Subgroups — #431×#6923 #30614321

Order 15616.

1318 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₆₁⋊#431	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄²×#6923	C₂	1	1	yes	maximal, characteristic
3	C₄⋊C₈×#6923	C₂	1	4	yes	maximal, complemented
4	C₂²⋊C₈×#6923	C₂	1	4	yes	maximal
5	#21461532	C₂	1	2	yes	maximal, complemented
6	C₄×C₈×#6923	C₂	1	2	yes	maximal, complemented
7	#431×D₆₁	C₂	1	1	yes	maximal, characteristic
8	C₂²×C₄×#6923	C₄	1	2	yes	—
9	C₂²×C₄×#6923	C₄	1	2	yes	—
10	C₂²×C₄×#6923	C₂²	1	2	yes	—
11	#16840781	C₄	1	2	yes	complemented
12	#16840780	C₄	1	2	yes	complemented
13	#16840779	C₄	1	2	yes	complemented
14	#16840778	C₄	1	2	yes	complemented
15	D₆₁⋊(C₄⋊C₈)	C₂²	1	2	yes	—
16	D₆₁⋊(C₂²⋊C₈)	C₂²	1	2	yes	—
17	C₄×D₆₁⋊C₈	C₂²	1	2	yes	—
18	C₂×C₈×#6923	C₂²	1	8	yes	—
19	C₄²×#6923	C₄	1	2	yes	—
20	C₄²×#6923	C₄	1	2	yes	—
21	C₄²×#6923	C₂²	1	1	yes	characteristic
22	C₄²×#6923	C₂²	1	2	yes	—
23	C₄²×#6923	C₂²	1	1	yes	characteristic
24	(C₂×#6923)⋊C₈	C₂²	1	8	yes	—
25	C₂×C₄²×D₆₁	C₂²	1	1	yes	characteristic
26	#16839815	C₄	1	1	yes	characteristic, complemented
27	#16839814	C₄	1	2	yes	complemented
28	#16839813	C₄	1	2	yes	complemented
29	#16839812	C₄	1	2	yes	complemented
30	C₄⋊C₈×D₆₁	C₂²	1	2	yes	—
31	C₂²⋊C₈×D₆₁	C₂²	1	2	yes	—
32	C₄×C₈×D₆₁	C₂²	1	2	yes	—
33	C₆₁×#431	C₄	1	1	yes	characteristic, complemented
34	C₂³×#6923	C₂×C₄	1	4	yes	—
35	C₂×D₆₁⋊C₈	C₂³	1	4	yes	—
36	C₂×C₄×#6923	—	2	8	no	—
37	C₂×C₄×#6923	—	2	8	no	—
38	C₂×C₄×#6923	C₈	1	16	yes	complemented
39	C₂×C₄×#6923	C₂×C₄	1	4	yes	—
40	C₂×C₄×#6923	C₂×C₄	1	2	yes	—
41	C₂×C₄×#6923	C₂×C₄	1	4	yes	—
42	C₂×C₄×#6923	C₂×C₄	1	2	yes	—
43	C₂×C₄×#6923	C₂×C₄	1	4	yes	—
44	C₂×C₄×#6923	C₂×C₄	1	2	yes	—
45	C₂×C₄×#6923	C₂×C₄	1	2	yes	—
46	C₂×C₄×#6923	C₂³	1	2	yes	—
47	C₂×C₄×#6923	C₂³	1	2	yes	—
48	#14519844	C₂×C₄	1	4	yes	complemented
49	C₄⋊#92420	C₂×C₄	1	4	yes	complemented
50	#14519834	C₂×C₄	1	4	yes	—
51	C₂²⋊#92420	C₂×C₄	1	4	yes	—
52	C₄×#92420	C₂×C₄	1	4	yes	complemented
53	C₄×#92420	C₂×C₄	1	4	yes	complemented
54	C₈×#6923	—	2	16	no	—
55	C₂²×C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
56	C₂²×C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
57	C₂²×C₄×D₆₁	C₂³	1	1	yes	characteristic
58	C₂×C₈×D₆₁	C₂³	1	4	yes	—
59	C₂×C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
62	C₄²×D₆₁	C₂×C₄	1	1	yes	characteristic
63	C₄²×D₆₁	C₂×C₄	1	1	yes	characteristic
64	C₄²×D₆₁	C₂×C₄	1	1	yes	characteristic
65	C₄²×D₆₁	C₂×C₄	1	1	yes	characteristic
66	C₄²×D₆₁	C₂×C₄	1	1	yes	characteristic
67	C₄²×D₆₁	C₂×C₄	1	1	yes	characteristic
68	C₄²×D₆₁	C₂³	1	1	yes	characteristic
69	C₄²×D₆₁	C₂³	1	1	yes	characteristic
70	C₄⋊#92418	C₂×C₄	1	2	yes	complemented
71	#14519706	C₂×C₄	1	4	yes	complemented
72	C₂²⋊#92418	C₂×C₄	1	2	yes	—
73	#14519689	C₂×C₄	1	4	yes	—
74	C₄×#92418	C₂×C₄	1	2	yes	complemented
75	C₈×Dic₆₁	C₂×C₄	1	4	yes	complemented
76	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
77	C₄⋊C₈×C₆₁	C₂×C₄	1	2	yes	complemented
78	C₂²⋊C₈×C₆₁	C₂×C₄	1	2	yes	—
79	C₄×C₈×C₆₁	C₂×C₄	1	2	yes	complemented
80	C₂³×D₆₁	C₂²×C₄	1	1	yes	characteristic
81	C₂²×#6923	—	2	8	no	—
82	C₂²×#6923	—	2	8	no	—
83	C₂²×#6923	C₂×C₈	1	16	yes	—
84	C₂²×#6923	C₂²×C₄	1	4	yes	—
85	C₂²×#6923	C₂²×C₄	1	4	yes	—
86	C₂²×C₄×C₆₁	C₄²	1	1	yes	characteristic
87	C₂²×C₄×C₆₁	C₄²	1	1	yes	characteristic
88	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
89	C₂²×Dic₆₁	C₄²	1	1	yes	characteristic
90	C₂²×Dic₆₁	C₄²	1	1	yes	characteristic
91	C₂²×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
92	C₂×C₄×D₆₁	—	2	4	no	—
93	C₂×C₄×D₆₁	—	2	4	no	—
94	C₂×C₄×D₆₁	C₄²	1	1	yes	characteristic
95	C₂×C₄×D₆₁	C₄²	1	1	yes	characteristic
96	C₂×C₄×D₆₁	C₄²	1	1	yes	characteristic
97	C₂×C₄×D₆₁	C₄²	1	1	yes	characteristic
98	C₂×C₄×D₆₁	C₂×C₈	1	8	yes	—
99	C₂×C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
100	C₂×C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
102	C₂×C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
103	C₂×C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
104	C₂×C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₄×D₆₁	C₂⁴	1	1	yes	characteristic
107	C₂×#92420	C₂²×C₄	1	8	yes	—
108	C₄×#6923	—	2	8	no	—
109	C₄×#6923	—	2	8	no	—
110	C₄×#6923	—	2	4	no	—
111	C₄×#6923	—	2	4	no	—
112	C₄×#6923	C₂×C₈	1	8	yes	—
113	C₄×#6923	C₂×C₈	1	16	yes	—
114	C₄×#6923	C₂×C₈	1	8	yes	—
115	C₄×#6923	M₁₆	1	8	yes	—
116	C₄×#6923	#41	1	8	yes	—
117	D₆₁⋊C₈	—	2	8	no	—
118	C₂×C₈×C₆₁	C₂²×C₄	1	4	yes	—
119	C₄²×C₆₁	C₄²	1	1	yes	characteristic
120	C₄²×C₆₁	C₄²	1	1	yes	characteristic
121	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
122	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
123	C₄×Dic₆₁	C₄²	1	1	yes	characteristic
124	C₄×Dic₆₁	C₄²	1	1	yes	characteristic
125	C₄×Dic₆₁	C₄²	1	1	yes	characteristic
126	C₄×Dic₆₁	C₄²	1	1	yes	characteristic
127	C₄×Dic₆₁	C₄²	1	1	yes	characteristic
128	C₄×Dic₆₁	C₄²	1	1	yes	characteristic
129	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
130	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
131	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
132	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
133	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
134	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
135	C₂×#92418	C₂²×C₄	1	4	yes	—
136	C₈×D₆₁	—	2	8	no	—
137	C₂³×C₆₁	C₂×C₄²	1	1	yes	characteristic
138	C₂²×D₆₁	—	2	2	no	—
139	C₂²×D₆₁	—	2	2	no	—
140	C₂²×D₆₁	C₂×C₄²	1	1	yes	characteristic
141	C₂²×D₆₁	C₂²×C₈	1	4	yes	—
142	C₂²×D₆₁	C₂³×C₄	1	1	yes	characteristic
143	C₂×#6923	—	2	4	no	—
144	C₂×#6923	—	2	4	no	—
145	C₂×#6923	—	2	32	no	—
146	C₂×#6923	#117	1	8	yes	—
147	C₂×#6923	C₂²×C₈	1	8	yes	—
148	C₂×#6923	C₂²×C₈	1	8	yes	—
149	C₂×#6923	C₂×M₁₆	1	8	yes	—
150	C₂×C₄×C₆₁	—	2	2	no	—
151	C₂×C₄×C₆₁	—	2	2	no	—
152	C₂×C₄×C₆₁	C₄×C₈	1	4	yes	complemented
153	C₂×C₄×C₆₁	C₂×C₄²	1	1	yes	characteristic
154	C₂×C₄×C₆₁	C₂×C₄²	1	1	yes	characteristic
155	C₂×C₄×C₆₁	C₂×C₄²	1	1	yes	characteristic
156	C₂×C₄×C₆₁	C₂×C₄²	1	1	yes	characteristic
157	C₂×C₄×C₆₁	C₂×C₄²	1	1	yes	characteristic
158	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
159	C₂×Dic₆₁	—	2	2	no	—
160	C₂×Dic₆₁	—	2	2	no	—
161	C₂×Dic₆₁	C₄×C₈	1	4	yes	complemented
162	C₂×Dic₆₁	C₂×C₄²	1	1	yes	characteristic
163	C₂×Dic₆₁	C₂×C₄²	1	1	yes	characteristic
164	C₂×Dic₆₁	C₂×C₄²	1	1	yes	characteristic
165	C₂×Dic₆₁	C₂×C₄²	1	1	yes	characteristic
166	C₂×Dic₆₁	C₂×C₄²	1	1	yes	characteristic
167	C₂×Dic₆₁	C₂³×C₄	1	1	yes	characteristic
168	C₄×D₆₁	—	2	2	no	—
169	C₄×D₆₁	—	2	2	no	—
170	C₄×D₆₁	—	2	2	no	—
171	C₄×D₆₁	—	2	2	no	—
172	C₄×D₆₁	—	2	2	no	—
173	C₄×D₆₁	—	2	2	no	—
174	C₄×D₆₁	C₄×C₈	1	4	yes	complemented
175	C₄×D₆₁	C₄×C₈	1	4	yes	complemented
176	C₄×D₆₁	C₂²×C₈	1	4	yes	—
177	C₄×D₆₁	C₂²×C₈	1	4	yes	—
178	C₄×D₆₁	C₂×M₁₆	1	4	yes	—
179	C₄×D₆₁	C₂×#41	1	4	yes	—
180	#92420	—	2	8	no	—
181	C₈×C₆₁	—	2	4	no	—
182	#92418	—	2	4	no	—
183	C₄×#431	—	61	1	no	maximal, Sylow
184	C₂²×C₆₁	—	2	1	no	—
185	C₂²×C₆₁	—	2	1	no	—
186	C₂²×C₆₁	C₂×C₄×C₈	1	2	yes	—
187	C₂²×C₆₁	C₂²×C₄²	1	1	yes	characteristic
188	C₂×D₆₁	—	2	1	no	—
189	C₂×D₆₁	—	2	1	no	—
190	C₂×D₆₁	—	2	8	no	—
191	C₂×D₆₁	C₂×C₄×C₈	1	2	yes	—
192	C₂×D₆₁	C₂×#117	1	2	yes	—
193	C₂×D₆₁	C₂³×C₈	1	2	yes	—
194	C₂×D₆₁	C₂²×M₁₆	1	2	yes	—
195	#6923	—	2	8	no	—
196	#6923	#431	1	16	yes	direct product factor
197	C₄×C₆₁	—	2	1	no	—
198	C₄×C₆₁	—	2	1	no	—
199	C₄×C₆₁	C₂×C₄×C₈	1	2	yes	—
200	C₄×C₆₁	C₂×C₄×C₈	1	2	yes	—
201	C₄×C₆₁	C₄×M₁₆	1	2	yes	—
202	C₄×C₆₁	C₄×#41	1	2	yes	—
203	Dic₆₁	—	2	1	no	—
204	Dic₆₁	—	2	1	no	—
205	Dic₆₁	C₂×C₄×C₈	1	2	yes	—
206	Dic₆₁	C₂×C₄×C₈	1	2	yes	—
207	Dic₆₁	C₄×M₁₆	1	2	yes	—
208	Dic₆₁	C₄×#41	1	2	yes	—
209	C₂×#431	—	61	1	no	—
210	C₂×#431	—	61	1	no	—
211	C₂×C₄³	—	61	1	no	—
212	C₄×C₄⋊C₈	—	61	4	no	—
213	C₄×C₂²⋊C₈	—	61	4	no	—
214	#1744	—	61	2	no	—
215	C₄²×C₈	—	61	2	no	—
216	C₂×C₆₁	—	2	2	no	—
217	C₂×C₆₁	C₄×#117	1	1	yes	characteristic
218	C₂×C₆₁	C₂²×C₄×C₈	1	1	yes	characteristic
219	C₂×C₆₁	C₂×C₄×M₁₆	1	1	yes	characteristic
220	D₆₁	—	2	2	no	—
221	D₆₁	C₂×#431	1	4	yes	—
222	C₂²×C₄²	—	61	2	no	—
223	C₂²×C₄²	—	61	1	no	—
224	C₂²×C₄²	—	61	2	no	—
225	C₂²×C₄²	—	61	2	no	—
226	#431	—	61	2	no	—
227	#431	—	61	2	no	—
228	#431	—	61	2	no	—
229	#431	—	61	2	no	—
230	#431	—	61	1	no	—
231	#431	—	61	2	no	—
232	#431	—	61	2	no	—
233	#431	—	61	2	no	—
234	#431	#6923	1	1	yes	characteristic, direct product factor
235	C₂×C₄⋊C₈	—	61	2	no	—
236	C₂×C₄⋊C₈	—	61	2	no	—
237	C₂×C₂²⋊C₈	—	61	2	no	—
238	C₂×C₂²⋊C₈	—	61	2	no	—
239	C₂×C₄×C₈	—	61	2	no	—
240	C₂×C₄×C₈	—	61	2	no	—
241	C₂×C₄×C₈	—	61	8	no	—
242	C₄³	—	61	1	no	—
243	C₄³	—	61	1	no	—
244	C₄³	—	61	2	no	—
245	C₄³	—	61	2	no	—
246	C₄³	—	61	2	no	—
247	#336	—	61	8	no	—
248	C₆₁	C₄×#431	1	1	yes	characteristic, complemented, Sylow
249	C₂³×C₄	—	61	1	no	—
250	C₂³×C₄	—	61	4	no	—
251	C₂³×C₄	—	61	1	no	—
252	C₂³×C₄	—	61	1	no	—
253	C₂²×C₈	—	61	4	no	—
254	C₂²×C₈	—	61	4	no	—
255	C₂×C₄²	—	61	16	no	—
256	C₂×C₄²	—	61	2	no	—
257	C₂×C₄²	—	61	4	no	—
258	C₂×C₄²	—	61	2	no	—
259	C₂×C₄²	—	61	2	no	—
260	C₂×C₄²	—	61	2	no	—
261	C₂×C₄²	—	61	1	no	—
262	C₂×C₄²	—	61	1	no	—
263	C₂×C₄²	—	61	1	no	—
264	C₂×C₄²	—	61	1	no	—
265	C₂×C₄²	—	61	1	no	—
266	C₂×C₄²	—	61	1	no	—
267	C₂×C₄²	—	61	1	no	—
268	C₂×C₄²	—	61	1	no	—
269	C₂×C₄²	—	61	1	no	—
270	C₂×C₄²	—	61	1	no	—
271	C₂×C₄²	—	61	1	no	—
272	C₂×C₄²	—	61	4	no	—
273	C₂×C₄²	—	61	4	no	—
274	C₂×C₄²	—	61	2	no	—
275	C₂×C₄²	—	61	2	no	—
276	C₂×C₄²	—	122	8	no	—
277	C₂×C₄²	—	122	8	no	—
278	C₂×C₄²	C₂×#6923	1	1	yes	characteristic
279	C₄⋊C₈	—	61	4	no	—
280	C₄⋊C₈	—	61	4	no	—
281	C₄⋊C₈	—	61	4	no	—
282	C₄⋊C₈	—	61	2	no	—
283	C₄⋊C₈	C₂×#6923	1	2	yes	complemented
284	C₂²⋊C₈	—	61	4	no	—
285	C₂²⋊C₈	—	61	4	no	—
286	C₂²⋊C₈	—	61	2	no	—
287	C₂²⋊C₈	—	61	4	no	—
288	C₂²⋊C₈	C₂×#6923	1	2	yes	—
289	C₄×C₈	—	61	4	no	—
290	C₄×C₈	—	61	4	no	—
291	C₄×C₈	—	61	4	no	—
292	C₄×C₈	—	61	2	no	—
293	C₄×C₈	—	122	16	no	—
294	C₄×C₈	C₂×#6923	1	2	yes	complemented
295	C₂⁴	—	61	1	no	—
296	C₂²×C₄	—	61	4	no	—
297	C₂²×C₄	—	61	1	no	—
298	C₂²×C₄	—	61	8	no	—
299	C₂²×C₄	—	61	1	no	—
300	C₂²×C₄	—	61	1	no	—
301	C₂²×C₄	—	61	1	no	—
302	C₂²×C₄	—	61	1	no	—
303	C₂²×C₄	—	61	1	no	—
304	C₂²×C₄	—	61	1	no	—
305	C₂²×C₄	—	61	4	no	—
306	C₂²×C₄	—	61	16	no	—
307	C₂²×C₄	—	61	1	no	—
308	C₂²×C₄	—	61	1	no	—
309	C₂²×C₄	—	61	1	no	—
310	C₂²×C₄	—	61	1	no	—
311	C₂²×C₄	—	61	1	no	—
312	C₂²×C₄	—	61	1	no	—
313	C₂²×C₄	—	61	1	no	—
314	C₂²×C₄	—	61	1	no	—
315	C₂²×C₄	—	122	4	no	—
316	C₂²×C₄	—	122	4	no	—
317	C₂²×C₄	—	122	8	no	—
318	C₂²×C₄	—	122	8	no	—
319	C₂²×C₄	C₄×#6923	1	1	yes	characteristic
320	C₂²×C₄	C₄×#6923	1	1	yes	characteristic
321	C₂²×C₄	C₂²×#6923	1	1	yes	characteristic
322	C₂×C₈	—	61	8	no	—
323	C₂×C₈	—	61	4	no	—
324	C₂×C₈	—	122	8	no	—
325	C₂×C₈	—	122	8	no	—
326	C₂×C₈	C₂²×#6923	1	4	yes	—
327	C₄²	—	61	8	no	—
328	C₄²	—	61	8	no	—
329	C₄²	—	61	16	no	—
330	C₄²	—	61	8	no	—
331	C₄²	—	61	8	no	—
332	C₄²	—	61	1	no	—
333	C₄²	—	61	1	no	—
334	C₄²	—	61	1	no	—
335	C₄²	—	61	1	no	—
336	C₄²	—	61	1	no	—
337	C₄²	—	61	1	no	—
338	C₄²	—	61	1	no	—
339	C₄²	—	61	1	no	—
340	C₄²	—	61	1	no	—
341	C₄²	—	61	1	no	—
342	C₄²	—	61	1	no	—
343	C₄²	—	61	1	no	—
344	C₄²	—	122	8	no	—
345	C₄²	—	122	8	no	—
346	C₄²	—	122	4	no	—
347	C₄²	—	122	4	no	—
348	C₄²	C₄×#6923	1	1	yes	characteristic
349	C₄²	C₄×#6923	1	1	yes	characteristic
350	C₄²	C₂²×#6923	1	1	yes	characteristic
351	C₄²	C₂²×#6923	1	1	yes	characteristic
352	C₂³	—	61	1	no	—
353	C₂³	—	61	4	no	—
354	C₂³	—	61	1	no	—
355	C₂³	—	122	2	no	—
356	C₂³	—	122	2	no	—
357	C₂³	C₂×C₄×#6923	1	1	yes	characteristic
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	61	8	no	—
361	C₂×C₄	—	61	8	no	—
362	C₂×C₄	—	61	8	no	—
363	C₂×C₄	—	61	4	no	—
364	C₂×C₄	—	61	1	no	—
365	C₂×C₄	—	61	1	no	—
366	C₂×C₄	—	61	1	no	—
367	C₂×C₄	—	61	1	no	—
368	C₂×C₄	—	61	4	no	—
369	C₂×C₄	—	61	4	no	—
370	C₂×C₄	—	61	4	no	—
371	C₂×C₄	—	61	4	no	—
372	C₂×C₄	—	61	4	no	—
373	C₂×C₄	—	61	4	no	—
374	C₂×C₄	—	61	8	no	—
375	C₂×C₄	—	61	1	no	—
376	C₂×C₄	—	61	1	no	—
377	C₂×C₄	—	122	2	no	—
378	C₂×C₄	—	122	2	no	—
379	C₂×C₄	—	122	2	no	—
380	C₂×C₄	—	122	2	no	—
381	C₂×C₄	—	122	2	no	—
382	C₂×C₄	—	122	2	no	—
383	C₂×C₄	—	122	32	no	—
384	C₂×C₄	—	122	4	no	—
385	C₂×C₄	—	122	4	no	—
386	C₂×C₄	—	122	2	no	—
387	C₂×C₄	—	122	2	no	—
388	C₂×C₄	C₈×#6923	1	4	yes	complemented
389	C₂×C₄	C₂×C₄×#6923	1	1	yes	characteristic
390	C₂×C₄	C₂×C₄×#6923	1	1	yes	characteristic
391	C₂×C₄	C₂×C₄×#6923	1	1	yes	characteristic
392	C₂×C₄	C₂×C₄×#6923	1	1	yes	characteristic
393	C₂×C₄	C₂×C₄×#6923	1	1	yes	characteristic
394	C₂×C₄	C₂³×#6923	1	1	yes	characteristic
395	C₈	—	2	4	no	—
396	C₈	—	122	8	no	—
397	C₈	—	122	4	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	2	1	no	—
400	C₂²	—	61	2	no	—
401	C₂²	—	61	2	no	—
402	C₂²	—	61	2	no	—
403	C₂²	—	61	2	no	—
404	C₂²	—	122	8	no	—
405	C₂²	—	122	1	no	—
406	C₂²	—	122	1	no	—
407	C₂²	C₂×C₈×#6923	1	2	yes	—
408	C₂²	C₂²×C₄×#6923	1	1	yes	characteristic
409	C₄	—	2	1	no	—
410	C₄	—	2	1	no	—
411	C₄	—	61	16	no	—
412	C₄	—	61	2	no	—
413	C₄	—	61	2	no	—
414	C₄	—	61	2	no	—
415	C₄	—	61	2	no	—
416	C₄	—	122	8	no	—
417	C₄	—	122	1	no	—
418	C₄	—	122	1	no	—
419	C₄	C₂×C₈×#6923	1	2	yes	—
420	C₄	C₂×C₈×#6923	1	2	yes	—
421	C₄	M₁₆×#6923	1	2	yes	—
422	C₄	#41×#6923	1	2	yes	—
423	C₂	—	2	2	no	—
424	C₂	—	61	4	no	—
425	C₂	—	122	2	no	—
426	C₂	#117×#6923	1	1	yes	characteristic
427	C₂	C₂²×C₈×#6923	1	1	yes	characteristic
428	C₂	C₂×M₁₆×#6923	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	C₂²×#6923
commutator	C₂×C₆₁	C₂²×C₄×C₈
Frattini	C₂×C₄	C₂³×#6923
Fitting	C₆₁×#431	C₄
socle	C₂²×C₆₁	C₂²×C₄²
prime radical	C₂³×D₆₁	C₂²×C₄
cosocle	C₂×C₄×D₆₁	C₂⁴
hypercenter	#431	#6923
hypocenter	C₆₁	C₄×#431
LCS	G ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₄² ◁ #431

Complements

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

N	H ≅ G/N	type
3. C₄⋊C₈×#6923	C₂	semidirect
5. #21461532	C₂	semidirect
6. C₄×C₈×#6923	C₂	semidirect
11. #16840781	C₄	semidirect
12. #16840780	C₄	semidirect
13. #16840779	C₄	semidirect
14. #16840778	C₄	semidirect
26. #16839815	C₄	semidirect
27. #16839814	C₄	semidirect
28. #16839813	C₄	semidirect
29. #16839812	C₄	semidirect
33. C₆₁×#431	C₄	semidirect
38. C₂×C₄×#6923	C₈	semidirect
48. #14519844	C₂×C₄	semidirect
49. C₄⋊#92420	C₂×C₄	semidirect
52. C₄×#92420	C₂×C₄	semidirect
53. C₄×#92420	C₂×C₄	semidirect
70. C₄⋊#92418	C₂×C₄	semidirect
71. #14519706	C₂×C₄	semidirect
74. C₄×#92418	C₂×C₄	semidirect
75. C₈×Dic₆₁	C₂×C₄	semidirect
77. C₄⋊C₈×C₆₁	C₂×C₄	semidirect
79. C₄×C₈×C₆₁	C₂×C₄	semidirect
152. C₂×C₄×C₆₁	C₄×C₈	semidirect
161. C₂×Dic₆₁	C₄×C₈	semidirect
174. C₄×D₆₁	C₄×C₈	semidirect
175. C₄×D₆₁	C₄×C₈	semidirect
196. #6923	#431	direct (N × H)
234. #431	#6923	direct (N × H)
248. C₆₁	C₄×#431	semidirect
283. C₄⋊C₈	C₂×#6923	semidirect
294. C₄×C₈	C₂×#6923	semidirect
388. C₂×C₄	C₈×#6923	semidirect

Maximal subgroups

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

subgroup	index
D₆₁⋊#431	2
C₂×C₄²×#6923	2
C₄⋊C₈×#6923	2
C₂²⋊C₈×#6923	2
#21461532	2
C₄×C₈×#6923	2
#431×D₆₁	2
C₄×#431	61