Subgroups — #20260488

Order 6208.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#11715895	C₂	1	2	yes	maximal
2	C₄×C₈×C₉₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#11715895	—	2	2	no	—
4	C₂×C₈×C₉₇	C₄	1	1	yes	characteristic
5	C₂×C₈×C₉₇	C₄	1	1	yes	characteristic
6	C₄²×C₉₇	C₂²	1	1	yes	characteristic
7	C₂×C₄×C₉₇	C₂×C₄	1	1	yes	characteristic
8	C₂×C₄×C₉₇	D₄	1	1	yes	characteristic
9	C₂×C₄×C₉₇	Q₈	1	1	yes	characteristic
10	C₈×C₉₇	—	2	1	no	—
11	C₈×C₉₇	C₈	1	2	yes	complemented
12	#11715895	—	4	2	no	—
13	C₂²×C₉₇	C₄⋊C₄	1	1	yes	characteristic
14	C₄×C₉₇	—	2	1	no	—
15	C₄×C₉₇	C₂×C₈	1	1	yes	characteristic
16	C₄×C₉₇	M₁₆	1	1	yes	characteristic
17	C₄×C₉₇	D₈	1	1	yes	characteristic
18	C₄×C₉₇	Q₁₆	1	1	yes	characteristic
19	C₂×C₉₇	C₄⋊C₈	1	1	yes	characteristic
20	C₂×C₉₇	#107	1	1	yes	characteristic
21	C₂×C₉₇	#108	1	1	yes	characteristic
22	C₉₇	#335	1	1	yes	characteristic, complemented, Sylow
23	#335	—	97	1	no	maximal, Sylow
24	C₄⋊C₈	—	97	2	no	—
25	C₄×C₈	D₉₇	1	1	yes	characteristic
26	C₂×C₈	—	194	2	no	—
27	C₂×C₈	Dic₉₇	1	1	yes	characteristic
28	C₂×C₈	Dic₉₇	1	1	yes	characteristic
29	C₄²	C₂×D₉₇	1	1	yes	characteristic
30	C₂×C₄	Dic₁₉₄	1	1	yes	characteristic
31	C₂×C₄	D₃₈₈	1	1	yes	characteristic
32	C₂×C₄	C₂×Dic₉₇	1	1	yes	characteristic
33	C₈	—	2	1	no	—
34	C₈	—	388	2	no	—
35	C₈	#11715895	1	2	yes	complemented
36	C₂²	C₄⋊Dic₉₇	1	1	yes	characteristic
37	C₄	—	2	1	no	—
38	C₄	C₂×#11715895	1	1	yes	characteristic
39	C₄	#13095495	1	1	yes	characteristic
40	C₄	D₇₇₆	1	1	yes	characteristic
41	C₄	Dic₃₈₈	1	1	yes	characteristic
42	C₂	C₄⋊#11715895	1	1	yes	characteristic
43	C₂	#15690744	1	1	yes	characteristic
44	C₂	#15690746	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₃₈₈
commutator	C₄×C₉₇	C₂×C₈
Frattini	C₄²	C₂×D₉₇
Fitting	C₄×C₈×C₉₇	C₂
socle	C₂²×C₉₇	C₄⋊C₄
hypercenter	C₄×C₈	D₉₇
hypocenter	C₉₇	#335
LCS	G ▷ C₄×C₉₇ ▷ C₂×C₉₇ ▷ C₉₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
11. C₈×C₉₇	C₈	semidirect
22. C₉₇	#335	semidirect
35. C₈	#11715895	semidirect