Subgroups — #16843881

Order 3968.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14521413	C₂	1	1	yes	maximal, characteristic
2	#14520842	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#353	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#127	C₂²	1	1	yes	characteristic
5	#11758447	C₄	1	1	yes	characteristic, complemented
6	C₃₁×#99	—	2	1	no	—
7	#11758422	—	2	1	no	—
8	#11758420	—	2	1	no	—
9	#11758420	—	2	1	no	—
10	#11758391	C₄	1	1	yes	characteristic, complemented
11	C₂×D₄×C₃₁	—	4	1	no	—
12	C₂×D₄×C₃₁	D₄	1	1	yes	characteristic
13	C₂×D₄×C₃₁	D₄	1	1	yes	characteristic
14	C₂²⋊C₄×C₃₁	—	4	1	no	—
15	C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
16	C₂²⋊Dic₃₁	—	4	1	no	—
17	C₄⋊Dic₃₁	—	2	1	no	—
18	Dic₃₁⋊C₄	—	4	1	no	—
19	C₂×C₃₁⋊C₈	—	2	1	no	—
20	C₂³×C₃₁	—	2	1	no	—
21	C₂³×C₃₁	—	2	1	no	—
22	D₄×C₃₁	—	4	1	no	—
23	D₄×C₃₁	—	4	1	no	—
24	D₄×C₃₁	—	8	2	no	—
25	C₂×C₄×C₃₁	—	2	1	no	—
26	C₂×C₄×C₃₁	—	8	1	no	—
27	C₂×C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
28	C₂×Dic₃₁	—	4	1	no	—
29	C₂×Dic₃₁	—	8	1	no	—
30	C₃₁⋊C₈	—	4	1	no	—
31	#1412	—	31	1	no	maximal, Sylow
32	C₂²×C₃₁	—	4	1	no	—
33	C₂²×C₃₁	—	4	1	no	—
34	C₂²×C₃₁	—	8	1	no	—
35	C₂²×C₃₁	—	8	1	no	—
36	C₂²×C₃₁	#99	1	1	yes	characteristic
37	C₄×C₃₁	—	2	1	no	—
38	C₄×C₃₁	—	4	1	no	—
39	C₄×C₃₁	—	16	1	no	—
40	Dic₃₁	—	8	1	no	—
41	Dic₃₁	—	16	1	no	—
42	#490	—	31	1	no	—
43	#353	—	31	1	no	—
44	#353	D₃₁	1	1	yes	characteristic
45	C₂×C₃₁	—	2	1	no	—
46	C₂×C₃₁	—	8	1	no	—
47	C₂×C₃₁	—	8	1	no	—
48	C₂×C₃₁	#354	1	1	yes	characteristic
49	#127	C₂×D₃₁	1	1	yes	characteristic
50	#125	—	31	1	no	—
51	#102	—	62	1	no	—
52	#102	—	62	1	no	—
53	#99	—	2	1	no	—
54	#99	—	62	1	no	—
55	#97	—	31	1	no	—
56	C₃₁	#1412	1	1	yes	characteristic, complemented, Sylow
57	C₂×D₄	—	4	1	no	—
58	C₂×D₄	D₁₂₄	1	1	yes	characteristic
59	C₂×D₄	C₂²⋊D₃₁	1	1	yes	characteristic
60	C₂×C₈	—	62	1	no	—
61	C₄⋊C₄	—	62	1	no	—
62	C₄⋊C₄	—	124	1	no	—
63	C₂²⋊C₄	—	4	1	no	—
64	C₂²⋊C₄	—	124	1	no	—
65	C₄²	C₄×D₃₁	1	1	yes	characteristic
66	C₂³	—	2	1	no	—
67	C₂³	—	2	1	no	—
68	D₄	—	4	1	no	—
69	D₄	—	4	1	no	—
70	D₄	—	8	2	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	8	1	no	—
73	C₂×C₄	—	124	1	no	—
74	C₂×C₄	—	248	1	no	—
75	C₂×C₄	(C₂×D₃₁)⋊C₄	1	1	yes	characteristic
76	C₈	—	124	1	no	—
77	C₂²	—	4	1	no	—
78	C₂²	—	4	1	no	—
79	C₂²	—	8	1	no	—
80	C₂²	—	8	1	no	—
81	C₂²	#11758394	1	1	yes	characteristic
82	C₄	—	2	1	no	—
83	C₄	—	4	1	no	—
84	C₄	—	16	1	no	—
85	C₄	—	496	1	no	—
86	C₄	—	248	1	no	—
87	C₂	—	2	1	no	—
88	C₂	—	8	1	no	—
89	C₂	—	8	1	no	—
90	C₂	#14520843	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14520843
commutator	C₄²×C₃₁	C₂×C₄
Frattini	#127	C₂×D₃₁
Fitting	C₃₁×#353	C₂
socle	C₂×C₃₁	#354
prime radical, cosocle	C₃₁×#127	C₂²
hypercenter	#353	D₃₁
hypocenter	C₃₁	#1412
LCS	G ▷ C₄²×C₃₁ ▷ C₂×C₄×C₃₁ ▷ C₂²×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ #127 ◁ #353

Complements

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

N	H ≅ G/N	type
5. #11758447	C₄	semidirect
10. #11758391	C₄	semidirect
56. C₃₁	#1412	semidirect

Maximal subgroups

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

subgroup	index
#14521413	2
#14520842	2
C₃₁×#353	2
#1412	31