Subgroups — #44542913

Order 31936.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₉₉₆	C₂	1	1	yes	maximal, characteristic
2	#30630291	C₂	1	1	yes	maximal, characteristic
3	#108×C₄₉₉	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₉₉₈	—	2	1	no	—
5	Dic₁₉₉₆	—	2	1	no	—
6	Dic₁₉₉₆	C₄	1	2	yes	—
7	C₄₉₉⋊C₁₆	—	2	1	no	—
8	M₁₆×C₄₉₉	—	2	1	no	—
9	C₂×C₈×C₄₉₉	C₂²	1	1	yes	characteristic
10	Dic₉₉₈	—	2	2	no	—
11	Dic₉₉₈	—	4	1	no	—
12	C₂×Dic₄₉₉	—	4	1	no	—
13	C₂×C₄×C₄₉₉	D₄	1	1	yes	characteristic
14	C₈×C₄₉₉	—	4	1	no	—
15	C₈×C₄₉₉	C₂×C₄	1	1	yes	characteristic
16	C₈×C₄₉₉	D₄	1	1	yes	characteristic
17	C₂²×C₄₉₉	SD₁₆	1	1	yes	characteristic
18	C₄×C₄₉₉	C₂²⋊C₄	1	1	yes	characteristic
19	C₄×C₄₉₉	D₈	1	1	yes	characteristic
20	Dic₄₉₉	—	4	2	no	—
21	C₂×C₄₉₉	—	2	1	no	—
22	C₂×C₄₉₉	#102	1	1	yes	characteristic
23	C₄₉₉	#362	1	1	yes	characteristic, complemented, Sylow
24	#362	—	499	1	no	maximal, Sylow
25	C₂×Q₁₆	—	499	1	no	—
26	M₃₂	—	499	1	no	—
27	#108	D₄₉₉	1	1	yes	characteristic
28	C₂×Q₈	—	998	1	no	—
29	Q₁₆	—	998	1	no	—
30	Q₁₆	—	499	2	no	—
31	M₁₆	—	2	1	no	—
32	C₂×C₈	C₂×D₄₉₉	1	1	yes	characteristic
33	C₁₆	—	998	1	no	—
34	Q₈	—	1996	1	no	—
35	Q₈	—	998	2	no	—
36	C₂×C₄	—	1996	1	no	—
37	C₂×C₄	C₂²⋊D₄₉₉	1	1	yes	characteristic
38	C₈	—	4	1	no	—
39	C₈	C₄×D₄₉₉	1	1	yes	characteristic
40	C₈	D₁₉₉₆	1	1	yes	characteristic
41	C₂²	#22547798	1	1	yes	characteristic
42	C₄	—	1996	2	no	—
43	C₄	(C₂×D₄₉₉)⋊C₄	1	1	yes	characteristic
44	C₄	#22547796	1	1	yes	characteristic
45	C₂	—	2	1	no	—
46	C₂	#30630271	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#30630271
commutator	C₈×C₄₉₉	C₂×C₄
Frattini	C₂×C₈	C₂×D₄₉₉
Fitting	#108×C₄₉₉	C₂
socle	C₂×C₄₉₉	#102
prime radical	C₂²×C₄₉₉	SD₁₆
cosocle	C₂×C₈×C₄₉₉	C₂²
hypercenter	#108	D₄₉₉
hypocenter	C₄₉₉	#362
LCS	G ▷ C₈×C₄₉₉ ▷ C₄×C₄₉₉ ▷ C₂×C₄₉₉ ▷ C₄₉₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #108

Complements

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

N	H ≅ G/N	type
23. C₄₉₉	#362	semidirect

Maximal subgroups

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

subgroup	index
C₂×Dic₁₉₉₆	2
#30630291	2
#108×C₄₉₉	2
#362	499