Subgroups — C₂²×#19150712 #36378199

Order 22592.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19150712	C₂	1	6	yes	maximal, direct product factor
2	C₂²×C₈×C₃₅₃	C₂	1	1	yes	maximal, characteristic
3	#19150712	C₂²	1	4	yes	direct product factor
4	C₂²×C₄×C₃₅₃	C₄	1	1	yes	characteristic
5	C₂×C₈×C₃₅₃	C₄	1	3	yes	—
6	C₂×C₈×C₃₅₃	C₂²	1	3	yes	—
7	C₂³×C₃₅₃	C₈	1	1	yes	characteristic
8	C₂×C₄×C₃₅₃	C₈	1	3	yes	—
9	C₂×C₄×C₃₅₃	C₂×C₄	1	3	yes	—
10	C₈×C₃₅₃	C₂×C₄	1	3	yes	—
11	C₈×C₃₅₃	C₂³	1	1	yes	characteristic
12	C₂²×C₃₅₃	C₁₆	1	4	yes	complemented
13	C₂²×C₃₅₃	C₂×C₈	1	3	yes	—
14	C₄×C₃₅₃	C₂×C₈	1	3	yes	—
15	C₄×C₃₅₃	C₂²×C₄	1	1	yes	characteristic
16	C₂×C₃₅₃	C₂×C₁₆	1	6	yes	complemented
17	C₂×C₃₅₃	C₂²×C₈	1	1	yes	characteristic
18	C₃₅₃	C₂²×C₁₆	1	1	yes	characteristic, complemented, Sylow
19	C₂²×C₁₆	—	353	1	no	maximal, Sylow
20	C₂²×C₈	D₃₅₃	1	1	yes	characteristic
21	C₂×C₁₆	—	353	6	no	—
22	C₂²×C₄	Dic₃₅₃	1	1	yes	characteristic
23	C₂×C₈	Dic₃₅₃	1	3	yes	—
24	C₂×C₈	C₂×D₃₅₃	1	3	yes	—
25	C₁₆	—	353	4	no	—
26	C₂³	#15667725	1	1	yes	characteristic
27	C₂×C₄	#15667725	1	3	yes	—
28	C₂×C₄	C₂×Dic₃₅₃	1	3	yes	—
29	C₈	C₂×Dic₃₅₃	1	3	yes	—
30	C₈	C₂²×D₃₅₃	1	1	yes	characteristic
31	C₂²	#19150712	1	4	yes	direct product factor
32	C₂²	C₂×#15667725	1	3	yes	—
33	C₄	C₂×#15667725	1	3	yes	—
34	C₄	C₂²×Dic₃₅₃	1	1	yes	characteristic
35	C₂	C₂×#19150712	1	6	yes	direct product factor
36	C₂	C₂²×#15667725	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²×C₈	D₃₅₃
commutator, hypocenter	C₃₅₃	C₂²×C₁₆
Frattini	C₈	C₂²×D₃₅₃
Fitting	C₂²×C₈×C₃₅₃	C₂
socle, prime radical	C₂³×C₃₅₃	C₈
cosocle	C₈×C₃₅₃	C₂³
LCS	G ▷ C₃₅₃
UCS	C₁ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
1. C₂×#19150712	C₂	direct (N × H)
3. #19150712	C₂²	direct (N × H)
12. C₂²×C₃₅₃	C₁₆	semidirect
16. C₂×C₃₅₃	C₂×C₁₆	semidirect
18. C₃₅₃	C₂²×C₁₆	semidirect
31. C₂²	#19150712	direct (N × H)
35. C₂	C₂×#19150712	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#19150712	2
C₂²×C₈×C₃₅₃	2
C₂²×C₁₆	353

Subgroups — C22×#19150712 #36378199

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#19150712 #36378199