Subgroups — #102×C₁₁₅₁ #49145708

Order 36832.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×C₁₁₅₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×C₁₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄⋊C₄×C₁₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂³×C₁₁₅₁	—	2	1	no	—
5	D₄×C₁₁₅₁	—	2	1	no	—
6	D₄×C₁₁₅₁	C₄	1	2	yes	complemented
7	C₂×C₄×C₁₁₅₁	—	2	1	no	—
8	C₂×C₄×C₁₁₅₁	C₂²	1	1	yes	characteristic
9	C₈×C₁₁₅₁	—	2	1	no	—
10	C₂²×C₁₁₅₁	—	2	2	no	—
11	C₂²×C₁₁₅₁	—	4	1	no	—
12	C₂²×C₁₁₅₁	—	4	1	no	—
13	C₂²×C₁₁₅₁	D₄	1	1	yes	characteristic
14	C₄×C₁₁₅₁	—	4	1	no	—
15	C₄×C₁₁₅₁	C₂×C₄	1	1	yes	characteristic
16	C₄×C₁₁₅₁	D₄	1	1	yes	characteristic
17	C₂×C₁₁₅₁	—	4	2	no	—
18	C₂×C₁₁₅₁	C₂²⋊C₄	1	1	yes	characteristic
19	C₂×C₁₁₅₁	D₈	1	1	yes	characteristic
20	C₂×C₁₁₅₁	SD₁₆	1	1	yes	characteristic
21	C₁₁₅₁	#102	1	1	yes	characteristic, direct product factor, Sylow
22	#102	C₁₁₅₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
23	C₂×D₄	C₂×C₁₁₅₁	1	1	yes	characteristic
24	C₂×C₈	C₂×C₁₁₅₁	1	1	yes	characteristic, complemented
25	C₄⋊C₄	C₂×C₁₁₅₁	1	1	yes	characteristic, complemented
26	C₂³	—	2	1	no	—
27	D₄	—	2	1	no	—
28	D₄	C₄×C₁₁₅₁	1	2	yes	complemented
29	C₂×C₄	—	2	1	no	—
30	C₂×C₄	C₂²×C₁₁₅₁	1	1	yes	characteristic
31	C₈	—	2	1	no	—
32	C₂²	—	2	2	no	—
33	C₂²	—	4	1	no	—
34	C₂²	—	4	1	no	—
35	C₂²	D₄×C₁₁₅₁	1	1	yes	characteristic
36	C₄	—	4	1	no	—
37	C₄	C₂×C₄×C₁₁₅₁	1	1	yes	characteristic
38	C₄	D₄×C₁₁₅₁	1	1	yes	characteristic
39	C₂	—	4	2	no	—
40	C₂	C₂²⋊C₄×C₁₁₅₁	1	1	yes	characteristic
41	C₂	D₈×C₁₁₅₁	1	1	yes	characteristic
42	C₂	SD₁₆×C₁₁₅₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₁₅₁	D₄
commutator	C₄	C₂×C₄×C₁₁₅₁
Frattini, cosocle	C₂×C₄	C₂²×C₁₁₅₁
prime radical	C₂×D₄×C₁₁₅₁	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁₅₁ ◁ C₂×C₄×C₁₁₅₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₈×C₁₁₅₁	C₂	semidirect
3. C₄⋊C₄×C₁₁₅₁	C₂	semidirect
6. D₄×C₁₁₅₁	C₄	semidirect
21. C₁₁₅₁	#102	direct (N × H)
22. #102	C₁₁₅₁	direct (N × H)
24. C₂×C₈	C₂×C₁₁₅₁	semidirect
25. C₄⋊C₄	C₂×C₁₁₅₁	semidirect
28. D₄	C₄×C₁₁₅₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄×C₁₁₅₁	2
C₂×C₈×C₁₁₅₁	2
C₄⋊C₄×C₁₁₅₁	2
#102	1151

Subgroups — #102×C1151 #49145708

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #102×C₁₁₅₁ #49145708