Subgroups — C₂×#16812055 #20293054

Order 6848.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₄₂₈	C₂	1	1	yes	maximal, characteristic
2	#16812055	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₁₀₇⋊C₁₆	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₁₆×C₁₀₇	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₂₁₄	—	2	1	no	—
6	Dic₄₂₈	—	2	1	no	—
7	Dic₄₂₈	C₂²	1	2	yes	—
8	C₁₀₇⋊C₁₆	C₂²	1	2	yes	—
9	C₂×Q₈×C₁₀₇	—	2	1	no	—
10	Q₁₆×C₁₀₇	—	2	1	no	—
11	Q₁₆×C₁₀₇	C₂²	1	2	yes	—
12	C₂×C₈×C₁₀₇	C₂²	1	1	yes	characteristic
13	Q₈×C₁₀₇	—	2	2	no	—
14	Q₈×C₁₀₇	—	4	1	no	—
15	C₂×C₄×C₁₀₇	—	4	1	no	—
16	C₂×C₄×C₁₀₇	D₄	1	1	yes	characteristic
17	C₂×Dic₁₀₇	—	4	1	no	—
18	Dic₂₁₄	—	2	2	no	—
19	Dic₂₁₄	—	4	1	no	—
20	C₈×C₁₀₇	D₄	1	1	yes	characteristic
21	C₈×C₁₀₇	C₂³	1	1	yes	characteristic
22	C₂²×C₁₀₇	D₈	1	1	yes	characteristic
23	C₄×C₁₀₇	—	4	2	no	—
24	C₄×C₁₀₇	D₈	1	1	yes	characteristic
25	C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
26	Dic₁₀₇	—	4	2	no	—
27	C₂×C₁₀₇	Q₃₂	1	2	yes	complemented
28	C₂×C₁₀₇	C₂×D₈	1	1	yes	characteristic
29	C₁₀₇	C₂×Q₃₂	1	1	yes	characteristic, complemented, Sylow
30	C₂×Q₃₂	—	107	1	no	maximal, Sylow
31	C₂×Q₁₆	—	107	1	no	—
32	C₂×Q₁₆	D₁₀₇	1	1	yes	characteristic
33	Q₃₂	—	107	4	no	—
34	C₂×C₁₆	—	107	1	no	—
35	C₂×Q₈	—	2	1	no	—
36	C₂×Q₈	—	214	1	no	—
37	Q₁₆	—	2	1	no	—
38	Q₁₆	—	107	2	no	—
39	Q₁₆	—	214	1	no	—
40	Q₁₆	C₂×D₁₀₇	1	2	yes	—
41	C₂×C₈	C₂×D₁₀₇	1	1	yes	characteristic
42	C₁₆	—	107	2	no	—
43	Q₈	—	2	2	no	—
44	Q₈	—	4	1	no	—
45	Q₈	—	428	1	no	—
46	Q₈	—	214	2	no	—
47	C₂×C₄	—	4	1	no	—
48	C₂×C₄	—	428	1	no	—
49	C₂×C₄	C₂²⋊D₁₀₇	1	1	yes	characteristic
50	C₈	C₂²⋊D₁₀₇	1	1	yes	characteristic
51	C₈	C₂²×D₁₀₇	1	1	yes	characteristic
52	C₂²	#13133803	1	1	yes	characteristic
53	C₄	—	4	2	no	—
54	C₄	—	428	2	no	—
55	C₄	#13133803	1	1	yes	characteristic
56	C₄	C₂×C₂²⋊D₁₀₇	1	1	yes	characteristic
57	C₂	#16812055	1	2	yes	direct product factor
58	C₂	C₂×#13133803	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#13133803
commutator	C₈×C₁₀₇	C₂³
Frattini	C₈	C₂²×D₁₀₇
Fitting	C₂×Q₁₆×C₁₀₇	C₂
socle	C₂²×C₁₀₇	D₈
hypercenter	C₂×Q₁₆	D₁₀₇
hypocenter	C₁₀₇	C₂×Q₃₂
LCS	G ▷ C₈×C₁₀₇ ▷ C₄×C₁₀₇ ▷ C₂×C₁₀₇ ▷ C₁₀₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
2. #16812055	C₂	direct (N × H)
27. C₂×C₁₀₇	Q₃₂	semidirect
29. C₁₀₇	C₂×Q₃₂	semidirect
57. C₂	#16812055	direct (N × H)

Subgroups — C2×#16812055 #20293054

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#16812055 #20293054