Subgroups — #30616608

Order 15616.

826 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21462297	C₂	1	1	yes	maximal, characteristic
2	#21462256	C₂	1	1	yes	maximal, characteristic
3	#21461932	C₂	1	1	yes	maximal, characteristic, complemented
4	#21461932	C₂	1	1	yes	maximal, characteristic, complemented
5	#21461931	C₂	1	1	yes	maximal, characteristic, complemented
6	#21461930	C₂	1	1	yes	maximal, characteristic, complemented
7	#21461770	C₂	1	1	yes	maximal, characteristic
8	#21461770	C₂	1	1	yes	maximal, characteristic
9	#21461769	C₂	1	1	yes	maximal, characteristic
10	#21461768	C₂	1	1	yes	maximal, characteristic
11	#21461633	C₂	1	1	yes	maximal, characteristic, complemented
12	#21461633	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×#14519846	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×#14519845	C₂	1	1	yes	maximal, characteristic, complemented
15	#433×D₆₁	C₂	1	1	yes	maximal, characteristic
16	C₂×#14519856	C₂²	1	1	yes	characteristic
17	C₂²×C₄⋊#6923	C₂²	1	1	yes	characteristic
18	C₂×#14519846	C₂²	1	1	yes	characteristic
19	C₂×#14519846	C₂²	1	1	yes	characteristic
20	C₂×#14519846	C₂²	1	1	yes	characteristic
21	C₂×#14519846	C₂²	1	1	yes	characteristic
22	C₂×#14519845	C₂²	1	1	yes	characteristic
23	C₂×#14519845	C₂²	1	1	yes	characteristic
24	C₂×#14519845	C₂²	1	1	yes	characteristic
25	C₂×#14519845	C₂²	1	1	yes	characteristic
26	#16840712	—	2	1	no	—
27	#16840712	—	2	1	no	—
28	#16840711	—	2	1	no	—
29	#16840711	—	2	1	no	—
30	#16840708	C₂²	1	1	yes	characteristic
31	#16840706	C₂²	1	1	yes	characteristic
32	#16840704	C₂²	1	1	yes	characteristic
33	#16840704	C₂²	1	1	yes	characteristic
34	C₄⋊C₄×#6923	—	2	1	no	—
35	C₄⋊C₄×#6923	—	2	1	no	—
36	C₄×C₄⋊#6923	C₂²	1	1	yes	characteristic
37	C₄×C₄⋊#6923	C₂²	1	1	yes	characteristic
38	C₄×C₄⋊#6923	C₂²	1	1	yes	characteristic
39	C₄×C₄⋊#6923	C₂²	1	1	yes	characteristic
40	C₄×C₄⋊#6923	C₂²	1	1	yes	characteristic
41	C₄×C₄⋊#6923	C₂²	1	1	yes	characteristic
42	C₂²⋊C₄×#6923	—	2	1	no	—
43	C₂²⋊C₄×#6923	—	2	1	no	—
44	#16840636	C₂²	1	1	yes	characteristic
45	#16840636	C₂²	1	1	yes	characteristic
46	#16840636	C₂²	1	1	yes	characteristic
47	#16840636	C₂²	1	1	yes	characteristic
48	#16840636	C₂²	1	1	yes	characteristic
49	#16840636	C₂²	1	1	yes	characteristic
50	#16840636	C₂²	1	1	yes	characteristic
51	#16840636	C₂²	1	1	yes	characteristic
52	#117×D₆₁	C₂²	1	1	yes	characteristic
53	#16839824	C₄	1	1	yes	characteristic, complemented
54	#16839823	C₄	1	1	yes	characteristic, complemented
55	#16839822	C₄	1	1	yes	characteristic, complemented
56	#16839822	C₄	1	1	yes	characteristic, complemented
57	#16839821	C₄	1	1	yes	characteristic, complemented
58	#16839820	C₄	1	1	yes	characteristic, complemented
59	#16839820	C₄	1	1	yes	characteristic, complemented
60	C₄⋊C₈×D₆₁	C₂²	1	1	yes	characteristic
61	C₄⋊C₈×D₆₁	C₂²	1	1	yes	characteristic
62	C₂²⋊C₈×D₆₁	C₂²	1	1	yes	characteristic
63	C₂²⋊C₈×D₆₁	C₂²	1	1	yes	characteristic
64	#97×D₆₁	C₂²	1	1	yes	characteristic
65	C₄×C₈×D₆₁	C₂²	1	1	yes	characteristic
66	C₆₁×#433	C₄	1	1	yes	characteristic, complemented
67	C₂³×#6923	—	2	1	no	—
68	#14519856	—	2	2	no	—
69	#14519856	—	2	2	no	—
70	C₂×C₄⋊#6923	—	2	1	no	—
71	C₂×C₄⋊#6923	—	2	2	no	—
72	C₂×C₄⋊#6923	—	2	2	no	—
73	C₂×C₄⋊#6923	—	2	1	no	—
74	C₂×C₄⋊#6923	—	2	1	no	—
75	C₂×C₄⋊#6923	C₂³	1	1	yes	characteristic
76	C₂×C₄⋊#6923	C₂³	1	1	yes	characteristic
77	C₂×C₄⋊#6923	C₂³	1	1	yes	characteristic
78	C₂×C₄⋊#6923	C₂³	1	1	yes	characteristic
79	C₂×C₄⋊#6923	C₂³	1	1	yes	characteristic
80	C₂×C₄⋊#6923	C₂³	1	1	yes	characteristic
81	C₂×C₄⋊#6923	C₂³	1	1	yes	characteristic
82	C₂×C₄⋊#6923	C₂³	1	1	yes	characteristic
83	C₂×C₂²⋊#6923	—	2	1	no	—
84	C₂×C₂²⋊#6923	—	2	1	no	—
85	C₂×C₂²⋊#6923	—	2	1	no	—
86	C₂×C₄×#6923	—	2	1	no	—
87	C₂×C₄×#6923	—	2	1	no	—
88	C₂×C₄×#6923	—	2	1	no	—
89	C₂×C₄×#6923	—	2	1	no	—
90	C₂×C₄×#6923	—	2	1	no	—
91	C₂×C₄×#6923	—	2	1	no	—
92	C₂×C₄×#6923	—	2	1	no	—
93	#14519846	—	2	2	no	—
94	#14519846	—	2	2	no	—
95	#14519846	—	2	2	no	—
96	#14519846	—	2	2	no	—
97	#14519845	—	2	2	no	—
98	#14519845	—	2	2	no	—
99	#14519845	—	2	2	no	—
100	#14519845	—	2	2	no	—
101	(C₂×#6923)⋊C₄	—	2	1	no	—
102	(C₂×#6923)⋊C₄	—	2	1	no	—
103	(C₂×#6923)⋊C₄	—	2	1	no	—
104	(C₂×#6923)⋊C₄	—	2	1	no	—
105	(C₂×#6923)⋊C₄	—	2	1	no	—
106	(C₂×#6923)⋊C₄	—	2	1	no	—
107	(C₂×#6923)⋊C₄	—	2	1	no	—
108	(C₂×#6923)⋊C₄	—	2	1	no	—
109	(C₂×#6923)⋊C₄	—	2	1	no	—
110	(C₂×#6923)⋊C₄	—	2	1	no	—
111	C₂²×C₄×D₆₁	C₂³	1	1	yes	characteristic
112	C₂×C₈×D₆₁	C₂³	1	1	yes	characteristic
113	C₂×C₈×D₆₁	C₂³	1	1	yes	characteristic
114	C₂×C₈×D₆₁	C₂³	1	1	yes	characteristic
115	C₂×C₈×D₆₁	C₂³	1	1	yes	characteristic
116	#14519736	C₂×C₄	1	1	yes	characteristic
117	#14519735	Q₈	1	1	yes	characteristic
118	#14519735	Q₈	1	1	yes	characteristic
119	#14519734	C₂×C₄	1	1	yes	characteristic
120	#14519734	C₂×C₄	1	1	yes	characteristic
121	#14519733	Q₈	1	1	yes	characteristic
122	#14519733	Q₈	1	1	yes	characteristic
123	C₄⋊C₄×D₆₁	D₄	1	1	yes	characteristic
124	C₄⋊C₄×D₆₁	D₄	1	1	yes	characteristic
125	C₂²⋊C₄×D₆₁	D₄	1	1	yes	characteristic
126	C₂²⋊C₄×D₆₁	D₄	1	1	yes	characteristic
127	C₄²×D₆₁	C₂³	1	1	yes	characteristic
128	C₄²×D₆₁	C₂³	1	1	yes	characteristic
129	C₄⋊#92418	C₂×C₄	1	1	yes	characteristic, complemented
130	C₄⋊#92418	C₂×C₄	1	1	yes	characteristic, complemented
131	#14519706	C₂×C₄	1	1	yes	characteristic, complemented
132	#14519706	C₂×C₄	1	1	yes	characteristic, complemented
133	#14519706	C₂×C₄	1	1	yes	characteristic, complemented
134	#14519706	C₂×C₄	1	1	yes	characteristic, complemented
135	C₂²⋊#92418	C₂×C₄	1	1	yes	characteristic
136	C₂²⋊#92418	C₂×C₄	1	1	yes	characteristic
137	#14519689	C₂×C₄	1	1	yes	characteristic
138	#14519689	C₂×C₄	1	1	yes	characteristic
139	#14519689	C₂×C₄	1	1	yes	characteristic
140	#14519689	C₂×C₄	1	1	yes	characteristic
141	#14519688	C₂×C₄	1	1	yes	characteristic, complemented
142	#14519687	C₂×C₄	1	1	yes	characteristic, complemented
143	#14519687	C₂×C₄	1	1	yes	characteristic, complemented
144	C₄×#92418	C₂×C₄	1	1	yes	characteristic, complemented
145	C₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic, complemented
146	C₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic, complemented
147	#117×C₆₁	C₂×C₄	1	1	yes	characteristic
148	C₄⋊C₈×C₆₁	C₂×C₄	1	1	yes	characteristic, complemented
149	C₄⋊C₈×C₆₁	C₂×C₄	1	1	yes	characteristic, complemented
150	C₂²⋊C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
151	C₂²⋊C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
152	#97×C₆₁	C₂×C₄	1	1	yes	characteristic, complemented
153	C₄×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic, complemented
154	C₂³×D₆₁	C₂×D₄	1	1	yes	characteristic
155	C₂²×#6923	—	2	1	no	—
156	C₂²×#6923	—	2	1	no	—
157	C₂²×#6923	—	2	1	no	—
158	C₂²×#6923	—	2	1	no	—
159	C₂²×#6923	—	2	4	no	—
160	C₂²×#6923	—	2	1	no	—
161	C₂²×#6923	—	2	1	no	—
162	C₂²×#6923	—	2	1	no	—
163	C₂²×#6923	—	2	1	no	—
164	C₂²×#6923	—	8	1	no	—
165	C₂²×#6923	—	8	1	no	—
166	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
167	C₂²×Dic₆₁	C₂×Q₈	1	1	yes	characteristic
168	C₂×C₄×D₆₁	—	2	1	no	—
169	C₂×C₄×D₆₁	—	2	1	no	—
170	C₂×C₄×D₆₁	—	2	1	no	—
171	C₂×C₄×D₆₁	—	2	1	no	—
172	C₂×C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
173	C₂×C₄×D₆₁	C₂×D₄	1	1	yes	characteristic
174	C₂×C₄×D₆₁	C₂×D₄	1	1	yes	characteristic
175	C₂×C₄×D₆₁	C₂×D₄	1	1	yes	characteristic
176	C₂×C₄×D₆₁	C₂×D₄	1	1	yes	characteristic
177	C₂×C₄×D₆₁	C₂×D₄	1	1	yes	characteristic
178	C₂×C₄×D₆₁	C₂×Q₈	1	1	yes	characteristic
179	C₂×C₄×D₆₁	C₂⁴	1	1	yes	characteristic
180	C₂²⋊#6923	—	2	4	no	—
181	C₂²⋊#6923	—	8	1	no	—
182	C₂²⋊#6923	—	8	1	no	—
183	C₄⋊#6923	—	2	4	no	—
184	C₄⋊#6923	—	2	1	no	—
185	C₄⋊#6923	—	2	1	no	—
186	C₄⋊#6923	—	2	1	no	—
187	C₄⋊#6923	—	2	1	no	—
188	C₄⋊#6923	—	2	1	no	—
189	C₄⋊#6923	—	2	1	no	—
190	C₄⋊#6923	—	2	1	no	—
191	C₄⋊#6923	—	2	1	no	—
192	C₄⋊#6923	—	2	1	no	—
193	C₄⋊#6923	—	2	1	no	—
194	C₄⋊#6923	—	2	1	no	—
195	C₄⋊#6923	—	2	1	no	—
196	C₄⋊#6923	—	8	1	no	—
197	C₄⋊#6923	—	8	1	no	—
198	C₄⋊#6923	#41	1	2	yes	—
199	C₄⋊#6923	#41	1	2	yes	—
200	C₄⋊#6923	#41	1	2	yes	—
201	C₄⋊#6923	#41	1	2	yes	—
202	C₄×#6923	—	2	4	no	—
203	C₄×#6923	—	8	1	no	—
204	C₄×#6923	—	8	1	no	—
205	C₄×#6923	—	8	1	no	—
206	C₄×#6923	—	8	1	no	—
207	C₄×#6923	—	8	1	no	—
208	C₄×#6923	—	8	1	no	—
209	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
210	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
211	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
212	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
213	C₄⋊C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
214	C₄⋊C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
215	C₂²⋊C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
216	C₂²⋊C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
217	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
218	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
219	C₂²⋊Dic₆₁	C₄⋊C₄	1	1	yes	characteristic
220	C₂²⋊Dic₆₁	C₄⋊C₄	1	1	yes	characteristic
221	#11758198	C₄⋊C₄	1	1	yes	characteristic
222	#11758198	C₄⋊C₄	1	1	yes	characteristic
223	#11758198	C₄⋊C₄	1	1	yes	characteristic
224	#11758198	C₄⋊C₄	1	1	yes	characteristic
225	C₄⋊Dic₆₁	C₄⋊C₄	1	1	yes	characteristic
226	C₄⋊Dic₆₁	C₄⋊C₄	1	1	yes	characteristic
227	#11758196	C₄⋊C₄	1	1	yes	characteristic
228	#11758196	C₄⋊C₄	1	1	yes	characteristic
229	#11758196	C₄⋊C₄	1	1	yes	characteristic
230	#11758196	C₄⋊C₄	1	1	yes	characteristic
231	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
232	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
233	C₄×Dic₆₁	C₂×Q₈	1	1	yes	characteristic
234	C₄×Dic₆₁	C₂×Q₈	1	1	yes	characteristic
235	C₄×Dic₆₁	C₂×Q₈	1	1	yes	characteristic
236	C₄×Dic₆₁	C₂×Q₈	1	1	yes	characteristic
237	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
238	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
239	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
240	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
241	C₈×D₆₁	—	2	1	no	—
242	C₈×D₆₁	—	2	1	no	—
243	C₈×D₆₁	—	2	1	no	—
244	C₈×D₆₁	—	2	1	no	—
245	C₈×D₆₁	—	2	1	no	—
246	C₈×D₆₁	—	2	1	no	—
247	C₈×D₆₁	—	2	1	no	—
248	C₈×D₆₁	—	2	1	no	—
249	C₂³×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
250	C₂²×D₆₁	—	2	1	no	—
251	C₂²×D₆₁	—	2	1	no	—
252	C₂²×D₆₁	—	2	1	no	—
253	C₂²×D₆₁	—	2	1	no	—
254	C₂²×D₆₁	—	2	1	no	—
255	C₂²×D₆₁	—	2	1	no	—
256	C₂²×D₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
257	C₂²×D₆₁	C₂²×D₄	1	1	yes	characteristic
258	C₂×#6923	—	2	2	no	—
259	C₂×#6923	—	2	2	no	—
260	C₂×#6923	—	2	2	no	—
261	C₂×#6923	—	2	2	no	—
262	C₂×#6923	—	4	1	no	—
263	C₂×#6923	—	4	1	no	—
264	C₂×#6923	—	4	1	no	—
265	C₂×#6923	—	4	1	no	—
266	C₂×#6923	—	4	1	no	—
267	C₂×#6923	—	4	1	no	—
268	C₂×#6923	—	4	1	no	—
269	C₂×#6923	—	4	1	no	—
270	C₂×#6923	—	4	1	no	—
271	C₂×#6923	—	4	1	no	—
272	C₂×#6923	—	4	1	no	—
273	C₂×#6923	—	4	1	no	—
274	C₂×#6923	—	4	1	no	—
275	C₂×#6923	—	4	1	no	—
276	C₂×#6923	—	4	1	no	—
277	C₂×#6923	—	4	1	no	—
278	C₂×#6923	—	4	1	no	—
279	C₂×#6923	—	4	1	no	—
280	C₂×#6923	—	4	1	no	—
281	C₂×#6923	—	4	1	no	—
282	C₂×#6923	—	8	4	no	—
283	C₂×C₄×C₆₁	—	2	1	no	—
284	C₂×C₄×C₆₁	—	2	1	no	—
285	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
286	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
287	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
288	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
289	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
290	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
291	C₂×Dic₆₁	—	2	1	no	—
292	C₂×Dic₆₁	—	2	1	no	—
293	C₂×Dic₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
294	C₂×Dic₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
295	C₂×Dic₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
296	C₂×Dic₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
297	C₂×Dic₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
298	C₂×Dic₆₁	C₂²×Q₈	1	1	yes	characteristic
299	C₄×D₆₁	—	2	1	no	—
300	C₄×D₆₁	—	2	1	no	—
301	C₄×D₆₁	—	2	1	no	—
302	C₄×D₆₁	—	2	1	no	—
303	C₄×D₆₁	—	2	1	no	—
304	C₄×D₆₁	—	2	1	no	—
305	C₄×D₆₁	—	2	1	no	—
306	C₄×D₆₁	—	2	1	no	—
307	C₄×D₆₁	—	2	1	no	—
308	C₄×D₆₁	—	2	1	no	—
309	C₄×D₆₁	—	2	1	no	—
310	C₄×D₆₁	—	2	1	no	—
311	C₄×D₆₁	—	2	1	no	—
312	C₄×D₆₁	—	2	1	no	—
313	C₄×D₆₁	C₂×#41	1	1	yes	characteristic
314	C₄×D₆₁	C₂×#41	1	1	yes	characteristic
315	C₄×D₆₁	C₂×#41	1	1	yes	characteristic
316	C₄×D₆₁	C₂×#41	1	1	yes	characteristic
317	C₈×C₆₁	—	2	1	no	—
318	C₈×C₆₁	—	2	1	no	—
319	C₈×C₆₁	—	2	1	no	—
320	C₈×C₆₁	—	2	1	no	—
321	#92418	—	2	1	no	—
322	#92418	—	2	1	no	—
323	#92418	—	2	1	no	—
324	#92418	—	2	1	no	—
325	#21367	—	61	1	no	maximal, Sylow
326	C₂²×C₆₁	—	2	1	no	—
327	C₂²×C₆₁	—	2	1	no	—
328	C₂²×C₆₁	—	2	1	no	—
329	C₂²×C₆₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
330	C₂×D₆₁	—	2	1	no	—
331	C₂×D₆₁	—	2	1	no	—
332	C₂×D₆₁	—	2	1	no	—
333	C₂×D₆₁	—	4	1	no	—
334	C₂×D₆₁	—	4	1	no	—
335	C₂×D₆₁	—	4	1	no	—
336	C₂×D₆₁	—	4	1	no	—
337	C₂×D₆₁	#525	1	1	yes	characteristic
338	C₂×D₆₁	#525	1	1	yes	characteristic
339	C₂×D₆₁	#576	1	1	yes	characteristic
340	C₂×D₆₁	#577	1	1	yes	characteristic
341	C₂×D₆₁	#577	1	1	yes	characteristic
342	C₂×D₆₁	#578	1	1	yes	characteristic
343	#6923	—	4	2	no	—
344	#6923	—	4	2	no	—
345	#6923	—	4	2	no	—
346	#6923	—	4	2	no	—
347	#6923	—	8	1	no	—
348	#6923	—	8	1	no	—
349	#6923	—	8	1	no	—
350	#6923	—	8	1	no	—
351	C₄×C₆₁	—	2	1	no	—
352	C₄×C₆₁	—	2	1	no	—
353	C₄×C₆₁	—	2	1	no	—
354	C₄×C₆₁	—	2	1	no	—
355	C₄×C₆₁	—	2	1	no	—
356	C₄×C₆₁	C₄×#41	1	1	yes	characteristic
357	C₄×C₆₁	C₄×#41	1	1	yes	characteristic
358	Dic₆₁	—	2	1	no	—
359	Dic₆₁	—	2	1	no	—
360	Dic₆₁	—	2	1	no	—
361	Dic₆₁	—	2	1	no	—
362	Dic₆₁	—	2	1	no	—
363	Dic₆₁	#533	1	1	yes	characteristic
364	Dic₆₁	#533	1	1	yes	characteristic
365	C₂×#433	—	61	1	no	—
366	#2314	—	61	1	no	—
367	#2274	—	61	1	no	—
368	#1949	—	61	1	no	—
369	#1949	—	61	1	no	—
370	#1948	—	61	1	no	—
371	#1947	—	61	1	no	—
372	#1854	—	61	1	no	—
373	#1854	—	61	1	no	—
374	#1853	—	61	1	no	—
375	#1852	—	61	1	no	—
376	#1776	—	61	1	no	—
377	#1776	—	61	1	no	—
378	C₄×#107	—	61	1	no	—
379	C₄×#106	—	61	1	no	—
380	C₂×C₆₁	—	4	1	no	—
381	C₂×C₆₁	#2296	1	1	yes	characteristic
382	C₂×C₆₁	#2912	1	1	yes	characteristic
383	C₂×C₆₁	#2913	1	1	yes	characteristic
384	D₆₁	—	4	1	no	—
385	D₆₁	#3118	1	1	yes	characteristic
386	D₆₁	#3119	1	1	yes	characteristic
387	D₆₁	#3120	1	1	yes	characteristic
388	D₆₁	#3121	1	1	yes	characteristic
389	C₂×#117	—	61	1	no	—
390	C₂×#117	—	61	1	no	—
391	C₂²×C₄⋊C₄	—	61	1	no	—
392	#433	—	61	1	no	—
393	#433	—	61	1	no	—
394	#433	—	61	1	no	—
395	#433	—	61	1	no	—
396	#433	—	61	1	no	—
397	#433	—	61	1	no	—
398	#433	—	61	1	no	—
399	#433	#6923	1	1	yes	characteristic, complemented
400	C₂×#107	—	61	1	no	—
401	C₂×#107	—	61	1	no	—
402	C₂×#107	—	61	1	no	—
403	C₂×#107	—	61	1	no	—
404	C₂×#106	—	61	1	no	—
405	C₂×#106	—	61	1	no	—
406	C₂×#106	—	61	1	no	—
407	C₂×#106	—	61	1	no	—
408	C₂×C₄⋊C₈	—	61	1	no	—
409	C₂×C₄⋊C₈	—	61	1	no	—
410	C₂×C₂²⋊C₈	—	61	1	no	—
411	C₂×C₂²⋊C₈	—	61	1	no	—
412	C₂×#97	—	61	1	no	—
413	C₂×C₄×C₈	—	61	1	no	—
414	#388	—	122	1	no	—
415	#388	—	122	1	no	—
416	#387	—	122	1	no	—
417	#387	—	122	1	no	—
418	#384	—	61	1	no	—
419	#382	—	61	1	no	—
420	#380	—	61	1	no	—
421	#380	—	61	1	no	—
422	C₄×C₄⋊C₄	—	61	1	no	—
423	C₄×C₄⋊C₄	—	61	1	no	—
424	C₄×C₄⋊C₄	—	61	1	no	—
425	C₄×C₄⋊C₄	—	61	1	no	—
426	C₄×C₄⋊C₄	—	61	1	no	—
427	C₄×C₄⋊C₄	—	61	1	no	—
428	C₄×C₄⋊C₄	—	122	1	no	—
429	C₄×C₄⋊C₄	—	122	1	no	—
430	C₄×C₂²⋊C₄	—	122	1	no	—
431	C₄×C₂²⋊C₄	—	122	1	no	—
432	#340	—	61	1	no	—
433	#340	—	61	1	no	—
434	#340	—	61	1	no	—
435	#340	—	61	1	no	—
436	#340	—	61	1	no	—
437	#340	—	61	1	no	—
438	#340	—	61	1	no	—
439	#340	—	61	1	no	—
440	C₆₁	#21367	1	1	yes	characteristic, complemented, Sylow
441	C₂³×C₄	—	61	1	no	—
442	C₂³×C₄	—	122	1	no	—
443	C₂²×C₈	—	61	1	no	—
444	C₂²×C₈	—	61	1	no	—
445	C₂²×C₈	—	61	1	no	—
446	C₂²×C₈	—	61	1	no	—
447	#117	—	61	1	no	—
448	#117	—	61	1	no	—
449	#117	—	61	1	no	—
450	#117	—	61	1	no	—
451	#117	—	61	1	no	—
452	#117	—	61	1	no	—
453	#117	—	61	1	no	—
454	#117	—	122	2	no	—
455	#117	—	122	2	no	—
456	#117	C₂×#6923	1	1	yes	characteristic
457	C₂×C₄⋊C₄	—	61	1	no	—
458	C₂×C₄⋊C₄	—	61	1	no	—
459	C₂×C₄⋊C₄	—	61	1	no	—
460	C₂×C₄⋊C₄	—	61	1	no	—
461	C₂×C₄⋊C₄	—	61	1	no	—
462	C₂×C₄⋊C₄	—	61	1	no	—
463	C₂×C₄⋊C₄	—	61	1	no	—
464	C₂×C₄⋊C₄	—	61	1	no	—
465	C₂×C₄⋊C₄	—	61	1	no	—
466	C₂×C₄⋊C₄	—	61	1	no	—
467	C₂×C₄⋊C₄	—	122	2	no	—
468	C₂×C₄⋊C₄	—	122	2	no	—
469	C₂×C₄⋊C₄	—	122	1	no	—
470	C₂×C₄⋊C₄	—	122	1	no	—
471	C₂×C₄⋊C₄	—	122	1	no	—
472	C₂×C₂²⋊C₄	—	61	1	no	—
473	C₂×C₂²⋊C₄	—	61	1	no	—
474	C₂×C₂²⋊C₄	—	122	1	no	—
475	C₂×C₂²⋊C₄	—	122	1	no	—
476	C₂×C₂²⋊C₄	—	122	1	no	—
477	C₂×C₄²	—	61	1	no	—
478	C₂×C₄²	—	61	1	no	—
479	C₂×C₄²	—	122	1	no	—
480	C₂×C₄²	—	122	1	no	—
481	C₂×C₄²	—	122	1	no	—
482	C₂×C₄²	—	122	1	no	—
483	C₂×C₄²	—	122	1	no	—
484	C₂×C₄²	—	122	1	no	—
485	C₂×C₄²	—	122	1	no	—
486	#107	—	122	2	no	—
487	#107	—	122	2	no	—
488	#107	—	122	2	no	—
489	#107	—	122	2	no	—
490	#106	—	122	2	no	—
491	#106	—	122	2	no	—
492	#106	—	122	2	no	—
493	#106	—	122	2	no	—
494	C₄⋊C₈	—	61	1	no	—
495	C₄⋊C₈	—	61	1	no	—
496	C₄⋊C₈	—	61	1	no	—
497	C₄⋊C₈	—	61	1	no	—
498	C₄⋊C₈	—	61	1	no	—
499	C₄⋊C₈	—	61	1	no	—
500	C₄⋊C₈	C₂×#6923	1	1	yes	characteristic, complemented
501	C₄⋊C₈	C₂×#6923	1	1	yes	characteristic, complemented
502	C₂²⋊C₈	—	61	1	no	—
503	C₂²⋊C₈	—	61	1	no	—
504	C₂²⋊C₈	—	61	1	no	—
505	C₂²⋊C₈	—	61	1	no	—
506	C₂²⋊C₈	—	61	1	no	—
507	C₂²⋊C₈	—	61	1	no	—
508	C₂²⋊C₈	C₂×#6923	1	1	yes	characteristic
509	C₂²⋊C₈	C₂×#6923	1	1	yes	characteristic
510	#97	—	61	1	no	—
511	#97	—	61	1	no	—
512	#97	—	61	1	no	—
513	#97	C₂×#6923	1	1	yes	characteristic, complemented
514	C₄×C₈	—	61	1	no	—
515	C₄×C₈	—	61	1	no	—
516	C₄×C₈	—	61	1	no	—
517	C₄×C₈	C₂×#6923	1	1	yes	characteristic, complemented
518	#95	—	122	1	no	—
519	#95	—	122	1	no	—
520	#95	—	122	1	no	—
521	#95	—	122	1	no	—
522	#95	—	122	1	no	—
523	#95	—	122	1	no	—
524	#95	—	122	1	no	—
525	#95	—	122	1	no	—
526	#95	—	122	1	no	—
527	#95	—	122	1	no	—
528	C₂⁴	—	61	1	no	—
529	C₂²×C₄	—	61	1	no	—
530	C₂²×C₄	—	61	1	no	—
531	C₂²×C₄	—	61	1	no	—
532	C₂²×C₄	—	61	1	no	—
533	C₂²×C₄	—	61	1	no	—
534	C₂²×C₄	—	61	1	no	—
535	C₂²×C₄	—	61	1	no	—
536	C₂²×C₄	—	61	1	no	—
537	C₂²×C₄	—	61	1	no	—
538	C₂²×C₄	—	122	1	no	—
539	C₂²×C₄	—	122	1	no	—
540	C₂²×C₄	—	122	1	no	—
541	C₂²×C₄	—	122	1	no	—
542	C₂²×C₄	—	122	4	no	—
543	C₂²×C₄	—	122	1	no	—
544	C₂²×C₄	—	122	1	no	—
545	C₂²×C₄	—	122	1	no	—
546	C₂²×C₄	—	122	1	no	—
547	C₂²×C₄	—	122	1	no	—
548	C₂²×C₄	—	122	1	no	—
549	C₂²×C₄	—	122	1	no	—
550	C₂²×C₄	—	122	1	no	—
551	C₂²×C₄	—	488	1	no	—
552	C₂²×C₄	—	488	1	no	—
553	C₂²×C₄	C₂²×#6923	1	1	yes	characteristic
554	C₂×C₈	—	61	1	no	—
555	C₂×C₈	—	61	1	no	—
556	C₂×C₈	—	61	1	no	—
557	C₂×C₈	—	61	1	no	—
558	C₂×C₈	—	122	1	no	—
559	C₂×C₈	—	122	1	no	—
560	C₂×C₈	—	122	1	no	—
561	C₂×C₈	—	122	1	no	—
562	C₂×C₈	—	122	1	no	—
563	C₂×C₈	—	122	1	no	—
564	C₂×C₈	—	122	1	no	—
565	C₂×C₈	—	122	1	no	—
566	C₂×C₈	C₂²×#6923	1	1	yes	characteristic
567	C₂×C₈	C₂²×#6923	1	1	yes	characteristic
568	C₂×C₈	C₂²×#6923	1	1	yes	characteristic
569	C₂×C₈	C₂²×#6923	1	1	yes	characteristic
570	C₄⋊C₄	—	61	1	no	—
571	C₄⋊C₄	—	61	1	no	—
572	C₄⋊C₄	—	61	1	no	—
573	C₄⋊C₄	—	61	1	no	—
574	C₄⋊C₄	—	61	1	no	—
575	C₄⋊C₄	—	61	1	no	—
576	C₄⋊C₄	—	61	2	no	—
577	C₄⋊C₄	—	61	2	no	—
578	C₄⋊C₄	—	61	2	no	—
579	C₄⋊C₄	—	61	2	no	—
580	C₄⋊C₄	—	122	1	no	—
581	C₄⋊C₄	—	122	1	no	—
582	C₄⋊C₄	—	122	1	no	—
583	C₄⋊C₄	—	122	1	no	—
584	C₄⋊C₄	—	122	1	no	—
585	C₄⋊C₄	—	122	1	no	—
586	C₄⋊C₄	—	122	1	no	—
587	C₄⋊C₄	—	122	1	no	—
588	C₄⋊C₄	—	122	1	no	—
589	C₄⋊C₄	—	122	1	no	—
590	C₄⋊C₄	—	122	1	no	—
591	C₄⋊C₄	—	122	1	no	—
592	C₄⋊C₄	—	122	4	no	—
593	C₄⋊C₄	—	488	1	no	—
594	C₄⋊C₄	—	488	1	no	—
595	C₄⋊C₄	C₄⋊#6923	1	1	yes	characteristic
596	C₄⋊C₄	C₄⋊#6923	1	1	yes	characteristic
597	C₂²⋊C₄	—	61	1	no	—
598	C₂²⋊C₄	—	61	1	no	—
599	C₂²⋊C₄	—	61	1	no	—
600	C₂²⋊C₄	—	61	1	no	—
601	C₂²⋊C₄	—	61	1	no	—
602	C₂²⋊C₄	—	61	1	no	—
603	C₂²⋊C₄	—	122	4	no	—
604	C₂²⋊C₄	—	488	1	no	—
605	C₂²⋊C₄	—	488	1	no	—
606	C₂²⋊C₄	C₄⋊#6923	1	1	yes	characteristic
607	C₂²⋊C₄	C₄⋊#6923	1	1	yes	characteristic
608	C₄²	—	61	1	no	—
609	C₄²	—	61	1	no	—
610	C₄²	—	61	1	no	—
611	C₄²	—	61	1	no	—
612	C₄²	—	61	1	no	—
613	C₄²	—	61	1	no	—
614	C₄²	—	122	4	no	—
615	C₄²	—	488	1	no	—
616	C₄²	—	488	1	no	—
617	C₄²	—	488	1	no	—
618	C₄²	—	488	1	no	—
619	C₄²	—	488	1	no	—
620	C₄²	—	488	1	no	—
621	C₄²	C₂²×#6923	1	1	yes	characteristic
622	C₄²	C₂²×#6923	1	1	yes	characteristic
623	C₂³	—	61	1	no	—
624	C₂³	—	61	1	no	—
625	C₂³	—	122	1	no	—
626	C₂³	—	122	1	no	—
627	C₂³	—	122	1	no	—
628	C₂³	—	122	1	no	—
629	C₂³	—	122	1	no	—
630	C₂³	—	122	1	no	—
631	C₂³	C₂×C₄⋊#6923	1	1	yes	characteristic
632	C₂×C₄	—	2	1	no	—
633	C₂×C₄	—	2	1	no	—
634	C₂×C₄	—	61	1	no	—
635	C₂×C₄	—	61	1	no	—
636	C₂×C₄	—	61	1	no	—
637	C₂×C₄	—	61	1	no	—
638	C₂×C₄	—	61	1	no	—
639	C₂×C₄	—	61	1	no	—
640	C₂×C₄	—	61	1	no	—
641	C₂×C₄	—	61	1	no	—
642	C₂×C₄	—	61	1	no	—
643	C₂×C₄	—	61	1	no	—
644	C₂×C₄	—	122	1	no	—
645	C₂×C₄	—	122	1	no	—
646	C₂×C₄	—	122	1	no	—
647	C₂×C₄	—	122	1	no	—
648	C₂×C₄	—	122	1	no	—
649	C₂×C₄	—	122	1	no	—
650	C₂×C₄	—	122	1	no	—
651	C₂×C₄	—	122	1	no	—
652	C₂×C₄	—	122	1	no	—
653	C₂×C₄	—	122	1	no	—
654	C₂×C₄	—	122	1	no	—
655	C₂×C₄	—	122	1	no	—
656	C₂×C₄	—	122	1	no	—
657	C₂×C₄	—	122	1	no	—
658	C₂×C₄	—	122	1	no	—
659	C₂×C₄	—	122	1	no	—
660	C₂×C₄	—	122	2	no	—
661	C₂×C₄	—	122	2	no	—
662	C₂×C₄	—	122	2	no	—
663	C₂×C₄	—	122	2	no	—
664	C₂×C₄	—	488	4	no	—
665	C₂×C₄	—	244	1	no	—
666	C₂×C₄	—	244	1	no	—
667	C₂×C₄	—	244	1	no	—
668	C₂×C₄	—	244	1	no	—
669	C₂×C₄	—	244	1	no	—
670	C₂×C₄	—	244	1	no	—
671	C₂×C₄	—	244	1	no	—
672	C₂×C₄	—	244	1	no	—
673	C₂×C₄	—	244	1	no	—
674	C₂×C₄	—	244	1	no	—
675	C₂×C₄	—	244	1	no	—
676	C₂×C₄	—	244	1	no	—
677	C₂×C₄	—	244	1	no	—
678	C₂×C₄	—	244	1	no	—
679	C₂×C₄	—	244	1	no	—
680	C₂×C₄	—	244	1	no	—
681	C₂×C₄	—	244	1	no	—
682	C₂×C₄	—	244	1	no	—
683	C₂×C₄	—	244	1	no	—
684	C₂×C₄	—	244	1	no	—
685	C₂×C₄	C₂×C₄⋊#6923	1	1	yes	characteristic
686	C₂×C₄	C₂×C₄⋊#6923	1	1	yes	characteristic
687	C₂×C₄	C₂×C₄⋊#6923	1	1	yes	characteristic
688	C₂×C₄	C₂×C₄⋊#6923	1	1	yes	characteristic
689	C₂×C₄	C₂×C₄⋊#6923	1	1	yes	characteristic
690	C₂×C₄	C₂³×#6923	1	1	yes	characteristic
691	C₈	—	2	1	no	—
692	C₈	—	2	1	no	—
693	C₈	—	2	1	no	—
694	C₈	—	2	1	no	—
695	C₈	—	122	1	no	—
696	C₈	—	122	1	no	—
697	C₈	—	122	1	no	—
698	C₈	—	122	1	no	—
699	C₂²	—	2	1	no	—
700	C₂²	—	2	1	no	—
701	C₂²	—	2	1	no	—
702	C₂²	—	61	1	no	—
703	C₂²	—	61	1	no	—
704	C₂²	—	61	1	no	—
705	C₂²	—	61	1	no	—
706	C₂²	—	61	1	no	—
707	C₂²	—	61	1	no	—
708	C₂²	—	122	1	no	—
709	C₂²	—	122	1	no	—
710	C₂²	—	122	1	no	—
711	C₂²	—	244	1	no	—
712	C₂²	—	244	1	no	—
713	C₂²	—	244	1	no	—
714	C₂²	—	244	1	no	—
715	C₂²	C₂²×C₄⋊#6923	1	1	yes	characteristic
716	C₄	—	2	1	no	—
717	C₄	—	2	1	no	—
718	C₄	—	2	1	no	—
719	C₄	—	2	1	no	—
720	C₄	—	2	1	no	—
721	C₄	—	61	1	no	—
722	C₄	—	61	1	no	—
723	C₄	—	122	1	no	—
724	C₄	—	122	1	no	—
725	C₄	—	122	1	no	—
726	C₄	—	122	1	no	—
727	C₄	—	122	1	no	—
728	C₄	—	488	1	no	—
729	C₄	—	488	1	no	—
730	C₄	—	488	1	no	—
731	C₄	—	488	1	no	—
732	C₄	—	244	2	no	—
733	C₄	—	244	2	no	—
734	C₄	—	244	2	no	—
735	C₄	—	244	2	no	—
736	C₄	#41×#6923	1	1	yes	characteristic
737	C₄	#41×#6923	1	1	yes	characteristic
738	C₂	—	4	1	no	—
739	C₂	—	61	1	no	—
740	C₂	—	61	1	no	—
741	C₂	—	61	1	no	—
742	C₂	—	61	1	no	—
743	C₂	—	244	1	no	—
744	C₂	#21462279	1	1	yes	characteristic
745	C₂	#21462473	1	1	yes	characteristic
746	C₂	#21462474	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×C₄⋊#6923
commutator	C₂×C₄×C₆₁	C₂³×C₄
Frattini	C₂×C₄	C₂³×#6923
Fitting	C₆₁×#433	C₄
socle	C₂²×C₆₁	C₂²×C₄⋊C₄
prime radical	C₂³×D₆₁	C₂×D₄
cosocle	C₂×C₄×D₆₁	C₂⁴
hypercenter	#433	#6923
hypocenter	C₆₁	#21367
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ #117 ◁ #433

Complements

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

N	H ≅ G/N	type
3. #21461932	C₂	semidirect
4. #21461932	C₂	semidirect
5. #21461931	C₂	semidirect
6. #21461930	C₂	semidirect
11. #21461633	C₂	semidirect
12. #21461633	C₂	semidirect
13. C₄×#14519846	C₂	semidirect
14. C₄×#14519845	C₂	semidirect
53. #16839824	C₄	semidirect
54. #16839823	C₄	semidirect
55. #16839822	C₄	semidirect
56. #16839822	C₄	semidirect
57. #16839821	C₄	semidirect
58. #16839820	C₄	semidirect
59. #16839820	C₄	semidirect
66. C₆₁×#433	C₄	semidirect
129. C₄⋊#92418	C₂×C₄	semidirect
130. C₄⋊#92418	C₂×C₄	semidirect
131. #14519706	C₂×C₄	semidirect
132. #14519706	C₂×C₄	semidirect
133. #14519706	C₂×C₄	semidirect
134. #14519706	C₂×C₄	semidirect
141. #14519688	C₂×C₄	semidirect
142. #14519687	C₂×C₄	semidirect
143. #14519687	C₂×C₄	semidirect
144. C₄×#92418	C₂×C₄	semidirect
145. C₈×Dic₆₁	C₂×C₄	semidirect
146. C₈×Dic₆₁	C₂×C₄	semidirect
148. C₄⋊C₈×C₆₁	C₂×C₄	semidirect
149. C₄⋊C₈×C₆₁	C₂×C₄	semidirect
152. #97×C₆₁	C₂×C₄	semidirect
153. C₄×C₈×C₆₁	C₂×C₄	semidirect
399. #433	#6923	semidirect
440. C₆₁	#21367	semidirect
500. C₄⋊C₈	C₂×#6923	semidirect
501. C₄⋊C₈	C₂×#6923	semidirect
513. #97	C₂×#6923	semidirect
517. C₄×C₈	C₂×#6923	semidirect

Maximal subgroups

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

subgroup	index
#21462297	2
#21462256	2
#21461932	2
#21461931	2
#21461930	2
#21461770	2
#21461769	2
#21461768	2
#21461633	2
C₄×#14519846	2
C₄×#14519845	2
#433×D₆₁	2
#21367	61