Subgroups — C₂²×#20269746 #41003252

Order 26944.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20269746	C₂	1	6	yes	maximal, direct product factor
2	C₂²×C₈×C₄₂₁	C₂	1	1	yes	maximal, characteristic
3	#20269746	C₂²	1	4	yes	direct product factor
4	C₂²×C₄×C₄₂₁	C₄	1	1	yes	characteristic
5	C₂×C₈×C₄₂₁	C₄	1	3	yes	—
6	C₂×C₈×C₄₂₁	C₂²	1	3	yes	—
7	C₂³×C₄₂₁	C₈	1	1	yes	characteristic
8	C₂×C₄×C₄₂₁	C₈	1	3	yes	—
9	C₂×C₄×C₄₂₁	C₂×C₄	1	3	yes	—
10	C₈×C₄₂₁	C₂×C₄	1	3	yes	—
11	C₈×C₄₂₁	C₂³	1	1	yes	characteristic
12	C₂²×C₄₂₁	C₁₆	1	4	yes	complemented
13	C₂²×C₄₂₁	C₂×C₈	1	3	yes	—
14	C₄×C₄₂₁	C₂×C₈	1	3	yes	—
15	C₄×C₄₂₁	C₂²×C₄	1	1	yes	characteristic
16	C₂×C₄₂₁	C₂×C₁₆	1	6	yes	complemented
17	C₂×C₄₂₁	C₂²×C₈	1	1	yes	characteristic
18	C₄₂₁	C₂²×C₁₆	1	1	yes	characteristic, complemented, Sylow
19	C₂²×C₁₆	—	421	1	no	maximal, Sylow
20	C₂²×C₈	D₄₂₁	1	1	yes	characteristic
21	C₂×C₁₆	—	421	6	no	—
22	C₂²×C₄	Dic₄₂₁	1	1	yes	characteristic
23	C₂×C₈	Dic₄₂₁	1	3	yes	—
24	C₂×C₈	C₂×D₄₂₁	1	3	yes	—
25	C₁₆	—	421	4	no	—
26	C₂³	#16809890	1	1	yes	characteristic
27	C₂×C₄	#16809890	1	3	yes	—
28	C₂×C₄	C₂×Dic₄₂₁	1	3	yes	—
29	C₈	C₂×Dic₄₂₁	1	3	yes	—
30	C₈	C₂²×D₄₂₁	1	1	yes	characteristic
31	C₂²	#20269746	1	4	yes	direct product factor
32	C₂²	C₂×#16809890	1	3	yes	—
33	C₄	C₂×#16809890	1	3	yes	—
34	C₄	C₂²×Dic₄₂₁	1	1	yes	characteristic
35	C₂	C₂×#20269746	1	6	yes	direct product factor
36	C₂	C₂²×#16809890	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²×C₈	D₄₂₁
commutator, hypocenter	C₄₂₁	C₂²×C₁₆
Frattini	C₈	C₂²×D₄₂₁
Fitting	C₂²×C₈×C₄₂₁	C₂
socle, prime radical	C₂³×C₄₂₁	C₈
cosocle	C₈×C₄₂₁	C₂³
LCS	G ▷ C₄₂₁
UCS	C₁ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
1. C₂×#20269746	C₂	direct (N × H)
3. #20269746	C₂²	direct (N × H)
12. C₂²×C₄₂₁	C₁₆	semidirect
16. C₂×C₄₂₁	C₂×C₁₆	semidirect
18. C₄₂₁	C₂²×C₁₆	semidirect
31. C₂²	#20269746	direct (N × H)
35. C₂	C₂×#20269746	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×#20269746	2
C₂²×C₈×C₄₂₁	2
C₂²×C₁₆	421

Subgroups — C22×#20269746 #41003252

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#20269746 #41003252