Subgroups — #72316852

Order 2048.

At least 9826 conjugacy classes of subgroups; only the 1080 normal subgroups are shown.

The subgroup lattice has 702 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72316814	C₂	1	2	yes	maximal, complemented
2	#72316806	C₂	1	1	yes	maximal, characteristic, complemented
3	#72316800	C₂	1	1	yes	maximal, characteristic, complemented
4	#72316786	C₂	1	2	yes	maximal, complemented
5	#72316752	C₂	1	4	yes	maximal, complemented
6	#72316731	C₂	1	4	yes	maximal, complemented
7	#72316710	C₂	1	4	yes	maximal, complemented
8	#72316695	C₂	1	4	yes	maximal, complemented
9	C₂×#6629390	C₂	1	1	yes	maximal, characteristic, complemented
10	#72285551	C₂	1	1	yes	maximal, characteristic, complemented
11	#72282454	C₂	1	2	yes	maximal, complemented
12	#72282229	C₂	1	2	yes	maximal, complemented
13	#72281567	C₂	1	1	yes	maximal, characteristic, complemented
14	#72280000	C₂	1	1	yes	maximal, characteristic, complemented
15	#72257824	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄×#585	C₂²	1	1	yes	characteristic
17	#7628157	C₂²	1	1	yes	characteristic
18	C₂×#34963	C₂²	1	1	yes	characteristic
19	#7511831	C₂²	1	2	yes	complemented
20	#7511830	C₂²	1	2	yes	complemented
21	#7511802	C₂²	1	2	yes	complemented
22	#7511801	C₂²	1	2	yes	complemented
23	#7509825	C₂²	1	1	yes	characteristic, complemented
24	#7505972	C₂²	1	1	yes	characteristic, complemented
25	#7505968	C₂²	1	1	yes	characteristic, complemented
26	#7503347	C₂²	1	1	yes	characteristic, complemented
27	#6629391	C₂²	1	2	yes	complemented
28	#6629390	C₂²	1	4	yes	—
29	#6629390	C₂²	1	4	yes	—
30	#6629390	C₂²	1	2	yes	complemented
31	#6629387	C₂²	1	2	yes	—
32	#6629386	C₂²	1	2	yes	—
33	#6629119	C₂²	1	2	yes	complemented
34	C₂×#32976	C₂²	1	2	yes	—
35	#6628982	C₂²	1	2	yes	complemented
36	C₂×#32926	C₂²	1	2	yes	—
37	#6372358	C₂²	1	1	yes	characteristic
38	#6370937	C₂²	1	1	yes	characteristic
39	C₂×#20723	C₂²	1	1	yes	characteristic
40	#6342561	C₂²	1	1	yes	characteristic
41	#482633	C₂²	1	4	yes	complemented
42	#482630	C₂²	1	2	yes	complemented
43	#482629	C₂²	1	2	yes	complemented
44	#482427	C₂²	1	2	yes	complemented
45	#482424	C₂²	1	2	yes	complemented
46	#482361	C₂²	1	2	yes	complemented
47	#482357	C₂²	1	2	yes	complemented
48	#482236	C₂²	1	2	yes	complemented
49	#482234	C₂²	1	4	yes	complemented
50	#482234	C₂²	1	2	yes	complemented
51	#184941	C₂²	1	4	yes	complemented
52	#184939	C₂²	1	2	yes	—
53	#184939	C₂²	1	2	yes	—
54	#184929	C₂²	1	4	yes	complemented
55	#144282	C₂²	1	8	yes	complemented
56	#144281	C₂²	1	8	yes	complemented
57	#144267	C₂²	1	8	yes	complemented
58	#144266	C₂²	1	8	yes	complemented
59	#144266	C₂²	1	8	yes	complemented
60	#144264	C₂²	1	8	yes	complemented
61	#144205	C₂²	1	8	yes	complemented
62	#144204	C₂²	1	8	yes	complemented
63	#127396	C₂²	1	4	yes	complemented
64	#127395	C₂²	1	2	yes	complemented
65	#127395	C₂²	1	2	yes	complemented
66	#127377	C₂²	1	4	yes	complemented
67	C₂²×#585	D₄	1	1	yes	characteristic
68	C₄×#585	D₄	1	2	yes	—
69	C₄×#585	D₄	1	2	yes	—
70	C₄×#585	C₂³	1	2	yes	—
71	C₄×#585	C₂³	1	2	yes	—
72	C₂×C₄×H(5,𝔽₂)	D₄	1	2	yes	—
73	C₂×C₄×H(5,𝔽₂)	C₂³	1	2	yes	—
74	C₂×#3428	D₄	1	1	yes	characteristic
75	C₂²×C₄×#41	D₄	1	1	yes	characteristic, complemented
76	C₂²×C₄×#41	C₂³	1	1	yes	characteristic
77	C₂³×C₄×D₄	D₄	1	1	yes	characteristic, complemented
78	C₂×#2920	D₄	1	1	yes	characteristic, complemented
79	C₂²×C₄×M₁₆	D₄	1	1	yes	characteristic, complemented
80	#34971	D₄	1	1	yes	characteristic, complemented
81	#34971	C₂³	1	1	yes	characteristic
82	#34963	D₄	1	2	yes	complemented
83	#34963	D₄	1	2	yes	complemented
84	#34963	D₄	1	1	yes	characteristic, complemented
85	#34963	C₂³	1	2	yes	—
86	#34963	C₂³	1	2	yes	—
87	#34963	C₂³	1	1	yes	characteristic
88	#34952	D₄	1	1	yes	characteristic, complemented
89	#34952	C₂³	1	1	yes	characteristic
90	#34935	D₄	1	1	yes	characteristic, complemented
91	#34935	C₂³	1	1	yes	characteristic
92	#34809	D₄	1	1	yes	characteristic, complemented
93	#34809	C₂³	1	1	yes	characteristic
94	C₂×#2487	D₄	1	1	yes	characteristic, complemented
95	C₂×#2487	C₂³	1	1	yes	characteristic
96	#34736	D₄	1	1	yes	characteristic, complemented
97	#34736	C₂³	1	1	yes	characteristic
98	C₂×#2408	D₄	1	1	yes	characteristic, complemented
99	C₂×#2408	C₂³	1	1	yes	characteristic
100	#34012	D₄	1	1	yes	characteristic, complemented
101	C₂×#2283	D₄	1	1	yes	characteristic, complemented
102	#32976	C₂³	1	4	yes	—
103	#32976	C₂³	1	8	yes	—
104	#32975	C₂³	1	4	yes	—
105	#32927	C₂³	1	4	yes	—
106	#32926	C₂³	1	4	yes	—
107	#32926	C₂³	1	8	yes	—
108	#32460	C₂³	1	2	yes	complemented
109	#32459	C₂³	1	2	yes	complemented
110	#31669	C₂³	1	2	yes	complemented
111	#31667	C₂³	1	2	yes	complemented
112	#31667	C₂³	1	2	yes	complemented
113	#31666	C₂³	1	2	yes	complemented
114	#31058	C₂³	1	2	yes	complemented
115	#31056	C₂³	1	2	yes	complemented
116	#21380	D₄	1	2	yes	complemented
117	#21380	C₂³	1	2	yes	—
118	#21373	D₄	1	2	yes	complemented
119	#21373	C₂³	1	2	yes	—
120	#21303	D₄	1	1	yes	characteristic, complemented
121	#21303	D₄	1	1	yes	characteristic, complemented
122	#21190	C₂³	1	1	yes	characteristic
123	#21190	C₂³	1	1	yes	characteristic
124	#20723	D₄	1	2	yes	complemented
125	#20723	D₄	1	2	yes	complemented
126	#20723	D₄	1	2	yes	complemented
127	#20723	C₂³	1	2	yes	—
128	#20723	C₂³	1	2	yes	—
129	#20723	C₂³	1	2	yes	—
130	#20722	D₄	1	2	yes	complemented
131	#20722	C₂³	1	2	yes	—
132	#20688	D₄	1	2	yes	complemented
133	C₂×#1820	D₄	1	2	yes	complemented
134	#20632	C₂³	1	2	yes	—
135	C₂×#1799	C₂³	1	2	yes	—
136	C₄×#410	D₄	1	2	yes	complemented
137	C₂×C₄×#99	D₄	1	2	yes	complemented
138	#17366	C₂³	1	2	yes	—
139	#17364	C₂³	1	2	yes	—
140	#17349	C₂³	1	2	yes	—
141	#11899	C₂³	1	4	yes	complemented
142	#11899	C₂³	1	8	yes	complemented
143	#11898	C₂³	1	4	yes	complemented
144	#11874	C₂³	1	4	yes	complemented
145	#11873	C₂³	1	8	yes	complemented
146	#11873	C₂³	1	4	yes	complemented
147	#8318	C₂³	1	8	yes	—
148	#8318	C₂³	1	8	yes	—
149	#7237	C₂³	1	8	yes	complemented
150	#7237	C₂³	1	8	yes	complemented
151	C₂×#585	C₂×D₄	1	2	yes	—
152	C₂×#585	C₂×D₄	1	2	yes	—
153	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
154	C₂³×#41	C₂×D₄	1	1	yes	characteristic
155	C₂³×#41	C₂×D₄	1	1	yes	characteristic
156	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
157	C₄×H(5,𝔽₂)	C₂×D₄	1	4	yes	—
158	C₄×H(5,𝔽₂)	C₂×D₄	1	4	yes	—
159	C₄×H(5,𝔽₂)	C₂×D₄	1	4	yes	—
160	C₄×H(5,𝔽₂)	C₂⁴	1	4	yes	—
161	#3428	C₂×D₄	1	2	yes	—
162	#3428	C₂×D₄	1	2	yes	—
163	C₂×#518	C₂×D₄	1	2	yes	—
164	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
165	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
166	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
167	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
168	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
169	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
170	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
171	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
172	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
173	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
174	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
175	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
176	C₂×C₄×#41	#41	1	1	yes	characteristic
177	C₂×C₄×#41	#41	1	1	yes	characteristic
178	C₂×C₄×#41	C₂⁴	1	1	yes	characteristic
179	C₂×C₄×#41	C₂⁴	1	1	yes	characteristic
180	C₂²×C₄×Q₈	C₂×D₄	1	1	yes	characteristic
181	C₂²×C₄×Q₈	C₂×D₄	1	1	yes	characteristic, complemented
182	C₂²×C₄×Q₈	C₂×D₄	1	1	yes	characteristic, complemented
183	C₂²×C₄×Q₈	#41	1	1	yes	characteristic
184	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
185	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
186	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
187	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
188	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
189	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
190	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
191	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic, complemented
192	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic, complemented
193	C₂²×C₄×D₄	C₂⁴	1	1	yes	characteristic
194	C₂²×#117	C₂×D₄	1	1	yes	characteristic
195	C₂²×#117	C₂×D₄	1	1	yes	characteristic
196	C₂²×#117	C₂×D₄	1	1	yes	characteristic
197	C₂²×#117	#41	1	1	yes	characteristic
198	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
199	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
200	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
201	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
202	C₂×#432	C₂×D₄	1	2	yes	complemented
203	C₂×#431	C₂×D₄	1	2	yes	complemented
204	C₂×#423	C₂×D₄	1	1	yes	characteristic
205	C₂×#423	C₂×D₄	1	1	yes	characteristic
206	C₂×C₄×M₁₆	C₂×D₄	1	1	yes	characteristic
207	C₂×C₄×M₁₆	C₂×D₄	1	1	yes	characteristic
208	C₂×C₄×M₁₆	C₂×D₄	1	2	yes	complemented
209	C₂²×C₄×C₈	C₂×D₄	1	2	yes	complemented
210	#2487	C₂×D₄	1	2	yes	—
211	#2487	C₂×D₄	1	2	yes	—
212	#2487	C₂×D₄	1	1	yes	characteristic
213	#2487	C₂×D₄	1	2	yes	—
214	#2487	C₂×D₄	1	1	yes	characteristic, complemented
215	#2487	C₂×D₄	1	1	yes	characteristic, complemented
216	#2487	C₂⁴	1	1	yes	characteristic
217	#2487	C₂⁴	1	2	yes	—
218	#2486	C₂×D₄	1	1	yes	characteristic
219	#2486	C₂×D₄	1	1	yes	characteristic, complemented
220	#2486	C₂×D₄	1	1	yes	characteristic, complemented
221	#2486	C₂⁴	1	1	yes	characteristic
222	#2409	C₂×D₄	1	1	yes	characteristic
223	#2409	C₂×D₄	1	1	yes	characteristic, complemented
224	#2409	C₂×D₄	1	1	yes	characteristic, complemented
225	#2409	C₂⁴	1	1	yes	characteristic
226	#2408	C₂×D₄	1	2	yes	—
227	#2408	C₂×D₄	1	1	yes	characteristic
228	#2408	C₂×D₄	1	2	yes	—
229	#2408	C₂×D₄	1	2	yes	—
230	#2408	C₂×D₄	1	1	yes	characteristic, complemented
231	#2408	C₂×D₄	1	1	yes	characteristic, complemented
232	#2408	C₂⁴	1	1	yes	characteristic
233	#2408	C₂⁴	1	2	yes	—
234	#2285	C₂×D₄	1	1	yes	characteristic, complemented
235	#2285	C₂×D₄	1	1	yes	characteristic, complemented
236	#2283	C₂×D₄	1	2	yes	—
237	#2283	C₂×D₄	1	2	yes	—
238	#2283	C₂×D₄	1	1	yes	characteristic, complemented
239	#2283	C₂×D₄	1	1	yes	characteristic, complemented
240	#2280	C₂×D₄	1	1	yes	characteristic
241	#2280	C₂×D₄	1	1	yes	characteristic
242	C₂×#380	C₂×D₄	1	1	yes	characteristic
243	C₂×#380	C₂×D₄	1	1	yes	characteristic
244	#1984	C₂×D₄	1	2	yes	complemented
245	#1984	C₂×D₄	1	2	yes	complemented
246	#1984	C₂×D₄	1	2	yes	complemented
247	#1984	C₂×D₄	1	2	yes	complemented
248	#1954	C₂×D₄	1	2	yes	—
249	#1954	C₂×D₄	1	2	yes	—
250	#1954	C₂⁴	1	2	yes	—
251	#1954	C₂⁴	1	2	yes	—
252	#1820	C₂×D₄	1	4	yes	—
253	#1820	C₂×D₄	1	4	yes	—
254	#1820	C₂×D₄	1	4	yes	complemented
255	#1819	C₂×D₄	1	4	yes	—
256	#1799	C₂×D₄	1	4	yes	—
257	#1799	C₂×D₄	1	4	yes	complemented
258	#1799	C₂⁴	1	4	yes	—
259	#1799	C₂⁴	1	4	yes	—
260	C₄×#99	C₂×D₄	1	4	yes	—
261	C₄×#99	C₂×D₄	1	4	yes	—
262	C₄×#99	C₂×D₄	1	4	yes	—
263	C₄×#99	C₂×D₄	1	4	yes	complemented
264	#1740	C₂×D₄	1	4	yes	complemented
265	C₂×#342	C₂×D₄	1	4	yes	—
266	#1460	C₂⁴	1	4	yes	—
267	C₂×H(5,𝔽₂)	C₂²×D₄	1	4	yes	—
268	C₂²×#41	#120	1	1	yes	characteristic
269	C₂²×#41	#120	1	1	yes	characteristic
270	C₂²×#41	#120	1	1	yes	characteristic
271	C₂²×#41	#120	1	1	yes	characteristic
272	C₂²×#41	#121	1	1	yes	characteristic
273	C₂²×#41	#121	1	1	yes	characteristic
274	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
275	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
276	C₂³×Q₈	#121	1	1	yes	characteristic
277	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
278	C₂³×D₄	#120	1	1	yes	characteristic
279	C₂³×D₄	#120	1	1	yes	characteristic
280	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
281	C₂³×D₄	C₂²×D₄	1	2	yes	—
282	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
283	C₂⁴×C₄	#120	1	1	yes	characteristic
284	C₂⁴×C₄	#120	1	1	yes	characteristic
285	C₂⁴×C₄	#120	1	1	yes	characteristic
286	C₂⁴×C₄	#120	1	1	yes	characteristic
287	C₂⁴×C₄	#120	1	1	yes	characteristic
288	C₂⁴×C₄	#121	1	1	yes	characteristic
289	C₂⁴×C₄	#127	1	1	yes	characteristic
290	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
291	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
292	#518	C₂²×D₄	1	4	yes	—
293	C₂×C₄×Q₈	#120	1	1	yes	characteristic
294	C₂×C₄×Q₈	#120	1	1	yes	characteristic
295	C₂×C₄×Q₈	#121	1	1	yes	characteristic
296	C₂×C₄×Q₈	#121	1	1	yes	characteristic
297	C₂×C₄×Q₈	#121	1	1	yes	characteristic
298	C₂×C₄×Q₈	#121	1	1	yes	characteristic
299	C₂×C₄×Q₈	#121	1	1	yes	characteristic
300	C₂×C₄×Q₈	#121	1	1	yes	characteristic
301	C₂×C₄×Q₈	#121	1	1	yes	characteristic
302	C₂×C₄×Q₈	#121	1	1	yes	characteristic
303	C₂×C₄×Q₈	#127	1	1	yes	characteristic
304	C₂×C₄×Q₈	#127	1	1	yes	characteristic
305	C₂×C₄×Q₈	C₂²×D₄	1	1	yes	characteristic
306	C₂×C₄×Q₈	C₂²×D₄	1	1	yes	characteristic
307	C₂×C₄×Q₈	C₂×#41	1	1	yes	characteristic
308	C₂×C₄×Q₈	C₂×#41	1	1	yes	characteristic
309	C₂×C₄×D₄	#120	1	1	yes	characteristic
310	C₂×C₄×D₄	#120	1	1	yes	characteristic
311	C₂×C₄×D₄	#120	1	1	yes	characteristic
312	C₂×C₄×D₄	#120	1	1	yes	characteristic
313	C₂×C₄×D₄	#120	1	1	yes	characteristic
314	C₂×C₄×D₄	#120	1	1	yes	characteristic
315	C₂×C₄×D₄	#120	1	1	yes	characteristic
316	C₂×C₄×D₄	#120	1	1	yes	characteristic
317	C₂×C₄×D₄	#120	1	1	yes	characteristic
318	C₂×C₄×D₄	#120	1	1	yes	characteristic
319	C₂×C₄×D₄	#120	1	1	yes	characteristic
320	C₂×C₄×D₄	#120	1	1	yes	characteristic
321	C₂×C₄×D₄	#120	1	1	yes	characteristic
322	C₂×C₄×D₄	#120	1	1	yes	characteristic
323	C₂×C₄×D₄	#120	1	1	yes	characteristic
324	C₂×C₄×D₄	#120	1	1	yes	characteristic
325	C₂×C₄×D₄	#121	1	1	yes	characteristic
326	C₂×C₄×D₄	#121	1	1	yes	characteristic
327	C₂×C₄×D₄	#121	1	1	yes	characteristic
328	C₂×C₄×D₄	#121	1	1	yes	characteristic
329	C₂×C₄×D₄	#121	1	1	yes	characteristic
330	C₂×C₄×D₄	#121	1	1	yes	characteristic
331	C₂×C₄×D₄	#121	1	1	yes	characteristic
332	C₂×C₄×D₄	#121	1	1	yes	characteristic
333	C₂×C₄×D₄	#121	1	1	yes	characteristic
334	C₂×C₄×D₄	#121	1	1	yes	characteristic
335	C₂×C₄×D₄	#127	1	1	yes	characteristic
336	C₂×C₄×D₄	#127	1	1	yes	characteristic
337	C₂×C₄×D₄	#127	1	1	yes	characteristic
338	C₂×C₄×D₄	#127	1	1	yes	characteristic
339	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
340	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
341	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
342	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
343	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
344	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
345	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
346	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
347	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
348	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
349	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
350	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
351	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
352	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
353	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
354	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
355	C₂×C₄×D₄	C₂×#41	1	1	yes	characteristic
356	C₂×C₄×D₄	C₂⁵	1	1	yes	characteristic
357	C₂×#117	#120	1	1	yes	characteristic
358	C₂×#117	#120	1	1	yes	characteristic
359	C₂×#117	#120	1	1	yes	characteristic
360	C₂×#117	#120	1	1	yes	characteristic
361	C₂×#117	#121	1	1	yes	characteristic
362	C₂×#117	#121	1	1	yes	characteristic
363	C₂×#117	#121	1	1	yes	characteristic
364	C₂×#117	#121	1	1	yes	characteristic
365	C₂×#117	#121	1	1	yes	characteristic
366	C₂×#117	#121	1	1	yes	characteristic
367	C₂×#117	#121	1	1	yes	characteristic
368	C₂×#117	#121	1	1	yes	characteristic
369	C₂×#117	#121	1	1	yes	characteristic
370	C₂×#117	#121	1	1	yes	characteristic
371	C₂×#117	#127	1	1	yes	characteristic
372	C₂×#117	#127	1	1	yes	characteristic
373	C₂×#117	#127	1	1	yes	characteristic
374	C₂×#117	#127	1	1	yes	characteristic
375	C₂×#117	C₂²×D₄	1	1	yes	characteristic
376	C₂×#117	C₂²×D₄	1	1	yes	characteristic
377	C₂×#117	C₂²×D₄	1	1	yes	characteristic
378	C₂×#117	C₂²×D₄	1	1	yes	characteristic
379	C₂×#117	C₂×#41	1	1	yes	characteristic
380	C₂×#117	C₂×#41	1	1	yes	characteristic
381	C₂²×C₄⋊C₄	#121	1	1	yes	characteristic
382	C₂²×C₄⋊C₄	#121	1	1	yes	characteristic
383	C₂²×C₄⋊C₄	#121	1	1	yes	characteristic
384	C₂²×C₄⋊C₄	#127	1	1	yes	characteristic
385	C₂²×C₄⋊C₄	#127	1	1	yes	characteristic
386	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
387	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
388	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
389	C₂²×C₄⋊C₄	C₂×#41	1	1	yes	characteristic
390	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
391	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
392	C₂²×C₂²⋊C₄	#121	1	1	yes	characteristic
393	C₂²×C₂²⋊C₄	#121	1	1	yes	characteristic
394	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
395	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
396	C₂²×C₄²	#120	1	1	yes	characteristic
397	C₂²×C₄²	#120	1	1	yes	characteristic
398	C₂²×C₄²	#120	1	1	yes	characteristic
399	C₂²×C₄²	#120	1	1	yes	characteristic
400	C₂²×C₄²	#120	1	1	yes	characteristic
401	C₂²×C₄²	#120	1	1	yes	characteristic
402	C₂²×C₄²	#120	1	1	yes	characteristic
403	C₂²×C₄²	#120	1	1	yes	characteristic
404	C₂²×C₄²	#120	1	1	yes	characteristic
405	C₂²×C₄²	#120	1	1	yes	characteristic
406	C₂²×C₄²	#120	1	1	yes	characteristic
407	C₂²×C₄²	#120	1	1	yes	characteristic
408	C₂²×C₄²	#120	1	1	yes	characteristic
409	C₂²×C₄²	#121	1	1	yes	characteristic
410	C₂²×C₄²	#121	1	1	yes	characteristic
411	C₂²×C₄²	#121	1	1	yes	characteristic
412	C₂²×C₄²	#121	1	1	yes	characteristic
413	C₂²×C₄²	#121	1	1	yes	characteristic
414	C₂²×C₄²	#121	1	1	yes	characteristic
415	C₂²×C₄²	#121	1	1	yes	characteristic
416	C₂²×C₄²	#121	1	1	yes	characteristic
417	C₂²×C₄²	#121	1	1	yes	characteristic
418	C₂²×C₄²	#121	1	1	yes	characteristic
419	C₂²×C₄²	#121	1	1	yes	characteristic
420	C₂²×C₄²	#127	1	1	yes	characteristic
421	C₂²×C₄²	#127	1	1	yes	characteristic
422	C₂²×C₄²	#127	1	1	yes	characteristic
423	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
424	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
425	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
426	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
427	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
428	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
429	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
430	C₂×C₄⋊C₈	C₂²×D₄	1	2	yes	—
431	C₂×C₄⋊C₈	C₂²×D₄	1	2	yes	—
432	C₂×C₄×C₈	C₂²×D₄	1	2	yes	—
433	C₂×C₄×C₈	C₂²×D₄	1	2	yes	—
434	#380	C₂²×D₄	1	2	yes	—
435	#380	C₂²×D₄	1	1	yes	characteristic
436	#380	C₂²×D₄	1	1	yes	characteristic
437	#380	C₂²×D₄	1	2	yes	—
438	#380	C₂²×D₄	1	1	yes	characteristic
439	#380	C₂²×D₄	1	1	yes	characteristic
440	#342	C₂²×D₄	1	8	yes	—
441	#342	C₂²×D₄	1	8	yes	—
442	C₂⁵	#392	1	1	yes	characteristic
443	C₂⁵	C₂×#120	1	1	yes	characteristic
444	C₂⁵	C₂×#120	1	1	yes	characteristic
445	H(5,𝔽₂)	#575	1	8	yes	—
446	C₂²×Q₈	#392	1	1	yes	characteristic
447	C₂²×Q₈	#392	1	1	yes	characteristic
448	C₂²×Q₈	C₂×#121	1	1	yes	characteristic
449	C₂²×Q₈	C₂×#121	1	1	yes	characteristic
450	C₂²×D₄	#392	1	1	yes	characteristic
451	C₂²×D₄	#392	1	1	yes	characteristic
452	C₂²×D₄	#392	1	1	yes	characteristic
453	C₂²×D₄	#392	1	1	yes	characteristic
454	C₂²×D₄	C₂×#120	1	1	yes	characteristic
455	C₂²×D₄	C₂×#120	1	1	yes	characteristic
456	C₂²×D₄	C₂×#120	1	1	yes	characteristic
457	C₂²×D₄	C₂×#120	1	1	yes	characteristic
458	C₂²×D₄	C₂×#120	1	1	yes	characteristic
459	C₂²×D₄	C₂×#120	1	1	yes	characteristic
460	C₂²×D₄	C₂×#121	1	1	yes	characteristic
461	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
462	C₂³×C₄	#392	1	1	yes	characteristic
463	C₂³×C₄	#392	1	1	yes	characteristic
464	C₂³×C₄	#392	1	1	yes	characteristic
465	C₂³×C₄	#392	1	1	yes	characteristic
466	C₂³×C₄	#392	1	1	yes	characteristic
467	C₂³×C₄	#392	1	1	yes	characteristic
468	C₂³×C₄	#392	1	1	yes	characteristic
469	C₂³×C₄	#392	1	1	yes	characteristic
470	C₂³×C₄	#392	1	1	yes	characteristic
471	C₂³×C₄	#392	1	1	yes	characteristic
472	C₂³×C₄	#392	1	1	yes	characteristic
473	C₂³×C₄	#392	1	1	yes	characteristic
474	C₂³×C₄	#392	1	1	yes	characteristic
475	C₂³×C₄	#392	1	1	yes	characteristic
476	C₂³×C₄	#392	1	1	yes	characteristic
477	C₂³×C₄	#392	1	1	yes	characteristic
478	C₂³×C₄	#392	1	1	yes	characteristic
479	C₂³×C₄	#392	1	1	yes	characteristic
480	C₂³×C₄	#392	1	1	yes	characteristic
481	C₂³×C₄	#392	1	1	yes	characteristic
482	C₂³×C₄	#392	1	1	yes	characteristic
483	C₂³×C₄	C₂×#120	1	1	yes	characteristic
484	C₂³×C₄	C₂×#120	1	1	yes	characteristic
485	C₂³×C₄	C₂×#120	1	1	yes	characteristic
486	C₂³×C₄	C₂×#120	1	1	yes	characteristic
487	C₂³×C₄	C₂×#120	1	1	yes	characteristic
488	C₂³×C₄	C₂×#120	1	1	yes	characteristic
489	C₂³×C₄	C₂×#120	1	1	yes	characteristic
490	C₂³×C₄	C₂×#120	1	1	yes	characteristic
491	C₂³×C₄	C₂×#120	1	1	yes	characteristic
492	C₂³×C₄	C₂×#120	1	1	yes	characteristic
493	C₂³×C₄	C₂×#120	1	1	yes	characteristic
494	C₂³×C₄	C₂×#120	1	1	yes	characteristic
495	C₂³×C₄	C₂×#120	1	1	yes	characteristic
496	C₂³×C₄	C₂×#120	1	1	yes	characteristic
497	C₂³×C₄	C₂×#120	1	1	yes	characteristic
498	C₂³×C₄	C₂×#121	1	1	yes	characteristic
499	C₂³×C₄	C₂×#121	1	1	yes	characteristic
500	C₂³×C₄	C₂×#121	1	1	yes	characteristic
501	C₂³×C₄	C₂×#121	1	1	yes	characteristic
502	C₂³×C₄	C₂×#121	1	1	yes	characteristic
503	C₂³×C₄	C₂×#121	1	1	yes	characteristic
504	C₂³×C₄	C₂×#121	1	1	yes	characteristic
505	C₂³×C₄	C₂×#127	1	1	yes	characteristic
506	C₂³×C₄	C₂×#127	1	1	yes	characteristic
507	C₂³×C₄	C₂×#127	1	1	yes	characteristic
508	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
509	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
510	C₂×C₄⋊C₄	#392	1	1	yes	characteristic
511	C₂×C₄⋊C₄	#392	1	1	yes	characteristic
512	C₂×C₄⋊C₄	#392	1	1	yes	characteristic
513	C₂×C₄⋊C₄	#392	1	1	yes	characteristic
514	C₂×C₄⋊C₄	#392	1	1	yes	characteristic
515	C₂×C₄⋊C₄	#392	1	1	yes	characteristic
516	C₂×C₄⋊C₄	#392	1	1	yes	characteristic
517	C₂×C₄⋊C₄	#392	1	1	yes	characteristic
518	C₂×C₄⋊C₄	#392	1	1	yes	characteristic
519	C₂×C₄⋊C₄	#392	1	1	yes	characteristic
520	C₂×C₄⋊C₄	C₂×#121	1	1	yes	characteristic
521	C₂×C₄⋊C₄	C₂×#121	1	1	yes	characteristic
522	C₂×C₄⋊C₄	C₂×#121	1	1	yes	characteristic
523	C₂×C₄⋊C₄	C₂×#121	1	1	yes	characteristic
524	C₂×C₄⋊C₄	C₂×#121	1	1	yes	characteristic
525	C₂×C₄⋊C₄	C₂×#121	1	1	yes	characteristic
526	C₂×C₄⋊C₄	C₂×#121	1	1	yes	characteristic
527	C₂×C₄⋊C₄	C₂×#121	1	1	yes	characteristic
528	C₂×C₄⋊C₄	C₂×#121	1	1	yes	characteristic
529	C₂×C₄⋊C₄	C₂×#127	1	1	yes	characteristic
530	C₂×C₄⋊C₄	C₂×#127	1	1	yes	characteristic
531	C₂×C₄⋊C₄	C₂×#127	1	1	yes	characteristic
532	C₂×C₄⋊C₄	C₂×#127	1	1	yes	characteristic
533	C₂×C₄⋊C₄	C₂²×#41	1	1	yes	characteristic
534	C₂×C₂²⋊C₄	#392	1	1	yes	characteristic
535	C₂×C₂²⋊C₄	#392	1	1	yes	characteristic
536	C₂×C₂²⋊C₄	#392	1	1	yes	characteristic
537	C₂×C₂²⋊C₄	#392	1	1	yes	characteristic
538	C₂×C₂²⋊C₄	#392	1	1	yes	characteristic
539	C₂×C₂²⋊C₄	#392	1	1	yes	characteristic
540	C₂×C₂²⋊C₄	#392	1	1	yes	characteristic
541	C₂×C₂²⋊C₄	#392	1	1	yes	characteristic
542	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
543	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
544	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
545	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
546	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
547	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
548	C₂×C₂²⋊C₄	C₂×#121	1	1	yes	characteristic
549	C₂×C₂²⋊C₄	C₂×#121	1	1	yes	characteristic
550	C₂×C₂²⋊C₄	C₂×#121	1	1	yes	characteristic
551	C₂×C₂²⋊C₄	C₂×#121	1	1	yes	characteristic
552	C₂×C₂²⋊C₄	C₂×#121	1	1	yes	characteristic
553	C₂×C₂²⋊C₄	C₂×#121	1	1	yes	characteristic
554	C₂×C₂²⋊C₄	C₂×#127	1	1	yes	characteristic
555	C₂×C₂²⋊C₄	C₂×#127	1	1	yes	characteristic
556	C₂×C₂²⋊C₄	C₂³×D₄	1	1	yes	characteristic
557	C₂×C₂²⋊C₄	C₂³×D₄	1	1	yes	characteristic
558	C₂×C₄²	#392	1	1	yes	characteristic
559	C₂×C₄²	#392	1	1	yes	characteristic
560	C₂×C₄²	#392	1	1	yes	characteristic
561	C₂×C₄²	#392	1	1	yes	characteristic
562	C₂×C₄²	#392	1	1	yes	characteristic
563	C₂×C₄²	#392	1	1	yes	characteristic
564	C₂×C₄²	#392	1	1	yes	characteristic
565	C₂×C₄²	#392	1	1	yes	characteristic
566	C₂×C₄²	#392	1	1	yes	characteristic
567	C₂×C₄²	#392	1	1	yes	characteristic
568	C₂×C₄²	#392	1	1	yes	characteristic
569	C₂×C₄²	#392	1	1	yes	characteristic
570	C₂×C₄²	#392	1	1	yes	characteristic
571	C₂×C₄²	#392	1	1	yes	characteristic
572	C₂×C₄²	#392	1	1	yes	characteristic
573	C₂×C₄²	#392	1	1	yes	characteristic
574	C₂×C₄²	#392	1	1	yes	characteristic
575	C₂×C₄²	#392	1	1	yes	characteristic
576	C₂×C₄²	B(4,𝔽₂)	1	1	yes	characteristic
577	C₂×C₄²	B(4,𝔽₂)	1	1	yes	characteristic
578	C₂×C₄²	B(4,𝔽₂)	1	1	yes	characteristic
579	C₂×C₄²	B(4,𝔽₂)	1	1	yes	characteristic
580	C₂×C₄²	B(4,𝔽₂)	1	1	yes	characteristic
581	C₂×C₄²	B(4,𝔽₂)	1	1	yes	characteristic
582	C₂×C₄²	B(4,𝔽₂)	1	1	yes	characteristic
583	C₂×C₄²	B(4,𝔽₂)	1	1	yes	characteristic
584	C₂×C₄²	C₂×#120	1	1	yes	characteristic
585	C₂×C₄²	C₂×#120	1	1	yes	characteristic
586	C₂×C₄²	C₂×#120	1	1	yes	characteristic
587	C₂×C₄²	C₂×#120	1	1	yes	characteristic
588	C₂×C₄²	C₂×#120	1	1	yes	characteristic
589	C₂×C₄²	C₂×#120	1	1	yes	characteristic
590	C₂×C₄²	C₂×#120	1	1	yes	characteristic
591	C₂×C₄²	C₂×#121	1	1	yes	characteristic
592	C₂×C₄²	C₂×#121	1	1	yes	characteristic
593	C₂×C₄²	C₂×#121	1	1	yes	characteristic
594	C₂×C₄²	C₂×#121	1	1	yes	characteristic
595	C₂×C₄²	C₂×#121	1	1	yes	characteristic
596	C₂×C₄²	C₂×#121	1	1	yes	characteristic
597	C₂×C₄²	C₂×#121	1	1	yes	characteristic
598	C₂×C₄²	C₂×#121	1	1	yes	characteristic
599	C₂×C₄²	C₂×#121	1	1	yes	characteristic
600	C₂×C₄²	C₂×#121	1	1	yes	characteristic
601	C₂×C₄²	C₂×#121	1	1	yes	characteristic
602	C₂×C₄²	C₂×#127	1	1	yes	characteristic
603	C₂×C₄²	C₂×#127	1	1	yes	characteristic
604	C₂×C₄²	C₂×#127	1	1	yes	characteristic
605	C₂×C₄²	C₂³×D₄	1	1	yes	characteristic
606	C₂⁴	C₂×#392	1	1	yes	characteristic
607	C₂⁴	C₂×#392	1	1	yes	characteristic
608	C₂⁴	C₂×#392	1	1	yes	characteristic
609	C₂⁴	C₂×#392	1	1	yes	characteristic
610	C₂⁴	C₂×#392	1	1	yes	characteristic
611	C₂⁴	C₂²×#120	1	1	yes	characteristic
612	C₂⁴	C₂²×#120	1	1	yes	characteristic
613	C₂×D₄	#2010	1	4	yes	—
614	C₂×D₄	C₂×#575	1	4	yes	—
615	C₂²×C₄	#2021	1	1	yes	characteristic
616	C₂²×C₄	#2021	1	1	yes	characteristic
617	C₂²×C₄	#2021	1	1	yes	characteristic
618	C₂²×C₄	#2021	1	1	yes	characteristic
619	C₂²×C₄	#2021	1	1	yes	characteristic
620	C₂²×C₄	#2021	1	1	yes	characteristic
621	C₂²×C₄	#2021	1	1	yes	characteristic
622	C₂²×C₄	#2021	1	1	yes	characteristic
623	C₂²×C₄	C₂×#392	1	1	yes	characteristic
624	C₂²×C₄	C₂×#392	1	1	yes	characteristic
625	C₂²×C₄	C₂×#392	1	1	yes	characteristic
626	C₂²×C₄	C₂×#392	1	1	yes	characteristic
627	C₂²×C₄	C₂×#392	1	1	yes	characteristic
628	C₂²×C₄	C₂×#392	1	1	yes	characteristic
629	C₂²×C₄	C₂×#392	1	1	yes	characteristic
630	C₂²×C₄	C₂×#392	1	1	yes	characteristic
631	C₂²×C₄	C₂×#392	1	1	yes	characteristic
632	C₂²×C₄	C₂×#392	1	1	yes	characteristic
633	C₂²×C₄	C₂×#392	1	1	yes	characteristic
634	C₂²×C₄	C₂×#392	1	1	yes	characteristic
635	C₂²×C₄	C₂×#392	1	1	yes	characteristic
636	C₂²×C₄	C₂×#392	1	1	yes	characteristic
637	C₂²×C₄	C₂×#392	1	1	yes	characteristic
638	C₂²×C₄	C₂×#392	1	1	yes	characteristic
639	C₂²×C₄	C₂×#392	1	1	yes	characteristic
640	C₂²×C₄	C₂×#392	1	1	yes	characteristic
641	C₂²×C₄	C₂×#392	1	1	yes	characteristic
642	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
643	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
644	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
645	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
646	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
647	C₂²×C₄	C₂²×#121	1	1	yes	characteristic
648	C₂²×C₄	C₂²×#121	1	1	yes	characteristic
649	C₂²×C₄	C₂²×#121	1	1	yes	characteristic
650	C₂²×C₄	C₂²×#127	1	1	yes	characteristic
651	C₄²	#2021	1	1	yes	characteristic
652	C₄²	#2021	1	1	yes	characteristic
653	C₄²	#2021	1	1	yes	characteristic
654	C₄²	#2021	1	1	yes	characteristic
655	C₄²	#2021	1	1	yes	characteristic
656	C₄²	#2021	1	1	yes	characteristic
657	C₄²	#2021	1	1	yes	characteristic
658	C₄²	#2021	1	1	yes	characteristic
659	C₄²	C₂×B(4,𝔽₂)	1	1	yes	characteristic
660	C₄²	C₂×B(4,𝔽₂)	1	1	yes	characteristic
661	C₄²	C₂×B(4,𝔽₂)	1	1	yes	characteristic
662	C₄²	C₂×B(4,𝔽₂)	1	1	yes	characteristic
663	C₄²	C₂×B(4,𝔽₂)	1	1	yes	characteristic
664	C₄²	C₂×B(4,𝔽₂)	1	1	yes	characteristic
665	C₄²	C₂×B(4,𝔽₂)	1	1	yes	characteristic
666	C₄²	C₂×B(4,𝔽₂)	1	1	yes	characteristic
667	C₂³	C₂×#2010	1	2	yes	—
668	C₂³	C₂×#2010	1	2	yes	—
669	C₂³	C₂×#2021	1	1	yes	characteristic
670	C₂³	C₂×#2021	1	1	yes	characteristic
671	C₂³	C₂²×#392	1	1	yes	characteristic
672	C₂³	#60359	1	2	yes	—
673	C₂³	#60359	1	2	yes	—
674	C₂×C₄	C₂×#2010	1	2	yes	—
675	C₂×C₄	C₂×#2021	1	1	yes	characteristic
676	C₂×C₄	C₂×#2021	1	1	yes	characteristic
677	C₂×C₄	C₂×#2021	1	1	yes	characteristic
678	C₂×C₄	C₂×#2021	1	1	yes	characteristic
679	C₂×C₄	C₂×#2021	1	1	yes	characteristic
680	C₂×C₄	C₂×#2021	1	1	yes	characteristic
681	C₂×C₄	C₂×#2021	1	1	yes	characteristic
682	C₂×C₄	C₂×#2021	1	1	yes	characteristic
683	C₂×C₄	C₂×#2021	1	1	yes	characteristic
684	C₂×C₄	C₂×#2021	1	1	yes	characteristic
685	C₂×C₄	#33546	1	2	yes	—
686	C₂×C₄	#33550	1	2	yes	—
687	C₂×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
688	C₂×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
689	C₂×C₄	#60444	1	2	yes	—
690	C₂²	#498885	1	2	yes	—
691	C₂²	#6431698	1	1	yes	characteristic
692	C₂²	C₂²×#2010	1	1	yes	characteristic
693	C₂²	C₂²×#2021	1	1	yes	characteristic
694	C₄	#498885	1	2	yes	—
695	C₄	#498898	1	2	yes	—
696	C₄	C₂×#33546	1	1	yes	characteristic
697	C₄	C₂×#33550	1	1	yes	characteristic
698	C₂	C₂×#498885	1	1	yes	characteristic
699	C₂	C₂×#498898	1	1	yes	characteristic
700	C₂	#72281041	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×#2021
commutator, Frattini, cosocle	C₂×C₄×D₄	C₂⁵
socle	C₂²	C₂²×#2021
LCS	G ▷ C₂×C₄×D₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ C₂²×C₄×#41 ◁ G
LECS	G ▷ C₂×C₄×D₄ ▷ C₂³ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72316814	C₂	semidirect
2. #72316806	C₂	semidirect
3. #72316800	C₂	semidirect
4. #72316786	C₂	semidirect
5. #72316752	C₂	semidirect
6. #72316731	C₂	semidirect
7. #72316710	C₂	semidirect
8. #72316695	C₂	semidirect
9. C₂×#6629390	C₂	semidirect
10. #72285551	C₂	semidirect
11. #72282454	C₂	semidirect
12. #72282229	C₂	semidirect
13. #72281567	C₂	semidirect
14. #72280000	C₂	semidirect
15. #72257824	C₂	semidirect
19. #7511831	C₂²	semidirect
20. #7511830	C₂²	semidirect
21. #7511802	C₂²	semidirect
22. #7511801	C₂²	semidirect
23. #7509825	C₂²	semidirect
24. #7505972	C₂²	semidirect
25. #7505968	C₂²	semidirect
26. #7503347	C₂²	semidirect
27. #6629391	C₂²	semidirect
30. #6629390	C₂²	semidirect
33. #6629119	C₂²	semidirect
35. #6628982	C₂²	semidirect
41. #482633	C₂²	semidirect
42. #482630	C₂²	semidirect
43. #482629	C₂²	semidirect
44. #482427	C₂²	semidirect
45. #482424	C₂²	semidirect
46. #482361	C₂²	semidirect
47. #482357	C₂²	semidirect
48. #482236	C₂²	semidirect
49. #482234	C₂²	semidirect
50. #482234	C₂²	semidirect
51. #184941	C₂²	semidirect
54. #184929	C₂²	semidirect
55. #144282	C₂²	semidirect
56. #144281	C₂²	semidirect
57. #144267	C₂²	semidirect
58. #144266	C₂²	semidirect
59. #144266	C₂²	semidirect
60. #144264	C₂²	semidirect
61. #144205	C₂²	semidirect
62. #144204	C₂²	semidirect
63. #127396	C₂²	semidirect
64. #127395	C₂²	semidirect
65. #127395	C₂²	semidirect
66. #127377	C₂²	semidirect
75. C₂²×C₄×#41	D₄	semidirect
77. C₂³×C₄×D₄	D₄	semidirect
78. C₂×#2920	D₄	semidirect
79. C₂²×C₄×M₁₆	D₄	semidirect
80. #34971	D₄	semidirect
82. #34963	D₄	semidirect
83. #34963	D₄	semidirect
84. #34963	D₄	semidirect
88. #34952	D₄	semidirect
90. #34935	D₄	semidirect
92. #34809	D₄	semidirect
94. C₂×#2487	D₄	semidirect
96. #34736	D₄	semidirect
98. C₂×#2408	D₄	semidirect
100. #34012	D₄	semidirect
101. C₂×#2283	D₄	semidirect
108. #32460	C₂³	semidirect
109. #32459	C₂³	semidirect
110. #31669	C₂³	semidirect
111. #31667	C₂³	semidirect
112. #31667	C₂³	semidirect
113. #31666	C₂³	semidirect
114. #31058	C₂³	semidirect
115. #31056	C₂³	semidirect
116. #21380	D₄	semidirect
118. #21373	D₄	semidirect
120. #21303	D₄	semidirect
121. #21303	D₄	semidirect
124. #20723	D₄	semidirect
125. #20723	D₄	semidirect
126. #20723	D₄	semidirect
130. #20722	D₄	semidirect
132. #20688	D₄	semidirect
133. C₂×#1820	D₄	semidirect
136. C₄×#410	D₄	semidirect
137. C₂×C₄×#99	D₄	semidirect
141. #11899	C₂³	semidirect
142. #11899	C₂³	semidirect
143. #11898	C₂³	semidirect
144. #11874	C₂³	semidirect
145. #11873	C₂³	semidirect
146. #11873	C₂³	semidirect
149. #7237	C₂³	semidirect
150. #7237	C₂³	semidirect
181. C₂²×C₄×Q₈	C₂×D₄	semidirect
182. C₂²×C₄×Q₈	C₂×D₄	semidirect
191. C₂²×C₄×D₄	C₂×D₄	semidirect
192. C₂²×C₄×D₄	C₂×D₄	semidirect
202. C₂×#432	C₂×D₄	semidirect
203. C₂×#431	C₂×D₄	semidirect
208. C₂×C₄×M₁₆	C₂×D₄	semidirect
209. C₂²×C₄×C₈	C₂×D₄	semidirect
214. #2487	C₂×D₄	semidirect
215. #2487	C₂×D₄	semidirect
219. #2486	C₂×D₄	semidirect
220. #2486	C₂×D₄	semidirect
223. #2409	C₂×D₄	semidirect
224. #2409	C₂×D₄	semidirect
230. #2408	C₂×D₄	semidirect
231. #2408	C₂×D₄	semidirect
234. #2285	C₂×D₄	semidirect
235. #2285	C₂×D₄	semidirect
238. #2283	C₂×D₄	semidirect
239. #2283	C₂×D₄	semidirect
244. #1984	C₂×D₄	semidirect
245. #1984	C₂×D₄	semidirect
246. #1984	C₂×D₄	semidirect
247. #1984	C₂×D₄	semidirect
254. #1820	C₂×D₄	semidirect
257. #1799	C₂×D₄	semidirect
263. C₄×#99	C₂×D₄	semidirect
264. #1740	C₂×D₄	semidirect

Maximal subgroups

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

subgroup	index
#72316814	2
#72316806	2
#72316800	2
#72316786	2
#72316752	2
#72316731	2
#72316710	2
#72316695	2
C₂×#6629390	2
#72285551	2
#72282454	2
#72282229	2
#72281567	2
#72280000	2
#72257824	2