Subgroups — #20292378

Order 6848.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊(C₁₀₇⋊C₈)	C₂	1	2	yes	maximal
2	C₄×C₈×C₁₀₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₀₇⋊C₈	—	2	2	no	—
4	C₂×C₈×C₁₀₇	C₄	1	1	yes	characteristic
5	C₂×C₈×C₁₀₇	C₄	1	1	yes	characteristic
6	C₄²×C₁₀₇	C₂²	1	1	yes	characteristic
7	C₂×C₄×C₁₀₇	C₂×C₄	1	1	yes	characteristic
8	C₂×C₄×C₁₀₇	D₄	1	1	yes	characteristic
9	C₂×C₄×C₁₀₇	Q₈	1	1	yes	characteristic
10	C₈×C₁₀₇	—	2	1	no	—
11	C₈×C₁₀₇	C₈	1	2	yes	complemented
12	C₁₀₇⋊C₈	—	4	2	no	—
13	C₂²×C₁₀₇	C₄⋊C₄	1	1	yes	characteristic
14	C₄×C₁₀₇	—	2	1	no	—
15	C₄×C₁₀₇	C₂×C₈	1	1	yes	characteristic
16	C₄×C₁₀₇	M₁₆	1	1	yes	characteristic
17	C₄×C₁₀₇	SD₁₆	1	2	yes	—
18	C₂×C₁₀₇	C₄⋊C₈	1	1	yes	characteristic
19	C₂×C₁₀₇	#106	1	1	yes	characteristic
20	C₂×C₁₀₇	#108	1	1	yes	characteristic
21	C₁₀₇	#334	1	1	yes	characteristic, complemented, Sylow
22	#334	—	107	1	no	maximal, Sylow
23	C₄⋊C₈	—	107	2	no	—
24	C₄×C₈	D₁₀₇	1	1	yes	characteristic
25	C₂×C₈	—	214	2	no	—
26	C₂×C₈	Dic₁₀₇	1	1	yes	characteristic
27	C₂×C₈	Dic₁₀₇	1	1	yes	characteristic
28	C₄²	C₂×D₁₀₇	1	1	yes	characteristic
29	C₂×C₄	Dic₂₁₄	1	1	yes	characteristic
30	C₂×C₄	D₄₂₈	1	1	yes	characteristic
31	C₂×C₄	C₂×Dic₁₀₇	1	1	yes	characteristic
32	C₈	—	2	1	no	—
33	C₈	—	428	2	no	—
34	C₈	C₁₀₇⋊C₈	1	2	yes	complemented
35	C₂²	C₄⋊Dic₁₀₇	1	1	yes	characteristic
36	C₄	—	2	1	no	—
37	C₄	C₂×C₁₀₇⋊C₈	1	1	yes	characteristic
38	C₄	#13133802	1	1	yes	characteristic
39	C₄	#13133807	1	2	yes	—
40	C₂	C₄⋊(C₁₀₇⋊C₈)	1	1	yes	characteristic
41	C₂	#16812041	1	1	yes	characteristic
42	C₂	#16812045	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₄₂₈
commutator	C₄×C₁₀₇	C₂×C₈
Frattini	C₄²	C₂×D₁₀₇
Fitting	C₄×C₈×C₁₀₇	C₂
socle	C₂²×C₁₀₇	C₄⋊C₄
hypercenter	C₄×C₈	D₁₀₇
hypocenter	C₁₀₇	#334
LCS	G ▷ C₄×C₁₀₇ ▷ C₂×C₁₀₇ ▷ C₁₀₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
11. C₈×C₁₀₇	C₈	semidirect
21. C₁₀₇	#334	semidirect
34. C₈	C₁₀₇⋊C₈	semidirect