Subgroups — #95×D₁₉₉ #27163861

Order 12736.

330 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₁₉₉	C₂	1	3	yes	maximal
2	C₁₉₉⋊#95	C₂	1	3	yes	maximal, complemented
3	#95×C₁₉₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂³×D₁₉₉	C₂²	1	1	yes	characteristic
5	C₂²×Dic₁₉₉	C₂²	1	3	yes	—
6	C₂×C₄×D₁₉₉	—	2	12	no	—
7	C₂×C₄×D₁₉₉	C₄	1	12	yes	complemented
8	C₂²×C₄×C₁₉₉	C₂²	1	3	yes	—
9	C₂²×D₁₉₉	C₂×C₄	1	6	yes	—
10	C₂²×D₁₉₉	D₄	1	6	yes	—
11	C₂²×D₁₉₉	Q₈	1	2	yes	—
12	C₂×Dic₁₉₉	—	2	6	no	—
13	C₂×Dic₁₉₉	C₂×C₄	1	6	yes	complemented
14	C₄×D₁₉₉	—	2	24	no	—
15	C₂³×C₁₉₉	C₂³	1	1	yes	characteristic
16	C₂×C₄×C₁₉₉	—	2	6	no	—
17	C₂×C₄×C₁₉₉	C₂×C₄	1	6	yes	complemented
18	C₂²×C₁₉₉	C₂²×C₄	1	3	yes	—
19	C₂²×C₁₉₉	C₂×D₄	1	3	yes	—
20	C₂²×C₁₉₉	C₂×Q₈	1	1	yes	characteristic
21	C₂×D₁₉₉	C₄²	1	4	yes	—
22	C₂×D₁₉₉	C₂²⋊C₄	1	12	yes	—
23	C₂×D₁₉₉	C₄⋊C₄	1	12	yes	—
24	C₄×C₁₉₉	—	2	6	no	—
25	Dic₁₉₉	—	2	6	no	—
26	C₂×C₁₉₉	C₂×C₄²	1	1	yes	characteristic
27	C₂×C₁₉₉	C₂×C₂²⋊C₄	1	3	yes	—
28	C₂×C₁₉₉	C₂×C₄⋊C₄	1	3	yes	—
29	D₁₉₉	#95	1	8	yes	direct product factor
30	C₁₉₉	C₂×#95	1	1	yes	characteristic, complemented, Sylow
31	C₂×#95	—	199	1	no	maximal, Sylow
32	C₂³×C₄	—	199	3	no	—
33	#95	—	199	3	no	—
34	#95	D₁₉₉	1	1	yes	characteristic, direct product factor
35	C₂⁴	—	199	1	no	—
36	C₂²×C₄	—	398	12	no	—
37	C₂²×C₄	—	199	3	no	—
38	C₂²×C₄	—	199	12	no	—
39	C₂²×C₄	C₂×D₁₉₉	1	3	yes	—
40	C₂³	—	199	6	no	—
41	C₂³	—	199	6	no	—
42	C₂³	—	199	2	no	—
43	C₂³	C₂²×D₁₉₉	1	1	yes	characteristic
44	C₂×C₄	—	2	6	no	—
45	C₂×C₄	—	398	24	no	—
46	C₂×C₄	—	398	6	no	—
47	C₂×C₄	—	199	6	no	—
48	C₂×C₄	C₄×D₁₉₉	1	6	yes	complemented
49	C₂²	—	199	4	no	—
50	C₂²	—	199	12	no	—
51	C₂²	—	199	12	no	—
52	C₂²	C₂×C₄×D₁₉₉	1	3	yes	—
53	C₂²	D₄×D₁₉₉	1	3	yes	—
54	C₂²	Q₈×D₁₉₉	1	1	yes	characteristic
55	C₄	—	2	6	no	—
56	C₄	—	398	6	no	—
57	C₂	—	199	8	no	—
58	C₂	C₄²×D₁₉₉	1	1	yes	characteristic
59	C₂	C₂²⋊C₄×D₁₉₉	1	3	yes	—
60	C₂	C₄⋊C₄×D₁₉₉	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₁₉₉
commutator	C₂×C₁₉₉	C₂×C₄²
Fitting	#95×C₁₉₉	C₂
socle, cosocle	C₂³×C₁₉₉	C₂³
prime radical	C₂³×D₁₉₉	C₂²
hypercenter	#95	D₁₉₉
hypocenter	C₁₉₉	C₂×#95
LCS	G ▷ C₂×C₁₉₉ ▷ C₁₉₉
UCS	C₁ ◁ C₂³ ◁ #95

Complements

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

N	H ≅ G/N	type
2. C₁₉₉⋊#95	C₂	semidirect
3. #95×C₁₉₉	C₂	semidirect
7. C₂×C₄×D₁₉₉	C₄	semidirect
13. C₂×Dic₁₉₉	C₂×C₄	semidirect
17. C₂×C₄×C₁₉₉	C₂×C₄	semidirect
29. D₁₉₉	#95	direct (N × H)
30. C₁₉₉	C₂×#95	semidirect
34. #95	D₁₉₉	direct (N × H)
48. C₂×C₄	C₄×D₁₉₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄×D₁₉₉	2
C₁₉₉⋊#95	2
#95×C₁₉₉	2
C₂×#95	199

Subgroups — #95×D199 #27163861

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #95×D₁₉₉ #27163861