Subgroups — #27135034

Order 12352.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15690530	C₂	1	1	yes	maximal, characteristic
2	C₈×Dic₁₉₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₆×C₁₉₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#13095393	C₄	1	1	yes	characteristic
5	C₄×Dic₁₉₃	C₄	1	1	yes	characteristic
6	#15690530	C₄	1	2	yes	complemented
7	C₂×C₈×C₁₉₃	C₂²	1	1	yes	characteristic
8	C₁₆×C₁₉₃	C₄	1	2	yes	complemented
9	C₂×Dic₁₉₃	C₈	1	2	yes	—
10	#13095393	C₈	1	2	yes	—
11	C₂×C₄×C₁₉₃	C₂×C₄	1	1	yes	characteristic
12	C₈×C₁₉₃	C₂×C₄	1	1	yes	characteristic
13	C₈×C₁₉₃	C₂×C₄	1	1	yes	characteristic
14	C₂²×C₁₉₃	C₂×C₈	1	1	yes	characteristic
15	C₄×C₁₉₃	C₄²	1	1	yes	characteristic
16	C₄×C₁₉₃	C₂×C₈	1	1	yes	characteristic
17	Dic₁₉₃	—	2	2	no	—
18	C₂×C₁₉₃	C₄×C₈	1	1	yes	characteristic
19	C₂×C₁₉₃	M₃₂	1	2	yes	—
20	C₁₉₃	#346	1	1	yes	characteristic, complemented, Sylow
21	#346	—	193	1	no	maximal, Sylow
22	C₂×C₁₆	—	193	1	no	—
23	C₂×C₁₆	D₁₉₃	1	1	yes	characteristic
24	C₄×C₈	—	193	1	no	—
25	C₂×C₈	—	193	1	no	—
26	C₂×C₈	C₂×D₁₉₃	1	1	yes	characteristic
27	C₄²	—	193	1	no	—
28	C₁₆	—	193	2	no	—
29	C₁₆	Dic₁₉₃	1	2	yes	complemented
30	C₂×C₄	—	193	2	no	—
31	C₂×C₄	C₄×D₁₉₃	1	1	yes	characteristic
32	C₈	—	193	2	no	—
33	C₈	C₄×D₁₉₃	1	1	yes	characteristic
34	C₈	C₂×Dic₁₉₃	1	1	yes	characteristic
35	C₂²	C₈×D₁₉₃	1	1	yes	characteristic
36	C₄	—	386	2	no	—
37	C₄	C₄×Dic₁₉₃	1	1	yes	characteristic
38	C₄	C₈×D₁₉₃	1	1	yes	characteristic
39	C₂	C₈×Dic₁₉₃	1	1	yes	characteristic
40	C₂	#20259838	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂×D₁₉₃
commutator	C₂×C₁₉₃	C₄×C₈
Fitting	C₂×C₁₆×C₁₉₃	C₂
socle, prime radical	C₂²×C₁₉₃	C₂×C₈
cosocle	C₂×C₈×C₁₉₃	C₂²
hypercenter	C₂×C₁₆	D₁₉₃
hypocenter	C₁₉₃	#346
LCS	G ▷ C₂×C₁₉₃ ▷ C₁₉₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
6. #15690530	C₄	semidirect
8. C₁₆×C₁₉₃	C₄	semidirect
20. C₁₉₃	#346	semidirect
29. C₁₆	Dic₁₉₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#15690530	2
C₈×Dic₁₉₃	2
C₂×C₁₆×C₁₉₃	2
#346	193