Subgroups — #72322570

Order 2048.

At least 6411 conjugacy classes of subgroups; only the 814 normal subgroups are shown.

The subgroup lattice has 686 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72322562	C₂	1	1	yes	maximal, characteristic, complemented
2	#72322557	C₂	1	1	yes	maximal, characteristic, complemented
3	#72322550	C₂	1	1	yes	maximal, characteristic, complemented
4	#72322547	C₂	1	1	yes	maximal, characteristic, complemented
5	#72322530	C₂	1	1	yes	maximal, characteristic, complemented
6	#72322489	C₂	1	1	yes	maximal, characteristic, complemented
7	#72322409	C₂	1	1	yes	maximal, characteristic, complemented
8	#72322351	C₂	1	1	yes	maximal, characteristic, complemented
9	#72322295	C₂	1	1	yes	maximal, characteristic, complemented
10	#72322220	C₂	1	1	yes	maximal, characteristic, complemented
11	#72321996	C₂	1	1	yes	maximal, characteristic, complemented
12	#72321654	C₂	1	1	yes	maximal, characteristic, complemented
13	#72321324	C₂	1	1	yes	maximal, characteristic, complemented
14	#72321084	C₂	1	1	yes	maximal, characteristic, complemented
15	#72321017	C₂	1	1	yes	maximal, characteristic, complemented
16	#72320946	C₂	1	1	yes	maximal, characteristic, complemented
17	#72320676	C₂	1	1	yes	maximal, characteristic, complemented
18	#72320276	C₂	1	1	yes	maximal, characteristic, complemented
19	#72320048	C₂	1	1	yes	maximal, characteristic, complemented
20	#72309654	C₂	1	1	yes	maximal, characteristic, complemented
21	#72256927	C₂	1	1	yes	maximal, characteristic, complemented
22	#72256925	C₂	1	1	yes	maximal, characteristic, complemented
23	#72256887	C₂	1	1	yes	maximal, characteristic, complemented
24	#72250701	C₂	1	1	yes	maximal, characteristic, complemented
25	#72250667	C₂	1	1	yes	maximal, characteristic, complemented
26	#72250652	C₂	1	1	yes	maximal, characteristic, complemented
27	#72250638	C₂	1	1	yes	maximal, characteristic, complemented
28	#72250299	C₂	1	1	yes	maximal, characteristic, complemented
29	C₂×#500001	C₂	1	1	yes	maximal, characteristic, complemented
30	#72231555	C₂	1	1	yes	maximal, characteristic, complemented
31	C₂×#495739	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#61293	C₂²	1	1	yes	characteristic
33	C₂×#60176	C₂²	1	1	yes	characteristic, complemented
34	C₂×#33595	C₂²	1	1	yes	characteristic
35	C₂×#33539	C₂²	1	1	yes	characteristic
36	C₂×#33539	C₂²	1	1	yes	characteristic
37	C₂×#33533	C₂²	1	1	yes	characteristic
38	C₂×#33531	C₂²	1	1	yes	characteristic, complemented
39	#7622822	C₂²	1	1	yes	characteristic
40	C₂×#33468	C₂²	1	1	yes	characteristic
41	C₂²×AGL(1,ℤ/16)	C₂²	1	1	yes	characteristic
42	C₂×#33388	C₂²	1	1	yes	characteristic, complemented
43	#6629756	C₂²	1	1	yes	characteristic, complemented
44	#6444706	C₂²	1	1	yes	characteristic, complemented
45	#6444669	C₂²	1	1	yes	characteristic, complemented
46	#6444277	C₂²	1	1	yes	characteristic
47	#6444242	C₂²	1	1	yes	characteristic
48	#6443262	C₂²	1	1	yes	characteristic, complemented
49	#6442790	C₂²	1	1	yes	characteristic
50	C₂×#24288	C₂²	1	1	yes	characteristic
51	#6382785	C₂²	1	1	yes	characteristic, complemented
52	C₂×#23188	C₂²	1	1	yes	characteristic, complemented
53	#6381967	C₂²	1	1	yes	characteristic
54	#6381963	C₂²	1	1	yes	characteristic
55	#6379857	C₂²	1	1	yes	characteristic, complemented
56	#6379178	C₂²	1	1	yes	characteristic, complemented
57	#6373021	C₂²	1	1	yes	characteristic
58	C₂×#21559	C₂²	1	1	yes	characteristic
59	#499306	C₂²	1	1	yes	characteristic, complemented
60	C₂×#13459	C₂²	1	1	yes	characteristic, complemented
61	#499056	C₂²	1	1	yes	characteristic
62	#499054	C₂²	1	1	yes	characteristic, complemented
63	C₂×#13396	C₂²	1	1	yes	characteristic, complemented
64	C₂×#13373	C₂²	1	1	yes	characteristic, complemented
65	C₂×#13373	C₂²	1	1	yes	characteristic, complemented
66	#498860	C₂²	1	1	yes	characteristic
67	#498853	C₂²	1	1	yes	characteristic
68	#498853	C₂²	1	1	yes	characteristic
69	C₂×#13310	C₂²	1	1	yes	characteristic
70	C₂×#13310	C₂²	1	1	yes	characteristic
71	#495242	C₂²	1	1	yes	characteristic
72	C₂×#13249	C₂²	1	1	yes	characteristic, complemented
73	C₂×#13215	C₂²	1	1	yes	characteristic, complemented
74	#494923	C₂²	1	1	yes	characteristic, complemented
75	#494893	C₂²	1	1	yes	characteristic, complemented
76	#494844	C₂²	1	1	yes	characteristic, complemented
77	C₂×#13079	C₂²	1	1	yes	characteristic, complemented
78	C₂×#13077	C₂²	1	1	yes	characteristic
79	#494647	C₂²	1	1	yes	characteristic
80	#494568	C₂²	1	1	yes	characteristic
81	C₂×#13040	C₂²	1	1	yes	characteristic, complemented
82	#494559	C₂²	1	1	yes	characteristic
83	C₂×#13037	C₂²	1	1	yes	characteristic
84	C₂×#13037	C₂²	1	1	yes	characteristic, complemented
85	C₂×#13037	C₂²	1	1	yes	characteristic, complemented
86	C₂×#13033	C₂²	1	1	yes	characteristic
87	C₂×#13033	C₂²	1	1	yes	characteristic
88	C₂×#13030	C₂²	1	1	yes	characteristic
89	C₂×#13030	C₂²	1	1	yes	characteristic
90	C₂×#13005	C₂²	1	1	yes	characteristic
91	C₂×#13005	C₂²	1	1	yes	characteristic
92	C₂×#12988	C₂²	1	1	yes	characteristic
93	C₂×#12956	C₂²	1	1	yes	characteristic, complemented
94	#494334	C₂²	1	1	yes	characteristic, complemented
95	C₂×#12953	C₂²	1	1	yes	characteristic, complemented
96	#494324	C₂²	1	1	yes	characteristic, complemented
97	C₂×#12949	C₂²	1	1	yes	characteristic, complemented
98	C₂×#12934	C₂²	1	1	yes	characteristic, complemented
99	#494267	C₂²	1	1	yes	characteristic, complemented
100	C₂×#12874	C₂²	1	1	yes	characteristic, complemented
101	C₂×#12750	C₂²	1	1	yes	characteristic, complemented
102	C₂×#12750	C₂²	1	1	yes	characteristic, complemented
103	#493085	C₂²	1	1	yes	characteristic, complemented
104	C₂×#12649	C₂²	1	1	yes	characteristic, complemented
105	C₂×#12647	C₂²	1	1	yes	characteristic, complemented
106	#492979	C₂²	1	1	yes	characteristic, complemented
107	C₂×#12609	C₂²	1	1	yes	characteristic, complemented
108	#416201	C₂²	1	1	yes	characteristic
109	#415114	C₂²	1	1	yes	characteristic, complemented
110	#414978	C₂²	1	1	yes	characteristic
111	#413511	C₂²	1	1	yes	characteristic, complemented
112	#393095	C₂²	1	1	yes	characteristic
113	#368649	C₂²	1	1	yes	characteristic, complemented
114	#368388	C₂²	1	1	yes	characteristic, complemented
115	#365078	C₂²	1	1	yes	characteristic
116	#363501	C₂²	1	1	yes	characteristic, complemented
117	#361674	C₂²	1	1	yes	characteristic, complemented
118	#360416	C₂²	1	1	yes	characteristic, complemented
119	#149453	C₂²	1	1	yes	characteristic, complemented
120	#149301	C₂²	1	1	yes	characteristic, complemented
121	#149236	C₂²	1	1	yes	characteristic, complemented
122	#149069	C₂²	1	1	yes	characteristic, complemented
123	#148789	C₂²	1	1	yes	characteristic, complemented
124	#148783	C₂²	1	1	yes	characteristic, complemented
125	#148742	C₂²	1	1	yes	characteristic, complemented
126	#148635	C₂²	1	1	yes	characteristic, complemented
127	#148570	C₂²	1	1	yes	characteristic, complemented
128	#148566	C₂²	1	1	yes	characteristic, complemented
129	#148509	C₂²	1	1	yes	characteristic, complemented
130	#148447	C₂²	1	1	yes	characteristic, complemented
131	#148373	C₂²	1	1	yes	characteristic, complemented
132	#148365	C₂²	1	1	yes	characteristic, complemented
133	#148294	C₂²	1	1	yes	characteristic, complemented
134	#148226	C₂²	1	1	yes	characteristic, complemented
135	#148164	C₂²	1	1	yes	characteristic, complemented
136	#148125	C₂²	1	1	yes	characteristic, complemented
137	#148114	C₂²	1	1	yes	characteristic, complemented
138	#148114	C₂²	1	1	yes	characteristic, complemented
139	#148112	C₂²	1	1	yes	characteristic, complemented
140	#148112	C₂²	1	1	yes	characteristic, complemented
141	#148105	C₂²	1	1	yes	characteristic, complemented
142	#148077	C₂²	1	1	yes	characteristic, complemented
143	#147982	C₂²	1	1	yes	characteristic, complemented
144	#147953	C₂²	1	1	yes	characteristic
145	#147953	C₂²	1	1	yes	characteristic
146	#147947	C₂²	1	1	yes	characteristic, complemented
147	#147947	C₂²	1	1	yes	characteristic, complemented
148	#147938	C₂²	1	1	yes	characteristic
149	#147938	C₂²	1	1	yes	characteristic
150	#147904	C₂²	1	1	yes	characteristic
151	#147904	C₂²	1	1	yes	characteristic
152	#147887	C₂²	1	1	yes	characteristic, complemented
153	#147878	C₂²	1	1	yes	characteristic, complemented
154	#147878	C₂²	1	1	yes	characteristic, complemented
155	#147684	C₂²	1	1	yes	characteristic
156	#147684	C₂²	1	1	yes	characteristic
157	#147658	C₂²	1	1	yes	characteristic, complemented
158	#147638	C₂²	1	1	yes	characteristic
159	#147636	C₂²	1	1	yes	characteristic, complemented
160	#147634	C₂²	1	1	yes	characteristic
161	#147630	C₂²	1	1	yes	characteristic
162	#147542	C₂²	1	1	yes	characteristic
163	#147465	C₂²	1	1	yes	characteristic, complemented
164	#147446	C₂²	1	1	yes	characteristic, complemented
165	#147446	C₂²	1	1	yes	characteristic, complemented
166	#147427	C₂²	1	1	yes	characteristic, complemented
167	#147382	C₂²	1	1	yes	characteristic, complemented
168	#147283	C₂²	1	1	yes	characteristic, complemented
169	#147283	C₂²	1	1	yes	characteristic, complemented
170	#147243	C₂²	1	1	yes	characteristic, complemented
171	#147199	C₂²	1	1	yes	characteristic, complemented
172	#147194	C₂²	1	1	yes	characteristic, complemented
173	#147125	C₂²	1	1	yes	characteristic, complemented
174	#147125	C₂²	1	1	yes	characteristic, complemented
175	#147058	C₂²	1	1	yes	characteristic, complemented
176	#146981	C₂²	1	1	yes	characteristic, complemented
177	#146905	C₂²	1	1	yes	characteristic, complemented
178	#146802	C₂²	1	1	yes	characteristic, complemented
179	#146799	C₂²	1	1	yes	characteristic, complemented
180	#146799	C₂²	1	1	yes	characteristic, complemented
181	#146792	C₂²	1	1	yes	characteristic, complemented
182	#146761	C₂²	1	1	yes	characteristic, complemented
183	#146551	C₂²	1	1	yes	characteristic, complemented
184	#146535	C₂²	1	1	yes	characteristic, complemented
185	#146408	C₂²	1	1	yes	characteristic, complemented
186	#146385	C₂²	1	1	yes	characteristic, complemented
187	C₂×#3584	C₂³	1	1	yes	characteristic
188	C₂²×#576	C₂³	1	1	yes	characteristic
189	C₂×#3414	C₂³	1	1	yes	characteristic
190	C₂×#3414	C₂³	1	1	yes	characteristic
191	C₂²×#509	C₂³	1	1	yes	characteristic
192	C₂²×#509	C₂³	1	1	yes	characteristic
193	C₂²×#509	C₂³	1	1	yes	characteristic
194	C₂²×#509	C₂³	1	1	yes	characteristic
195	C₂×#3407	C₂³	1	1	yes	characteristic
196	C₂×#3162	C₂³	1	1	yes	characteristic
197	C₂×#3155	C₂³	1	1	yes	characteristic
198	C₂²×#493	C₂³	1	1	yes	characteristic
199	C₂×#3067	C₂³	1	1	yes	characteristic
200	C₂×#3067	C₂³	1	1	yes	characteristic
201	C₂×#3060	C₂³	1	1	yes	characteristic
202	C₂×#3058	C₂³	1	1	yes	characteristic
203	C₂×#3058	C₂³	1	1	yes	characteristic
204	C₂×#3058	C₂³	1	1	yes	characteristic
205	C₂×#2957	C₂³	1	1	yes	characteristic
206	C₂²×#444	C₂³	1	1	yes	characteristic
207	C₂×#2952	C₂³	1	1	yes	characteristic
208	C₂×#2948	C₂³	1	1	yes	characteristic
209	C₂×#2943	C₂³	1	1	yes	characteristic
210	C₂²×#442	C₂³	1	1	yes	characteristic
211	C₂²×#442	C₂³	1	1	yes	characteristic
212	C₂×#2932	C₂³	1	1	yes	characteristic
213	C₂×#2912	C₂³	1	1	yes	characteristic
214	C₂×#2912	C₂³	1	1	yes	characteristic
215	C₂×#2875	C₂³	1	1	yes	characteristic
216	#34744	D₄	1	1	yes	characteristic
217	C₂×#2155	C₂³	1	1	yes	characteristic
218	C₂×#2155	C₂³	1	1	yes	characteristic
219	C₂²×#365	C₂³	1	1	yes	characteristic
220	C₂²×#365	C₂³	1	1	yes	characteristic
221	C₂×#2153	C₂³	1	1	yes	characteristic
222	C₂×#2148	C₂³	1	1	yes	characteristic
223	C₂×#2148	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	C₂²×#361	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	C₂×#2145	C₂³	1	1	yes	characteristic
236	C₂×#2145	C₂³	1	1	yes	characteristic
237	C₂×#2145	C₂³	1	1	yes	characteristic
238	C₂²×#360	C₂³	1	1	yes	characteristic
239	C₂²×#360	C₂³	1	1	yes	characteristic
240	C₂²×#360	C₂³	1	1	yes	characteristic
241	C₂²×#360	C₂³	1	1	yes	characteristic
242	C₂×#2143	C₂³	1	1	yes	characteristic
243	C₂×#2143	C₂³	1	1	yes	characteristic
244	#33380	C₂³	1	1	yes	characteristic
245	#33380	C₂³	1	1	yes	characteristic
246	C₂×#2140	C₂³	1	1	yes	characteristic
247	C₂×#2140	C₂³	1	1	yes	characteristic
248	C₂×#2140	C₂³	1	1	yes	characteristic
249	C₂×#2140	C₂³	1	1	yes	characteristic
250	C₂×#2117	C₂³	1	1	yes	characteristic
251	C₂×#2117	C₂³	1	1	yes	characteristic
252	C₂×#2117	C₂³	1	1	yes	characteristic
253	C₂×#2117	C₂³	1	1	yes	characteristic
254	C₂×#2115	C₂³	1	1	yes	characteristic
255	C₂×#2115	C₂³	1	1	yes	characteristic
256	#33333	C₂³	1	1	yes	characteristic
257	C₂×#2110	C₂³	1	1	yes	characteristic
258	C₂²×#347	C₂³	1	1	yes	characteristic
259	C₂²×#347	C₂³	1	1	yes	characteristic
260	#25426	D₄	1	2	yes	—
261	#25426	D₄	1	2	yes	—
262	#25424	D₄	1	2	yes	—
263	#25424	D₄	1	2	yes	—
264	#23031	D₄	1	2	yes	—
265	#23031	D₄	1	2	yes	—
266	#23029	D₄	1	2	yes	—
267	#23029	D₄	1	2	yes	—
268	C₂×#1976	C₂³	1	1	yes	characteristic
269	C₂×#1976	C₂³	1	1	yes	characteristic
270	#21240	C₂³	1	1	yes	characteristic
271	C₂×#1975	C₂³	1	1	yes	characteristic
272	C₂×#1975	C₂³	1	1	yes	characteristic
273	C₂×#1975	C₂³	1	1	yes	characteristic
274	#21233	C₂³	1	1	yes	characteristic
275	#21233	C₂³	1	1	yes	characteristic
276	#21228	C₂³	1	1	yes	characteristic
277	C₂×#1972	C₂³	1	1	yes	characteristic
278	C₂×#1972	C₂³	1	1	yes	characteristic
279	#21224	C₂³	1	1	yes	characteristic
280	#21224	C₂³	1	1	yes	characteristic
281	#21224	C₂³	1	1	yes	characteristic
282	C₂×#1953	C₂³	1	1	yes	characteristic
283	C₂×#1946	C₂³	1	1	yes	characteristic
284	#21157	C₂³	1	1	yes	characteristic
285	#21155	C₂³	1	1	yes	characteristic
286	#21154	C₂³	1	1	yes	characteristic
287	#21151	C₂³	1	1	yes	characteristic
288	#21052	D₄	1	1	yes	characteristic
289	#21048	D₄	1	1	yes	characteristic
290	#21027	D₄	1	1	yes	characteristic
291	#21023	D₄	1	1	yes	characteristic
292	#20900	D₄	1	1	yes	characteristic
293	#20838	D₄	1	1	yes	characteristic
294	C₂×#1833	C₂³	1	1	yes	characteristic
295	#20684	D₄	1	1	yes	characteristic
296	C₂×#1814	C₂³	1	1	yes	characteristic
297	C₂×#1814	C₂³	1	1	yes	characteristic
298	C₂×#1813	C₂³	1	1	yes	characteristic
299	C₂×#1812	C₂³	1	1	yes	characteristic
300	#20668	C₂³	1	1	yes	characteristic
301	#20662	C₂³	1	1	yes	characteristic
302	#20454	C₂³	1	1	yes	characteristic
303	C₂×C₄×#106	C₂³	1	1	yes	characteristic
304	C₂×#1773	C₂³	1	1	yes	characteristic
305	#20436	C₂³	1	1	yes	characteristic
306	C₂×#1770	C₂³	1	1	yes	characteristic
307	#20384	C₂³	1	1	yes	characteristic
308	#20383	C₂³	1	1	yes	characteristic
309	#20383	C₂³	1	1	yes	characteristic
310	#13005	D₄	1	8	yes	complemented
311	C₂×#1389	C₂³	1	1	yes	characteristic
312	C₂×#1389	C₂³	1	1	yes	characteristic
313	C₂×#1389	C₂³	1	1	yes	characteristic
314	C₂×#1389	C₂³	1	1	yes	characteristic
315	#12569	C₂³	1	1	yes	characteristic
316	#12569	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×#1384	C₂³	1	1	yes	characteristic
324	C₂×#1384	C₂³	1	1	yes	characteristic
325	C₂×#1384	C₂³	1	1	yes	characteristic
326	C₂×#1384	C₂³	1	1	yes	characteristic
327	#12563	C₂³	1	1	yes	characteristic
328	#12563	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	#12549	C₂³	1	1	yes	characteristic
342	#12547	C₂³	1	1	yes	characteristic
343	C₂×#1375	C₂³	1	1	yes	characteristic
344	C₂×#1375	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	#12544	C₂³	1	1	yes	characteristic
350	#12544	C₂³	1	1	yes	characteristic
351	#12544	C₂³	1	1	yes	characteristic
352	#12544	C₂³	1	1	yes	characteristic
353	#10873	C₂³	1	1	yes	characteristic
354	#10868	C₂³	1	1	yes	characteristic
355	#10864	C₂³	1	1	yes	characteristic
356	#10864	C₂³	1	1	yes	characteristic
357	#10860	C₂³	1	1	yes	characteristic
358	#10860	C₂³	1	1	yes	characteristic
359	C₂²×#135	C₂⁴	1	1	yes	characteristic
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	C₂²×#131	C₂⁴	1	1	yes	characteristic
367	C₂×#532	C₂×D₄	1	1	yes	characteristic
368	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
369	#3414	#41	1	4	yes	complemented
370	C₂²×SD₃₂	#41	1	2	yes	complemented
371	C₂²×SD₃₂	#41	1	2	yes	complemented
372	C₂²×D₁₆	#41	1	2	yes	complemented
373	C₂²×D₁₆	#41	1	2	yes	complemented
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×#470	C₂×D₄	1	2	yes	—
386	C₂×#469	C₂×D₄	1	2	yes	—
387	C₂×#469	C₂×D₄	1	2	yes	—
388	C₂×#469	C₂×D₄	1	2	yes	—
389	C₂×#466	C₂×D₄	1	2	yes	—
390	C₂×#466	C₂×D₄	1	2	yes	—
391	C₂×#442	C₂×D₄	1	1	yes	characteristic
392	C₂×#442	C₂×D₄	1	1	yes	characteristic
393	C₂×#442	C₂×D₄	1	2	yes	—
394	C₂×#442	C₂×D₄	1	2	yes	—
395	C₂×#441	C₂×D₄	1	1	yes	characteristic
396	C₂×#441	C₂×D₄	1	1	yes	characteristic
397	C₂²×#108	C₂⁴	1	1	yes	characteristic
398	C₂²×#108	C₂⁴	1	1	yes	characteristic
399	C₂²×#108	C₂⁴	1	1	yes	characteristic
400	C₂²×#108	C₂⁴	1	1	yes	characteristic
401	#2912	C₂×D₄	1	4	yes	—
402	C₂×#427	C₂×D₄	1	2	yes	—
403	C₂×#427	C₂⁴	1	1	yes	characteristic
404	C₂×#427	C₂⁴	1	1	yes	characteristic
405	C₂×#427	C₂⁴	1	1	yes	characteristic
406	C₂×#427	C₂⁴	1	1	yes	characteristic
407	C₂×#427	C₂⁴	1	1	yes	characteristic
408	C₂²×#106	C₂×D₄	1	2	yes	—
409	C₂²×#106	C₂⁴	1	1	yes	characteristic
410	C₂²×#106	C₂⁴	1	1	yes	characteristic
411	C₂×#424	C₂×D₄	1	1	yes	characteristic
412	C₂×#423	C₂×D₄	1	1	yes	characteristic
413	C₂²×C₄⋊C₈	C₂×D₄	1	1	yes	characteristic
414	C₂×#408	C₂×D₄	1	1	yes	characteristic
415	C₂×#408	C₂×D₄	1	1	yes	characteristic
416	C₂×#408	C₂×D₄	1	1	yes	characteristic
417	C₂×#408	C₂×D₄	1	1	yes	characteristic
418	C₂×#408	C₂×D₄	1	1	yes	characteristic
419	C₂×#405	C₂×D₄	1	1	yes	characteristic
420	C₂×#405	C₂⁴	1	1	yes	characteristic
421	C₂×#405	C₂⁴	1	1	yes	characteristic
422	C₂×C₄×M₁₆	C₂×D₄	1	1	yes	characteristic
423	C₂²×#97	C₂⁴	1	1	yes	characteristic
424	C₂²×#97	C₂⁴	1	1	yes	characteristic
425	C₂²×C₄×C₈	C₂⁴	1	1	yes	characteristic
426	#2297	C₂×D₄	1	1	yes	characteristic
427	#2297	C₂×D₄	1	1	yes	characteristic
428	#2297	C₂×D₄	1	1	yes	characteristic
429	#2296	C₂×D₄	1	1	yes	characteristic
430	C₂×C₄×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
431	#2145	C₂×D₄	1	4	yes	—
432	C₂×#360	C₂×D₄	1	4	yes	—
433	#2117	C₂×D₄	1	4	yes	—
434	#1972	C₂×D₄	1	2	yes	—
435	#1972	C₂×D₄	1	2	yes	—
436	#1972	C₂×D₄	1	2	yes	—
437	#1972	C₂×D₄	1	2	yes	—
438	#1943	C₂×D₄	1	1	yes	characteristic
439	#1943	C₂×D₄	1	1	yes	characteristic
440	#1943	C₂×D₄	1	1	yes	characteristic
441	#1943	C₂×D₄	1	1	yes	characteristic
442	#1941	C₂×D₄	1	2	yes	—
443	#1941	C₂×D₄	1	2	yes	—
444	#1776	C₂×D₄	1	2	yes	—
445	#1776	C₂×D₄	1	2	yes	—
446	#1753	C₂×D₄	1	2	yes	—
447	#1753	C₂×D₄	1	2	yes	—
448	#1752	C₂×D₄	1	2	yes	—
449	#1752	C₂×D₄	1	2	yes	—
450	#1729	C₂×D₄	1	1	yes	characteristic
451	#1729	C₂×D₄	1	1	yes	characteristic
452	#1729	C₂×D₄	1	1	yes	characteristic
453	#1729	C₂×D₄	1	1	yes	characteristic
454	#1728	C₂×D₄	1	1	yes	characteristic
455	#1728	C₂×D₄	1	1	yes	characteristic
456	#1728	C₂×D₄	1	1	yes	characteristic
457	#1728	C₂×D₄	1	1	yes	characteristic
458	C₂×#336	C₂×D₄	1	1	yes	characteristic
459	C₂×#336	C₂×D₄	1	1	yes	characteristic
460	#1389	C₂×D₄	1	4	yes	—
461	#1383	C₂×D₄	1	4	yes	—
462	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
463	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
464	C₂×#135	C₂²×D₄	1	2	yes	—
465	C₂×#135	C₂×#41	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×Q₁₆	C₂×#41	1	1	yes	characteristic
471	C₂²×D₈	C₂²×D₄	1	2	yes	—
472	C₂²×D₈	C₂²×D₄	1	2	yes	—
473	C₂²×D₈	C₂²×D₄	1	1	yes	characteristic
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	1	yes	characteristic
478	C₂×#131	C₂²×D₄	1	2	yes	—
479	C₂×#131	H(5,𝔽₂)	1	2	yes	—
480	C₂²×M₁₆	C₂²×D₄	1	1	yes	characteristic
481	C₂²×M₁₆	C₂²×D₄	1	1	yes	characteristic
482	C₂²×M₁₆	C₂²×D₄	1	1	yes	characteristic
483	C₂²×M₁₆	C₂²×D₄	1	1	yes	characteristic
484	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
485	C₂³×C₈	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	2	yes	—
489	C₂³×C₈	C₂⁵	1	1	yes	characteristic
490	C₂×C₄⋊Q₈	AGL(1,ℤ/8)	1	1	yes	characteristic
491	C₂×#127	AGL(1,ℤ/8)	1	1	yes	characteristic
492	C₂×#124	AGL(1,ℤ/8)	1	1	yes	characteristic
493	C₂×#124	AGL(1,ℤ/8)	1	1	yes	characteristic
494	C₂×#117	C₂²×D₄	1	1	yes	characteristic
495	C₂×#117	C₂²×D₄	1	1	yes	characteristic
496	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
497	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
498	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
499	C₂×M₃₂	C₂²×D₄	1	2	yes	—
500	C₂×M₃₂	C₂²×D₄	1	2	yes	—
501	C₂×M₃₂	C₂×#41	1	2	yes	—
502	C₂²×C₁₆	C₂×#41	1	2	yes	—
503	C₂²×C₁₆	C₂×#41	1	2	yes	—
504	C₂×#108	C₂²×D₄	1	2	yes	—
505	#427	C₂²×D₄	1	2	yes	—
506	#427	H(5,𝔽₂)	1	2	yes	—
507	C₂×#107	C₂²×D₄	1	1	yes	characteristic
508	C₂×#107	C₂²×D₄	1	1	yes	characteristic
509	C₂×#106	C₂²×D₄	1	2	yes	—
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×#106	C₂²×D₄	1	1	yes	characteristic
514	C₂×#106	C₂²×D₄	1	2	yes	—
515	C₂×#106	C₂²×D₄	1	2	yes	—
516	C₂×#106	H(5,𝔽₂)	1	2	yes	—
517	C₂×C₂²⋊C₈	#120	1	2	yes	—
518	C₂×C₂²⋊C₈	#120	1	2	yes	—
519	C₂×#97	C₂²×D₄	1	1	yes	characteristic
520	C₂×#97	C₂²×D₄	1	1	yes	characteristic
521	C₂×#97	C₂²×D₄	1	1	yes	characteristic
522	C₂×#97	C₂²×D₄	1	1	yes	characteristic
523	C₂×#97	C₂²×D₄	1	2	yes	—
524	C₂×C₄×C₈	C₂²×D₄	1	2	yes	—
525	#386	AGL(1,ℤ/8)	1	2	yes	—
526	#386	AGL(1,ℤ/8)	1	2	yes	—
527	C₄×C₂²⋊C₄	#120	1	2	yes	—
528	C₄×C₂²⋊C₄	#120	1	2	yes	—
529	#336	#120	1	2	yes	—
530	#336	#120	1	2	yes	—
531	#336	#120	1	2	yes	—
532	#336	#120	1	2	yes	—
533	C₂×#41	D₄²	1	2	yes	—
534	C₂×#41	#576	1	2	yes	—
535	C₂²×Q₈	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
536	C₂²×Q₈	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
537	C₂²×D₄	C₂×AGL(1,ℤ/8)	1	2	yes	—
538	C₂²×D₄	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×#120	1	2	yes	—
541	C₂³×C₄	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
542	C₂³×C₄	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
543	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
544	C₂×Q₁₆	#525	1	2	yes	complemented
545	C₂×Q₁₆	#546	1	2	yes	—
546	C₂×D₈	#525	1	4	yes	—
547	C₂×D₈	#525	1	2	yes	complemented
548	C₂×D₈	#546	1	2	yes	—
549	C₂×M₁₆	D₄²	1	2	yes	—
550	C₂²×C₈	C₂×#120	1	1	yes	characteristic
551	C₂²×C₈	C₂×#120	1	1	yes	characteristic
552	C₂²×C₈	C₂×#120	1	2	yes	—
553	C₂²×C₈	C₂×#120	1	2	yes	—
554	C₂²×C₈	C₂³×D₄	1	1	yes	characteristic
555	C₂²×C₈	C₂³×D₄	1	1	yes	characteristic
556	C₂²×C₈	C₂³×D₄	1	1	yes	characteristic
557	C₂²×C₈	C₂²×#41	1	1	yes	characteristic
558	C₂²×C₈	C₂²×#41	1	1	yes	characteristic
559	C₂²×C₈	C₂²×#41	1	1	yes	characteristic
560	C₂²×C₈	C₂×H(5,𝔽₂)	1	1	yes	characteristic
561	C₂²×C₈	C₂×H(5,𝔽₂)	1	1	yes	characteristic
562	C₂²×C₈	C₂×H(5,𝔽₂)	1	1	yes	characteristic
563	C₂²×C₈	C₂×H(5,𝔽₂)	1	1	yes	characteristic
564	C₂²×C₈	#585	1	1	yes	characteristic
565	C₂²×C₈	#585	1	1	yes	characteristic
566	C₂²×C₈	#585	1	1	yes	characteristic
567	C₂²×C₈	#585	1	1	yes	characteristic
568	C₂×C₂²⋊C₄	C₂×AGL(1,ℤ/8)	1	2	yes	—
569	C₂×C₄²	C₂×#120	1	1	yes	characteristic
570	C₂×C₄²	C₂×#120	1	2	yes	—
571	C₂×C₄²	C₂×#120	1	1	yes	characteristic
572	C₂×C₄²	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
573	C₂×C₄²	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
574	#106	D₄²	1	2	yes	—
575	#106	D₄²	1	4	yes	—
576	#106	D₄²	1	2	yes	—
577	C₂⁴	#3003	1	2	yes	—
578	C₂⁴	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
579	C₂×Q₈	#3264	1	2	yes	—
580	C₂×D₄	#3264	1	2	yes	—
581	C₂²×C₄	#3003	1	2	yes	—
582	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
583	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
584	C₂²×C₄	D₄×#41	1	1	yes	characteristic
585	C₂²×C₄	D₄×#41	1	1	yes	characteristic
586	C₂²×C₄	D₄×#41	1	1	yes	characteristic
587	C₂²×C₄	#3484	1	1	yes	characteristic
588	C₂²×C₄	#3488	1	1	yes	characteristic
589	C₂²×C₄	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
590	C₂²×C₄	C₂×#576	1	1	yes	characteristic
591	C₂²×C₄	#3584	1	1	yes	characteristic
592	C₂²×C₄	#3585	1	1	yes	characteristic
593	C₂²×C₄	#3585	1	1	yes	characteristic
594	C₂²×C₄	#3585	1	1	yes	characteristic
595	C₂²×C₄	#3585	1	1	yes	characteristic
596	C₂×C₈	C₂×#525	1	1	yes	characteristic
597	C₂×C₈	C₂×#525	1	1	yes	characteristic
598	C₂×C₈	#3449	1	1	yes	characteristic
599	C₂×C₈	#3459	1	1	yes	characteristic
600	C₂×C₈	C₂×D₄²	1	1	yes	characteristic
601	C₂×C₈	C₂×D₄²	1	1	yes	characteristic
602	C₂×C₈	C₂×#546	1	1	yes	characteristic
603	C₂×C₈	D₄×#41	1	1	yes	characteristic
604	C₂×C₈	D₄×#41	1	1	yes	characteristic
605	C₂×C₈	D₄×#41	1	1	yes	characteristic
606	C₂×C₈	D₄×#41	1	1	yes	characteristic
607	C₂×C₈	#3481	1	1	yes	characteristic
608	C₂×C₈	#3484	1	1	yes	characteristic
609	C₂×C₈	#3484	1	1	yes	characteristic
610	C₂×C₈	#3485	1	1	yes	characteristic
611	C₂×C₈	#3485	1	1	yes	characteristic
612	C₂×C₈	#3488	1	1	yes	characteristic
613	C₂×C₈	#3488	1	1	yes	characteristic
614	C₂×C₈	#3490	1	1	yes	characteristic
615	C₂×C₈	#3505	1	1	yes	characteristic
616	C₂×C₈	#3505	1	1	yes	characteristic
617	C₂×C₈	#3513	1	1	yes	characteristic
618	C₂×C₈	#3513	1	1	yes	characteristic
619	C₂×C₈	#3519	1	1	yes	characteristic
620	C₂×C₈	#3533	1	1	yes	characteristic
621	C₂×C₈	#3540	1	1	yes	characteristic
622	C₂×C₈	#3540	1	1	yes	characteristic
623	C₂×C₈	#3542	1	1	yes	characteristic
624	C₂³	C₂×#3003	1	1	yes	characteristic
625	C₂³	D₄×AGL(1,ℤ/8)	1	1	yes	characteristic
626	C₂³	#61437	1	1	yes	characteristic
627	C₂³	#61451	1	1	yes	characteristic
628	C₂³	#61451	1	1	yes	characteristic
629	C₂³	#61591	1	1	yes	characteristic
630	C₂³	#61961	1	1	yes	characteristic
631	C₂×C₄	#34736	1	1	yes	characteristic
632	C₂×C₄	D₄×#120	1	1	yes	characteristic
633	C₂×C₄	#36099	1	1	yes	characteristic
634	C₂×C₄	#36212	1	1	yes	characteristic
635	C₂×C₄	#37825	1	1	yes	characteristic
636	C₂×C₄	#58992	1	1	yes	characteristic
637	C₂×C₄	#59179	1	1	yes	characteristic
638	C₂×C₄	#60369	1	1	yes	characteristic
639	C₂×C₄	#60372	1	1	yes	characteristic
640	C₂×C₄	#60376	1	1	yes	characteristic
641	C₂×C₄	C₂×#3264	1	1	yes	characteristic
642	C₂×C₄	#61059	1	1	yes	characteristic
643	C₂×C₄	#61077	1	1	yes	characteristic
644	C₂×C₄	#61451	1	1	yes	characteristic
645	C₂×C₄	#61451	1	1	yes	characteristic
646	C₂×C₄	#61451	1	1	yes	characteristic
647	C₂×C₄	#61489	1	1	yes	characteristic
648	C₂×C₄	#61505	1	1	yes	characteristic
649	C₂×C₄	#61505	1	1	yes	characteristic
650	C₂×C₄	#61519	1	1	yes	characteristic
651	C₂×C₄	#61519	1	1	yes	characteristic
652	C₂×C₄	#61548	1	1	yes	characteristic
653	C₂×C₄	#61571	1	1	yes	characteristic
654	C₂×C₄	#61616	1	1	yes	characteristic
655	C₂×C₄	#61651	1	1	yes	characteristic
656	C₂×C₄	#61989	1	1	yes	characteristic
657	C₂×C₄	#62007	1	1	yes	characteristic
658	C₂×C₄	#62083	1	1	yes	characteristic
659	C₈	#34655	1	1	yes	characteristic
660	C₈	#35352	1	1	yes	characteristic
661	C₈	#36096	1	1	yes	characteristic
662	C₈	#37658	1	1	yes	characteristic
663	C₈	#37800	1	1	yes	characteristic
664	C₈	#39869	1	1	yes	characteristic
665	C₈	#59000	1	1	yes	characteristic
666	C₈	#59029	1	1	yes	characteristic
667	C₂²	#6453969	1	1	yes	characteristic
668	C₂²	#6573549	1	1	yes	characteristic
669	C₂²	#6577402	1	1	yes	characteristic
670	C₂²	#6595872	1	1	yes	characteristic
671	C₂²	#6742022	1	1	yes	characteristic
672	C₂²	#7515320	1	1	yes	characteristic
673	C₂²	#7584844	1	1	yes	characteristic
674	C₄	#648002	1	1	yes	characteristic
675	C₄	#6454097	1	1	yes	characteristic
676	C₄	#6573792	1	1	yes	characteristic
677	C₄	#6577212	1	1	yes	characteristic
678	C₄	#6596042	1	1	yes	characteristic
679	C₄	#6742229	1	1	yes	characteristic
680	C₄	#7515180	1	1	yes	characteristic
681	C₄	#7584689	1	1	yes	characteristic
682	C₂	#72213937	1	1	yes	characteristic
683	C₂	#72249723	1	1	yes	characteristic
684	C₂	#72249759	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#6453969
commutator, Frattini, cosocle	C₂³×C₈	C₂⁵
LCS	G ▷ C₂³×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #6373021 ◁ 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. #72322562	C₂	semidirect
2. #72322557	C₂	semidirect
3. #72322550	C₂	semidirect
4. #72322547	C₂	semidirect
5. #72322530	C₂	semidirect
6. #72322489	C₂	semidirect
7. #72322409	C₂	semidirect
8. #72322351	C₂	semidirect
9. #72322295	C₂	semidirect
10. #72322220	C₂	semidirect
11. #72321996	C₂	semidirect
12. #72321654	C₂	semidirect
13. #72321324	C₂	semidirect
14. #72321084	C₂	semidirect
15. #72321017	C₂	semidirect
16. #72320946	C₂	semidirect
17. #72320676	C₂	semidirect
18. #72320276	C₂	semidirect
19. #72320048	C₂	semidirect
20. #72309654	C₂	semidirect
21. #72256927	C₂	semidirect
22. #72256925	C₂	semidirect
23. #72256887	C₂	semidirect
24. #72250701	C₂	semidirect
25. #72250667	C₂	semidirect
26. #72250652	C₂	semidirect
27. #72250638	C₂	semidirect
28. #72250299	C₂	semidirect
29. C₂×#500001	C₂	semidirect
30. #72231555	C₂	semidirect
31. C₂×#495739	C₂	semidirect
33. C₂×#60176	C₂²	semidirect
38. C₂×#33531	C₂²	semidirect
42. C₂×#33388	C₂²	semidirect
43. #6629756	C₂²	semidirect
44. #6444706	C₂²	semidirect
45. #6444669	C₂²	semidirect
48. #6443262	C₂²	semidirect
51. #6382785	C₂²	semidirect
52. C₂×#23188	C₂²	semidirect
55. #6379857	C₂²	semidirect
56. #6379178	C₂²	semidirect
59. #499306	C₂²	semidirect
60. C₂×#13459	C₂²	semidirect
62. #499054	C₂²	semidirect
63. C₂×#13396	C₂²	semidirect
64. C₂×#13373	C₂²	semidirect
65. C₂×#13373	C₂²	semidirect
72. C₂×#13249	C₂²	semidirect
73. C₂×#13215	C₂²	semidirect
74. #494923	C₂²	semidirect
75. #494893	C₂²	semidirect
76. #494844	C₂²	semidirect
77. C₂×#13079	C₂²	semidirect
81. C₂×#13040	C₂²	semidirect
84. C₂×#13037	C₂²	semidirect
85. C₂×#13037	C₂²	semidirect
93. C₂×#12956	C₂²	semidirect
94. #494334	C₂²	semidirect
95. C₂×#12953	C₂²	semidirect
96. #494324	C₂²	semidirect
97. C₂×#12949	C₂²	semidirect
98. C₂×#12934	C₂²	semidirect
99. #494267	C₂²	semidirect
100. C₂×#12874	C₂²	semidirect
101. C₂×#12750	C₂²	semidirect
102. C₂×#12750	C₂²	semidirect
103. #493085	C₂²	semidirect
104. C₂×#12649	C₂²	semidirect
105. C₂×#12647	C₂²	semidirect
106. #492979	C₂²	semidirect
107. C₂×#12609	C₂²	semidirect
109. #415114	C₂²	semidirect
111. #413511	C₂²	semidirect
113. #368649	C₂²	semidirect
114. #368388	C₂²	semidirect
116. #363501	C₂²	semidirect
117. #361674	C₂²	semidirect
118. #360416	C₂²	semidirect
119. #149453	C₂²	semidirect
120. #149301	C₂²	semidirect
121. #149236	C₂²	semidirect
122. #149069	C₂²	semidirect
123. #148789	C₂²	semidirect
124. #148783	C₂²	semidirect
125. #148742	C₂²	semidirect
126. #148635	C₂²	semidirect
127. #148570	C₂²	semidirect
128. #148566	C₂²	semidirect
129. #148509	C₂²	semidirect
130. #148447	C₂²	semidirect
131. #148373	C₂²	semidirect
132. #148365	C₂²	semidirect
133. #148294	C₂²	semidirect
134. #148226	C₂²	semidirect
135. #148164	C₂²	semidirect
136. #148125	C₂²	semidirect
137. #148114	C₂²	semidirect
138. #148114	C₂²	semidirect
139. #148112	C₂²	semidirect
140. #148112	C₂²	semidirect
141. #148105	C₂²	semidirect
142. #148077	C₂²	semidirect
143. #147982	C₂²	semidirect
146. #147947	C₂²	semidirect
147. #147947	C₂²	semidirect
152. #147887	C₂²	semidirect
153. #147878	C₂²	semidirect
154. #147878	C₂²	semidirect
157. #147658	C₂²	semidirect
159. #147636	C₂²	semidirect
163. #147465	C₂²	semidirect
164. #147446	C₂²	semidirect
165. #147446	C₂²	semidirect
166. #147427	C₂²	semidirect
167. #147382	C₂²	semidirect
168. #147283	C₂²	semidirect
169. #147283	C₂²	semidirect
170. #147243	C₂²	semidirect
171. #147199	C₂²	semidirect
172. #147194	C₂²	semidirect
173. #147125	C₂²	semidirect
174. #147125	C₂²	semidirect
175. #147058	C₂²	semidirect
176. #146981	C₂²	semidirect
177. #146905	C₂²	semidirect
178. #146802	C₂²	semidirect
179. #146799	C₂²	semidirect
180. #146799	C₂²	semidirect
181. #146792	C₂²	semidirect
182. #146761	C₂²	semidirect
183. #146551	C₂²	semidirect
184. #146535	C₂²	semidirect
185. #146408	C₂²	semidirect
186. #146385	C₂²	semidirect
310. #13005	D₄	semidirect
369. #3414	#41	semidirect
370. C₂²×SD₃₂	#41	semidirect
371. C₂²×SD₃₂	#41	semidirect
372. C₂²×D₁₆	#41	semidirect
373. C₂²×D₁₆	#41	semidirect
544. C₂×Q₁₆	#525	semidirect
547. C₂×D₈	#525	semidirect

Maximal subgroups

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

subgroup	index
#72322562	2
#72322557	2
#72322550	2
#72322547	2
#72322530	2
#72322489	2
#72322409	2
#72322351	2
#72322295	2
#72322220	2
#72321996	2
#72321654	2
#72321324	2
#72321084	2
#72321017	2
#72320946	2
#72320676	2
#72320276	2
#72320048	2
#72309654	2
#72256927	2
#72256925	2
#72256887	2
#72250701	2
#72250667	2
#72250652	2
#72250638	2
#72250299	2
C₂×#500001	2
#72231555	2
C₂×#495739	2