Subgroups — #72306381

Order 2048.

At least 6829 conjugacy classes of subgroups; only the 502 normal subgroups are shown.

The subgroup lattice has 349 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72306380	C₂	1	1	yes	maximal, characteristic, complemented
2	#72306379	C₂	1	1	yes	maximal, characteristic
3	#72306378	C₂	1	1	yes	maximal, characteristic, complemented
4	#72306374	C₂	1	1	yes	maximal, characteristic, complemented
5	#72306367	C₂	1	1	yes	maximal, characteristic, complemented
6	#72306332	C₂	1	2	yes	maximal, complemented
7	#72306304	C₂	1	2	yes	maximal, complemented
8	#72306300	C₂	1	2	yes	maximal, complemented
9	#72306288	C₂	1	2	yes	maximal, complemented
10	#72279260	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#152674	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#62836	C₂²	1	1	yes	characteristic
13	C₂×#24001	C₄	1	1	yes	characteristic, complemented
14	C₂×#23999	C₂²	1	1	yes	characteristic
15	C₂×#23898	C₄	1	1	yes	characteristic, complemented
16	#6437459	C₄	1	1	yes	characteristic, complemented
17	#6437458	C₂²	1	1	yes	characteristic
18	C₂×#23909	C₂²	1	1	yes	characteristic
19	#6431798	C₄	1	1	yes	characteristic, complemented
20	#6343930	C₂²	1	2	yes	—
21	#6343928	C₂²	1	2	yes	—
22	C₂×#17675	C₂²	1	1	yes	characteristic
23	C₂×#17663	C₂²	1	1	yes	characteristic
24	C₂×#13569	C₂²	1	2	yes	complemented
25	C₂×#13569	C₂²	1	2	yes	complemented
26	C₂×#12728	C₂²	1	2	yes	—
27	#493433	C₂²	1	2	yes	—
28	C₂×#12695	C₂²	1	1	yes	characteristic
29	C₂×#12695	C₂²	1	1	yes	characteristic
30	#382439	C₄	1	1	yes	characteristic, complemented
31	#363975	C₄	1	1	yes	characteristic, complemented
32	#363973	C₂²	1	1	yes	characteristic
33	#359604	C₂²	1	1	yes	characteristic
34	#359602	C₄	1	1	yes	characteristic, complemented
35	#359560	C₄	1	1	yes	characteristic, complemented
36	#359460	C₂²	1	1	yes	characteristic
37	#151803	C₂²	1	2	yes	complemented
38	#151803	C₂²	1	2	yes	complemented
39	C₂×#7481	C₂²	1	2	yes	complemented
40	C₂×#7481	C₂²	1	2	yes	complemented
41	C₂×#7481	C₂²	1	2	yes	complemented
42	C₂×#7481	C₂²	1	2	yes	complemented
43	#62848	C₂×C₄	1	1	yes	characteristic
44	C₂×#3510	D₄	1	1	yes	characteristic
45	C₂×#3510	C₂³	1	1	yes	characteristic
46	C₂×#3500	D₄	1	1	yes	characteristic
47	C₂×#3500	C₂³	1	1	yes	characteristic
48	C₂×#3509	C₂×C₄	1	1	yes	characteristic
49	C₂×#3499	C₂×C₄	1	1	yes	characteristic
50	C₂×#3508	D₄	1	1	yes	characteristic
51	C₂×#3498	D₄	1	1	yes	characteristic
52	C₂×#3487	C₂×C₄	1	1	yes	characteristic
53	C₂×#3487	C₂×C₄	1	1	yes	characteristic
54	C₂×#3487	D₄	1	1	yes	characteristic
55	C₂×#3485	C₂×C₄	1	1	yes	characteristic
56	C₂×#3485	D₄	1	1	yes	characteristic
57	C₂×#3444	D₄	1	1	yes	characteristic
58	C₂×#3444	D₄	1	1	yes	characteristic
59	C₂²×#532	C₂³	1	1	yes	characteristic
60	C₂×#3020	C₂×C₄	1	1	yes	characteristic
61	C₂×#3020	C₂×C₄	1	1	yes	characteristic
62	C₂²×#456	C₂×C₄	1	1	yes	characteristic
63	C₂²×#454	C₂³	1	1	yes	characteristic
64	C₂×#2884	C₂×C₄	1	1	yes	characteristic
65	C₂×#2884	C₂×C₄	1	1	yes	characteristic
66	#34174	C₂×C₄	1	1	yes	characteristic
67	C₂²×#354	C₂³	1	2	yes	—
68	C₂²×#354	C₂³	1	2	yes	—
69	C₂×#1912	C₂×C₄	1	1	yes	characteristic
70	C₂×#1912	C₂×C₄	1	1	yes	characteristic
71	C₂×#1912	C₂×C₄	1	1	yes	characteristic
72	C₂×#1912	C₂×C₄	1	1	yes	characteristic
73	#20954	C₂×C₄	1	1	yes	characteristic
74	#20954	C₂×C₄	1	1	yes	characteristic
75	C₂×#1888	C₂³	1	1	yes	characteristic
76	C₂×#1888	C₂³	1	1	yes	characteristic
77	C₂×#1888	C₂³	1	1	yes	characteristic
78	C₂×#1886	C₂×C₄	1	1	yes	characteristic
79	C₂×#1886	C₂×C₄	1	1	yes	characteristic
80	C₂×#1886	C₂×C₄	1	1	yes	characteristic
81	C₂×#1830	C₂×C₄	1	1	yes	characteristic
82	C₂×#1830	C₂×C₄	1	1	yes	characteristic
83	#20593	C₂×C₄	1	1	yes	characteristic
84	#20593	C₂×C₄	1	1	yes	characteristic
85	C₂×#1785	C₂×C₄	1	1	yes	characteristic
86	C₂×#1785	C₂×C₄	1	1	yes	characteristic
87	#20355	C₂×C₄	1	1	yes	characteristic
88	#17686	D₄	1	8	yes	complemented
89	#17675	D₄	1	2	yes	complemented
90	#17675	D₄	1	2	yes	complemented
91	#17675	D₄	1	4	yes	complemented
92	#17666	D₄	1	4	yes	complemented
93	C₂×#1536	D₄	1	2	yes	complemented
94	C₂×#1533	C₂³	1	2	yes	—
95	C₂×#1533	C₂³	1	2	yes	—
96	C₂×#1525	D₄	1	2	yes	complemented
97	C₂²×2₋¹⁺⁴	C₂²⋊C₄	1	1	yes	characteristic
98	C₂²×2₋¹⁺⁴	C₂²×C₄	1	1	yes	characteristic
99	C₂²×2₋¹⁺⁴	C₂²×C₄	1	1	yes	characteristic
100	C₂²×H(5,𝔽₂)	C₂²⋊C₄	1	1	yes	characteristic
101	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
102	C₂³×#41	C₂²×C₄	1	1	yes	characteristic
103	C₂³×#41	C₂×D₄	1	1	yes	characteristic
104	#3510	C₂×D₄	1	4	yes	—
105	#3510	#41	1	4	yes	—
106	C₂×#536	C₂²⋊C₄	1	1	yes	characteristic
107	C₂×#536	C₂²⋊C₄	1	1	yes	characteristic
108	C₂×#536	C₂²×C₄	1	1	yes	characteristic
109	C₂×#536	C₂²×C₄	1	1	yes	characteristic
110	C₂×#536	#41	1	2	yes	—
111	C₂×#535	C₂²⋊C₄	1	1	yes	characteristic
112	C₂×#535	C₂²⋊C₄	1	1	yes	characteristic
113	C₂×#535	C₂×D₄	1	1	yes	characteristic
114	C₂×#535	C₂×D₄	1	1	yes	characteristic
115	C₂×#535	#41	1	2	yes	—
116	C₂×#533	C₂²⋊C₄	1	1	yes	characteristic
117	C₂×#533	C₂×D₄	1	1	yes	characteristic
118	C₂×#532	C₂²⋊C₄	1	1	yes	characteristic
119	C₂×#532	C₂×D₄	1	1	yes	characteristic
120	C₂×#532	C₂×D₄	1	1	yes	characteristic
121	C₂×#532	C₂×D₄	1	1	yes	characteristic
122	C₂×#532	C₂×D₄	1	2	yes	—
123	C₂×#532	C₂×D₄	1	1	yes	characteristic
124	C₂×#532	C₂×D₄	1	1	yes	characteristic
125	C₂×#532	#41	1	1	yes	characteristic
126	C₂×#532	#41	1	1	yes	characteristic
127	C₂×#532	#41	1	1	yes	characteristic
128	C₂×#532	#41	1	1	yes	characteristic
129	C₂²×C₄⋊Q₈	C₂²×C₄	1	1	yes	characteristic
130	C₂²×#127	C₂×D₄	1	1	yes	characteristic
131	C₂²×#124	C₂×D₄	1	2	yes	—
132	C₂²×#124	C₂×D₄	1	1	yes	characteristic
133	C₂²×#124	C₂⁴	1	1	yes	characteristic
134	C₂×#525	C₂²⋊C₄	1	1	yes	characteristic
135	C₂×#525	C₂²⋊C₄	1	1	yes	characteristic
136	C₂×#525	C₂²⋊C₄	1	1	yes	characteristic
137	C₂×#525	C₂²⋊C₄	1	1	yes	characteristic
138	C₂×#519	C₂²⋊C₄	1	1	yes	characteristic
139	C₂×#519	C₂²×C₄	1	1	yes	characteristic
140	C₂×#519	C₂²×C₄	1	1	yes	characteristic
141	C₂×#519	C₂²×C₄	1	1	yes	characteristic
142	C₂×#519	C₂²×C₄	1	1	yes	characteristic
143	C₂×#518	C₂²⋊C₄	1	1	yes	characteristic
144	C₂×#518	C₂×D₄	1	1	yes	characteristic
145	C₂×C₄×#41	C₂²⋊C₄	1	1	yes	characteristic
146	C₂×C₄×#41	C₂²⋊C₄	1	1	yes	characteristic
147	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
148	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
149	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
150	C₂²×#101	C₂²×C₄	1	1	yes	characteristic
151	C₂²×#101	C₂²×C₄	1	1	yes	characteristic
152	C₂²×#101	C₂²×C₄	1	1	yes	characteristic
153	C₂²×#101	C₂²×C₄	1	1	yes	characteristic
154	#1533	C₂×D₄	1	4	yes	—
155	#1533	C₂×D₄	1	4	yes	—
156	#1533	C₂×D₄	1	4	yes	—
157	#1533	C₂×D₄	1	4	yes	—
158	C₂×#329	C₂×D₄	1	4	yes	—
159	C₂×#329	C₂×D₄	1	4	yes	—
160	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
161	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
162	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
163	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
164	C₂²×#41	C₄×D₄	1	1	yes	characteristic
165	C₂²×#41	C₄×D₄	1	1	yes	characteristic
166	C₂²×#41	C₄×D₄	1	1	yes	characteristic
167	C₂²×#41	C₄×D₄	1	1	yes	characteristic
168	C₂²×#41	C₄×D₄	1	2	yes	—
169	C₂²×#41	#121	1	1	yes	characteristic
170	C₂²×#41	#121	1	1	yes	characteristic
171	C₂²×#41	#121	1	1	yes	characteristic
172	C₂²×#41	#121	1	1	yes	characteristic
173	C₂²×#41	#121	1	2	yes	—
174	C₂³×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
175	C₂³×Q₈	C₄×D₄	1	2	yes	—
176	C₂³×Q₈	C₂³×C₄	1	1	yes	characteristic
177	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
178	C₂³×D₄	#121	1	2	yes	—
179	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
180	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
181	#536	C₄×D₄	1	4	yes	—
182	#535	#121	1	4	yes	—
183	#533	#99	1	2	yes	—
184	#533	#99	1	2	yes	—
185	#533	#120	1	2	yes	—
186	#533	#123	1	2	yes	—
187	C₂×C₄⋊Q₈	#99	1	1	yes	characteristic
188	C₂×C₄⋊Q₈	C₄×D₄	1	1	yes	characteristic
189	C₂×C₄⋊Q₈	C₄×D₄	1	1	yes	characteristic
190	C₂×C₄⋊Q₈	C₄×D₄	1	1	yes	characteristic
191	C₂×C₄⋊Q₈	C₄×D₄	1	1	yes	characteristic
192	C₂×C₄⋊Q₈	C₄×D₄	1	2	yes	—
193	C₂×C₄⋊Q₈	#123	1	1	yes	characteristic
194	C₂×#127	#99	1	1	yes	characteristic
195	C₂×#127	#121	1	1	yes	characteristic
196	C₂×#127	#121	1	1	yes	characteristic
197	C₂×#127	#121	1	1	yes	characteristic
198	C₂×#127	#121	1	1	yes	characteristic
199	C₂×#127	#121	1	2	yes	—
200	C₂×#127	#123	1	1	yes	characteristic
201	C₂×#124	#99	1	1	yes	characteristic
202	C₂×#124	#99	1	1	yes	characteristic
203	C₂×#124	C₄×D₄	1	2	yes	—
204	C₂×#124	#120	1	1	yes	characteristic
205	C₂×#124	#120	1	1	yes	characteristic
206	C₂×#124	#120	1	1	yes	characteristic
207	C₂×#124	#120	1	1	yes	characteristic
208	C₂×#124	#121	1	2	yes	—
209	C₂×#124	#123	1	1	yes	characteristic
210	C₂×#124	#123	1	1	yes	characteristic
211	C₂×#124	C₂²×D₄	1	2	yes	—
212	C₂×#124	C₂²×D₄	1	2	yes	—
213	C₂×#124	C₂²×D₄	1	1	yes	characteristic
214	C₂×#124	C₂²×D₄	1	1	yes	characteristic
215	C₂×#124	C₂×#41	1	2	yes	—
216	C₂×#124	C₂×#41	1	2	yes	—
217	C₂×#124	C₂×#41	1	1	yes	characteristic
218	C₂×#124	C₂×#41	1	1	yes	characteristic
219	#525	#99	1	2	yes	—
220	#525	#99	1	2	yes	—
221	C₂×#123	#99	1	2	yes	—
222	C₂×#120	#99	1	2	yes	—
223	#519	C₄×D₄	1	4	yes	—
224	#518	#121	1	4	yes	—
225	C₄×#41	#120	1	2	yes	—
226	C₄×#41	#123	1	2	yes	—
227	C₂×#117	C₂×C₂²⋊C₄	1	1	yes	characteristic
228	C₂×#117	C₂×C₂²⋊C₄	1	1	yes	characteristic
229	C₂×#117	C₂×C₂²⋊C₄	1	1	yes	characteristic
230	C₂×#117	C₂×C₂²⋊C₄	1	1	yes	characteristic
231	C₂×#117	#123	1	2	yes	—
232	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
233	C₂²×C₄²	#120	1	1	yes	characteristic
234	C₂²×C₄²	#120	1	1	yes	characteristic
235	C₂²×C₄²	#120	1	2	yes	—
236	C₂²×C₄²	#123	1	1	yes	characteristic
237	C₂²×C₄²	#123	1	1	yes	characteristic
238	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
239	#329	#120	1	8	yes	—
240	#329	#120	1	8	yes	—
241	C₂⁵	C₂×#99	1	1	yes	characteristic
242	C₂×#41	#386	1	2	yes	—
243	C₂×#41	C₂×#99	1	2	yes	—
244	C₂²×Q₈	#386	1	1	yes	characteristic
245	C₂²×Q₈	#386	1	1	yes	characteristic
246	C₂²×Q₈	#386	1	1	yes	characteristic
247	C₂²×Q₈	#386	1	1	yes	characteristic
248	C₂²×Q₈	C₂×#99	1	1	yes	characteristic
249	C₂²×Q₈	C₂×#99	1	1	yes	characteristic
250	C₂²×Q₈	C₂×C₄×D₄	1	2	yes	—
251	C₂²×Q₈	C₂×C₄×D₄	1	1	yes	characteristic
252	C₂²×Q₈	C₂×C₄×D₄	1	1	yes	characteristic
253	C₂²×Q₈	C₂×C₄×D₄	1	2	yes	—
254	C₂²×D₄	#386	1	1	yes	characteristic
255	C₂²×D₄	#386	1	1	yes	characteristic
256	C₂²×D₄	#386	1	1	yes	characteristic
257	C₂²×D₄	#386	1	1	yes	characteristic
258	C₂²×D₄	C₂×#99	1	1	yes	characteristic
259	C₂²×D₄	C₂×#99	1	1	yes	characteristic
260	C₂²×D₄	C₂×#99	1	2	yes	—
261	C₂²×D₄	C₂×#121	1	2	yes	—
262	C₂²×D₄	C₂×#121	1	1	yes	characteristic
263	C₂²×D₄	C₂×#121	1	1	yes	characteristic
264	C₂²×D₄	C₂×#121	1	2	yes	—
265	C₂³×C₄	#386	1	2	yes	—
266	C₂³×C₄	#386	1	1	yes	characteristic
267	C₂³×C₄	#386	1	1	yes	characteristic
268	C₂³×C₄	C₂×#99	1	1	yes	characteristic
269	C₂³×C₄	C₂×#99	1	1	yes	characteristic
270	C₂³×C₄	C₂×#99	1	1	yes	characteristic
271	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
272	#124	C₂×#120	1	2	yes	—
273	#124	C₂×#120	1	2	yes	—
274	#124	#525	1	2	yes	—
275	#124	#525	1	2	yes	—
276	#124	#525	1	2	yes	—
277	#124	#525	1	2	yes	—
278	#124	#525	1	2	yes	—
279	#124	#525	1	2	yes	—
280	#117	#386	1	2	yes	—
281	#117	#386	1	2	yes	—
282	#117	#386	1	2	yes	—
283	#117	C₂×#99	1	2	yes	—
284	#117	C₂×#99	1	2	yes	—
285	#117	C₂×#99	1	2	yes	—
286	C₂×C₂²⋊C₄	C₂×#99	1	2	yes	—
287	C₂×C₄²	#386	1	2	yes	—
288	C₂×C₄²	#386	1	1	yes	characteristic
289	C₂×C₄²	#386	1	1	yes	characteristic
290	C₂×C₄²	C₂×#99	1	1	yes	characteristic
291	C₂×C₄²	C₂×#99	1	1	yes	characteristic
292	C₂×C₄²	C₂×#99	1	1	yes	characteristic
293	C₂×C₄²	C₂×#99	1	1	yes	characteristic
294	C₂×C₄²	C₂×#120	1	1	yes	characteristic
295	C₂×C₄²	C₂×#120	1	1	yes	characteristic
296	C₂×C₄²	C₂×#120	1	1	yes	characteristic
297	C₂×C₄²	C₂×#123	1	1	yes	characteristic
298	C₂×C₄²	C₂×#123	1	1	yes	characteristic
299	C₂×C₄²	C₂×#123	1	1	yes	characteristic
300	C₂⁴	#1898	1	2	yes	—
301	C₂⁴	#1898	1	1	yes	characteristic
302	C₂⁴	#1898	1	1	yes	characteristic
303	C₂⁴	C₂²×#99	1	1	yes	characteristic
304	C₂×Q₈	#1898	1	2	yes	—
305	C₂×Q₈	C₄×#120	1	2	yes	—
306	C₂×Q₈	C₄×#120	1	2	yes	—
307	C₂×D₄	#1898	1	2	yes	—
308	C₂×D₄	#2847	1	2	yes	—
309	C₂×D₄	#2847	1	2	yes	—
310	C₂²×C₄	#1898	1	1	yes	characteristic
311	C₂²×C₄	#1898	1	1	yes	characteristic
312	C₂²×C₄	#1898	1	2	yes	—
313	C₂²×C₄	C₂×#386	1	1	yes	characteristic
314	C₂²×C₄	C₂×#386	1	1	yes	characteristic
315	C₂²×C₄	C₂×#386	1	1	yes	characteristic
316	C₂²×C₄	C₂²×#99	1	1	yes	characteristic
317	C₂²×C₄	C₂²×#99	1	1	yes	characteristic
318	C₂²×C₄	C₂²×#99	1	1	yes	characteristic
319	C₂²⋊C₄	#1898	1	4	yes	—
320	C₄²	#1898	1	1	yes	characteristic
321	C₄²	#1898	1	1	yes	characteristic
322	C₄²	#1898	1	1	yes	characteristic
323	C₄²	#1898	1	1	yes	characteristic
324	C₄²	#1898	1	4	yes	—
325	C₄²	#2846	1	1	yes	characteristic
326	C₄²	#2849	1	1	yes	characteristic
327	C₄²	#2849	1	1	yes	characteristic
328	C₄²	#2849	1	1	yes	characteristic
329	C₂³	C₂×#1898	1	1	yes	characteristic
330	C₂³	C₂×#1898	1	1	yes	characteristic
331	C₂³	C₂×#1898	1	1	yes	characteristic
332	C₂³	#33348	1	1	yes	characteristic
333	C₂³	#33348	1	1	yes	characteristic
334	C₂³	#33348	1	1	yes	characteristic
335	C₂³	#33350	1	1	yes	characteristic
336	C₂×C₄	#14694	1	1	yes	characteristic
337	C₂×C₄	C₂×#1898	1	1	yes	characteristic
338	C₂×C₄	C₂×#1898	1	1	yes	characteristic
339	C₂×C₄	C₂×#1898	1	1	yes	characteristic
340	C₂²	#392675	1	1	yes	characteristic
341	C₂²	#494682	1	1	yes	characteristic
342	C₂²	#494682	1	1	yes	characteristic
343	C₂²	#494683	1	1	yes	characteristic
344	C₂²	#494685	1	1	yes	characteristic
345	C₂²	#494685	1	1	yes	characteristic
346	C₂²	#494687	1	1	yes	characteristic
347	C₂	#72306284	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂	#72306284
commutator	C₂³×Q₈	C₂³×C₄
Frattini, cosocle	C₂²×#124	C₂⁴
prime radical	#72306379	C₂
LCS	G ▷ C₂³×Q₈ ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂ ◁ C₂⁴ ◁ C₂×#525 ◁ C₂×#62836 ◁ G
LECS	G ▷ C₂²×#124 ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72306380	C₂	semidirect
3. #72306378	C₂	semidirect
4. #72306374	C₂	semidirect
5. #72306367	C₂	semidirect
6. #72306332	C₂	semidirect
7. #72306304	C₂	semidirect
8. #72306300	C₂	semidirect
9. #72306288	C₂	semidirect
10. #72279260	C₂	semidirect
11. C₂×#152674	C₂	semidirect
13. C₂×#24001	C₄	semidirect
15. C₂×#23898	C₄	semidirect
16. #6437459	C₄	semidirect
19. #6431798	C₄	semidirect
24. C₂×#13569	C₂²	semidirect
25. C₂×#13569	C₂²	semidirect
30. #382439	C₄	semidirect
31. #363975	C₄	semidirect
34. #359602	C₄	semidirect
35. #359560	C₄	semidirect
37. #151803	C₂²	semidirect
38. #151803	C₂²	semidirect
39. C₂×#7481	C₂²	semidirect
40. C₂×#7481	C₂²	semidirect
41. C₂×#7481	C₂²	semidirect
42. C₂×#7481	C₂²	semidirect
88. #17686	D₄	semidirect
89. #17675	D₄	semidirect
90. #17675	D₄	semidirect
91. #17675	D₄	semidirect
92. #17666	D₄	semidirect
93. C₂×#1536	D₄	semidirect
96. C₂×#1525	D₄	semidirect

Maximal subgroups

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

subgroup	index
#72306380	2
#72306379	2
#72306378	2
#72306374	2
#72306367	2
#72306332	2
#72306304	2
#72306300	2
#72306288	2
#72279260	2
C₂×#152674	2