Subgroups — #27136180

Order 12352.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15690558	C₂	1	2	yes	maximal
2	C₈×Dic₁₉₃	C₂	1	1	yes	maximal, characteristic
3	#15690558	—	2	2	no	—
4	C₂×#13095393	C₂²	1	1	yes	characteristic
5	C₄×Dic₁₉₃	C₄	1	1	yes	characteristic
6	C₂×C₈×C₁₉₃	C₄	1	1	yes	characteristic
7	C₂×Dic₁₉₃	C₈	1	1	yes	characteristic
8	C₂×Dic₁₉₃	C₈	1	1	yes	characteristic
9	#13095393	D₄	1	1	yes	characteristic
10	#13095393	Q₈	1	1	yes	characteristic
11	C₂×C₄×C₁₉₃	C₂×C₄	1	1	yes	characteristic
12	C₈×C₁₉₃	—	2	1	no	—
13	C₂²×C₁₉₃	C₂×C₈	1	1	yes	characteristic
14	C₄×C₁₉₃	C₄⋊C₄	1	1	yes	characteristic
15	C₄×C₁₉₃	M₁₆	1	1	yes	characteristic
16	Dic₁₉₃	—	2	1	no	—
17	Dic₁₉₃	C₁₆	1	2	yes	complemented
18	C₂×C₁₉₃	C₄⋊C₈	1	1	yes	characteristic
19	C₂×C₁₉₃	C₂×C₁₆	1	1	yes	characteristic
20	C₂×C₁₉₃	M₃₂	1	1	yes	characteristic
21	C₁₉₃	C₄⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
22	C₄⋊C₁₆	—	193	1	no	maximal, Sylow
23	C₂×C₁₆	—	193	2	no	—
24	C₄×C₈	—	193	1	no	—
25	C₂×C₈	—	193	1	no	—
26	C₂×C₈	#11715871	1	1	yes	characteristic
27	C₄²	—	193	1	no	—
28	C₁₆	—	386	2	no	—
29	C₂×C₄	—	193	1	no	—
30	C₂×C₄	—	193	1	no	—
31	C₂×C₄	C₂×#11715871	1	1	yes	characteristic
32	C₈	—	2	1	no	—
33	C₈	—	193	1	no	—
34	C₈	—	193	1	no	—
35	C₂²	#15690563	1	1	yes	characteristic
36	C₄	—	386	1	no	—
37	C₄	—	193	2	no	—
38	C₄	C₄⋊#11715871	1	1	yes	characteristic
39	C₄	#15690564	1	1	yes	characteristic
40	C₂	#20259966	1	1	yes	characteristic
41	C₂	#20259972	1	1	yes	characteristic
42	C₂	#20259974	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂×#11715871
commutator	C₂×C₁₉₃	C₂×C₁₆
Fitting	C₂×C₈×C₁₉₃	C₄
socle, prime radical	C₂²×C₁₉₃	C₂×C₈
cosocle	C₂×#13095393	C₂²
hypercenter	C₂×C₈	#11715871
hypocenter	C₁₉₃	C₄⋊C₁₆
LCS	G ▷ C₂×C₁₉₃ ▷ C₁₉₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
17. Dic₁₉₃	C₁₆	semidirect
21. 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×#15690558	2
C₈×Dic₁₉₃	2
C₄⋊C₁₆	193