Subgroups — #72334280

Order 4096.

At least 22540 conjugacy classes of subgroups; only the 487 normal subgroups are shown.

The subgroup lattice has 385 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72334279	C₂	1	1	yes	maximal, characteristic, complemented
2	#72334276	C₂	1	2	yes	maximal, complemented
3	#72327288	C₂	1	1	yes	maximal, characteristic
4	#72327248	C₄	1	1	yes	characteristic, complemented
5	#72327244	C₄	1	1	yes	characteristic, complemented
6	#72327231	C₄	1	1	yes	characteristic, complemented
7	#72326786	C₄	1	1	yes	characteristic, complemented
8	#72318215	C₄	1	1	yes	characteristic, complemented
9	#72316299	C₂	1	2	yes	maximal, complemented
10	#72310517	C₂	1	1	yes	maximal, characteristic, complemented
11	#72309392	C₂	1	1	yes	maximal, characteristic, complemented
12	#72309387	C₂	1	2	yes	maximal, complemented
13	#72309335	C₂²	1	1	yes	characteristic
14	#72283093	C₂²	1	1	yes	characteristic
15	#72247307	C₂²	1	2	yes	complemented
16	#72237617	C₂	1	1	yes	maximal, characteristic, complemented
17	#72237035	C₂²	1	2	yes	complemented
18	#72235865	C₂²	1	2	yes	complemented
19	#72235058	C₂²	1	2	yes	complemented
20	C₂×#97550	C₂²	1	1	yes	characteristic, complemented
21	#72234672	C₂	1	1	yes	maximal, characteristic, complemented
22	#72234670	C₂²	1	1	yes	characteristic, complemented
23	#72226352	C₂	1	1	yes	maximal, characteristic, complemented
24	#72226347	C₂²	1	2	yes	complemented
25	#72225873	C₂²	1	1	yes	characteristic, complemented
26	#72225776	C₂²	1	1	yes	characteristic, complemented
27	#72225733	C₂²	1	1	yes	characteristic
28	#72225660	C₄	1	1	yes	characteristic, complemented
29	#72225655	C₂²	1	1	yes	characteristic
30	#72219048	C₂	1	2	yes	maximal, complemented
31	#72219038	C₂²	1	2	yes	—
32	#72219038	C₂²	1	2	yes	complemented
33	#72219035	C₂²	1	2	yes	—
34	#72219034	C₂²	1	2	yes	complemented
35	#72219022	C₂²	1	2	yes	complemented
36	#72218920	C₂²	1	1	yes	characteristic
37	#72218789	C₂²	1	2	yes	complemented
38	C₂×#133822	C₂²	1	2	yes	complemented
39	#72217730	C₂²	1	1	yes	characteristic
40	C₂×#449475	C₂²	1	1	yes	characteristic
41	#72216646	C₄	1	1	yes	characteristic, complemented
42	#72210024	C₄	1	1	yes	characteristic, complemented
43	#10586066	D₄	1	1	yes	characteristic
44	#8093108	C₂×C₄	1	1	yes	characteristic, complemented
45	#8093107	C₂×C₄	1	1	yes	characteristic, complemented
46	#7670230	C₂×C₄	1	1	yes	characteristic, complemented
47	#7670203	C₂×C₄	1	1	yes	characteristic, complemented
48	#7642273	C₂³	1	1	yes	characteristic
49	#7642244	C₂³	1	1	yes	characteristic
50	#7642244	C₂³	1	1	yes	characteristic
51	C₂²×#2846	D₄	1	1	yes	characteristic
52	C₂²×#2846	D₄	1	1	yes	characteristic
53	C₂²×#2846	C₂³	1	1	yes	characteristic
54	C₂×#35346	C₂³	1	1	yes	characteristic
55	#6629262	C₂×C₄	1	1	yes	characteristic
56	#6629262	D₄	1	1	yes	characteristic
57	#6628896	C₂×C₄	1	1	yes	characteristic
58	#6628896	D₄	1	1	yes	characteristic
59	#6451874	D₄	1	1	yes	characteristic
60	#6451874	D₄	1	1	yes	characteristic
61	#6432953	C₂×C₄	1	1	yes	characteristic
62	#6432953	C₂×C₄	1	1	yes	characteristic
63	#6432953	D₄	1	1	yes	characteristic
64	#6432953	D₄	1	1	yes	characteristic
65	#6374210	D₄	1	1	yes	characteristic
66	#6374210	D₄	1	1	yes	characteristic
67	#6370693	D₄	1	1	yes	characteristic
68	#515285	C₂³	1	2	yes	—
69	#449521	C₂×C₄	1	1	yes	characteristic, complemented
70	#449521	C₂×C₄	1	1	yes	characteristic, complemented
71	#449475	C₂×C₄	1	1	yes	characteristic
72	#449475	C₂×C₄	1	1	yes	characteristic
73	#449475	C₂×C₄	1	1	yes	characteristic
74	#449475	C₂×C₄	1	1	yes	characteristic
75	#449475	C₂×C₄	1	1	yes	characteristic, complemented
76	#449475	C₂×C₄	1	1	yes	characteristic, complemented
77	#449475	D₄	1	1	yes	characteristic
78	#449475	D₄	1	1	yes	characteristic
79	#449475	D₄	1	1	yes	characteristic
80	#449475	D₄	1	1	yes	characteristic
81	#418213	C₂×C₄	1	1	yes	characteristic, complemented
82	#418132	C₂×C₄	1	1	yes	characteristic, complemented
83	#417896	C₂×C₄	1	1	yes	characteristic
84	#417896	C₂×C₄	1	1	yes	characteristic
85	#417896	C₂×C₄	1	1	yes	characteristic, complemented
86	#417896	D₄	1	1	yes	characteristic
87	#417896	D₄	1	1	yes	characteristic
88	#417824	C₂×C₄	1	1	yes	characteristic
89	#417824	C₂×C₄	1	1	yes	characteristic
90	#417824	C₂×C₄	1	1	yes	characteristic, complemented
91	#417824	D₄	1	1	yes	characteristic
92	#417824	D₄	1	1	yes	characteristic
93	#392699	D₄	1	4	yes	complemented
94	#391735	C₂×C₄	1	1	yes	characteristic, complemented
95	#391709	C₂×C₄	1	1	yes	characteristic, complemented
96	#382422	C₂³	1	1	yes	characteristic
97	#375666	C₂×C₄	1	1	yes	characteristic, complemented
98	#374004	C₂×C₄	1	1	yes	characteristic, complemented
99	#359705	D₄	1	1	yes	characteristic
100	#359705	D₄	1	1	yes	characteristic
101	C₂×#10965	D₄	1	1	yes	characteristic
102	C₂×#10965	D₄	1	1	yes	characteristic
103	C₂×#10965	C₂³	1	2	yes	—
104	C₂×#10965	C₂³	1	1	yes	characteristic
105	#201687	D₄	1	4	yes	complemented
106	C₂×#8547	C₂³	1	2	yes	—
107	C₂×#8541	C₂³	1	2	yes	—
108	C₂⁸	C₂×D₄	1	1	yes	characteristic
109	C₂×H(7,𝔽₂)	C₂²⋊C₄	1	1	yes	characteristic, complemented
110	C₂³×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
111	#62842	C₂²⋊C₄	1	1	yes	characteristic, complemented
112	#62842	C₂²⋊C₄	1	1	yes	characteristic, complemented
113	C₂×#3490	C₂×D₄	1	1	yes	characteristic
114	C₂×#3484	C₂×D₄	1	1	yes	characteristic
115	C₂×#3484	C₂×D₄	1	1	yes	characteristic
116	C₂³×#120	C₂×D₄	1	1	yes	characteristic
117	C₂³×#120	C₂×D₄	1	1	yes	characteristic
118	C₂³×#120	C₂⁴	1	1	yes	characteristic
119	#62652	C₂²⋊C₄	1	1	yes	characteristic, complemented
120	C₂²×#518	C₂×D₄	1	2	yes	complemented
121	#36714	#41	1	4	yes	—
122	C₂×#2846	C₂²⋊C₄	1	1	yes	characteristic
123	C₂×#2846	C₂²⋊C₄	1	1	yes	characteristic
124	C₂×#2846	C₂²⋊C₄	1	1	yes	characteristic
125	C₂×#2846	C₂²⋊C₄	1	1	yes	characteristic
126	C₂×#2846	C₂²⋊C₄	1	1	yes	characteristic
127	C₂×#2846	C₂²⋊C₄	1	1	yes	characteristic
128	C₂×#2846	C₂²⋊C₄	1	1	yes	characteristic
129	C₂×#2846	C₂²⋊C₄	1	1	yes	characteristic
130	C₂×#2846	C₂²×C₄	1	1	yes	characteristic
131	C₂×#2846	C₂²×C₄	1	1	yes	characteristic
132	C₂×#2846	C₂×D₄	1	1	yes	characteristic
133	C₂×#2846	C₂×D₄	1	1	yes	characteristic
134	#35390	C₂²×C₄	1	1	yes	characteristic
135	#35390	C₂×D₄	1	1	yes	characteristic
136	#35367	C₂²×C₄	1	1	yes	characteristic
137	#35367	C₂×D₄	1	1	yes	characteristic
138	#35350	C₂²×C₄	1	1	yes	characteristic
139	#35350	C₂²×C₄	1	1	yes	characteristic
140	#35350	C₂×D₄	1	1	yes	characteristic
141	#35350	C₂×D₄	1	1	yes	characteristic
142	#35346	C₂²×C₄	1	1	yes	characteristic
143	#35346	C₂²×C₄	1	1	yes	characteristic
144	#35346	C₂²×C₄	1	1	yes	characteristic
145	#35346	C₂²×C₄	1	1	yes	characteristic
146	#35346	C₂×D₄	1	1	yes	characteristic
147	#35346	C₂×D₄	1	1	yes	characteristic
148	#35346	C₂×D₄	1	1	yes	characteristic
149	#35346	C₂×D₄	1	1	yes	characteristic
150	#35346	C₂×D₄	1	1	yes	characteristic
151	#35346	C₂×D₄	1	1	yes	characteristic
152	#35346	C₂×D₄	1	1	yes	characteristic
153	#35346	C₂×D₄	1	1	yes	characteristic
154	#34980	C₂×D₄	1	4	yes	—
155	#34176	C₂×D₄	1	1	yes	characteristic
156	#34171	C₂×D₄	1	1	yes	characteristic
157	#34171	C₂×D₄	1	1	yes	characteristic
158	C₂×#2308	C₂×D₄	1	1	yes	characteristic
159	C₂×#2308	C₂×D₄	1	1	yes	characteristic
160	C₂×#2308	C₂×D₄	1	1	yes	characteristic
161	C₂×#2308	C₂×D₄	1	2	yes	complemented
162	C₂²×#379	C₂×D₄	1	1	yes	characteristic
163	C₂²×#379	C₂×D₄	1	1	yes	characteristic
164	C₂²×#379	C₂×D₄	1	1	yes	characteristic
165	#23468	C₂²⋊C₄	1	1	yes	characteristic, complemented
166	#23468	C₂²⋊C₄	1	1	yes	characteristic, complemented
167	#23468	C₂²⋊C₄	1	1	yes	characteristic, complemented
168	#23468	C₂²⋊C₄	1	1	yes	characteristic, complemented
169	#23444	C₂²⋊C₄	1	1	yes	characteristic, complemented
170	#23444	C₂²⋊C₄	1	1	yes	characteristic, complemented
171	#23444	C₂²⋊C₄	1	1	yes	characteristic, complemented
172	#23444	C₂²⋊C₄	1	1	yes	characteristic, complemented
173	#20689	C₂²⋊C₄	1	1	yes	characteristic, complemented
174	#20689	C₂²⋊C₄	1	1	yes	characteristic, complemented
175	#20689	C₂²⋊C₄	1	1	yes	characteristic, complemented
176	#20689	C₂²⋊C₄	1	1	yes	characteristic, complemented
177	C₂×#1819	C₂×D₄	1	1	yes	characteristic
178	C₂×#1819	C₂×D₄	1	1	yes	characteristic
179	#20585	C₂²⋊C₄	1	1	yes	characteristic, complemented
180	#20585	C₂²⋊C₄	1	1	yes	characteristic, complemented
181	#20585	C₂²⋊C₄	1	1	yes	characteristic, complemented
182	#20585	C₂²⋊C₄	1	1	yes	characteristic, complemented
183	#20585	C₂²⋊C₄	1	1	yes	characteristic, complemented
184	#20585	C₂²⋊C₄	1	1	yes	characteristic, complemented
185	#20585	C₂²⋊C₄	1	1	yes	characteristic, complemented
186	#20585	C₂²⋊C₄	1	1	yes	characteristic, complemented
187	C₂×#1781	C₂×D₄	1	4	yes	complemented
188	#10965	C₂²⋊C₄	1	1	yes	characteristic
189	#10965	C₂²⋊C₄	1	1	yes	characteristic
190	#10965	C₂²⋊C₄	1	1	yes	characteristic
191	#10965	C₂²⋊C₄	1	1	yes	characteristic
192	#10965	C₂²⋊C₄	1	1	yes	characteristic
193	#10965	C₂²⋊C₄	1	1	yes	characteristic
194	#10965	C₂²⋊C₄	1	1	yes	characteristic
195	#10965	C₂²⋊C₄	1	1	yes	characteristic
196	#10965	C₂²×C₄	1	1	yes	characteristic
197	#10965	C₂²×C₄	1	1	yes	characteristic
198	#10965	C₂²×C₄	1	1	yes	characteristic
199	#10965	C₂²×C₄	1	1	yes	characteristic
200	#10965	C₂×D₄	1	1	yes	characteristic
201	#10965	C₂×D₄	1	1	yes	characteristic
202	#10965	C₂×D₄	1	1	yes	characteristic
203	#10965	C₂×D₄	1	1	yes	characteristic
204	#10938	C₂²⋊C₄	1	1	yes	characteristic, complemented
205	#10938	C₂²⋊C₄	1	1	yes	characteristic, complemented
206	#10938	C₂²⋊C₄	1	1	yes	characteristic, complemented
207	#10938	C₂²⋊C₄	1	1	yes	characteristic, complemented
208	#10938	C₂²⋊C₄	1	1	yes	characteristic, complemented
209	#10938	C₂²⋊C₄	1	1	yes	characteristic, complemented
210	#10938	C₂²⋊C₄	1	1	yes	characteristic, complemented
211	#10938	C₂²⋊C₄	1	1	yes	characteristic, complemented
212	C₂⁷	C₂×C₂²⋊C₄	1	1	yes	characteristic
213	C₂⁷	C₂×C₂²⋊C₄	1	1	yes	characteristic
214	C₂⁷	C₂²×D₄	1	1	yes	characteristic
215	C₂²×H(5,𝔽₂)	C₂×C₂²⋊C₄	1	1	yes	characteristic
216	C₂²×H(5,𝔽₂)	C₂×C₂²⋊C₄	1	1	yes	characteristic
217	C₂²×H(5,𝔽₂)	C₂×C₂²⋊C₄	1	1	yes	characteristic
218	C₂²×H(5,𝔽₂)	C₂×C₂²⋊C₄	1	1	yes	characteristic
219	C₂²×H(5,𝔽₂)	#120	1	1	yes	characteristic
220	C₂²×H(5,𝔽₂)	#120	1	1	yes	characteristic
221	C₂⁴×D₄	#120	1	1	yes	characteristic
222	C₂⁴×D₄	#120	1	1	yes	characteristic
223	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
224	C₂⁴×D₄	C₂²×D₄	1	2	yes	—
225	C₂×#543	C₂×C₂²⋊C₄	1	1	yes	characteristic
226	C₂×#534	C₂×C₂²⋊C₄	1	1	yes	characteristic
227	C₂×#534	#123	1	2	yes	—
228	C₂²×#120	C₂×C₂²⋊C₄	1	1	yes	characteristic
229	C₂²×#120	C₂×C₂²⋊C₄	1	1	yes	characteristic
230	C₂²×#120	C₂×C₂²⋊C₄	1	1	yes	characteristic
231	C₂²×#120	C₂×C₂²⋊C₄	1	1	yes	characteristic
232	C₂²×#120	#120	1	1	yes	characteristic
233	C₂²×#120	#120	1	1	yes	characteristic
234	C₂²×#120	#120	1	1	yes	characteristic
235	C₂²×#120	#120	1	1	yes	characteristic
236	C₂²×#120	#120	1	2	yes	—
237	C₂²×#120	C₂³×C₄	1	1	yes	characteristic
238	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
239	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
240	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
241	C₂²×#120	C₂×#41	1	2	yes	—
242	C₂²×#120	H(5,𝔽₂)	1	2	yes	—
243	C₂×#518	C₂×C₂²⋊C₄	1	1	yes	characteristic
244	C₂×#518	C₂×C₂²⋊C₄	1	1	yes	characteristic
245	C₂³×C₂²⋊C₄	#120	1	1	yes	characteristic
246	C₂³×C₂²⋊C₄	#120	1	1	yes	characteristic
247	C₂³×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
248	C₂³×C₂²⋊C₄	H(5,𝔽₂)	1	2	yes	—
249	#2405	C₄×D₄	1	4	yes	—
250	#2405	#121	1	4	yes	—
251	#2403	C₄×D₄	1	4	yes	—
252	#2403	#121	1	4	yes	—
253	#2309	#123	1	2	yes	—
254	#2308	C₂×C₂²⋊C₄	1	1	yes	characteristic
255	#2308	C₂×C₂²⋊C₄	1	1	yes	characteristic
256	#2308	C₂×C₂²⋊C₄	1	1	yes	characteristic
257	#2308	C₂×C₂²⋊C₄	1	1	yes	characteristic
258	#2308	C₂×C₂²⋊C₄	1	1	yes	characteristic
259	#2308	C₂×C₂²⋊C₄	1	1	yes	characteristic
260	#2308	C₂×C₂²⋊C₄	1	1	yes	characteristic
261	#2308	C₂×C₂²⋊C₄	1	1	yes	characteristic
262	#2308	C₂×C₂²⋊C₄	1	1	yes	characteristic
263	#2308	C₂×C₂²⋊C₄	1	1	yes	characteristic
264	#2308	#120	1	1	yes	characteristic
265	#2308	#120	1	1	yes	characteristic
266	#2308	#120	1	1	yes	characteristic
267	#2308	#120	1	1	yes	characteristic
268	#2308	#120	1	1	yes	characteristic
269	#2308	#120	1	1	yes	characteristic
270	C₂×#379	C₂×C₂²⋊C₄	1	1	yes	characteristic
271	C₂×#379	C₂×C₂²⋊C₄	1	1	yes	characteristic
272	C₂×#379	C₂×C₂²⋊C₄	1	1	yes	characteristic
273	C₂×#379	C₂×C₂²⋊C₄	1	1	yes	characteristic
274	C₂×#379	C₂×C₂²⋊C₄	1	1	yes	characteristic
275	C₂×#379	C₂×C₂²⋊C₄	1	1	yes	characteristic
276	C₂×#379	#120	1	2	yes	—
277	#2273	C₂×C₂²⋊C₄	1	1	yes	characteristic
278	#2273	C₂×C₂²⋊C₄	1	1	yes	characteristic
279	C₂×#342	C₂×C₂²⋊C₄	1	1	yes	characteristic
280	C₂×#342	C₂×C₂²⋊C₄	1	1	yes	characteristic
281	C₂×#342	C₂×C₂²⋊C₄	1	1	yes	characteristic
282	C₂×#342	C₂×C₂²⋊C₄	1	1	yes	characteristic
283	C₂⁶	B(4,𝔽₂)	1	1	yes	characteristic
284	C₂⁶	B(4,𝔽₂)	1	1	yes	characteristic
285	C₂⁶	C₂²×C₂²⋊C₄	1	1	yes	characteristic
286	C₂⁶	C₂×#120	1	1	yes	characteristic
287	C₂⁶	C₂×#120	1	1	yes	characteristic
288	C₂⁶	C₂×#120	1	1	yes	characteristic
289	C₂⁶	D₄²	1	2	yes	—
290	C₂⁶	#546	1	2	yes	—
291	C₂³×D₄	#379	1	1	yes	characteristic
292	C₂³×D₄	#379	1	1	yes	characteristic
293	C₂³×D₄	#379	1	1	yes	characteristic
294	C₂³×D₄	#379	1	1	yes	characteristic
295	C₂³×D₄	#386	1	2	yes	—
296	C₂³×D₄	B(4,𝔽₂)	1	4	yes	—
297	C₂³×D₄	#458	1	1	yes	characteristic
298	C₂³×D₄	#458	1	1	yes	characteristic
299	C₂³×D₄	#458	1	1	yes	characteristic
300	C₂³×D₄	#458	1	1	yes	characteristic
301	C₂³×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
302	C₂³×D₄	C₂×C₄×D₄	1	2	yes	—
303	C₂³×D₄	C₂×#120	1	1	yes	characteristic
304	C₂³×D₄	C₂×#121	1	2	yes	—
305	C₂³×D₄	C₂×#123	1	1	yes	characteristic
306	C₂³×D₄	#534	1	1	yes	characteristic
307	C₂³×D₄	D₄²	1	2	yes	—
308	C₂³×D₄	D₄²	1	2	yes	—
309	C₂⁴×C₄	B(4,𝔽₂)	1	1	yes	characteristic
310	C₂⁴×C₄	B(4,𝔽₂)	1	1	yes	characteristic
311	C₂⁴×C₄	#534	1	1	yes	characteristic
312	C₂⁴×C₄	D₄²	1	2	yes	—
313	C₂²×C₂²⋊C₄	#379	1	1	yes	characteristic
314	C₂²×C₂²⋊C₄	#379	1	1	yes	characteristic
315	C₂²×C₂²⋊C₄	#379	1	1	yes	characteristic
316	C₂²×C₂²⋊C₄	#379	1	1	yes	characteristic
317	C₂²×C₂²⋊C₄	#386	1	2	yes	—
318	C₂²×C₂²⋊C₄	B(4,𝔽₂)	1	4	yes	—
319	C₂²×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
320	C₂²×C₂²⋊C₄	#518	1	2	yes	—
321	C₂²×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
322	C₂²×C₂²⋊C₄	#534	1	2	yes	—
323	C₂²×C₂²⋊C₄	#546	1	2	yes	—
324	C₂²×C₂²⋊C₄	#546	1	2	yes	—
325	C₂²×C₂²⋊C₄	#546	1	2	yes	—
326	#379	#386	1	2	yes	—
327	#379	#386	1	2	yes	—
328	C₂⁵	#1790	1	1	yes	characteristic
329	C₂⁵	#1790	1	1	yes	characteristic
330	C₂⁵	#1790	1	1	yes	characteristic
331	C₂⁵	#1790	1	1	yes	characteristic
332	C₂⁵	#1889	1	2	yes	complemented
333	C₂⁵	C₂×#379	1	1	yes	characteristic
334	C₂⁵	C₂×#386	1	1	yes	characteristic
335	C₂⁵	D₄×C₂²⋊C₄	1	2	yes	—
336	C₂⁵	#2403	1	1	yes	characteristic
337	C₂⁵	#2403	1	1	yes	characteristic
338	C₂⁵	#2405	1	1	yes	characteristic
339	C₂⁵	#2410	1	2	yes	—
340	C₂⁵	C₂×B(4,𝔽₂)	1	1	yes	characteristic
341	C₂⁵	C₂×B(4,𝔽₂)	1	1	yes	characteristic
342	C₂⁵	C₂×B(4,𝔽₂)	1	4	yes	—
343	C₂⁵	C₂×#458	1	1	yes	characteristic
344	C₂⁵	C₂×#458	1	1	yes	characteristic
345	C₂³×C₄	#1790	1	1	yes	characteristic
346	C₂³×C₄	#1790	1	1	yes	characteristic
347	C₂³×C₄	#1790	1	1	yes	characteristic
348	C₂³×C₄	#1790	1	1	yes	characteristic
349	C₂³×C₄	#1889	1	4	yes	complemented
350	C₂³×C₄	#1889	1	2	yes	complemented
351	C₂³×C₄	#2308	1	1	yes	characteristic
352	C₂³×C₄	D₄×C₂²⋊C₄	1	2	yes	—
353	C₂³×C₄	#2405	1	1	yes	characteristic
354	C₂³×C₄	#2410	1	2	yes	—
355	C₂⁴	#12753	1	2	yes	complemented
356	C₂⁴	#13867	1	1	yes	characteristic
357	C₂⁴	C₂×#1790	1	1	yes	characteristic
358	C₂⁴	C₂×#1790	1	1	yes	characteristic
359	C₂⁴	C₂×#1889	1	2	yes	—
360	C₂⁴	#23895	1	2	yes	—
361	C₂⁴	#23900	1	1	yes	characteristic
362	C₂⁴	#23900	1	2	yes	—
363	C₂⁴	#23900	1	2	yes	—
364	C₂⁴	#23901	1	1	yes	characteristic
365	C₂⁴	#24056	1	1	yes	characteristic
366	C₂⁴	#24056	1	1	yes	characteristic
367	C₂²×C₄	#12753	1	2	yes	complemented
368	C₂³	#245225	1	2	yes	—
369	C₂³	#245226	1	2	yes	—
370	C₂³	#359501	1	1	yes	characteristic
371	C₂³	#359549	1	1	yes	characteristic
372	C₂³	#359552	1	1	yes	characteristic
373	C₂³	C₂×#12753	1	1	yes	characteristic
374	C₂³	C₂×#12753	1	1	yes	characteristic
375	C₂³	#493562	1	1	yes	characteristic
376	C₂³	#493562	1	1	yes	characteristic
377	C₂²	B(5,𝔽₂)	1	2	yes	—
378	C₂²	#72233445	1	2	yes	—
379	C₂²	#72235131	1	1	yes	characteristic
380	C₂²	#72235131	1	1	yes	characteristic
381	C₂²	#72236754	1	1	yes	characteristic
382	C₂	#72246469	1	2	yes	—
383	C₂	#72266446	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#72236754
commutator	C₂²×#120	C₂³×C₄
Frattini, cosocle	C₂³×#120	C₂⁴
prime radical	#72327288	C₂
LCS	G ▷ C₂²×#120 ▷ C₂⁴ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁵ ◁ C₂³×#120 ◁ G
LECS	G ▷ C₂³×#120 ▷ C₂⁴ ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72334279	C₂	semidirect
2. #72334276	C₂	semidirect
4. #72327248	C₄	semidirect
5. #72327244	C₄	semidirect
6. #72327231	C₄	semidirect
7. #72326786	C₄	semidirect
8. #72318215	C₄	semidirect
9. #72316299	C₂	semidirect
10. #72310517	C₂	semidirect
11. #72309392	C₂	semidirect
12. #72309387	C₂	semidirect
15. #72247307	C₂²	semidirect
16. #72237617	C₂	semidirect
17. #72237035	C₂²	semidirect
18. #72235865	C₂²	semidirect
19. #72235058	C₂²	semidirect
20. C₂×#97550	C₂²	semidirect
21. #72234672	C₂	semidirect
22. #72234670	C₂²	semidirect
23. #72226352	C₂	semidirect
24. #72226347	C₂²	semidirect
25. #72225873	C₂²	semidirect
26. #72225776	C₂²	semidirect
28. #72225660	C₄	semidirect
30. #72219048	C₂	semidirect
32. #72219038	C₂²	semidirect
34. #72219034	C₂²	semidirect
35. #72219022	C₂²	semidirect
37. #72218789	C₂²	semidirect
38. C₂×#133822	C₂²	semidirect
41. #72216646	C₄	semidirect
42. #72210024	C₄	semidirect
44. #8093108	C₂×C₄	semidirect
45. #8093107	C₂×C₄	semidirect
46. #7670230	C₂×C₄	semidirect
47. #7670203	C₂×C₄	semidirect
69. #449521	C₂×C₄	semidirect
70. #449521	C₂×C₄	semidirect
75. #449475	C₂×C₄	semidirect
76. #449475	C₂×C₄	semidirect
81. #418213	C₂×C₄	semidirect
82. #418132	C₂×C₄	semidirect
85. #417896	C₂×C₄	semidirect
90. #417824	C₂×C₄	semidirect
93. #392699	D₄	semidirect
94. #391735	C₂×C₄	semidirect
95. #391709	C₂×C₄	semidirect
97. #375666	C₂×C₄	semidirect
98. #374004	C₂×C₄	semidirect
105. #201687	D₄	semidirect
109. C₂×H(7,𝔽₂)	C₂²⋊C₄	semidirect
111. #62842	C₂²⋊C₄	semidirect
112. #62842	C₂²⋊C₄	semidirect
119. #62652	C₂²⋊C₄	semidirect
120. C₂²×#518	C₂×D₄	semidirect
161. C₂×#2308	C₂×D₄	semidirect
165. #23468	C₂²⋊C₄	semidirect
166. #23468	C₂²⋊C₄	semidirect
167. #23468	C₂²⋊C₄	semidirect
168. #23468	C₂²⋊C₄	semidirect
169. #23444	C₂²⋊C₄	semidirect
170. #23444	C₂²⋊C₄	semidirect
171. #23444	C₂²⋊C₄	semidirect
172. #23444	C₂²⋊C₄	semidirect
173. #20689	C₂²⋊C₄	semidirect
174. #20689	C₂²⋊C₄	semidirect
175. #20689	C₂²⋊C₄	semidirect
176. #20689	C₂²⋊C₄	semidirect
179. #20585	C₂²⋊C₄	semidirect
180. #20585	C₂²⋊C₄	semidirect
181. #20585	C₂²⋊C₄	semidirect
182. #20585	C₂²⋊C₄	semidirect
183. #20585	C₂²⋊C₄	semidirect
184. #20585	C₂²⋊C₄	semidirect
185. #20585	C₂²⋊C₄	semidirect
186. #20585	C₂²⋊C₄	semidirect
187. C₂×#1781	C₂×D₄	semidirect
204. #10938	C₂²⋊C₄	semidirect
205. #10938	C₂²⋊C₄	semidirect
206. #10938	C₂²⋊C₄	semidirect
207. #10938	C₂²⋊C₄	semidirect
208. #10938	C₂²⋊C₄	semidirect
209. #10938	C₂²⋊C₄	semidirect
210. #10938	C₂²⋊C₄	semidirect
211. #10938	C₂²⋊C₄	semidirect
332. C₂⁵	#1889	semidirect
349. C₂³×C₄	#1889	semidirect
350. C₂³×C₄	#1889	semidirect
355. C₂⁴	#12753	semidirect
367. C₂²×C₄	#12753	semidirect

Maximal subgroups

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

subgroup	index
#72334279	2
#72334276	2
#72327288	2
#72316299	2
#72310517	2
#72309392	2
#72309387	2
#72237617	2
#72234672	2
#72226352	2
#72219048	2