Subgroups — #38740913

Order 25216.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20263232	C₂	1	1	yes	maximal, characteristic
2	#27160905	C₂	1	1	yes	maximal, characteristic
3	#366×C₁₉₇	C₂	1	1	yes	maximal, characteristic
4	#20263260	—	2	1	no	—
5	#20263232	C₄	1	2	yes	complemented
6	C₂×C₁₆×C₁₉₇	C₂²	1	1	yes	characteristic
7	#107×C₁₉₇	—	2	1	no	—
8	C₄⋊Dic₁₉₇	—	4	1	no	—
9	C₂×C₈×C₁₉₇	D₄	1	1	yes	characteristic
10	C₄⋊C₄×C₁₉₇	—	4	1	no	—
11	C₁₆×C₁₉₇	C₂×C₄	1	1	yes	characteristic
12	C₁₆×C₁₉₇	Q₈	1	1	yes	characteristic
13	C₂×Dic₁₉₇	—	8	1	no	—
14	C₂×C₄×C₁₉₇	—	8	1	no	—
15	C₂×C₄×C₁₉₇	D₈	1	1	yes	characteristic
16	C₈×C₁₉₇	C₄⋊C₄	1	1	yes	characteristic
17	C₈×C₁₉₇	Q₁₆	1	1	yes	characteristic
18	C₂²×C₁₉₇	D₁₆	1	1	yes	characteristic
19	C₄×C₁₉₇	—	16	1	no	—
20	C₄×C₁₉₇	#107	1	1	yes	characteristic
21	C₄×C₁₉₇	Q₃₂	1	1	yes	characteristic
22	Dic₁₉₇	—	16	1	no	—
23	C₂×C₁₉₇	#366	1	1	yes	characteristic
24	C₂×C₁₉₇	SD₆₄	1	1	yes	characteristic
25	C₂×C₁₉₇	SD₆₄	1	1	yes	characteristic
26	C₁₉₇	#1424	1	1	yes	characteristic, complemented, Sylow
27	#1424	—	197	1	no	maximal, Sylow
28	C₂×C₃₂	—	197	1	no	—
29	#366	—	197	1	no	—
30	#366	D₁₉₇	1	1	yes	characteristic
31	C₂×C₁₆	C₂×D₁₉₇	1	1	yes	characteristic
32	#107	—	2	1	no	—
33	#107	—	394	1	no	—
34	C₃₂	—	197	2	no	—
35	C₂×C₈	C₂²⋊D₁₉₇	1	1	yes	characteristic
36	C₄⋊C₄	—	4	1	no	—
37	C₄⋊C₄	—	788	1	no	—
38	C₁₆	C₄×D₁₉₇	1	1	yes	characteristic
39	C₁₆	Dic₃₉₄	1	1	yes	characteristic
40	C₂×C₄	—	8	1	no	—
41	C₂×C₄	—	1576	1	no	—
42	C₂×C₄	#15691343	1	1	yes	characteristic
43	C₈	#15691337	1	1	yes	characteristic
44	C₈	#15691348	1	1	yes	characteristic
45	C₂²	#20263267	1	1	yes	characteristic
46	C₄	—	16	1	no	—
47	C₄	—	3152	1	no	—
48	C₄	#20263259	1	1	yes	characteristic
49	C₄	#20263272	1	1	yes	characteristic
50	C₂	#27160904	1	1	yes	characteristic
51	C₂	#27160916	1	1	yes	characteristic
52	C₂	#27160917	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#20263267
commutator	C₁₆×C₁₉₇	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₁₉₇
Fitting	#366×C₁₉₇	C₂
socle, prime radical	C₂²×C₁₉₇	D₁₆
cosocle	C₂×C₁₆×C₁₉₇	C₂²
hypercenter	#366	D₁₉₇
hypocenter	C₁₉₇	#1424
LCS	G ▷ C₁₆×C₁₉₇ ▷ C₈×C₁₉₇ ▷ C₄×C₁₉₇ ▷ C₂×C₁₉₇ ▷ C₁₉₇
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. #20263232	C₄	semidirect
26. C₁₉₇	#1424	semidirect

Maximal subgroups

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

subgroup	index
C₂×#20263232	2
#27160905	2
#366×C₁₉₇	2
#1424	197