Subgroups — C₁₁×#19638 #14596831

Order 2816.

754 conjugacy classes of subgroups.

The subgroup lattice has 298 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3206	C₂	1	2	yes	maximal, complemented
2	C₁₁×#3169	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₁×#500	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#3141	C₂	1	2	yes	maximal, complemented
5	C₁₁×#1719	C₂	1	4	yes	maximal, complemented
6	C₁₁×#1710	C₂	1	2	yes	maximal, complemented
7	C₁₁×#1706	C₂	1	2	yes	maximal, complemented
8	C₈×C₁₁×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁×#532	C₂²	1	2	yes	—
10	C₂×C₁₁×C₄⋊Q₈	C₂²	1	2	yes	—
11	C₁₁×#500	—	2	2	no	—
12	C₁₁×#500	C₂²	1	2	yes	—
13	C₁₁×#500	C₂²	1	2	yes	—
14	C₁₁×#500	C₂²	1	1	yes	characteristic
15	C₁₁×#493	C₂²	1	1	yes	characteristic
16	C₁₁×#492	C₂²	1	4	yes	—
17	C₁₁×#489	—	2	4	no	—
18	C₁₁×#487	C₂²	1	4	yes	—
19	C₁₁×#487	C₂²	1	4	yes	—
20	C₁₁×#486	C₂²	1	2	yes	—
21	C₁₁×#486	C₂²	1	4	yes	—
22	C₁₁×#466	—	2	2	no	—
23	C₁₁×#461	—	2	4	no	—
24	C₁₁×#448	—	2	4	no	—
25	C₄×C₁₁×D₈	—	2	2	no	—
26	C₁₁×#431	C₂²	1	1	yes	characteristic
27	C₂×C₁₁×#107	—	2	2	no	—
28	C₁₁×#417	—	2	4	no	—
29	C₄×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
31	C₁₁×#322	C₂²	1	2	yes	—
32	C₈²×C₁₁	C₂²	1	2	yes	—
33	C₂×C₁₁×#41	—	2	2	no	—
34	C₂²×Q₈×C₁₁	—	2	2	no	—
35	C₂×C₁₁×SD₁₆	—	2	8	no	—
36	C₂×C₁₁×D₈	—	2	2	no	—
37	C₂×C₁₁×M₁₆	D₄	1	2	yes	—
38	C₂²×C₈×C₁₁	D₄	1	2	yes	—
39	C₁₁×C₄⋊Q₈	—	2	2	no	—
40	C₁₁×C₄⋊Q₈	—	2	2	no	—
41	C₁₁×C₄⋊Q₈	—	2	2	no	—
42	C₁₁×C₄⋊Q₈	C₂³	1	4	yes	—
43	C₁₁×C₄⋊Q₈	C₂³	1	2	yes	—
44	C₁₁×#127	C₂³	1	2	yes	—
45	C₁₁×#124	—	2	2	no	—
46	C₁₁×#121	—	2	2	no	—
47	C₁₁×#121	—	2	2	no	—
48	C₄×D₄×C₁₁	—	2	2	no	—
49	C₄×D₄×C₁₁	—	2	2	no	—
50	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
51	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
52	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
53	C₁₁×#107	—	2	4	no	—
54	C₁₁×#107	—	2	4	no	—
55	C₁₁×#107	—	2	2	no	—
56	C₁₁×C₄⋊C₈	D₄	1	2	yes	—
57	C₁₁×#103	—	2	8	no	—
58	C₁₁×#103	—	2	8	no	—
59	C₁₁×#102	—	2	8	no	—
60	C₁₁×#102	—	2	4	no	—
61	C₁₁×C₂²⋊C₈	D₄	1	2	yes	—
62	C₁₁×#97	D₄	1	2	yes	—
63	C₄×C₈×C₁₁	D₄	1	2	yes	—
64	C₄×C₈×C₁₁	C₂³	1	2	yes	—
65	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
66	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
67	C₄×C₈×C₁₁	C₂³	1	2	yes	—
68	#19638	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
69	C₁₁×#41	—	4	8	no	—
70	C₂×Q₈×C₁₁	—	2	2	no	—
71	C₂×Q₈×C₁₁	—	2	4	no	—
72	C₂×Q₈×C₁₁	—	4	2	no	—
73	C₂×Q₈×C₁₁	—	8	4	no	—
74	C₂×D₄×C₁₁	—	2	2	no	—
75	C₂×D₄×C₁₁	—	2	2	no	—
76	C₂×D₄×C₁₁	—	2	2	no	—
77	C₂×D₄×C₁₁	—	4	2	no	—
78	C₂²×C₄×C₁₁	—	4	2	no	—
79	C₂²×C₄×C₁₁	—	4	2	no	—
80	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
83	C₁₁×SD₁₆	—	8	8	no	—
84	C₁₁×D₈	—	4	4	no	—
85	C₁₁×M₁₆	—	2	4	no	—
86	C₂×C₈×C₁₁	—	2	4	no	—
87	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
88	C₂×C₈×C₁₁	C₂×D₄	1	4	yes	—
89	C₂×C₈×C₁₁	C₂×D₄	1	4	yes	—
90	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
91	C₁₁×C₄⋊C₄	—	2	4	no	—
92	C₁₁×C₄⋊C₄	—	2	2	no	—
93	C₁₁×C₄⋊C₄	—	2	2	no	—
94	C₁₁×C₄⋊C₄	—	2	4	no	—
95	C₁₁×C₄⋊C₄	—	4	2	no	—
96	C₁₁×C₄⋊C₄	—	4	2	no	—
97	C₁₁×C₂²⋊C₄	—	4	2	no	—
98	C₁₁×C₂²⋊C₄	—	4	2	no	—
99	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
100	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
101	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
102	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
103	#3206	C₂×C₁₁	1	2	yes	complemented
104	#3169	C₂×C₁₁	1	1	yes	characteristic
105	C₂×#500	C₂×C₁₁	1	1	yes	characteristic, complemented
106	#3141	C₂×C₁₁	1	2	yes	complemented
107	#1719	C₂×C₁₁	1	4	yes	complemented
108	#1710	C₂×C₁₁	1	2	yes	complemented
109	#1706	C₂×C₁₁	1	2	yes	complemented
110	C₈×M₁₆	C₂×C₁₁	1	1	yes	characteristic, complemented
111	C₂³×C₁₁	—	4	2	no	—
112	C₂³×C₁₁	#127	1	1	yes	characteristic
113	Q₈×C₁₁	—	4	4	no	—
114	Q₈×C₁₁	—	4	8	no	—
115	Q₈×C₁₁	—	8	4	no	—
116	D₄×C₁₁	—	4	4	no	—
117	D₄×C₁₁	—	4	4	no	—
118	D₄×C₁₁	—	4	4	no	—
119	D₄×C₁₁	—	8	4	no	—
120	C₂×C₄×C₁₁	—	2	2	no	—
121	C₂×C₄×C₁₁	—	2	2	no	—
122	C₂×C₄×C₁₁	—	4	2	no	—
123	C₂×C₄×C₁₁	—	4	4	no	—
124	C₂×C₄×C₁₁	—	8	4	no	—
125	C₂×C₄×C₁₁	—	8	4	no	—
126	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
127	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
128	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
129	C₂×C₄×C₁₁	#135	1	4	yes	—
130	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
131	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
132	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
133	C₈×C₁₁	—	2	4	no	—
134	C₈×C₁₁	—	2	2	no	—
135	C₈×C₁₁	—	2	4	no	—
136	C₈×C₁₁	#137	1	4	yes	—
137	#532	C₂²×C₁₁	1	2	yes	—
138	C₂×C₄⋊Q₈	C₂²×C₁₁	1	2	yes	—
139	#500	—	2	2	no	—
140	#500	C₂²×C₁₁	1	2	yes	—
141	#500	C₂²×C₁₁	1	2	yes	—
142	#500	C₂²×C₁₁	1	1	yes	characteristic
143	#493	C₂²×C₁₁	1	1	yes	characteristic
144	#492	C₂²×C₁₁	1	4	yes	—
145	#489	—	2	4	no	—
146	#487	C₂²×C₁₁	1	4	yes	—
147	#487	C₂²×C₁₁	1	4	yes	—
148	#486	C₂²×C₁₁	1	4	yes	—
149	#486	C₂²×C₁₁	1	2	yes	—
150	#466	—	2	2	no	—
151	#461	—	2	4	no	—
152	#448	—	2	4	no	—
153	C₄×D₈	—	2	2	no	—
154	#431	C₂²×C₁₁	1	1	yes	characteristic
155	C₂×#107	—	2	2	no	—
156	#417	—	2	4	no	—
157	C₄×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
158	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
159	#322	C₂²×C₁₁	1	2	yes	—
160	C₈²	C₂²×C₁₁	1	2	yes	—
161	C₂²×C₁₁	—	2	1	no	—
162	C₂²×C₁₁	—	2	1	no	—
163	C₂²×C₁₁	—	8	2	no	—
164	C₂²×C₁₁	—	8	2	no	—
165	C₂²×C₁₁	—	8	2	no	—
166	C₂²×C₁₁	#495	1	2	yes	—
167	C₂²×C₁₁	C₂×#127	1	1	yes	characteristic
168	C₄×C₁₁	—	2	1	no	—
169	C₄×C₁₁	—	2	1	no	—
170	C₄×C₁₁	—	8	2	no	—
171	C₄×C₁₁	—	8	4	no	—
172	C₄×C₁₁	#495	1	2	yes	—
173	C₄×C₁₁	C₂×#135	1	2	yes	—
174	C₄×C₁₁	C₂×#137	1	2	yes	—
175	C₄×C₁₁	#576	1	2	yes	—
176	C₂×#41	—	2	2	no	—
177	C₂²×Q₈	—	2	2	no	—
178	C₂×SD₁₆	—	2	8	no	—
179	C₂×D₈	—	2	2	no	—
180	C₂×M₁₆	D₄×C₁₁	1	2	yes	—
181	C₂²×C₈	D₄×C₁₁	1	2	yes	—
182	C₄⋊Q₈	—	2	2	no	—
183	C₄⋊Q₈	—	2	2	no	—
184	C₄⋊Q₈	—	2	2	no	—
185	C₄⋊Q₈	C₂³×C₁₁	1	4	yes	—
186	C₄⋊Q₈	C₂³×C₁₁	1	2	yes	—
187	#127	C₂³×C₁₁	1	2	yes	—
188	#124	—	2	2	no	—
189	#121	—	2	2	no	—
190	#121	—	2	2	no	—
191	C₄×D₄	—	2	2	no	—
192	C₄×D₄	—	2	2	no	—
193	C₂×C₄⋊C₄	—	2	2	no	—
194	C₂×C₄⋊C₄	—	2	2	no	—
195	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
196	#107	—	2	4	no	—
197	#107	—	2	4	no	—
198	#107	—	2	2	no	—
199	C₄⋊C₈	D₄×C₁₁	1	2	yes	—
200	#103	—	2	8	no	—
201	#103	—	2	8	no	—
202	#102	—	2	8	no	—
203	#102	—	2	4	no	—
204	C₂²⋊C₈	D₄×C₁₁	1	2	yes	—
205	#97	D₄×C₁₁	1	2	yes	—
206	C₄×C₈	D₄×C₁₁	1	2	yes	—
207	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
208	C₄×C₈	C₂³×C₁₁	1	2	yes	—
209	C₄×C₈	C₂³×C₁₁	1	2	yes	—
210	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
211	C₂×C₁₁	—	2	2	no	—
212	C₂×C₁₁	—	16	2	no	—
213	C₂×C₁₁	C₂×#495	1	1	yes	characteristic
214	C₂×C₁₁	#3152	1	1	yes	characteristic
215	C₂×C₁₁	#3155	1	1	yes	characteristic
216	#41	—	4	8	no	—
217	C₂×Q₈	—	2	2	no	—
218	C₂×Q₈	—	2	4	no	—
219	C₂×Q₈	—	4	2	no	—
220	C₂×Q₈	—	8	4	no	—
221	C₂×D₄	—	2	2	no	—
222	C₂×D₄	—	2	2	no	—
223	C₂×D₄	—	2	2	no	—
224	C₂×D₄	—	4	2	no	—
225	C₂²×C₄	—	4	2	no	—
226	C₂²×C₄	—	4	2	no	—
227	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
228	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
229	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
230	SD₁₆	—	8	8	no	—
231	D₈	—	4	4	no	—
232	M₁₆	—	2	4	no	—
233	C₂×C₈	—	2	4	no	—
234	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
235	C₂×C₈	C₂×D₄×C₁₁	1	4	yes	—
236	C₂×C₈	C₂×D₄×C₁₁	1	4	yes	—
237	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
238	C₄⋊C₄	—	2	4	no	—
239	C₄⋊C₄	—	2	2	no	—
240	C₄⋊C₄	—	2	2	no	—
241	C₄⋊C₄	—	2	4	no	—
242	C₄⋊C₄	—	4	2	no	—
243	C₄⋊C₄	—	4	2	no	—
244	C₂²⋊C₄	—	4	2	no	—
245	C₂²⋊C₄	—	4	2	no	—
246	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
247	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
248	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
249	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
250	C₁₁	#19638	1	1	yes	characteristic, direct product factor, Sylow
251	C₂³	—	4	2	no	—
252	C₂³	C₁₁×#127	1	1	yes	characteristic
253	Q₈	—	4	4	no	—
254	Q₈	—	4	8	no	—
255	Q₈	—	8	4	no	—
256	D₄	—	4	4	no	—
257	D₄	—	4	4	no	—
258	D₄	—	4	4	no	—
259	D₄	—	8	4	no	—
260	C₂×C₄	—	2	2	no	—
261	C₂×C₄	—	2	2	no	—
262	C₂×C₄	—	4	2	no	—
263	C₂×C₄	—	4	4	no	—
264	C₂×C₄	—	8	4	no	—
265	C₂×C₄	—	8	4	no	—
266	C₂×C₄	C₁₁×#127	1	1	yes	characteristic
267	C₂×C₄	C₁₁×#127	1	1	yes	characteristic
268	C₂×C₄	C₁₁×#127	1	1	yes	characteristic
269	C₂×C₄	C₁₁×#135	1	4	yes	—
270	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
271	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
272	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
273	C₈	—	2	4	no	—
274	C₈	—	2	2	no	—
275	C₈	—	2	4	no	—
276	C₈	C₁₁×#137	1	4	yes	—
277	C₂²	—	2	1	no	—
278	C₂²	—	2	1	no	—
279	C₂²	—	8	2	no	—
280	C₂²	—	8	2	no	—
281	C₂²	—	8	2	no	—
282	C₂²	C₁₁×#495	1	2	yes	—
283	C₂²	C₂×C₁₁×#127	1	1	yes	characteristic
284	C₄	—	2	1	no	—
285	C₄	—	2	1	no	—
286	C₄	—	8	2	no	—
287	C₄	—	8	4	no	—
288	C₄	C₁₁×#495	1	2	yes	—
289	C₄	C₂×C₁₁×#135	1	2	yes	—
290	C₄	C₂×C₁₁×#137	1	2	yes	—
291	C₄	C₁₁×#576	1	2	yes	—
292	C₂	—	2	2	no	—
293	C₂	—	16	2	no	—
294	C₂	C₂×C₁₁×#495	1	1	yes	characteristic
295	C₂	C₁₁×#3152	1	1	yes	characteristic
296	C₂	C₁₁×#3155	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂×#127
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₁
prime radical	C₁₁×#3169	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₁×#3206	C₂	semidirect
3. C₂×C₁₁×#500	C₂	semidirect
4. C₁₁×#3141	C₂	semidirect
5. C₁₁×#1719	C₂	semidirect
6. C₁₁×#1710	C₂	semidirect
7. C₁₁×#1706	C₂	semidirect
8. C₈×C₁₁×M₁₆	C₂	semidirect
68. #19638	C₁₁	direct (N × H)
103. #3206	C₂×C₁₁	semidirect
105. C₂×#500	C₂×C₁₁	semidirect
106. #3141	C₂×C₁₁	semidirect
107. #1719	C₂×C₁₁	semidirect
108. #1710	C₂×C₁₁	semidirect
109. #1706	C₂×C₁₁	semidirect
110. C₈×M₁₆	C₂×C₁₁	semidirect
250. C₁₁	#19638	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₁×#3206	2
C₁₁×#3169	2
C₂×C₁₁×#500	2
C₁₁×#3141	2
C₁₁×#1719	2
C₁₁×#1710	2
C₁₁×#1706	2
C₈×C₁₁×M₁₆	2
#19638	11

Subgroups — C11×#19638 #14596831

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#19638 #14596831