Subgroups — C₂²⋊#20294111 #42122937

Order 27712.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20294111	C₂	1	2	yes	maximal, complemented
2	C₂²×#16812367	C₂	1	1	yes	maximal, characteristic
3	#20294111	—	2	2	no	—
4	C₂×#16812367	—	2	2	no	—
5	C₂×#16812367	C₄	1	1	yes	characteristic
6	C₂×#16812367	C₂²	1	1	yes	characteristic
7	C₂²×#13181884	C₄	1	1	yes	characteristic
8	#16812367	—	2	1	no	—
9	#16812367	D₄	1	2	yes	—
10	C₂×#13181884	—	2	1	no	—
11	C₂×#13181884	—	2	1	no	—
12	C₂×#13181884	C₈	1	1	yes	characteristic
13	C₂×#13181884	C₂×C₄	1	1	yes	characteristic
14	C₂²×D₄₃₃	C₈	1	1	yes	characteristic
15	C₂²×C₄₃₃	C₁₆	1	1	yes	characteristic, complemented
16	C₂×D₄₃₃	—	2	1	no	—
17	C₂×D₄₃₃	—	2	1	no	—
18	C₂×D₄₃₃	C₁₆	1	1	yes	characteristic, complemented
19	C₂×D₄₃₃	C₂×C₈	1	1	yes	characteristic
20	#13181884	—	2	1	no	—
21	#13181884	C₂²⋊C₄	1	1	yes	characteristic
22	#13181884	M₁₆	1	1	yes	characteristic
23	C₂×C₄₃₃	—	2	1	no	—
24	C₂×C₄₃₃	C₂×C₁₆	1	1	yes	characteristic
25	D₄₃₃	—	2	1	no	—
26	D₄₃₃	C₂²⋊C₈	1	1	yes	characteristic
27	D₄₃₃	M₃₂	1	1	yes	characteristic
28	C₄₃₃	C₂²⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
29	C₂²⋊C₁₆	—	433	1	no	maximal, Sylow
30	C₂²×C₈	—	433	1	no	—
31	C₂×C₁₆	—	433	2	no	—
32	C₂²×C₄	—	433	1	no	—
33	C₂×C₈	—	866	2	no	—
34	C₂×C₈	—	433	1	no	—
35	C₂×C₈	—	433	1	no	—
36	C₁₆	—	866	2	no	—
37	C₂³	—	433	1	no	—
38	C₂×C₄	—	866	1	no	—
39	C₂×C₄	—	866	1	no	—
40	C₂×C₄	—	433	1	no	—
41	C₂×C₄	—	433	1	no	—
42	C₈	—	866	1	no	—
43	C₈	—	433	2	no	—
44	C₂²	—	866	1	no	—
45	C₂²	—	866	1	no	—
46	C₂²	—	433	1	no	—
47	C₂²	—	433	1	no	—
48	C₂²	#20294111	1	1	yes	characteristic, complemented
49	C₄	—	866	1	no	—
50	C₄	—	433	1	no	—
51	C₄	—	433	1	no	—
52	C₂	—	2	1	no	—
53	C₂	—	866	1	no	—
54	C₂	—	433	1	no	—
55	C₂	—	433	1	no	—
56	C₂	C₂×#20294111	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂×#20294111
commutator, socle	C₂×C₄₃₃	C₂×C₁₆
Fitting	C₂²×C₄₃₃	C₁₆
prime radical	C₂²×D₄₃₃	C₈
cosocle	C₂×#16812367	C₂²
hypercenter	C₂²	#20294111
hypocenter	C₄₃₃	C₂²⋊C₁₆
LCS	G ▷ C₂×C₄₃₃ ▷ C₄₃₃
UCS	C₁ ◁ C₂ ◁ C₂²

Complements

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

N	H ≅ G/N	type
1. C₂×#20294111	C₂	semidirect
15. C₂²×C₄₃₃	C₁₆	semidirect
18. C₂×D₄₃₃	C₁₆	semidirect
28. C₄₃₃	C₂²⋊C₁₆	semidirect
48. C₂²	#20294111	semidirect

Maximal subgroups

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

subgroup	index
C₂×#20294111	2
C₂²×#16812367	2
C₂²⋊C₁₆	433

Subgroups — C22⋊#20294111 #42122937

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²⋊#20294111 #42122937