Subgroups — #27169331

Order 12928.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15692161	C₂	1	1	yes	maximal, characteristic
2	#20265003	C₂	1	1	yes	maximal, characteristic
3	#366×C₁₀₁	C₂	1	1	yes	maximal, characteristic
4	#15692189	—	2	1	no	—
5	#15692161	C₄	1	2	yes	complemented
6	C₂×C₁₆×C₁₀₁	C₂²	1	1	yes	characteristic
7	#107×C₁₀₁	—	2	1	no	—
8	C₄⋊Dic₁₀₁	—	4	1	no	—
9	C₂×C₈×C₁₀₁	D₄	1	1	yes	characteristic
10	C₄⋊C₄×C₁₀₁	—	4	1	no	—
11	C₁₆×C₁₀₁	C₂×C₄	1	1	yes	characteristic
12	C₁₆×C₁₀₁	Q₈	1	1	yes	characteristic
13	C₂×C₄×C₁₀₁	—	8	1	no	—
14	C₂×C₄×C₁₀₁	D₈	1	1	yes	characteristic
15	C₂×Dic₁₀₁	—	8	1	no	—
16	C₈×C₁₀₁	C₄⋊C₄	1	1	yes	characteristic
17	C₈×C₁₀₁	Q₁₆	1	1	yes	characteristic
18	C₂²×C₁₀₁	D₁₆	1	1	yes	characteristic
19	C₄×C₁₀₁	—	16	1	no	—
20	C₄×C₁₀₁	#107	1	1	yes	characteristic
21	C₄×C₁₀₁	Q₃₂	1	1	yes	characteristic
22	Dic₁₀₁	—	16	1	no	—
23	C₂×C₁₀₁	#366	1	1	yes	characteristic
24	C₂×C₁₀₁	D₃₂	1	1	yes	characteristic
25	C₂×C₁₀₁	Q₆₄	1	1	yes	characteristic
26	#1423	—	101	1	no	maximal, Sylow
27	C₁₀₁	#1423	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃₂	—	101	1	no	—
29	#366	—	101	1	no	—
30	#366	D₁₀₁	1	1	yes	characteristic
31	C₂×C₁₆	C₂×D₁₀₁	1	1	yes	characteristic
32	#107	—	2	1	no	—
33	#107	—	202	1	no	—
34	C₃₂	—	101	2	no	—
35	C₂×C₈	C₂²⋊D₁₀₁	1	1	yes	characteristic
36	C₄⋊C₄	—	4	1	no	—
37	C₄⋊C₄	—	404	1	no	—
38	C₁₆	Dic₂₀₂	1	1	yes	characteristic
39	C₁₆	C₄×D₁₀₁	1	1	yes	characteristic
40	C₂×C₄	—	8	1	no	—
41	C₂×C₄	—	808	1	no	—
42	C₂×C₄	#13108059	1	1	yes	characteristic
43	C₈	#13108053	1	1	yes	characteristic
44	C₈	#13108064	1	1	yes	characteristic
45	C₂²	#15692196	1	1	yes	characteristic
46	C₄	—	16	1	no	—
47	C₄	—	1616	1	no	—
48	C₄	#15692188	1	1	yes	characteristic
49	C₄	#15692201	1	1	yes	characteristic
50	C₂	#20265002	1	1	yes	characteristic
51	C₂	#20265012	1	1	yes	characteristic
52	C₂	#20265017	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#15692196
commutator	C₁₆×C₁₀₁	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₁₀₁
Fitting	#366×C₁₀₁	C₂
socle, prime radical	C₂²×C₁₀₁	D₁₆
cosocle	C₂×C₁₆×C₁₀₁	C₂²
hypercenter	#366	D₁₀₁
hypocenter	C₁₀₁	#1423
LCS	G ▷ C₁₆×C₁₀₁ ▷ C₈×C₁₀₁ ▷ C₄×C₁₀₁ ▷ C₂×C₁₀₁ ▷ C₁₀₁
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. #15692161	C₄	semidirect
27. C₁₀₁	#1423	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15692161	2
#20265003	2
#366×C₁₀₁	2
#1423	101