Subgroups — #27135077

Order 12352.

50 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	—	2	1	no	—
7	C₂×C₈×C₁₉₃	C₂²	1	1	yes	characteristic
8	C₁₆×C₁₉₃	—	2	1	no	—
9	C₂×Dic₁₉₃	C₈	1	1	yes	characteristic
10	C₂×Dic₁₉₃	C₈	1	1	yes	characteristic
11	#13095393	—	2	1	no	—
12	C₂×C₄×C₁₉₃	C₂×C₄	1	1	yes	characteristic
13	C₈×C₁₉₃	D₄	1	1	yes	characteristic
14	C₈×C₁₉₃	Q₈	1	1	yes	characteristic
15	C₂²×C₁₉₃	C₂×C₈	1	1	yes	characteristic
16	C₄×C₁₉₃	C₄⋊C₄	1	1	yes	characteristic
17	C₄×C₁₉₃	M₁₆	1	1	yes	characteristic
18	Dic₁₉₃	—	2	1	no	—
19	Dic₁₉₃	C₁₆	1	2	yes	complemented
20	C₂×C₁₉₃	C₄⋊C₈	1	1	yes	characteristic
21	C₂×C₁₉₃	C₂×C₁₆	1	1	yes	characteristic
22	C₂×C₁₉₃	M₃₂	1	1	yes	characteristic
23	C₁₉₃	C₄⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
24	C₄⋊C₁₆	—	193	1	no	maximal, Sylow
25	C₂×C₁₆	—	193	1	no	—
26	C₂×C₁₆	D₁₉₃	1	1	yes	characteristic
27	C₄×C₈	—	193	1	no	—
28	C₂×C₈	—	193	1	no	—
29	C₂×C₈	C₂×D₁₉₃	1	1	yes	characteristic
30	C₄²	—	193	1	no	—
31	C₁₆	—	2	1	no	—
32	C₁₆	—	386	1	no	—
33	C₂×C₄	—	193	1	no	—
34	C₂×C₄	—	193	1	no	—
35	C₂×C₄	C₄×D₁₉₃	1	1	yes	characteristic
36	C₈	—	386	1	no	—
37	C₈	C₂²⋊D₁₉₃	1	1	yes	characteristic
38	C₈	Dic₃₈₆	1	1	yes	characteristic
39	C₂²	C₈×D₁₉₃	1	1	yes	characteristic
40	C₄	—	386	1	no	—
41	C₄	—	193	2	no	—
42	C₄	#15690534	1	1	yes	characteristic
43	C₄	#15690538	1	1	yes	characteristic
44	C₂	#20259828	1	1	yes	characteristic
45	C₂	C₁₆×D₁₉₃	1	1	yes	characteristic
46	C₂	#20259838	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂×D₁₉₃
commutator	C₂×C₁₉₃	C₂×C₁₆
Fitting	C₂×C₁₆×C₁₉₃	C₂
socle, prime radical	C₂²×C₁₉₃	C₂×C₈
cosocle	C₂×C₈×C₁₉₃	C₂²
hypercenter	C₂×C₁₆	D₁₉₃
hypocenter	C₁₉₃	C₄⋊C₁₆
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
19. Dic₁₉₃	C₁₆	semidirect
23. C₁₉₃	C₄⋊C₁₆	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
C₄⋊C₁₆	193