Subgroups — #72258525

Order 2048.

At least 11887 conjugacy classes of subgroups; only the 1268 normal subgroups are shown.

The subgroup lattice has 464 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72258515	C₂	1	2	yes	maximal, complemented
2	#72258512	C₂	1	2	yes	maximal, complemented
3	#72240571	C₂	1	1	yes	maximal, characteristic, complemented
4	#72240111	C₂	1	4	yes	maximal, complemented
5	#72237496	C₂	1	4	yes	maximal, complemented
6	#72236600	C₂	1	1	yes	maximal, characteristic, complemented
7	#72236586	C₂	1	1	yes	maximal, characteristic, complemented
8	#72235219	C₂	1	1	yes	maximal, characteristic, complemented
9	#72234959	C₂	1	8	yes	maximal, complemented
10	#72233581	C₂	1	2	yes	maximal, complemented
11	#72226123	C₂	1	1	yes	maximal, characteristic, complemented
12	#72225690	C₂	1	1	yes	maximal, characteristic, complemented
13	#72225610	C₂	1	2	yes	maximal, complemented
14	#72219460	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#62817	C₂²	1	1	yes	characteristic, complemented
16	C₂×#62842	C₂²	1	1	yes	characteristic
17	C₂×#62842	C₂²	1	1	yes	characteristic, complemented
18	#7752089	C₂²	1	4	yes	complemented
19	#7721725	C₂²	1	4	yes	—
20	#7643563	C₂²	1	1	yes	characteristic, complemented
21	#7642244	C₂²	1	1	yes	characteristic, complemented
22	#7630668	C₂²	1	1	yes	characteristic
23	#7630442	C₂²	1	2	yes	complemented
24	C₂×#35346	C₂²	1	1	yes	characteristic
25	#7626386	C₂²	1	1	yes	characteristic, complemented
26	#6628892	C₂²	1	2	yes	complemented
27	C₂×#32898	C₂²	1	2	yes	complemented
28	#6470225	C₂²	1	8	yes	complemented
29	#6437621	C₂²	1	2	yes	—
30	#6437621	C₂²	1	2	yes	complemented
31	#6437621	C₂²	1	4	yes	complemented
32	#6437621	C₂²	1	2	yes	complemented
33	C₂×#20984	C₂²	1	2	yes	complemented
34	C₂×#20585	C₂²	1	1	yes	characteristic, complemented
35	#616960	C₂²	1	2	yes	complemented
36	#394061	C₂²	1	4	yes	complemented
37	#393929	C₂²	1	4	yes	complemented
38	#392699	C₂²	1	2	yes	complemented
39	#392658	C₂²	1	2	yes	complemented
40	#392111	C₂²	1	1	yes	characteristic, complemented
41	#392111	C₂²	1	1	yes	characteristic, complemented
42	#359442	C₂²	1	2	yes	complemented
43	#359434	C₂²	1	2	yes	complemented
44	#233549	C₂²	1	8	yes	complemented
45	#233541	C₂²	1	8	yes	complemented
46	#201687	C₂²	1	4	yes	complemented
47	#201678	C₂²	1	8	yes	complemented
48	C₂×#9495	C₂²	1	4	yes	complemented
49	#188049	C₂²	1	4	yes	complemented
50	C₂×#8541	C₂²	1	2	yes	complemented
51	#187944	C₂²	1	2	yes	complemented
52	#187944	C₂²	1	2	yes	complemented
53	#187944	C₂²	1	2	yes	complemented
54	#187944	C₂²	1	4	yes	complemented
55	#187928	C₂²	1	8	yes	complemented
56	#115631	C₂²	1	4	yes	complemented
57	#115204	C₂²	1	8	yes	complemented
58	#115133	C₂²	1	4	yes	complemented
59	#111467	C₂²	1	8	yes	complemented
60	#107194	C₂²	1	8	yes	complemented
61	#107114	C₂²	1	2	yes	complemented
62	#105808	C₂²	1	2	yes	complemented
63	C₂³×H(5,𝔽₂)	D₄	1	1	yes	characteristic, complemented
64	C₂³×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
65	C₂³×H(5,𝔽₂)	C₂³	1	1	yes	characteristic, complemented
66	C₂×#3485	D₄	1	1	yes	characteristic, complemented
67	C₂×#3485	D₄	1	1	yes	characteristic, complemented
68	C₂×#3485	D₄	1	2	yes	complemented
69	C₂×#3485	D₄	1	1	yes	characteristic, complemented
70	C₂×#3484	D₄	1	1	yes	characteristic, complemented
71	C₂×#3484	C₂³	1	1	yes	characteristic
72	C₂×#3484	C₂³	1	1	yes	characteristic
73	C₂×#3484	C₂³	1	2	yes	—
74	C₂×#3484	C₂³	1	4	yes	—
75	C₂×#3484	C₂³	1	1	yes	characteristic
76	C₂²×#534	D₄	1	2	yes	complemented
77	C₂²×#534	C₂³	1	2	yes	—
78	C₂²×#534	C₂³	1	2	yes	—
79	C₂²×#534	C₂³	1	2	yes	complemented
80	C₂³×#120	D₄	1	1	yes	characteristic, complemented
81	C₂³×#120	D₄	1	1	yes	characteristic, complemented
82	C₂³×#120	C₂³	1	1	yes	characteristic
83	C₂²×#518	D₄	1	1	yes	characteristic, complemented
84	C₂²×#518	C₂³	1	1	yes	characteristic, complemented
85	#37436	C₂³	1	4	yes	—
86	#37117	D₄	1	4	yes	complemented
87	#36721	D₄	1	4	yes	complemented
88	#36717	D₄	1	4	yes	complemented
89	#36714	D₄	1	4	yes	complemented
90	#35512	D₄	1	4	yes	complemented
91	#35355	D₄	1	4	yes	complemented
92	#35354	D₄	1	4	yes	complemented
93	#35346	D₄	1	4	yes	complemented
94	#35088	D₄	1	2	yes	complemented
95	#34980	D₄	1	2	yes	complemented
96	#34980	C₂³	1	4	yes	—
97	#34980	C₂³	1	4	yes	—
98	#34980	C₂³	1	2	yes	—
99	#34980	C₂³	1	4	yes	complemented
100	#34980	C₂³	1	4	yes	complemented
101	C₂×#2404	D₄	1	2	yes	complemented
102	C₂×#2404	D₄	1	2	yes	complemented
103	C₂×#2403	C₂³	1	2	yes	—
104	C₂×#2403	C₂³	1	2	yes	—
105	C₂×#2403	C₂³	1	4	yes	complemented
106	C₂×#2613	C₂³	1	2	yes	—
107	#34356	C₂³	1	4	yes	—
108	#34172	D₄	1	1	yes	characteristic, complemented
109	#34171	D₄	1	1	yes	characteristic, complemented
110	#34171	C₂³	1	1	yes	characteristic
111	C₂×#2308	D₄	1	1	yes	characteristic, complemented
112	C₂×#2308	D₄	1	1	yes	characteristic, complemented
113	C₂×#2308	C₂³	1	1	yes	characteristic
114	C₂×#2308	C₂³	1	2	yes	complemented
115	#23901	D₄	1	8	yes	complemented
116	#23900	D₄	1	8	yes	complemented
117	#21746	C₂³	1	8	yes	—
118	#21746	C₂³	1	8	yes	complemented
119	#21746	C₂³	1	8	yes	complemented
120	C₂×#1898	C₂³	1	4	yes	—
121	C₂×#1898	C₂³	1	4	yes	complemented
122	C₂×#1898	C₂³	1	4	yes	complemented
123	C₂×#1781	C₂³	1	2	yes	—
124	C₂×#1781	C₂³	1	2	yes	—
125	C₂×#1781	C₂³	1	4	yes	complemented
126	C₂×#1781	C₂³	1	4	yes	complemented
127	C₂×#1781	C₂³	1	2	yes	complemented
128	C₂×#1781	C₂³	1	2	yes	complemented
129	C₂×#1781	C₂³	1	2	yes	complemented
130	C₂×#1781	C₂³	1	2	yes	complemented
131	C₂×#1781	C₂³	1	8	yes	complemented
132	#14335	C₂³	1	2	yes	—
133	#14335	C₂³	1	2	yes	complemented
134	#13867	C₂³	1	4	yes	complemented
135	#10735	C₂³	1	4	yes	complemented
136	#10725	C₂³	1	4	yes	complemented
137	#8101	C₂³	1	8	yes	complemented
138	C₂×#1304	C₂³	1	8	yes	complemented
139	C₂⁷	C₂×D₄	1	1	yes	characteristic, complemented
140	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
141	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
142	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
143	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic, complemented
144	C₂²×H(5,𝔽₂)	C₂×D₄	1	4	yes	complemented
145	C₂³×#41	C₂×D₄	1	1	yes	characteristic
146	C₂³×#41	C₂×D₄	1	1	yes	characteristic
147	C₂³×#41	C₂×D₄	1	1	yes	characteristic
148	C₂³×#41	C₂×D₄	1	1	yes	characteristic
149	C₂³×#41	C₂×D₄	1	1	yes	characteristic
150	C₂³×#41	C₂×D₄	1	1	yes	characteristic
151	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
152	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
153	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
154	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
155	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
156	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
157	C₂⁴×D₄	C₂×D₄	1	2	yes	—
158	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
159	C₂⁴×D₄	C₂⁴	1	2	yes	—
160	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
161	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
162	C₂⁴×D₄	C₂⁴	1	2	yes	—
163	#3484	C₂×D₄	1	8	yes	—
164	C₂×#534	C₂×D₄	1	2	yes	—
165	C₂×#534	C₂×D₄	1	2	yes	—
166	C₂×#534	C₂×D₄	1	2	yes	—
167	C₂×#534	C₂×D₄	1	2	yes	—
168	C₂×#534	C₂×D₄	1	2	yes	—
169	C₂×#534	C₂×D₄	1	2	yes	—
170	C₂×#534	C₂×D₄	1	2	yes	complemented
171	C₂×#534	C₂×D₄	1	4	yes	complemented
172	C₂×#534	C₂×D₄	1	4	yes	complemented
173	C₂²×#123	C₂×D₄	1	2	yes	—
174	C₂²×#123	C₂×D₄	1	2	yes	—
175	C₂²×#123	C₂×D₄	1	4	yes	—
176	C₂²×#123	C₂×D₄	1	2	yes	complemented
177	C₂²×#123	C₂×D₄	1	4	yes	complemented
178	C₂²×#121	C₂×D₄	1	4	yes	—
179	C₂²×#121	C₂×D₄	1	4	yes	—
180	C₂²×#120	C₂×D₄	1	2	yes	—
181	C₂²×#120	C₂×D₄	1	2	yes	—
182	C₂²×#120	C₂×D₄	1	4	yes	—
183	C₂²×#120	C₂×D₄	1	2	yes	complemented
184	C₂²×#120	C₂×D₄	1	2	yes	complemented
185	C₂²×#120	C₂×D₄	1	2	yes	complemented
186	C₂²×#120	C₂×D₄	1	4	yes	complemented
187	C₂²×#120	C₂⁴	1	2	yes	—
188	C₂²×#120	C₂⁴	1	2	yes	—
189	C₂²×#120	C₂⁴	1	2	yes	—
190	C₂×#518	C₂×D₄	1	1	yes	characteristic
191	C₂×#518	C₂×D₄	1	1	yes	characteristic
192	C₂×#518	C₂×D₄	1	2	yes	—
193	C₂×#518	C₂×D₄	1	4	yes	complemented
194	C₂×#518	C₂×D₄	1	1	yes	characteristic, complemented
195	C₂×#518	C₂×D₄	1	1	yes	characteristic, complemented
196	C₂×#518	C₂×D₄	1	1	yes	characteristic, complemented
197	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
198	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	complemented
199	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
200	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
201	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
202	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
203	#2849	C₂×D₄	1	8	yes	complemented
204	#2846	C₂×D₄	1	8	yes	complemented
205	#2483	C₂×D₄	1	4	yes	complemented
206	#2405	C₂×D₄	1	4	yes	—
207	#2405	C₂×D₄	1	4	yes	—
208	#2405	C₂×D₄	1	4	yes	complemented
209	#2405	C₂×D₄	1	4	yes	complemented
210	#2405	C₂×D₄	1	4	yes	complemented
211	#2405	C₂×D₄	1	4	yes	complemented
212	#2403	C₂×D₄	1	4	yes	—
213	#2403	C₂×D₄	1	4	yes	—
214	#2403	C₂×D₄	1	4	yes	—
215	#2403	C₂×D₄	1	4	yes	—
216	#2403	C₂×D₄	1	4	yes	—
217	#2403	C₂×D₄	1	4	yes	—
218	#2403	C₂×D₄	1	4	yes	complemented
219	#2403	C₂×D₄	1	4	yes	complemented
220	#2403	C₂×D₄	1	4	yes	complemented
221	#2312	C₂×D₄	1	4	yes	complemented
222	#2312	C₂×D₄	1	4	yes	complemented
223	#2309	C₂×D₄	1	4	yes	complemented
224	#2308	C₂×D₄	1	2	yes	—
225	#2308	C₂×D₄	1	2	yes	—
226	#2308	C₂×D₄	1	4	yes	complemented
227	#2308	C₂×D₄	1	2	yes	complemented
228	C₂×#386	C₂×D₄	1	2	yes	—
229	C₂×#386	C₂×D₄	1	2	yes	—
230	C₂×#386	C₂×D₄	1	2	yes	complemented
231	C₂×#386	C₂×D₄	1	2	yes	complemented
232	C₂×#381	C₂×D₄	1	2	yes	complemented
233	C₂×#381	C₂×D₄	1	2	yes	complemented
234	C₂×#379	C₂×D₄	1	2	yes	complemented
235	C₂×#379	C₂⁴	1	4	yes	—
236	C₂×#379	C₂⁴	1	4	yes	—
237	C₂×#379	C₂⁴	1	4	yes	—
238	C₂×#379	C₂⁴	1	2	yes	—
239	C₂×#379	C₂⁴	1	2	yes	—
240	#1898	C₂×D₄	1	16	yes	complemented
241	#1781	C₂×D₄	1	8	yes	complemented
242	C₂⁶	#120	1	1	yes	characteristic
243	C₂⁶	#120	1	1	yes	characteristic
244	C₂⁶	#120	1	2	yes	complemented
245	C₂⁶	C₂²×D₄	1	1	yes	characteristic
246	C₂⁶	C₂²×D₄	1	1	yes	characteristic
247	C₂⁶	C₂²×D₄	1	1	yes	characteristic
248	C₂⁶	C₂²×D₄	1	2	yes	—
249	C₂⁶	C₂²×D₄	1	2	yes	complemented
250	C₂⁶	C₂⁵	1	1	yes	characteristic
251	C₂×H(5,𝔽₂)	#120	1	4	yes	—
252	C₂³×Q₈	#120	1	1	yes	characteristic
253	C₂³×Q₈	#120	1	1	yes	characteristic
254	C₂³×D₄	#120	1	1	yes	characteristic
255	C₂³×D₄	#120	1	1	yes	characteristic
256	C₂³×D₄	#120	1	1	yes	characteristic
257	C₂³×D₄	#120	1	1	yes	characteristic
258	C₂³×D₄	#120	1	1	yes	characteristic
259	C₂³×D₄	#120	1	1	yes	characteristic
260	C₂³×D₄	#120	1	2	yes	complemented
261	C₂³×D₄	#120	1	2	yes	complemented
262	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
263	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
264	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
265	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
266	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
267	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
268	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
269	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
270	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
271	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
272	C₂³×D₄	C₂²×D₄	1	2	yes	—
273	C₂³×D₄	C₂²×D₄	1	2	yes	—
274	C₂³×D₄	C₂²×D₄	1	4	yes	—
275	C₂³×D₄	C₂²×D₄	1	4	yes	—
276	C₂³×D₄	C₂²×D₄	1	4	yes	—
277	C₂³×D₄	C₂²×D₄	1	4	yes	—
278	C₂³×D₄	C₂²×D₄	1	4	yes	—
279	C₂³×D₄	C₂²×D₄	1	4	yes	—
280	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
281	C₂³×D₄	C₂²×D₄	1	2	yes	—
282	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
283	C₂³×D₄	C₂²×D₄	1	4	yes	—
284	C₂³×D₄	C₂²×D₄	1	4	yes	—
285	C₂³×D₄	H(5,𝔽₂)	1	4	yes	—
286	C₂⁴×C₄	#120	1	1	yes	characteristic
287	C₂⁴×C₄	#120	1	1	yes	characteristic
288	C₂⁴×C₄	#120	1	1	yes	characteristic
289	C₂⁴×C₄	#120	1	1	yes	characteristic
290	C₂⁴×C₄	#120	1	1	yes	characteristic
291	C₂⁴×C₄	#120	1	1	yes	characteristic
292	C₂⁴×C₄	#120	1	2	yes	complemented
293	C₂⁴×C₄	#120	1	4	yes	complemented
294	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
295	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
296	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
297	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
298	C₂⁴×C₄	C₂²×D₄	1	2	yes	complemented
299	#534	#120	1	8	yes	—
300	C₂×#123	#120	1	4	yes	complemented
301	C₂×#123	#120	1	2	yes	complemented
302	C₂×#123	#120	1	2	yes	complemented
303	C₂×#120	#120	1	2	yes	—
304	C₂×#120	#120	1	4	yes	—
305	C₂×#120	#120	1	2	yes	—
306	C₂×#120	#120	1	2	yes	—
307	C₂×#120	#120	1	4	yes	—
308	C₂×#120	#120	1	2	yes	—
309	C₂×#120	#120	1	2	yes	complemented
310	C₂×#120	#120	1	4	yes	complemented
311	C₂×#120	#120	1	2	yes	complemented
312	C₂×#120	C₂²×D₄	1	8	yes	—
313	C₂×#120	H(5,𝔽₂)	1	8	yes	—
314	#518	#120	1	4	yes	—
315	C₂²×C₄⋊C₄	#120	1	4	yes	complemented
316	C₂²×C₄⋊C₄	#120	1	4	yes	complemented
317	C₂²×C₂²⋊C₄	#120	1	4	yes	complemented
318	C₂²×C₂²⋊C₄	#120	1	4	yes	complemented
319	C₂²×C₂²⋊C₄	#120	1	4	yes	complemented
320	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
321	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
322	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
323	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
324	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
325	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
326	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
327	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
328	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
329	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
330	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	complemented
331	#386	#120	1	4	yes	—
332	#386	#120	1	4	yes	—
333	#386	#120	1	4	yes	—
334	#386	#120	1	4	yes	—
335	#386	#120	1	4	yes	complemented
336	#386	#120	1	4	yes	complemented
337	#386	#120	1	4	yes	complemented
338	#386	#120	1	4	yes	complemented
339	#379	C₂²×D₄	1	4	yes	—
340	#379	C₂²×D₄	1	4	yes	—
341	#379	C₂²×D₄	1	4	yes	—
342	#379	C₂²×D₄	1	4	yes	—
343	#379	C₂²×D₄	1	8	yes	complemented
344	C₂⁵	B(4,𝔽₂)	1	4	yes	complemented
345	C₂⁵	C₂×#120	1	1	yes	characteristic
346	C₂⁵	C₂×#120	1	2	yes	—
347	C₂⁵	C₂×#120	1	2	yes	—
348	C₂⁵	C₂×#120	1	1	yes	characteristic
349	C₂⁵	C₂×#120	1	1	yes	characteristic
350	C₂⁵	C₂×#120	1	1	yes	characteristic
351	C₂⁵	C₂×#120	1	1	yes	characteristic
352	C₂⁵	C₂×#120	1	1	yes	characteristic
353	C₂⁵	C₂×#120	1	2	yes	—
354	C₂⁵	C₂×#120	1	2	yes	—
355	C₂⁵	C₂×#120	1	2	yes	—
356	C₂⁵	C₂×#120	1	2	yes	—
357	C₂⁵	C₂×#120	1	2	yes	—
358	C₂⁵	D₄²	1	4	yes	—
359	C₂⁵	C₂³×D₄	1	1	yes	characteristic
360	C₂⁵	C₂³×D₄	1	1	yes	characteristic
361	C₂⁵	C₂³×D₄	1	1	yes	characteristic
362	C₂⁵	C₂³×D₄	1	4	yes	—
363	C₂⁵	C₂³×D₄	1	2	yes	—
364	C₂⁵	C₂×H(5,𝔽₂)	1	4	yes	—
365	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
366	C₂²×D₄	B(4,𝔽₂)	1	4	yes	complemented
367	C₂²×D₄	C₂×#120	1	2	yes	—
368	C₂²×D₄	C₂×#120	1	4	yes	—
369	C₂²×D₄	C₂×#120	1	2	yes	—
370	C₂²×D₄	C₂×#120	1	2	yes	—
371	C₂²×D₄	C₂×#120	1	4	yes	—
372	C₂²×D₄	C₂×#120	1	2	yes	—
373	C₂²×D₄	C₂×#120	1	2	yes	—
374	C₂²×D₄	C₂×#120	1	2	yes	—
375	C₂²×D₄	C₂×#120	1	4	yes	—
376	C₂²×D₄	#534	1	2	yes	—
377	C₂²×D₄	#534	1	2	yes	—
378	C₂²×D₄	#534	1	4	yes	—
379	C₂²×D₄	D₄²	1	4	yes	—
380	C₂²×D₄	D₄²	1	4	yes	—
381	C₂²×D₄	D₄²	1	16	yes	—
382	C₂³×C₄	C₂×#120	1	1	yes	characteristic
383	C₂³×C₄	C₂×#120	1	1	yes	characteristic
384	C₂³×C₄	C₂×#120	1	1	yes	characteristic
385	C₂³×C₄	C₂×#120	1	1	yes	characteristic
386	C₂³×C₄	C₂×#120	1	1	yes	characteristic
387	C₂³×C₄	C₂×#120	1	1	yes	characteristic
388	C₂³×C₄	C₂×#120	1	2	yes	—
389	C₂³×C₄	C₂×#120	1	2	yes	—
390	C₂³×C₄	C₂×#120	1	4	yes	—
391	C₂³×C₄	C₂×#120	1	4	yes	—
392	C₂³×C₄	C₂×#120	1	4	yes	—
393	C₂³×C₄	C₂×#120	1	4	yes	—
394	C₂³×C₄	C₂×#120	1	2	yes	—
395	C₂³×C₄	C₂×#120	1	4	yes	—
396	C₂³×C₄	D₄²	1	4	yes	—
397	C₂×C₂²⋊C₄	C₂×#120	1	4	yes	—
398	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
399	C₂×C₂²⋊C₄	C₂×#120	1	4	yes	—
400	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
401	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
402	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
403	C₂×C₂²⋊C₄	C₂×#120	1	4	yes	—
404	C₂×C₂²⋊C₄	#534	1	4	yes	—
405	C₂×C₂²⋊C₄	D₄²	1	16	yes	—
406	C₂⁴	#2403	1	2	yes	—
407	C₂⁴	#2403	1	2	yes	—
408	C₂⁴	#2403	1	4	yes	—
409	C₂⁴	#2846	1	1	yes	characteristic
410	C₂⁴	#2846	1	2	yes	—
411	C₂⁴	#2846	1	1	yes	characteristic
412	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
413	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
414	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
415	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
416	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
417	C₂⁴	#3026	1	2	yes	—
418	C₂⁴	#3026	1	2	yes	—
419	C₂⁴	C₂²×#120	1	2	yes	—
420	C₂⁴	C₂²×#120	1	2	yes	—
421	C₂⁴	C₂²×#120	1	2	yes	—
422	C₂⁴	C₂²×#120	1	1	yes	characteristic
423	C₂⁴	C₂²×#120	1	1	yes	characteristic
424	C₂⁴	C₂×#534	1	1	yes	characteristic
425	C₂⁴	C₂×#534	1	2	yes	—
426	C₂⁴	C₂×D₄²	1	2	yes	—
427	C₂⁴	C₂×D₄²	1	2	yes	—
428	C₂⁴	C₂×D₄²	1	8	yes	—
429	C₂⁴	#3484	1	2	yes	—
430	C₂⁴	#3484	1	2	yes	—
431	C₂⁴	#3484	1	8	yes	—
432	C₂²×C₄	#2403	1	2	yes	—
433	C₂²×C₄	#2403	1	2	yes	—
434	C₂²×C₄	#2403	1	8	yes	—
435	C₂²×C₄	#2403	1	4	yes	—
436	C₂²×C₄	#2846	1	2	yes	—
437	C₂²×C₄	#2846	1	2	yes	—
438	C₂²×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
439	C₂³	#23900	1	4	yes	—
440	C₂³	#32898	1	2	yes	—
441	C₂³	#32898	1	4	yes	—
442	C₂³	#32898	1	2	yes	—
443	C₂³	C₂×#2403	1	2	yes	—
444	C₂³	C₂×#2403	1	1	yes	characteristic
445	C₂³	#34980	1	2	yes	—
446	C₂³	#34980	1	1	yes	characteristic
447	C₂³	D₄×#120	1	4	yes	—
448	C₂³	D₄×#120	1	4	yes	—
449	C₂³	C₂×#2846	1	1	yes	characteristic
450	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
451	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
452	C₂³	C₂×#3026	1	1	yes	characteristic
453	C₂³	C₂×#3026	1	1	yes	characteristic
454	C₂²	#612424	1	1	yes	characteristic
455	C₂²	C₂×#23900	1	1	yes	characteristic
456	C₂²	#6437621	1	1	yes	characteristic
457	C₂²	#6470225	1	1	yes	characteristic
458	C₂²	#6470225	1	1	yes	characteristic
459	C₂²	C₂×#32898	1	1	yes	characteristic
460	C₂²	C₂×#32898	1	1	yes	characteristic
461	C₂	#72214832	1	1	yes	characteristic
462	C₂	#72234172	1	2	yes	—

	subgroup	G/H
center, socle	C₂²	#612424
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. #72258515	C₂	semidirect
2. #72258512	C₂	semidirect
3. #72240571	C₂	semidirect
4. #72240111	C₂	semidirect
5. #72237496	C₂	semidirect
6. #72236600	C₂	semidirect
7. #72236586	C₂	semidirect
8. #72235219	C₂	semidirect
9. #72234959	C₂	semidirect
10. #72233581	C₂	semidirect
11. #72226123	C₂	semidirect
12. #72225690	C₂	semidirect
13. #72225610	C₂	semidirect
14. #72219460	C₂	semidirect
15. C₂×#62817	C₂²	semidirect
17. C₂×#62842	C₂²	semidirect
18. #7752089	C₂²	semidirect
20. #7643563	C₂²	semidirect
21. #7642244	C₂²	semidirect
23. #7630442	C₂²	semidirect
25. #7626386	C₂²	semidirect
26. #6628892	C₂²	semidirect
27. C₂×#32898	C₂²	semidirect
28. #6470225	C₂²	semidirect
30. #6437621	C₂²	semidirect
31. #6437621	C₂²	semidirect
32. #6437621	C₂²	semidirect
33. C₂×#20984	C₂²	semidirect
34. C₂×#20585	C₂²	semidirect
35. #616960	C₂²	semidirect
36. #394061	C₂²	semidirect
37. #393929	C₂²	semidirect
38. #392699	C₂²	semidirect
39. #392658	C₂²	semidirect
40. #392111	C₂²	semidirect
41. #392111	C₂²	semidirect
42. #359442	C₂²	semidirect
43. #359434	C₂²	semidirect
44. #233549	C₂²	semidirect
45. #233541	C₂²	semidirect
46. #201687	C₂²	semidirect
47. #201678	C₂²	semidirect
48. C₂×#9495	C₂²	semidirect
49. #188049	C₂²	semidirect
50. C₂×#8541	C₂²	semidirect
51. #187944	C₂²	semidirect
52. #187944	C₂²	semidirect
53. #187944	C₂²	semidirect
54. #187944	C₂²	semidirect
55. #187928	C₂²	semidirect
56. #115631	C₂²	semidirect
57. #115204	C₂²	semidirect
58. #115133	C₂²	semidirect
59. #111467	C₂²	semidirect
60. #107194	C₂²	semidirect
61. #107114	C₂²	semidirect
62. #105808	C₂²	semidirect
63. C₂³×H(5,𝔽₂)	D₄	semidirect
65. C₂³×H(5,𝔽₂)	C₂³	semidirect
66. C₂×#3485	D₄	semidirect
67. C₂×#3485	D₄	semidirect
68. C₂×#3485	D₄	semidirect
69. C₂×#3485	D₄	semidirect
70. C₂×#3484	D₄	semidirect
76. C₂²×#534	D₄	semidirect
79. C₂²×#534	C₂³	semidirect
80. C₂³×#120	D₄	semidirect
81. C₂³×#120	D₄	semidirect
83. C₂²×#518	D₄	semidirect
84. C₂²×#518	C₂³	semidirect
86. #37117	D₄	semidirect
87. #36721	D₄	semidirect
88. #36717	D₄	semidirect
89. #36714	D₄	semidirect
90. #35512	D₄	semidirect
91. #35355	D₄	semidirect
92. #35354	D₄	semidirect
93. #35346	D₄	semidirect
94. #35088	D₄	semidirect
95. #34980	D₄	semidirect
99. #34980	C₂³	semidirect
100. #34980	C₂³	semidirect
101. C₂×#2404	D₄	semidirect
102. C₂×#2404	D₄	semidirect
105. C₂×#2403	C₂³	semidirect
108. #34172	D₄	semidirect
109. #34171	D₄	semidirect
111. C₂×#2308	D₄	semidirect
112. C₂×#2308	D₄	semidirect
114. C₂×#2308	C₂³	semidirect
115. #23901	D₄	semidirect
116. #23900	D₄	semidirect
118. #21746	C₂³	semidirect
119. #21746	C₂³	semidirect
121. C₂×#1898	C₂³	semidirect
122. C₂×#1898	C₂³	semidirect
125. C₂×#1781	C₂³	semidirect
126. C₂×#1781	C₂³	semidirect
127. C₂×#1781	C₂³	semidirect
128. C₂×#1781	C₂³	semidirect
129. C₂×#1781	C₂³	semidirect
130. C₂×#1781	C₂³	semidirect
131. C₂×#1781	C₂³	semidirect
133. #14335	C₂³	semidirect
134. #13867	C₂³	semidirect
135. #10735	C₂³	semidirect
136. #10725	C₂³	semidirect
137. #8101	C₂³	semidirect
138. C₂×#1304	C₂³	semidirect
139. C₂⁷	C₂×D₄	semidirect
143. C₂²×H(5,𝔽₂)	C₂×D₄	semidirect
144. C₂²×H(5,𝔽₂)	C₂×D₄	semidirect
170. C₂×#534	C₂×D₄	semidirect
171. C₂×#534	C₂×D₄	semidirect
172. C₂×#534	C₂×D₄	semidirect
176. C₂²×#123	C₂×D₄	semidirect
177. C₂²×#123	C₂×D₄	semidirect
183. C₂²×#120	C₂×D₄	semidirect
184. C₂²×#120	C₂×D₄	semidirect
185. C₂²×#120	C₂×D₄	semidirect
186. C₂²×#120	C₂×D₄	semidirect
193. C₂×#518	C₂×D₄	semidirect
194. C₂×#518	C₂×D₄	semidirect
195. C₂×#518	C₂×D₄	semidirect
196. C₂×#518	C₂×D₄	semidirect
198. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
199. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
200. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
201. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
203. #2849	C₂×D₄	semidirect
204. #2846	C₂×D₄	semidirect
205. #2483	C₂×D₄	semidirect
208. #2405	C₂×D₄	semidirect
209. #2405	C₂×D₄	semidirect
210. #2405	C₂×D₄	semidirect
211. #2405	C₂×D₄	semidirect
218. #2403	C₂×D₄	semidirect
219. #2403	C₂×D₄	semidirect
220. #2403	C₂×D₄	semidirect
221. #2312	C₂×D₄	semidirect
222. #2312	C₂×D₄	semidirect
223. #2309	C₂×D₄	semidirect
226. #2308	C₂×D₄	semidirect
227. #2308	C₂×D₄	semidirect
230. C₂×#386	C₂×D₄	semidirect
231. C₂×#386	C₂×D₄	semidirect
232. C₂×#381	C₂×D₄	semidirect
233. C₂×#381	C₂×D₄	semidirect
234. C₂×#379	C₂×D₄	semidirect
240. #1898	C₂×D₄	semidirect
241. #1781	C₂×D₄	semidirect
244. C₂⁶	#120	semidirect
249. C₂⁶	C₂²×D₄	semidirect
260. C₂³×D₄	#120	semidirect
261. C₂³×D₄	#120	semidirect
292. C₂⁴×C₄	#120	semidirect
293. C₂⁴×C₄	#120	semidirect
298. C₂⁴×C₄	C₂²×D₄	semidirect
300. C₂×#123	#120	semidirect
301. C₂×#123	#120	semidirect
302. C₂×#123	#120	semidirect
309. C₂×#120	#120	semidirect
310. C₂×#120	#120	semidirect
311. C₂×#120	#120	semidirect
315. C₂²×C₄⋊C₄	#120	semidirect
316. C₂²×C₄⋊C₄	#120	semidirect
317. C₂²×C₂²⋊C₄	#120	semidirect
318. C₂²×C₂²⋊C₄	#120	semidirect
319. C₂²×C₂²⋊C₄	#120	semidirect
330. C₂²×C₂²⋊C₄	C₂²×D₄	semidirect
335. #386	#120	semidirect
336. #386	#120	semidirect
337. #386	#120	semidirect
338. #386	#120	semidirect
343. #379	C₂²×D₄	semidirect
344. C₂⁵	B(4,𝔽₂)	semidirect
366. C₂²×D₄	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
#72258515	2
#72258512	2
#72240571	2
#72240111	2
#72237496	2
#72236600	2
#72236586	2
#72235219	2
#72234959	2
#72233581	2
#72226123	2
#72225690	2
#72225610	2
#72219460	2