Subgroups — #34094994

Order 20032.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#14578816	C₂	1	1	yes	maximal, characteristic
2	C₄×#14578816	C₂	1	1	yes	maximal, characteristic
3	C₈×Dic₃₁₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#14578816	C₄	1	2	yes	—
5	C₂×#14578816	C₄	1	2	yes	—
6	C₂×#14578809	C₄	1	1	yes	characteristic
7	C₄×Dic₃₁₃	C₂²	1	1	yes	characteristic
8	C₂×C₈×C₃₁₃	C₄	1	1	yes	characteristic
9	#14578816	—	2	2	no	—
10	#14578816	C₈	1	4	yes	complemented
11	C₂×Dic₃₁₃	C₂×C₄	1	1	yes	characteristic
12	C₂×Dic₃₁₃	C₂×C₄	1	1	yes	characteristic
13	#14578809	—	2	1	no	—
14	C₂×C₄×C₃₁₃	C₂×C₄	1	1	yes	characteristic
15	C₈×C₃₁₃	—	2	1	no	—
16	C₂²×C₃₁₃	C₄²	1	1	yes	characteristic
17	C₄×C₃₁₃	M₁₆	1	1	yes	characteristic
18	C₄×C₃₁₃	M₁₆	1	1	yes	characteristic
19	Dic₃₁₃	C₂×C₈	1	2	yes	—
20	Dic₃₁₃	M₁₆	1	2	yes	—
21	C₂×C₃₁₃	C₄×C₈	1	1	yes	characteristic
22	C₂×C₃₁₃	#97	1	1	yes	characteristic
23	C₂×C₃₁₃	#97	1	1	yes	characteristic
24	C₃₁₃	#322	1	1	yes	characteristic, complemented, Sylow
25	#322	—	313	1	no	maximal, Sylow
26	C₄×C₈	—	313	1	no	—
27	C₄×C₈	—	313	1	no	—
28	C₄×C₈	—	313	1	no	—
29	C₂×C₈	—	313	2	no	—
30	C₂×C₈	—	313	2	no	—
31	C₂×C₈	—	313	1	no	—
32	C₂×C₈	#11929411	1	1	yes	characteristic
33	C₄²	—	313	1	no	—
34	C₂×C₄	—	313	1	no	—
35	C₂×C₄	—	313	1	no	—
36	C₂×C₄	C₂×#11929411	1	1	yes	characteristic
37	C₈	—	2	1	no	—
38	C₈	—	313	4	no	—
39	C₈	—	626	2	no	—
40	C₈	—	626	1	no	—
41	C₂²	C₄×#11929411	1	1	yes	characteristic
42	C₄	—	313	2	no	—
43	C₄	—	313	2	no	—
44	C₄	#19097570	1	1	yes	characteristic
45	C₄	#19097571	1	1	yes	characteristic
46	C₂	C₈×#11929411	1	1	yes	characteristic
47	C₂	#23756551	1	1	yes	characteristic
48	C₂	#23756552	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂×#11929411
commutator	C₂×C₃₁₃	C₄×C₈
Fitting	C₂×C₈×C₃₁₃	C₄
socle, prime radical	C₂²×C₃₁₃	C₄²
cosocle	C₄×Dic₃₁₃	C₂²
hypercenter	C₂×C₈	#11929411
hypocenter	C₃₁₃	#322
LCS	G ▷ C₂×C₃₁₃ ▷ C₃₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
10. #14578816	C₈	semidirect
24. C₃₁₃	#322	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
#322	313