Subgroups — C₁₉₉⋊#564 #27164773

Order 12736.

172 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20263947	C₂	1	2	yes	maximal
2	#20263946	C₂	1	4	yes	maximal
3	#20263945	C₂	1	4	yes	maximal
4	#20263945	C₂	1	4	yes	maximal
5	#125×C₁₉₉	C₂	1	1	yes	maximal, characteristic
6	C₄⋊Dic₁₉₉	C₂²	1	2	yes	—
7	C₄⋊Dic₁₉₉	C₂²	1	4	yes	—
8	C₄⋊Dic₁₉₉	C₂²	1	2	yes	—
9	Dic₁₉₉⋊C₄	C₂²	1	4	yes	—
10	Dic₁₉₉⋊C₄	C₂²	1	4	yes	—
11	Dic₁₉₉⋊C₄	C₂²	1	4	yes	—
12	Dic₁₉₉⋊C₄	C₂²	1	4	yes	—
13	C₄×Dic₁₉₉	C₂²	1	4	yes	—
14	C₄⋊C₄×C₁₉₉	C₂²	1	2	yes	—
15	C₄⋊C₄×C₁₉₉	C₂²	1	4	yes	—
16	C₄²×C₁₉₉	C₂²	1	1	yes	characteristic
17	C₂×Dic₁₉₉	C₂³	1	4	yes	—
18	C₂×Dic₁₉₉	C₂³	1	4	yes	—
19	C₂×C₄×C₁₉₉	C₂³	1	1	yes	characteristic
20	C₂×C₄×C₁₉₉	C₂³	1	2	yes	—
21	C₂×C₄×C₁₉₉	C₂³	1	4	yes	—
22	C₂²×C₁₉₉	C₂⁴	1	1	yes	characteristic
23	C₄×C₁₉₉	—	2	2	no	—
24	C₄×C₁₉₉	—	2	4	no	—
25	C₄×C₁₉₉	—	2	1	no	—
26	Dic₁₉₉	—	2	4	no	—
27	Dic₁₉₉	—	2	4	no	—
28	C₂×C₁₉₉	2₋¹⁺⁴	1	2	yes	—
29	C₂×C₁₉₉	2₋¹⁺⁴	1	1	yes	characteristic
30	C₁₉₉	#564	1	1	yes	characteristic, complemented, Sylow
31	#564	—	199	1	no	maximal, Sylow
32	#125	—	199	4	no	—
33	#125	—	199	4	no	—
34	#125	—	199	4	no	—
35	#125	—	199	2	no	—
36	#125	D₁₉₉	1	1	yes	characteristic
37	C₄⋊C₄	—	199	4	no	—
38	C₄⋊C₄	—	199	4	no	—
39	C₄⋊C₄	—	199	4	no	—
40	C₄⋊C₄	—	199	4	no	—
41	C₄⋊C₄	—	199	4	no	—
42	C₄⋊C₄	—	199	2	no	—
43	C₄⋊C₄	—	199	2	no	—
44	C₄⋊C₄	C₂×D₁₉₉	1	2	yes	—
45	C₄⋊C₄	C₂×D₁₉₉	1	4	yes	—
46	C₄²	—	199	4	no	—
47	C₄²	C₂×D₁₉₉	1	1	yes	characteristic
48	C₂×C₄	—	199	4	no	—
49	C₂×C₄	—	199	4	no	—
50	C₂×C₄	C₂²×D₁₉₉	1	4	yes	—
51	C₂×C₄	C₂²×D₁₉₉	1	2	yes	—
52	C₂×C₄	C₂²×D₁₉₉	1	1	yes	characteristic
53	C₂²	C₂³×D₁₉₉	1	1	yes	characteristic
54	C₄	—	2	4	no	—
55	C₄	—	2	2	no	—
56	C₄	—	2	1	no	—
57	C₄	—	398	4	no	—
58	C₄	—	398	4	no	—
59	C₂	#20264002	1	2	yes	—
60	C₂	#20264003	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₁₉₉
commutator, socle, prime radical, cosocle	C₂²×C₁₉₉	C₂⁴
Fitting	#125×C₁₉₉	C₂
hypercenter	#125	D₁₉₉
hypocenter	C₁₉₉	#564
LCS	G ▷ C₂²×C₁₉₉ ▷ C₁₉₉
UCS	C₁ ◁ C₂² ◁ #125

Complements

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

N	H ≅ G/N	type
30. C₁₉₉	#564	semidirect

Maximal subgroups

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

subgroup	index
#20263947	2
#20263946	2
#20263945	2
#125×C₁₉₉	2
#564	199

Subgroups — C199⋊#564 #27164773

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉₉⋊#564 #27164773