Subgroups — #28338738

Order 13696.

116 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20293028	C₂	1	2	yes	maximal
2	#20292454	C₂	1	2	yes	maximal
3	#20292453	C₂	1	1	yes	maximal, characteristic
4	C₁₆×Dic₁₀₇	C₂	1	1	yes	maximal, characteristic
5	#366×C₁₀₇	C₂	1	1	yes	maximal, characteristic
6	#16812100	—	2	2	no	—
7	C₂×C₁₀₇⋊C₁₆	C₂²	1	1	yes	characteristic
8	#16812043	C₂²	1	2	yes	—
9	#16812040	—	2	2	no	—
10	C₈×Dic₁₀₇	C₂²	1	1	yes	characteristic
11	C₂×C₁₆×C₁₀₇	C₂²	1	1	yes	characteristic
12	#107×C₁₀₇	C₂²	1	2	yes	—
13	C₂×C₁₀₇⋊C₈	D₄	1	1	yes	characteristic
14	C₄⋊Dic₁₀₇	—	2	2	no	—
15	C₄⋊Dic₁₀₇	—	4	2	no	—
16	Dic₁₀₇⋊C₄	—	4	2	no	—
17	C₄×Dic₁₀₇	D₄	1	1	yes	characteristic
18	C₁₀₇⋊C₁₆	Q₈	1	2	yes	—
19	C₂×C₈×C₁₀₇	C₂³	1	1	yes	characteristic
20	C₄⋊C₄×C₁₀₇	—	2	2	no	—
21	C₁₆×C₁₀₇	Q₈	1	2	yes	—
22	C₂×C₄×C₁₀₇	—	4	2	no	—
23	C₂×C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
24	C₂×Dic₁₀₇	—	4	2	no	—
25	C₂×Dic₁₀₇	D₈	1	1	yes	characteristic
26	C₂×Dic₁₀₇	D₈	1	1	yes	characteristic
27	C₈×C₁₀₇	C₂×Q₈	1	1	yes	characteristic
28	C₈×C₁₀₇	C₂×Q₈	1	1	yes	characteristic
29	C₁₀₇⋊C₈	Q₁₆	1	2	yes	—
30	C₂²×C₁₀₇	C₂×D₈	1	1	yes	characteristic
31	C₄×C₁₀₇	—	8	2	no	—
32	C₄×C₁₀₇	C₄⋊Q₈	1	1	yes	characteristic
33	C₄×C₁₀₇	C₂×Q₁₆	1	1	yes	characteristic
34	Dic₁₀₇	—	2	1	no	—
35	Dic₁₀₇	—	2	1	no	—
36	Dic₁₀₇	—	8	2	no	—
37	C₂×C₁₀₇	#500	1	1	yes	characteristic
38	C₂×C₁₀₇	#508	1	1	yes	characteristic
39	C₂×C₁₀₇	#508	1	1	yes	characteristic
40	#2253	—	107	1	no	maximal, Sylow
41	C₁₀₇	#2253	1	1	yes	characteristic, complemented, Sylow
42	#499	—	107	2	no	—
43	#367	—	107	2	no	—
44	#366	—	107	1	no	—
45	#366	D₁₀₇	1	1	yes	characteristic
46	C₄×C₁₆	—	107	1	no	—
47	#125	—	214	2	no	—
48	C₂×C₁₆	—	107	1	no	—
49	C₂×C₁₆	C₂×D₁₀₇	1	1	yes	characteristic
50	#107	—	107	2	no	—
51	#107	C₂×D₁₀₇	1	2	yes	—
52	#106	—	214	2	no	—
53	C₄×C₈	—	107	1	no	—
54	C₂×C₈	—	107	1	no	—
55	C₂×C₈	C₂²×D₁₀₇	1	1	yes	characteristic
56	C₄⋊C₄	—	2	2	no	—
57	C₄⋊C₄	—	428	2	no	—
58	C₄⋊C₄	—	428	2	no	—
59	C₄⋊C₄	—	214	2	no	—
60	C₄²	—	107	1	no	—
61	C₁₆	—	107	2	no	—
62	C₁₆	Dic₂₁₄	1	2	yes	—
63	C₂×C₄	—	4	2	no	—
64	C₂×C₄	—	107	1	no	—
65	C₂×C₄	—	107	1	no	—
66	C₂×C₄	—	428	2	no	—
67	C₂×C₄	D₄×D₁₀₇	1	1	yes	characteristic
68	C₈	—	107	2	no	—
69	C₈	Q₈×D₁₀₇	1	1	yes	characteristic
70	C₈	C₂×Dic₂₁₄	1	1	yes	characteristic
71	C₂²	D₈×D₁₀₇	1	1	yes	characteristic
72	C₄	—	8	2	no	—
73	C₄	—	856	2	no	—
74	C₄	—	214	1	no	—
75	C₄	—	214	1	no	—
76	C₄	#16812108	1	1	yes	characteristic
77	C₄	Q₁₆×D₁₀₇	1	1	yes	characteristic
78	C₂	#20293031	1	1	yes	characteristic
79	C₂	#20293056	1	1	yes	characteristic
80	C₂	#20293060	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₈×D₁₀₇
commutator, cosocle	C₂×C₈×C₁₀₇	C₂³
Frattini	C₂×C₈	C₂²×D₁₀₇
Fitting	#366×C₁₀₇	C₂
socle, prime radical	C₂²×C₁₀₇	C₂×D₈
hypercenter	#366	D₁₀₇
hypocenter	C₁₀₇	#2253
LCS	G ▷ C₂×C₈×C₁₀₇ ▷ C₄×C₁₀₇ ▷ C₂×C₁₀₇ ▷ C₁₀₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #366

Complements

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

N	H ≅ G/N	type
41. C₁₀₇	#2253	semidirect

Maximal subgroups

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

subgroup	index
#20293028	2
#20292454	2
#20292453	2
C₁₆×Dic₁₀₇	2
#366×C₁₀₇	2
#2253	107