Subgroups — #20293035

Order 6848.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16812108	C₂	1	1	yes	maximal, characteristic
2	#16812100	C₂	1	1	yes	maximal, characteristic
3	#16812042	C₂	1	1	yes	maximal, characteristic
4	#16812041	C₂	1	1	yes	maximal, characteristic
5	#16812040	C₂	1	1	yes	maximal, characteristic
6	#16812019	C₂	1	1	yes	maximal, characteristic
7	#107×C₁₀₇	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₂₁₄	—	2	1	no	—
9	C₂×C₁₀₇⋊C₈	C₂²	1	1	yes	characteristic
10	C₄⋊Dic₁₀₇	—	2	1	no	—
11	C₄⋊Dic₁₀₇	C₂²	1	1	yes	characteristic
12	C₄⋊Dic₁₀₇	C₂²	1	1	yes	characteristic
13	Dic₁₀₇⋊C₄	—	2	1	no	—
14	Dic₁₀₇⋊C₄	—	2	1	no	—
15	C₄×Dic₁₀₇	C₂²	1	1	yes	characteristic
16	C₂×C₈×C₁₀₇	C₂²	1	1	yes	characteristic
17	C₄⋊C₄×C₁₀₇	C₂²	1	1	yes	characteristic
18	C₄⋊C₄×C₁₀₇	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₁₀₇	—	2	1	no	—
20	C₂×C₄×C₁₀₇	—	2	1	no	—
21	C₂×C₄×C₁₀₇	C₂³	1	1	yes	characteristic
22	C₂×Dic₁₀₇	—	2	1	no	—
23	C₂×Dic₁₀₇	—	2	1	no	—
24	C₂×Dic₁₀₇	D₄	1	1	yes	characteristic
25	C₂×Dic₁₀₇	D₄	1	1	yes	characteristic
26	Dic₂₁₄	—	4	2	no	—
27	C₈×C₁₀₇	Q₈	1	2	yes	complemented
28	C₁₀₇⋊C₈	Q₈	1	2	yes	complemented
29	C₂²×C₁₀₇	C₂×D₄	1	1	yes	characteristic
30	C₄×C₁₀₇	—	4	1	no	—
31	C₄×C₁₀₇	—	4	1	no	—
32	C₄×C₁₀₇	C₂×Q₈	1	1	yes	characteristic
33	C₄×C₁₀₇	C₂×Q₈	1	1	yes	characteristic
34	Dic₁₀₇	—	2	1	no	—
35	Dic₁₀₇	—	2	1	no	—
36	Dic₁₀₇	—	4	1	no	—
37	Dic₁₀₇	—	4	1	no	—
38	C₂×C₁₀₇	C₄⋊Q₈	1	1	yes	characteristic
39	C₂×C₁₀₇	AGL(1,ℤ/8)	1	1	yes	characteristic
40	C₂×C₁₀₇	#137	1	1	yes	characteristic
41	C₁₀₇	#501	1	1	yes	characteristic, complemented, Sylow
42	#501	—	107	1	no	maximal, Sylow
43	C₄⋊Q₈	—	107	1	no	—
44	#125	—	107	1	no	—
45	#107	—	107	1	no	—
46	#107	D₁₀₇	1	1	yes	characteristic
47	#106	—	107	1	no	—
48	#106	—	107	1	no	—
49	#97	—	107	1	no	—
50	C₂×Q₈	—	214	1	no	—
51	C₂×C₈	—	107	1	no	—
52	C₂×C₈	C₂×D₁₀₇	1	1	yes	characteristic
53	C₄⋊C₄	—	107	1	no	—
54	C₄⋊C₄	—	107	1	no	—
55	C₄⋊C₄	—	214	1	no	—
56	C₄⋊C₄	—	214	1	no	—
57	C₄⋊C₄	—	214	1	no	—
58	C₄⋊C₄	C₂×D₁₀₇	1	1	yes	characteristic
59	C₄⋊C₄	C₂×D₁₀₇	1	1	yes	characteristic
60	C₄²	—	107	1	no	—
61	Q₈	—	428	2	no	—
62	C₂×C₄	—	2	1	no	—
63	C₂×C₄	—	2	1	no	—
64	C₂×C₄	—	107	1	no	—
65	C₂×C₄	—	107	1	no	—
66	C₂×C₄	—	214	1	no	—
67	C₂×C₄	—	214	1	no	—
68	C₂×C₄	C₂²×D₁₀₇	1	1	yes	characteristic
69	C₈	—	107	2	no	—
70	C₈	Dic₂₁₄	1	2	yes	complemented
71	C₂²	D₄×D₁₀₇	1	1	yes	characteristic
72	C₄	—	4	1	no	—
73	C₄	—	4	1	no	—
74	C₄	—	428	1	no	—
75	C₄	—	428	1	no	—
76	C₄	—	214	1	no	—
77	C₄	—	214	1	no	—
78	C₄	Q₈×D₁₀₇	1	1	yes	characteristic
79	C₄	C₂×Dic₂₁₄	1	1	yes	characteristic
80	C₂	#16812108	1	1	yes	characteristic
81	C₂	#16812133	1	1	yes	characteristic
82	C₂	#16812141	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₁₀₇
commutator	C₂×C₄×C₁₀₇	C₂³
Frattini	C₂×C₄	C₂²×D₁₀₇
Fitting	#107×C₁₀₇	C₂
socle	C₂²×C₁₀₇	C₂×D₄
hypercenter	#107	D₁₀₇
hypocenter	C₁₀₇	#501
LCS	G ▷ C₂×C₄×C₁₀₇ ▷ C₂×C₁₀₇ ▷ C₁₀₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #107

Complements

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

N	H ≅ G/N	type
27. C₈×C₁₀₇	Q₈	semidirect
28. C₁₀₇⋊C₈	Q₈	semidirect
41. C₁₀₇	#501	semidirect
70. C₈	Dic₂₁₄	semidirect