Subgroups — #72267708

Order 2048.

At least 8717 conjugacy classes of subgroups; only the 780 normal subgroups are shown.

The subgroup lattice has 458 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72267704	C₂	1	1	yes	maximal, characteristic, complemented
2	#72267467	C₂	1	1	yes	maximal, characteristic, complemented
3	#72267465	C₂	1	2	yes	maximal, complemented
4	#72267451	C₂	1	1	yes	maximal, characteristic, complemented
5	#72267448	C₂	1	2	yes	maximal, complemented
6	#72267447	C₂	1	2	yes	maximal, complemented
7	#72267284	C₂	1	2	yes	maximal, complemented
8	#72267275	C₂	1	2	yes	maximal, complemented
9	#72266879	C₂	1	2	yes	maximal, complemented
10	#72266869	C₂	1	2	yes	maximal, complemented
11	#72266862	C₂	1	1	yes	maximal, characteristic, complemented
12	#72266853	C₂	1	2	yes	maximal, complemented
13	#72266766	C₂	1	2	yes	maximal, complemented
14	#72266753	C₂	1	2	yes	maximal, complemented
15	#72266739	C₂	1	1	yes	maximal, characteristic, complemented
16	#72213520	C₂	1	2	yes	maximal, complemented
17	#72213149	C₂	1	2	yes	maximal, complemented
18	#72212205	C₂	1	1	yes	maximal, characteristic, complemented
19	#72210333	C₂	1	1	yes	maximal, characteristic
20	C₂⁴×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
21	C₂×#32892	C₂²	1	2	yes	—
22	C₂×#32892	C₂²	1	2	yes	—
23	C₂×#32892	C₂²	1	2	yes	—
24	C₂×#32889	C₂²	1	2	yes	—
25	C₂×#32889	C₂²	1	2	yes	—
26	C₂×#32889	C₂²	1	2	yes	—
27	C₂×#20617	C₂²	1	2	yes	—
28	C₂×#20617	C₂²	1	2	yes	—
29	C₂²×#1784	C₂²	1	1	yes	characteristic
30	#4963786	C₂²	1	1	yes	characteristic, complemented
31	#4941686	C₂²	1	1	yes	characteristic, complemented
32	#4933524	C₂²	1	1	yes	characteristic, complemented
33	#4933483	C₂²	1	1	yes	characteristic, complemented
34	#4312070	C₂²	1	1	yes	characteristic, complemented
35	#4311774	C₂²	1	1	yes	characteristic, complemented
36	#1505962	C₂²	1	1	yes	characteristic, complemented
37	#1494872	C₂²	1	1	yes	characteristic, complemented
38	#1425995	C₂²	1	1	yes	characteristic, complemented
39	#1424124	C₂²	1	1	yes	characteristic, complemented
40	#613102	C₂²	1	1	yes	characteristic
41	#613016	C₂²	1	1	yes	characteristic
42	#571072	C₂²	1	1	yes	characteristic, complemented
43	#570800	C₂²	1	1	yes	characteristic, complemented
44	#517416	C₂²	1	1	yes	characteristic
45	C₂×#13378	C₂²	1	4	yes	complemented
46	C₂×#13358	C₂²	1	4	yes	complemented
47	C₂×#13094	C₂²	1	2	yes	complemented
48	C₂×#13092	C₂²	1	2	yes	complemented
49	C₂×#13058	C₂²	1	4	yes	complemented
50	C₂×#13055	C₂²	1	4	yes	complemented
51	#392129	C₂²	1	2	yes	—
52	#392129	C₂²	1	2	yes	—
53	#392129	C₂²	1	2	yes	—
54	#392129	C₂²	1	2	yes	—
55	#392129	C₂²	1	2	yes	—
56	#392129	C₂²	1	2	yes	—
57	#392129	C₂²	1	2	yes	—
58	#392129	C₂²	1	2	yes	—
59	#392129	C₂²	1	2	yes	—
60	#392129	C₂²	1	2	yes	—
61	#392114	C₂²	1	1	yes	characteristic
62	#392114	C₂²	1	1	yes	characteristic
63	#148577	C₂²	1	2	yes	complemented
64	#148577	C₂²	1	2	yes	complemented
65	#148577	C₂²	1	2	yes	complemented
66	#148577	C₂²	1	2	yes	complemented
67	#148577	C₂²	1	2	yes	complemented
68	#148577	C₂²	1	2	yes	complemented
69	#148577	C₂²	1	2	yes	complemented
70	#148577	C₂²	1	2	yes	complemented
71	#148173	C₂²	1	4	yes	complemented
72	#148172	C₂²	1	4	yes	complemented
73	#148172	C₂²	1	4	yes	complemented
74	#148172	C₂²	1	4	yes	complemented
75	#148172	C₂²	1	4	yes	complemented
76	#148172	C₂²	1	4	yes	complemented
77	#147778	C₂²	1	4	yes	complemented
78	#147778	C₂²	1	4	yes	complemented
79	#147777	C₂²	1	4	yes	complemented
80	#147777	C₂²	1	4	yes	complemented
81	#147565	C₂²	1	2	yes	complemented
82	#147565	C₂²	1	2	yes	complemented
83	#147563	C₂²	1	2	yes	complemented
84	#147563	C₂²	1	2	yes	complemented
85	#147497	C₂²	1	4	yes	complemented
86	#147496	C₂²	1	4	yes	complemented
87	#146573	C₂²	1	2	yes	complemented
88	#146573	C₂²	1	2	yes	complemented
89	#146471	C₂²	1	2	yes	complemented
90	#146471	C₂²	1	2	yes	complemented
91	C₂³×2₋¹⁺⁴	C₂³	1	2	yes	—
92	C₂³×2₋¹⁺⁴	C₂³	1	2	yes	—
93	C₂³×2₋¹⁺⁴	C₂³	1	2	yes	—
94	C₂⁵×Q₈	C₂³	1	1	yes	characteristic
95	C₂²×#456	C₂³	1	4	yes	—
96	C₂²×#454	C₂³	1	4	yes	—
97	C₂³×#101	C₂³	1	2	yes	—
98	C₂×#2811	C₂³	1	1	yes	characteristic, complemented
99	C₂×#2731	C₂³	1	1	yes	characteristic, complemented
100	C₂×#2848	D₄	1	1	yes	characteristic
101	C₂×#2847	D₄	1	1	yes	characteristic
102	C₂×#2436	D₄	1	1	yes	characteristic
103	C₂×#2436	D₄	1	1	yes	characteristic
104	C₂×#2436	D₄	1	1	yes	characteristic
105	C₂×#2436	C₂³	1	1	yes	characteristic
106	C₂×#2436	C₂³	1	1	yes	characteristic
107	C₂×#2436	C₂³	1	1	yes	characteristic
108	C₂×#2434	D₄	1	1	yes	characteristic
109	C₂×#2434	D₄	1	1	yes	characteristic
110	C₂×#2434	D₄	1	1	yes	characteristic
111	C₂×#2434	C₂³	1	1	yes	characteristic
112	C₂×#2434	C₂³	1	1	yes	characteristic
113	C₂×#2434	C₂³	1	1	yes	characteristic
114	C₂×#2379	C₂³	1	1	yes	characteristic, complemented
115	C₂×#2369	C₂³	1	1	yes	characteristic, complemented
116	C₂×#2310	D₄	1	1	yes	characteristic
117	C₂×#2310	D₄	1	1	yes	characteristic
118	C₂×#2310	C₂³	1	1	yes	characteristic
119	C₂×#2310	C₂³	1	1	yes	characteristic
120	C₂×#2280	D₄	1	1	yes	characteristic
121	C₂×#2280	D₄	1	1	yes	characteristic
122	C₂²×#356	C₂³	1	4	yes	complemented
123	C₂²×#355	C₂³	1	4	yes	complemented
124	C₂×#1793	C₂³	1	4	yes	—
125	C₂×#1793	C₂³	1	4	yes	—
126	C₂×#1793	C₂³	1	4	yes	—
127	C₂×#1793	C₂³	1	4	yes	—
128	C₂×#1793	C₂³	1	4	yes	—
129	C₂×#1793	C₂³	1	4	yes	—
130	C₂×#1793	C₂³	1	4	yes	—
131	C₂×#1793	C₂³	1	4	yes	—
132	C₂×#1793	C₂³	1	4	yes	—
133	C₂×#1793	C₂³	1	4	yes	—
134	C₂×#1784	C₂³	1	2	yes	—
135	C₂×#1784	C₂³	1	2	yes	—
136	C₂×#1784	C₂³	1	2	yes	—
137	C₂×#1784	C₂³	1	2	yes	—
138	C₂×#1784	C₂³	1	2	yes	—
139	C₂×#1784	C₂³	1	2	yes	—
140	C₂×#1784	C₂³	1	2	yes	—
141	C₂×#1784	C₂³	1	2	yes	—
142	#14501	C₂³	1	1	yes	characteristic, complemented
143	#14501	C₂³	1	1	yes	characteristic, complemented
144	#14501	C₂³	1	1	yes	characteristic, complemented
145	#14501	C₂³	1	1	yes	characteristic, complemented
146	#14501	C₂³	1	1	yes	characteristic, complemented
147	#14492	C₂³	1	1	yes	characteristic, complemented
148	#14492	C₂³	1	1	yes	characteristic, complemented
149	#14467	C₂³	1	1	yes	characteristic, complemented
150	#14450	C₂³	1	1	yes	characteristic, complemented
151	#14450	C₂³	1	1	yes	characteristic, complemented
152	#13922	D₄	1	1	yes	characteristic
153	#13922	D₄	1	1	yes	characteristic
154	#13922	D₄	1	1	yes	characteristic
155	#13922	D₄	1	1	yes	characteristic
156	#13922	D₄	1	1	yes	characteristic
157	#13922	D₄	1	1	yes	characteristic
158	#13922	D₄	1	1	yes	characteristic
159	#13922	D₄	1	1	yes	characteristic
160	#13922	D₄	1	1	yes	characteristic
161	#13922	D₄	1	1	yes	characteristic
162	#13922	C₂³	1	1	yes	characteristic
163	#13922	C₂³	1	1	yes	characteristic
164	#13922	C₂³	1	1	yes	characteristic
165	#13922	C₂³	1	1	yes	characteristic
166	#13922	C₂³	1	1	yes	characteristic
167	#13922	C₂³	1	1	yes	characteristic
168	#13922	C₂³	1	1	yes	characteristic
169	#13922	C₂³	1	1	yes	characteristic
170	#13922	C₂³	1	1	yes	characteristic
171	#13922	C₂³	1	1	yes	characteristic
172	#13834	C₂³	1	1	yes	characteristic, complemented
173	#13826	C₂³	1	1	yes	characteristic, complemented
174	C₄×#379	D₄	1	1	yes	characteristic
175	C₄×#379	D₄	1	1	yes	characteristic
176	C₂×#1394	C₂³	1	4	yes	complemented
177	C₂×#1394	C₂³	1	4	yes	complemented
178	C₂×#1394	C₂³	1	4	yes	complemented
179	C₂×#1394	C₂³	1	4	yes	complemented
180	C₂×#1394	C₂³	1	4	yes	complemented
181	C₂×#1394	C₂³	1	4	yes	complemented
182	C₂×#1394	C₂³	1	4	yes	complemented
183	C₂×#1394	C₂³	1	4	yes	complemented
184	C₂×#1394	C₂³	1	4	yes	complemented
185	C₂×#1394	C₂³	1	4	yes	complemented
186	C₂²×2₋¹⁺⁴	#41	1	8	yes	—
187	C₂²×2₋¹⁺⁴	C₂⁴	1	4	yes	—
188	C₂⁴×Q₈	C₂×D₄	1	1	yes	characteristic
189	C₂⁴×Q₈	C₂×D₄	1	1	yes	characteristic
190	C₂⁴×Q₈	C₂×D₄	1	1	yes	characteristic
191	C₂⁴×Q₈	C₂×D₄	1	1	yes	characteristic
192	C₂⁴×Q₈	C₂×D₄	1	1	yes	characteristic
193	C₂⁴×Q₈	C₂×D₄	1	1	yes	characteristic
194	C₂⁴×Q₈	C₂×D₄	1	1	yes	characteristic
195	C₂⁴×Q₈	C₂×D₄	1	1	yes	characteristic
196	C₂⁴×Q₈	C₂×D₄	1	1	yes	characteristic
197	C₂⁴×Q₈	C₂⁴	1	1	yes	characteristic
198	C₂⁴×Q₈	C₂⁴	1	1	yes	characteristic
199	C₂⁴×Q₈	C₂⁴	1	1	yes	characteristic
200	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
201	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
202	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
203	C₂²×C₄⋊Q₈	C₂×D₄	1	1	yes	characteristic
204	C₂²×C₄⋊Q₈	C₂×D₄	1	1	yes	characteristic
205	C₂²×C₄⋊Q₈	C₂×D₄	1	1	yes	characteristic
206	C₂²×C₄⋊Q₈	C₂⁴	1	1	yes	characteristic
207	C₂²×#124	C₂×D₄	1	1	yes	characteristic
208	C₂²×#124	C₂×D₄	1	1	yes	characteristic
209	C₂²×#124	C₂×D₄	1	1	yes	characteristic
210	C₂²×#124	C₂⁴	1	1	yes	characteristic
211	C₂²×C₂²⋊Q₈	C₂×D₄	1	1	yes	characteristic
212	C₂²×C₂²⋊Q₈	C₂×D₄	1	1	yes	characteristic
213	C₂²×C₂²⋊Q₈	C₂×D₄	1	1	yes	characteristic
214	C₂²×#121	C₂×D₄	1	1	yes	characteristic
215	C₂²×#121	C₂×D₄	1	1	yes	characteristic
216	C₂²×#121	C₂×D₄	1	1	yes	characteristic
217	C₂²×#117	C₂×D₄	1	1	yes	characteristic
218	C₂²×#117	C₂×D₄	1	1	yes	characteristic
219	C₂²×#117	C₂×D₄	1	1	yes	characteristic
220	C₂²×#117	C₂×D₄	1	1	yes	characteristic
221	C₂²×#101	C₂⁴	1	4	yes	—
222	C₂²×#101	C₂⁴	1	4	yes	—
223	C₂²×#101	C₂⁴	1	4	yes	—
224	C₂×#391	C₂×D₄	1	1	yes	characteristic
225	C₂×#391	C₂×D₄	1	1	yes	characteristic
226	C₂×#391	C₂×D₄	1	1	yes	characteristic
227	C₂×#391	C₂×D₄	1	1	yes	characteristic
228	C₂×#391	C₂×D₄	1	1	yes	characteristic
229	C₂×#391	C₂×D₄	1	1	yes	characteristic
230	C₂×#391	C₂×D₄	1	1	yes	characteristic
231	C₂×#391	C₂×D₄	1	1	yes	characteristic
232	C₂×#391	C₂×D₄	1	1	yes	characteristic
233	C₂×#391	C₂×D₄	1	1	yes	characteristic
234	C₂×#391	C₂×D₄	1	1	yes	characteristic
235	C₂×#391	C₂×D₄	1	1	yes	characteristic
236	C₂×#391	C₂×D₄	1	1	yes	characteristic
237	C₂×#391	C₂×D₄	1	1	yes	characteristic
238	C₂×#391	C₂×D₄	1	1	yes	characteristic
239	C₂×#391	C₂×D₄	1	1	yes	characteristic
240	C₂×#391	C₂×D₄	1	1	yes	characteristic
241	C₂×#391	C₂×D₄	1	1	yes	characteristic
242	C₂×#391	C₂×D₄	1	1	yes	characteristic
243	C₂×#391	C₂×D₄	1	1	yes	characteristic
244	C₂×#391	C₂×D₄	1	1	yes	characteristic
245	C₂×#391	C₂×D₄	1	1	yes	characteristic
246	C₂×#391	C₂×D₄	1	1	yes	characteristic
247	C₂×#391	C₂×D₄	1	1	yes	characteristic
248	C₂×#391	C₂×D₄	1	1	yes	characteristic
249	C₂×#391	C₂×D₄	1	1	yes	characteristic
250	C₂×#391	C₂×D₄	1	1	yes	characteristic
251	C₂×#391	C₂×D₄	1	1	yes	characteristic
252	C₂×#391	C₂×D₄	1	1	yes	characteristic
253	C₂×#391	C₂×D₄	1	1	yes	characteristic
254	C₂×#391	C₂⁴	1	1	yes	characteristic
255	C₂×#391	C₂⁴	1	1	yes	characteristic
256	C₂×#391	C₂⁴	1	1	yes	characteristic
257	C₂×#391	C₂⁴	1	1	yes	characteristic
258	C₂×#391	C₂⁴	1	1	yes	characteristic
259	C₂×#391	C₂⁴	1	1	yes	characteristic
260	C₂×#391	C₂⁴	1	1	yes	characteristic
261	C₂×#391	C₂⁴	1	1	yes	characteristic
262	C₂×#391	C₂⁴	1	1	yes	characteristic
263	C₂×#391	C₂⁴	1	1	yes	characteristic
264	C₂×#380	C₂×D₄	1	1	yes	characteristic
265	C₂×#380	C₂×D₄	1	1	yes	characteristic
266	C₂×#380	C₂×D₄	1	1	yes	characteristic
267	C₂×#380	C₂×D₄	1	1	yes	characteristic
268	C₂×#380	C₂×D₄	1	1	yes	characteristic
269	C₂×#380	C₂×D₄	1	1	yes	characteristic
270	C₂×#380	C₂×D₄	1	1	yes	characteristic
271	C₂×#380	C₂×D₄	1	1	yes	characteristic
272	C₂×#380	C₂×D₄	1	1	yes	characteristic
273	C₂×#380	C₂×D₄	1	1	yes	characteristic
274	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
275	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
276	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
277	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
278	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
279	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
280	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
281	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
282	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
283	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
284	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
285	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
286	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
287	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
288	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
289	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
290	C₂⁶	#120	1	1	yes	characteristic
291	C₂×2₋¹⁺⁴	C₂×#41	1	8	yes	—
292	C₂×2₋¹⁺⁴	H(5,𝔽₂)	1	8	yes	—
293	C₂×2₋¹⁺⁴	H(5,𝔽₂)	1	8	yes	—
294	C₂³×Q₈	#120	1	1	yes	characteristic
295	C₂³×Q₈	#120	1	1	yes	characteristic
296	C₂³×Q₈	#120	1	1	yes	characteristic
297	C₂³×Q₈	#120	1	1	yes	characteristic
298	C₂³×Q₈	#120	1	1	yes	characteristic
299	C₂³×Q₈	#120	1	1	yes	characteristic
300	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
301	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
302	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
303	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
304	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
305	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
306	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
307	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
308	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
309	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
310	C₂³×Q₈	C₂×#41	1	4	yes	—
311	C₂³×Q₈	H(5,𝔽₂)	1	4	yes	—
312	C₂³×Q₈	C₂⁵	1	1	yes	characteristic
313	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
314	C₂⁴×C₄	#120	1	1	yes	characteristic
315	C₂⁴×C₄	#120	1	1	yes	characteristic
316	C₂⁴×C₄	#120	1	1	yes	characteristic
317	C₂⁴×C₄	#120	1	1	yes	characteristic
318	C₂⁴×C₄	#120	1	1	yes	characteristic
319	C₂⁴×C₄	#120	1	1	yes	characteristic
320	C₂⁴×C₄	#120	1	1	yes	characteristic
321	C₂⁴×C₄	#120	1	1	yes	characteristic
322	C₂⁴×C₄	#120	1	1	yes	characteristic
323	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
324	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
325	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
326	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
327	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
328	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
329	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
330	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
331	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
332	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
333	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
334	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
335	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
336	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
337	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
338	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
339	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
340	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
341	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
342	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
343	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
344	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
345	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
346	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
347	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
348	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
349	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
350	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
351	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
352	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
353	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
354	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
355	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
356	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
357	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
358	C₂⁵	C₂×#120	1	1	yes	characteristic
359	C₂⁵	C₂×#120	1	1	yes	characteristic
360	C₂⁵	C₂×#120	1	1	yes	characteristic
361	2₋¹⁺⁴	#538	1	16	yes	—
362	C₂²×Q₈	B(4,𝔽₂)	1	4	yes	—
363	C₂²×Q₈	B(4,𝔽₂)	1	4	yes	—
364	C₂²×Q₈	#525	1	2	yes	—
365	C₂²×Q₈	#535	1	2	yes	—
366	C₂²×Q₈	#546	1	4	yes	—
367	C₂²×Q₈	#546	1	4	yes	—
368	C₂²×Q₈	C₂²×#41	1	2	yes	—
369	C₂²×Q₈	C₂×H(5,𝔽₂)	1	2	yes	—
370	C₂²×Q₈	C₂×H(5,𝔽₂)	1	4	yes	—
371	C₂²×Q₈	C₂×H(5,𝔽₂)	1	4	yes	—
372	C₂³×C₄	B(4,𝔽₂)	1	4	yes	—
373	C₂³×C₄	C₂×#120	1	1	yes	characteristic
374	C₂³×C₄	C₂×#120	1	1	yes	characteristic
375	C₂³×C₄	C₂×#120	1	1	yes	characteristic
376	C₂³×C₄	C₂×#120	1	1	yes	characteristic
377	C₂³×C₄	C₂×#120	1	1	yes	characteristic
378	C₂³×C₄	C₂×#120	1	1	yes	characteristic
379	C₂³×C₄	C₂×#120	1	1	yes	characteristic
380	C₂³×C₄	C₂×#120	1	1	yes	characteristic
381	C₂³×C₄	C₂×#120	1	1	yes	characteristic
382	C₂³×C₄	#525	1	2	yes	—
383	C₂³×C₄	#535	1	2	yes	—
384	C₂³×C₄	#546	1	4	yes	—
385	C₂³×C₄	#546	1	4	yes	—
386	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
387	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
388	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
389	C₂⁴	#2404	1	2	yes	—
390	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
391	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
392	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
393	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
394	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
395	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
396	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
397	C₂⁴	C₂²×#120	1	1	yes	characteristic
398	C₂×Q₈	C₂×#538	1	4	yes	—
399	C₂×Q₈	#3490	1	4	yes	—
400	C₂×Q₈	#3532	1	4	yes	—
401	C₂×Q₈	#3532	1	4	yes	—
402	C₂²×C₄	#2404	1	2	yes	—
403	C₂²×C₄	#2404	1	2	yes	—
404	C₂²×C₄	#2404	1	2	yes	—
405	C₂²×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
406	C₂²×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
407	C₂²×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
408	C₂²×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
409	C₂²×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
410	C₂²×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
411	C₂²×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
412	C₂²×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
413	C₂²×C₄	C₂×#525	1	1	yes	characteristic
414	C₂²×C₄	C₂×#535	1	1	yes	characteristic
415	C₂²×C₄	C₂×#546	1	2	yes	—
416	C₂²×C₄	C₂×#546	1	2	yes	—
417	C₂²×C₄	#3484	1	2	yes	—
418	C₂²×C₄	#3484	1	2	yes	—
419	C₂²×C₄	#3484	1	2	yes	—
420	C₂²×C₄	#3484	1	2	yes	—
421	C₂²×C₄	#3484	1	2	yes	—
422	C₂²×C₄	#3484	1	2	yes	—
423	C₂³	#23984	1	2	yes	—
424	C₂³	#23984	1	2	yes	—
425	C₂³	#33568	1	2	yes	—
426	C₂³	#33569	1	2	yes	—
427	C₂³	C₂×#2404	1	1	yes	characteristic
428	C₂³	#35346	1	1	yes	characteristic
429	C₂³	#35346	1	1	yes	characteristic
430	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
431	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
432	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
433	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
434	C₂×C₄	#23984	1	4	yes	—
435	C₂×C₄	#34988	1	2	yes	—
436	C₂×C₄	#36703	1	2	yes	—
437	C₂×C₄	#37660	1	4	yes	—
438	C₂×C₄	#37660	1	4	yes	—
439	C₂²	#619644	1	1	yes	characteristic
440	C₂²	C₂×#23984	1	1	yes	characteristic
441	C₂²	C₂×#23984	1	1	yes	characteristic
442	C₂²	#6499867	1	1	yes	characteristic
443	C₂²	#6499867	1	1	yes	characteristic
444	C₂²	#6499867	1	1	yes	characteristic
445	C₂²	#6499867	1	1	yes	characteristic
446	C₂²	C₂×#33568	1	1	yes	characteristic
447	C₂²	C₂×#33569	1	1	yes	characteristic
448	C₂²	#7622904	1	1	yes	characteristic
449	C₂²	#7622904	1	1	yes	characteristic
450	C₂	#72210404	1	1	yes	characteristic
451	C₂	#72212257	1	1	yes	characteristic
452	C₂	#72213178	1	1	yes	characteristic
453	C₂	#72222883	1	1	yes	characteristic
454	C₂	#72267418	1	1	yes	characteristic
455	C₂	#72267535	1	1	yes	characteristic
456	C₂	#72267625	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂²×B(4,𝔽₂)
commutator, Frattini, cosocle	C₂³×Q₈	C₂⁵
prime radical	#72210333	C₂
LCS	G ▷ C₂³×Q₈ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₂⁶ ◁ C₂⁵×Q₈ ◁ G
LECS	G ▷ C₂³×Q₈ ▷ C₂² ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72267704	C₂	semidirect
2. #72267467	C₂	semidirect
3. #72267465	C₂	semidirect
4. #72267451	C₂	semidirect
5. #72267448	C₂	semidirect
6. #72267447	C₂	semidirect
7. #72267284	C₂	semidirect
8. #72267275	C₂	semidirect
9. #72266879	C₂	semidirect
10. #72266869	C₂	semidirect
11. #72266862	C₂	semidirect
12. #72266853	C₂	semidirect
13. #72266766	C₂	semidirect
14. #72266753	C₂	semidirect
15. #72266739	C₂	semidirect
16. #72213520	C₂	semidirect
17. #72213149	C₂	semidirect
18. #72212205	C₂	semidirect
30. #4963786	C₂²	semidirect
31. #4941686	C₂²	semidirect
32. #4933524	C₂²	semidirect
33. #4933483	C₂²	semidirect
34. #4312070	C₂²	semidirect
35. #4311774	C₂²	semidirect
36. #1505962	C₂²	semidirect
37. #1494872	C₂²	semidirect
38. #1425995	C₂²	semidirect
39. #1424124	C₂²	semidirect
42. #571072	C₂²	semidirect
43. #570800	C₂²	semidirect
45. C₂×#13378	C₂²	semidirect
46. C₂×#13358	C₂²	semidirect
47. C₂×#13094	C₂²	semidirect
48. C₂×#13092	C₂²	semidirect
49. C₂×#13058	C₂²	semidirect
50. C₂×#13055	C₂²	semidirect
63. #148577	C₂²	semidirect
64. #148577	C₂²	semidirect
65. #148577	C₂²	semidirect
66. #148577	C₂²	semidirect
67. #148577	C₂²	semidirect
68. #148577	C₂²	semidirect
69. #148577	C₂²	semidirect
70. #148577	C₂²	semidirect
71. #148173	C₂²	semidirect
72. #148172	C₂²	semidirect
73. #148172	C₂²	semidirect
74. #148172	C₂²	semidirect
75. #148172	C₂²	semidirect
76. #148172	C₂²	semidirect
77. #147778	C₂²	semidirect
78. #147778	C₂²	semidirect
79. #147777	C₂²	semidirect
80. #147777	C₂²	semidirect
81. #147565	C₂²	semidirect
82. #147565	C₂²	semidirect
83. #147563	C₂²	semidirect
84. #147563	C₂²	semidirect
85. #147497	C₂²	semidirect
86. #147496	C₂²	semidirect
87. #146573	C₂²	semidirect
88. #146573	C₂²	semidirect
89. #146471	C₂²	semidirect
90. #146471	C₂²	semidirect
98. C₂×#2811	C₂³	semidirect
99. C₂×#2731	C₂³	semidirect
114. C₂×#2379	C₂³	semidirect
115. C₂×#2369	C₂³	semidirect
122. C₂²×#356	C₂³	semidirect
123. C₂²×#355	C₂³	semidirect
142. #14501	C₂³	semidirect
143. #14501	C₂³	semidirect
144. #14501	C₂³	semidirect
145. #14501	C₂³	semidirect
146. #14501	C₂³	semidirect
147. #14492	C₂³	semidirect
148. #14492	C₂³	semidirect
149. #14467	C₂³	semidirect
150. #14450	C₂³	semidirect
151. #14450	C₂³	semidirect
172. #13834	C₂³	semidirect
173. #13826	C₂³	semidirect
176. C₂×#1394	C₂³	semidirect
177. C₂×#1394	C₂³	semidirect
178. C₂×#1394	C₂³	semidirect
179. C₂×#1394	C₂³	semidirect
180. C₂×#1394	C₂³	semidirect
181. C₂×#1394	C₂³	semidirect
182. C₂×#1394	C₂³	semidirect
183. C₂×#1394	C₂³	semidirect
184. C₂×#1394	C₂³	semidirect
185. C₂×#1394	C₂³	semidirect

Maximal subgroups

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

subgroup	index
#72267704	2
#72267467	2
#72267465	2
#72267451	2
#72267448	2
#72267447	2
#72267284	2
#72267275	2
#72266879	2
#72266869	2
#72266862	2
#72266853	2
#72266766	2
#72266753	2
#72266739	2
#72213520	2
#72213149	2
#72212205	2
#72210333	2