Subgroups — #20261648

Order 6208.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15690883	C₂	1	1	yes	maximal, characteristic
2	#15690879	C₂	1	1	yes	maximal, characteristic
3	Q₁₆×D₉₇	C₂	1	1	yes	maximal, characteristic
4	C₄⋊#87604	—	2	1	no	—
5	#13095514	—	2	1	no	—
6	Q₈×D₉₇	—	2	1	no	—
7	Dic₃₈₈	C₄	1	1	yes	characteristic, complemented
8	#13095501	—	2	1	no	—
9	C₈×D₉₇	C₂²	1	1	yes	characteristic
10	Q₁₆×C₉₇	C₄	1	1	yes	characteristic, complemented
11	C₂×#87604	—	4	1	no	—
12	Q₈×C₉₇	—	2	1	no	—
13	C₄×D₉₇	—	4	1	no	—
14	C₄×D₉₇	D₄	1	1	yes	characteristic
15	Dic₁₉₄	—	2	1	no	—
16	Dic₁₉₄	—	4	1	no	—
17	C₈×C₉₇	C₂×C₄	1	1	yes	characteristic
18	#11715895	D₄	1	1	yes	characteristic
19	C₂×D₉₇	D₈	1	1	yes	characteristic
20	#87604	—	8	1	no	—
21	C₄×C₉₇	—	4	1	no	—
22	C₄×C₉₇	C₂²⋊C₄	1	1	yes	characteristic
23	Dic₉₇	—	4	1	no	—
24	Dic₉₇	SD₁₆	1	1	yes	characteristic
25	C₂×C₉₇	#102	1	1	yes	characteristic
26	D₉₇	SD₃₂	1	1	yes	characteristic
27	D₉₇	Q₃₂	1	1	yes	characteristic
28	C₉₇	#358	1	1	yes	characteristic, complemented, Sylow
29	#358	—	97	1	no	maximal, Sylow
30	C₂×Q₁₆	—	97	1	no	—
31	C₂×C₁₆	—	97	1	no	—
32	#107	—	97	1	no	—
33	C₂×Q₈	—	194	1	no	—
34	Q₁₆	—	97	1	no	—
35	Q₁₆	—	194	1	no	—
36	Q₁₆	#87604	1	1	yes	characteristic, complemented
37	C₂×C₈	—	97	1	no	—
38	C₄⋊C₄	—	194	1	no	—
39	C₁₆	—	194	1	no	—
40	Q₈	—	2	1	no	—
41	Q₈	—	388	1	no	—
42	Q₈	—	194	1	no	—
43	C₂×C₄	—	97	1	no	—
44	C₂×C₄	—	388	1	no	—
45	C₂×C₄	—	388	1	no	—
46	C₈	—	97	1	no	—
47	C₈	C₂×#87604	1	1	yes	characteristic
48	C₂²	—	97	1	no	—
49	C₄	—	4	1	no	—
50	C₄	—	776	1	no	—
51	C₄	—	97	1	no	—
52	C₄	—	388	1	no	—
53	C₄	C₂²⋊#87604	1	1	yes	characteristic
54	C₂	—	97	1	no	—
55	C₂	—	97	1	no	—
56	C₂	#15690872	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#15690872
commutator	C₈×C₉₇	C₂×C₄
Frattini	C₈	C₂×#87604
Fitting	Q₁₆×C₉₇	C₄
socle	C₂×C₉₇	#102
hypercenter	Q₁₆	#87604
hypocenter	C₉₇	#358
LCS	G ▷ C₈×C₉₇ ▷ C₄×C₉₇ ▷ C₂×C₉₇ ▷ C₉₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ Q₁₆

Complements

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

N	H ≅ G/N	type
7. Dic₃₈₈	C₄	semidirect
10. Q₁₆×C₉₇	C₄	semidirect
28. C₉₇	#358	semidirect
36. Q₁₆	#87604	semidirect