Subgroups — C₈×C₃₁×#99 #21464918

Order 7936.

614 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×D₄×C₃₁	C₂	1	1	yes	maximal, characteristic
2	C₄×C₃₁×#99	C₂	1	1	yes	maximal, characteristic
3	C₈×C₂²⋊C₄×C₃₁	C₂	1	2	yes	maximal, complemented
4	C₃₁×#1459	C₂	1	1	yes	maximal, characteristic
5	C₃₁×#1282	C₂	1	2	yes	maximal, complemented
6	C₂³×C₈×C₃₁	C₄	1	1	yes	characteristic, complemented
7	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic
8	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
9	C₈×D₄×C₃₁	—	2	2	no	—
10	C₈×D₄×C₃₁	—	2	2	no	—
11	C₂×C₃₁×C₄⋊C₈	C₄	1	1	yes	characteristic, complemented
12	C₂×C₃₁×#99	C₄	1	2	yes	—
13	C₂×C₃₁×C₂²⋊C₈	C₄	1	1	yes	characteristic, complemented
14	C₂×C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
15	C₂×C₃₁×C₂²⋊C₈	C₂²	1	2	yes	—
16	C₂×C₄×C₈×C₃₁	—	2	2	no	—
17	C₂×C₄×C₈×C₃₁	C₄	1	1	yes	characteristic, complemented
18	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
19	C₃₁×#342	C₄	1	2	yes	—
20	C₃₁×#336	—	2	2	no	—
21	C₃₁×#324	C₄	1	2	yes	complemented
22	C₃₁×#323	C₄	1	2	yes	complemented
23	C₂²×D₄×C₃₁	C₂×C₄	1	1	yes	characteristic
24	C₂³×C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
25	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
26	C₂²×C₈×C₃₁	—	2	2	no	—
27	C₂²×C₈×C₃₁	—	2	1	no	—
28	C₂²×C₈×C₃₁	—	2	1	no	—
29	C₂²×C₈×C₃₁	—	4	2	no	—
30	C₂²×C₈×C₃₁	—	4	2	no	—
31	C₂²×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₈×C₃₁	D₄	1	2	yes	—
36	C₂²×C₈×C₃₁	D₄	1	2	yes	—
37	C₄×D₄×C₃₁	—	2	2	no	—
38	C₄×D₄×C₃₁	—	2	2	no	—
39	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
40	C₂×C₂²⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
41	C₂×C₂²⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
42	C₂×C₂²⋊C₄×C₃₁	C₂×C₄	1	4	yes	—
43	C₂×C₄²×C₃₁	—	2	2	no	—
44	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
45	C₃₁×C₄⋊C₈	—	2	2	no	—
46	C₃₁×#99	C₈	1	8	yes	direct product factor
47	C₃₁×C₂²⋊C₈	—	2	2	no	—
48	C₃₁×C₂²⋊C₈	—	2	2	no	—
49	C₃₁×C₂²⋊C₈	—	2	2	no	—
50	C₃₁×C₂²⋊C₈	C₂×C₄	1	4	yes	—
51	C₄×C₈×C₃₁	—	2	1	no	—
52	C₄×C₈×C₃₁	—	2	1	no	—
53	C₄×C₈×C₃₁	—	4	4	no	—
54	C₃₁×#95	—	2	2	no	—
55	C₂⁴×C₃₁	C₄²	1	1	yes	characteristic
56	C₂⁴×C₃₁	C₂²×C₄	1	1	yes	characteristic
57	C₂×D₄×C₃₁	—	2	2	no	—
58	C₂×D₄×C₃₁	—	2	2	no	—
59	C₂×D₄×C₃₁	C₂×C₈	1	4	yes	—
60	C₂²×C₄×C₃₁	—	2	4	no	—
61	C₂²×C₄×C₃₁	—	2	1	no	—
62	C₂²×C₄×C₃₁	—	2	1	no	—
63	C₂²×C₄×C₃₁	—	4	1	no	—
64	C₂²×C₄×C₃₁	—	4	1	no	—
65	C₂²×C₄×C₃₁	—	4	1	no	—
66	C₂²×C₄×C₃₁	—	4	1	no	—
67	C₂²×C₄×C₃₁	C₄²	1	1	yes	characteristic
68	C₂²×C₄×C₃₁	C₄²	1	1	yes	characteristic
69	C₂²×C₄×C₃₁	C₄²	1	1	yes	characteristic
70	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
71	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
72	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
73	C₂²×C₄×C₃₁	#41	1	2	yes	—
74	C₂×C₈×C₃₁	—	2	4	no	—
75	C₂×C₈×C₃₁	—	2	2	no	—
76	C₂×C₈×C₃₁	—	2	1	no	—
77	C₂×C₈×C₃₁	—	2	1	no	—
78	C₂×C₈×C₃₁	—	2	4	no	—
79	C₂×C₈×C₃₁	—	4	1	no	—
80	C₂×C₈×C₃₁	—	4	2	no	—
81	C₂×C₈×C₃₁	—	4	2	no	—
82	C₂×C₈×C₃₁	—	4	2	no	—
83	C₂×C₈×C₃₁	—	4	2	no	—
84	C₂×C₈×C₃₁	—	4	2	no	—
85	C₂×C₈×C₃₁	—	4	1	no	—
86	C₂×C₈×C₃₁	—	4	1	no	—
87	C₂×C₈×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
88	C₂×C₈×C₃₁	C₂²⋊C₄	1	2	yes	—
89	C₂×C₈×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
90	C₄⋊C₄×C₃₁	—	2	2	no	—
91	C₂²⋊C₄×C₃₁	—	2	2	no	—
92	C₂²⋊C₄×C₃₁	—	2	4	no	—
93	C₂²⋊C₄×C₃₁	—	2	2	no	—
94	C₂²⋊C₄×C₃₁	C₂×C₈	1	8	yes	complemented
95	C₄²×C₃₁	—	2	1	no	—
96	C₄²×C₃₁	—	2	1	no	—
97	C₄²×C₃₁	—	4	2	no	—
98	C₄²×C₃₁	—	4	2	no	—
99	C₈×#99	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
100	C₂³×C₃₁	—	2	1	no	—
101	C₂³×C₃₁	—	2	1	no	—
102	C₂³×C₃₁	—	4	1	no	—
103	C₂³×C₃₁	—	4	1	no	—
104	C₂³×C₃₁	—	4	1	no	—
105	C₂³×C₃₁	—	4	1	no	—
106	C₂³×C₃₁	C₄×C₈	1	2	yes	complemented
107	C₂³×C₃₁	C₂×C₄²	1	1	yes	characteristic
108	C₂³×C₃₁	C₄×D₄	1	2	yes	—
109	C₂³×C₃₁	C₂²×C₈	1	2	yes	—
110	C₂³×C₃₁	#131	1	2	yes	—
111	D₄×C₃₁	—	2	8	no	—
112	C₂×C₄×C₃₁	—	2	1	no	—
113	C₂×C₄×C₃₁	—	2	1	no	—
114	C₂×C₄×C₃₁	—	2	2	no	—
115	C₂×C₄×C₃₁	—	2	1	no	—
116	C₂×C₄×C₃₁	—	2	2	no	—
117	C₂×C₄×C₃₁	—	2	1	no	—
118	C₂×C₄×C₃₁	—	2	1	no	—
119	C₂×C₄×C₃₁	—	2	1	no	—
120	C₂×C₄×C₃₁	—	2	8	no	—
121	C₂×C₄×C₃₁	—	4	1	no	—
122	C₂×C₄×C₃₁	—	4	2	no	—
123	C₂×C₄×C₃₁	—	4	2	no	—
124	C₂×C₄×C₃₁	—	4	4	no	—
125	C₂×C₄×C₃₁	—	4	4	no	—
126	C₂×C₄×C₃₁	—	4	1	no	—
127	C₂×C₄×C₃₁	—	4	1	no	—
128	C₂×C₄×C₃₁	—	4	1	no	—
129	C₂×C₄×C₃₁	—	4	1	no	—
130	C₂×C₄×C₃₁	C₄×C₈	1	2	yes	complemented
131	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
132	C₂×C₄×C₃₁	#117	1	1	yes	characteristic
133	C₂×C₄×C₃₁	C₄×D₄	1	2	yes	—
134	C₈×C₃₁	—	2	1	no	—
135	C₈×C₃₁	—	2	2	no	—
136	C₈×C₃₁	—	4	4	no	—
137	C₈×C₃₁	—	4	1	no	—
138	C₈×C₃₁	—	4	1	no	—
139	C₈×C₃₁	#99	1	2	yes	direct product factor
140	C₂×C₈×D₄	C₂×C₃₁	1	1	yes	characteristic
141	C₄×#99	C₂×C₃₁	1	1	yes	characteristic
142	C₈×C₂²⋊C₄	C₂×C₃₁	1	2	yes	complemented
143	#1459	C₂×C₃₁	1	1	yes	characteristic
144	#1282	C₂×C₃₁	1	2	yes	complemented
145	C₂²×C₃₁	—	2	2	no	—
146	C₂²×C₃₁	—	2	1	no	—
147	C₂²×C₃₁	—	2	2	no	—
148	C₂²×C₃₁	—	2	1	no	—
149	C₂²×C₃₁	—	2	2	no	—
150	C₂²×C₃₁	—	4	2	no	—
151	C₂²×C₃₁	—	4	2	no	—
152	C₂²×C₃₁	—	4	2	no	—
153	C₂²×C₃₁	—	4	2	no	—
154	C₂²×C₃₁	—	4	1	no	—
155	C₂²×C₃₁	—	4	1	no	—
156	C₂²×C₃₁	C₄×C₂²⋊C₄	1	1	yes	characteristic
157	C₂²×C₃₁	C₂×C₄×C₈	1	1	yes	characteristic
158	C₂²×C₃₁	#405	1	1	yes	characteristic
159	C₂²×C₃₁	C₈×D₄	1	4	yes	—
160	C₄×C₃₁	—	2	2	no	—
161	C₄×C₃₁	—	2	2	no	—
162	C₄×C₃₁	—	2	1	no	—
163	C₄×C₃₁	—	4	8	no	—
164	C₄×C₃₁	—	4	1	no	—
165	C₄×C₃₁	—	4	1	no	—
166	C₄×C₃₁	C₂×#99	1	1	yes	characteristic
167	C₄×C₃₁	#410	1	1	yes	characteristic
168	C₂³×C₈	C₄×C₃₁	1	1	yes	characteristic, complemented
169	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
170	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
171	C₈×D₄	—	2	2	no	—
172	C₈×D₄	—	2	2	no	—
173	C₂×C₄⋊C₈	C₄×C₃₁	1	1	yes	characteristic, complemented
174	C₂×#99	C₄×C₃₁	1	2	yes	—
175	C₂×C₂²⋊C₈	C₄×C₃₁	1	1	yes	characteristic, complemented
176	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
177	C₂×C₂²⋊C₈	C₂²×C₃₁	1	2	yes	—
178	C₂×C₄×C₈	—	2	2	no	—
179	C₂×C₄×C₈	C₄×C₃₁	1	1	yes	characteristic, complemented
180	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
181	#342	C₄×C₃₁	1	2	yes	—
182	#336	—	2	2	no	—
183	#324	C₄×C₃₁	1	2	yes	complemented
184	#323	C₄×C₃₁	1	2	yes	complemented
185	C₂×C₃₁	—	2	4	no	—
186	C₂×C₃₁	—	2	1	no	—
187	C₂×C₃₁	—	2	1	no	—
188	C₂×C₃₁	—	4	2	no	—
189	C₂×C₃₁	C₈×C₂²⋊C₄	1	1	yes	characteristic
190	C₂×C₃₁	C₄×#99	1	1	yes	characteristic
191	C₂×C₃₁	#1757	1	1	yes	characteristic
192	C₂²×D₄	C₂×C₄×C₃₁	1	1	yes	characteristic
193	C₂³×C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
194	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
195	C₂²×C₈	—	2	2	no	—
196	C₂²×C₈	—	2	1	no	—
197	C₂²×C₈	—	2	1	no	—
198	C₂²×C₈	—	4	2	no	—
199	C₂²×C₈	—	4	2	no	—
200	C₂²×C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
201	C₂²×C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
202	C₂²×C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
203	C₂²×C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
204	C₂²×C₈	D₄×C₃₁	1	2	yes	—
205	C₂²×C₈	D₄×C₃₁	1	2	yes	—
206	C₄×D₄	—	2	2	no	—
207	C₄×D₄	—	2	2	no	—
208	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
209	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
210	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
211	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	4	yes	—
212	C₂×C₄²	—	2	2	no	—
213	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
214	C₄⋊C₈	—	2	2	no	—
215	#99	C₈×C₃₁	1	8	yes	direct product factor
216	C₂²⋊C₈	—	2	2	no	—
217	C₂²⋊C₈	—	2	2	no	—
218	C₂²⋊C₈	—	2	2	no	—
219	C₂²⋊C₈	C₂×C₄×C₃₁	1	4	yes	—
220	C₄×C₈	—	2	1	no	—
221	C₄×C₈	—	2	1	no	—
222	C₄×C₈	—	4	4	no	—
223	#95	—	2	2	no	—
224	C₃₁	C₈×#99	1	1	yes	characteristic, direct product factor, Sylow
225	C₂⁴	C₄²×C₃₁	1	1	yes	characteristic
226	C₂⁴	C₂²×C₄×C₃₁	1	1	yes	characteristic
227	C₂×D₄	—	2	2	no	—
228	C₂×D₄	—	2	2	no	—
229	C₂×D₄	C₂×C₈×C₃₁	1	4	yes	—
230	C₂²×C₄	—	2	4	no	—
231	C₂²×C₄	—	2	1	no	—
232	C₂²×C₄	—	2	1	no	—
233	C₂²×C₄	—	4	1	no	—
234	C₂²×C₄	—	4	1	no	—
235	C₂²×C₄	—	4	1	no	—
236	C₂²×C₄	—	4	1	no	—
237	C₂²×C₄	C₄²×C₃₁	1	1	yes	characteristic
238	C₂²×C₄	C₄²×C₃₁	1	1	yes	characteristic
239	C₂²×C₄	C₄²×C₃₁	1	1	yes	characteristic
240	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
241	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
242	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
243	C₂²×C₄	#41×C₃₁	1	2	yes	—
244	C₂×C₈	—	2	4	no	—
245	C₂×C₈	—	2	2	no	—
246	C₂×C₈	—	2	1	no	—
247	C₂×C₈	—	2	1	no	—
248	C₂×C₈	—	2	4	no	—
249	C₂×C₈	—	4	1	no	—
250	C₂×C₈	—	4	2	no	—
251	C₂×C₈	—	4	2	no	—
252	C₂×C₈	—	4	2	no	—
253	C₂×C₈	—	4	2	no	—
254	C₂×C₈	—	4	2	no	—
255	C₂×C₈	—	4	1	no	—
256	C₂×C₈	—	4	1	no	—
257	C₂×C₈	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
258	C₂×C₈	C₂²⋊C₄×C₃₁	1	2	yes	—
259	C₂×C₈	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
260	C₄⋊C₄	—	2	2	no	—
261	C₂²⋊C₄	—	2	2	no	—
262	C₂²⋊C₄	—	2	4	no	—
263	C₂²⋊C₄	—	2	2	no	—
264	C₂²⋊C₄	C₂×C₈×C₃₁	1	8	yes	complemented
265	C₄²	—	2	1	no	—
266	C₄²	—	2	1	no	—
267	C₄²	—	4	2	no	—
268	C₄²	—	4	2	no	—
269	C₂³	—	2	1	no	—
270	C₂³	—	2	1	no	—
271	C₂³	—	4	1	no	—
272	C₂³	—	4	1	no	—
273	C₂³	—	4	1	no	—
274	C₂³	—	4	1	no	—
275	C₂³	C₄×C₈×C₃₁	1	2	yes	complemented
276	C₂³	C₂×C₄²×C₃₁	1	1	yes	characteristic
277	C₂³	C₄×D₄×C₃₁	1	2	yes	—
278	C₂³	C₂²×C₈×C₃₁	1	2	yes	—
279	C₂³	C₃₁×#131	1	2	yes	—
280	D₄	—	2	8	no	—
281	C₂×C₄	—	2	1	no	—
282	C₂×C₄	—	2	1	no	—
283	C₂×C₄	—	2	2	no	—
284	C₂×C₄	—	2	1	no	—
285	C₂×C₄	—	2	2	no	—
286	C₂×C₄	—	2	1	no	—
287	C₂×C₄	—	2	8	no	—
288	C₂×C₄	—	2	1	no	—
289	C₂×C₄	—	2	1	no	—
290	C₂×C₄	—	4	1	no	—
291	C₂×C₄	—	4	2	no	—
292	C₂×C₄	—	4	2	no	—
293	C₂×C₄	—	4	4	no	—
294	C₂×C₄	—	4	4	no	—
295	C₂×C₄	—	4	1	no	—
296	C₂×C₄	—	4	1	no	—
297	C₂×C₄	—	4	1	no	—
298	C₂×C₄	—	4	1	no	—
299	C₂×C₄	C₄×C₈×C₃₁	1	2	yes	complemented
300	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
301	C₂×C₄	C₃₁×#117	1	1	yes	characteristic
302	C₂×C₄	C₄×D₄×C₃₁	1	2	yes	—
303	C₈	—	2	1	no	—
304	C₈	—	2	2	no	—
305	C₈	—	4	4	no	—
306	C₈	—	4	1	no	—
307	C₈	—	4	1	no	—
308	C₈	C₃₁×#99	1	2	yes	direct product factor
309	C₂²	—	2	2	no	—
310	C₂²	—	2	1	no	—
311	C₂²	—	2	2	no	—
312	C₂²	—	2	1	no	—
313	C₂²	—	2	2	no	—
314	C₂²	—	4	2	no	—
315	C₂²	—	4	2	no	—
316	C₂²	—	4	2	no	—
317	C₂²	—	4	2	no	—
318	C₂²	—	4	1	no	—
319	C₂²	—	4	1	no	—
320	C₂²	C₄×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
321	C₂²	C₂×C₄×C₈×C₃₁	1	1	yes	characteristic
322	C₂²	C₃₁×#405	1	1	yes	characteristic
323	C₂²	C₈×D₄×C₃₁	1	4	yes	—
324	C₄	—	2	2	no	—
325	C₄	—	2	2	no	—
326	C₄	—	2	1	no	—
327	C₄	—	4	8	no	—
328	C₄	—	4	1	no	—
329	C₄	—	4	1	no	—
330	C₄	C₂×C₃₁×#99	1	1	yes	characteristic
331	C₄	C₃₁×#410	1	1	yes	characteristic
332	C₂	—	2	4	no	—
333	C₂	—	2	1	no	—
334	C₂	—	2	1	no	—
335	C₂	—	4	2	no	—
336	C₂	C₈×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
337	C₂	C₄×C₃₁×#99	1	1	yes	characteristic
338	C₂	C₃₁×#1757	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈×C₃₁	C₂²⋊C₄
commutator	C₂²	C₂×C₄×C₈×C₃₁
Frattini, cosocle	C₂³×C₄	C₂³×C₃₁
socle	C₂²×C₃₁	C₄×C₂²⋊C₄
prime radical	C₂²×D₄×C₃₁	C₂×C₄
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₃₁ ◁ C₂³×C₈×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₈×C₂²⋊C₄×C₃₁	C₂	semidirect
5. C₃₁×#1282	C₂	semidirect
6. C₂³×C₈×C₃₁	C₄	semidirect
11. C₂×C₃₁×C₄⋊C₈	C₄	semidirect
13. C₂×C₃₁×C₂²⋊C₈	C₄	semidirect
17. C₂×C₄×C₈×C₃₁	C₄	semidirect
21. C₃₁×#324	C₄	semidirect
22. C₃₁×#323	C₄	semidirect
46. C₃₁×#99	C₈	direct (N × H)
94. C₂²⋊C₄×C₃₁	C₂×C₈	semidirect
99. C₈×#99	C₃₁	direct (N × H)
106. C₂³×C₃₁	C₄×C₈	semidirect
130. C₂×C₄×C₃₁	C₄×C₈	semidirect
139. C₈×C₃₁	#99	direct (N × H)
142. C₈×C₂²⋊C₄	C₂×C₃₁	semidirect
144. #1282	C₂×C₃₁	semidirect
168. C₂³×C₈	C₄×C₃₁	semidirect
173. C₂×C₄⋊C₈	C₄×C₃₁	semidirect
175. C₂×C₂²⋊C₈	C₄×C₃₁	semidirect
179. C₂×C₄×C₈	C₄×C₃₁	semidirect
183. #324	C₄×C₃₁	semidirect
184. #323	C₄×C₃₁	semidirect
215. #99	C₈×C₃₁	direct (N × H)
224. C₃₁	C₈×#99	direct (N × H)
264. C₂²⋊C₄	C₂×C₈×C₃₁	semidirect
275. C₂³	C₄×C₈×C₃₁	semidirect
299. C₂×C₄	C₄×C₈×C₃₁	semidirect
308. C₈	C₃₁×#99	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₈×D₄×C₃₁	2
C₄×C₃₁×#99	2
C₈×C₂²⋊C₄×C₃₁	2
C₃₁×#1459	2
C₃₁×#1282	2
C₈×#99	31

Subgroups — C8×C31×#99 #21464918

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×C₃₁×#99 #21464918