Subgroups — C₁₁×#23248 #14600441

Order 2816.

716 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₁×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#1985	C₂	1	2	yes	maximal
3	C₁₁×#1984	C₂	1	2	yes	maximal
4	C₁₁×#1940	C₂	1	2	yes	maximal
5	C₁₁×#1939	C₂	1	1	yes	maximal, characteristic
6	C₁₁×#1939	C₂	1	1	yes	maximal, characteristic
7	C₁₁×#1771	C₂	1	2	yes	maximal
8	C₁₁×#1770	C₂	1	1	yes	maximal, characteristic
9	C₈×C₁₁×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
10	C₁₁×#1767	C₂	1	1	yes	maximal, characteristic
11	C₄×C₁₁×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₁×C₄⋊Q₈	C₄	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₁₁	C₂²	1	2	yes	—
14	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
17	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
18	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₁×#97	C₂²	1	2	yes	—
21	C₂×C₁₁×#97	C₂²	1	2	yes	—
22	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
25	C₁₁×#391	C₄	1	2	yes	—
26	C₁₁×#389	C₄	1	1	yes	characteristic
27	C₁₁×#389	C₄	1	1	yes	characteristic
28	C₁₁×#389	C₄	1	2	yes	—
29	C₁₁×#384	C₄	1	1	yes	characteristic
30	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
31	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
32	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
33	C₄³×C₁₁	C₂²	1	1	yes	characteristic
34	C₁₁×#336	C₂²	1	2	yes	—
35	C₁₁×#336	C₂²	1	2	yes	—
36	C₁₁×#336	C₂²	1	2	yes	—
37	C₁₁×#336	C₂²	1	2	yes	—
38	C₁₁×#336	C₂²	1	1	yes	characteristic
39	C₁₁×#336	C₂²	1	2	yes	—
40	C₁₁×#336	C₂²	1	1	yes	characteristic
41	C₂²×Q₈×C₁₁	C₂×C₄	1	2	yes	—
42	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
43	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
45	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
48	C₁₁×C₄⋊Q₈	—	2	4	no	—
49	C₄×Q₈×C₁₁	—	4	2	no	—
50	C₄×Q₈×C₁₁	—	4	2	no	—
51	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
52	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
53	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
54	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
55	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
56	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
57	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
58	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
59	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
66	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
67	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
69	C₁₁×C₄⋊C₈	—	2	2	no	—
70	C₁₁×C₄⋊C₈	—	2	2	no	—
71	C₁₁×C₄⋊C₈	—	4	2	no	—
72	C₁₁×C₄⋊C₈	—	4	2	no	—
73	C₁₁×C₄⋊C₈	Q₈	1	4	yes	complemented
74	C₁₁×C₄⋊C₈	Q₈	1	4	yes	complemented
75	C₁₁×#97	—	2	4	no	—
76	C₁₁×#97	—	4	2	no	—
77	C₄×C₈×C₁₁	—	2	2	no	—
78	C₄×C₈×C₁₁	—	2	2	no	—
79	C₄×C₈×C₁₁	—	4	2	no	—
80	C₁₁×#95	C₂×C₄	1	2	yes	—
81	C₁₁×#95	C₂×C₄	1	2	yes	—
82	C₁₁×#95	C₂×C₄	1	2	yes	—
83	C₁₁×#95	C₂×C₄	1	2	yes	—
84	#23248	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
85	C₂×Q₈×C₁₁	—	2	4	no	—
86	C₂×Q₈×C₁₁	—	2	4	no	—
87	C₂×Q₈×C₁₁	—	4	2	no	—
88	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
89	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
90	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
91	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
96	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
99	C₂×C₈×C₁₁	—	2	1	no	—
100	C₂×C₈×C₁₁	—	2	1	no	—
101	C₂×C₈×C₁₁	—	2	2	no	—
102	C₂×C₈×C₁₁	—	2	1	no	—
103	C₂×C₈×C₁₁	—	2	1	no	—
104	C₂×C₈×C₁₁	—	2	2	no	—
105	C₂×C₈×C₁₁	—	2	1	no	—
106	C₂×C₈×C₁₁	—	2	1	no	—
107	C₂×C₈×C₁₁	—	2	2	no	—
108	C₂×C₈×C₁₁	—	2	1	no	—
109	C₂×C₈×C₁₁	—	2	2	no	—
110	C₂×C₈×C₁₁	—	2	1	no	—
111	C₂×C₈×C₁₁	—	2	1	no	—
112	C₂×C₈×C₁₁	—	2	1	no	—
113	C₂×C₈×C₁₁	—	2	2	no	—
114	C₂×C₈×C₁₁	C₂×Q₈	1	2	yes	—
115	C₂×C₈×C₁₁	C₂×Q₈	1	4	yes	—
116	C₂×C₈×C₁₁	C₂×Q₈	1	2	yes	—
117	C₁₁×C₄⋊C₄	—	2	4	no	—
118	C₁₁×C₄⋊C₄	—	2	2	no	—
119	C₁₁×C₄⋊C₄	—	2	2	no	—
120	C₁₁×C₄⋊C₄	—	2	2	no	—
121	C₁₁×C₄⋊C₄	—	4	2	no	—
122	C₁₁×C₄⋊C₄	—	4	2	no	—
123	C₁₁×C₄⋊C₄	—	4	2	no	—
124	C₁₁×C₄⋊C₄	—	4	2	no	—
125	C₁₁×C₄⋊C₄	M₁₆	1	4	yes	—
126	C₄²×C₁₁	—	2	2	no	—
127	C₄²×C₁₁	—	2	2	no	—
128	C₄²×C₁₁	—	2	2	no	—
129	C₄²×C₁₁	—	2	2	no	—
130	C₄²×C₁₁	—	2	2	no	—
131	C₄²×C₁₁	—	2	2	no	—
132	C₄²×C₁₁	—	2	2	no	—
133	C₄²×C₁₁	—	2	1	no	—
134	C₄²×C₁₁	—	2	1	no	—
135	C₄²×C₁₁	—	4	1	no	—
136	C₄²×C₁₁	C₂×Q₈	1	2	yes	—
137	C₄²×C₁₁	C₂×Q₈	1	2	yes	—
138	C₄²×C₁₁	#41	1	2	yes	—
139	C₄²×C₁₁	#41	1	2	yes	—
140	C₄×C₄⋊Q₈	C₂×C₁₁	1	1	yes	characteristic
141	#1985	C₂×C₁₁	1	2	yes	—
142	#1984	C₂×C₁₁	1	2	yes	—
143	#1940	C₂×C₁₁	1	2	yes	—
144	#1939	C₂×C₁₁	1	1	yes	characteristic
145	#1939	C₂×C₁₁	1	1	yes	characteristic
146	#1771	C₂×C₁₁	1	2	yes	—
147	#1770	C₂×C₁₁	1	1	yes	characteristic
148	C₈×C₄⋊C₄	C₂×C₁₁	1	1	yes	characteristic
149	#1767	C₂×C₁₁	1	1	yes	characteristic
150	C₄×C₄⋊C₈	C₂×C₁₁	1	1	yes	characteristic
151	C₂³×C₁₁	C₂³×C₄	1	1	yes	characteristic
152	Q₈×C₁₁	—	4	8	no	—
153	C₂×C₄×C₁₁	—	2	1	no	—
154	C₂×C₄×C₁₁	—	2	2	no	—
155	C₂×C₄×C₁₁	—	2	1	no	—
156	C₂×C₄×C₁₁	—	2	1	no	—
157	C₂×C₄×C₁₁	—	2	1	no	—
158	C₂×C₄×C₁₁	—	2	1	no	—
159	C₂×C₄×C₁₁	—	2	1	no	—
160	C₂×C₄×C₁₁	—	2	2	no	—
161	C₂×C₄×C₁₁	—	2	1	no	—
162	C₂×C₄×C₁₁	—	2	1	no	—
163	C₂×C₄×C₁₁	—	2	1	no	—
164	C₂×C₄×C₁₁	—	2	2	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	—	2	1	no	—
169	C₂×C₄×C₁₁	—	2	2	no	—
170	C₂×C₄×C₁₁	—	2	2	no	—
171	C₂×C₄×C₁₁	—	2	2	no	—
172	C₂×C₄×C₁₁	—	2	1	no	—
173	C₂×C₄×C₁₁	—	2	2	no	—
174	C₂×C₄×C₁₁	—	2	2	no	—
175	C₂×C₄×C₁₁	C₄×Q₈	1	2	yes	—
176	C₂×C₄×C₁₁	C₄×Q₈	1	2	yes	—
177	C₂×C₄×C₁₁	C₄×Q₈	1	2	yes	—
178	C₂×C₄×C₁₁	C₄×Q₈	1	2	yes	—
179	C₂×C₄×C₁₁	C₂×M₁₆	1	4	yes	—
180	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
181	C₂×C₄×C₁₁	#131	1	2	yes	—
182	C₂×C₄×C₁₁	#131	1	2	yes	—
183	C₂×C₄×C₁₁	C₂²×Q₈	1	1	yes	characteristic
184	C₂×C₄×C₁₁	C₂²×Q₈	1	1	yes	characteristic
185	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
186	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
187	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
188	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
189	C₈×C₁₁	—	2	2	no	—
190	C₈×C₁₁	—	2	2	no	—
191	C₈×C₁₁	—	2	4	no	—
192	C₈×C₁₁	—	4	1	no	—
193	C₈×C₁₁	—	4	1	no	—
194	C₈×C₁₁	—	4	2	no	—
195	C₂×C₄⋊Q₈	C₄×C₁₁	1	1	yes	characteristic
196	C₂×C₄×Q₈	C₂²×C₁₁	1	2	yes	—
197	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
198	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
199	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
200	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
201	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
202	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
203	C₂×#97	C₂²×C₁₁	1	2	yes	—
204	C₂×#97	C₂²×C₁₁	1	2	yes	—
205	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
206	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
207	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	—
208	#391	C₄×C₁₁	1	2	yes	—
209	#389	C₄×C₁₁	1	1	yes	characteristic
210	#389	C₄×C₁₁	1	1	yes	characteristic
211	#389	C₄×C₁₁	1	2	yes	—
212	#384	C₄×C₁₁	1	1	yes	characteristic
213	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
214	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
215	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
216	C₄³	C₂²×C₁₁	1	1	yes	characteristic
217	#336	C₂²×C₁₁	1	2	yes	—
218	#336	C₂²×C₁₁	1	2	yes	—
219	#336	C₂²×C₁₁	1	2	yes	—
220	#336	C₂²×C₁₁	1	2	yes	—
221	#336	C₂²×C₁₁	1	1	yes	characteristic
222	#336	C₂²×C₁₁	1	2	yes	—
223	#336	C₂²×C₁₁	1	1	yes	characteristic
224	C₂²×C₁₁	C₂×C₄×Q₈	1	1	yes	characteristic
225	C₂²×C₁₁	C₂×C₄×Q₈	1	1	yes	characteristic
226	C₂²×C₁₁	#518	1	1	yes	characteristic
227	C₂²×C₁₁	C₂²×M₁₆	1	1	yes	characteristic
228	C₂²×C₁₁	C₂×#131	1	1	yes	characteristic
229	C₂²×C₁₁	C₂×#131	1	1	yes	characteristic
230	C₂²×C₁₁	#568	1	1	yes	characteristic
231	C₄×C₁₁	—	2	2	no	—
232	C₄×C₁₁	—	2	2	no	—
233	C₄×C₁₁	—	2	2	no	—
234	C₄×C₁₁	—	2	4	no	—
235	C₄×C₁₁	—	2	2	no	—
236	C₄×C₁₁	—	4	2	no	—
237	C₄×C₁₁	—	4	1	no	—
238	C₄×C₁₁	—	4	2	no	—
239	C₄×C₁₁	—	4	2	no	—
240	C₄×C₁₁	#446	1	4	yes	—
241	C₄×C₁₁	#554	1	1	yes	characteristic
242	C₄×C₁₁	#554	1	1	yes	characteristic
243	C₄×C₁₁	#555	1	1	yes	characteristic
244	C₄×C₁₁	Q₈²	1	1	yes	characteristic
245	C₂²×Q₈	C₂×C₄×C₁₁	1	2	yes	—
246	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
247	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
248	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
249	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
250	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
251	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
252	C₄⋊Q₈	—	2	4	no	—
253	C₄×Q₈	—	4	2	no	—
254	C₄×Q₈	—	4	2	no	—
255	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
256	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
257	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
258	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
259	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
260	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
261	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
262	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
263	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
264	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
265	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
266	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
267	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
268	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
269	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
270	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
271	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
272	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
273	C₄⋊C₈	—	2	2	no	—
274	C₄⋊C₈	—	2	2	no	—
275	C₄⋊C₈	—	4	2	no	—
276	C₄⋊C₈	—	4	2	no	—
277	C₄⋊C₈	Q₈×C₁₁	1	4	yes	complemented
278	C₄⋊C₈	Q₈×C₁₁	1	4	yes	complemented
279	#97	—	2	4	no	—
280	#97	—	4	2	no	—
281	C₄×C₈	—	2	2	no	—
282	C₄×C₈	—	2	2	no	—
283	C₄×C₈	—	4	2	no	—
284	#95	C₂×C₄×C₁₁	1	2	yes	—
285	#95	C₂×C₄×C₁₁	1	2	yes	—
286	#95	C₂×C₄×C₁₁	1	2	yes	—
287	#95	C₂×C₄×C₁₁	1	2	yes	—
288	C₂×C₁₁	#2369	1	1	yes	characteristic
289	C₂×C₁₁	C₂×#446	1	1	yes	characteristic
290	C₂×C₁₁	#2960	1	1	yes	characteristic
291	C₂×C₁₁	#2962	1	1	yes	characteristic
292	C₂×C₁₁	Q₈×M₁₆	1	1	yes	characteristic
293	C₂×C₁₁	#2974	1	1	yes	characteristic
294	C₂×C₁₁	#2981	1	1	yes	characteristic
295	C₂×Q₈	—	2	4	no	—
296	C₂×Q₈	—	2	4	no	—
297	C₂×Q₈	—	4	2	no	—
298	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
299	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
300	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
301	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
302	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
303	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
304	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
305	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
306	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
307	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
308	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
309	C₂×C₈	—	2	1	no	—
310	C₂×C₈	—	2	1	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	1	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	1	no	—
315	C₂×C₈	—	2	1	no	—
316	C₂×C₈	—	2	1	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	2	1	no	—
319	C₂×C₈	—	2	1	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	1	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	C₂×Q₈×C₁₁	1	2	yes	—
325	C₂×C₈	C₂×Q₈×C₁₁	1	2	yes	—
326	C₂×C₈	C₂×Q₈×C₁₁	1	4	yes	—
327	C₄⋊C₄	—	2	4	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	4	2	no	—
332	C₄⋊C₄	—	4	2	no	—
333	C₄⋊C₄	—	4	2	no	—
334	C₄⋊C₄	—	4	2	no	—
335	C₄⋊C₄	C₁₁×M₁₆	1	4	yes	—
336	C₄²	—	2	2	no	—
337	C₄²	—	2	2	no	—
338	C₄²	—	2	2	no	—
339	C₄²	—	2	2	no	—
340	C₄²	—	2	2	no	—
341	C₄²	—	2	2	no	—
342	C₄²	—	2	2	no	—
343	C₄²	—	2	1	no	—
344	C₄²	—	2	1	no	—
345	C₄²	—	4	1	no	—
346	C₄²	C₂×Q₈×C₁₁	1	2	yes	—
347	C₄²	C₂×Q₈×C₁₁	1	2	yes	—
348	C₄²	C₁₁×#41	1	2	yes	—
349	C₄²	C₁₁×#41	1	2	yes	—
350	C₁₁	#23248	1	1	yes	characteristic, direct product factor, Sylow
351	C₂³	C₂³×C₄×C₁₁	1	1	yes	characteristic
352	Q₈	—	4	8	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	C₄×Q₈×C₁₁	1	2	yes	—
376	C₂×C₄	C₄×Q₈×C₁₁	1	2	yes	—
377	C₂×C₄	C₄×Q₈×C₁₁	1	2	yes	—
378	C₂×C₄	C₄×Q₈×C₁₁	1	2	yes	—
379	C₂×C₄	C₂×C₁₁×M₁₆	1	4	yes	—
380	C₂×C₄	C₂×C₁₁×M₁₆	1	2	yes	—
381	C₂×C₄	C₁₁×#131	1	2	yes	—
382	C₂×C₄	C₁₁×#131	1	2	yes	—
383	C₂×C₄	C₂²×Q₈×C₁₁	1	1	yes	characteristic
384	C₂×C₄	C₂²×Q₈×C₁₁	1	1	yes	characteristic
385	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
386	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
387	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
388	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
389	C₈	—	2	2	no	—
390	C₈	—	2	2	no	—
391	C₈	—	2	4	no	—
392	C₈	—	4	1	no	—
393	C₈	—	4	1	no	—
394	C₈	—	4	2	no	—
395	C₂²	C₂×C₄×Q₈×C₁₁	1	1	yes	characteristic
396	C₂²	C₂×C₄×Q₈×C₁₁	1	1	yes	characteristic
397	C₂²	C₁₁×#518	1	1	yes	characteristic
398	C₂²	C₂²×C₁₁×M₁₆	1	1	yes	characteristic
399	C₂²	C₂×C₁₁×#131	1	1	yes	characteristic
400	C₂²	C₂×C₁₁×#131	1	1	yes	characteristic
401	C₂²	C₁₁×#568	1	1	yes	characteristic
402	C₄	—	2	2	no	—
403	C₄	—	2	2	no	—
404	C₄	—	2	2	no	—
405	C₄	—	2	4	no	—
406	C₄	—	2	2	no	—
407	C₄	—	4	2	no	—
408	C₄	—	4	1	no	—
409	C₄	—	4	2	no	—
410	C₄	—	4	2	no	—
411	C₄	C₁₁×#446	1	4	yes	—
412	C₄	C₁₁×#554	1	1	yes	characteristic
413	C₄	C₁₁×#554	1	1	yes	characteristic
414	C₄	C₁₁×#555	1	1	yes	characteristic
415	C₄	Q₈²×C₁₁	1	1	yes	characteristic
416	C₂	C₁₁×#2369	1	1	yes	characteristic
417	C₂	C₂×C₁₁×#446	1	1	yes	characteristic
418	C₂	C₁₁×#2960	1	1	yes	characteristic
419	C₂	C₁₁×#2962	1	1	yes	characteristic
420	C₂	Q₈×C₁₁×M₁₆	1	1	yes	characteristic
421	C₂	C₁₁×#2974	1	1	yes	characteristic
422	C₂	C₁₁×#2981	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
73. C₁₁×C₄⋊C₈	Q₈	semidirect
74. C₁₁×C₄⋊C₈	Q₈	semidirect
84. #23248	C₁₁	direct (N × H)
277. C₄⋊C₈	Q₈×C₁₁	semidirect
278. C₄⋊C₈	Q₈×C₁₁	semidirect
350. C₁₁	#23248	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₁₁×C₄⋊Q₈	2
C₁₁×#1985	2
C₁₁×#1984	2
C₁₁×#1940	2
C₁₁×#1939	2
C₁₁×#1771	2
C₁₁×#1770	2
C₈×C₁₁×C₄⋊C₄	2
C₁₁×#1767	2
C₄×C₁₁×C₄⋊C₈	2
#23248	11

Subgroups — C11×#23248 #14600441

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#23248 #14600441