Subgroups — #44542959

Order 31936.

218 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×Dic₄₉₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂²⋊Dic₄₉₉	C₂	1	1	yes	maximal, characteristic
3	C₄₉₉⋊#95	C₂	1	4	yes	maximal, complemented
4	C₂×C₂²⋊C₄×C₄₉₉	C₂	1	1	yes	maximal, characteristic
5	C₂²×Dic₄₉₉	—	2	2	no	—
6	C₂²×Dic₄₉₉	—	2	2	no	—
7	C₂²×Dic₄₉₉	C₄	1	4	yes	complemented
8	C₂²×Dic₄₉₉	C₂²	1	2	yes	—
9	C₂²×Dic₄₉₉	C₂²	1	2	yes	—
10	C₂²⋊Dic₄₉₉	—	2	2	no	—
11	C₂⁴×C₄₉₉	C₂²	1	1	yes	characteristic
12	C₂²×C₄×C₄₉₉	C₂²	1	2	yes	—
13	C₂²⋊C₄×C₄₉₉	—	2	2	no	—
14	C₂×Dic₄₉₉	—	2	8	no	—
15	C₂×Dic₄₉₉	—	2	2	no	—
16	C₂×Dic₄₉₉	—	2	2	no	—
17	C₂×Dic₄₉₉	—	2	2	no	—
18	C₂×Dic₄₉₉	—	2	4	no	—
19	C₂×Dic₄₉₉	C₂×C₄	1	4	yes	—
20	C₂³×C₄₉₉	—	2	4	no	—
21	C₂³×C₄₉₉	C₂×C₄	1	2	yes	—
22	C₂³×C₄₉₉	D₄	1	2	yes	—
23	C₂³×C₄₉₉	D₄	1	2	yes	—
24	C₂³×C₄₉₉	C₂³	1	1	yes	characteristic
25	C₂×C₄×C₄₉₉	—	2	2	no	—
26	C₂×C₄×C₄₉₉	—	2	4	no	—
27	C₂²×C₄₉₉	—	2	4	no	—
28	C₂²×C₄₉₉	—	2	4	no	—
29	C₂²×C₄₉₉	—	2	4	no	—
30	C₂²×C₄₉₉	C₂²⋊C₄	1	4	yes	—
31	C₂²×C₄₉₉	C₂²×C₄	1	1	yes	characteristic
32	C₂²×C₄₉₉	C₂×D₄	1	1	yes	characteristic
33	C₂²×C₄₉₉	C₂×D₄	1	1	yes	characteristic
34	C₂²×C₄₉₉	#41	1	4	yes	—
35	C₄×C₄₉₉	—	4	2	no	—
36	Dic₄₉₉	—	2	4	no	—
37	Dic₄₉₉	—	4	2	no	—
38	C₂×C₄₉₉	—	2	4	no	—
39	C₂×C₄₉₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
40	C₂×C₄₉₉	#117	1	2	yes	—
41	C₂×C₄₉₉	#123	1	2	yes	—
42	C₂×C₄₉₉	#123	1	2	yes	—
43	C₄₉₉	#381	1	1	yes	characteristic, complemented, Sylow
44	#381	—	499	1	no	maximal, Sylow
45	C₂³×C₄	—	499	1	no	—
46	C₂×C₂²⋊C₄	—	499	1	no	—
47	C₂×C₂²⋊C₄	D₄₉₉	1	1	yes	characteristic
48	#95	—	499	4	no	—
49	C₂⁴	C₂×D₄₉₉	1	1	yes	characteristic
50	C₂²×C₄	—	998	2	no	—
51	C₂²×C₄	—	998	2	no	—
52	C₂²×C₄	—	499	2	no	—
53	C₂²×C₄	—	499	4	no	—
54	C₂²×C₄	—	499	2	no	—
55	C₂²×C₄	C₂×D₄₉₉	1	2	yes	—
56	C₂²⋊C₄	—	2	2	no	—
57	C₂²⋊C₄	—	998	2	no	—
58	C₂³	—	2	4	no	—
59	C₂³	C₄×D₄₉₉	1	2	yes	—
60	C₂³	C₂²⋊D₄₉₉	1	2	yes	—
61	C₂³	D₁₉₉₆	1	2	yes	—
62	C₂³	C₂²×D₄₉₉	1	1	yes	characteristic
63	C₂×C₄	—	2	2	no	—
64	C₂×C₄	—	2	4	no	—
65	C₂×C₄	—	998	2	no	—
66	C₂×C₄	—	998	4	no	—
67	C₂×C₄	—	998	8	no	—
68	C₂×C₄	—	998	2	no	—
69	C₂×C₄	—	998	2	no	—
70	C₂×C₄	—	499	4	no	—
71	C₂²	—	2	4	no	—
72	C₂²	—	2	4	no	—
73	C₂²	—	2	4	no	—
74	C₂²	(C₂×D₄₉₉)⋊C₄	1	4	yes	—
75	C₂²	C₂×C₄×D₄₉₉	1	1	yes	characteristic
76	C₂²	C₂×C₂²⋊D₄₉₉	1	1	yes	characteristic
77	C₂²	C₂×D₁₉₉₆	1	1	yes	characteristic
78	C₂²	#22547810	1	4	yes	—
79	C₄	—	4	2	no	—
80	C₄	—	1996	2	no	—
81	C₄	—	998	4	no	—
82	C₂	—	2	4	no	—
83	C₂	C₂×(C₂×D₄₉₉)⋊C₄	1	1	yes	characteristic
84	C₂	#30630307	1	2	yes	—
85	C₂	#30630332	1	2	yes	—
86	C₂	#30630335	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₄₉₉
commutator	C₂²×C₄₉₉	C₂²×C₄
Fitting	C₂×C₂²⋊C₄×C₄₉₉	C₂
socle, cosocle	C₂³×C₄₉₉	C₂³
prime radical	C₂⁴×C₄₉₉	C₂²
hypercenter	C₂×C₂²⋊C₄	D₄₉₉
hypocenter	C₄₉₉	#381
LCS	G ▷ C₂²×C₄₉₉ ▷ C₄₉₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
3. C₄₉₉⋊#95	C₂	semidirect
7. C₂²×Dic₄₉₉	C₄	semidirect
43. C₄₉₉	#381	semidirect

Maximal subgroups

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

subgroup	index
C₂³×Dic₄₉₉	2
C₂×C₂²⋊Dic₄₉₉	2
C₄₉₉⋊#95	2
C₂×C₂²⋊C₄×C₄₉₉	2
#381	499