Subgroups — #20260516

Order 6208.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13095494	C₂	1	1	yes	maximal, characteristic
2	#15690750	C₂	1	1	yes	maximal, characteristic, complemented
3	M₃₂×C₉₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×D₉₇	C₄	1	1	yes	characteristic
5	#13095494	—	2	1	no	—
6	#13095494	—	2	1	no	—
7	C₂×#11715895	C₄	1	1	yes	characteristic
8	#13095486	—	2	1	no	—
9	C₂×C₈×C₉₇	C₂²	1	1	yes	characteristic
10	C₁₆×C₉₇	—	2	1	no	—
11	C₂²×D₉₇	C₈	1	1	yes	characteristic
12	C₂×C₄×C₉₇	C₂×C₄	1	1	yes	characteristic
13	C₂×Dic₉₇	C₈	1	1	yes	characteristic
14	C₄×D₉₇	—	2	1	no	—
15	C₄×D₉₇	—	2	1	no	—
16	C₈×C₉₇	D₄	1	1	yes	characteristic
17	C₈×C₉₇	D₄	1	1	yes	characteristic
18	#11715895	—	2	1	no	—
19	C₂²×C₉₇	C₂×C₈	1	1	yes	characteristic
20	C₂×D₉₇	—	2	1	no	—
21	C₂×D₉₇	—	4	1	no	—
22	C₄×C₉₇	C₂²⋊C₄	1	1	yes	characteristic
23	C₄×C₉₇	M₁₆	1	1	yes	characteristic
24	Dic₉₇	—	2	1	no	—
25	C₂×C₉₇	—	2	1	no	—
26	C₂×C₉₇	C₂²⋊C₈	1	1	yes	characteristic
27	D₉₇	—	4	1	no	—
28	C₉₇	#349	1	1	yes	characteristic, complemented, Sylow
29	#349	—	97	1	no	maximal, Sylow
30	C₂×M₁₆	—	97	1	no	—
31	M₃₂	—	97	1	no	—
32	M₃₂	D₉₇	1	1	yes	characteristic, complemented
33	C₂²×C₄	—	97	1	no	—
34	M₁₆	—	194	1	no	—
35	M₁₆	—	194	1	no	—
36	C₂×C₈	—	97	1	no	—
37	C₂×C₈	C₂×D₉₇	1	1	yes	characteristic
38	C₁₆	—	2	1	no	—
39	C₁₆	—	194	1	no	—
40	C₂³	—	97	1	no	—
41	C₂×C₄	—	97	1	no	—
42	C₂×C₄	—	194	1	no	—
43	C₂×C₄	—	194	1	no	—
44	C₂×C₄	C₄×D₉₇	1	1	yes	characteristic
45	C₈	—	194	1	no	—
46	C₈	D₃₈₈	1	1	yes	characteristic
47	C₈	C₂²⋊D₉₇	1	1	yes	characteristic
48	C₂²	—	388	1	no	—
49	C₂²	—	194	1	no	—
50	C₂²	C₈×D₉₇	1	1	yes	characteristic
51	C₄	—	194	1	no	—
52	C₄	#13095488	1	1	yes	characteristic
53	C₄	#13095494	1	1	yes	characteristic
54	C₂	—	2	1	no	—
55	C₂	—	388	1	no	—
56	C₂	#15690722	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#13095488
commutator	C₂²×C₉₇	C₂×C₈
Frattini	C₂×C₈	C₂×D₉₇
Fitting	M₃₂×C₉₇	C₂
socle	C₂×C₉₇	C₂²⋊C₈
hypercenter	M₃₂	D₉₇
hypocenter	C₉₇	#349
LCS	G ▷ C₂²×C₉₇ ▷ C₂×C₉₇ ▷ C₉₇
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ M₃₂

Complements

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

N	H ≅ G/N	type
2. #15690750	C₂	semidirect
3. M₃₂×C₉₇	C₂	semidirect
28. C₉₇	#349	semidirect
32. M₃₂	D₉₇	semidirect