Subgroups — #20292408

Order 6848.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13133801	C₂	1	1	yes	maximal, characteristic
2	#16812049	C₂	1	1	yes	maximal, characteristic, complemented
3	M₃₂×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×D₁₀₇	C₄	1	1	yes	characteristic
5	#13133801	—	2	1	no	—
6	#13133801	—	2	1	no	—
7	C₂×C₁₀₇⋊C₈	C₄	1	1	yes	characteristic
8	C₁₀₇⋊C₁₆	—	2	1	no	—
9	C₂×C₈×C₁₀₇	C₂²	1	1	yes	characteristic
10	C₁₆×C₁₀₇	—	2	1	no	—
11	C₂²×D₁₀₇	C₈	1	1	yes	characteristic
12	C₂×C₄×C₁₀₇	C₂×C₄	1	1	yes	characteristic
13	C₂×Dic₁₀₇	C₈	1	1	yes	characteristic
14	C₄×D₁₀₇	—	2	1	no	—
15	C₄×D₁₀₇	—	2	1	no	—
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	C₂×C₈	1	1	yes	characteristic
20	C₂×D₁₀₇	—	2	1	no	—
21	C₂×D₁₀₇	—	4	1	no	—
22	C₄×C₁₀₇	C₂²⋊C₄	1	1	yes	characteristic
23	C₄×C₁₀₇	M₁₆	1	1	yes	characteristic
24	Dic₁₀₇	—	2	1	no	—
25	C₂×C₁₀₇	—	2	1	no	—
26	C₂×C₁₀₇	C₂²⋊C₈	1	1	yes	characteristic
27	D₁₀₇	—	4	1	no	—
28	C₁₀₇	#349	1	1	yes	characteristic, complemented, Sylow
29	#349	—	107	1	no	maximal, Sylow
30	C₂×M₁₆	—	107	1	no	—
31	M₃₂	—	107	1	no	—
32	M₃₂	D₁₀₇	1	1	yes	characteristic, complemented
33	C₂²×C₄	—	107	1	no	—
34	M₁₆	—	214	1	no	—
35	M₁₆	—	214	1	no	—
36	C₂×C₈	—	107	1	no	—
37	C₂×C₈	C₂×D₁₀₇	1	1	yes	characteristic
38	C₁₆	—	2	1	no	—
39	C₁₆	—	214	1	no	—
40	C₂³	—	107	1	no	—
41	C₂×C₄	—	107	1	no	—
42	C₂×C₄	—	214	1	no	—
43	C₂×C₄	—	214	1	no	—
44	C₂×C₄	C₄×D₁₀₇	1	1	yes	characteristic
45	C₈	—	214	1	no	—
46	C₈	D₄₂₈	1	1	yes	characteristic
47	C₈	C₂²⋊D₁₀₇	1	1	yes	characteristic
48	C₂²	—	428	1	no	—
49	C₂²	—	214	1	no	—
50	C₂²	C₈×D₁₀₇	1	1	yes	characteristic
51	C₄	—	214	1	no	—
52	C₄	(C₂×D₁₀₇)⋊C₄	1	1	yes	characteristic
53	C₄	#13133801	1	1	yes	characteristic
54	C₂	—	2	1	no	—
55	C₂	—	428	1	no	—
56	C₂	(C₂×D₁₀₇)⋊C₈	1	1	yes	characteristic

	subgroup	G/H
center	C₄	(C₂×D₁₀₇)⋊C₄
commutator	C₂²×C₁₀₇	C₂×C₈
Frattini	C₂×C₈	C₂×D₁₀₇
Fitting	M₃₂×C₁₀₇	C₂
socle	C₂×C₁₀₇	C₂²⋊C₈
hypercenter	M₃₂	D₁₀₇
hypocenter	C₁₀₇	#349
LCS	G ▷ C₂²×C₁₀₇ ▷ C₂×C₁₀₇ ▷ C₁₀₇
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ M₃₂

Complements

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

N	H ≅ G/N	type
2. #16812049	C₂	semidirect
3. M₃₂×C₁₀₇	C₂	semidirect
28. C₁₀₇	#349	semidirect
32. M₃₂	D₁₀₇	semidirect