Subgroups — #20292992

Order 6848.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16812106	C₂	1	1	yes	maximal, characteristic
2	#16812101	C₂	1	1	yes	maximal, characteristic, complemented
3	#16812031	C₂	1	4	yes	maximal, complemented
4	#97×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₄₂₈	—	2	2	no	—
6	C₂×D₄₂₈	C₂²	1	2	yes	—
7	C₄⋊Dic₁₀₇	C₂²	1	2	yes	—
8	Dic₁₀₇⋊C₄	—	2	2	no	—
9	C₂×C₈×C₁₀₇	C₂²	1	2	yes	—
10	C₄²×C₁₀₇	C₂²	1	1	yes	characteristic
11	C₂²×D₁₀₇	—	2	2	no	—
12	C₂×C₄×C₁₀₇	D₄	1	2	yes	—
13	C₂×C₄×C₁₀₇	C₂³	1	1	yes	characteristic
14	C₂×Dic₁₀₇	—	2	2	no	—
15	D₄₂₈	—	2	4	no	—
16	D₄₂₈	—	4	4	no	—
17	C₈×C₁₀₇	—	2	2	no	—
18	C₂²×C₁₀₇	C₂×D₄	1	1	yes	characteristic
19	C₂×D₁₀₇	—	4	2	no	—
20	C₂×D₁₀₇	—	4	4	no	—
21	C₄×C₁₀₇	—	2	2	no	—
22	C₄×C₁₀₇	#41	1	2	yes	—
23	Dic₁₀₇	—	4	2	no	—
24	C₂×C₁₀₇	#124	1	1	yes	characteristic
25	C₂×C₁₀₇	AGL(1,ℤ/8)	1	2	yes	—
26	D₁₀₇	—	8	2	no	—
27	C₁₀₇	#490	1	1	yes	characteristic, complemented, Sylow
28	#490	—	107	1	no	maximal, Sylow
29	#127	—	107	1	no	—
30	#125	—	107	1	no	—
31	#102	—	107	4	no	—
32	#97	D₁₀₇	1	1	yes	characteristic, complemented
33	C₂×D₄	—	107	2	no	—
34	C₂×D₄	—	214	2	no	—
35	C₂×C₈	C₂×D₁₀₇	1	2	yes	—
36	C₄⋊C₄	—	107	2	no	—
37	C₄⋊C₄	—	214	2	no	—
38	C₄²	C₂×D₁₀₇	1	1	yes	characteristic
39	C₂³	—	214	2	no	—
40	D₄	—	428	4	no	—
41	D₄	—	214	4	no	—
42	C₂×C₄	—	214	2	no	—
43	C₂×C₄	D₄₂₈	1	2	yes	—
44	C₂×C₄	C₂²×D₁₀₇	1	1	yes	characteristic
45	C₈	—	2	2	no	—
46	C₂²	—	428	2	no	—
47	C₂²	—	428	4	no	—
48	C₂²	C₂×D₄₂₈	1	1	yes	characteristic
49	C₄	—	2	2	no	—
50	C₄	—	428	2	no	—
51	C₄	#13133818	1	2	yes	—
52	C₂	—	856	2	no	—
53	C₂	#16812097	1	1	yes	characteristic
54	C₂	#16812137	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₄₂₈
commutator	C₂×C₄×C₁₀₇	C₂³
Frattini	C₂×C₄	C₂²×D₁₀₇
Fitting	#97×C₁₀₇	C₂
socle	C₂²×C₁₀₇	C₂×D₄
hypercenter	#97	D₁₀₇
hypocenter	C₁₀₇	#490
LCS	G ▷ C₂×C₄×C₁₀₇ ▷ C₂×C₁₀₇ ▷ C₁₀₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #97

Complements

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

N	H ≅ G/N	type
2. #16812101	C₂	semidirect
3. #16812031	C₂	semidirect
4. #97×C₁₀₇	C₂	semidirect
27. C₁₀₇	#490	semidirect
32. #97	D₁₀₇	semidirect