Subgroups — C₁₁×#13197 #14590390

Order 2816.

424 conjugacy classes of subgroups.

The subgroup lattice has 296 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#443	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₁×#364	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#2117	C₂	1	2	yes	maximal, complemented
4	C₁₁×#2115	C₂	1	2	yes	maximal, complemented
5	C₄×C₁₁×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₁×#135	C₄	1	1	yes	characteristic
7	C₂×C₁₁×#131	C₂²	1	2	yes	—
8	C₂×C₁₁×M₃₂	C₂²	1	2	yes	—
9	C₂×C₁₁×M₃₂	C₂²	1	1	yes	characteristic
10	C₂×C₁₁×M₃₂	C₂²	1	1	yes	characteristic
11	C₁₁×#443	—	2	1	no	—
12	C₁₁×#443	—	2	1	no	—
13	C₁₁×#443	—	2	1	no	—
14	C₁₁×#443	—	2	1	no	—
15	C₂×C₁₁×#108	C₄	1	1	yes	characteristic
16	C₂×C₁₁×#104	C₄	1	2	yes	—
17	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
18	C₁₁×#364	—	2	1	no	—
19	C₁₁×#364	—	2	1	no	—
20	C₁₁×#350	—	2	4	no	—
21	C₁₁×#349	—	2	4	no	—
22	C₁₁×#346	—	2	1	no	—
23	C₄×C₁₁×C₁₆	—	2	1	no	—
24	C₂×C₁₁×#41	C₂×C₄	1	2	yes	—
25	C₁₁×#135	—	2	1	no	—
26	C₁₁×#135	—	2	1	no	—
27	C₁₁×#135	—	2	1	no	—
28	C₁₁×#135	—	2	1	no	—
29	C₂×C₁₁×Q₁₆	C₈	1	1	yes	characteristic
30	C₂×C₁₁×SD₁₆	C₈	1	2	yes	—
31	C₂×C₁₁×D₈	C₈	1	1	yes	characteristic
32	C₁₁×#131	—	2	2	no	—
33	C₁₁×#131	—	2	2	no	—
34	C₁₁×#131	—	2	2	no	—
35	C₁₁×#131	—	2	2	no	—
36	C₂×C₁₁×M₁₆	—	2	2	no	—
37	C₂×C₁₁×M₁₆	C₂×C₄	1	2	yes	—
38	C₂²×C₈×C₁₁	—	2	2	no	—
39	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
41	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
42	C₁₁×M₃₂	—	2	1	no	—
43	C₁₁×M₃₂	—	2	1	no	—
44	C₁₁×M₃₂	—	2	2	no	—
45	C₁₁×M₃₂	—	2	2	no	—
46	C₁₁×M₃₂	D₄	1	2	yes	—
47	C₁₁×M₃₂	D₄	1	2	yes	—
48	C₂×C₁₁×C₁₆	—	2	1	no	—
49	C₂×C₁₁×C₁₆	—	2	1	no	—
50	C₂×C₁₁×C₁₆	—	2	2	no	—
51	C₁₁×#108	—	2	1	no	—
52	C₁₁×#108	—	2	1	no	—
53	C₁₁×#104	—	2	2	no	—
54	C₁₁×#104	—	2	2	no	—
55	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
56	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
57	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
58	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
59	#13197	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
60	C₁₁×#41	—	2	2	no	—
61	C₁₁×#41	—	2	2	no	—
62	C₁₁×#41	—	2	2	no	—
63	C₁₁×#41	—	2	2	no	—
64	C₂×Q₈×C₁₁	C₂×C₈	1	2	yes	—
65	C₂×D₄×C₁₁	—	2	2	no	—
66	C₂×D₄×C₁₁	C₂×C₈	1	2	yes	—
67	C₂²×C₄×C₁₁	—	2	1	no	—
68	C₂²×C₄×C₁₁	—	2	2	no	—
69	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
70	C₁₁×Q₁₆	—	2	1	no	—
71	C₁₁×Q₁₆	—	2	1	no	—
72	C₁₁×SD₁₆	—	2	2	no	—
73	C₁₁×SD₁₆	—	2	2	no	—
74	C₁₁×D₈	—	2	1	no	—
75	C₁₁×D₈	—	2	1	no	—
76	C₁₁×M₁₆	—	2	2	no	—
77	C₁₁×M₁₆	—	2	2	no	—
78	C₁₁×M₁₆	—	4	2	no	—
79	C₁₁×M₁₆	—	4	2	no	—
80	C₂×C₈×C₁₁	—	2	2	no	—
81	C₂×C₈×C₁₁	—	4	2	no	—
82	C₂×C₈×C₁₁	—	4	2	no	—
83	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
84	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
85	C₂×C₈×C₁₁	C₂×C₈	1	1	yes	characteristic
86	C₂×C₈×C₁₁	C₂×C₈	1	1	yes	characteristic
87	C₂×C₈×C₁₁	M₁₆	1	1	yes	characteristic
88	C₂×C₈×C₁₁	M₁₆	1	1	yes	characteristic
89	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
90	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
91	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
92	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
93	C₂×C₈×C₁₁	#41	1	1	yes	characteristic
94	C₂×C₈×C₁₁	#41	1	1	yes	characteristic
95	C₄²×C₁₁	—	2	1	no	—
96	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
97	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
98	C₁₁×C₁₆	—	2	2	no	—
99	C₁₁×C₁₆	—	2	2	no	—
100	C₁₁×C₁₆	—	4	2	no	—
101	C₂×#443	C₂×C₁₁	1	1	yes	characteristic
102	C₂×#364	C₂×C₁₁	1	1	yes	characteristic, complemented
103	#2117	C₂×C₁₁	1	2	yes	complemented
104	#2115	C₂×C₁₁	1	2	yes	complemented
105	C₄×M₃₂	C₂×C₁₁	1	1	yes	characteristic, complemented
106	C₂³×C₁₁	—	2	2	no	—
107	C₂³×C₁₁	#131	1	1	yes	characteristic
108	Q₈×C₁₁	—	2	2	no	—
109	Q₈×C₁₁	—	2	2	no	—
110	D₄×C₁₁	—	2	2	no	—
111	D₄×C₁₁	—	2	2	no	—
112	D₄×C₁₁	—	4	2	no	—
113	D₄×C₁₁	—	4	2	no	—
114	C₂×C₄×C₁₁	—	2	1	no	—
115	C₂×C₄×C₁₁	—	2	1	no	—
116	C₂×C₄×C₁₁	—	2	2	no	—
117	C₂×C₄×C₁₁	—	4	2	no	—
118	C₂×C₄×C₁₁	—	4	2	no	—
119	C₂×C₄×C₁₁	—	4	2	no	—
120	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
121	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
122	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
123	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
124	C₂×C₄×C₁₁	C₂×M₁₆	1	1	yes	characteristic
125	C₂×C₄×C₁₁	#131	1	1	yes	characteristic
126	C₈×C₁₁	—	4	2	no	—
127	C₈×C₁₁	C₂²⋊C₈	1	1	yes	characteristic
128	C₈×C₁₁	C₂²⋊C₈	1	1	yes	characteristic
129	C₈×C₁₁	C₂²⋊C₈	1	1	yes	characteristic
130	C₈×C₁₁	C₂²⋊C₈	1	1	yes	characteristic
131	C₈×C₁₁	#121	1	1	yes	characteristic
132	C₈×C₁₁	#121	1	1	yes	characteristic
133	C₈×C₁₁	#124	1	1	yes	characteristic
134	C₈×C₁₁	#127	1	1	yes	characteristic
135	C₂×#135	C₄×C₁₁	1	1	yes	characteristic
136	C₂×#131	C₂²×C₁₁	1	2	yes	—
137	C₂×M₃₂	C₂²×C₁₁	1	2	yes	—
138	C₂×M₃₂	C₂²×C₁₁	1	1	yes	characteristic
139	C₂×M₃₂	C₂²×C₁₁	1	1	yes	characteristic
140	#443	—	2	1	no	—
141	#443	—	2	1	no	—
142	#443	—	2	1	no	—
143	#443	—	2	1	no	—
144	C₂×#108	C₄×C₁₁	1	1	yes	characteristic
145	C₂×#104	C₄×C₁₁	1	2	yes	—
146	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
147	#364	—	2	1	no	—
148	#364	—	2	1	no	—
149	#350	—	2	4	no	—
150	#349	—	2	4	no	—
151	#346	—	2	1	no	—
152	C₄×C₁₆	—	2	1	no	—
153	C₂²×C₁₁	—	4	1	no	—
154	C₂²×C₁₁	—	4	2	no	—
155	C₂²×C₁₁	—	8	2	no	—
156	C₂²×C₁₁	#408	1	1	yes	characteristic
157	C₂²×C₁₁	C₈×D₄	1	1	yes	characteristic
158	C₂²×C₁₁	#436	1	1	yes	characteristic
159	C₄×C₁₁	—	2	2	no	—
160	C₄×C₁₁	—	4	1	no	—
161	C₄×C₁₁	—	4	2	no	—
162	C₄×C₁₁	#390	1	1	yes	characteristic
163	C₄×C₁₁	C₂×C₂²⋊C₈	1	1	yes	characteristic
164	C₄×C₁₁	C₈×D₄	1	1	yes	characteristic
165	C₄×C₁₁	#436	1	1	yes	characteristic
166	C₂×#41	C₂×C₄×C₁₁	1	2	yes	—
167	#135	—	2	1	no	—
168	#135	—	2	1	no	—
169	#135	—	2	1	no	—
170	#135	—	2	1	no	—
171	C₂×Q₁₆	C₈×C₁₁	1	1	yes	characteristic
172	C₂×SD₁₆	C₈×C₁₁	1	2	yes	—
173	C₂×D₈	C₈×C₁₁	1	1	yes	characteristic
174	#131	—	2	2	no	—
175	#131	—	2	2	no	—
176	#131	—	2	2	no	—
177	#131	—	2	2	no	—
178	C₂×M₁₆	—	2	2	no	—
179	C₂×M₁₆	C₂×C₄×C₁₁	1	2	yes	—
180	C₂²×C₈	—	2	2	no	—
181	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
182	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
183	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
184	M₃₂	—	2	1	no	—
185	M₃₂	—	2	1	no	—
186	M₃₂	—	2	2	no	—
187	M₃₂	—	2	2	no	—
188	M₃₂	D₄×C₁₁	1	2	yes	—
189	M₃₂	D₄×C₁₁	1	2	yes	—
190	C₂×C₁₆	—	2	1	no	—
191	C₂×C₁₆	—	2	1	no	—
192	C₂×C₁₆	—	2	2	no	—
193	#108	—	2	1	no	—
194	#108	—	2	1	no	—
195	#104	—	2	2	no	—
196	#104	—	2	2	no	—
197	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
198	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
199	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
200	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
201	C₂×C₁₁	—	2	1	no	—
202	C₂×C₁₁	—	2	1	no	—
203	C₂×C₁₁	—	2	1	no	—
204	C₂×C₁₁	—	8	2	no	—
205	C₂×C₁₁	#1954	1	1	yes	characteristic
206	#41	—	2	2	no	—
207	#41	—	2	2	no	—
208	#41	—	2	2	no	—
209	#41	—	2	2	no	—
210	C₂×Q₈	C₂×C₈×C₁₁	1	2	yes	—
211	C₂×D₄	—	2	2	no	—
212	C₂×D₄	C₂×C₈×C₁₁	1	2	yes	—
213	C₂²×C₄	—	2	1	no	—
214	C₂²×C₄	—	2	2	no	—
215	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
216	Q₁₆	—	2	1	no	—
217	Q₁₆	—	2	1	no	—
218	SD₁₆	—	2	2	no	—
219	SD₁₆	—	2	2	no	—
220	D₈	—	2	1	no	—
221	D₈	—	2	1	no	—
222	M₁₆	—	2	2	no	—
223	M₁₆	—	2	2	no	—
224	M₁₆	—	4	2	no	—
225	M₁₆	—	4	2	no	—
226	C₂×C₈	—	2	2	no	—
227	C₂×C₈	—	4	2	no	—
228	C₂×C₈	—	4	2	no	—
229	C₂×C₈	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
230	C₂×C₈	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
231	C₂×C₈	C₂×C₈×C₁₁	1	1	yes	characteristic
232	C₂×C₈	C₂×C₈×C₁₁	1	1	yes	characteristic
233	C₂×C₈	C₁₁×M₁₆	1	1	yes	characteristic
234	C₂×C₈	C₁₁×M₁₆	1	1	yes	characteristic
235	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
236	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
237	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
238	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
239	C₂×C₈	C₁₁×#41	1	1	yes	characteristic
240	C₂×C₈	C₁₁×#41	1	1	yes	characteristic
241	C₄²	—	2	1	no	—
242	C₄²	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
243	C₄²	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
244	C₁₆	—	2	2	no	—
245	C₁₆	—	2	2	no	—
246	C₁₆	—	4	2	no	—
247	C₁₁	#13197	1	1	yes	characteristic, direct product factor, Sylow
248	C₂³	—	2	2	no	—
249	C₂³	C₁₁×#131	1	1	yes	characteristic
250	Q₈	—	2	2	no	—
251	Q₈	—	2	2	no	—
252	D₄	—	2	2	no	—
253	D₄	—	2	2	no	—
254	D₄	—	4	2	no	—
255	D₄	—	4	2	no	—
256	C₂×C₄	—	2	1	no	—
257	C₂×C₄	—	2	1	no	—
258	C₂×C₄	—	2	2	no	—
259	C₂×C₄	—	4	2	no	—
260	C₂×C₄	—	4	2	no	—
261	C₂×C₄	—	4	2	no	—
262	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
263	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
264	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
265	C₂×C₄	C₂²×C₈×C₁₁	1	1	yes	characteristic
266	C₂×C₄	C₂×C₁₁×M₁₆	1	1	yes	characteristic
267	C₂×C₄	C₁₁×#131	1	1	yes	characteristic
268	C₈	—	4	2	no	—
269	C₈	C₁₁×C₂²⋊C₈	1	1	yes	characteristic
270	C₈	C₁₁×C₂²⋊C₈	1	1	yes	characteristic
271	C₈	C₁₁×C₂²⋊C₈	1	1	yes	characteristic
272	C₈	C₁₁×C₂²⋊C₈	1	1	yes	characteristic
273	C₈	C₁₁×#121	1	1	yes	characteristic
274	C₈	C₁₁×#121	1	1	yes	characteristic
275	C₈	C₁₁×#124	1	1	yes	characteristic
276	C₈	C₁₁×#127	1	1	yes	characteristic
277	C₂²	—	4	1	no	—
278	C₂²	—	4	2	no	—
279	C₂²	—	8	2	no	—
280	C₂²	C₁₁×#408	1	1	yes	characteristic
281	C₂²	C₈×D₄×C₁₁	1	1	yes	characteristic
282	C₂²	C₁₁×#436	1	1	yes	characteristic
283	C₄	—	2	2	no	—
284	C₄	—	4	1	no	—
285	C₄	—	4	2	no	—
286	C₄	C₁₁×#390	1	1	yes	characteristic
287	C₄	C₂×C₁₁×C₂²⋊C₈	1	1	yes	characteristic
288	C₄	C₈×D₄×C₁₁	1	1	yes	characteristic
289	C₄	C₁₁×#436	1	1	yes	characteristic
290	C₂	—	2	1	no	—
291	C₂	—	2	1	no	—
292	C₂	—	2	1	no	—
293	C₂	—	8	2	no	—
294	C₂	C₁₁×#1954	1	1	yes	characteristic

	subgroup	G/H
center	C₈×C₁₁	#121
commutator	C₂×C₄	C₂²×C₈×C₁₁
Frattini, cosocle	C₂²×C₈	C₂³×C₁₁
socle	C₂×C₁₁	#1954
prime radical	C₂×C₁₁×#135	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₁₁ ◁ C₂²×C₈×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₁×#364	C₂	semidirect
3. C₁₁×#2117	C₂	semidirect
4. C₁₁×#2115	C₂	semidirect
5. C₄×C₁₁×M₃₂	C₂	semidirect
59. #13197	C₁₁	direct (N × H)
102. C₂×#364	C₂×C₁₁	semidirect
103. #2117	C₂×C₁₁	semidirect
104. #2115	C₂×C₁₁	semidirect
105. C₄×M₃₂	C₂×C₁₁	semidirect
247. C₁₁	#13197	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₁×#443	2
C₂×C₁₁×#364	2
C₁₁×#2117	2
C₁₁×#2115	2
C₄×C₁₁×M₃₂	2
#13197	11

Subgroups — C11×#13197 #14590390

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#13197 #14590390