Subgroups — #1367×C₂₁₁ #41008987

Order 27008.

76 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	—	2	2	no	—
4	C₄×C₈×C₂₁₁	C₄	1	1	yes	characteristic
5	C₄×C₈×C₂₁₁	C₄	1	1	yes	characteristic
6	C₄×C₈×C₂₁₁	C₂²	1	1	yes	characteristic
7	C₂×C₈×C₂₁₁	—	2	1	no	—
8	C₂×C₈×C₂₁₁	C₈	1	1	yes	characteristic
9	C₂×C₈×C₂₁₁	C₈	1	1	yes	characteristic
10	C₂×C₈×C₂₁₁	D₄	1	1	yes	characteristic
11	C₂×C₈×C₂₁₁	Q₈	1	1	yes	characteristic
12	C₄²×C₂₁₁	C₂×C₄	1	1	yes	characteristic
13	C₁₆×C₂₁₁	—	4	2	no	—
14	C₂×C₄×C₂₁₁	C₄⋊C₄	1	1	yes	characteristic
15	C₂×C₄×C₂₁₁	C₂×C₈	1	1	yes	characteristic
16	C₂×C₄×C₂₁₁	M₁₆	1	1	yes	characteristic
17	C₈×C₂₁₁	—	2	2	no	—
18	C₈×C₂₁₁	—	2	1	no	—
19	C₈×C₂₁₁	—	2	1	no	—
20	C₈×C₂₁₁	C₁₆	1	2	yes	complemented
21	C₈×C₂₁₁	SD₁₆	1	2	yes	—
22	C₂²×C₂₁₁	C₄⋊C₈	1	1	yes	characteristic
23	C₄×C₂₁₁	—	2	1	no	—
24	C₄×C₂₁₁	#106	1	1	yes	characteristic
25	C₄×C₂₁₁	#108	1	1	yes	characteristic
26	C₄×C₂₁₁	C₂×C₁₆	1	1	yes	characteristic
27	C₄×C₂₁₁	M₃₂	1	1	yes	characteristic
28	C₂×C₂₁₁	#334	1	1	yes	characteristic
29	C₂×C₂₁₁	C₄⋊C₁₆	1	1	yes	characteristic
30	C₂×C₂₁₁	#364	1	1	yes	characteristic
31	C₂₁₁	#1367	1	1	yes	characteristic, direct product factor, Sylow
32	#1367	C₂₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
33	C₄⋊C₁₆	C₂×C₂₁₁	1	2	yes	—
34	C₈²	C₂×C₂₁₁	1	1	yes	characteristic
35	C₂×C₁₆	—	2	2	no	—
36	C₄×C₈	C₄×C₂₁₁	1	1	yes	characteristic
37	C₄×C₈	C₄×C₂₁₁	1	1	yes	characteristic
38	C₄×C₈	C₂²×C₂₁₁	1	1	yes	characteristic
39	C₂×C₈	—	2	1	no	—
40	C₂×C₈	C₈×C₂₁₁	1	1	yes	characteristic
41	C₂×C₈	C₈×C₂₁₁	1	1	yes	characteristic
42	C₂×C₈	D₄×C₂₁₁	1	1	yes	characteristic
43	C₂×C₈	Q₈×C₂₁₁	1	1	yes	characteristic
44	C₄²	C₂×C₄×C₂₁₁	1	1	yes	characteristic
45	C₁₆	—	4	2	no	—
46	C₂×C₄	C₄⋊C₄×C₂₁₁	1	1	yes	characteristic
47	C₂×C₄	C₂×C₈×C₂₁₁	1	1	yes	characteristic
48	C₂×C₄	M₁₆×C₂₁₁	1	1	yes	characteristic
49	C₈	—	2	2	no	—
50	C₈	—	2	1	no	—
51	C₈	—	2	1	no	—
52	C₈	C₁₆×C₂₁₁	1	2	yes	complemented
53	C₈	SD₁₆×C₂₁₁	1	2	yes	—
54	C₂²	C₄⋊C₈×C₂₁₁	1	1	yes	characteristic
55	C₄	—	2	1	no	—
56	C₄	#106×C₂₁₁	1	1	yes	characteristic
57	C₄	#108×C₂₁₁	1	1	yes	characteristic
58	C₄	C₂×C₁₆×C₂₁₁	1	1	yes	characteristic
59	C₄	M₃₂×C₂₁₁	1	1	yes	characteristic
60	C₂	#334×C₂₁₁	1	1	yes	characteristic
61	C₂	C₄⋊C₁₆×C₂₁₁	1	1	yes	characteristic
62	C₂	#364×C₂₁₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈×C₂₁₁	D₄
commutator	C₄	C₂×C₁₆×C₂₁₁
Frattini, cosocle	C₄×C₈	C₂²×C₂₁₁
socle, prime radical	C₂²×C₂₁₁	C₄⋊C₈
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₂₁₁ ◁ C₄×C₈×C₂₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
20. C₈×C₂₁₁	C₁₆	semidirect
31. C₂₁₁	#1367	direct (N × H)
32. #1367	C₂₁₁	direct (N × H)
52. C₈	C₁₆×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
#1367	211

Subgroups — #1367×C211 #41008987

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1367×C₂₁₁ #41008987