Subgroups — #34095048

Order 20032.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23756571	C₂	1	2	yes	maximal, complemented
2	C₂×#19097545	C₂	1	1	yes	maximal, characteristic
3	#19097564	—	2	2	no	—
4	#19097545	—	2	2	no	—
5	C₂×#14578809	C₄	1	1	yes	characteristic
6	C₂×#14578809	C₂²	1	1	yes	characteristic
7	C₂²×C₄×C₃₁₃	C₄	1	1	yes	characteristic
8	#14578809	—	2	1	no	—
9	#14578809	D₄	1	2	yes	—
10	C₂³×C₃₁₃	C₈	1	1	yes	characteristic
11	C₂×C₄×C₃₁₃	—	2	1	no	—
12	C₂×C₄×C₃₁₃	—	2	1	no	—
13	C₂×C₄×C₃₁₃	C₈	1	1	yes	characteristic
14	C₂×C₄×C₃₁₃	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₃₁₃	—	2	1	no	—
16	C₂²×C₃₁₃	—	4	1	no	—
17	C₂²×C₃₁₃	C₂×C₈	1	1	yes	characteristic
18	C₄×C₃₁₃	—	2	1	no	—
19	C₄×C₃₁₃	C₂²⋊C₄	1	1	yes	characteristic
20	C₄×C₃₁₃	M₁₆	1	1	yes	characteristic
21	C₂×C₃₁₃	—	2	1	no	—
22	C₂×C₃₁₃	—	4	1	no	—
23	C₂×C₃₁₃	C₂²⋊C₈	1	1	yes	characteristic
24	C₃₁₃	#349	1	1	yes	characteristic, complemented, Sylow
25	#349	—	313	1	no	maximal, Sylow
26	C₂×M₁₆	—	313	1	no	—
27	M₃₂	—	313	2	no	—
28	C₂²×C₄	#11929411	1	1	yes	characteristic
29	M₁₆	—	626	2	no	—
30	C₂×C₈	—	313	1	no	—
31	C₂×C₈	—	313	1	no	—
32	C₁₆	—	626	2	no	—
33	C₂³	#14578816	1	1	yes	characteristic
34	C₂×C₄	—	2	1	no	—
35	C₂×C₄	—	2	1	no	—
36	C₂×C₄	#14578816	1	1	yes	characteristic
37	C₂×C₄	C₂×#11929411	1	1	yes	characteristic
38	C₈	—	313	2	no	—
39	C₈	—	626	1	no	—
40	C₂²	—	2	1	no	—
41	C₂²	—	4	1	no	—
42	C₂²	C₂×#14578816	1	1	yes	characteristic
43	C₄	—	2	1	no	—
44	C₄	C₂²⋊#11929411	1	1	yes	characteristic
45	C₄	#19097570	1	1	yes	characteristic
46	C₂	—	2	1	no	—
47	C₂	—	4	1	no	—
48	C₂	C₂²⋊#14578816	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²⋊#11929411
commutator	C₂²×C₃₁₃	C₂×C₈
Frattini	C₂×C₄	C₂×#11929411
Fitting	C₂²×C₄×C₃₁₃	C₄
socle	C₂×C₃₁₃	C₂²⋊C₈
prime radical	C₂³×C₃₁₃	C₈
cosocle	C₂×#14578809	C₂²
hypercenter	C₂²×C₄	#11929411
hypocenter	C₃₁₃	#349
LCS	G ▷ C₂²×C₃₁₃ ▷ C₂×C₃₁₃ ▷ C₃₁₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
1. #23756571	C₂	semidirect
24. C₃₁₃	#349	semidirect

Maximal subgroups

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

subgroup	index
#23756571	2
C₂×#19097545	2
#349	313