Subgroups — #50305673

Order 38336.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#34062721	C₂	1	1	yes	maximal, characteristic
2	#34062655	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₆×C₅₉₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#23751078	C₄	1	1	yes	characteristic
5	#23751062	C₄	1	1	yes	characteristic
6	#23751061	—	2	1	no	—
7	C₈×D₅₉₉	—	2	1	no	—
8	C₅₉₉⋊C₁₆	—	2	1	no	—
9	C₂×C₈×C₅₉₉	C₂²	1	1	yes	characteristic
10	C₁₆×C₅₉₉	—	2	1	no	—
11	Dic₁₁₉₈	C₈	1	1	yes	characteristic
12	D₂₃₉₆	C₈	1	1	yes	characteristic
13	C₂²⋊D₅₉₉	—	2	1	no	—
14	C₄×D₅₉₉	—	2	1	no	—
15	C₅₉₉⋊C₈	—	2	1	no	—
16	C₂×C₄×C₅₉₉	C₂×C₄	1	1	yes	characteristic
17	C₈×C₅₉₉	D₄	1	1	yes	characteristic
18	C₈×C₅₉₉	D₄	1	1	yes	characteristic
19	C₂²×C₅₉₉	M₁₆	1	1	yes	characteristic
20	C₂×D₅₉₉	—	2	1	no	—
21	C₄×C₅₉₉	C₂²⋊C₄	1	1	yes	characteristic
22	C₄×C₅₉₉	C₂×C₈	1	1	yes	characteristic
23	Dic₅₉₉	—	2	1	no	—
24	C₂×C₅₉₉	—	2	1	no	—
25	C₂×C₅₉₉	C₂²⋊C₈	1	1	yes	characteristic
26	D₅₉₉	—	4	1	no	—
27	C₅₉₉	#350	1	1	yes	characteristic, complemented, Sylow
28	#350	—	599	1	no	maximal, Sylow
29	#131	—	599	1	no	—
30	M₃₂	—	599	1	no	—
31	C₂×C₁₆	D₅₉₉	1	1	yes	characteristic, complemented
32	#41	—	599	1	no	—
33	M₁₆	—	599	1	no	—
34	M₁₆	—	1198	1	no	—
35	C₂×C₈	—	1198	1	no	—
36	C₂×C₈	C₂×D₅₉₉	1	1	yes	characteristic
37	C₁₆	—	2	1	no	—
38	C₁₆	—	1198	1	no	—
39	Q₈	—	599	1	no	—
40	D₄	—	599	1	no	—
41	D₄	—	1198	1	no	—
42	C₂×C₄	—	1198	1	no	—
43	C₂×C₄	C₄×D₅₉₉	1	1	yes	characteristic
44	C₈	—	1198	1	no	—
45	C₈	C₂²⋊D₅₉₉	1	1	yes	characteristic
46	C₈	D₂₃₉₆	1	1	yes	characteristic
47	C₂²	—	1198	1	no	—
48	C₂²	#23751061	1	1	yes	characteristic
49	C₄	—	1198	1	no	—
50	C₄	(C₂×D₅₉₉)⋊C₄	1	1	yes	characteristic
51	C₄	C₈×D₅₉₉	1	1	yes	characteristic
52	C₂	—	2	1	no	—
53	C₂	—	2396	1	no	—
54	C₂	(C₂×D₅₉₉)⋊C₈	1	1	yes	characteristic

	subgroup	G/H
center	C₈	D₂₃₉₆
commutator	C₄×C₅₉₉	C₂×C₈
Frattini	C₂×C₈	C₂×D₅₉₉
Fitting	C₂×C₁₆×C₅₉₉	C₂
socle	C₂×C₅₉₉	C₂²⋊C₈
prime radical	#23751078	C₄
cosocle	C₂×C₈×C₅₉₉	C₂²
hypercenter	C₂×C₁₆	D₅₉₉
hypocenter	C₅₉₉	#350
LCS	G ▷ C₄×C₅₉₉ ▷ C₂×C₅₉₉ ▷ C₅₉₉
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
2. #34062655	C₂	semidirect
3. C₂×C₁₆×C₅₉₉	C₂	semidirect
27. C₅₉₉	#350	semidirect
31. C₂×C₁₆	D₅₉₉	semidirect

Maximal subgroups

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

subgroup	index
#34062721	2
#34062655	2
C₂×C₁₆×C₅₉₉	2
#350	599