Subgroups — #20292881

Order 6848.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₈₅₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#13133801	C₂	1	1	yes	maximal, characteristic, complemented
3	#16812084	C₂	1	2	yes	maximal, complemented
4	#16812029	C₂	1	2	yes	maximal, complemented
5	#106×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₄₂₈	—	2	2	no	—
7	C₂×D₄₂₈	C₂²	1	2	yes	—
8	C₂×C₄×D₁₀₇	C₂²	1	1	yes	characteristic
9	D₈₅₆	—	2	2	no	—
10	#13133801	—	2	2	no	—
11	C₂×C₁₀₇⋊C₈	C₂²	1	1	yes	characteristic
12	(C₂×D₁₀₇)⋊C₄	—	2	2	no	—
13	C₂×C₈×C₁₀₇	C₂²	1	1	yes	characteristic
14	C₄⋊C₄×C₁₀₇	C₂²	1	2	yes	—
15	C₂²×D₁₀₇	—	2	2	no	—
16	C₂²×D₁₀₇	D₄	1	1	yes	characteristic
17	C₂×C₄×C₁₀₇	—	2	2	no	—
18	C₂×C₄×C₁₀₇	C₂³	1	1	yes	characteristic
19	C₂×Dic₁₀₇	D₄	1	1	yes	characteristic
20	D₄₂₈	—	2	2	no	—
21	D₄₂₈	—	2	2	no	—
22	D₄₂₈	—	4	4	no	—
23	C₄×D₁₀₇	—	2	1	no	—
24	C₄×D₁₀₇	—	2	1	no	—
25	C₈×C₁₀₇	D₄	1	2	yes	complemented
26	C₁₀₇⋊C₈	—	2	1	no	—
27	C₂²×C₁₀₇	C₂×D₄	1	1	yes	characteristic
28	C₂×D₁₀₇	—	2	1	no	—
29	C₂×D₁₀₇	—	2	2	no	—
30	C₂×D₁₀₇	—	4	2	no	—
31	C₂×D₁₀₇	—	4	2	no	—
32	C₂×D₁₀₇	—	4	2	no	—
33	C₄×C₁₀₇	—	4	2	no	—
34	C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
35	C₄×C₁₀₇	#41	1	1	yes	characteristic
36	Dic₁₀₇	—	2	1	no	—
37	C₂×C₁₀₇	#121	1	1	yes	characteristic
38	C₂×C₁₀₇	AGL(1,ℤ/8)	1	2	yes	—
39	D₁₀₇	—	4	1	no	—
40	D₁₀₇	—	8	2	no	—
41	C₁₀₇	#469	1	1	yes	characteristic, complemented, Sylow
42	#469	—	107	1	no	maximal, Sylow
43	C₂×D₈	—	107	1	no	—
44	C₂×M₁₆	—	107	1	no	—
45	#121	—	107	2	no	—
46	#106	D₁₀₇	1	1	yes	characteristic, complemented
47	#102	—	107	2	no	—
48	C₂×D₄	—	107	2	no	—
49	C₂×D₄	—	214	2	no	—
50	C₂²×C₄	—	107	1	no	—
51	D₈	—	214	2	no	—
52	M₁₆	—	214	2	no	—
53	C₂×C₈	—	107	1	no	—
54	C₂×C₈	C₂×D₁₀₇	1	1	yes	characteristic
55	C₄⋊C₄	C₂×D₁₀₇	1	2	yes	—
56	C₂²⋊C₄	—	214	2	no	—
57	C₂³	—	107	1	no	—
58	C₂³	—	214	2	no	—
59	D₄	—	428	4	no	—
60	D₄	—	214	2	no	—
61	D₄	—	214	2	no	—
62	C₂×C₄	—	2	2	no	—
63	C₂×C₄	—	107	1	no	—
64	C₂×C₄	—	214	1	no	—
65	C₂×C₄	—	214	1	no	—
66	C₂×C₄	C₂²×D₁₀₇	1	1	yes	characteristic
67	C₈	—	214	1	no	—
68	C₈	D₄₂₈	1	2	yes	complemented
69	C₂²	—	428	2	no	—
70	C₂²	—	428	2	no	—
71	C₂²	—	428	2	no	—
72	C₂²	—	214	1	no	—
73	C₂²	—	214	2	no	—
74	C₂²	D₄×D₁₀₇	1	1	yes	characteristic
75	C₄	—	4	2	no	—
76	C₄	—	214	1	no	—
77	C₄	C₂×D₄₂₈	1	1	yes	characteristic
78	C₄	#13133819	1	1	yes	characteristic
79	C₂	—	856	2	no	—
80	C₂	—	428	1	no	—
81	C₂	#16812084	1	1	yes	characteristic
82	C₂	#16812136	1	2	yes	—

	subgroup	G/H
center	C₂²	D₄×D₁₀₇
commutator	C₂×C₄×C₁₀₇	C₂³
Frattini	C₂×C₄	C₂²×D₁₀₇
Fitting	#106×C₁₀₇	C₂
socle	C₂²×C₁₀₇	C₂×D₄
hypercenter	#106	D₁₀₇
hypocenter	C₁₀₇	#469
LCS	G ▷ C₂×C₄×C₁₀₇ ▷ C₂×C₁₀₇ ▷ C₁₀₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

Complements

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

N	H ≅ G/N	type
1. C₂×D₈₅₆	C₂	semidirect
2. C₂×#13133801	C₂	semidirect
3. #16812084	C₂	semidirect
4. #16812029	C₂	semidirect
5. #106×C₁₀₇	C₂	semidirect
25. C₈×C₁₀₇	D₄	semidirect
41. C₁₀₇	#469	semidirect
46. #106	D₁₀₇	semidirect
68. C₈	D₄₂₈	semidirect