Subgroups — #14521327

Order 1984.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×Dic₃₁	C₂	1	1	yes	maximal, characteristic
2	#11758465	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#102	C₂	1	1	yes	maximal, characteristic
4	#11758420	C₂	1	1	yes	maximal, characteristic
5	#11758406	C₂	1	1	yes	maximal, characteristic, complemented
6	Dic₃₁⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	#11758395	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×D₄×C₃₁	C₂²	1	1	yes	characteristic
9	C₂²×Dic₃₁	—	2	1	no	—
10	C₂×Dic₆₂	—	2	1	no	—
11	C₂×C₈×C₃₁	C₂²	1	1	yes	characteristic
12	C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
13	C₂²⋊Dic₃₁	—	2	1	no	—
14	C₄⋊Dic₃₁	C₂²	1	1	yes	characteristic
15	C₄⋊Dic₃₁	C₂²	1	1	yes	characteristic
16	Dic₃₁⋊C₄	—	2	1	no	—
17	C₄×Dic₃₁	C₂²	1	1	yes	characteristic
18	C₂×C₃₁⋊C₈	C₂²	1	1	yes	characteristic
19	C₂³×C₃₁	—	2	1	no	—
20	D₄×C₃₁	—	2	1	no	—
21	D₄×C₃₁	Q₈	1	2	yes	complemented
22	C₂×C₄×C₃₁	—	2	1	no	—
23	C₂×C₄×C₃₁	C₂³	1	1	yes	characteristic
24	C₂×Dic₃₁	—	2	1	no	—
25	C₂×Dic₃₁	—	2	1	no	—
26	C₂×Dic₃₁	—	4	2	no	—
27	C₂×Dic₃₁	D₄	1	1	yes	characteristic
28	C₂×Dic₃₁	D₄	1	1	yes	characteristic
29	Dic₆₂	—	4	2	no	—
30	C₈×C₃₁	—	2	1	no	—
31	C₃₁⋊C₈	—	2	1	no	—
32	C₂²×C₃₁	—	2	2	no	—
33	C₂²×C₃₁	—	4	1	no	—
34	C₂²×C₃₁	—	4	1	no	—
35	C₂²×C₃₁	C₂×D₄	1	1	yes	characteristic
36	C₄×C₃₁	—	4	1	no	—
37	C₄×C₃₁	C₂×Q₈	1	1	yes	characteristic
38	C₄×C₃₁	#41	1	1	yes	characteristic
39	Dic₃₁	—	2	1	no	—
40	Dic₃₁	—	4	1	no	—
41	Dic₃₁	—	4	1	no	—
42	Dic₃₁	D₈	1	2	yes	—
43	#474	—	31	1	no	maximal, Sylow
44	C₂×C₃₁	—	4	2	no	—
45	C₂×C₃₁	C₂²⋊Q₈	1	1	yes	characteristic
46	C₂×C₃₁	C₂×D₈	1	1	yes	characteristic
47	C₂×C₃₁	#137	1	1	yes	characteristic
48	C₄⋊Q₈	—	31	1	no	—
49	C₄×D₄	—	31	1	no	—
50	#107	—	31	1	no	—
51	#107	—	31	1	no	—
52	C₄⋊C₈	—	31	1	no	—
53	#102	—	31	1	no	—
54	#102	D₃₁	1	1	yes	characteristic
55	C₃₁	#474	1	1	yes	characteristic, complemented, Sylow
56	C₂×Q₈	—	62	1	no	—
57	C₂×D₄	C₂×D₃₁	1	1	yes	characteristic
58	C₂²×C₄	—	62	1	no	—
59	C₂×C₈	—	31	1	no	—
60	C₂×C₈	C₂×D₃₁	1	1	yes	characteristic
61	C₄⋊C₄	—	31	1	no	—
62	C₄⋊C₄	—	31	1	no	—
63	C₄⋊C₄	—	62	1	no	—
64	C₄⋊C₄	C₂×D₃₁	1	1	yes	characteristic
65	C₂²⋊C₄	—	62	1	no	—
66	C₄²	—	31	1	no	—
67	C₂³	—	2	1	no	—
68	Q₈	—	124	2	no	—
69	D₄	—	2	1	no	—
70	D₄	Dic₆₂	1	2	yes	complemented
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	31	1	no	—
73	C₂×C₄	—	31	1	no	—
74	C₂×C₄	—	62	1	no	—
75	C₂×C₄	—	62	1	no	—
76	C₂×C₄	—	124	2	no	—
77	C₂×C₄	C₂²×D₃₁	1	1	yes	characteristic
78	C₈	—	2	1	no	—
79	C₈	—	62	1	no	—
80	C₂²	—	2	2	no	—
81	C₂²	—	4	1	no	—
82	C₂²	—	4	1	no	—
83	C₂²	D₄×D₃₁	1	1	yes	characteristic
84	C₄	—	4	1	no	—
85	C₄	—	31	2	no	—
86	C₄	—	62	1	no	—
87	C₄	—	124	1	no	—
88	C₄	—	124	1	no	—
89	C₄	C₂×Dic₆₂	1	1	yes	characteristic
90	C₄	#92497	1	1	yes	characteristic
91	C₂	—	4	2	no	—
92	C₂	#11758455	1	1	yes	characteristic
93	C₂	D₈×D₃₁	1	1	yes	characteristic
94	C₂	#11758492	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₃₁
commutator, cosocle	C₂×C₄×C₃₁	C₂³
Frattini	C₂×C₄	C₂²×D₃₁
Fitting	C₃₁×#102	C₂
socle	C₂²×C₃₁	C₂×D₄
prime radical	C₂×D₄×C₃₁	C₂²
hypercenter	#102	D₃₁
hypocenter	C₃₁	#474
LCS	G ▷ C₂×C₄×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #102

Complements

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

N	H ≅ G/N	type
2. #11758465	C₂	semidirect
5. #11758406	C₂	semidirect
6. Dic₃₁⋊C₈	C₂	semidirect
7. #11758395	C₂	semidirect
21. D₄×C₃₁	Q₈	semidirect
55. C₃₁	#474	semidirect
70. D₄	Dic₆₂	semidirect

Maximal subgroups

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

subgroup	index
D₄×Dic₃₁	2
#11758465	2
C₃₁×#102	2
#11758420	2
#11758406	2
Dic₃₁⋊C₈	2
#11758395	2
#474	31