Subgroups — C₃₁×#33842 #21490601

Order 7936.

664 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#510	C₂	1	2	yes	maximal, complemented
2	D₄×Q₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3283	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#2247	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#2219	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2209	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#2208	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#2189	C₂	1	2	yes	maximal, complemented
9	C₃₁×#2188	C₂	1	2	yes	maximal, complemented
10	C₄×C₃₁×SD₃₂	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#2169	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃₁×#135	C₂²	1	2	yes	—
13	C₂²×Q₁₆×C₃₁	C₂²	1	2	yes	—
14	D₄×Q₈×C₃₁	—	2	1	no	—
15	C₃₁×#547	—	2	1	no	—
16	C₃₁×#510	—	2	8	no	—
17	C₂×C₃₁×Q₃₂	C₂²	1	2	yes	—
18	C₂×C₃₁×Q₃₂	C₂²	1	2	yes	—
19	C₂×C₃₁×Q₃₂	C₂²	1	2	yes	—
20	C₂×C₃₁×SD₃₂	C₂²	1	2	yes	—
21	C₂×C₃₁×SD₃₂	C₂²	1	1	yes	characteristic
22	C₂×C₃₁×M₃₂	C₂²	1	2	yes	—
23	C₃₁×#494	C₂²	1	1	yes	characteristic
24	C₃₁×#494	C₂²	1	1	yes	characteristic
25	C₃₁×#467	C₂²	1	2	yes	—
26	C₃₁×#467	C₂²	1	2	yes	—
27	C₃₁×#462	—	2	1	no	—
28	C₃₁×#461	—	2	1	no	—
29	C₃₁×#452	—	2	2	no	—
30	C₃₁×#451	—	2	2	no	—
31	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
32	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
33	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
34	C₃₁×#367	C₂²	1	1	yes	characteristic
35	C₃₁×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
36	C₃₁×#358	C₂²	1	1	yes	characteristic
37	C₃₁×#358	C₂²	1	2	yes	—
38	C₃₁×#358	C₂²	1	2	yes	—
39	C₃₁×#357	C₂²	1	1	yes	characteristic
40	C₃₁×C₂²⋊C₁₆	C₂²	1	2	yes	—
41	C₄×C₁₆×C₃₁	C₂²	1	1	yes	characteristic
42	C₂×#41×C₃₁	—	2	2	no	—
43	C₂²×Q₈×C₃₁	—	2	2	no	—
44	C₃₁×#135	—	2	4	no	—
45	C₃₁×#135	—	4	2	no	—
46	C₂×Q₁₆×C₃₁	—	2	4	no	—
47	C₂×Q₁₆×C₃₁	—	2	2	no	—
48	C₂×Q₁₆×C₃₁	—	2	1	no	—
49	C₂×Q₁₆×C₃₁	—	2	1	no	—
50	C₂×Q₁₆×C₃₁	—	4	2	no	—
51	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
52	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
53	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
54	C₂×SD₁₆×C₃₁	—	2	2	no	—
55	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
57	C₃₁×C₄⋊Q₈	—	2	1	no	—
58	C₃₁×C₄⋊Q₈	—	2	1	no	—
59	C₃₁×C₄⋊Q₈	—	4	1	no	—
60	C₃₁×#123	—	4	2	no	—
61	C₃₁×C₂²⋊Q₈	—	2	2	no	—
62	C₃₁×C₂²⋊Q₈	—	2	2	no	—
63	C₃₁×C₂²⋊Q₈	—	4	2	no	—
64	C₃₁×#121	—	4	1	no	—
65	C₄×Q₈×C₃₁	—	2	1	no	—
66	C₄×D₄×C₃₁	—	2	1	no	—
67	C₄×D₄×C₃₁	—	4	1	no	—
68	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₃₁	—	4	1	no	—
70	C₃₁×Q₃₂	—	2	4	no	—
71	C₃₁×Q₃₂	—	2	4	no	—
72	C₃₁×Q₃₂	—	4	2	no	—
73	C₃₁×SD₃₂	—	2	4	no	—
74	C₃₁×SD₃₂	D₄	1	4	yes	complemented
75	C₃₁×M₃₂	—	2	4	no	—
76	C₂×C₁₆×C₃₁	C₂³	1	2	yes	—
77	C₂×C₁₆×C₃₁	C₂³	1	1	yes	characteristic
78	C₂×C₁₆×C₃₁	C₂³	1	1	yes	characteristic
79	C₃₁×#107	C₂³	1	1	yes	characteristic
80	C₃₁×#107	C₂³	1	1	yes	characteristic
81	C₃₁×C₄⋊C₈	D₄	1	1	yes	characteristic
82	C₃₁×#103	—	2	1	no	—
83	C₃₁×#103	—	2	2	no	—
84	C₃₁×#103	—	2	2	no	—
85	C₃₁×#102	—	2	1	no	—
86	C₃₁×C₂²⋊C₈	D₄	1	2	yes	—
87	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
88	#41×C₃₁	—	4	4	no	—
89	#41×C₃₁	—	8	2	no	—
90	C₂×Q₈×C₃₁	—	2	1	no	—
91	C₂×Q₈×C₃₁	—	2	2	no	—
92	C₂×Q₈×C₃₁	—	2	2	no	—
93	C₂×Q₈×C₃₁	—	4	4	no	—
94	C₂×Q₈×C₃₁	—	4	2	no	—
95	C₂×Q₈×C₃₁	—	8	2	no	—
96	C₂×D₄×C₃₁	—	2	1	no	—
97	C₂×D₄×C₃₁	—	4	2	no	—
98	C₂×D₄×C₃₁	D₈	1	1	yes	characteristic
99	C₂²×C₄×C₃₁	—	4	2	no	—
100	C₂²×C₄×C₃₁	—	4	1	no	—
101	C₂²×C₄×C₃₁	—	4	2	no	—
102	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
103	Q₁₆×C₃₁	—	2	2	no	—
104	Q₁₆×C₃₁	—	2	2	no	—
105	Q₁₆×C₃₁	—	2	1	no	—
106	Q₁₆×C₃₁	—	2	2	no	—
107	Q₁₆×C₃₁	—	2	2	no	—
108	Q₁₆×C₃₁	—	4	4	no	—
109	Q₁₆×C₃₁	—	8	1	no	—
110	Q₁₆×C₃₁	—	8	1	no	—
111	Q₁₆×C₃₁	C₂×D₄	1	2	yes	—
112	SD₁₆×C₃₁	—	4	4	no	—
113	D₈×C₃₁	—	2	1	no	—
114	D₈×C₃₁	C₂×D₄	1	2	yes	—
115	C₂×C₈×C₃₁	—	2	2	no	—
116	C₂×C₈×C₃₁	—	2	2	no	—
117	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
118	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
119	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
120	C₄⋊C₄×C₃₁	—	2	1	no	—
121	C₄⋊C₄×C₃₁	—	2	1	no	—
122	C₄⋊C₄×C₃₁	—	4	1	no	—
123	C₄⋊C₄×C₃₁	—	4	2	no	—
124	C₄⋊C₄×C₃₁	—	4	1	no	—
125	C₄⋊C₄×C₃₁	—	4	1	no	—
126	C₄⋊C₄×C₃₁	—	4	2	no	—
127	C₄⋊C₄×C₃₁	—	4	1	no	—
128	C₄⋊C₄×C₃₁	—	4	1	no	—
129	C₄⋊C₄×C₃₁	D₈	1	1	yes	characteristic
130	C₂²⋊C₄×C₃₁	—	4	2	no	—
131	C₂²⋊C₄×C₃₁	—	4	2	no	—
132	C₂²⋊C₄×C₃₁	—	4	1	no	—
133	C₂²⋊C₄×C₃₁	D₈	1	2	yes	—
134	C₄²×C₃₁	—	4	1	no	—
135	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
136	C₁₆×C₃₁	—	2	2	no	—
137	C₁₆×C₃₁	—	2	1	no	—
138	C₁₆×C₃₁	C₂×D₄	1	2	yes	—
139	#33842	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
140	C₂³×C₃₁	—	4	1	no	—
141	C₂³×C₃₁	C₂×D₈	1	2	yes	—
142	Q₈×C₃₁	—	2	2	no	—
143	Q₈×C₃₁	—	4	1	no	—
144	Q₈×C₃₁	—	4	2	no	—
145	Q₈×C₃₁	—	4	2	no	—
146	Q₈×C₃₁	—	4	2	no	—
147	Q₈×C₃₁	—	4	2	no	—
148	Q₈×C₃₁	—	8	4	no	—
149	D₄×C₃₁	—	2	2	no	—
150	D₄×C₃₁	—	2	2	no	—
151	D₄×C₃₁	—	4	1	no	—
152	D₄×C₃₁	—	8	4	no	—
153	C₂×C₄×C₃₁	—	2	2	no	—
154	C₂×C₄×C₃₁	—	2	2	no	—
155	C₂×C₄×C₃₁	—	4	1	no	—
156	C₂×C₄×C₃₁	—	4	1	no	—
157	C₂×C₄×C₃₁	—	4	1	no	—
158	C₂×C₄×C₃₁	—	4	2	no	—
159	C₂×C₄×C₃₁	—	4	2	no	—
160	C₂×C₄×C₃₁	—	8	4	no	—
161	C₂×C₄×C₃₁	—	8	4	no	—
162	C₂×C₄×C₃₁	—	8	2	no	—
163	C₂×C₄×C₃₁	C₂×D₈	1	1	yes	characteristic
164	C₂×C₄×C₃₁	C₂×D₈	1	2	yes	—
165	C₂×C₄×C₃₁	C₂×D₈	1	1	yes	characteristic
166	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
167	C₈×C₃₁	—	2	2	no	—
168	C₈×C₃₁	—	2	1	no	—
169	C₈×C₃₁	C₂²×D₄	1	1	yes	characteristic
170	C₈×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
171	C₂×#510	C₂×C₃₁	1	2	yes	complemented
172	D₄×Q₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
173	#3283	C₂×C₃₁	1	1	yes	characteristic
174	#2247	C₂×C₃₁	1	1	yes	characteristic, complemented
175	#2219	C₂×C₃₁	1	2	yes	complemented
176	#2209	C₂×C₃₁	1	1	yes	characteristic, complemented
177	#2208	C₂×C₃₁	1	1	yes	characteristic, complemented
178	#2189	C₂×C₃₁	1	2	yes	complemented
179	#2188	C₂×C₃₁	1	2	yes	complemented
180	C₄×SD₃₂	C₂×C₃₁	1	1	yes	characteristic, complemented
181	#2169	C₂×C₃₁	1	1	yes	characteristic, complemented
182	C₂²×C₃₁	—	2	2	no	—
183	C₂²×C₃₁	—	2	2	no	—
184	C₂²×C₃₁	—	2	2	no	—
185	C₂²×C₃₁	—	4	2	no	—
186	C₂²×C₃₁	—	8	1	no	—
187	C₂²×C₃₁	—	8	1	no	—
188	C₂²×C₃₁	C₂²×D₈	1	1	yes	characteristic
189	C₄×C₃₁	—	2	1	no	—
190	C₄×C₃₁	—	2	2	no	—
191	C₄×C₃₁	—	4	2	no	—
192	C₄×C₃₁	—	8	1	no	—
193	C₄×C₃₁	—	8	1	no	—
194	C₄×C₃₁	—	8	2	no	—
195	C₄×C₃₁	—	8	2	no	—
196	C₄×C₃₁	#510	1	2	yes	complemented
197	C₄×C₃₁	D₄²	1	1	yes	characteristic
198	C₄×C₃₁	#576	1	1	yes	characteristic
199	C₂×#135	C₂²×C₃₁	1	2	yes	—
200	C₂²×Q₁₆	C₂²×C₃₁	1	2	yes	—
201	D₄×Q₈	—	2	1	no	—
202	#547	—	2	1	no	—
203	#510	—	2	8	no	—
204	C₂×Q₃₂	C₂²×C₃₁	1	2	yes	—
205	C₂×Q₃₂	C₂²×C₃₁	1	2	yes	—
206	C₂×Q₃₂	C₂²×C₃₁	1	2	yes	—
207	C₂×SD₃₂	C₂²×C₃₁	1	2	yes	—
208	C₂×SD₃₂	C₂²×C₃₁	1	1	yes	characteristic
209	C₂×M₃₂	C₂²×C₃₁	1	2	yes	—
210	#494	C₂²×C₃₁	1	1	yes	characteristic
211	#494	C₂²×C₃₁	1	1	yes	characteristic
212	#467	C₂²×C₃₁	1	2	yes	—
213	#467	C₂²×C₃₁	1	2	yes	—
214	#462	—	2	1	no	—
215	#461	—	2	1	no	—
216	#452	—	2	2	no	—
217	#451	—	2	2	no	—
218	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
219	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
220	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
221	#367	C₂²×C₃₁	1	1	yes	characteristic
222	C₄⋊C₁₆	C₂²×C₃₁	1	1	yes	characteristic
223	#358	C₂²×C₃₁	1	1	yes	characteristic
224	#358	C₂²×C₃₁	1	2	yes	—
225	#358	C₂²×C₃₁	1	2	yes	—
226	#357	C₂²×C₃₁	1	1	yes	characteristic
227	C₂²⋊C₁₆	C₂²×C₃₁	1	2	yes	—
228	C₄×C₁₆	C₂²×C₃₁	1	1	yes	characteristic
229	C₂×C₃₁	—	4	2	no	—
230	C₂×C₃₁	—	8	2	no	—
231	C₂×C₃₁	D₄×D₈	1	1	yes	characteristic
232	C₂×C₃₁	C₂×#510	1	1	yes	characteristic
233	C₂×C₃₁	#3417	1	1	yes	characteristic
234	C₂×#41	—	2	2	no	—
235	C₂²×Q₈	—	2	2	no	—
236	#135	—	2	4	no	—
237	#135	—	4	2	no	—
238	C₂×Q₁₆	—	2	4	no	—
239	C₂×Q₁₆	—	2	2	no	—
240	C₂×Q₁₆	—	2	1	no	—
241	C₂×Q₁₆	—	2	1	no	—
242	C₂×Q₁₆	—	4	2	no	—
243	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
244	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
245	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
246	C₂×SD₁₆	—	2	2	no	—
247	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
248	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
249	C₄⋊Q₈	—	2	1	no	—
250	C₄⋊Q₈	—	2	1	no	—
251	C₄⋊Q₈	—	4	1	no	—
252	#123	—	4	2	no	—
253	C₂²⋊Q₈	—	2	2	no	—
254	C₂²⋊Q₈	—	2	2	no	—
255	C₂²⋊Q₈	—	4	2	no	—
256	#121	—	4	1	no	—
257	C₄×Q₈	—	2	1	no	—
258	C₄×D₄	—	2	1	no	—
259	C₄×D₄	—	4	1	no	—
260	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
261	C₂×C₄⋊C₄	—	4	1	no	—
262	Q₃₂	—	2	4	no	—
263	Q₃₂	—	2	4	no	—
264	Q₃₂	—	4	2	no	—
265	SD₃₂	—	2	4	no	—
266	SD₃₂	D₄×C₃₁	1	4	yes	complemented
267	M₃₂	—	2	4	no	—
268	C₂×C₁₆	C₂³×C₃₁	1	1	yes	characteristic
269	C₂×C₁₆	C₂³×C₃₁	1	2	yes	—
270	C₂×C₁₆	C₂³×C₃₁	1	1	yes	characteristic
271	#107	C₂³×C₃₁	1	1	yes	characteristic
272	#107	C₂³×C₃₁	1	1	yes	characteristic
273	C₄⋊C₈	D₄×C₃₁	1	1	yes	characteristic
274	#103	—	2	1	no	—
275	#103	—	2	2	no	—
276	#103	—	2	2	no	—
277	#102	—	2	1	no	—
278	C₂²⋊C₈	D₄×C₃₁	1	2	yes	—
279	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
280	C₃₁	#33842	1	1	yes	characteristic, direct product factor, Sylow
281	#41	—	4	4	no	—
282	#41	—	8	2	no	—
283	C₂×Q₈	—	2	1	no	—
284	C₂×Q₈	—	2	2	no	—
285	C₂×Q₈	—	2	2	no	—
286	C₂×Q₈	—	4	4	no	—
287	C₂×Q₈	—	4	2	no	—
288	C₂×Q₈	—	8	2	no	—
289	C₂×D₄	—	2	1	no	—
290	C₂×D₄	—	4	2	no	—
291	C₂×D₄	D₈×C₃₁	1	1	yes	characteristic
292	C₂²×C₄	—	4	2	no	—
293	C₂²×C₄	—	4	1	no	—
294	C₂²×C₄	—	4	2	no	—
295	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
296	Q₁₆	—	2	2	no	—
297	Q₁₆	—	2	2	no	—
298	Q₁₆	—	2	1	no	—
299	Q₁₆	—	2	2	no	—
300	Q₁₆	—	2	2	no	—
301	Q₁₆	—	4	4	no	—
302	Q₁₆	—	8	1	no	—
303	Q₁₆	—	8	1	no	—
304	Q₁₆	C₂×D₄×C₃₁	1	2	yes	—
305	SD₁₆	—	4	4	no	—
306	D₈	—	2	1	no	—
307	D₈	C₂×D₄×C₃₁	1	2	yes	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
311	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
312	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
313	C₄⋊C₄	—	2	1	no	—
314	C₄⋊C₄	—	2	1	no	—
315	C₄⋊C₄	—	4	1	no	—
316	C₄⋊C₄	—	4	2	no	—
317	C₄⋊C₄	—	4	1	no	—
318	C₄⋊C₄	—	4	1	no	—
319	C₄⋊C₄	—	4	2	no	—
320	C₄⋊C₄	—	4	1	no	—
321	C₄⋊C₄	—	4	1	no	—
322	C₄⋊C₄	D₈×C₃₁	1	1	yes	characteristic
323	C₂²⋊C₄	—	4	2	no	—
324	C₂²⋊C₄	—	4	2	no	—
325	C₂²⋊C₄	—	4	1	no	—
326	C₂²⋊C₄	D₈×C₃₁	1	2	yes	—
327	C₄²	—	4	1	no	—
328	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
329	C₁₆	—	2	2	no	—
330	C₁₆	—	2	1	no	—
331	C₁₆	C₂×D₄×C₃₁	1	2	yes	—
332	C₂³	—	4	1	no	—
333	C₂³	C₂×D₈×C₃₁	1	2	yes	—
334	Q₈	—	2	2	no	—
335	Q₈	—	4	1	no	—
336	Q₈	—	4	2	no	—
337	Q₈	—	4	2	no	—
338	Q₈	—	4	2	no	—
339	Q₈	—	4	2	no	—
340	Q₈	—	8	4	no	—
341	D₄	—	2	2	no	—
342	D₄	—	2	2	no	—
343	D₄	—	4	1	no	—
344	D₄	—	8	4	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	4	1	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	8	4	no	—
353	C₂×C₄	—	8	4	no	—
354	C₂×C₄	—	8	2	no	—
355	C₂×C₄	C₂×D₈×C₃₁	1	1	yes	characteristic
356	C₂×C₄	C₂×D₈×C₃₁	1	2	yes	—
357	C₂×C₄	C₂×D₈×C₃₁	1	1	yes	characteristic
358	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
359	C₈	—	2	2	no	—
360	C₈	—	2	1	no	—
361	C₈	C₂²×D₄×C₃₁	1	1	yes	characteristic
362	C₈	C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
363	C₂²	—	2	2	no	—
364	C₂²	—	2	2	no	—
365	C₂²	—	2	2	no	—
366	C₂²	—	4	2	no	—
367	C₂²	—	8	1	no	—
368	C₂²	—	8	1	no	—
369	C₂²	C₂²×D₈×C₃₁	1	1	yes	characteristic
370	C₄	—	2	1	no	—
371	C₄	—	2	2	no	—
372	C₄	—	4	2	no	—
373	C₄	—	8	1	no	—
374	C₄	—	8	1	no	—
375	C₄	—	8	2	no	—
376	C₄	—	8	2	no	—
377	C₄	C₃₁×#510	1	2	yes	complemented
378	C₄	D₄²×C₃₁	1	1	yes	characteristic
379	C₄	C₃₁×#576	1	1	yes	characteristic
380	C₂	—	4	2	no	—
381	C₂	—	8	2	no	—
382	C₂	D₄×D₈×C₃₁	1	1	yes	characteristic
383	C₂	C₂×C₃₁×#510	1	1	yes	characteristic
384	C₂	C₃₁×#3417	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₃₁
prime radical	C₃₁×#3283	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₄×D₄×C₃₁ ◁ C₈×D₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×#510	C₂	semidirect
2. D₄×Q₁₆×C₃₁	C₂	semidirect
4. C₃₁×#2247	C₂	semidirect
5. C₃₁×#2219	C₂	semidirect
6. C₃₁×#2209	C₂	semidirect
7. C₃₁×#2208	C₂	semidirect
8. C₃₁×#2189	C₂	semidirect
9. C₃₁×#2188	C₂	semidirect
10. C₄×C₃₁×SD₃₂	C₂	semidirect
11. C₃₁×#2169	C₂	semidirect
74. C₃₁×SD₃₂	D₄	semidirect
139. #33842	C₃₁	direct (N × H)
171. C₂×#510	C₂×C₃₁	semidirect
172. D₄×Q₁₆	C₂×C₃₁	semidirect
174. #2247	C₂×C₃₁	semidirect
175. #2219	C₂×C₃₁	semidirect
176. #2209	C₂×C₃₁	semidirect
177. #2208	C₂×C₃₁	semidirect
178. #2189	C₂×C₃₁	semidirect
179. #2188	C₂×C₃₁	semidirect
180. C₄×SD₃₂	C₂×C₃₁	semidirect
181. #2169	C₂×C₃₁	semidirect
196. C₄×C₃₁	#510	semidirect
266. SD₃₂	D₄×C₃₁	semidirect
280. C₃₁	#33842	direct (N × H)
377. C₄	C₃₁×#510	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#510	2
D₄×Q₁₆×C₃₁	2
C₃₁×#3283	2
C₃₁×#2247	2
C₃₁×#2219	2
C₃₁×#2209	2
C₃₁×#2208	2
C₃₁×#2189	2
C₃₁×#2188	2
C₄×C₃₁×SD₃₂	2
C₃₁×#2169	2
#33842	31

Subgroups — C31×#33842 #21490601

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#33842 #21490601