Subgroups — #20261633

Order 6208.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15690884	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#13095514	C₂	1	1	yes	maximal, characteristic, complemented
3	#15690817	C₂	1	1	yes	maximal, characteristic
4	#13095514	—	2	1	no	—
5	#13095514	—	2	1	no	—
6	#13095495	—	2	1	no	—
7	#13095495	C₄	1	1	yes	characteristic
8	C₂×#11715895	—	2	1	no	—
9	C₂×#11715895	C₂²	1	1	yes	characteristic
10	#41×C₉₇	C₄	1	1	yes	characteristic
11	Q₈×C₉₇	C₈	1	1	yes	characteristic
12	D₄×C₉₇	—	2	1	no	—
13	D₄×C₉₇	C₈	1	1	yes	characteristic
14	C₂×C₄×C₉₇	—	2	1	no	—
15	C₂×C₄×C₉₇	C₂×C₄	1	1	yes	characteristic
16	#11715895	—	2	1	no	—
17	#11715895	D₄	1	1	yes	characteristic
18	#11715895	D₄	1	1	yes	characteristic
19	C₂²×C₉₇	—	2	1	no	—
20	C₂²×C₉₇	M₁₆	1	1	yes	characteristic
21	C₄×C₉₇	—	2	1	no	—
22	C₄×C₉₇	C₂²⋊C₄	1	1	yes	characteristic
23	C₄×C₉₇	C₂×C₈	1	1	yes	characteristic
24	C₂×C₉₇	—	2	1	no	—
25	C₂×C₉₇	—	4	1	no	—
26	C₂×C₉₇	C₂²⋊C₈	1	1	yes	characteristic
27	C₉₇	#350	1	1	yes	characteristic, complemented, Sylow
28	#350	—	97	1	no	maximal, Sylow
29	#131	—	97	1	no	—
30	M₃₂	—	97	1	no	—
31	C₂×C₁₆	—	97	1	no	—
32	#41	#87604	1	1	yes	characteristic
33	M₁₆	—	97	1	no	—
34	M₁₆	—	194	1	no	—
35	C₂×C₈	—	97	1	no	—
36	C₂×C₈	—	194	1	no	—
37	C₁₆	—	194	1	no	—
38	C₁₆	—	194	1	no	—
39	Q₈	#11715897	1	1	yes	characteristic
40	D₄	—	2	1	no	—
41	D₄	#11715897	1	1	yes	characteristic
42	C₂×C₄	—	2	1	no	—
43	C₂×C₄	C₂×#87604	1	1	yes	characteristic
44	C₈	—	97	1	no	—
45	C₈	—	97	1	no	—
46	C₈	—	194	1	no	—
47	C₂²	—	2	1	no	—
48	C₂²	#13095520	1	1	yes	characteristic
49	C₄	—	2	1	no	—
50	C₄	C₂²⋊#87604	1	1	yes	characteristic
51	C₄	C₂×#11715897	1	1	yes	characteristic
52	C₂	—	2	1	no	—
53	C₂	—	4	1	no	—
54	C₂	C₂²⋊#11715897	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²⋊#87604
commutator	C₄×C₉₇	C₂×C₈
Frattini	C₂×C₄	C₂×#87604
Fitting	#41×C₉₇	C₄
socle	C₂×C₉₇	C₂²⋊C₈
hypercenter	#41	#87604
hypocenter	C₉₇	#350
LCS	G ▷ C₄×C₉₇ ▷ C₂×C₉₇ ▷ C₉₇
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ #41

Complements

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

N	H ≅ G/N	type
1. #15690884	C₂	semidirect
2. C₂×#13095514	C₂	semidirect
27. C₉₇	#350	semidirect