Subgroups — C₁₁×#19204 #14596397

Order 2816.

646 conjugacy classes of subgroups.

The subgroup lattice has 312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3229	C₂	1	2	yes	maximal
2	C₂×C₁₁×#494	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#2960	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#1690	C₂	1	4	yes	maximal, complemented
5	C₁₁×#1670	C₂	1	4	yes	maximal, complemented
6	C₁₁×#1564	C₂	1	1	yes	maximal, characteristic
7	C₁₁×#1546	C₂	1	2	yes	maximal
8	C₂²×C₁₁×Q₁₆	—	2	1	no	—
9	C₂²×C₁₁×Q₁₆	—	2	1	no	—
10	C₁₁×#533	C₂²	1	1	yes	characteristic
11	C₂×C₁₁×C₄⋊Q₈	C₂²	1	2	yes	—
12	C₁₁×#498	—	2	2	no	—
13	C₁₁×#494	—	2	1	no	—
14	C₁₁×#494	—	2	1	no	—
15	C₁₁×#494	C₂²	1	2	yes	—
16	C₁₁×#494	C₂²	1	2	yes	—
17	C₁₁×#487	—	2	2	no	—
18	C₁₁×#483	—	2	4	no	—
19	C₁₁×#475	C₂²	1	8	yes	—
20	C₁₁×#446	—	2	1	no	—
21	C₁₁×#446	C₂²	1	2	yes	—
22	C₈×Q₈×C₁₁	—	2	1	no	—
23	C₈×Q₈×C₁₁	C₂²	1	2	yes	—
24	C₁₁×#431	C₂²	1	2	yes	—
25	C₁₁×#424	—	2	1	no	—
26	C₁₁×#423	C₂²	1	1	yes	characteristic
27	C₁₁×#405	—	2	1	no	—
28	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
29	C₁₁×#335	C₂²	1	2	yes	—
30	C₁₁×#334	C₂²	1	2	yes	—
31	C₁₁×#332	C₂²	1	8	yes	—
32	C₂²×Q₈×C₁₁	—	2	2	no	—
33	C₂×C₁₁×Q₁₆	—	2	2	no	—
34	C₂×C₁₁×Q₁₆	—	2	2	no	—
35	C₂×C₁₁×Q₁₆	—	2	2	no	—
36	C₂×C₁₁×Q₁₆	—	2	2	no	—
37	C₂×C₁₁×Q₁₆	—	4	4	no	—
38	C₂×C₁₁×Q₁₆	—	4	4	no	—
39	C₂×C₁₁×M₁₆	—	2	1	no	—
40	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
41	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
42	C₁₁×C₄⋊Q₈	—	2	2	no	—
43	C₁₁×C₄⋊Q₈	—	2	2	no	—
44	C₁₁×C₄⋊Q₈	—	2	2	no	—
45	C₁₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
46	C₁₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
47	C₁₁×C₄⋊Q₈	C₂³	1	4	yes	—
48	C₁₁×#125	—	2	1	no	—
49	C₁₁×C₂²⋊Q₈	—	2	1	no	—
50	C₁₁×C₂²⋊Q₈	D₄	1	2	yes	—
51	C₄×Q₈×C₁₁	—	2	1	no	—
52	C₄×Q₈×C₁₁	C₂³	1	2	yes	—
53	C₁₁×#117	—	2	1	no	—
54	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
55	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
56	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
57	C₁₁×#106	—	2	8	no	—
58	C₁₁×C₄⋊C₈	—	2	2	no	—
59	C₁₁×C₄⋊C₈	—	2	2	no	—
60	C₁₁×C₄⋊C₈	—	2	1	no	—
61	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
62	C₁₁×C₄⋊C₈	C₂³	1	4	yes	—
63	C₁₁×#103	—	2	8	no	—
64	C₁₁×C₂²⋊C₈	—	2	2	no	—
65	C₁₁×#97	—	2	2	no	—
66	C₄×C₈×C₁₁	—	2	2	no	—
67	C₄×C₈×C₁₁	—	2	2	no	—
68	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
69	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
70	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
71	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
72	#19204	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
73	C₂×Q₈×C₁₁	—	2	1	no	—
74	C₂×Q₈×C₁₁	—	2	4	no	—
75	C₂×Q₈×C₁₁	—	4	2	no	—
76	C₂×Q₈×C₁₁	—	4	4	no	—
77	C₂×Q₈×C₁₁	—	4	4	no	—
78	C₂×Q₈×C₁₁	C₂×D₄	1	2	yes	—
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	#41	1	1	yes	characteristic
83	C₁₁×Q₁₆	—	4	4	no	—
84	C₁₁×Q₁₆	—	4	4	no	—
85	C₁₁×Q₁₆	—	4	4	no	—
86	C₁₁×Q₁₆	—	4	4	no	—
87	C₁₁×M₁₆	—	4	2	no	—
88	C₂×C₈×C₁₁	—	2	2	no	—
89	C₂×C₈×C₁₁	—	2	2	no	—
90	C₂×C₈×C₁₁	—	2	4	no	—
91	C₂×C₈×C₁₁	SD₁₆	1	4	yes	—
92	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
93	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
94	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
95	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
96	C₁₁×C₄⋊C₄	—	2	1	no	—
97	C₁₁×C₄⋊C₄	—	2	1	no	—
98	C₁₁×C₄⋊C₄	—	2	1	no	—
99	C₁₁×C₄⋊C₄	—	2	2	no	—
100	C₁₁×C₄⋊C₄	—	2	2	no	—
101	C₁₁×C₄⋊C₄	—	2	4	no	—
102	C₁₁×C₄⋊C₄	—	2	4	no	—
103	C₁₁×C₄⋊C₄	—	4	2	no	—
104	C₁₁×C₄⋊C₄	—	4	2	no	—
105	C₁₁×C₄⋊C₄	C₂×D₄	1	2	yes	—
106	C₁₁×C₂²⋊C₄	—	2	2	no	—
107	C₄²×C₁₁	—	2	2	no	—
108	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
109	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
110	C₄²×C₁₁	#41	1	1	yes	characteristic
111	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
112	#3229	C₂×C₁₁	1	2	yes	—
113	C₂×#494	C₂×C₁₁	1	1	yes	characteristic
114	#2960	C₂×C₁₁	1	1	yes	characteristic
115	#1690	C₂×C₁₁	1	4	yes	complemented
116	#1670	C₂×C₁₁	1	4	yes	complemented
117	#1564	C₂×C₁₁	1	1	yes	characteristic
118	#1546	C₂×C₁₁	1	2	yes	—
119	C₂³×C₁₁	#121	1	1	yes	characteristic
120	Q₈×C₁₁	—	2	4	no	—
121	Q₈×C₁₁	—	4	2	no	—
122	Q₈×C₁₁	—	4	4	no	—
123	Q₈×C₁₁	—	4	4	no	—
124	Q₈×C₁₁	—	8	4	no	—
125	C₂×C₄×C₁₁	—	2	2	no	—
126	C₂×C₄×C₁₁	—	2	2	no	—
127	C₂×C₄×C₁₁	—	2	2	no	—
128	C₂×C₄×C₁₁	—	2	2	no	—
129	C₂×C₄×C₁₁	—	4	4	no	—
130	C₂×C₄×C₁₁	—	8	4	no	—
131	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
132	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
133	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
134	C₂×C₄×C₁₁	C₂×SD₁₆	1	2	yes	—
135	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	2	yes	—
136	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
137	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
138	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
139	C₈×C₁₁	—	2	1	no	—
140	C₈×C₁₁	—	2	1	no	—
141	C₈×C₁₁	—	4	2	no	—
142	C₈×C₁₁	—	4	4	no	—
143	C₈×C₁₁	C₂×SD₁₆	1	2	yes	—
144	C₈×C₁₁	C₂×SD₁₆	1	2	yes	—
145	C₂²×Q₁₆	—	2	1	no	—
146	C₂²×Q₁₆	—	2	1	no	—
147	#533	C₂²×C₁₁	1	1	yes	characteristic
148	C₂×C₄⋊Q₈	C₂²×C₁₁	1	2	yes	—
149	#498	—	2	2	no	—
150	#494	—	2	1	no	—
151	#494	—	2	1	no	—
152	#494	C₂²×C₁₁	1	2	yes	—
153	#494	C₂²×C₁₁	1	2	yes	—
154	#487	—	2	2	no	—
155	#483	—	2	4	no	—
156	#475	C₂²×C₁₁	1	8	yes	—
157	#446	—	2	1	no	—
158	#446	C₂²×C₁₁	1	2	yes	—
159	C₈×Q₈	—	2	1	no	—
160	C₈×Q₈	C₂²×C₁₁	1	2	yes	—
161	#431	C₂²×C₁₁	1	2	yes	—
162	#424	—	2	1	no	—
163	#423	C₂²×C₁₁	1	1	yes	characteristic
164	#405	—	2	1	no	—
165	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
166	#335	C₂²×C₁₁	1	2	yes	—
167	#334	C₂²×C₁₁	1	2	yes	—
168	#332	C₂²×C₁₁	1	8	yes	—
169	C₂²×C₁₁	—	2	1	no	—
170	C₂²×C₁₁	—	2	1	no	—
171	C₂²×C₁₁	#460	1	2	yes	—
172	C₂²×C₁₁	C₂×#121	1	1	yes	characteristic
173	C₄×C₁₁	—	2	1	no	—
174	C₄×C₁₁	—	2	1	no	—
175	C₄×C₁₁	—	4	2	no	—
176	C₄×C₁₁	—	4	2	no	—
177	C₄×C₁₁	—	8	4	no	—
178	C₄×C₁₁	#460	1	2	yes	—
179	C₄×C₁₁	#473	1	2	yes	—
180	C₄×C₁₁	C₂²×SD₁₆	1	1	yes	characteristic
181	C₄×C₁₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
182	C₄×C₁₁	#578	1	2	yes	—
183	C₂²×Q₈	—	2	2	no	—
184	C₂×Q₁₆	—	2	2	no	—
185	C₂×Q₁₆	—	2	2	no	—
186	C₂×Q₁₆	—	2	2	no	—
187	C₂×Q₁₆	—	2	2	no	—
188	C₂×Q₁₆	—	4	4	no	—
189	C₂×Q₁₆	—	4	4	no	—
190	C₂×M₁₆	—	2	1	no	—
191	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
192	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
193	C₄⋊Q₈	—	2	2	no	—
194	C₄⋊Q₈	—	2	2	no	—
195	C₄⋊Q₈	—	2	2	no	—
196	C₄⋊Q₈	D₄×C₁₁	1	1	yes	characteristic
197	C₄⋊Q₈	D₄×C₁₁	1	1	yes	characteristic
198	C₄⋊Q₈	C₂³×C₁₁	1	4	yes	—
199	#125	—	2	1	no	—
200	C₂²⋊Q₈	—	2	1	no	—
201	C₂²⋊Q₈	D₄×C₁₁	1	2	yes	—
202	C₄×Q₈	—	2	1	no	—
203	C₄×Q₈	C₂³×C₁₁	1	2	yes	—
204	#117	—	2	1	no	—
205	C₂×C₄⋊C₄	—	2	2	no	—
206	C₂×C₄⋊C₄	—	2	2	no	—
207	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
208	#106	—	2	8	no	—
209	C₄⋊C₈	—	2	2	no	—
210	C₄⋊C₈	—	2	2	no	—
211	C₄⋊C₈	—	2	1	no	—
212	C₄⋊C₈	C₂³×C₁₁	1	2	yes	—
213	C₄⋊C₈	C₂³×C₁₁	1	4	yes	—
214	#103	—	2	8	no	—
215	C₂²⋊C₈	—	2	2	no	—
216	#97	—	2	2	no	—
217	C₄×C₈	—	2	2	no	—
218	C₄×C₈	—	2	2	no	—
219	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
220	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
221	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
222	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
223	C₂×C₁₁	—	2	2	no	—
224	C₂×C₁₁	C₂×#460	1	1	yes	characteristic
225	C₂×C₁₁	#3059	1	1	yes	characteristic
226	C₂×C₁₁	C₂×#473	1	1	yes	characteristic
227	C₂×Q₈	—	2	1	no	—
228	C₂×Q₈	—	2	4	no	—
229	C₂×Q₈	—	4	2	no	—
230	C₂×Q₈	—	4	4	no	—
231	C₂×Q₈	—	4	4	no	—
232	C₂×Q₈	C₂×D₄×C₁₁	1	2	yes	—
233	C₂²×C₄	—	4	2	no	—
234	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
235	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
236	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
237	Q₁₆	—	4	4	no	—
238	Q₁₆	—	4	4	no	—
239	Q₁₆	—	4	4	no	—
240	Q₁₆	—	4	4	no	—
241	M₁₆	—	4	2	no	—
242	C₂×C₈	—	2	2	no	—
243	C₂×C₈	—	2	2	no	—
244	C₂×C₈	—	2	4	no	—
245	C₂×C₈	C₁₁×SD₁₆	1	4	yes	—
246	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
247	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
248	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
249	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
250	C₄⋊C₄	—	2	1	no	—
251	C₄⋊C₄	—	2	1	no	—
252	C₄⋊C₄	—	2	1	no	—
253	C₄⋊C₄	—	2	2	no	—
254	C₄⋊C₄	—	2	2	no	—
255	C₄⋊C₄	—	2	4	no	—
256	C₄⋊C₄	—	2	4	no	—
257	C₄⋊C₄	—	4	2	no	—
258	C₄⋊C₄	—	4	2	no	—
259	C₄⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
260	C₂²⋊C₄	—	2	2	no	—
261	C₄²	—	2	2	no	—
262	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
263	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
264	C₄²	C₁₁×#41	1	1	yes	characteristic
265	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
266	C₁₁	#19204	1	1	yes	characteristic, direct product factor, Sylow
267	C₂³	C₁₁×#121	1	1	yes	characteristic
268	Q₈	—	2	4	no	—
269	Q₈	—	4	2	no	—
270	Q₈	—	4	4	no	—
271	Q₈	—	4	4	no	—
272	Q₈	—	8	4	no	—
273	C₂×C₄	—	2	2	no	—
274	C₂×C₄	—	2	2	no	—
275	C₂×C₄	—	2	2	no	—
276	C₂×C₄	—	2	2	no	—
277	C₂×C₄	—	4	4	no	—
278	C₂×C₄	—	8	4	no	—
279	C₂×C₄	C₁₁×#121	1	1	yes	characteristic
280	C₂×C₄	C₁₁×#121	1	1	yes	characteristic
281	C₂×C₄	C₁₁×#121	1	1	yes	characteristic
282	C₂×C₄	C₂×C₁₁×SD₁₆	1	2	yes	—
283	C₂×C₄	C₁₁×AGL(1,ℤ/8)	1	2	yes	—
284	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
285	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
286	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
287	C₈	—	2	1	no	—
288	C₈	—	2	1	no	—
289	C₈	—	4	2	no	—
290	C₈	—	4	4	no	—
291	C₈	C₂×C₁₁×SD₁₆	1	2	yes	—
292	C₈	C₂×C₁₁×SD₁₆	1	2	yes	—
293	C₂²	—	2	1	no	—
294	C₂²	—	2	1	no	—
295	C₂²	C₁₁×#460	1	2	yes	—
296	C₂²	C₂×C₁₁×#121	1	1	yes	characteristic
297	C₄	—	2	1	no	—
298	C₄	—	2	1	no	—
299	C₄	—	4	2	no	—
300	C₄	—	4	2	no	—
301	C₄	—	8	4	no	—
302	C₄	C₁₁×#460	1	2	yes	—
303	C₄	C₁₁×#473	1	2	yes	—
304	C₄	C₂²×C₁₁×SD₁₆	1	1	yes	characteristic
305	C₄	C₂×C₁₁×AGL(1,ℤ/8)	1	1	yes	characteristic
306	C₄	C₁₁×#578	1	2	yes	—
307	C₂	—	2	2	no	—
308	C₂	C₂×C₁₁×#460	1	1	yes	characteristic
309	C₂	C₁₁×#3059	1	1	yes	characteristic
310	C₂	C₂×C₁₁×#473	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₁
prime radical	C₂³×C₁₁	#121
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
4. C₁₁×#1690	C₂	semidirect
5. C₁₁×#1670	C₂	semidirect
72. #19204	C₁₁	direct (N × H)
115. #1690	C₂×C₁₁	semidirect
116. #1670	C₂×C₁₁	semidirect
266. C₁₁	#19204	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×#3229	2
C₂×C₁₁×#494	2
C₁₁×#2960	2
C₁₁×#1690	2
C₁₁×#1670	2
C₁₁×#1564	2
C₁₁×#1546	2
#19204	11

Subgroups — C11×#19204 #14596397

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#19204 #14596397