Subgroups — #34095015

Order 20032.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#14578816	C₂	1	2	yes	maximal
2	C₈×Dic₃₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#14578816	—	2	2	no	—
4	C₂×#14578809	C₄	1	1	yes	characteristic
5	C₄×Dic₃₁₃	C₂²	1	1	yes	characteristic
6	C₂×C₈×C₃₁₃	C₄	1	1	yes	characteristic
7	#14578816	—	4	2	no	—
8	C₂×Dic₃₁₃	D₄	1	1	yes	characteristic
9	C₂×Dic₃₁₃	Q₈	1	1	yes	characteristic
10	#14578809	—	2	1	no	—
11	C₂×C₄×C₃₁₃	C₂×C₄	1	1	yes	characteristic
12	C₈×C₃₁₃	C₈	1	2	yes	complemented
13	C₂²×C₃₁₃	C₄⋊C₄	1	1	yes	characteristic
14	C₄×C₃₁₃	C₂×C₈	1	1	yes	characteristic
15	C₄×C₃₁₃	M₁₆	1	1	yes	characteristic
16	Dic₃₁₃	—	2	1	no	—
17	Dic₃₁₃	D₈	1	1	yes	characteristic
18	Dic₃₁₃	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	—	313	1	no	—
26	C₂×C₈	—	313	1	no	—
27	C₂×C₈	—	626	2	no	—
28	C₂×C₈	#11929411	1	1	yes	characteristic
29	C₄²	—	313	1	no	—
30	C₂×C₄	—	313	1	no	—
31	C₂×C₄	—	313	1	no	—
32	C₂×C₄	C₂×#11929411	1	1	yes	characteristic
33	C₈	—	626	1	no	—
34	C₈	—	1252	2	no	—
35	C₈	#14578816	1	2	yes	complemented
36	C₂²	C₄⋊#11929411	1	1	yes	characteristic
37	C₄	—	313	1	no	—
38	C₄	—	313	1	no	—
39	C₄	—	626	1	no	—
40	C₄	C₂×#14578816	1	1	yes	characteristic
41	C₄	#19097571	1	1	yes	characteristic
42	C₂	C₄⋊#14578816	1	1	yes	characteristic
43	C₂	#23756566	1	1	yes	characteristic
44	C₂	#23756568	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₄⋊#11929411
commutator	C₄×C₃₁₃	C₂×C₈
Frattini	C₂×C₄	C₂×#11929411
Fitting	C₂×C₈×C₃₁₃	C₄
socle, prime radical	C₂²×C₃₁₃	C₄⋊C₄
cosocle	C₄×Dic₃₁₃	C₂²
hypercenter	C₂×C₈	#11929411
hypocenter	C₃₁₃	#335
LCS	G ▷ C₄×C₃₁₃ ▷ C₂×C₃₁₃ ▷ C₃₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×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	#14578816	semidirect

Maximal subgroups

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

subgroup	index
C₄⋊#14578816	2
C₈×Dic₃₁₃	2
#335	313