Subgroups — #20259930

Order 6176.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15690555	C₂	1	1	yes	maximal, characteristic
2	#15690545	C₂	1	2	yes	maximal, complemented
3	#15690542	C₂	1	2	yes	maximal, complemented
4	#15690539	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×Q₈×C₁₉₃	C₂	1	1	yes	maximal, characteristic, complemented
6	Dic₃₈₆	C₂²	1	1	yes	characteristic
7	D₇₇₂	C₂²	1	1	yes	characteristic
8	C₂²⋊D₁₉₃	—	2	1	no	—
9	C₄×D₁₉₃	—	2	1	no	—
10	#13095393	C₂²	1	2	yes	—
11	Q₈×C₁₉₃	—	2	1	no	—
12	Q₈×C₁₉₃	C₂²	1	2	yes	—
13	C₂×C₄×C₁₉₃	—	2	1	no	—
14	C₂×C₄×C₁₉₃	C₂²	1	1	yes	characteristic
15	C₂²×C₁₉₃	D₄	1	1	yes	characteristic
16	C₂×D₁₉₃	—	2	1	no	—
17	C₄×C₁₉₃	—	2	2	no	—
18	C₄×C₁₉₃	D₄	1	1	yes	characteristic
19	C₄×C₁₉₃	C₂³	1	1	yes	characteristic
20	Dic₁₉₃	—	2	1	no	—
21	C₂×C₁₉₃	—	2	1	no	—
22	C₂×C₁₉₃	C₂×D₄	1	1	yes	characteristic
23	D₁₉₃	—	4	1	no	—
24	C₁₉₃	#137	1	1	yes	characteristic, complemented, Sylow
25	#137	—	193	1	no	maximal, Sylow
26	#41	—	193	1	no	—
27	C₂×Q₈	D₁₉₃	1	1	yes	characteristic, complemented
28	Q₁₆	—	193	2	no	—
29	SD₁₆	—	193	2	no	—
30	M₁₆	—	193	1	no	—
31	Q₈	—	2	1	no	—
32	Q₈	—	193	1	no	—
33	Q₈	C₂×D₁₉₃	1	2	yes	—
34	D₄	—	386	1	no	—
35	D₄	—	193	1	no	—
36	C₂×C₄	—	2	1	no	—
37	C₂×C₄	—	386	1	no	—
38	C₂×C₄	C₂×D₁₉₃	1	1	yes	characteristic
39	C₈	—	193	2	no	—
40	C₂²	—	386	1	no	—
41	C₂²	C₂²⋊D₁₉₃	1	1	yes	characteristic
42	C₄	—	2	2	no	—
43	C₄	—	386	1	no	—
44	C₄	C₂²⋊D₁₉₃	1	1	yes	characteristic
45	C₄	C₂²×D₁₉₃	1	1	yes	characteristic
46	C₂	—	2	1	no	—
47	C₂	—	772	1	no	—
48	C₂	C₂×C₂²⋊D₁₉₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×C₂²⋊D₁₉₃
commutator	C₄×C₁₉₃	C₂³
Frattini	C₄	C₂²×D₁₉₃
Fitting	C₂×Q₈×C₁₉₃	C₂
socle	C₂×C₁₉₃	C₂×D₄
hypercenter	C₂×Q₈	D₁₉₃
hypocenter	C₁₉₃	#137
LCS	G ▷ C₄×C₁₉₃ ▷ C₂×C₁₉₃ ▷ C₁₉₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
2. #15690545	C₂	semidirect
3. #15690542	C₂	semidirect
4. #15690539	C₂	semidirect
5. C₂×Q₈×C₁₉₃	C₂	semidirect
24. C₁₉₃	#137	semidirect
27. C₂×Q₈	D₁₉₃	semidirect