Subgroups — #20292497

Order 6848.

186 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊Dic₁₀₇	C₂	1	6	yes	maximal
2	C₂×C₄²×C₁₀₇	C₂	1	1	yes	maximal, characteristic
3	C₂²×Dic₁₀₇	C₂²	1	4	yes	—
4	C₄⋊Dic₁₀₇	—	2	12	no	—
5	C₂²×C₄×C₁₀₇	C₂²	1	3	yes	—
6	C₄²×C₁₀₇	C₄	1	4	yes	complemented
7	C₂³×C₁₀₇	C₂³	1	1	yes	characteristic
8	C₂×C₄×C₁₀₇	C₂×C₄	1	6	yes	—
9	C₂×C₄×C₁₀₇	D₄	1	6	yes	—
10	C₂×C₄×C₁₀₇	Q₈	1	6	yes	—
11	C₂×Dic₁₀₇	—	2	12	no	—
12	C₂²×C₁₀₇	C₂²×C₄	1	1	yes	characteristic
13	C₂²×C₁₀₇	C₂×D₄	1	3	yes	—
14	C₂²×C₁₀₇	C₂×Q₈	1	3	yes	—
15	C₄×C₁₀₇	C₄⋊C₄	1	12	yes	complemented
16	Dic₁₀₇	—	4	4	no	—
17	C₂×C₁₀₇	C₂×C₄⋊C₄	1	3	yes	—
18	C₂×C₁₀₇	#127	1	1	yes	characteristic
19	C₂×C₁₀₇	C₄⋊Q₈	1	3	yes	—
20	C₁₀₇	#384	1	1	yes	characteristic, complemented, Sylow
21	#384	—	107	1	no	maximal, Sylow
22	C₂×C₄⋊C₄	—	107	6	no	—
23	C₂×C₄²	D₁₀₇	1	1	yes	characteristic
24	C₂²×C₄	—	107	4	no	—
25	C₂²×C₄	C₂×D₁₀₇	1	3	yes	—
26	C₄⋊C₄	—	214	12	no	—
27	C₄²	Dic₁₀₇	1	4	yes	complemented
28	C₂³	C₂²×D₁₀₇	1	1	yes	characteristic
29	C₂×C₄	—	214	12	no	—
30	C₂×C₄	Dic₂₁₄	1	6	yes	—
31	C₂×C₄	D₄₂₈	1	6	yes	—
32	C₂×C₄	C₂×Dic₁₀₇	1	6	yes	—
33	C₂²	C₂²×Dic₁₀₇	1	1	yes	characteristic
34	C₂²	C₂×D₄₂₈	1	3	yes	—
35	C₂²	C₂×Dic₂₁₄	1	3	yes	—
36	C₄	—	428	4	no	—
37	C₄	C₄⋊Dic₁₀₇	1	12	yes	complemented
38	C₂	C₂×C₄⋊Dic₁₀₇	1	3	yes	—
39	C₂	#16812106	1	1	yes	characteristic
40	C₂	#16812109	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₁₀₇
commutator	C₂²×C₁₀₇	C₂²×C₄
Fitting	C₂×C₄²×C₁₀₇	C₂
socle	C₂³×C₁₀₇	C₂³
hypercenter	C₂×C₄²	D₁₀₇
hypocenter	C₁₀₇	#384
LCS	G ▷ C₂²×C₁₀₇ ▷ C₁₀₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
6. C₄²×C₁₀₇	C₄	semidirect
15. C₄×C₁₀₇	C₄⋊C₄	semidirect
20. C₁₀₇	#384	semidirect
27. C₄²	Dic₁₀₇	semidirect
37. C₄	C₄⋊Dic₁₀₇	semidirect