Subgroups — C₂²⋊#16838782 #29508813

Order 15424.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16838782	C₂	1	2	yes	maximal, complemented
2	C₂²×#14515356	C₂	1	1	yes	maximal, characteristic
3	#16838782	—	2	2	no	—
4	C₂×#14515356	—	2	2	no	—
5	C₂×#14515356	C₄	1	1	yes	characteristic
6	C₂×#14515356	C₂²	1	1	yes	characteristic
7	C₂²×Dic₂₄₁	C₄	1	1	yes	characteristic
8	#14515356	—	2	1	no	—
9	#14515356	D₄	1	2	yes	—
10	C₂×Dic₂₄₁	—	2	1	no	—
11	C₂×Dic₂₄₁	—	2	1	no	—
12	C₂×Dic₂₄₁	C₈	1	1	yes	characteristic
13	C₂×Dic₂₄₁	C₂×C₄	1	1	yes	characteristic
14	C₂³×C₂₄₁	C₈	1	1	yes	characteristic
15	C₂²×C₂₄₁	—	2	1	no	—
16	C₂²×C₂₄₁	—	2	1	no	—
17	C₂²×C₂₄₁	C₁₆	1	2	yes	complemented
18	C₂²×C₂₄₁	C₂×C₈	1	1	yes	characteristic
19	Dic₂₄₁	—	2	1	no	—
20	Dic₂₄₁	C₂²⋊C₄	1	1	yes	characteristic
21	Dic₂₄₁	M₁₆	1	1	yes	characteristic
22	C₂×C₂₄₁	—	2	2	no	—
23	C₂×C₂₄₁	C₂²⋊C₈	1	1	yes	characteristic
24	C₂×C₂₄₁	C₂×C₁₆	1	1	yes	characteristic
25	C₂×C₂₄₁	M₃₂	1	1	yes	characteristic
26	C₂₄₁	C₂²⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
27	C₂²⋊C₁₆	—	241	1	no	maximal, Sylow
28	C₂²×C₈	—	241	1	no	—
29	C₂×C₁₆	—	241	2	no	—
30	C₂²×C₄	—	241	1	no	—
31	C₂×C₈	—	482	2	no	—
32	C₂×C₈	—	241	1	no	—
33	C₂×C₈	—	241	1	no	—
34	C₁₆	—	482	2	no	—
35	C₂³	#14515358	1	1	yes	characteristic
36	C₂×C₄	—	482	1	no	—
37	C₂×C₄	—	482	1	no	—
38	C₂×C₄	—	241	1	no	—
39	C₂×C₄	—	241	1	no	—
40	C₈	—	482	1	no	—
41	C₈	—	241	2	no	—
42	C₂²	—	2	1	no	—
43	C₂²	—	2	1	no	—
44	C₂²	#16838782	1	2	yes	complemented
45	C₂²	C₂×#14515358	1	1	yes	characteristic
46	C₄	—	482	1	no	—
47	C₄	—	241	1	no	—
48	C₄	—	241	1	no	—
49	C₂	—	2	2	no	—
50	C₂	C₂²⋊#14515358	1	1	yes	characteristic
51	C₂	C₂×#16838782	1	1	yes	characteristic
52	C₂	#21440738	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂×#14515358
commutator	C₂×C₂₄₁	C₂×C₁₆
Fitting, prime radical	C₂³×C₂₄₁	C₈
socle	C₂²×C₂₄₁	C₂×C₈
cosocle	C₂×#14515356	C₂²
hypercenter	C₂³	#14515358
hypocenter	C₂₄₁	C₂²⋊C₁₆
LCS	G ▷ C₂×C₂₄₁ ▷ C₂₄₁
UCS	C₁ ◁ C₂² ◁ C₂³

Complements

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

N	H ≅ G/N	type
1. C₂×#16838782	C₂	semidirect
17. C₂²×C₂₄₁	C₁₆	semidirect
26. C₂₄₁	C₂²⋊C₁₆	semidirect
44. C₂²	#16838782	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16838782	2
C₂²×#14515356	2
C₂²⋊C₁₆	241

Subgroups — C22⋊#16838782 #29508813

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²⋊#16838782 #29508813