Subgroups — #36378884

Order 22592.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19150749	C₂	1	2	yes	maximal, complemented
2	C₂×#19150745	C₂	1	1	yes	maximal, characteristic
3	#19150749	—	2	2	no	—
4	#19150745	—	2	2	no	—
5	C₂×#15667732	C₄	1	1	yes	characteristic
6	C₂×#15667732	C₂²	1	1	yes	characteristic
7	C₂×C₄×D₃₅₃	C₄	1	1	yes	characteristic
8	#15667732	—	2	1	no	—
9	#15667732	D₄	1	2	yes	—
10	C₂²×D₃₅₃	C₈	1	1	yes	characteristic
11	C₂×Dic₃₅₃	C₂×C₄	1	1	yes	characteristic
12	C₄×D₃₅₃	—	2	1	no	—
13	C₄×D₃₅₃	—	2	1	no	—
14	C₂×C₄×C₃₅₃	C₈	1	1	yes	characteristic
15	C₂²×C₃₅₃	C₂×C₈	1	1	yes	characteristic
16	C₂×D₃₅₃	—	2	1	no	—
17	C₂×D₃₅₃	—	2	1	no	—
18	C₂×D₃₅₃	C₁₆	1	2	yes	complemented
19	C₄×C₃₅₃	—	2	1	no	—
20	Dic₃₅₃	C₂²⋊C₄	1	1	yes	characteristic
21	Dic₃₅₃	M₁₆	1	1	yes	characteristic
22	C₂×C₃₅₃	C₂²⋊C₈	1	1	yes	characteristic
23	C₂×C₃₅₃	C₂×C₁₆	1	1	yes	characteristic
24	C₂×C₃₅₃	M₃₂	1	1	yes	characteristic
25	D₃₅₃	—	2	2	no	—
26	C₃₅₃	C₂²⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
27	C₂²⋊C₁₆	—	353	1	no	maximal, Sylow
28	C₂²×C₈	—	353	1	no	—
29	C₂×C₁₆	—	353	2	no	—
30	C₂²×C₄	—	353	1	no	—
31	C₂×C₈	—	353	1	no	—
32	C₂×C₈	—	353	1	no	—
33	C₂×C₈	—	706	2	no	—
34	C₁₆	—	706	2	no	—
35	C₂³	—	353	1	no	—
36	C₂×C₄	—	353	1	no	—
37	C₂×C₄	—	706	1	no	—
38	C₂×C₄	—	706	1	no	—
39	C₂×C₄	#15667734	1	1	yes	characteristic
40	C₈	—	353	2	no	—
41	C₈	—	706	1	no	—
42	C₂²	—	353	2	no	—
43	C₂²	—	706	1	no	—
44	C₂²	—	706	1	no	—
45	C₂²	C₂×#15667734	1	1	yes	characteristic
46	C₄	—	2	1	no	—
47	C₄	—	353	1	no	—
48	C₄	—	353	1	no	—
49	C₂	—	706	2	no	—
50	C₂	C₂²⋊#15667734	1	1	yes	characteristic
51	C₂	#26015087	1	1	yes	characteristic
52	C₂	#26015089	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂×#15667734
commutator	C₂×C₃₅₃	C₂×C₁₆
Fitting	C₂×C₄×C₃₅₃	C₈
socle	C₂²×C₃₅₃	C₂×C₈
prime radical	C₂²×D₃₅₃	C₈
cosocle	C₂×#15667732	C₂²
hypercenter	C₂×C₄	#15667734
hypocenter	C₃₅₃	C₂²⋊C₁₆
LCS	G ▷ C₂×C₃₅₃ ▷ C₃₅₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
1. C₂×#19150749	C₂	semidirect
18. C₂×D₃₅₃	C₁₆	semidirect
26. C₃₅₃	C₂²⋊C₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19150749	2
C₂×#19150745	2
C₂²⋊C₁₆	353