Subgroups — #20292444

Order 6848.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₄₂₈	C₂	1	1	yes	maximal, characteristic
2	#16812045	C₂	1	1	yes	maximal, characteristic
3	M₃₂×C₁₀₇	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₂₁₄	—	2	1	no	—
5	Dic₄₂₈	—	2	1	no	—
6	Dic₄₂₈	C₄	1	2	yes	—
7	#13133802	—	2	1	no	—
8	C₂×C₈×C₁₀₇	C₂²	1	1	yes	characteristic
9	C₁₆×C₁₀₇	—	2	1	no	—
10	C₂×C₄×C₁₀₇	D₄	1	1	yes	characteristic
11	C₂×Dic₁₀₇	—	4	1	no	—
12	Dic₂₁₄	—	2	2	no	—
13	Dic₂₁₄	—	4	1	no	—
14	C₈×C₁₀₇	C₂×C₄	1	1	yes	characteristic
15	C₈×C₁₀₇	D₄	1	1	yes	characteristic
16	C₁₀₇⋊C₈	—	4	1	no	—
17	C₂²×C₁₀₇	SD₁₆	1	1	yes	characteristic
18	C₄×C₁₀₇	C₂²⋊C₄	1	1	yes	characteristic
19	C₄×C₁₀₇	D₈	1	1	yes	characteristic
20	Dic₁₀₇	—	4	2	no	—
21	C₂×C₁₀₇	—	2	1	no	—
22	C₂×C₁₀₇	#102	1	1	yes	characteristic
23	C₁₀₇	#362	1	1	yes	characteristic, complemented, Sylow
24	#362	—	107	1	no	maximal, Sylow
25	C₂×Q₁₆	—	107	1	no	—
26	M₃₂	D₁₀₇	1	1	yes	characteristic
27	#108	—	107	1	no	—
28	C₂×Q₈	—	214	1	no	—
29	Q₁₆	—	107	2	no	—
30	Q₁₆	—	214	1	no	—
31	M₁₆	—	214	1	no	—
32	C₂×C₈	C₂×D₁₀₇	1	1	yes	characteristic
33	C₁₆	—	2	1	no	—
34	Q₈	—	428	1	no	—
35	Q₈	—	214	2	no	—
36	C₂×C₄	—	428	1	no	—
37	C₂×C₄	D₄₂₈	1	1	yes	characteristic
38	C₈	—	428	1	no	—
39	C₈	C₄×D₁₀₇	1	1	yes	characteristic
40	C₈	C₂²⋊D₁₀₇	1	1	yes	characteristic
41	C₂²	#13133807	1	1	yes	characteristic
42	C₄	—	428	2	no	—
43	C₄	(C₂×D₁₀₇)⋊C₄	1	1	yes	characteristic
44	C₄	D₈₅₆	1	1	yes	characteristic
45	C₂	—	2	1	no	—
46	C₂	#16812031	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#16812031
commutator	C₈×C₁₀₇	C₂×C₄
Frattini	C₂×C₈	C₂×D₁₀₇
Fitting	M₃₂×C₁₀₇	C₂
socle	C₂×C₁₀₇	#102
hypercenter	M₃₂	D₁₀₇
hypocenter	C₁₀₇	#362
LCS	G ▷ C₈×C₁₀₇ ▷ C₄×C₁₀₇ ▷ C₂×C₁₀₇ ▷ C₁₀₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ M₃₂

Complements

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

N	H ≅ G/N	type
23. C₁₀₇	#362	semidirect