Subgroups — #20293012

Order 6848.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13133805	C₂	1	2	yes	maximal, complemented
2	C₂×D₈₅₆	C₂	1	1	yes	maximal, characteristic
3	#16812098	C₂	1	2	yes	maximal, complemented
4	C₈×Dic₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×Q₁₆×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₄₂₈	C₂²	1	2	yes	—
7	#13133805	—	2	4	no	—
8	D₈₅₆	—	2	2	no	—
9	C₂×C₁₀₇⋊C₈	C₂²	1	1	yes	characteristic
10	(C₂×D₁₀₇)⋊C₄	—	2	4	no	—
11	C₄×Dic₁₀₇	C₂²	1	1	yes	characteristic
12	C₂×Q₈×C₁₀₇	C₂²	1	2	yes	—
13	Q₁₆×C₁₀₇	—	2	2	no	—
14	C₂×C₈×C₁₀₇	C₂²	1	1	yes	characteristic
15	C₂²×D₁₀₇	—	2	2	no	—
16	Q₈×C₁₀₇	—	2	2	no	—
17	Q₈×C₁₀₇	—	2	2	no	—
18	C₂×C₄×C₁₀₇	—	2	2	no	—
19	C₂×C₄×C₁₀₇	C₂³	1	1	yes	characteristic
20	C₂×Dic₁₀₇	D₄	1	2	yes	—
21	D₄₂₈	—	2	2	no	—
22	D₄₂₈	—	2	2	no	—
23	C₈×C₁₀₇	D₄	1	2	yes	—
24	C₁₀₇⋊C₈	D₄	1	2	yes	—
25	C₂²×C₁₀₇	C₂×D₄	1	1	yes	characteristic
26	C₂×D₁₀₇	—	4	2	no	—
27	C₂×D₁₀₇	—	4	4	no	—
28	C₄×C₁₀₇	—	4	2	no	—
29	C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
30	C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
31	Dic₁₀₇	—	2	2	no	—
32	C₂×C₁₀₇	#127	1	1	yes	characteristic
33	C₂×C₁₀₇	#135	1	2	yes	—
34	D₁₀₇	—	8	2	no	—
35	C₁₀₇	#495	1	1	yes	characteristic, complemented, Sylow
36	#495	—	107	1	no	maximal, Sylow
37	C₂×Q₁₆	D₁₀₇	1	1	yes	characteristic, complemented
38	C₂×SD₁₆	—	107	2	no	—
39	C₂×D₈	—	107	1	no	—
40	#124	—	107	2	no	—
41	C₄×C₈	—	107	1	no	—
42	C₂×Q₈	C₂×D₁₀₇	1	2	yes	—
43	C₂×D₄	—	107	2	no	—
44	Q₁₆	—	2	2	no	—
45	SD₁₆	—	214	4	no	—
46	D₈	—	214	2	no	—
47	C₂×C₈	—	107	1	no	—
48	C₂×C₈	C₂×D₁₀₇	1	1	yes	characteristic
49	C₂²⋊C₄	—	214	4	no	—
50	C₄²	—	107	1	no	—
51	C₂³	—	214	2	no	—
52	Q₈	—	2	2	no	—
53	Q₈	—	2	2	no	—
54	D₄	—	214	2	no	—
55	D₄	—	214	2	no	—
56	C₂×C₄	—	2	2	no	—
57	C₂×C₄	—	107	2	no	—
58	C₂×C₄	C₂²×D₁₀₇	1	1	yes	characteristic
59	C₈	—	107	2	no	—
60	C₈	C₂²⋊D₁₀₇	1	2	yes	—
61	C₂²	—	428	2	no	—
62	C₂²	—	428	4	no	—
63	C₂²	D₄×D₁₀₇	1	1	yes	characteristic
64	C₄	—	4	2	no	—
65	C₄	—	214	2	no	—
66	C₄	D₄×D₁₀₇	1	1	yes	characteristic
67	C₄	C₂×C₂²⋊D₁₀₇	1	1	yes	characteristic
68	C₂	—	856	2	no	—
69	C₂	#16812105	1	1	yes	characteristic
70	C₂	#16812132	1	2	yes	—

	subgroup	G/H
center	C₂²	D₄×D₁₀₇
commutator	C₂×C₄×C₁₀₇	C₂³
Frattini	C₂×C₄	C₂²×D₁₀₇
Fitting	C₂×Q₁₆×C₁₀₇	C₂
socle	C₂²×C₁₀₇	C₂×D₄
hypercenter	C₂×Q₁₆	D₁₀₇
hypocenter	C₁₀₇	#495
LCS	G ▷ C₂×C₄×C₁₀₇ ▷ C₂×C₁₀₇ ▷ C₁₀₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×#13133805	C₂	semidirect
3. #16812098	C₂	semidirect
4. C₈×Dic₁₀₇	C₂	semidirect
5. C₂×Q₁₆×C₁₀₇	C₂	semidirect
35. C₁₀₇	#495	semidirect
37. C₂×Q₁₆	D₁₀₇	semidirect