Subgroups — #20293060

Order 6848.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16812132	C₂	1	2	yes	maximal, complemented
2	#16812052	C₂	1	2	yes	maximal, complemented
3	D₁₇₁₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₆×D₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
5	Q₃₂×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
6	#13133819	—	2	2	no	—
7	#13133805	—	2	2	no	—
8	D₈₅₆	C₂²	1	2	yes	—
9	C₈×D₁₀₇	C₂²	1	1	yes	characteristic
10	C₁₀₇⋊C₁₆	C₂²	1	1	yes	characteristic
11	Q₁₆×C₁₀₇	C₂²	1	2	yes	—
12	C₁₆×C₁₀₇	C₂²	1	1	yes	characteristic
13	Q₈×C₁₀₇	—	2	2	no	—
14	D₄₂₈	—	2	2	no	—
15	D₄₂₈	—	4	2	no	—
16	C₄×D₁₀₇	—	4	2	no	—
17	C₄×D₁₀₇	D₄	1	1	yes	characteristic
18	C₈×C₁₀₇	C₂³	1	1	yes	characteristic
19	C₁₀₇⋊C₈	D₄	1	1	yes	characteristic
20	C₂×D₁₀₇	—	4	2	no	—
21	C₂×D₁₀₇	D₈	1	1	yes	characteristic
22	C₄×C₁₀₇	—	4	2	no	—
23	C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
24	Dic₁₀₇	D₈	1	1	yes	characteristic
25	C₂×C₁₀₇	C₂×D₈	1	1	yes	characteristic
26	D₁₀₇	—	2	1	no	—
27	D₁₀₇	—	8	2	no	—
28	C₁₀₇	#508	1	1	yes	characteristic, complemented, Sylow
29	#508	—	107	1	no	maximal, Sylow
30	#135	—	107	2	no	—
31	Q₃₂	D₁₀₇	1	1	yes	characteristic, complemented
32	SD₃₂	—	107	2	no	—
33	D₁₆	—	107	1	no	—
34	C₂×C₁₆	—	107	1	no	—
35	#41	—	214	2	no	—
36	Q₁₆	C₂×D₁₀₇	1	2	yes	—
37	SD₁₆	—	214	2	no	—
38	D₈	—	107	2	no	—
39	C₂×C₈	—	107	1	no	—
40	C₁₆	—	107	1	no	—
41	C₁₆	C₂×D₁₀₇	1	1	yes	characteristic
42	Q₈	—	2	2	no	—
43	D₄	—	428	2	no	—
44	D₄	—	214	2	no	—
45	C₂×C₄	—	107	1	no	—
46	C₂×C₄	—	428	2	no	—
47	C₈	—	107	1	no	—
48	C₈	C₂²×D₁₀₇	1	1	yes	characteristic
49	C₂²	—	107	1	no	—
50	C₂²	—	428	2	no	—
51	C₄	—	4	2	no	—
52	C₄	—	107	1	no	—
53	C₄	D₄×D₁₀₇	1	1	yes	characteristic
54	C₂	—	856	2	no	—
55	C₂	—	214	1	no	—
56	C₂	D₈×D₁₀₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₈×D₁₀₇
commutator	C₈×C₁₀₇	C₂³
Frattini	C₈	C₂²×D₁₀₇
Fitting	Q₃₂×C₁₀₇	C₂
socle	C₂×C₁₀₇	C₂×D₈
hypercenter	Q₃₂	D₁₀₇
hypocenter	C₁₀₇	#508
LCS	G ▷ C₈×C₁₀₇ ▷ C₄×C₁₀₇ ▷ C₂×C₁₀₇ ▷ C₁₀₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ Q₃₂

Complements

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

N	H ≅ G/N	type
1. #16812132	C₂	semidirect
2. #16812052	C₂	semidirect
3. D₁₇₁₂	C₂	semidirect
4. C₁₆×D₁₀₇	C₂	semidirect
5. Q₃₂×C₁₀₇	C₂	semidirect
28. C₁₀₇	#508	semidirect
31. Q₃₂	D₁₀₇	semidirect