Subgroups — C₁₁×#3475 #13066313

Order 1408.

1132 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#556	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁×#555	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#554	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#553	C₂	1	2	yes	maximal, complemented
5	C₁₁×#552	C₂	1	2	yes	maximal, complemented
6	C₁₁×#552	C₂	1	2	yes	maximal, complemented
7	C₁₁×#551	C₂	1	4	yes	maximal, complemented
8	C₁₁×#547	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁×#546	C₂	1	2	yes	maximal, complemented
10	C₁₁×#533	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₁×#529	C₂	1	4	yes	maximal, complemented
12	C₁₁×#529	C₂	1	2	yes	maximal, complemented
13	C₁₁×#525	C₂	1	2	yes	maximal, complemented
14	C₄×C₁₁×#41	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₁₁×#41	C₂	1	2	yes	maximal, complemented
16	C₂×C₄×D₄×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₁₁×#117	C₂	1	2	yes	maximal, complemented
18	C₂×C₁₁×#41	C₂²	1	1	yes	characteristic
19	C₂×C₁₁×#41	C₂²	1	2	yes	—
20	C₂²×D₄×C₁₁	C₂²	1	1	yes	characteristic
21	C₂³×C₄×C₁₁	C₂²	1	2	yes	—
22	C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
23	C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
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×#125	C₂²	1	4	yes	complemented
28	C₁₁×#125	C₂²	1	2	yes	complemented
29	C₁₁×#125	C₂²	1	2	yes	complemented
30	C₁₁×#124	C₂²	1	2	yes	—
31	C₁₁×#124	C₂²	1	4	yes	complemented
32	C₁₁×#123	C₂²	1	4	yes	—
33	C₁₁×#123	C₂²	1	4	yes	—
34	C₁₁×#123	C₂²	1	4	yes	complemented
35	C₁₁×#123	C₂²	1	4	yes	complemented
36	C₁₁×C₂²⋊Q₈	C₂²	1	2	yes	—
37	C₁₁×C₂²⋊Q₈	C₂²	1	2	yes	—
38	C₁₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
39	C₁₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
40	C₁₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
41	C₁₁×C₂²⋊Q₈	C₂²	1	4	yes	complemented
42	C₁₁×#121	C₂²	1	4	yes	—
43	C₁₁×#121	C₂²	1	2	yes	—
44	C₁₁×#121	C₂²	1	2	yes	complemented
45	C₁₁×#121	C₂²	1	2	yes	complemented
46	C₁₁×#120	C₂²	1	4	yes	—
47	C₄×Q₈×C₁₁	C₂²	1	2	yes	complemented
48	C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic, complemented
49	C₄×Q₈×C₁₁	C₂²	1	2	yes	complemented
50	C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic, complemented
51	C₄×Q₈×C₁₁	C₂²	1	2	yes	complemented
52	C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
53	C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
54	C₄×D₄×C₁₁	C₂²	1	2	yes	—
55	C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
56	C₄×D₄×C₁₁	C₂²	1	2	yes	—
57	C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
58	C₄×D₄×C₁₁	C₂²	1	2	yes	—
59	C₄×D₄×C₁₁	C₂²	1	2	yes	—
60	C₄×D₄×C₁₁	C₂²	1	2	yes	—
61	C₄×D₄×C₁₁	C₂²	1	4	yes	complemented
62	C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic, complemented
63	C₄×D₄×C₁₁	C₂²	1	4	yes	complemented
64	C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic, complemented
65	C₄×D₄×C₁₁	C₂²	1	4	yes	complemented
66	C₁₁×#117	C₂²	1	1	yes	characteristic
67	C₁₁×#117	C₂²	1	2	yes	—
68	C₁₁×#117	C₂²	1	4	yes	—
69	C₁₁×#117	C₂²	1	4	yes	complemented
70	C₁₁×#117	C₂²	1	2	yes	complemented
71	C₁₁×#117	C₂²	1	2	yes	complemented
72	C₁₁×#117	C₂²	1	2	yes	complemented
73	C₁₁×#117	C₂²	1	4	yes	complemented
74	C₁₁×#117	C₂²	1	2	yes	complemented
75	C₂×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
76	C₂×C₁₁×C₄⋊C₄	C₂²	1	2	yes	complemented
77	C₂×C₁₁×C₄⋊C₄	C₂²	1	2	yes	complemented
78	C₂×C₁₁×C₂²⋊C₄	C₂²	1	4	yes	—
79	C₂×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	—
80	C₂×C₄²×C₁₁	C₂²	1	1	yes	characteristic
81	C₂×C₄²×C₁₁	C₂²	1	4	yes	complemented
82	C₂×C₄²×C₁₁	C₂²	1	2	yes	complemented
83	C₂⁴×C₁₁	C₂³	1	2	yes	—
84	C₁₁×#41	—	2	8	no	—
85	C₁₁×#41	—	2	4	no	—
86	C₂×Q₈×C₁₁	C₂³	1	2	yes	—
87	C₂×Q₈×C₁₁	C₂³	1	1	yes	characteristic
88	C₂×Q₈×C₁₁	C₂³	1	2	yes	—
89	C₂×D₄×C₁₁	—	2	4	no	—
90	C₂×D₄×C₁₁	C₂³	1	2	yes	—
91	C₂×D₄×C₁₁	C₂³	1	2	yes	—
92	C₂×D₄×C₁₁	C₂³	1	1	yes	characteristic
93	C₂×D₄×C₁₁	C₂³	1	4	yes	—
94	C₂×D₄×C₁₁	C₂³	1	1	yes	characteristic
95	C₂×D₄×C₁₁	C₂³	1	4	yes	—
96	C₂×D₄×C₁₁	C₂³	1	1	yes	characteristic
97	C₂²×C₄×C₁₁	—	2	8	no	—
98	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
99	C₂²×C₄×C₁₁	C₂³	1	4	yes	—
100	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
101	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
102	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
103	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
104	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
105	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
106	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
107	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
108	C₂²×C₄×C₁₁	C₂³	1	4	yes	—
109	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
110	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
111	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
112	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
113	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
114	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
115	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
116	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
117	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
118	C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
119	C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
120	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
121	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
122	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
123	C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
124	C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
125	C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
126	C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
127	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
128	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
129	C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
130	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
131	C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
132	C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
133	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
134	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
135	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
136	C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
137	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
138	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
139	C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
140	C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
141	C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
142	C₄²×C₁₁	C₂³	1	1	yes	characteristic
143	C₄²×C₁₁	C₂³	1	1	yes	characteristic
144	C₄²×C₁₁	C₂³	1	4	yes	—
145	C₄²×C₁₁	C₂³	1	4	yes	—
146	C₄²×C₁₁	C₂³	1	2	yes	—
147	C₄²×C₁₁	C₂³	1	2	yes	—
148	C₄²×C₁₁	C₂³	1	1	yes	characteristic
149	C₄²×C₁₁	C₂³	1	1	yes	characteristic
150	C₄²×C₁₁	C₂³	1	2	yes	—
151	C₄²×C₁₁	C₂³	1	4	yes	—
152	#3475	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
153	C₂³×C₁₁	—	2	4	no	—
154	C₂³×C₁₁	—	2	4	no	—
155	C₂³×C₁₁	—	4	2	no	—
156	C₂³×C₁₁	C₂⁴	1	2	yes	—
157	C₂³×C₁₁	C₂⁴	1	2	yes	—
158	C₂³×C₁₁	C₂⁴	1	1	yes	characteristic
159	C₂³×C₁₁	C₂⁴	1	2	yes	—
160	Q₈×C₁₁	—	2	2	no	—
161	Q₈×C₁₁	—	2	4	no	—
162	Q₈×C₁₁	—	4	2	no	—
163	D₄×C₁₁	—	2	4	no	—
164	D₄×C₁₁	—	2	4	no	—
165	D₄×C₁₁	—	2	8	no	—
166	D₄×C₁₁	—	2	2	no	—
167	D₄×C₁₁	—	2	2	no	—
168	D₄×C₁₁	—	4	4	no	—
169	D₄×C₁₁	#41	1	4	yes	complemented
170	C₂×C₄×C₁₁	—	2	4	no	—
171	C₂×C₄×C₁₁	—	2	8	no	—
172	C₂×C₄×C₁₁	—	2	4	no	—
173	C₂×C₄×C₁₁	—	2	4	no	—
174	C₂×C₄×C₁₁	—	2	4	no	—
175	C₂×C₄×C₁₁	—	2	4	no	—
176	C₂×C₄×C₁₁	—	2	2	no	—
177	C₂×C₄×C₁₁	—	2	4	no	—
178	C₂×C₄×C₁₁	—	2	4	no	—
179	C₂×C₄×C₁₁	—	4	2	no	—
180	C₂×C₄×C₁₁	—	4	4	no	—
181	C₂×C₄×C₁₁	—	4	1	no	—
182	C₂×C₄×C₁₁	#41	1	4	yes	complemented
183	C₂×C₄×C₁₁	C₂⁴	1	2	yes	—
184	C₂×C₄×C₁₁	C₂⁴	1	2	yes	—
185	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
186	C₂×C₄×C₁₁	C₂⁴	1	2	yes	—
187	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
188	C₂×C₄×C₁₁	C₂⁴	1	4	yes	—
189	C₂×C₄×C₁₁	C₂⁴	1	2	yes	—
190	C₂×C₄×C₁₁	C₂⁴	1	4	yes	—
191	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
192	C₂×C₄×C₁₁	C₂⁴	1	2	yes	—
193	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
194	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
195	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
196	#556	C₂×C₁₁	1	1	yes	characteristic, complemented
197	#555	C₂×C₁₁	1	1	yes	characteristic, complemented
198	#554	C₂×C₁₁	1	1	yes	characteristic, complemented
199	#553	C₂×C₁₁	1	2	yes	complemented
200	#552	C₂×C₁₁	1	2	yes	complemented
201	#552	C₂×C₁₁	1	2	yes	complemented
202	#551	C₂×C₁₁	1	4	yes	complemented
203	#547	C₂×C₁₁	1	1	yes	characteristic, complemented
204	#546	C₂×C₁₁	1	2	yes	complemented
205	#533	C₂×C₁₁	1	1	yes	characteristic, complemented
206	#529	C₂×C₁₁	1	4	yes	complemented
207	#529	C₂×C₁₁	1	2	yes	complemented
208	#525	C₂×C₁₁	1	2	yes	complemented
209	C₄×#41	C₂×C₁₁	1	1	yes	characteristic, complemented
210	C₄×#41	C₂×C₁₁	1	2	yes	complemented
211	C₂×C₄×D₄	C₂×C₁₁	1	1	yes	characteristic, complemented
212	C₂×#117	C₂×C₁₁	1	2	yes	complemented
213	C₂²×C₁₁	—	2	2	no	—
214	C₂²×C₁₁	—	2	1	no	—
215	C₂²×C₁₁	—	2	2	no	—
216	C₂²×C₁₁	—	2	1	no	—
217	C₂²×C₁₁	—	2	2	no	—
218	C₂²×C₁₁	—	2	2	no	—
219	C₂²×C₁₁	—	2	2	no	—
220	C₂²×C₁₁	—	2	2	no	—
221	C₂²×C₁₁	—	2	2	no	—
222	C₂²×C₁₁	—	2	2	no	—
223	C₂²×C₁₁	—	4	8	no	—
224	C₂²×C₁₁	C₂×#41	1	2	yes	—
225	C₂²×C₁₁	C₂×#41	1	4	yes	—
226	C₂²×C₁₁	C₂⁵	1	1	yes	characteristic
227	C₄×C₁₁	—	2	2	no	—
228	C₄×C₁₁	—	2	2	no	—
229	C₄×C₁₁	—	2	2	no	—
230	C₄×C₁₁	—	2	1	no	—
231	C₄×C₁₁	—	2	4	no	—
232	C₄×C₁₁	—	2	2	no	—
233	C₄×C₁₁	—	2	1	no	—
234	C₄×C₁₁	—	2	2	no	—
235	C₄×C₁₁	—	2	4	no	—
236	C₄×C₁₁	—	2	1	no	—
237	C₄×C₁₁	C₂×#41	1	2	yes	—
238	C₄×C₁₁	C₂×#41	1	2	yes	—
239	C₄×C₁₁	C₂×#41	1	2	yes	—
240	C₂×#41	C₂²×C₁₁	1	1	yes	characteristic
241	C₂×#41	C₂²×C₁₁	1	2	yes	—
242	C₂²×D₄	C₂²×C₁₁	1	1	yes	characteristic
243	C₂³×C₄	C₂²×C₁₁	1	2	yes	—
244	C₄⋊Q₈	C₂²×C₁₁	1	1	yes	characteristic, complemented
245	C₄⋊Q₈	C₂²×C₁₁	1	1	yes	characteristic, complemented
246	#126	C₂²×C₁₁	1	4	yes	complemented
247	#126	C₂²×C₁₁	1	4	yes	complemented
248	#126	C₂²×C₁₁	1	4	yes	complemented
249	#125	C₂²×C₁₁	1	4	yes	complemented
250	#125	C₂²×C₁₁	1	2	yes	complemented
251	#125	C₂²×C₁₁	1	2	yes	complemented
252	#124	C₂²×C₁₁	1	2	yes	—
253	#124	C₂²×C₁₁	1	4	yes	complemented
254	#123	C₂²×C₁₁	1	4	yes	—
255	#123	C₂²×C₁₁	1	4	yes	—
256	#123	C₂²×C₁₁	1	4	yes	complemented
257	#123	C₂²×C₁₁	1	4	yes	complemented
258	C₂²⋊Q₈	C₂²×C₁₁	1	2	yes	—
259	C₂²⋊Q₈	C₂²×C₁₁	1	2	yes	—
260	C₂²⋊Q₈	C₂²×C₁₁	1	2	yes	complemented
261	C₂²⋊Q₈	C₂²×C₁₁	1	2	yes	complemented
262	C₂²⋊Q₈	C₂²×C₁₁	1	2	yes	complemented
263	C₂²⋊Q₈	C₂²×C₁₁	1	4	yes	complemented
264	#121	C₂²×C₁₁	1	4	yes	—
265	#121	C₂²×C₁₁	1	2	yes	—
266	#121	C₂²×C₁₁	1	2	yes	complemented
267	#121	C₂²×C₁₁	1	2	yes	complemented
268	#120	C₂²×C₁₁	1	4	yes	—
269	C₄×Q₈	C₂²×C₁₁	1	2	yes	complemented
270	C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic, complemented
271	C₄×Q₈	C₂²×C₁₁	1	2	yes	complemented
272	C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic, complemented
273	C₄×Q₈	C₂²×C₁₁	1	2	yes	complemented
274	C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic
275	C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic
276	C₄×D₄	C₂²×C₁₁	1	2	yes	—
277	C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic
278	C₄×D₄	C₂²×C₁₁	1	2	yes	—
279	C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic
280	C₄×D₄	C₂²×C₁₁	1	2	yes	—
281	C₄×D₄	C₂²×C₁₁	1	2	yes	—
282	C₄×D₄	C₂²×C₁₁	1	2	yes	—
283	C₄×D₄	C₂²×C₁₁	1	4	yes	complemented
284	C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic, complemented
285	C₄×D₄	C₂²×C₁₁	1	4	yes	complemented
286	C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic, complemented
287	C₄×D₄	C₂²×C₁₁	1	4	yes	complemented
288	#117	C₂²×C₁₁	1	1	yes	characteristic
289	#117	C₂²×C₁₁	1	2	yes	—
290	#117	C₂²×C₁₁	1	4	yes	—
291	#117	C₂²×C₁₁	1	4	yes	complemented
292	#117	C₂²×C₁₁	1	2	yes	complemented
293	#117	C₂²×C₁₁	1	2	yes	complemented
294	#117	C₂²×C₁₁	1	2	yes	complemented
295	#117	C₂²×C₁₁	1	4	yes	complemented
296	#117	C₂²×C₁₁	1	2	yes	complemented
297	C₂×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
298	C₂×C₄⋊C₄	C₂²×C₁₁	1	2	yes	complemented
299	C₂×C₄⋊C₄	C₂²×C₁₁	1	2	yes	complemented
300	C₂×C₂²⋊C₄	C₂²×C₁₁	1	4	yes	—
301	C₂×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	—
302	C₂×C₄²	C₂²×C₁₁	1	1	yes	characteristic
303	C₂×C₄²	C₂²×C₁₁	1	4	yes	complemented
304	C₂×C₄²	C₂²×C₁₁	1	2	yes	complemented
305	C₂×C₁₁	—	2	2	no	—
306	C₂×C₁₁	—	2	4	no	—
307	C₂×C₁₁	—	4	2	no	—
308	C₂×C₁₁	—	4	2	no	—
309	C₂×C₁₁	C₂²×#41	1	1	yes	characteristic
310	C₂×C₁₁	C₂²×#41	1	1	yes	characteristic
311	C₂×C₁₁	#585	1	1	yes	characteristic
312	C₂⁴	C₂³×C₁₁	1	2	yes	—
313	#41	—	2	8	no	—
314	#41	—	2	4	no	—
315	C₂×Q₈	C₂³×C₁₁	1	2	yes	—
316	C₂×Q₈	C₂³×C₁₁	1	1	yes	characteristic
317	C₂×Q₈	C₂³×C₁₁	1	2	yes	—
318	C₂×D₄	—	2	4	no	—
319	C₂×D₄	C₂³×C₁₁	1	2	yes	—
320	C₂×D₄	C₂³×C₁₁	1	2	yes	—
321	C₂×D₄	C₂³×C₁₁	1	1	yes	characteristic
322	C₂×D₄	C₂³×C₁₁	1	4	yes	—
323	C₂×D₄	C₂³×C₁₁	1	1	yes	characteristic
324	C₂×D₄	C₂³×C₁₁	1	4	yes	—
325	C₂×D₄	C₂³×C₁₁	1	1	yes	characteristic
326	C₂²×C₄	—	2	8	no	—
327	C₂²×C₄	C₂³×C₁₁	1	1	yes	characteristic
328	C₂²×C₄	C₂³×C₁₁	1	2	yes	—
329	C₂²×C₄	C₂³×C₁₁	1	4	yes	—
330	C₂²×C₄	C₂³×C₁₁	1	2	yes	—
331	C₂²×C₄	C₂³×C₁₁	1	2	yes	—
332	C₂²×C₄	C₂³×C₁₁	1	2	yes	—
333	C₂²×C₄	C₂³×C₁₁	1	2	yes	—
334	C₂²×C₄	C₂³×C₁₁	1	2	yes	—
335	C₂²×C₄	C₂³×C₁₁	1	2	yes	—
336	C₂²×C₄	C₂³×C₁₁	1	1	yes	characteristic
337	C₂²×C₄	C₂³×C₁₁	1	4	yes	—
338	C₂²×C₄	C₂³×C₁₁	1	2	yes	—
339	C₂²×C₄	C₂³×C₁₁	1	1	yes	characteristic
340	C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
341	C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
342	C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
343	C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
344	C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
345	C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
346	C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
347	C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
348	C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
349	C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
350	C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
351	C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
352	C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
353	C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
354	C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
355	C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
356	C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
357	C₂²⋊C₄	C₂³×C₁₁	1	2	yes	—
358	C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
359	C₂²⋊C₄	C₂³×C₁₁	1	2	yes	—
360	C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
361	C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
362	C₂²⋊C₄	C₂³×C₁₁	1	2	yes	—
363	C₂²⋊C₄	C₂³×C₁₁	1	2	yes	—
364	C₂²⋊C₄	C₂³×C₁₁	1	2	yes	—
365	C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
366	C₂²⋊C₄	C₂³×C₁₁	1	2	yes	—
367	C₂²⋊C₄	C₂³×C₁₁	1	2	yes	—
368	C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
369	C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
370	C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
371	C₄²	C₂³×C₁₁	1	1	yes	characteristic
372	C₄²	C₂³×C₁₁	1	1	yes	characteristic
373	C₄²	C₂³×C₁₁	1	1	yes	characteristic
374	C₄²	C₂³×C₁₁	1	1	yes	characteristic
375	C₄²	C₂³×C₁₁	1	2	yes	—
376	C₄²	C₂³×C₁₁	1	4	yes	—
377	C₄²	C₂³×C₁₁	1	4	yes	—
378	C₄²	C₂³×C₁₁	1	4	yes	—
379	C₄²	C₂³×C₁₁	1	2	yes	—
380	C₄²	C₂³×C₁₁	1	2	yes	—
381	C₁₁	#3475	1	1	yes	characteristic, direct product factor, Sylow
382	C₂³	—	2	4	no	—
383	C₂³	—	2	4	no	—
384	C₂³	—	4	2	no	—
385	C₂³	C₂⁴×C₁₁	1	2	yes	—
386	C₂³	C₂⁴×C₁₁	1	2	yes	—
387	C₂³	C₂⁴×C₁₁	1	1	yes	characteristic
388	C₂³	C₂⁴×C₁₁	1	2	yes	—
389	Q₈	—	2	2	no	—
390	Q₈	—	2	4	no	—
391	Q₈	—	4	2	no	—
392	D₄	—	2	4	no	—
393	D₄	—	2	4	no	—
394	D₄	—	2	8	no	—
395	D₄	—	2	2	no	—
396	D₄	—	2	2	no	—
397	D₄	—	4	4	no	—
398	D₄	C₁₁×#41	1	4	yes	complemented
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	2	8	no	—
401	C₂×C₄	—	2	4	no	—
402	C₂×C₄	—	2	4	no	—
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	4	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	C₁₁×#41	1	4	yes	complemented
412	C₂×C₄	C₂⁴×C₁₁	1	2	yes	—
413	C₂×C₄	C₂⁴×C₁₁	1	2	yes	—
414	C₂×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
415	C₂×C₄	C₂⁴×C₁₁	1	2	yes	—
416	C₂×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
417	C₂×C₄	C₂⁴×C₁₁	1	4	yes	—
418	C₂×C₄	C₂⁴×C₁₁	1	2	yes	—
419	C₂×C₄	C₂⁴×C₁₁	1	4	yes	—
420	C₂×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
421	C₂×C₄	C₂⁴×C₁₁	1	2	yes	—
422	C₂×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
423	C₂×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
424	C₂×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
425	C₂²	—	2	2	no	—
426	C₂²	—	2	1	no	—
427	C₂²	—	2	2	no	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	2	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	2	2	no	—
432	C₂²	—	2	2	no	—
433	C₂²	—	2	2	no	—
434	C₂²	—	2	2	no	—
435	C₂²	—	4	8	no	—
436	C₂²	C₂×C₁₁×#41	1	2	yes	—
437	C₂²	C₂×C₁₁×#41	1	4	yes	—
438	C₂²	C₂⁵×C₁₁	1	1	yes	characteristic
439	C₄	—	2	2	no	—
440	C₄	—	2	2	no	—
441	C₄	—	2	2	no	—
442	C₄	—	2	1	no	—
443	C₄	—	2	4	no	—
444	C₄	—	2	2	no	—
445	C₄	—	2	1	no	—
446	C₄	—	2	2	no	—
447	C₄	—	2	4	no	—
448	C₄	—	2	1	no	—
449	C₄	C₂×C₁₁×#41	1	2	yes	—
450	C₄	C₂×C₁₁×#41	1	2	yes	—
451	C₄	C₂×C₁₁×#41	1	2	yes	—
452	C₂	—	2	2	no	—
453	C₂	—	2	4	no	—
454	C₂	—	4	2	no	—
455	C₂	—	4	2	no	—
456	C₂	C₂²×C₁₁×#41	1	1	yes	characteristic
457	C₂	C₂²×C₁₁×#41	1	1	yes	characteristic
458	C₂	C₁₁×#585	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₁	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁵×C₁₁
socle	C₂²×C₁₁	C₂⁵
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₁×#556	C₂	semidirect
2. C₁₁×#555	C₂	semidirect
3. C₁₁×#554	C₂	semidirect
4. C₁₁×#553	C₂	semidirect
5. C₁₁×#552	C₂	semidirect
6. C₁₁×#552	C₂	semidirect
7. C₁₁×#551	C₂	semidirect
8. C₁₁×#547	C₂	semidirect
9. C₁₁×#546	C₂	semidirect
10. C₁₁×#533	C₂	semidirect
11. C₁₁×#529	C₂	semidirect
12. C₁₁×#529	C₂	semidirect
13. C₁₁×#525	C₂	semidirect
14. C₄×C₁₁×#41	C₂	semidirect
15. C₄×C₁₁×#41	C₂	semidirect
16. C₂×C₄×D₄×C₁₁	C₂	semidirect
17. C₂×C₁₁×#117	C₂	semidirect
22. C₁₁×C₄⋊Q₈	C₂²	semidirect
23. C₁₁×C₄⋊Q₈	C₂²	semidirect
24. C₁₁×#126	C₂²	semidirect
25. C₁₁×#126	C₂²	semidirect
26. C₁₁×#126	C₂²	semidirect
27. C₁₁×#125	C₂²	semidirect
28. C₁₁×#125	C₂²	semidirect
29. C₁₁×#125	C₂²	semidirect
31. C₁₁×#124	C₂²	semidirect
34. C₁₁×#123	C₂²	semidirect
35. C₁₁×#123	C₂²	semidirect
38. C₁₁×C₂²⋊Q₈	C₂²	semidirect
39. C₁₁×C₂²⋊Q₈	C₂²	semidirect
40. C₁₁×C₂²⋊Q₈	C₂²	semidirect
41. C₁₁×C₂²⋊Q₈	C₂²	semidirect
44. C₁₁×#121	C₂²	semidirect
45. C₁₁×#121	C₂²	semidirect
47. C₄×Q₈×C₁₁	C₂²	semidirect
48. C₄×Q₈×C₁₁	C₂²	semidirect
49. C₄×Q₈×C₁₁	C₂²	semidirect
50. C₄×Q₈×C₁₁	C₂²	semidirect
51. C₄×Q₈×C₁₁	C₂²	semidirect
61. C₄×D₄×C₁₁	C₂²	semidirect
62. C₄×D₄×C₁₁	C₂²	semidirect
63. C₄×D₄×C₁₁	C₂²	semidirect
64. C₄×D₄×C₁₁	C₂²	semidirect
65. 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. C₁₁×#117	C₂²	semidirect
76. C₂×C₁₁×C₄⋊C₄	C₂²	semidirect
77. C₂×C₁₁×C₄⋊C₄	C₂²	semidirect
81. C₂×C₄²×C₁₁	C₂²	semidirect
82. C₂×C₄²×C₁₁	C₂²	semidirect
152. #3475	C₁₁	direct (N × H)
169. D₄×C₁₁	#41	semidirect
182. C₂×C₄×C₁₁	#41	semidirect
196. #556	C₂×C₁₁	semidirect
197. #555	C₂×C₁₁	semidirect
198. #554	C₂×C₁₁	semidirect
199. #553	C₂×C₁₁	semidirect
200. #552	C₂×C₁₁	semidirect
201. #552	C₂×C₁₁	semidirect
202. #551	C₂×C₁₁	semidirect
203. #547	C₂×C₁₁	semidirect
204. #546	C₂×C₁₁	semidirect
205. #533	C₂×C₁₁	semidirect
206. #529	C₂×C₁₁	semidirect
207. #529	C₂×C₁₁	semidirect
208. #525	C₂×C₁₁	semidirect
209. C₄×#41	C₂×C₁₁	semidirect
210. C₄×#41	C₂×C₁₁	semidirect
211. C₂×C₄×D₄	C₂×C₁₁	semidirect
212. C₂×#117	C₂×C₁₁	semidirect
244. C₄⋊Q₈	C₂²×C₁₁	semidirect
245. C₄⋊Q₈	C₂²×C₁₁	semidirect
246. #126	C₂²×C₁₁	semidirect
247. #126	C₂²×C₁₁	semidirect
248. #126	C₂²×C₁₁	semidirect
249. #125	C₂²×C₁₁	semidirect
250. #125	C₂²×C₁₁	semidirect
251. #125	C₂²×C₁₁	semidirect
253. #124	C₂²×C₁₁	semidirect
256. #123	C₂²×C₁₁	semidirect
257. #123	C₂²×C₁₁	semidirect
260. C₂²⋊Q₈	C₂²×C₁₁	semidirect
261. C₂²⋊Q₈	C₂²×C₁₁	semidirect
262. C₂²⋊Q₈	C₂²×C₁₁	semidirect
263. C₂²⋊Q₈	C₂²×C₁₁	semidirect
266. #121	C₂²×C₁₁	semidirect
267. #121	C₂²×C₁₁	semidirect
269. C₄×Q₈	C₂²×C₁₁	semidirect
270. C₄×Q₈	C₂²×C₁₁	semidirect
271. C₄×Q₈	C₂²×C₁₁	semidirect
272. C₄×Q₈	C₂²×C₁₁	semidirect
273. C₄×Q₈	C₂²×C₁₁	semidirect
283. C₄×D₄	C₂²×C₁₁	semidirect
284. C₄×D₄	C₂²×C₁₁	semidirect
285. C₄×D₄	C₂²×C₁₁	semidirect
286. C₄×D₄	C₂²×C₁₁	semidirect
287. C₄×D₄	C₂²×C₁₁	semidirect
291. #117	C₂²×C₁₁	semidirect
292. #117	C₂²×C₁₁	semidirect
293. #117	C₂²×C₁₁	semidirect
294. #117	C₂²×C₁₁	semidirect
295. #117	C₂²×C₁₁	semidirect
296. #117	C₂²×C₁₁	semidirect
298. C₂×C₄⋊C₄	C₂²×C₁₁	semidirect
299. C₂×C₄⋊C₄	C₂²×C₁₁	semidirect
303. C₂×C₄²	C₂²×C₁₁	semidirect
304. C₂×C₄²	C₂²×C₁₁	semidirect
381. C₁₁	#3475	direct (N × H)
398. D₄	C₁₁×#41	semidirect
411. C₂×C₄	C₁₁×#41	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×#556	2
C₁₁×#555	2
C₁₁×#554	2
C₁₁×#553	2
C₁₁×#552	2
C₁₁×#551	2
C₁₁×#547	2
C₁₁×#546	2
C₁₁×#533	2
C₁₁×#529	2
C₁₁×#525	2
C₄×C₁₁×#41	2
C₂×C₄×D₄×C₁₁	2
C₂×C₁₁×#117	2
#3475	11

Subgroups — C11×#3475 #13066313

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#3475 #13066313