Subgroups — #20292410

Order 6848.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16812115	C₂	1	1	yes	maximal, characteristic
2	#16812049	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₆×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#13133818	C₄	1	1	yes	characteristic
5	#13133802	C₄	1	1	yes	characteristic
6	#13133801	—	2	1	no	—
7	C₈×D₁₀₇	—	2	1	no	—
8	C₁₀₇⋊C₁₆	—	2	1	no	—
9	C₂×C₈×C₁₀₇	C₂²	1	1	yes	characteristic
10	C₁₆×C₁₀₇	—	2	1	no	—
11	C₂×C₄×C₁₀₇	C₂×C₄	1	1	yes	characteristic
12	C₂²⋊D₁₀₇	—	2	1	no	—
13	D₄₂₈	C₈	1	1	yes	characteristic
14	C₄×D₁₀₇	—	2	1	no	—
15	Dic₂₁₄	C₈	1	1	yes	characteristic
16	C₈×C₁₀₇	D₄	1	1	yes	characteristic
17	C₈×C₁₀₇	D₄	1	1	yes	characteristic
18	C₁₀₇⋊C₈	—	2	1	no	—
19	C₂²×C₁₀₇	M₁₆	1	1	yes	characteristic
20	C₂×D₁₀₇	—	2	1	no	—
21	C₄×C₁₀₇	C₂²⋊C₄	1	1	yes	characteristic
22	C₄×C₁₀₇	C₂×C₈	1	1	yes	characteristic
23	Dic₁₀₇	—	2	1	no	—
24	C₂×C₁₀₇	—	2	1	no	—
25	C₂×C₁₀₇	C₂²⋊C₈	1	1	yes	characteristic
26	D₁₀₇	—	4	1	no	—
27	C₁₀₇	#350	1	1	yes	characteristic, complemented, Sylow
28	#350	—	107	1	no	maximal, Sylow
29	#131	—	107	1	no	—
30	M₃₂	—	107	1	no	—
31	C₂×C₁₆	D₁₀₇	1	1	yes	characteristic, complemented
32	#41	—	107	1	no	—
33	M₁₆	—	107	1	no	—
34	M₁₆	—	214	1	no	—
35	C₂×C₈	—	214	1	no	—
36	C₂×C₈	C₂×D₁₀₇	1	1	yes	characteristic
37	C₁₆	—	2	1	no	—
38	C₁₆	—	214	1	no	—
39	Q₈	—	107	1	no	—
40	D₄	—	107	1	no	—
41	D₄	—	214	1	no	—
42	C₂×C₄	—	214	1	no	—
43	C₂×C₄	C₄×D₁₀₇	1	1	yes	characteristic
44	C₈	—	214	1	no	—
45	C₈	D₄₂₈	1	1	yes	characteristic
46	C₈	C₂²⋊D₁₀₇	1	1	yes	characteristic
47	C₂²	—	214	1	no	—
48	C₂²	#13133801	1	1	yes	characteristic
49	C₄	—	214	1	no	—
50	C₄	(C₂×D₁₀₇)⋊C₄	1	1	yes	characteristic
51	C₄	C₈×D₁₀₇	1	1	yes	characteristic
52	C₂	—	2	1	no	—
53	C₂	—	428	1	no	—
54	C₂	(C₂×D₁₀₇)⋊C₈	1	1	yes	characteristic

	subgroup	G/H
center	C₈	D₄₂₈
commutator	C₄×C₁₀₇	C₂×C₈
Frattini	C₂×C₈	C₂×D₁₀₇
Fitting	C₂×C₁₆×C₁₀₇	C₂
socle	C₂×C₁₀₇	C₂²⋊C₈
hypercenter	C₂×C₁₆	D₁₀₇
hypocenter	C₁₀₇	#350
LCS	G ▷ C₄×C₁₀₇ ▷ C₂×C₁₀₇ ▷ C₁₀₇
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
2. #16812049	C₂	semidirect
3. C₂×C₁₆×C₁₀₇	C₂	semidirect
27. C₁₀₇	#350	semidirect
31. C₂×C₁₆	D₁₀₇	semidirect