Subgroups — C₁₁×#2151 #13064989

Order 1408.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×M₃₂	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₁×C₁₆	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#405	C₂	1	1	yes	maximal, characteristic
4	C₁₁×C₄⋊C₁₆	C₂	1	4	yes	maximal, complemented
5	C₂×C₁₁×M₁₆	C₄	1	1	yes	characteristic
6	C₂²×C₈×C₁₁	C₂²	1	1	yes	characteristic
7	C₁₁×#117	C₄	1	1	yes	characteristic
8	C₁₁×M₃₂	—	2	2	no	—
9	C₂×C₁₁×C₁₆	—	2	2	no	—
10	C₂×C₁₁×C₁₆	C₂²	1	2	yes	—
11	C₂×C₁₁×C₁₆	C₂²	1	2	yes	—
12	C₁₁×#97	C₄	1	2	yes	—
13	C₄×C₈×C₁₁	C₂²	1	2	yes	—
14	C₂²×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
15	C₁₁×M₁₆	—	2	2	no	—
16	C₂×C₈×C₁₁	C₂×C₄	1	2	yes	—
17	C₂×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈×C₁₁	D₄	1	2	yes	—
19	C₂×C₈×C₁₁	Q₈	1	2	yes	—
20	C₂×C₈×C₁₁	C₂³	1	1	yes	characteristic
21	C₁₁×C₄⋊C₄	C₈	1	2	yes	—
22	C₁₁×C₂²⋊C₄	C₈	1	2	yes	—
23	C₄²×C₁₁	C₂×C₄	1	2	yes	—
24	C₁₁×C₁₆	—	2	2	no	—
25	C₁₁×C₁₆	—	2	2	no	—
26	#2151	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
27	C₂³×C₁₁	C₂×C₈	1	1	yes	characteristic
28	C₂×C₄×C₁₁	C₄⋊C₄	1	2	yes	—
29	C₂×C₄×C₁₁	C₂×C₈	1	4	yes	—
30	C₂×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
31	C₂×C₄×C₁₁	M₁₆	1	2	yes	—
32	C₂×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
33	C₈×C₁₁	—	2	2	no	—
34	C₈×C₁₁	C₄⋊C₄	1	2	yes	—
35	C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
36	C₈×C₁₁	C₂×Q₈	1	1	yes	characteristic
37	C₂×M₃₂	C₂×C₁₁	1	1	yes	characteristic
38	C₂²×C₁₆	C₂×C₁₁	1	1	yes	characteristic
39	#405	C₂×C₁₁	1	1	yes	characteristic
40	C₄⋊C₁₆	C₂×C₁₁	1	4	yes	complemented
41	C₂²×C₁₁	—	2	2	no	—
42	C₂²×C₁₁	C₄⋊C₈	1	2	yes	—
43	C₂²×C₁₁	C₂²×C₈	1	1	yes	characteristic
44	C₄×C₁₁	—	2	4	no	—
45	C₄×C₁₁	C₄⋊C₈	1	2	yes	—
46	C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
47	C₄×C₁₁	C₂×M₁₆	1	1	yes	characteristic
48	C₂×M₁₆	C₄×C₁₁	1	1	yes	characteristic
49	C₂²×C₈	C₂²×C₁₁	1	1	yes	characteristic
50	#117	C₄×C₁₁	1	1	yes	characteristic
51	M₃₂	—	2	2	no	—
52	C₂×C₁₆	—	2	2	no	—
53	C₂×C₁₆	C₂²×C₁₁	1	2	yes	—
54	C₂×C₁₆	C₂²×C₁₁	1	2	yes	—
55	#97	C₄×C₁₁	1	2	yes	—
56	C₄×C₈	C₂²×C₁₁	1	2	yes	—
57	C₂×C₁₁	—	2	2	no	—
58	C₂×C₁₁	C₂×C₄⋊C₈	1	1	yes	characteristic
59	C₂×C₁₁	#504	1	2	yes	—
60	C₂²×C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
61	M₁₆	—	2	2	no	—
62	C₂×C₈	C₂×C₄×C₁₁	1	2	yes	—
63	C₂×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
64	C₂×C₈	D₄×C₁₁	1	2	yes	—
65	C₂×C₈	Q₈×C₁₁	1	2	yes	—
66	C₂×C₈	C₂³×C₁₁	1	1	yes	characteristic
67	C₄⋊C₄	C₈×C₁₁	1	2	yes	—
68	C₂²⋊C₄	C₈×C₁₁	1	2	yes	—
69	C₄²	C₂×C₄×C₁₁	1	2	yes	—
70	C₁₆	—	2	2	no	—
71	C₁₆	—	2	2	no	—
72	C₁₁	#2151	1	1	yes	characteristic, direct product factor, Sylow
73	C₂³	C₂×C₈×C₁₁	1	1	yes	characteristic
74	C₂×C₄	C₁₁×C₄⋊C₄	1	2	yes	—
75	C₂×C₄	C₂×C₈×C₁₁	1	4	yes	—
76	C₂×C₄	C₂×C₈×C₁₁	1	1	yes	characteristic
77	C₂×C₄	C₁₁×M₁₆	1	2	yes	—
78	C₂×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
79	C₈	—	2	2	no	—
80	C₈	C₁₁×C₄⋊C₄	1	2	yes	—
81	C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
82	C₈	C₂×Q₈×C₁₁	1	1	yes	characteristic
83	C₂²	—	2	2	no	—
84	C₂²	C₁₁×C₄⋊C₈	1	2	yes	—
85	C₂²	C₂²×C₈×C₁₁	1	1	yes	characteristic
86	C₄	—	2	4	no	—
87	C₄	C₁₁×C₄⋊C₈	1	2	yes	—
88	C₄	C₂×C₁₁×C₄⋊C₄	1	1	yes	characteristic
89	C₄	C₂×C₁₁×M₁₆	1	1	yes	characteristic
90	C₂	—	2	2	no	—
91	C₂	C₂×C₁₁×C₄⋊C₈	1	1	yes	characteristic
92	C₂	C₁₁×#504	1	2	yes	—

	subgroup	G/H
center	C₂×C₈×C₁₁	C₂³
commutator	C₂²	C₂²×C₈×C₁₁
Frattini, cosocle	C₂×C₈	C₂³×C₁₁
socle	C₂²×C₁₁	C₂²×C₈
prime radical	C₂³×C₁₁	C₂×C₈
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₁×C₄⋊C₁₆	C₂	semidirect
26. #2151	C₁₁	direct (N × H)
40. C₄⋊C₁₆	C₂×C₁₁	semidirect
72. C₁₁	#2151	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×C₁₁×M₃₂	2
C₂²×C₁₁×C₁₆	2
C₁₁×#405	2
C₁₁×C₄⋊C₁₆	2
#2151	11

Subgroups — C11×#2151 #13064989

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#2151 #13064989