Subgroups — #335×C₄₉₁ #44536192

Order 31424.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊C₈×C₄₉₁	C₂	1	2	yes	maximal
2	C₄×C₈×C₄₉₁	C₂	1	1	yes	maximal, characteristic
3	C₂×C₈×C₄₉₁	—	2	2	no	—
4	C₂×C₈×C₄₉₁	C₄	1	1	yes	characteristic
5	C₂×C₈×C₄₉₁	C₄	1	1	yes	characteristic
6	C₄²×C₄₉₁	C₂²	1	1	yes	characteristic
7	C₂×C₄×C₄₉₁	C₂×C₄	1	1	yes	characteristic
8	C₂×C₄×C₄₉₁	D₄	1	1	yes	characteristic
9	C₂×C₄×C₄₉₁	Q₈	1	1	yes	characteristic
10	C₈×C₄₉₁	—	2	1	no	—
11	C₈×C₄₉₁	—	4	2	no	—
12	C₈×C₄₉₁	C₈	1	2	yes	complemented
13	C₂²×C₄₉₁	C₄⋊C₄	1	1	yes	characteristic
14	C₄×C₄₉₁	—	2	1	no	—
15	C₄×C₄₉₁	C₂×C₈	1	1	yes	characteristic
16	C₄×C₄₉₁	M₁₆	1	1	yes	characteristic
17	C₄×C₄₉₁	D₈	1	1	yes	characteristic
18	C₄×C₄₉₁	Q₁₆	1	1	yes	characteristic
19	C₂×C₄₉₁	C₄⋊C₈	1	1	yes	characteristic
20	C₂×C₄₉₁	#107	1	1	yes	characteristic
21	C₂×C₄₉₁	#108	1	1	yes	characteristic
22	C₄₉₁	#335	1	1	yes	characteristic, direct product factor, Sylow
23	#335	C₄₉₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
24	C₄⋊C₈	C₂×C₄₉₁	1	2	yes	—
25	C₄×C₈	C₂×C₄₉₁	1	1	yes	characteristic
26	C₂×C₈	—	2	2	no	—
27	C₂×C₈	C₄×C₄₉₁	1	1	yes	characteristic
28	C₂×C₈	C₄×C₄₉₁	1	1	yes	characteristic
29	C₄²	C₂²×C₄₉₁	1	1	yes	characteristic
30	C₂×C₄	C₂×C₄×C₄₉₁	1	1	yes	characteristic
31	C₂×C₄	D₄×C₄₉₁	1	1	yes	characteristic
32	C₂×C₄	Q₈×C₄₉₁	1	1	yes	characteristic
33	C₈	—	2	1	no	—
34	C₈	—	4	2	no	—
35	C₈	C₈×C₄₉₁	1	2	yes	complemented
36	C₂²	C₄⋊C₄×C₄₉₁	1	1	yes	characteristic
37	C₄	—	2	1	no	—
38	C₄	C₂×C₈×C₄₉₁	1	1	yes	characteristic
39	C₄	M₁₆×C₄₉₁	1	1	yes	characteristic
40	C₄	D₈×C₄₉₁	1	1	yes	characteristic
41	C₄	Q₁₆×C₄₉₁	1	1	yes	characteristic
42	C₂	C₄⋊C₈×C₄₉₁	1	1	yes	characteristic
43	C₂	#107×C₄₉₁	1	1	yes	characteristic
44	C₂	#108×C₄₉₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₄₉₁	D₄
commutator	C₄	C₂×C₈×C₄₉₁
Frattini, cosocle	C₄²	C₂²×C₄₉₁
socle, prime radical	C₂²×C₄₉₁	C₄⋊C₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₉₁ ◁ C₄²×C₄₉₁ ◁ G

Complements

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

N	H ≅ G/N	type
12. C₈×C₄₉₁	C₈	semidirect
22. C₄₉₁	#335	direct (N × H)
23. #335	C₄₉₁	direct (N × H)
35. C₈	C₈×C₄₉₁	semidirect

Maximal subgroups

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

subgroup	index
C₄⋊C₈×C₄₉₁	2
C₄×C₈×C₄₉₁	2
#335	491

Subgroups — #335×C491 #44536192

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #335×C₄₉₁ #44536192