Subgroups — C₂×#16812101 #20293149

Order 6848.

226 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16812101	C₂	1	8	yes	maximal, direct product factor
2	C₂×C₄⋊Dic₁₀₇	C₂	1	2	yes	maximal
3	C₂×Dic₁₀₇⋊C₄	C₂	1	4	yes	maximal
4	C₂×C₄²×C₁₀₇	C₂	1	1	yes	maximal, characteristic
5	C₂²×Dic₁₀₇	C₂²	1	4	yes	—
6	C₄⋊Dic₁₀₇	C₂²	1	8	yes	—
7	Dic₁₀₇⋊C₄	C₂²	1	16	yes	—
8	C₂²×C₄×C₁₀₇	C₂²	1	2	yes	—
9	C₂²×C₄×C₁₀₇	C₂²	1	1	yes	characteristic
10	C₄²×C₁₀₇	C₂²	1	4	yes	—
11	C₂³×C₁₀₇	C₂³	1	1	yes	characteristic
12	C₂×C₄×C₁₀₇	—	2	4	no	—
13	C₂×C₄×C₁₀₇	Q₈	1	4	yes	—
14	C₂×C₄×C₁₀₇	C₂³	1	4	yes	—
15	C₂×C₄×C₁₀₇	C₂³	1	2	yes	—
16	C₂×Dic₁₀₇	—	2	8	no	—
17	C₂×Dic₁₀₇	C₂³	1	8	yes	—
18	C₂²×C₁₀₇	C₂×Q₈	1	2	yes	—
19	C₂²×C₁₀₇	#41	1	4	yes	—
20	C₂²×C₁₀₇	C₂⁴	1	1	yes	characteristic
21	C₄×C₁₀₇	—	2	4	no	—
22	C₄×C₁₀₇	C₂×Q₈	1	4	yes	—
23	Dic₁₀₇	—	2	8	no	—
24	C₂×C₁₀₇	#125	1	4	yes	complemented
25	C₂×C₁₀₇	C₂²×Q₈	1	1	yes	characteristic
26	C₂×C₁₀₇	C₂×#41	1	2	yes	—
27	C₁₀₇	C₂×#125	1	1	yes	characteristic, complemented, Sylow
28	C₂×#125	—	107	1	no	maximal, Sylow
29	#125	—	107	8	no	—
30	C₂×C₄⋊C₄	—	107	4	no	—
31	C₂×C₄⋊C₄	—	107	2	no	—
32	C₂×C₄²	D₁₀₇	1	1	yes	characteristic
33	C₂²×C₄	—	107	4	no	—
34	C₂²×C₄	C₂×D₁₀₇	1	2	yes	—
35	C₂²×C₄	C₂×D₁₀₇	1	1	yes	characteristic
36	C₄⋊C₄	—	107	16	no	—
37	C₄⋊C₄	—	107	8	no	—
38	C₄²	C₂×D₁₀₇	1	4	yes	—
39	C₂³	C₂²×D₁₀₇	1	1	yes	characteristic
40	C₂×C₄	—	2	4	no	—
41	C₂×C₄	—	107	8	no	—
42	C₂×C₄	—	214	8	no	—
43	C₂×C₄	Dic₂₁₄	1	4	yes	—
44	C₂×C₄	C₂²×D₁₀₇	1	4	yes	—
45	C₂×C₄	C₂²×D₁₀₇	1	2	yes	—
46	C₂²	C₂×Dic₂₁₄	1	2	yes	—
47	C₂²	#13133818	1	4	yes	—
48	C₂²	C₂³×D₁₀₇	1	1	yes	characteristic
49	C₄	—	2	4	no	—
50	C₄	—	214	8	no	—
51	C₄	C₂×Dic₂₁₄	1	4	yes	—
52	C₂	#16812101	1	4	yes	direct product factor
53	C₂	C₂²×Dic₂₁₄	1	1	yes	characteristic
54	C₂	C₂×#13133818	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂²×D₁₀₇
commutator	C₂²×C₁₀₇	C₂⁴
Frattini	C₂²	C₂³×D₁₀₇
Fitting	C₂×C₄²×C₁₀₇	C₂
socle	C₂³×C₁₀₇	C₂³
hypercenter	C₂×C₄²	D₁₀₇
hypocenter	C₁₀₇	C₂×#125
LCS	G ▷ C₂²×C₁₀₇ ▷ C₁₀₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
1. #16812101	C₂	direct (N × H)
24. C₂×C₁₀₇	#125	semidirect
27. C₁₀₇	C₂×#125	semidirect
52. C₂	#16812101	direct (N × H)

Subgroups — C2×#16812101 #20293149

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#16812101 #20293149