Subgroups — #72313398

Order 4096.

At least 18031 conjugacy classes of subgroups; only the 569 normal subgroups are shown.

The subgroup lattice has 340 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72312643	C₂	1	2	yes	maximal, complemented
2	#72312241	C₂	1	2	yes	maximal, complemented
3	#72265785	C₂	1	1	yes	maximal, characteristic, complemented
4	#72238352	C₂	1	2	yes	maximal, complemented
5	#72237628	C₂	1	1	yes	maximal, characteristic
6	#72237627	C₄	1	2	yes	complemented
7	#72237618	C₄	1	1	yes	characteristic, complemented
8	#72237581	C₂	1	2	yes	maximal, complemented
9	#72234668	C₂²	1	1	yes	characteristic
10	#72234661	C₂²	1	2	yes	—
11	#72234625	C₂²	1	1	yes	characteristic
12	#72232592	C₄	1	1	yes	characteristic, complemented
13	#72219455	C₂	1	2	yes	maximal, complemented
14	#72219444	C₂	1	2	yes	maximal, complemented
15	#72219418	C₂²	1	2	yes	complemented
16	#72219415	C₂²	1	2	yes	complemented
17	#72219414	C₂²	1	2	yes	complemented
18	#72219414	C₂²	1	2	yes	complemented
19	#72219311	C₂²	1	2	yes	complemented
20	#72219310	C₂²	1	2	yes	complemented
21	#72219309	C₂	1	1	yes	maximal, characteristic, complemented
22	#72219301	C₂²	1	1	yes	characteristic, complemented
23	#72219300	C₂²	1	2	yes	—
24	#72219300	C₂²	1	2	yes	—
25	#72219300	C₂²	1	2	yes	complemented
26	#72219300	C₂²	1	2	yes	complemented
27	#72219299	C₂²	1	1	yes	characteristic, complemented
28	C₂×#394058	C₂²	1	2	yes	—
29	C₂×#7670203	C₂²	1	1	yes	characteristic
30	#72218518	C₂²	1	1	yes	characteristic, complemented
31	#72218306	C₂²	1	2	yes	complemented
32	#72218291	C₂²	1	1	yes	characteristic, complemented
33	#72217789	C₄	1	1	yes	characteristic, complemented
34	#72217699	C₄	1	2	yes	complemented
35	#72217511	C₄	1	1	yes	characteristic, complemented
36	#72215179	C₂²	1	2	yes	complemented
37	C₂×#62817	C₂×C₄	1	1	yes	characteristic, complemented
38	C₂²×#3484	D₄	1	1	yes	characteristic
39	C₂²×#3484	C₂³	1	1	yes	characteristic
40	C₂⁴×#120	C₂×C₄	1	1	yes	characteristic
41	C₂⁴×#120	C₂³	1	1	yes	characteristic
42	#7641845	C₂×C₄	1	2	yes	—
43	#7641845	C₂×C₄	1	2	yes	—
44	C₂²×#2846	C₂×C₄	1	1	yes	characteristic
45	C₂²×#2846	C₂×C₄	1	2	yes	complemented
46	C₂×#35390	D₄	1	1	yes	characteristic
47	C₂×#35348	D₄	1	1	yes	characteristic
48	C₂×#35348	D₄	1	1	yes	characteristic
49	C₂×#35346	D₄	1	1	yes	characteristic
50	C₂×#34981	C₂×C₄	1	1	yes	characteristic
51	C₂×#34981	D₄	1	1	yes	characteristic
52	C₂×#34980	D₄	1	1	yes	characteristic
53	C₂×#34980	C₂³	1	1	yes	characteristic
54	C₂×#34980	C₂³	1	2	yes	—
55	#7626202	C₂×C₄	1	1	yes	characteristic, complemented
56	C₂×#34198	C₂×C₄	1	1	yes	characteristic
57	C₂×#34198	D₄	1	1	yes	characteristic
58	#6440460	D₄	1	2	yes	—
59	#6440460	D₄	1	2	yes	—
60	#6440460	D₄	1	2	yes	—
61	#6440460	D₄	1	2	yes	—
62	#6437621	D₄	1	2	yes	—
63	#6437621	D₄	1	2	yes	—
64	#6437621	D₄	1	2	yes	—
65	#6437621	D₄	1	2	yes	—
66	C₂×#21746	C₂×C₄	1	2	yes	—
67	C₂×#21746	C₂×C₄	1	2	yes	—
68	C₂×#21746	C₂×C₄	1	1	yes	characteristic, complemented
69	C₂×#21746	C₂×C₄	1	2	yes	complemented
70	C₂×#21746	C₂×C₄	1	1	yes	characteristic, complemented
71	C₂²×#1898	C₂×C₄	1	2	yes	complemented
72	C₂²×#1781	C₂³	1	2	yes	—
73	C₂×#14679	C₂×C₄	1	2	yes	complemented
74	#392113	C₂³	1	2	yes	—
75	#392113	C₂³	1	2	yes	—
76	#392109	C₂³	1	2	yes	—
77	#392109	C₂³	1	2	yes	—
78	#355913	C₂×C₄	1	2	yes	complemented
79	C₂×#10735	C₂×C₄	1	2	yes	complemented
80	#147567	D₄	1	8	yes	complemented
81	C₂⁸	C₂²×C₄	1	1	yes	characteristic
82	C₂³×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
83	C₂⁵×D₄	C₂²⋊C₄	1	1	yes	characteristic
84	C₂⁵×D₄	C₂⁴	1	1	yes	characteristic
85	C₂×#3484	C₂×D₄	1	2	yes	—
86	C₂×#3484	C₂×D₄	1	2	yes	—
87	C₂×#3484	C₂×D₄	1	2	yes	—
88	C₂×#3484	C₂×D₄	1	2	yes	—
89	C₂²×#534	C₂²⋊C₄	1	1	yes	characteristic
90	C₂²×#534	C₂×D₄	1	1	yes	characteristic
91	C₂²×#534	C₂×D₄	1	1	yes	characteristic
92	C₂²×#534	C₂×D₄	1	2	yes	—
93	C₂²×#534	C₂×D₄	1	2	yes	—
94	C₂²×#534	C₂×D₄	1	1	yes	characteristic
95	C₂²×#534	C₂×D₄	1	1	yes	characteristic
96	C₂³×#120	C₂²⋊C₄	1	1	yes	characteristic
97	C₂³×#120	C₂²⋊C₄	1	1	yes	characteristic
98	C₂³×#120	C₂²⋊C₄	1	1	yes	characteristic
99	C₂³×#120	C₂²⋊C₄	1	1	yes	characteristic
100	C₂³×#120	C₂²×C₄	1	1	yes	characteristic
101	C₂³×#120	C₂²×C₄	1	1	yes	characteristic
102	C₂³×#120	C₂²×C₄	1	2	yes	—
103	C₂³×#120	C₂²×C₄	1	1	yes	characteristic
104	C₂³×#120	C₂×D₄	1	1	yes	characteristic
105	C₂³×#120	C₂×D₄	1	1	yes	characteristic
106	C₂³×#120	C₂×D₄	1	1	yes	characteristic
107	C₂³×#120	C₂×D₄	1	1	yes	characteristic
108	C₂²×#518	C₂²⋊C₄	1	1	yes	characteristic
109	C₂²×#518	C₂×D₄	1	1	yes	characteristic
110	C₂⁴×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
111	C₂⁴×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
112	#34992	C₂²⋊C₄	1	2	yes	—
113	#34992	C₂²⋊C₄	1	2	yes	—
114	#34992	C₂²⋊C₄	1	2	yes	—
115	#34992	C₂²⋊C₄	1	2	yes	—
116	#34980	C₂²⋊C₄	1	2	yes	—
117	#34980	C₂²⋊C₄	1	2	yes	—
118	#34980	C₂²⋊C₄	1	2	yes	—
119	#34980	C₂²⋊C₄	1	2	yes	—
120	#34980	C₂×D₄	1	4	yes	—
121	#34980	#41	1	4	yes	—
122	C₂×#2315	C₂²⋊C₄	1	1	yes	characteristic
123	C₂×#2315	C₂²⋊C₄	1	1	yes	characteristic
124	C₂×#2308	C₂²⋊C₄	1	1	yes	characteristic
125	C₂×#2308	C₂²⋊C₄	1	1	yes	characteristic
126	C₂×#2308	C₂²⋊C₄	1	1	yes	characteristic
127	C₂×#2308	C₂×D₄	1	2	yes	—
128	C₂×#2308	C₂×D₄	1	2	yes	—
129	C₂×#2308	C₂×D₄	1	1	yes	characteristic
130	C₂×#2308	C₂×D₄	1	1	yes	characteristic
131	C₂²×#379	C₂²⋊C₄	1	1	yes	characteristic
132	C₂²×#379	C₂²⋊C₄	1	1	yes	characteristic
133	C₂²×#379	C₂²×C₄	1	2	yes	—
134	C₂²×#379	C₂²×C₄	1	2	yes	—
135	C₂²×#379	C₂²×C₄	1	2	yes	—
136	C₂²×#379	C₂²×C₄	1	1	yes	characteristic
137	C₂×#2273	C₂²⋊C₄	1	1	yes	characteristic
138	C₂×#1898	C₂²⋊C₄	1	2	yes	—
139	C₂×#1898	C₂²⋊C₄	1	2	yes	—
140	C₂×#1898	C₂²⋊C₄	1	2	yes	—
141	C₂×#1898	C₂²⋊C₄	1	2	yes	—
142	C₂×#1898	C₂²⋊C₄	1	2	yes	—
143	C₂×#1898	C₂²⋊C₄	1	2	yes	—
144	C₂×#1898	C₂²⋊C₄	1	2	yes	—
145	C₂×#1898	C₂²⋊C₄	1	2	yes	—
146	C₂×#1783	C₂×D₄	1	4	yes	complemented
147	C₂×#1781	C₂×D₄	1	2	yes	—
148	C₂×#1781	C₂×D₄	1	2	yes	—
149	C₂×#1781	C₂×D₄	1	2	yes	—
150	C₂×#1781	C₂×D₄	1	2	yes	—
151	C₂×#1781	C₂×D₄	1	4	yes	complemented
152	C₂⁷	#99	1	1	yes	characteristic, complemented
153	C₂⁷	C₂×C₂²⋊C₄	1	1	yes	characteristic
154	C₂⁷	C₂×C₂²⋊C₄	1	1	yes	characteristic
155	C₂⁷	C₂³×C₄	1	1	yes	characteristic
156	C₂⁷	H(5,𝔽₂)	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	C₂²×H(5,𝔽₂)	#120	1	1	yes	characteristic
160	C₂²×H(5,𝔽₂)	#120	1	1	yes	characteristic
161	C₂⁴×D₄	#99	1	1	yes	characteristic, complemented
162	C₂⁴×D₄	#99	1	1	yes	characteristic, complemented
163	C₂⁴×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
164	C₂⁴×D₄	C₂×C₂²⋊C₄	1	2	yes	—
165	C₂⁴×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
166	C₂⁴×D₄	C₂×C₂²⋊C₄	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	C₂²×D₄	1	2	yes	—
170	C₂⁴×D₄	C₂²×D₄	1	2	yes	—
171	C₂⁴×D₄	C₂²×D₄	1	2	yes	—
172	C₂⁴×D₄	C₂×#41	1	2	yes	—
173	C₂⁴×D₄	H(5,𝔽₂)	1	1	yes	characteristic
174	C₂⁴×D₄	H(5,𝔽₂)	1	1	yes	characteristic
175	C₂⁵×C₄	#99	1	1	yes	characteristic, complemented
176	C₂⁵×C₄	H(5,𝔽₂)	1	1	yes	characteristic
177	C₂×#534	#99	1	2	yes	complemented
178	C₂×#534	#99	1	2	yes	complemented
179	C₂×#534	#120	1	2	yes	—
180	C₂×#534	#120	1	2	yes	—
181	C₂×#534	#120	1	2	yes	—
182	C₂×#534	#120	1	2	yes	—
183	C₂×#534	#120	1	2	yes	—
184	C₂×#534	#121	1	4	yes	—
185	C₂×#534	#123	1	2	yes	—
186	C₂²×#120	#99	1	2	yes	complemented
187	C₂²×#120	#99	1	2	yes	complemented
188	C₂²×#120	C₂×C₂²⋊C₄	1	2	yes	—
189	C₂²×#120	C₂×C₂²⋊C₄	1	2	yes	—
190	C₂²×#120	C₂×C₂²⋊C₄	1	2	yes	—
191	C₂²×#120	C₂×C₂²⋊C₄	1	2	yes	—
192	C₂²×#120	C₄×D₄	1	4	yes	—
193	C₂×#518	#120	1	2	yes	—
194	C₂×#518	#120	1	2	yes	—
195	C₂³×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
196	C₂³×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
197	C₂³×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
198	C₂³×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
199	C₂³×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
200	C₂³×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
201	C₂³×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
202	C₂³×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
203	C₂³×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
204	C₂³×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
205	#2849	#99	1	4	yes	complemented
206	#2846	#99	1	4	yes	complemented
207	#2622	#99	1	8	yes	complemented
208	#2308	#120	1	2	yes	—
209	#2308	#121	1	4	yes	—
210	#2308	#123	1	2	yes	—
211	C₂×#381	#99	1	2	yes	complemented
212	C₂×#379	#99	1	2	yes	complemented
213	C₂×#379	C₂×C₂²⋊C₄	1	2	yes	—
214	C₂×#379	C₂×C₂²⋊C₄	1	2	yes	—
215	C₂×#379	C₂×C₂²⋊C₄	1	2	yes	—
216	C₂×#379	C₂×C₂²⋊C₄	1	2	yes	—
217	C₂×#379	C₄×D₄	1	4	yes	—
218	C₂⁶	C₂×#99	1	1	yes	characteristic
219	C₂⁶	C₂×#99	1	1	yes	characteristic
220	C₂⁶	C₂×#99	1	1	yes	characteristic
221	C₂⁶	C₂×#99	1	2	yes	—
222	C₂⁶	C₂×#99	1	2	yes	—
223	C₂⁶	C₂×#99	1	1	yes	characteristic
224	C₂⁶	C₂×#99	1	1	yes	characteristic
225	C₂⁶	C₂²×C₂²⋊C₄	1	1	yes	characteristic
226	C₂⁶	C₂²×C₂²⋊C₄	1	2	yes	—
227	C₂⁶	C₂×C₄×D₄	1	2	yes	—
228	C₂⁶	#518	1	1	yes	characteristic
229	C₂⁶	#518	1	1	yes	characteristic
230	C₂⁶	#534	1	1	yes	characteristic
231	C₂⁶	#534	1	1	yes	characteristic
232	C₂⁶	D₄²	1	2	yes	—
233	C₂⁶	#546	1	2	yes	—
234	C₂³×D₄	#379	1	1	yes	characteristic
235	C₂³×D₄	#379	1	1	yes	characteristic
236	C₂³×D₄	#379	1	1	yes	characteristic
237	C₂³×D₄	#379	1	1	yes	characteristic
238	C₂³×D₄	#386	1	2	yes	—
239	C₂³×D₄	C₂×#99	1	2	yes	—
240	C₂³×D₄	C₂×#99	1	1	yes	characteristic
241	C₂³×D₄	C₂×#99	1	1	yes	characteristic
242	C₂³×D₄	C₂×#99	1	1	yes	characteristic
243	C₂³×D₄	C₂×#99	1	1	yes	characteristic
244	C₂³×D₄	C₂×#120	1	1	yes	characteristic
245	C₂³×D₄	C₂×#120	1	1	yes	characteristic
246	C₂³×D₄	C₂×#120	1	1	yes	characteristic
247	C₂³×D₄	C₂×#120	1	2	yes	—
248	C₂³×D₄	C₂×#121	1	2	yes	—
249	C₂³×D₄	C₂×#123	1	1	yes	characteristic
250	C₂³×D₄	D₄²	1	2	yes	—
251	C₂³×D₄	D₄²	1	2	yes	—
252	C₂³×D₄	#546	1	2	yes	—
253	C₂³×D₄	#546	1	2	yes	—
254	C₂⁴×C₄	C₂×#99	1	1	yes	characteristic
255	C₂⁴×C₄	C₂×#99	1	2	yes	—
256	C₂⁴×C₄	C₂×#99	1	1	yes	characteristic
257	C₂⁴×C₄	C₂×#99	1	1	yes	characteristic
258	C₂⁴×C₄	#534	1	1	yes	characteristic
259	C₂⁴×C₄	#534	1	1	yes	characteristic
260	C₂⁴×C₄	D₄²	1	2	yes	—
261	C₂⁴×C₄	#546	1	2	yes	—
262	C₂×#120	C₂×#99	1	4	yes	—
263	C₂×#120	C₂×#99	1	4	yes	—
264	C₂²×C₂²⋊C₄	#379	1	2	yes	—
265	C₂²×C₂²⋊C₄	#379	1	2	yes	—
266	C₂²×C₂²⋊C₄	#386	1	2	yes	—
267	C₂²×C₂²⋊C₄	#386	1	2	yes	—
268	C₂²×C₂²⋊C₄	#386	1	2	yes	—
269	C₂²×C₂²⋊C₄	C₂×#99	1	4	yes	—
270	C₂²×C₂²⋊C₄	C₂×#99	1	2	yes	—
271	C₂²×C₂²⋊C₄	C₂×#99	1	2	yes	—
272	C₂²×C₂²⋊C₄	C₂×#99	1	2	yes	—
273	C₂²×C₂²⋊C₄	C₂×#99	1	2	yes	—
274	#379	C₂×#99	1	4	yes	—
275	#379	C₂×#99	1	4	yes	—
276	C₂⁵	#1781	1	1	yes	characteristic
277	C₂⁵	#1781	1	1	yes	characteristic
278	C₂⁵	#1781	1	1	yes	characteristic
279	C₂⁵	#1781	1	1	yes	characteristic
280	C₂⁵	#1898	1	2	yes	—
281	C₂⁵	C₂×#379	1	1	yes	characteristic
282	C₂⁵	C₂×#386	1	1	yes	characteristic
283	C₂⁵	#2308	1	1	yes	characteristic
284	C₂⁵	D₄×C₂²⋊C₄	1	2	yes	—
285	C₂⁵	D₄×C₂²⋊C₄	1	2	yes	—
286	C₂⁵	#2403	1	1	yes	characteristic
287	C₂⁵	#2405	1	1	yes	characteristic
288	C₂⁵	#2410	1	2	yes	—
289	C₂⁵	C₂²×#99	1	2	yes	—
290	C₂⁵	C₂²×#99	1	1	yes	characteristic
291	C₂⁵	C₂²×#99	1	1	yes	characteristic
292	C₂⁵	C₂²×#99	1	2	yes	—
293	C₂⁵	C₂²×#99	1	1	yes	characteristic
294	C₂⁵	C₂²×#99	1	1	yes	characteristic
295	C₂⁵	#2883	1	2	yes	—
296	C₂⁵	#2883	1	2	yes	—
297	C₂²×D₄	#1781	1	4	yes	—
298	C₂³×C₄	#1781	1	1	yes	characteristic
299	C₂³×C₄	#1781	1	1	yes	characteristic
300	C₂³×C₄	#1781	1	1	yes	characteristic
301	C₂³×C₄	#1781	1	1	yes	characteristic
302	C₂³×C₄	#1898	1	2	yes	—
303	C₂³×C₄	#2403	1	1	yes	characteristic
304	C₂³×C₄	#2405	1	1	yes	characteristic
305	C₂³×C₄	#2410	1	2	yes	—
306	C₂×C₂²⋊C₄	#1781	1	4	yes	—
307	C₂×C₂²⋊C₄	#1898	1	4	yes	—
308	C₂⁴	#8541	1	2	yes	—
309	C₂⁴	#13867	1	1	yes	characteristic
310	C₂⁴	C₂×#1781	1	1	yes	characteristic
311	C₂⁴	C₂×#1781	1	1	yes	characteristic
312	C₂⁴	C₂×#1781	1	2	yes	—
313	C₂⁴	#20585	1	2	yes	—
314	C₂⁴	C₂×#1898	1	1	yes	characteristic
315	C₂⁴	C₂×#1898	1	1	yes	characteristic
316	C₂⁴	#21746	1	1	yes	characteristic
317	C₂⁴	#21746	1	1	yes	characteristic
318	C₂⁴	D₄×#99	1	2	yes	—
319	C₂⁴	D₄×#99	1	2	yes	—
320	C₂⁴	D₄×#99	1	2	yes	—
321	C₂⁴	D₄×#99	1	2	yes	—
322	C₂⁴	#23895	1	2	yes	—
323	C₂²×C₄	#8541	1	2	yes	—
324	C₂²×C₄	#23895	1	2	yes	—
325	C₂³	C₂×#8541	1	1	yes	characteristic
326	C₂³	#188035	1	2	yes	—
327	C₂³	#188049	1	1	yes	characteristic
328	C₂³	#359428	1	1	yes	characteristic
329	C₂³	#359528	1	2	yes	—
330	C₂³	#359549	1	1	yes	characteristic
331	C₂³	#359549	1	1	yes	characteristic
332	C₂³	#359579	1	2	yes	—
333	C₂²	#72218180	1	1	yes	characteristic
334	C₂²	#72219457	1	1	yes	characteristic
335	C₂²	#72233304	1	2	yes	—
336	C₂²	#72233304	1	2	yes	—
337	C₂²	#72236600	1	1	yes	characteristic
338	C₂	#72236821	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂	#72236821
commutator	C₂⁷	C₂³×C₄
Frattini, cosocle	C₂⁵×D₄	C₂⁴
prime radical	#72237628	C₂
LCS	G ▷ C₂⁷ ▷ 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. #72312643	C₂	semidirect
2. #72312241	C₂	semidirect
3. #72265785	C₂	semidirect
4. #72238352	C₂	semidirect
6. #72237627	C₄	semidirect
7. #72237618	C₄	semidirect
8. #72237581	C₂	semidirect
12. #72232592	C₄	semidirect
13. #72219455	C₂	semidirect
14. #72219444	C₂	semidirect
15. #72219418	C₂²	semidirect
16. #72219415	C₂²	semidirect
17. #72219414	C₂²	semidirect
18. #72219414	C₂²	semidirect
19. #72219311	C₂²	semidirect
20. #72219310	C₂²	semidirect
21. #72219309	C₂	semidirect
22. #72219301	C₂²	semidirect
25. #72219300	C₂²	semidirect
26. #72219300	C₂²	semidirect
27. #72219299	C₂²	semidirect
30. #72218518	C₂²	semidirect
31. #72218306	C₂²	semidirect
32. #72218291	C₂²	semidirect
33. #72217789	C₄	semidirect
34. #72217699	C₄	semidirect
35. #72217511	C₄	semidirect
36. #72215179	C₂²	semidirect
37. C₂×#62817	C₂×C₄	semidirect
45. C₂²×#2846	C₂×C₄	semidirect
55. #7626202	C₂×C₄	semidirect
68. C₂×#21746	C₂×C₄	semidirect
69. C₂×#21746	C₂×C₄	semidirect
70. C₂×#21746	C₂×C₄	semidirect
71. C₂²×#1898	C₂×C₄	semidirect
73. C₂×#14679	C₂×C₄	semidirect
78. #355913	C₂×C₄	semidirect
79. C₂×#10735	C₂×C₄	semidirect
80. #147567	D₄	semidirect
146. C₂×#1783	C₂×D₄	semidirect
151. C₂×#1781	C₂×D₄	semidirect
152. C₂⁷	#99	semidirect
161. C₂⁴×D₄	#99	semidirect
162. C₂⁴×D₄	#99	semidirect
175. C₂⁵×C₄	#99	semidirect
177. C₂×#534	#99	semidirect
178. C₂×#534	#99	semidirect
186. C₂²×#120	#99	semidirect
187. C₂²×#120	#99	semidirect
205. #2849	#99	semidirect
206. #2846	#99	semidirect
207. #2622	#99	semidirect
211. C₂×#381	#99	semidirect
212. C₂×#379	#99	semidirect

Maximal subgroups

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

subgroup	index
#72312643	2
#72312241	2
#72265785	2
#72238352	2
#72237628	2
#72237581	2
#72219455	2
#72219444	2
#72219309	2