Subgroups — #16854754

Order 3968.

412 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14521556	C₂	1	1	yes	maximal, characteristic
2	#14521125	C₂	1	1	yes	maximal, characteristic, complemented
3	#14521124	C₂	1	1	yes	maximal, characteristic, complemented
4	#14521123	C₂	1	1	yes	maximal, characteristic, complemented
5	#14521120	C₂	1	1	yes	maximal, characteristic, complemented
6	#14521118	C₂	1	1	yes	maximal, characteristic, complemented
7	#14521117	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈×C₂²⋊D₃₁	C₂	1	1	yes	maximal, characteristic, complemented
9	(C₂²⋊D₃₁)⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
10	#14521107	C₂	1	1	yes	maximal, characteristic, complemented
11	#14521107	C₂	1	1	yes	maximal, characteristic, complemented
12	#14521016	C₂	1	1	yes	maximal, characteristic, complemented
13	#14521011	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²⋊C₈×D₃₁	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#408	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#41×C₃₁	C₂²	1	1	yes	characteristic
17	C₂²×C₄×D₃₁	C₂²	1	1	yes	characteristic
18	C₂×M₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
19	C₂²×C₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
20	#11758523	C₄	1	1	yes	characteristic
21	#11758523	C₄	1	1	yes	characteristic
22	#11758515	C₄	1	1	yes	characteristic
23	#11758515	C₄	1	1	yes	characteristic
24	#11758514	C₄	1	1	yes	characteristic
25	#11758514	C₄	1	1	yes	characteristic
26	#11758512	C₄	1	1	yes	characteristic
27	#11758512	C₄	1	1	yes	characteristic
28	C₄×C₂²⋊D₃₁	C₂²	1	1	yes	characteristic
29	C₄×C₂²⋊D₃₁	C₂²	1	1	yes	characteristic
30	C₄×C₂²⋊D₃₁	C₂²	1	1	yes	characteristic
31	C₄×C₂²⋊D₃₁	C₂²	1	1	yes	characteristic
32	#11758503	C₂²	1	1	yes	characteristic
33	C₂×#92474	C₂²	1	1	yes	characteristic, complemented
34	C₂²×C₃₁⋊C₈	C₂²	1	1	yes	characteristic, complemented
35	C₂×#92469	C₂²	1	1	yes	characteristic
36	C₂×#92469	C₂²	1	1	yes	characteristic
37	C₂×C₈×D₃₁	C₂²	1	1	yes	characteristic
38	C₂×C₈×D₃₁	C₂²	1	1	yes	characteristic
39	C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
40	C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
41	C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
42	C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
43	C₂²⋊(C₃₁⋊C₈)	C₂²	1	1	yes	characteristic
44	C₂²⋊(C₃₁⋊C₈)	C₂²	1	1	yes	characteristic
45	C₂²⋊(C₃₁⋊C₈)	C₂²	1	1	yes	characteristic, complemented
46	C₂²⋊(C₃₁⋊C₈)	C₂²	1	1	yes	characteristic, complemented
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
50	(C₂×D₃₁)⋊C₈	C₂²	1	1	yes	characteristic
51	#11758403	C₂²	1	1	yes	characteristic, complemented
52	#11758403	C₂²	1	1	yes	characteristic, complemented
53	Dic₃₁⋊C₈	C₂²	1	1	yes	characteristic, complemented
54	Dic₃₁⋊C₈	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	C₈×Dic₃₁	C₂²	1	1	yes	characteristic, complemented
58	C₈×Dic₃₁	C₂²	1	1	yes	characteristic, complemented
59	C₂³×D₃₁	C₂×C₄	1	1	yes	characteristic
60	#41×C₃₁	—	4	1	no	—
61	#41×C₃₁	—	4	1	no	—
62	C₂×Q₈×C₃₁	C₂×C₄	1	1	yes	characteristic
63	C₂×D₄×C₃₁	C₂×C₄	1	1	yes	characteristic
64	C₂×D₄×C₃₁	C₂×C₄	1	1	yes	characteristic
65	C₂×D₄×C₃₁	C₂×C₄	1	1	yes	characteristic
66	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
67	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
68	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
69	C₂×C₂²⋊D₃₁	C₂×C₄	1	1	yes	characteristic
70	C₂×C₂²⋊D₃₁	C₂×C₄	1	1	yes	characteristic
71	C₂×C₂²⋊D₃₁	C₂×C₄	1	1	yes	characteristic
72	C₂×C₂²⋊D₃₁	C₂×C₄	1	1	yes	characteristic
73	C₂²×Dic₃₁	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄×D₃₁	—	4	1	no	—
75	C₂×C₄×D₃₁	—	4	1	no	—
76	C₂×C₄×D₃₁	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄×D₃₁	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
79	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
80	M₁₆×C₃₁	—	4	1	no	—
81	C₂×C₈×C₃₁	—	4	1	no	—
82	C₂×C₈×C₃₁	C₂³	1	1	yes	characteristic
83	C₂×C₈×C₃₁	C₂³	1	1	yes	characteristic
84	C₂×C₈×C₃₁	C₂³	1	1	yes	characteristic
85	C₂×C₈×C₃₁	C₂³	1	1	yes	characteristic
86	C₂²⋊Dic₃₁	C₂×C₄	1	1	yes	characteristic
87	C₂²⋊Dic₃₁	C₂×C₄	1	1	yes	characteristic
88	C₂²⋊Dic₃₁	C₂×C₄	1	1	yes	characteristic
89	C₂²⋊Dic₃₁	C₂×C₄	1	1	yes	characteristic
90	C₂²⋊Dic₃₁	C₂×C₄	1	1	yes	characteristic
91	C₂²⋊Dic₃₁	C₂×C₄	1	1	yes	characteristic
92	(C₂×D₃₁)⋊C₄	C₂×C₄	1	1	yes	characteristic
93	(C₂×D₃₁)⋊C₄	C₂×C₄	1	1	yes	characteristic
94	(C₂×D₃₁)⋊C₄	C₂×C₄	1	1	yes	characteristic
95	(C₂×D₃₁)⋊C₄	C₂×C₄	1	1	yes	characteristic
96	C₄⋊Dic₃₁	C₂×C₄	1	1	yes	characteristic
97	C₄⋊Dic₃₁	C₂×C₄	1	1	yes	characteristic
98	Dic₃₁⋊C₄	C₂×C₄	1	1	yes	characteristic
99	Dic₃₁⋊C₄	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	C₂³	1	1	yes	characteristic
103	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
104	#92474	—	4	1	no	—
105	C₂×C₃₁⋊C₈	—	4	1	no	—
106	C₂×C₃₁⋊C₈	C₂³	1	1	yes	characteristic
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	#92469	—	4	1	no	—
111	#92469	—	4	1	no	—
112	C₈×D₃₁	—	4	1	no	—
113	C₈×D₃₁	—	4	1	no	—
114	C₂³×C₃₁	C₂²×C₄	1	1	yes	characteristic
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	C₂²×C₄	1	1	yes	characteristic
121	C₂²×D₃₁	C₂²×C₄	1	1	yes	characteristic
122	Q₈×C₃₁	—	4	1	no	—
123	D₄×C₃₁	—	4	1	no	—
124	D₄×C₃₁	—	4	1	no	—
125	D₄×C₃₁	—	4	1	no	—
126	C₂×C₄×C₃₁	—	2	1	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	—	2	1	no	—
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	C₂²⋊D₃₁	—	4	1	no	—
139	C₂²⋊D₃₁	—	4	1	no	—
140	C₂×Dic₃₁	—	4	1	no	—
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	C₂×Dic₃₁	C₂²×C₄	1	1	yes	characteristic
146	C₂×Dic₃₁	C₂²×C₄	1	1	yes	characteristic
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	—	4	1	no	—
152	C₄×D₃₁	—	4	1	no	—
153	C₈×C₃₁	—	2	1	no	—
154	C₈×C₃₁	—	2	1	no	—
155	C₈×C₃₁	—	2	1	no	—
156	C₈×C₃₁	—	2	1	no	—
157	C₃₁⋊C₈	—	2	1	no	—
158	C₃₁⋊C₈	—	2	1	no	—
159	C₃₁⋊C₈	—	2	1	no	—
160	C₃₁⋊C₈	—	2	1	no	—
161	#2976	—	31	1	no	maximal, Sylow
162	C₂²×C₃₁	—	2	1	no	—
163	C₂²×C₃₁	—	2	1	no	—
164	C₂²×C₃₁	—	2	1	no	—
165	C₂²×C₃₁	—	2	1	no	—
166	C₂²×C₃₁	—	2	1	no	—
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	C₂³×C₄	1	1	yes	characteristic
172	C₂×D₃₁	—	2	1	no	—
173	C₂×D₃₁	—	2	1	no	—
174	C₂×D₃₁	—	2	1	no	—
175	C₂×D₃₁	—	2	1	no	—
176	C₂×D₃₁	—	2	1	no	—
177	C₂×D₃₁	—	4	4	no	—
178	C₂×D₃₁	#131	1	2	yes	—
179	C₄×C₃₁	—	2	1	no	—
180	C₄×C₃₁	—	2	1	no	—
181	C₄×C₃₁	—	2	1	no	—
182	C₄×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
183	C₄×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
184	Dic₃₁	—	2	1	no	—
185	Dic₃₁	—	2	1	no	—
186	Dic₃₁	—	2	1	no	—
187	Dic₃₁	—	2	1	no	—
188	Dic₃₁	—	2	1	no	—
189	Dic₃₁	—	2	1	no	—
190	#525	—	31	1	no	—
191	#436	—	31	1	no	—
192	#436	—	31	1	no	—
193	#435	—	31	1	no	—
194	#435	—	31	1	no	—
195	#435	—	31	1	no	—
196	#435	—	31	1	no	—
197	C₈×D₄	—	31	1	no	—
198	C₈×D₄	—	31	1	no	—
199	#433	—	31	1	no	—
200	#433	—	31	1	no	—
201	#408	—	31	1	no	—
202	#408	D₃₁	1	1	yes	characteristic, complemented
203	#407	—	31	1	no	—
204	C₂×C₂²⋊C₈	—	31	1	no	—
205	C₂×C₃₁	—	4	1	no	—
206	C₂×C₃₁	—	4	1	no	—
207	C₂×C₃₁	—	4	1	no	—
208	C₂×C₃₁	#518	1	1	yes	characteristic
209	C₂×C₃₁	C₂×#131	1	1	yes	characteristic
210	C₂×C₃₁	#568	1	1	yes	characteristic
211	D₃₁	—	2	2	no	—
212	D₃₁	—	4	1	no	—
213	C₂×#41	C₂×D₃₁	1	1	yes	characteristic
214	C₂³×C₄	—	31	1	no	—
215	C₂×M₁₆	—	31	1	no	—
216	C₂×M₁₆	—	31	1	no	—
217	C₂×M₁₆	—	31	1	no	—
218	C₂×M₁₆	C₂×D₃₁	1	1	yes	characteristic, complemented
219	C₂²×C₈	—	31	1	no	—
220	C₂²×C₈	—	31	1	no	—
221	C₂²×C₈	—	31	1	no	—
222	C₂²×C₈	C₂×D₃₁	1	1	yes	characteristic, complemented
223	#123	—	31	1	no	—
224	#123	—	31	1	no	—
225	C₂²⋊Q₈	—	31	1	no	—
226	C₂²⋊Q₈	—	31	1	no	—
227	#121	—	31	1	no	—
228	#121	—	31	1	no	—
229	#120	—	31	1	no	—
230	#120	—	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	#117	—	31	1	no	—
236	C₄⋊C₈	—	31	1	no	—
237	C₄⋊C₈	—	31	1	no	—
238	C₄⋊C₈	—	31	1	no	—
239	C₄⋊C₈	—	31	1	no	—
240	C₂²⋊C₈	—	31	1	no	—
241	C₂²⋊C₈	—	31	1	no	—
242	C₂²⋊C₈	—	31	1	no	—
243	C₂²⋊C₈	—	31	1	no	—
244	C₂²⋊C₈	—	31	1	no	—
245	C₂²⋊C₈	—	31	1	no	—
246	C₂²⋊C₈	—	31	1	no	—
247	C₂²⋊C₈	—	31	1	no	—
248	C₂²⋊C₈	C₂×D₃₁	1	1	yes	characteristic
249	C₂²⋊C₈	C₂×D₃₁	1	1	yes	characteristic
250	C₂²⋊C₈	C₂×D₃₁	1	1	yes	characteristic, complemented
251	C₂²⋊C₈	C₂×D₃₁	1	1	yes	characteristic, complemented
252	#97	—	31	1	no	—
253	#97	—	31	1	no	—
254	C₄×C₈	—	31	1	no	—
255	C₄×C₈	—	31	1	no	—
256	C₃₁	#2976	1	1	yes	characteristic, complemented, Sylow
257	C₂⁴	—	31	1	no	—
258	#41	—	4	1	no	—
259	#41	—	4	1	no	—
260	C₂×Q₈	C₄×D₃₁	1	1	yes	characteristic
261	C₂×D₄	—	31	1	no	—
262	C₂×D₄	—	31	1	no	—
263	C₂×D₄	—	31	1	no	—
264	C₂×D₄	—	31	1	no	—
265	C₂×D₄	C₄×D₃₁	1	1	yes	characteristic
266	C₂×D₄	C₄×D₃₁	1	1	yes	characteristic
267	C₂×D₄	C₄×D₃₁	1	1	yes	characteristic
268	C₂²×C₄	—	31	1	no	—
269	C₂²×C₄	—	31	1	no	—
270	C₂²×C₄	—	31	1	no	—
271	C₂²×C₄	—	31	1	no	—
272	C₂²×C₄	—	31	1	no	—
273	C₂²×C₄	—	124	1	no	—
274	C₂²×C₄	—	124	1	no	—
275	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
276	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
277	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
278	M₁₆	—	4	1	no	—
279	M₁₆	—	124	1	no	—
280	M₁₆	—	124	1	no	—
281	M₁₆	—	124	1	no	—
282	C₂×C₈	—	4	1	no	—
283	C₂×C₈	—	31	1	no	—
284	C₂×C₈	—	31	1	no	—
285	C₂×C₈	—	31	1	no	—
286	C₂×C₈	—	31	1	no	—
287	C₂×C₈	—	124	1	no	—
288	C₂×C₈	—	124	1	no	—
289	C₂×C₈	—	124	1	no	—
290	C₂×C₈	C₂²×D₃₁	1	1	yes	characteristic
291	C₂×C₈	C₂²×D₃₁	1	1	yes	characteristic
292	C₂×C₈	C₂²×D₃₁	1	1	yes	characteristic
293	C₂×C₈	C₂²×D₃₁	1	1	yes	characteristic
294	C₄⋊C₄	—	31	1	no	—
295	C₄⋊C₄	—	31	1	no	—
296	C₄⋊C₄	—	31	1	no	—
297	C₄⋊C₄	—	31	1	no	—
298	C₄⋊C₄	—	31	1	no	—
299	C₄⋊C₄	—	31	1	no	—
300	C₂²⋊C₄	—	31	1	no	—
301	C₂²⋊C₄	—	31	1	no	—
302	C₂²⋊C₄	—	31	1	no	—
303	C₂²⋊C₄	—	31	1	no	—
304	C₂²⋊C₄	—	31	1	no	—
305	C₂²⋊C₄	—	31	1	no	—
306	C₂²⋊C₄	—	31	1	no	—
307	C₂²⋊C₄	—	31	1	no	—
308	C₂²⋊C₄	—	31	1	no	—
309	C₂²⋊C₄	—	31	1	no	—
310	C₄²	—	31	1	no	—
311	C₄²	—	31	1	no	—
312	C₂³	—	31	1	no	—
313	C₂³	—	31	1	no	—
314	C₂³	—	62	2	no	—
315	C₂³	—	124	1	no	—
316	C₂³	—	124	1	no	—
317	C₂³	C₂×C₄×D₃₁	1	1	yes	characteristic
318	C₂³	C₂×C₄×D₃₁	1	1	yes	characteristic
319	C₂³	C₂×C₄×D₃₁	1	1	yes	characteristic
320	Q₈	—	4	1	no	—
321	D₄	—	4	1	no	—
322	D₄	—	4	1	no	—
323	D₄	—	4	1	no	—
324	D₄	—	62	2	no	—
325	D₄	—	62	2	no	—
326	D₄	—	124	1	no	—
327	D₄	—	124	1	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	31	1	no	—
335	C₂×C₄	—	31	1	no	—
336	C₂×C₄	—	31	1	no	—
337	C₂×C₄	—	31	1	no	—
338	C₂×C₄	—	31	1	no	—
339	C₂×C₄	—	31	1	no	—
340	C₂×C₄	—	62	1	no	—
341	C₂×C₄	—	62	1	no	—
342	C₂×C₄	—	62	1	no	—
343	C₂×C₄	—	62	1	no	—
344	C₂×C₄	—	124	1	no	—
345	C₂×C₄	—	124	1	no	—
346	C₂×C₄	—	124	1	no	—
347	C₂×C₄	C₂×C₄×D₃₁	1	1	yes	characteristic
348	C₂×C₄	C₂×C₄×D₃₁	1	1	yes	characteristic
349	C₂×C₄	C₂×C₄×D₃₁	1	1	yes	characteristic
350	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
351	C₈	—	2	1	no	—
352	C₈	—	2	1	no	—
353	C₈	—	2	1	no	—
354	C₈	—	2	1	no	—
355	C₈	—	62	1	no	—
356	C₈	—	62	1	no	—
357	C₈	—	62	1	no	—
358	C₈	—	62	1	no	—
359	C₂²	—	2	1	no	—
360	C₂²	—	2	1	no	—
361	C₂²	—	2	1	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	2	1	no	—
364	C₂²	—	2	1	no	—
365	C₂²	—	2	1	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	2	1	no	—
368	C₂²	—	31	2	no	—
369	C₂²	—	62	1	no	—
370	C₂²	—	62	1	no	—
371	C₂²	—	62	1	no	—
372	C₂²	—	62	1	no	—
373	C₂²	—	62	1	no	—
374	C₂²	—	124	4	no	—
375	C₂²	C₂²×C₄×D₃₁	1	1	yes	characteristic
376	C₄	—	2	1	no	—
377	C₄	—	2	1	no	—
378	C₄	—	2	1	no	—
379	C₄	—	62	1	no	—
380	C₄	—	62	1	no	—
381	C₄	—	62	1	no	—
382	C₄	—	62	1	no	—
383	C₄	—	62	1	no	—
384	C₄	—	62	1	no	—
385	C₄	#11758561	1	1	yes	characteristic
386	C₄	#11758561	1	1	yes	characteristic
387	C₂	—	4	1	no	—
388	C₂	—	4	1	no	—
389	C₂	—	4	1	no	—
390	C₂	—	62	2	no	—
391	C₂	—	124	1	no	—
392	C₂	#14521522	1	1	yes	characteristic
393	C₂	#131×D₃₁	1	1	yes	characteristic
394	C₂	#14521814	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₃₁
commutator, socle	C₂²×C₃₁	C₂³×C₄
Fitting	C₃₁×#408	C₂
prime radical	#14521556	C₂
cosocle	C₂×C₄×C₃₁	C₂⁴
hypercenter	#408	D₃₁
hypocenter	C₃₁	#2976
LCS	G ▷ C₂²×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂×C₄ ◁ #408

Complements

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

N	H ≅ G/N	type
2. #14521125	C₂	semidirect
3. #14521124	C₂	semidirect
4. #14521123	C₂	semidirect
5. #14521120	C₂	semidirect
6. #14521118	C₂	semidirect
7. #14521117	C₂	semidirect
8. C₈×C₂²⋊D₃₁	C₂	semidirect
9. (C₂²⋊D₃₁)⋊C₈	C₂	semidirect
10. #14521107	C₂	semidirect
11. #14521107	C₂	semidirect
12. #14521016	C₂	semidirect
13. #14521011	C₂	semidirect
14. C₂²⋊C₈×D₃₁	C₂	semidirect
15. C₃₁×#408	C₂	semidirect
18. C₂×M₁₆×C₃₁	C₂²	semidirect
19. C₂²×C₈×C₃₁	C₂²	semidirect
33. C₂×#92474	C₂²	semidirect
34. C₂²×C₃₁⋊C₈	C₂²	semidirect
41. C₃₁×C₂²⋊C₈	C₂²	semidirect
42. C₃₁×C₂²⋊C₈	C₂²	semidirect
45. C₂²⋊(C₃₁⋊C₈)	C₂²	semidirect
46. C₂²⋊(C₃₁⋊C₈)	C₂²	semidirect
51. #11758403	C₂²	semidirect
52. #11758403	C₂²	semidirect
53. Dic₃₁⋊C₈	C₂²	semidirect
54. Dic₃₁⋊C₈	C₂²	semidirect
55. Dic₃₁⋊C₈	C₂²	semidirect
56. Dic₃₁⋊C₈	C₂²	semidirect
57. C₈×Dic₃₁	C₂²	semidirect
58. C₈×Dic₃₁	C₂²	semidirect
202. #408	D₃₁	semidirect
218. C₂×M₁₆	C₂×D₃₁	semidirect
222. C₂²×C₈	C₂×D₃₁	semidirect
250. C₂²⋊C₈	C₂×D₃₁	semidirect
251. C₂²⋊C₈	C₂×D₃₁	semidirect
256. C₃₁	#2976	semidirect

Maximal subgroups

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

subgroup	index
#14521556	2
#14521125	2
#14521124	2
#14521123	2
#14521120	2
#14521118	2
#14521117	2
C₈×C₂²⋊D₃₁	2
(C₂²⋊D₃₁)⋊C₈	2
#14521107	2
#14521016	2
#14521011	2
C₂²⋊C₈×D₃₁	2
C₃₁×#408	2
#2976	31