Subgroups — #16854736

Order 3968.

456 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×D₄×D₃₁	C₂	1	1	yes	maximal, characteristic
2	#14521123	C₂	1	1	yes	maximal, characteristic, complemented
3	#14521122	C₂	1	1	yes	maximal, characteristic, complemented
4	#14521121	C₂	1	1	yes	maximal, characteristic, complemented
5	#14521120	C₂	1	1	yes	maximal, characteristic, complemented
6	#14521119	C₂	1	1	yes	maximal, characteristic, complemented
7	#14521118	C₂	1	1	yes	maximal, characteristic, complemented
8	#14521117	C₂	1	1	yes	maximal, characteristic, complemented
9	#14521105	C₂	1	1	yes	maximal, characteristic, complemented
10	#14521104	C₂	1	1	yes	maximal, characteristic, complemented
11	#14521012	C₂	1	1	yes	maximal, characteristic, complemented
12	#14521011	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×(C₂×D₃₁)⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²⋊C₈×D₃₁	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#435	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×D₄×D₃₁	C₄	1	1	yes	characteristic
17	C₂²×C₄×D₃₁	C₂²	1	1	yes	characteristic
18	C₂²×C₄×D₃₁	C₂²	1	1	yes	characteristic
19	C₂×M₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
20	C₂²×C₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
21	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
22	D₄×Dic₃₁	C₄	1	1	yes	characteristic
23	C₄×C₂²⋊D₃₁	C₂²	1	1	yes	characteristic
24	C₄×C₂²⋊D₃₁	C₂²	1	1	yes	characteristic
25	C₂×#92474	C₂²	1	1	yes	characteristic, complemented
26	C₂²×C₃₁⋊C₈	C₂²	1	1	yes	characteristic, complemented
27	C₂×#92469	C₂²	1	1	yes	characteristic, complemented
28	C₂×#92469	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₈×D₃₁	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₈×D₃₁	C₂²	1	1	yes	characteristic, complemented
31	#11758470	C₄	1	1	yes	characteristic
32	C₄⋊C₄×D₃₁	C₄	1	1	yes	characteristic
33	(C₂²⋊D₃₁)⋊C₄	C₄	1	1	yes	characteristic
34	(C₂²⋊D₃₁)⋊C₄	C₄	1	1	yes	characteristic
35	C₂²⋊C₄×D₃₁	C₄	1	1	yes	characteristic
36	C₂²⋊C₄×D₃₁	C₄	1	1	yes	characteristic
37	C₄×D₁₂₄	C₂²	1	1	yes	characteristic
38	C₄²×D₃₁	C₂²	1	1	yes	characteristic
39	C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
40	C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
41	C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
42	C₃₁×#97	C₂²	1	1	yes	characteristic, complemented
43	C₂²⋊(C₃₁⋊C₈)	C₂²	1	1	yes	characteristic, complemented
44	C₂²⋊(C₃₁⋊C₈)	C₂²	1	1	yes	characteristic, complemented
45	(C₂×D₃₁)⋊C₈	C₂²	1	1	yes	characteristic
46	(C₂×D₃₁)⋊C₈	C₂²	1	1	yes	characteristic
47	(C₂×D₃₁)⋊C₈	C₂²	1	1	yes	characteristic
48	(C₂×D₃₁)⋊C₈	C₂²	1	1	yes	characteristic
49	(C₂×D₃₁)⋊C₈	C₂²	1	1	yes	characteristic, complemented
50	(C₂×D₃₁)⋊C₈	C₂²	1	1	yes	characteristic, complemented
51	(C₂×D₃₁)⋊C₈	C₂²	1	1	yes	characteristic, complemented
52	(C₂×D₃₁)⋊C₈	C₂²	1	1	yes	characteristic, complemented
53	#11758403	C₂²	1	1	yes	characteristic, complemented
54	#11758403	C₂²	1	1	yes	characteristic, complemented
55	Dic₃₁⋊C₈	C₂²	1	1	yes	characteristic, complemented
56	Dic₃₁⋊C₈	C₂²	1	1	yes	characteristic, complemented
57	C₄⋊(C₃₁⋊C₈)	C₂²	1	1	yes	characteristic, complemented
58	#11758391	C₂²	1	1	yes	characteristic, complemented
59	C₂³×D₃₁	C₂×C₄	1	1	yes	characteristic
60	C₂³×D₃₁	C₂×C₄	1	1	yes	characteristic
61	C₂×D₄×C₃₁	C₂×C₄	1	1	yes	characteristic
62	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
63	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
64	C₂×C₂²⋊D₃₁	C₂×C₄	1	1	yes	characteristic
65	C₂×C₂²⋊D₃₁	C₂×C₄	1	1	yes	characteristic
66	C₂²×Dic₃₁	C₂×C₄	1	1	yes	characteristic
67	C₂²×Dic₃₁	C₂×C₄	1	1	yes	characteristic
68	D₄×D₃₁	—	2	4	no	—
69	C₂×D₁₂₄	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄×D₃₁	—	4	1	no	—
71	C₂×C₄×D₃₁	—	4	1	no	—
72	C₂×C₄×D₃₁	—	4	1	no	—
73	C₂×C₄×D₃₁	—	4	1	no	—
74	C₂×C₄×D₃₁	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄×D₃₁	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄×D₃₁	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄×D₃₁	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄×D₃₁	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄×D₃₁	C₂×C₄	1	1	yes	characteristic
80	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
81	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
82	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
83	M₁₆×C₃₁	—	4	1	no	—
84	C₂×C₈×C₃₁	—	4	1	no	—
85	C₂×C₈×C₃₁	C₂³	1	1	yes	characteristic
86	C₂×C₈×C₃₁	C₂³	1	1	yes	characteristic
87	C₂×C₈×C₃₁	C₂³	1	1	yes	characteristic
88	C₂×C₈×C₃₁	C₂³	1	1	yes	characteristic
89	C₄⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
90	C₂²⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
91	C₂²⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
92	C₄²×C₃₁	C₂³	1	1	yes	characteristic
93	C₂²⋊Dic₃₁	C₂×C₄	1	1	yes	characteristic
94	C₂²⋊Dic₃₁	C₂×C₄	1	1	yes	characteristic
95	(C₂×D₃₁)⋊C₄	C₂×C₄	1	1	yes	characteristic
96	(C₂×D₃₁)⋊C₄	C₂×C₄	1	1	yes	characteristic
97	(C₂×D₃₁)⋊C₄	C₂×C₄	1	1	yes	characteristic
98	(C₂×D₃₁)⋊C₄	C₂×C₄	1	1	yes	characteristic
99	C₄⋊Dic₃₁	C₂×C₄	1	1	yes	characteristic
100	Dic₃₁⋊C₄	C₂×C₄	1	1	yes	characteristic
101	Dic₃₁⋊C₄	C₂×C₄	1	1	yes	characteristic
102	C₄×Dic₃₁	C₂×C₄	1	1	yes	characteristic
103	C₄×Dic₃₁	C₂×C₄	1	1	yes	characteristic
104	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
105	#92474	—	4	1	no	—
106	C₂×C₃₁⋊C₈	—	4	1	no	—
107	C₂×C₃₁⋊C₈	C₂³	1	1	yes	characteristic
108	C₂×C₃₁⋊C₈	C₂³	1	1	yes	characteristic
109	C₂×C₃₁⋊C₈	C₂³	1	1	yes	characteristic
110	C₂×C₃₁⋊C₈	C₂³	1	1	yes	characteristic
111	#92469	—	4	1	no	—
112	#92469	—	4	1	no	—
113	C₈×D₃₁	—	4	1	no	—
114	C₈×D₃₁	—	4	1	no	—
115	C₂³×C₃₁	C₂²×C₄	1	1	yes	characteristic
116	C₂³×C₃₁	C₂²×C₄	1	1	yes	characteristic
117	C₂²×D₃₁	—	2	2	no	—
118	C₂²×D₃₁	—	4	1	no	—
119	C₂²×D₃₁	—	4	1	no	—
120	C₂²×D₃₁	—	4	1	no	—
121	C₂²×D₃₁	—	4	1	no	—
122	C₂²×D₃₁	M₁₆	1	4	yes	complemented
123	C₂²×D₃₁	C₂²×C₄	1	1	yes	characteristic
124	C₂²×D₃₁	C₂²×C₄	1	1	yes	characteristic
125	C₂²×D₃₁	C₂²×C₄	1	1	yes	characteristic
126	D₄×C₃₁	—	2	2	no	—
127	C₂×C₄×C₃₁	—	2	1	no	—
128	C₂×C₄×C₃₁	—	2	1	no	—
129	C₂×C₄×C₃₁	—	2	1	no	—
130	C₂×C₄×C₃₁	—	2	1	no	—
131	C₂×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
136	C₂²⋊D₃₁	—	2	2	no	—
137	C₂²⋊D₃₁	—	2	2	no	—
138	C₂×Dic₃₁	—	4	1	no	—
139	C₂×Dic₃₁	—	4	1	no	—
140	C₂×Dic₃₁	C₂²×C₄	1	1	yes	characteristic
141	C₂×Dic₃₁	C₂²×C₄	1	1	yes	characteristic
142	C₂×Dic₃₁	C₂²×C₄	1	1	yes	characteristic
143	C₂×Dic₃₁	C₂²×C₄	1	1	yes	characteristic
144	C₂×Dic₃₁	C₂²×C₄	1	1	yes	characteristic
145	D₁₂₄	—	2	2	no	—
146	C₄×D₃₁	—	2	2	no	—
147	C₄×D₃₁	—	2	1	no	—
148	C₄×D₃₁	—	2	1	no	—
149	C₄×D₃₁	—	2	1	no	—
150	C₄×D₃₁	—	2	1	no	—
151	C₄×D₃₁	—	2	1	no	—
152	C₄×D₃₁	—	2	1	no	—
153	C₄×D₃₁	—	4	1	no	—
154	C₄×D₃₁	—	4	1	no	—
155	C₄×D₃₁	—	4	1	no	—
156	C₄×D₃₁	—	4	1	no	—
157	C₄×D₃₁	—	4	1	no	—
158	C₈×C₃₁	—	2	1	no	—
159	C₈×C₃₁	—	2	1	no	—
160	C₈×C₃₁	—	2	1	no	—
161	C₈×C₃₁	—	2	1	no	—
162	C₃₁⋊C₈	—	2	1	no	—
163	C₃₁⋊C₈	—	2	1	no	—
164	C₃₁⋊C₈	—	2	1	no	—
165	C₃₁⋊C₈	—	2	1	no	—
166	#2973	—	31	1	no	maximal, Sylow
167	C₂²×C₃₁	—	2	1	no	—
168	C₂²×C₃₁	—	2	1	no	—
169	C₂²×C₃₁	—	2	1	no	—
170	C₂²×C₃₁	—	2	1	no	—
171	C₂²×C₃₁	—	2	1	no	—
172	C₂²×C₃₁	C₂×M₁₆	1	2	yes	—
173	C₂²×C₃₁	C₂³×C₄	1	1	yes	characteristic
174	C₂×D₃₁	—	2	1	no	—
175	C₂×D₃₁	—	2	1	no	—
176	C₂×D₃₁	—	2	1	no	—
177	C₂×D₃₁	—	2	1	no	—
178	C₂×D₃₁	—	2	1	no	—
179	C₂×D₃₁	—	2	1	no	—
180	C₂×D₃₁	—	2	1	no	—
181	C₂×D₃₁	—	4	4	no	—
182	C₂×D₃₁	—	4	4	no	—
183	C₂×D₃₁	C₂×M₁₆	1	2	yes	—
184	C₂×D₃₁	C₂×M₁₆	1	2	yes	—
185	C₄×C₃₁	—	2	1	no	—
186	C₄×C₃₁	—	2	1	no	—
187	C₄×C₃₁	—	2	1	no	—
188	C₄×C₃₁	—	2	1	no	—
189	C₄×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
190	C₄×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
191	Dic₃₁	—	2	1	no	—
192	Dic₃₁	—	2	1	no	—
193	Dic₃₁	—	2	1	no	—
194	Dic₃₁	—	2	1	no	—
195	Dic₃₁	—	2	1	no	—
196	C₂×C₄×D₄	—	31	1	no	—
197	#435	—	31	1	no	—
198	#435	—	31	1	no	—
199	#435	—	31	1	no	—
200	#435	—	31	1	no	—
201	#435	—	31	1	no	—
202	#435	—	31	1	no	—
203	#435	—	31	1	no	—
204	#435	D₃₁	1	1	yes	characteristic, complemented
205	#432	—	31	1	no	—
206	#432	—	31	1	no	—
207	#407	—	31	1	no	—
208	#407	—	31	1	no	—
209	C₂×C₂²⋊C₈	—	31	1	no	—
210	C₂×C₂²⋊C₈	—	31	1	no	—
211	C₂×C₃₁	—	2	2	no	—
212	C₂×C₃₁	—	4	1	no	—
213	C₂×C₃₁	#518	1	1	yes	characteristic
214	C₂×C₃₁	C₂²×M₁₆	1	1	yes	characteristic
215	C₂×C₃₁	#568	1	1	yes	characteristic
216	D₃₁	—	2	2	no	—
217	D₃₁	—	2	2	no	—
218	D₃₁	—	4	1	no	—
219	C₂²×D₄	—	31	1	no	—
220	C₂³×C₄	—	31	1	no	—
221	C₂³×C₄	—	31	1	no	—
222	C₂×M₁₆	—	31	1	no	—
223	C₂×M₁₆	—	31	1	no	—
224	C₂×M₁₆	—	31	1	no	—
225	C₂×M₁₆	C₂×D₃₁	1	1	yes	characteristic, complemented
226	C₂²×C₈	—	31	1	no	—
227	C₂²×C₈	—	31	1	no	—
228	C₂²×C₈	—	31	1	no	—
229	C₂²×C₈	C₂×D₃₁	1	1	yes	characteristic, complemented
230	C₄×D₄	—	31	1	no	—
231	C₄×D₄	—	31	1	no	—
232	C₄×D₄	—	31	1	no	—
233	C₄×D₄	—	31	1	no	—
234	C₄×D₄	—	31	1	no	—
235	C₄×D₄	—	31	1	no	—
236	C₄×D₄	—	31	1	no	—
237	C₄×D₄	C₂×D₃₁	1	1	yes	characteristic
238	C₂×C₄⋊C₄	—	31	1	no	—
239	C₂×C₂²⋊C₄	—	31	1	no	—
240	C₂×C₂²⋊C₄	—	31	1	no	—
241	C₂×C₄²	—	31	1	no	—
242	C₄⋊C₈	—	31	1	no	—
243	C₄⋊C₈	—	31	1	no	—
244	C₄⋊C₈	—	31	1	no	—
245	C₄⋊C₈	C₂×D₃₁	1	1	yes	characteristic, complemented
246	C₂²⋊C₈	—	31	1	no	—
247	C₂²⋊C₈	—	31	1	no	—
248	C₂²⋊C₈	—	31	1	no	—
249	C₂²⋊C₈	—	31	1	no	—
250	C₂²⋊C₈	—	31	1	no	—
251	C₂²⋊C₈	—	31	1	no	—
252	C₂²⋊C₈	—	31	1	no	—
253	C₂²⋊C₈	—	31	1	no	—
254	C₂²⋊C₈	—	31	1	no	—
255	C₂²⋊C₈	—	31	1	no	—
256	C₂²⋊C₈	C₂×D₃₁	1	1	yes	characteristic, complemented
257	C₂²⋊C₈	C₂×D₃₁	1	1	yes	characteristic, complemented
258	#97	—	31	1	no	—
259	#97	—	31	1	no	—
260	#97	—	31	1	no	—
261	#97	C₂×D₃₁	1	1	yes	characteristic, complemented
262	C₃₁	#2973	1	1	yes	characteristic, complemented, Sylow
263	C₂⁴	—	31	1	no	—
264	C₂⁴	—	31	1	no	—
265	C₂×D₄	—	31	1	no	—
266	C₂×D₄	—	31	1	no	—
267	C₂×D₄	—	31	1	no	—
268	C₂×D₄	—	62	4	no	—
269	C₂×D₄	C₄×D₃₁	1	1	yes	characteristic
270	C₂²×C₄	—	31	1	no	—
271	C₂²×C₄	—	31	1	no	—
272	C₂²×C₄	—	31	1	no	—
273	C₂²×C₄	—	31	1	no	—
274	C₂²×C₄	—	31	1	no	—
275	C₂²×C₄	—	31	1	no	—
276	C₂²×C₄	—	31	1	no	—
277	C₂²×C₄	—	31	1	no	—
278	C₂²×C₄	—	31	1	no	—
279	C₂²×C₄	—	31	1	no	—
280	C₂²×C₄	—	31	1	no	—
281	C₂²×C₄	—	124	1	no	—
282	C₂²×C₄	—	124	1	no	—
283	C₂²×C₄	—	124	1	no	—
284	C₂²×C₄	—	124	1	no	—
285	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
286	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
287	M₁₆	—	4	1	no	—
288	M₁₆	—	124	1	no	—
289	M₁₆	—	124	1	no	—
290	M₁₆	—	124	1	no	—
291	C₂×C₈	—	4	1	no	—
292	C₂×C₈	—	31	1	no	—
293	C₂×C₈	—	31	1	no	—
294	C₂×C₈	—	31	1	no	—
295	C₂×C₈	—	31	1	no	—
296	C₂×C₈	—	124	1	no	—
297	C₂×C₈	—	124	1	no	—
298	C₂×C₈	—	124	1	no	—
299	C₂×C₈	C₂²×D₃₁	1	1	yes	characteristic
300	C₂×C₈	C₂²×D₃₁	1	1	yes	characteristic
301	C₂×C₈	C₂²×D₃₁	1	1	yes	characteristic
302	C₂×C₈	C₂²×D₃₁	1	1	yes	characteristic
303	C₄⋊C₄	—	31	1	no	—
304	C₄⋊C₄	—	31	1	no	—
305	C₄⋊C₄	—	31	1	no	—
306	C₄⋊C₄	C₄×D₃₁	1	1	yes	characteristic
307	C₂²⋊C₄	—	31	1	no	—
308	C₂²⋊C₄	—	31	1	no	—
309	C₂²⋊C₄	—	31	1	no	—
310	C₂²⋊C₄	—	31	1	no	—
311	C₂²⋊C₄	—	31	1	no	—
312	C₂²⋊C₄	—	31	1	no	—
313	C₂²⋊C₄	C₄×D₃₁	1	1	yes	characteristic
314	C₂²⋊C₄	C₄×D₃₁	1	1	yes	characteristic
315	C₄²	—	31	1	no	—
316	C₄²	—	31	1	no	—
317	C₄²	—	31	1	no	—
318	C₄²	C₂²×D₃₁	1	1	yes	characteristic
319	C₂³	—	31	1	no	—
320	C₂³	—	31	1	no	—
321	C₂³	—	31	4	no	—
322	C₂³	—	31	1	no	—
323	C₂³	—	62	2	no	—
324	C₂³	—	124	1	no	—
325	C₂³	—	124	1	no	—
326	C₂³	—	124	1	no	—
327	C₂³	—	124	1	no	—
328	C₂³	C₂×C₄×D₃₁	1	1	yes	characteristic
329	C₂³	C₂×C₄×D₃₁	1	1	yes	characteristic
330	D₄	—	2	2	no	—
331	D₄	—	62	2	no	—
332	D₄	—	62	2	no	—
333	D₄	—	62	2	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	31	1	no	—
339	C₂×C₄	—	31	1	no	—
340	C₂×C₄	—	31	1	no	—
341	C₂×C₄	—	31	1	no	—
342	C₂×C₄	—	31	1	no	—
343	C₂×C₄	—	62	2	no	—
344	C₂×C₄	—	62	1	no	—
345	C₂×C₄	—	62	1	no	—
346	C₂×C₄	—	62	1	no	—
347	C₂×C₄	—	62	1	no	—
348	C₂×C₄	—	62	1	no	—
349	C₂×C₄	—	62	1	no	—
350	C₂×C₄	—	124	1	no	—
351	C₂×C₄	—	124	1	no	—
352	C₂×C₄	—	124	1	no	—
353	C₂×C₄	—	124	1	no	—
354	C₂×C₄	—	124	1	no	—
355	C₂×C₄	—	124	1	no	—
356	C₂×C₄	—	124	1	no	—
357	C₂×C₄	C₂×C₄×D₃₁	1	1	yes	characteristic
358	C₂×C₄	C₂×C₄×D₃₁	1	1	yes	characteristic
359	C₂×C₄	C₂×C₄×D₃₁	1	1	yes	characteristic
360	C₂×C₄	C₂×C₄×D₃₁	1	1	yes	characteristic
361	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
362	C₈	—	2	1	no	—
363	C₈	—	2	1	no	—
364	C₈	—	2	1	no	—
365	C₈	—	2	1	no	—
366	C₈	—	62	1	no	—
367	C₈	—	62	1	no	—
368	C₈	—	62	1	no	—
369	C₈	—	62	1	no	—
370	C₂²	—	2	1	no	—
371	C₂²	—	2	1	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	2	1	no	—
375	C₂²	—	31	2	no	—
376	C₂²	—	31	2	no	—
377	C₂²	—	62	1	no	—
378	C₂²	—	62	1	no	—
379	C₂²	—	62	1	no	—
380	C₂²	—	62	1	no	—
381	C₂²	—	62	1	no	—
382	C₂²	—	62	1	no	—
383	C₂²	—	62	1	no	—
384	C₂²	—	124	4	no	—
385	C₂²	—	124	4	no	—
386	C₂²	M₁₆×D₃₁	1	2	yes	—
387	C₂²	C₂²×C₄×D₃₁	1	1	yes	characteristic
388	C₄	—	2	1	no	—
389	C₄	—	2	1	no	—
390	C₄	—	2	1	no	—
391	C₄	—	2	1	no	—
392	C₄	—	62	1	no	—
393	C₄	—	62	1	no	—
394	C₄	—	62	1	no	—
395	C₄	—	62	1	no	—
396	C₄	—	62	1	no	—
397	C₄	#11758561	1	1	yes	characteristic
398	C₄	#11758566	1	1	yes	characteristic
399	C₂	—	2	2	no	—
400	C₂	—	4	1	no	—
401	C₂	—	62	2	no	—
402	C₂	—	62	2	no	—
403	C₂	—	124	1	no	—
404	C₂	#14521521	1	1	yes	characteristic
405	C₂	C₂×M₁₆×D₃₁	1	1	yes	characteristic
406	C₂	#14521814	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₃₁
commutator, socle	C₂²×C₃₁	C₂³×C₄
Fitting	C₃₁×#435	C₂
prime radical	C₂×D₄×D₃₁	C₄
cosocle	C₂×C₄×C₃₁	C₂⁴
hypercenter	#435	D₃₁
hypocenter	C₃₁	#2973
LCS	G ▷ C₂²×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂×C₄ ◁ #435

Complements

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

N	H ≅ G/N	type
2. #14521123	C₂	semidirect
3. #14521122	C₂	semidirect
4. #14521121	C₂	semidirect
5. #14521120	C₂	semidirect
6. #14521119	C₂	semidirect
7. #14521118	C₂	semidirect
8. #14521117	C₂	semidirect
9. #14521105	C₂	semidirect
10. #14521104	C₂	semidirect
11. #14521012	C₂	semidirect
12. #14521011	C₂	semidirect
13. C₂×(C₂×D₃₁)⋊C₈	C₂	semidirect
14. C₂²⋊C₈×D₃₁	C₂	semidirect
15. C₃₁×#435	C₂	semidirect
19. C₂×M₁₆×C₃₁	C₂²	semidirect
20. C₂²×C₈×C₃₁	C₂²	semidirect
25. C₂×#92474	C₂²	semidirect
26. C₂²×C₃₁⋊C₈	C₂²	semidirect
27. C₂×#92469	C₂²	semidirect
28. C₂×#92469	C₂²	semidirect
29. C₂×C₈×D₃₁	C₂²	semidirect
30. C₂×C₈×D₃₁	C₂²	semidirect
39. C₃₁×C₄⋊C₈	C₂²	semidirect
40. C₃₁×C₂²⋊C₈	C₂²	semidirect
41. C₃₁×C₂²⋊C₈	C₂²	semidirect
42. C₃₁×#97	C₂²	semidirect
43. C₂²⋊(C₃₁⋊C₈)	C₂²	semidirect
44. C₂²⋊(C₃₁⋊C₈)	C₂²	semidirect
49. (C₂×D₃₁)⋊C₈	C₂²	semidirect
50. (C₂×D₃₁)⋊C₈	C₂²	semidirect
51. (C₂×D₃₁)⋊C₈	C₂²	semidirect
52. (C₂×D₃₁)⋊C₈	C₂²	semidirect
53. #11758403	C₂²	semidirect
54. #11758403	C₂²	semidirect
55. Dic₃₁⋊C₈	C₂²	semidirect
56. Dic₃₁⋊C₈	C₂²	semidirect
57. C₄⋊(C₃₁⋊C₈)	C₂²	semidirect
58. #11758391	C₂²	semidirect
122. C₂²×D₃₁	M₁₆	semidirect
204. #435	D₃₁	semidirect
225. C₂×M₁₆	C₂×D₃₁	semidirect
229. C₂²×C₈	C₂×D₃₁	semidirect
245. C₄⋊C₈	C₂×D₃₁	semidirect
256. C₂²⋊C₈	C₂×D₃₁	semidirect
257. C₂²⋊C₈	C₂×D₃₁	semidirect
261. #97	C₂×D₃₁	semidirect
262. C₃₁	#2973	semidirect

Maximal subgroups

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

subgroup	index
C₄×D₄×D₃₁	2
#14521123	2
#14521122	2
#14521121	2
#14521120	2
#14521119	2
#14521118	2
#14521117	2
#14521105	2
#14521104	2
#14521012	2
#14521011	2
C₂×(C₂×D₃₁)⋊C₈	2
C₂²⋊C₈×D₃₁	2
C₃₁×#435	2
#2973	31