Subgroups — #36378684

Order 22592.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26015066	C₂	1	2	yes	maximal, complemented
2	C₂×#19150720	C₂	1	1	yes	maximal, characteristic
3	#19150740	—	2	2	no	—
4	C₂×C₄×D₃₅₃	C₄	1	1	yes	characteristic
5	#19150720	—	2	2	no	—
6	C₂×#15667725	C₂²	1	1	yes	characteristic
7	C₂×C₈×C₃₅₃	C₄	1	1	yes	characteristic
8	C₂²×D₃₅₃	C₈	1	1	yes	characteristic
9	C₂×Dic₃₅₃	C₈	1	1	yes	characteristic
10	C₄×D₃₅₃	—	2	1	no	—
11	C₄×D₃₅₃	—	2	1	no	—
12	#15667725	D₄	1	2	yes	—
13	C₂×C₄×C₃₅₃	C₂×C₄	1	1	yes	characteristic
14	C₈×C₃₅₃	—	2	1	no	—
15	C₂²×C₃₅₃	C₂×C₈	1	1	yes	characteristic
16	C₂×D₃₅₃	—	2	1	no	—
17	C₂×D₃₅₃	—	4	1	no	—
18	C₄×C₃₅₃	C₂²⋊C₄	1	1	yes	characteristic
19	C₄×C₃₅₃	M₁₆	1	1	yes	characteristic
20	Dic₃₅₃	—	2	1	no	—
21	C₂×C₃₅₃	—	2	1	no	—
22	C₂×C₃₅₃	C₂²⋊C₈	1	1	yes	characteristic
23	D₃₅₃	—	4	1	no	—
24	C₃₅₃	#349	1	1	yes	characteristic, complemented, Sylow
25	#349	—	353	1	no	maximal, Sylow
26	C₂×M₁₆	—	353	1	no	—
27	M₃₂	—	353	2	no	—
28	C₂²×C₄	—	353	1	no	—
29	M₁₆	—	706	2	no	—
30	C₂×C₈	—	353	1	no	—
31	C₂×C₈	#13083443	1	1	yes	characteristic
32	C₁₆	—	706	2	no	—
33	C₂³	—	353	1	no	—
34	C₂×C₄	—	353	1	no	—
35	C₂×C₄	—	706	1	no	—
36	C₂×C₄	—	706	1	no	—
37	C₂×C₄	C₂×#13083443	1	1	yes	characteristic
38	C₈	—	2	1	no	—
39	C₈	—	353	2	no	—
40	C₂²	—	1412	1	no	—
41	C₂²	—	706	1	no	—
42	C₂²	#19150745	1	1	yes	characteristic
43	C₄	—	706	1	no	—
44	C₄	C₂²⋊#13083443	1	1	yes	characteristic
45	C₄	#19150747	1	1	yes	characteristic
46	C₂	—	2	1	no	—
47	C₂	—	1412	1	no	—
48	C₂	#26015049	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²⋊#13083443
commutator	C₂²×C₃₅₃	C₂×C₈
Frattini	C₂×C₄	C₂×#13083443
Fitting	C₂×C₈×C₃₅₃	C₄
socle	C₂×C₃₅₃	C₂²⋊C₈
prime radical	C₂²×D₃₅₃	C₈
cosocle	C₂×#15667725	C₂²
hypercenter	C₂×C₈	#13083443
hypocenter	C₃₅₃	#349
LCS	G ▷ C₂²×C₃₅₃ ▷ C₂×C₃₅₃ ▷ C₃₅₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
1. #26015066	C₂	semidirect
24. C₃₅₃	#349	semidirect

Maximal subgroups

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

subgroup	index
#26015066	2
C₂×#19150720	2
#349	353