Subgroups — #20293240

Order 6848.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16812109	C₂	1	1	yes	maximal, characteristic, complemented
2	#16812104	C₂	1	4	yes	maximal
3	#16812100	C₂	1	4	yes	maximal, complemented
4	#16812089	C₂	1	2	yes	maximal
5	#16812074	C₂	1	2	yes	maximal, complemented
6	#16812066	C₂	1	1	yes	maximal, characteristic
7	#125×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×Dic₂₁₄	C₂²	1	2	yes	—
9	C₂×C₄×D₁₀₇	C₂²	1	1	yes	characteristic
10	C₄⋊Dic₁₀₇	C₂²	1	4	yes	—
11	C₄⋊Dic₁₀₇	C₂²	1	4	yes	—
12	Dic₁₀₇⋊C₄	C₂²	1	2	yes	—
13	Dic₁₀₇⋊C₄	C₂²	1	4	yes	—
14	(C₂×D₁₀₇)⋊C₄	C₂²	1	2	yes	—
15	(C₂×D₁₀₇)⋊C₄	C₂²	1	4	yes	—
16	C₄×Dic₁₀₇	C₂²	1	1	yes	characteristic
17	C₄×Dic₁₀₇	C₂²	1	4	yes	—
18	C₄⋊C₄×C₁₀₇	C₂²	1	2	yes	—
19	C₄⋊C₄×C₁₀₇	C₂²	1	4	yes	—
20	C₄²×C₁₀₇	C₂²	1	1	yes	characteristic
21	C₂²×D₁₀₇	C₂³	1	1	yes	characteristic
22	C₂×C₄×C₁₀₇	C₂³	1	2	yes	—
23	C₂×C₄×C₁₀₇	C₂³	1	4	yes	—
24	C₂×C₄×C₁₀₇	C₂³	1	1	yes	characteristic
25	C₂×Dic₁₀₇	C₂³	1	2	yes	—
26	C₂×Dic₁₀₇	C₂³	1	4	yes	—
27	C₂×Dic₁₀₇	C₂³	1	1	yes	characteristic
28	C₄×D₁₀₇	—	2	2	no	—
29	Dic₂₁₄	—	2	4	no	—
30	C₂²×C₁₀₇	C₂⁴	1	1	yes	characteristic
31	C₂×D₁₀₇	—	2	1	no	—
32	C₂×D₁₀₇	—	2	2	no	—
33	C₄×C₁₀₇	—	2	2	no	—
34	C₄×C₁₀₇	—	2	4	no	—
35	C₄×C₁₀₇	#41	1	2	yes	—
36	Dic₁₀₇	—	2	4	no	—
37	Dic₁₀₇	—	2	1	no	—
38	Dic₁₀₇	—	2	2	no	—
39	C₂×C₁₀₇	C₂×#41	1	1	yes	characteristic
40	C₂×C₁₀₇	2₋¹⁺⁴	1	2	yes	—
41	D₁₀₇	—	4	1	no	—
42	C₁₀₇	#541	1	1	yes	characteristic, complemented, Sylow
43	#541	—	107	1	no	maximal, Sylow
44	C₄⋊Q₈	—	107	1	no	—
45	#126	—	107	4	no	—
46	#125	—	107	4	no	—
47	#125	D₁₀₇	1	1	yes	characteristic, complemented
48	C₂²⋊Q₈	—	107	2	no	—
49	C₄×Q₈	—	107	2	no	—
50	#117	—	107	1	no	—
51	C₂×Q₈	—	107	2	no	—
52	C₂²×C₄	—	107	1	no	—
53	C₄⋊C₄	—	107	2	no	—
54	C₄⋊C₄	—	107	4	no	—
55	C₄⋊C₄	—	107	4	no	—
56	C₄⋊C₄	—	107	4	no	—
57	C₄⋊C₄	C₂×D₁₀₇	1	2	yes	—
58	C₄⋊C₄	C₂×D₁₀₇	1	4	yes	—
59	C₂²⋊C₄	—	107	2	no	—
60	C₂²⋊C₄	—	107	4	no	—
61	C₄²	—	107	1	no	—
62	C₄²	—	107	4	no	—
63	C₄²	C₂×D₁₀₇	1	1	yes	characteristic
64	C₂³	—	107	1	no	—
65	Q₈	—	214	4	no	—
66	C₂×C₄	—	107	2	no	—
67	C₂×C₄	—	107	4	no	—
68	C₂×C₄	—	107	1	no	—
69	C₂×C₄	—	214	2	no	—
70	C₂×C₄	C₂²×D₁₀₇	1	4	yes	—
71	C₂×C₄	C₂²×D₁₀₇	1	2	yes	—
72	C₂×C₄	C₂²×D₁₀₇	1	1	yes	characteristic
73	C₂²	—	214	1	no	—
74	C₂²	—	214	2	no	—
75	C₂²	C₂³×D₁₀₇	1	1	yes	characteristic
76	C₄	—	2	4	no	—
77	C₄	—	2	2	no	—
78	C₄	—	214	1	no	—
79	C₄	—	214	4	no	—
80	C₄	—	214	2	no	—
81	C₄	#13133819	1	2	yes	—
82	C₂	—	428	1	no	—
83	C₂	C₂×#13133819	1	1	yes	characteristic
84	C₂	#16812156	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₁₀₇
commutator, socle	C₂²×C₁₀₇	C₂⁴
Fitting	#125×C₁₀₇	C₂
hypercenter	#125	D₁₀₇
hypocenter	C₁₀₇	#541
LCS	G ▷ C₂²×C₁₀₇ ▷ C₁₀₇
UCS	C₁ ◁ C₂² ◁ #125

Complements

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

N	H ≅ G/N	type
1. #16812109	C₂	semidirect
3. #16812100	C₂	semidirect
5. #16812074	C₂	semidirect
7. #125×C₁₀₇	C₂	semidirect
42. C₁₀₇	#541	semidirect
47. #125	D₁₀₇	semidirect