Subgroups — #28334662

Order 13696.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₀₇⋊C₃₂	C₂	1	1	yes	maximal, characteristic
2	#20292453	C₂	1	1	yes	maximal, characteristic
3	#366×C₁₀₇	C₂	1	1	yes	maximal, characteristic
4	#16812043	—	2	1	no	—
5	C₁₀₇⋊C₃₂	C₄	1	2	yes	complemented
6	C₂×C₁₆×C₁₀₇	C₂²	1	1	yes	characteristic
7	#107×C₁₀₇	—	2	1	no	—
8	C₄⋊Dic₁₀₇	—	4	1	no	—
9	C₂×C₈×C₁₀₇	D₄	1	1	yes	characteristic
10	C₄⋊C₄×C₁₀₇	—	4	1	no	—
11	C₁₆×C₁₀₇	C₂×C₄	1	1	yes	characteristic
12	C₁₆×C₁₀₇	Q₈	1	1	yes	characteristic
13	C₂×C₄×C₁₀₇	—	8	1	no	—
14	C₂×C₄×C₁₀₇	D₈	1	1	yes	characteristic
15	C₂×Dic₁₀₇	—	8	1	no	—
16	C₈×C₁₀₇	C₄⋊C₄	1	1	yes	characteristic
17	C₈×C₁₀₇	Q₁₆	1	1	yes	characteristic
18	C₂²×C₁₀₇	D₁₆	1	1	yes	characteristic
19	C₄×C₁₀₇	—	16	1	no	—
20	C₄×C₁₀₇	#107	1	1	yes	characteristic
21	C₄×C₁₀₇	Q₃₂	1	1	yes	characteristic
22	Dic₁₀₇	—	16	1	no	—
23	C₂×C₁₀₇	#366	1	1	yes	characteristic
24	C₂×C₁₀₇	SD₆₄	1	1	yes	characteristic
25	C₂×C₁₀₇	SD₆₄	1	1	yes	characteristic
26	#1424	—	107	1	no	maximal, Sylow
27	C₁₀₇	#1424	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃₂	—	107	1	no	—
29	#366	—	107	1	no	—
30	#366	D₁₀₇	1	1	yes	characteristic
31	C₂×C₁₆	C₂×D₁₀₇	1	1	yes	characteristic
32	#107	—	2	1	no	—
33	#107	—	214	1	no	—
34	C₃₂	—	107	2	no	—
35	C₂×C₈	C₂²⋊D₁₀₇	1	1	yes	characteristic
36	C₄⋊C₄	—	4	1	no	—
37	C₄⋊C₄	—	428	1	no	—
38	C₁₆	Dic₂₁₄	1	1	yes	characteristic
39	C₁₆	C₄×D₁₀₇	1	1	yes	characteristic
40	C₂×C₄	—	8	1	no	—
41	C₂×C₄	—	856	1	no	—
42	C₂×C₄	#13133803	1	1	yes	characteristic
43	C₈	Dic₁₀₇⋊C₄	1	1	yes	characteristic
44	C₈	#13133808	1	1	yes	characteristic
45	C₂²	#16812050	1	1	yes	characteristic
46	C₄	—	16	1	no	—
47	C₄	—	1712	1	no	—
48	C₄	#16812042	1	1	yes	characteristic
49	C₄	#16812055	1	1	yes	characteristic
50	C₂	#20292452	1	1	yes	characteristic
51	C₂	#20292464	1	1	yes	characteristic
52	C₂	#20292465	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#16812050
commutator	C₁₆×C₁₀₇	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₁₀₇
Fitting	#366×C₁₀₇	C₂
socle, prime radical	C₂²×C₁₀₇	D₁₆
cosocle	C₂×C₁₆×C₁₀₇	C₂²
hypercenter	#366	D₁₀₇
hypocenter	C₁₀₇	#1424
LCS	G ▷ C₁₆×C₁₀₇ ▷ C₈×C₁₀₇ ▷ C₄×C₁₀₇ ▷ C₂×C₁₀₇ ▷ C₁₀₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #366

Complements

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

N	H ≅ G/N	type
5. C₁₀₇⋊C₃₂	C₄	semidirect
27. C₁₀₇	#1424	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₀₇⋊C₃₂	2
#20292453	2
#366×C₁₀₇	2
#1424	107