Subgroups — #72262241

Order 2048.

At least 28385 conjugacy classes of subgroups; only the 1242 normal subgroups are shown.

The subgroup lattice has 924 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72262240	C₂	1	1	yes	maximal, characteristic, complemented
2	#72262238	C₂	1	2	yes	maximal, complemented
3	#72262237	C₂	1	2	yes	maximal, complemented
4	#72262236	C₂	1	1	yes	maximal, characteristic, complemented
5	#72262235	C₂	1	1	yes	maximal, characteristic, complemented
6	#72262233	C₂	1	1	yes	maximal, characteristic, complemented
7	#72262225	C₂	1	1	yes	maximal, characteristic, complemented
8	#72262193	C₂	1	2	yes	maximal, complemented
9	#72262128	C₂	1	2	yes	maximal, complemented
10	C₂×#511853	C₂	1	2	yes	maximal, complemented
11	#72237806	C₂	1	2	yes	maximal, complemented
12	#72235270	C₂	1	1	yes	maximal, characteristic, complemented
13	#72234644	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×#33551	C₂	1	1	yes	maximal, characteristic, complemented
15	#72234157	C₂	1	2	yes	maximal, complemented
16	#72233855	C₂	1	1	yes	maximal, characteristic, complemented
17	#72233135	C₂	1	2	yes	maximal, complemented
18	#72232838	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#499787	C₂	1	1	yes	maximal, characteristic, complemented
20	#72232728	C₂	1	1	yes	maximal, characteristic, complemented
21	#72232683	C₂	1	1	yes	maximal, characteristic, complemented
22	#72225632	C₂	1	1	yes	maximal, characteristic, complemented
23	#72218980	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#63012	C₂²	1	1	yes	characteristic, complemented
25	C₂²×#3532	C₂²	1	1	yes	characteristic
26	C₂²×#3026	C₂²	1	1	yes	characteristic, complemented
27	C₂³×B(4,𝔽₂)	C₂²	1	1	yes	characteristic, complemented
28	C₂²×#3019	C₂²	1	1	yes	characteristic, complemented
29	#7829278	C₂²	1	1	yes	characteristic, complemented
30	#7829277	C₂²	1	1	yes	characteristic, complemented
31	#7819711	C₂²	1	1	yes	characteristic, complemented
32	#7819709	C₂²	1	1	yes	characteristic, complemented
33	#7772009	C₂²	1	1	yes	characteristic
34	#7768137	C₂²	1	1	yes	characteristic
35	#7733187	C₂²	1	1	yes	characteristic, complemented
36	#7733150	C₂²	1	1	yes	characteristic, complemented
37	#7680651	C₂²	1	1	yes	characteristic
38	#7675392	C₂²	1	1	yes	characteristic
39	#7670206	C₂²	1	1	yes	characteristic
40	C₂×#58990	C₂²	1	1	yes	characteristic
41	#7627347	C₂²	1	1	yes	characteristic, complemented
42	C₂×#33557	C₂²	1	2	yes	complemented
43	C₂×#33551	C₂²	1	2	yes	—
44	C₂×#33551	C₂²	1	2	yes	complemented
45	C₂×#33551	C₂²	1	2	yes	complemented
46	C₂×#33551	C₂²	1	2	yes	complemented
47	C₂×#33551	C₂²	1	2	yes	complemented
48	C₂²×#2196	C₂²	1	2	yes	complemented
49	C₂²×#2127	C₂²	1	1	yes	characteristic, complemented
50	C₂²×#2121	C₂²	1	1	yes	characteristic, complemented
51	C₂³×AΣL(1,𝔽₁₆)	C₂²	1	1	yes	characteristic, complemented
52	#6628892	C₂²	1	1	yes	characteristic, complemented
53	C₂×#32898	C₂²	1	1	yes	characteristic, complemented
54	C₂×#32888	C₂²	1	1	yes	characteristic, complemented
55	C₂×#23996	C₂²	1	2	yes	complemented
56	C₂×#23996	C₂²	1	2	yes	complemented
57	C₂×#23998	C₂²	1	2	yes	complemented
58	#6370693	C₂²	1	1	yes	characteristic, complemented
59	#498931	C₂²	1	2	yes	complemented
60	#498927	C₂²	1	2	yes	complemented
61	#498923	C₂²	1	2	yes	complemented
62	C₂×#13346	C₂²	1	2	yes	complemented
63	#498890	C₂²	1	2	yes	complemented
64	C₂×#13343	C₂²	1	2	yes	complemented
65	C₂×#13088	C₂²	1	1	yes	characteristic, complemented
66	C₂×#13088	C₂²	1	1	yes	characteristic, complemented
67	#494695	C₂²	1	1	yes	characteristic, complemented
68	C₂×#13086	C₂²	1	1	yes	characteristic, complemented
69	#494677	C₂²	1	1	yes	characteristic, complemented
70	C₂×#13082	C₂²	1	1	yes	characteristic, complemented
71	#494600	C₂²	1	2	yes	complemented
72	#494582	C₂²	1	2	yes	complemented
73	C₂×#13041	C₂²	1	2	yes	complemented
74	C₂×#12767	C₂²	1	2	yes	complemented
75	C₂×#12759	C₂²	1	2	yes	complemented
76	C₂×#12753	C₂²	1	2	yes	complemented
77	C₂×#12753	C₂²	1	2	yes	complemented
78	C₂×#12753	C₂²	1	2	yes	complemented
79	C₂×#12753	C₂²	1	2	yes	complemented
80	C₂×#12753	C₂²	1	2	yes	complemented
81	C₂×#12727	C₂²	1	2	yes	complemented
82	C₂×#12725	C₂²	1	2	yes	complemented
83	C₂×#12725	C₂²	1	2	yes	complemented
84	#493370	C₂²	1	1	yes	characteristic, complemented
85	#493357	C₂²	1	1	yes	characteristic, complemented
86	C₂×#12687	C₂²	1	1	yes	characteristic, complemented
87	#405274	C₂²	1	2	yes	complemented
88	#405271	C₂²	1	2	yes	complemented
89	#405268	C₂²	1	2	yes	complemented
90	#394275	C₂²	1	2	yes	complemented
91	#394273	C₂²	1	2	yes	complemented
92	#394273	C₂²	1	2	yes	complemented
93	#374058	C₂²	1	1	yes	characteristic, complemented
94	#374052	C₂²	1	1	yes	characteristic, complemented
95	#374038	C₂²	1	1	yes	characteristic, complemented
96	#364545	C₂²	1	2	yes	complemented
97	#364532	C₂²	1	2	yes	complemented
98	#364526	C₂²	1	2	yes	complemented
99	#359894	C₂²	1	1	yes	characteristic, complemented
100	#359892	C₂²	1	1	yes	characteristic, complemented
101	#359892	C₂²	1	1	yes	characteristic, complemented
102	#359509	C₂²	1	1	yes	characteristic, complemented
103	#359501	C₂²	1	1	yes	characteristic, complemented
104	#359442	C₂²	1	1	yes	characteristic, complemented
105	#147829	C₂²	1	2	yes	complemented
106	#147824	C₂²	1	2	yes	complemented
107	#147819	C₂²	1	2	yes	complemented
108	#147811	C₂²	1	2	yes	complemented
109	#147783	C₂²	1	2	yes	complemented
110	#147779	C₂²	1	2	yes	complemented
111	#147741	C₂²	1	2	yes	complemented
112	#147732	C₂²	1	2	yes	complemented
113	#147732	C₂²	1	2	yes	complemented
114	#147610	C₂²	1	2	yes	complemented
115	#147609	C₂²	1	2	yes	complemented
116	#147603	C₂²	1	2	yes	complemented
117	#146705	C₂²	1	2	yes	complemented
118	#146692	C₂²	1	2	yes	complemented
119	#146675	C₂²	1	2	yes	complemented
120	#146654	C₂²	1	2	yes	complemented
121	#146609	C₂²	1	2	yes	complemented
122	#146599	C₂²	1	2	yes	complemented
123	C₂³×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
124	C₂×#3508	C₂³	1	1	yes	characteristic
125	C₂×#3490	C₂³	1	1	yes	characteristic
126	C₂×#3490	C₂³	1	1	yes	characteristic
127	C₂×#3543	C₂³	1	1	yes	characteristic
128	C₂×#3532	D₄	1	1	yes	characteristic, complemented
129	C₂×#3532	D₄	1	1	yes	characteristic, complemented
130	C₂×#3532	D₄	1	1	yes	characteristic, complemented
131	C₂×#3532	D₄	1	1	yes	characteristic, complemented
132	C₂×#3532	C₂³	1	1	yes	characteristic
133	C₂×#3532	C₂³	1	1	yes	characteristic
134	C₂×#3532	C₂³	1	1	yes	characteristic
135	C₂×#3532	C₂³	1	1	yes	characteristic
136	C₂×#3532	C₂³	1	1	yes	characteristic
137	C₂²×#551	D₄	1	1	yes	characteristic, complemented
138	C₂²×D₄²	D₄	1	1	yes	characteristic, complemented
139	C₂²×D₄²	C₂³	1	1	yes	characteristic
140	C₂²×H(3,𝔽₄)	D₄	1	1	yes	characteristic, complemented
141	C₂²×#560	D₄	1	1	yes	characteristic, complemented
142	C₂²×#535	C₂³	1	1	yes	characteristic
143	C₂²×#534	C₂³	1	1	yes	characteristic
144	C₂³×#120	C₂³	1	1	yes	characteristic
145	C₂×#3026	C₂³	1	2	yes	—
146	C₂×#3026	C₂³	1	2	yes	—
147	C₂×#3026	C₂³	1	2	yes	complemented
148	C₂²×B(4,𝔽₂)	C₂³	1	2	yes	—
149	C₂²×B(4,𝔽₂)	C₂³	1	2	yes	—
150	C₂²×B(4,𝔽₂)	C₂³	1	2	yes	complemented
151	C₂×#3019	C₂³	1	2	yes	—
152	C₂×#3019	C₂³	1	2	yes	—
153	C₂²×#453	C₂³	1	2	yes	complemented
154	C₂³×#100	C₂³	1	1	yes	characteristic
155	C₂×#2883	C₂³	1	2	yes	complemented
156	C₂×#2883	C₂³	1	2	yes	complemented
157	C₂³×#99	C₂³	1	1	yes	characteristic
158	C₂³×#99	C₂³	1	1	yes	characteristic
159	#59189	D₄	1	1	yes	characteristic, complemented
160	#59162	D₄	1	1	yes	characteristic, complemented
161	#59126	D₄	1	1	yes	characteristic, complemented
162	#58990	D₄	1	1	yes	characteristic, complemented
163	#58990	D₄	1	1	yes	characteristic, complemented
164	#58990	D₄	1	1	yes	characteristic, complemented
165	#58990	D₄	1	1	yes	characteristic, complemented
166	#58990	D₄	1	1	yes	characteristic, complemented
167	#58990	D₄	1	1	yes	characteristic, complemented
168	#58990	D₄	1	1	yes	characteristic, complemented
169	#58990	D₄	1	1	yes	characteristic, complemented
170	#58990	D₄	1	1	yes	characteristic, complemented
171	C₂×#2679	C₂³	1	1	yes	characteristic
172	C₂×#2669	C₂³	1	1	yes	characteristic
173	#52012	D₄	1	1	yes	characteristic, complemented
174	#52004	D₄	1	1	yes	characteristic, complemented
175	#51902	D₄	1	1	yes	characteristic, complemented
176	#51895	D₄	1	1	yes	characteristic, complemented
177	#50646	D₄	1	1	yes	characteristic, complemented
178	#50635	D₄	1	1	yes	characteristic, complemented
179	#47846	D₄	1	1	yes	characteristic, complemented
180	#47827	D₄	1	1	yes	characteristic, complemented
181	#46324	D₄	1	1	yes	characteristic, complemented
182	#45977	D₄	1	1	yes	characteristic, complemented
183	#45455	D₄	1	1	yes	characteristic, complemented
184	#45438	D₄	1	1	yes	characteristic, complemented
185	#37232	C₂³	1	1	yes	characteristic
186	#37129	C₂³	1	1	yes	characteristic
187	#36737	C₂³	1	1	yes	characteristic
188	#36702	C₂³	1	1	yes	characteristic
189	C₂×#2846	D₄	1	1	yes	characteristic, complemented
190	#35556	D₄	1	1	yes	characteristic, complemented
191	#35541	C₂³	1	1	yes	characteristic
192	#35528	D₄	1	1	yes	characteristic, complemented
193	#35528	C₂³	1	1	yes	characteristic
194	#35367	D₄	1	1	yes	characteristic, complemented
195	#35360	D₄	1	1	yes	characteristic, complemented
196	#35360	C₂³	1	1	yes	characteristic
197	#35350	C₂³	1	1	yes	characteristic
198	#35348	D₄	1	1	yes	characteristic, complemented
199	#35348	D₄	1	1	yes	characteristic, complemented
200	#35348	C₂³	1	1	yes	characteristic
201	#35348	C₂³	1	1	yes	characteristic
202	#35272	D₄	1	1	yes	characteristic, complemented
203	#35254	D₄	1	1	yes	characteristic, complemented
204	#35250	D₄	1	1	yes	characteristic, complemented
205	#34993	D₄	1	1	yes	characteristic, complemented
206	#34992	D₄	1	1	yes	characteristic, complemented
207	#34982	D₄	1	1	yes	characteristic, complemented
208	#34982	D₄	1	1	yes	characteristic, complemented
209	#34981	D₄	1	1	yes	characteristic, complemented
210	#34981	D₄	1	1	yes	characteristic, complemented
211	#34980	C₂³	1	1	yes	characteristic
212	#34739	D₄	1	1	yes	characteristic, complemented
213	C₂×#2433	C₂³	1	1	yes	characteristic
214	C₂×#2403	D₄	1	1	yes	characteristic, complemented
215	C₂×#2403	C₂³	1	1	yes	characteristic
216	#34408	C₂³	1	1	yes	characteristic
217	#34406	C₂³	1	1	yes	characteristic
218	#34273	C₂³	1	1	yes	characteristic
219	#34269	C₂³	1	1	yes	characteristic
220	#34204	D₄	1	1	yes	characteristic, complemented
221	#34198	D₄	1	1	yes	characteristic, complemented
222	#34198	C₂³	1	1	yes	characteristic
223	#34171	D₄	1	1	yes	characteristic, complemented
224	#34171	C₂³	1	1	yes	characteristic
225	#34171	C₂³	1	1	yes	characteristic
226	C₂×#2358	C₂³	1	1	yes	characteristic
227	C₂²⋊C₄×#41	D₄	1	1	yes	characteristic, complemented
228	C₂×D₄×C₂²⋊C₄	D₄	1	1	yes	characteristic, complemented
229	C₂²×#379	D₄	1	1	yes	characteristic, complemented
230	#33551	D₄	1	16	yes	complemented
231	C₂×#2127	C₂³	1	2	yes	—
232	C₂×#2127	C₂³	1	2	yes	—
233	C₂×#2127	C₂³	1	2	yes	—
234	C₂×#2127	C₂³	1	2	yes	—
235	C₂²×#353	C₂³	1	2	yes	complemented
236	C₂²×#353	C₂³	1	2	yes	complemented
237	C₂×#2121	C₂³	1	2	yes	—
238	C₂×#2121	C₂³	1	2	yes	—
239	C₂×#2121	C₂³	1	2	yes	—
240	C₂×#2121	C₂³	1	2	yes	—
241	C₂×#2121	C₂³	1	2	yes	complemented
242	C₂×#2121	C₂³	1	2	yes	complemented
243	C₂²×AΣL(1,𝔽₁₆)	C₂³	1	2	yes	—
244	C₂²×AΣL(1,𝔽₁₆)	C₂³	1	2	yes	—
245	C₂²×AΣL(1,𝔽₁₆)	C₂³	1	2	yes	—
246	C₂²×AΣL(1,𝔽₁₆)	C₂³	1	2	yes	—
247	C₂²×AΣL(1,𝔽₁₆)	C₂³	1	2	yes	complemented
248	C₂²×AΣL(1,𝔽₁₆)	C₂³	1	2	yes	complemented
249	C₂×#1913	C₂³	1	2	yes	—
250	C₂×#1913	C₂³	1	2	yes	—
251	C₂×#1913	C₂³	1	2	yes	complemented
252	C₂×#1911	C₂³	1	2	yes	—
253	C₂×#1911	C₂³	1	2	yes	—
254	C₂×#1889	C₂³	1	2	yes	—
255	C₂×#1889	C₂³	1	2	yes	—
256	C₂×#1889	C₂³	1	2	yes	complemented
257	C₂×#1887	C₂³	1	2	yes	complemented
258	C₂×#1829	C₂³	1	2	yes	complemented
259	C₂×#1828	C₂³	1	2	yes	complemented
260	C₂×#1828	C₂³	1	2	yes	complemented
261	C₂×#1792	C₂³	1	2	yes	complemented
262	#20609	C₂³	1	2	yes	complemented
263	C₂×#1790	C₂³	1	2	yes	complemented
264	C₂×#1783	C₂³	1	1	yes	characteristic
265	C₂×#1781	C₂³	1	1	yes	characteristic
266	C₂×#1781	C₂³	1	1	yes	characteristic
267	C₂×#1393	C₂³	1	2	yes	complemented
268	C₂×#1393	C₂³	1	2	yes	complemented
269	#12574	C₂³	1	2	yes	complemented
270	#12574	C₂³	1	2	yes	complemented
271	C₂×#1390	C₂³	1	2	yes	complemented
272	C₂×#1390	C₂³	1	2	yes	complemented
273	#10769	C₂³	1	2	yes	complemented
274	#10768	C₂³	1	2	yes	complemented
275	#10768	C₂³	1	2	yes	complemented
276	#10754	C₂³	1	2	yes	complemented
277	#10749	C₂³	1	2	yes	complemented
278	#10745	C₂³	1	2	yes	complemented
279	C₂⁷	C₂×D₄	1	1	yes	characteristic
280	C₂²×H(5,𝔽₂)	C₂⁴	1	2	yes	—
281	C₂³×#41	C₂×D₄	1	1	yes	characteristic
282	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
283	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
284	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
285	#3532	C₂×D₄	1	8	yes	—
286	C₂×H(3,𝔽₄)	C₂×D₄	1	1	yes	characteristic
287	C₂×H(3,𝔽₄)	C₂×D₄	1	1	yes	characteristic
288	C₂×H(3,𝔽₄)	C₂×D₄	1	1	yes	characteristic
289	C₂×H(3,𝔽₄)	C₂×D₄	1	1	yes	characteristic
290	C₂×H(3,𝔽₄)	C₂×D₄	1	1	yes	characteristic, complemented
291	C₂×#560	C₂×D₄	1	1	yes	characteristic
292	C₂×#560	C₂×D₄	1	1	yes	characteristic
293	C₂×#560	C₂×D₄	1	1	yes	characteristic
294	C₂×#560	C₂×D₄	1	1	yes	characteristic
295	C₂×#560	C₂×D₄	1	1	yes	characteristic, complemented
296	C₂×#560	C₂×D₄	1	1	yes	characteristic, complemented
297	C₂×#560	C₂×D₄	1	1	yes	characteristic, complemented
298	C₂×#559	C₂×D₄	1	1	yes	characteristic, complemented
299	C₂×#551	C₂×D₄	1	1	yes	characteristic
300	C₂×#551	C₂×D₄	1	1	yes	characteristic
301	C₂×#551	C₂×D₄	1	1	yes	characteristic
302	C₂×#551	C₂×D₄	1	1	yes	characteristic
303	C₂×#551	C₂×D₄	1	1	yes	characteristic, complemented
304	C₂×D₄²	C₂×D₄	1	1	yes	characteristic
305	C₂×D₄²	C₂×D₄	1	1	yes	characteristic
306	C₂×D₄²	C₂×D₄	1	1	yes	characteristic
307	C₂×D₄²	C₂×D₄	1	1	yes	characteristic
308	C₂×D₄²	C₂×D₄	1	1	yes	characteristic, complemented
309	C₂×D₄²	C₂×D₄	1	1	yes	characteristic, complemented
310	C₂×D₄²	C₂×D₄	1	1	yes	characteristic, complemented
311	C₂×D₄²	C₂×D₄	1	1	yes	characteristic, complemented
312	C₂×D₄²	C₂×D₄	1	1	yes	characteristic, complemented
313	C₂×D₄²	C₂×D₄	1	1	yes	characteristic, complemented
314	C₂×#543	C₂×D₄	1	1	yes	characteristic, complemented
315	C₂×#543	C₂×D₄	1	1	yes	characteristic, complemented
316	C₂×#535	C₂×D₄	1	1	yes	characteristic
317	C₂×#535	C₂×D₄	1	1	yes	characteristic
318	C₂×#535	C₂×D₄	1	1	yes	characteristic
319	C₂×#535	C₂×D₄	1	1	yes	characteristic
320	C₂×#535	C₂×D₄	1	1	yes	characteristic
321	C₂×#535	C₂×D₄	1	1	yes	characteristic
322	C₂×#535	C₂×D₄	1	1	yes	characteristic, complemented
323	C₂×#535	C₂×D₄	1	1	yes	characteristic, complemented
324	C₂×#535	C₂⁴	1	1	yes	characteristic
325	C₂×#535	C₂⁴	1	1	yes	characteristic
326	C₂×#534	C₂×D₄	1	1	yes	characteristic
327	C₂×#534	C₂×D₄	1	1	yes	characteristic
328	C₂×#534	C₂×D₄	1	1	yes	characteristic
329	C₂×#534	C₂×D₄	1	1	yes	characteristic
330	C₂×#534	C₂×D₄	1	1	yes	characteristic
331	C₂×#534	C₂×D₄	1	1	yes	characteristic
332	C₂×#534	C₂×D₄	1	1	yes	characteristic
333	C₂×#534	C₂⁴	1	1	yes	characteristic
334	C₂×#534	C₂⁴	1	1	yes	characteristic
335	C₂×#534	C₂⁴	1	1	yes	characteristic
336	C₂×#533	C₂×D₄	1	1	yes	characteristic, complemented
337	C₂²×#127	C₂×D₄	1	1	yes	characteristic
338	C₂²×#127	C₂×D₄	1	1	yes	characteristic
339	C₂²×#127	C₂×D₄	1	1	yes	characteristic
340	C₂²×#127	C₂⁴	1	1	yes	characteristic
341	C₂²×#124	C₂×D₄	1	1	yes	characteristic
342	C₂²×#124	C₂×D₄	1	1	yes	characteristic
343	C₂²×#123	C₂×D₄	1	1	yes	characteristic
344	C₂²×#123	C₂×D₄	1	1	yes	characteristic
345	C₂²×#121	C₂×D₄	1	1	yes	characteristic
346	C₂²×#120	C₂×D₄	1	1	yes	characteristic
347	C₂²×#120	C₂×D₄	1	1	yes	characteristic
348	C₂²×#120	C₂×D₄	1	1	yes	characteristic
349	C₂²×#120	C₂×D₄	1	1	yes	characteristic
350	C₂²×#120	C₂×D₄	1	1	yes	characteristic
351	C₂²×#120	C₂×D₄	1	1	yes	characteristic
352	C₂²×#120	C₂×D₄	1	1	yes	characteristic
353	C₂²×#120	C₂×D₄	1	1	yes	characteristic
354	C₂²×#120	C₂×D₄	1	1	yes	characteristic
355	C₂²×#120	C₂×D₄	1	1	yes	characteristic
356	C₂²×#120	C₂×D₄	1	1	yes	characteristic
357	C₂²×#120	C₂×D₄	1	1	yes	characteristic
358	C₂²×#120	C₂×D₄	1	1	yes	characteristic
359	C₂²×#120	C₂×D₄	1	1	yes	characteristic
360	C₂²×#120	C₂×D₄	1	1	yes	characteristic, complemented
361	C₂²×#120	C₂×D₄	1	1	yes	characteristic, complemented
362	C₂²×#120	C₂×D₄	1	1	yes	characteristic, complemented
363	C₂²×#120	C₂×D₄	1	1	yes	characteristic, complemented
364	C₂²×#120	C₂⁴	1	1	yes	characteristic
365	C₂²×#120	C₂⁴	1	1	yes	characteristic
366	C₂²×#120	C₂⁴	1	1	yes	characteristic
367	C₂×#518	C₂×D₄	1	1	yes	characteristic, complemented
368	C₂×#518	C₂×D₄	1	1	yes	characteristic, complemented
369	C₂×#518	C₂×D₄	1	1	yes	characteristic, complemented
370	C₂×#518	C₂×D₄	1	1	yes	characteristic, complemented
371	C₂×#518	C₂⁴	1	2	yes	—
372	C₂×#518	C₂⁴	1	1	yes	characteristic
373	C₂×#518	C₂⁴	1	1	yes	characteristic
374	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic, complemented
375	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic, complemented
376	C₂²×#117	C₂×D₄	1	1	yes	characteristic
377	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
378	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
379	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
380	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
381	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
382	#3026	C₂×D₄	1	8	yes	complemented
383	C₂×B(4,𝔽₂)	C₂×D₄	1	8	yes	complemented
384	#3019	C₂×D₄	1	8	yes	complemented
385	C₂²×#100	C₂⁴	1	2	yes	—
386	C₂²×#100	C₂⁴	1	2	yes	—
387	C₂²×#99	C₂⁴	1	2	yes	—
388	C₂²×#99	C₂⁴	1	2	yes	—
389	C₂²×#99	C₂⁴	1	2	yes	—
390	C₂²×#99	C₂⁴	1	2	yes	—
391	#2724	C₂×D₄	1	1	yes	characteristic, complemented
392	#2717	C₂×D₄	1	1	yes	characteristic, complemented
393	#2709	C₂×D₄	1	1	yes	characteristic, complemented
394	#2709	C₂×D₄	1	1	yes	characteristic, complemented
395	#2709	C₂×D₄	1	1	yes	characteristic, complemented
396	#2697	C₂×D₄	1	1	yes	characteristic, complemented
397	#2697	C₂×D₄	1	1	yes	characteristic, complemented
398	#2684	C₂×D₄	1	1	yes	characteristic, complemented
399	#2684	C₂×D₄	1	1	yes	characteristic, complemented
400	#2684	C₂×D₄	1	1	yes	characteristic, complemented
401	#2679	C₂×D₄	1	1	yes	characteristic, complemented
402	#2679	C₂×D₄	1	1	yes	characteristic, complemented
403	#2679	C₂×D₄	1	1	yes	characteristic, complemented
404	#2679	C₂×D₄	1	1	yes	characteristic, complemented
405	#2679	C₂×D₄	1	1	yes	characteristic, complemented
406	#2669	C₂×D₄	1	1	yes	characteristic, complemented
407	#2669	C₂×D₄	1	1	yes	characteristic, complemented
408	#2669	C₂×D₄	1	1	yes	characteristic, complemented
409	#2669	C₂×D₄	1	1	yes	characteristic, complemented
410	#2669	C₂×D₄	1	1	yes	characteristic, complemented
411	#2669	C₂×D₄	1	1	yes	characteristic, complemented
412	#2669	C₂×D₄	1	1	yes	characteristic, complemented
413	#2669	C₂×D₄	1	1	yes	characteristic, complemented
414	#2669	C₂×D₄	1	1	yes	characteristic, complemented
415	#2433	C₂×D₄	1	1	yes	characteristic
416	#2433	C₂×D₄	1	1	yes	characteristic
417	#2433	C₂×D₄	1	1	yes	characteristic
418	#2433	C₂×D₄	1	1	yes	characteristic
419	#2433	C₂×D₄	1	1	yes	characteristic
420	#2433	C₂×D₄	1	1	yes	characteristic
421	#2433	C₂×D₄	1	1	yes	characteristic
422	#2433	C₂×D₄	1	1	yes	characteristic
423	#2405	C₂×D₄	1	1	yes	characteristic
424	#2405	C₂×D₄	1	1	yes	characteristic
425	#2405	C₂×D₄	1	1	yes	characteristic
426	#2405	C₂×D₄	1	1	yes	characteristic
427	#2403	C₂×D₄	1	1	yes	characteristic
428	#2403	C₂×D₄	1	1	yes	characteristic
429	#2403	C₂×D₄	1	1	yes	characteristic
430	#2403	C₂×D₄	1	1	yes	characteristic
431	#2403	C₂×D₄	1	1	yes	characteristic
432	#2403	C₂×D₄	1	1	yes	characteristic
433	#2403	C₂×D₄	1	1	yes	characteristic
434	#2403	C₂×D₄	1	1	yes	characteristic
435	#2403	C₂×D₄	1	1	yes	characteristic
436	#2403	C₂×D₄	1	1	yes	characteristic
437	#2403	C₂×D₄	1	1	yes	characteristic
438	#2403	C₂×D₄	1	1	yes	characteristic
439	#2380	C₂×D₄	1	1	yes	characteristic, complemented
440	#2379	C₂×D₄	1	1	yes	characteristic, complemented
441	#2376	C₂×D₄	1	1	yes	characteristic, complemented
442	#2375	C₂×D₄	1	1	yes	characteristic, complemented
443	#2374	C₂×D₄	1	1	yes	characteristic, complemented
444	#2372	C₂×D₄	1	1	yes	characteristic, complemented
445	#2366	C₂×D₄	1	1	yes	characteristic, complemented
446	#2358	C₂×D₄	1	1	yes	characteristic, complemented
447	#2358	C₂×D₄	1	1	yes	characteristic, complemented
448	#2358	C₂×D₄	1	1	yes	characteristic, complemented
449	#2358	C₂×D₄	1	1	yes	characteristic, complemented
450	#2358	C₂×D₄	1	1	yes	characteristic, complemented
451	#2316	C₂×D₄	1	1	yes	characteristic, complemented
452	#2315	C₂×D₄	1	1	yes	characteristic, complemented
453	#2315	C₂×D₄	1	1	yes	characteristic, complemented
454	#2315	C₂×D₄	1	1	yes	characteristic, complemented
455	#2315	C₂×D₄	1	1	yes	characteristic, complemented
456	#2315	C₂×D₄	1	1	yes	characteristic, complemented
457	#2315	C₂×D₄	1	1	yes	characteristic, complemented
458	#2315	C₂×D₄	1	1	yes	characteristic, complemented
459	#2311	C₂×D₄	1	1	yes	characteristic, complemented
460	#2311	C₂×D₄	1	1	yes	characteristic, complemented
461	#2309	C₂×D₄	1	1	yes	characteristic
462	#2309	C₂×D₄	1	1	yes	characteristic
463	#2309	C₂×D₄	1	1	yes	characteristic, complemented
464	#2308	C₂×D₄	1	1	yes	characteristic
465	#2308	C₂×D₄	1	1	yes	characteristic
466	#2308	C₂×D₄	1	1	yes	characteristic
467	#2308	C₂×D₄	1	1	yes	characteristic
468	#2308	C₂×D₄	1	1	yes	characteristic
469	#2308	C₂×D₄	1	1	yes	characteristic, complemented
470	#2308	C₂×D₄	1	1	yes	characteristic, complemented
471	#2308	C₂×D₄	1	1	yes	characteristic, complemented
472	#2308	C₂⁴	1	1	yes	characteristic
473	#2297	C₂×D₄	1	1	yes	characteristic, complemented
474	#2297	C₂×D₄	1	1	yes	characteristic, complemented
475	#2296	C₂×D₄	1	1	yes	characteristic, complemented
476	#2296	C₂×D₄	1	1	yes	characteristic, complemented
477	C₂×#390	C₂×D₄	1	1	yes	characteristic
478	C₂×#390	C₂⁴	1	1	yes	characteristic
479	C₂×#386	C₂×D₄	1	1	yes	characteristic
480	C₂×#386	C₂×D₄	1	1	yes	characteristic, complemented
481	C₂×#386	C₂×D₄	1	1	yes	characteristic, complemented
482	C₂×#386	C₂⁴	1	1	yes	characteristic
483	#2285	C₂×D₄	1	1	yes	characteristic, complemented
484	#2280	C₂×D₄	1	1	yes	characteristic
485	#2280	C₂×D₄	1	1	yes	characteristic
486	C₂×#380	C₂×D₄	1	1	yes	characteristic, complemented
487	C₂×#379	C₂×D₄	1	1	yes	characteristic
488	C₂×#379	C₂×D₄	1	1	yes	characteristic
489	C₂×#379	C₂×D₄	1	1	yes	characteristic
490	C₂×#379	C₂×D₄	1	1	yes	characteristic
491	C₂×#379	C₂×D₄	1	1	yes	characteristic
492	C₂×#379	C₂×D₄	1	1	yes	characteristic
493	C₂×#379	C₂×D₄	1	1	yes	characteristic, complemented
494	C₂×#379	C₂×D₄	1	1	yes	characteristic, complemented
495	C₂×#379	C₂×D₄	1	1	yes	characteristic, complemented
496	C₂×#379	C₂×D₄	1	1	yes	characteristic, complemented
497	C₂×#379	C₂×D₄	1	1	yes	characteristic, complemented
498	#2274	C₂×D₄	1	1	yes	characteristic, complemented
499	#2273	C₂×D₄	1	1	yes	characteristic, complemented
500	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
501	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
502	#2127	C₂×D₄	1	8	yes	complemented
503	#2121	C₂×D₄	1	8	yes	complemented
504	C₂×AΣL(1,𝔽₁₆)	C₂×D₄	1	8	yes	complemented
505	C₂⁶	#120	1	1	yes	characteristic
506	C₂⁶	#120	1	1	yes	characteristic
507	C₂⁶	#120	1	1	yes	characteristic
508	C₂⁶	#120	1	1	yes	characteristic
509	C₂⁶	#120	1	1	yes	characteristic
510	C₂⁶	C₂²×D₄	1	1	yes	characteristic
511	C₂⁶	C₂²×D₄	1	1	yes	characteristic
512	C₂⁶	C₂²×D₄	1	1	yes	characteristic
513	C₂⁶	C₂²×D₄	1	1	yes	characteristic
514	C₂⁶	C₂²×D₄	1	1	yes	characteristic
515	C₂×H(5,𝔽₂)	C₂²×D₄	1	4	yes	—
516	C₂²×#41	#120	1	1	yes	characteristic
517	C₂²×#41	#120	1	1	yes	characteristic
518	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
519	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
520	C₂³×Q₈	#120	1	1	yes	characteristic
521	C₂³×D₄	#120	1	1	yes	characteristic
522	C₂³×D₄	#120	1	1	yes	characteristic
523	C₂³×D₄	#120	1	1	yes	characteristic
524	C₂³×D₄	#120	1	1	yes	characteristic
525	C₂³×D₄	#120	1	1	yes	characteristic
526	C₂³×D₄	#120	1	1	yes	characteristic
527	C₂³×D₄	#120	1	1	yes	characteristic
528	C₂³×D₄	#120	1	1	yes	characteristic
529	C₂³×D₄	#120	1	1	yes	characteristic
530	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
531	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
532	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
533	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
534	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
535	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
536	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
537	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
538	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
539	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
540	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
541	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
542	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
543	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
544	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
545	C₂³×D₄	C₂⁵	1	1	yes	characteristic
546	C₂⁴×C₄	#120	1	1	yes	characteristic
547	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
548	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
549	H(3,𝔽₄)	#120	1	4	yes	complemented
550	#560	#120	1	4	yes	complemented
551	#551	#120	1	4	yes	complemented
552	D₄²	#120	1	4	yes	complemented
553	#535	C₂²×D₄	1	4	yes	—
554	#535	H(5,𝔽₂)	1	4	yes	—
555	#534	C₂²×D₄	1	4	yes	—
556	#534	H(5,𝔽₂)	1	4	yes	—
557	C₂×#127	#120	1	1	yes	characteristic
558	C₂×#127	#120	1	1	yes	characteristic
559	C₂×#127	#120	1	1	yes	characteristic
560	C₂×#127	#120	1	1	yes	characteristic
561	C₂×#127	#120	1	1	yes	characteristic
562	C₂×#127	#120	1	1	yes	characteristic
563	C₂×#127	#120	1	1	yes	characteristic
564	C₂×#127	#120	1	1	yes	characteristic
565	C₂×#127	C₂²×D₄	1	1	yes	characteristic
566	C₂×#127	C₂²×D₄	1	1	yes	characteristic
567	C₂×#127	C₂²×D₄	1	1	yes	characteristic
568	C₂×#127	C₂²×D₄	1	1	yes	characteristic
569	C₂×#127	C₂²×D₄	1	1	yes	characteristic
570	C₂×#127	C₂²×D₄	1	1	yes	characteristic
571	C₂×#127	C₂²×D₄	1	1	yes	characteristic
572	C₂×#127	C₂²×D₄	1	1	yes	characteristic
573	C₂×#124	#120	1	1	yes	characteristic
574	C₂×#124	#120	1	1	yes	characteristic
575	C₂×#124	#120	1	1	yes	characteristic
576	C₂×#124	#120	1	1	yes	characteristic
577	C₂×#124	C₂²×D₄	1	1	yes	characteristic
578	C₂×#124	C₂²×D₄	1	1	yes	characteristic
579	C₂×#124	C₂²×D₄	1	1	yes	characteristic
580	C₂×#124	C₂²×D₄	1	1	yes	characteristic
581	C₂×#123	#120	1	1	yes	characteristic
582	C₂×#123	#120	1	1	yes	characteristic
583	C₂×#123	#120	1	1	yes	characteristic
584	C₂×#123	#120	1	1	yes	characteristic
585	C₂×#123	#120	1	1	yes	characteristic
586	C₂×#123	#120	1	1	yes	characteristic
587	C₂×#123	C₂²×D₄	1	1	yes	characteristic
588	C₂×#123	C₂²×D₄	1	1	yes	characteristic
589	C₂×#123	C₂²×D₄	1	1	yes	characteristic
590	C₂×#123	C₂²×D₄	1	1	yes	characteristic
591	C₂×#123	C₂²×D₄	1	1	yes	characteristic
592	C₂×#123	C₂²×D₄	1	1	yes	characteristic
593	C₂×#121	#120	1	1	yes	characteristic
594	C₂×#121	#120	1	1	yes	characteristic
595	C₂×#121	#120	1	1	yes	characteristic
596	C₂×#121	#120	1	1	yes	characteristic
597	C₂×#120	#120	1	1	yes	characteristic
598	C₂×#120	#120	1	1	yes	characteristic
599	C₂×#120	#120	1	1	yes	characteristic
600	C₂×#120	#120	1	1	yes	characteristic
601	C₂×#120	#120	1	1	yes	characteristic
602	C₂×#120	#120	1	1	yes	characteristic
603	C₂×#120	#120	1	1	yes	characteristic
604	C₂×#120	#120	1	1	yes	characteristic
605	C₂×#120	#120	1	1	yes	characteristic
606	C₂×#120	#120	1	1	yes	characteristic
607	C₂×#120	#120	1	1	yes	characteristic
608	C₂×#120	#120	1	1	yes	characteristic
609	C₂×#120	#120	1	1	yes	characteristic
610	C₂×#120	#120	1	1	yes	characteristic
611	C₂×#120	#120	1	1	yes	characteristic
612	C₂×#120	#120	1	1	yes	characteristic
613	C₂×#120	#120	1	1	yes	characteristic
614	C₂×#120	#120	1	1	yes	characteristic
615	C₂×#120	C₂²×D₄	1	1	yes	characteristic
616	C₂×#120	C₂²×D₄	1	1	yes	characteristic
617	C₂×#120	C₂²×D₄	1	1	yes	characteristic
618	C₂×#120	C₂²×D₄	1	1	yes	characteristic
619	C₂×#120	C₂²×D₄	1	1	yes	characteristic
620	C₂×#120	C₂²×D₄	1	1	yes	characteristic
621	C₂×#120	C₂²×D₄	1	1	yes	characteristic
622	C₂×#120	C₂²×D₄	1	1	yes	characteristic
623	C₂×#120	C₂²×D₄	1	1	yes	characteristic
624	C₂×#120	C₂²×D₄	1	1	yes	characteristic
625	C₂×#120	C₂²×D₄	1	1	yes	characteristic
626	C₂×#120	C₂²×D₄	1	1	yes	characteristic
627	C₂×#120	C₂²×D₄	1	1	yes	characteristic
628	C₂×#120	C₂²×D₄	1	1	yes	characteristic
629	C₂×#120	C₂²×D₄	1	1	yes	characteristic
630	C₂×#120	C₂²×D₄	1	1	yes	characteristic
631	C₂×#120	C₂²×D₄	1	1	yes	characteristic
632	C₂×#120	C₂²×D₄	1	1	yes	characteristic
633	C₂×#120	C₂²×D₄	1	4	yes	—
634	C₂×#120	H(5,𝔽₂)	1	4	yes	—
635	C₂×#117	#120	1	1	yes	characteristic
636	C₂×#117	#120	1	1	yes	characteristic
637	C₂×#117	C₂²×D₄	1	1	yes	characteristic
638	C₂×#117	C₂²×D₄	1	1	yes	characteristic
639	C₂×#117	C₂²×D₄	1	1	yes	characteristic
640	C₂×#117	C₂²×D₄	1	1	yes	characteristic
641	C₂×#117	C₂²×D₄	1	1	yes	characteristic
642	C₂×#117	C₂²×D₄	1	1	yes	characteristic
643	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
644	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
645	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
646	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
647	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
648	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
649	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
650	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
651	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
652	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
653	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
654	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
655	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
656	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
657	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
658	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
659	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
660	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
661	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
662	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
663	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
664	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
665	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
666	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
667	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
668	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
669	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
670	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
671	C₂²×C₄²	#120	1	1	yes	characteristic
672	C₂²×C₄²	#120	1	1	yes	characteristic
673	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
674	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
675	C₂×#100	C₂²×D₄	1	4	yes	—
676	C₂×#99	C₂²×D₄	1	4	yes	—
677	C₂×#99	C₂²×D₄	1	4	yes	—
678	#390	#120	1	1	yes	characteristic
679	#390	#120	1	1	yes	characteristic
680	#390	#120	1	1	yes	characteristic
681	#390	#120	1	1	yes	characteristic
682	#390	C₂²×D₄	1	1	yes	characteristic
683	#390	C₂²×D₄	1	1	yes	characteristic
684	#390	C₂²×D₄	1	1	yes	characteristic
685	#390	C₂²×D₄	1	1	yes	characteristic
686	#386	#120	1	1	yes	characteristic
687	#386	#120	1	1	yes	characteristic
688	#386	#120	1	1	yes	characteristic
689	#386	#120	1	1	yes	characteristic
690	#386	#120	1	1	yes	characteristic
691	#386	#120	1	1	yes	characteristic
692	#386	#120	1	1	yes	characteristic
693	#386	#120	1	1	yes	characteristic
694	#386	C₂²×D₄	1	1	yes	characteristic
695	#386	C₂²×D₄	1	1	yes	characteristic
696	#386	C₂²×D₄	1	1	yes	characteristic
697	#386	C₂²×D₄	1	1	yes	characteristic
698	#386	C₂²×D₄	1	1	yes	characteristic
699	#386	C₂²×D₄	1	1	yes	characteristic
700	#386	C₂²×D₄	1	1	yes	characteristic
701	#386	C₂²×D₄	1	1	yes	characteristic
702	#381	#120	1	1	yes	characteristic
703	#381	#120	1	1	yes	characteristic
704	#381	#120	1	1	yes	characteristic
705	#381	#120	1	1	yes	characteristic
706	#379	#120	1	1	yes	characteristic
707	#379	#120	1	1	yes	characteristic
708	#379	#120	1	1	yes	characteristic
709	#379	#120	1	1	yes	characteristic
710	#379	#120	1	1	yes	characteristic
711	#379	#120	1	1	yes	characteristic
712	#379	#120	1	1	yes	characteristic
713	#379	#120	1	1	yes	characteristic
714	#379	#120	1	1	yes	characteristic
715	#379	#120	1	1	yes	characteristic
716	#379	#120	1	1	yes	characteristic
717	#379	#120	1	1	yes	characteristic
718	#379	#120	1	1	yes	characteristic
719	#379	#120	1	1	yes	characteristic
720	#379	#120	1	1	yes	characteristic
721	#379	#120	1	1	yes	characteristic
722	#379	#120	1	1	yes	characteristic
723	#379	#120	1	1	yes	characteristic
724	#379	#120	1	1	yes	characteristic
725	#379	#120	1	1	yes	characteristic
726	C₄×C₂²⋊C₄	#120	1	1	yes	characteristic
727	C₄×C₂²⋊C₄	#120	1	1	yes	characteristic
728	C₄×C₂²⋊C₄	#120	1	1	yes	characteristic
729	C₄×C₂²⋊C₄	#120	1	1	yes	characteristic
730	C₂⁵	C₂×#120	1	1	yes	characteristic
731	C₂⁵	C₂×#120	1	1	yes	characteristic
732	C₂⁵	C₂×#120	1	1	yes	characteristic
733	C₂⁵	C₂×#120	1	1	yes	characteristic
734	C₂⁵	C₂×#120	1	1	yes	characteristic
735	C₂⁵	C₂×#120	1	1	yes	characteristic
736	C₂⁵	C₂×#120	1	1	yes	characteristic
737	C₂⁵	C₂×#120	1	1	yes	characteristic
738	C₂⁵	C₂×#120	1	1	yes	characteristic
739	C₂⁵	C₂×#120	1	1	yes	characteristic
740	C₂⁵	C₂×#120	1	1	yes	characteristic
741	C₂⁵	C₂×#120	1	1	yes	characteristic
742	C₂⁵	C₂×#120	1	1	yes	characteristic
743	C₂⁵	C₂×#120	1	1	yes	characteristic
744	C₂⁵	C₂×#120	1	1	yes	characteristic
745	C₂⁵	C₂×#120	1	1	yes	characteristic
746	C₂⁵	C₂×#120	1	1	yes	characteristic
747	C₂⁵	C₂×#120	1	1	yes	characteristic
748	C₂⁵	C₂×#120	1	1	yes	characteristic
749	C₂⁵	C₂×#120	1	1	yes	characteristic
750	C₂⁵	D₄²	1	4	yes	—
751	C₂⁵	C₂³×D₄	1	1	yes	characteristic
752	C₂⁵	C₂³×D₄	1	1	yes	characteristic
753	C₂×#41	D₄²	1	4	yes	—
754	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
755	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
756	C₂²×D₄	C₂×#120	1	1	yes	characteristic
757	C₂²×D₄	C₂×#120	1	1	yes	characteristic
758	C₂²×D₄	C₂×#120	1	1	yes	characteristic
759	C₂²×D₄	C₂×#120	1	1	yes	characteristic
760	C₂²×D₄	C₂×#120	1	1	yes	characteristic
761	C₂²×D₄	C₂×#120	1	1	yes	characteristic
762	C₂²×D₄	C₂×#120	1	1	yes	characteristic
763	C₂²×D₄	C₂×#120	1	1	yes	characteristic
764	C₂²×D₄	C₂×#120	1	1	yes	characteristic
765	C₂²×D₄	C₂×#120	1	1	yes	characteristic
766	C₂²×D₄	C₂×#120	1	1	yes	characteristic
767	C₂²×D₄	C₂×#120	1	1	yes	characteristic
768	C₂²×D₄	C₂×#120	1	1	yes	characteristic
769	C₂²×D₄	C₂×#120	1	1	yes	characteristic
770	C₂²×D₄	C₂×#120	1	1	yes	characteristic
771	C₂²×D₄	C₂×#120	1	1	yes	characteristic
772	C₂²×D₄	D₄²	1	4	yes	—
773	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
774	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
775	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
776	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
777	C₂²×D₄	C₂³×D₄	1	2	yes	—
778	C₂²×D₄	C₂×H(5,𝔽₂)	1	2	yes	—
779	C₂²×D₄	C₂×H(5,𝔽₂)	1	2	yes	—
780	C₂²×D₄	C₂×H(5,𝔽₂)	1	2	yes	—
781	C₂³×C₄	C₂×#120	1	1	yes	characteristic
782	C₂³×C₄	C₂×#120	1	1	yes	characteristic
783	C₂³×C₄	C₂×#120	1	1	yes	characteristic
784	C₂³×C₄	C₂×#120	1	1	yes	characteristic
785	C₂³×C₄	C₂×#120	1	1	yes	characteristic
786	C₂³×C₄	C₂×#120	1	1	yes	characteristic
787	C₂³×C₄	C₂×#120	1	1	yes	characteristic
788	C₂³×C₄	C₂×#120	1	1	yes	characteristic
789	C₂³×C₄	C₂×#120	1	1	yes	characteristic
790	C₂³×C₄	C₂×#120	1	1	yes	characteristic
791	C₂³×C₄	C₂×#120	1	1	yes	characteristic
792	C₂³×C₄	C₂×#120	1	1	yes	characteristic
793	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
794	#127	C₂×#120	1	2	yes	—
795	#127	#534	1	2	yes	—
796	#127	D₄²	1	4	yes	—
797	#124	C₂×#120	1	2	yes	—
798	#124	#534	1	2	yes	—
799	#124	D₄²	1	4	yes	—
800	#123	C₂×#120	1	2	yes	—
801	#123	#534	1	2	yes	—
802	#123	D₄²	1	4	yes	—
803	#120	C₂×#120	1	2	yes	—
804	#120	C₂×#120	1	2	yes	—
805	#120	C₂×#120	1	2	yes	—
806	#120	#534	1	2	yes	—
807	#120	#534	1	2	yes	—
808	#120	#534	1	2	yes	—
809	#120	D₄²	1	4	yes	—
810	#120	D₄²	1	4	yes	—
811	#120	D₄²	1	4	yes	—
812	#117	D₄²	1	4	yes	—
813	C₂×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
814	C₂×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
815	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
816	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
817	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
818	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
819	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
820	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
821	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
822	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
823	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
824	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
825	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
826	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
827	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
828	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
829	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
830	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
831	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
832	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
833	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
834	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
835	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
836	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
837	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
838	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
839	C₂×C₂²⋊C₄	D₄²	1	4	yes	—
840	C₂×C₂²⋊C₄	D₄²	1	4	yes	—
841	C₂×C₄²	C₂×#120	1	1	yes	characteristic
842	C₂×C₄²	C₂×#120	1	1	yes	characteristic
843	C₂×C₄²	C₂×#120	1	1	yes	characteristic
844	C₂×C₄²	C₂×#120	1	1	yes	characteristic
845	C₂×C₄²	C₂×#120	1	1	yes	characteristic
846	C₂×C₄²	C₂×#120	1	1	yes	characteristic
847	C₂×C₄²	C₂×#120	1	1	yes	characteristic
848	C₂×C₄²	C₂×#120	1	1	yes	characteristic
849	C₂⁴	#2403	1	2	yes	—
850	C₂⁴	#2403	1	2	yes	—
851	C₂⁴	#2403	1	2	yes	—
852	C₂⁴	#2846	1	1	yes	characteristic
853	C₂⁴	#2846	1	1	yes	characteristic
854	C₂⁴	#2846	1	1	yes	characteristic
855	C₂⁴	#2846	1	1	yes	characteristic
856	C₂⁴	#2846	1	1	yes	characteristic
857	C₂⁴	#2846	1	1	yes	characteristic
858	C₂⁴	#3025	1	1	yes	characteristic
859	C₂⁴	#3025	1	1	yes	characteristic
860	C₂⁴	#3027	1	1	yes	characteristic
861	C₂⁴	#3027	1	1	yes	characteristic
862	C₂⁴	C₂²×#120	1	1	yes	characteristic
863	C₂⁴	C₂²×#120	1	1	yes	characteristic
864	C₂⁴	C₂²×#120	1	1	yes	characteristic
865	C₂⁴	C₂²×#120	1	1	yes	characteristic
866	C₂⁴	C₂²×#120	1	1	yes	characteristic
867	C₂⁴	C₂×D₄²	1	2	yes	—
868	C₂⁴	C₂×D₄²	1	2	yes	—
869	C₂⁴	#3484	1	2	yes	—
870	C₂⁴	#3484	1	2	yes	—
871	C₂×Q₈	#2403	1	2	yes	—
872	C₂×D₄	#2403	1	2	yes	—
873	C₂×D₄	C₂²×#120	1	1	yes	characteristic
874	C₂×D₄	C₂×#534	1	1	yes	characteristic
875	C₂×D₄	C₂×#534	1	1	yes	characteristic
876	C₂×D₄	C₂×#534	1	1	yes	characteristic
877	C₂×D₄	C₂×D₄²	1	2	yes	—
878	C₂×D₄	C₂×D₄²	1	2	yes	—
879	C₂×D₄	C₂×D₄²	1	2	yes	—
880	C₂×D₄	#3484	1	2	yes	—
881	C₂×D₄	#3484	1	2	yes	—
882	C₂×D₄	#3484	1	2	yes	—
883	C₂²×C₄	#2403	1	2	yes	—
884	C₂²×C₄	#2846	1	1	yes	characteristic
885	C₂²×C₄	#2846	1	1	yes	characteristic
886	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
887	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
888	C₂²×C₄	C₂×D₄²	1	2	yes	—
889	C₂²×C₄	#3484	1	2	yes	—
890	C₂²⋊C₄	#2403	1	2	yes	—
891	C₂²⋊C₄	#2403	1	2	yes	—
892	C₂²⋊C₄	#2403	1	2	yes	—
893	C₂²⋊C₄	#2403	1	2	yes	—
894	C₄²	#2403	1	2	yes	—
895	C₄²	#2403	1	2	yes	—
896	C₂³	#32899	1	1	yes	characteristic
897	C₂³	#32899	1	1	yes	characteristic
898	C₂³	#32899	1	1	yes	characteristic
899	C₂³	#32899	1	1	yes	characteristic
900	C₂³	C₂×#2403	1	1	yes	characteristic
901	C₂³	C₂×#2403	1	1	yes	characteristic
902	C₂³	#34980	1	1	yes	characteristic
903	C₂³	#34980	1	1	yes	characteristic
904	C₂³	D₄×#120	1	2	yes	—
905	C₂³	D₄×#120	1	2	yes	—
906	C₂³	D₄×#120	1	2	yes	—
907	C₂³	C₂×#2846	1	1	yes	characteristic
908	C₂³	C₂×#3025	1	1	yes	characteristic
909	C₂³	C₂×#3027	1	1	yes	characteristic
910	C₂³	#60399	1	2	yes	—
911	C₂×C₄	C₂×#2403	1	1	yes	characteristic
912	C₂×C₄	#34980	1	1	yes	characteristic
913	C₂×C₄	D₄×#120	1	2	yes	—
914	C₂²	#511853	1	2	yes	complemented
915	C₂²	#612424	1	1	yes	characteristic
916	C₂²	#6573710	1	2	yes	—
917	C₂²	#6573716	1	2	yes	—
918	C₂²	C₂×#32899	1	1	yes	characteristic
919	C₂²	#6628896	1	1	yes	characteristic
920	C₂	C₂×#511853	1	1	yes	characteristic
921	C₂	#72240574	1	1	yes	characteristic
922	C₂	#72240647	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂×#32899
commutator, Frattini, cosocle	C₂³×D₄	C₂⁵
LCS	G ▷ C₂³×D₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁵ ◁ #34171 ◁ G
LECS	G ▷ C₂³×D₄ ▷ C₂² ▷ C₂ ▷ C₁

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. #72262240	C₂	semidirect
2. #72262238	C₂	semidirect
3. #72262237	C₂	semidirect
4. #72262236	C₂	semidirect
5. #72262235	C₂	semidirect
6. #72262233	C₂	semidirect
7. #72262225	C₂	semidirect
8. #72262193	C₂	semidirect
9. #72262128	C₂	semidirect
10. C₂×#511853	C₂	semidirect
11. #72237806	C₂	semidirect
12. #72235270	C₂	semidirect
13. #72234644	C₂	semidirect
14. C₂²×#33551	C₂	semidirect
15. #72234157	C₂	semidirect
16. #72233855	C₂	semidirect
17. #72233135	C₂	semidirect
18. #72232838	C₂	semidirect
19. C₂×#499787	C₂	semidirect
20. #72232728	C₂	semidirect
21. #72232683	C₂	semidirect
22. #72225632	C₂	semidirect
23. #72218980	C₂	semidirect
24. C₂×#63012	C₂²	semidirect
26. C₂²×#3026	C₂²	semidirect
27. C₂³×B(4,𝔽₂)	C₂²	semidirect
28. C₂²×#3019	C₂²	semidirect
29. #7829278	C₂²	semidirect
30. #7829277	C₂²	semidirect
31. #7819711	C₂²	semidirect
32. #7819709	C₂²	semidirect
35. #7733187	C₂²	semidirect
36. #7733150	C₂²	semidirect
41. #7627347	C₂²	semidirect
42. C₂×#33557	C₂²	semidirect
44. C₂×#33551	C₂²	semidirect
45. C₂×#33551	C₂²	semidirect
46. C₂×#33551	C₂²	semidirect
47. C₂×#33551	C₂²	semidirect
48. C₂²×#2196	C₂²	semidirect
49. C₂²×#2127	C₂²	semidirect
50. C₂²×#2121	C₂²	semidirect
51. C₂³×AΣL(1,𝔽₁₆)	C₂²	semidirect
52. #6628892	C₂²	semidirect
53. C₂×#32898	C₂²	semidirect
54. C₂×#32888	C₂²	semidirect
55. C₂×#23996	C₂²	semidirect
56. C₂×#23996	C₂²	semidirect
57. C₂×#23998	C₂²	semidirect
58. #6370693	C₂²	semidirect
59. #498931	C₂²	semidirect
60. #498927	C₂²	semidirect
61. #498923	C₂²	semidirect
62. C₂×#13346	C₂²	semidirect
63. #498890	C₂²	semidirect
64. C₂×#13343	C₂²	semidirect
65. C₂×#13088	C₂²	semidirect
66. C₂×#13088	C₂²	semidirect
67. #494695	C₂²	semidirect
68. C₂×#13086	C₂²	semidirect
69. #494677	C₂²	semidirect
70. C₂×#13082	C₂²	semidirect
71. #494600	C₂²	semidirect
72. #494582	C₂²	semidirect
73. C₂×#13041	C₂²	semidirect
74. C₂×#12767	C₂²	semidirect
75. C₂×#12759	C₂²	semidirect
76. C₂×#12753	C₂²	semidirect
77. C₂×#12753	C₂²	semidirect
78. C₂×#12753	C₂²	semidirect
79. C₂×#12753	C₂²	semidirect
80. C₂×#12753	C₂²	semidirect
81. C₂×#12727	C₂²	semidirect
82. C₂×#12725	C₂²	semidirect
83. C₂×#12725	C₂²	semidirect
84. #493370	C₂²	semidirect
85. #493357	C₂²	semidirect
86. C₂×#12687	C₂²	semidirect
87. #405274	C₂²	semidirect
88. #405271	C₂²	semidirect
89. #405268	C₂²	semidirect
90. #394275	C₂²	semidirect
91. #394273	C₂²	semidirect
92. #394273	C₂²	semidirect
93. #374058	C₂²	semidirect
94. #374052	C₂²	semidirect
95. #374038	C₂²	semidirect
96. #364545	C₂²	semidirect
97. #364532	C₂²	semidirect
98. #364526	C₂²	semidirect
99. #359894	C₂²	semidirect
100. #359892	C₂²	semidirect
101. #359892	C₂²	semidirect
102. #359509	C₂²	semidirect
103. #359501	C₂²	semidirect
104. #359442	C₂²	semidirect
105. #147829	C₂²	semidirect
106. #147824	C₂²	semidirect
107. #147819	C₂²	semidirect
108. #147811	C₂²	semidirect
109. #147783	C₂²	semidirect
110. #147779	C₂²	semidirect
111. #147741	C₂²	semidirect
112. #147732	C₂²	semidirect
113. #147732	C₂²	semidirect
114. #147610	C₂²	semidirect
115. #147609	C₂²	semidirect
116. #147603	C₂²	semidirect
117. #146705	C₂²	semidirect
118. #146692	C₂²	semidirect
119. #146675	C₂²	semidirect
120. #146654	C₂²	semidirect
121. #146609	C₂²	semidirect
122. #146599	C₂²	semidirect
128. C₂×#3532	D₄	semidirect
129. C₂×#3532	D₄	semidirect
130. C₂×#3532	D₄	semidirect
131. C₂×#3532	D₄	semidirect
137. C₂²×#551	D₄	semidirect
138. C₂²×D₄²	D₄	semidirect
140. C₂²×H(3,𝔽₄)	D₄	semidirect
141. C₂²×#560	D₄	semidirect
147. C₂×#3026	C₂³	semidirect
150. C₂²×B(4,𝔽₂)	C₂³	semidirect
153. C₂²×#453	C₂³	semidirect
155. C₂×#2883	C₂³	semidirect
156. C₂×#2883	C₂³	semidirect
159. #59189	D₄	semidirect
160. #59162	D₄	semidirect
161. #59126	D₄	semidirect
162. #58990	D₄	semidirect
163. #58990	D₄	semidirect
164. #58990	D₄	semidirect
165. #58990	D₄	semidirect
166. #58990	D₄	semidirect
167. #58990	D₄	semidirect
168. #58990	D₄	semidirect
169. #58990	D₄	semidirect
170. #58990	D₄	semidirect
173. #52012	D₄	semidirect
174. #52004	D₄	semidirect
175. #51902	D₄	semidirect
176. #51895	D₄	semidirect
177. #50646	D₄	semidirect
178. #50635	D₄	semidirect
179. #47846	D₄	semidirect
180. #47827	D₄	semidirect
181. #46324	D₄	semidirect
182. #45977	D₄	semidirect
183. #45455	D₄	semidirect
184. #45438	D₄	semidirect
189. C₂×#2846	D₄	semidirect
190. #35556	D₄	semidirect
192. #35528	D₄	semidirect
194. #35367	D₄	semidirect
195. #35360	D₄	semidirect
198. #35348	D₄	semidirect
199. #35348	D₄	semidirect
202. #35272	D₄	semidirect
203. #35254	D₄	semidirect
204. #35250	D₄	semidirect
205. #34993	D₄	semidirect
206. #34992	D₄	semidirect
207. #34982	D₄	semidirect
208. #34982	D₄	semidirect
209. #34981	D₄	semidirect
210. #34981	D₄	semidirect
212. #34739	D₄	semidirect
214. C₂×#2403	D₄	semidirect
220. #34204	D₄	semidirect
221. #34198	D₄	semidirect
223. #34171	D₄	semidirect
227. C₂²⋊C₄×#41	D₄	semidirect
228. C₂×D₄×C₂²⋊C₄	D₄	semidirect
229. C₂²×#379	D₄	semidirect
230. #33551	D₄	semidirect
235. C₂²×#353	C₂³	semidirect
236. C₂²×#353	C₂³	semidirect
241. C₂×#2121	C₂³	semidirect
242. C₂×#2121	C₂³	semidirect
247. C₂²×AΣL(1,𝔽₁₆)	C₂³	semidirect
248. C₂²×AΣL(1,𝔽₁₆)	C₂³	semidirect
251. C₂×#1913	C₂³	semidirect
256. C₂×#1889	C₂³	semidirect
257. C₂×#1887	C₂³	semidirect
258. C₂×#1829	C₂³	semidirect
259. C₂×#1828	C₂³	semidirect
260. C₂×#1828	C₂³	semidirect
261. C₂×#1792	C₂³	semidirect
262. #20609	C₂³	semidirect
263. C₂×#1790	C₂³	semidirect
267. C₂×#1393	C₂³	semidirect
268. C₂×#1393	C₂³	semidirect
269. #12574	C₂³	semidirect
270. #12574	C₂³	semidirect
271. C₂×#1390	C₂³	semidirect
272. C₂×#1390	C₂³	semidirect
273. #10769	C₂³	semidirect
274. #10768	C₂³	semidirect
275. #10768	C₂³	semidirect
276. #10754	C₂³	semidirect
277. #10749	C₂³	semidirect
278. #10745	C₂³	semidirect
290. C₂×H(3,𝔽₄)	C₂×D₄	semidirect
295. C₂×#560	C₂×D₄	semidirect
296. C₂×#560	C₂×D₄	semidirect
297. C₂×#560	C₂×D₄	semidirect
298. C₂×#559	C₂×D₄	semidirect
303. C₂×#551	C₂×D₄	semidirect
308. C₂×D₄²	C₂×D₄	semidirect
309. C₂×D₄²	C₂×D₄	semidirect
310. C₂×D₄²	C₂×D₄	semidirect
311. C₂×D₄²	C₂×D₄	semidirect
312. C₂×D₄²	C₂×D₄	semidirect
313. C₂×D₄²	C₂×D₄	semidirect
314. C₂×#543	C₂×D₄	semidirect
315. C₂×#543	C₂×D₄	semidirect
322. C₂×#535	C₂×D₄	semidirect
323. C₂×#535	C₂×D₄	semidirect
336. C₂×#533	C₂×D₄	semidirect
360. C₂²×#120	C₂×D₄	semidirect
361. C₂²×#120	C₂×D₄	semidirect
362. C₂²×#120	C₂×D₄	semidirect
363. C₂²×#120	C₂×D₄	semidirect
367. C₂×#518	C₂×D₄	semidirect
368. C₂×#518	C₂×D₄	semidirect
369. C₂×#518	C₂×D₄	semidirect
370. C₂×#518	C₂×D₄	semidirect
374. C₂×C₄×#41	C₂×D₄	semidirect
375. C₂×C₄×#41	C₂×D₄	semidirect
379. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
380. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
381. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
382. #3026	C₂×D₄	semidirect
383. C₂×B(4,𝔽₂)	C₂×D₄	semidirect
384. #3019	C₂×D₄	semidirect
391. #2724	C₂×D₄	semidirect
392. #2717	C₂×D₄	semidirect
393. #2709	C₂×D₄	semidirect
394. #2709	C₂×D₄	semidirect
395. #2709	C₂×D₄	semidirect
396. #2697	C₂×D₄	semidirect
397. #2697	C₂×D₄	semidirect
398. #2684	C₂×D₄	semidirect
399. #2684	C₂×D₄	semidirect
400. #2684	C₂×D₄	semidirect
401. #2679	C₂×D₄	semidirect
402. #2679	C₂×D₄	semidirect
403. #2679	C₂×D₄	semidirect
404. #2679	C₂×D₄	semidirect
405. #2679	C₂×D₄	semidirect
406. #2669	C₂×D₄	semidirect
407. #2669	C₂×D₄	semidirect
408. #2669	C₂×D₄	semidirect
409. #2669	C₂×D₄	semidirect
410. #2669	C₂×D₄	semidirect
411. #2669	C₂×D₄	semidirect
412. #2669	C₂×D₄	semidirect
413. #2669	C₂×D₄	semidirect
414. #2669	C₂×D₄	semidirect
439. #2380	C₂×D₄	semidirect
440. #2379	C₂×D₄	semidirect
441. #2376	C₂×D₄	semidirect
442. #2375	C₂×D₄	semidirect
443. #2374	C₂×D₄	semidirect
444. #2372	C₂×D₄	semidirect
445. #2366	C₂×D₄	semidirect
446. #2358	C₂×D₄	semidirect
447. #2358	C₂×D₄	semidirect
448. #2358	C₂×D₄	semidirect
449. #2358	C₂×D₄	semidirect
450. #2358	C₂×D₄	semidirect
451. #2316	C₂×D₄	semidirect
452. #2315	C₂×D₄	semidirect
453. #2315	C₂×D₄	semidirect
454. #2315	C₂×D₄	semidirect
455. #2315	C₂×D₄	semidirect
456. #2315	C₂×D₄	semidirect
457. #2315	C₂×D₄	semidirect
458. #2315	C₂×D₄	semidirect
459. #2311	C₂×D₄	semidirect
460. #2311	C₂×D₄	semidirect
463. #2309	C₂×D₄	semidirect
469. #2308	C₂×D₄	semidirect
470. #2308	C₂×D₄	semidirect
471. #2308	C₂×D₄	semidirect
473. #2297	C₂×D₄	semidirect
474. #2297	C₂×D₄	semidirect
475. #2296	C₂×D₄	semidirect
476. #2296	C₂×D₄	semidirect
480. C₂×#386	C₂×D₄	semidirect
481. C₂×#386	C₂×D₄	semidirect
483. #2285	C₂×D₄	semidirect
486. C₂×#380	C₂×D₄	semidirect
493. C₂×#379	C₂×D₄	semidirect
494. C₂×#379	C₂×D₄	semidirect
495. C₂×#379	C₂×D₄	semidirect
496. C₂×#379	C₂×D₄	semidirect
497. C₂×#379	C₂×D₄	semidirect
498. #2274	C₂×D₄	semidirect
499. #2273	C₂×D₄	semidirect
501. C₂×C₄×C₂²⋊C₄	C₂×D₄	semidirect
502. #2127	C₂×D₄	semidirect
503. #2121	C₂×D₄	semidirect
504. C₂×AΣL(1,𝔽₁₆)	C₂×D₄	semidirect
549. H(3,𝔽₄)	#120	semidirect
550. #560	#120	semidirect
551. #551	#120	semidirect
552. D₄²	#120	semidirect
914. C₂²	#511853	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#72262240	2
#72262238	2
#72262237	2
#72262236	2
#72262235	2
#72262233	2
#72262225	2
#72262193	2
#72262128	2
C₂×#511853	2
#72237806	2
#72235270	2
#72234644	2
C₂²×#33551	2
#72234157	2
#72233855	2
#72233135	2
#72232838	2
C₂×#499787	2
#72232728	2
#72232683	2
#72225632	2
#72218980	2