Subgroups — #20260476

Order 6208.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15690802	C₂	1	1	yes	maximal, characteristic
2	#15690721	C₂	1	1	yes	maximal, characteristic
3	#97×C₉₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#11715895	—	2	1	no	—
5	C₄⋊Dic₉₇	C₄	1	1	yes	characteristic
6	C₄⋊Dic₉₇	C₄	1	1	yes	characteristic
7	#13095490	—	2	1	no	—
8	#13095490	—	2	1	no	—
9	C₂×C₈×C₉₇	—	2	1	no	—
10	C₄²×C₉₇	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₉₇	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄×C₉₇	D₄	1	1	yes	characteristic
13	C₂×C₄×C₉₇	D₄	1	1	yes	characteristic
14	C₂×Dic₉₇	—	2	1	no	—
15	C₂×Dic₉₇	—	2	1	no	—
16	C₈×C₉₇	—	2	2	no	—
17	#11715895	—	2	2	no	—
18	C₂²×C₉₇	C₂²⋊C₄	1	1	yes	characteristic
19	C₄×C₉₇	—	2	1	no	—
20	C₄×C₉₇	—	2	1	no	—
21	C₄×C₉₇	—	2	1	no	—
22	Dic₉₇	—	4	1	no	—
23	Dic₉₇	—	4	1	no	—
24	C₂×C₉₇	#101	1	1	yes	characteristic
25	C₂×C₉₇	#104	1	1	yes	characteristic
26	C₂×C₉₇	#104	1	1	yes	characteristic
27	C₉₇	#330	1	1	yes	characteristic, complemented, Sylow
28	#330	—	97	1	no	maximal, Sylow
29	#125	—	97	1	no	—
30	#97	—	97	1	no	—
31	#97	D₉₇	1	1	yes	characteristic
32	C₂×C₈	—	2	1	no	—
33	C₂×C₈	—	194	1	no	—
34	C₄⋊C₄	—	97	1	no	—
35	C₄⋊C₄	—	97	1	no	—
36	C₄⋊C₄	—	194	1	no	—
37	C₄⋊C₄	—	194	1	no	—
38	C₄²	C₂×D₉₇	1	1	yes	characteristic
39	C₂×C₄	—	194	1	no	—
40	C₂×C₄	—	194	1	no	—
41	C₂×C₄	C₄×D₉₇	1	1	yes	characteristic
42	C₂×C₄	D₃₈₈	1	1	yes	characteristic
43	C₂×C₄	C₂²⋊D₉₇	1	1	yes	characteristic
44	C₈	—	2	2	no	—
45	C₈	—	194	2	no	—
46	C₂²	#13095488	1	1	yes	characteristic
47	C₄	—	2	1	no	—
48	C₄	—	2	1	no	—
49	C₄	—	2	1	no	—
50	C₄	—	388	1	no	—
51	C₄	—	388	1	no	—
52	C₂	#15690728	1	1	yes	characteristic
53	C₂	#15690736	1	1	yes	characteristic
54	C₂	#15690738	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#13095488
commutator	C₂×C₄×C₉₇	C₂×C₄
Frattini	C₄²	C₂×D₉₇
Fitting	#97×C₉₇	C₂
socle	C₂²×C₉₇	C₂²⋊C₄
hypercenter	#97	D₉₇
hypocenter	C₉₇	#330
LCS	G ▷ C₂×C₄×C₉₇ ▷ C₂²×C₉₇ ▷ C₉₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #97

Complements

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

N	H ≅ G/N	type
27. C₉₇	#330	semidirect