Subgroups — #29699926

Order 15616.

736 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21446760	C₂	1	2	yes	maximal
2	#21446385	C₂	1	2	yes	maximal
3	#21446378	C₂	1	2	yes	maximal
4	#21445971	C₂	1	1	yes	maximal, characteristic
5	#21445936	C₂	1	1	yes	maximal, characteristic
6	#21445936	C₂	1	1	yes	maximal, characteristic
7	#21445694	C₂	1	2	yes	maximal
8	#21445672	C₂	1	1	yes	maximal, characteristic
9	#21445672	C₂	1	1	yes	maximal, characteristic
10	C₄×C₄⋊#92418	C₂	1	1	yes	maximal, characteristic
11	C₄²×Q₈×C₆₁	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄⋊#92418	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊#92418	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊#92418	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊#92418	C₂²	1	2	yes	—
16	C₂×C₄⋊#92418	C₂²	1	2	yes	—
17	C₂×C₄⋊#92418	C₂²	1	1	yes	characteristic
18	C₂×#14519688	C₂²	1	2	yes	—
19	C₂×#14519688	C₂²	1	2	yes	—
20	C₂×C₄×#92418	C₂²	1	2	yes	—
21	#16839517	C₂²	1	2	yes	—
22	#16839517	C₂²	1	2	yes	—
23	#16839517	C₂²	1	2	yes	—
24	#16839517	C₂²	1	2	yes	—
25	#16839517	C₂²	1	2	yes	—
26	#16839517	C₂²	1	2	yes	—
27	#16839517	C₂²	1	2	yes	—
28	C₂×C₄×Q₈×C₆₁	C₄	1	1	yes	characteristic
29	C₂×C₄×Q₈×C₆₁	C₄	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
31	C₄×C₄⋊C₄×C₆₁	C₄	1	1	yes	characteristic
32	C₄×C₄⋊C₄×C₆₁	C₄	1	1	yes	characteristic
33	C₄×C₄⋊C₄×C₆₁	C₄	1	1	yes	characteristic
34	C₄×C₄⋊C₄×C₆₁	C₄	1	1	yes	characteristic
35	C₄×C₄⋊C₄×C₆₁	C₄	1	1	yes	characteristic
36	C₄×C₄⋊C₄×C₆₁	C₄	1	1	yes	characteristic
37	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
38	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
39	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
40	C₄³×C₆₁	C₂²	1	1	yes	characteristic
41	C₄³×C₆₁	C₂²	1	1	yes	characteristic
42	C₄³×C₆₁	C₂²	1	1	yes	characteristic
43	C₂²×#92418	C₂³	1	2	yes	—
44	C₂²×#92418	C₂³	1	2	yes	—
45	C₂²×#92418	C₂³	1	2	yes	—
46	C₂²×#92418	C₂³	1	2	yes	—
47	C₄⋊#92418	—	2	4	no	—
48	C₄⋊#92418	—	2	2	no	—
49	C₄⋊#92418	—	2	2	no	—
50	C₄⋊#92418	—	2	2	no	—
51	C₄⋊#92418	—	4	2	no	—
52	C₄⋊#92418	Q₈	1	4	yes	complemented
53	#14519688	—	2	4	no	—
54	#14519688	—	4	2	no	—
55	C₄×#92418	—	4	2	no	—
56	C₂²×Q₈×C₆₁	C₂×C₄	1	1	yes	characteristic
57	C₄×Q₈×C₆₁	—	2	4	no	—
58	C₄×Q₈×C₆₁	—	2	4	no	—
59	C₄×Q₈×C₆₁	—	2	2	no	—
60	C₄×Q₈×C₆₁	—	2	2	no	—
61	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
80	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
81	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
82	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
83	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
84	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
86	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
89	#95×C₆₁	C₂×C₄	1	1	yes	characteristic
90	#95×C₆₁	C₂×C₄	1	1	yes	characteristic
91	#95×C₆₁	C₂×C₄	1	1	yes	characteristic
92	#95×C₆₁	C₂×C₄	1	1	yes	characteristic
93	#95×C₆₁	C₂×C₄	1	1	yes	characteristic
94	#95×C₆₁	C₂×C₄	1	1	yes	characteristic
95	C₂×Q₈×C₆₁	—	2	2	no	—
96	C₂×Q₈×C₆₁	—	2	2	no	—
97	C₂×Q₈×C₆₁	—	2	2	no	—
98	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
113	C₄⋊C₄×C₆₁	—	2	2	no	—
114	C₄⋊C₄×C₆₁	—	2	2	no	—
115	C₄⋊C₄×C₆₁	—	2	2	no	—
116	C₄⋊C₄×C₆₁	—	2	2	no	—
117	C₄⋊C₄×C₆₁	—	2	2	no	—
118	C₄⋊C₄×C₆₁	—	2	2	no	—
119	C₄⋊C₄×C₆₁	—	2	2	no	—
120	C₄⋊C₄×C₆₁	—	2	2	no	—
121	C₄⋊C₄×C₆₁	M₁₆	1	4	yes	—
122	C₄²×C₆₁	—	2	2	no	—
123	C₄²×C₆₁	—	2	2	no	—
124	C₄²×C₆₁	—	2	2	no	—
125	C₄²×C₆₁	—	2	2	no	—
126	C₄²×C₆₁	—	2	2	no	—
127	C₄²×C₆₁	—	2	2	no	—
128	C₄²×C₆₁	—	2	2	no	—
129	C₄²×C₆₁	—	2	2	no	—
130	C₄²×C₆₁	—	2	1	no	—
131	C₄²×C₆₁	—	2	1	no	—
132	C₄²×C₆₁	—	2	1	no	—
133	C₄²×C₆₁	—	2	1	no	—
134	C₄²×C₆₁	—	2	1	no	—
135	C₄²×C₆₁	—	2	1	no	—
136	C₄²×C₆₁	—	2	1	no	—
137	C₄²×C₆₁	—	2	1	no	—
138	C₄²×C₆₁	—	2	1	no	—
139	C₄²×C₆₁	—	2	1	no	—
140	C₄²×C₆₁	—	4	1	no	—
141	C₄²×C₆₁	—	4	1	no	—
142	C₄²×C₆₁	—	4	1	no	—
143	C₄²×C₆₁	M₁₆	1	4	yes	—
144	C₄²×C₆₁	C₂×Q₈	1	2	yes	—
145	C₄²×C₆₁	#41	1	2	yes	—
146	C₄²×C₆₁	#41	1	2	yes	—
147	C₄²×C₆₁	#41	1	2	yes	—
148	C₂×#92418	—	2	2	no	—
149	C₂×#92418	—	2	2	no	—
150	C₂×#92418	—	2	2	no	—
151	C₂×#92418	—	2	2	no	—
152	C₂×#92418	—	2	2	no	—
153	C₂×#92418	—	2	2	no	—
154	C₂×#92418	—	2	2	no	—
155	C₂×#92418	—	2	2	no	—
156	C₂×#92418	—	2	2	no	—
157	C₂×#92418	—	2	2	no	—
158	C₂×#92418	—	2	2	no	—
159	C₂×#92418	C₂×Q₈	1	4	yes	—
160	C₂³×C₆₁	C₂³×C₄	1	1	yes	characteristic
161	Q₈×C₆₁	—	2	8	no	—
162	C₂×C₄×C₆₁	—	2	1	no	—
163	C₂×C₄×C₆₁	—	2	1	no	—
164	C₂×C₄×C₆₁	—	2	1	no	—
165	C₂×C₄×C₆₁	—	2	1	no	—
166	C₂×C₄×C₆₁	—	2	1	no	—
167	C₂×C₄×C₆₁	—	2	1	no	—
168	C₂×C₄×C₆₁	—	2	1	no	—
169	C₂×C₄×C₆₁	—	2	1	no	—
170	C₂×C₄×C₆₁	—	2	1	no	—
171	C₂×C₄×C₆₁	—	2	1	no	—
172	C₂×C₄×C₆₁	—	2	1	no	—
173	C₂×C₄×C₆₁	—	2	1	no	—
174	C₂×C₄×C₆₁	—	2	1	no	—
175	C₂×C₄×C₆₁	—	2	1	no	—
176	C₂×C₄×C₆₁	—	2	1	no	—
177	C₂×C₄×C₆₁	—	2	1	no	—
178	C₂×C₄×C₆₁	—	2	1	no	—
179	C₂×C₄×C₆₁	—	2	1	no	—
180	C₂×C₄×C₆₁	—	2	1	no	—
181	C₂×C₄×C₆₁	—	2	1	no	—
182	C₂×C₄×C₆₁	—	2	1	no	—
183	C₂×C₄×C₆₁	—	2	1	no	—
184	C₂×C₄×C₆₁	—	2	1	no	—
185	C₂×C₄×C₆₁	—	2	1	no	—
186	C₂×C₄×C₆₁	—	2	1	no	—
187	C₂×C₄×C₆₁	—	2	1	no	—
188	C₂×C₄×C₆₁	—	2	1	no	—
189	C₂×C₄×C₆₁	—	2	1	no	—
190	C₂×C₄×C₆₁	—	2	1	no	—
191	C₂×C₄×C₆₁	—	2	1	no	—
192	C₂×C₄×C₆₁	—	2	1	no	—
193	C₂×C₄×C₆₁	#117	1	2	yes	—
194	C₂×C₄×C₆₁	#117	1	2	yes	—
195	C₂×C₄×C₆₁	C₄×Q₈	1	2	yes	—
196	C₂×C₄×C₆₁	C₄×Q₈	1	2	yes	—
197	C₂×C₄×C₆₁	C₂×M₁₆	1	2	yes	—
198	C₂×C₄×C₆₁	C₂×M₁₆	1	2	yes	—
199	C₂×C₄×C₆₁	C₂×M₁₆	1	2	yes	—
200	C₂×C₄×C₆₁	C₂×M₁₆	1	2	yes	—
201	C₂×C₄×C₆₁	C₂×M₁₆	1	2	yes	—
202	C₂×C₄×C₆₁	C₂×M₁₆	1	2	yes	—
203	C₂×C₄×C₆₁	#131	1	2	yes	—
204	C₂×C₄×C₆₁	C₂²×Q₈	1	1	yes	characteristic
205	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
206	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
207	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
208	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
209	C₂×C₄×C₆₁	2₋¹⁺⁴	1	1	yes	characteristic
210	#92418	—	2	4	no	—
211	#92418	—	4	2	no	—
212	#92418	—	4	2	no	—
213	#92418	—	4	2	no	—
214	#22823	—	61	1	no	maximal, Sylow
215	C₂²×C₆₁	C₂×#117	1	1	yes	characteristic
216	C₂²×C₆₁	C₂×C₄×Q₈	1	1	yes	characteristic
217	C₂²×C₆₁	#520	1	1	yes	characteristic
218	C₂²×C₆₁	C₂²×M₁₆	1	1	yes	characteristic
219	C₂²×C₆₁	C₂²×M₁₆	1	1	yes	characteristic
220	C₂²×C₆₁	C₂×#131	1	1	yes	characteristic
221	C₂²×C₆₁	#568	1	1	yes	characteristic
222	C₄×C₆₁	—	2	2	no	—
223	C₄×C₆₁	—	2	2	no	—
224	C₄×C₆₁	—	2	2	no	—
225	C₄×C₆₁	—	2	2	no	—
226	C₄×C₆₁	—	2	2	no	—
227	C₄×C₆₁	—	2	2	no	—
228	C₄×C₆₁	—	2	2	no	—
229	C₄×C₆₁	—	2	2	no	—
230	C₄×C₆₁	—	4	1	no	—
231	C₄×C₆₁	—	4	1	no	—
232	C₄×C₆₁	—	4	1	no	—
233	C₄×C₆₁	—	4	1	no	—
234	C₄×C₆₁	—	4	1	no	—
235	C₄×C₆₁	#446	1	4	yes	—
236	C₄×C₆₁	#554	1	1	yes	characteristic
237	C₄×C₆₁	#556	1	1	yes	characteristic
238	C₄×C₆₁	#557	1	1	yes	characteristic
239	C₄×C₆₁	#559	1	1	yes	characteristic
240	C₄²×Q₈	D₆₁	1	1	yes	characteristic
241	#1985	—	61	2	no	—
242	#1917	—	61	2	no	—
243	#1916	—	61	2	no	—
244	#1842	—	61	1	no	—
245	#1831	—	61	1	no	—
246	#1831	—	61	1	no	—
247	#1771	—	61	2	no	—
248	#1767	—	61	1	no	—
249	#1767	—	61	1	no	—
250	C₄×C₄⋊C₈	—	61	1	no	—
251	C₂×C₆₁	#2355	1	1	yes	characteristic
252	C₂×C₆₁	#2920	1	1	yes	characteristic
253	C₂×C₆₁	#2925	1	1	yes	characteristic
254	C₂×C₆₁	C₂×#446	1	1	yes	characteristic
255	C₂×C₆₁	Q₈×M₁₆	1	1	yes	characteristic
256	C₂×C₆₁	#2989	1	1	yes	characteristic
257	C₂×C₆₁	#2990	1	1	yes	characteristic
258	C₂×C₄×Q₈	Dic₆₁	1	1	yes	characteristic
259	C₂×C₄×Q₈	Dic₆₁	1	1	yes	characteristic
260	C₂×C₄×Q₈	C₂×D₆₁	1	1	yes	characteristic
261	C₂×C₄⋊C₈	—	61	1	no	—
262	C₂×C₄⋊C₈	—	61	1	no	—
263	C₂×C₄⋊C₈	—	61	1	no	—
264	C₂×C₄⋊C₈	—	61	1	no	—
265	C₂×C₄⋊C₈	—	61	2	no	—
266	C₂×C₄⋊C₈	—	61	2	no	—
267	C₂×#97	—	61	2	no	—
268	C₂×#97	—	61	2	no	—
269	C₂×C₄×C₈	—	61	2	no	—
270	C₄×C₄⋊C₄	Dic₆₁	1	1	yes	characteristic
271	C₄×C₄⋊C₄	Dic₆₁	1	1	yes	characteristic
272	C₄×C₄⋊C₄	Dic₆₁	1	1	yes	characteristic
273	C₄×C₄⋊C₄	Dic₆₁	1	1	yes	characteristic
274	C₄×C₄⋊C₄	Dic₆₁	1	1	yes	characteristic
275	C₄×C₄⋊C₄	Dic₆₁	1	1	yes	characteristic
276	C₄×C₄⋊C₄	C₂×D₆₁	1	1	yes	characteristic
277	C₄×C₄⋊C₄	C₂×D₆₁	1	1	yes	characteristic
278	C₄×C₄⋊C₄	C₂×D₆₁	1	1	yes	characteristic
279	C₄³	C₂×D₆₁	1	1	yes	characteristic
280	C₄³	C₂×D₆₁	1	1	yes	characteristic
281	C₄³	C₂×D₆₁	1	1	yes	characteristic
282	#336	—	61	2	no	—
283	#336	—	61	2	no	—
284	#336	—	61	2	no	—
285	#336	—	61	2	no	—
286	#336	—	61	2	no	—
287	#336	—	61	2	no	—
288	#336	—	61	2	no	—
289	C₆₁	#22823	1	1	yes	characteristic, complemented, Sylow
290	C₂²×Q₈	C₂×Dic₆₁	1	1	yes	characteristic
291	C₂²×C₈	—	61	2	no	—
292	C₂²×C₈	—	61	2	no	—
293	C₂²×C₈	—	61	2	no	—
294	C₂²×C₈	—	61	2	no	—
295	C₄×Q₈	—	2	4	no	—
296	C₄×Q₈	—	2	4	no	—
297	C₄×Q₈	—	2	2	no	—
298	C₄×Q₈	—	2	2	no	—
299	C₂×C₄⋊C₄	C₂×Dic₆₁	1	1	yes	characteristic
300	C₂×C₄⋊C₄	C₂×Dic₆₁	1	1	yes	characteristic
301	C₂×C₄⋊C₄	C₂×Dic₆₁	1	1	yes	characteristic
302	C₂×C₄⋊C₄	C₂×Dic₆₁	1	1	yes	characteristic
303	C₂×C₄⋊C₄	C₂×Dic₆₁	1	1	yes	characteristic
304	C₂×C₄⋊C₄	C₂×Dic₆₁	1	1	yes	characteristic
305	C₂×C₄⋊C₄	C₂×Dic₆₁	1	1	yes	characteristic
306	C₂×C₄⋊C₄	C₂×Dic₆₁	1	1	yes	characteristic
307	C₂×C₄⋊C₄	C₂×Dic₆₁	1	1	yes	characteristic
308	C₂×C₄²	C₂×Dic₆₁	1	1	yes	characteristic
309	C₂×C₄²	C₂×Dic₆₁	1	1	yes	characteristic
310	C₂×C₄²	C₂×Dic₆₁	1	1	yes	characteristic
311	C₂×C₄²	C₂×Dic₆₁	1	1	yes	characteristic
312	C₂×C₄²	C₂×Dic₆₁	1	1	yes	characteristic
313	C₂×C₄²	C₂×Dic₆₁	1	1	yes	characteristic
314	C₂×C₄²	C₂×Dic₆₁	1	1	yes	characteristic
315	C₂×C₄²	C₂×Dic₆₁	1	1	yes	characteristic
316	C₂×C₄²	C₂×Dic₆₁	1	1	yes	characteristic
317	C₂×C₄²	C₂×Dic₆₁	1	1	yes	characteristic
318	C₂×C₄²	C₂×Dic₆₁	1	1	yes	characteristic
319	C₂×C₄²	C₂×Dic₆₁	1	1	yes	characteristic
320	C₂×C₄²	C₂²×D₆₁	1	1	yes	characteristic
321	C₂×C₄²	C₂²×D₆₁	1	1	yes	characteristic
322	C₂×C₄²	C₂²×D₆₁	1	1	yes	characteristic
323	C₂×C₄²	C₂²×D₆₁	1	1	yes	characteristic
324	C₂×C₄²	C₂²×D₆₁	1	1	yes	characteristic
325	C₂×C₄²	C₂²×D₆₁	1	1	yes	characteristic
326	C₂×C₄²	C₂²×D₆₁	1	1	yes	characteristic
327	C₄⋊C₈	—	61	4	no	—
328	C₄⋊C₈	—	122	4	no	—
329	C₄⋊C₈	—	122	2	no	—
330	C₄⋊C₈	—	122	2	no	—
331	C₄⋊C₈	—	122	2	no	—
332	C₄⋊C₈	—	244	2	no	—
333	#97	—	122	4	no	—
334	#97	—	244	2	no	—
335	C₄×C₈	—	244	2	no	—
336	#95	C₂×Dic₆₁	1	1	yes	characteristic
337	#95	C₂×Dic₆₁	1	1	yes	characteristic
338	#95	C₂×Dic₆₁	1	1	yes	characteristic
339	#95	C₂×Dic₆₁	1	1	yes	characteristic
340	#95	C₂×Dic₆₁	1	1	yes	characteristic
341	#95	C₂×Dic₆₁	1	1	yes	characteristic
342	C₂×Q₈	—	2	2	no	—
343	C₂×Q₈	—	2	2	no	—
344	C₂×Q₈	—	2	2	no	—
345	C₂²×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
346	C₂²×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
347	C₂²×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
348	C₂²×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
349	C₂²×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
350	C₂²×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
351	C₂²×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
352	C₂²×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
353	C₂²×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
354	C₂²×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
355	C₂²×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
356	C₂²×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
357	C₂²×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
358	C₂²×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
359	C₂²×C₄	C₂³×D₆₁	1	1	yes	characteristic
360	C₂×C₈	—	61	4	no	—
361	C₂×C₈	—	122	2	no	—
362	C₂×C₈	—	122	2	no	—
363	C₂×C₈	—	122	2	no	—
364	C₂×C₈	—	122	2	no	—
365	C₂×C₈	—	122	2	no	—
366	C₂×C₈	—	122	2	no	—
367	C₂×C₈	—	122	2	no	—
368	C₂×C₈	—	122	2	no	—
369	C₂×C₈	—	122	2	no	—
370	C₂×C₈	—	122	2	no	—
371	C₂×C₈	—	122	2	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	#11758194	1	4	yes	—
381	C₄²	—	2	1	no	—
382	C₄²	—	2	1	no	—
383	C₄²	—	2	1	no	—
384	C₄²	—	2	1	no	—
385	C₄²	—	2	1	no	—
386	C₄²	—	2	1	no	—
387	C₄²	—	2	1	no	—
388	C₄²	—	2	1	no	—
389	C₄²	—	2	1	no	—
390	C₄²	—	2	1	no	—
391	C₄²	—	2	2	no	—
392	C₄²	—	2	2	no	—
393	C₄²	—	2	2	no	—
394	C₄²	—	2	2	no	—
395	C₄²	—	2	2	no	—
396	C₄²	—	2	2	no	—
397	C₄²	—	2	2	no	—
398	C₄²	—	2	2	no	—
399	C₄²	—	4	1	no	—
400	C₄²	—	4	1	no	—
401	C₄²	—	4	1	no	—
402	C₄²	#11758194	1	4	yes	—
403	C₄²	#11758222	1	2	yes	—
404	C₄²	#11758222	1	2	yes	—
405	C₄²	Q₈×D₆₁	1	2	yes	—
406	C₄²	#11758226	1	2	yes	—
407	C₂³	C₂³×Dic₆₁	1	1	yes	characteristic
408	Q₈	—	2	8	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	#14519736	1	2	yes	—
441	C₂×C₄	#14519736	1	2	yes	—
442	C₂×C₄	Q₈×Dic₆₁	1	2	yes	—
443	C₂×C₄	Q₈×Dic₆₁	1	2	yes	—
444	C₂×C₄	C₂×#11758194	1	2	yes	—
445	C₂×C₄	C₂×#11758194	1	2	yes	—
446	C₂×C₄	C₂×#11758194	1	2	yes	—
447	C₂×C₄	C₂×#11758194	1	2	yes	—
448	C₂×C₄	C₂×#11758194	1	2	yes	—
449	C₂×C₄	C₂×#11758194	1	2	yes	—
450	C₂×C₄	#14519784	1	2	yes	—
451	C₂×C₄	C₂×Q₈×D₆₁	1	1	yes	characteristic
452	C₂×C₄	C₂×#11758222	1	1	yes	characteristic
453	C₂×C₄	C₂×#11758222	1	1	yes	characteristic
454	C₂×C₄	C₂×#11758226	1	1	yes	characteristic
455	C₂×C₄	#14519823	1	1	yes	characteristic
456	C₂×C₄	#14519824	1	1	yes	characteristic
457	C₈	—	122	4	no	—
458	C₈	—	244	2	no	—
459	C₈	—	244	2	no	—
460	C₈	—	244	2	no	—
461	C₂²	C₂×#14519736	1	1	yes	characteristic
462	C₂²	C₂×Q₈×Dic₆₁	1	1	yes	characteristic
463	C₂²	#16840245	1	1	yes	characteristic
464	C₂²	C₂²×#11758194	1	1	yes	characteristic
465	C₂²	C₂²×#11758194	1	1	yes	characteristic
466	C₂²	C₂×#14519784	1	1	yes	characteristic
467	C₂²	#16840529	1	1	yes	characteristic
468	C₄	—	2	2	no	—
469	C₄	—	2	2	no	—
470	C₄	—	2	2	no	—
471	C₄	—	2	2	no	—
472	C₄	—	2	2	no	—
473	C₄	—	2	2	no	—
474	C₄	—	2	2	no	—
475	C₄	—	2	2	no	—
476	C₄	—	4	1	no	—
477	C₄	—	4	1	no	—
478	C₄	—	4	1	no	—
479	C₄	—	4	1	no	—
480	C₄	—	4	1	no	—
481	C₄	#16839893	1	4	yes	—
482	C₄	#16840472	1	1	yes	characteristic
483	C₄	#16840485	1	1	yes	characteristic
484	C₄	#16840490	1	1	yes	characteristic
485	C₄	#16840497	1	1	yes	characteristic
486	C₂	#21448776	1	1	yes	characteristic
487	C₂	#21454452	1	1	yes	characteristic
488	C₂	#21454485	1	1	yes	characteristic
489	C₂	C₂×#16839893	1	1	yes	characteristic
490	C₂	Q₈×#11758194	1	1	yes	characteristic
491	C₂	#21454936	1	1	yes	characteristic
492	C₂	#21454944	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₆₁
commutator, socle, prime radical	C₂³×C₆₁	C₂³×C₄
Fitting	C₄²×Q₈×C₆₁	C₂
cosocle	C₂²×C₄×C₆₁	C₂⁴
hypercenter	C₄²×Q₈	D₆₁
hypocenter	C₆₁	#22823
LCS	G ▷ C₂³×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₄²×Q₈

Complements

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

N	H ≅ G/N	type
52. C₄⋊#92418	Q₈	semidirect
289. C₆₁	#22823	semidirect

Maximal subgroups

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

subgroup	index
#21446760	2
#21446385	2
#21446378	2
#21445971	2
#21445936	2
#21445694	2
#21445672	2
C₄×C₄⋊#92418	2
C₄²×Q₈×C₆₁	2
#22823	61