Subgroups — #38767052

Order 25472.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27163844	C₂	1	2	yes	maximal
2	C₂×C₃₂×C₁₉₉	C₂	1	1	yes	maximal, characteristic
3	#20263889	—	2	2	no	—
4	C₂×C₁₆×C₁₉₉	C₂²	1	1	yes	characteristic
5	C₃₂×C₁₉₉	C₄	1	2	yes	complemented
6	C₄⋊Dic₁₉₉	—	4	2	no	—
7	C₂×C₈×C₁₉₉	D₄	1	1	yes	characteristic
8	C₁₆×C₁₉₉	C₂×C₄	1	1	yes	characteristic
9	C₁₆×C₁₉₉	Q₈	1	1	yes	characteristic
10	C₂×Dic₁₉₉	—	8	2	no	—
11	C₂×C₄×C₁₉₉	D₈	1	1	yes	characteristic
12	C₈×C₁₉₉	C₄⋊C₄	1	1	yes	characteristic
13	C₈×C₁₉₉	Q₁₆	1	1	yes	characteristic
14	C₂²×C₁₉₉	D₁₆	1	1	yes	characteristic
15	C₄×C₁₉₉	#107	1	1	yes	characteristic
16	C₄×C₁₉₉	Q₃₂	1	1	yes	characteristic
17	Dic₁₉₉	—	16	2	no	—
18	C₂×C₁₉₉	#366	1	1	yes	characteristic
19	C₂×C₁₉₉	SD₆₄	1	2	yes	—
20	C₁₉₉	#1424	1	1	yes	characteristic, complemented, Sylow
21	#1424	—	199	1	no	maximal, Sylow
22	C₂×C₃₂	D₁₉₉	1	1	yes	characteristic
23	#366	—	199	2	no	—
24	C₂×C₁₆	C₂×D₁₉₉	1	1	yes	characteristic
25	#107	—	398	2	no	—
26	C₃₂	Dic₁₉₉	1	2	yes	complemented
27	C₂×C₈	D₇₉₆	1	1	yes	characteristic
28	C₄⋊C₄	—	796	2	no	—
29	C₁₆	C₂×Dic₁₉₉	1	1	yes	characteristic
30	C₁₆	Dic₃₉₈	1	1	yes	characteristic
31	C₂×C₄	—	1592	2	no	—
32	C₂×C₄	D₁₅₉₂	1	1	yes	characteristic
33	C₈	C₄⋊Dic₁₉₉	1	1	yes	characteristic
34	C₈	Dic₇₉₆	1	1	yes	characteristic
35	C₂²	D₃₁₈₄	1	1	yes	characteristic
36	C₄	—	3184	2	no	—
37	C₄	#20263889	1	1	yes	characteristic
38	C₄	Dic₁₅₉₂	1	1	yes	characteristic
39	C₂	#27163844	1	1	yes	characteristic
40	C₂	#27163857	1	2	yes	—

	subgroup	G/H
center	C₂²	D₃₁₈₄
commutator	C₁₆×C₁₉₉	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₁₉₉
Fitting	C₂×C₃₂×C₁₉₉	C₂
socle, prime radical	C₂²×C₁₉₉	D₁₆
cosocle	C₂×C₁₆×C₁₉₉	C₂²
hypercenter	C₂×C₃₂	D₁₉₉
hypocenter	C₁₉₉	#1424
LCS	G ▷ C₁₆×C₁₉₉ ▷ C₈×C₁₉₉ ▷ C₄×C₁₉₉ ▷ C₂×C₁₉₉ ▷ C₁₉₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
5. C₃₂×C₁₉₉	C₄	semidirect
20. C₁₉₉	#1424	semidirect
26. C₃₂	Dic₁₉₉	semidirect

Maximal subgroups

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

subgroup	index
#27163844	2
C₂×C₃₂×C₁₉₉	2
#1424	199