Subgroups — #341×C₄₂₁ #41002313

Order 26944.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₁₆×C₄₂₁	C₂	1	2	yes	maximal
2	C₂²×C₈×C₄₂₁	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₄×C₄₂₁	C₂²	1	1	yes	characteristic
4	M₁₆×C₄₂₁	—	2	2	no	—
5	M₁₆×C₄₂₁	C₄	1	4	yes	—
6	C₂×C₈×C₄₂₁	—	2	2	no	—
7	C₂×C₈×C₄₂₁	—	2	2	no	—
8	C₂×C₈×C₄₂₁	C₄	1	2	yes	—
9	C₂³×C₄₂₁	Q₈	1	1	yes	characteristic
10	C₂×C₄×C₄₂₁	C₂×C₄	1	1	yes	characteristic
11	C₂×C₄×C₄₂₁	C₂×C₄	1	2	yes	—
12	C₂×C₄×C₄₂₁	D₄	1	2	yes	—
13	C₂×C₄×C₄₂₁	D₄	1	1	yes	characteristic
14	C₈×C₄₂₁	—	2	2	no	—
15	C₈×C₄₂₁	—	2	4	no	—
16	C₂²×C₄₂₁	—	2	2	no	—
17	C₂²×C₄₂₁	C₄⋊C₄	1	2	yes	—
18	C₂²×C₄₂₁	C₄⋊C₄	1	1	yes	characteristic
19	C₄×C₄₂₁	C₄²	1	1	yes	characteristic
20	C₄×C₄₂₁	C₂²⋊C₄	1	1	yes	characteristic
21	C₄×C₄₂₁	C₂²⋊C₄	1	2	yes	—
22	C₂×C₄₂₁	—	2	2	no	—
23	C₂×C₄₂₁	#95	1	1	yes	characteristic
24	C₂×C₄₂₁	#108	1	2	yes	—
25	C₄₂₁	#341	1	1	yes	characteristic, direct product factor, Sylow
26	#341	C₄₂₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
27	C₂×M₁₆	C₂×C₄₂₁	1	2	yes	—
28	C₂²×C₈	C₂×C₄₂₁	1	1	yes	characteristic
29	C₂²×C₄	C₂²×C₄₂₁	1	1	yes	characteristic
30	M₁₆	—	2	2	no	—
31	M₁₆	C₄×C₄₂₁	1	4	yes	—
32	C₂×C₈	—	2	2	no	—
33	C₂×C₈	—	2	2	no	—
34	C₂×C₈	C₄×C₄₂₁	1	2	yes	—
35	C₂³	Q₈×C₄₂₁	1	1	yes	characteristic
36	C₂×C₄	C₂×C₄×C₄₂₁	1	1	yes	characteristic
37	C₂×C₄	C₂×C₄×C₄₂₁	1	2	yes	—
38	C₂×C₄	D₄×C₄₂₁	1	1	yes	characteristic
39	C₂×C₄	D₄×C₄₂₁	1	2	yes	—
40	C₈	—	2	2	no	—
41	C₈	—	2	4	no	—
42	C₂²	—	2	2	no	—
43	C₂²	C₄⋊C₄×C₄₂₁	1	2	yes	—
44	C₂²	C₄⋊C₄×C₄₂₁	1	1	yes	characteristic
45	C₄	C₄²×C₄₂₁	1	1	yes	characteristic
46	C₄	C₂²⋊C₄×C₄₂₁	1	1	yes	characteristic
47	C₄	C₂²⋊C₄×C₄₂₁	1	2	yes	—
48	C₂	—	2	2	no	—
49	C₂	#95×C₄₂₁	1	1	yes	characteristic
50	C₂	#108×C₄₂₁	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₄₂₁	D₄
commutator	C₄	C₄²×C₄₂₁
Frattini, cosocle	C₂²×C₄	C₂²×C₄₂₁
socle	C₂²×C₄₂₁	C₄⋊C₄
prime radical	C₂³×C₄₂₁	Q₈
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₂₁ ◁ C₂²×C₄×C₄₂₁ ◁ G

Complements

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

N	H ≅ G/N	type
25. C₄₂₁	#341	direct (N × H)
26. #341	C₄₂₁	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×M₁₆×C₄₂₁	2
C₂²×C₈×C₄₂₁	2
#341	421

Subgroups — #341×C421 #41002313

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #341×C₄₂₁ #41002313