Subgroups — #20261027

Order 6208.

96 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	#15690743	C₂	1	2	yes	maximal
3	C₄⋊#11715895	C₂	1	1	yes	maximal, characteristic
4	#15690733	C₂	1	2	yes	maximal
5	C₄⋊Q₈×C₉₇	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₁₉₄	C₂²	1	1	yes	characteristic
7	C₂×#11715895	C₂²	1	2	yes	—
8	C₄⋊Dic₉₇	C₂²	1	1	yes	characteristic
9	#13095490	—	2	1	no	—
10	C₄×Dic₉₇	—	2	1	no	—
11	C₂×Q₈×C₉₇	—	2	1	no	—
12	C₄⋊C₄×C₉₇	—	2	1	no	—
13	C₄⋊C₄×C₉₇	C₂²	1	2	yes	—
14	C₄²×C₉₇	C₂²	1	1	yes	characteristic
15	Q₈×C₉₇	—	4	2	no	—
16	C₂×C₄×C₉₇	—	2	2	no	—
17	C₂×C₄×C₉₇	D₄	1	1	yes	characteristic
18	C₂×C₄×C₉₇	D₄	1	1	yes	characteristic
19	C₂×C₄×C₉₇	C₂³	1	1	yes	characteristic
20	C₂×Dic₉₇	—	2	1	no	—
21	C₂×Dic₉₇	—	2	1	no	—
22	Dic₁₉₄	—	2	1	no	—
23	Dic₁₉₄	Q₈	1	2	yes	complemented
24	#11715895	—	2	2	no	—
25	C₂²×C₉₇	C₂×D₄	1	1	yes	characteristic
26	C₄×C₉₇	—	2	1	no	—
27	C₄×C₉₇	—	4	2	no	—
28	C₄×C₉₇	Q₁₆	1	2	yes	—
29	C₄×C₉₇	C₂×Q₈	1	1	yes	characteristic
30	C₄×C₉₇	#41	1	1	yes	characteristic
31	Dic₉₇	—	2	2	no	—
32	Dic₉₇	—	4	1	no	—
33	C₂×C₉₇	C₂²⋊Q₈	1	1	yes	characteristic
34	C₂×C₉₇	C₂×Q₁₆	1	1	yes	characteristic
35	C₂×C₉₇	AGL(1,ℤ/8)	1	1	yes	characteristic
36	C₉₇	#477	1	1	yes	characteristic, complemented, Sylow
37	#477	—	97	1	no	maximal, Sylow
38	C₄⋊Q₈	D₉₇	1	1	yes	characteristic
39	C₄×Q₈	—	97	1	no	—
40	#107	—	97	2	no	—
41	C₄⋊C₈	—	97	1	no	—
42	#103	—	97	2	no	—
43	C₂×Q₈	—	2	1	no	—
44	C₂×Q₈	—	97	1	no	—
45	C₂×C₈	—	97	2	no	—
46	C₄⋊C₄	—	2	1	no	—
47	C₄⋊C₄	—	97	1	no	—
48	C₄⋊C₄	—	194	1	no	—
49	C₄⋊C₄	C₂×D₉₇	1	2	yes	—
50	C₄²	—	194	1	no	—
51	C₄²	C₂×D₉₇	1	1	yes	characteristic
52	Q₈	—	4	2	no	—
53	Q₈	—	97	2	no	—
54	Q₈	—	194	1	no	—
55	C₂×C₄	—	2	2	no	—
56	C₂×C₄	—	194	1	no	—
57	C₂×C₄	—	194	1	no	—
58	C₂×C₄	C₂²⋊D₉₇	1	1	yes	characteristic
59	C₂×C₄	C₂²⋊D₉₇	1	1	yes	characteristic
60	C₂×C₄	C₂²×D₉₇	1	1	yes	characteristic
61	C₈	—	194	2	no	—
62	C₂²	C₂×C₂²⋊D₉₇	1	1	yes	characteristic
63	C₄	—	2	1	no	—
64	C₄	—	4	2	no	—
65	C₄	—	388	1	no	—
66	C₄	—	194	2	no	—
67	C₄	#13095501	1	2	yes	—
68	C₄	Q₈×D₉₇	1	1	yes	characteristic
69	C₄	#13095512	1	1	yes	characteristic
70	C₂	#15690786	1	1	yes	characteristic
71	C₂	C₂×#13095501	1	1	yes	characteristic
72	C₂	#15690836	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₉₇
commutator	C₂×C₄×C₉₇	C₂³
Frattini	C₂×C₄	C₂²×D₉₇
Fitting	C₄⋊Q₈×C₉₇	C₂
socle	C₂²×C₉₇	C₂×D₄
hypercenter	C₄⋊Q₈	D₉₇
hypocenter	C₉₇	#477
LCS	G ▷ C₂×C₄×C₉₇ ▷ C₂×C₉₇ ▷ C₉₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
23. Dic₁₉₄	Q₈	semidirect
36. C₉₇	#477	semidirect