Subgroups — C₁₁×#33483 #14610676

Order 2816.

516 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#2966	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2183	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₈×C₁₁×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#2169	C₂	1	2	yes	maximal, complemented
5	C₁₁×#2169	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁×#2168	C₂	1	2	yes	maximal, complemented
7	D₄×C₁₁×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₁×#2164	C₂	1	2	yes	maximal, complemented
9	C₁₁×#2162	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₁×#2108	C₂	1	2	yes	maximal, complemented
11	C₄×C₁₁×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₁×#529	C₄	1	1	yes	characteristic
13	C₂×C₁₁×M₃₂	C₂²	1	1	yes	characteristic
14	C₂×C₁₁×M₃₂	C₂²	1	1	yes	characteristic
15	C₂×C₁₁×M₃₂	C₂²	1	2	yes	—
16	C₂²×C₁₁×C₁₆	C₂²	1	2	yes	—
17	C₁₁×#446	C₄	1	1	yes	characteristic
18	C₈×Q₈×C₁₁	C₂²	1	1	yes	characteristic
19	C₁₁×#436	C₄	1	1	yes	characteristic
20	C₁₁×#435	C₄	1	2	yes	—
21	C₈×D₄×C₁₁	C₂²	1	1	yes	characteristic
22	C₈×D₄×C₁₁	C₂²	1	2	yes	—
23	C₁₁×#433	C₄	1	2	yes	—
24	C₁₁×#432	C₄	1	1	yes	characteristic
25	C₁₁×#405	C₂²	1	2	yes	—
26	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
27	C₁₁×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
28	C₁₁×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
29	C₁₁×C₄⋊C₁₆	C₂²	1	2	yes	—
30	C₁₁×C₄⋊C₁₆	C₂²	1	2	yes	—
31	C₁₁×C₂²⋊C₁₆	C₂²	1	2	yes	—
32	C₁₁×C₂²⋊C₁₆	C₂²	1	2	yes	—
33	C₁₁×C₂²⋊C₁₆	C₂²	1	2	yes	—
34	C₁₁×#346	C₂²	1	1	yes	characteristic
35	C₁₁×#346	C₂²	1	2	yes	—
36	C₁₁×#346	C₂²	1	1	yes	characteristic
37	C₄×C₁₁×C₁₆	C₂²	1	2	yes	—
38	C₄×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
39	C₄×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
40	C₄×C₁₁×C₁₆	C₂²	1	2	yes	—
41	C₂×C₁₁×M₁₆	C₂×C₄	1	2	yes	—
42	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
43	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
44	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
45	C₁₁×#126	C₈	1	2	yes	—
46	C₁₁×#125	C₈	1	1	yes	characteristic
47	C₁₁×#124	C₈	1	1	yes	characteristic
48	C₁₁×#123	C₈	1	2	yes	—
49	C₁₁×C₂²⋊Q₈	C₈	1	1	yes	characteristic
50	C₁₁×#121	C₈	1	1	yes	characteristic
51	C₄×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
52	C₄×D₄×C₁₁	C₂×C₄	1	2	yes	—
53	C₄×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
54	C₁₁×#117	C₂×C₄	1	2	yes	—
55	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
56	C₁₁×M₃₂	—	2	2	no	—
57	C₁₁×M₃₂	—	2	2	no	—
58	C₁₁×M₃₂	—	2	4	no	—
59	C₂×C₁₁×C₁₆	—	2	4	no	—
60	C₂×C₁₁×C₁₆	C₂³	1	2	yes	—
61	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
62	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
63	C₂×C₁₁×C₁₆	C₂³	1	2	yes	—
64	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
65	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
66	C₁₁×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
67	C₁₁×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
68	C₁₁×C₄⋊C₈	C₂×C₄	1	2	yes	—
69	C₁₁×C₄⋊C₈	C₂×C₄	1	2	yes	—
70	C₁₁×C₂²⋊C₈	C₂×C₄	1	2	yes	—
71	C₁₁×C₂²⋊C₈	C₂×C₄	1	2	yes	—
72	C₁₁×C₂²⋊C₈	C₂×C₄	1	2	yes	—
73	C₁₁×#97	C₂×C₄	1	2	yes	—
74	C₁₁×#97	C₂×C₄	1	2	yes	—
75	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
76	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
77	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
78	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
79	C₄×C₈×C₁₁	C₂³	1	2	yes	—
80	#33483	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
81	C₂×Q₈×C₁₁	C₂×C₈	1	1	yes	characteristic
82	C₂×D₄×C₁₁	C₂×C₈	1	1	yes	characteristic
83	C₂×D₄×C₁₁	C₂×C₈	1	2	yes	—
84	C₂²×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
85	C₂²×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
86	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
88	C₁₁×M₁₆	—	2	4	no	—
89	C₂×C₈×C₁₁	—	2	2	no	—
90	C₂×C₈×C₁₁	—	2	2	no	—
91	C₂×C₈×C₁₁	—	2	2	no	—
92	C₂×C₈×C₁₁	—	2	1	no	—
93	C₂×C₈×C₁₁	—	2	1	no	—
94	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
95	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
96	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
97	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
98	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
99	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
100	C₁₁×C₄⋊C₄	C₂×C₈	1	2	yes	—
101	C₁₁×C₄⋊C₄	C₂×C₈	1	2	yes	—
102	C₁₁×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
103	C₁₁×C₄⋊C₄	C₂×C₈	1	2	yes	—
104	C₁₁×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
105	C₁₁×C₄⋊C₄	C₂×C₈	1	2	yes	—
106	C₁₁×C₂²⋊C₄	C₂×C₈	1	2	yes	—
107	C₁₁×C₂²⋊C₄	C₂×C₈	1	2	yes	—
108	C₁₁×C₂²⋊C₄	C₂×C₈	1	2	yes	—
109	C₁₁×C₂²⋊C₄	C₂×C₈	1	2	yes	—
110	C₁₁×C₂²⋊C₄	C₂×C₈	1	2	yes	—
111	C₄²×C₁₁	C₂×C₈	1	1	yes	characteristic
112	C₄²×C₁₁	C₂×C₈	1	1	yes	characteristic
113	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
114	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
115	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
116	C₁₁×C₁₆	—	2	2	no	—
117	C₁₁×C₁₆	—	2	1	no	—
118	C₁₁×C₁₆	—	2	1	no	—
119	C₁₁×C₁₆	—	2	2	no	—
120	C₁₁×C₁₆	#41	1	2	yes	—
121	C₁₁×C₁₆	#41	1	2	yes	—
122	#2966	C₂×C₁₁	1	1	yes	characteristic
123	#2183	C₂×C₁₁	1	1	yes	characteristic, complemented
124	Q₈×C₁₆	C₂×C₁₁	1	1	yes	characteristic, complemented
125	#2169	C₂×C₁₁	1	1	yes	characteristic, complemented
126	#2169	C₂×C₁₁	1	2	yes	complemented
127	#2168	C₂×C₁₁	1	2	yes	complemented
128	D₄×C₁₆	C₂×C₁₁	1	1	yes	characteristic, complemented
129	#2164	C₂×C₁₁	1	2	yes	complemented
130	#2162	C₂×C₁₁	1	1	yes	characteristic, complemented
131	#2108	C₂×C₁₁	1	2	yes	complemented
132	C₄×M₃₂	C₂×C₁₁	1	1	yes	characteristic, complemented
133	C₂³×C₁₁	C₂²×C₈	1	2	yes	—
134	C₂³×C₁₁	C₂²×C₈	1	1	yes	characteristic
135	Q₈×C₁₁	—	2	2	no	—
136	D₄×C₁₁	—	2	2	no	—
137	D₄×C₁₁	—	4	2	no	—
138	C₂×C₄×C₁₁	—	2	2	no	—
139	C₂×C₄×C₁₁	—	2	1	no	—
140	C₂×C₄×C₁₁	—	2	1	no	—
141	C₂×C₄×C₁₁	—	2	2	no	—
142	C₂×C₄×C₁₁	—	2	2	no	—
143	C₂×C₄×C₁₁	—	4	1	no	—
144	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
145	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
146	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
147	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
148	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
149	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
150	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
151	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
152	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
153	C₈×C₁₁	—	2	2	no	—
154	C₈×C₁₁	—	2	1	no	—
155	C₈×C₁₁	—	2	1	no	—
156	C₈×C₁₁	—	2	2	no	—
157	C₈×C₁₁	#131	1	2	yes	—
158	C₈×C₁₁	C₂×#41	1	1	yes	characteristic
159	C₈×C₁₁	C₂×#41	1	1	yes	characteristic
160	#529	C₄×C₁₁	1	1	yes	characteristic
161	C₂×M₃₂	C₂²×C₁₁	1	1	yes	characteristic
162	C₂×M₃₂	C₂²×C₁₁	1	1	yes	characteristic
163	C₂×M₃₂	C₂²×C₁₁	1	2	yes	—
164	C₂²×C₁₆	C₂²×C₁₁	1	2	yes	—
165	#446	C₄×C₁₁	1	1	yes	characteristic
166	C₈×Q₈	C₂²×C₁₁	1	1	yes	characteristic
167	#436	C₄×C₁₁	1	1	yes	characteristic
168	#435	C₄×C₁₁	1	2	yes	—
169	C₈×D₄	C₂²×C₁₁	1	1	yes	characteristic
170	C₈×D₄	C₂²×C₁₁	1	2	yes	—
171	#433	C₄×C₁₁	1	2	yes	—
172	#432	C₄×C₁₁	1	1	yes	characteristic
173	#405	C₂²×C₁₁	1	2	yes	—
174	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
175	C₄⋊C₁₆	C₂²×C₁₁	1	1	yes	characteristic
176	C₄⋊C₁₆	C₂²×C₁₁	1	1	yes	characteristic
177	C₄⋊C₁₆	C₂²×C₁₁	1	2	yes	—
178	C₄⋊C₁₆	C₂²×C₁₁	1	2	yes	—
179	C₂²⋊C₁₆	C₂²×C₁₁	1	2	yes	—
180	C₂²⋊C₁₆	C₂²×C₁₁	1	2	yes	—
181	C₂²⋊C₁₆	C₂²×C₁₁	1	2	yes	—
182	#346	C₂²×C₁₁	1	1	yes	characteristic
183	#346	C₂²×C₁₁	1	1	yes	characteristic
184	#346	C₂²×C₁₁	1	2	yes	—
185	C₄×C₁₆	C₂²×C₁₁	1	1	yes	characteristic
186	C₄×C₁₆	C₂²×C₁₁	1	1	yes	characteristic
187	C₄×C₁₆	C₂²×C₁₁	1	2	yes	—
188	C₄×C₁₆	C₂²×C₁₁	1	2	yes	—
189	C₂²×C₁₁	—	2	1	no	—
190	C₂²×C₁₁	—	2	2	no	—
191	C₂²×C₁₁	—	2	1	no	—
192	C₂²×C₁₁	—	2	2	no	—
193	C₂²×C₁₁	—	2	1	no	—
194	C₂²×C₁₁	—	2	2	no	—
195	C₂²×C₁₁	C₂³×C₈	1	1	yes	characteristic
196	C₄×C₁₁	—	2	1	no	—
197	C₄×C₁₁	—	2	2	no	—
198	C₄×C₁₁	—	2	1	no	—
199	C₄×C₁₁	—	2	1	no	—
200	C₄×C₁₁	—	2	2	no	—
201	C₄×C₁₁	—	2	1	no	—
202	C₄×C₁₁	—	2	2	no	—
203	C₄×C₁₁	#504	1	2	yes	—
204	C₄×C₁₁	C₄×#41	1	1	yes	characteristic
205	C₄×C₁₁	C₂×#131	1	1	yes	characteristic
206	C₂×M₁₆	C₂×C₄×C₁₁	1	2	yes	—
207	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
208	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
209	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
210	#126	C₈×C₁₁	1	2	yes	—
211	#125	C₈×C₁₁	1	1	yes	characteristic
212	#124	C₈×C₁₁	1	1	yes	characteristic
213	#123	C₈×C₁₁	1	2	yes	—
214	C₂²⋊Q₈	C₈×C₁₁	1	1	yes	characteristic
215	#121	C₈×C₁₁	1	1	yes	characteristic
216	C₄×Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
217	C₄×D₄	C₂×C₄×C₁₁	1	2	yes	—
218	C₄×D₄	C₂×C₄×C₁₁	1	1	yes	characteristic
219	#117	C₂×C₄×C₁₁	1	2	yes	—
220	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
221	M₃₂	—	2	2	no	—
222	M₃₂	—	2	2	no	—
223	M₃₂	—	2	4	no	—
224	C₂×C₁₆	—	2	4	no	—
225	C₂×C₁₆	C₂³×C₁₁	1	2	yes	—
226	C₂×C₁₆	C₂³×C₁₁	1	1	yes	characteristic
227	C₂×C₁₆	C₂³×C₁₁	1	1	yes	characteristic
228	C₂×C₁₆	C₂³×C₁₁	1	2	yes	—
229	C₂×C₁₆	C₂³×C₁₁	1	1	yes	characteristic
230	C₂×C₁₆	C₂³×C₁₁	1	1	yes	characteristic
231	C₄⋊C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
232	C₄⋊C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
233	C₄⋊C₈	C₂×C₄×C₁₁	1	2	yes	—
234	C₄⋊C₈	C₂×C₄×C₁₁	1	2	yes	—
235	C₂²⋊C₈	C₂×C₄×C₁₁	1	2	yes	—
236	C₂²⋊C₈	C₂×C₄×C₁₁	1	2	yes	—
237	C₂²⋊C₈	C₂×C₄×C₁₁	1	2	yes	—
238	#97	C₂×C₄×C₁₁	1	2	yes	—
239	#97	C₂×C₄×C₁₁	1	2	yes	—
240	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
241	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
242	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
243	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
244	C₄×C₈	C₂³×C₁₁	1	2	yes	—
245	C₂×C₁₁	—	4	1	no	—
246	C₂×C₁₁	—	4	2	no	—
247	C₂×C₁₁	C₈×#41	1	1	yes	characteristic
248	C₂×C₁₁	C₂×#504	1	1	yes	characteristic
249	C₂×C₁₁	#3407	1	1	yes	characteristic
250	C₂×Q₈	C₂×C₈×C₁₁	1	1	yes	characteristic
251	C₂×D₄	C₂×C₈×C₁₁	1	1	yes	characteristic
252	C₂×D₄	C₂×C₈×C₁₁	1	2	yes	—
253	C₂²×C₄	C₂×C₈×C₁₁	1	1	yes	characteristic
254	C₂²×C₄	C₂×C₈×C₁₁	1	1	yes	characteristic
255	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
256	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
257	M₁₆	—	2	4	no	—
258	C₂×C₈	—	2	2	no	—
259	C₂×C₈	—	2	2	no	—
260	C₂×C₈	—	2	1	no	—
261	C₂×C₈	—	2	1	no	—
262	C₂×C₈	—	2	2	no	—
263	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
264	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
265	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
266	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
267	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
268	C₂×C₈	C₂⁴×C₁₁	1	1	yes	characteristic
269	C₄⋊C₄	C₂×C₈×C₁₁	1	2	yes	—
270	C₄⋊C₄	C₂×C₈×C₁₁	1	2	yes	—
271	C₄⋊C₄	C₂×C₈×C₁₁	1	1	yes	characteristic
272	C₄⋊C₄	C₂×C₈×C₁₁	1	2	yes	—
273	C₄⋊C₄	C₂×C₈×C₁₁	1	1	yes	characteristic
274	C₄⋊C₄	C₂×C₈×C₁₁	1	2	yes	—
275	C₂²⋊C₄	C₂×C₈×C₁₁	1	2	yes	—
276	C₂²⋊C₄	C₂×C₈×C₁₁	1	2	yes	—
277	C₂²⋊C₄	C₂×C₈×C₁₁	1	2	yes	—
278	C₂²⋊C₄	C₂×C₈×C₁₁	1	2	yes	—
279	C₂²⋊C₄	C₂×C₈×C₁₁	1	2	yes	—
280	C₄²	C₂×C₈×C₁₁	1	1	yes	characteristic
281	C₄²	C₂×C₈×C₁₁	1	1	yes	characteristic
282	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
283	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
284	C₄²	C₂²×C₄×C₁₁	1	2	yes	—
285	C₁₆	—	2	2	no	—
286	C₁₆	—	2	1	no	—
287	C₁₆	—	2	1	no	—
288	C₁₆	—	2	2	no	—
289	C₁₆	C₁₁×#41	1	2	yes	—
290	C₁₆	C₁₁×#41	1	2	yes	—
291	C₁₁	#33483	1	1	yes	characteristic, direct product factor, Sylow
292	C₂³	C₂²×C₈×C₁₁	1	2	yes	—
293	C₂³	C₂²×C₈×C₁₁	1	1	yes	characteristic
294	Q₈	—	2	2	no	—
295	D₄	—	2	2	no	—
296	D₄	—	4	2	no	—
297	C₂×C₄	—	2	2	no	—
298	C₂×C₄	—	2	2	no	—
299	C₂×C₄	—	2	1	no	—
300	C₂×C₄	—	2	1	no	—
301	C₂×C₄	—	2	2	no	—
302	C₂×C₄	—	4	1	no	—
303	C₂×C₄	C₂²×C₈×C₁₁	1	1	yes	characteristic
304	C₂×C₄	C₂²×C₈×C₁₁	1	1	yes	characteristic
305	C₂×C₄	C₂²×C₈×C₁₁	1	1	yes	characteristic
306	C₂×C₄	C₂²×C₈×C₁₁	1	1	yes	characteristic
307	C₂×C₄	C₂²×C₈×C₁₁	1	2	yes	—
308	C₂×C₄	C₂²×C₈×C₁₁	1	2	yes	—
309	C₂×C₄	C₂²×C₈×C₁₁	1	2	yes	—
310	C₂×C₄	C₂²×C₈×C₁₁	1	1	yes	characteristic
311	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
312	C₈	—	2	2	no	—
313	C₈	—	2	1	no	—
314	C₈	—	2	1	no	—
315	C₈	—	2	2	no	—
316	C₈	C₁₁×#131	1	2	yes	—
317	C₈	C₂×C₁₁×#41	1	1	yes	characteristic
318	C₈	C₂×C₁₁×#41	1	1	yes	characteristic
319	C₂²	—	2	1	no	—
320	C₂²	—	2	2	no	—
321	C₂²	—	2	1	no	—
322	C₂²	—	2	2	no	—
323	C₂²	—	2	1	no	—
324	C₂²	—	2	2	no	—
325	C₂²	C₂³×C₈×C₁₁	1	1	yes	characteristic
326	C₄	—	2	1	no	—
327	C₄	—	2	2	no	—
328	C₄	—	2	1	no	—
329	C₄	—	2	1	no	—
330	C₄	—	2	2	no	—
331	C₄	—	2	1	no	—
332	C₄	—	2	2	no	—
333	C₄	C₁₁×#504	1	2	yes	—
334	C₄	C₄×C₁₁×#41	1	1	yes	characteristic
335	C₄	C₂×C₁₁×#131	1	1	yes	characteristic
336	C₂	—	4	1	no	—
337	C₂	—	4	2	no	—
338	C₂	C₈×C₁₁×#41	1	1	yes	characteristic
339	C₂	C₂×C₁₁×#504	1	1	yes	characteristic
340	C₂	C₁₁×#3407	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈×C₁₁	C₂⁴
commutator	C₂²	C₂³×C₈×C₁₁
Frattini, cosocle	C₂×C₈	C₂⁴×C₁₁
socle	C₂²×C₁₁	C₂³×C₈
prime radical	C₁₁×#121	C₈
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₁×#2183	C₂	semidirect
3. Q₈×C₁₁×C₁₆	C₂	semidirect
4. C₁₁×#2169	C₂	semidirect
5. C₁₁×#2169	C₂	semidirect
6. C₁₁×#2168	C₂	semidirect
7. D₄×C₁₁×C₁₆	C₂	semidirect
8. C₁₁×#2164	C₂	semidirect
9. C₁₁×#2162	C₂	semidirect
10. C₁₁×#2108	C₂	semidirect
11. C₄×C₁₁×M₃₂	C₂	semidirect
80. #33483	C₁₁	direct (N × H)
123. #2183	C₂×C₁₁	semidirect
124. Q₈×C₁₆	C₂×C₁₁	semidirect
125. #2169	C₂×C₁₁	semidirect
126. #2169	C₂×C₁₁	semidirect
127. #2168	C₂×C₁₁	semidirect
128. D₄×C₁₆	C₂×C₁₁	semidirect
129. #2164	C₂×C₁₁	semidirect
130. #2162	C₂×C₁₁	semidirect
131. #2108	C₂×C₁₁	semidirect
132. C₄×M₃₂	C₂×C₁₁	semidirect
291. C₁₁	#33483	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×#2966	2
C₁₁×#2183	2
Q₈×C₁₁×C₁₆	2
C₁₁×#2169	2
C₁₁×#2168	2
D₄×C₁₁×C₁₆	2
C₁₁×#2164	2
C₁₁×#2162	2
C₁₁×#2108	2
C₄×C₁₁×M₃₂	2
#33483	11

Subgroups — C11×#33483 #14610676

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#33483 #14610676