Subgroups — #1311×C₂₁₁ #41008931

Order 27008.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₆×C₂₁₁	C₂	1	2	yes	maximal
2	C₈²×C₂₁₁	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₆×C₂₁₁	C₄	1	4	yes	—
4	C₄×C₈×C₂₁₁	C₄	1	2	yes	—
5	C₄×C₈×C₂₁₁	C₂²	1	1	yes	characteristic
6	C₂×C₈×C₂₁₁	C₈	1	4	yes	—
7	C₂×C₈×C₂₁₁	C₂×C₄	1	2	yes	—
8	C₄²×C₂₁₁	C₂×C₄	1	1	yes	characteristic
9	C₁₆×C₂₁₁	C₈	1	8	yes	complemented
10	C₂×C₄×C₂₁₁	C₄²	1	1	yes	characteristic
11	C₂×C₄×C₂₁₁	C₂×C₈	1	2	yes	—
12	C₈×C₂₁₁	—	2	4	no	—
13	C₈×C₂₁₁	C₂×C₈	1	4	yes	—
14	C₂²×C₂₁₁	C₄×C₈	1	1	yes	characteristic
15	C₄×C₂₁₁	C₄×C₈	1	2	yes	—
16	C₄×C₂₁₁	M₃₂	1	4	yes	—
17	C₂×C₂₁₁	C₈²	1	1	yes	characteristic
18	C₂×C₂₁₁	#346	1	2	yes	—
19	C₂₁₁	#1311	1	1	yes	characteristic, direct product factor, Sylow
20	#1311	C₂₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₄×C₁₆	C₂×C₂₁₁	1	2	yes	—
22	C₈²	C₂×C₂₁₁	1	1	yes	characteristic
23	C₂×C₁₆	C₄×C₂₁₁	1	4	yes	—
24	C₄×C₈	C₄×C₂₁₁	1	2	yes	—
25	C₄×C₈	C₂²×C₂₁₁	1	1	yes	characteristic
26	C₂×C₈	C₈×C₂₁₁	1	4	yes	—
27	C₂×C₈	C₂×C₄×C₂₁₁	1	2	yes	—
28	C₄²	C₂×C₄×C₂₁₁	1	1	yes	characteristic
29	C₁₆	C₈×C₂₁₁	1	8	yes	complemented
30	C₂×C₄	C₄²×C₂₁₁	1	1	yes	characteristic
31	C₂×C₄	C₂×C₈×C₂₁₁	1	2	yes	—
32	C₈	—	2	4	no	—
33	C₈	C₂×C₈×C₂₁₁	1	4	yes	—
34	C₂²	C₄×C₈×C₂₁₁	1	1	yes	characteristic
35	C₄	C₄×C₈×C₂₁₁	1	2	yes	—
36	C₄	M₃₂×C₂₁₁	1	4	yes	—
37	C₂	C₈²×C₂₁₁	1	1	yes	characteristic
38	C₂	#346×C₂₁₁	1	2	yes	—

	subgroup	G/H
center	C₄×C₈×C₂₁₁	C₂²
commutator	C₂	C₈²×C₂₁₁
Frattini, cosocle	C₄×C₈	C₂²×C₂₁₁
socle, prime radical	C₂²×C₂₁₁	C₄×C₈
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₈×C₂₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
9. C₁₆×C₂₁₁	C₈	semidirect
19. C₂₁₁	#1311	direct (N × H)
20. #1311	C₂₁₁	direct (N × H)
29. C₁₆	C₈×C₂₁₁	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₁₆×C₂₁₁	2
C₈²×C₂₁₁	2
#1311	211

Subgroups — #1311×C211 #41008931

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1311×C₂₁₁ #41008931