Subgroups — #72302102

Order 4096.

At least 10143 conjugacy classes of subgroups; only the 757 normal subgroups are shown.

The subgroup lattice has 415 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72302095	C₂	1	2	yes	maximal, complemented
2	#72302073	C₂	1	2	yes	maximal, complemented
3	#72302046	C₂	1	2	yes	maximal, complemented
4	#72302045	C₂²	1	2	yes	complemented
5	#72302013	C₂	1	2	yes	maximal, complemented
6	#72302012	C₂²	1	2	yes	complemented
7	#72266983	C₂	1	2	yes	maximal, complemented
8	#72266980	C₂	1	2	yes	maximal, complemented
9	#72266940	C₂²	1	2	yes	complemented
10	#72266920	C₂²	1	2	yes	complemented
11	#72266878	C₂²	1	2	yes	complemented
12	#72266878	C₂²	1	2	yes	complemented
13	#72266840	C₂²	1	2	yes	complemented
14	#72266811	C₂²	1	2	yes	complemented
15	#72234688	C₂	1	1	yes	maximal, characteristic
16	#72234688	C₂	1	1	yes	maximal, characteristic
17	#72234620	C₄	1	2	yes	complemented
18	#72234592	C₄	1	2	yes	complemented
19	#72233654	C₂²	1	2	yes	—
20	#72233654	C₂²	1	2	yes	—
21	#72225776	C₂²	1	2	yes	—
22	#72225776	C₂²	1	1	yes	characteristic
23	#72225776	C₂²	1	1	yes	characteristic
24	#72219311	C₄	1	2	yes	complemented
25	#72219309	C₂	1	1	yes	maximal, characteristic
26	#72219303	C₂²	1	2	yes	—
27	#72219302	C₂²	1	2	yes	—
28	#72219301	C₂²	1	1	yes	characteristic
29	#72219301	C₂²	1	1	yes	characteristic
30	#72219301	C₂²	1	2	yes	—
31	#72219301	C₂²	1	1	yes	characteristic
32	#72219299	C₂²	1	1	yes	characteristic
33	C₂×#7670203	C₂²	1	1	yes	characteristic
34	#72218518	C₄	1	2	yes	complemented
35	C₂²×#3484	C₂³	1	1	yes	characteristic
36	C₂²×#3484	C₂³	1	1	yes	characteristic
37	C₂⁴×#120	C₂×C₄	1	1	yes	characteristic
38	C₂⁴×#120	D₄	1	1	yes	characteristic
39	C₂²×#2846	Q₈	1	1	yes	characteristic
40	C₂×#35390	Q₈	1	1	yes	characteristic
41	C₂×#35348	C₂×C₄	1	1	yes	characteristic
42	C₂×#35348	D₄	1	1	yes	characteristic
43	C₂×#35346	C₂³	1	1	yes	characteristic
44	C₂×#34981	Q₈	1	1	yes	characteristic
45	C₂×#34981	Q₈	1	1	yes	characteristic
46	C₂×#34980	C₂×C₄	1	1	yes	characteristic
47	C₂×#34980	D₄	1	1	yes	characteristic
48	C₂×#34198	C₂×C₄	1	1	yes	characteristic
49	C₂×#34198	D₄	1	1	yes	characteristic
50	#6370704	C₂³	1	2	yes	—
51	#6370693	C₂³	1	2	yes	—
52	#6370693	C₂³	1	2	yes	—
53	#6370693	C₂³	1	2	yes	—
54	#6370693	C₂³	1	2	yes	—
55	#6370693	C₂³	1	2	yes	—
56	#494700	D₄	1	8	yes	—
57	#392231	C₂×C₄	1	2	yes	—
58	#392231	C₂×C₄	1	2	yes	—
59	#392109	C₂×C₄	1	2	yes	—
60	#392109	C₂×C₄	1	2	yes	—
61	#359501	D₄	1	4	yes	—
62	#359501	D₄	1	4	yes	—
63	#359442	D₄	1	4	yes	—
64	#359442	D₄	1	4	yes	—
65	#190116	C₂×C₄	1	4	yes	—
66	#188049	C₂×C₄	1	4	yes	—
67	C₂×#8541	C₂×C₄	1	4	yes	—
68	C₂×#8541	C₂×C₄	1	4	yes	—
69	C₂⁸	C₄⋊C₄	1	1	yes	characteristic, complemented
70	C₂³×H(5,𝔽₂)	C₂⁴	1	1	yes	characteristic
71	C₂⁵×D₄	C₂²×C₄	1	1	yes	characteristic
72	C₂⁵×D₄	C₂×D₄	1	1	yes	characteristic
73	C₂²×#535	#41	1	2	yes	—
74	C₂²×#535	#41	1	2	yes	—
75	C₂²×#534	C₄⋊C₄	1	1	yes	characteristic, complemented
76	C₂²×#534	C₂²×C₄	1	1	yes	characteristic
77	C₂²×#534	C₂×D₄	1	2	yes	—
78	C₂²×#534	C₂×D₄	1	1	yes	characteristic
79	C₂²×#534	C₂×D₄	1	2	yes	—
80	C₂²×#534	C₂×Q₈	1	1	yes	characteristic
81	C₂²×#534	C₂×Q₈	1	1	yes	characteristic
82	C₂²×#525	#41	1	2	yes	—
83	C₂²×#525	#41	1	2	yes	—
84	C₂³×#120	C₄⋊C₄	1	1	yes	characteristic, complemented
85	C₂³×#120	C₄⋊C₄	1	1	yes	characteristic, complemented
86	C₂³×#120	C₄⋊C₄	1	1	yes	characteristic, complemented
87	C₂³×#120	C₄⋊C₄	1	1	yes	characteristic, complemented
88	C₂³×#120	C₂²×C₄	1	1	yes	characteristic
89	C₂³×#120	C₂²×C₄	1	1	yes	characteristic
90	C₂³×#120	C₂×D₄	1	2	yes	—
91	C₂³×#120	C₂×D₄	1	1	yes	characteristic
92	C₂³×#120	C₂×D₄	1	1	yes	characteristic
93	C₂³×#120	C₂×D₄	1	2	yes	—
94	C₂³×#120	C₂×Q₈	1	1	yes	characteristic
95	C₂³×#120	C₂×Q₈	1	1	yes	characteristic
96	C₂³×#120	C₂×Q₈	1	1	yes	characteristic
97	C₂²×#518	C₂²×C₄	1	1	yes	characteristic
98	C₂²×#518	C₂×D₄	1	1	yes	characteristic
99	C₂⁴×C₂²⋊C₄	C₄⋊C₄	1	1	yes	characteristic, complemented
100	C₂⁴×C₂²⋊C₄	C₄⋊C₄	1	1	yes	characteristic, complemented
101	C₂×#2883	C₂×D₄	1	4	yes	—
102	#35346	C₂×D₄	1	4	yes	—
103	#35346	#41	1	4	yes	—
104	#34171	C₂×D₄	1	4	yes	—
105	#34171	C₂×D₄	1	4	yes	—
106	C₂×#2315	C₄⋊C₄	1	1	yes	characteristic, complemented
107	C₂×#2315	C₄⋊C₄	1	1	yes	characteristic, complemented
108	C₂×#2308	C₄⋊C₄	1	1	yes	characteristic, complemented
109	C₂×#2308	C₄⋊C₄	1	1	yes	characteristic, complemented
110	C₂×#2308	C₂²×C₄	1	1	yes	characteristic
111	C₂×#2308	C₂×D₄	1	1	yes	characteristic
112	C₂×#2308	C₂×Q₈	1	1	yes	characteristic
113	C₂²×#379	C₄⋊C₄	1	1	yes	characteristic, complemented
114	C₂²×#379	C₄⋊C₄	1	1	yes	characteristic, complemented
115	C₂²×#379	C₄⋊C₄	1	1	yes	characteristic, complemented
116	C₂×#2273	C₄⋊C₄	1	1	yes	characteristic, complemented
117	#20592	C₂×D₄	1	4	yes	—
118	C₂×#1781	C₂²⋊C₄	1	4	yes	complemented
119	C₂×#1781	C₂²×C₄	1	4	yes	—
120	C₂×#1781	C₂²×C₄	1	4	yes	—
121	C₂×#1781	C₂×D₄	1	4	yes	—
122	C₂×#1781	C₂×D₄	1	4	yes	—
123	#14679	C₂²⋊C₄	1	4	yes	complemented
124	#10735	C₂²⋊C₄	1	8	yes	complemented
125	C₂⁷	C₂×C₂²⋊C₄	1	1	yes	characteristic
126	C₂⁷	C₂×C₄⋊C₄	1	1	yes	characteristic
127	C₂⁷	C₂×C₄⋊C₄	1	1	yes	characteristic
128	C₂⁷	C₂×C₄⋊C₄	1	1	yes	characteristic
129	C₂⁷	#120	1	1	yes	characteristic
130	C₂²×H(5,𝔽₂)	C₂²×D₄	1	2	yes	—
131	C₂²×H(5,𝔽₂)	C₂×#41	1	2	yes	—
132	C₂²×H(5,𝔽₂)	H(5,𝔽₂)	1	2	yes	—
133	C₂²×H(5,𝔽₂)	H(5,𝔽₂)	1	1	yes	characteristic
134	C₂²×H(5,𝔽₂)	H(5,𝔽₂)	1	1	yes	characteristic
135	C₂²×H(5,𝔽₂)	H(5,𝔽₂)	1	2	yes	—
136	C₂²×H(5,𝔽₂)	H(5,𝔽₂)	1	2	yes	—
137	C₂²×H(5,𝔽₂)	H(5,𝔽₂)	1	2	yes	—
138	C₂²×H(5,𝔽₂)	H(5,𝔽₂)	1	1	yes	characteristic
139	C₂²×H(5,𝔽₂)	H(5,𝔽₂)	1	1	yes	characteristic
140	C₂³×#41	C₂×#41	1	2	yes	—
141	C₂³×#41	C₂×#41	1	2	yes	—
142	C₂³×#41	H(5,𝔽₂)	1	2	yes	—
143	C₂⁴×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
144	C₂⁴×D₄	C₂×C₄⋊C₄	1	1	yes	characteristic
145	C₂⁴×D₄	C₂×C₄⋊C₄	1	1	yes	characteristic
146	C₂⁴×D₄	#117	1	1	yes	characteristic
147	C₂⁴×D₄	#120	1	1	yes	characteristic
148	C₂⁴×D₄	#123	1	1	yes	characteristic
149	C₂⁴×D₄	C₂³×C₄	1	1	yes	characteristic
150	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
151	C₂⁴×D₄	C₂²×D₄	1	2	yes	—
152	C₂⁴×D₄	C₂²×D₄	1	2	yes	—
153	C₂⁴×D₄	C₂²×Q₈	1	1	yes	characteristic
154	C₂⁴×D₄	H(5,𝔽₂)	1	2	yes	—
155	C₂⁵×C₄	#117	1	1	yes	characteristic
156	C₂⁵×C₄	#123	1	1	yes	characteristic
157	C₂²×#123	C₄×D₄	1	2	yes	—
158	C₂²×#123	#121	1	2	yes	—
159	C₂²×#123	C₂²⋊Q₈	1	2	yes	—
160	C₂²×#123	C₂²⋊Q₈	1	2	yes	—
161	C₂²×#120	C₄×D₄	1	2	yes	—
162	C₂²×#120	C₄×D₄	1	2	yes	—
163	C₂²×#120	C₄×D₄	1	4	yes	—
164	C₂²×#120	C₄×D₄	1	2	yes	—
165	C₂²×#120	#120	1	2	yes	—
166	C₂²×#120	#121	1	2	yes	—
167	C₂²×#120	#121	1	2	yes	—
168	C₂²×#120	#121	1	2	yes	—
169	C₂²×#120	C₂²⋊Q₈	1	2	yes	—
170	C₂²×#120	C₂²⋊Q₈	1	2	yes	—
171	C₂²×#120	C₂²⋊Q₈	1	2	yes	—
172	C₂²×#120	C₂²⋊Q₈	1	2	yes	—
173	C₂²×#120	C₂²⋊Q₈	1	2	yes	—
174	C₂²×#120	C₂²⋊Q₈	1	2	yes	—
175	C₂²×#120	C₂²⋊Q₈	1	4	yes	—
176	C₂²×#120	#123	1	2	yes	—
177	C₂²×#117	#117	1	2	yes	—
178	C₂²×#117	#123	1	2	yes	—
179	C₂³×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
180	C₂³×C₂²⋊C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
181	C₂³×C₂²⋊C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
182	C₂³×C₂²⋊C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
183	C₂³×C₂²⋊C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
184	C₂³×C₂²⋊C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
185	C₂³×C₂²⋊C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
186	C₂³×C₂²⋊C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
187	C₂³×C₂²⋊C₄	#120	1	2	yes	—
188	#2308	C₄×D₄	1	4	yes	—
189	#2308	#120	1	2	yes	—
190	#2308	C₂²⋊Q₈	1	4	yes	—
191	#2308	#123	1	2	yes	—
192	C₂×#379	C₂×C₂²⋊C₄	1	8	yes	—
193	C₂⁶	#380	1	1	yes	characteristic
194	C₂⁶	#380	1	1	yes	characteristic
195	C₂⁶	#380	1	1	yes	characteristic
196	C₂⁶	#385	1	1	yes	characteristic
197	C₂⁶	#385	1	1	yes	characteristic
198	C₂⁶	#385	1	1	yes	characteristic
199	C₂⁶	#385	1	2	yes	—
200	C₂⁶	C₂²×C₂²⋊C₄	1	1	yes	characteristic
201	C₂⁶	C₂²×C₄⋊C₄	1	1	yes	characteristic
202	C₂⁶	C₂×#120	1	1	yes	characteristic
203	C₂⁶	#543	1	1	yes	characteristic
204	C₂⁶	D₄²	1	2	yes	—
205	C₂²×#41	#534	1	2	yes	—
206	C₂²×#41	#535	1	2	yes	—
207	C₂²×#41	#538	1	2	yes	—
208	C₂²×#41	#538	1	2	yes	—
209	C₂²×#41	#538	1	2	yes	—
210	C₂²×#41	#538	1	2	yes	—
211	C₂²×#41	#538	1	2	yes	—
212	C₂²×#41	#538	1	2	yes	—
213	C₂²×#41	#538	1	2	yes	—
214	C₂²×#41	#538	1	2	yes	—
215	C₂²×#41	#538	1	2	yes	—
216	C₂²×#41	#538	1	2	yes	—
217	C₂²×#41	#546	1	2	yes	—
218	C₂²×#41	#546	1	2	yes	—
219	C₂²×#41	#546	1	2	yes	—
220	C₂²×#41	#546	1	2	yes	—
221	C₂²×#41	#551	1	2	yes	—
222	C₂²×#41	#551	1	2	yes	—
223	C₂²×#41	#551	1	2	yes	—
224	C₂²×#41	#551	1	2	yes	—
225	C₂²×#41	#560	1	2	yes	—
226	C₂²×#41	#560	1	2	yes	—
227	C₂²×#41	#560	1	2	yes	—
228	C₂²×#41	#560	1	2	yes	—
229	C₂³×Q₈	#551	1	2	yes	—
230	C₂³×D₄	C₂×C₄×D₄	1	2	yes	—
231	C₂³×D₄	C₂×C₄×D₄	1	2	yes	—
232	C₂³×D₄	#518	1	1	yes	characteristic
233	C₂³×D₄	#518	1	1	yes	characteristic
234	C₂³×D₄	#518	1	1	yes	characteristic
235	C₂³×D₄	#518	1	1	yes	characteristic
236	C₂³×D₄	#518	1	2	yes	—
237	C₂³×D₄	#518	1	2	yes	—
238	C₂³×D₄	C₂×#120	1	1	yes	characteristic
239	C₂³×D₄	C₂×#121	1	2	yes	—
240	C₂³×D₄	C₂×C₂²⋊Q₈	1	2	yes	—
241	C₂³×D₄	C₂×C₂²⋊Q₈	1	2	yes	—
242	C₂³×D₄	C₂×C₂²⋊Q₈	1	2	yes	—
243	C₂³×D₄	C₂×#123	1	1	yes	characteristic
244	C₂³×D₄	#534	1	2	yes	—
245	C₂³×D₄	#534	1	2	yes	—
246	C₂³×D₄	#534	1	1	yes	characteristic
247	C₂³×D₄	#534	1	2	yes	—
248	C₂³×D₄	#534	1	2	yes	—
249	C₂³×D₄	#534	1	2	yes	—
250	C₂³×D₄	#534	1	2	yes	—
251	C₂³×D₄	#534	1	2	yes	—
252	C₂³×D₄	#534	1	2	yes	—
253	C₂³×D₄	#534	1	1	yes	characteristic
254	C₂³×D₄	#535	1	2	yes	—
255	C₂³×D₄	#535	1	2	yes	—
256	C₂³×D₄	#535	1	2	yes	—
257	C₂³×D₄	#535	1	2	yes	—
258	C₂³×D₄	#535	1	2	yes	—
259	C₂³×D₄	#538	1	2	yes	—
260	C₂³×D₄	#538	1	2	yes	—
261	C₂³×D₄	#543	1	1	yes	characteristic
262	C₂³×D₄	#543	1	1	yes	characteristic
263	C₂³×D₄	#543	1	1	yes	characteristic
264	C₂³×D₄	#543	1	1	yes	characteristic
265	C₂³×D₄	#543	1	2	yes	—
266	C₂³×D₄	D₄²	1	2	yes	—
267	C₂³×D₄	D₄²	1	2	yes	—
268	C₂³×D₄	D₄²	1	2	yes	—
269	C₂³×D₄	D₄²	1	2	yes	—
270	C₂³×D₄	D₄²	1	2	yes	—
271	C₂³×D₄	#546	1	2	yes	—
272	C₂³×D₄	#546	1	2	yes	—
273	C₂³×D₄	#546	1	2	yes	—
274	C₂³×D₄	#546	1	2	yes	—
275	C₂³×D₄	#546	1	2	yes	—
276	C₂³×D₄	#546	1	2	yes	—
277	C₂³×D₄	#560	1	2	yes	—
278	C₂³×D₄	#560	1	2	yes	—
279	C₂³×D₄	H(3,𝔽₄)	1	2	yes	—
280	C₂³×D₄	H(3,𝔽₄)	1	2	yes	—
281	C₂⁴×C₄	#380	1	1	yes	characteristic
282	C₂⁴×C₄	#385	1	1	yes	characteristic
283	C₂⁴×C₄	C₂×#117	1	1	yes	characteristic
284	C₂⁴×C₄	C₂×#123	1	1	yes	characteristic
285	C₂⁴×C₄	#543	1	1	yes	characteristic
286	C₂⁴×C₄	#546	1	2	yes	—
287	C₂⁴×C₄	#546	1	2	yes	—
288	C₂⁴×C₄	#551	1	2	yes	—
289	C₂²×C₂²⋊C₄	#380	1	2	yes	—
290	C₂²×C₂²⋊C₄	#380	1	2	yes	—
291	C₂²×C₂²⋊C₄	#385	1	2	yes	—
292	C₂²×C₂²⋊C₄	#385	1	2	yes	—
293	C₂²×C₂²⋊C₄	#385	1	2	yes	—
294	C₂²×C₂²⋊C₄	#385	1	2	yes	—
295	C₂²×C₂²⋊C₄	#385	1	2	yes	—
296	C₂⁵	C₂×#380	1	1	yes	characteristic
297	C₂⁵	C₂×#385	1	1	yes	characteristic
298	C₂⁵	C₂×#385	1	1	yes	characteristic
299	C₂⁵	#2308	1	1	yes	characteristic
300	C₂⁵	#2309	1	1	yes	characteristic
301	C₂⁵	#2315	1	1	yes	characteristic
302	C₂⁵	#2315	1	1	yes	characteristic
303	C₂⁵	#2315	1	1	yes	characteristic
304	C₂⁵	#2315	1	1	yes	characteristic
305	C₂⁵	D₄×C₂²⋊C₄	1	2	yes	—
306	C₂⁵	D₄×C₂²⋊C₄	1	2	yes	—
307	C₂⁵	#2403	1	1	yes	characteristic
308	C₂⁵	#2405	1	1	yes	characteristic
309	C₂⁵	#2410	1	2	yes	—
310	C₂⁵	#2437	1	2	yes	—
311	C₂⁵	#2613	1	2	yes	—
312	C₂⁵	#2626	1	2	yes	—
313	C₂⁵	#2669	1	2	yes	—
314	C₂⁵	#2670	1	2	yes	—
315	C₂⁵	#2678	1	2	yes	—
316	C₂⁵	#2679	1	2	yes	—
317	C₂⁵	#2840	1	1	yes	characteristic
318	C₂⁵	#2842	1	1	yes	characteristic
319	C₂²×Q₈	#2685	1	2	yes	—
320	C₂²×Q₈	#2697	1	2	yes	—
321	C₂²×Q₈	#2735	1	2	yes	—
322	C₂²×Q₈	#2735	1	2	yes	—
323	C₂²×D₄	#2321	1	2	yes	—
324	C₂²×D₄	#2321	1	2	yes	—
325	C₂²×D₄	#2321	1	2	yes	—
326	C₂²×D₄	#2321	1	2	yes	—
327	C₂²×D₄	#2358	1	2	yes	—
328	C₂²×D₄	#2358	1	2	yes	—
329	C₂²×D₄	#2375	1	2	yes	—
330	C₂²×D₄	#2375	1	2	yes	—
331	C₂²×D₄	#2410	1	2	yes	—
332	C₂²×D₄	#2412	1	2	yes	—
333	C₂²×D₄	#2437	1	2	yes	—
334	C₂²×D₄	#2437	1	2	yes	—
335	C₂²×D₄	#2437	1	2	yes	—
336	C₂²×D₄	#2437	1	2	yes	—
337	C₂²×D₄	#2613	1	2	yes	—
338	C₂²×D₄	#2617	1	2	yes	—
339	C₂²×D₄	#2617	1	2	yes	—
340	C₂²×D₄	#2622	1	2	yes	—
341	C₂²×D₄	#2626	1	2	yes	—
342	C₂²×D₄	#2626	1	2	yes	—
343	C₂²×D₄	#2626	1	2	yes	—
344	C₂²×D₄	#2626	1	2	yes	—
345	C₂²×D₄	#2668	1	2	yes	—
346	C₂²×D₄	#2668	1	2	yes	—
347	C₂²×D₄	#2669	1	2	yes	—
348	C₂²×D₄	#2669	1	2	yes	—
349	C₂²×D₄	#2670	1	2	yes	—
350	C₂²×D₄	#2670	1	2	yes	—
351	C₂²×D₄	#2678	1	2	yes	—
352	C₂²×D₄	#2678	1	2	yes	—
353	C₂²×D₄	#2684	1	2	yes	—
354	C₂²×D₄	#2684	1	2	yes	—
355	C₂²×D₄	#2685	1	2	yes	—
356	C₂²×D₄	#2697	1	2	yes	—
357	C₂²×D₄	#2812	1	2	yes	—
358	C₂²×D₄	#2812	1	2	yes	—
359	C₂³×C₄	#2312	1	1	yes	characteristic
360	C₂³×C₄	#2312	1	1	yes	characteristic
361	C₂³×C₄	#2342	1	2	yes	—
362	C₂³×C₄	#2342	1	2	yes	—
363	C₂³×C₄	#2405	1	1	yes	characteristic
364	C₂³×C₄	#2412	1	2	yes	—
365	C₂³×C₄	#2437	1	2	yes	—
366	C₂³×C₄	#2483	1	1	yes	characteristic
367	C₂³×C₄	#2622	1	2	yes	—
368	C₂³×C₄	#2626	1	2	yes	—
369	C₂³×C₄	#2668	1	2	yes	—
370	C₂³×C₄	#2678	1	2	yes	—
371	C₂³×C₄	#2678	1	2	yes	—
372	C₂³×C₄	#2678	1	2	yes	—
373	C₂³×C₄	#2684	1	2	yes	—
374	C₂³×C₄	#2685	1	2	yes	—
375	C₂³×C₄	#2685	1	2	yes	—
376	C₂³×C₄	#2685	1	2	yes	—
377	C₂³×C₄	#2685	1	2	yes	—
378	C₂³×C₄	#2697	1	2	yes	—
379	C₂³×C₄	#2735	1	2	yes	—
380	C₂³×C₄	#2736	1	2	yes	—
381	C₂³×C₄	#2842	1	1	yes	characteristic
382	C₂³×C₄	#2842	1	1	yes	characteristic
383	C₂⁴	#13877	1	1	yes	characteristic
384	C₂⁴	#13877	1	1	yes	characteristic
385	C₂⁴	#14127	1	1	yes	characteristic
386	C₂⁴	#14262	1	1	yes	characteristic
387	C₂⁴	#14262	1	1	yes	characteristic
388	C₂⁴	#14338	1	1	yes	characteristic
389	C₂⁴	#14357	1	2	yes	—
390	C₂⁴	#14358	1	2	yes	—
391	C₂⁴	#14673	1	1	yes	characteristic
392	C₂⁴	#16249	1	2	yes	—
393	C₂⁴	#16255	1	2	yes	—
394	C₂⁴	#16297	1	2	yes	—
395	C₂⁴	#16298	1	2	yes	—
396	C₂⁴	#21776	1	4	yes	—
397	C₂⁴	#23895	1	4	yes	—
398	C₂²×C₄	#14365	1	2	yes	—
399	C₂²×C₄	#14366	1	2	yes	—
400	C₂²×C₄	#16255	1	2	yes	—
401	C₂²×C₄	#16298	1	2	yes	—
402	C₂²×C₄	#16298	1	2	yes	—
403	C₂²×C₄	#16391	1	2	yes	—
404	C₂³	#155632	1	1	yes	characteristic
405	C₂³	#373637	1	2	yes	—
406	C₂³	#380263	1	2	yes	—
407	C₂³	#382544	1	2	yes	—
408	C₂³	#383139	1	4	yes	—
409	C₂³	#453952	1	4	yes	—
410	C₂²	#72265603	1	1	yes	characteristic
411	C₂²	#72265702	1	1	yes	characteristic
412	C₂²	#72265866	1	1	yes	characteristic
413	C₂	#72266086	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂	#72266086
commutator	C₂⁴×D₄	C₂³×C₄
Frattini, cosocle	C₂³×H(5,𝔽₂)	C₂⁴
prime radical	C₂×#7670203	C₂²
LCS	G ▷ C₂⁴×D₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂ ◁ C₂³ ◁ C₂³×H(5,𝔽₂) ◁ G
LECS	G ▷ C₂³×H(5,𝔽₂) ▷ C₂³ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72302095	C₂	semidirect
2. #72302073	C₂	semidirect
3. #72302046	C₂	semidirect
4. #72302045	C₂²	semidirect
5. #72302013	C₂	semidirect
6. #72302012	C₂²	semidirect
7. #72266983	C₂	semidirect
8. #72266980	C₂	semidirect
9. #72266940	C₂²	semidirect
10. #72266920	C₂²	semidirect
11. #72266878	C₂²	semidirect
12. #72266878	C₂²	semidirect
13. #72266840	C₂²	semidirect
14. #72266811	C₂²	semidirect
17. #72234620	C₄	semidirect
18. #72234592	C₄	semidirect
24. #72219311	C₄	semidirect
34. #72218518	C₄	semidirect
69. C₂⁸	C₄⋊C₄	semidirect
75. C₂²×#534	C₄⋊C₄	semidirect
84. C₂³×#120	C₄⋊C₄	semidirect
85. C₂³×#120	C₄⋊C₄	semidirect
86. C₂³×#120	C₄⋊C₄	semidirect
87. C₂³×#120	C₄⋊C₄	semidirect
99. C₂⁴×C₂²⋊C₄	C₄⋊C₄	semidirect
100. C₂⁴×C₂²⋊C₄	C₄⋊C₄	semidirect
106. C₂×#2315	C₄⋊C₄	semidirect
107. C₂×#2315	C₄⋊C₄	semidirect
108. C₂×#2308	C₄⋊C₄	semidirect
109. C₂×#2308	C₄⋊C₄	semidirect
113. C₂²×#379	C₄⋊C₄	semidirect
114. C₂²×#379	C₄⋊C₄	semidirect
115. C₂²×#379	C₄⋊C₄	semidirect
116. C₂×#2273	C₄⋊C₄	semidirect
118. C₂×#1781	C₂²⋊C₄	semidirect
123. #14679	C₂²⋊C₄	semidirect
124. #10735	C₂²⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
#72302095	2
#72302073	2
#72302046	2
#72302013	2
#72266983	2
#72266980	2
#72234688	2
#72219309	2