Subgroups — #72260690

Order 2048.

At least 7346 conjugacy classes of subgroups; only the 442 normal subgroups are shown.

The subgroup lattice has 357 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72260685	C₂	1	2	yes	maximal, complemented
2	#72260683	C₂	1	1	yes	maximal, characteristic, complemented
3	#72260601	C₂	1	1	yes	maximal, characteristic
4	#72260565	C₂	1	1	yes	maximal, characteristic, complemented
5	#72260439	C₂	1	1	yes	maximal, characteristic, complemented
6	#72238524	C₂	1	1	yes	maximal, characteristic, complemented
7	#72235062	C₂	1	1	yes	maximal, characteristic, complemented
8	#72234781	C₂	1	1	yes	maximal, characteristic, complemented
9	#72215536	C₂	1	2	yes	maximal, complemented
10	#72215527	C₂	1	2	yes	maximal, complemented
11	#72214206	C₂	1	2	yes	maximal, complemented
12	C₂×#52004	C₂²	1	1	yes	characteristic
13	C₂×#36098	C₂²	1	1	yes	characteristic
14	#6385984	C₂²	1	1	yes	characteristic, complemented
15	#6385972	C₂²	1	1	yes	characteristic, complemented
16	#6342764	C₂²	1	1	yes	characteristic, complemented
17	#5021210	C₄	1	1	yes	characteristic, complemented
18	#4941252	C₄	1	1	yes	characteristic, complemented
19	#4607561	C₄	1	1	yes	characteristic, complemented
20	#4420593	C₂²	1	1	yes	characteristic
21	#2925513	C₄	1	1	yes	characteristic, complemented
22	#2032498	C₄	1	1	yes	characteristic, complemented
23	#2031998	C₄	1	1	yes	characteristic, complemented
24	#1419350	C₄	1	1	yes	characteristic, complemented
25	#850465	C₂²	1	1	yes	characteristic
26	#686202	C₂²	1	1	yes	characteristic
27	#647656	C₄	1	1	yes	characteristic, complemented
28	#616967	C₂²	1	1	yes	characteristic
29	#605076	C₂²	1	1	yes	characteristic
30	#496228	C₂²	1	2	yes	—
31	#496228	C₂²	1	2	yes	complemented
32	#493385	C₂²	1	2	yes	complemented
33	#493352	C₂²	1	2	yes	complemented
34	#359513	C₂²	1	2	yes	complemented
35	#359507	C₂²	1	2	yes	complemented
36	#201819	C₂²	1	2	yes	—
37	#201819	C₂²	1	2	yes	complemented
38	#188085	C₂²	1	1	yes	characteristic, complemented
39	#128059	C₂²	1	2	yes	complemented
40	#128034	C₂²	1	2	yes	complemented
41	#107117	C₂²	1	2	yes	complemented
42	#106740	C₂²	1	2	yes	complemented
43	C₂²×#546	C₂³	1	1	yes	characteristic
44	C₂²×D₄²	C₂×C₄	1	1	yes	characteristic, complemented
45	C₂²×#535	C₂³	1	1	yes	characteristic
46	C₂²×#525	C₂³	1	1	yes	characteristic
47	C₂³×#120	D₄	1	1	yes	characteristic
48	C₂⁴×C₂²⋊C₄	D₄	1	1	yes	characteristic
49	#60064	C₂³	1	2	yes	—
50	C₂×#2669	C₂×C₄	1	1	yes	characteristic, complemented
51	C₂×#2669	C₂×C₄	1	1	yes	characteristic, complemented
52	C₂×#2849	D₄	1	1	yes	characteristic
53	C₂×#2847	C₂×C₄	1	1	yes	characteristic
54	C₂×#2846	C₂×C₄	1	1	yes	characteristic
55	C₂×#2539	C₂×C₄	1	1	yes	characteristic
56	C₂×#2534	D₄	1	1	yes	characteristic
57	C₂×#2534	D₄	1	1	yes	characteristic
58	C₂×#2411	D₄	1	1	yes	characteristic
59	C₂×#2404	C₂³	1	1	yes	characteristic
60	C₂×#2404	C₂³	1	1	yes	characteristic
61	C₂×#2412	C₂×C₄	1	1	yes	characteristic
62	C₂×#2405	D₄	1	1	yes	characteristic
63	C₂×#2617	D₄	1	1	yes	characteristic
64	C₂×#2613	D₄	1	1	yes	characteristic
65	C₂²×#392	D₄	1	1	yes	characteristic
66	C₂×#2380	C₂×C₄	1	1	yes	characteristic, complemented
67	C₂×#2342	D₄	1	1	yes	characteristic
68	C₂×C₄×#120	D₄	1	1	yes	characteristic
69	#20591	C₂³	1	2	yes	—
70	#20591	C₂³	1	2	yes	—
71	#20584	C₂³	1	2	yes	—
72	#15984	C₂×C₄	1	1	yes	characteristic
73	#15984	D₄	1	1	yes	characteristic
74	#15948	C₂×C₄	1	1	yes	characteristic
75	#15948	C₂×C₄	1	1	yes	characteristic, complemented
76	#15948	D₄	1	1	yes	characteristic
77	#15947	C₂×C₄	1	1	yes	characteristic
78	#15947	C₂×C₄	1	1	yes	characteristic, complemented
79	#15947	D₄	1	1	yes	characteristic
80	#15763	D₄	1	1	yes	characteristic
81	#15763	D₄	1	1	yes	characteristic
82	#15463	C₂×C₄	1	1	yes	characteristic, complemented
83	#15310	C₂×C₄	1	1	yes	characteristic
84	#15310	C₂×C₄	1	1	yes	characteristic
85	#15266	C₂×C₄	1	1	yes	characteristic, complemented
86	#15264	D₄	1	1	yes	characteristic
87	#15264	D₄	1	1	yes	characteristic
88	#15261	C₂×C₄	1	1	yes	characteristic, complemented
89	#15261	C₂×C₄	1	1	yes	characteristic, complemented
90	#15258	C₂×C₄	1	1	yes	characteristic
91	#15258	C₂×C₄	1	1	yes	characteristic
92	#15258	C₂×C₄	1	1	yes	characteristic, complemented
93	#15258	C₂×C₄	1	1	yes	characteristic, complemented
94	#15257	C₂×C₄	1	1	yes	characteristic
95	#15257	D₄	1	1	yes	characteristic
96	#14666	C₂×C₄	1	1	yes	characteristic, complemented
97	#14659	D₄	1	1	yes	characteristic
98	#14410	C₂×C₄	1	1	yes	characteristic, complemented
99	#14358	C₂×C₄	1	1	yes	characteristic, complemented
100	#14344	D₄	1	1	yes	characteristic
101	#14337	C₂³	1	1	yes	characteristic
102	#14135	D₄	1	1	yes	characteristic
103	#14134	C₂×C₄	1	1	yes	characteristic, complemented
104	#13956	C₂³	1	1	yes	characteristic
105	#13868	D₄	1	1	yes	characteristic
106	#13087	D₄	1	8	yes	complemented
107	C₂⁷	C₂²⋊C₄	1	1	yes	characteristic
108	C₂³×#41	C₂⁴	1	1	yes	characteristic
109	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
110	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
111	C₂⁵×C₄	C₂²⋊C₄	1	1	yes	characteristic
112	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
113	C₂²×#127	C₂²×C₄	1	1	yes	characteristic
114	C₂²×#127	C₂²×C₄	1	1	yes	characteristic
115	C₂²×#124	C₂×D₄	1	1	yes	characteristic
116	C₂²×#124	C₂×D₄	1	1	yes	characteristic
117	C₂²×#124	C₂×D₄	1	1	yes	characteristic
118	C₂²×#123	C₂²⋊C₄	1	1	yes	characteristic
119	C₂²×#123	C₂²⋊C₄	1	1	yes	characteristic
120	C₂²×#123	C₂²×C₄	1	1	yes	characteristic
121	C₂²×#123	C₂×D₄	1	1	yes	characteristic
122	C₂²×#123	C₂×D₄	1	1	yes	characteristic
123	C₂²×#123	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₂²⋊Q₈	C₂×D₄	1	1	yes	characteristic
125	C₂²×#121	C₂²×C₄	1	1	yes	characteristic
126	C₂²×#121	C₂×D₄	1	1	yes	characteristic
127	C₂²×#121	C₂×D₄	1	1	yes	characteristic
128	C₂²×#120	C₂²⋊C₄	1	1	yes	characteristic
129	C₂²×#120	C₂²⋊C₄	1	1	yes	characteristic
130	C₂²×#120	C₂²⋊C₄	1	1	yes	characteristic
131	C₂²×#120	C₂²⋊C₄	1	1	yes	characteristic
132	C₂²×#120	C₂²⋊C₄	1	1	yes	characteristic
133	C₂²×#120	C₂²×C₄	1	1	yes	characteristic
134	C₂²×#120	C₂²×C₄	1	1	yes	characteristic
135	C₂²×#120	C₂²×C₄	1	1	yes	characteristic
136	C₂²×#120	C₂²×C₄	1	1	yes	characteristic
137	C₂²×#120	C₂×D₄	1	1	yes	characteristic
138	C₂²×#120	C₂×D₄	1	1	yes	characteristic
139	C₂²×#120	C₂×D₄	1	1	yes	characteristic
140	C₂²×#120	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
143	C₂²×#117	C₂×D₄	1	1	yes	characteristic
144	C₂²×#117	C₂×D₄	1	1	yes	characteristic
145	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
146	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
147	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
148	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
149	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
150	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
151	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
152	C₂×#410	C₂×D₄	1	4	yes	complemented
153	#2404	C₂×D₄	1	4	yes	—
154	#2404	#41	1	4	yes	—
155	C₂×#394	C₂²⋊C₄	1	1	yes	characteristic
156	C₂×#394	C₂²⋊C₄	1	1	yes	characteristic
157	C₂×#392	C₂²⋊C₄	1	1	yes	characteristic
158	C₂×#392	C₂²⋊C₄	1	1	yes	characteristic
159	C₂×#392	C₂²⋊C₄	1	1	yes	characteristic
160	C₂×#392	C₂²⋊C₄	1	1	yes	characteristic
161	C₂×#392	C₂²⋊C₄	1	1	yes	characteristic
162	C₂×#392	C₂²⋊C₄	1	1	yes	characteristic
163	C₂×#386	C₂²⋊C₄	1	1	yes	characteristic
164	C₂×#386	C₂²⋊C₄	1	1	yes	characteristic
165	C₂×#386	C₂²⋊C₄	1	1	yes	characteristic
166	C₂×#386	C₂²×C₄	1	1	yes	characteristic
167	C₂×#386	C₂²×C₄	1	1	yes	characteristic
168	C₂×#386	C₂×D₄	1	1	yes	characteristic
169	C₂×#386	C₂×D₄	1	1	yes	characteristic
170	C₂×#385	C₂²⋊C₄	1	1	yes	characteristic
171	C₂×#381	C₂²⋊C₄	1	1	yes	characteristic
172	C₂×#381	C₂²⋊C₄	1	1	yes	characteristic
173	C₂×#381	C₂×D₄	1	1	yes	characteristic
174	C₂×#381	C₂×D₄	1	1	yes	characteristic
175	C₂×#381	C₂×D₄	1	1	yes	characteristic
176	C₂×#380	C₂²⋊C₄	1	1	yes	characteristic
177	C₂×#380	C₂×D₄	1	1	yes	characteristic
178	C₂×#380	C₂×D₄	1	1	yes	characteristic
179	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic
180	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic
181	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic
182	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic
183	C₂×C₄×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
184	C₂²×#95	C₂×D₄	1	1	yes	characteristic
185	#1785	C₂×D₄	1	4	yes	complemented
186	#1446	C₂×D₄	1	1	yes	characteristic
187	#1446	C₂×D₄	1	1	yes	characteristic
188	#1440	C₂²⋊C₄	1	1	yes	characteristic
189	#1440	C₂²⋊C₄	1	1	yes	characteristic
190	#1438	C₂²⋊C₄	1	1	yes	characteristic
191	#1438	C₂²⋊C₄	1	1	yes	characteristic
192	#1438	C₂²⋊C₄	1	1	yes	characteristic
193	#1438	C₂²⋊C₄	1	1	yes	characteristic
194	#1438	C₂²⋊C₄	1	1	yes	characteristic
195	#1438	C₂²⋊C₄	1	1	yes	characteristic
196	#1438	C₂²×C₄	1	1	yes	characteristic
197	#1438	C₂²×C₄	1	1	yes	characteristic
198	#1438	C₂²×C₄	1	1	yes	characteristic
199	#1438	C₂²×C₄	1	1	yes	characteristic
200	#1438	C₂×D₄	1	1	yes	characteristic
201	#1438	C₂×D₄	1	1	yes	characteristic
202	#1437	C₂²⋊C₄	1	1	yes	characteristic
203	#1437	C₂²⋊C₄	1	1	yes	characteristic
204	#1437	C₂²⋊C₄	1	1	yes	characteristic
205	#1437	C₂²⋊C₄	1	1	yes	characteristic
206	#1437	C₂²⋊C₄	1	1	yes	characteristic
207	#1437	C₂²⋊C₄	1	1	yes	characteristic
208	#1436	C₂²⋊C₄	1	1	yes	characteristic
209	#1436	C₂²⋊C₄	1	1	yes	characteristic
210	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
211	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
212	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
213	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
214	C₂⁶	#120	1	1	yes	characteristic
215	C₂²×#41	C₂²×D₄	1	2	yes	—
216	C₂²×#41	C₂×#41	1	2	yes	—
217	C₂²×#41	H(5,𝔽₂)	1	2	yes	—
218	C₂²×#41	H(5,𝔽₂)	1	2	yes	—
219	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
220	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
221	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
222	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
223	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
224	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
225	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
226	C₂³×D₄	#120	1	1	yes	characteristic
227	C₂³×D₄	#120	1	1	yes	characteristic
228	C₂³×D₄	C₂³×C₄	1	1	yes	characteristic
229	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
230	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
231	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
232	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
233	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
234	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
235	C₂⁴×C₄	#120	1	1	yes	characteristic
236	C₂⁴×C₄	#120	1	1	yes	characteristic
237	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
238	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
239	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
240	C₂×#120	C₄×D₄	1	4	yes	—
241	C₂×#120	#120	1	2	yes	—
242	C₂×#120	#123	1	2	yes	—
243	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
244	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
245	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
246	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
247	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
248	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
249	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
250	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
251	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
252	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
253	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
254	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
255	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
256	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
257	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
258	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
259	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
260	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
261	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
262	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
263	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
264	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
265	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
266	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
267	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
268	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
269	C₂²×C₂²⋊C₄	#121	1	4	yes	—
270	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
271	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
272	C₂²×C₄²	#120	1	1	yes	characteristic
273	#386	C₄×D₄	1	4	yes	—
274	#386	#120	1	2	yes	—
275	#386	#123	1	2	yes	—
276	#381	#121	1	4	yes	—
277	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
278	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
279	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
280	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
281	C₂⁵	#379	1	1	yes	characteristic
282	C₂⁵	#379	1	1	yes	characteristic
283	C₂⁵	#379	1	1	yes	characteristic
284	C₂⁵	#386	1	2	yes	—
285	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
286	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
287	C₂⁵	C₂×#120	1	1	yes	characteristic
288	C₂²×Q₈	D₄²	1	2	yes	—
289	C₂²×Q₈	#546	1	2	yes	—
290	C₂²×D₄	C₂×C₄×D₄	1	2	yes	—
291	C₂²×D₄	#518	1	2	yes	—
292	C₂²×D₄	C₂×#120	1	1	yes	characteristic
293	C₂²×D₄	C₂×#123	1	1	yes	characteristic
294	C₂²×D₄	#534	1	1	yes	characteristic
295	C₂²×D₄	#534	1	1	yes	characteristic
296	C₂²×D₄	D₄²	1	2	yes	—
297	C₂²×D₄	#546	1	2	yes	—
298	C₂³×C₄	#379	1	1	yes	characteristic
299	C₂³×C₄	#379	1	1	yes	characteristic
300	C₂³×C₄	#379	1	1	yes	characteristic
301	C₂³×C₄	#379	1	1	yes	characteristic
302	C₂³×C₄	#379	1	1	yes	characteristic
303	C₂³×C₄	#386	1	2	yes	—
304	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
305	C₂³×C₄	C₂×#120	1	1	yes	characteristic
306	C₂³×C₄	C₂×#120	1	1	yes	characteristic
307	C₂³×C₄	C₂×#120	1	1	yes	characteristic
308	C₂³×C₄	C₂×#121	1	2	yes	—
309	C₂³×C₄	#534	1	2	yes	—
310	C₂³×C₄	D₄²	1	2	yes	—
311	C₂³×C₄	D₄²	1	2	yes	—
312	C₂³×C₄	#546	1	2	yes	—
313	C₂³×C₄	#546	1	2	yes	—
314	C₂×C₂²⋊C₄	#386	1	2	yes	—
315	C₂×C₂²⋊C₄	#386	1	2	yes	—
316	C₂×C₂²⋊C₄	B(4,𝔽₂)	1	1	yes	characteristic
317	C₂×C₂²⋊C₄	B(4,𝔽₂)	1	1	yes	characteristic
318	C₂×C₂²⋊C₄	#458	1	1	yes	characteristic
319	C₂×C₂²⋊C₄	#458	1	1	yes	characteristic
320	C₂⁴	#1790	1	1	yes	characteristic
321	C₂⁴	#1790	1	1	yes	characteristic
322	C₂⁴	C₂×#379	1	1	yes	characteristic
323	C₂⁴	C₂×#386	1	1	yes	characteristic
324	C₂⁴	#2308	1	1	yes	characteristic
325	C₂⁴	D₄×C₂²⋊C₄	1	2	yes	—
326	C₂⁴	#2403	1	1	yes	characteristic
327	C₂⁴	#2405	1	1	yes	characteristic
328	C₂²×C₄	#1790	1	1	yes	characteristic
329	C₂²×C₄	#1790	1	1	yes	characteristic
330	C₂²×C₄	D₄×C₂²⋊C₄	1	2	yes	—
331	C₂²×C₄	#2403	1	1	yes	characteristic
332	C₂²×C₄	#2405	1	1	yes	characteristic
333	C₂²×C₄	#2410	1	2	yes	—
334	C₂²×C₄	#2410	1	2	yes	—
335	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
336	C₂²×C₄	C₂×#458	1	1	yes	characteristic
337	C₂²×C₄	#3026	1	2	yes	—
338	C₂³	#12755	1	2	yes	—
339	C₂³	#13867	1	1	yes	characteristic
340	C₂³	C₂×#1790	1	1	yes	characteristic
341	C₂³	#20609	1	1	yes	characteristic
342	C₂³	#21776	1	2	yes	—
343	C₂³	#23895	1	2	yes	—
344	C₂×C₄	#24404	1	2	yes	—
345	C₂×C₄	#24405	1	2	yes	—
346	C₂²	#359531	1	1	yes	characteristic
347	C₂²	#359549	1	1	yes	characteristic
348	C₂²	#359591	1	1	yes	characteristic
349	C₂²	C₂×#12755	1	1	yes	characteristic
350	C₂²	#493569	1	1	yes	characteristic
351	C₂²	#493641	1	1	yes	characteristic
352	C₂²	#493648	1	1	yes	characteristic
353	C₂	#72232729	1	1	yes	characteristic
354	C₂	#72232821	1	1	yes	characteristic
355	C₂	#72260446	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#359531
commutator	C₂³×D₄	C₂³×C₄
Frattini, cosocle	C₂³×#41	C₂⁴
prime radical	#72260601	C₂
LCS	G ▷ C₂³×D₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂²×#546 ◁ G
LECS	G ▷ C₂³×#41 ▷ C₂³ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72260685	C₂	semidirect
2. #72260683	C₂	semidirect
4. #72260565	C₂	semidirect
5. #72260439	C₂	semidirect
6. #72238524	C₂	semidirect
7. #72235062	C₂	semidirect
8. #72234781	C₂	semidirect
9. #72215536	C₂	semidirect
10. #72215527	C₂	semidirect
11. #72214206	C₂	semidirect
14. #6385984	C₂²	semidirect
15. #6385972	C₂²	semidirect
16. #6342764	C₂²	semidirect
17. #5021210	C₄	semidirect
18. #4941252	C₄	semidirect
19. #4607561	C₄	semidirect
21. #2925513	C₄	semidirect
22. #2032498	C₄	semidirect
23. #2031998	C₄	semidirect
24. #1419350	C₄	semidirect
27. #647656	C₄	semidirect
31. #496228	C₂²	semidirect
32. #493385	C₂²	semidirect
33. #493352	C₂²	semidirect
34. #359513	C₂²	semidirect
35. #359507	C₂²	semidirect
37. #201819	C₂²	semidirect
38. #188085	C₂²	semidirect
39. #128059	C₂²	semidirect
40. #128034	C₂²	semidirect
41. #107117	C₂²	semidirect
42. #106740	C₂²	semidirect
44. C₂²×D₄²	C₂×C₄	semidirect
50. C₂×#2669	C₂×C₄	semidirect
51. C₂×#2669	C₂×C₄	semidirect
66. C₂×#2380	C₂×C₄	semidirect
75. #15948	C₂×C₄	semidirect
78. #15947	C₂×C₄	semidirect
82. #15463	C₂×C₄	semidirect
85. #15266	C₂×C₄	semidirect
88. #15261	C₂×C₄	semidirect
89. #15261	C₂×C₄	semidirect
92. #15258	C₂×C₄	semidirect
93. #15258	C₂×C₄	semidirect
96. #14666	C₂×C₄	semidirect
98. #14410	C₂×C₄	semidirect
99. #14358	C₂×C₄	semidirect
103. #14134	C₂×C₄	semidirect
106. #13087	D₄	semidirect
152. C₂×#410	C₂×D₄	semidirect
185. #1785	C₂×D₄	semidirect

Maximal subgroups

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

subgroup	index
#72260685	2
#72260683	2
#72260601	2
#72260565	2
#72260439	2
#72238524	2
#72235062	2
#72234781	2
#72215536	2
#72215527	2
#72214206	2