Subgroups — #44543447

Order 31936.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30630350	C₂	1	1	yes	maximal, characteristic
2	#30630349	C₂	1	1	yes	maximal, characteristic
3	#30630276	C₂	1	1	yes	maximal, characteristic
4	#30630275	C₂	1	1	yes	maximal, characteristic
5	#30630274	C₂	1	1	yes	maximal, characteristic
6	C₈×Dic₄₉₉	C₂	1	1	yes	maximal, characteristic
7	#103×C₄₉₉	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₉₉₈	—	2	1	no	—
9	C₂×Dic₉₉₈	C₂²	1	1	yes	characteristic
10	C₂×C₄₉₉⋊C₈	C₂²	1	1	yes	characteristic
11	C₄⋊Dic₄₉₉	C₂²	1	1	yes	characteristic
12	Dic₄₉₉⋊C₄	—	2	1	no	—
13	Dic₄₉₉⋊C₄	—	2	1	no	—
14	Dic₄₉₉⋊C₄	—	2	1	no	—
15	C₄×Dic₄₉₉	C₂²	1	1	yes	characteristic
16	C₂×Q₈×C₄₉₉	C₂²	1	1	yes	characteristic
17	C₂×C₈×C₄₉₉	C₂²	1	1	yes	characteristic
18	C₄⋊C₄×C₄₉₉	C₂²	1	1	yes	characteristic
19	Dic₉₉₈	—	2	1	no	—
20	Dic₉₉₈	—	2	1	no	—
21	Dic₉₉₈	—	4	2	no	—
22	C₂×Dic₄₉₉	—	2	1	no	—
23	C₂×Dic₄₉₉	—	2	1	no	—
24	C₂×Dic₄₉₉	D₄	1	1	yes	characteristic
25	C₂×Dic₄₉₉	D₄	1	1	yes	characteristic
26	C₄₉₉⋊C₈	—	2	1	no	—
27	Q₈×C₄₉₉	—	2	1	no	—
28	Q₈×C₄₉₉	—	2	1	no	—
29	C₂×C₄×C₄₉₉	—	2	1	no	—
30	C₂×C₄×C₄₉₉	—	2	1	no	—
31	C₂×C₄×C₄₉₉	C₂³	1	1	yes	characteristic
32	C₈×C₄₉₉	—	2	1	no	—
33	C₂²×C₄₉₉	C₂×D₄	1	1	yes	characteristic
34	C₄×C₄₉₉	—	4	1	no	—
35	C₄×C₄₉₉	—	4	1	no	—
36	C₄×C₄₉₉	#41	1	1	yes	characteristic
37	C₄×C₄₉₉	#41	1	1	yes	characteristic
38	Dic₄₉₉	—	4	1	no	—
39	Dic₄₉₉	—	4	1	no	—
40	Dic₄₉₉	SD₁₆	1	2	yes	—
41	Dic₄₉₉	Q₁₆	1	2	yes	—
42	C₂×C₄₉₉	#124	1	1	yes	characteristic
43	C₂×C₄₉₉	C₂×SD₁₆	1	1	yes	characteristic
44	C₂×C₄₉₉	C₂×Q₁₆	1	1	yes	characteristic
45	C₄₉₉	#487	1	1	yes	characteristic, complemented, Sylow
46	#487	—	499	1	no	maximal, Sylow
47	C₄⋊Q₈	—	499	1	no	—
48	C₄⋊Q₈	—	499	1	no	—
49	#103	—	499	1	no	—
50	#103	—	499	1	no	—
51	#103	—	499	1	no	—
52	#103	D₄₉₉	1	1	yes	characteristic
53	C₄×C₈	—	499	1	no	—
54	C₂×Q₈	—	998	1	no	—
55	C₂×Q₈	—	499	1	no	—
56	C₂×Q₈	C₂×D₄₉₉	1	1	yes	characteristic
57	C₂×C₈	—	499	1	no	—
58	C₂×C₈	C₂×D₄₉₉	1	1	yes	characteristic
59	C₄⋊C₄	—	998	1	no	—
60	C₄⋊C₄	—	998	1	no	—
61	C₄⋊C₄	—	998	1	no	—
62	C₄⋊C₄	—	499	1	no	—
63	C₄⋊C₄	C₂×D₄₉₉	1	1	yes	characteristic
64	C₄²	—	499	1	no	—
65	Q₈	—	2	1	no	—
66	Q₈	—	2	1	no	—
67	Q₈	—	1996	2	no	—
68	Q₈	—	998	1	no	—
69	Q₈	—	998	1	no	—
70	C₂×C₄	—	2	1	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	998	1	no	—
73	C₂×C₄	—	998	1	no	—
74	C₂×C₄	—	499	1	no	—
75	C₂×C₄	—	499	1	no	—
76	C₂×C₄	C₂²×D₄₉₉	1	1	yes	characteristic
77	C₈	—	2	1	no	—
78	C₈	—	998	1	no	—
79	C₂²	D₄×D₄₉₉	1	1	yes	characteristic
80	C₄	—	4	1	no	—
81	C₄	—	4	1	no	—
82	C₄	—	1996	1	no	—
83	C₄	—	1996	1	no	—
84	C₄	—	499	2	no	—
85	C₄	—	499	2	no	—
86	C₄	#22547810	1	1	yes	characteristic
87	C₄	#22547811	1	1	yes	characteristic
88	C₂	#30630337	1	1	yes	characteristic
89	C₂	SD₁₆×D₄₉₉	1	1	yes	characteristic
90	C₂	Q₁₆×D₄₉₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₄₉₉
commutator, cosocle	C₂×C₄×C₄₉₉	C₂³
Frattini	C₂×C₄	C₂²×D₄₉₉
Fitting	#103×C₄₉₉	C₂
socle, prime radical	C₂²×C₄₉₉	C₂×D₄
hypercenter	#103	D₄₉₉
hypocenter	C₄₉₉	#487
LCS	G ▷ C₂×C₄×C₄₉₉ ▷ C₂×C₄₉₉ ▷ C₄₉₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #103

Complements

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

N	H ≅ G/N	type
45. C₄₉₉	#487	semidirect

Maximal subgroups

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

subgroup	index
#30630350	2
#30630349	2
#30630276	2
#30630275	2
#30630274	2
C₈×Dic₄₉₉	2
#103×C₄₉₉	2
#487	499