Subgroups — #16845310

Order 3968.

190 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14521447	C₂	1	1	yes	maximal, characteristic, complemented
2	#14521401	C₂	1	2	yes	maximal, complemented
3	#14521395	C₂	1	2	yes	maximal
4	C₈×C₃₁⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#492	C₂	1	1	yes	maximal, characteristic
6	C₂×SD₁₆×C₃₁	—	2	2	no	—
7	C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
8	C₃₁×#127	C₂²	1	1	yes	characteristic
9	#11758446	C₂²	1	2	yes	—
10	C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
11	#11758420	—	2	4	no	—
12	#11758405	—	2	2	no	—
13	#11758398	—	2	4	no	—
14	C₄×C₃₁⋊C₈	C₂²	1	2	yes	—
15	C₂×Q₈×C₃₁	—	2	1	no	—
16	C₂×D₄×C₃₁	—	2	2	no	—
17	C₂×D₄×C₃₁	—	2	1	no	—
18	C₂×Dic₆₂	—	2	2	no	—
19	SD₁₆×C₃₁	—	4	4	no	—
20	C₂×C₈×C₃₁	D₄	1	2	yes	—
21	C₄⋊C₄×C₃₁	—	2	2	no	—
22	C₄²×C₃₁	C₂³	1	1	yes	characteristic
23	C₄⋊Dic₃₁	—	2	2	no	—
24	C₄⋊Dic₃₁	—	2	2	no	—
25	C₂×C₃₁⋊C₈	D₄	1	4	yes	—
26	C₂³×C₃₁	—	4	1	no	—
27	Q₈×C₃₁	—	4	2	no	—
28	D₄×C₃₁	—	4	2	no	—
29	D₄×C₃₁	—	4	4	no	—
30	C₂×C₄×C₃₁	—	4	1	no	—
31	C₂×C₄×C₃₁	C₂×D₄	1	2	yes	—
32	C₂×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
33	C₂×Dic₃₁	—	4	2	no	—
34	Dic₆₂	—	4	4	no	—
35	C₈×C₃₁	SD₁₆	1	4	yes	—
36	C₃₁⋊C₈	—	2	4	no	—
37	#1708	—	31	1	no	maximal, Sylow
38	C₂²×C₃₁	—	8	1	no	—
39	C₂²×C₃₁	—	8	2	no	—
40	C₂²×C₃₁	#127	1	1	yes	characteristic
41	C₄×C₃₁	—	8	1	no	—
42	C₄×C₃₁	C₂×SD₁₆	1	2	yes	—
43	C₄×C₃₁	#135	1	4	yes	—
44	Dic₃₁	—	8	2	no	—
45	#498	—	31	1	no	—
46	#492	D₃₁	1	1	yes	characteristic
47	#487	—	31	2	no	—
48	#486	—	31	2	no	—
49	C₈²	—	31	1	no	—
50	C₂×C₃₁	—	16	1	no	—
51	C₂×C₃₁	#492	1	1	yes	characteristic
52	C₂×C₃₁	#495	1	2	yes	—
53	C₂×SD₁₆	—	2	2	no	—
54	C₄⋊Q₈	—	31	2	no	—
55	C₄⋊Q₈	C₂×D₃₁	1	1	yes	characteristic
56	#127	C₂×D₃₁	1	1	yes	characteristic
57	#106	—	62	2	no	—
58	#103	—	62	4	no	—
59	#102	—	62	4	no	—
60	C₄×C₈	—	31	2	no	—
61	C₄×C₈	C₂×D₃₁	1	1	yes	characteristic
62	C₃₁	#1708	1	1	yes	characteristic, complemented, Sylow
63	C₂×Q₈	—	2	1	no	—
64	C₂×Q₈	—	62	2	no	—
65	C₂×D₄	—	2	2	no	—
66	C₂×D₄	—	2	1	no	—
67	SD₁₆	—	4	4	no	—
68	C₂×C₈	—	31	4	no	—
69	C₂×C₈	C₂²⋊D₃₁	1	2	yes	—
70	C₄⋊C₄	—	2	2	no	—
71	C₄⋊C₄	—	62	2	no	—
72	C₄⋊C₄	—	62	2	no	—
73	C₄²	C₂²×D₃₁	1	1	yes	characteristic
74	C₂³	—	4	1	no	—
75	Q₈	—	4	2	no	—
76	Q₈	—	124	4	no	—
77	D₄	—	4	4	no	—
78	D₄	—	4	2	no	—
79	C₂×C₄	—	4	1	no	—
80	C₂×C₄	—	124	2	no	—
81	C₂×C₄	D₄×D₃₁	1	2	yes	—
82	C₂×C₄	C₂×C₂²⋊D₃₁	1	1	yes	characteristic
83	C₈	—	62	4	no	—
84	C₈	#92480	1	4	yes	—
85	C₂²	—	8	1	no	—
86	C₂²	—	8	2	no	—
87	C₂²	#11758517	1	1	yes	characteristic
88	C₄	—	8	1	no	—
89	C₄	—	248	2	no	—
90	C₄	#11758493	1	4	yes	—
91	C₄	C₂×#92480	1	2	yes	—
92	C₂	—	16	1	no	—
93	C₂	#14521421	1	1	yes	characteristic
94	C₂	#14521430	1	2	yes	—

	subgroup	G/H
center	C₂²	#11758517
commutator, cosocle	C₄²×C₃₁	C₂³
Frattini	C₄²	C₂²×D₃₁
Fitting	C₃₁×#492	C₂
socle	C₂²×C₃₁	#127
prime radical	C₃₁×#127	C₂²
hypercenter	#492	D₃₁
hypocenter	C₃₁	#1708
LCS	G ▷ C₄²×C₃₁ ▷ C₂²×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #492

Complements

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

N	H ≅ G/N	type
1. #14521447	C₂	semidirect
2. #14521401	C₂	semidirect
4. C₈×C₃₁⋊C₈	C₂	semidirect
62. C₃₁	#1708	semidirect

Maximal subgroups

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

subgroup	index
#14521447	2
#14521401	2
#14521395	2
C₈×C₃₁⋊C₈	2
C₃₁×#492	2
#1708	31