Subgroups — #72265925

Order 2048.

At least 9529 conjugacy classes of subgroups; only the 1052 normal subgroups are shown.

The subgroup lattice has 374 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72265924	C₂	1	2	yes	maximal, complemented
2	#72252238	C₂	1	2	yes	maximal, complemented
3	#72251607	C₂	1	1	yes	maximal, characteristic, complemented
4	#72251605	C₂	1	1	yes	maximal, characteristic, complemented
5	#72249444	C₂	1	1	yes	maximal, characteristic, complemented
6	#72236600	C₂	1	2	yes	maximal, complemented
7	#72236586	C₂	1	2	yes	maximal, complemented
8	#72234959	C₂	1	8	yes	maximal, complemented
9	#72234958	C₂	1	8	yes	maximal, complemented
10	#72233065	C₂	1	2	yes	maximal, complemented
11	#72219038	C₂	1	2	yes	maximal, complemented
12	C₂×#62842	C₂²	1	1	yes	characteristic, complemented
13	#7752093	C₂²	1	4	yes	complemented
14	#7752089	C₂²	1	4	yes	complemented
15	#7712875	C₂²	1	2	yes	—
16	#7642244	C₂²	1	2	yes	—
17	#7630668	C₂²	1	2	yes	—
18	C₂×#35346	C₂²	1	1	yes	characteristic
19	C₂×#35346	C₂²	1	1	yes	characteristic, complemented
20	#6628892	C₂²	1	4	yes	complemented
21	#6470225	C₂²	1	4	yes	complemented
22	#6437621	C₂²	1	4	yes	complemented
23	C₂×#20585	C₂²	1	1	yes	characteristic, complemented
24	C₂×#20585	C₂²	1	1	yes	characteristic, complemented
25	#515285	C₂²	1	1	yes	characteristic, complemented
26	#394061	C₂²	1	8	yes	complemented
27	#393929	C₂²	1	8	yes	complemented
28	#392699	C₂²	1	4	yes	complemented
29	#392111	C₂²	1	2	yes	complemented
30	#359442	C₂²	1	4	yes	complemented
31	#353314	C₂²	1	1	yes	characteristic, complemented
32	#238082	C₂²	1	4	yes	complemented
33	#233549	C₂²	1	4	yes	complemented
34	#233541	C₂²	1	8	yes	complemented
35	#201687	C₂²	1	4	yes	complemented
36	#201687	C₂²	1	4	yes	complemented
37	#201678	C₂²	1	8	yes	complemented
38	#201664	C₂²	1	4	yes	complemented
39	C₂×#8746	C₂²	1	2	yes	complemented
40	C₂×#8541	C₂²	1	2	yes	complemented
41	#187944	C₂²	1	4	yes	complemented
42	#187928	C₂²	1	4	yes	complemented
43	#122191	C₂²	1	4	yes	complemented
44	#115631	C₂²	1	8	yes	complemented
45	#115204	C₂²	1	8	yes	complemented
46	#115133	C₂²	1	8	yes	complemented
47	#111467	C₂²	1	4	yes	complemented
48	#107194	C₂²	1	8	yes	complemented
49	#107114	C₂²	1	4	yes	complemented
50	#106766	C₂²	1	4	yes	complemented
51	C₂³×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
52	C₂³×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
53	C₂×#3485	D₄	1	2	yes	complemented
54	C₂×#3484	D₄	1	2	yes	complemented
55	C₂×#3484	C₂³	1	2	yes	—
56	C₂×#3484	C₂³	1	2	yes	—
57	C₂²×#534	C₂³	1	4	yes	—
58	C₂³×#120	D₄	1	1	yes	characteristic, complemented
59	C₂³×#120	D₄	1	1	yes	characteristic, complemented
60	C₂³×#120	C₂³	1	1	yes	characteristic
61	C₂²×#518	C₂³	1	1	yes	characteristic
62	#46999	D₄	1	2	yes	complemented
63	#46997	D₄	1	4	yes	complemented
64	#46996	D₄	1	2	yes	complemented
65	#46837	D₄	1	2	yes	complemented
66	#46387	D₄	1	2	yes	complemented
67	#46386	D₄	1	4	yes	complemented
68	#37475	C₂³	1	2	yes	—
69	#37436	C₂³	1	2	yes	—
70	#36714	D₄	1	4	yes	complemented
71	#36714	D₄	1	4	yes	complemented
72	#35350	D₄	1	2	yes	complemented
73	#35350	D₄	1	2	yes	complemented
74	#35346	D₄	1	2	yes	complemented
75	#35346	D₄	1	2	yes	complemented
76	#35088	D₄	1	4	yes	complemented
77	#34980	D₄	1	4	yes	complemented
78	#34980	C₂³	1	4	yes	—
79	#34980	C₂³	1	8	yes	—
80	#34980	C₂³	1	4	yes	—
81	C₂×#2404	D₄	1	4	yes	complemented
82	C₂×#2403	C₂³	1	4	yes	—
83	C₂×#2403	C₂³	1	4	yes	—
84	C₂×#2613	C₂³	1	4	yes	—
85	#34356	C₂³	1	4	yes	—
86	#34172	D₄	1	2	yes	complemented
87	#34171	D₄	1	2	yes	complemented
88	#34171	C₂³	1	2	yes	—
89	#34171	C₂³	1	2	yes	—
90	C₂×#2308	D₄	1	1	yes	characteristic, complemented
91	C₂×#2308	D₄	1	1	yes	characteristic, complemented
92	C₂×#2308	C₂³	1	1	yes	characteristic
93	C₂×#2308	C₂³	1	1	yes	characteristic
94	C₂×#2308	C₂³	1	1	yes	characteristic
95	#21746	C₂³	1	8	yes	—
96	#21746	C₂³	1	8	yes	—
97	C₂×#1898	C₂³	1	8	yes	—
98	C₂×#1781	C₂³	1	8	yes	—
99	C₂×#1781	C₂³	1	4	yes	—
100	C₂×#1781	C₂³	1	4	yes	—
101	C₂×#1781	C₂³	1	4	yes	—
102	C₂×#1781	C₂³	1	4	yes	—
103	C₂×#1781	C₂³	1	4	yes	—
104	C₂×#1781	C₂³	1	4	yes	—
105	#14335	C₂³	1	4	yes	—
106	#13867	C₂³	1	4	yes	—
107	#10735	C₂³	1	8	yes	—
108	#10725	C₂³	1	4	yes	—
109	#8101	C₂³	1	8	yes	—
110	#8101	C₂³	1	8	yes	—
111	C₂×#1304	C₂³	1	4	yes	—
112	C₂×#1304	C₂³	1	4	yes	—
113	C₂⁷	C₂×D₄	1	1	yes	characteristic
114	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	complemented
115	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	complemented
116	C₂³×#41	C₂×D₄	1	2	yes	—
117	C₂³×#41	C₂×D₄	1	2	yes	—
118	C₂³×#41	C₂×D₄	1	2	yes	—
119	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
120	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
121	C₂⁴×D₄	C₂×D₄	1	2	yes	—
122	C₂⁴×D₄	C₂×D₄	1	2	yes	—
123	C₂⁴×D₄	C₂⁴	1	2	yes	—
124	C₂⁴×D₄	C₂⁴	1	2	yes	—
125	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
126	C₂⁴×D₄	C₂⁴	1	2	yes	—
127	C₂×#534	C₂×D₄	1	4	yes	—
128	C₂×#534	C₂×D₄	1	4	yes	—
129	C₂×#534	C₂×D₄	1	4	yes	complemented
130	C₂×#534	C₂×D₄	1	4	yes	complemented
131	C₂²×#123	C₂×D₄	1	4	yes	complemented
132	C₂²×#120	C₂×D₄	1	4	yes	—
133	C₂²×#120	C₂×D₄	1	4	yes	—
134	C₂²×#120	C₂×D₄	1	2	yes	—
135	C₂²×#120	C₂×D₄	1	2	yes	—
136	C₂²×#120	C₂×D₄	1	2	yes	—
137	C₂²×#120	C₂×D₄	1	2	yes	—
138	C₂²×#120	C₂×D₄	1	4	yes	complemented
139	C₂²×#120	C₂⁴	1	4	yes	—
140	C₂×#518	C₂×D₄	1	2	yes	complemented
141	C₂×#518	C₂×D₄	1	2	yes	complemented
142	C₂×#518	C₂×D₄	1	2	yes	complemented
143	C₂×#518	C₂×D₄	1	2	yes	complemented
144	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
145	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
146	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
147	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
148	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
149	#2842	C₂×D₄	1	4	yes	complemented
150	#2842	C₂×D₄	1	2	yes	complemented
151	#2840	C₂×D₄	1	2	yes	complemented
152	#2483	C₂×D₄	1	2	yes	complemented
153	#2405	C₂×D₄	1	4	yes	—
154	#2405	C₂×D₄	1	4	yes	—
155	#2405	C₂×D₄	1	4	yes	—
156	#2405	C₂×D₄	1	4	yes	—
157	#2405	C₂×D₄	1	4	yes	complemented
158	#2405	C₂×D₄	1	4	yes	complemented
159	#2405	C₂×D₄	1	4	yes	complemented
160	#2403	C₂×D₄	1	4	yes	—
161	#2403	C₂×D₄	1	4	yes	—
162	#2403	C₂×D₄	1	4	yes	—
163	#2403	C₂×D₄	1	4	yes	—
164	#2403	C₂×D₄	1	4	yes	complemented
165	#2403	C₂×D₄	1	4	yes	complemented
166	#2403	C₂×D₄	1	2	yes	complemented
167	#2312	C₂×D₄	1	4	yes	complemented
168	#2312	C₂×D₄	1	4	yes	complemented
169	#2309	C₂×D₄	1	4	yes	complemented
170	#2309	C₂×D₄	1	4	yes	complemented
171	#2308	C₂×D₄	1	2	yes	—
172	#2308	C₂×D₄	1	2	yes	—
173	#2308	C₂×D₄	1	2	yes	—
174	#2308	C₂×D₄	1	2	yes	—
175	#2308	C₂×D₄	1	4	yes	—
176	#2308	C₂×D₄	1	4	yes	—
177	#2308	C₂×D₄	1	2	yes	complemented
178	#2308	C₂×D₄	1	2	yes	complemented
179	#2308	C₂×D₄	1	4	yes	complemented
180	#2308	C₂×D₄	1	4	yes	complemented
181	C₂×#386	C₂×D₄	1	4	yes	—
182	C₂×#386	C₂×D₄	1	4	yes	—
183	C₂×#381	C₂×D₄	1	2	yes	—
184	C₂×#381	C₂×D₄	1	4	yes	complemented
185	C₂×#379	C₂×D₄	1	4	yes	complemented
186	C₂×#379	C₂⁴	1	2	yes	—
187	C₂×#379	C₂⁴	1	8	yes	—
188	C₂×#379	C₂⁴	1	2	yes	—
189	C₂×#379	C₂⁴	1	2	yes	—
190	C₂×#379	C₂⁴	1	4	yes	—
191	C₂⁶	#120	1	1	yes	characteristic
192	C₂⁶	#120	1	1	yes	characteristic
193	C₂⁶	#120	1	1	yes	characteristic
194	C₂⁶	#120	1	2	yes	—
195	C₂⁶	#120	1	1	yes	characteristic
196	C₂⁶	C₂²×D₄	1	1	yes	characteristic
197	C₂⁶	C₂²×D₄	1	2	yes	—
198	C₂⁶	C₂²×D₄	1	2	yes	—
199	C₂⁶	H(5,𝔽₂)	1	2	yes	complemented
200	C₂⁶	C₂⁵	1	1	yes	characteristic
201	C₂³×Q₈	#120	1	2	yes	—
202	C₂³×D₄	#120	1	2	yes	—
203	C₂³×D₄	#120	1	2	yes	—
204	C₂³×D₄	#120	1	2	yes	—
205	C₂³×D₄	C₂²×D₄	1	2	yes	—
206	C₂³×D₄	C₂²×D₄	1	2	yes	—
207	C₂³×D₄	C₂²×D₄	1	2	yes	—
208	C₂³×D₄	C₂²×D₄	1	2	yes	—
209	C₂³×D₄	C₂²×D₄	1	2	yes	—
210	C₂³×D₄	C₂²×D₄	1	2	yes	—
211	C₂³×D₄	C₂²×D₄	1	4	yes	—
212	C₂³×D₄	C₂²×D₄	1	2	yes	—
213	C₂³×D₄	C₂²×D₄	1	2	yes	—
214	C₂³×D₄	C₂²×D₄	1	2	yes	—
215	C₂³×D₄	C₂²×D₄	1	4	yes	—
216	C₂³×D₄	C₂²×D₄	1	2	yes	—
217	C₂³×D₄	C₂²×D₄	1	4	yes	—
218	C₂³×D₄	C₂²×D₄	1	2	yes	—
219	C₂³×D₄	C₂²×D₄	1	2	yes	—
220	C₂³×D₄	C₂²×D₄	1	2	yes	—
221	C₂³×D₄	C₂²×D₄	1	2	yes	—
222	C₂⁴×C₄	#120	1	1	yes	characteristic
223	C₂⁴×C₄	#120	1	2	yes	—
224	C₂⁴×C₄	#120	1	1	yes	characteristic
225	C₂⁴×C₄	#120	1	2	yes	—
226	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
227	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
228	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
229	C₂⁴×C₄	H(5,𝔽₂)	1	2	yes	complemented
230	C₂×#123	#120	1	4	yes	—
231	C₂×#123	#120	1	4	yes	—
232	C₂×#123	#120	1	4	yes	—
233	C₂×#123	#120	1	4	yes	—
234	C₂×#120	#120	1	4	yes	—
235	C₂×#120	#120	1	4	yes	—
236	C₂×#120	#120	1	4	yes	—
237	C₂×#120	#120	1	4	yes	—
238	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
239	C₂²×C₂²⋊C₄	#120	1	2	yes	—
240	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
241	C₂²×C₂²⋊C₄	#120	1	2	yes	—
242	C₂²×C₂²⋊C₄	#120	1	2	yes	—
243	C₂²×C₂²⋊C₄	#120	1	2	yes	—
244	C₂²×C₂²⋊C₄	#120	1	2	yes	—
245	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
246	C₂²×C₂²⋊C₄	#120	1	2	yes	—
247	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
248	C₂²×C₂²⋊C₄	#120	1	2	yes	—
249	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
250	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
251	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
252	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
253	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
254	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
255	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
256	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
257	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
258	C₂²×C₂²⋊C₄	H(5,𝔽₂)	1	4	yes	complemented
259	#386	#120	1	4	yes	—
260	#386	#120	1	4	yes	—
261	#386	#120	1	4	yes	—
262	#386	#120	1	4	yes	—
263	#386	#120	1	4	yes	—
264	#386	#120	1	4	yes	—
265	#386	#120	1	4	yes	—
266	#386	#120	1	4	yes	—
267	#381	#120	1	2	yes	—
268	#381	#120	1	2	yes	—
269	#381	#120	1	2	yes	—
270	#381	#120	1	2	yes	—
271	#379	C₂²×D₄	1	2	yes	—
272	#379	C₂²×D₄	1	2	yes	—
273	#379	C₂²×D₄	1	2	yes	—
274	#379	C₂²×D₄	1	2	yes	—
275	#379	C₂²×D₄	1	4	yes	—
276	#379	C₂²×D₄	1	4	yes	—
277	#379	C₂²×D₄	1	4	yes	—
278	#379	C₂²×D₄	1	4	yes	—
279	#379	H(5,𝔽₂)	1	4	yes	complemented
280	C₂⁵	B(4,𝔽₂)	1	4	yes	complemented
281	C₂⁵	C₂×#120	1	2	yes	—
282	C₂⁵	C₂×#120	1	1	yes	characteristic
283	C₂⁵	C₂×#120	1	1	yes	characteristic
284	C₂⁵	C₂×#120	1	1	yes	characteristic
285	C₂⁵	C₂×#120	1	1	yes	characteristic
286	C₂⁵	C₂×#120	1	2	yes	—
287	C₂⁵	C₂×#120	1	1	yes	characteristic
288	C₂⁵	C₂×#120	1	1	yes	characteristic
289	C₂⁵	C₂×#120	1	2	yes	—
290	C₂⁵	C₂×#120	1	4	yes	—
291	C₂⁵	C₂×#120	1	2	yes	—
292	C₂⁵	C₂³×D₄	1	1	yes	characteristic
293	C₂⁵	C₂³×D₄	1	2	yes	—
294	C₂⁵	C₂³×D₄	1	2	yes	—
295	C₂⁵	C₂³×D₄	1	2	yes	—
296	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
297	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
298	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
299	C₂⁵	#585	1	2	yes	—
300	C₂²×D₄	C₂×#120	1	4	yes	—
301	C₂²×D₄	C₂×#120	1	4	yes	—
302	C₂²×D₄	C₂×#120	1	4	yes	—
303	C₂²×D₄	C₂×#120	1	4	yes	—
304	C₂³×C₄	B(4,𝔽₂)	1	4	yes	complemented
305	C₂³×C₄	C₂×#120	1	2	yes	—
306	C₂³×C₄	C₂×#120	1	2	yes	—
307	C₂³×C₄	C₂×#120	1	2	yes	—
308	C₂³×C₄	C₂×#120	1	4	yes	—
309	C₂³×C₄	C₂×#120	1	4	yes	—
310	C₂³×C₄	C₂×#120	1	4	yes	—
311	C₂³×C₄	C₂×#120	1	2	yes	—
312	C₂³×C₄	C₂×#120	1	2	yes	—
313	C₂³×C₄	C₂×#120	1	2	yes	—
314	C₂³×C₄	C₂×#120	1	2	yes	—
315	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
316	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
317	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
318	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
319	C₂×C₂²⋊C₄	C₂×#120	1	4	yes	—
320	C₂×C₂²⋊C₄	C₂×#120	1	4	yes	—
321	C₂×C₂²⋊C₄	C₂×#120	1	4	yes	—
322	C₂×C₂²⋊C₄	C₂×#120	1	4	yes	—
323	C₂⁴	#2846	1	1	yes	characteristic
324	C₂⁴	#2846	1	1	yes	characteristic
325	C₂⁴	#2846	1	1	yes	characteristic
326	C₂⁴	#2846	1	1	yes	characteristic
327	C₂⁴	C₂×B(4,𝔽₂)	1	4	yes	—
328	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
329	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
330	C₂⁴	#3026	1	2	yes	—
331	C₂⁴	#3026	1	2	yes	—
332	C₂⁴	C₂²×#120	1	1	yes	characteristic
333	C₂⁴	C₂²×#120	1	4	yes	—
334	C₂⁴	C₂²×#120	1	1	yes	characteristic
335	C₂⁴	C₂²×#120	1	1	yes	characteristic
336	C₂⁴	#3484	1	1	yes	characteristic
337	C₂⁴	#3484	1	1	yes	characteristic
338	C₂⁴	#3484	1	1	yes	characteristic
339	C₂⁴	#3484	1	4	yes	—
340	C₂⁴	#3484	1	4	yes	—
341	C₂⁴	#3485	1	1	yes	characteristic
342	C₂⁴	#3488	1	4	yes	—
343	C₂⁴	#3496	1	4	yes	—
344	C₂⁴	#3496	1	4	yes	—
345	C₂⁴	#3498	1	4	yes	—
346	C₂²×C₄	#2846	1	4	yes	—
347	C₂²×C₄	C₂×B(4,𝔽₂)	1	4	yes	—
348	C₂³	#32898	1	2	yes	—
349	C₂³	#32898	1	2	yes	—
350	C₂³	#32898	1	2	yes	—
351	C₂³	#32898	1	2	yes	—
352	C₂³	#35346	1	1	yes	characteristic
353	C₂³	#35346	1	1	yes	characteristic
354	C₂³	#35347	1	1	yes	characteristic
355	C₂³	#35347	1	1	yes	characteristic
356	C₂³	#35512	1	1	yes	characteristic
357	C₂³	#35527	1	1	yes	characteristic
358	C₂³	#35680	1	8	yes	—
359	C₂³	C₂×#2846	1	1	yes	characteristic
360	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
361	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
362	C₂³	C₂×#3026	1	1	yes	characteristic
363	C₂³	C₂×#3026	1	1	yes	characteristic
364	C₂²	#4928938	1	1	yes	characteristic
365	C₂²	#6499867	1	1	yes	characteristic
366	C₂²	#6499870	1	1	yes	characteristic
367	C₂²	#6500010	1	1	yes	characteristic
368	C₂²	#6500010	1	1	yes	characteristic
369	C₂²	C₂×#32898	1	1	yes	characteristic
370	C₂²	C₂×#32898	1	1	yes	characteristic
371	C₂	#72234953	1	2	yes	—
372	C₂	#72240103	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#4928938
commutator, Frattini, cosocle	C₂⁶	C₂⁵
LCS	G ▷ C₂⁶ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁶ ◁ G
LECS	G ▷ C₂⁶ ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72265924	C₂	semidirect
2. #72252238	C₂	semidirect
3. #72251607	C₂	semidirect
4. #72251605	C₂	semidirect
5. #72249444	C₂	semidirect
6. #72236600	C₂	semidirect
7. #72236586	C₂	semidirect
8. #72234959	C₂	semidirect
9. #72234958	C₂	semidirect
10. #72233065	C₂	semidirect
11. #72219038	C₂	semidirect
12. C₂×#62842	C₂²	semidirect
13. #7752093	C₂²	semidirect
14. #7752089	C₂²	semidirect
19. C₂×#35346	C₂²	semidirect
20. #6628892	C₂²	semidirect
21. #6470225	C₂²	semidirect
22. #6437621	C₂²	semidirect
23. C₂×#20585	C₂²	semidirect
24. C₂×#20585	C₂²	semidirect
25. #515285	C₂²	semidirect
26. #394061	C₂²	semidirect
27. #393929	C₂²	semidirect
28. #392699	C₂²	semidirect
29. #392111	C₂²	semidirect
30. #359442	C₂²	semidirect
31. #353314	C₂²	semidirect
32. #238082	C₂²	semidirect
33. #233549	C₂²	semidirect
34. #233541	C₂²	semidirect
35. #201687	C₂²	semidirect
36. #201687	C₂²	semidirect
37. #201678	C₂²	semidirect
38. #201664	C₂²	semidirect
39. C₂×#8746	C₂²	semidirect
40. C₂×#8541	C₂²	semidirect
41. #187944	C₂²	semidirect
42. #187928	C₂²	semidirect
43. #122191	C₂²	semidirect
44. #115631	C₂²	semidirect
45. #115204	C₂²	semidirect
46. #115133	C₂²	semidirect
47. #111467	C₂²	semidirect
48. #107194	C₂²	semidirect
49. #107114	C₂²	semidirect
50. #106766	C₂²	semidirect
53. C₂×#3485	D₄	semidirect
54. C₂×#3484	D₄	semidirect
58. C₂³×#120	D₄	semidirect
59. C₂³×#120	D₄	semidirect
62. #46999	D₄	semidirect
63. #46997	D₄	semidirect
64. #46996	D₄	semidirect
65. #46837	D₄	semidirect
66. #46387	D₄	semidirect
67. #46386	D₄	semidirect
70. #36714	D₄	semidirect
71. #36714	D₄	semidirect
72. #35350	D₄	semidirect
73. #35350	D₄	semidirect
74. #35346	D₄	semidirect
75. #35346	D₄	semidirect
76. #35088	D₄	semidirect
77. #34980	D₄	semidirect
81. C₂×#2404	D₄	semidirect
86. #34172	D₄	semidirect
87. #34171	D₄	semidirect
90. C₂×#2308	D₄	semidirect
91. C₂×#2308	D₄	semidirect
114. C₂²×H(5,𝔽₂)	C₂×D₄	semidirect
115. C₂²×H(5,𝔽₂)	C₂×D₄	semidirect
129. C₂×#534	C₂×D₄	semidirect
130. C₂×#534	C₂×D₄	semidirect
131. C₂²×#123	C₂×D₄	semidirect
138. C₂²×#120	C₂×D₄	semidirect
140. C₂×#518	C₂×D₄	semidirect
141. C₂×#518	C₂×D₄	semidirect
142. C₂×#518	C₂×D₄	semidirect
143. C₂×#518	C₂×D₄	semidirect
149. #2842	C₂×D₄	semidirect
150. #2842	C₂×D₄	semidirect
151. #2840	C₂×D₄	semidirect
152. #2483	C₂×D₄	semidirect
157. #2405	C₂×D₄	semidirect
158. #2405	C₂×D₄	semidirect
159. #2405	C₂×D₄	semidirect
164. #2403	C₂×D₄	semidirect
165. #2403	C₂×D₄	semidirect
166. #2403	C₂×D₄	semidirect
167. #2312	C₂×D₄	semidirect
168. #2312	C₂×D₄	semidirect
169. #2309	C₂×D₄	semidirect
170. #2309	C₂×D₄	semidirect
177. #2308	C₂×D₄	semidirect
178. #2308	C₂×D₄	semidirect
179. #2308	C₂×D₄	semidirect
180. #2308	C₂×D₄	semidirect
184. C₂×#381	C₂×D₄	semidirect
185. C₂×#379	C₂×D₄	semidirect
199. C₂⁶	H(5,𝔽₂)	semidirect
229. C₂⁴×C₄	H(5,𝔽₂)	semidirect
258. C₂²×C₂²⋊C₄	H(5,𝔽₂)	semidirect
279. #379	H(5,𝔽₂)	semidirect
280. C₂⁵	B(4,𝔽₂)	semidirect
304. C₂³×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
#72265924	2
#72252238	2
#72251607	2
#72251605	2
#72249444	2
#72236600	2
#72236586	2
#72234959	2
#72234958	2
#72233065	2
#72219038	2