Subgroups — #335×C₂₉₃ #34035596

Order 18752.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊C₈×C₂₉₃	C₂	1	2	yes	maximal
2	C₄×C₈×C₂₉₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₈×C₂₉₃	—	2	2	no	—
4	C₂×C₈×C₂₉₃	C₄	1	1	yes	characteristic
5	C₂×C₈×C₂₉₃	C₄	1	1	yes	characteristic
6	C₄²×C₂₉₃	C₂²	1	1	yes	characteristic
7	C₂×C₄×C₂₉₃	C₂×C₄	1	1	yes	characteristic
8	C₂×C₄×C₂₉₃	D₄	1	1	yes	characteristic
9	C₂×C₄×C₂₉₃	Q₈	1	1	yes	characteristic
10	C₈×C₂₉₃	—	2	1	no	—
11	C₈×C₂₉₃	—	4	2	no	—
12	C₈×C₂₉₃	C₈	1	2	yes	complemented
13	C₂²×C₂₉₃	C₄⋊C₄	1	1	yes	characteristic
14	C₄×C₂₉₃	—	2	1	no	—
15	C₄×C₂₉₃	C₂×C₈	1	1	yes	characteristic
16	C₄×C₂₉₃	M₁₆	1	1	yes	characteristic
17	C₄×C₂₉₃	D₈	1	1	yes	characteristic
18	C₄×C₂₉₃	Q₁₆	1	1	yes	characteristic
19	C₂×C₂₉₃	C₄⋊C₈	1	1	yes	characteristic
20	C₂×C₂₉₃	#107	1	1	yes	characteristic
21	C₂×C₂₉₃	#108	1	1	yes	characteristic
22	C₂₉₃	#335	1	1	yes	characteristic, direct product factor, Sylow
23	#335	C₂₉₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
24	C₄⋊C₈	C₂×C₂₉₃	1	2	yes	—
25	C₄×C₈	C₂×C₂₉₃	1	1	yes	characteristic
26	C₂×C₈	—	2	2	no	—
27	C₂×C₈	C₄×C₂₉₃	1	1	yes	characteristic
28	C₂×C₈	C₄×C₂₉₃	1	1	yes	characteristic
29	C₄²	C₂²×C₂₉₃	1	1	yes	characteristic
30	C₂×C₄	C₂×C₄×C₂₉₃	1	1	yes	characteristic
31	C₂×C₄	D₄×C₂₉₃	1	1	yes	characteristic
32	C₂×C₄	Q₈×C₂₉₃	1	1	yes	characteristic
33	C₈	—	2	1	no	—
34	C₈	—	4	2	no	—
35	C₈	C₈×C₂₉₃	1	2	yes	complemented
36	C₂²	C₄⋊C₄×C₂₉₃	1	1	yes	characteristic
37	C₄	—	2	1	no	—
38	C₄	C₂×C₈×C₂₉₃	1	1	yes	characteristic
39	C₄	M₁₆×C₂₉₃	1	1	yes	characteristic
40	C₄	D₈×C₂₉₃	1	1	yes	characteristic
41	C₄	Q₁₆×C₂₉₃	1	1	yes	characteristic
42	C₂	C₄⋊C₈×C₂₉₃	1	1	yes	characteristic
43	C₂	#107×C₂₉₃	1	1	yes	characteristic
44	C₂	#108×C₂₉₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₉₃	D₄
commutator	C₄	C₂×C₈×C₂₉₃
Frattini, cosocle	C₄²	C₂²×C₂₉₃
socle, prime radical	C₂²×C₂₉₃	C₄⋊C₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₉₃ ◁ C₄²×C₂₉₃ ◁ G

Complements

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

N	H ≅ G/N	type
12. C₈×C₂₉₃	C₈	semidirect
22. C₂₉₃	#335	direct (N × H)
23. #335	C₂₉₃	direct (N × H)
35. C₈	C₈×C₂₉₃	semidirect

Maximal subgroups

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

subgroup	index
C₄⋊C₈×C₂₉₃	2
C₄×C₈×C₂₉₃	2
#335	293

Subgroups — #335×C293 #34035596

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #335×C₂₉₃ #34035596