Subgroups — #72256243

Order 2048.

At least 9929 conjugacy classes of subgroups; only the 790 normal subgroups are shown.

The subgroup lattice has 358 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72255841	C₂	1	1	yes	maximal, characteristic, complemented
2	#72255841	C₂	1	1	yes	maximal, characteristic, complemented
3	#72240419	C₂	1	1	yes	maximal, characteristic, complemented
4	#72238349	C₂	1	1	yes	maximal, characteristic, complemented
5	#72236631	C₂	1	1	yes	maximal, characteristic, complemented
6	#72236508	C₂	1	1	yes	maximal, characteristic, complemented
7	#72235130	C₂	1	1	yes	maximal, characteristic, complemented
8	#72234693	C₂	1	1	yes	maximal, characteristic, complemented
9	#72233581	C₂	1	1	yes	maximal, characteristic, complemented
10	#72233445	C₂	1	8	yes	maximal, complemented
11	#72225712	C₂	1	1	yes	maximal, characteristic, complemented
12	#72218838	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#139750	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#144378	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#6499874	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#511790	C₂	1	1	yes	maximal, characteristic, complemented
17	B(5,𝔽₂)	C₂	1	8	yes	maximal, complemented
18	#10586404	C₂²	1	1	yes	characteristic, complemented
19	C₂×#62817	C₂²	1	1	yes	characteristic, complemented
20	C₂×#60399	C₂²	1	1	yes	characteristic
21	#6499875	C₂²	1	4	yes	complemented
22	#6499874	C₂²	1	8	yes	complemented
23	#6499874	C₂²	1	4	yes	complemented
24	C₂×#23895	C₂²	1	1	yes	characteristic
25	C₂×#23895	C₂²	1	1	yes	characteristic
26	C₂×#23895	C₂²	1	1	yes	characteristic, complemented
27	C₂×#23895	C₂²	1	1	yes	characteristic, complemented
28	#6437621	C₂²	1	1	yes	characteristic
29	#6437621	C₂²	1	1	yes	characteristic, complemented
30	#6437621	C₂²	1	1	yes	characteristic, complemented
31	C₂×#23900	C₂²	1	1	yes	characteristic
32	C₂×#23900	C₂²	1	1	yes	characteristic, complemented
33	C₂×#23900	C₂²	1	1	yes	characteristic, complemented
34	C₂×#23897	C₂²	1	1	yes	characteristic, complemented
35	C₂×#21776	C₂²	1	1	yes	characteristic, complemented
36	C₂×#21776	C₂²	1	1	yes	characteristic, complemented
37	#616960	C₂²	1	1	yes	characteristic, complemented
38	#511791	C₂²	1	4	yes	complemented
39	#511790	C₂²	1	8	yes	complemented
40	#511790	C₂²	1	4	yes	complemented
41	C₂×#12707	C₂²	1	1	yes	characteristic, complemented
42	C₂×#12707	C₂²	1	1	yes	characteristic, complemented
43	C₂×#12707	C₂²	1	1	yes	characteristic, complemented
44	C₂×#12705	C₂²	1	1	yes	characteristic, complemented
45	C₂×#12705	C₂²	1	1	yes	characteristic, complemented
46	#493357	C₂²	1	1	yes	characteristic, complemented
47	C₂×#12687	C₂²	1	1	yes	characteristic, complemented
48	#347048	C₂²	1	4	yes	complemented
49	#347044	C₂²	1	4	yes	complemented
50	#347042	C₂²	1	4	yes	complemented
51	#347042	C₂²	1	4	yes	complemented
52	#188049	C₂²	1	1	yes	characteristic, complemented
53	C₂×#8541	C₂²	1	1	yes	characteristic, complemented
54	#187944	C₂²	1	1	yes	characteristic, complemented
55	#187944	C₂²	1	1	yes	characteristic, complemented
56	#187944	C₂²	1	1	yes	characteristic, complemented
57	#187944	C₂²	1	1	yes	characteristic, complemented
58	#186835	C₂²	1	1	yes	characteristic, complemented
59	#144379	C₂²	1	4	yes	complemented
60	#144378	C₂²	1	4	yes	complemented
61	#144378	C₂²	1	8	yes	complemented
62	#144367	C₂²	1	4	yes	complemented
63	#144366	C₂²	1	4	yes	complemented
64	#144364	C₂²	1	8	yes	complemented
65	#139750	C₂²	1	4	yes	complemented
66	#139750	C₂²	1	8	yes	complemented
67	#139749	C₂²	1	4	yes	complemented
68	#139743	C₂²	1	8	yes	complemented
69	#139743	C₂²	1	8	yes	complemented
70	#133839	C₂²	1	8	yes	complemented
71	C₂×#7316	C₂²	1	1	yes	characteristic, complemented
72	C₂×#7310	C₂²	1	1	yes	characteristic, complemented
73	C₂×#7310	C₂²	1	1	yes	characteristic, complemented
74	#128009	C₂²	1	1	yes	characteristic, complemented
75	C₂×H(7,𝔽₂)	D₄	1	1	yes	characteristic, complemented
76	#62820	C₂³	1	2	yes	complemented
77	#62817	C₂³	1	4	yes	—
78	#62817	C₂³	1	2	yes	complemented
79	C₂×#3484	C₂³	1	1	yes	characteristic
80	C₂×#3484	C₂³	1	1	yes	characteristic
81	C₂×#3484	C₂³	1	1	yes	characteristic
82	C₂×#3484	C₂³	1	1	yes	characteristic
83	C₂×#3484	C₂³	1	1	yes	characteristic
84	C₂²×#534	C₂³	1	1	yes	characteristic
85	C₂³×#120	C₂³	1	1	yes	characteristic
86	#60399	D₄	1	4	yes	complemented
87	#60399	C₂³	1	4	yes	—
88	C₂×#3026	D₄	1	2	yes	complemented
89	C₂×#3026	D₄	1	2	yes	complemented
90	C₂×#2883	D₄	1	1	yes	characteristic, complemented
91	C₂×#2883	D₄	1	1	yes	characteristic, complemented
92	C₂×#2883	D₄	1	1	yes	characteristic, complemented
93	C₂×#2846	D₄	1	2	yes	complemented
94	#34980	D₄	1	2	yes	complemented
95	#23901	D₄	1	2	yes	complemented
96	#23901	C₂³	1	2	yes	—
97	#23901	C₂³	1	2	yes	complemented
98	#23901	C₂³	1	2	yes	complemented
99	#23900	D₄	1	2	yes	complemented
100	#23900	D₄	1	4	yes	complemented
101	#23900	C₂³	1	4	yes	—
102	#23900	C₂³	1	2	yes	—
103	#23900	C₂³	1	4	yes	—
104	#23900	C₂³	1	2	yes	complemented
105	#23900	C₂³	1	2	yes	complemented
106	#23900	C₂³	1	4	yes	complemented
107	#23897	C₂³	1	4	yes	complemented
108	#23895	D₄	1	4	yes	complemented
109	#23895	D₄	1	4	yes	complemented
110	#23895	C₂³	1	4	yes	—
111	#23895	C₂³	1	4	yes	—
112	#23895	C₂³	1	4	yes	—
113	#23895	C₂³	1	4	yes	complemented
114	#21776	C₂³	1	4	yes	—
115	#21776	C₂³	1	4	yes	complemented
116	C₂×#1913	D₄	1	2	yes	complemented
117	C₂×#1913	D₄	1	2	yes	complemented
118	C₂×#1898	D₄	1	2	yes	complemented
119	C₂×#1898	D₄	1	2	yes	complemented
120	C₂×#1783	C₂³	1	1	yes	characteristic
121	C₂×#1781	C₂³	1	1	yes	characteristic
122	C₂×#1781	C₂³	1	1	yes	characteristic
123	C₂×#1781	C₂³	1	1	yes	characteristic
124	C₂×#1781	C₂³	1	1	yes	characteristic
125	C₂×#1781	C₂³	1	1	yes	characteristic
126	C₂×#1781	C₂³	1	1	yes	characteristic
127	#15948	C₂³	1	2	yes	complemented
128	#15947	C₂³	1	2	yes	complemented
129	#14335	C₂³	1	1	yes	characteristic
130	#12707	C₂³	1	4	yes	complemented
131	#12707	C₂³	1	4	yes	complemented
132	#12707	C₂³	1	4	yes	complemented
133	#12705	C₂³	1	4	yes	—
134	#12705	C₂³	1	4	yes	complemented
135	#12688	C₂³	1	2	yes	complemented
136	#12687	C₂³	1	4	yes	complemented
137	#12687	C₂³	1	2	yes	complemented
138	#8543	C₂³	1	2	yes	complemented
139	#8541	C₂³	1	4	yes	complemented
140	#8541	C₂³	1	2	yes	complemented
141	#8534	C₂³	1	4	yes	—
142	#8534	C₂³	1	4	yes	complemented
143	#8534	C₂³	1	4	yes	complemented
144	#8534	C₂³	1	4	yes	complemented
145	#8453	C₂³	1	4	yes	complemented
146	#7316	C₂³	1	4	yes	complemented
147	#7310	C₂³	1	4	yes	complemented
148	#7310	C₂³	1	4	yes	complemented
149	#7307	C₂³	1	4	yes	complemented
150	C₂⁷	C₂×D₄	1	1	yes	characteristic, complemented
151	H(7,𝔽₂)	C₂×D₄	1	4	yes	complemented
152	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
153	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
154	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
155	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic, complemented
156	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic, complemented
157	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic, complemented
158	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
159	#3484	C₂×D₄	1	2	yes	—
160	#3484	C₂×D₄	1	2	yes	—
161	#3484	C₂×D₄	1	2	yes	—
162	#3484	C₂×D₄	1	2	yes	—
163	#3484	C₂×D₄	1	2	yes	—
164	#3484	C₂×D₄	1	2	yes	—
165	#3484	C₂×D₄	1	2	yes	—
166	#3484	C₂×D₄	1	2	yes	complemented
167	#3484	C₂×D₄	1	2	yes	complemented
168	#3484	C₂⁴	1	2	yes	—
169	#3484	C₂⁴	1	2	yes	—
170	#3484	C₂⁴	1	2	yes	—
171	#3484	C₂⁴	1	2	yes	—
172	#3484	C₂⁴	1	2	yes	—
173	C₂×#534	C₂×D₄	1	2	yes	—
174	C₂×#534	C₂×D₄	1	2	yes	—
175	C₂²×#123	C₂×D₄	1	1	yes	characteristic, complemented
176	C₂²×#123	C₂⁴	1	1	yes	characteristic
177	C₂²×#120	C₂×D₄	1	2	yes	—
178	C₂²×#120	C₂×D₄	1	2	yes	—
179	C₂²×#120	C₂×D₄	1	2	yes	complemented
180	C₂²×#120	C₂×D₄	1	1	yes	characteristic, complemented
181	C₂²×#120	C₂⁴	1	2	yes	—
182	C₂²×#120	C₂⁴	1	1	yes	characteristic
183	C₂×#518	C₂×D₄	1	1	yes	characteristic
184	C₂×#518	C₂×D₄	1	1	yes	characteristic
185	C₂×#518	C₂×D₄	1	1	yes	characteristic
186	C₂×#518	C₂×D₄	1	1	yes	characteristic, complemented
187	C₂×#518	C₂×D₄	1	1	yes	characteristic, complemented
188	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
189	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
190	#3026	C₂×D₄	1	8	yes	complemented
191	#3026	C₂×D₄	1	8	yes	complemented
192	#2883	C₂×D₄	1	4	yes	complemented
193	#2883	C₂×D₄	1	4	yes	complemented
194	#2883	C₂×D₄	1	4	yes	complemented
195	C₂²×#99	C₂×D₄	1	2	yes	complemented
196	C₂²×#99	C₂×D₄	1	2	yes	complemented
197	#2849	C₂×D₄	1	4	yes	complemented
198	#2846	C₂×D₄	1	8	yes	complemented
199	#2846	C₂×D₄	1	4	yes	complemented
200	C₂×#379	C₂×D₄	1	2	yes	complemented
201	C₂×#379	C₂×D₄	1	2	yes	complemented
202	#1913	C₂×D₄	1	8	yes	complemented
203	#1913	C₂×D₄	1	8	yes	complemented
204	#1898	C₂×D₄	1	8	yes	complemented
205	#1898	C₂×D₄	1	4	yes	complemented
206	#1898	C₂×D₄	1	4	yes	complemented
207	#1783	C₂⁴	1	2	yes	—
208	#1781	C₂×D₄	1	2	yes	complemented
209	#1781	C₂×D₄	1	2	yes	complemented
210	#1781	C₂×D₄	1	2	yes	complemented
211	#1781	C₂×D₄	1	2	yes	complemented
212	#1781	C₂⁴	1	2	yes	—
213	#1781	C₂⁴	1	2	yes	—
214	#1781	C₂⁴	1	2	yes	—
215	#1781	C₂⁴	1	2	yes	—
216	#1781	C₂⁴	1	2	yes	—
217	#1781	C₂⁴	1	2	yes	—
218	#1438	C₂⁴	1	2	yes	—
219	C₂⁶	C₂²×D₄	1	1	yes	characteristic
220	C₂⁶	C₂²×D₄	1	1	yes	characteristic
221	C₂⁶	C₂²×D₄	1	2	yes	—
222	C₂⁶	C₂²×D₄	1	1	yes	characteristic, complemented
223	C₂×H(5,𝔽₂)	#120	1	2	yes	—
224	C₂×H(5,𝔽₂)	#120	1	2	yes	—
225	C₂×H(5,𝔽₂)	C₂²×D₄	1	2	yes	—
226	C₂×H(5,𝔽₂)	C₂²×D₄	1	2	yes	—
227	C₂×H(5,𝔽₂)	C₂²×D₄	1	2	yes	—
228	C₂×H(5,𝔽₂)	C₂²×D₄	1	2	yes	—
229	C₂×H(5,𝔽₂)	C₂²×D₄	1	2	yes	complemented
230	C₂³×D₄	#120	1	2	yes	—
231	C₂³×D₄	#120	1	2	yes	—
232	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
233	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
234	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
235	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
236	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
237	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
238	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
239	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
240	C₂³×D₄	H(5,𝔽₂)	1	1	yes	characteristic
241	C₂³×D₄	H(5,𝔽₂)	1	1	yes	characteristic
242	C₂³×D₄	H(5,𝔽₂)	1	1	yes	characteristic
243	C₂³×D₄	C₂⁵	1	1	yes	characteristic
244	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic, complemented
245	C₂⁴×C₄	H(5,𝔽₂)	1	1	yes	characteristic
246	#534	#120	1	4	yes	—
247	#534	#120	1	4	yes	—
248	#534	C₂²×D₄	1	4	yes	—
249	#534	C₂²×D₄	1	4	yes	—
250	C₂×#120	#120	1	4	yes	—
251	C₂×#120	#120	1	4	yes	—
252	C₂×#120	C₂²×D₄	1	4	yes	—
253	C₂×#120	C₂²×D₄	1	4	yes	—
254	#518	#120	1	2	yes	—
255	#518	#120	1	2	yes	—
256	#518	C₂²×D₄	1	2	yes	—
257	#518	C₂²×D₄	1	2	yes	—
258	#518	C₂²×D₄	1	2	yes	—
259	#518	C₂²×D₄	1	2	yes	—
260	#518	C₂²×D₄	1	2	yes	complemented
261	C₂²×C₂²⋊C₄	#120	1	2	yes	—
262	C₂²×C₂²⋊C₄	#120	1	2	yes	—
263	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
264	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic, complemented
265	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic, complemented
266	C₂×#99	C₂²×D₄	1	4	yes	—
267	C₂×#99	C₂²×D₄	1	4	yes	complemented
268	#379	C₂²×D₄	1	4	yes	—
269	#379	C₂²×D₄	1	4	yes	complemented
270	C₂⁵	B(4,𝔽₂)	1	2	yes	complemented
271	C₂⁵	B(4,𝔽₂)	1	2	yes	complemented
272	C₂⁵	C₂×#120	1	1	yes	characteristic
273	C₂⁵	C₂×#120	1	1	yes	characteristic
274	C₂⁵	C₂×#120	1	1	yes	characteristic
275	C₂⁵	C₂×#120	1	1	yes	characteristic
276	C₂⁵	D₄²	1	1	yes	characteristic
277	C₂⁵	D₄²	1	1	yes	characteristic
278	C₂⁵	D₄²	1	1	yes	characteristic
279	C₂⁵	D₄²	1	1	yes	characteristic
280	C₂⁵	D₄²	1	1	yes	characteristic
281	C₂⁵	D₄²	1	1	yes	characteristic
282	C₂⁵	D₄²	1	1	yes	characteristic
283	C₂⁵	C₂³×D₄	1	1	yes	characteristic
284	C₂⁵	C₂³×D₄	1	1	yes	characteristic
285	C₂²×D₄	B(4,𝔽₂)	1	4	yes	complemented
286	C₂²×D₄	B(4,𝔽₂)	1	4	yes	complemented
287	C₂²×D₄	C₂×#120	1	1	yes	characteristic
288	C₂²×D₄	C₂×#120	1	1	yes	characteristic
289	C₂²×D₄	C₂×#120	1	1	yes	characteristic
290	C₂²×D₄	C₂×#120	1	1	yes	characteristic
291	C₂²×D₄	C₂×#120	1	4	yes	—
292	C₂²×D₄	C₂×#120	1	4	yes	—
293	C₂²×D₄	#534	1	1	yes	characteristic
294	C₂²×D₄	#534	1	1	yes	characteristic
295	C₂²×D₄	D₄²	1	1	yes	characteristic
296	C₂²×D₄	D₄²	1	1	yes	characteristic
297	C₂²×D₄	D₄²	1	1	yes	characteristic
298	C₂²×D₄	D₄²	1	1	yes	characteristic
299	C₂²×D₄	D₄²	1	1	yes	characteristic
300	C₂²×D₄	D₄²	1	1	yes	characteristic
301	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
302	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
303	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
304	C₂²×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
305	C₂³×C₄	B(4,𝔽₂)	1	2	yes	complemented
306	C₂³×C₄	B(4,𝔽₂)	1	2	yes	complemented
307	C₂³×C₄	#534	1	1	yes	characteristic
308	C₂³×C₄	#534	1	1	yes	characteristic
309	C₂³×C₄	D₄²	1	1	yes	characteristic
310	C₂³×C₄	D₄²	1	1	yes	characteristic
311	C₂³×C₄	D₄²	1	1	yes	characteristic
312	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
313	C₂×C₂²⋊C₄	C₂×#120	1	4	yes	—
314	C₂×C₂²⋊C₄	C₂×#120	1	4	yes	—
315	C₂⁴	#2403	1	1	yes	characteristic
316	C₂⁴	#2403	1	1	yes	characteristic
317	C₂⁴	#2403	1	1	yes	characteristic
318	C₂⁴	#2403	1	1	yes	characteristic
319	C₂⁴	#2403	1	1	yes	characteristic
320	C₂⁴	#2403	1	1	yes	characteristic
321	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
322	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
323	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
324	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
325	C₂⁴	C₂×B(4,𝔽₂)	1	4	yes	—
326	C₂⁴	C₂×B(4,𝔽₂)	1	4	yes	—
327	C₂⁴	C₂²×#120	1	1	yes	characteristic
328	C₂⁴	C₂²×#120	1	1	yes	characteristic
329	C₂⁴	C₂×D₄²	1	1	yes	characteristic
330	C₂⁴	C₂×D₄²	1	1	yes	characteristic
331	C₂⁴	C₂×D₄²	1	1	yes	characteristic
332	C₂²×C₄	#2403	1	1	yes	characteristic
333	C₂²×C₄	#2403	1	1	yes	characteristic
334	C₂²×C₄	C₂×B(4,𝔽₂)	1	4	yes	—
335	C₂²×C₄	C₂×B(4,𝔽₂)	1	4	yes	—
336	C₂²×C₄	C₂×#534	1	1	yes	characteristic
337	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
338	C₂³	#23895	1	1	yes	characteristic
339	C₂³	#23895	1	1	yes	characteristic
340	C₂³	#23900	1	2	yes	—
341	C₂³	#23900	1	2	yes	—
342	C₂³	#23900	1	1	yes	characteristic
343	C₂³	#23900	1	1	yes	characteristic
344	C₂³	#23900	1	1	yes	characteristic
345	C₂³	#23900	1	1	yes	characteristic
346	C₂³	C₂×#2403	1	1	yes	characteristic
347	C₂³	C₂²×B(4,𝔽₂)	1	2	yes	—
348	C₂³	C₂²×B(4,𝔽₂)	1	2	yes	—
349	C₂²	#245225	1	1	yes	characteristic
350	C₂²	#245225	1	1	yes	characteristic
351	C₂²	#245225	1	1	yes	characteristic
352	C₂²	#245225	1	1	yes	characteristic
353	C₂²	C₂×#23900	1	1	yes	characteristic
354	C₂²	C₂×#23900	1	1	yes	characteristic
355	C₂²	C₂×#23895	1	1	yes	characteristic
356	C₂	C₂×#245225	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂	C₂×#245225
commutator, Frattini, cosocle	C₂³×D₄	C₂⁵
LCS	G ▷ C₂³×D₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂ ◁ C₂⁴ ◁ C₂⁴×D₄ ◁ G
LECS	G ▷ C₂³×D₄ ▷ C₂³ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72255841	C₂	semidirect
2. #72255841	C₂	semidirect
3. #72240419	C₂	semidirect
4. #72238349	C₂	semidirect
5. #72236631	C₂	semidirect
6. #72236508	C₂	semidirect
7. #72235130	C₂	semidirect
8. #72234693	C₂	semidirect
9. #72233581	C₂	semidirect
10. #72233445	C₂	semidirect
11. #72225712	C₂	semidirect
12. #72218838	C₂	semidirect
13. C₂×#139750	C₂	semidirect
14. C₂×#144378	C₂	semidirect
15. C₂×#6499874	C₂	semidirect
16. C₂×#511790	C₂	semidirect
17. B(5,𝔽₂)	C₂	semidirect
18. #10586404	C₂²	semidirect
19. C₂×#62817	C₂²	semidirect
21. #6499875	C₂²	semidirect
22. #6499874	C₂²	semidirect
23. #6499874	C₂²	semidirect
26. C₂×#23895	C₂²	semidirect
27. C₂×#23895	C₂²	semidirect
29. #6437621	C₂²	semidirect
30. #6437621	C₂²	semidirect
32. C₂×#23900	C₂²	semidirect
33. C₂×#23900	C₂²	semidirect
34. C₂×#23897	C₂²	semidirect
35. C₂×#21776	C₂²	semidirect
36. C₂×#21776	C₂²	semidirect
37. #616960	C₂²	semidirect
38. #511791	C₂²	semidirect
39. #511790	C₂²	semidirect
40. #511790	C₂²	semidirect
41. C₂×#12707	C₂²	semidirect
42. C₂×#12707	C₂²	semidirect
43. C₂×#12707	C₂²	semidirect
44. C₂×#12705	C₂²	semidirect
45. C₂×#12705	C₂²	semidirect
46. #493357	C₂²	semidirect
47. C₂×#12687	C₂²	semidirect
48. #347048	C₂²	semidirect
49. #347044	C₂²	semidirect
50. #347042	C₂²	semidirect
51. #347042	C₂²	semidirect
52. #188049	C₂²	semidirect
53. C₂×#8541	C₂²	semidirect
54. #187944	C₂²	semidirect
55. #187944	C₂²	semidirect
56. #187944	C₂²	semidirect
57. #187944	C₂²	semidirect
58. #186835	C₂²	semidirect
59. #144379	C₂²	semidirect
60. #144378	C₂²	semidirect
61. #144378	C₂²	semidirect
62. #144367	C₂²	semidirect
63. #144366	C₂²	semidirect
64. #144364	C₂²	semidirect
65. #139750	C₂²	semidirect
66. #139750	C₂²	semidirect
67. #139749	C₂²	semidirect
68. #139743	C₂²	semidirect
69. #139743	C₂²	semidirect
70. #133839	C₂²	semidirect
71. C₂×#7316	C₂²	semidirect
72. C₂×#7310	C₂²	semidirect
73. C₂×#7310	C₂²	semidirect
74. #128009	C₂²	semidirect
75. C₂×H(7,𝔽₂)	D₄	semidirect
76. #62820	C₂³	semidirect
78. #62817	C₂³	semidirect
86. #60399	D₄	semidirect
88. C₂×#3026	D₄	semidirect
89. C₂×#3026	D₄	semidirect
90. C₂×#2883	D₄	semidirect
91. C₂×#2883	D₄	semidirect
92. C₂×#2883	D₄	semidirect
93. C₂×#2846	D₄	semidirect
94. #34980	D₄	semidirect
95. #23901	D₄	semidirect
97. #23901	C₂³	semidirect
98. #23901	C₂³	semidirect
99. #23900	D₄	semidirect
100. #23900	D₄	semidirect
104. #23900	C₂³	semidirect
105. #23900	C₂³	semidirect
106. #23900	C₂³	semidirect
107. #23897	C₂³	semidirect
108. #23895	D₄	semidirect
109. #23895	D₄	semidirect
113. #23895	C₂³	semidirect
115. #21776	C₂³	semidirect
116. C₂×#1913	D₄	semidirect
117. C₂×#1913	D₄	semidirect
118. C₂×#1898	D₄	semidirect
119. C₂×#1898	D₄	semidirect
127. #15948	C₂³	semidirect
128. #15947	C₂³	semidirect
130. #12707	C₂³	semidirect
131. #12707	C₂³	semidirect
132. #12707	C₂³	semidirect
134. #12705	C₂³	semidirect
135. #12688	C₂³	semidirect
136. #12687	C₂³	semidirect
137. #12687	C₂³	semidirect
138. #8543	C₂³	semidirect
139. #8541	C₂³	semidirect
140. #8541	C₂³	semidirect
142. #8534	C₂³	semidirect
143. #8534	C₂³	semidirect
144. #8534	C₂³	semidirect
145. #8453	C₂³	semidirect
146. #7316	C₂³	semidirect
147. #7310	C₂³	semidirect
148. #7310	C₂³	semidirect
149. #7307	C₂³	semidirect
150. C₂⁷	C₂×D₄	semidirect
151. H(7,𝔽₂)	C₂×D₄	semidirect
155. C₂²×H(5,𝔽₂)	C₂×D₄	semidirect
156. C₂²×H(5,𝔽₂)	C₂×D₄	semidirect
157. C₂⁴×D₄	C₂×D₄	semidirect
166. #3484	C₂×D₄	semidirect
167. #3484	C₂×D₄	semidirect
175. C₂²×#123	C₂×D₄	semidirect
179. C₂²×#120	C₂×D₄	semidirect
180. C₂²×#120	C₂×D₄	semidirect
186. C₂×#518	C₂×D₄	semidirect
187. C₂×#518	C₂×D₄	semidirect
188. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
189. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
190. #3026	C₂×D₄	semidirect
191. #3026	C₂×D₄	semidirect
192. #2883	C₂×D₄	semidirect
193. #2883	C₂×D₄	semidirect
194. #2883	C₂×D₄	semidirect
195. C₂²×#99	C₂×D₄	semidirect
196. C₂²×#99	C₂×D₄	semidirect
197. #2849	C₂×D₄	semidirect
198. #2846	C₂×D₄	semidirect
199. #2846	C₂×D₄	semidirect
200. C₂×#379	C₂×D₄	semidirect
201. C₂×#379	C₂×D₄	semidirect
202. #1913	C₂×D₄	semidirect
203. #1913	C₂×D₄	semidirect
204. #1898	C₂×D₄	semidirect
205. #1898	C₂×D₄	semidirect
206. #1898	C₂×D₄	semidirect
208. #1781	C₂×D₄	semidirect
209. #1781	C₂×D₄	semidirect
210. #1781	C₂×D₄	semidirect
211. #1781	C₂×D₄	semidirect
222. C₂⁶	C₂²×D₄	semidirect
229. C₂×H(5,𝔽₂)	C₂²×D₄	semidirect
244. C₂⁴×C₄	C₂²×D₄	semidirect
260. #518	C₂²×D₄	semidirect
264. C₂²×C₂²⋊C₄	C₂²×D₄	semidirect
265. C₂²×C₂²⋊C₄	C₂²×D₄	semidirect
267. C₂×#99	C₂²×D₄	semidirect
269. #379	C₂²×D₄	semidirect
270. C₂⁵	B(4,𝔽₂)	semidirect
271. C₂⁵	B(4,𝔽₂)	semidirect
285. C₂²×D₄	B(4,𝔽₂)	semidirect
286. C₂²×D₄	B(4,𝔽₂)	semidirect
305. C₂³×C₄	B(4,𝔽₂)	semidirect
306. 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
#72255841	2
#72240419	2
#72238349	2
#72236631	2
#72236508	2
#72235130	2
#72234693	2
#72233581	2
#72233445	2
#72225712	2
#72218838	2
C₂×#139750	2
C₂×#144378	2
C₂×#6499874	2
C₂×#511790	2
B(5,𝔽₂)	2