Subgroups — #38766990

Order 25472.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27163852	C₂	1	2	yes	maximal, complemented
2	C₂×M₃₂×C₁₉₉	C₂	1	1	yes	maximal, characteristic
3	C₁₉₉⋊C₃₂	—	2	2	no	—
4	C₂²×C₈×C₁₉₉	C₄	1	1	yes	characteristic
5	M₃₂×C₁₉₉	—	2	2	no	—
6	C₂×C₁₆×C₁₉₉	C₄	1	1	yes	characteristic
7	C₂×C₁₆×C₁₉₉	C₂²	1	1	yes	characteristic
8	C₂²×C₄×C₁₉₉	C₈	1	1	yes	characteristic
9	C₂×C₈×C₁₉₉	—	2	1	no	—
10	C₂×C₈×C₁₉₉	—	2	1	no	—
11	C₂×C₈×C₁₉₉	C₈	1	1	yes	characteristic
12	C₂×C₈×C₁₉₉	C₂×C₄	1	1	yes	characteristic
13	C₁₆×C₁₉₉	—	2	1	no	—
14	C₁₆×C₁₉₉	D₄	1	2	yes	—
15	C₂³×C₁₉₉	C₁₆	1	1	yes	characteristic
16	C₂×C₄×C₁₉₉	—	2	1	no	—
17	C₂×C₄×C₁₉₉	—	2	1	no	—
18	C₂×C₄×C₁₉₉	C₁₆	1	1	yes	characteristic
19	C₂×C₄×C₁₉₉	C₂×C₈	1	1	yes	characteristic
20	C₈×C₁₉₉	—	2	1	no	—
21	C₈×C₁₉₉	C₂²⋊C₄	1	1	yes	characteristic
22	C₈×C₁₉₉	M₁₆	1	1	yes	characteristic
23	C₂²×C₁₉₉	—	2	1	no	—
24	C₂²×C₁₉₉	—	4	1	no	—
25	C₂²×C₁₉₉	C₂×C₁₆	1	1	yes	characteristic
26	C₄×C₁₉₉	—	2	1	no	—
27	C₄×C₁₉₉	C₂²⋊C₈	1	1	yes	characteristic
28	C₄×C₁₉₉	M₃₂	1	1	yes	characteristic
29	C₂×C₁₉₉	—	2	1	no	—
30	C₂×C₁₉₉	—	4	1	no	—
31	C₂×C₁₉₉	C₂²⋊C₁₆	1	1	yes	characteristic
32	C₁₉₉	#1400	1	1	yes	characteristic, complemented, Sylow
33	#1400	—	199	1	no	maximal, Sylow
34	C₂×M₃₂	D₁₉₉	1	1	yes	characteristic
35	M₆₄	—	199	2	no	—
36	C₂²×C₈	Dic₁₉₉	1	1	yes	characteristic
37	M₃₂	—	2	2	no	—
38	C₂×C₁₆	Dic₁₉₉	1	1	yes	characteristic
39	C₂×C₁₆	C₂×D₁₉₉	1	1	yes	characteristic
40	C₃₂	—	398	2	no	—
41	C₂²×C₄	C₁₉₉⋊C₈	1	1	yes	characteristic
42	C₂×C₈	—	2	1	no	—
43	C₂×C₈	—	2	1	no	—
44	C₂×C₈	C₁₉₉⋊C₈	1	1	yes	characteristic
45	C₂×C₈	C₂×Dic₁₉₉	1	1	yes	characteristic
46	C₁₆	—	2	1	no	—
47	C₁₆	C₂²⋊D₁₉₉	1	2	yes	—
48	C₂³	C₁₉₉⋊C₁₆	1	1	yes	characteristic
49	C₂×C₄	—	2	1	no	—
50	C₂×C₄	—	2	1	no	—
51	C₂×C₄	C₁₉₉⋊C₁₆	1	1	yes	characteristic
52	C₂×C₄	C₂×C₁₉₉⋊C₈	1	1	yes	characteristic
53	C₈	—	2	1	no	—
54	C₈	C₂²⋊Dic₁₉₉	1	1	yes	characteristic
55	C₈	#15691870	1	1	yes	characteristic
56	C₂²	—	2	1	no	—
57	C₂²	—	4	1	no	—
58	C₂²	C₂×C₁₉₉⋊C₁₆	1	1	yes	characteristic
59	C₄	—	2	1	no	—
60	C₄	C₂²⋊(C₁₉₉⋊C₈)	1	1	yes	characteristic
61	C₄	#20263895	1	1	yes	characteristic
62	C₂	—	2	1	no	—
63	C₂	—	4	1	no	—
64	C₂	C₂²⋊(C₁₉₉⋊C₁₆)	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂²⋊Dic₁₉₉
commutator	C₂²×C₁₉₉	C₂×C₁₆
Frattini	C₂×C₁₆	C₂×D₁₉₉
Fitting	C₂×M₃₂×C₁₉₉	C₂
socle	C₂×C₁₉₉	C₂²⋊C₁₆
prime radical	C₂³×C₁₉₉	C₁₆
cosocle	C₂×C₁₆×C₁₉₉	C₂²
hypercenter	C₂×M₃₂	D₁₉₉
hypocenter	C₁₉₉	#1400
LCS	G ▷ C₂²×C₁₉₉ ▷ C₂×C₁₉₉ ▷ C₁₉₉
UCS	C₁ ◁ C₈ ◁ C₂×C₁₆ ◁ C₂×M₃₂

Complements

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

N	H ≅ G/N	type
1. #27163852	C₂	semidirect
32. C₁₉₉	#1400	semidirect

Maximal subgroups

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

subgroup	index
#27163852	2
C₂×M₃₂×C₁₉₉	2
#1400	199