Subgroups — #99×C₁₁₈₁ #49180263

Order 37792.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×C₁₁₈₁	C₂	1	1	yes	maximal, characteristic
2	C₂²⋊C₄×C₁₁₈₁	C₂	1	2	yes	maximal, complemented
3	C₂³×C₁₁₈₁	C₄	1	1	yes	characteristic, complemented
4	C₂³×C₁₁₈₁	C₂²	1	1	yes	characteristic
5	D₄×C₁₁₈₁	—	2	2	no	—
6	C₂×C₄×C₁₁₈₁	—	2	2	no	—
7	C₂×C₄×C₁₁₈₁	C₄	1	1	yes	characteristic, complemented
8	C₂²×C₁₁₈₁	—	2	1	no	—
9	C₂²×C₁₁₈₁	—	4	1	no	—
10	C₂²×C₁₁₈₁	—	4	1	no	—
11	C₂²×C₁₁₈₁	C₂×C₄	1	1	yes	characteristic
12	C₂²×C₁₁₈₁	D₄	1	2	yes	—
13	C₄×C₁₁₈₁	—	2	1	no	—
14	C₄×C₁₁₈₁	—	4	2	no	—
15	C₂×C₁₁₈₁	—	2	2	no	—
16	C₂×C₁₁₈₁	—	2	1	no	—
17	C₂×C₁₁₈₁	—	4	1	no	—
18	C₂×C₁₁₈₁	C₂²⋊C₄	1	1	yes	characteristic
19	C₁₁₈₁	#99	1	1	yes	characteristic, direct product factor, Sylow
20	#99	C₁₁₈₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₂×D₄	C₂×C₁₁₈₁	1	1	yes	characteristic
22	C₂²⋊C₄	C₂×C₁₁₈₁	1	2	yes	complemented
23	C₂³	C₄×C₁₁₈₁	1	1	yes	characteristic, complemented
24	C₂³	C₂²×C₁₁₈₁	1	1	yes	characteristic
25	D₄	—	2	2	no	—
26	C₂×C₄	—	2	2	no	—
27	C₂×C₄	C₄×C₁₁₈₁	1	1	yes	characteristic, complemented
28	C₂²	—	2	1	no	—
29	C₂²	—	4	1	no	—
30	C₂²	—	4	1	no	—
31	C₂²	C₂×C₄×C₁₁₈₁	1	1	yes	characteristic
32	C₂²	D₄×C₁₁₈₁	1	2	yes	—
33	C₄	—	2	1	no	—
34	C₄	—	4	2	no	—
35	C₂	—	2	2	no	—
36	C₂	—	2	1	no	—
37	C₂	—	4	1	no	—
38	C₂	C₂²⋊C₄×C₁₁₈₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₁₈₁	C₂²⋊C₄
commutator	C₂²	C₂×C₄×C₁₁₈₁
Frattini, cosocle	C₂³	C₂²×C₁₁₈₁
prime radical	C₂×D₄×C₁₁₈₁	C₂
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₁₈₁ ◁ C₂³×C₁₁₈₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²⋊C₄×C₁₁₈₁	C₂	semidirect
3. C₂³×C₁₁₈₁	C₄	semidirect
7. C₂×C₄×C₁₁₈₁	C₄	semidirect
19. C₁₁₈₁	#99	direct (N × H)
20. #99	C₁₁₈₁	direct (N × H)
22. C₂²⋊C₄	C₂×C₁₁₈₁	semidirect
23. C₂³	C₄×C₁₁₈₁	semidirect
27. C₂×C₄	C₄×C₁₁₈₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄×C₁₁₈₁	2
C₂²⋊C₄×C₁₁₈₁	2
#99	1181

Subgroups — #99×C1181 #49180263

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #99×C₁₁₈₁ #49180263