Subgroups — C₁₁×#33337 #14610530

Order 2816.

1128 conjugacy classes of subgroups.

The subgroup lattice has 252 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#568	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#3407	C₂	1	2	yes	maximal, complemented
3	C₁₁×#2115	C₂	1	6	yes	maximal, complemented
4	C₂×C₁₁×#349	C₂	1	6	yes	maximal, complemented
5	C₂²×C₁₁×#41	C₄	1	1	yes	characteristic
6	C₁₁×#568	—	2	8	no	—
7	C₂×C₁₁×#131	C₄	1	3	yes	—
8	C₂×C₁₁×#131	C₄	1	1	yes	characteristic
9	C₂×C₁₁×#131	C₂²	1	3	yes	—
10	C₂×C₁₁×#131	C₂²	1	1	yes	characteristic
11	C₂²×C₁₁×M₁₆	C₄	1	3	yes	—
12	C₂²×C₁₁×M₁₆	C₂²	1	3	yes	—
13	C₁₁×#504	—	2	8	no	—
14	C₂×C₁₁×M₃₂	C₂²	1	12	yes	complemented
15	C₁₁×#349	C₂²	1	4	yes	—
16	C₁₁×#349	C₂²	1	12	yes	complemented
17	C₂×C₁₁×#41	—	2	4	no	—
18	C₂×C₁₁×#41	—	2	4	no	—
19	C₂×C₁₁×#41	C₈	1	1	yes	characteristic
20	C₂×C₁₁×#41	C₈	1	3	yes	—
21	C₂×C₁₁×#41	C₂×C₄	1	3	yes	—
22	C₂×C₁₁×#41	C₂×C₄	1	1	yes	characteristic
23	C₂²×Q₈×C₁₁	C₈	1	1	yes	characteristic
24	C₂²×D₄×C₁₁	C₈	1	3	yes	—
25	C₂³×C₄×C₁₁	C₂×C₄	1	3	yes	—
26	C₁₁×#131	—	2	4	no	—
27	C₁₁×#131	—	2	12	no	—
28	C₁₁×#131	—	2	12	no	—
29	C₁₁×#131	D₄	1	8	yes	—
30	C₂×C₁₁×M₁₆	—	2	12	no	—
31	C₂×C₁₁×M₁₆	—	2	12	no	—
32	C₂×C₁₁×M₁₆	C₂×C₄	1	3	yes	—
33	C₂×C₁₁×M₁₆	C₂×C₄	1	3	yes	—
34	C₂×C₁₁×M₁₆	C₂×C₄	1	3	yes	—
35	C₂×C₁₁×M₁₆	C₂×C₄	1	3	yes	—
36	C₂×C₁₁×M₁₆	C₂³	1	1	yes	characteristic
37	C₂×C₁₁×M₁₆	C₂³	1	3	yes	—
38	C₂²×C₈×C₁₁	C₂×C₄	1	6	yes	—
39	C₂²×C₈×C₁₁	C₂×C₄	1	3	yes	—
40	C₂²×C₈×C₁₁	C₂³	1	3	yes	—
41	C₁₁×M₃₂	—	2	12	no	—
42	C₁₁×M₃₂	C₂³	1	8	yes	—
43	C₂×C₁₁×C₁₆	—	2	12	no	—
44	#33337	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
45	C₂⁴×C₁₁	C₂×C₈	1	3	yes	—
46	C₁₁×#41	—	2	4	no	—
47	C₁₁×#41	—	2	12	no	—
48	C₁₁×#41	—	2	6	no	—
49	C₁₁×#41	—	2	6	no	—
50	C₁₁×#41	C₂²⋊C₄	1	4	yes	—
51	C₁₁×#41	M₁₆	1	4	yes	—
52	C₂×Q₈×C₁₁	—	2	4	no	—
53	C₂×Q₈×C₁₁	C₂×C₈	1	3	yes	—
54	C₂×Q₈×C₁₁	C₂×C₈	1	1	yes	characteristic
55	C₂×D₄×C₁₁	—	2	12	no	—
56	C₂×D₄×C₁₁	C₂×C₈	1	6	yes	—
57	C₂×D₄×C₁₁	C₂×C₈	1	3	yes	—
58	C₂×D₄×C₁₁	C₂×C₈	1	3	yes	—
59	C₂²×C₄×C₁₁	—	2	6	no	—
60	C₂²×C₄×C₁₁	—	2	6	no	—
61	C₂²×C₄×C₁₁	C₂×C₈	1	3	yes	—
62	C₂²×C₄×C₁₁	C₂×C₈	1	3	yes	—
63	C₂²×C₄×C₁₁	C₂×C₈	1	3	yes	—
64	C₂²×C₄×C₁₁	C₂²×C₄	1	3	yes	—
65	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
66	C₂²×C₄×C₁₁	C₂²×C₄	1	3	yes	—
67	C₁₁×M₁₆	—	2	6	no	—
68	C₁₁×M₁₆	—	2	6	no	—
69	C₁₁×M₁₆	—	2	2	no	—
70	C₁₁×M₁₆	—	2	6	no	—
71	C₁₁×M₁₆	—	2	6	no	—
72	C₁₁×M₁₆	C₂²⋊C₄	1	12	yes	—
73	C₂×C₈×C₁₁	—	2	12	no	—
74	C₂×C₈×C₁₁	—	2	6	no	—
75	C₂×C₈×C₁₁	C₂²×C₄	1	3	yes	—
76	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
77	C₂×C₈×C₁₁	C₂²×C₄	1	3	yes	—
78	C₂×C₈×C₁₁	C₂×D₄	1	12	yes	—
79	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
80	C₁₁×C₁₆	—	2	8	no	—
81	C₂×#568	C₂×C₁₁	1	1	yes	characteristic
82	#3407	C₂×C₁₁	1	2	yes	complemented
83	#2115	C₂×C₁₁	1	6	yes	complemented
84	C₂×#349	C₂×C₁₁	1	6	yes	complemented
85	C₂³×C₁₁	—	2	6	no	—
86	C₂³×C₁₁	—	8	3	no	—
87	C₂³×C₁₁	C₂²×C₈	1	1	yes	characteristic
88	C₂³×C₁₁	C₂²×C₈	1	3	yes	—
89	C₂³×C₁₁	C₂²×C₈	1	3	yes	—
90	Q₈×C₁₁	—	2	6	no	—
91	Q₈×C₁₁	C₂²⋊C₈	1	4	yes	—
92	D₄×C₁₁	—	2	12	no	—
93	D₄×C₁₁	—	2	6	no	—
94	D₄×C₁₁	C₂²⋊C₈	1	12	yes	—
95	C₂×C₄×C₁₁	—	2	6	no	—
96	C₂×C₄×C₁₁	—	2	3	no	—
97	C₂×C₄×C₁₁	—	2	1	no	—
98	C₂×C₄×C₁₁	—	2	1	no	—
99	C₂×C₄×C₁₁	—	2	3	no	—
100	C₂×C₄×C₁₁	—	2	6	no	—
101	C₂×C₄×C₁₁	—	2	6	no	—
102	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	6	yes	—
103	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
104	C₂×C₄×C₁₁	C₂²×C₈	1	3	yes	—
105	C₂×C₄×C₁₁	C₂²×C₈	1	3	yes	—
106	C₂×C₄×C₁₁	C₂×M₁₆	1	6	yes	—
107	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
108	C₈×C₁₁	—	2	3	no	—
109	C₈×C₁₁	—	2	1	no	—
110	C₈×C₁₁	C₂×C₂²⋊C₄	1	6	yes	—
111	C₈×C₁₁	C₂²×D₄	1	2	yes	—
112	C₂²×#41	C₄×C₁₁	1	1	yes	characteristic
113	#568	—	2	8	no	—
114	C₂×#131	C₄×C₁₁	1	3	yes	—
115	C₂×#131	C₄×C₁₁	1	1	yes	characteristic
116	C₂×#131	C₂²×C₁₁	1	3	yes	—
117	C₂×#131	C₂²×C₁₁	1	1	yes	characteristic
118	C₂²×M₁₆	C₄×C₁₁	1	3	yes	—
119	C₂²×M₁₆	C₂²×C₁₁	1	3	yes	—
120	#504	—	2	8	no	—
121	C₂×M₃₂	C₂²×C₁₁	1	12	yes	complemented
122	#349	C₂²×C₁₁	1	4	yes	—
123	#349	C₂²×C₁₁	1	12	yes	complemented
124	C₂²×C₁₁	—	2	1	no	—
125	C₂²×C₁₁	—	2	3	no	—
126	C₂²×C₁₁	—	4	3	no	—
127	C₂²×C₁₁	—	4	1	no	—
128	C₂²×C₁₁	—	4	3	no	—
129	C₂²×C₁₁	—	8	6	no	—
130	C₂²×C₁₁	C₂×C₂²⋊C₈	1	6	yes	—
131	C₂²×C₁₁	C₂³×C₈	1	1	yes	characteristic
132	C₄×C₁₁	—	2	1	no	—
133	C₄×C₁₁	—	2	3	no	—
134	C₄×C₁₁	C₂×C₂²⋊C₈	1	6	yes	—
135	C₄×C₁₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
136	C₄×C₁₁	C₂²×M₁₆	1	1	yes	characteristic
137	C₂×#41	—	2	4	no	—
138	C₂×#41	—	2	4	no	—
139	C₂×#41	C₈×C₁₁	1	1	yes	characteristic
140	C₂×#41	C₈×C₁₁	1	3	yes	—
141	C₂×#41	C₂×C₄×C₁₁	1	3	yes	—
142	C₂×#41	C₂×C₄×C₁₁	1	1	yes	characteristic
143	C₂²×Q₈	C₈×C₁₁	1	1	yes	characteristic
144	C₂²×D₄	C₈×C₁₁	1	3	yes	—
145	C₂³×C₄	C₂×C₄×C₁₁	1	3	yes	—
146	#131	—	2	4	no	—
147	#131	—	2	12	no	—
148	#131	—	2	12	no	—
149	#131	D₄×C₁₁	1	8	yes	—
150	C₂×M₁₆	—	2	12	no	—
151	C₂×M₁₆	—	2	12	no	—
152	C₂×M₁₆	C₂×C₄×C₁₁	1	3	yes	—
153	C₂×M₁₆	C₂×C₄×C₁₁	1	3	yes	—
154	C₂×M₁₆	C₂×C₄×C₁₁	1	3	yes	—
155	C₂×M₁₆	C₂×C₄×C₁₁	1	3	yes	—
156	C₂×M₁₆	C₂³×C₁₁	1	1	yes	characteristic
157	C₂×M₁₆	C₂³×C₁₁	1	3	yes	—
158	C₂²×C₈	C₂×C₄×C₁₁	1	6	yes	—
159	C₂²×C₈	C₂×C₄×C₁₁	1	3	yes	—
160	C₂²×C₈	C₂³×C₁₁	1	3	yes	—
161	M₃₂	—	2	12	no	—
162	M₃₂	C₂³×C₁₁	1	8	yes	—
163	C₂×C₁₆	—	2	12	no	—
164	C₂×C₁₁	—	2	1	no	—
165	C₂×C₁₁	—	2	6	no	—
166	C₂×C₁₁	—	4	3	no	—
167	C₂×C₁₁	—	4	1	no	—
168	C₂×C₁₁	C₂²×C₂²⋊C₈	1	1	yes	characteristic
169	C₂⁴	C₂×C₈×C₁₁	1	3	yes	—
170	#41	—	2	4	no	—
171	#41	—	2	12	no	—
172	#41	—	2	6	no	—
173	#41	—	2	6	no	—
174	#41	C₁₁×C₂²⋊C₄	1	4	yes	—
175	#41	C₁₁×M₁₆	1	4	yes	—
176	C₂×Q₈	—	2	4	no	—
177	C₂×Q₈	C₂×C₈×C₁₁	1	3	yes	—
178	C₂×Q₈	C₂×C₈×C₁₁	1	1	yes	characteristic
179	C₂×D₄	—	2	12	no	—
180	C₂×D₄	C₂×C₈×C₁₁	1	6	yes	—
181	C₂×D₄	C₂×C₈×C₁₁	1	3	yes	—
182	C₂×D₄	C₂×C₈×C₁₁	1	3	yes	—
183	C₂²×C₄	—	2	6	no	—
184	C₂²×C₄	—	2	6	no	—
185	C₂²×C₄	C₂×C₈×C₁₁	1	3	yes	—
186	C₂²×C₄	C₂×C₈×C₁₁	1	3	yes	—
187	C₂²×C₄	C₂×C₈×C₁₁	1	3	yes	—
188	C₂²×C₄	C₂²×C₄×C₁₁	1	3	yes	—
189	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
190	C₂²×C₄	C₂²×C₄×C₁₁	1	3	yes	—
191	M₁₆	—	2	6	no	—
192	M₁₆	—	2	6	no	—
193	M₁₆	—	2	6	no	—
194	M₁₆	—	2	2	no	—
195	M₁₆	—	2	6	no	—
196	M₁₆	C₁₁×C₂²⋊C₄	1	12	yes	—
197	C₂×C₈	—	2	6	no	—
198	C₂×C₈	—	2	12	no	—
199	C₂×C₈	C₂²×C₄×C₁₁	1	3	yes	—
200	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
201	C₂×C₈	C₂²×C₄×C₁₁	1	3	yes	—
202	C₂×C₈	C₂×D₄×C₁₁	1	12	yes	—
203	C₂×C₈	C₂⁴×C₁₁	1	1	yes	characteristic
204	C₁₆	—	2	8	no	—
205	C₁₁	#33337	1	1	yes	characteristic, direct product factor, Sylow
206	C₂³	—	2	6	no	—
207	C₂³	—	8	3	no	—
208	C₂³	C₂²×C₈×C₁₁	1	1	yes	characteristic
209	C₂³	C₂²×C₈×C₁₁	1	3	yes	—
210	C₂³	C₂²×C₈×C₁₁	1	3	yes	—
211	Q₈	—	2	6	no	—
212	Q₈	C₁₁×C₂²⋊C₈	1	4	yes	—
213	D₄	—	2	12	no	—
214	D₄	—	2	6	no	—
215	D₄	C₁₁×C₂²⋊C₈	1	12	yes	—
216	C₂×C₄	—	2	6	no	—
217	C₂×C₄	—	2	3	no	—
218	C₂×C₄	—	2	1	no	—
219	C₂×C₄	—	2	6	no	—
220	C₂×C₄	—	2	6	no	—
221	C₂×C₄	—	2	1	no	—
222	C₂×C₄	—	2	3	no	—
223	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	6	yes	—
224	C₂×C₄	C₂²×C₈×C₁₁	1	1	yes	characteristic
225	C₂×C₄	C₂²×C₈×C₁₁	1	3	yes	—
226	C₂×C₄	C₂²×C₈×C₁₁	1	3	yes	—
227	C₂×C₄	C₂×C₁₁×M₁₆	1	6	yes	—
228	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
229	C₈	—	2	1	no	—
230	C₈	—	2	3	no	—
231	C₈	C₂×C₁₁×C₂²⋊C₄	1	6	yes	—
232	C₈	C₂²×D₄×C₁₁	1	2	yes	—
233	C₂²	—	2	1	no	—
234	C₂²	—	2	3	no	—
235	C₂²	—	4	3	no	—
236	C₂²	—	4	1	no	—
237	C₂²	—	4	3	no	—
238	C₂²	—	8	6	no	—
239	C₂²	C₂×C₁₁×C₂²⋊C₈	1	6	yes	—
240	C₂²	C₂³×C₈×C₁₁	1	1	yes	characteristic
241	C₄	—	2	1	no	—
242	C₄	—	2	3	no	—
243	C₄	C₂×C₁₁×C₂²⋊C₈	1	6	yes	—
244	C₄	C₂²×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
245	C₄	C₂²×C₁₁×M₁₆	1	1	yes	characteristic
246	C₂	—	2	1	no	—
247	C₂	—	2	6	no	—
248	C₂	—	4	1	no	—
249	C₂	—	4	3	no	—
250	C₂	C₂²×C₁₁×C₂²⋊C₈	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₁₁	C₂²×C₂²⋊C₄
commutator	C₂²	C₂³×C₈×C₁₁
Frattini, cosocle	C₂×C₈	C₂⁴×C₁₁
socle	C₂×C₁₁	C₂²×C₂²⋊C₈
prime radical	C₂²×C₁₁×#41	C₄
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₁ ◁ C₂×C₁₁×#131 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₁×#3407	C₂	semidirect
3. C₁₁×#2115	C₂	semidirect
4. C₂×C₁₁×#349	C₂	semidirect
14. C₂×C₁₁×M₃₂	C₂²	semidirect
16. C₁₁×#349	C₂²	semidirect
44. #33337	C₁₁	direct (N × H)
82. #3407	C₂×C₁₁	semidirect
83. #2115	C₂×C₁₁	semidirect
84. C₂×#349	C₂×C₁₁	semidirect
121. C₂×M₃₂	C₂²×C₁₁	semidirect
123. #349	C₂²×C₁₁	semidirect
205. C₁₁	#33337	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×#568	2
C₁₁×#3407	2
C₁₁×#2115	2
C₂×C₁₁×#349	2
#33337	11

Subgroups — C11×#33337 #14610530

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#33337 #14610530