Subgroups — C₁₁×#11245 #14588438

Order 2816.

624 conjugacy classes of subgroups.

The subgroup lattice has 304 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#2911	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2905	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₁×#344	C₂	1	2	yes	maximal
4	C₂×C₁₁×#338	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₁×H(3,ℤ/4)	C₂	1	2	yes	maximal
6	C₂²×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
7	C₂²×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
8	C₂²×C₁₁×M₁₆	C₂²	1	2	yes	—
9	C₂×C₁₁×#117	C₂²	1	2	yes	—
10	C₂×C₁₁×#117	C₂²	1	1	yes	characteristic
11	C₁₁×#428	—	2	4	no	—
12	C₁₁×#427	—	2	2	no	—
13	C₁₁×#424	—	2	2	no	—
14	C₁₁×#424	—	2	2	no	—
15	C₁₁×#423	C₄	1	4	yes	complemented
16	C₁₁×#344	—	2	4	no	—
17	C₁₁×#338	—	2	2	no	—
18	C₁₁×H(3,ℤ/4)	—	2	4	no	—
19	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
20	C₂×C₁₁×M₁₆	—	2	2	no	—
21	C₂×C₁₁×M₁₆	—	2	2	no	—
22	C₂×C₁₁×M₁₆	—	2	2	no	—
23	C₂×C₁₁×M₁₆	—	2	2	no	—
24	C₂×C₁₁×M₁₆	—	2	2	no	—
25	C₂×C₁₁×M₁₆	—	2	1	no	—
26	C₂×C₁₁×M₁₆	—	2	2	no	—
27	C₂×C₁₁×M₁₆	—	2	2	no	—
28	C₂×C₁₁×M₁₆	—	2	2	no	—
29	C₂×C₁₁×M₁₆	—	2	2	no	—
30	C₂×C₁₁×M₁₆	—	2	2	no	—
31	C₂×C₁₁×M₁₆	C₂×C₄	1	2	yes	—
32	C₂×C₁₁×M₁₆	C₂×C₄	1	2	yes	—
33	C₂×C₁₁×M₁₆	D₄	1	2	yes	—
34	C₂²×C₈×C₁₁	—	2	1	no	—
35	C₂²×C₈×C₁₁	D₄	1	2	yes	—
36	C₂²×C₈×C₁₁	Q₈	1	4	yes	—
37	C₁₁×#117	—	2	1	no	—
38	C₁₁×#117	—	2	1	no	—
39	C₁₁×#117	—	2	2	no	—
40	C₁₁×#117	—	2	2	no	—
41	C₁₁×#117	—	2	2	no	—
42	C₁₁×#117	D₄	1	4	yes	—
43	C₁₁×#117	D₄	1	2	yes	—
44	C₁₁×#117	Q₈	1	2	yes	—
45	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
46	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
47	C₂×C₁₁×C₂²⋊C₄	—	2	1	no	—
48	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
49	C₂×C₄²×C₁₁	—	2	2	no	—
50	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
51	C₁₁×#107	—	2	4	no	—
52	C₁₁×#106	—	2	4	no	—
53	C₁₁×C₄⋊C₈	—	2	8	no	—
54	#11245	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
55	C₂⁴×C₁₁	#41	1	1	yes	characteristic
56	C₂²×C₄×C₁₁	—	2	2	no	—
57	C₂²×C₄×C₁₁	—	4	2	no	—
58	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
59	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
60	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
61	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
62	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
63	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
64	C₂²×C₄×C₁₁	C₂×Q₈	1	2	yes	—
65	C₂²×C₄×C₁₁	#41	1	2	yes	—
66	C₂²×C₄×C₁₁	#41	1	2	yes	—
67	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
68	C₁₁×M₁₆	—	2	4	no	—
69	C₁₁×M₁₆	—	2	4	no	—
70	C₁₁×M₁₆	—	2	4	no	—
71	C₁₁×M₁₆	—	4	1	no	—
72	C₁₁×M₁₆	—	4	2	no	—
73	C₁₁×M₁₆	—	4	2	no	—
74	C₁₁×M₁₆	—	4	2	no	—
75	C₁₁×M₁₆	—	4	1	no	—
76	C₁₁×M₁₆	—	4	2	no	—
77	C₂×C₈×C₁₁	—	2	2	no	—
78	C₂×C₈×C₁₁	—	2	2	no	—
79	C₂×C₈×C₁₁	—	2	4	no	—
80	C₂×C₈×C₁₁	—	2	4	no	—
81	C₂×C₈×C₁₁	—	2	4	no	—
82	C₂×C₈×C₁₁	—	2	2	no	—
83	C₂×C₈×C₁₁	—	4	2	no	—
84	C₂×C₈×C₁₁	C₂²⋊C₄	1	4	yes	—
85	C₁₁×C₄⋊C₄	—	2	2	no	—
86	C₁₁×C₄⋊C₄	—	2	2	no	—
87	C₁₁×C₄⋊C₄	—	2	4	no	—
88	C₁₁×C₄⋊C₄	—	4	2	no	—
89	C₁₁×C₂²⋊C₄	—	2	2	no	—
90	C₁₁×C₂²⋊C₄	—	2	2	no	—
91	C₁₁×C₂²⋊C₄	—	2	4	no	—
92	C₁₁×C₂²⋊C₄	—	4	2	no	—
93	C₄²×C₁₁	—	2	2	no	—
94	C₄²×C₁₁	—	2	4	no	—
95	C₄²×C₁₁	—	4	2	no	—
96	C₄²×C₁₁	C₄⋊C₄	1	4	yes	—
97	#2911	C₂×C₁₁	1	1	yes	characteristic
98	#2905	C₂×C₁₁	1	1	yes	characteristic
99	C₂×#344	C₂×C₁₁	1	2	yes	—
100	C₂×#338	C₂×C₁₁	1	1	yes	characteristic
101	C₂×H(3,ℤ/4)	C₂×C₁₁	1	2	yes	—
102	C₂³×C₁₁	—	8	1	no	—
103	C₂³×C₁₁	#117	1	1	yes	characteristic
104	C₂³×C₁₁	#121	1	1	yes	characteristic
105	C₂³×C₁₁	C₂²⋊Q₈	1	1	yes	characteristic
106	C₂³×C₁₁	#123	1	2	yes	—
107	C₂³×C₁₁	#125	1	2	yes	—
108	C₂×C₄×C₁₁	—	2	4	no	—
109	C₂×C₄×C₁₁	—	4	4	no	—
110	C₂×C₄×C₁₁	—	8	2	no	—
111	C₂×C₄×C₁₁	—	8	4	no	—
112	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
113	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
114	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
115	C₂×C₄×C₁₁	C₄×Q₈	1	2	yes	—
116	C₂×C₄×C₁₁	#120	1	1	yes	characteristic
117	C₂×C₄×C₁₁	#121	1	2	yes	—
118	C₂×C₄×C₁₁	#121	1	2	yes	—
119	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
120	C₂×C₄×C₁₁	C₂²⋊Q₈	1	2	yes	—
121	C₂×C₄×C₁₁	C₂²⋊Q₈	1	2	yes	—
122	C₂×C₄×C₁₁	C₂²⋊Q₈	1	2	yes	—
123	C₂×C₄×C₁₁	C₂²⋊Q₈	1	1	yes	characteristic
124	C₂×C₄×C₁₁	#123	1	1	yes	characteristic
125	C₂×C₄×C₁₁	#124	1	1	yes	characteristic
126	C₂×C₄×C₁₁	#125	1	2	yes	—
127	C₂×C₄×C₁₁	#126	1	2	yes	—
128	C₂×C₄×C₁₁	C₄⋊Q₈	1	2	yes	—
129	C₂×C₄×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
130	C₈×C₁₁	—	2	4	no	—
131	C₈×C₁₁	—	4	2	no	—
132	C₈×C₁₁	—	4	4	no	—
133	C₂²×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
134	C₂²×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
135	C₂²×M₁₆	C₂²×C₁₁	1	2	yes	—
136	C₂×#117	C₂²×C₁₁	1	2	yes	—
137	C₂×#117	C₂²×C₁₁	1	1	yes	characteristic
138	#428	—	2	4	no	—
139	#427	—	2	2	no	—
140	#424	—	2	2	no	—
141	#424	—	2	2	no	—
142	#423	C₄×C₁₁	1	4	yes	complemented
143	#344	—	2	4	no	—
144	#338	—	2	2	no	—
145	H(3,ℤ/4)	—	2	4	no	—
146	C₂²×C₁₁	—	4	1	no	—
147	C₂²×C₁₁	—	4	2	no	—
148	C₂²×C₁₁	—	4	1	no	—
149	C₂²×C₁₁	—	4	1	no	—
150	C₂²×C₁₁	—	4	2	no	—
151	C₂²×C₁₁	#380	1	1	yes	characteristic
152	C₂²×C₁₁	#387	1	2	yes	—
153	C₂²×C₁₁	#394	1	1	yes	characteristic
154	C₂²×C₁₁	#398	1	2	yes	—
155	C₂²×C₁₁	#398	1	1	yes	characteristic
156	C₄×C₁₁	—	4	4	no	—
157	C₄×C₁₁	—	8	4	no	—
158	C₄×C₁₁	#386	1	1	yes	characteristic
159	C₄×C₁₁	#389	1	2	yes	—
160	C₄×C₁₁	#391	1	1	yes	characteristic
161	C₄×C₁₁	#395	1	1	yes	characteristic
162	C₄×C₁₁	#396	1	2	yes	—
163	C₄×C₁₁	#400	1	1	yes	characteristic
164	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
165	C₂×M₁₆	—	2	2	no	—
166	C₂×M₁₆	—	2	2	no	—
167	C₂×M₁₆	—	2	2	no	—
168	C₂×M₁₆	—	2	2	no	—
169	C₂×M₁₆	—	2	2	no	—
170	C₂×M₁₆	—	2	1	no	—
171	C₂×M₁₆	—	2	2	no	—
172	C₂×M₁₆	—	2	2	no	—
173	C₂×M₁₆	—	2	2	no	—
174	C₂×M₁₆	—	2	2	no	—
175	C₂×M₁₆	—	2	2	no	—
176	C₂×M₁₆	C₂×C₄×C₁₁	1	2	yes	—
177	C₂×M₁₆	C₂×C₄×C₁₁	1	2	yes	—
178	C₂×M₁₆	D₄×C₁₁	1	2	yes	—
179	C₂²×C₈	—	2	1	no	—
180	C₂²×C₈	D₄×C₁₁	1	2	yes	—
181	C₂²×C₈	Q₈×C₁₁	1	4	yes	—
182	#117	—	2	1	no	—
183	#117	—	2	1	no	—
184	#117	—	2	2	no	—
185	#117	—	2	2	no	—
186	#117	—	2	2	no	—
187	#117	D₄×C₁₁	1	4	yes	—
188	#117	D₄×C₁₁	1	2	yes	—
189	#117	Q₈×C₁₁	1	2	yes	—
190	C₂×C₄⋊C₄	—	2	1	no	—
191	C₂×C₄⋊C₄	—	2	2	no	—
192	C₂×C₂²⋊C₄	—	2	1	no	—
193	C₂×C₂²⋊C₄	—	2	2	no	—
194	C₂×C₄²	—	2	2	no	—
195	C₂×C₄²	C₂×C₄×C₁₁	1	2	yes	—
196	#107	—	2	4	no	—
197	#106	—	2	4	no	—
198	C₄⋊C₈	—	2	8	no	—
199	C₂×C₁₁	—	2	1	no	—
200	C₂×C₁₁	—	2	1	no	—
201	C₂×C₁₁	—	2	2	no	—
202	C₂×C₁₁	—	2	2	no	—
203	C₂×C₁₁	—	2	1	no	—
204	C₂×C₁₁	#1441	1	1	yes	characteristic
205	C₂⁴	C₁₁×#41	1	1	yes	characteristic
206	C₂²×C₄	—	2	2	no	—
207	C₂²×C₄	—	4	2	no	—
208	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
209	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
210	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
211	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
212	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
213	C₂²×C₄	C₂×Q₈×C₁₁	1	1	yes	characteristic
214	C₂²×C₄	C₂×Q₈×C₁₁	1	2	yes	—
215	C₂²×C₄	C₁₁×#41	1	2	yes	—
216	C₂²×C₄	C₁₁×#41	1	2	yes	—
217	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
218	M₁₆	—	2	4	no	—
219	M₁₆	—	2	4	no	—
220	M₁₆	—	2	4	no	—
221	M₁₆	—	4	1	no	—
222	M₁₆	—	4	2	no	—
223	M₁₆	—	4	2	no	—
224	M₁₆	—	4	2	no	—
225	M₁₆	—	4	1	no	—
226	M₁₆	—	4	2	no	—
227	C₂×C₈	—	2	2	no	—
228	C₂×C₈	—	2	2	no	—
229	C₂×C₈	—	2	2	no	—
230	C₂×C₈	—	2	4	no	—
231	C₂×C₈	—	2	4	no	—
232	C₂×C₈	—	2	4	no	—
233	C₂×C₈	—	4	2	no	—
234	C₂×C₈	C₁₁×C₂²⋊C₄	1	4	yes	—
235	C₄⋊C₄	—	2	2	no	—
236	C₄⋊C₄	—	2	2	no	—
237	C₄⋊C₄	—	2	4	no	—
238	C₄⋊C₄	—	4	2	no	—
239	C₂²⋊C₄	—	2	2	no	—
240	C₂²⋊C₄	—	2	2	no	—
241	C₂²⋊C₄	—	2	4	no	—
242	C₂²⋊C₄	—	4	2	no	—
243	C₄²	—	2	2	no	—
244	C₄²	—	2	4	no	—
245	C₄²	—	4	2	no	—
246	C₄²	C₁₁×C₄⋊C₄	1	4	yes	—
247	C₁₁	#11245	1	1	yes	characteristic, direct product factor, Sylow
248	C₂³	—	8	1	no	—
249	C₂³	C₁₁×#117	1	1	yes	characteristic
250	C₂³	C₁₁×#121	1	1	yes	characteristic
251	C₂³	C₁₁×C₂²⋊Q₈	1	1	yes	characteristic
252	C₂³	C₁₁×#123	1	2	yes	—
253	C₂³	C₁₁×#125	1	2	yes	—
254	C₂×C₄	—	2	4	no	—
255	C₂×C₄	—	4	4	no	—
256	C₂×C₄	—	8	2	no	—
257	C₂×C₄	—	8	4	no	—
258	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
259	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	1	yes	characteristic
260	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
261	C₂×C₄	C₄×Q₈×C₁₁	1	2	yes	—
262	C₂×C₄	C₁₁×#120	1	1	yes	characteristic
263	C₂×C₄	C₁₁×#121	1	2	yes	—
264	C₂×C₄	C₁₁×#121	1	2	yes	—
265	C₂×C₄	C₁₁×#121	1	1	yes	characteristic
266	C₂×C₄	C₁₁×C₂²⋊Q₈	1	2	yes	—
267	C₂×C₄	C₁₁×C₂²⋊Q₈	1	2	yes	—
268	C₂×C₄	C₁₁×C₂²⋊Q₈	1	2	yes	—
269	C₂×C₄	C₁₁×C₂²⋊Q₈	1	1	yes	characteristic
270	C₂×C₄	C₁₁×#123	1	1	yes	characteristic
271	C₂×C₄	C₁₁×#124	1	1	yes	characteristic
272	C₂×C₄	C₁₁×#125	1	2	yes	—
273	C₂×C₄	C₁₁×#126	1	2	yes	—
274	C₂×C₄	C₁₁×C₄⋊Q₈	1	2	yes	—
275	C₂×C₄	C₁₁×C₄⋊Q₈	1	1	yes	characteristic
276	C₈	—	2	4	no	—
277	C₈	—	4	2	no	—
278	C₈	—	4	4	no	—
279	C₂²	—	4	1	no	—
280	C₂²	—	4	2	no	—
281	C₂²	—	4	1	no	—
282	C₂²	—	4	1	no	—
283	C₂²	—	4	2	no	—
284	C₂²	C₁₁×#380	1	1	yes	characteristic
285	C₂²	C₁₁×#387	1	2	yes	—
286	C₂²	C₁₁×#394	1	1	yes	characteristic
287	C₂²	C₁₁×#398	1	2	yes	—
288	C₂²	C₁₁×#398	1	1	yes	characteristic
289	C₄	—	4	4	no	—
290	C₄	—	8	4	no	—
291	C₄	C₁₁×#386	1	1	yes	characteristic
292	C₄	C₁₁×#389	1	2	yes	—
293	C₄	C₁₁×#391	1	1	yes	characteristic
294	C₄	C₁₁×#395	1	1	yes	characteristic
295	C₄	C₁₁×#396	1	2	yes	—
296	C₄	C₁₁×#400	1	1	yes	characteristic
297	C₂	—	2	1	no	—
298	C₂	—	2	1	no	—
299	C₂	—	2	2	no	—
300	C₂	—	2	2	no	—
301	C₂	—	2	1	no	—
302	C₂	C₁₁×#1441	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₁₁	#391
commutator	C₂²×C₄	C₂²×C₄×C₁₁
Frattini, cosocle	C₂³×C₄	C₂³×C₁₁
socle	C₂×C₁₁	#1441
prime radical	C₂⁴×C₁₁	#41
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₁ ◁ C₂³×C₄×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
15. C₁₁×#423	C₄	semidirect
54. #11245	C₁₁	direct (N × H)
142. #423	C₄×C₁₁	semidirect
247. C₁₁	#11245	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×#2911	2
C₁₁×#2905	2
C₂×C₁₁×#344	2
C₂×C₁₁×#338	2
C₂×C₁₁×H(3,ℤ/4)	2
#11245	11

Subgroups — C11×#11245 #14588438

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#11245 #14588438