Subgroups — #38766942

Order 25472.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20263889	C₂	1	2	yes	maximal
2	C₂²×C₁₆×C₁₉₉	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄⋊Dic₁₉₉	—	2	2	no	—
4	#20263889	—	2	2	no	—
5	#20263889	C₄	1	4	yes	complemented
6	C₂²×C₈×C₁₉₉	C₂²	1	1	yes	characteristic
7	C₂×C₁₆×C₁₉₉	—	2	2	no	—
8	C₂×C₁₆×C₁₉₉	C₄	1	2	yes	complemented
9	C₂²×Dic₁₉₉	—	4	2	no	—
10	C₄⋊Dic₁₉₉	—	2	4	no	—
11	C₄⋊Dic₁₉₉	—	4	2	no	—
12	C₂²×C₄×C₁₉₉	D₄	1	1	yes	characteristic
13	C₂×C₈×C₁₉₉	C₂×C₄	1	2	yes	—
14	C₂×C₈×C₁₉₉	C₂×C₄	1	1	yes	characteristic
15	C₂×C₈×C₁₉₉	D₄	1	2	yes	—
16	C₂×C₈×C₁₉₉	Q₈	1	1	yes	characteristic
17	C₁₆×C₁₉₉	—	2	2	no	—
18	C₂×Dic₁₉₉	—	4	4	no	—
19	C₂×Dic₁₉₉	—	8	2	no	—
20	C₂×Dic₁₉₉	—	8	2	no	—
21	C₂³×C₁₉₉	D₈	1	1	yes	characteristic
22	C₂×C₄×C₁₉₉	C₂²⋊C₄	1	2	yes	—
23	C₂×C₄×C₁₉₉	C₄⋊C₄	1	1	yes	characteristic
24	C₂×C₄×C₁₉₉	SD₁₆	1	2	yes	—
25	C₂×C₄×C₁₉₉	Q₁₆	1	1	yes	characteristic
26	C₈×C₁₉₉	C₄²	1	1	yes	characteristic
27	C₈×C₁₉₉	C₂²⋊C₄	1	1	yes	characteristic
28	C₈×C₁₉₉	C₄⋊C₄	1	2	yes	—
29	C₂²×C₁₉₉	#102	1	2	yes	—
30	C₂²×C₁₉₉	#107	1	1	yes	characteristic
31	C₂²×C₁₉₉	D₁₆	1	1	yes	characteristic
32	C₂²×C₁₉₉	SD₃₂	1	2	yes	—
33	C₂²×C₁₉₉	Q₃₂	1	1	yes	characteristic
34	C₄×C₁₉₉	#95	1	1	yes	characteristic
35	C₄×C₁₉₉	#103	1	2	yes	—
36	C₄×C₁₉₉	#106	1	1	yes	characteristic
37	Dic₁₉₉	—	8	4	no	—
38	C₂×C₁₉₉	#340	1	1	yes	characteristic
39	C₂×C₁₉₉	#357	1	2	yes	—
40	C₂×C₁₉₉	#358	1	2	yes	—
41	C₂×C₁₉₉	#366	1	1	yes	characteristic
42	C₂×C₁₉₉	#367	1	1	yes	characteristic
43	C₁₉₉	#1380	1	1	yes	characteristic, complemented, Sylow
44	#1380	—	199	1	no	maximal, Sylow
45	C₂²×C₁₆	D₁₉₉	1	1	yes	characteristic
46	C₂×#107	—	199	2	no	—
47	C₂²×C₈	C₂×D₁₉₉	1	1	yes	characteristic
48	C₂×C₄⋊C₄	—	398	2	no	—
49	C₂×C₁₆	—	2	2	no	—
50	C₂×C₁₆	Dic₁₉₉	1	2	yes	complemented
51	#107	—	398	2	no	—
52	#107	—	199	4	no	—
53	C₂²×C₄	—	796	2	no	—
54	C₂²×C₄	D₇₉₆	1	1	yes	characteristic
55	C₂×C₈	C₄×D₁₉₉	1	2	yes	—
56	C₂×C₈	C₂×Dic₁₉₉	1	1	yes	characteristic
57	C₂×C₈	C₂²⋊D₁₉₉	1	2	yes	—
58	C₂×C₈	Dic₃₉₈	1	1	yes	characteristic
59	C₄⋊C₄	—	796	2	no	—
60	C₄⋊C₄	—	398	4	no	—
61	C₁₆	—	2	2	no	—
62	C₂³	D₁₅₉₂	1	1	yes	characteristic
63	C₂×C₄	—	796	4	no	—
64	C₂×C₄	—	1592	2	no	—
65	C₂×C₄	—	1592	2	no	—
66	C₂×C₄	(C₂×D₁₉₉)⋊C₄	1	2	yes	—
67	C₂×C₄	C₄⋊Dic₁₉₉	1	1	yes	characteristic
68	C₂×C₄	#15691875	1	2	yes	—
69	C₂×C₄	Dic₇₉₆	1	1	yes	characteristic
70	C₈	C₄×Dic₁₉₉	1	1	yes	characteristic
71	C₈	C₂²⋊Dic₁₉₉	1	1	yes	characteristic
72	C₈	Dic₁₉₉⋊C₄	1	2	yes	—
73	C₂²	#20263877	1	2	yes	—
74	C₂²	#20263889	1	1	yes	characteristic
75	C₂²	D₃₁₈₄	1	1	yes	characteristic
76	C₂²	#20263900	1	2	yes	—
77	C₂²	Dic₁₅₉₂	1	1	yes	characteristic
78	C₄	—	1592	4	no	—
79	C₄	C₁₉₉⋊#95	1	1	yes	characteristic
80	C₄	#20263880	1	2	yes	—
81	C₄	#20263887	1	1	yes	characteristic
82	C₂	#27163781	1	1	yes	characteristic
83	C₂	#27163820	1	2	yes	—
84	C₂	#27163823	1	2	yes	—
85	C₂	#27163844	1	1	yes	characteristic
86	C₂	#27163846	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₁₅₉₂
commutator	C₈×C₁₉₉	C₄²
Frattini	C₂²×C₈	C₂×D₁₉₉
Fitting	C₂²×C₁₆×C₁₉₉	C₂
socle, prime radical	C₂³×C₁₉₉	D₈
cosocle	C₂²×C₈×C₁₉₉	C₂²
hypercenter	C₂²×C₁₆	D₁₉₉
hypocenter	C₁₉₉	#1380
LCS	G ▷ C₈×C₁₉₉ ▷ C₄×C₁₉₉ ▷ C₂×C₁₉₉ ▷ C₁₉₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆

Complements

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

N	H ≅ G/N	type
5. #20263889	C₄	semidirect
8. C₂×C₁₆×C₁₉₉	C₄	semidirect
43. C₁₉₉	#1380	semidirect
50. C₂×C₁₆	Dic₁₉₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#20263889	2
C₂²×C₁₆×C₁₉₉	2
#1380	199