Subgroups — #1365×C₂₁₁ #41008985

Order 27008.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#500×C₂₁₁	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₁₆×C₂₁₁	C₂	1	1	yes	maximal, characteristic
3	#335×C₂₁₁	C₂	1	1	yes	maximal, characteristic
4	C₄⋊Q₈×C₂₁₁	—	2	1	no	—
5	C₂×C₁₆×C₂₁₁	—	2	1	no	—
6	#107×C₂₁₁	—	2	1	no	—
7	#107×C₂₁₁	C₄	1	2	yes	—
8	C₄⋊C₈×C₂₁₁	—	2	1	no	—
9	C₄×C₈×C₂₁₁	C₂²	1	1	yes	characteristic
10	C₂×Q₈×C₂₁₁	—	4	1	no	—
11	C₂×C₈×C₂₁₁	—	4	1	no	—
12	C₂×C₈×C₂₁₁	C₂×C₄	1	1	yes	characteristic
13	C₂×C₈×C₂₁₁	D₄	1	1	yes	characteristic
14	C₄⋊C₄×C₂₁₁	—	2	2	no	—
15	C₄⋊C₄×C₂₁₁	—	4	1	no	—
16	C₄²×C₂₁₁	D₄	1	1	yes	characteristic
17	C₁₆×C₂₁₁	—	4	1	no	—
18	Q₈×C₂₁₁	—	8	2	no	—
19	C₂×C₄×C₂₁₁	—	4	2	no	—
20	C₂×C₄×C₂₁₁	C₂²⋊C₄	1	1	yes	characteristic
21	C₂×C₄×C₂₁₁	D₈	1	1	yes	characteristic
22	C₂×C₄×C₂₁₁	SD₁₆	1	1	yes	characteristic
23	C₈×C₂₁₁	—	2	1	no	—
24	C₈×C₂₁₁	—	8	1	no	—
25	C₈×C₂₁₁	SD₁₆	1	1	yes	characteristic
26	C₈×C₂₁₁	Q₁₆	1	1	yes	characteristic
27	C₂²×C₂₁₁	#102	1	1	yes	characteristic
28	C₄×C₂₁₁	—	2	1	no	—
29	C₄×C₂₁₁	—	8	2	no	—
30	C₄×C₂₁₁	#101	1	1	yes	characteristic
31	C₄×C₂₁₁	#103	1	1	yes	characteristic
32	C₄×C₂₁₁	SD₃₂	1	1	yes	characteristic
33	C₄×C₂₁₁	Q₃₂	1	1	yes	characteristic
34	C₂×C₂₁₁	#332	1	1	yes	characteristic
35	C₂×C₂₁₁	#358	1	1	yes	characteristic
36	C₂×C₂₁₁	#361	1	1	yes	characteristic
37	C₂₁₁	#1365	1	1	yes	characteristic, direct product factor, Sylow
38	#1365	C₂₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
39	#500	C₂×C₂₁₁	1	1	yes	characteristic
40	C₄⋊C₁₆	C₂×C₂₁₁	1	1	yes	characteristic
41	#335	C₂×C₂₁₁	1	1	yes	characteristic
42	C₄⋊Q₈	—	2	1	no	—
43	C₂×C₁₆	—	2	1	no	—
44	#107	—	2	1	no	—
45	#107	C₄×C₂₁₁	1	2	yes	—
46	C₄⋊C₈	—	2	1	no	—
47	C₄×C₈	C₂²×C₂₁₁	1	1	yes	characteristic
48	C₂×Q₈	—	4	1	no	—
49	C₂×C₈	—	4	1	no	—
50	C₂×C₈	C₂×C₄×C₂₁₁	1	1	yes	characteristic
51	C₂×C₈	D₄×C₂₁₁	1	1	yes	characteristic
52	C₄⋊C₄	—	2	2	no	—
53	C₄⋊C₄	—	4	1	no	—
54	C₄²	D₄×C₂₁₁	1	1	yes	characteristic
55	C₁₆	—	4	1	no	—
56	Q₈	—	8	2	no	—
57	C₂×C₄	—	4	2	no	—
58	C₂×C₄	C₂²⋊C₄×C₂₁₁	1	1	yes	characteristic
59	C₂×C₄	D₈×C₂₁₁	1	1	yes	characteristic
60	C₂×C₄	SD₁₆×C₂₁₁	1	1	yes	characteristic
61	C₈	—	2	1	no	—
62	C₈	—	8	1	no	—
63	C₈	SD₁₆×C₂₁₁	1	1	yes	characteristic
64	C₈	Q₁₆×C₂₁₁	1	1	yes	characteristic
65	C₂²	#102×C₂₁₁	1	1	yes	characteristic
66	C₄	—	2	1	no	—
67	C₄	—	8	2	no	—
68	C₄	#101×C₂₁₁	1	1	yes	characteristic
69	C₄	#103×C₂₁₁	1	1	yes	characteristic
70	C₄	SD₃₂×C₂₁₁	1	1	yes	characteristic
71	C₄	Q₃₂×C₂₁₁	1	1	yes	characteristic
72	C₂	#332×C₂₁₁	1	1	yes	characteristic
73	C₂	#358×C₂₁₁	1	1	yes	characteristic
74	C₂	#361×C₂₁₁	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂²×C₂₁₁	#102
commutator	C₂×C₈	C₂×C₄×C₂₁₁
Frattini, cosocle	C₄×C₈	C₂²×C₂₁₁
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₁₁ ◁ C₄²×C₂₁₁ ◁ C₄×C₈×C₂₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
37. C₂₁₁	#1365	direct (N × H)
38. #1365	C₂₁₁	direct (N × H)

Maximal subgroups

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

subgroup	index
#500×C₂₁₁	2
C₄⋊C₁₆×C₂₁₁	2
#335×C₂₁₁	2
#1365	211

Subgroups — #1365×C211 #41008985

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1365×C₂₁₁ #41008985