Subgroups — #20261775

Order 6208.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×#87604	C₂	1	2	yes	maximal
2	#15690878	C₂	1	1	yes	maximal, characteristic
3	#15690873	C₂	1	2	yes	maximal
4	#15690864	C₂	1	1	yes	maximal, characteristic
5	Q₁₆×D₉₇	C₂	1	1	yes	maximal, characteristic
6	#13095519	C₂²	1	1	yes	characteristic
7	C₄⋊#87604	—	2	2	no	—
8	C₄⋊#87604	C₂²	1	2	yes	—
9	C₄×#87604	—	2	2	no	—
10	C₄×#87604	C₂²	1	1	yes	characteristic
11	Q₈×D₉₇	C₂²	1	2	yes	—
12	Dic₃₈₈	C₄	1	1	yes	characteristic, complemented
13	#13095501	C₄	1	2	yes	complemented
14	C₈×D₉₇	C₂²	1	1	yes	characteristic
15	Q₁₆×C₉₇	C₄	1	1	yes	characteristic, complemented
16	C₂×#87604	—	2	2	no	—
17	C₂×#87604	D₄	1	2	yes	—
18	Q₈×C₉₇	C₂×C₄	1	2	yes	—
19	C₄×D₉₇	—	2	2	no	—
20	C₄×D₉₇	C₂³	1	1	yes	characteristic
21	Dic₁₉₄	—	2	2	no	—
22	Dic₁₉₄	C₂×C₄	1	2	yes	—
23	#11715897	—	2	1	no	—
24	C₈×C₉₇	C₂×C₄	1	1	yes	characteristic
25	#11715895	C₂×C₄	1	1	yes	characteristic
26	C₂×D₉₇	C₂×D₄	1	1	yes	characteristic
27	#87604	—	2	2	no	—
28	#87604	—	4	2	no	—
29	C₄×C₉₇	—	2	2	no	—
30	C₄×C₉₇	C₂²×C₄	1	1	yes	characteristic
31	Dic₉₇	—	2	2	no	—
32	Dic₉₇	#41	1	1	yes	characteristic
33	C₂×C₉₇	C₄×D₄	1	1	yes	characteristic
34	D₉₇	#137	1	2	yes	—
35	C₉₇	#441	1	1	yes	characteristic, complemented, Sylow
36	#441	—	97	1	no	maximal, Sylow
37	C₂×Q₁₆	—	97	1	no	—
38	C₄×Q₈	—	97	2	no	—
39	#106	—	97	1	no	—
40	#103	—	97	2	no	—
41	#97	—	97	1	no	—
42	C₂×Q₈	—	97	2	no	—
43	Q₁₆	—	97	2	no	—
44	Q₁₆	—	97	1	no	—
45	Q₁₆	#87604	1	1	yes	characteristic, complemented
46	C₂×C₈	—	97	1	no	—
47	C₂×C₈	—	97	1	no	—
48	C₄⋊C₄	—	97	2	no	—
49	C₄⋊C₄	—	194	2	no	—
50	C₄²	—	97	1	no	—
51	C₄²	—	194	2	no	—
52	Q₈	—	97	2	no	—
53	Q₈	—	194	2	no	—
54	Q₈	C₂×#87604	1	2	yes	—
55	C₂×C₄	—	97	1	no	—
56	C₂×C₄	—	97	2	no	—
57	C₂×C₄	—	194	2	no	—
58	C₂×C₄	—	194	2	no	—
59	C₈	—	97	1	no	—
60	C₈	—	194	1	no	—
61	C₈	C₂×#87604	1	1	yes	characteristic
62	C₂²	—	97	1	no	—
63	C₄	—	2	2	no	—
64	C₄	—	97	1	no	—
65	C₄	—	388	2	no	—
66	C₄	—	194	2	no	—
67	C₄	—	194	2	no	—
68	C₄	C₂²×#87604	1	1	yes	characteristic
69	C₂	—	97	2	no	—
70	C₂	D₄×#87604	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×#87604
commutator	C₄×C₉₇	C₂²×C₄
Frattini	C₄	C₂²×#87604
Fitting	Q₁₆×C₉₇	C₄
socle	C₂×C₉₇	C₄×D₄
hypercenter	Q₁₆	#87604
hypocenter	C₉₇	#441
LCS	G ▷ C₄×C₉₇ ▷ C₂×C₉₇ ▷ C₉₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ Q₁₆

Complements

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

N	H ≅ G/N	type
12. Dic₃₈₈	C₄	semidirect
13. #13095501	C₄	semidirect
15. Q₁₆×C₉₇	C₄	semidirect
35. C₉₇	#441	semidirect
45. Q₁₆	#87604	semidirect