Subgroups — #20292425

Order 6848.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16812107	C₂	1	1	yes	maximal, characteristic
2	#16812028	C₂	1	1	yes	maximal, characteristic
3	#101×C₁₀₇	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₂₁₄	C₄	1	1	yes	characteristic
5	#13133802	—	2	1	no	—
6	Dic₁₀₇⋊C₄	—	2	1	no	—
7	Dic₁₀₇⋊C₄	—	2	1	no	—
8	C₄×Dic₁₀₇	C₄	1	1	yes	characteristic
9	C₂×Q₈×C₁₀₇	C₂²	1	1	yes	characteristic
10	M₁₆×C₁₀₇	—	2	1	no	—
11	Q₈×C₁₀₇	—	4	1	no	—
12	C₂×C₄×C₁₀₇	C₂×C₄	1	1	yes	characteristic
13	C₂×C₄×C₁₀₇	D₄	1	1	yes	characteristic
14	C₂×C₄×C₁₀₇	D₄	1	1	yes	characteristic
15	C₂×Dic₁₀₇	—	2	1	no	—
16	C₂×Dic₁₀₇	—	2	1	no	—
17	Dic₂₁₄	—	4	1	no	—
18	C₈×C₁₀₇	—	4	1	no	—
19	C₁₀₇⋊C₈	—	4	1	no	—
20	C₂²×C₁₀₇	C₂²⋊C₄	1	1	yes	characteristic
21	C₄×C₁₀₇	—	2	1	no	—
22	C₄×C₁₀₇	—	2	1	no	—
23	C₄×C₁₀₇	—	2	1	no	—
24	Dic₁₀₇	—	2	2	no	—
25	Dic₁₀₇	—	4	1	no	—
26	C₂×C₁₀₇	—	2	1	no	—
27	C₂×C₁₀₇	#99	1	1	yes	characteristic
28	C₁₀₇	#356	1	1	yes	characteristic, complemented, Sylow
29	#356	—	107	1	no	maximal, Sylow
30	C₄⋊Q₈	—	107	1	no	—
31	#101	—	107	1	no	—
32	#101	D₁₀₇	1	1	yes	characteristic
33	C₂×Q₈	—	107	1	no	—
34	C₂×Q₈	C₂×D₁₀₇	1	1	yes	characteristic
35	M₁₆	—	2	1	no	—
36	M₁₆	—	214	1	no	—
37	C₄⋊C₄	—	214	1	no	—
38	C₄⋊C₄	—	214	1	no	—
39	C₄²	—	107	1	no	—
40	Q₈	—	4	1	no	—
41	Q₈	—	428	1	no	—
42	C₂×C₄	—	214	1	no	—
43	C₂×C₄	—	214	1	no	—
44	C₂×C₄	C₄×D₁₀₇	1	1	yes	characteristic
45	C₂×C₄	D₄₂₈	1	1	yes	characteristic
46	C₂×C₄	C₂²⋊D₁₀₇	1	1	yes	characteristic
47	C₈	—	4	1	no	—
48	C₈	—	428	1	no	—
49	C₂²	(C₂×D₁₀₇)⋊C₄	1	1	yes	characteristic
50	C₄	—	2	1	no	—
51	C₄	—	2	1	no	—
52	C₄	—	2	1	no	—
53	C₄	—	428	1	no	—
54	C₄	—	214	2	no	—
55	C₂	—	2	1	no	—
56	C₂	#16812023	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#16812023
commutator	C₂×C₄×C₁₀₇	C₂×C₄
Frattini	C₂×Q₈	C₂×D₁₀₇
Fitting	#101×C₁₀₇	C₂
socle	C₂×C₁₀₇	#99
hypercenter	#101	D₁₀₇
hypocenter	C₁₀₇	#356
LCS	G ▷ C₂×C₄×C₁₀₇ ▷ C₂²×C₁₀₇ ▷ C₂×C₁₀₇ ▷ C₁₀₇
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×Q₈ ◁ #101

Complements

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

N	H ≅ G/N	type
28. C₁₀₇	#356	semidirect