Subgroups — #20292434

Order 6848.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₀₇⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	#16812045	C₂	1	1	yes	maximal, characteristic, complemented
3	#135×C₁₀₇	C₂	1	1	yes	maximal, characteristic
4	#13133802	—	2	1	no	—
5	C₁₀₇⋊C₁₆	—	2	1	no	—
6	#41×C₁₀₇	—	2	1	no	—
7	Q₁₆×C₁₀₇	C₄	1	1	yes	characteristic
8	SD₁₆×C₁₀₇	—	2	1	no	—
9	D₈×C₁₀₇	C₄	1	1	yes	characteristic
10	C₂×C₈×C₁₀₇	C₂²	1	1	yes	characteristic
11	Q₈×C₁₀₇	—	2	1	no	—
12	D₄×C₁₀₇	—	2	1	no	—
13	D₄×C₁₀₇	—	4	1	no	—
14	C₂×C₄×C₁₀₇	—	4	1	no	—
15	C₂×C₄×C₁₀₇	D₄	1	1	yes	characteristic
16	C₈×C₁₀₇	C₂×C₄	1	1	yes	characteristic
17	C₈×C₁₀₇	D₄	1	1	yes	characteristic
18	C₁₀₇⋊C₈	—	4	1	no	—
19	C₂²×C₁₀₇	—	4	1	no	—
20	C₂²×C₁₀₇	SD₁₆	1	1	yes	characteristic
21	C₄×C₁₀₇	—	4	1	no	—
22	C₄×C₁₀₇	C₂²⋊C₄	1	1	yes	characteristic
23	C₄×C₁₀₇	D₈	1	1	yes	characteristic
24	C₂×C₁₀₇	—	2	1	no	—
25	C₂×C₁₀₇	—	8	1	no	—
26	C₂×C₁₀₇	#102	1	1	yes	characteristic
27	C₁₀₇	#359	1	1	yes	characteristic, complemented, Sylow
28	#359	—	107	1	no	maximal, Sylow
29	#135	D₁₀₇	1	1	yes	characteristic
30	C₂×C₁₆	—	107	1	no	—
31	#108	—	107	1	no	—
32	#41	—	2	1	no	—
33	Q₁₆	Dic₁₀₇	1	1	yes	characteristic
34	SD₁₆	—	2	1	no	—
35	D₈	Dic₁₀₇	1	1	yes	characteristic
36	M₁₆	—	214	1	no	—
37	C₂×C₈	C₂×D₁₀₇	1	1	yes	characteristic
38	C₁₆	—	214	1	no	—
39	Q₈	—	2	1	no	—
40	D₄	—	2	1	no	—
41	D₄	—	4	1	no	—
42	C₂×C₄	—	4	1	no	—
43	C₂×C₄	C₂²⋊D₁₀₇	1	1	yes	characteristic
44	C₈	—	428	1	no	—
45	C₈	C₂×Dic₁₀₇	1	1	yes	characteristic
46	C₈	C₂²⋊D₁₀₇	1	1	yes	characteristic
47	C₂²	—	4	1	no	—
48	C₂²	#13133806	1	1	yes	characteristic
49	C₄	—	4	1	no	—
50	C₄	C₂²⋊Dic₁₀₇	1	1	yes	characteristic
51	C₄	#13133803	1	1	yes	characteristic
52	C₂	—	2	1	no	—
53	C₂	—	8	1	no	—
54	C₂	#16812030	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#13133803
commutator	C₈×C₁₀₇	C₂×C₄
Frattini	C₂×C₈	C₂×D₁₀₇
Fitting	#135×C₁₀₇	C₂
socle	C₂×C₁₀₇	#102
hypercenter	#135	D₁₀₇
hypocenter	C₁₀₇	#359
LCS	G ▷ C₈×C₁₀₇ ▷ C₄×C₁₀₇ ▷ C₂×C₁₀₇ ▷ C₁₀₇
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #135

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₀₇⋊C₁₆	C₂	semidirect
2. #16812045	C₂	semidirect
27. C₁₀₇	#359	semidirect