Subgroups — #16847597

Order 3968.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14521166	C₂	1	2	yes	maximal, complemented
2	#14520879	C₂	1	1	yes	maximal, characteristic, complemented
3	#14520856	C₂	1	2	yes	maximal, complemented
4	#14520824	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#508	C₂	1	1	yes	maximal, characteristic
6	C₃₁×#135	C₂²	1	2	yes	—
7	#11758525	—	2	2	no	—
8	C₃₁×Q₃₂	C₄	1	1	yes	characteristic, complemented
9	C₃₁×SD₃₂	C₄	1	2	yes	complemented
10	C₃₁×D₁₆	C₄	1	1	yes	characteristic, complemented
11	C₂×C₁₆×C₃₁	C₂²	1	1	yes	characteristic
12	#11758425	—	2	2	no	—
13	#11758407	C₂²	1	2	yes	—
14	C₈×Dic₃₁	C₂²	1	1	yes	characteristic
15	C₂×C₃₁⋊C₁₆	C₂²	1	1	yes	characteristic
16	#41×C₃₁	—	2	2	no	—
17	Q₁₆×C₃₁	C₂×C₄	1	2	yes	—
18	SD₁₆×C₃₁	—	2	2	no	—
19	D₈×C₃₁	C₂×C₄	1	2	yes	—
20	C₂×C₈×C₃₁	C₂³	1	1	yes	characteristic
21	C₄×Dic₃₁	D₄	1	1	yes	characteristic
22	#92474	—	2	2	no	—
23	#92474	—	4	2	no	—
24	C₂×C₃₁⋊C₈	—	4	2	no	—
25	C₂×C₃₁⋊C₈	D₄	1	1	yes	characteristic
26	C₁₆×C₃₁	C₂×C₄	1	1	yes	characteristic
27	C₁₆×C₃₁	C₂×C₄	1	1	yes	characteristic
28	C₃₁⋊C₁₆	—	2	1	no	—
29	Q₈×C₃₁	—	2	2	no	—
30	D₄×C₃₁	—	2	2	no	—
31	D₄×C₃₁	—	4	2	no	—
32	C₂×C₄×C₃₁	—	4	2	no	—
33	C₂×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
34	C₂×Dic₃₁	—	2	1	no	—
35	C₈×C₃₁	C₂²×C₄	1	1	yes	characteristic
36	C₈×C₃₁	#41	1	1	yes	characteristic
37	C₃₁⋊C₈	—	4	2	no	—
38	C₃₁⋊C₈	D₈	1	2	yes	—
39	#2179	—	31	1	no	maximal, Sylow
40	C₂²×C₃₁	—	4	2	no	—
41	C₂²×C₃₁	#135	1	1	yes	characteristic
42	C₄×C₃₁	—	4	2	no	—
43	C₄×C₃₁	C₄×D₄	1	1	yes	characteristic
44	C₄×C₃₁	C₂×D₈	1	1	yes	characteristic
45	Dic₃₁	—	4	1	no	—
46	#508	D₃₁	1	1	yes	characteristic
47	#443	—	31	2	no	—
48	#368	—	31	1	no	—
49	#359	—	31	2	no	—
50	#346	—	31	1	no	—
51	C₂×C₃₁	—	2	1	no	—
52	C₂×C₃₁	—	8	2	no	—
53	C₂×C₃₁	C₄×D₈	1	1	yes	characteristic
54	#135	C₂×D₃₁	1	2	yes	—
55	#131	—	62	2	no	—
56	Q₃₂	Dic₃₁	1	1	yes	characteristic, complemented
57	SD₃₂	Dic₃₁	1	2	yes	complemented
58	D₁₆	Dic₃₁	1	1	yes	characteristic, complemented
59	C₂×C₁₆	—	31	1	no	—
60	C₂×C₁₆	C₂×D₃₁	1	1	yes	characteristic
61	#108	—	31	2	no	—
62	#104	—	62	2	no	—
63	C₄×C₈	—	31	1	no	—
64	C₃₁	#2179	1	1	yes	characteristic, complemented, Sylow
65	#41	—	2	2	no	—
66	Q₁₆	C₂×Dic₃₁	1	2	yes	—
67	SD₁₆	—	2	2	no	—
68	D₈	C₂×Dic₃₁	1	2	yes	—
69	M₁₆	—	62	2	no	—
70	M₁₆	—	124	2	no	—
71	C₂×C₈	—	31	1	no	—
72	C₂×C₈	—	124	2	no	—
73	C₂×C₈	C₂²×D₃₁	1	1	yes	characteristic
74	C₄²	—	31	1	no	—
75	C₁₆	—	62	1	no	—
76	C₁₆	C₂×Dic₃₁	1	1	yes	characteristic
77	C₁₆	C₂×Dic₃₁	1	1	yes	characteristic
78	Q₈	—	2	2	no	—
79	D₄	—	2	2	no	—
80	D₄	—	4	2	no	—
81	C₂×C₄	—	4	2	no	—
82	C₂×C₄	—	62	1	no	—
83	C₂×C₄	D₄×D₃₁	1	1	yes	characteristic
84	C₈	—	31	2	no	—
85	C₈	—	124	2	no	—
86	C₈	#92497	1	1	yes	characteristic
87	C₈	C₂²×Dic₃₁	1	1	yes	characteristic
88	C₂²	—	4	2	no	—
89	C₂²	#11758489	1	1	yes	characteristic
90	C₄	—	4	2	no	—
91	C₄	—	124	1	no	—
92	C₄	D₈×D₃₁	1	1	yes	characteristic
93	C₄	D₄×Dic₃₁	1	1	yes	characteristic
94	C₂	—	2	1	no	—
95	C₂	—	8	2	no	—
96	C₂	D₈×Dic₃₁	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₈×D₃₁
commutator	C₈×C₃₁	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₃₁
Fitting, prime radical	C₃₁×#508	C₂
socle	C₂×C₃₁	C₄×D₈
cosocle	C₂×C₈×C₃₁	C₂³
hypercenter	#508	D₃₁
hypocenter	C₃₁	#2179
LCS	G ▷ C₈×C₃₁ ▷ C₄×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #508

Complements

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

N	H ≅ G/N	type
1. #14521166	C₂	semidirect
2. #14520879	C₂	semidirect
3. #14520856	C₂	semidirect
4. #14520824	C₂	semidirect
8. C₃₁×Q₃₂	C₄	semidirect
9. C₃₁×SD₃₂	C₄	semidirect
10. C₃₁×D₁₆	C₄	semidirect
56. Q₃₂	Dic₃₁	semidirect
57. SD₃₂	Dic₃₁	semidirect
58. D₁₆	Dic₃₁	semidirect
64. C₃₁	#2179	semidirect

Maximal subgroups

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

subgroup	index
#14521166	2
#14520879	2
#14520856	2
#14520824	2
C₃₁×#508	2
#2179	31