Subgroups — #44543307

Order 31936.

108 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	C₂×#22547801	C₂	1	1	yes	maximal, characteristic
3	#30630349	C₂	1	1	yes	maximal, characteristic
4	#30630316	C₂	1	1	yes	maximal, characteristic
5	Dic₄₉₉⋊C₈	C₂	1	1	yes	maximal, characteristic
6	#30630274	C₂	1	1	yes	maximal, characteristic
7	#103×C₄₉₉	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₉₉₈	C₂²	1	1	yes	characteristic
9	C₂×Dic₉₉₈	C₂²	1	1	yes	characteristic
10	Dic₁₉₉₆	—	2	2	no	—
11	#22547801	—	2	2	no	—
12	C₂×C₄₉₉⋊C₈	C₂²	1	1	yes	characteristic
13	Dic₄₉₉⋊C₄	—	2	1	no	—
14	Dic₄₉₉⋊C₄	—	2	1	no	—
15	Dic₄₉₉⋊C₄	—	2	1	no	—
16	C₄×Dic₄₉₉	—	2	1	no	—
17	C₄×Dic₄₉₉	C₂²	1	1	yes	characteristic
18	C₂×Q₈×C₄₉₉	C₂²	1	1	yes	characteristic
19	C₂×C₈×C₄₉₉	C₂²	1	1	yes	characteristic
20	C₄⋊C₄×C₄₉₉	C₂²	1	1	yes	characteristic
21	Dic₉₉₈	—	2	1	no	—
22	Dic₉₉₈	—	2	1	no	—
23	Dic₉₉₈	—	2	1	no	—
24	Dic₉₉₈	D₄	1	2	yes	—
25	C₂×Dic₄₉₉	—	2	1	no	—
26	C₂×Dic₄₉₉	—	2	1	no	—
27	C₂×Dic₄₉₉	D₄	1	1	yes	characteristic
28	C₂×Dic₄₉₉	D₄	1	1	yes	characteristic
29	C₄₉₉⋊C₈	—	2	1	no	—
30	Q₈×C₄₉₉	—	2	1	no	—
31	Q₈×C₄₉₉	—	2	1	no	—
32	C₂×C₄×C₄₉₉	—	2	1	no	—
33	C₂×C₄×C₄₉₉	—	2	1	no	—
34	C₂×C₄×C₄₉₉	C₂³	1	1	yes	characteristic
35	C₈×C₄₉₉	—	2	1	no	—
36	C₂²×C₄₉₉	C₂×D₄	1	1	yes	characteristic
37	C₄×C₄₉₉	—	4	1	no	—
38	C₄×C₄₉₉	—	4	1	no	—
39	C₄×C₄₉₉	C₂×D₄	1	1	yes	characteristic
40	C₄×C₄₉₉	#41	1	1	yes	characteristic
41	Dic₄₉₉	—	2	2	no	—
42	Dic₄₉₉	—	2	1	no	—
43	Dic₄₉₉	—	4	1	no	—
44	Dic₄₉₉	Q₁₆	1	2	yes	complemented
45	C₂×C₄₉₉	#121	1	1	yes	characteristic
46	C₂×C₄₉₉	C₂×Q₁₆	1	1	yes	characteristic
47	C₂×C₄₉₉	#137	1	1	yes	characteristic
48	C₄₉₉	#462	1	1	yes	characteristic, complemented, Sylow
49	#462	—	499	1	no	maximal, Sylow
50	C₂×Q₁₆	—	499	1	no	—
51	C₂×Q₁₆	—	499	1	no	—
52	C₄⋊Q₈	—	499	1	no	—
53	C₄×Q₈	—	499	1	no	—
54	C₄⋊C₈	—	499	1	no	—
55	#103	—	499	1	no	—
56	#103	D₄₉₉	1	1	yes	characteristic
57	C₂×Q₈	—	499	1	no	—
58	C₂×Q₈	—	499	1	no	—
59	C₂×Q₈	C₂×D₄₉₉	1	1	yes	characteristic
60	Q₁₆	—	998	2	no	—
61	Q₁₆	—	998	2	no	—
62	C₂×C₈	—	499	1	no	—
63	C₂×C₈	C₂×D₄₉₉	1	1	yes	characteristic
64	C₄⋊C₄	—	998	1	no	—
65	C₄⋊C₄	—	998	1	no	—
66	C₄⋊C₄	—	998	1	no	—
67	C₄⋊C₄	C₂×D₄₉₉	1	1	yes	characteristic
68	C₄²	—	998	1	no	—
69	C₄²	—	499	1	no	—
70	Q₈	—	2	1	no	—
71	Q₈	—	2	1	no	—
72	Q₈	—	998	1	no	—
73	Q₈	—	998	1	no	—
74	Q₈	—	998	1	no	—
75	Q₈	—	499	2	no	—
76	C₂×C₄	—	2	1	no	—
77	C₂×C₄	—	2	1	no	—
78	C₂×C₄	—	998	1	no	—
79	C₂×C₄	—	998	1	no	—
80	C₂×C₄	—	499	1	no	—
81	C₂×C₄	—	499	1	no	—
82	C₂×C₄	C₂²×D₄₉₉	1	1	yes	characteristic
83	C₈	—	2	1	no	—
84	C₈	—	998	1	no	—
85	C₂²	D₄×D₄₉₉	1	1	yes	characteristic
86	C₄	—	4	1	no	—
87	C₄	—	4	1	no	—
88	C₄	—	1996	1	no	—
89	C₄	—	998	2	no	—
90	C₄	—	998	1	no	—
91	C₄	—	499	2	no	—
92	C₄	D₄×D₄₉₉	1	1	yes	characteristic
93	C₄	#22547811	1	1	yes	characteristic
94	C₂	#30630324	1	1	yes	characteristic
95	C₂	Q₁₆×D₄₉₉	1	1	yes	characteristic
96	C₂	#30630380	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	#462
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
44. Dic₄₉₉	Q₁₆	semidirect
48. C₄₉₉	#462	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
C₂×#22547801	2
#30630349	2
#30630316	2
Dic₄₉₉⋊C₈	2
#30630274	2
#103×C₄₉₉	2
#462	499