Subgroups — #1281×C₂₁₁ #41008901

Order 27008.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#431×C₂₁₁	C₂	1	2	yes	maximal
2	C₂×#97×C₂₁₁	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₈×C₂₁₁	C₄	1	2	yes	—
4	C₂×C₄²×C₂₁₁	C₂²	1	1	yes	characteristic
5	C₄⋊C₈×C₂₁₁	—	2	2	no	—
6	C₂²⋊C₈×C₂₁₁	C₄	1	4	yes	—
7	#97×C₂₁₁	—	2	2	no	—
8	C₄×C₈×C₂₁₁	—	2	2	no	—
9	C₂²×C₄×C₂₁₁	C₂×C₄	1	2	yes	—
10	C₂²×C₄×C₂₁₁	C₂×C₄	1	1	yes	characteristic
11	C₂×C₈×C₂₁₁	—	2	2	no	—
12	C₂×C₈×C₂₁₁	—	2	2	no	—
13	C₂×C₈×C₂₁₁	—	2	4	no	—
14	C₂×C₈×C₂₁₁	C₈	1	4	yes	complemented
15	C₄²×C₂₁₁	D₄	1	1	yes	characteristic
16	C₄²×C₂₁₁	D₄	1	2	yes	—
17	C₄²×C₂₁₁	Q₈	1	1	yes	characteristic
18	C₂³×C₂₁₁	C₄²	1	1	yes	characteristic
19	C₂×C₄×C₂₁₁	—	4	2	no	—
20	C₂×C₄×C₂₁₁	C₂²⋊C₄	1	2	yes	—
21	C₂×C₄×C₂₁₁	C₂²⋊C₄	1	1	yes	characteristic
22	C₂×C₄×C₂₁₁	C₄⋊C₄	1	2	yes	—
23	C₂×C₄×C₂₁₁	C₄⋊C₄	1	1	yes	characteristic
24	C₂×C₄×C₂₁₁	C₂×C₈	1	2	yes	—
25	C₂×C₄×C₂₁₁	M₁₆	1	2	yes	—
26	C₈×C₂₁₁	—	2	4	no	—
27	C₈×C₂₁₁	—	4	4	no	—
28	C₂²×C₂₁₁	—	2	2	no	—
29	C₂²×C₂₁₁	#95	1	1	yes	characteristic
30	C₂²×C₂₁₁	C₄×C₈	1	1	yes	characteristic
31	C₂²×C₂₁₁	#97	1	1	yes	characteristic
32	C₄×C₂₁₁	—	2	2	no	—
33	C₄×C₂₁₁	—	2	2	no	—
34	C₄×C₂₁₁	C₂²⋊C₈	1	2	yes	—
35	C₄×C₂₁₁	C₄⋊C₈	1	2	yes	—
36	C₂×C₂₁₁	—	2	1	no	—
37	C₂×C₂₁₁	—	2	1	no	—
38	C₂×C₂₁₁	#336	1	1	yes	characteristic
39	C₂×C₂₁₁	#344	1	2	yes	—
40	C₂₁₁	#1281	1	1	yes	characteristic, direct product factor, Sylow
41	#1281	C₂₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	#431	C₂×C₂₁₁	1	2	yes	—
43	C₂×#97	C₂×C₂₁₁	1	1	yes	characteristic
44	C₂²×C₈	C₄×C₂₁₁	1	2	yes	—
45	C₂×C₄²	C₂²×C₂₁₁	1	1	yes	characteristic
46	C₄⋊C₈	—	2	2	no	—
47	C₂²⋊C₈	C₄×C₂₁₁	1	4	yes	—
48	#97	—	2	2	no	—
49	C₄×C₈	—	2	2	no	—
50	C₂²×C₄	C₂×C₄×C₂₁₁	1	2	yes	—
51	C₂²×C₄	C₂×C₄×C₂₁₁	1	1	yes	characteristic
52	C₂×C₈	—	2	2	no	—
53	C₂×C₈	—	2	2	no	—
54	C₂×C₈	—	2	4	no	—
55	C₂×C₈	C₈×C₂₁₁	1	4	yes	complemented
56	C₄²	D₄×C₂₁₁	1	2	yes	—
57	C₄²	D₄×C₂₁₁	1	1	yes	characteristic
58	C₄²	Q₈×C₂₁₁	1	1	yes	characteristic
59	C₂³	C₄²×C₂₁₁	1	1	yes	characteristic
60	C₂×C₄	—	4	2	no	—
61	C₂×C₄	C₂²⋊C₄×C₂₁₁	1	2	yes	—
62	C₂×C₄	C₂²⋊C₄×C₂₁₁	1	1	yes	characteristic
63	C₂×C₄	C₄⋊C₄×C₂₁₁	1	2	yes	—
64	C₂×C₄	C₄⋊C₄×C₂₁₁	1	1	yes	characteristic
65	C₂×C₄	C₂×C₈×C₂₁₁	1	2	yes	—
66	C₂×C₄	M₁₆×C₂₁₁	1	2	yes	—
67	C₈	—	2	4	no	—
68	C₈	—	4	4	no	—
69	C₂²	—	2	2	no	—
70	C₂²	#95×C₂₁₁	1	1	yes	characteristic
71	C₂²	C₄×C₈×C₂₁₁	1	1	yes	characteristic
72	C₂²	#97×C₂₁₁	1	1	yes	characteristic
73	C₄	—	2	2	no	—
74	C₄	—	2	2	no	—
75	C₄	C₂²⋊C₈×C₂₁₁	1	2	yes	—
76	C₄	C₄⋊C₈×C₂₁₁	1	2	yes	—
77	C₂	—	2	1	no	—
78	C₂	—	2	1	no	—
79	C₂	#336×C₂₁₁	1	1	yes	characteristic
80	C₂	#344×C₂₁₁	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₂₁₁	C₂²⋊C₄
commutator	C₂²	C₄×C₈×C₂₁₁
Frattini, cosocle	C₂×C₄²	C₂²×C₂₁₁
socle	C₂²×C₂₁₁	#95
prime radical	C₂³×C₂₁₁	C₄²
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₁₁ ◁ C₂×C₄²×C₂₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
14. C₂×C₈×C₂₁₁	C₈	semidirect
40. C₂₁₁	#1281	direct (N × H)
41. #1281	C₂₁₁	direct (N × H)
55. C₂×C₈	C₈×C₂₁₁	semidirect

Maximal subgroups

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

subgroup	index
#431×C₂₁₁	2
C₂×#97×C₂₁₁	2
#1281	211

Subgroups — #1281×C211 #41008901

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1281×C₂₁₁ #41008901