Subgroups — #72313501

Order 4096.

At least 26420 conjugacy classes of subgroups; only the 389 normal subgroups are shown.

The subgroup lattice has 331 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72313018	C₂	1	1	yes	maximal, characteristic, complemented
2	#72310388	C₂	1	1	yes	maximal, characteristic, complemented
3	#72310339	C₂	1	1	yes	maximal, characteristic, complemented
4	#72310337	C₂	1	1	yes	maximal, characteristic, complemented
5	#72309645	C₂	1	1	yes	maximal, characteristic, complemented
6	#72266831	C₂	1	1	yes	maximal, characteristic, complemented
7	#72266073	C₂²	1	1	yes	characteristic, complemented
8	#72262330	C₂	1	1	yes	maximal, characteristic, complemented
9	#72259008	C₂²	1	1	yes	characteristic, complemented
10	#72251547	C₂	1	1	yes	maximal, characteristic, complemented
11	#72238345	C₂	1	1	yes	maximal, characteristic, complemented
12	#72237400	C₂²	1	1	yes	characteristic, complemented
13	#72237032	C₂	1	1	yes	maximal, characteristic, complemented
14	#72234661	C₂²	1	1	yes	characteristic, complemented
15	#72225710	C₂	1	1	yes	maximal, characteristic, complemented
16	#72225650	C₂²	1	1	yes	characteristic
17	#72225619	C₂²	1	1	yes	characteristic
18	#72225617	C₂²	1	1	yes	characteristic
19	#72224136	C₂²	1	1	yes	characteristic
20	#72219455	C₂	1	1	yes	maximal, characteristic, complemented
21	#72219418	C₂²	1	1	yes	characteristic, complemented
22	#72219414	C₂²	1	1	yes	characteristic, complemented
23	#72219311	C₂²	1	1	yes	characteristic, complemented
24	#72219300	C₂²	1	1	yes	characteristic, complemented
25	C₂×#394058	C₂²	1	1	yes	characteristic
26	#72218868	C₂	1	1	yes	maximal, characteristic, complemented
27	#72218518	C₂²	1	1	yes	characteristic, complemented
28	#72218393	C₂	1	1	yes	maximal, characteristic, complemented
29	#72218381	C₂²	1	1	yes	characteristic, complemented
30	#72218381	C₂²	1	1	yes	characteristic, complemented
31	#72218375	C₂²	1	1	yes	characteristic, complemented
32	#72218313	C₂²	1	1	yes	characteristic, complemented
33	#72218133	C₂	1	1	yes	maximal, characteristic, complemented
34	#72218069	C₂²	1	1	yes	characteristic, complemented
35	#72218069	C₂²	1	1	yes	characteristic, complemented
36	#72218057	C₂²	1	1	yes	characteristic
37	#72218057	C₂²	1	1	yes	characteristic
38	#72218057	C₂²	1	1	yes	characteristic
39	#72218057	C₂²	1	1	yes	characteristic, complemented
40	#72218057	C₂²	1	1	yes	characteristic, complemented
41	#72218057	C₂²	1	1	yes	characteristic, complemented
42	#72218057	C₂²	1	1	yes	characteristic, complemented
43	C₂²×#23900	C₂²	1	1	yes	characteristic, complemented
44	#72217511	C₂²	1	1	yes	characteristic
45	#72215858	C₂²	1	1	yes	characteristic
46	#72215179	C₂²	1	1	yes	characteristic, complemented
47	#72213862	C₂²	1	1	yes	characteristic, complemented
48	#72213862	C₂²	1	1	yes	characteristic, complemented
49	#72210555	C₂²	1	1	yes	characteristic, complemented
50	#72210511	C₂²	1	1	yes	characteristic
51	#10586404	D₄	1	1	yes	characteristic, complemented
52	C₂×#62817	D₄	1	1	yes	characteristic, complemented
53	C₂²×#3484	C₂³	1	1	yes	characteristic
54	C₂⁴×#120	C₂³	1	1	yes	characteristic
55	#7642244	D₄	1	1	yes	characteristic, complemented
56	#7642244	D₄	1	1	yes	characteristic, complemented
57	C₂²×#2846	D₄	1	1	yes	characteristic, complemented
58	#7630939	C₂³	1	1	yes	characteristic
59	#7630939	C₂³	1	1	yes	characteristic
60	#7630939	C₂³	1	1	yes	characteristic
61	C₂×#34980	C₂³	1	1	yes	characteristic
62	#7626202	D₄	1	1	yes	characteristic, complemented
63	#6628867	D₄	1	2	yes	complemented
64	#6440460	D₄	1	1	yes	characteristic, complemented
65	C₂×#23895	D₄	1	1	yes	characteristic, complemented
66	#6437621	D₄	1	1	yes	characteristic, complemented
67	C₂×#23900	D₄	1	1	yes	characteristic, complemented
68	C₂×#23900	D₄	1	1	yes	characteristic, complemented
69	#6374210	D₄	1	1	yes	characteristic, complemented
70	#6374210	D₄	1	1	yes	characteristic, complemented
71	C₂×#21776	D₄	1	1	yes	characteristic, complemented
72	#6374128	D₄	1	1	yes	characteristic, complemented
73	C₂²×#1898	D₄	1	1	yes	characteristic, complemented
74	C₂²×#1781	C₂³	1	1	yes	characteristic
75	C₂²×#1781	C₂³	1	1	yes	characteristic
76	C₂²×#1781	C₂³	1	1	yes	characteristic
77	C₂²×#1781	C₂³	1	1	yes	characteristic
78	C₂×#14679	D₄	1	1	yes	characteristic, complemented
79	#494713	D₄	1	4	yes	complemented
80	#392696	D₄	1	2	yes	complemented
81	#392113	C₂³	1	1	yes	characteristic
82	#392109	C₂³	1	1	yes	characteristic
83	#392109	C₂³	1	1	yes	characteristic
84	#392109	C₂³	1	1	yes	characteristic
85	#392109	C₂³	1	1	yes	characteristic
86	#382544	D₄	1	1	yes	characteristic, complemented
87	#382434	D₄	1	1	yes	characteristic, complemented
88	#373637	D₄	1	1	yes	characteristic, complemented
89	#359811	D₄	1	1	yes	characteristic, complemented
90	#359549	D₄	1	1	yes	characteristic, complemented
91	#359549	D₄	1	1	yes	characteristic, complemented
92	#359501	D₄	1	1	yes	characteristic, complemented
93	#359501	D₄	1	1	yes	characteristic, complemented
94	#359442	D₄	1	1	yes	characteristic, complemented
95	#355096	D₄	1	1	yes	characteristic, complemented
96	C₂×#10735	D₄	1	1	yes	characteristic, complemented
97	#147569	D₄	1	4	yes	complemented
98	C₂⁸	C₂×D₄	1	1	yes	characteristic
99	C₂³×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic, complemented
100	C₂⁵×D₄	C₂⁴	1	1	yes	characteristic
101	C₂×#3484	C₂×D₄	1	1	yes	characteristic
102	C₂×#3484	C₂×D₄	1	1	yes	characteristic
103	C₂×#3484	C₂×D₄	1	1	yes	characteristic
104	C₂×#3484	C₂×D₄	1	1	yes	characteristic
105	C₂×#3484	C₂×D₄	1	1	yes	characteristic
106	C₂×#3484	C₂×D₄	1	1	yes	characteristic
107	C₂×#3484	C₂×D₄	1	1	yes	characteristic
108	C₂×#3484	C₂×D₄	1	1	yes	characteristic
109	C₂×#3484	C₂×D₄	1	1	yes	characteristic
110	C₂²×#534	C₂×D₄	1	1	yes	characteristic
111	C₂²×#534	C₂×D₄	1	1	yes	characteristic
112	C₂³×#120	C₂×D₄	1	1	yes	characteristic
113	C₂³×#120	C₂×D₄	1	1	yes	characteristic
114	C₂³×#120	C₂×D₄	1	1	yes	characteristic
115	C₂³×#120	C₂×D₄	1	1	yes	characteristic
116	C₂³×#120	C₂×D₄	1	1	yes	characteristic
117	C₂²×#518	C₂×D₄	1	1	yes	characteristic, complemented
118	C₂⁴×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
119	C₂³×#99	C₂×D₄	1	2	yes	complemented
120	#36614	#41	1	2	yes	—
121	#35222	C₂×D₄	1	2	yes	—
122	#35222	C₂×D₄	1	2	yes	—
123	#35222	C₂×D₄	1	2	yes	—
124	#34171	C₂×D₄	1	1	yes	characteristic
125	#34171	C₂×D₄	1	1	yes	characteristic
126	#34171	C₂×D₄	1	1	yes	characteristic
127	#34171	C₂×D₄	1	1	yes	characteristic
128	#34171	C₂×D₄	1	1	yes	characteristic
129	#34171	C₂×D₄	1	1	yes	characteristic
130	#34171	C₂×D₄	1	1	yes	characteristic
131	#34171	C₂×D₄	1	1	yes	characteristic
132	#34171	C₂×D₄	1	1	yes	characteristic
133	C₂×#2308	C₂×D₄	1	1	yes	characteristic
134	C₂×#2308	C₂×D₄	1	1	yes	characteristic
135	C₂²×#379	C₂×D₄	1	1	yes	characteristic
136	C₂²×#379	C₂×D₄	1	1	yes	characteristic
137	C₂²×#379	C₂×D₄	1	1	yes	characteristic
138	C₂×#1783	C₂×D₄	1	2	yes	complemented
139	C₂×#1781	C₂×D₄	1	1	yes	characteristic
140	C₂×#1781	C₂×D₄	1	1	yes	characteristic
141	C₂×#1781	C₂×D₄	1	1	yes	characteristic
142	C₂×#1781	C₂×D₄	1	1	yes	characteristic
143	C₂×#1781	C₂×D₄	1	1	yes	characteristic
144	C₂×#1781	C₂×D₄	1	1	yes	characteristic
145	C₂×#1781	C₂×D₄	1	1	yes	characteristic
146	C₂×#1781	C₂×D₄	1	1	yes	characteristic
147	C₂×#1781	C₂×D₄	1	1	yes	characteristic
148	C₂×#1781	C₂×D₄	1	1	yes	characteristic
149	C₂×#1781	C₂×D₄	1	2	yes	complemented
150	C₂×#1781	C₂×D₄	1	2	yes	complemented
151	C₂×#1781	C₂×D₄	1	2	yes	complemented
152	C₂⁷	#120	1	1	yes	characteristic
153	C₂⁷	#120	1	1	yes	characteristic
154	C₂⁷	C₂²×D₄	1	1	yes	characteristic
155	C₂⁷	H(5,𝔽₂)	1	1	yes	characteristic
156	C₂²×H(5,𝔽₂)	#120	1	1	yes	characteristic
157	C₂²×H(5,𝔽₂)	#120	1	1	yes	characteristic
158	C₂²×H(5,𝔽₂)	#120	1	1	yes	characteristic
159	C₂⁴×D₄	#120	1	1	yes	characteristic
160	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
161	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
162	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
163	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
164	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
165	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
166	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
167	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
168	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
169	C₂⁴×D₄	H(5,𝔽₂)	1	1	yes	characteristic
170	C₂⁴×D₄	H(5,𝔽₂)	1	1	yes	characteristic
171	C₂⁴×D₄	H(5,𝔽₂)	1	1	yes	characteristic
172	C₂⁵×C₄	C₂×#41	1	1	yes	characteristic
173	C₂×#535	#120	1	2	yes	—
174	C₂×#535	#120	1	2	yes	—
175	C₂×#535	#127	1	2	yes	—
176	C₂×#525	#121	1	2	yes	—
177	C₂×#525	#121	1	2	yes	—
178	C₂×#525	#121	1	2	yes	—
179	C₂×#518	#120	1	1	yes	characteristic
180	C₂×#518	#120	1	1	yes	characteristic
181	C₂×#518	#120	1	1	yes	characteristic
182	C₂×#518	#120	1	1	yes	characteristic
183	C₂×#518	#120	1	1	yes	characteristic
184	C₂×#518	#120	1	1	yes	characteristic
185	C₂×#518	#120	1	1	yes	characteristic
186	C₂×#518	#120	1	1	yes	characteristic
187	C₂×#518	#120	1	1	yes	characteristic
188	C₂³×C₂²⋊C₄	#120	1	1	yes	characteristic
189	C₂³×C₂²⋊C₄	#120	1	1	yes	characteristic
190	C₂³×C₂²⋊C₄	#120	1	1	yes	characteristic
191	C₂³×C₂²⋊C₄	#120	1	1	yes	characteristic
192	C₂³×C₂²⋊C₄	#120	1	1	yes	characteristic
193	C₂²×#99	#120	1	1	yes	characteristic
194	C₂²×#99	#120	1	1	yes	characteristic
195	C₂²×#99	#120	1	1	yes	characteristic
196	C₂²×#99	#120	1	1	yes	characteristic
197	#2309	#120	1	2	yes	—
198	#2309	#120	1	2	yes	—
199	#2309	#127	1	2	yes	—
200	#2280	#121	1	2	yes	—
201	#2280	#121	1	2	yes	—
202	#2280	#121	1	2	yes	—
203	C₂×#379	#120	1	1	yes	characteristic
204	C₂×#379	#120	1	1	yes	characteristic
205	C₂×#379	#120	1	1	yes	characteristic
206	C₂×#379	#120	1	1	yes	characteristic
207	C₂⁶	B(4,𝔽₂)	1	2	yes	—
208	C₂⁶	B(4,𝔽₂)	1	1	yes	characteristic
209	C₂⁶	C₂×#120	1	1	yes	characteristic
210	C₂⁶	C₂×#120	1	1	yes	characteristic
211	C₂⁶	C₂×#120	1	1	yes	characteristic
212	C₂⁶	#534	1	1	yes	characteristic
213	C₂⁶	#534	1	1	yes	characteristic
214	C₂⁶	#535	1	1	yes	characteristic
215	C₂⁶	D₄²	1	1	yes	characteristic
216	C₂⁶	D₄²	1	1	yes	characteristic
217	C₂⁶	D₄²	1	1	yes	characteristic
218	C₂⁶	D₄²	1	1	yes	characteristic
219	C₂⁶	D₄²	1	1	yes	characteristic
220	C₂⁶	D₄²	1	1	yes	characteristic
221	C₂⁶	#546	1	1	yes	characteristic
222	C₂²×#41	#392	1	2	yes	—
223	C₂³×D₄	C₂×#120	1	1	yes	characteristic
224	C₂³×D₄	C₂×#120	1	1	yes	characteristic
225	C₂³×D₄	C₂×#120	1	1	yes	characteristic
226	C₂³×D₄	C₂×#120	1	1	yes	characteristic
227	C₂³×D₄	C₂×#120	1	1	yes	characteristic
228	C₂³×D₄	C₂×#120	1	1	yes	characteristic
229	C₂³×D₄	C₂×#127	1	1	yes	characteristic
230	C₂³×D₄	#534	1	1	yes	characteristic
231	C₂³×D₄	#534	1	1	yes	characteristic
232	C₂³×D₄	#535	1	1	yes	characteristic
233	C₂³×D₄	D₄²	1	1	yes	characteristic
234	C₂³×D₄	D₄²	1	1	yes	characteristic
235	C₂³×D₄	D₄²	1	1	yes	characteristic
236	C₂³×D₄	D₄²	1	1	yes	characteristic
237	C₂³×D₄	D₄²	1	1	yes	characteristic
238	C₂³×D₄	D₄²	1	1	yes	characteristic
239	C₂⁴×C₄	B(4,𝔽₂)	1	1	yes	characteristic
240	C₂⁴×C₄	C₂×#121	1	1	yes	characteristic
241	C₂⁴×C₄	C₂×#121	1	1	yes	characteristic
242	C₂⁴×C₄	C₂×#121	1	1	yes	characteristic
243	C₂⁴×C₄	#546	1	1	yes	characteristic
244	C₂⁴×C₄	#546	1	1	yes	characteristic
245	C₂⁴×C₄	#546	1	1	yes	characteristic
246	C₂×#127	B(4,𝔽₂)	1	4	yes	—
247	C₂×#124	B(4,𝔽₂)	1	4	yes	—
248	C₂×#117	#392	1	2	yes	—
249	C₂×#117	#392	1	2	yes	—
250	C₂×#117	#392	1	2	yes	—
251	C₂²×C₂²⋊C₄	B(4,𝔽₂)	1	2	yes	—
252	C₂²×C₂²⋊C₄	B(4,𝔽₂)	1	2	yes	—
253	#379	B(4,𝔽₂)	1	2	yes	—
254	C₂⁵	#2403	1	1	yes	characteristic
255	C₂⁵	#2403	1	1	yes	characteristic
256	C₂⁵	#2403	1	1	yes	characteristic
257	C₂⁵	#2403	1	1	yes	characteristic
258	C₂⁵	#2408	1	1	yes	characteristic
259	C₂⁵	#2410	1	1	yes	characteristic
260	C₂⁵	#2410	1	1	yes	characteristic
261	C₂⁵	#2433	1	1	yes	characteristic
262	C₂⁵	#2433	1	1	yes	characteristic
263	C₂⁵	#2613	1	1	yes	characteristic
264	C₂⁵	#2846	1	1	yes	characteristic
265	C₂⁵	C₂×B(4,𝔽₂)	1	1	yes	characteristic
266	C₂⁵	C₂×B(4,𝔽₂)	1	1	yes	characteristic
267	C₂⁵	C₂×B(4,𝔽₂)	1	1	yes	characteristic
268	C₂⁵	C₂×B(4,𝔽₂)	1	1	yes	characteristic
269	C₂⁵	C₂×B(4,𝔽₂)	1	1	yes	characteristic
270	C₂⁵	#3025	1	1	yes	characteristic
271	C₂⁵	#3026	1	1	yes	characteristic
272	C₂⁵	#3026	1	1	yes	characteristic
273	C₂⁵	#3026	1	1	yes	characteristic
274	C₂⁵	#3026	1	1	yes	characteristic
275	C₂⁵	#3026	1	1	yes	characteristic
276	C₂⁵	#3027	1	1	yes	characteristic
277	C₂²×Q₈	#2021	1	2	yes	complemented
278	C₂²×D₄	#2021	1	2	yes	complemented
279	C₂²×D₄	C₂×B(4,𝔽₂)	1	4	yes	—
280	C₂³×C₄	C₂×#392	1	1	yes	characteristic
281	C₂³×C₄	#2408	1	1	yes	characteristic
282	C₂³×C₄	#2410	1	1	yes	characteristic
283	C₂³×C₄	#2410	1	1	yes	characteristic
284	C₂×C₄²	#2021	1	4	yes	complemented
285	C₂⁴	#14715	1	1	yes	characteristic
286	C₂⁴	#23895	1	2	yes	—
287	C₂⁴	#23895	1	2	yes	—
288	C₂⁴	#23900	1	2	yes	—
289	C₂⁴	#23900	1	1	yes	characteristic
290	C₂⁴	#23900	1	2	yes	—
291	C₂⁴	#23900	1	1	yes	characteristic
292	C₂⁴	#23903	1	1	yes	characteristic
293	C₂⁴	#23903	1	1	yes	characteristic
294	C₂⁴	#24260	1	1	yes	characteristic
295	C₂⁴	#24262	1	1	yes	characteristic
296	C₂⁴	#24404	1	1	yes	characteristic
297	C₂⁴	#24404	1	1	yes	characteristic
298	C₂⁴	#24404	1	1	yes	characteristic
299	C₂⁴	#24404	1	1	yes	characteristic
300	C₂⁴	#25771	1	1	yes	characteristic
301	C₂⁴	#25773	1	1	yes	characteristic
302	C₂⁴	#32898	1	1	yes	characteristic
303	C₂⁴	#32898	1	1	yes	characteristic
304	C₂⁴	#32898	1	1	yes	characteristic
305	C₂⁴	#32898	1	1	yes	characteristic
306	C₂⁴	#32898	1	1	yes	characteristic
307	C₂⁴	#32899	1	1	yes	characteristic
308	C₂²×C₄	C₂×#2021	1	2	yes	—
309	C₂³	#245225	1	2	yes	—
310	C₂³	#245246	1	2	yes	—
311	C₂³	#347042	1	1	yes	characteristic
312	C₂³	#347043	1	1	yes	characteristic
313	C₂³	#347043	1	1	yes	characteristic
314	C₂³	#347047	1	1	yes	characteristic
315	C₂³	#393933	1	1	yes	characteristic
316	C₂³	#393934	1	1	yes	characteristic
317	C₂³	#394058	1	1	yes	characteristic
318	C₂³	#394064	1	1	yes	characteristic
319	C₂³	#394064	1	1	yes	characteristic
320	C₂³	#394066	1	1	yes	characteristic
321	C₂³	#394066	1	1	yes	characteristic
322	C₂²	#72210600	1	1	yes	characteristic
323	C₂²	#72219236	1	1	yes	characteristic
324	C₂²	#72225609	1	1	yes	characteristic
325	C₂²	#72233127	1	1	yes	characteristic
326	C₂²	#72234155	1	1	yes	characteristic
327	C₂²	#72234959	1	1	yes	characteristic
328	C₂²	#72234959	1	1	yes	characteristic
329	C₂	#72258840	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂	#72258840
commutator, Frattini, cosocle	C₂⁵×D₄	C₂⁴
LCS	G ▷ C₂⁵×D₄ ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂ ◁ C₂⁴ ◁ C₂⁵×D₄ ◁ G
LECS	G ▷ C₂⁵×D₄ ▷ C₂⁴ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72313018	C₂	semidirect
2. #72310388	C₂	semidirect
3. #72310339	C₂	semidirect
4. #72310337	C₂	semidirect
5. #72309645	C₂	semidirect
6. #72266831	C₂	semidirect
7. #72266073	C₂²	semidirect
8. #72262330	C₂	semidirect
9. #72259008	C₂²	semidirect
10. #72251547	C₂	semidirect
11. #72238345	C₂	semidirect
12. #72237400	C₂²	semidirect
13. #72237032	C₂	semidirect
14. #72234661	C₂²	semidirect
15. #72225710	C₂	semidirect
20. #72219455	C₂	semidirect
21. #72219418	C₂²	semidirect
22. #72219414	C₂²	semidirect
23. #72219311	C₂²	semidirect
24. #72219300	C₂²	semidirect
26. #72218868	C₂	semidirect
27. #72218518	C₂²	semidirect
28. #72218393	C₂	semidirect
29. #72218381	C₂²	semidirect
30. #72218381	C₂²	semidirect
31. #72218375	C₂²	semidirect
32. #72218313	C₂²	semidirect
33. #72218133	C₂	semidirect
34. #72218069	C₂²	semidirect
35. #72218069	C₂²	semidirect
39. #72218057	C₂²	semidirect
40. #72218057	C₂²	semidirect
41. #72218057	C₂²	semidirect
42. #72218057	C₂²	semidirect
43. C₂²×#23900	C₂²	semidirect
46. #72215179	C₂²	semidirect
47. #72213862	C₂²	semidirect
48. #72213862	C₂²	semidirect
49. #72210555	C₂²	semidirect
51. #10586404	D₄	semidirect
52. C₂×#62817	D₄	semidirect
55. #7642244	D₄	semidirect
56. #7642244	D₄	semidirect
57. C₂²×#2846	D₄	semidirect
62. #7626202	D₄	semidirect
63. #6628867	D₄	semidirect
64. #6440460	D₄	semidirect
65. C₂×#23895	D₄	semidirect
66. #6437621	D₄	semidirect
67. C₂×#23900	D₄	semidirect
68. C₂×#23900	D₄	semidirect
69. #6374210	D₄	semidirect
70. #6374210	D₄	semidirect
71. C₂×#21776	D₄	semidirect
72. #6374128	D₄	semidirect
73. C₂²×#1898	D₄	semidirect
78. C₂×#14679	D₄	semidirect
79. #494713	D₄	semidirect
80. #392696	D₄	semidirect
86. #382544	D₄	semidirect
87. #382434	D₄	semidirect
88. #373637	D₄	semidirect
89. #359811	D₄	semidirect
90. #359549	D₄	semidirect
91. #359549	D₄	semidirect
92. #359501	D₄	semidirect
93. #359501	D₄	semidirect
94. #359442	D₄	semidirect
95. #355096	D₄	semidirect
96. C₂×#10735	D₄	semidirect
97. #147569	D₄	semidirect
99. C₂³×H(5,𝔽₂)	C₂×D₄	semidirect
117. C₂²×#518	C₂×D₄	semidirect
119. C₂³×#99	C₂×D₄	semidirect
138. C₂×#1783	C₂×D₄	semidirect
149. C₂×#1781	C₂×D₄	semidirect
150. C₂×#1781	C₂×D₄	semidirect
151. C₂×#1781	C₂×D₄	semidirect
277. C₂²×Q₈	#2021	semidirect
278. C₂²×D₄	#2021	semidirect
284. C₂×C₄²	#2021	semidirect

Maximal subgroups

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

subgroup	index
#72313018	2
#72310388	2
#72310339	2
#72310337	2
#72309645	2
#72266831	2
#72262330	2
#72251547	2
#72238345	2
#72237032	2
#72225710	2
#72219455	2
#72218868	2
#72218393	2
#72218133	2