Subgroups — C₂²⋊#19150751 #36378913

Order 22592.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19150751	C₂	1	2	yes	maximal, complemented
2	C₂²×#15667734	C₂	1	1	yes	maximal, characteristic
3	#19150751	—	2	2	no	—
4	C₂×#15667734	—	2	2	no	—
5	C₂×#15667734	C₄	1	1	yes	characteristic
6	C₂×#15667734	C₂²	1	1	yes	characteristic
7	C₂²×#13083443	C₄	1	1	yes	characteristic
8	#15667734	—	2	1	no	—
9	#15667734	D₄	1	2	yes	—
10	C₂×#13083443	—	2	1	no	—
11	C₂×#13083443	—	2	1	no	—
12	C₂×#13083443	C₈	1	1	yes	characteristic
13	C₂×#13083443	C₂×C₄	1	1	yes	characteristic
14	C₂²×D₃₅₃	C₈	1	1	yes	characteristic
15	C₂²×C₃₅₃	C₁₆	1	1	yes	characteristic, complemented
16	C₂×D₃₅₃	—	2	1	no	—
17	C₂×D₃₅₃	—	2	1	no	—
18	C₂×D₃₅₃	C₁₆	1	1	yes	characteristic, complemented
19	C₂×D₃₅₃	C₂×C₈	1	1	yes	characteristic
20	#13083443	—	2	1	no	—
21	#13083443	C₂²⋊C₄	1	1	yes	characteristic
22	#13083443	M₁₆	1	1	yes	characteristic
23	C₂×C₃₅₃	—	2	1	no	—
24	C₂×C₃₅₃	C₂×C₁₆	1	1	yes	characteristic
25	D₃₅₃	—	2	1	no	—
26	D₃₅₃	C₂²⋊C₈	1	1	yes	characteristic
27	D₃₅₃	M₃₂	1	1	yes	characteristic
28	C₃₅₃	C₂²⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
29	C₂²⋊C₁₆	—	353	1	no	maximal, Sylow
30	C₂²×C₈	—	353	1	no	—
31	C₂×C₁₆	—	353	2	no	—
32	C₂²×C₄	—	353	1	no	—
33	C₂×C₈	—	353	1	no	—
34	C₂×C₈	—	353	1	no	—
35	C₂×C₈	—	706	2	no	—
36	C₁₆	—	706	2	no	—
37	C₂³	—	353	1	no	—
38	C₂×C₄	—	353	1	no	—
39	C₂×C₄	—	353	1	no	—
40	C₂×C₄	—	706	1	no	—
41	C₂×C₄	—	706	1	no	—
42	C₈	—	353	2	no	—
43	C₈	—	706	1	no	—
44	C₂²	—	353	1	no	—
45	C₂²	—	353	1	no	—
46	C₂²	—	706	1	no	—
47	C₂²	—	706	1	no	—
48	C₂²	#19150751	1	1	yes	characteristic, complemented
49	C₄	—	353	1	no	—
50	C₄	—	353	1	no	—
51	C₄	—	706	1	no	—
52	C₂	—	2	1	no	—
53	C₂	—	353	1	no	—
54	C₂	—	353	1	no	—
55	C₂	—	706	1	no	—
56	C₂	C₂×#19150751	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂×#19150751
commutator, socle	C₂×C₃₅₃	C₂×C₁₆
Fitting	C₂²×C₃₅₃	C₁₆
prime radical	C₂²×D₃₅₃	C₈
cosocle	C₂×#15667734	C₂²
hypercenter	C₂²	#19150751
hypocenter	C₃₅₃	C₂²⋊C₁₆
LCS	G ▷ C₂×C₃₅₃ ▷ C₃₅₃
UCS	C₁ ◁ C₂ ◁ C₂²

Complements

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

N	H ≅ G/N	type
1. C₂×#19150751	C₂	semidirect
15. C₂²×C₃₅₃	C₁₆	semidirect
18. C₂×D₃₅₃	C₁₆	semidirect
28. C₃₅₃	C₂²⋊C₁₆	semidirect
48. C₂²	#19150751	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19150751	2
C₂²×#15667734	2
C₂²⋊C₁₆	353

Subgroups — C22⋊#19150751 #36378913

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²⋊#19150751 #36378913