Subgroups — #20260549

Order 6208.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₇₇₆	C₂	1	1	yes	maximal, characteristic
2	#15690746	C₂	1	1	yes	maximal, characteristic, complemented
3	M₃₂×C₉₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₃₈₈	—	2	1	no	—
5	D₇₇₆	—	2	1	no	—
6	D₇₇₆	C₄	1	2	yes	—
7	#13095495	—	2	1	no	—
8	C₂×C₈×C₉₇	C₂²	1	1	yes	characteristic
9	C₁₆×C₉₇	—	2	1	no	—
10	C₂²×D₉₇	—	4	1	no	—
11	C₂×C₄×C₉₇	D₄	1	1	yes	characteristic
12	D₃₈₈	—	2	2	no	—
13	D₃₈₈	—	4	1	no	—
14	C₈×C₉₇	C₂×C₄	1	1	yes	characteristic
15	C₈×C₉₇	D₄	1	1	yes	characteristic
16	#11715895	—	4	1	no	—
17	C₂²×C₉₇	SD₁₆	1	1	yes	characteristic
18	C₂×D₉₇	—	4	2	no	—
19	C₂×D₉₇	—	8	2	no	—
20	C₄×C₉₇	C₂²⋊C₄	1	1	yes	characteristic
21	C₄×C₉₇	D₈	1	1	yes	characteristic
22	C₂×C₉₇	—	2	1	no	—
23	C₂×C₉₇	#102	1	1	yes	characteristic
24	D₉₇	—	8	2	no	—
25	C₉₇	#361	1	1	yes	characteristic, complemented, Sylow
26	#361	—	97	1	no	maximal, Sylow
27	C₂×D₈	—	97	1	no	—
28	M₃₂	D₉₇	1	1	yes	characteristic, complemented
29	#108	—	97	1	no	—
30	C₂×D₄	—	194	1	no	—
31	D₈	—	97	2	no	—
32	D₈	—	194	1	no	—
33	M₁₆	—	194	1	no	—
34	C₂×C₈	C₂×D₉₇	1	1	yes	characteristic
35	C₁₆	—	2	1	no	—
36	C₂³	—	388	1	no	—
37	D₄	—	388	1	no	—
38	D₄	—	194	2	no	—
39	C₂×C₄	D₃₈₈	1	1	yes	characteristic
40	C₈	—	388	1	no	—
41	C₈	C₄×D₉₇	1	1	yes	characteristic
42	C₈	C₂²⋊D₉₇	1	1	yes	characteristic
43	C₂²	—	776	2	no	—
44	C₂²	—	388	2	no	—
45	C₂²	#13095500	1	1	yes	characteristic
46	C₄	#13095488	1	1	yes	characteristic
47	C₄	D₇₇₆	1	1	yes	characteristic
48	C₂	—	2	1	no	—
49	C₂	—	776	2	no	—
50	C₂	#15690732	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#15690732
commutator	C₈×C₉₇	C₂×C₄
Frattini	C₂×C₈	C₂×D₉₇
Fitting	M₃₂×C₉₇	C₂
socle	C₂×C₉₇	#102
hypercenter	M₃₂	D₉₇
hypocenter	C₉₇	#361
LCS	G ▷ C₈×C₉₇ ▷ C₄×C₉₇ ▷ C₂×C₉₇ ▷ C₉₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ M₃₂

Complements

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

N	H ≅ G/N	type
2. #15690746	C₂	semidirect
3. M₃₂×C₉₇	C₂	semidirect
25. C₉₇	#361	semidirect
28. M₃₂	D₉₇	semidirect