Subgroups — C₁₁×#12011 #14589204

Order 2816.

220 conjugacy classes of subgroups.

The subgroup lattice has 136 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#364	C₂	1	2	yes	maximal
2	C₄×C₁₁×M₃₂	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#1373	C₂	1	4	yes	maximal, complemented
4	C₂×C₁₁×M₃₂	—	2	2	no	—
5	C₂×C₁₁×M₃₂	C₄	1	1	yes	characteristic
6	C₂×C₁₁×M₃₂	C₄	1	1	yes	characteristic
7	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
8	C₁₁×#364	—	2	2	no	—
9	C₁₁×#364	C₂²	1	4	yes	—
10	C₁₁×#346	C₄	1	2	yes	—
11	C₄×C₁₁×C₁₆	C₂²	1	2	yes	—
12	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
13	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
14	C₂×C₄²×C₁₁	Q₈	1	1	yes	characteristic
15	C₁₁×M₃₂	—	2	2	no	—
16	C₁₁×M₃₂	—	2	4	no	—
17	C₁₁×M₃₂	—	4	2	no	—
18	C₁₁×M₃₂	C₈	1	4	yes	—
19	C₂×C₁₁×C₁₆	—	4	2	no	—
20	C₂×C₁₁×C₁₆	C₂×C₄	1	2	yes	—
21	C₂×C₁₁×C₁₆	C₂×C₄	1	2	yes	—
22	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
23	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
24	C₄×C₈×C₁₁	Q₈	1	1	yes	characteristic
25	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
26	#12011	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
27	C₂²×C₄×C₁₁	—	2	1	no	—
28	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
29	C₂×C₈×C₁₁	C₄⋊C₄	1	1	yes	characteristic
30	C₂×C₈×C₁₁	C₄⋊C₄	1	1	yes	characteristic
31	C₂×C₈×C₁₁	C₂×C₈	1	2	yes	—
32	C₂×C₈×C₁₁	M₁₆	1	2	yes	—
33	C₂×C₈×C₁₁	D₈	1	2	yes	—
34	C₂×C₈×C₁₁	Q₁₆	1	2	yes	—
35	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
36	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
37	C₄²×C₁₁	—	2	1	no	—
38	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
39	C₄²×C₁₁	C₂×Q₈	1	1	yes	characteristic
40	C₁₁×C₁₆	—	2	2	no	—
41	C₁₁×C₁₆	—	4	4	no	—
42	C₁₁×C₁₆	C₂×C₈	1	4	yes	—
43	C₂×#364	C₂×C₁₁	1	2	yes	—
44	C₄×M₃₂	C₂×C₁₁	1	1	yes	characteristic
45	#1373	C₂×C₁₁	1	4	yes	complemented
46	C₂³×C₁₁	#108	1	1	yes	characteristic
47	C₂×C₄×C₁₁	—	2	1	no	—
48	C₂×C₄×C₁₁	—	2	1	no	—
49	C₂×C₄×C₁₁	—	4	2	no	—
50	C₂×C₄×C₁₁	C₄⋊C₈	1	2	yes	—
51	C₂×C₄×C₁₁	#107	1	2	yes	—
52	C₂×C₄×C₁₁	#108	1	1	yes	characteristic
53	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
54	C₈×C₁₁	C₄⋊C₈	1	2	yes	—
55	C₈×C₁₁	#107	1	2	yes	—
56	C₈×C₁₁	C₂²×C₈	1	1	yes	characteristic
57	C₈×C₁₁	C₂×M₁₆	1	1	yes	characteristic
58	C₈×C₁₁	C₂×D₈	1	1	yes	characteristic
59	C₈×C₁₁	C₂×Q₁₆	1	1	yes	characteristic
60	C₂×M₃₂	—	2	2	no	—
61	C₂×M₃₂	C₄×C₁₁	1	1	yes	characteristic
62	C₂×M₃₂	C₄×C₁₁	1	1	yes	characteristic
63	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
64	#364	—	2	2	no	—
65	#364	C₂²×C₁₁	1	4	yes	—
66	#346	C₄×C₁₁	1	2	yes	—
67	C₄×C₁₆	C₂²×C₁₁	1	2	yes	—
68	C₂²×C₁₁	—	4	1	no	—
69	C₂²×C₁₁	#335	1	2	yes	—
70	C₂²×C₁₁	C₂×#108	1	1	yes	characteristic
71	C₄×C₁₁	—	2	2	no	—
72	C₄×C₁₁	—	4	1	no	—
73	C₄×C₁₁	#335	1	2	yes	—
74	C₄×C₁₁	C₂×C₄⋊C₈	1	1	yes	characteristic
75	C₄×C₁₁	C₂×#107	1	1	yes	characteristic
76	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
77	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
78	C₂×C₄²	Q₈×C₁₁	1	1	yes	characteristic
79	M₃₂	—	2	2	no	—
80	M₃₂	—	2	4	no	—
81	M₃₂	—	4	2	no	—
82	M₃₂	C₈×C₁₁	1	4	yes	—
83	C₂×C₁₆	—	4	2	no	—
84	C₂×C₁₆	C₂×C₄×C₁₁	1	2	yes	—
85	C₂×C₁₆	C₂×C₄×C₁₁	1	2	yes	—
86	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
87	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
88	C₄×C₈	Q₈×C₁₁	1	1	yes	characteristic
89	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
90	C₂×C₁₁	—	2	1	no	—
91	C₂×C₁₁	—	2	2	no	—
92	C₂×C₁₁	C₂×#335	1	1	yes	characteristic
93	C₂²×C₄	—	2	1	no	—
94	C₂²×C₄	C₁₁×C₄⋊C₄	1	1	yes	characteristic
95	C₂×C₈	C₁₁×C₄⋊C₄	1	1	yes	characteristic
96	C₂×C₈	C₁₁×C₄⋊C₄	1	1	yes	characteristic
97	C₂×C₈	C₂×C₈×C₁₁	1	2	yes	—
98	C₂×C₈	C₁₁×M₁₆	1	2	yes	—
99	C₂×C₈	C₁₁×D₈	1	2	yes	—
100	C₂×C₈	C₁₁×Q₁₆	1	2	yes	—
101	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
102	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
103	C₄²	—	2	1	no	—
104	C₄²	C₁₁×C₄⋊C₄	1	1	yes	characteristic
105	C₄²	C₂×Q₈×C₁₁	1	1	yes	characteristic
106	C₁₆	—	2	2	no	—
107	C₁₆	—	4	4	no	—
108	C₁₆	C₂×C₈×C₁₁	1	4	yes	—
109	C₁₁	#12011	1	1	yes	characteristic, direct product factor, Sylow
110	C₂³	C₁₁×#108	1	1	yes	characteristic
111	C₂×C₄	—	2	1	no	—
112	C₂×C₄	—	2	1	no	—
113	C₂×C₄	—	4	2	no	—
114	C₂×C₄	C₁₁×C₄⋊C₈	1	2	yes	—
115	C₂×C₄	C₁₁×#107	1	2	yes	—
116	C₂×C₄	C₁₁×#108	1	1	yes	characteristic
117	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	1	yes	characteristic
118	C₈	C₁₁×C₄⋊C₈	1	2	yes	—
119	C₈	C₁₁×#107	1	2	yes	—
120	C₈	C₂²×C₈×C₁₁	1	1	yes	characteristic
121	C₈	C₂×C₁₁×M₁₆	1	1	yes	characteristic
122	C₈	C₂×C₁₁×D₈	1	1	yes	characteristic
123	C₈	C₂×C₁₁×Q₁₆	1	1	yes	characteristic
124	C₂²	—	4	1	no	—
125	C₂²	C₁₁×#335	1	2	yes	—
126	C₂²	C₂×C₁₁×#108	1	1	yes	characteristic
127	C₄	—	2	2	no	—
128	C₄	—	4	1	no	—
129	C₄	C₁₁×#335	1	2	yes	—
130	C₄	C₂×C₁₁×C₄⋊C₈	1	1	yes	characteristic
131	C₄	C₂×C₁₁×#107	1	1	yes	characteristic
132	C₂	—	2	1	no	—
133	C₂	—	2	2	no	—
134	C₂	C₂×C₁₁×#335	1	1	yes	characteristic

	subgroup	G/H
center	C₈×C₁₁	C₂×D₈
commutator	C₈	C₂²×C₈×C₁₁
Frattini, cosocle	C₄×C₈	C₂³×C₁₁
socle	C₂×C₁₁	C₂×#335
prime radical	C₂³×C₁₁	#108
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₁₁ ◁ C₂²×C₈×C₁₁ ◁ C₂×C₄×C₈×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₁×#1373	C₂	semidirect
26. #12011	C₁₁	direct (N × H)
45. #1373	C₂×C₁₁	semidirect
109. C₁₁	#12011	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×#364	2
C₄×C₁₁×M₃₂	2
C₁₁×#1373	2
#12011	11

Subgroups — C11×#12011 #14589204

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#12011 #14589204