Subgroups — #14521258

Order 1984.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11758521	C₂	1	1	yes	maximal, characteristic
2	C₂×#92482	C₂	1	1	yes	maximal, characteristic
3	C₂×Dic₁₂₄	C₂	1	1	yes	maximal, characteristic
4	#11758464	C₂	1	1	yes	maximal, characteristic
5	C₃₁×#103	C₂	1	1	yes	maximal, characteristic
6	Dic₃₁⋊C₈	C₂	1	1	yes	maximal, characteristic
7	#11758398	C₂	1	1	yes	maximal, characteristic
8	C₂×Q₈×C₃₁	C₂²	1	1	yes	characteristic
9	C₂×Dic₆₂	C₂²	1	1	yes	characteristic
10	C₂×Dic₆₂	C₂²	1	1	yes	characteristic
11	C₂×C₈×C₃₁	C₂²	1	1	yes	characteristic
12	C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
13	#92482	—	2	2	no	—
14	Dic₃₁⋊C₄	—	2	1	no	—
15	Dic₃₁⋊C₄	—	2	1	no	—
16	Dic₃₁⋊C₄	—	2	1	no	—
17	C₄×Dic₃₁	—	2	1	no	—
18	C₄×Dic₃₁	C₂²	1	1	yes	characteristic
19	C₂×C₃₁⋊C₈	C₂²	1	1	yes	characteristic
20	Dic₁₂₄	—	2	2	no	—
21	Q₈×C₃₁	—	2	1	no	—
22	Q₈×C₃₁	—	2	1	no	—
23	C₂×C₄×C₃₁	—	2	1	no	—
24	C₂×C₄×C₃₁	—	2	1	no	—
25	C₂×C₄×C₃₁	C₂³	1	1	yes	characteristic
26	C₂×Dic₃₁	—	2	1	no	—
27	C₂×Dic₃₁	—	2	1	no	—
28	C₂×Dic₃₁	D₄	1	1	yes	characteristic
29	C₂×Dic₃₁	D₄	1	1	yes	characteristic
30	Dic₆₂	—	2	1	no	—
31	Dic₆₂	—	2	1	no	—
32	Dic₆₂	—	2	1	no	—
33	Dic₆₂	D₄	1	2	yes	—
34	C₈×C₃₁	—	2	1	no	—
35	C₃₁⋊C₈	—	2	1	no	—
36	C₂²×C₃₁	C₂×D₄	1	1	yes	characteristic
37	C₄×C₃₁	—	4	1	no	—
38	C₄×C₃₁	—	4	1	no	—
39	C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
40	C₄×C₃₁	#41	1	1	yes	characteristic
41	Dic₃₁	—	2	2	no	—
42	Dic₃₁	—	2	1	no	—
43	Dic₃₁	—	4	1	no	—
44	Dic₃₁	Q₁₆	1	2	yes	complemented
45	#462	—	31	1	no	maximal, Sylow
46	C₂×C₃₁	#121	1	1	yes	characteristic
47	C₂×C₃₁	C₂×Q₁₆	1	1	yes	characteristic
48	C₂×C₃₁	#137	1	1	yes	characteristic
49	C₂×Q₁₆	—	31	1	no	—
50	C₂×Q₁₆	—	31	1	no	—
51	C₄⋊Q₈	—	31	1	no	—
52	C₄×Q₈	—	31	1	no	—
53	C₄⋊C₈	—	31	1	no	—
54	#103	—	31	1	no	—
55	#103	D₃₁	1	1	yes	characteristic
56	C₃₁	#462	1	1	yes	characteristic, complemented, Sylow
57	C₂×Q₈	—	31	1	no	—
58	C₂×Q₈	—	31	1	no	—
59	C₂×Q₈	C₂×D₃₁	1	1	yes	characteristic
60	Q₁₆	—	62	2	no	—
61	Q₁₆	—	62	2	no	—
62	C₂×C₈	—	31	1	no	—
63	C₂×C₈	C₂×D₃₁	1	1	yes	characteristic
64	C₄⋊C₄	—	62	1	no	—
65	C₄⋊C₄	—	62	1	no	—
66	C₄⋊C₄	—	62	1	no	—
67	C₄⋊C₄	C₂×D₃₁	1	1	yes	characteristic
68	C₄²	—	31	1	no	—
69	C₄²	—	62	1	no	—
70	Q₈	—	2	1	no	—
71	Q₈	—	2	1	no	—
72	Q₈	—	31	2	no	—
73	Q₈	—	62	1	no	—
74	Q₈	—	62	1	no	—
75	Q₈	—	62	1	no	—
76	C₂×C₄	—	2	1	no	—
77	C₂×C₄	—	2	1	no	—
78	C₂×C₄	—	31	1	no	—
79	C₂×C₄	—	31	1	no	—
80	C₂×C₄	—	62	1	no	—
81	C₂×C₄	—	62	1	no	—
82	C₂×C₄	C₂²×D₃₁	1	1	yes	characteristic
83	C₈	—	2	1	no	—
84	C₈	—	62	1	no	—
85	C₂²	D₄×D₃₁	1	1	yes	characteristic
86	C₄	—	4	1	no	—
87	C₄	—	4	1	no	—
88	C₄	—	31	2	no	—
89	C₄	—	62	2	no	—
90	C₄	—	62	1	no	—
91	C₄	—	124	1	no	—
92	C₄	#92495	1	1	yes	characteristic
93	C₄	D₄×D₃₁	1	1	yes	characteristic
94	C₂	#11758461	1	1	yes	characteristic
95	C₂	#11758492	1	1	yes	characteristic
96	C₂	Q₁₆×D₃₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₃₁
commutator, cosocle	C₂×C₄×C₃₁	C₂³
Frattini	C₂×C₄	C₂²×D₃₁
Fitting	C₃₁×#103	C₂
socle, prime radical	C₂²×C₃₁	C₂×D₄
hypercenter	#103	D₃₁
hypocenter	C₃₁	#462
LCS	G ▷ C₂×C₄×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #103

Complements

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

N	H ≅ G/N	type
44. Dic₃₁	Q₁₆	semidirect
56. C₃₁	#462	semidirect

Maximal subgroups

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

subgroup	index
#11758521	2
C₂×#92482	2
C₂×Dic₁₂₄	2
#11758464	2
C₃₁×#103	2
Dic₃₁⋊C₈	2
#11758398	2
#462	31