Subgroups — #38767049

Order 25472.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉₉⋊C₃₂	C₂	1	1	yes	maximal, characteristic
2	#27163844	C₂	1	1	yes	maximal, characteristic
3	#366×C₁₉₉	C₂	1	1	yes	maximal, characteristic
4	#20263889	—	2	1	no	—
5	C₁₉₉⋊C₃₂	C₄	1	2	yes	complemented
6	C₂×C₁₆×C₁₉₉	C₂²	1	1	yes	characteristic
7	#107×C₁₉₉	—	2	1	no	—
8	C₄⋊Dic₁₉₉	—	4	1	no	—
9	C₂×C₈×C₁₉₉	D₄	1	1	yes	characteristic
10	C₄⋊C₄×C₁₉₉	—	4	1	no	—
11	C₁₆×C₁₉₉	C₂×C₄	1	1	yes	characteristic
12	C₁₆×C₁₉₉	Q₈	1	1	yes	characteristic
13	C₂×Dic₁₉₉	—	8	1	no	—
14	C₂×C₄×C₁₉₉	—	8	1	no	—
15	C₂×C₄×C₁₉₉	D₈	1	1	yes	characteristic
16	C₈×C₁₉₉	C₄⋊C₄	1	1	yes	characteristic
17	C₈×C₁₉₉	Q₁₆	1	1	yes	characteristic
18	C₂²×C₁₉₉	D₁₆	1	1	yes	characteristic
19	C₄×C₁₉₉	—	16	1	no	—
20	C₄×C₁₉₉	#107	1	1	yes	characteristic
21	C₄×C₁₉₉	Q₃₂	1	1	yes	characteristic
22	Dic₁₉₉	—	16	1	no	—
23	C₂×C₁₉₉	#366	1	1	yes	characteristic
24	C₂×C₁₉₉	D₃₂	1	1	yes	characteristic
25	C₂×C₁₉₉	Q₆₄	1	1	yes	characteristic
26	C₁₉₉	#1423	1	1	yes	characteristic, complemented, Sylow
27	#1423	—	199	1	no	maximal, Sylow
28	C₂×C₃₂	—	199	1	no	—
29	#366	—	199	1	no	—
30	#366	D₁₉₉	1	1	yes	characteristic
31	C₂×C₁₆	C₂×D₁₉₉	1	1	yes	characteristic
32	#107	—	2	1	no	—
33	#107	—	398	1	no	—
34	C₃₂	—	199	2	no	—
35	C₂×C₈	C₂²⋊D₁₉₉	1	1	yes	characteristic
36	C₄⋊C₄	—	4	1	no	—
37	C₄⋊C₄	—	796	1	no	—
38	C₁₆	C₄×D₁₉₉	1	1	yes	characteristic
39	C₁₆	Dic₃₉₈	1	1	yes	characteristic
40	C₂×C₄	—	8	1	no	—
41	C₂×C₄	—	1592	1	no	—
42	C₂×C₄	#15691871	1	1	yes	characteristic
43	C₈	Dic₁₉₉⋊C₄	1	1	yes	characteristic
44	C₈	#15691876	1	1	yes	characteristic
45	C₂²	#20263896	1	1	yes	characteristic
46	C₄	—	16	1	no	—
47	C₄	—	3184	1	no	—
48	C₄	#20263888	1	1	yes	characteristic
49	C₄	#20263901	1	1	yes	characteristic
50	C₂	#27163843	1	1	yes	characteristic
51	C₂	#27163853	1	1	yes	characteristic
52	C₂	#27163858	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#20263896
commutator	C₁₆×C₁₉₉	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₁₉₉
Fitting	#366×C₁₉₉	C₂
socle, prime radical	C₂²×C₁₉₉	D₁₆
cosocle	C₂×C₁₆×C₁₉₉	C₂²
hypercenter	#366	D₁₉₉
hypocenter	C₁₉₉	#1423
LCS	G ▷ C₁₆×C₁₉₉ ▷ C₈×C₁₉₉ ▷ C₄×C₁₉₉ ▷ C₂×C₁₉₉ ▷ C₁₉₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #366

Complements

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

N	H ≅ G/N	type
5. C₁₉₉⋊C₃₂	C₄	semidirect
26. C₁₉₉	#1423	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₉₉⋊C₃₂	2
#27163844	2
#366×C₁₉₉	2
#1423	199