Subgroups — #20260465

Order 6208.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×Dic₁₉₄	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×Dic₁₉₄	C₄	1	1	yes	characteristic
5	C₂×#11715895	—	2	1	no	—
6	C₄⋊Dic₉₇	C₄	1	1	yes	characteristic
7	#13095490	—	2	1	no	—
8	C₄×Dic₉₇	—	2	1	no	—
9	C₂×C₈×C₉₇	—	2	1	no	—
10	C₄²×C₉₇	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₉₇	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄×C₉₇	D₄	1	1	yes	characteristic
13	C₂×C₄×C₉₇	D₄	1	1	yes	characteristic
14	C₂×Dic₉₇	—	2	1	no	—
15	C₂×Dic₉₇	—	2	1	no	—
16	Dic₁₉₄	—	2	1	no	—
17	Dic₁₉₄	C₈	1	2	yes	complemented
18	C₈×C₉₇	—	4	1	no	—
19	#11715895	—	2	2	no	—
20	C₂²×C₉₇	C₂²⋊C₄	1	1	yes	characteristic
21	C₄×C₉₇	—	2	1	no	—
22	C₄×C₉₇	C₂×C₈	1	1	yes	characteristic
23	C₄×C₉₇	M₁₆	1	1	yes	characteristic
24	C₄×C₉₇	SD₁₆	1	1	yes	characteristic
25	C₄×C₉₇	Q₁₆	1	1	yes	characteristic
26	Dic₉₇	—	2	2	no	—
27	Dic₉₇	—	4	1	no	—
28	C₂×C₉₇	C₂²⋊C₈	1	1	yes	characteristic
29	C₂×C₉₇	#103	1	1	yes	characteristic
30	C₂×C₉₇	#104	1	1	yes	characteristic
31	C₉₇	Q₈⋊C₈	1	1	yes	characteristic, complemented, Sylow
32	Q₈⋊C₈	—	97	1	no	maximal, Sylow
33	C₄×Q₈	—	97	1	no	—
34	C₄⋊C₈	D₉₇	1	1	yes	characteristic
35	C₄×C₈	—	97	1	no	—
36	C₂×Q₈	—	97	1	no	—
37	C₂×C₈	—	2	1	no	—
38	C₂×C₈	—	194	1	no	—
39	C₄⋊C₄	—	97	1	no	—
40	C₄⋊C₄	—	194	1	no	—
41	C₄²	—	194	1	no	—
42	C₄²	C₂×D₉₇	1	1	yes	characteristic
43	Q₈	—	97	2	no	—
44	Q₈	—	194	1	no	—
45	C₂×C₄	—	194	1	no	—
46	C₂×C₄	—	194	1	no	—
47	C₂×C₄	C₄×D₉₇	1	1	yes	characteristic
48	C₂×C₄	D₃₈₈	1	1	yes	characteristic
49	C₂×C₄	C₂²⋊D₉₇	1	1	yes	characteristic
50	C₈	—	4	1	no	—
51	C₈	—	194	2	no	—
52	C₂²	#13095488	1	1	yes	characteristic
53	C₄	—	2	1	no	—
54	C₄	—	388	1	no	—
55	C₄	—	194	2	no	—
56	C₄	C₈×D₉₇	1	1	yes	characteristic
57	C₄	#13095494	1	1	yes	characteristic
58	C₄	#13095499	1	1	yes	characteristic
59	C₄	#13095501	1	1	yes	characteristic
60	C₂	#15690722	1	1	yes	characteristic
61	C₂	#15690733	1	1	yes	characteristic
62	C₂	#15690736	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	C₂²⋊C₄
hypercenter	C₄⋊C₈	D₉₇
hypocenter	C₉₇	Q₈⋊C₈
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
17. Dic₁₉₄	C₈	semidirect
31. C₉₇	Q₈⋊C₈	semidirect