Subgroups — C₁₁×#3540 #13066378

Order 1408.

1058 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×H(3,𝔽₄)	C₂	1	2	yes	maximal, complemented
2	C₁₁×#560	C₂	1	2	yes	maximal, complemented
3	C₁₁×#559	C₂	1	2	yes	maximal, complemented
4	C₁₁×#556	C₂	1	2	yes	maximal, complemented
5	C₁₁×#555	C₂	1	2	yes	maximal, complemented
6	C₁₁×#551	C₂	1	2	yes	maximal, complemented
7	C₁₁×#548	C₂	1	2	yes	maximal, complemented
8	C₁₁×#546	C₂	1	2	yes	maximal, complemented
9	C₁₁×#542	C₂	1	2	yes	maximal, complemented
10	C₁₁×#542	C₂	1	4	yes	maximal, complemented
11	C₁₁×#538	C₂	1	4	yes	maximal, complemented
12	C₁₁×#536	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₁×#535	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₁×#525	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₁×#525	C₂	1	2	yes	maximal, complemented
16	C₂×C₁₁×#41	C₂²	1	1	yes	characteristic
17	C₂×C₁₁×#41	C₂²	1	2	yes	—
18	C₂²×Q₈×C₁₁	C₂²	1	1	yes	characteristic, complemented
19	C₂²×D₄×C₁₁	C₂²	1	1	yes	characteristic, complemented
20	C₂³×C₄×C₁₁	C₂²	1	1	yes	characteristic, complemented
21	C₁₁×C₄⋊Q₈	C₂²	1	2	yes	complemented
22	C₁₁×C₄⋊Q₈	C₂²	1	2	yes	complemented
23	C₁₁×#127	C₂²	1	2	yes	—
24	C₁₁×#126	C₂²	1	4	yes	complemented
25	C₁₁×#126	C₂²	1	4	yes	complemented
26	C₁₁×#126	C₂²	1	4	yes	complemented
27	C₁₁×#124	C₂²	1	2	yes	—
28	C₁₁×#124	C₂²	1	4	yes	—
29	C₁₁×#124	C₂²	1	2	yes	complemented
30	C₁₁×#124	C₂²	1	4	yes	complemented
31	C₁₁×#124	C₂²	1	2	yes	complemented
32	C₁₁×#124	C₂²	1	4	yes	complemented
33	C₁₁×#124	C₂²	1	4	yes	complemented
34	C₁₁×#124	C₂²	1	4	yes	complemented
35	C₁₁×#123	C₂²	1	1	yes	characteristic
36	C₁₁×#123	C₂²	1	4	yes	complemented
37	C₁₁×#123	C₂²	1	1	yes	characteristic, complemented
38	C₁₁×#123	C₂²	1	2	yes	complemented
39	C₁₁×#123	C₂²	1	2	yes	complemented
40	C₁₁×#123	C₂²	1	4	yes	complemented
41	C₁₁×#123	C₂²	1	4	yes	complemented
42	C₁₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
43	C₁₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
44	C₁₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
45	C₁₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
46	C₁₁×C₂²⋊Q₈	C₂²	1	4	yes	complemented
47	C₁₁×C₂²⋊Q₈	C₂²	1	4	yes	complemented
48	C₁₁×#121	C₂²	1	2	yes	—
49	C₁₁×#121	C₂²	1	2	yes	—
50	C₁₁×#121	C₂²	1	2	yes	—
51	C₁₁×#121	C₂²	1	4	yes	—
52	C₁₁×#121	C₂²	1	2	yes	complemented
53	C₁₁×#121	C₂²	1	4	yes	complemented
54	C₁₁×#121	C₂²	1	4	yes	complemented
55	C₁₁×#120	C₂²	1	1	yes	characteristic
56	C₁₁×#120	C₂²	1	2	yes	—
57	C₁₁×#120	C₂²	1	4	yes	—
58	C₁₁×#120	C₂²	1	1	yes	characteristic, complemented
59	C₁₁×#120	C₂²	1	4	yes	complemented
60	C₁₁×#120	C₂²	1	2	yes	complemented
61	C₄×Q₈×C₁₁	C₂²	1	2	yes	complemented
62	C₄×Q₈×C₁₁	C₂²	1	4	yes	complemented
63	C₄×D₄×C₁₁	C₂²	1	2	yes	—
64	C₄×D₄×C₁₁	C₂²	1	4	yes	complemented
65	C₄×D₄×C₁₁	C₂²	1	2	yes	complemented
66	C₄×D₄×C₁₁	C₂²	1	4	yes	complemented
67	C₄×D₄×C₁₁	C₂²	1	4	yes	complemented
68	C₄×D₄×C₁₁	C₂²	1	2	yes	complemented
69	C₁₁×#117	C₂²	1	1	yes	characteristic, complemented
70	C₁₁×#117	C₂²	1	2	yes	complemented
71	C₁₁×#117	C₂²	1	1	yes	characteristic, complemented
72	C₁₁×#117	C₂²	1	1	yes	characteristic, complemented
73	C₁₁×#117	C₂²	1	4	yes	complemented
74	C₂×C₁₁×C₂²⋊C₄	C₂²	1	4	yes	complemented
75	C₂⁴×C₁₁	C₂³	1	2	yes	—
76	C₂⁴×C₁₁	C₂³	1	1	yes	characteristic
77	C₁₁×#41	—	4	2	no	—
78	C₁₁×#41	—	4	4	no	—
79	C₂×Q₈×C₁₁	—	4	2	no	—
80	C₂×Q₈×C₁₁	C₂³	1	2	yes	—
81	C₂×Q₈×C₁₁	C₂³	1	4	yes	—
82	C₂×Q₈×C₁₁	C₂³	1	2	yes	—
83	C₂×Q₈×C₁₁	C₂³	1	1	yes	characteristic
84	C₂×D₄×C₁₁	—	4	2	no	—
85	C₂×D₄×C₁₁	C₂³	1	2	yes	—
86	C₂×D₄×C₁₁	C₂³	1	2	yes	—
87	C₂×D₄×C₁₁	C₂³	1	4	yes	—
88	C₂×D₄×C₁₁	C₂³	1	4	yes	—
89	C₂×D₄×C₁₁	C₂³	1	2	yes	—
90	C₂×D₄×C₁₁	C₂³	1	4	yes	—
91	C₂×D₄×C₁₁	C₂³	1	1	yes	characteristic
92	C₂×D₄×C₁₁	C₂³	1	4	yes	—
93	C₂×D₄×C₁₁	C₂³	1	1	yes	characteristic
94	C₂×D₄×C₁₁	C₂³	1	1	yes	characteristic
95	C₂×D₄×C₁₁	C₂³	1	2	yes	—
96	C₂²×C₄×C₁₁	—	4	2	no	—
97	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
98	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
99	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
100	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
101	C₂²×C₄×C₁₁	C₂³	1	4	yes	—
102	C₂²×C₄×C₁₁	C₂³	1	4	yes	—
103	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
104	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
105	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
106	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
107	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
108	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
109	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
110	C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
111	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
112	C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
113	C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
114	C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
115	C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
116	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
117	C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
118	C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
119	C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
120	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
121	C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
122	C₁₁×C₂²⋊C₄	C₂³	1	1	yes	characteristic
123	C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
124	C₁₁×C₂²⋊C₄	C₂³	1	1	yes	characteristic
125	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
126	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
127	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
128	C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
129	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
130	C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
131	C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
132	C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
133	C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
134	C₄²×C₁₁	C₂³	1	2	yes	—
135	C₄²×C₁₁	C₂³	1	4	yes	—
136	C₄²×C₁₁	C₂³	1	2	yes	—
137	C₄²×C₁₁	C₂³	1	2	yes	—
138	C₄²×C₁₁	C₂³	1	4	yes	—
139	#3540	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
140	C₂³×C₁₁	—	4	1	no	—
141	C₂³×C₁₁	—	4	2	no	—
142	C₂³×C₁₁	—	4	2	no	—
143	C₂³×C₁₁	—	4	4	no	—
144	C₂³×C₁₁	C₂⁴	1	1	yes	characteristic
145	C₂³×C₁₁	C₂⁴	1	1	yes	characteristic
146	C₂³×C₁₁	C₂⁴	1	2	yes	—
147	C₂³×C₁₁	C₂⁴	1	4	yes	—
148	C₂³×C₁₁	C₂⁴	1	1	yes	characteristic
149	Q₈×C₁₁	—	2	4	no	—
150	Q₈×C₁₁	—	4	2	no	—
151	Q₈×C₁₁	—	4	4	no	—
152	Q₈×C₁₁	—	4	1	no	—
153	D₄×C₁₁	—	2	4	no	—
154	D₄×C₁₁	—	4	2	no	—
155	D₄×C₁₁	—	4	2	no	—
156	D₄×C₁₁	—	4	4	no	—
157	D₄×C₁₁	—	4	4	no	—
158	D₄×C₁₁	—	4	4	no	—
159	D₄×C₁₁	—	4	2	no	—
160	D₄×C₁₁	—	4	1	no	—
161	D₄×C₁₁	—	4	1	no	—
162	D₄×C₁₁	—	4	1	no	—
163	D₄×C₁₁	—	4	4	no	—
164	C₂×C₄×C₁₁	—	2	4	no	—
165	C₂×C₄×C₁₁	—	2	2	no	—
166	C₂×C₄×C₁₁	—	2	2	no	—
167	C₂×C₄×C₁₁	—	2	2	no	—
168	C₂×C₄×C₁₁	—	4	1	no	—
169	C₂×C₄×C₁₁	—	4	2	no	—
170	C₂×C₄×C₁₁	—	4	4	no	—
171	C₂×C₄×C₁₁	—	4	2	no	—
172	C₂×C₄×C₁₁	—	4	4	no	—
173	C₂×C₄×C₁₁	C₂⁴	1	2	yes	—
174	C₂×C₄×C₁₁	C₂⁴	1	4	yes	—
175	C₂×C₄×C₁₁	C₂⁴	1	4	yes	—
176	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
177	C₂×C₄×C₁₁	C₂⁴	1	2	yes	—
178	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
179	C₂×C₄×C₁₁	C₂⁴	1	2	yes	—
180	C₂×C₄×C₁₁	C₂⁴	1	4	yes	—
181	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
182	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
183	H(3,𝔽₄)	C₂×C₁₁	1	2	yes	complemented
184	#560	C₂×C₁₁	1	2	yes	complemented
185	#559	C₂×C₁₁	1	2	yes	complemented
186	#556	C₂×C₁₁	1	2	yes	complemented
187	#555	C₂×C₁₁	1	2	yes	complemented
188	#551	C₂×C₁₁	1	2	yes	complemented
189	#548	C₂×C₁₁	1	2	yes	complemented
190	#546	C₂×C₁₁	1	2	yes	complemented
191	#542	C₂×C₁₁	1	2	yes	complemented
192	#542	C₂×C₁₁	1	4	yes	complemented
193	#538	C₂×C₁₁	1	4	yes	complemented
194	#536	C₂×C₁₁	1	1	yes	characteristic, complemented
195	#535	C₂×C₁₁	1	1	yes	characteristic, complemented
196	#525	C₂×C₁₁	1	1	yes	characteristic, complemented
197	#525	C₂×C₁₁	1	2	yes	complemented
198	C₂²×C₁₁	—	2	1	no	—
199	C₂²×C₁₁	—	2	2	no	—
200	C₂²×C₁₁	—	2	1	no	—
201	C₂²×C₁₁	—	2	1	no	—
202	C₂²×C₁₁	—	2	4	no	—
203	C₂²×C₁₁	—	2	4	no	—
204	C₂²×C₁₁	—	2	2	no	—
205	C₂²×C₁₁	—	2	2	no	—
206	C₂²×C₁₁	—	2	2	no	—
207	C₂²×C₁₁	—	2	2	no	—
208	C₂²×C₁₁	—	2	4	no	—
209	C₂²×C₁₁	—	2	2	no	—
210	C₂²×C₁₁	—	4	4	no	—
211	C₂²×C₁₁	—	8	4	no	—
212	C₂²×C₁₁	C₂⁵	1	1	yes	characteristic
213	C₄×C₁₁	—	2	2	no	—
214	C₄×C₁₁	—	2	1	no	—
215	C₄×C₁₁	—	2	1	no	—
216	C₄×C₁₁	—	2	1	no	—
217	C₄×C₁₁	—	2	4	no	—
218	C₄×C₁₁	—	2	2	no	—
219	C₄×C₁₁	—	2	4	no	—
220	C₄×C₁₁	—	2	4	no	—
221	C₄×C₁₁	—	2	2	no	—
222	C₄×C₁₁	H(5,𝔽₂)	1	2	yes	—
223	C₂×#41	C₂²×C₁₁	1	1	yes	characteristic
224	C₂×#41	C₂²×C₁₁	1	2	yes	—
225	C₂²×Q₈	C₂²×C₁₁	1	1	yes	characteristic, complemented
226	C₂²×D₄	C₂²×C₁₁	1	1	yes	characteristic, complemented
227	C₂³×C₄	C₂²×C₁₁	1	1	yes	characteristic, complemented
228	C₄⋊Q₈	C₂²×C₁₁	1	2	yes	complemented
229	C₄⋊Q₈	C₂²×C₁₁	1	2	yes	complemented
230	#127	C₂²×C₁₁	1	2	yes	—
231	#126	C₂²×C₁₁	1	4	yes	complemented
232	#126	C₂²×C₁₁	1	4	yes	complemented
233	#126	C₂²×C₁₁	1	4	yes	complemented
234	#124	C₂²×C₁₁	1	2	yes	—
235	#124	C₂²×C₁₁	1	4	yes	—
236	#124	C₂²×C₁₁	1	2	yes	complemented
237	#124	C₂²×C₁₁	1	4	yes	complemented
238	#124	C₂²×C₁₁	1	2	yes	complemented
239	#124	C₂²×C₁₁	1	4	yes	complemented
240	#124	C₂²×C₁₁	1	4	yes	complemented
241	#124	C₂²×C₁₁	1	4	yes	complemented
242	#123	C₂²×C₁₁	1	1	yes	characteristic
243	#123	C₂²×C₁₁	1	4	yes	complemented
244	#123	C₂²×C₁₁	1	1	yes	characteristic, complemented
245	#123	C₂²×C₁₁	1	2	yes	complemented
246	#123	C₂²×C₁₁	1	2	yes	complemented
247	#123	C₂²×C₁₁	1	4	yes	complemented
248	#123	C₂²×C₁₁	1	4	yes	complemented
249	C₂²⋊Q₈	C₂²×C₁₁	1	2	yes	complemented
250	C₂²⋊Q₈	C₂²×C₁₁	1	2	yes	complemented
251	C₂²⋊Q₈	C₂²×C₁₁	1	2	yes	complemented
252	C₂²⋊Q₈	C₂²×C₁₁	1	2	yes	complemented
253	C₂²⋊Q₈	C₂²×C₁₁	1	4	yes	complemented
254	C₂²⋊Q₈	C₂²×C₁₁	1	4	yes	complemented
255	#121	C₂²×C₁₁	1	2	yes	—
256	#121	C₂²×C₁₁	1	2	yes	—
257	#121	C₂²×C₁₁	1	2	yes	—
258	#121	C₂²×C₁₁	1	4	yes	—
259	#121	C₂²×C₁₁	1	2	yes	complemented
260	#121	C₂²×C₁₁	1	4	yes	complemented
261	#121	C₂²×C₁₁	1	4	yes	complemented
262	#120	C₂²×C₁₁	1	1	yes	characteristic
263	#120	C₂²×C₁₁	1	2	yes	—
264	#120	C₂²×C₁₁	1	4	yes	—
265	#120	C₂²×C₁₁	1	1	yes	characteristic, complemented
266	#120	C₂²×C₁₁	1	4	yes	complemented
267	#120	C₂²×C₁₁	1	2	yes	complemented
268	C₄×Q₈	C₂²×C₁₁	1	2	yes	complemented
269	C₄×Q₈	C₂²×C₁₁	1	4	yes	complemented
270	C₄×D₄	C₂²×C₁₁	1	2	yes	—
271	C₄×D₄	C₂²×C₁₁	1	4	yes	complemented
272	C₄×D₄	C₂²×C₁₁	1	2	yes	complemented
273	C₄×D₄	C₂²×C₁₁	1	4	yes	complemented
274	C₄×D₄	C₂²×C₁₁	1	4	yes	complemented
275	C₄×D₄	C₂²×C₁₁	1	2	yes	complemented
276	#117	C₂²×C₁₁	1	1	yes	characteristic, complemented
277	#117	C₂²×C₁₁	1	2	yes	complemented
278	#117	C₂²×C₁₁	1	1	yes	characteristic, complemented
279	#117	C₂²×C₁₁	1	1	yes	characteristic, complemented
280	#117	C₂²×C₁₁	1	4	yes	complemented
281	C₂×C₂²⋊C₄	C₂²×C₁₁	1	4	yes	complemented
282	C₂×C₁₁	—	4	1	no	—
283	C₂×C₁₁	—	4	2	no	—
284	C₂×C₁₁	—	4	1	no	—
285	C₂×C₁₁	—	4	4	no	—
286	C₂×C₁₁	—	4	1	no	—
287	C₂×C₁₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
288	C₂×C₁₁	#585	1	2	yes	—
289	C₂⁴	C₂³×C₁₁	1	2	yes	—
290	C₂⁴	C₂³×C₁₁	1	1	yes	characteristic
291	#41	—	4	2	no	—
292	#41	—	4	4	no	—
293	C₂×Q₈	—	4	2	no	—
294	C₂×Q₈	C₂³×C₁₁	1	2	yes	—
295	C₂×Q₈	C₂³×C₁₁	1	4	yes	—
296	C₂×Q₈	C₂³×C₁₁	1	2	yes	—
297	C₂×Q₈	C₂³×C₁₁	1	1	yes	characteristic
298	C₂×D₄	—	4	2	no	—
299	C₂×D₄	C₂³×C₁₁	1	2	yes	—
300	C₂×D₄	C₂³×C₁₁	1	2	yes	—
301	C₂×D₄	C₂³×C₁₁	1	4	yes	—
302	C₂×D₄	C₂³×C₁₁	1	4	yes	—
303	C₂×D₄	C₂³×C₁₁	1	2	yes	—
304	C₂×D₄	C₂³×C₁₁	1	4	yes	—
305	C₂×D₄	C₂³×C₁₁	1	1	yes	characteristic
306	C₂×D₄	C₂³×C₁₁	1	4	yes	—
307	C₂×D₄	C₂³×C₁₁	1	1	yes	characteristic
308	C₂×D₄	C₂³×C₁₁	1	1	yes	characteristic
309	C₂×D₄	C₂³×C₁₁	1	2	yes	—
310	C₂²×C₄	—	4	2	no	—
311	C₂²×C₄	C₂³×C₁₁	1	1	yes	characteristic
312	C₂²×C₄	C₂³×C₁₁	1	2	yes	—
313	C₂²×C₄	C₂³×C₁₁	1	1	yes	characteristic
314	C₂²×C₄	C₂³×C₁₁	1	1	yes	characteristic
315	C₂²×C₄	C₂³×C₁₁	1	4	yes	—
316	C₂²×C₄	C₂³×C₁₁	1	4	yes	—
317	C₂²×C₄	C₂³×C₁₁	1	1	yes	characteristic
318	C₂²×C₄	C₂³×C₁₁	1	2	yes	—
319	C₂²×C₄	C₂³×C₁₁	1	2	yes	—
320	C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
321	C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
322	C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
323	C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
324	C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
325	C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
326	C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
327	C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
328	C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
329	C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
330	C₂²⋊C₄	C₂³×C₁₁	1	2	yes	—
331	C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
332	C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
333	C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
334	C₂²⋊C₄	C₂³×C₁₁	1	2	yes	—
335	C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
336	C₂²⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
337	C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
338	C₂²⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
339	C₂²⋊C₄	C₂³×C₁₁	1	2	yes	—
340	C₂²⋊C₄	C₂³×C₁₁	1	2	yes	—
341	C₂²⋊C₄	C₂³×C₁₁	1	2	yes	—
342	C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
343	C₂²⋊C₄	C₂³×C₁₁	1	2	yes	—
344	C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
345	C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
346	C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
347	C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
348	C₄²	C₂³×C₁₁	1	2	yes	—
349	C₄²	C₂³×C₁₁	1	4	yes	—
350	C₄²	C₂³×C₁₁	1	2	yes	—
351	C₄²	C₂³×C₁₁	1	2	yes	—
352	C₄²	C₂³×C₁₁	1	4	yes	—
353	C₁₁	#3540	1	1	yes	characteristic, direct product factor, Sylow
354	C₂³	—	4	1	no	—
355	C₂³	—	4	2	no	—
356	C₂³	—	4	2	no	—
357	C₂³	—	4	4	no	—
358	C₂³	C₂⁴×C₁₁	1	1	yes	characteristic
359	C₂³	C₂⁴×C₁₁	1	1	yes	characteristic
360	C₂³	C₂⁴×C₁₁	1	2	yes	—
361	C₂³	C₂⁴×C₁₁	1	4	yes	—
362	C₂³	C₂⁴×C₁₁	1	1	yes	characteristic
363	Q₈	—	2	4	no	—
364	Q₈	—	4	2	no	—
365	Q₈	—	4	4	no	—
366	Q₈	—	4	1	no	—
367	D₄	—	2	4	no	—
368	D₄	—	4	2	no	—
369	D₄	—	4	2	no	—
370	D₄	—	4	4	no	—
371	D₄	—	4	4	no	—
372	D₄	—	4	4	no	—
373	D₄	—	4	2	no	—
374	D₄	—	4	1	no	—
375	D₄	—	4	1	no	—
376	D₄	—	4	1	no	—
377	D₄	—	4	4	no	—
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	4	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	4	no	—
387	C₂×C₄	C₂⁴×C₁₁	1	2	yes	—
388	C₂×C₄	C₂⁴×C₁₁	1	4	yes	—
389	C₂×C₄	C₂⁴×C₁₁	1	4	yes	—
390	C₂×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
391	C₂×C₄	C₂⁴×C₁₁	1	2	yes	—
392	C₂×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
393	C₂×C₄	C₂⁴×C₁₁	1	2	yes	—
394	C₂×C₄	C₂⁴×C₁₁	1	4	yes	—
395	C₂×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
396	C₂×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
397	C₂²	—	2	1	no	—
398	C₂²	—	2	2	no	—
399	C₂²	—	2	1	no	—
400	C₂²	—	2	1	no	—
401	C₂²	—	2	4	no	—
402	C₂²	—	2	4	no	—
403	C₂²	—	2	2	no	—
404	C₂²	—	2	2	no	—
405	C₂²	—	2	2	no	—
406	C₂²	—	2	2	no	—
407	C₂²	—	2	4	no	—
408	C₂²	—	2	2	no	—
409	C₂²	—	4	4	no	—
410	C₂²	—	8	4	no	—
411	C₂²	C₂⁵×C₁₁	1	1	yes	characteristic
412	C₄	—	2	2	no	—
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	2	1	no	—
416	C₄	—	2	4	no	—
417	C₄	—	2	2	no	—
418	C₄	—	2	4	no	—
419	C₄	—	2	4	no	—
420	C₄	—	2	2	no	—
421	C₄	C₁₁×H(5,𝔽₂)	1	2	yes	—
422	C₂	—	4	2	no	—
423	C₂	—	4	1	no	—
424	C₂	—	4	1	no	—
425	C₂	—	4	4	no	—
426	C₂	—	4	1	no	—
427	C₂	C₂×C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
428	C₂	C₁₁×#585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₁₁
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₁×H(3,𝔽₄)	C₂	semidirect
2. C₁₁×#560	C₂	semidirect
3. C₁₁×#559	C₂	semidirect
4. C₁₁×#556	C₂	semidirect
5. C₁₁×#555	C₂	semidirect
6. C₁₁×#551	C₂	semidirect
7. C₁₁×#548	C₂	semidirect
8. C₁₁×#546	C₂	semidirect
9. C₁₁×#542	C₂	semidirect
10. C₁₁×#542	C₂	semidirect
11. C₁₁×#538	C₂	semidirect
12. C₁₁×#536	C₂	semidirect
13. C₁₁×#535	C₂	semidirect
14. C₁₁×#525	C₂	semidirect
15. C₁₁×#525	C₂	semidirect
18. C₂²×Q₈×C₁₁	C₂²	semidirect
19. C₂²×D₄×C₁₁	C₂²	semidirect
20. C₂³×C₄×C₁₁	C₂²	semidirect
21. C₁₁×C₄⋊Q₈	C₂²	semidirect
22. C₁₁×C₄⋊Q₈	C₂²	semidirect
24. C₁₁×#126	C₂²	semidirect
25. C₁₁×#126	C₂²	semidirect
26. C₁₁×#126	C₂²	semidirect
29. C₁₁×#124	C₂²	semidirect
30. C₁₁×#124	C₂²	semidirect
31. C₁₁×#124	C₂²	semidirect
32. C₁₁×#124	C₂²	semidirect
33. C₁₁×#124	C₂²	semidirect
34. C₁₁×#124	C₂²	semidirect
36. C₁₁×#123	C₂²	semidirect
37. C₁₁×#123	C₂²	semidirect
38. C₁₁×#123	C₂²	semidirect
39. C₁₁×#123	C₂²	semidirect
40. C₁₁×#123	C₂²	semidirect
41. C₁₁×#123	C₂²	semidirect
42. C₁₁×C₂²⋊Q₈	C₂²	semidirect
43. C₁₁×C₂²⋊Q₈	C₂²	semidirect
44. C₁₁×C₂²⋊Q₈	C₂²	semidirect
45. C₁₁×C₂²⋊Q₈	C₂²	semidirect
46. C₁₁×C₂²⋊Q₈	C₂²	semidirect
47. C₁₁×C₂²⋊Q₈	C₂²	semidirect
52. C₁₁×#121	C₂²	semidirect
53. C₁₁×#121	C₂²	semidirect
54. C₁₁×#121	C₂²	semidirect
58. C₁₁×#120	C₂²	semidirect
59. C₁₁×#120	C₂²	semidirect
60. C₁₁×#120	C₂²	semidirect
61. C₄×Q₈×C₁₁	C₂²	semidirect
62. C₄×Q₈×C₁₁	C₂²	semidirect
64. C₄×D₄×C₁₁	C₂²	semidirect
65. C₄×D₄×C₁₁	C₂²	semidirect
66. C₄×D₄×C₁₁	C₂²	semidirect
67. C₄×D₄×C₁₁	C₂²	semidirect
68. C₄×D₄×C₁₁	C₂²	semidirect
69. C₁₁×#117	C₂²	semidirect
70. C₁₁×#117	C₂²	semidirect
71. C₁₁×#117	C₂²	semidirect
72. C₁₁×#117	C₂²	semidirect
73. C₁₁×#117	C₂²	semidirect
74. C₂×C₁₁×C₂²⋊C₄	C₂²	semidirect
139. #3540	C₁₁	direct (N × H)
183. H(3,𝔽₄)	C₂×C₁₁	semidirect
184. #560	C₂×C₁₁	semidirect
185. #559	C₂×C₁₁	semidirect
186. #556	C₂×C₁₁	semidirect
187. #555	C₂×C₁₁	semidirect
188. #551	C₂×C₁₁	semidirect
189. #548	C₂×C₁₁	semidirect
190. #546	C₂×C₁₁	semidirect
191. #542	C₂×C₁₁	semidirect
192. #542	C₂×C₁₁	semidirect
193. #538	C₂×C₁₁	semidirect
194. #536	C₂×C₁₁	semidirect
195. #535	C₂×C₁₁	semidirect
196. #525	C₂×C₁₁	semidirect
197. #525	C₂×C₁₁	semidirect
225. C₂²×Q₈	C₂²×C₁₁	semidirect
226. C₂²×D₄	C₂²×C₁₁	semidirect
227. C₂³×C₄	C₂²×C₁₁	semidirect
228. C₄⋊Q₈	C₂²×C₁₁	semidirect
229. C₄⋊Q₈	C₂²×C₁₁	semidirect
231. #126	C₂²×C₁₁	semidirect
232. #126	C₂²×C₁₁	semidirect
233. #126	C₂²×C₁₁	semidirect
236. #124	C₂²×C₁₁	semidirect
237. #124	C₂²×C₁₁	semidirect
238. #124	C₂²×C₁₁	semidirect
239. #124	C₂²×C₁₁	semidirect
240. #124	C₂²×C₁₁	semidirect
241. #124	C₂²×C₁₁	semidirect
243. #123	C₂²×C₁₁	semidirect
244. #123	C₂²×C₁₁	semidirect
245. #123	C₂²×C₁₁	semidirect
246. #123	C₂²×C₁₁	semidirect
247. #123	C₂²×C₁₁	semidirect
248. #123	C₂²×C₁₁	semidirect
249. C₂²⋊Q₈	C₂²×C₁₁	semidirect
250. C₂²⋊Q₈	C₂²×C₁₁	semidirect
251. C₂²⋊Q₈	C₂²×C₁₁	semidirect
252. C₂²⋊Q₈	C₂²×C₁₁	semidirect
253. C₂²⋊Q₈	C₂²×C₁₁	semidirect
254. C₂²⋊Q₈	C₂²×C₁₁	semidirect
259. #121	C₂²×C₁₁	semidirect
260. #121	C₂²×C₁₁	semidirect
261. #121	C₂²×C₁₁	semidirect
265. #120	C₂²×C₁₁	semidirect
266. #120	C₂²×C₁₁	semidirect
267. #120	C₂²×C₁₁	semidirect
268. C₄×Q₈	C₂²×C₁₁	semidirect
269. C₄×Q₈	C₂²×C₁₁	semidirect
271. C₄×D₄	C₂²×C₁₁	semidirect
272. C₄×D₄	C₂²×C₁₁	semidirect
273. C₄×D₄	C₂²×C₁₁	semidirect
274. C₄×D₄	C₂²×C₁₁	semidirect
275. C₄×D₄	C₂²×C₁₁	semidirect
276. #117	C₂²×C₁₁	semidirect
277. #117	C₂²×C₁₁	semidirect
278. #117	C₂²×C₁₁	semidirect
279. #117	C₂²×C₁₁	semidirect
280. #117	C₂²×C₁₁	semidirect
281. C₂×C₂²⋊C₄	C₂²×C₁₁	semidirect
353. C₁₁	#3540	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×H(3,𝔽₄)	2
C₁₁×#560	2
C₁₁×#559	2
C₁₁×#556	2
C₁₁×#555	2
C₁₁×#551	2
C₁₁×#548	2
C₁₁×#546	2
C₁₁×#542	2
C₁₁×#538	2
C₁₁×#536	2
C₁₁×#535	2
C₁₁×#525	2
#3540	11

Subgroups — C11×#3540 #13066378

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#3540 #13066378