Subgroups — #34062637

Order 19168.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₂₃₉₆	C₂	1	1	yes	maximal, characteristic
2	C₄⋊Dic₅₉₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₈×C₅₉₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×D₅₉₉	—	2	1	no	—
5	D₂₃₉₆	—	2	1	no	—
6	D₂₃₉₆	C₄	1	2	yes	complemented
7	C₂×Dic₅₉₉	—	2	1	no	—
8	C₂×C₄×C₅₉₉	C₂²	1	1	yes	characteristic
9	C₈×C₅₉₉	—	2	1	no	—
10	C₂²×C₅₉₉	D₄	1	1	yes	characteristic
11	C₂×D₅₉₉	—	2	2	no	—
12	C₂×D₅₉₉	—	4	1	no	—
13	C₂×D₅₉₉	—	4	1	no	—
14	C₄×C₅₉₉	C₂×C₄	1	1	yes	characteristic
15	C₄×C₅₉₉	D₄	1	1	yes	characteristic
16	Dic₅₉₉	—	4	1	no	—
17	C₂×C₅₉₉	C₂²⋊C₄	1	1	yes	characteristic
18	C₂×C₅₉₉	D₈	1	1	yes	characteristic
19	C₂×C₅₉₉	SD₁₆	1	1	yes	characteristic
20	D₅₉₉	—	4	2	no	—
21	C₅₉₉	#102	1	1	yes	characteristic, complemented, Sylow
22	#102	—	599	1	no	maximal, Sylow
23	C₂×D₄	—	599	1	no	—
24	C₂×C₈	D₅₉₉	1	1	yes	characteristic, complemented
25	C₄⋊C₄	—	599	1	no	—
26	C₂³	—	1198	1	no	—
27	D₄	—	599	2	no	—
28	D₄	—	1198	1	no	—
29	C₂×C₄	—	1198	1	no	—
30	C₂×C₄	C₂×D₅₉₉	1	1	yes	characteristic
31	C₈	—	2	1	no	—
32	C₂²	—	2396	1	no	—
33	C₂²	—	2396	1	no	—
34	C₂²	—	1198	2	no	—
35	C₂²	D₂₃₉₆	1	1	yes	characteristic
36	C₄	—	2396	1	no	—
37	C₄	C₄×D₅₉₉	1	1	yes	characteristic
38	C₄	C₂²⋊D₅₉₉	1	1	yes	characteristic
39	C₂	—	2396	2	no	—
40	C₂	(C₂×D₅₉₉)⋊C₄	1	1	yes	characteristic
41	C₂	D₄₇₉₂	1	1	yes	characteristic
42	C₂	#23751067	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₂₃₉₆
commutator	C₄×C₅₉₉	C₂×C₄
Frattini	C₂×C₄	C₂×D₅₉₉
Fitting	C₂×C₈×C₅₉₉	C₂
socle	C₂²×C₅₉₉	D₄
prime radical	C₂×D₂₃₉₆	C₂
cosocle	C₂×C₄×C₅₉₉	C₂²
hypercenter	C₂×C₈	D₅₉₉
hypocenter	C₅₉₉	#102
LCS	G ▷ C₄×C₅₉₉ ▷ C₂×C₅₉₉ ▷ C₅₉₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
2. C₄⋊Dic₅₉₉	C₂	semidirect
3. C₂×C₈×C₅₉₉	C₂	semidirect
6. D₂₃₉₆	C₄	semidirect
21. C₅₉₉	#102	semidirect
24. C₂×C₈	D₅₉₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₂₃₉₆	2
C₄⋊Dic₅₉₉	2
C₂×C₈×C₅₉₉	2
#102	599