Subgroups — #72262336

Order 2048.

At least 17141 conjugacy classes of subgroups; only the 1640 normal subgroups are shown.

The subgroup lattice has 755 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72262332	C₂	1	2	yes	maximal, complemented
2	#72262329	C₂	1	1	yes	maximal, characteristic, complemented
3	#72262237	C₂	1	4	yes	maximal, complemented
4	#72262227	C₂	1	2	yes	maximal, complemented
5	#72262176	C₂	1	2	yes	maximal, complemented
6	#72262135	C₂	1	1	yes	maximal, characteristic, complemented
7	#72256627	C₂	1	1	yes	maximal, characteristic, complemented
8	#72249513	C₂	1	2	yes	maximal, complemented
9	C₂×#493480	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#493635	C₂	1	1	yes	maximal, characteristic, complemented
11	#72234696	C₂	1	2	yes	maximal, complemented
12	#72234630	C₂	1	2	yes	maximal, complemented
13	#72234161	C₂	1	2	yes	maximal, complemented
14	#72234160	C₂	1	2	yes	maximal, complemented
15	C₂×#7622880	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#6499855	C₂	1	1	yes	maximal, characteristic, complemented
17	#72213329	C₂	1	4	yes	maximal, complemented
18	C₂×#63011	C₂²	1	1	yes	characteristic
19	C₂×#62832	C₂²	1	1	yes	characteristic
20	C₂×#60399	C₂²	1	2	yes	complemented
21	C₂×#60399	C₂²	1	1	yes	characteristic, complemented
22	C₂×#60388	C₂²	1	1	yes	characteristic
23	C₂×#60388	C₂²	1	1	yes	characteristic, complemented
24	#7829277	C₂²	1	2	yes	complemented
25	#7792761	C₂²	1	2	yes	complemented
26	#7737455	C₂²	1	1	yes	characteristic, complemented
27	#7737454	C₂²	1	1	yes	characteristic, complemented
28	#7711201	C₂²	1	1	yes	characteristic, complemented
29	C₂×#59126	C₂²	1	1	yes	characteristic, complemented
30	#7659296	C₂²	1	2	yes	—
31	#7648640	C₂²	1	2	yes	—
32	#7627298	C₂²	1	1	yes	characteristic
33	C₂×#33557	C₂²	1	2	yes	complemented
34	C₂×#33551	C₂²	1	4	yes	complemented
35	C₂²×#2196	C₂²	1	2	yes	complemented
36	C₂×#33359	C₂²	1	1	yes	characteristic
37	C₂×#33359	C₂²	1	1	yes	characteristic
38	C₂×#33359	C₂²	1	2	yes	complemented
39	C₂×#33348	C₂²	1	2	yes	complemented
40	C₂×#33348	C₂²	1	2	yes	complemented
41	C₂×#23998	C₂²	1	2	yes	complemented
42	C₂×#23998	C₂²	1	2	yes	complemented
43	C₂×#23897	C₂²	1	2	yes	complemented
44	C₂×#23906	C₂²	1	2	yes	complemented
45	C₂×#21782	C₂²	1	1	yes	characteristic
46	C₂×#21782	C₂²	1	1	yes	characteristic, complemented
47	C₂×#21778	C₂²	1	1	yes	characteristic, complemented
48	C₂×#21776	C₂²	1	2	yes	complemented
49	C₂×#21776	C₂²	1	2	yes	complemented
50	#6370735	C₂²	1	2	yes	complemented
51	#498931	C₂²	1	4	yes	complemented
52	#498927	C₂²	1	4	yes	complemented
53	#498923	C₂²	1	4	yes	complemented
54	C₂×#13346	C₂²	1	4	yes	complemented
55	#494600	C₂²	1	4	yes	complemented
56	#494596	C₂²	1	2	yes	complemented
57	C₂×#13047	C₂²	1	2	yes	complemented
58	C₂×#12767	C₂²	1	2	yes	complemented
59	C₂×#12759	C₂²	1	2	yes	complemented
60	C₂×#12753	C₂²	1	4	yes	complemented
61	C₂×#12727	C₂²	1	2	yes	complemented
62	C₂×#12727	C₂²	1	2	yes	complemented
63	C₂×#12707	C₂²	1	2	yes	complemented
64	C₂×#12693	C₂²	1	2	yes	complemented
65	#492887	C₂²	1	2	yes	complemented
66	#492887	C₂²	1	2	yes	complemented
67	#405274	C₂²	1	4	yes	complemented
68	#405268	C₂²	1	4	yes	complemented
69	#394066	C₂²	1	4	yes	complemented
70	#394064	C₂²	1	4	yes	complemented
71	#355922	C₂²	1	2	yes	complemented
72	#147829	C₂²	1	4	yes	complemented
73	#147824	C₂²	1	4	yes	complemented
74	#147819	C₂²	1	4	yes	complemented
75	#147811	C₂²	1	4	yes	complemented
76	#147609	C₂²	1	4	yes	complemented
77	#147603	C₂²	1	4	yes	complemented
78	#147567	C₂²	1	4	yes	complemented
79	#147555	C₂²	1	4	yes	complemented
80	#146654	C₂²	1	4	yes	complemented
81	#146639	C₂²	1	2	yes	complemented
82	#146622	C₂²	1	2	yes	complemented
83	C₂×H(7,𝔽₂)	C₂³	1	1	yes	characteristic
84	C₂×#3508	D₄	1	1	yes	characteristic, complemented
85	C₂×#3508	D₄	1	1	yes	characteristic, complemented
86	C₂×#3508	C₂³	1	1	yes	characteristic
87	C₂×#3508	C₂³	1	1	yes	characteristic
88	C₂×#3498	D₄	1	1	yes	characteristic, complemented
89	C₂×#3498	D₄	1	1	yes	characteristic, complemented
90	C₂×#3498	C₂³	1	1	yes	characteristic
91	C₂×#3498	C₂³	1	1	yes	characteristic
92	C₂×#3484	D₄	1	1	yes	characteristic, complemented
93	C₂×#3484	D₄	1	1	yes	characteristic, complemented
94	C₂×#3484	C₂³	1	2	yes	—
95	C₂×#3484	C₂³	1	1	yes	characteristic
96	C₂×#3484	C₂³	1	1	yes	characteristic
97	C₂×#3484	C₂³	1	2	yes	complemented
98	C₂×#3549	D₄	1	1	yes	characteristic, complemented
99	C₂×#3543	D₄	1	1	yes	characteristic, complemented
100	C₂×#3543	C₂³	1	1	yes	characteristic
101	C₂×#3537	D₄	1	2	yes	complemented
102	C₂×#3532	D₄	1	2	yes	complemented
103	C₂×#3532	C₂³	1	2	yes	—
104	C₂×#3481	D₄	1	1	yes	characteristic, complemented
105	C₂²×D₄²	D₄	1	1	yes	characteristic, complemented
106	C₂²×D₄²	C₂³	1	1	yes	characteristic
107	C₂×#3444	D₄	1	1	yes	characteristic, complemented
108	C₂×#3444	D₄	1	1	yes	characteristic, complemented
109	C₂³×#127	C₂³	1	1	yes	characteristic
110	C₂×#3026	C₂³	1	4	yes	—
111	C₂²×B(4,𝔽₂)	C₂³	1	4	yes	—
112	#60388	D₄	1	8	yes	complemented
113	C₂×#3019	C₂³	1	2	yes	—
114	C₂×#3019	C₂³	1	2	yes	complemented
115	C₂²×#453	C₂³	1	2	yes	—
116	C₂²×#453	C₂³	1	2	yes	complemented
117	C₂×#2888	C₂³	1	1	yes	characteristic
118	C₂×#2888	C₂³	1	1	yes	characteristic
119	C₂×#2883	C₂³	1	1	yes	characteristic
120	C₂×#2883	C₂³	1	2	yes	—
121	C₂×#2883	C₂³	1	2	yes	—
122	C₂×#2883	C₂³	1	2	yes	complemented
123	#52165	D₄	1	2	yes	complemented
124	C₂×#2669	D₄	1	2	yes	complemented
125	C₂×#2669	C₂³	1	2	yes	—
126	#37297	D₄	1	2	yes	complemented
127	#37273	D₄	1	2	yes	complemented
128	#37269	D₄	1	2	yes	complemented
129	#37232	D₄	1	2	yes	complemented
130	#37232	C₂³	1	2	yes	—
131	#36737	D₄	1	2	yes	complemented
132	#36737	C₂³	1	2	yes	—
133	#36702	D₄	1	2	yes	complemented
134	#36702	C₂³	1	2	yes	—
135	#35360	D₄	1	2	yes	complemented
136	#35360	C₂³	1	2	yes	—
137	#35350	D₄	1	2	yes	complemented
138	#35350	C₂³	1	2	yes	—
139	#35348	D₄	1	2	yes	complemented
140	#35348	D₄	1	2	yes	complemented
141	#34984	D₄	1	2	yes	complemented
142	#34980	D₄	1	2	yes	complemented
143	#34980	C₂³	1	2	yes	—
144	C₂×#2408	D₄	1	2	yes	complemented
145	C₂×#2403	D₄	1	2	yes	complemented
146	C₂×#2403	C₂³	1	2	yes	—
147	#34411	D₄	1	2	yes	complemented
148	#34406	D₄	1	2	yes	complemented
149	#34406	C₂³	1	2	yes	—
150	#34368	D₄	1	1	yes	characteristic, complemented
151	#34364	D₄	1	1	yes	characteristic, complemented
152	#34364	C₂³	1	1	yes	characteristic
153	#34256	C₂³	1	2	yes	—
154	#34155	D₄	1	1	yes	characteristic, complemented
155	C₂×#2366	D₄	1	1	yes	characteristic, complemented
156	C₂×#2366	C₂³	1	1	yes	characteristic
157	#33359	D₄	1	8	yes	complemented
158	C₂×#2127	C₂³	1	2	yes	—
159	C₂×#2127	C₂³	1	2	yes	—
160	C₂×#2127	C₂³	1	4	yes	complemented
161	C₂²×#353	C₂³	1	2	yes	—
162	C₂²×#353	C₂³	1	2	yes	—
163	C₂²×#353	C₂³	1	4	yes	complemented
164	C₂×#2121	C₂³	1	4	yes	—
165	C₂×#2121	C₂³	1	4	yes	—
166	C₂²×AΣL(1,𝔽₁₆)	C₂³	1	4	yes	—
167	C₂²×AΣL(1,𝔽₁₆)	C₂³	1	4	yes	—
168	#21782	D₄	1	8	yes	complemented
169	C₂×#1913	C₂³	1	4	yes	—
170	C₂×#1911	C₂³	1	2	yes	—
171	C₂×#1911	C₂³	1	2	yes	complemented
172	C₂×#1889	C₂³	1	4	yes	—
173	C₂×#1887	C₂³	1	2	yes	—
174	C₂×#1887	C₂³	1	2	yes	complemented
175	C₂×#1829	C₂³	1	2	yes	complemented
176	C₂×#1828	C₂³	1	4	yes	complemented
177	#20609	C₂³	1	4	yes	complemented
178	C₂×#1790	C₂³	1	4	yes	complemented
179	C₂×#1783	C₂³	1	2	yes	complemented
180	C₂×#1781	C₂³	1	4	yes	complemented
181	#12574	C₂³	1	4	yes	complemented
182	#12574	C₂³	1	4	yes	complemented
183	C₂×#1390	C₂³	1	4	yes	complemented
184	C₂×#1390	C₂³	1	4	yes	complemented
185	#10754	C₂³	1	4	yes	complemented
186	#10745	C₂³	1	4	yes	complemented
187	H(7,𝔽₂)	C₂×D₄	1	4	yes	complemented
188	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
189	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
190	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic, complemented
191	C₂²×H(5,𝔽₂)	C₂⁴	1	2	yes	—
192	C₂²×H(5,𝔽₂)	C₂⁴	1	1	yes	characteristic
193	C₂⁴×D₄	C₂×D₄	1	2	yes	—
194	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic, complemented
195	C₂⁴×D₄	C₂×D₄	1	2	yes	complemented
196	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
197	C₂×H(3,𝔽₄)	C₂×D₄	1	2	yes	—
198	C₂×#560	C₂×D₄	1	2	yes	—
199	C₂×#560	C₂×D₄	1	2	yes	—
200	#3498	C₂×D₄	1	4	yes	—
201	#3498	C₂×D₄	1	4	yes	—
202	#3498	C₂×D₄	1	4	yes	—
203	#3498	#41	1	4	yes	—
204	C₂×#559	C₂×D₄	1	1	yes	characteristic
205	C₂×#551	C₂×D₄	1	2	yes	—
206	C₂×D₄²	C₂×D₄	1	2	yes	—
207	C₂×D₄²	C₂×D₄	1	2	yes	—
208	C₂×D₄²	C₂×D₄	1	1	yes	characteristic
209	C₂×D₄²	C₂×D₄	1	1	yes	characteristic
210	C₂×D₄²	C₂×D₄	1	1	yes	characteristic
211	C₂×#535	C₂×D₄	1	2	yes	—
212	C₂×#535	C₂×D₄	1	1	yes	characteristic
213	C₂×#535	C₂×D₄	1	1	yes	characteristic
214	C₂×#535	C₂×D₄	1	2	yes	—
215	C₂×#535	C₂×D₄	1	1	yes	characteristic
216	C₂×#535	C₂×D₄	1	1	yes	characteristic
217	C₂×#535	C₂×D₄	1	2	yes	—
218	C₂×#535	C₂×D₄	1	2	yes	—
219	C₂×#535	C₂×D₄	1	1	yes	characteristic
220	C₂×#535	C₂×D₄	1	1	yes	characteristic
221	C₂×#535	C₂×D₄	1	1	yes	characteristic
222	C₂×#535	C₂×D₄	1	1	yes	characteristic
223	C₂×#535	C₂×D₄	1	1	yes	characteristic, complemented
224	C₂×#535	C₂×D₄	1	1	yes	characteristic, complemented
225	C₂×#535	C₂⁴	1	1	yes	characteristic
226	C₂×#535	C₂⁴	1	1	yes	characteristic
227	C₂×#534	C₂×D₄	1	2	yes	—
228	C₂×#534	C₂×D₄	1	2	yes	—
229	C₂×#534	C₂×D₄	1	2	yes	—
230	C₂×#534	C₂×D₄	1	2	yes	—
231	C₂×#534	C₂×D₄	1	2	yes	—
232	C₂×#534	C₂×D₄	1	2	yes	complemented
233	C₂×#534	C₂⁴	1	2	yes	—
234	C₂×#533	C₂×D₄	1	1	yes	characteristic, complemented
235	C₂×#533	C₂×D₄	1	1	yes	characteristic, complemented
236	C₂×#532	C₂×D₄	1	1	yes	characteristic
237	C₂×#532	C₂×D₄	1	1	yes	characteristic
238	C₂×#532	C₂×D₄	1	2	yes	—
239	C₂×#532	C₂×D₄	1	1	yes	characteristic
240	C₂×#532	C₂×D₄	1	1	yes	characteristic
241	C₂²×#127	C₂×D₄	1	2	yes	—
242	C₂²×#127	C₂×D₄	1	1	yes	characteristic
243	C₂²×#127	C₂×D₄	1	1	yes	characteristic
244	C₂²×#127	C₂×D₄	1	1	yes	characteristic, complemented
245	C₂²×#127	C₂×D₄	1	1	yes	characteristic, complemented
246	C₂²×#127	C₂⁴	1	1	yes	characteristic
247	C₂²×#127	C₂⁴	1	1	yes	characteristic
248	C₂×#525	C₂×D₄	1	2	yes	—
249	C₂×#525	C₂×D₄	1	2	yes	—
250	C₂×#525	C₂×D₄	1	1	yes	characteristic
251	C₂×#525	C₂×D₄	1	1	yes	characteristic
252	C₂×#525	C₂×D₄	1	1	yes	characteristic, complemented
253	C₂×#525	C₂×D₄	1	1	yes	characteristic, complemented
254	C₂²×#120	C₂×D₄	1	2	yes	—
255	C₂²×#120	C₂×D₄	1	2	yes	—
256	C₂²×#120	C₂×D₄	1	2	yes	—
257	C₂²×#120	C₂×D₄	1	2	yes	—
258	C₂²×#120	C₂×D₄	1	2	yes	—
259	C₂²×#120	C₂×D₄	1	2	yes	complemented
260	C₂²×#120	C₂×D₄	1	2	yes	complemented
261	C₂²×#120	C₂⁴	1	2	yes	—
262	C₂×#518	C₂×D₄	1	2	yes	—
263	C₂×#518	C₂×D₄	1	2	yes	—
264	C₂×#518	C₂×D₄	1	1	yes	characteristic, complemented
265	C₂×#518	C₂×D₄	1	1	yes	characteristic, complemented
266	C₂×#518	C₂×D₄	1	1	yes	characteristic, complemented
267	C₂×#518	C₂⁴	1	2	yes	—
268	C₂×#518	C₂⁴	1	1	yes	characteristic
269	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
270	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
271	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic, complemented
272	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic, complemented
273	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
274	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic, complemented
275	#3019	C₂×D₄	1	8	yes	complemented
276	C₂×#453	C₂×D₄	1	8	yes	complemented
277	#2888	C₂×D₄	1	4	yes	complemented
278	#2888	C₂×D₄	1	4	yes	complemented
279	C₂²×#100	C₂⁴	1	2	yes	—
280	C₂²×#100	C₂⁴	1	2	yes	—
281	#2883	C₂×D₄	1	8	yes	complemented
282	#2883	C₂×D₄	1	4	yes	complemented
283	C₂²×#99	C₂⁴	1	4	yes	—
284	C₂²×#99	C₂⁴	1	4	yes	—
285	#2717	C₂×D₄	1	2	yes	complemented
286	#2709	C₂×D₄	1	2	yes	complemented
287	#2709	C₂×D₄	1	2	yes	complemented
288	#2709	C₂×D₄	1	2	yes	complemented
289	#2684	C₂×D₄	1	2	yes	complemented
290	#2684	C₂×D₄	1	2	yes	complemented
291	#2684	C₂×D₄	1	2	yes	complemented
292	#2669	C₂×D₄	1	2	yes	complemented
293	#2669	C₂×D₄	1	2	yes	complemented
294	#2669	C₂×D₄	1	2	yes	complemented
295	#2669	C₂×D₄	1	2	yes	complemented
296	#2669	C₂×D₄	1	2	yes	complemented
297	#2669	C₂×D₄	1	2	yes	complemented
298	#2669	C₂×D₄	1	2	yes	complemented
299	#2669	C₂×D₄	1	2	yes	complemented
300	#2669	C₂×D₄	1	2	yes	complemented
301	#2380	C₂×D₄	1	2	yes	complemented
302	#2380	C₂×D₄	1	2	yes	complemented
303	#2379	C₂×D₄	1	2	yes	complemented
304	#2372	C₂×D₄	1	2	yes	complemented
305	#2366	C₂×D₄	1	2	yes	complemented
306	#2366	C₂×D₄	1	1	yes	characteristic, complemented
307	#2366	C₂×D₄	1	1	yes	characteristic, complemented
308	#2366	C₂×D₄	1	1	yes	characteristic, complemented
309	#2366	C₂×D₄	1	2	yes	complemented
310	#2366	C₂×D₄	1	1	yes	characteristic, complemented
311	#2315	C₂×D₄	1	2	yes	complemented
312	#2315	C₂×D₄	1	2	yes	complemented
313	#2315	C₂×D₄	1	2	yes	complemented
314	#2311	C₂×D₄	1	2	yes	—
315	#2311	C₂×D₄	1	2	yes	—
316	#2308	C₂×D₄	1	2	yes	—
317	#2308	C₂×D₄	1	2	yes	—
318	#2308	C₂×D₄	1	2	yes	—
319	#2308	C₂×D₄	1	2	yes	complemented
320	#2308	C₂×D₄	1	2	yes	complemented
321	#2308	C₂⁴	1	2	yes	—
322	#2297	C₂×D₄	1	2	yes	—
323	#2297	C₂×D₄	1	2	yes	—
324	C₂×#386	C₂×D₄	1	2	yes	—
325	C₂×#386	C₂×D₄	1	2	yes	—
326	C₂×#386	C₂×D₄	1	2	yes	—
327	C₂×#386	C₂×D₄	1	2	yes	complemented
328	C₂×#386	C₂×D₄	1	2	yes	complemented
329	C₂×#386	C₂⁴	1	2	yes	—
330	C₂×#380	C₂×D₄	1	2	yes	complemented
331	C₂×#379	C₂×D₄	1	2	yes	complemented
332	C₂×#379	C₂×D₄	1	2	yes	complemented
333	C₂×#379	C₂×D₄	1	2	yes	complemented
334	C₂×#379	C₂×D₄	1	2	yes	complemented
335	#2127	C₂×D₄	1	8	yes	complemented
336	C₂×#353	C₂×D₄	1	8	yes	complemented
337	#1911	C₂×D₄	1	8	yes	complemented
338	#1887	C₂×D₄	1	8	yes	complemented
339	C₂⁶	#120	1	2	yes	—
340	C₂⁶	C₂²×D₄	1	2	yes	—
341	C₂⁶	C₂²×D₄	1	2	yes	—
342	C₂×H(5,𝔽₂)	#120	1	4	yes	—
343	C₂×H(5,𝔽₂)	#121	1	4	yes	—
344	C₂×H(5,𝔽₂)	C₂²×D₄	1	4	yes	—
345	C₂×H(5,𝔽₂)	C₂²×D₄	1	2	yes	—
346	C₂×H(5,𝔽₂)	C₂²×D₄	1	2	yes	—
347	C₂×H(5,𝔽₂)	C₂²×D₄	1	2	yes	—
348	C₂×H(5,𝔽₂)	C₂×#41	1	2	yes	—
349	C₂×H(5,𝔽₂)	H(5,𝔽₂)	1	4	yes	—
350	C₂×H(5,𝔽₂)	H(5,𝔽₂)	1	4	yes	—
351	C₂²×#41	#120	1	2	yes	—
352	C₂²×#41	#120	1	1	yes	characteristic
353	C₂²×#41	#120	1	1	yes	characteristic
354	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
355	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
356	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
357	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
358	C₂²×#41	C₂²×D₄	1	2	yes	—
359	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
360	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
361	C₂³×D₄	#120	1	2	yes	—
362	C₂³×D₄	#120	1	2	yes	—
363	C₂³×D₄	#120	1	2	yes	—
364	C₂³×D₄	#120	1	1	yes	characteristic
365	C₂³×D₄	#120	1	1	yes	characteristic
366	C₂³×D₄	C₂²×D₄	1	2	yes	—
367	C₂³×D₄	C₂²×D₄	1	2	yes	—
368	C₂³×D₄	C₂²×D₄	1	2	yes	—
369	C₂³×D₄	C₂²×D₄	1	2	yes	—
370	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
371	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
372	C₂³×D₄	C₂²×D₄	1	2	yes	—
373	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
374	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
375	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
376	C₂³×D₄	C₂⁵	1	1	yes	characteristic
377	C₂⁴×C₄	#120	1	2	yes	—
378	C₂⁴×C₄	#120	1	2	yes	—
379	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
380	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
381	#535	#120	1	4	yes	—
382	#535	#120	1	4	yes	—
383	#535	#120	1	4	yes	—
384	#535	#121	1	4	yes	—
385	#535	#121	1	4	yes	—
386	#535	#121	1	4	yes	—
387	#535	#121	1	4	yes	—
388	#535	#121	1	4	yes	—
389	#535	#127	1	4	yes	—
390	#535	#127	1	4	yes	—
391	#535	C₂²×D₄	1	2	yes	—
392	#535	C₂²×D₄	1	2	yes	—
393	#535	C₂²×D₄	1	2	yes	—
394	#535	C₂×#41	1	2	yes	—
395	#532	#120	1	4	yes	—
396	#532	#120	1	4	yes	—
397	#532	#121	1	4	yes	—
398	#532	#121	1	4	yes	—
399	#532	#121	1	4	yes	—
400	#532	#127	1	4	yes	—
401	C₂×C₄⋊Q₈	#120	1	1	yes	characteristic
402	C₂×C₄⋊Q₈	#120	1	1	yes	characteristic
403	C₂×#127	#120	1	1	yes	characteristic
404	C₂×#127	#120	1	2	yes	—
405	C₂×#127	#120	1	1	yes	characteristic
406	C₂×#127	#120	1	1	yes	characteristic
407	C₂×#127	#120	1	1	yes	characteristic
408	C₂×#127	#120	1	4	yes	—
409	C₂×#127	#121	1	4	yes	—
410	C₂×#127	#121	1	4	yes	—
411	C₂×#127	#127	1	4	yes	—
412	C₂×#127	C₂²×D₄	1	2	yes	—
413	C₂×#127	C₂²×D₄	1	2	yes	—
414	C₂×#127	C₂²×D₄	1	2	yes	—
415	C₂×#127	C₂²×D₄	1	1	yes	characteristic
416	C₂×#127	C₂²×D₄	1	1	yes	characteristic
417	C₂×#127	C₂²×D₄	1	1	yes	characteristic
418	C₂×#127	C₂²×D₄	1	2	yes	—
419	C₂×#127	C₂²×D₄	1	1	yes	characteristic
420	C₂×#127	C₂²×D₄	1	1	yes	characteristic
421	C₂×#127	C₂²×D₄	1	1	yes	characteristic
422	C₂×#127	C₂²×D₄	1	2	yes	—
423	C₂×#127	C₂²×D₄	1	2	yes	—
424	C₂×#127	C₂×#41	1	2	yes	—
425	C₂×#124	#120	1	1	yes	characteristic
426	C₂×#124	#120	1	1	yes	characteristic
427	C₂×#124	#120	1	2	yes	—
428	C₂×#124	#120	1	1	yes	characteristic
429	C₂×#124	#120	1	1	yes	characteristic
430	C₂×#124	#120	1	1	yes	characteristic
431	C₂×#124	#120	1	1	yes	characteristic
432	C₂×#124	C₂²×D₄	1	2	yes	—
433	C₂×#124	C₂²×D₄	1	1	yes	characteristic
434	C₂×#124	C₂²×D₄	1	1	yes	characteristic
435	C₂×#123	#120	1	1	yes	characteristic
436	C₂×#123	#120	1	2	yes	—
437	C₂×#123	#120	1	1	yes	characteristic
438	C₂×#123	#120	1	2	yes	—
439	C₂×#123	#120	1	2	yes	—
440	C₂×#123	C₂²×D₄	1	2	yes	—
441	C₂×#123	C₂²×D₄	1	2	yes	—
442	C₂×#120	#120	1	1	yes	characteristic
443	C₂×#120	#120	1	2	yes	—
444	C₂×#120	#120	1	2	yes	—
445	C₂×#120	#120	1	2	yes	—
446	C₂×#120	#120	1	2	yes	—
447	C₂×#120	#120	1	1	yes	characteristic
448	C₂×#120	#120	1	2	yes	—
449	C₂×#120	#120	1	2	yes	—
450	C₂×#120	#120	1	2	yes	—
451	C₂×#120	#120	1	2	yes	—
452	C₂×#120	#120	1	2	yes	—
453	C₂×#120	#120	1	2	yes	—
454	C₂×#120	#120	1	2	yes	—
455	C₂×#120	C₂²×D₄	1	2	yes	—
456	C₂×#120	C₂²×D₄	1	2	yes	—
457	C₂×#120	C₂²×D₄	1	2	yes	—
458	C₂×#120	C₂²×D₄	1	2	yes	—
459	C₂×#120	C₂²×D₄	1	2	yes	—
460	C₂×#120	C₂²×D₄	1	2	yes	—
461	#518	C₂²×D₄	1	4	yes	—
462	C₄×#41	#120	1	4	yes	—
463	C₄×#41	#121	1	4	yes	—
464	C₂×#117	#120	1	2	yes	—
465	C₂×#117	#120	1	2	yes	—
466	C₂×#117	#120	1	2	yes	—
467	C₂×#117	#120	1	2	yes	—
468	C₂×#117	#120	1	2	yes	—
469	C₂×#117	#120	1	1	yes	characteristic
470	C₂×#117	#120	1	1	yes	characteristic
471	C₂×#117	C₂²×D₄	1	1	yes	characteristic
472	C₂×#117	C₂²×D₄	1	1	yes	characteristic
473	C₂×#117	C₂²×D₄	1	1	yes	characteristic
474	C₂×#117	C₂²×D₄	1	1	yes	characteristic
475	C₂²×C₄⋊C₄	#120	1	2	yes	—
476	C₂²×C₂²⋊C₄	#120	1	2	yes	—
477	C₂²×C₂²⋊C₄	#120	1	2	yes	—
478	C₂²×C₂²⋊C₄	#120	1	2	yes	—
479	C₂²×C₂²⋊C₄	#120	1	2	yes	—
480	C₂²×C₂²⋊C₄	#120	1	2	yes	—
481	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
482	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
483	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
484	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
485	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
486	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
487	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
488	C₂²×C₄²	#120	1	2	yes	—
489	C₂²×C₄²	#120	1	1	yes	characteristic
490	C₂²×C₄²	#120	1	1	yes	characteristic
491	C₂²×C₄²	#120	1	2	yes	—
492	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
493	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
494	C₂×#100	C₂²×D₄	1	4	yes	—
495	C₂×#100	C₂²×D₄	1	4	yes	—
496	C₂×#99	C₂²×D₄	1	8	yes	—
497	#386	#120	1	2	yes	—
498	#386	#120	1	2	yes	—
499	#386	#120	1	2	yes	—
500	#386	#120	1	2	yes	—
501	#386	#120	1	2	yes	—
502	#386	#120	1	2	yes	—
503	#386	#120	1	2	yes	—
504	#386	#120	1	2	yes	—
505	#386	C₂²×D₄	1	2	yes	—
506	#386	C₂²×D₄	1	2	yes	—
507	#386	C₂²×D₄	1	2	yes	—
508	#386	C₂²×D₄	1	2	yes	—
509	#386	C₂²×D₄	1	2	yes	—
510	#386	C₂²×D₄	1	2	yes	—
511	#386	C₂²×D₄	1	2	yes	—
512	#386	C₂²×D₄	1	2	yes	—
513	C₂⁵	C₂×#120	1	1	yes	characteristic
514	C₂⁵	C₂×#120	1	2	yes	—
515	C₂⁵	C₂×#120	1	2	yes	—
516	C₂⁵	C₂×#120	1	2	yes	—
517	C₂⁵	C₂×#120	1	2	yes	—
518	C₂⁵	C₂×#120	1	2	yes	—
519	C₂⁵	C₂×#120	1	2	yes	—
520	C₂⁵	C₂³×D₄	1	2	yes	—
521	C₂×#41	#392	1	4	yes	complemented
522	C₂×#41	#392	1	4	yes	complemented
523	C₂×#41	C₂×#120	1	2	yes	—
524	C₂×#41	C₂×#120	1	2	yes	—
525	C₂×#41	C₂×#120	1	2	yes	—
526	C₂×#41	C₂×#120	1	2	yes	—
527	C₂×#41	C₂×#121	1	2	yes	—
528	C₂×#41	C₂×#121	1	2	yes	—
529	C₂×#41	C₂×#121	1	2	yes	—
530	C₂×#41	C₂×#121	1	2	yes	—
531	C₂×#41	C₂×#121	1	2	yes	—
532	C₂×#41	C₂×#127	1	2	yes	—
533	C₂×#41	#534	1	2	yes	—
534	C₂×#41	#534	1	2	yes	—
535	C₂×#41	#534	1	4	yes	—
536	C₂×#41	#534	1	2	yes	—
537	C₂×#41	#534	1	2	yes	—
538	C₂×#41	#535	1	4	yes	—
539	C₂×#41	D₄²	1	4	yes	—
540	C₂×#41	D₄²	1	4	yes	—
541	C₂×#41	D₄²	1	4	yes	—
542	C₂×#41	#546	1	4	yes	—
543	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
544	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
545	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
546	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
547	C₂²×D₄	#392	1	4	yes	complemented
548	C₂²×D₄	#392	1	4	yes	complemented
549	C₂²×D₄	C₂×#120	1	1	yes	characteristic
550	C₂²×D₄	C₂×#120	1	2	yes	—
551	C₂²×D₄	C₂×#120	1	1	yes	characteristic
552	C₂²×D₄	C₂×#120	1	2	yes	—
553	C₂²×D₄	C₂×#120	1	2	yes	—
554	C₂²×D₄	C₂×#120	1	2	yes	—
555	C₂²×D₄	C₂×#120	1	2	yes	—
556	C₂²×D₄	C₂×#120	1	2	yes	—
557	C₂²×D₄	C₂×#120	1	1	yes	characteristic
558	C₂²×D₄	C₂×#120	1	2	yes	—
559	C₂²×D₄	C₂×#120	1	1	yes	characteristic
560	C₂²×D₄	C₂×#120	1	1	yes	characteristic
561	C₂²×D₄	C₂×#120	1	1	yes	characteristic
562	C₂²×D₄	C₂×#120	1	2	yes	—
563	C₂²×D₄	C₂×#120	1	1	yes	characteristic
564	C₂²×D₄	C₂×#120	1	1	yes	characteristic
565	C₂²×D₄	C₂×#121	1	2	yes	—
566	C₂²×D₄	C₂×#121	1	2	yes	—
567	C₂²×D₄	C₂×#121	1	2	yes	—
568	C₂²×D₄	C₂×#127	1	2	yes	—
569	C₂²×D₄	#534	1	4	yes	—
570	C₂²×D₄	#535	1	4	yes	—
571	C₂²×D₄	D₄²	1	4	yes	—
572	C₂²×D₄	D₄²	1	4	yes	—
573	C₂²×D₄	D₄²	1	4	yes	—
574	C₂²×D₄	D₄²	1	4	yes	—
575	C₂²×D₄	D₄²	1	4	yes	—
576	C₂²×D₄	D₄²	1	4	yes	—
577	C₂²×D₄	D₄²	1	4	yes	—
578	C₂²×D₄	D₄²	1	4	yes	—
579	C₂²×D₄	D₄²	1	4	yes	—
580	C₂²×D₄	#546	1	4	yes	—
581	C₂²×D₄	#546	1	4	yes	—
582	C₂²×D₄	#546	1	4	yes	—
583	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
584	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
585	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
586	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
587	C₂²×D₄	C₂³×D₄	1	2	yes	—
588	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
589	C₂²×D₄	C₂²×#41	1	1	yes	characteristic
590	C₂²×D₄	C₂×H(5,𝔽₂)	1	2	yes	—
591	C₂²×D₄	C₂×H(5,𝔽₂)	1	2	yes	—
592	C₂³×C₄	C₂×#120	1	1	yes	characteristic
593	C₂³×C₄	C₂×#120	1	2	yes	—
594	C₂³×C₄	C₂×#120	1	2	yes	—
595	C₂³×C₄	C₂×#120	1	2	yes	—
596	C₂³×C₄	C₂×#120	1	2	yes	—
597	C₂³×C₄	C₂×#120	1	2	yes	—
598	C₂³×C₄	C₂×#120	1	2	yes	—
599	C₂³×C₄	C₂×#120	1	2	yes	—
600	C₂³×C₄	C₂×#120	1	1	yes	characteristic
601	C₂³×C₄	C₂×#120	1	1	yes	characteristic
602	C₂³×C₄	C₂×#120	1	2	yes	—
603	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
604	C₄⋊Q₈	#392	1	4	yes	complemented
605	#127	#392	1	4	yes	complemented
606	#127	#392	1	4	yes	complemented
607	#127	#392	1	4	yes	complemented
608	#127	C₂×#120	1	2	yes	—
609	#127	C₂×#120	1	2	yes	—
610	#127	C₂×#120	1	2	yes	—
611	#127	C₂×#121	1	2	yes	—
612	#127	C₂×#121	1	2	yes	—
613	#127	C₂×#121	1	2	yes	—
614	#127	C₂×#121	1	2	yes	—
615	#127	C₂×#121	1	2	yes	—
616	#127	C₂×#121	1	2	yes	—
617	#127	C₂×#127	1	2	yes	—
618	#127	C₂×#127	1	2	yes	—
619	#127	C₂×#127	1	2	yes	—
620	#124	#392	1	4	yes	complemented
621	#124	#392	1	4	yes	complemented
622	#124	#392	1	4	yes	complemented
623	#124	#392	1	4	yes	complemented
624	#124	C₂×#120	1	2	yes	—
625	#124	C₂×#121	1	2	yes	—
626	#124	C₂×#121	1	2	yes	—
627	#124	C₂×#127	1	2	yes	—
628	#117	#392	1	4	yes	complemented
629	#117	#392	1	4	yes	complemented
630	#117	C₂×#120	1	2	yes	—
631	#117	C₂×#121	1	2	yes	—
632	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
633	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
634	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
635	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
636	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
637	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
638	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
639	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
640	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
641	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
642	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
643	C₂×C₄²	#392	1	4	yes	complemented
644	C₂×C₄²	#392	1	4	yes	complemented
645	C₂×C₄²	C₂×#120	1	1	yes	characteristic
646	C₂×C₄²	C₂×#120	1	2	yes	—
647	C₂×C₄²	C₂×#120	1	1	yes	characteristic
648	C₂×C₄²	C₂×#120	1	1	yes	characteristic
649	C₂×C₄²	C₂×#120	1	1	yes	characteristic
650	C₂×C₄²	C₂×#120	1	1	yes	characteristic
651	C₂×C₄²	C₂×#120	1	1	yes	characteristic
652	C₂×C₄²	C₂×#120	1	2	yes	—
653	C₂×C₄²	C₂×#121	1	2	yes	—
654	C₂⁴	#2403	1	4	yes	—
655	C₂⁴	#2408	1	4	yes	—
656	C₂⁴	#2410	1	4	yes	—
657	C₂⁴	#2433	1	4	yes	—
658	C₂⁴	#2846	1	1	yes	characteristic
659	C₂⁴	#2846	1	2	yes	—
660	C₂⁴	#2846	1	1	yes	characteristic
661	C₂⁴	C₂²×#120	1	2	yes	—
662	C₂⁴	C₂²×#120	1	2	yes	—
663	C₂⁴	C₂²×#120	1	1	yes	characteristic
664	C₂⁴	C₂×D₄²	1	2	yes	—
665	C₂⁴	C₂×D₄²	1	2	yes	—
666	C₂⁴	C₂×D₄²	1	2	yes	—
667	C₂⁴	C₂×#546	1	2	yes	—
668	C₂×Q₈	C₂×#392	1	2	yes	—
669	C₂×Q₈	C₂×#392	1	2	yes	—
670	C₂×Q₈	#2403	1	2	yes	—
671	C₂×Q₈	#2410	1	2	yes	—
672	C₂×Q₈	#2613	1	2	yes	—
673	C₂×D₄	C₂×#392	1	2	yes	—
674	C₂×D₄	C₂×#392	1	2	yes	—
675	C₂×D₄	C₂×#392	1	2	yes	—
676	C₂×D₄	C₂×#392	1	2	yes	—
677	C₂×D₄	#2403	1	2	yes	—
678	C₂×D₄	#2403	1	2	yes	—
679	C₂×D₄	#2403	1	2	yes	—
680	C₂×D₄	#2403	1	4	yes	—
681	C₂×D₄	#2403	1	4	yes	—
682	C₂×D₄	#2403	1	4	yes	—
683	C₂×D₄	#2408	1	4	yes	—
684	C₂×D₄	#2408	1	4	yes	—
685	C₂×D₄	#2410	1	2	yes	—
686	C₂×D₄	#2410	1	2	yes	—
687	C₂×D₄	#2410	1	2	yes	—
688	C₂×D₄	#2410	1	4	yes	—
689	C₂×D₄	#2410	1	4	yes	—
690	C₂×D₄	#2410	1	4	yes	—
691	C₂×D₄	#2433	1	4	yes	—
692	C₂×D₄	#2433	1	4	yes	—
693	C₂×D₄	#2613	1	2	yes	—
694	C₂×D₄	C₂²×#120	1	1	yes	characteristic
695	C₂×D₄	C₂²×#121	1	1	yes	characteristic
696	C₂×D₄	C₂²×#121	1	1	yes	characteristic
697	C₂×D₄	C₂²×#127	1	1	yes	characteristic
698	C₂×D₄	C₂×#534	1	2	yes	—
699	C₂×D₄	C₂×#535	1	2	yes	—
700	C₂×D₄	C₂×D₄²	1	2	yes	—
701	C₂×D₄	C₂×D₄²	1	2	yes	—
702	C₂×D₄	C₂×D₄²	1	2	yes	—
703	C₂×D₄	C₂×#546	1	2	yes	—
704	C₂²×C₄	C₂×#392	1	2	yes	—
705	C₂²×C₄	C₂×#392	1	2	yes	—
706	C₂²×C₄	#2403	1	4	yes	—
707	C₂²×C₄	#2403	1	4	yes	—
708	C₂²×C₄	#2408	1	4	yes	—
709	C₂²×C₄	#2410	1	4	yes	—
710	C₂²×C₄	#2410	1	4	yes	—
711	C₂²×C₄	#2433	1	4	yes	—
712	C₂²×C₄	#2613	1	2	yes	—
713	C₂²×C₄	#2613	1	2	yes	—
714	C₂²×C₄	#2846	1	1	yes	characteristic
715	C₂²×C₄	#2846	1	2	yes	—
716	C₂²×C₄	#2846	1	1	yes	characteristic
717	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
718	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
719	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
720	C₂²×C₄	C₂²×#121	1	1	yes	characteristic
721	C₂²×C₄	C₂×#534	1	1	yes	characteristic
722	C₂²×C₄	C₂×#534	1	1	yes	characteristic
723	C₄²	C₂×#392	1	2	yes	—
724	C₄²	C₂×#392	1	2	yes	—
725	C₄²	C₂×#392	1	2	yes	—
726	C₄²	C₂×#392	1	2	yes	—
727	C₂³	#14715	1	2	yes	—
728	C₂³	#14715	1	2	yes	—
729	C₂³	#14715	1	4	yes	—
730	C₂³	C₂×#2403	1	2	yes	—
731	C₂³	C₂×#2403	1	1	yes	characteristic
732	C₂³	C₂×#2410	1	2	yes	—
733	C₂³	C₂×#2410	1	1	yes	characteristic
734	C₂³	C₂×#2408	1	2	yes	—
735	C₂³	C₂×#2433	1	2	yes	—
736	C₂³	C₂×#2846	1	1	yes	characteristic
737	C₂³	#60399	1	2	yes	—
738	C₂³	#60399	1	2	yes	—
739	C₂×C₄	#14715	1	2	yes	—
740	C₂×C₄	#14715	1	2	yes	—
741	C₂×C₄	#14715	1	4	yes	—
742	C₂×C₄	C₂²×#392	1	1	yes	characteristic
743	C₂×C₄	C₂×#2613	1	1	yes	characteristic
744	C₂×C₄	C₂×#2403	1	1	yes	characteristic
745	C₂×C₄	C₂×#2410	1	1	yes	characteristic
746	C₂²	C₂×#14715	1	1	yes	characteristic
747	C₂²	#6437632	1	2	yes	—
748	C₂²	#6437999	1	2	yes	—
749	C₂²	#6628896	1	1	yes	characteristic
750	C₂²	#6628896	1	1	yes	characteristic
751	C₂	#72216366	1	1	yes	characteristic
752	C₂	#72238078	1	1	yes	characteristic
753	C₂	#72249650	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#6628896
commutator, Frattini, cosocle	C₂³×D₄	C₂⁵
LCS	G ▷ C₂³×D₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁴ ◁ C₂×#3484 ◁ 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. #72262332	C₂	semidirect
2. #72262329	C₂	semidirect
3. #72262237	C₂	semidirect
4. #72262227	C₂	semidirect
5. #72262176	C₂	semidirect
6. #72262135	C₂	semidirect
7. #72256627	C₂	semidirect
8. #72249513	C₂	semidirect
9. C₂×#493480	C₂	semidirect
10. C₂×#493635	C₂	semidirect
11. #72234696	C₂	semidirect
12. #72234630	C₂	semidirect
13. #72234161	C₂	semidirect
14. #72234160	C₂	semidirect
15. C₂×#7622880	C₂	semidirect
16. C₂×#6499855	C₂	semidirect
17. #72213329	C₂	semidirect
20. C₂×#60399	C₂²	semidirect
21. C₂×#60399	C₂²	semidirect
23. C₂×#60388	C₂²	semidirect
24. #7829277	C₂²	semidirect
25. #7792761	C₂²	semidirect
26. #7737455	C₂²	semidirect
27. #7737454	C₂²	semidirect
28. #7711201	C₂²	semidirect
29. C₂×#59126	C₂²	semidirect
33. C₂×#33557	C₂²	semidirect
34. C₂×#33551	C₂²	semidirect
35. C₂²×#2196	C₂²	semidirect
38. C₂×#33359	C₂²	semidirect
39. C₂×#33348	C₂²	semidirect
40. C₂×#33348	C₂²	semidirect
41. C₂×#23998	C₂²	semidirect
42. C₂×#23998	C₂²	semidirect
43. C₂×#23897	C₂²	semidirect
44. C₂×#23906	C₂²	semidirect
46. C₂×#21782	C₂²	semidirect
47. C₂×#21778	C₂²	semidirect
48. C₂×#21776	C₂²	semidirect
49. C₂×#21776	C₂²	semidirect
50. #6370735	C₂²	semidirect
51. #498931	C₂²	semidirect
52. #498927	C₂²	semidirect
53. #498923	C₂²	semidirect
54. C₂×#13346	C₂²	semidirect
55. #494600	C₂²	semidirect
56. #494596	C₂²	semidirect
57. C₂×#13047	C₂²	semidirect
58. C₂×#12767	C₂²	semidirect
59. C₂×#12759	C₂²	semidirect
60. C₂×#12753	C₂²	semidirect
61. C₂×#12727	C₂²	semidirect
62. C₂×#12727	C₂²	semidirect
63. C₂×#12707	C₂²	semidirect
64. C₂×#12693	C₂²	semidirect
65. #492887	C₂²	semidirect
66. #492887	C₂²	semidirect
67. #405274	C₂²	semidirect
68. #405268	C₂²	semidirect
69. #394066	C₂²	semidirect
70. #394064	C₂²	semidirect
71. #355922	C₂²	semidirect
72. #147829	C₂²	semidirect
73. #147824	C₂²	semidirect
74. #147819	C₂²	semidirect
75. #147811	C₂²	semidirect
76. #147609	C₂²	semidirect
77. #147603	C₂²	semidirect
78. #147567	C₂²	semidirect
79. #147555	C₂²	semidirect
80. #146654	C₂²	semidirect
81. #146639	C₂²	semidirect
82. #146622	C₂²	semidirect
84. C₂×#3508	D₄	semidirect
85. C₂×#3508	D₄	semidirect
88. C₂×#3498	D₄	semidirect
89. C₂×#3498	D₄	semidirect
92. C₂×#3484	D₄	semidirect
93. C₂×#3484	D₄	semidirect
97. C₂×#3484	C₂³	semidirect
98. C₂×#3549	D₄	semidirect
99. C₂×#3543	D₄	semidirect
101. C₂×#3537	D₄	semidirect
102. C₂×#3532	D₄	semidirect
104. C₂×#3481	D₄	semidirect
105. C₂²×D₄²	D₄	semidirect
107. C₂×#3444	D₄	semidirect
108. C₂×#3444	D₄	semidirect
112. #60388	D₄	semidirect
114. C₂×#3019	C₂³	semidirect
116. C₂²×#453	C₂³	semidirect
122. C₂×#2883	C₂³	semidirect
123. #52165	D₄	semidirect
124. C₂×#2669	D₄	semidirect
126. #37297	D₄	semidirect
127. #37273	D₄	semidirect
128. #37269	D₄	semidirect
129. #37232	D₄	semidirect
131. #36737	D₄	semidirect
133. #36702	D₄	semidirect
135. #35360	D₄	semidirect
137. #35350	D₄	semidirect
139. #35348	D₄	semidirect
140. #35348	D₄	semidirect
141. #34984	D₄	semidirect
142. #34980	D₄	semidirect
144. C₂×#2408	D₄	semidirect
145. C₂×#2403	D₄	semidirect
147. #34411	D₄	semidirect
148. #34406	D₄	semidirect
150. #34368	D₄	semidirect
151. #34364	D₄	semidirect
154. #34155	D₄	semidirect
155. C₂×#2366	D₄	semidirect
157. #33359	D₄	semidirect
160. C₂×#2127	C₂³	semidirect
163. C₂²×#353	C₂³	semidirect
168. #21782	D₄	semidirect
171. C₂×#1911	C₂³	semidirect
174. C₂×#1887	C₂³	semidirect
175. C₂×#1829	C₂³	semidirect
176. C₂×#1828	C₂³	semidirect
177. #20609	C₂³	semidirect
178. C₂×#1790	C₂³	semidirect
179. C₂×#1783	C₂³	semidirect
180. C₂×#1781	C₂³	semidirect
181. #12574	C₂³	semidirect
182. #12574	C₂³	semidirect
183. C₂×#1390	C₂³	semidirect
184. C₂×#1390	C₂³	semidirect
185. #10754	C₂³	semidirect
186. #10745	C₂³	semidirect
187. H(7,𝔽₂)	C₂×D₄	semidirect
190. C₂²×H(5,𝔽₂)	C₂×D₄	semidirect
194. C₂⁴×D₄	C₂×D₄	semidirect
195. C₂⁴×D₄	C₂×D₄	semidirect
223. C₂×#535	C₂×D₄	semidirect
224. C₂×#535	C₂×D₄	semidirect
232. C₂×#534	C₂×D₄	semidirect
234. C₂×#533	C₂×D₄	semidirect
235. C₂×#533	C₂×D₄	semidirect
244. C₂²×#127	C₂×D₄	semidirect
245. C₂²×#127	C₂×D₄	semidirect
252. C₂×#525	C₂×D₄	semidirect
253. C₂×#525	C₂×D₄	semidirect
259. C₂²×#120	C₂×D₄	semidirect
260. C₂²×#120	C₂×D₄	semidirect
264. C₂×#518	C₂×D₄	semidirect
265. C₂×#518	C₂×D₄	semidirect
266. C₂×#518	C₂×D₄	semidirect
271. C₂×C₄×#41	C₂×D₄	semidirect
272. C₂×C₄×#41	C₂×D₄	semidirect
274. C₂³×C₄²	C₂×D₄	semidirect
275. #3019	C₂×D₄	semidirect
276. C₂×#453	C₂×D₄	semidirect
277. #2888	C₂×D₄	semidirect
278. #2888	C₂×D₄	semidirect
281. #2883	C₂×D₄	semidirect
282. #2883	C₂×D₄	semidirect
285. #2717	C₂×D₄	semidirect
286. #2709	C₂×D₄	semidirect
287. #2709	C₂×D₄	semidirect
288. #2709	C₂×D₄	semidirect
289. #2684	C₂×D₄	semidirect
290. #2684	C₂×D₄	semidirect
291. #2684	C₂×D₄	semidirect
292. #2669	C₂×D₄	semidirect
293. #2669	C₂×D₄	semidirect
294. #2669	C₂×D₄	semidirect
295. #2669	C₂×D₄	semidirect
296. #2669	C₂×D₄	semidirect
297. #2669	C₂×D₄	semidirect
298. #2669	C₂×D₄	semidirect
299. #2669	C₂×D₄	semidirect
300. #2669	C₂×D₄	semidirect
301. #2380	C₂×D₄	semidirect
302. #2380	C₂×D₄	semidirect
303. #2379	C₂×D₄	semidirect
304. #2372	C₂×D₄	semidirect
305. #2366	C₂×D₄	semidirect
306. #2366	C₂×D₄	semidirect
307. #2366	C₂×D₄	semidirect
308. #2366	C₂×D₄	semidirect
309. #2366	C₂×D₄	semidirect
310. #2366	C₂×D₄	semidirect
311. #2315	C₂×D₄	semidirect
312. #2315	C₂×D₄	semidirect
313. #2315	C₂×D₄	semidirect
319. #2308	C₂×D₄	semidirect
320. #2308	C₂×D₄	semidirect
327. C₂×#386	C₂×D₄	semidirect
328. C₂×#386	C₂×D₄	semidirect
330. C₂×#380	C₂×D₄	semidirect
331. C₂×#379	C₂×D₄	semidirect
332. C₂×#379	C₂×D₄	semidirect
333. C₂×#379	C₂×D₄	semidirect
334. C₂×#379	C₂×D₄	semidirect
335. #2127	C₂×D₄	semidirect
336. C₂×#353	C₂×D₄	semidirect
337. #1911	C₂×D₄	semidirect
338. #1887	C₂×D₄	semidirect
521. C₂×#41	#392	semidirect
522. C₂×#41	#392	semidirect
547. C₂²×D₄	#392	semidirect
548. C₂²×D₄	#392	semidirect
604. C₄⋊Q₈	#392	semidirect
605. #127	#392	semidirect
606. #127	#392	semidirect
607. #127	#392	semidirect
620. #124	#392	semidirect
621. #124	#392	semidirect
622. #124	#392	semidirect
623. #124	#392	semidirect
628. #117	#392	semidirect
629. #117	#392	semidirect
643. C₂×C₄²	#392	semidirect
644. C₂×C₄²	#392	semidirect

Maximal subgroups

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

subgroup	index
#72262332	2
#72262329	2
#72262237	2
#72262227	2
#72262176	2
#72262135	2
#72256627	2
#72249513	2
C₂×#493480	2
C₂×#493635	2
#72234696	2
#72234630	2
#72234161	2
#72234160	2
C₂×#7622880	2
C₂×#6499855	2
#72213329	2