Subgroups — C₁₁×#33458 #14610651

Order 2816.

646 conjugacy classes of subgroups.

The subgroup lattice has 208 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₁×Q₃₂	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2950	C₂	1	2	yes	maximal
3	C₁₁×#2176	C₂	1	4	yes	maximal, complemented
4	C₄×C₁₁×Q₃₂	C₂	1	4	yes	maximal, complemented
5	C₁₁×#2158	C₂	1	1	yes	maximal, characteristic
6	C₁₁×#2141	C₂	1	2	yes	maximal
7	C₁₁×#2108	C₂	1	1	yes	maximal, characteristic
8	C₂²×C₁₁×Q₁₆	C₂²	1	2	yes	—
9	C₁₁×#519	—	2	2	no	—
10	C₂×C₁₁×Q₃₂	C₄	1	8	yes	complemented
11	C₂×C₁₁×Q₃₂	C₂²	1	2	yes	—
12	C₂×C₁₁×Q₃₂	C₂²	1	2	yes	—
13	C₂×C₁₁×M₃₂	C₂²	1	1	yes	characteristic
14	C₂²×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
15	C₁₁×#441	—	2	4	no	—
16	C₄×C₁₁×Q₁₆	C₂²	1	8	yes	—
17	C₁₁×#427	C₂²	1	2	yes	—
18	C₁₁×#419	—	2	2	no	—
19	C₁₁×#405	C₂²	1	1	yes	characteristic
20	C₁₁×#367	C₂²	1	2	yes	—
21	C₁₁×#366	C₂²	1	2	yes	—
22	C₁₁×#358	C₂²	1	8	yes	—
23	C₁₁×#346	C₂²	1	2	yes	—
24	C₄×C₁₁×C₁₆	C₂²	1	2	yes	—
25	C₂²×Q₈×C₁₁	—	2	2	no	—
26	C₂×C₁₁×Q₁₆	—	2	2	no	—
27	C₂×C₁₁×Q₁₆	—	2	4	no	—
28	C₂×C₁₁×Q₁₆	C₂×C₄	1	8	yes	—
29	C₂×C₁₁×Q₁₆	C₂³	1	4	yes	—
30	C₂×C₁₁×M₁₆	D₄	1	1	yes	characteristic
31	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
32	C₄×Q₈×C₁₁	—	2	8	no	—
33	C₄×Q₈×C₁₁	—	4	4	no	—
34	C₁₁×#117	—	2	2	no	—
35	C₁₁×#117	—	4	4	no	—
36	C₁₁×#117	D₄	1	1	yes	characteristic
37	C₁₁×Q₃₂	C₂×C₄	1	8	yes	—
38	C₁₁×Q₃₂	C₂×C₄	1	8	yes	—
39	C₁₁×M₃₂	—	2	2	no	—
40	C₂×C₁₁×C₁₆	C₂×C₄	1	4	yes	—
41	C₂×C₁₁×C₁₆	C₂³	1	2	yes	—
42	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
43	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
44	C₁₁×#107	C₂³	1	4	yes	—
45	C₁₁×#106	—	2	2	no	—
46	C₁₁×#103	—	2	8	no	—
47	C₁₁×#97	D₄	1	2	yes	—
48	C₄×C₈×C₁₁	C₂³	1	2	yes	—
49	#33458	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
50	C₂×Q₈×C₁₁	—	2	8	no	—
51	C₂×Q₈×C₁₁	—	2	4	no	—
52	C₂×Q₈×C₁₁	—	4	2	no	—
53	C₂×Q₈×C₁₁	—	4	4	no	—
54	C₂²×C₄×C₁₁	—	4	2	no	—
55	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
56	C₁₁×Q₁₆	—	2	8	no	—
57	C₁₁×Q₁₆	—	2	4	no	—
58	C₁₁×Q₁₆	C₂²×C₄	1	8	yes	—
59	C₁₁×M₁₆	—	2	2	no	—
60	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
61	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
62	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
63	C₂×C₈×C₁₁	#41	1	2	yes	—
64	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
65	C₁₁×C₄⋊C₄	—	2	4	no	—
66	C₁₁×C₄⋊C₄	—	4	8	no	—
67	C₁₁×C₄⋊C₄	D₈	1	2	yes	—
68	C₁₁×C₂²⋊C₄	—	4	2	no	—
69	C₁₁×C₂²⋊C₄	D₈	1	2	yes	—
70	C₄²×C₁₁	—	4	2	no	—
71	C₄²×C₁₁	—	4	8	no	—
72	C₄²×C₁₁	C₂×D₄	1	2	yes	—
73	C₁₁×C₁₆	—	2	2	no	—
74	C₁₁×C₁₆	C₂²×C₄	1	2	yes	—
75	C₁₁×C₁₆	C₂²×C₄	1	2	yes	—
76	C₂²×Q₃₂	C₂×C₁₁	1	1	yes	characteristic
77	#2950	C₂×C₁₁	1	2	yes	—
78	#2176	C₂×C₁₁	1	4	yes	complemented
79	C₄×Q₃₂	C₂×C₁₁	1	4	yes	complemented
80	#2158	C₂×C₁₁	1	1	yes	characteristic
81	#2141	C₂×C₁₁	1	2	yes	—
82	#2108	C₂×C₁₁	1	1	yes	characteristic
83	C₂³×C₁₁	C₂×D₈	1	1	yes	characteristic
84	Q₈×C₁₁	—	2	8	no	—
85	Q₈×C₁₁	—	4	4	no	—
86	Q₈×C₁₁	—	4	8	no	—
87	C₂×C₄×C₁₁	—	4	4	no	—
88	C₂×C₄×C₁₁	—	4	8	no	—
89	C₂×C₄×C₁₁	—	4	4	no	—
90	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
91	C₂×C₄×C₁₁	C₂×D₈	1	4	yes	—
92	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
93	C₂×C₄×C₁₁	#135	1	2	yes	—
94	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
95	C₈×C₁₁	—	2	2	no	—
96	C₈×C₁₁	C₄×D₄	1	2	yes	—
97	C₈×C₁₁	C₂³×C₄	1	1	yes	characteristic
98	C₈×C₁₁	C₂×#41	1	1	yes	characteristic
99	C₂²×Q₁₆	C₂²×C₁₁	1	2	yes	—
100	#519	—	2	2	no	—
101	C₂×Q₃₂	C₄×C₁₁	1	8	yes	complemented
102	C₂×Q₃₂	C₂²×C₁₁	1	2	yes	—
103	C₂×Q₃₂	C₂²×C₁₁	1	2	yes	—
104	C₂×M₃₂	C₂²×C₁₁	1	1	yes	characteristic
105	C₂²×C₁₆	C₂²×C₁₁	1	1	yes	characteristic
106	#441	—	2	4	no	—
107	C₄×Q₁₆	C₂²×C₁₁	1	8	yes	—
108	#427	C₂²×C₁₁	1	2	yes	—
109	#419	—	2	2	no	—
110	#405	C₂²×C₁₁	1	1	yes	characteristic
111	#367	C₂²×C₁₁	1	2	yes	—
112	#366	C₂²×C₁₁	1	2	yes	—
113	#358	C₂²×C₁₁	1	8	yes	—
114	#346	C₂²×C₁₁	1	2	yes	—
115	C₄×C₁₆	C₂²×C₁₁	1	2	yes	—
116	C₂²×C₁₁	—	2	2	no	—
117	C₂²×C₁₁	C₄×D₈	1	2	yes	—
118	C₂²×C₁₁	C₂²×D₈	1	1	yes	characteristic
119	C₄×C₁₁	—	2	4	no	—
120	C₄×C₁₁	—	4	8	no	—
121	C₄×C₁₁	—	8	4	no	—
122	C₄×C₁₁	C₄×D₈	1	2	yes	—
123	C₄×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
124	C₄×C₁₁	C₂×#135	1	1	yes	characteristic
125	C₂²×Q₈	—	2	2	no	—
126	C₂×Q₁₆	—	2	2	no	—
127	C₂×Q₁₆	—	2	4	no	—
128	C₂×Q₁₆	C₂×C₄×C₁₁	1	8	yes	—
129	C₂×Q₁₆	C₂³×C₁₁	1	4	yes	—
130	C₂×M₁₆	D₄×C₁₁	1	1	yes	characteristic
131	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
132	C₄×Q₈	—	2	8	no	—
133	C₄×Q₈	—	4	4	no	—
134	#117	—	2	2	no	—
135	#117	—	4	4	no	—
136	#117	D₄×C₁₁	1	1	yes	characteristic
137	Q₃₂	C₂×C₄×C₁₁	1	8	yes	—
138	Q₃₂	C₂×C₄×C₁₁	1	8	yes	—
139	M₃₂	—	2	2	no	—
140	C₂×C₁₆	C₂×C₄×C₁₁	1	4	yes	—
141	C₂×C₁₆	C₂³×C₁₁	1	2	yes	—
142	C₂×C₁₆	C₂³×C₁₁	1	1	yes	characteristic
143	C₂×C₁₆	C₂³×C₁₁	1	1	yes	characteristic
144	#107	C₂³×C₁₁	1	4	yes	—
145	#106	—	2	2	no	—
146	#103	—	2	8	no	—
147	#97	D₄×C₁₁	1	2	yes	—
148	C₄×C₈	C₂³×C₁₁	1	2	yes	—
149	C₂×C₁₁	—	2	2	no	—
150	C₂×C₁₁	C₂×C₄×D₈	1	1	yes	characteristic
151	C₂×C₁₁	#3417	1	2	yes	—
152	C₂×Q₈	—	2	8	no	—
153	C₂×Q₈	—	2	4	no	—
154	C₂×Q₈	—	4	2	no	—
155	C₂×Q₈	—	4	4	no	—
156	C₂²×C₄	—	4	2	no	—
157	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
158	Q₁₆	—	2	8	no	—
159	Q₁₆	—	2	4	no	—
160	Q₁₆	C₂²×C₄×C₁₁	1	8	yes	—
161	M₁₆	—	2	2	no	—
162	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
163	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
164	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
165	C₂×C₈	C₁₁×#41	1	2	yes	—
166	C₂×C₈	C₂⁴×C₁₁	1	1	yes	characteristic
167	C₄⋊C₄	—	2	4	no	—
168	C₄⋊C₄	—	4	8	no	—
169	C₄⋊C₄	C₁₁×D₈	1	2	yes	—
170	C₂²⋊C₄	—	4	2	no	—
171	C₂²⋊C₄	C₁₁×D₈	1	2	yes	—
172	C₄²	—	4	2	no	—
173	C₄²	—	4	8	no	—
174	C₄²	C₂×D₄×C₁₁	1	2	yes	—
175	C₁₆	—	2	2	no	—
176	C₁₆	C₂²×C₄×C₁₁	1	2	yes	—
177	C₁₆	C₂²×C₄×C₁₁	1	2	yes	—
178	C₁₁	#33458	1	1	yes	characteristic, direct product factor, Sylow
179	C₂³	C₂×C₁₁×D₈	1	1	yes	characteristic
180	Q₈	—	2	8	no	—
181	Q₈	—	4	4	no	—
182	Q₈	—	4	8	no	—
183	C₂×C₄	—	4	4	no	—
184	C₂×C₄	—	4	8	no	—
185	C₂×C₄	—	4	4	no	—
186	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
187	C₂×C₄	C₂×C₁₁×D₈	1	4	yes	—
188	C₂×C₄	C₂×C₁₁×D₈	1	1	yes	characteristic
189	C₂×C₄	C₁₁×#135	1	2	yes	—
190	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
191	C₈	—	2	2	no	—
192	C₈	C₄×D₄×C₁₁	1	2	yes	—
193	C₈	C₂³×C₄×C₁₁	1	1	yes	characteristic
194	C₈	C₂×C₁₁×#41	1	1	yes	characteristic
195	C₂²	—	2	2	no	—
196	C₂²	C₄×C₁₁×D₈	1	2	yes	—
197	C₂²	C₂²×C₁₁×D₈	1	1	yes	characteristic
198	C₄	—	2	4	no	—
199	C₄	—	4	8	no	—
200	C₄	—	8	4	no	—
201	C₄	C₄×C₁₁×D₈	1	2	yes	—
202	C₄	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
203	C₄	C₂×C₁₁×#135	1	1	yes	characteristic
204	C₂	—	2	2	no	—
205	C₂	C₂×C₄×C₁₁×D₈	1	1	yes	characteristic
206	C₂	C₁₁×#3417	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂²×D₈
commutator	C₈	C₂³×C₄×C₁₁
Frattini, cosocle	C₂×C₈	C₂⁴×C₁₁
prime radical	C₂³×C₁₁	C₂×D₈
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₁₁×#117 ◁ C₁₁×#405 ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₁×#2176	C₂	semidirect
4. C₄×C₁₁×Q₃₂	C₂	semidirect
10. C₂×C₁₁×Q₃₂	C₄	semidirect
49. #33458	C₁₁	direct (N × H)
78. #2176	C₂×C₁₁	semidirect
79. C₄×Q₃₂	C₂×C₁₁	semidirect
101. C₂×Q₃₂	C₄×C₁₁	semidirect
178. C₁₁	#33458	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₁×Q₃₂	2
C₁₁×#2950	2
C₁₁×#2176	2
C₄×C₁₁×Q₃₂	2
C₁₁×#2158	2
C₁₁×#2141	2
C₁₁×#2108	2
#33458	11

Subgroups — C11×#33458 #14610651

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#33458 #14610651