Subgroups — #50305672

Order 38336.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#34062655	C₂	1	2	yes	maximal, complemented
2	C₂×M₁₆×C₅₉₉	C₂	1	1	yes	maximal, characteristic
3	C₅₉₉⋊C₁₆	—	2	2	no	—
4	C₂²×C₄×C₅₉₉	C₄	1	1	yes	characteristic
5	M₁₆×C₅₉₉	—	2	2	no	—
6	C₂×C₈×C₅₉₉	C₄	1	1	yes	characteristic
7	C₂×C₈×C₅₉₉	C₂²	1	1	yes	characteristic
8	C₂³×C₅₉₉	C₈	1	1	yes	characteristic
9	C₂×C₄×C₅₉₉	—	2	1	no	—
10	C₂×C₄×C₅₉₉	—	2	1	no	—
11	C₂×C₄×C₅₉₉	C₈	1	1	yes	characteristic
12	C₂×C₄×C₅₉₉	C₂×C₄	1	1	yes	characteristic
13	C₈×C₅₉₉	—	2	1	no	—
14	C₈×C₅₉₉	D₄	1	2	yes	—
15	C₂²×C₅₉₉	—	2	1	no	—
16	C₂²×C₅₉₉	—	4	1	no	—
17	C₂²×C₅₉₉	C₂×C₈	1	1	yes	characteristic
18	C₄×C₅₉₉	—	2	1	no	—
19	C₄×C₅₉₉	C₂²⋊C₄	1	1	yes	characteristic
20	C₄×C₅₉₉	M₁₆	1	1	yes	characteristic
21	C₂×C₅₉₉	—	2	1	no	—
22	C₂×C₅₉₉	—	4	1	no	—
23	C₂×C₅₉₉	C₂²⋊C₈	1	1	yes	characteristic
24	C₅₉₉	#349	1	1	yes	characteristic, complemented, Sylow
25	#349	—	599	1	no	maximal, Sylow
26	C₂×M₁₆	D₅₉₉	1	1	yes	characteristic
27	M₃₂	—	599	2	no	—
28	C₂²×C₄	Dic₅₉₉	1	1	yes	characteristic
29	M₁₆	—	2	2	no	—
30	C₂×C₈	Dic₅₉₉	1	1	yes	characteristic
31	C₂×C₈	C₂×D₅₉₉	1	1	yes	characteristic
32	C₁₆	—	1198	2	no	—
33	C₂³	C₅₉₉⋊C₈	1	1	yes	characteristic
34	C₂×C₄	—	2	1	no	—
35	C₂×C₄	—	2	1	no	—
36	C₂×C₄	C₅₉₉⋊C₈	1	1	yes	characteristic
37	C₂×C₄	C₂×Dic₅₉₉	1	1	yes	characteristic
38	C₈	—	2	1	no	—
39	C₈	C₂²⋊D₅₉₉	1	2	yes	—
40	C₂²	—	2	1	no	—
41	C₂²	—	4	1	no	—
42	C₂²	C₂×C₅₉₉⋊C₈	1	1	yes	characteristic
43	C₄	—	2	1	no	—
44	C₄	C₂²⋊Dic₅₉₉	1	1	yes	characteristic
45	C₄	#23751062	1	1	yes	characteristic
46	C₂	—	2	1	no	—
47	C₂	—	4	1	no	—
48	C₂	C₂²⋊(C₅₉₉⋊C₈)	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²⋊Dic₅₉₉
commutator	C₂²×C₅₉₉	C₂×C₈
Frattini	C₂×C₈	C₂×D₅₉₉
Fitting	C₂×M₁₆×C₅₉₉	C₂
socle	C₂×C₅₉₉	C₂²⋊C₈
prime radical	C₂³×C₅₉₉	C₈
cosocle	C₂×C₈×C₅₉₉	C₂²
hypercenter	C₂×M₁₆	D₅₉₉
hypocenter	C₅₉₉	#349
LCS	G ▷ C₂²×C₅₉₉ ▷ C₂×C₅₉₉ ▷ C₅₉₉
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
1. #34062655	C₂	semidirect
24. C₅₉₉	#349	semidirect

Maximal subgroups

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

subgroup	index
#34062655	2
C₂×M₁₆×C₅₉₉	2
#349	599