Subgroups — #72320850

Order 2048.

At least 6123 conjugacy classes of subgroups; only the 858 normal subgroups are shown.

The subgroup lattice has 693 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72320830	C₂	1	1	yes	maximal, characteristic, complemented
2	#72320808	C₂	1	1	yes	maximal, characteristic, complemented
3	#72320778	C₂	1	1	yes	maximal, characteristic, complemented
4	#72320756	C₂	1	1	yes	maximal, characteristic, complemented
5	#72320747	C₂	1	1	yes	maximal, characteristic, complemented
6	#72320737	C₂	1	1	yes	maximal, characteristic, complemented
7	#72320716	C₂	1	1	yes	maximal, characteristic, complemented
8	#72320700	C₂	1	1	yes	maximal, characteristic, complemented
9	#72320676	C₂	1	1	yes	maximal, characteristic, complemented
10	#72320655	C₂	1	1	yes	maximal, characteristic, complemented
11	#72320637	C₂	1	1	yes	maximal, characteristic, complemented
12	#72320621	C₂	1	1	yes	maximal, characteristic, complemented
13	#72320609	C₂	1	1	yes	maximal, characteristic, complemented
14	#72320592	C₂	1	1	yes	maximal, characteristic, complemented
15	#72320575	C₂	1	1	yes	maximal, characteristic, complemented
16	#72320401	C₂	1	1	yes	maximal, characteristic, complemented
17	#72319989	C₂	1	1	yes	maximal, characteristic, complemented
18	#72309672	C₂	1	1	yes	maximal, characteristic, complemented
19	#72308040	C₂	1	1	yes	maximal, characteristic, complemented
20	#72252627	C₂	1	1	yes	maximal, characteristic, complemented
21	#72250542	C₂	1	1	yes	maximal, characteristic, complemented
22	#72250515	C₂	1	1	yes	maximal, characteristic, complemented
23	#72250218	C₂	1	1	yes	maximal, characteristic, complemented
24	#72250205	C₂	1	1	yes	maximal, characteristic, complemented
25	#72250199	C₂	1	1	yes	maximal, characteristic, complemented
26	#72250169	C₂	1	1	yes	maximal, characteristic, complemented
27	#72249959	C₂	1	1	yes	maximal, characteristic, complemented
28	#72239492	C₂	1	1	yes	maximal, characteristic, complemented
29	C₂×#500743	C₂	1	1	yes	maximal, characteristic
30	C₂×#495739	C₂	1	1	yes	maximal, characteristic, complemented
31	#72231532	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#61049	C₂²	1	1	yes	characteristic
33	C₂×#60176	C₂²	1	1	yes	characteristic
34	C₂×#33595	C₂²	1	1	yes	characteristic
35	C₂×#33539	C₂²	1	1	yes	characteristic
36	C₂×#33517	C₂²	1	1	yes	characteristic
37	C₂×#33471	C₂²	1	1	yes	characteristic
38	C₂×#33468	C₂²	1	1	yes	characteristic, complemented
39	C₂²×AGL(1,ℤ/16)	C₂²	1	1	yes	characteristic
40	#7622612	C₂²	1	1	yes	characteristic
41	#6629756	C₂²	1	1	yes	characteristic
42	C₂×#28180	C₂²	1	1	yes	characteristic
43	#6457372	C₂²	1	1	yes	characteristic
44	#6457180	C₂²	1	1	yes	characteristic
45	#6444562	C₂²	1	1	yes	characteristic
46	#6444520	C₂²	1	1	yes	characteristic
47	#6444096	C₂²	1	1	yes	characteristic
48	#6444059	C₂²	1	1	yes	characteristic
49	#6380164	C₂²	1	1	yes	characteristic, complemented
50	#6380143	C₂²	1	1	yes	characteristic
51	#6380131	C₂²	1	1	yes	characteristic
52	#6379155	C₂²	1	1	yes	characteristic
53	#6379134	C₂²	1	1	yes	characteristic
54	C₂×#22436	C₂²	1	1	yes	characteristic
55	#6373016	C₂²	1	1	yes	characteristic
56	C₂×#21559	C₂²	1	1	yes	characteristic, complemented
57	#499545	C₂²	1	1	yes	characteristic, complemented
58	#499441	C₂²	1	1	yes	characteristic, complemented
59	#499364	C₂²	1	1	yes	characteristic, complemented
60	#499079	C₂²	1	1	yes	characteristic
61	C₂×#13396	C₂²	1	1	yes	characteristic
62	C₂×#13396	C₂²	1	1	yes	characteristic
63	C₂×#13395	C₂²	1	1	yes	characteristic
64	C₂×#13395	C₂²	1	1	yes	characteristic
65	C₂×#13310	C₂²	1	1	yes	characteristic
66	C₂×#13309	C₂²	1	1	yes	characteristic
67	C₂×#13215	C₂²	1	1	yes	characteristic
68	C₂×#13200	C₂²	1	1	yes	characteristic
69	#495044	C₂²	1	1	yes	characteristic, complemented
70	#495043	C₂²	1	1	yes	characteristic, complemented
71	C₂×#13155	C₂²	1	1	yes	characteristic, complemented
72	#494777	C₂²	1	1	yes	characteristic, complemented
73	C₂×#13040	C₂²	1	1	yes	characteristic, complemented
74	C₂×#13037	C₂²	1	1	yes	characteristic
75	C₂×#13033	C₂²	1	1	yes	characteristic
76	C₂×#13030	C₂²	1	1	yes	characteristic, complemented
77	#494536	C₂²	1	1	yes	characteristic, complemented
78	#494535	C₂²	1	1	yes	characteristic, complemented
79	C₂×#13005	C₂²	1	1	yes	characteristic, complemented
80	#494340	C₂²	1	1	yes	characteristic
81	#494339	C₂²	1	1	yes	characteristic, complemented
82	C₂×#12956	C₂²	1	1	yes	characteristic
83	#494335	C₂²	1	1	yes	characteristic, complemented
84	#494334	C₂²	1	1	yes	characteristic, complemented
85	C₂×#12953	C₂²	1	1	yes	characteristic
86	C₂×#12953	C₂²	1	1	yes	characteristic
87	#494325	C₂²	1	1	yes	characteristic, complemented
88	C₂×#12949	C₂²	1	1	yes	characteristic, complemented
89	C₂×#12949	C₂²	1	1	yes	characteristic, complemented
90	C₂×#12934	C₂²	1	1	yes	characteristic, complemented
91	C₂×#12934	C₂²	1	1	yes	characteristic, complemented
92	#494153	C₂²	1	1	yes	characteristic, complemented
93	C₂×#12826	C₂²	1	1	yes	characteristic
94	#493777	C₂²	1	1	yes	characteristic
95	#493773	C₂²	1	1	yes	characteristic, complemented
96	C₂×#12750	C₂²	1	1	yes	characteristic
97	C₂×#12750	C₂²	1	1	yes	characteristic
98	#493551	C₂²	1	1	yes	characteristic
99	C₂×#12736	C₂²	1	1	yes	characteristic
100	C₂×#12736	C₂²	1	1	yes	characteristic
101	#493512	C₂²	1	1	yes	characteristic
102	#493129	C₂²	1	1	yes	characteristic, complemented
103	C₂×#12649	C₂²	1	1	yes	characteristic, complemented
104	C₂×#12647	C₂²	1	1	yes	characteristic
105	C₂×#12609	C₂²	1	1	yes	characteristic, complemented
106	#416318	C₂²	1	1	yes	characteristic, complemented
107	#415479	C₂²	1	1	yes	characteristic, complemented
108	#414967	C₂²	1	1	yes	characteristic
109	#412773	C₂²	1	1	yes	characteristic, complemented
110	#392952	C₂²	1	1	yes	characteristic, complemented
111	#368420	C₂²	1	1	yes	characteristic, complemented
112	#365313	C₂²	1	1	yes	characteristic, complemented
113	#365077	C₂²	1	1	yes	characteristic, complemented
114	#365034	C₂²	1	1	yes	characteristic, complemented
115	#365015	C₂²	1	1	yes	characteristic, complemented
116	#360971	C₂²	1	1	yes	characteristic, complemented
117	#149374	C₂²	1	1	yes	characteristic, complemented
118	#149339	C₂²	1	1	yes	characteristic, complemented
119	#149236	C₂²	1	1	yes	characteristic, complemented
120	#149236	C₂²	1	1	yes	characteristic, complemented
121	#149191	C₂²	1	1	yes	characteristic, complemented
122	#149191	C₂²	1	1	yes	characteristic, complemented
123	#149045	C₂²	1	1	yes	characteristic, complemented
124	#148987	C₂²	1	1	yes	characteristic, complemented
125	#148869	C₂²	1	1	yes	characteristic, complemented
126	#148744	C₂²	1	1	yes	characteristic, complemented
127	#148741	C₂²	1	1	yes	characteristic, complemented
128	#148682	C₂²	1	1	yes	characteristic, complemented
129	#148635	C₂²	1	1	yes	characteristic, complemented
130	#148635	C₂²	1	1	yes	characteristic, complemented
131	#148595	C₂²	1	1	yes	characteristic, complemented
132	#148570	C₂²	1	1	yes	characteristic, complemented
133	#148570	C₂²	1	1	yes	characteristic, complemented
134	#148543	C₂²	1	1	yes	characteristic, complemented
135	#148432	C₂²	1	1	yes	characteristic, complemented
136	#148411	C₂²	1	1	yes	characteristic, complemented
137	#148373	C₂²	1	1	yes	characteristic, complemented
138	#148373	C₂²	1	1	yes	characteristic, complemented
139	#148345	C₂²	1	1	yes	characteristic, complemented
140	#148319	C₂²	1	1	yes	characteristic, complemented
141	#148284	C₂²	1	1	yes	characteristic, complemented
142	#148284	C₂²	1	1	yes	characteristic, complemented
143	#148282	C₂²	1	1	yes	characteristic, complemented
144	#148282	C₂²	1	1	yes	characteristic, complemented
145	#148195	C₂²	1	1	yes	characteristic, complemented
146	#148193	C₂²	1	1	yes	characteristic, complemented
147	#148164	C₂²	1	1	yes	characteristic, complemented
148	#148164	C₂²	1	1	yes	characteristic, complemented
149	#148114	C₂²	1	1	yes	characteristic, complemented
150	#148060	C₂²	1	1	yes	characteristic, complemented
151	#147961	C₂²	1	1	yes	characteristic, complemented
152	#147957	C₂²	1	1	yes	characteristic, complemented
153	#147953	C₂²	1	1	yes	characteristic, complemented
154	#147947	C₂²	1	1	yes	characteristic, complemented
155	#147938	C₂²	1	1	yes	characteristic, complemented
156	#147887	C₂²	1	1	yes	characteristic
157	#147684	C₂²	1	1	yes	characteristic, complemented
158	#147662	C₂²	1	1	yes	characteristic
159	#147642	C₂²	1	1	yes	characteristic
160	#147642	C₂²	1	1	yes	characteristic, complemented
161	#147621	C₂²	1	1	yes	characteristic, complemented
162	#147545	C₂²	1	1	yes	characteristic
163	#147465	C₂²	1	1	yes	characteristic, complemented
164	#147427	C₂²	1	1	yes	characteristic, complemented
165	#147405	C₂²	1	1	yes	characteristic, complemented
166	#147404	C₂²	1	1	yes	characteristic, complemented
167	#147372	C₂²	1	1	yes	characteristic, complemented
168	#147372	C₂²	1	1	yes	characteristic, complemented
169	#147362	C₂²	1	1	yes	characteristic, complemented
170	#147360	C₂²	1	1	yes	characteristic, complemented
171	#147243	C₂²	1	1	yes	characteristic, complemented
172	#147199	C₂²	1	1	yes	characteristic, complemented
173	#147195	C₂²	1	1	yes	characteristic, complemented
174	#147130	C₂²	1	1	yes	characteristic, complemented
175	#146802	C₂²	1	1	yes	characteristic, complemented
176	#146799	C₂²	1	1	yes	characteristic
177	#146799	C₂²	1	1	yes	characteristic
178	#146799	C₂²	1	1	yes	characteristic
179	#146799	C₂²	1	1	yes	characteristic
180	#146783	C₂²	1	1	yes	characteristic
181	#146772	C₂²	1	1	yes	characteristic
182	#146763	C₂²	1	1	yes	characteristic, complemented
183	#146750	C₂²	1	1	yes	characteristic
184	#146734	C₂²	1	1	yes	characteristic
185	#146557	C₂²	1	1	yes	characteristic, complemented
186	#146385	C₂²	1	1	yes	characteristic, complemented
187	C₂²×#576	C₂³	1	1	yes	characteristic
188	C₂⁴×D₈	C₂³	1	1	yes	characteristic
189	C₂×#3414	C₂³	1	1	yes	characteristic
190	C₂²×#509	C₂³	1	1	yes	characteristic
191	C₂²×#509	C₂³	1	1	yes	characteristic
192	C₂×#3155	C₂³	1	1	yes	characteristic
193	C₂×#3067	C₂³	1	1	yes	characteristic
194	C₂×#3058	C₂³	1	1	yes	characteristic
195	C₂×#3050	C₂³	1	1	yes	characteristic
196	C₂×#3050	C₂³	1	1	yes	characteristic
197	C₂×#2957	C₂³	1	1	yes	characteristic
198	C₂²×#444	C₂³	1	1	yes	characteristic
199	#60167	C₂³	1	1	yes	characteristic
200	C₂×#2952	C₂³	1	1	yes	characteristic
201	C₂×#2948	C₂³	1	1	yes	characteristic
202	C₂×#2948	C₂³	1	1	yes	characteristic
203	C₂×#2948	C₂³	1	1	yes	characteristic
204	C₂×#2943	C₂³	1	1	yes	characteristic
205	C₂²×#442	C₂³	1	1	yes	characteristic
206	C₂²×#442	C₂³	1	1	yes	characteristic
207	C₂×#2929	C₂³	1	1	yes	characteristic
208	C₂×#2912	C₂³	1	1	yes	characteristic
209	C₂×#2875	C₂³	1	1	yes	characteristic
210	#34742	D₄	1	1	yes	characteristic
211	#33539	D₄	1	8	yes	—
212	#33409	C₂³	1	1	yes	characteristic
213	C₂×#2155	C₂³	1	1	yes	characteristic
214	C₂×#2155	C₂³	1	1	yes	characteristic
215	C₂×#2155	C₂³	1	1	yes	characteristic
216	C₂×#2155	C₂³	1	1	yes	characteristic
217	C₂²×#365	C₂³	1	1	yes	characteristic
218	C₂²×#365	C₂³	1	1	yes	characteristic
219	C₂×#2153	C₂³	1	1	yes	characteristic
220	#33397	C₂³	1	1	yes	characteristic
221	C₂×#2148	C₂³	1	1	yes	characteristic
222	C₂×#2148	C₂³	1	1	yes	characteristic
223	C₂²×#361	C₂³	1	1	yes	characteristic
224	C₂²×#361	C₂³	1	1	yes	characteristic
225	C₂²×#361	C₂³	1	1	yes	characteristic
226	C₂²×#361	C₂³	1	1	yes	characteristic
227	C₂²×#361	C₂³	1	1	yes	characteristic
228	C₂²×#361	C₂³	1	1	yes	characteristic
229	C₂²×#361	C₂³	1	1	yes	characteristic
230	C₂²×#361	C₂³	1	1	yes	characteristic
231	C₂×#2145	C₂³	1	1	yes	characteristic
232	C₂×#2145	C₂³	1	1	yes	characteristic
233	C₂×#2145	C₂³	1	1	yes	characteristic
234	C₂×#2145	C₂³	1	1	yes	characteristic
235	C₂²×#360	C₂³	1	1	yes	characteristic
236	C₂²×#360	C₂³	1	1	yes	characteristic
237	C₂×#2143	C₂³	1	1	yes	characteristic
238	C₂×#2143	C₂³	1	1	yes	characteristic
239	#33380	C₂³	1	1	yes	characteristic
240	#33380	C₂³	1	1	yes	characteristic
241	C₂×#2140	C₂³	1	1	yes	characteristic
242	C₂×#2140	C₂³	1	1	yes	characteristic
243	C₂×#2140	C₂³	1	1	yes	characteristic
244	C₂×#2140	C₂³	1	1	yes	characteristic
245	C₂×#2140	C₂³	1	1	yes	characteristic
246	C₂×#2140	C₂³	1	1	yes	characteristic
247	C₂×#2117	C₂³	1	1	yes	characteristic
248	C₂×#2117	C₂³	1	1	yes	characteristic
249	C₂×#2117	C₂³	1	1	yes	characteristic
250	C₂×#2117	C₂³	1	1	yes	characteristic
251	C₂×#2112	C₂³	1	1	yes	characteristic
252	C₂×#2112	C₂³	1	1	yes	characteristic
253	C₂×#2112	C₂³	1	1	yes	characteristic
254	C₂×#2112	C₂³	1	1	yes	characteristic
255	C₂×#2110	C₂³	1	1	yes	characteristic
256	C₂²×#347	C₂³	1	1	yes	characteristic
257	C₂²×#347	C₂³	1	1	yes	characteristic
258	#33324	C₂³	1	1	yes	characteristic
259	#26264	D₄	1	2	yes	complemented
260	#26264	D₄	1	2	yes	complemented
261	#26263	D₄	1	2	yes	complemented
262	#26263	D₄	1	2	yes	complemented
263	#22672	D₄	1	2	yes	complemented
264	#22672	D₄	1	2	yes	complemented
265	#22670	D₄	1	2	yes	complemented
266	#22670	D₄	1	2	yes	complemented
267	C₂×#1976	C₂³	1	1	yes	characteristic
268	C₂×#1975	C₂³	1	1	yes	characteristic
269	#21233	C₂³	1	1	yes	characteristic
270	#21233	C₂³	1	1	yes	characteristic
271	#21229	C₂³	1	1	yes	characteristic
272	#21228	C₂³	1	1	yes	characteristic
273	C₂×#1972	C₂³	1	1	yes	characteristic
274	C₂×#1972	C₂³	1	1	yes	characteristic
275	C₂×#1953	C₂³	1	1	yes	characteristic
276	C₂×#1953	C₂³	1	1	yes	characteristic
277	#21163	C₂³	1	1	yes	characteristic
278	C₂×#1946	C₂³	1	1	yes	characteristic
279	#21157	C₂³	1	1	yes	characteristic
280	#21157	C₂³	1	1	yes	characteristic
281	#21155	C₂³	1	1	yes	characteristic
282	#21154	C₂³	1	1	yes	characteristic
283	#21053	D₄	1	1	yes	characteristic
284	#21049	D₄	1	1	yes	characteristic
285	#21026	D₄	1	1	yes	characteristic
286	#21022	D₄	1	1	yes	characteristic
287	#20899	D₄	1	1	yes	characteristic
288	#20839	D₄	1	1	yes	characteristic
289	#20807	C₂³	1	1	yes	characteristic
290	#20802	C₂³	1	1	yes	characteristic
291	#20799	C₂³	1	1	yes	characteristic
292	C₂×#1833	C₂³	1	1	yes	characteristic
293	#20684	D₄	1	1	yes	characteristic
294	#20678	C₂³	1	1	yes	characteristic
295	C₂×#1814	C₂³	1	1	yes	characteristic
296	C₂×#1814	C₂³	1	1	yes	characteristic
297	C₂×#1810	C₂³	1	1	yes	characteristic
298	C₂×#1810	C₂³	1	1	yes	characteristic
299	#20662	C₂³	1	1	yes	characteristic
300	#20658	C₂³	1	1	yes	characteristic
301	#20658	C₂³	1	1	yes	characteristic
302	C₂×#1807	C₂³	1	1	yes	characteristic
303	C₂×#1773	C₂³	1	1	yes	characteristic
304	#20438	C₂³	1	1	yes	characteristic
305	#20436	C₂³	1	1	yes	characteristic
306	#20385	C₂³	1	1	yes	characteristic
307	#20384	C₂³	1	1	yes	characteristic
308	C₂×#1752	C₂³	1	1	yes	characteristic
309	C₂×#1389	C₂³	1	1	yes	characteristic
310	C₂×#1389	C₂³	1	1	yes	characteristic
311	C₂×#1389	C₂³	1	1	yes	characteristic
312	C₂×#1389	C₂³	1	1	yes	characteristic
313	#12569	C₂³	1	1	yes	characteristic
314	#12569	C₂³	1	1	yes	characteristic
315	#12567	C₂³	1	1	yes	characteristic
316	#12567	C₂³	1	1	yes	characteristic
317	#12567	C₂³	1	1	yes	characteristic
318	#12567	C₂³	1	1	yes	characteristic
319	C₂×#1386	C₂³	1	1	yes	characteristic
320	C₂×#1386	C₂³	1	1	yes	characteristic
321	C₂×#1386	C₂³	1	1	yes	characteristic
322	C₂×#1386	C₂³	1	1	yes	characteristic
323	C₂×#1386	C₂³	1	1	yes	characteristic
324	C₂×#1386	C₂³	1	1	yes	characteristic
325	C₂×#1384	C₂³	1	1	yes	characteristic
326	C₂×#1384	C₂³	1	1	yes	characteristic
327	C₂×#1384	C₂³	1	1	yes	characteristic
328	C₂×#1384	C₂³	1	1	yes	characteristic
329	C₂×#1383	C₂³	1	1	yes	characteristic
330	C₂×#1383	C₂³	1	1	yes	characteristic
331	C₂×#1383	C₂³	1	1	yes	characteristic
332	C₂×#1383	C₂³	1	1	yes	characteristic
333	C₂×#1383	C₂³	1	1	yes	characteristic
334	C₂×#1383	C₂³	1	1	yes	characteristic
335	#12561	C₂³	1	1	yes	characteristic
336	#12561	C₂³	1	1	yes	characteristic
337	C₂×#1378	C₂³	1	1	yes	characteristic
338	C₂×#1378	C₂³	1	1	yes	characteristic
339	C₂×#1378	C₂³	1	1	yes	characteristic
340	C₂×#1378	C₂³	1	1	yes	characteristic
341	#12551	C₂³	1	1	yes	characteristic
342	#12551	C₂³	1	1	yes	characteristic
343	#12549	C₂³	1	1	yes	characteristic
344	#12547	C₂³	1	1	yes	characteristic
345	C₂×#1375	C₂³	1	1	yes	characteristic
346	C₂×#1375	C₂³	1	1	yes	characteristic
347	C₂×#1375	C₂³	1	1	yes	characteristic
348	C₂×#1375	C₂³	1	1	yes	characteristic
349	C₂×#1375	C₂³	1	1	yes	characteristic
350	C₂×#1375	C₂³	1	1	yes	characteristic
351	#10871	C₂³	1	1	yes	characteristic
352	#10868	C₂³	1	1	yes	characteristic
353	#10867	C₂³	1	1	yes	characteristic
354	#10866	C₂³	1	1	yes	characteristic
355	#10860	C₂³	1	1	yes	characteristic
356	#10860	C₂³	1	1	yes	characteristic
357	#10860	C₂³	1	1	yes	characteristic
358	#10860	C₂³	1	1	yes	characteristic
359	C₂×#576	C₂×D₄	1	4	yes	—
360	C₂²×#135	C₂⁴	1	1	yes	characteristic
361	C₂²×#135	C₂⁴	1	1	yes	characteristic
362	C₂³×D₈	C₂⁴	1	1	yes	characteristic
363	C₂³×D₈	C₂⁴	1	1	yes	characteristic
364	C₂²×#131	C₂×D₄	1	1	yes	characteristic
365	C₂²×#131	C₂⁴	1	1	yes	characteristic
366	C₂⁴×C₈	C₂⁴	1	1	yes	characteristic
367	C₂×#525	C₂×D₄	1	1	yes	characteristic
368	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
369	#3414	C₂×D₄	1	4	yes	—
370	C₂×#509	C₂×D₄	1	4	yes	—
371	C₂×#509	#41	1	4	yes	—
372	C₂²×SD₃₂	#41	1	2	yes	—
373	C₂²×D₁₆	#41	1	2	yes	—
374	C₂²×M₃₂	C₂⁴	1	1	yes	characteristic
375	C₂²×M₃₂	C₂⁴	1	1	yes	characteristic
376	C₂²×M₃₂	C₂⁴	1	1	yes	characteristic
377	C₂²×M₃₂	C₂⁴	1	1	yes	characteristic
378	C₂²×M₃₂	C₂⁴	1	1	yes	characteristic
379	C₂²×M₃₂	C₂⁴	1	1	yes	characteristic
380	C₂²×M₃₂	C₂⁴	1	1	yes	characteristic
381	C₂²×M₃₂	C₂⁴	1	1	yes	characteristic
382	C₂×#495	C₂×D₄	1	2	yes	—
383	C₂×#493	C₂×D₄	1	2	yes	—
384	#3067	C₂×D₄	1	4	yes	—
385	C₂×#442	C₂×D₄	1	1	yes	characteristic
386	C₂×#442	C₂×D₄	1	2	yes	—
387	C₂×#442	C₂×D₄	1	2	yes	—
388	C₂×#442	C₂×D₄	1	2	yes	—
389	C₂×#442	C₂×D₄	1	2	yes	—
390	C₂×#442	C₂×D₄	1	1	yes	characteristic
391	C₂×#441	C₂×D₄	1	1	yes	characteristic
392	C₂×#441	C₂×D₄	1	1	yes	characteristic
393	C₂×C₄×D₈	C₂×D₄	1	2	yes	—
394	C₂×C₄×D₈	C₂×D₄	1	2	yes	—
395	C₂²×#108	C₂⁴	1	1	yes	characteristic
396	C₂²×#108	C₂⁴	1	1	yes	characteristic
397	C₂²×#108	C₂⁴	1	1	yes	characteristic
398	C₂²×#108	C₂⁴	1	1	yes	characteristic
399	C₂×#427	C₂⁴	1	1	yes	characteristic
400	C₂×#427	C₂⁴	1	1	yes	characteristic
401	C₂×#427	C₂⁴	1	1	yes	characteristic
402	C₂×#427	C₂⁴	1	1	yes	characteristic
403	C₂×#427	C₂⁴	1	1	yes	characteristic
404	C₂×#427	C₂⁴	1	1	yes	characteristic
405	C₂²×#106	C₂⁴	1	1	yes	characteristic
406	C₂²×#106	C₂⁴	1	1	yes	characteristic
407	C₂×#424	C₂×D₄	1	1	yes	characteristic
408	C₂×#424	C₂×D₄	1	1	yes	characteristic
409	C₂×#423	C₂×D₄	1	1	yes	characteristic
410	C₂×#408	C₂×D₄	1	1	yes	characteristic
411	C₂×#408	C₂×D₄	1	1	yes	characteristic
412	C₂×#407	C₂×D₄	1	1	yes	characteristic
413	C₂×#407	C₂×D₄	1	1	yes	characteristic
414	C₂²×C₂²⋊C₈	C₂×D₄	1	1	yes	characteristic
415	C₂×#405	C₂×D₄	1	1	yes	characteristic
416	C₂×#405	C₂⁴	1	1	yes	characteristic
417	C₂×#405	C₂⁴	1	1	yes	characteristic
418	C₂×#405	C₂⁴	1	1	yes	characteristic
419	C₂×C₄×M₁₆	C₂×D₄	1	1	yes	characteristic
420	C₂²×#97	C₂⁴	1	1	yes	characteristic
421	C₂²×#97	C₂⁴	1	1	yes	characteristic
422	#2297	C₂×D₄	1	1	yes	characteristic
423	#2296	C₂×D₄	1	1	yes	characteristic
424	#2285	C₂×D₄	1	1	yes	characteristic
425	#2280	C₂×D₄	1	1	yes	characteristic
426	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
427	C₂×#361	C₂×D₄	1	4	yes	—
428	#2143	C₂×D₄	1	4	yes	—
429	C₂×#357	#41	1	2	yes	—
430	C₂×#357	#41	1	2	yes	—
431	#2117	C₂×D₄	1	4	yes	—
432	#1972	C₂×D₄	1	2	yes	—
433	#1972	C₂×D₄	1	2	yes	—
434	#1972	C₂×D₄	1	2	yes	—
435	#1972	C₂×D₄	1	2	yes	—
436	#1972	C₂×D₄	1	2	yes	—
437	#1971	C₂×D₄	1	2	yes	—
438	#1943	C₂×D₄	1	2	yes	—
439	#1943	C₂×D₄	1	2	yes	—
440	#1943	C₂×D₄	1	1	yes	characteristic
441	#1943	C₂×D₄	1	1	yes	characteristic
442	#1943	C₂×D₄	1	1	yes	characteristic
443	#1943	C₂×D₄	1	1	yes	characteristic
444	#1941	C₂×D₄	1	2	yes	—
445	#1941	C₂×D₄	1	2	yes	—
446	#1846	C₂×D₄	1	2	yes	—
447	#1844	C₂×D₄	1	2	yes	—
448	#1771	C₂×D₄	1	2	yes	—
449	#1771	C₂×D₄	1	2	yes	—
450	#1770	C₂×D₄	1	2	yes	—
451	#1770	C₂×D₄	1	2	yes	—
452	#1729	C₂×D₄	1	1	yes	characteristic
453	#1729	C₂×D₄	1	1	yes	characteristic
454	#1729	C₂×D₄	1	1	yes	characteristic
455	#1729	C₂×D₄	1	1	yes	characteristic
456	#1729	C₂×D₄	1	1	yes	characteristic
457	#1729	C₂×D₄	1	1	yes	characteristic
458	#1728	C₂×D₄	1	1	yes	characteristic
459	#1728	C₂×D₄	1	1	yes	characteristic
460	C₂×#336	C₂×D₄	1	1	yes	characteristic
461	C₂×#336	C₂×D₄	1	1	yes	characteristic
462	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
463	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
464	C₂×#135	C₂²×D₄	1	2	yes	—
465	C₂×#135	C₂²×D₄	1	2	yes	—
466	C₂×#135	C₂×#41	1	2	yes	—
467	C₂×#135	H(5,𝔽₂)	1	2	yes	—
468	C₂²×Q₁₆	C₂²×D₄	1	1	yes	characteristic
469	C₂²×Q₁₆	C₂×#41	1	1	yes	characteristic
470	C₂²×D₈	C₂²×D₄	1	2	yes	—
471	C₂²×D₈	C₂²×D₄	1	1	yes	characteristic
472	C₂²×D₈	C₂²×D₄	1	2	yes	—
473	C₂²×D₈	C₂²×D₄	1	2	yes	—
474	C₂²×D₈	C₂×#41	1	1	yes	characteristic
475	C₂²×D₈	C₂×#41	1	2	yes	—
476	C₂²×D₈	C₂×#41	1	2	yes	—
477	C₂²×D₈	C₂×#41	1	2	yes	—
478	C₂²×D₈	H(5,𝔽₂)	1	2	yes	—
479	C₂²×D₈	2₋¹⁺⁴	1	2	yes	—
480	C₂×#131	C₂²×D₄	1	2	yes	—
481	C₂×#131	H(5,𝔽₂)	1	2	yes	—
482	C₂²×M₁₆	C₂²×D₄	1	1	yes	characteristic
483	C₂²×M₁₆	C₂²×D₄	1	1	yes	characteristic
484	C₂²×M₁₆	C₂²×D₄	1	1	yes	characteristic
485	C₂²×M₁₆	C₂²×D₄	1	1	yes	characteristic
486	C₂³×C₈	C₂²×D₄	1	1	yes	characteristic
487	C₂³×C₈	C₂²×D₄	1	1	yes	characteristic
488	C₂³×C₈	C₂²×D₄	1	1	yes	characteristic
489	C₂³×C₈	C₂⁵	1	1	yes	characteristic
490	C₂×#117	C₂²×D₄	1	1	yes	characteristic
491	C₂×#117	C₂²×D₄	1	1	yes	characteristic
492	C₂×#117	C₂²×D₄	1	1	yes	characteristic
493	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
494	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
495	C₂×SD₃₂	#123	1	8	yes	complemented
496	C₂×D₁₆	#123	1	8	yes	complemented
497	C₂×M₃₂	C₂²×D₄	1	2	yes	—
498	C₂×M₃₂	C₂²×D₄	1	2	yes	—
499	C₂×M₃₂	C₂×#41	1	2	yes	—
500	C₂²×C₁₆	C₂×#41	1	2	yes	—
501	C₂²×C₁₆	C₂×#41	1	2	yes	—
502	C₂×#108	C₂²×D₄	1	2	yes	—
503	C₂×#107	C₂²×D₄	1	1	yes	characteristic
504	C₂×#107	C₂²×D₄	1	1	yes	characteristic
505	C₂×#107	C₂×#41	1	1	yes	characteristic
506	C₂×#107	C₂×#41	1	1	yes	characteristic
507	C₂×#106	C₂²×D₄	1	2	yes	—
508	C₂×#106	C₂²×D₄	1	2	yes	—
509	C₂×#106	C₂²×D₄	1	1	yes	characteristic
510	C₂×#106	C₂²×D₄	1	1	yes	characteristic
511	C₂×#106	C₂²×D₄	1	1	yes	characteristic
512	C₂×#106	C₂²×D₄	1	1	yes	characteristic
513	C₂×C₄⋊C₈	#120	1	2	yes	—
514	C₂×C₄⋊C₈	#120	1	2	yes	—
515	C₂×#97	C₂²×D₄	1	1	yes	characteristic
516	C₂×#97	C₂²×D₄	1	1	yes	characteristic
517	C₂×#97	C₂²×D₄	1	1	yes	characteristic
518	C₂×#97	C₂²×D₄	1	1	yes	characteristic
519	C₂×#97	C₂²×D₄	1	2	yes	—
520	C₂×#97	C₂²×D₄	1	2	yes	—
521	C₂×C₄×C₈	C₂²×D₄	1	2	yes	—
522	C₂×C₄×C₈	C₂²×D₄	1	2	yes	—
523	#391	AGL(1,ℤ/8)	1	1	yes	characteristic
524	#391	AGL(1,ℤ/8)	1	1	yes	characteristic
525	#390	AGL(1,ℤ/8)	1	1	yes	characteristic
526	#390	AGL(1,ℤ/8)	1	1	yes	characteristic
527	#381	AGL(1,ℤ/8)	1	2	yes	—
528	#379	AGL(1,ℤ/8)	1	2	yes	—
529	C₄×C₄⋊C₄	#120	1	2	yes	—
530	C₄×C₄⋊C₄	#120	1	2	yes	—
531	#336	#120	1	2	yes	—
532	#336	#120	1	2	yes	—
533	#336	#120	1	2	yes	—
534	#336	#120	1	2	yes	—
535	C₂⁵	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
536	C₂×#41	D₄²	1	2	yes	—
537	C₂×#41	#577	1	2	yes	—
538	C₂²×Q₈	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
539	C₂²×D₄	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
540	C₂³×C₄	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
541	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
542	C₂×Q₁₆	C₂×#123	1	2	yes	complemented
543	C₂×Q₁₆	D₄²	1	2	yes	—
544	C₂×D₈	C₂×#123	1	4	yes	—
545	C₂×D₈	C₂×#123	1	2	yes	complemented
546	C₂×D₈	#525	1	4	yes	—
547	C₂×D₈	#539	1	4	yes	—
548	C₂×D₈	D₄²	1	2	yes	—
549	C₂×D₈	D₄²	1	4	yes	—
550	C₂×D₈	#547	1	4	yes	—
551	C₂×D₈	#548	1	4	yes	—
552	C₂×D₈	#553	1	4	yes	—
553	C₂×M₁₆	D₄²	1	2	yes	—
554	C₂²×C₈	C₂×#120	1	1	yes	characteristic
555	C₂²×C₈	C₂×#120	1	1	yes	characteristic
556	C₂²×C₈	C₂×#120	1	2	yes	—
557	C₂²×C₈	C₂×#120	1	2	yes	—
558	C₂²×C₈	C₂³×D₄	1	1	yes	characteristic
559	C₂²×C₈	C₂³×D₄	1	1	yes	characteristic
560	C₂²×C₈	C₂³×D₄	1	1	yes	characteristic
561	C₂²×C₈	C₂²×#41	1	1	yes	characteristic
562	C₂²×C₈	C₂²×#41	1	1	yes	characteristic
563	C₂²×C₈	C₂²×#41	1	1	yes	characteristic
564	C₂²×C₈	C₂×H(5,𝔽₂)	1	1	yes	characteristic
565	C₂²×C₈	C₂×H(5,𝔽₂)	1	1	yes	characteristic
566	C₂²×C₈	C₂×H(5,𝔽₂)	1	1	yes	characteristic
567	C₂²×C₈	C₂×2₋¹⁺⁴	1	1	yes	characteristic
568	C₂²×C₈	#585	1	1	yes	characteristic
569	C₂²×C₈	#585	1	1	yes	characteristic
570	C₂²×C₈	#585	1	1	yes	characteristic
571	C₂²×C₈	#585	1	1	yes	characteristic
572	C₂×C₄⋊C₄	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
573	C₂×C₄⋊C₄	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
574	C₂×C₂²⋊C₄	C₂×AGL(1,ℤ/8)	1	2	yes	—
575	C₂×C₂²⋊C₄	C₂×AGL(1,ℤ/8)	1	2	yes	—
576	C₂×C₄²	C₂×#120	1	1	yes	characteristic
577	C₂×C₄²	C₂×#120	1	2	yes	—
578	C₂×C₄²	C₂×#120	1	1	yes	characteristic
579	C₂×C₄²	C₂×#120	1	2	yes	—
580	C₂×C₄²	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
581	C₂×C₄²	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
582	C₂×C₁₆	C₂×#123	1	4	yes	complemented
583	C₂⁴	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
584	C₂×Q₈	#3272	1	2	yes	—
585	C₂×D₄	#3272	1	2	yes	—
586	C₂²×C₄	#3003	1	2	yes	—
587	C₂²×C₄	#3003	1	2	yes	—
588	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
589	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
590	C₂²×C₄	D₄×#41	1	1	yes	characteristic
591	C₂²×C₄	D₄×#41	1	1	yes	characteristic
592	C₂²×C₄	D₄×#41	1	1	yes	characteristic
593	C₂²×C₄	#3484	1	1	yes	characteristic
594	C₂²×C₄	#3489	1	1	yes	characteristic
595	C₂²×C₄	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
596	C₂²×C₄	C₂×#577	1	1	yes	characteristic
597	C₂²×C₄	#3584	1	1	yes	characteristic
598	C₂²×C₄	#3585	1	1	yes	characteristic
599	C₂²×C₄	#3585	1	1	yes	characteristic
600	C₂²×C₄	#3585	1	1	yes	characteristic
601	C₂²×C₄	#3585	1	1	yes	characteristic
602	D₈	#2443	1	8	yes	—
603	C₂×C₈	C₂²×#123	1	1	yes	characteristic
604	C₂×C₈	C₂×#525	1	1	yes	characteristic
605	C₂×C₈	#3449	1	1	yes	characteristic
606	C₂×C₈	C₂×#539	1	1	yes	characteristic
607	C₂×C₈	C₂×D₄²	1	1	yes	characteristic
608	C₂×C₈	C₂×D₄²	1	1	yes	characteristic
609	C₂×C₈	C₂×#547	1	1	yes	characteristic
610	C₂×C₈	C₂×#548	1	1	yes	characteristic
611	C₂×C₈	D₄×#41	1	1	yes	characteristic
612	C₂×C₈	D₄×#41	1	1	yes	characteristic
613	C₂×C₈	D₄×#41	1	1	yes	characteristic
614	C₂×C₈	C₂×#553	1	1	yes	characteristic
615	C₂×C₈	#3484	1	1	yes	characteristic
616	C₂×C₈	#3484	1	1	yes	characteristic
617	C₂×C₈	#3485	1	1	yes	characteristic
618	C₂×C₈	#3485	1	1	yes	characteristic
619	C₂×C₈	#3487	1	1	yes	characteristic
620	C₂×C₈	#3489	1	1	yes	characteristic
621	C₂×C₈	#3513	1	1	yes	characteristic
622	C₂×C₈	#3513	1	1	yes	characteristic
623	C₂×C₈	#3513	1	1	yes	characteristic
624	C₂×C₈	#3513	1	1	yes	characteristic
625	C₂×C₈	#3513	1	1	yes	characteristic
626	C₂×C₈	#3513	1	1	yes	characteristic
627	C₂×C₈	#3533	1	1	yes	characteristic
628	C₂×C₈	#3533	1	1	yes	characteristic
629	C₂×C₈	#3535	1	1	yes	characteristic
630	C₂×C₈	#3535	1	1	yes	characteristic
631	C₂³	C₂×#3003	1	1	yes	characteristic
632	C₂³	D₄×AGL(1,ℤ/8)	1	1	yes	characteristic
633	C₂³	#61437	1	1	yes	characteristic
634	C₂³	#61451	1	1	yes	characteristic
635	C₂³	#61451	1	1	yes	characteristic
636	C₂³	#61600	1	1	yes	characteristic
637	C₂³	#62110	1	1	yes	characteristic
638	C₂×C₄	#34736	1	1	yes	characteristic
639	C₂×C₄	D₄×#120	1	1	yes	characteristic
640	C₂×C₄	D₄×#123	1	1	yes	characteristic
641	C₂×C₄	#36428	1	1	yes	characteristic
642	C₂×C₄	#37712	1	1	yes	characteristic
643	C₂×C₄	#58995	1	1	yes	characteristic
644	C₂×C₄	#59190	1	1	yes	characteristic
645	C₂×C₄	#60369	1	1	yes	characteristic
646	C₂×C₄	#60373	1	1	yes	characteristic
647	C₂×C₄	#60376	1	1	yes	characteristic
648	C₂×C₄	C₂×#3272	1	1	yes	characteristic
649	C₂×C₄	#61058	1	1	yes	characteristic
650	C₂×C₄	#61074	1	1	yes	characteristic
651	C₂×C₄	#61451	1	1	yes	characteristic
652	C₂×C₄	#61451	1	1	yes	characteristic
653	C₂×C₄	#61451	1	1	yes	characteristic
654	C₂×C₄	#61472	1	1	yes	characteristic
655	C₂×C₄	#61505	1	1	yes	characteristic
656	C₂×C₄	#61507	1	1	yes	characteristic
657	C₂×C₄	#61522	1	1	yes	characteristic
658	C₂×C₄	#61522	1	1	yes	characteristic
659	C₂×C₄	#61536	1	1	yes	characteristic
660	C₂×C₄	#61582	1	1	yes	characteristic
661	C₂×C₄	#61614	1	1	yes	characteristic
662	C₂×C₄	#61648	1	1	yes	characteristic
663	C₂×C₄	#62137	1	1	yes	characteristic
664	C₂×C₄	#62156	1	1	yes	characteristic
665	C₂×C₄	#62231	1	1	yes	characteristic
666	C₈	C₂×#2443	1	1	yes	characteristic
667	C₈	#35356	1	1	yes	characteristic
668	C₈	D₄×#123	1	1	yes	characteristic
669	C₈	#37655	1	1	yes	characteristic
670	C₈	#37712	1	1	yes	characteristic
671	C₈	#39116	1	1	yes	characteristic
672	C₈	#58995	1	1	yes	characteristic
673	C₈	#59190	1	1	yes	characteristic
674	C₂²	#6453969	1	1	yes	characteristic
675	C₂²	#6573573	1	1	yes	characteristic
676	C₂²	#6574826	1	1	yes	characteristic
677	C₂²	#6617180	1	1	yes	characteristic
678	C₂²	#6695110	1	1	yes	characteristic
679	C₂²	#7518005	1	1	yes	characteristic
680	C₂²	#7589775	1	1	yes	characteristic
681	C₄	#647794	1	1	yes	characteristic
682	C₄	#6454073	1	1	yes	characteristic
683	C₄	#6573784	1	1	yes	characteristic
684	C₄	#6575004	1	1	yes	characteristic
685	C₄	#6617389	1	1	yes	characteristic
686	C₄	#6695188	1	1	yes	characteristic
687	C₄	#7518135	1	1	yes	characteristic
688	C₄	#7589657	1	1	yes	characteristic
689	C₂	#72213937	1	1	yes	characteristic
690	C₂	#72249733	1	1	yes	characteristic
691	C₂	#72249759	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#6453969
commutator, Frattini, cosocle	C₂³×C₈	C₂⁵
prime radical	C₂×#500743	C₂
LCS	G ▷ C₂³×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #6373016 ◁ G
LECS	G ▷ C₂³×C₈ ▷ C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72320830	C₂	semidirect
2. #72320808	C₂	semidirect
3. #72320778	C₂	semidirect
4. #72320756	C₂	semidirect
5. #72320747	C₂	semidirect
6. #72320737	C₂	semidirect
7. #72320716	C₂	semidirect
8. #72320700	C₂	semidirect
9. #72320676	C₂	semidirect
10. #72320655	C₂	semidirect
11. #72320637	C₂	semidirect
12. #72320621	C₂	semidirect
13. #72320609	C₂	semidirect
14. #72320592	C₂	semidirect
15. #72320575	C₂	semidirect
16. #72320401	C₂	semidirect
17. #72319989	C₂	semidirect
18. #72309672	C₂	semidirect
19. #72308040	C₂	semidirect
20. #72252627	C₂	semidirect
21. #72250542	C₂	semidirect
22. #72250515	C₂	semidirect
23. #72250218	C₂	semidirect
24. #72250205	C₂	semidirect
25. #72250199	C₂	semidirect
26. #72250169	C₂	semidirect
27. #72249959	C₂	semidirect
28. #72239492	C₂	semidirect
30. C₂×#495739	C₂	semidirect
31. #72231532	C₂	semidirect
38. C₂×#33468	C₂²	semidirect
49. #6380164	C₂²	semidirect
56. C₂×#21559	C₂²	semidirect
57. #499545	C₂²	semidirect
58. #499441	C₂²	semidirect
59. #499364	C₂²	semidirect
69. #495044	C₂²	semidirect
70. #495043	C₂²	semidirect
71. C₂×#13155	C₂²	semidirect
72. #494777	C₂²	semidirect
73. C₂×#13040	C₂²	semidirect
76. C₂×#13030	C₂²	semidirect
77. #494536	C₂²	semidirect
78. #494535	C₂²	semidirect
79. C₂×#13005	C₂²	semidirect
81. #494339	C₂²	semidirect
83. #494335	C₂²	semidirect
84. #494334	C₂²	semidirect
87. #494325	C₂²	semidirect
88. C₂×#12949	C₂²	semidirect
89. C₂×#12949	C₂²	semidirect
90. C₂×#12934	C₂²	semidirect
91. C₂×#12934	C₂²	semidirect
92. #494153	C₂²	semidirect
95. #493773	C₂²	semidirect
102. #493129	C₂²	semidirect
103. C₂×#12649	C₂²	semidirect
105. C₂×#12609	C₂²	semidirect
106. #416318	C₂²	semidirect
107. #415479	C₂²	semidirect
109. #412773	C₂²	semidirect
110. #392952	C₂²	semidirect
111. #368420	C₂²	semidirect
112. #365313	C₂²	semidirect
113. #365077	C₂²	semidirect
114. #365034	C₂²	semidirect
115. #365015	C₂²	semidirect
116. #360971	C₂²	semidirect
117. #149374	C₂²	semidirect
118. #149339	C₂²	semidirect
119. #149236	C₂²	semidirect
120. #149236	C₂²	semidirect
121. #149191	C₂²	semidirect
122. #149191	C₂²	semidirect
123. #149045	C₂²	semidirect
124. #148987	C₂²	semidirect
125. #148869	C₂²	semidirect
126. #148744	C₂²	semidirect
127. #148741	C₂²	semidirect
128. #148682	C₂²	semidirect
129. #148635	C₂²	semidirect
130. #148635	C₂²	semidirect
131. #148595	C₂²	semidirect
132. #148570	C₂²	semidirect
133. #148570	C₂²	semidirect
134. #148543	C₂²	semidirect
135. #148432	C₂²	semidirect
136. #148411	C₂²	semidirect
137. #148373	C₂²	semidirect
138. #148373	C₂²	semidirect
139. #148345	C₂²	semidirect
140. #148319	C₂²	semidirect
141. #148284	C₂²	semidirect
142. #148284	C₂²	semidirect
143. #148282	C₂²	semidirect
144. #148282	C₂²	semidirect
145. #148195	C₂²	semidirect
146. #148193	C₂²	semidirect
147. #148164	C₂²	semidirect
148. #148164	C₂²	semidirect
149. #148114	C₂²	semidirect
150. #148060	C₂²	semidirect
151. #147961	C₂²	semidirect
152. #147957	C₂²	semidirect
153. #147953	C₂²	semidirect
154. #147947	C₂²	semidirect
155. #147938	C₂²	semidirect
157. #147684	C₂²	semidirect
160. #147642	C₂²	semidirect
161. #147621	C₂²	semidirect
163. #147465	C₂²	semidirect
164. #147427	C₂²	semidirect
165. #147405	C₂²	semidirect
166. #147404	C₂²	semidirect
167. #147372	C₂²	semidirect
168. #147372	C₂²	semidirect
169. #147362	C₂²	semidirect
170. #147360	C₂²	semidirect
171. #147243	C₂²	semidirect
172. #147199	C₂²	semidirect
173. #147195	C₂²	semidirect
174. #147130	C₂²	semidirect
175. #146802	C₂²	semidirect
182. #146763	C₂²	semidirect
185. #146557	C₂²	semidirect
186. #146385	C₂²	semidirect
259. #26264	D₄	semidirect
260. #26264	D₄	semidirect
261. #26263	D₄	semidirect
262. #26263	D₄	semidirect
263. #22672	D₄	semidirect
264. #22672	D₄	semidirect
265. #22670	D₄	semidirect
266. #22670	D₄	semidirect
495. C₂×SD₃₂	#123	semidirect
496. C₂×D₁₆	#123	semidirect
542. C₂×Q₁₆	C₂×#123	semidirect
545. C₂×D₈	C₂×#123	semidirect
582. C₂×C₁₆	C₂×#123	semidirect

Maximal subgroups

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

subgroup	index
#72320830	2
#72320808	2
#72320778	2
#72320756	2
#72320747	2
#72320737	2
#72320716	2
#72320700	2
#72320676	2
#72320655	2
#72320637	2
#72320621	2
#72320609	2
#72320592	2
#72320575	2
#72320401	2
#72319989	2
#72309672	2
#72308040	2
#72252627	2
#72250542	2
#72250515	2
#72250218	2
#72250205	2
#72250199	2
#72250169	2
#72249959	2
#72239492	2
C₂×#500743	2
C₂×#495739	2
#72231532	2