Subgroups — #72262769

Order 4096.

At least 11460 conjugacy classes of subgroups; only the 1061 normal subgroups are shown.

The subgroup lattice has 323 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72262765	C₂	1	2	yes	maximal, complemented
2	#72262702	C₂	1	1	yes	maximal, characteristic, complemented
3	#72262701	C₂²	1	1	yes	characteristic, complemented
4	#72262647	C₂	1	2	yes	maximal, complemented
5	#72262637	C₂²	1	1	yes	characteristic, complemented
6	#72262616	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#72216370	C₂	1	2	yes	maximal, complemented
8	C₂×#135513	C₂²	1	2	yes	complemented
9	#72256315	C₂	1	4	yes	maximal, complemented
10	#72256224	C₂	1	4	yes	maximal, complemented
11	#72256222	C₂²	1	4	yes	complemented
12	#72256017	C₂	1	4	yes	maximal, complemented
13	#72255990	C₂²	1	4	yes	complemented
14	#72255977	C₂²	1	4	yes	complemented
15	#72255971	C₂²	1	4	yes	complemented
16	#72255888	C₂	1	4	yes	maximal, complemented
17	#72255829	C₂²	1	4	yes	complemented
18	#72255793	C₂²	1	4	yes	complemented
19	C₂×#144380	C₂²	1	2	yes	complemented
20	C₂×#139759	C₂²	1	4	yes	complemented
21	#72249642	C₂	1	2	yes	maximal, complemented
22	#72249638	C₂²	1	2	yes	complemented
23	#72249612	C₂²	1	4	yes	complemented
24	#72249611	C₂²	1	2	yes	complemented
25	#72240419	C₂²	1	4	yes	complemented
26	C₂×#144633	C₂²	1	2	yes	complemented
27	C₂×#144631	C₂²	1	2	yes	complemented
28	#72238443	C₂²	1	4	yes	complemented
29	#72237854	C₂	1	1	yes	maximal, characteristic, complemented
30	#72237829	C₂²	1	4	yes	complemented
31	#72237480	C₂	1	2	yes	maximal, complemented
32	#72237476	C₂²	1	4	yes	complemented
33	#72237473	C₂²	1	4	yes	complemented
34	#72237472	C₂²	1	4	yes	complemented
35	#72237467	C₂²	1	4	yes	complemented
36	#72237039	C₂	1	2	yes	maximal, complemented
37	#72237037	C₂²	1	4	yes	complemented
38	#72237034	C₂²	1	2	yes	complemented
39	#72237033	C₂²	1	2	yes	complemented
40	#72236928	C₂²	1	4	yes	complemented
41	#72236636	C₂²	1	4	yes	complemented
42	#72235238	C₂²	1	4	yes	complemented
43	#72235234	C₂²	1	2	yes	complemented
44	#72234693	C₂²	1	4	yes	complemented
45	#72234675	C₂²	1	1	yes	characteristic, complemented
46	#72234668	C₂²	1	1	yes	characteristic, complemented
47	#72234625	C₂²	1	1	yes	characteristic
48	C₂×#511771	C₂²	1	4	yes	complemented
49	#72226366	C₂²	1	4	yes	complemented
50	C₂×#188035	C₂²	1	1	yes	characteristic, complemented
51	#72225712	C₂²	1	2	yes	complemented
52	C₂×#7266798	C₂²	1	2	yes	—
53	#72225665	C₂²	1	1	yes	characteristic, complemented
54	#72225641	C₂²	1	2	yes	complemented
55	#72225610	C₂²	1	4	yes	complemented
56	#72224136	C₂²	1	2	yes	—
57	#72219641	C₂²	1	2	yes	complemented
58	#72219393	C₂²	1	2	yes	complemented
59	#72219314	C₂²	1	2	yes	complemented
60	#72218838	C₂²	1	4	yes	complemented
61	#72218121	C₂²	1	4	yes	complemented
62	#72218104	C₂²	1	4	yes	complemented
63	C₂×#139750	C₂²	1	4	yes	complemented
64	C₂×#144378	C₂²	1	2	yes	complemented
65	C₂×#139731	C₂²	1	4	yes	complemented
66	C₂×#6499874	C₂²	1	2	yes	—
67	#10586404	C₂³	1	2	yes	—
68	C₂×#62817	C₂³	1	1	yes	characteristic
69	C₂³×D₄²	C₂³	1	1	yes	characteristic
70	C₂×#60399	D₄	1	4	yes	complemented
71	C₂×#60399	C₂³	1	2	yes	—
72	#7643002	C₂³	1	2	yes	—
73	#7642244	C₂³	1	2	yes	—
74	C₂×#34980	D₄	1	2	yes	complemented
75	C₂×#34980	C₂³	1	1	yes	characteristic
76	#7626202	C₂³	1	1	yes	characteristic
77	#7266798	D₄	1	16	yes	complemented
78	C₂×#32873	C₂³	1	2	yes	—
79	#6499871	D₄	1	4	yes	complemented
80	#6499870	D₄	1	4	yes	complemented
81	#6499869	D₄	1	4	yes	complemented
82	#6499867	D₄	1	4	yes	complemented
83	#6451874	D₄	1	4	yes	complemented
84	C₂×#23996	D₄	1	8	yes	complemented
85	C₂×#23895	C₂³	1	2	yes	—
86	C₂×#23895	C₂³	1	4	yes	—
87	#6437621	C₂³	1	4	yes	—
88	#6437621	C₂³	1	4	yes	—
89	C₂×#23900	C₂³	1	4	yes	—
90	C₂×#23900	C₂³	1	4	yes	—
91	C₂×#23906	C₂³	1	4	yes	—
92	C₂×#21776	D₄	1	4	yes	complemented
93	C₂×#21776	C₂³	1	2	yes	—
94	C₂×#21776	C₂³	1	4	yes	—
95	#6374128	C₂³	1	2	yes	—
96	C₂×#21746	D₄	1	2	yes	complemented
97	C₂×#21746	C₂³	1	1	yes	characteristic
98	C₂×#21746	C₂³	1	1	yes	characteristic
99	#617710	C₂³	1	2	yes	—
100	#616960	C₂³	1	2	yes	—
101	#556752	C₂³	1	1	yes	characteristic
102	C₂×#12707	C₂³	1	4	yes	—
103	C₂×#12705	C₂³	1	4	yes	—
104	C₂×#12705	C₂³	1	4	yes	—
105	C₂×#12693	C₂³	1	4	yes	—
106	#493357	C₂³	1	4	yes	—
107	C₂×#12687	C₂³	1	4	yes	—
108	C₂×#12687	C₂³	1	4	yes	—
109	#382436	C₂³	1	2	yes	—
110	#382434	C₂³	1	2	yes	—
111	#359558	C₂³	1	4	yes	—
112	#359549	C₂³	1	4	yes	—
113	#359442	C₂³	1	4	yes	—
114	#188109	C₂³	1	2	yes	—
115	#188049	C₂³	1	2	yes	—
116	C₂×#8546	C₂³	1	2	yes	—
117	C₂×#8541	C₂³	1	2	yes	—
118	#187944	C₂³	1	4	yes	—
119	#187944	C₂³	1	4	yes	—
120	#186835	C₂³	1	4	yes	—
121	#146479	C₂³	1	4	yes	—
122	#146475	C₂³	1	4	yes	—
123	#128033	C₂³	1	4	yes	—
124	C₂×#7316	C₂³	1	4	yes	—
125	C₂×#7314	C₂³	1	4	yes	—
126	C₂×#7311	C₂³	1	2	yes	—
127	C₂×#7310	C₂³	1	2	yes	—
128	C₂×#7310	C₂³	1	4	yes	—
129	#128009	C₂³	1	4	yes	—
130	#107114	C₂³	1	4	yes	—
131	C₂×H(7,𝔽₂)	C₂×D₄	1	2	yes	complemented
132	C₂⁵×D₄	C₂×D₄	1	1	yes	characteristic
133	#62820	C₂×D₄	1	4	yes	complemented
134	#62817	C₂×D₄	1	4	yes	complemented
135	C₂×#3490	C₂×D₄	1	4	yes	—
136	C₂×#3490	C₂×D₄	1	2	yes	—
137	C₂×#3484	C₂×D₄	1	4	yes	—
138	C₂×#3484	C₂⁴	1	4	yes	—
139	C₂×#3484	C₂⁴	1	2	yes	—
140	C₂²×#534	C₂⁴	1	2	yes	—
141	C₂³×#127	C₂⁴	1	1	yes	characteristic
142	C₂³×#120	C₂×D₄	1	2	yes	—
143	C₂³×#120	C₂⁴	1	1	yes	characteristic
144	C₂³×#120	C₂⁴	1	1	yes	characteristic
145	C₂×#3026	C₂×D₄	1	8	yes	complemented
146	C₂²×B(4,𝔽₂)	C₂×D₄	1	8	yes	—
147	C₂×#2883	C₂×D₄	1	4	yes	complemented
148	C₂×#2883	C₂×D₄	1	2	yes	complemented
149	C₂×#2883	C₂×D₄	1	4	yes	complemented
150	C₂×#2849	C₂×D₄	1	2	yes	—
151	C₂×#2846	C₂×D₄	1	2	yes	—
152	#34980	C₂×D₄	1	8	yes	—
153	C₂×#2613	C₂×D₄	1	2	yes	—
154	C₂×#2613	C₂×D₄	1	2	yes	—
155	#34171	C₂⁴	1	2	yes	—
156	C₂×#2308	C₂×D₄	1	2	yes	—
157	C₂²×#379	C₂×D₄	1	2	yes	—
158	C₂²×#379	C₂×D₄	1	1	yes	characteristic
159	#32873	C₂×D₄	1	8	yes	complemented
160	#23901	C₂×D₄	1	8	yes	complemented
161	#23900	C₂×D₄	1	8	yes	—
162	#23900	C₂×D₄	1	8	yes	—
163	#23900	C₂×D₄	1	16	yes	—
164	#23900	C₂×D₄	1	8	yes	complemented
165	#23895	C₂×D₄	1	8	yes	complemented
166	#21776	C₂×D₄	1	16	yes	complemented
167	#21747	C₂×D₄	1	4	yes	complemented
168	#21746	C₂×D₄	1	8	yes	—
169	#21746	C₂×D₄	1	4	yes	complemented
170	C₂×#1913	C₂×D₄	1	8	yes	complemented
171	C₂×#1898	C₂×D₄	1	8	yes	—
172	C₂×#1889	C₂×D₄	1	8	yes	—
173	C₂×#1828	C₂×D₄	1	4	yes	complemented
174	C₂×#1819	C₂×D₄	1	2	yes	—
175	C₂×#1783	C₂⁴	1	4	yes	—
176	C₂×#1781	C₂⁴	1	4	yes	—
177	C₂×#1781	C₂⁴	1	2	yes	—
178	C₂×#1781	C₂⁴	1	2	yes	—
179	C₂×#1781	C₂⁴	1	4	yes	—
180	#14335	C₂⁴	1	2	yes	—
181	C₂⁷	#120	1	1	yes	characteristic, complemented
182	C₂⁷	C₂²×D₄	1	1	yes	characteristic
183	C₂⁷	H(5,𝔽₂)	1	1	yes	characteristic, complemented
184	C₂²×H(5,𝔽₂)	C₂²×D₄	1	2	yes	—
185	C₂²×H(5,𝔽₂)	C₂²×D₄	1	4	yes	—
186	C₂⁴×D₄	#120	1	2	yes	—
187	C₂⁴×D₄	#120	1	2	yes	complemented
188	C₂⁴×D₄	C₂²×D₄	1	2	yes	—
189	C₂⁴×D₄	H(5,𝔽₂)	1	1	yes	characteristic, complemented
190	C₂⁴×D₄	C₂⁵	1	1	yes	characteristic
191	C₂⁵×C₄	#120	1	1	yes	characteristic, complemented
192	#3484	C₂²×D₄	1	8	yes	—
193	#3484	C₂²×D₄	1	8	yes	—
194	C₂×#543	#120	1	2	yes	—
195	C₂×#534	#120	1	2	yes	—
196	C₂×#534	C₂²×D₄	1	4	yes	—
197	C₂²×#123	C₂²×D₄	1	2	yes	—
198	C₂²×#123	C₂²×D₄	1	2	yes	—
199	C₂²×#120	#120	1	4	yes	—
200	C₂²×#120	C₂²×D₄	1	4	yes	—
201	C₂²×#120	C₂²×D₄	1	4	yes	—
202	C₂²×#120	C₂²×D₄	1	2	yes	—
203	C₂²×#120	C₂²×D₄	1	2	yes	—
204	C₂²×#120	C₂²×D₄	1	2	yes	—
205	C₂²×#120	C₂²×D₄	1	2	yes	—
206	C₂²×#120	C₂²×D₄	1	4	yes	—
207	C₂×#518	#120	1	4	yes	—
208	C₂×#518	C₂²×D₄	1	4	yes	—
209	C₂×#518	C₂²×D₄	1	2	yes	—
210	C₂×#518	H(5,𝔽₂)	1	2	yes	complemented
211	C₂×#518	H(5,𝔽₂)	1	2	yes	complemented
212	C₂³×C₂²⋊C₄	#120	1	2	yes	—
213	C₂³×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
214	C₂³×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
215	C₂³×C₂²⋊C₄	H(5,𝔽₂)	1	1	yes	characteristic, complemented
216	C₂³×C₄²	H(5,𝔽₂)	1	1	yes	characteristic, complemented
217	C₂×B(4,𝔽₂)	#120	1	16	yes	complemented
218	C₂×B(4,𝔽₂)	#120	1	16	yes	complemented
219	C₂²×#99	C₂²×D₄	1	8	yes	—
220	C₂×#381	#120	1	2	yes	complemented
221	C₂×#381	#120	1	2	yes	complemented
222	C₂×#379	#120	1	4	yes	complemented
223	C₂×#379	#120	1	4	yes	complemented
224	C₂×#379	#120	1	2	yes	complemented
225	C₂×#379	#120	1	2	yes	complemented
226	C₂×#379	#120	1	2	yes	complemented
227	C₂×#379	#120	1	1	yes	characteristic, complemented
228	C₂×#379	#120	1	1	yes	characteristic, complemented
229	C₂×#379	C₂²×D₄	1	4	yes	—
230	#1889	#120	1	16	yes	complemented
231	#1889	#120	1	16	yes	complemented
232	#1819	#120	1	4	yes	complemented
233	#1819	#120	1	4	yes	complemented
234	#1781	C₂²×D₄	1	8	yes	—
235	#1781	C₂²×D₄	1	8	yes	—
236	#1781	C₂²×D₄	1	4	yes	—
237	#1781	C₂²×D₄	1	4	yes	—
238	#1438	H(5,𝔽₂)	1	4	yes	complemented
239	C₂⁶	B(4,𝔽₂)	1	2	yes	complemented
240	C₂⁶	C₂×#120	1	1	yes	characteristic
241	C₂⁶	C₂×#120	1	2	yes	—
242	C₂⁶	C₂×#120	1	1	yes	characteristic
243	C₂⁶	C₂×#120	1	2	yes	—
244	C₂⁶	C₂×#120	1	2	yes	—
245	C₂⁶	C₂³×D₄	1	1	yes	characteristic
246	C₂⁶	C₂×H(5,𝔽₂)	1	1	yes	characteristic
247	C₂×H(5,𝔽₂)	C₂×#120	1	8	yes	—
248	C₂³×D₄	B(4,𝔽₂)	1	4	yes	complemented
249	C₂³×D₄	C₂×#120	1	4	yes	—
250	C₂³×D₄	C₂³×D₄	1	2	yes	—
251	C₂³×D₄	C₂³×D₄	1	2	yes	—
252	C₂³×D₄	C₂³×D₄	1	2	yes	—
253	C₂³×D₄	C₂×H(5,𝔽₂)	1	2	yes	—
254	C₂³×D₄	C₂×H(5,𝔽₂)	1	2	yes	—
255	C₂³×D₄	#585	1	2	yes	—
256	C₂⁴×C₄	B(4,𝔽₂)	1	2	yes	complemented
257	C₂⁴×C₄	C₂×#120	1	2	yes	—
258	C₂⁴×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
259	C₂×#120	C₂×#120	1	8	yes	—
260	C₂×#120	C₂×#120	1	8	yes	—
261	#518	C₂×#120	1	8	yes	—
262	C₂²×C₂²⋊C₄	C₂×#120	1	4	yes	—
263	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
264	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
265	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
266	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
267	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
268	C₂×#99	C₂×#120	1	16	yes	—
269	#379	C₂×#120	1	8	yes	—
270	C₂⁵	#2846	1	2	yes	—
271	C₂⁵	#2846	1	2	yes	—
272	C₂⁵	C₂×B(4,𝔽₂)	1	4	yes	—
273	C₂⁵	C₂×B(4,𝔽₂)	1	2	yes	—
274	C₂⁵	C₂×B(4,𝔽₂)	1	2	yes	—
275	C₂⁵	#3026	1	2	yes	—
276	C₂⁵	#3026	1	2	yes	—
277	C₂⁵	C₂²×#120	1	1	yes	characteristic
278	C₂⁵	C₂²×#120	1	1	yes	characteristic
279	C₂⁵	C₂²×#120	1	1	yes	characteristic
280	C₂⁵	#3484	1	1	yes	characteristic
281	C₂⁵	#3484	1	1	yes	characteristic
282	C₂⁵	#3484	1	2	yes	—
283	C₂⁵	#3484	1	1	yes	characteristic
284	C₂⁵	#3484	1	2	yes	—
285	C₂⁵	#3485	1	1	yes	characteristic
286	C₂⁵	#3488	1	2	yes	—
287	C₂²×D₄	C₂²×#120	1	4	yes	—
288	C₂²×D₄	#3496	1	4	yes	—
289	C₂²×D₄	#3496	1	4	yes	—
290	C₂²×D₄	#3498	1	4	yes	—
291	C₂³×C₄	C₂×B(4,𝔽₂)	1	4	yes	—
292	C₂³×C₄	#3484	1	2	yes	—
293	C₂³×C₄	#3484	1	2	yes	—
294	C₂³×C₄	#3488	1	2	yes	—
295	C₂×C₂²⋊C₄	#2846	1	4	yes	—
296	C₂⁴	#32898	1	2	yes	—
297	C₂⁴	#32898	1	2	yes	—
298	C₂⁴	#32898	1	2	yes	—
299	C₂⁴	#32898	1	2	yes	—
300	C₂⁴	#35346	1	1	yes	characteristic
301	C₂⁴	#35346	1	1	yes	characteristic
302	C₂⁴	#35347	1	1	yes	characteristic
303	C₂⁴	#35347	1	1	yes	characteristic
304	C₂⁴	#35512	1	1	yes	characteristic
305	C₂⁴	#35527	1	1	yes	characteristic
306	C₂⁴	#35680	1	4	yes	—
307	C₂⁴	C₂×#2846	1	1	yes	characteristic
308	C₂⁴	C₂²×B(4,𝔽₂)	1	2	yes	—
309	C₂⁴	C₂×#3026	1	2	yes	—
310	C₂²×C₄	#35680	1	4	yes	—
311	C₂³	#4928938	1	1	yes	characteristic
312	C₂³	#6499867	1	1	yes	characteristic
313	C₂³	#6499870	1	1	yes	characteristic
314	C₂³	#6499874	1	4	yes	—
315	C₂³	#6500010	1	2	yes	—
316	C₂³	C₂×#32898	1	2	yes	—
317	C₂²	#72216396	1	2	yes	—
318	C₂²	#72219157	1	2	yes	—
319	C₂²	#72234627	1	2	yes	—
320	C₂²	#72240103	1	1	yes	characteristic
321	C₂	#72251612	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂	#72251612
commutator, Frattini, cosocle	C₂⁴×D₄	C₂⁵
LCS	G ▷ C₂⁴×D₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂ ◁ C₂⁴ ◁ C₂⁴×D₄ ◁ G
LECS	G ▷ C₂⁴×D₄ ▷ C₂³ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72262765	C₂	semidirect
2. #72262702	C₂	semidirect
3. #72262701	C₂²	semidirect
4. #72262647	C₂	semidirect
5. #72262637	C₂²	semidirect
6. #72262616	C₂	semidirect
7. C₂×#72216370	C₂	semidirect
8. C₂×#135513	C₂²	semidirect
9. #72256315	C₂	semidirect
10. #72256224	C₂	semidirect
11. #72256222	C₂²	semidirect
12. #72256017	C₂	semidirect
13. #72255990	C₂²	semidirect
14. #72255977	C₂²	semidirect
15. #72255971	C₂²	semidirect
16. #72255888	C₂	semidirect
17. #72255829	C₂²	semidirect
18. #72255793	C₂²	semidirect
19. C₂×#144380	C₂²	semidirect
20. C₂×#139759	C₂²	semidirect
21. #72249642	C₂	semidirect
22. #72249638	C₂²	semidirect
23. #72249612	C₂²	semidirect
24. #72249611	C₂²	semidirect
25. #72240419	C₂²	semidirect
26. C₂×#144633	C₂²	semidirect
27. C₂×#144631	C₂²	semidirect
28. #72238443	C₂²	semidirect
29. #72237854	C₂	semidirect
30. #72237829	C₂²	semidirect
31. #72237480	C₂	semidirect
32. #72237476	C₂²	semidirect
33. #72237473	C₂²	semidirect
34. #72237472	C₂²	semidirect
35. #72237467	C₂²	semidirect
36. #72237039	C₂	semidirect
37. #72237037	C₂²	semidirect
38. #72237034	C₂²	semidirect
39. #72237033	C₂²	semidirect
40. #72236928	C₂²	semidirect
41. #72236636	C₂²	semidirect
42. #72235238	C₂²	semidirect
43. #72235234	C₂²	semidirect
44. #72234693	C₂²	semidirect
45. #72234675	C₂²	semidirect
46. #72234668	C₂²	semidirect
48. C₂×#511771	C₂²	semidirect
49. #72226366	C₂²	semidirect
50. C₂×#188035	C₂²	semidirect
51. #72225712	C₂²	semidirect
53. #72225665	C₂²	semidirect
54. #72225641	C₂²	semidirect
55. #72225610	C₂²	semidirect
57. #72219641	C₂²	semidirect
58. #72219393	C₂²	semidirect
59. #72219314	C₂²	semidirect
60. #72218838	C₂²	semidirect
61. #72218121	C₂²	semidirect
62. #72218104	C₂²	semidirect
63. C₂×#139750	C₂²	semidirect
64. C₂×#144378	C₂²	semidirect
65. C₂×#139731	C₂²	semidirect
70. C₂×#60399	D₄	semidirect
74. C₂×#34980	D₄	semidirect
77. #7266798	D₄	semidirect
79. #6499871	D₄	semidirect
80. #6499870	D₄	semidirect
81. #6499869	D₄	semidirect
82. #6499867	D₄	semidirect
83. #6451874	D₄	semidirect
84. C₂×#23996	D₄	semidirect
92. C₂×#21776	D₄	semidirect
96. C₂×#21746	D₄	semidirect
131. C₂×H(7,𝔽₂)	C₂×D₄	semidirect
133. #62820	C₂×D₄	semidirect
134. #62817	C₂×D₄	semidirect
145. C₂×#3026	C₂×D₄	semidirect
147. C₂×#2883	C₂×D₄	semidirect
148. C₂×#2883	C₂×D₄	semidirect
149. C₂×#2883	C₂×D₄	semidirect
159. #32873	C₂×D₄	semidirect
160. #23901	C₂×D₄	semidirect
164. #23900	C₂×D₄	semidirect
165. #23895	C₂×D₄	semidirect
166. #21776	C₂×D₄	semidirect
167. #21747	C₂×D₄	semidirect
169. #21746	C₂×D₄	semidirect
170. C₂×#1913	C₂×D₄	semidirect
173. C₂×#1828	C₂×D₄	semidirect
181. C₂⁷	#120	semidirect
183. C₂⁷	H(5,𝔽₂)	semidirect
187. C₂⁴×D₄	#120	semidirect
189. C₂⁴×D₄	H(5,𝔽₂)	semidirect
191. C₂⁵×C₄	#120	semidirect
210. C₂×#518	H(5,𝔽₂)	semidirect
211. C₂×#518	H(5,𝔽₂)	semidirect
215. C₂³×C₂²⋊C₄	H(5,𝔽₂)	semidirect
216. C₂³×C₄²	H(5,𝔽₂)	semidirect
217. C₂×B(4,𝔽₂)	#120	semidirect
218. C₂×B(4,𝔽₂)	#120	semidirect
220. C₂×#381	#120	semidirect
221. C₂×#381	#120	semidirect
222. C₂×#379	#120	semidirect
223. C₂×#379	#120	semidirect
224. C₂×#379	#120	semidirect
225. C₂×#379	#120	semidirect
226. C₂×#379	#120	semidirect
227. C₂×#379	#120	semidirect
228. C₂×#379	#120	semidirect
230. #1889	#120	semidirect
231. #1889	#120	semidirect
232. #1819	#120	semidirect
233. #1819	#120	semidirect
238. #1438	H(5,𝔽₂)	semidirect
239. C₂⁶	B(4,𝔽₂)	semidirect
248. C₂³×D₄	B(4,𝔽₂)	semidirect
256. C₂⁴×C₄	B(4,𝔽₂)	semidirect

Maximal subgroups

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

subgroup	index
#72262765	2
#72262702	2
#72262647	2
#72262616	2
C₂×#72216370	2
#72256315	2
#72256224	2
#72256017	2
#72255888	2
#72249642	2
#72237854	2
#72237480	2
#72237039	2