Subgroups — #20261585

Order 6208.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#11715897	C₂	1	1	yes	maximal, characteristic
2	C₄×#11715897	C₂	1	1	yes	maximal, characteristic
3	#15690775	C₂	1	1	yes	maximal, characteristic
4	C₂×#11715897	—	2	1	no	—
5	C₂×#11715897	—	2	1	no	—
6	C₂×Dic₁₉₄	C₄	1	1	yes	characteristic
7	#13095490	—	2	1	no	—
8	C₄×Dic₉₇	—	2	1	no	—
9	C₄×Dic₉₇	C₂²	1	1	yes	characteristic
10	C₄⋊C₄×C₉₇	C₄	1	1	yes	characteristic
11	C₂×C₄×C₉₇	—	2	1	no	—
12	C₂×C₄×C₉₇	C₂×C₄	1	1	yes	characteristic
13	C₂×Dic₉₇	—	2	1	no	—
14	C₂×Dic₉₇	D₄	1	1	yes	characteristic
15	C₂×Dic₉₇	D₄	1	1	yes	characteristic
16	Dic₁₉₄	—	2	1	no	—
17	Dic₁₉₄	C₈	1	2	yes	complemented
18	#11715897	—	2	2	no	—
19	#11715897	—	4	1	no	—
20	C₂²×C₉₇	C₂²⋊C₄	1	1	yes	characteristic
21	C₄×C₉₇	—	4	1	no	—
22	C₄×C₉₇	C₂×C₈	1	1	yes	characteristic
23	C₄×C₉₇	M₁₆	1	1	yes	characteristic
24	Dic₉₇	—	2	2	no	—
25	Dic₉₇	—	2	1	no	—
26	Dic₉₇	SD₁₆	1	1	yes	characteristic
27	Dic₉₇	Q₁₆	1	1	yes	characteristic
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	—	97	1	no	—
35	C₄×C₈	—	97	1	no	—
36	C₂×Q₈	—	97	1	no	—
37	C₂×C₈	—	194	1	no	—
38	C₂×C₈	—	194	1	no	—
39	C₄⋊C₄	—	194	1	no	—
40	C₄⋊C₄	#87604	1	1	yes	characteristic
41	C₄²	—	97	1	no	—
42	C₄²	—	194	1	no	—
43	Q₈	—	97	2	no	—
44	Q₈	—	194	1	no	—
45	C₂×C₄	—	2	1	no	—
46	C₂×C₄	—	97	1	no	—
47	C₂×C₄	—	97	1	no	—
48	C₂×C₄	—	194	1	no	—
49	C₂×C₄	C₂×#87604	1	1	yes	characteristic
50	C₈	—	388	1	no	—
51	C₈	—	194	2	no	—
52	C₂²	C₂²⋊#87604	1	1	yes	characteristic
53	C₄	—	4	1	no	—
54	C₄	—	97	1	no	—
55	C₄	—	97	1	no	—
56	C₄	—	194	2	no	—
57	C₄	—	194	1	no	—
58	C₄	#13095519	1	1	yes	characteristic
59	C₄	#13095521	1	1	yes	characteristic
60	C₂	#15690867	1	1	yes	characteristic
61	C₂	#15690873	1	1	yes	characteristic
62	C₂	#15690874	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²⋊#87604
commutator	C₄×C₉₇	C₂×C₈
Frattini	C₂×C₄	C₂×#87604
Fitting	C₄⋊C₄×C₉₇	C₄
socle	C₂²×C₉₇	C₂²⋊C₄
hypercenter	C₄⋊C₄	#87604
hypocenter	C₉₇	Q₈⋊C₈
LCS	G ▷ C₄×C₉₇ ▷ C₂×C₉₇ ▷ C₉₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₄⋊C₄

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