Subgroups — #20260487

Order 6208.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#11715895	C₂	1	1	yes	maximal, characteristic
2	C₄×#11715895	C₂	1	1	yes	maximal, characteristic
3	C₄⋊C₈×C₉₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#11715895	—	2	1	no	—
5	C₂×#11715895	C₄	1	1	yes	characteristic
6	C₂×#11715895	C₄	1	1	yes	characteristic
7	C₂×C₈×C₉₇	—	2	1	no	—
8	C₄²×C₉₇	C₂²	1	1	yes	characteristic
9	C₂×C₄×C₉₇	C₂×C₄	1	1	yes	characteristic
10	C₂×C₄×C₉₇	D₄	1	1	yes	characteristic
11	C₂×C₄×C₉₇	Q₈	1	1	yes	characteristic
12	C₈×C₉₇	—	4	1	no	—
13	#11715895	—	2	1	no	—
14	#11715895	—	4	1	no	—
15	#11715895	C₈	1	2	yes	complemented
16	C₂²×C₉₇	C₄⋊C₄	1	1	yes	characteristic
17	C₄×C₉₇	—	2	1	no	—
18	C₄×C₉₇	C₂×C₈	1	1	yes	characteristic
19	C₄×C₉₇	M₁₆	1	1	yes	characteristic
20	C₄×C₉₇	D₈	1	1	yes	characteristic
21	C₄×C₉₇	Q₁₆	1	1	yes	characteristic
22	C₂×C₉₇	C₄⋊C₈	1	1	yes	characteristic
23	C₂×C₉₇	#107	1	1	yes	characteristic
24	C₂×C₉₇	#108	1	1	yes	characteristic
25	C₉₇	#335	1	1	yes	characteristic, complemented, Sylow
26	#335	—	97	1	no	maximal, Sylow
27	C₄⋊C₈	—	97	1	no	—
28	C₄⋊C₈	D₉₇	1	1	yes	characteristic
29	C₄×C₈	—	97	1	no	—
30	C₂×C₈	—	2	1	no	—
31	C₂×C₈	—	97	1	no	—
32	C₂×C₈	—	97	1	no	—
33	C₂×C₈	—	194	1	no	—
34	C₄²	C₂×D₉₇	1	1	yes	characteristic
35	C₂×C₄	Dic₁₉₄	1	1	yes	characteristic
36	C₂×C₄	C₄×D₉₇	1	1	yes	characteristic
37	C₂×C₄	C₂²⋊D₉₇	1	1	yes	characteristic
38	C₈	—	4	1	no	—
39	C₈	—	97	2	no	—
40	C₈	—	388	1	no	—
41	C₈	—	194	1	no	—
42	C₂²	#13095490	1	1	yes	characteristic
43	C₄	—	2	1	no	—
44	C₄	C₈×D₉₇	1	1	yes	characteristic
45	C₄	#13095494	1	1	yes	characteristic
46	C₄	#13095496	1	1	yes	characteristic
47	C₄	#13095501	1	1	yes	characteristic
48	C₂	#15690739	1	1	yes	characteristic
49	C₂	#15690743	1	1	yes	characteristic
50	C₂	#15690745	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊D₉₇
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
15. #11715895	C₈	semidirect
25. C₉₇	#335	semidirect