Subgroups — C₁₁×#21293 #14598486

Order 2816.

746 conjugacy classes of subgroups.

The subgroup lattice has 286 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₁×#135	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2922	C₂	1	2	yes	maximal, complemented
3	C₁₁×#1975	C₂	1	2	yes	maximal
4	C₁₁×#1946	C₂	1	2	yes	maximal, complemented
5	C₁₁×#1938	C₂	1	4	yes	maximal, complemented
6	C₄×C₁₁×#108	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄×C₁₁×#104	C₂	1	2	yes	maximal, complemented
8	C₄×C₁₁×#97	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₁×#135	C₂²	1	1	yes	characteristic
10	C₄×C₁₁×#41	C₂²	1	2	yes	—
11	C₄×C₁₁×Q₁₆	C₄	1	2	yes	complemented
12	C₄×C₁₁×SD₁₆	C₄	1	4	yes	complemented
13	C₄×C₁₁×D₈	C₄	1	2	yes	complemented
14	C₁₁×#433	—	2	4	no	—
15	C₁₁×#431	—	2	4	no	—
16	C₂×C₁₁×#108	C₂²	1	2	yes	—
17	C₁₁×#427	C₂²	1	1	yes	characteristic
18	C₁₁×#424	C₂²	1	4	yes	—
19	C₂×C₁₁×#104	C₂²	1	4	yes	—
20	C₁₁×#416	C₂²	1	2	yes	—
21	C₁₁×#408	C₂²	1	4	yes	—
22	C₄×C₁₁×M₁₆	C₂²	1	2	yes	—
23	C₂×C₁₁×#97	C₂²	1	2	yes	—
24	C₂×C₁₁×#97	C₂²	1	2	yes	—
25	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
27	C₄³×C₁₁	C₂²	1	1	yes	characteristic
28	C₁₁×#341	C₂²	1	2	yes	—
29	C₁₁×#339	C₂²	1	4	yes	—
30	C₂×C₁₁×#41	C₂³	1	2	yes	—
31	C₁₁×#135	—	2	4	no	—
32	C₂×C₁₁×Q₁₆	C₂×C₄	1	1	yes	characteristic
33	C₂×C₁₁×SD₁₆	C₂×C₄	1	2	yes	—
34	C₂×C₁₁×D₈	C₂×C₄	1	1	yes	characteristic
35	C₂×C₁₁×M₁₆	C₂³	1	4	yes	—
36	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
37	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
38	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
39	C₄×Q₈×C₁₁	C₂×C₄	1	4	yes	—
40	C₄×D₄×C₁₁	—	2	4	no	—
41	C₄×D₄×C₁₁	C₂×C₄	1	4	yes	—
42	C₁₁×#117	—	2	2	no	—
43	C₁₁×#117	C₂³	1	2	yes	—
44	C₂×C₄²×C₁₁	—	2	2	no	—
45	C₂×C₄²×C₁₁	—	2	2	no	—
46	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
47	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
48	C₁₁×#108	—	2	4	no	—
49	C₁₁×#107	C₂×C₄	1	2	yes	—
50	C₁₁×#106	C₂×C₄	1	2	yes	—
51	C₁₁×C₄⋊C₈	—	2	8	no	—
52	C₁₁×#104	—	2	8	no	—
53	C₁₁×#103	C₂×C₄	1	4	yes	—
54	C₁₁×#102	C₂×C₄	1	4	yes	—
55	C₁₁×C₂²⋊C₈	—	2	8	no	—
56	C₁₁×#97	—	2	4	no	—
57	C₁₁×#97	—	2	2	no	—
58	C₁₁×#97	—	2	4	no	—
59	C₄×C₈×C₁₁	—	2	2	no	—
60	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
61	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
62	C₄×C₈×C₁₁	D₄	1	2	yes	—
63	C₄×C₈×C₁₁	D₄	1	2	yes	—
64	#21293	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
65	C₁₁×#41	—	2	4	no	—
66	C₁₁×#41	—	2	4	no	—
67	C₂×Q₈×C₁₁	C₂²×C₄	1	2	yes	—
68	C₂×D₄×C₁₁	—	2	2	no	—
69	C₂×D₄×C₁₁	C₂²×C₄	1	2	yes	—
70	C₂²×C₄×C₁₁	—	2	2	no	—
71	C₂²×C₄×C₁₁	—	2	4	no	—
72	C₂²×C₄×C₁₁	—	2	2	no	—
73	C₂²×C₄×C₁₁	#41	1	2	yes	—
74	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
75	C₁₁×Q₁₆	—	2	2	no	—
76	C₁₁×SD₁₆	—	2	4	no	—
77	C₁₁×D₈	—	2	2	no	—
78	C₁₁×M₁₆	—	2	4	no	—
79	C₁₁×M₁₆	—	2	4	no	—
80	C₂×C₈×C₁₁	—	2	4	no	—
81	C₂×C₈×C₁₁	—	2	2	no	—
82	C₂×C₈×C₁₁	—	2	2	no	—
83	C₂×C₈×C₁₁	—	2	2	no	—
84	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
85	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
86	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
87	C₂×C₈×C₁₁	C₂×D₄	1	4	yes	—
88	C₂×C₈×C₁₁	#41	1	4	yes	—
89	C₁₁×C₄⋊C₄	—	2	4	no	—
90	C₁₁×C₄⋊C₄	C₂²×C₄	1	4	yes	—
91	C₁₁×C₂²⋊C₄	—	2	2	no	—
92	C₁₁×C₂²⋊C₄	—	2	4	no	—
93	C₄²×C₁₁	—	2	4	no	—
94	C₄²×C₁₁	—	2	2	no	—
95	C₄²×C₁₁	—	2	2	no	—
96	C₄²×C₁₁	—	4	4	no	—
97	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
98	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
99	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
100	C₄²×C₁₁	#41	1	4	yes	—
101	C₄×#135	C₂×C₁₁	1	1	yes	characteristic
102	#2922	C₂×C₁₁	1	2	yes	complemented
103	#1975	C₂×C₁₁	1	2	yes	—
104	#1946	C₂×C₁₁	1	2	yes	complemented
105	#1938	C₂×C₁₁	1	4	yes	complemented
106	C₄×#108	C₂×C₁₁	1	1	yes	characteristic, complemented
107	C₄×#104	C₂×C₁₁	1	2	yes	complemented
108	C₄×#97	C₂×C₁₁	1	1	yes	characteristic, complemented
109	C₂³×C₁₁	—	2	2	no	—
110	C₂³×C₁₁	C₂×#41	1	1	yes	characteristic
111	Q₈×C₁₁	—	2	2	no	—
112	Q₈×C₁₁	—	2	2	no	—
113	D₄×C₁₁	—	2	2	no	—
114	D₄×C₁₁	—	2	2	no	—
115	D₄×C₁₁	—	4	4	no	—
116	C₂×C₄×C₁₁	—	2	4	no	—
117	C₂×C₄×C₁₁	—	2	4	no	—
118	C₂×C₄×C₁₁	—	2	2	no	—
119	C₂×C₄×C₁₁	—	2	4	no	—
120	C₂×C₄×C₁₁	—	4	4	no	—
121	C₂×C₄×C₁₁	—	4	4	no	—
122	C₂×C₄×C₁₁	—	4	8	no	—
123	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
124	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
125	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
126	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
127	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
128	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
129	C₈×C₁₁	—	2	2	no	—
130	C₈×C₁₁	—	2	4	no	—
131	C₈×C₁₁	—	4	4	no	—
132	C₈×C₁₁	#117	1	2	yes	—
133	C₈×C₁₁	#117	1	2	yes	—
134	C₂×#135	C₂²×C₁₁	1	1	yes	characteristic
135	C₄×#41	C₂²×C₁₁	1	2	yes	—
136	C₄×Q₁₆	C₄×C₁₁	1	2	yes	complemented
137	C₄×SD₁₆	C₄×C₁₁	1	4	yes	complemented
138	C₄×D₈	C₄×C₁₁	1	2	yes	complemented
139	#433	—	2	4	no	—
140	#431	—	2	4	no	—
141	C₂×#108	C₂²×C₁₁	1	2	yes	—
142	#427	C₂²×C₁₁	1	1	yes	characteristic
143	#424	C₂²×C₁₁	1	4	yes	—
144	C₂×#104	C₂²×C₁₁	1	4	yes	—
145	#416	C₂²×C₁₁	1	2	yes	—
146	#408	C₂²×C₁₁	1	4	yes	—
147	C₄×M₁₆	C₂²×C₁₁	1	2	yes	—
148	C₂×#97	C₂²×C₁₁	1	2	yes	—
149	C₂×#97	C₂²×C₁₁	1	2	yes	—
150	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
151	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
152	C₄³	C₂²×C₁₁	1	1	yes	characteristic
153	#341	C₂²×C₁₁	1	2	yes	—
154	#339	C₂²×C₁₁	1	4	yes	—
155	C₂²×C₁₁	—	2	2	no	—
156	C₂²×C₁₁	—	4	4	no	—
157	C₂²×C₁₁	—	4	2	no	—
158	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
159	C₂²×C₁₁	#529	1	2	yes	—
160	C₄×C₁₁	—	2	2	no	—
161	C₄×C₁₁	—	4	4	no	—
162	C₄×C₁₁	—	4	4	no	—
163	C₄×C₁₁	—	4	2	no	—
164	C₄×C₁₁	#444	1	4	yes	—
165	C₄×C₁₁	C₂×#117	1	1	yes	characteristic
166	C₄×C₁₁	C₄×#41	1	1	yes	characteristic
167	C₄×C₁₁	#532	1	2	yes	—
168	C₂×#41	C₂³×C₁₁	1	2	yes	—
169	#135	—	2	4	no	—
170	C₂×Q₁₆	C₂×C₄×C₁₁	1	1	yes	characteristic
171	C₂×SD₁₆	C₂×C₄×C₁₁	1	2	yes	—
172	C₂×D₈	C₂×C₄×C₁₁	1	1	yes	characteristic
173	C₂×M₁₆	C₂³×C₁₁	1	4	yes	—
174	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
175	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
176	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
177	C₄×Q₈	C₂×C₄×C₁₁	1	4	yes	—
178	C₄×D₄	—	2	4	no	—
179	C₄×D₄	C₂×C₄×C₁₁	1	4	yes	—
180	#117	—	2	2	no	—
181	#117	C₂³×C₁₁	1	2	yes	—
182	C₂×C₄²	—	2	2	no	—
183	C₂×C₄²	—	2	2	no	—
184	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
185	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
186	#108	—	2	4	no	—
187	#107	C₂×C₄×C₁₁	1	2	yes	—
188	#106	C₂×C₄×C₁₁	1	2	yes	—
189	C₄⋊C₈	—	2	8	no	—
190	#104	—	2	8	no	—
191	#103	C₂×C₄×C₁₁	1	4	yes	—
192	#102	C₂×C₄×C₁₁	1	4	yes	—
193	C₂²⋊C₈	—	2	8	no	—
194	#97	—	2	4	no	—
195	#97	—	2	2	no	—
196	#97	—	2	4	no	—
197	C₄×C₈	—	2	2	no	—
198	C₄×C₈	C₂×C₄×C₁₁	1	2	yes	—
199	C₄×C₈	C₂×C₄×C₁₁	1	2	yes	—
200	C₄×C₈	D₄×C₁₁	1	2	yes	—
201	C₄×C₈	D₄×C₁₁	1	2	yes	—
202	C₂×C₁₁	—	2	2	no	—
203	C₂×C₁₁	—	8	2	no	—
204	C₂×C₁₁	#2293	1	1	yes	characteristic
205	C₂×C₁₁	C₂×#444	1	2	yes	—
206	#41	—	2	4	no	—
207	#41	—	2	4	no	—
208	C₂×Q₈	C₂²×C₄×C₁₁	1	2	yes	—
209	C₂×D₄	—	2	2	no	—
210	C₂×D₄	C₂²×C₄×C₁₁	1	2	yes	—
211	C₂²×C₄	—	2	2	no	—
212	C₂²×C₄	—	2	4	no	—
213	C₂²×C₄	—	2	2	no	—
214	C₂²×C₄	C₁₁×#41	1	2	yes	—
215	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
216	Q₁₆	—	2	2	no	—
217	SD₁₆	—	2	4	no	—
218	D₈	—	2	2	no	—
219	M₁₆	—	2	4	no	—
220	M₁₆	—	2	4	no	—
221	C₂×C₈	—	2	2	no	—
222	C₂×C₈	—	2	2	no	—
223	C₂×C₈	—	2	2	no	—
224	C₂×C₈	—	2	4	no	—
225	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
226	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
227	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
228	C₂×C₈	C₂×D₄×C₁₁	1	4	yes	—
229	C₂×C₈	C₁₁×#41	1	4	yes	—
230	C₄⋊C₄	—	2	4	no	—
231	C₄⋊C₄	C₂²×C₄×C₁₁	1	4	yes	—
232	C₂²⋊C₄	—	2	2	no	—
233	C₂²⋊C₄	—	2	4	no	—
234	C₄²	—	2	4	no	—
235	C₄²	—	2	2	no	—
236	C₄²	—	2	2	no	—
237	C₄²	—	4	4	no	—
238	C₄²	C₂²×C₄×C₁₁	1	2	yes	—
239	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
240	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
241	C₄²	C₁₁×#41	1	4	yes	—
242	C₁₁	#21293	1	1	yes	characteristic, direct product factor, Sylow
243	C₂³	—	2	2	no	—
244	C₂³	C₂×C₁₁×#41	1	1	yes	characteristic
245	Q₈	—	2	2	no	—
246	Q₈	—	2	2	no	—
247	D₄	—	2	2	no	—
248	D₄	—	2	2	no	—
249	D₄	—	4	4	no	—
250	C₂×C₄	—	2	4	no	—
251	C₂×C₄	—	2	4	no	—
252	C₂×C₄	—	2	2	no	—
253	C₂×C₄	—	2	4	no	—
254	C₂×C₄	—	4	4	no	—
255	C₂×C₄	—	4	4	no	—
256	C₂×C₄	—	4	8	no	—
257	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
258	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
259	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
260	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
261	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
262	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
263	C₈	—	2	2	no	—
264	C₈	—	2	4	no	—
265	C₈	—	4	4	no	—
266	C₈	C₁₁×#117	1	2	yes	—
267	C₈	C₁₁×#117	1	2	yes	—
268	C₂²	—	2	2	no	—
269	C₂²	—	4	4	no	—
270	C₂²	—	4	2	no	—
271	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
272	C₂²	C₁₁×#529	1	2	yes	—
273	C₄	—	2	2	no	—
274	C₄	—	4	4	no	—
275	C₄	—	4	4	no	—
276	C₄	—	4	2	no	—
277	C₄	C₁₁×#444	1	4	yes	—
278	C₄	C₂×C₁₁×#117	1	1	yes	characteristic
279	C₄	C₄×C₁₁×#41	1	1	yes	characteristic
280	C₄	C₁₁×#532	1	2	yes	—
281	C₂	—	2	2	no	—
282	C₂	—	8	2	no	—
283	C₂	C₁₁×#2293	1	1	yes	characteristic
284	C₂	C₂×C₁₁×#444	1	2	yes	—

	subgroup	G/H
center	C₄²×C₁₁	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
socle	C₂²×C₁₁	C₂×C₄×D₄
prime radical	C₂×C₁₁×#135	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄²×C₁₁ ◁ C₂×C₄×C₈×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₁×#2922	C₂	semidirect
4. C₁₁×#1946	C₂	semidirect
5. C₁₁×#1938	C₂	semidirect
6. C₄×C₁₁×#108	C₂	semidirect
7. C₄×C₁₁×#104	C₂	semidirect
8. C₄×C₁₁×#97	C₂	semidirect
11. C₄×C₁₁×Q₁₆	C₄	semidirect
12. C₄×C₁₁×SD₁₆	C₄	semidirect
13. C₄×C₁₁×D₈	C₄	semidirect
64. #21293	C₁₁	direct (N × H)
102. #2922	C₂×C₁₁	semidirect
104. #1946	C₂×C₁₁	semidirect
105. #1938	C₂×C₁₁	semidirect
106. C₄×#108	C₂×C₁₁	semidirect
107. C₄×#104	C₂×C₁₁	semidirect
108. C₄×#97	C₂×C₁₁	semidirect
136. C₄×Q₁₆	C₄×C₁₁	semidirect
137. C₄×SD₁₆	C₄×C₁₁	semidirect
138. C₄×D₈	C₄×C₁₁	semidirect
242. C₁₁	#21293	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×#135	2
C₁₁×#2922	2
C₁₁×#1975	2
C₁₁×#1946	2
C₁₁×#1938	2
C₄×C₁₁×#108	2
C₄×C₁₁×#104	2
C₄×C₁₁×#97	2
#21293	11

Subgroups — C11×#21293 #14598486

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#21293 #14598486