Subgroups — #28334536

Order 13696.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20292448	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₀₇⋊C₁₆	C₂	1	1	yes	maximal, characteristic
3	#364×C₁₀₇	C₂	1	1	yes	maximal, characteristic
4	#16812049	—	2	1	no	—
5	C₂×C₁₀₇⋊C₁₆	C₄	1	1	yes	characteristic
6	C₂×C₁₀₇⋊C₁₆	C₄	1	1	yes	characteristic
7	M₃₂×C₁₀₇	—	2	1	no	—
8	C₄×C₈×C₁₀₇	C₂²	1	1	yes	characteristic
9	C₁₀₇⋊C₁₆	—	2	1	no	—
10	C₁₀₇⋊C₁₆	—	4	1	no	—
11	C₁₀₇⋊C₁₆	C₈	1	2	yes	—
12	C₂×C₈×C₁₀₇	C₂×C₄	1	1	yes	characteristic
13	C₂×C₈×C₁₀₇	D₄	1	1	yes	characteristic
14	C₄²×C₁₀₇	Q₈	1	1	yes	characteristic
15	C₁₆×C₁₀₇	—	4	1	no	—
16	C₂×C₄×C₁₀₇	—	2	1	no	—
17	C₂×C₄×C₁₀₇	C₄⋊C₄	1	1	yes	characteristic
18	C₈×C₁₀₇	C₂×C₈	1	1	yes	characteristic
19	C₈×C₁₀₇	M₁₆	1	1	yes	characteristic
20	C₈×C₁₀₇	D₈	1	1	yes	characteristic
21	C₈×C₁₀₇	Q₁₆	1	1	yes	characteristic
22	C₂²×C₁₀₇	#108	1	1	yes	characteristic
23	C₄×C₁₀₇	—	2	2	no	—
24	C₄×C₁₀₇	C₄⋊C₈	1	1	yes	characteristic
25	C₄×C₁₀₇	#107	1	1	yes	characteristic
26	C₂×C₁₀₇	—	2	1	no	—
27	C₂×C₁₀₇	#335	1	1	yes	characteristic
28	#1373	—	107	1	no	maximal, Sylow
29	C₁₀₇	#1373	1	1	yes	characteristic, complemented, Sylow
30	#364	—	107	1	no	—
31	#364	D₁₀₇	1	1	yes	characteristic
32	C₄×C₁₆	—	107	1	no	—
33	M₃₂	—	2	1	no	—
34	M₃₂	—	214	1	no	—
35	C₂×C₁₆	—	107	1	no	—
36	C₂×C₁₆	—	107	1	no	—
37	C₄×C₈	C₂×D₁₀₇	1	1	yes	characteristic
38	C₂×C₈	C₄×D₁₀₇	1	1	yes	characteristic
39	C₂×C₈	C₂²⋊D₁₀₇	1	1	yes	characteristic
40	C₄²	Dic₂₁₄	1	1	yes	characteristic
41	C₁₆	—	4	1	no	—
42	C₁₆	—	107	2	no	—
43	C₁₆	—	428	1	no	—
44	C₁₆	—	214	1	no	—
45	C₂×C₄	—	2	1	no	—
46	C₂×C₄	Dic₁₀₇⋊C₄	1	1	yes	characteristic
47	C₈	C₈×D₁₀₇	1	1	yes	characteristic
48	C₈	#13133801	1	1	yes	characteristic
49	C₈	#13133803	1	1	yes	characteristic
50	C₈	#13133808	1	1	yes	characteristic
51	C₂²	#16812044	1	1	yes	characteristic
52	C₄	—	2	2	no	—
53	C₄	Dic₁₀₇⋊C₈	1	1	yes	characteristic
54	C₄	#16812042	1	1	yes	characteristic
55	C₂	—	2	1	no	—
56	C₂	#20292379	1	1	yes	characteristic

	subgroup	G/H
center	C₈	#13133803
commutator	C₈×C₁₀₇	C₂×C₈
Frattini	C₄×C₈	C₂×D₁₀₇
Fitting	#364×C₁₀₇	C₂
socle	C₂×C₁₀₇	#335
prime radical	C₂²×C₁₀₇	#108
cosocle	C₄×C₈×C₁₀₇	C₂²
hypercenter	#364	D₁₀₇
hypocenter	C₁₀₇	#1373
LCS	G ▷ C₈×C₁₀₇ ▷ C₄×C₁₀₇ ▷ C₂×C₁₀₇ ▷ C₁₀₇
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #364

Complements

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

N	H ≅ G/N	type
29. C₁₀₇	#1373	semidirect

Maximal subgroups

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

subgroup	index
#20292448	2
C₄×C₁₀₇⋊C₁₆	2
#364×C₁₀₇	2
#1373	107