Subgroups — #20260474

Order 6208.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15690798	C₂	1	1	yes	maximal, characteristic
2	#15690721	C₂	1	1	yes	maximal, characteristic, complemented
3	#97×C₉₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×Dic₁₉₄	C₄	1	1	yes	characteristic
5	C₂×D₃₈₈	C₄	1	1	yes	characteristic
6	C₂×#11715895	—	2	1	no	—
7	#13095488	—	2	1	no	—
8	#13095488	—	2	1	no	—
9	C₂×C₈×C₉₇	—	2	1	no	—
10	C₄²×C₉₇	C₂²	1	1	yes	characteristic
11	C₂²×D₉₇	—	2	1	no	—
12	C₂×C₄×C₉₇	C₂×C₄	1	1	yes	characteristic
13	C₂×C₄×C₉₇	D₄	1	1	yes	characteristic
14	C₂×C₄×C₉₇	D₄	1	1	yes	characteristic
15	C₂×Dic₉₇	—	2	1	no	—
16	D₃₈₈	—	4	1	no	—
17	Dic₁₉₄	—	4	1	no	—
18	C₈×C₉₇	—	2	2	no	—
19	#11715895	—	2	2	no	—
20	C₂²×C₉₇	C₂²⋊C₄	1	1	yes	characteristic
21	C₂×D₉₇	—	4	1	no	—
22	C₂×D₉₇	—	4	1	no	—
23	C₂×D₉₇	—	4	1	no	—
24	C₄×C₉₇	—	2	1	no	—
25	C₄×C₉₇	—	2	1	no	—
26	C₄×C₉₇	—	2	1	no	—
27	Dic₉₇	—	4	1	no	—
28	C₂×C₉₇	#100	1	1	yes	characteristic
29	C₂×C₉₇	#104	1	1	yes	characteristic
30	C₂×C₉₇	#104	1	1	yes	characteristic
31	D₉₇	—	8	1	no	—
32	C₉₇	#329	1	1	yes	characteristic, complemented, Sylow
33	#329	—	97	1	no	maximal, Sylow
34	#124	—	97	1	no	—
35	#97	—	97	1	no	—
36	#97	D₉₇	1	1	yes	characteristic, complemented
37	C₂×Q₈	—	97	1	no	—
38	C₂×D₄	—	97	1	no	—
39	C₂×C₈	—	2	1	no	—
40	C₂×C₈	—	194	1	no	—
41	C₂²⋊C₄	—	194	1	no	—
42	C₂²⋊C₄	—	194	1	no	—
43	C₄²	C₂×D₉₇	1	1	yes	characteristic
44	C₂³	—	194	1	no	—
45	Q₈	—	388	1	no	—
46	D₄	—	388	1	no	—
47	C₂×C₄	—	194	1	no	—
48	C₂×C₄	C₄×D₉₇	1	1	yes	characteristic
49	C₂×C₄	D₃₈₈	1	1	yes	characteristic
50	C₂×C₄	C₂²⋊D₉₇	1	1	yes	characteristic
51	C₈	—	2	2	no	—
52	C₈	—	194	2	no	—
53	C₂²	—	388	1	no	—
54	C₂²	—	388	1	no	—
55	C₂²	—	388	1	no	—
56	C₂²	#13095488	1	1	yes	characteristic
57	C₄	—	2	1	no	—
58	C₄	—	2	1	no	—
59	C₄	—	2	1	no	—
60	C₄	—	388	1	no	—
61	C₂	—	776	1	no	—
62	C₂	#15690726	1	1	yes	characteristic
63	C₂	#15690736	1	1	yes	characteristic
64	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	#329
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
2. #15690721	C₂	semidirect
3. #97×C₉₇	C₂	semidirect
32. C₉₇	#329	semidirect
36. #97	D₉₇	semidirect