Subgroups — #20292546

Order 6848.

182 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₀₇⋊C₄	C₂	1	3	yes	maximal
2	C₁₀₇⋊#95	C₂	1	3	yes	maximal
3	C₂²×Q₈×C₁₀₇	C₂	1	1	yes	maximal, characteristic
4	C₂²×Dic₁₀₇	C₂²	1	1	yes	characteristic
5	C₂²×Dic₁₀₇	C₂²	1	3	yes	—
6	Dic₁₀₇⋊C₄	—	2	6	no	—
7	C₂×Q₈×C₁₀₇	—	2	6	no	—
8	C₂²×C₄×C₁₀₇	C₂²	1	3	yes	—
9	C₂³×C₁₀₇	C₂³	1	1	yes	characteristic
10	Q₈×C₁₀₇	—	2	8	no	—
11	C₂×C₄×C₁₀₇	—	2	6	no	—
12	C₂×C₄×C₁₀₇	D₄	1	6	yes	—
13	C₂×Dic₁₀₇	—	2	3	no	—
14	C₂×Dic₁₀₇	—	2	3	no	—
15	C₂×Dic₁₀₇	—	2	3	no	—
16	C₂×Dic₁₀₇	Q₈	1	6	yes	complemented
17	C₂²×C₁₀₇	C₂×D₄	1	3	yes	—
18	C₂²×C₁₀₇	C₂×Q₈	1	3	yes	—
19	C₂²×C₁₀₇	#41	1	1	yes	characteristic
20	C₄×C₁₀₇	—	2	6	no	—
21	Dic₁₀₇	—	2	6	no	—
22	Dic₁₀₇	—	4	1	no	—
23	C₂×C₁₀₇	#120	1	1	yes	characteristic
24	C₂×C₁₀₇	C₂²⋊Q₈	1	3	yes	—
25	C₂×C₁₀₇	C₄⋊Q₈	1	3	yes	—
26	C₁₀₇	#395	1	1	yes	characteristic, complemented, Sylow
27	#395	—	107	1	no	maximal, Sylow
28	C₂²×Q₈	D₁₀₇	1	1	yes	characteristic
29	C₂×C₄⋊C₄	—	107	3	no	—
30	#95	—	107	3	no	—
31	C₂×Q₈	—	2	6	no	—
32	C₂²×C₄	—	107	3	no	—
33	C₂²×C₄	—	107	1	no	—
34	C₂²×C₄	C₂×D₁₀₇	1	3	yes	—
35	C₄⋊C₄	—	214	6	no	—
36	C₂³	C₂²×D₁₀₇	1	1	yes	characteristic
37	Q₈	—	2	8	no	—
38	C₂×C₄	—	2	6	no	—
39	C₂×C₄	—	107	6	no	—
40	C₂×C₄	—	214	3	no	—
41	C₂×C₄	—	214	3	no	—
42	C₂×C₄	—	214	3	no	—
43	C₂×C₄	C₂²⋊D₁₀₇	1	6	yes	—
44	C₂²	C₂×C₂²⋊D₁₀₇	1	3	yes	—
45	C₂²	Q₈×D₁₀₇	1	3	yes	—
46	C₂²	#13133819	1	1	yes	characteristic
47	C₄	—	2	6	no	—
48	C₄	—	428	1	no	—
49	C₄	—	214	6	no	—
50	C₂	#16812078	1	1	yes	characteristic
51	C₂	#16812085	1	3	yes	—
52	C₂	#16812107	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₁₀₇
commutator, socle	C₂³×C₁₀₇	C₂³
Fitting	C₂²×Q₈×C₁₀₇	C₂
hypercenter	C₂²×Q₈	D₁₀₇
hypocenter	C₁₀₇	#395
LCS	G ▷ C₂³×C₁₀₇ ▷ C₁₀₇
UCS	C₁ ◁ C₂³ ◁ C₂²×Q₈

Complements

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

N	H ≅ G/N	type
16. C₂×Dic₁₀₇	Q₈	semidirect
26. C₁₀₇	#395	semidirect