Subgroups — #20292452

Order 6848.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₀₇⋊C₁₆	C₂	1	1	yes	maximal, characteristic
2	#16812043	C₂	1	1	yes	maximal, characteristic
3	#107×C₁₀₇	C₂	1	1	yes	maximal, characteristic
4	C₄⋊Dic₁₀₇	—	2	1	no	—
5	C₁₀₇⋊C₁₆	C₄	1	2	yes	complemented
6	C₂×C₈×C₁₀₇	C₂²	1	1	yes	characteristic
7	C₄⋊C₄×C₁₀₇	—	2	1	no	—
8	C₂×C₄×C₁₀₇	—	4	1	no	—
9	C₂×C₄×C₁₀₇	D₄	1	1	yes	characteristic
10	C₂×Dic₁₀₇	—	4	1	no	—
11	C₈×C₁₀₇	C₂×C₄	1	1	yes	characteristic
12	C₈×C₁₀₇	Q₈	1	1	yes	characteristic
13	C₂²×C₁₀₇	D₈	1	1	yes	characteristic
14	C₄×C₁₀₇	—	8	1	no	—
15	C₄×C₁₀₇	C₄⋊C₄	1	1	yes	characteristic
16	C₄×C₁₀₇	Q₁₆	1	1	yes	characteristic
17	Dic₁₀₇	—	8	1	no	—
18	C₂×C₁₀₇	#107	1	1	yes	characteristic
19	C₂×C₁₀₇	D₁₆	1	1	yes	characteristic
20	C₂×C₁₀₇	Q₃₂	1	1	yes	characteristic
21	C₁₀₇	#366	1	1	yes	characteristic, complemented, Sylow
22	#366	—	107	1	no	maximal, Sylow
23	C₂×C₁₆	—	107	1	no	—
24	#107	—	107	1	no	—
25	#107	D₁₀₇	1	1	yes	characteristic
26	C₂×C₈	C₂×D₁₀₇	1	1	yes	characteristic
27	C₄⋊C₄	—	2	1	no	—
28	C₄⋊C₄	—	214	1	no	—
29	C₁₆	—	107	2	no	—
30	C₂×C₄	—	4	1	no	—
31	C₂×C₄	—	428	1	no	—
32	C₂×C₄	C₂²⋊D₁₀₇	1	1	yes	characteristic
33	C₈	Dic₂₁₄	1	1	yes	characteristic
34	C₈	C₄×D₁₀₇	1	1	yes	characteristic
35	C₂²	#13133803	1	1	yes	characteristic
36	C₄	—	8	1	no	—
37	C₄	—	856	1	no	—
38	C₄	Dic₁₀₇⋊C₄	1	1	yes	characteristic
39	C₄	#13133808	1	1	yes	characteristic
40	C₂	#16812042	1	1	yes	characteristic
41	C₂	#16812050	1	1	yes	characteristic
42	C₂	#16812055	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#13133803
commutator	C₈×C₁₀₇	C₂×C₄
Frattini	C₂×C₈	C₂×D₁₀₇
Fitting	#107×C₁₀₇	C₂
socle	C₂²×C₁₀₇	D₈
hypercenter	#107	D₁₀₇
hypocenter	C₁₀₇	#366
LCS	G ▷ C₈×C₁₀₇ ▷ C₄×C₁₀₇ ▷ C₂×C₁₀₇ ▷ C₁₀₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #107

Complements

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

N	H ≅ G/N	type
5. C₁₀₇⋊C₁₆	C₄	semidirect
21. C₁₀₇	#366	semidirect