Subgroups — #20292432

Order 6848.

58 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	#16812043	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₆×C₁₀₇	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₂₁₄	—	2	1	no	—
5	Dic₄₂₈	—	2	1	no	—
6	Dic₄₂₈	C₄	1	2	yes	complemented
7	C₄⋊Dic₁₀₇	—	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	C₂×Dic₁₀₇	—	4	1	no	—
13	Dic₂₁₄	—	2	2	no	—
14	Dic₂₁₄	—	4	1	no	—
15	C₈×C₁₀₇	C₂×C₄	1	1	yes	characteristic
16	C₈×C₁₀₇	D₄	1	1	yes	characteristic
17	C₂²×C₁₀₇	D₈	1	1	yes	characteristic
18	C₄×C₁₀₇	C₂²⋊C₄	1	1	yes	characteristic
19	C₄×C₁₀₇	SD₁₆	1	1	yes	characteristic
20	Dic₁₀₇	—	4	2	no	—
21	Dic₁₀₇	—	8	1	no	—
22	C₂×C₁₀₇	#102	1	1	yes	characteristic
23	C₂×C₁₀₇	SD₃₂	1	1	yes	characteristic
24	C₂×C₁₀₇	Q₃₂	1	1	yes	characteristic
25	C₁₀₇	#358	1	1	yes	characteristic, complemented, Sylow
26	#358	—	107	1	no	maximal, Sylow
27	C₂×Q₁₆	—	107	1	no	—
28	C₂×C₁₆	D₁₀₇	1	1	yes	characteristic
29	#107	—	107	1	no	—
30	C₂×Q₈	—	214	1	no	—
31	Q₁₆	—	107	2	no	—
32	Q₁₆	—	214	1	no	—
33	C₂×C₈	C₂×D₁₀₇	1	1	yes	characteristic
34	C₄⋊C₄	—	214	1	no	—
35	C₁₆	—	2	1	no	—
36	Q₈	—	428	1	no	—
37	Q₈	—	214	2	no	—
38	C₂×C₄	—	428	1	no	—
39	C₂×C₄	—	428	1	no	—
40	C₂×C₄	D₄₂₈	1	1	yes	characteristic
41	C₈	C₄×D₁₀₇	1	1	yes	characteristic
42	C₈	C₂²⋊D₁₀₇	1	1	yes	characteristic
43	C₂²	D₈₅₆	1	1	yes	characteristic
44	C₄	—	856	1	no	—
45	C₄	—	428	2	no	—
46	C₄	(C₂×D₁₀₇)⋊C₄	1	1	yes	characteristic
47	C₄	#13133807	1	1	yes	characteristic
48	C₂	#16812031	1	1	yes	characteristic
49	C₂	#16812054	1	1	yes	characteristic
50	C₂	Dic₈₅₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₈₅₆
commutator	C₈×C₁₀₇	C₂×C₄
Frattini	C₂×C₈	C₂×D₁₀₇
Fitting	C₂×C₁₆×C₁₀₇	C₂
socle	C₂²×C₁₀₇	D₈
hypercenter	C₂×C₁₆	D₁₀₇
hypocenter	C₁₀₇	#358
LCS	G ▷ C₈×C₁₀₇ ▷ C₄×C₁₀₇ ▷ C₂×C₁₀₇ ▷ C₁₀₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
6. Dic₄₂₈	C₄	semidirect
25. C₁₀₇	#358	semidirect