Subgroups — #38742468

Order 25216.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27161037	C₂	1	3	yes	maximal
2	#27160836	C₂	1	3	yes	maximal
3	#338×C₁₉₇	C₂	1	1	yes	maximal, characteristic
4	C₂²×#13096802	C₂²	1	1	yes	characteristic
5	#20263285	C₂²	1	3	yes	—
6	#20263236	C₄	1	6	yes	complemented
7	C₈×Dic₁₉₇	C₄	1	6	yes	complemented
8	C₂×M₁₆×C₁₉₇	C₂²	1	3	yes	—
9	C₂×#13096802	C₂×C₄	1	3	yes	—
10	C₂×#13096802	C₂×C₄	1	3	yes	—
11	C₄⋊Dic₁₉₇	—	2	3	no	—
12	C₂²⋊Dic₁₉₇	—	2	3	no	—
13	C₄×Dic₁₉₇	C₂×C₄	1	6	yes	—
14	C₂²×C₄×C₁₉₇	C₂³	1	1	yes	characteristic
15	M₁₆×C₁₉₇	—	2	6	no	—
16	C₂×C₈×C₁₉₇	C₂×C₄	1	6	yes	—
17	C₂×Dic₁₉₇	—	2	6	no	—
18	#13096802	C₄²	1	1	yes	characteristic
19	#13096802	C₄²	1	3	yes	—
20	C₂³×C₁₉₇	#41	1	1	yes	characteristic
21	C₂×C₄×C₁₉₇	C₂²×C₄	1	3	yes	—
22	C₂×C₄×C₁₉₇	#41	1	3	yes	—
23	C₈×C₁₉₇	—	2	6	no	—
24	C₂²×C₁₉₇	—	4	1	no	—
25	C₂²×C₁₉₇	#117	1	3	yes	—
26	C₄×C₁₉₇	C₂×C₄²	1	1	yes	characteristic
27	C₄×C₁₉₇	#117	1	3	yes	—
28	Dic₁₉₇	—	4	6	no	—
29	C₂×C₁₉₇	—	2	3	no	—
30	C₂×C₁₉₇	#376	1	1	yes	characteristic
31	C₁₉₇	#1747	1	1	yes	characteristic, complemented, Sylow
32	#1747	—	197	1	no	maximal, Sylow
33	#405	—	197	3	no	—
34	#338	D₁₉₇	1	1	yes	characteristic
35	H(3,ℤ/4)	—	197	3	no	—
36	C₂×M₁₆	C₂×D₁₉₇	1	3	yes	—
37	C₂²×C₈	—	197	1	no	—
38	#117	—	197	3	no	—
39	#97	—	197	6	no	—
40	C₄×C₈	—	197	6	no	—
41	C₂²×C₄	C₂²×D₁₉₇	1	1	yes	characteristic
42	M₁₆	—	2	6	no	—
43	C₂×C₈	—	197	3	no	—
44	C₂×C₈	—	197	3	no	—
45	C₂×C₈	C₄×D₁₉₇	1	6	yes	—
46	C₄⋊C₄	—	394	3	no	—
47	C₂²⋊C₄	—	394	3	no	—
48	C₄²	—	197	6	no	—
49	C₂³	#15691359	1	1	yes	characteristic
50	C₂×C₄	—	394	6	no	—
51	C₂×C₄	C₂×C₄×D₁₉₇	1	3	yes	—
52	C₂×C₄	#15691357	1	3	yes	—
53	C₈	—	2	6	no	—
54	C₈	—	197	1	no	—
55	C₈	—	197	3	no	—
56	C₂²	—	4	1	no	—
57	C₂²	#20263284	1	3	yes	—
58	C₄	—	788	6	no	—
59	C₄	C₄²×D₁₉₇	1	1	yes	characteristic
60	C₄	#20263282	1	3	yes	—
61	C₂	—	2	3	no	—
62	C₂	#27160924	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₄²×D₁₉₇
commutator	C₄×C₁₉₇	C₂×C₄²
Frattini	C₂²×C₄	C₂²×D₁₉₇
Fitting	#338×C₁₉₇	C₂
socle	C₂×C₁₉₇	#376
prime radical	C₂³×C₁₉₇	#41
cosocle	C₂²×C₄×C₁₉₇	C₂³
hypercenter	#338	D₁₉₇
hypocenter	C₁₉₇	#1747
LCS	G ▷ C₄×C₁₉₇ ▷ C₁₉₇
UCS	C₁ ◁ C₄ ◁ #338

Complements

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

N	H ≅ G/N	type
6. #20263236	C₄	semidirect
7. C₈×Dic₁₉₇	C₄	semidirect
31. C₁₉₇	#1747	semidirect

Maximal subgroups

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

subgroup	index
#27161037	2
#27160836	2
#338×C₁₉₇	2
#1747	197