Subgroups — C₁₁×#33770 #14610963

Order 2816.

576 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3061	C₂	1	2	yes	maximal, complemented
2	C₁₁×#2235	C₂	1	2	yes	maximal, complemented
3	C₁₁×#2233	C₂	1	2	yes	maximal, complemented
4	C₁₁×#2219	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁×#2218	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁×#2217	C₂	1	2	yes	maximal, complemented
7	C₁₁×#2189	C₂	1	2	yes	maximal, complemented
8	C₁₁×#2186	C₂	1	2	yes	maximal, complemented
9	C₁₁×#2113	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₁×#135	C₂²	1	2	yes	—
11	C₂×C₁₁×#131	C₂²	1	1	yes	characteristic
12	C₁₁×#537	—	2	2	no	—
13	C₂×C₁₁×Q₃₂	C₂²	1	1	yes	characteristic
14	C₂×C₁₁×SD₃₂	C₂²	1	2	yes	—
15	C₂×C₁₁×D₁₆	C₂²	1	1	yes	characteristic
16	C₂×C₁₁×M₃₂	C₂²	1	1	yes	characteristic
17	C₂²×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
18	C₁₁×#468	—	2	2	no	—
19	C₁₁×#468	—	2	2	no	—
20	C₁₁×#467	C₂²	1	2	yes	—
21	C₁₁×#467	C₂²	1	2	yes	—
22	C₁₁×#466	C₂²	1	2	yes	—
23	C₁₁×#466	C₂²	1	2	yes	—
24	C₂×C₁₁×#107	C₂²	1	2	yes	—
25	C₁₁×#417	—	2	2	no	—
26	C₁₁×#367	C₂²	1	2	yes	—
27	C₁₁×#367	C₂²	1	1	yes	characteristic
28	C₁₁×#367	C₂²	1	1	yes	characteristic
29	C₁₁×#358	C₂²	1	2	yes	—
30	C₁₁×#358	C₂²	1	2	yes	—
31	C₁₁×#357	C₂²	1	2	yes	—
32	C₁₁×#357	C₂²	1	2	yes	—
33	C₁₁×C₂²⋊C₁₆	C₂²	1	2	yes	—
34	C₁₁×C₂²⋊C₁₆	C₂²	1	2	yes	—
35	C₂×C₁₁×#41	—	2	2	no	—
36	C₂×C₁₁×#41	D₄	1	1	yes	characteristic
37	C₁₁×#135	—	4	2	no	—
38	C₁₁×#135	—	4	2	no	—
39	C₂×C₁₁×Q₁₆	C₂³	1	2	yes	—
40	C₂×C₁₁×SD₁₆	—	2	2	no	—
41	C₂×C₁₁×D₈	C₂³	1	2	yes	—
42	C₁₁×#131	—	4	1	no	—
43	C₁₁×#131	—	4	1	no	—
44	C₂×C₁₁×M₁₆	D₄	1	2	yes	—
45	C₂×C₁₁×M₁₆	D₄	1	1	yes	characteristic
46	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
48	C₁₁×C₂²⋊Q₈	—	2	2	no	—
49	C₁₁×C₂²⋊Q₈	—	2	2	no	—
50	C₁₁×C₂²⋊Q₈	—	4	2	no	—
51	C₁₁×#121	—	2	2	no	—
52	C₁₁×#121	—	2	2	no	—
53	C₁₁×#121	—	4	2	no	—
54	C₁₁×#121	—	4	2	no	—
55	C₁₁×#121	—	4	2	no	—
56	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
57	C₁₁×Q₃₂	—	4	1	no	—
58	C₁₁×SD₃₂	—	4	2	no	—
59	C₁₁×D₁₆	—	4	1	no	—
60	C₁₁×M₃₂	—	4	1	no	—
61	C₂×C₁₁×C₁₆	—	4	1	no	—
62	C₂×C₁₁×C₁₆	C₂³	1	2	yes	—
63	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
64	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
65	C₁₁×#107	—	2	2	no	—
66	C₁₁×#107	C₂³	1	2	yes	—
67	C₁₁×#107	C₂³	1	2	yes	—
68	C₁₁×#103	—	2	2	no	—
69	C₁₁×#103	—	2	2	no	—
70	C₁₁×#102	—	2	2	no	—
71	C₁₁×#102	—	2	2	no	—
72	#33770	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
73	C₁₁×#41	—	4	1	no	—
74	C₁₁×#41	—	4	1	no	—
75	C₁₁×#41	—	4	4	no	—
76	C₁₁×#41	—	4	4	no	—
77	C₂×Q₈×C₁₁	—	2	2	no	—
78	C₂×Q₈×C₁₁	D₈	1	1	yes	characteristic
79	C₂×D₄×C₁₁	—	2	2	no	—
80	C₂×D₄×C₁₁	—	4	2	no	—
81	C₂×D₄×C₁₁	—	4	2	no	—
82	C₂×D₄×C₁₁	—	4	2	no	—
83	C₂×D₄×C₁₁	D₈	1	1	yes	characteristic
84	C₂×D₄×C₁₁	D₈	1	2	yes	—
85	C₂²×C₄×C₁₁	—	4	2	no	—
86	C₂²×C₄×C₁₁	—	4	2	no	—
87	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
88	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
89	C₁₁×Q₁₆	—	2	2	no	—
90	C₁₁×Q₁₆	—	2	2	no	—
91	C₁₁×SD₁₆	—	4	4	no	—
92	C₁₁×D₈	—	2	2	no	—
93	C₁₁×D₈	—	2	2	no	—
94	C₁₁×M₁₆	—	4	1	no	—
95	C₁₁×M₁₆	—	4	2	no	—
96	C₂×C₈×C₁₁	—	2	1	no	—
97	C₂×C₈×C₁₁	—	2	1	no	—
98	C₂×C₈×C₁₁	—	2	2	no	—
99	C₂×C₈×C₁₁	—	2	2	no	—
100	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
101	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
102	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
103	C₁₁×C₄⋊C₄	—	2	2	no	—
104	C₁₁×C₄⋊C₄	—	2	2	no	—
105	C₁₁×C₄⋊C₄	—	4	2	no	—
106	C₁₁×C₄⋊C₄	—	4	2	no	—
107	C₁₁×C₄⋊C₄	—	4	2	no	—
108	C₁₁×C₂²⋊C₄	—	4	2	no	—
109	C₁₁×C₂²⋊C₄	—	4	2	no	—
110	C₁₁×C₂²⋊C₄	—	4	2	no	—
111	C₁₁×C₂²⋊C₄	—	4	2	no	—
112	C₁₁×C₁₆	—	2	2	no	—
113	C₁₁×C₁₆	—	2	1	no	—
114	C₁₁×C₁₆	—	2	1	no	—
115	#3061	C₂×C₁₁	1	2	yes	complemented
116	#2235	C₂×C₁₁	1	2	yes	complemented
117	#2233	C₂×C₁₁	1	2	yes	complemented
118	#2219	C₂×C₁₁	1	1	yes	characteristic, complemented
119	#2218	C₂×C₁₁	1	1	yes	characteristic, complemented
120	#2217	C₂×C₁₁	1	2	yes	complemented
121	#2189	C₂×C₁₁	1	2	yes	complemented
122	#2186	C₂×C₁₁	1	2	yes	complemented
123	#2113	C₂×C₁₁	1	1	yes	characteristic, complemented
124	C₂³×C₁₁	—	4	2	no	—
125	C₂³×C₁₁	C₂×D₈	1	1	yes	characteristic
126	C₂³×C₁₁	C₂×D₈	1	2	yes	—
127	Q₈×C₁₁	—	4	1	no	—
128	Q₈×C₁₁	—	4	2	no	—
129	Q₈×C₁₁	—	4	2	no	—
130	D₄×C₁₁	—	4	2	no	—
131	D₄×C₁₁	—	4	1	no	—
132	D₄×C₁₁	—	4	2	no	—
133	D₄×C₁₁	—	4	2	no	—
134	D₄×C₁₁	—	8	4	no	—
135	D₄×C₁₁	—	16	2	no	—
136	D₄×C₁₁	—	16	2	no	—
137	C₂×C₄×C₁₁	—	2	1	no	—
138	C₂×C₄×C₁₁	—	2	2	no	—
139	C₂×C₄×C₁₁	—	2	1	no	—
140	C₂×C₄×C₁₁	—	2	2	no	—
141	C₂×C₄×C₁₁	—	4	2	no	—
142	C₂×C₄×C₁₁	—	4	2	no	—
143	C₂×C₄×C₁₁	—	4	2	no	—
144	C₂×C₄×C₁₁	—	8	4	no	—
145	C₂×C₄×C₁₁	—	16	2	no	—
146	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
147	C₂×C₄×C₁₁	C₂×D₈	1	2	yes	—
148	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
149	C₈×C₁₁	—	2	1	no	—
150	C₈×C₁₁	—	2	2	no	—
151	C₈×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
152	C₈×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
153	C₂×#135	C₂²×C₁₁	1	2	yes	—
154	C₂×#131	C₂²×C₁₁	1	1	yes	characteristic
155	#537	—	2	2	no	—
156	C₂×Q₃₂	C₂²×C₁₁	1	1	yes	characteristic
157	C₂×SD₃₂	C₂²×C₁₁	1	2	yes	—
158	C₂×D₁₆	C₂²×C₁₁	1	1	yes	characteristic
159	C₂×M₃₂	C₂²×C₁₁	1	1	yes	characteristic
160	C₂²×C₁₆	C₂²×C₁₁	1	1	yes	characteristic
161	#468	—	2	2	no	—
162	#468	—	2	2	no	—
163	#467	C₂²×C₁₁	1	2	yes	—
164	#467	C₂²×C₁₁	1	2	yes	—
165	#466	C₂²×C₁₁	1	2	yes	—
166	#466	C₂²×C₁₁	1	2	yes	—
167	C₂×#107	C₂²×C₁₁	1	2	yes	—
168	#417	—	2	2	no	—
169	#367	C₂²×C₁₁	1	2	yes	—
170	#367	C₂²×C₁₁	1	1	yes	characteristic
171	#367	C₂²×C₁₁	1	1	yes	characteristic
172	#358	C₂²×C₁₁	1	2	yes	—
173	#358	C₂²×C₁₁	1	2	yes	—
174	#357	C₂²×C₁₁	1	2	yes	—
175	#357	C₂²×C₁₁	1	2	yes	—
176	C₂²⋊C₁₆	C₂²×C₁₁	1	2	yes	—
177	C₂²⋊C₁₆	C₂²×C₁₁	1	2	yes	—
178	C₂²×C₁₁	—	2	2	no	—
179	C₂²×C₁₁	—	2	2	no	—
180	C₂²×C₁₁	—	2	2	no	—
181	C₂²×C₁₁	—	2	2	no	—
182	C₂²×C₁₁	—	2	1	no	—
183	C₂²×C₁₁	—	8	2	no	—
184	C₂²×C₁₁	—	8	2	no	—
185	C₂²×C₁₁	—	8	2	no	—
186	C₂²×C₁₁	C₂²×D₈	1	1	yes	characteristic
187	C₄×C₁₁	—	2	2	no	—
188	C₄×C₁₁	—	2	1	no	—
189	C₄×C₁₁	—	8	2	no	—
190	C₄×C₁₁	—	8	2	no	—
191	C₄×C₁₁	—	8	2	no	—
192	C₄×C₁₁	#534	1	1	yes	characteristic
193	C₄×C₁₁	#575	1	1	yes	characteristic
194	C₂×#41	—	2	2	no	—
195	C₂×#41	D₄×C₁₁	1	1	yes	characteristic
196	#135	—	4	2	no	—
197	#135	—	4	2	no	—
198	C₂×Q₁₆	C₂³×C₁₁	1	2	yes	—
199	C₂×SD₁₆	—	2	2	no	—
200	C₂×D₈	C₂³×C₁₁	1	2	yes	—
201	#131	—	4	1	no	—
202	#131	—	4	1	no	—
203	C₂×M₁₆	D₄×C₁₁	1	2	yes	—
204	C₂×M₁₆	D₄×C₁₁	1	1	yes	characteristic
205	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
206	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
207	C₂²⋊Q₈	—	2	2	no	—
208	C₂²⋊Q₈	—	2	2	no	—
209	C₂²⋊Q₈	—	4	2	no	—
210	#121	—	2	2	no	—
211	#121	—	2	2	no	—
212	#121	—	4	2	no	—
213	#121	—	4	2	no	—
214	#121	—	4	2	no	—
215	C₂×C₄⋊C₄	—	2	2	no	—
216	Q₃₂	—	4	1	no	—
217	SD₃₂	—	4	2	no	—
218	D₁₆	—	4	1	no	—
219	M₃₂	—	4	1	no	—
220	C₂×C₁₆	—	4	1	no	—
221	C₂×C₁₆	C₂³×C₁₁	1	1	yes	characteristic
222	C₂×C₁₆	C₂³×C₁₁	1	2	yes	—
223	C₂×C₁₆	C₂³×C₁₁	1	1	yes	characteristic
224	#107	—	2	2	no	—
225	#107	C₂³×C₁₁	1	2	yes	—
226	#107	C₂³×C₁₁	1	2	yes	—
227	#103	—	2	2	no	—
228	#103	—	2	2	no	—
229	#102	—	2	2	no	—
230	#102	—	2	2	no	—
231	C₂×C₁₁	—	4	2	no	—
232	C₂×C₁₁	—	4	1	no	—
233	C₂×C₁₁	—	16	2	no	—
234	C₂×C₁₁	#3186	1	1	yes	characteristic
235	C₂×C₁₁	#3416	1	2	yes	—
236	#41	—	4	1	no	—
237	#41	—	4	1	no	—
238	#41	—	4	4	no	—
239	#41	—	4	4	no	—
240	C₂×Q₈	—	2	2	no	—
241	C₂×Q₈	C₁₁×D₈	1	1	yes	characteristic
242	C₂×D₄	—	2	2	no	—
243	C₂×D₄	—	4	2	no	—
244	C₂×D₄	—	4	2	no	—
245	C₂×D₄	—	4	2	no	—
246	C₂×D₄	C₁₁×D₈	1	1	yes	characteristic
247	C₂×D₄	C₁₁×D₈	1	2	yes	—
248	C₂²×C₄	—	4	2	no	—
249	C₂²×C₄	—	4	2	no	—
250	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
251	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
252	Q₁₆	—	2	2	no	—
253	Q₁₆	—	2	2	no	—
254	SD₁₆	—	4	4	no	—
255	D₈	—	2	2	no	—
256	D₈	—	2	2	no	—
257	M₁₆	—	4	1	no	—
258	M₁₆	—	4	2	no	—
259	C₂×C₈	—	2	1	no	—
260	C₂×C₈	—	2	1	no	—
261	C₂×C₈	—	2	2	no	—
262	C₂×C₈	—	2	2	no	—
263	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
264	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
265	C₂×C₈	C₂⁴×C₁₁	1	1	yes	characteristic
266	C₄⋊C₄	—	2	2	no	—
267	C₄⋊C₄	—	2	2	no	—
268	C₄⋊C₄	—	4	2	no	—
269	C₄⋊C₄	—	4	2	no	—
270	C₄⋊C₄	—	4	2	no	—
271	C₂²⋊C₄	—	4	2	no	—
272	C₂²⋊C₄	—	4	2	no	—
273	C₂²⋊C₄	—	4	2	no	—
274	C₂²⋊C₄	—	4	2	no	—
275	C₁₆	—	2	2	no	—
276	C₁₆	—	2	1	no	—
277	C₁₆	—	2	1	no	—
278	C₁₁	#33770	1	1	yes	characteristic, direct product factor, Sylow
279	C₂³	—	4	2	no	—
280	C₂³	C₂×C₁₁×D₈	1	1	yes	characteristic
281	C₂³	C₂×C₁₁×D₈	1	2	yes	—
282	Q₈	—	4	1	no	—
283	Q₈	—	4	2	no	—
284	Q₈	—	4	2	no	—
285	D₄	—	4	2	no	—
286	D₄	—	4	1	no	—
287	D₄	—	4	2	no	—
288	D₄	—	4	2	no	—
289	D₄	—	8	4	no	—
290	D₄	—	16	2	no	—
291	D₄	—	16	2	no	—
292	C₂×C₄	—	2	1	no	—
293	C₂×C₄	—	2	2	no	—
294	C₂×C₄	—	2	1	no	—
295	C₂×C₄	—	2	2	no	—
296	C₂×C₄	—	4	2	no	—
297	C₂×C₄	—	4	2	no	—
298	C₂×C₄	—	4	2	no	—
299	C₂×C₄	—	8	4	no	—
300	C₂×C₄	—	16	2	no	—
301	C₂×C₄	C₂×C₁₁×D₈	1	1	yes	characteristic
302	C₂×C₄	C₂×C₁₁×D₈	1	2	yes	—
303	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
304	C₈	—	2	2	no	—
305	C₈	—	2	1	no	—
306	C₈	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
307	C₈	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
308	C₂²	—	2	2	no	—
309	C₂²	—	2	2	no	—
310	C₂²	—	2	2	no	—
311	C₂²	—	2	2	no	—
312	C₂²	—	2	1	no	—
313	C₂²	—	8	2	no	—
314	C₂²	—	8	2	no	—
315	C₂²	—	8	2	no	—
316	C₂²	C₂²×C₁₁×D₈	1	1	yes	characteristic
317	C₄	—	2	2	no	—
318	C₄	—	2	1	no	—
319	C₄	—	8	2	no	—
320	C₄	—	8	2	no	—
321	C₄	—	8	2	no	—
322	C₄	C₁₁×#534	1	1	yes	characteristic
323	C₄	C₁₁×#575	1	1	yes	characteristic
324	C₂	—	4	2	no	—
325	C₂	—	4	1	no	—
326	C₂	—	16	2	no	—
327	C₂	C₁₁×#3186	1	1	yes	characteristic
328	C₂	C₁₁×#3416	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₁
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂×C₁₁×#41 ◁ C₂×C₁₁×#131 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₁×#3061	C₂	semidirect
2. C₁₁×#2235	C₂	semidirect
3. C₁₁×#2233	C₂	semidirect
4. C₁₁×#2219	C₂	semidirect
5. C₁₁×#2218	C₂	semidirect
6. C₁₁×#2217	C₂	semidirect
7. C₁₁×#2189	C₂	semidirect
8. C₁₁×#2186	C₂	semidirect
9. C₁₁×#2113	C₂	semidirect
72. #33770	C₁₁	direct (N × H)
115. #3061	C₂×C₁₁	semidirect
116. #2235	C₂×C₁₁	semidirect
117. #2233	C₂×C₁₁	semidirect
118. #2219	C₂×C₁₁	semidirect
119. #2218	C₂×C₁₁	semidirect
120. #2217	C₂×C₁₁	semidirect
121. #2189	C₂×C₁₁	semidirect
122. #2186	C₂×C₁₁	semidirect
123. #2113	C₂×C₁₁	semidirect
278. C₁₁	#33770	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×#3061	2
C₁₁×#2235	2
C₁₁×#2233	2
C₁₁×#2219	2
C₁₁×#2218	2
C₁₁×#2217	2
C₁₁×#2189	2
C₁₁×#2186	2
C₁₁×#2113	2
#33770	11

Subgroups — C11×#33770 #14610963

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#33770 #14610963