Subgroups — #28334661

Order 13696.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20292453	C₂	1	2	yes	maximal
2	C₂×C₃₂×C₁₀₇	C₂	1	1	yes	maximal, characteristic
3	#16812043	—	2	2	no	—
4	C₂×C₁₆×C₁₀₇	C₂²	1	1	yes	characteristic
5	C₃₂×C₁₀₇	C₄	1	2	yes	complemented
6	C₄⋊Dic₁₀₇	—	4	2	no	—
7	C₂×C₈×C₁₀₇	D₄	1	1	yes	characteristic
8	C₁₆×C₁₀₇	C₂×C₄	1	1	yes	characteristic
9	C₁₆×C₁₀₇	Q₈	1	1	yes	characteristic
10	C₂×C₄×C₁₀₇	D₈	1	1	yes	characteristic
11	C₂×Dic₁₀₇	—	8	2	no	—
12	C₈×C₁₀₇	C₄⋊C₄	1	1	yes	characteristic
13	C₈×C₁₀₇	Q₁₆	1	1	yes	characteristic
14	C₂²×C₁₀₇	D₁₆	1	1	yes	characteristic
15	C₄×C₁₀₇	#107	1	1	yes	characteristic
16	C₄×C₁₀₇	Q₃₂	1	1	yes	characteristic
17	Dic₁₀₇	—	16	2	no	—
18	C₂×C₁₀₇	#366	1	1	yes	characteristic
19	C₂×C₁₀₇	D₃₂	1	1	yes	characteristic
20	C₂×C₁₀₇	Q₆₄	1	1	yes	characteristic
21	#1423	—	107	1	no	maximal, Sylow
22	C₁₀₇	#1423	1	1	yes	characteristic, complemented, Sylow
23	C₂×C₃₂	D₁₀₇	1	1	yes	characteristic
24	#366	—	107	2	no	—
25	C₂×C₁₆	C₂×D₁₀₇	1	1	yes	characteristic
26	#107	—	214	2	no	—
27	C₃₂	Dic₁₀₇	1	2	yes	complemented
28	C₂×C₈	D₄₂₈	1	1	yes	characteristic
29	C₄⋊C₄	—	428	2	no	—
30	C₁₆	Dic₂₁₄	1	1	yes	characteristic
31	C₁₆	C₂×Dic₁₀₇	1	1	yes	characteristic
32	C₂×C₄	—	856	2	no	—
33	C₂×C₄	D₈₅₆	1	1	yes	characteristic
34	C₈	C₄⋊Dic₁₀₇	1	1	yes	characteristic
35	C₈	Dic₄₂₈	1	1	yes	characteristic
36	C₂²	D₁₇₁₂	1	1	yes	characteristic
37	C₄	—	1712	2	no	—
38	C₄	#16812043	1	1	yes	characteristic
39	C₄	Dic₈₅₆	1	1	yes	characteristic
40	C₂	#20292453	1	1	yes	characteristic
41	C₂	D₃₄₂₄	1	1	yes	characteristic
42	C₂	Dic₁₇₁₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₁₇₁₂
commutator	C₁₆×C₁₀₇	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₁₀₇
Fitting	C₂×C₃₂×C₁₀₇	C₂
socle, prime radical	C₂²×C₁₀₇	D₁₆
cosocle	C₂×C₁₆×C₁₀₇	C₂²
hypercenter	C₂×C₃₂	D₁₀₇
hypocenter	C₁₀₇	#1423
LCS	G ▷ C₁₆×C₁₀₇ ▷ C₈×C₁₀₇ ▷ C₄×C₁₀₇ ▷ C₂×C₁₀₇ ▷ C₁₀₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
5. C₃₂×C₁₀₇	C₄	semidirect
22. C₁₀₇	#1423	semidirect
27. C₃₂	Dic₁₀₇	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#20292453	2
C₂×C₃₂×C₁₀₇	2
#1423	107