Subgroups — C₁₁×#12887 #14590080

Order 2816.

286 conjugacy classes of subgroups.

The subgroup lattice has 172 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₁×M₃₂	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#1848	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#1846	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#1383	C₂	1	4	yes	maximal
5	C₂×C₁₁×M₃₂	C₂²	1	2	yes	—
6	C₂×C₁₁×#108	—	2	1	no	—
7	C₂×C₁₁×#108	C₂²	1	2	yes	—
8	C₂×C₁₁×#107	—	2	1	no	—
9	C₂×C₁₁×#106	C₂²	1	2	yes	—
10	C₁₁×#423	—	2	1	no	—
11	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
12	C₁₁×#382	—	2	1	no	—
13	C₁₁×#346	C₄	1	2	yes	complemented
14	C₄×C₁₁×C₁₆	C₄	1	2	yes	complemented
15	C₂×C₁₁×M₁₆	—	2	2	no	—
16	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
17	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
18	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
19	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
20	C₁₁×M₃₂	—	2	2	no	—
21	C₁₁×M₃₂	—	2	2	no	—
22	C₂×C₁₁×C₁₆	C₂×C₄	1	4	yes	—
23	C₁₁×#108	—	2	4	no	—
24	C₁₁×#108	—	4	2	no	—
25	C₁₁×#107	—	4	2	no	—
26	C₁₁×#106	—	2	4	no	—
27	C₁₁×C₄⋊C₈	—	4	2	no	—
28	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
29	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
30	C₄×C₈×C₁₁	Q₈	1	1	yes	characteristic
31	C₄×C₈×C₁₁	Q₈	1	1	yes	characteristic
32	C₁₁×#95	—	4	2	no	—
33	#12887	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
34	C₂²×C₄×C₁₁	—	4	2	no	—
35	C₂²×C₄×C₁₁	SD₁₆	1	2	yes	—
36	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
37	C₁₁×M₁₆	—	4	2	no	—
38	C₁₁×M₁₆	—	4	2	no	—
39	C₂×C₈×C₁₁	—	4	2	no	—
40	C₂×C₈×C₁₁	C₄⋊C₄	1	1	yes	characteristic
41	C₂×C₈×C₁₁	C₄⋊C₄	1	1	yes	characteristic
42	C₂×C₈×C₁₁	D₈	1	2	yes	—
43	C₂×C₈×C₁₁	Q₁₆	1	2	yes	—
44	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
45	C₂×C₈×C₁₁	C₂×Q₈	1	1	yes	characteristic
46	C₂×C₈×C₁₁	#41	1	2	yes	—
47	C₂×C₈×C₁₁	#41	1	2	yes	—
48	C₁₁×C₄⋊C₄	—	4	2	no	—
49	C₁₁×C₄⋊C₄	—	4	2	no	—
50	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
51	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
52	C₄²×C₁₁	SD₁₆	1	2	yes	—
53	C₁₁×C₁₆	—	2	4	no	—
54	C₄×M₃₂	C₂×C₁₁	1	1	yes	characteristic
55	#1848	C₂×C₁₁	1	1	yes	characteristic
56	#1846	C₂×C₁₁	1	1	yes	characteristic
57	#1383	C₂×C₁₁	1	4	yes	—
58	C₂³×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
59	C₂×C₄×C₁₁	—	4	2	no	—
60	C₂×C₄×C₁₁	—	8	4	no	—
61	C₂×C₄×C₁₁	—	8	2	no	—
62	C₂×C₄×C₁₁	#106	1	2	yes	—
63	C₂×C₄×C₁₁	#106	1	2	yes	—
64	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
65	C₂×C₄×C₁₁	#124	1	1	yes	characteristic
66	C₂×C₄×C₁₁	#124	1	1	yes	characteristic
67	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
68	C₂×C₄×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
69	C₂×C₄×C₁₁	C₂×Q₁₆	1	1	yes	characteristic
70	C₈×C₁₁	—	8	2	no	—
71	C₈×C₁₁	#107	1	2	yes	—
72	C₈×C₁₁	#107	1	2	yes	—
73	C₈×C₁₁	#117	1	2	yes	—
74	C₈×C₁₁	#125	1	2	yes	—
75	C₂×M₃₂	C₂²×C₁₁	1	2	yes	—
76	C₂×#108	—	2	1	no	—
77	C₂×#108	C₂²×C₁₁	1	2	yes	—
78	C₂×#107	—	2	1	no	—
79	C₂×#106	C₂²×C₁₁	1	2	yes	—
80	#423	—	2	1	no	—
81	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
82	#382	—	2	1	no	—
83	#346	C₄×C₁₁	1	2	yes	complemented
84	C₄×C₁₆	C₄×C₁₁	1	2	yes	complemented
85	C₂²×C₁₁	—	2	2	no	—
86	C₂²×C₁₁	C₂×#106	1	1	yes	characteristic
87	C₂²×C₁₁	#486	1	1	yes	characteristic
88	C₂²×C₁₁	#487	1	1	yes	characteristic
89	C₄×C₁₁	—	2	2	no	—
90	C₄×C₁₁	—	2	2	no	—
91	C₄×C₁₁	—	16	2	no	—
92	C₄×C₁₁	#382	1	1	yes	characteristic
93	C₄×C₁₁	C₂×#107	1	1	yes	characteristic
94	C₄×C₁₁	#486	1	1	yes	characteristic
95	C₄×C₁₁	#487	1	1	yes	characteristic
96	C₂×M₁₆	—	2	2	no	—
97	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
98	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
99	C₂×C₄⋊C₄	—	2	2	no	—
100	C₂×C₄²	D₄×C₁₁	1	1	yes	characteristic
101	M₃₂	—	2	2	no	—
102	M₃₂	—	2	2	no	—
103	C₂×C₁₆	C₂×C₄×C₁₁	1	4	yes	—
104	#108	—	2	4	no	—
105	#108	—	4	2	no	—
106	#107	—	4	2	no	—
107	#106	—	2	4	no	—
108	C₄⋊C₈	—	4	2	no	—
109	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
110	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
111	C₄×C₈	Q₈×C₁₁	1	1	yes	characteristic
112	C₄×C₈	Q₈×C₁₁	1	1	yes	characteristic
113	#95	—	4	2	no	—
114	C₂×C₁₁	—	2	1	no	—
115	C₂×C₁₁	—	2	1	no	—
116	C₂×C₁₁	#1834	1	1	yes	characteristic
117	C₂×C₁₁	#2155	1	2	yes	—
118	C₂²×C₄	—	4	2	no	—
119	C₂²×C₄	C₁₁×SD₁₆	1	2	yes	—
120	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
121	M₁₆	—	4	2	no	—
122	M₁₆	—	4	2	no	—
123	C₂×C₈	—	4	2	no	—
124	C₂×C₈	C₁₁×C₄⋊C₄	1	1	yes	characteristic
125	C₂×C₈	C₁₁×C₄⋊C₄	1	1	yes	characteristic
126	C₂×C₈	C₁₁×D₈	1	2	yes	—
127	C₂×C₈	C₁₁×Q₁₆	1	2	yes	—
128	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
129	C₂×C₈	C₂×Q₈×C₁₁	1	1	yes	characteristic
130	C₂×C₈	C₁₁×#41	1	2	yes	—
131	C₂×C₈	C₁₁×#41	1	2	yes	—
132	C₄⋊C₄	—	4	2	no	—
133	C₄⋊C₄	—	4	2	no	—
134	C₄²	C₁₁×C₄⋊C₄	1	1	yes	characteristic
135	C₄²	C₁₁×C₄⋊C₄	1	1	yes	characteristic
136	C₄²	C₁₁×SD₁₆	1	2	yes	—
137	C₁₆	—	2	4	no	—
138	C₁₁	#12887	1	1	yes	characteristic, direct product factor, Sylow
139	C₂³	C₂×C₁₁×SD₁₆	1	1	yes	characteristic
140	C₂×C₄	—	4	2	no	—
141	C₂×C₄	—	8	4	no	—
142	C₂×C₄	—	8	2	no	—
143	C₂×C₄	C₁₁×#106	1	2	yes	—
144	C₂×C₄	C₁₁×#106	1	2	yes	—
145	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	1	yes	characteristic
146	C₂×C₄	C₁₁×#124	1	1	yes	characteristic
147	C₂×C₄	C₁₁×#124	1	1	yes	characteristic
148	C₂×C₄	C₂×C₁₁×D₈	1	1	yes	characteristic
149	C₂×C₄	C₂×C₁₁×SD₁₆	1	1	yes	characteristic
150	C₂×C₄	C₂×C₁₁×Q₁₆	1	1	yes	characteristic
151	C₈	—	8	2	no	—
152	C₈	C₁₁×#107	1	2	yes	—
153	C₈	C₁₁×#107	1	2	yes	—
154	C₈	C₁₁×#117	1	2	yes	—
155	C₈	C₁₁×#125	1	2	yes	—
156	C₂²	—	2	2	no	—
157	C₂²	C₂×C₁₁×#106	1	1	yes	characteristic
158	C₂²	C₁₁×#486	1	1	yes	characteristic
159	C₂²	C₁₁×#487	1	1	yes	characteristic
160	C₄	—	2	2	no	—
161	C₄	—	2	2	no	—
162	C₄	—	16	2	no	—
163	C₄	C₁₁×#382	1	1	yes	characteristic
164	C₄	C₂×C₁₁×#107	1	1	yes	characteristic
165	C₄	C₁₁×#486	1	1	yes	characteristic
166	C₄	C₁₁×#487	1	1	yes	characteristic
167	C₂	—	2	1	no	—
168	C₂	—	2	1	no	—
169	C₂	C₁₁×#1834	1	1	yes	characteristic
170	C₂	C₁₁×#2155	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂×#106
commutator	C₂×C₈	C₂²×C₄×C₁₁
Frattini, cosocle	C₂²×C₈	C₂³×C₁₁
prime radical	C₂³×C₁₁	C₂×SD₁₆
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ C₂×C₄×C₈×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
13. C₁₁×#346	C₄	semidirect
14. C₄×C₁₁×C₁₆	C₄	semidirect
33. #12887	C₁₁	direct (N × H)
83. #346	C₄×C₁₁	semidirect
84. C₄×C₁₆	C₄×C₁₁	semidirect
138. C₁₁	#12887	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₁₁×M₃₂	2
C₁₁×#1848	2
C₁₁×#1846	2
C₁₁×#1383	2
#12887	11

Subgroups — C11×#12887 #14590080

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#12887 #14590080