Subgroups — #34093905

Order 20032.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#14578809	C₂	1	2	yes	maximal
2	C₄×C₈×C₃₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#14578809	—	2	2	no	—
4	C₂×C₈×C₃₁₃	C₄	1	1	yes	characteristic
5	C₂×C₈×C₃₁₃	C₄	1	1	yes	characteristic
6	C₄²×C₃₁₃	C₂²	1	1	yes	characteristic
7	#14578809	—	4	2	no	—
8	C₂×C₄×C₃₁₃	C₂×C₄	1	1	yes	characteristic
9	C₂×C₄×C₃₁₃	D₄	1	1	yes	characteristic
10	C₂×C₄×C₃₁₃	Q₈	1	1	yes	characteristic
11	C₈×C₃₁₃	—	2	1	no	—
12	C₈×C₃₁₃	C₈	1	2	yes	complemented
13	C₂²×C₃₁₃	C₄⋊C₄	1	1	yes	characteristic
14	C₄×C₃₁₃	—	2	1	no	—
15	C₄×C₃₁₃	C₂×C₈	1	1	yes	characteristic
16	C₄×C₃₁₃	M₁₆	1	1	yes	characteristic
17	C₄×C₃₁₃	D₈	1	1	yes	characteristic
18	C₄×C₃₁₃	Q₁₆	1	1	yes	characteristic
19	C₂×C₃₁₃	C₄⋊C₈	1	1	yes	characteristic
20	C₂×C₃₁₃	#107	1	1	yes	characteristic
21	C₂×C₃₁₃	#108	1	1	yes	characteristic
22	C₃₁₃	#335	1	1	yes	characteristic, complemented, Sylow
23	#335	—	313	1	no	maximal, Sylow
24	C₄⋊C₈	—	313	2	no	—
25	C₄×C₈	D₃₁₃	1	1	yes	characteristic
26	C₂×C₈	—	626	2	no	—
27	C₂×C₈	Dic₃₁₃	1	1	yes	characteristic
28	C₂×C₈	Dic₃₁₃	1	1	yes	characteristic
29	C₄²	C₂×D₃₁₃	1	1	yes	characteristic
30	C₂×C₄	C₂×Dic₃₁₃	1	1	yes	characteristic
31	C₂×C₄	D₁₂₅₂	1	1	yes	characteristic
32	C₂×C₄	Dic₆₂₆	1	1	yes	characteristic
33	C₈	—	2	1	no	—
34	C₈	—	1252	2	no	—
35	C₈	#14578809	1	2	yes	complemented
36	C₂²	C₄⋊Dic₃₁₃	1	1	yes	characteristic
37	C₄	—	2	1	no	—
38	C₄	C₂×#14578809	1	1	yes	characteristic
39	C₄	#19097545	1	1	yes	characteristic
40	C₄	D₂₅₀₄	1	1	yes	characteristic
41	C₄	Dic₁₂₅₂	1	1	yes	characteristic
42	C₂	C₄⋊#14578809	1	1	yes	characteristic
43	C₂	#23756431	1	1	yes	characteristic
44	C₂	#23756433	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₁₂₅₂
commutator	C₄×C₃₁₃	C₂×C₈
Frattini	C₄²	C₂×D₃₁₃
Fitting	C₄×C₈×C₃₁₃	C₂
socle, prime radical	C₂²×C₃₁₃	C₄⋊C₄
cosocle	C₄²×C₃₁₃	C₂²
hypercenter	C₄×C₈	D₃₁₃
hypocenter	C₃₁₃	#335
LCS	G ▷ C₄×C₃₁₃ ▷ C₂×C₃₁₃ ▷ C₃₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
12. C₈×C₃₁₃	C₈	semidirect
22. C₃₁₃	#335	semidirect
35. C₈	#14578809	semidirect

Maximal subgroups

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

subgroup	index
C₄⋊#14578809	2
C₄×C₈×C₃₁₃	2
#335	313