Subgroups — #20260763

Order 6208.

114 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#11715895	C₂	1	1	yes	maximal, characteristic
2	#15690769	C₂	1	1	yes	maximal, characteristic
3	#15690739	C₂	1	4	yes	maximal, complemented
4	C₂×M₁₆×C₉₇	C₂	1	1	yes	maximal, characteristic
5	C₂×#11715895	—	2	2	no	—
6	C₂×#11715895	C₂²	1	2	yes	—
7	C₄⋊Dic₉₇	C₄	1	2	yes	—
8	C₂²⋊Dic₉₇	C₄	1	2	yes	—
9	C₄×Dic₉₇	C₂²	1	2	yes	—
10	C₂²×C₄×C₉₇	C₂²	1	1	yes	characteristic
11	M₁₆×C₉₇	—	2	2	no	—
12	C₂×C₈×C₉₇	C₂²	1	2	yes	—
13	C₂³×C₉₇	C₂×C₄	1	1	yes	characteristic
14	C₂×C₄×C₉₇	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄×C₉₇	D₄	1	2	yes	—
16	C₂×C₄×C₉₇	Q₈	1	2	yes	—
17	C₂×C₄×C₉₇	C₂³	1	1	yes	characteristic
18	C₂×Dic₉₇	C₂×C₄	1	4	yes	—
19	C₈×C₉₇	—	2	2	no	—
20	#11715895	—	2	2	no	—
21	C₂²×C₉₇	—	2	2	no	—
22	C₂²×C₉₇	C₄⋊C₄	1	2	yes	—
23	C₂²×C₉₇	C₂²×C₄	1	1	yes	characteristic
24	C₄×C₉₇	C₄⋊C₄	1	2	yes	—
25	C₄×C₉₇	C₂×D₄	1	1	yes	characteristic
26	C₄×C₉₇	C₂×Q₈	1	1	yes	characteristic
27	Dic₉₇	—	2	4	no	—
28	C₂×C₉₇	—	2	2	no	—
29	C₂×C₉₇	C₂×C₄⋊C₄	1	1	yes	characteristic
30	C₂×C₉₇	#131	1	2	yes	—
31	C₉₇	#424	1	1	yes	characteristic, complemented, Sylow
32	#424	—	97	1	no	maximal, Sylow
33	C₂×M₁₆	D₉₇	1	1	yes	characteristic
34	C₂²×C₈	—	97	1	no	—
35	#117	—	97	1	no	—
36	C₄⋊C₈	—	97	4	no	—
37	C₂²×C₄	C₂×D₉₇	1	1	yes	characteristic
38	M₁₆	—	2	2	no	—
39	C₂×C₈	—	97	2	no	—
40	C₂×C₈	—	194	2	no	—
41	C₂×C₈	C₂×D₉₇	1	2	yes	—
42	C₄⋊C₄	—	97	2	no	—
43	C₂²⋊C₄	—	97	2	no	—
44	C₄²	—	97	2	no	—
45	C₂³	C₄×D₉₇	1	1	yes	characteristic
46	C₂×C₄	—	97	4	no	—
47	C₂×C₄	Dic₁₉₄	1	2	yes	—
48	C₂×C₄	C₄×D₉₇	1	1	yes	characteristic
49	C₂×C₄	C₂²⋊D₉₇	1	2	yes	—
50	C₂×C₄	C₂²×D₉₇	1	1	yes	characteristic
51	C₈	—	2	2	no	—
52	C₈	—	194	2	no	—
53	C₂²	—	2	2	no	—
54	C₂²	#13095490	1	2	yes	—
55	C₂²	C₂×C₄×D₉₇	1	1	yes	characteristic
56	C₄	—	194	4	no	—
57	C₄	#13095490	1	2	yes	—
58	C₄	C₂×C₂²⋊D₉₇	1	1	yes	characteristic
59	C₄	C₂×Dic₁₉₄	1	1	yes	characteristic
60	C₂	—	2	2	no	—
61	C₂	C₂×#13095490	1	1	yes	characteristic
62	C₂	#15690818	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₉₇
commutator, socle	C₂²×C₉₇	C₂²×C₄
Fitting	C₂×M₁₆×C₉₇	C₂
hypercenter	C₂×M₁₆	D₉₇
hypocenter	C₉₇	#424
LCS	G ▷ C₂²×C₉₇ ▷ C₉₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
3. #15690739	C₂	semidirect
31. C₉₇	#424	semidirect