Subgroups — C₁₁×#23151 #14600344

Order 2816.

772 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#446	C₂	1	2	yes	maximal
2	C₄×C₁₁×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#1985	C₂	1	2	yes	maximal
4	C₁₁×#1939	C₂	1	1	yes	maximal, characteristic
5	C₁₁×#1939	C₂	1	1	yes	maximal, characteristic
6	C₁₁×#1917	C₂	1	2	yes	maximal
7	C₁₁×#1916	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	C₁₁×#446	—	2	8	no	—
15	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
16	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
17	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₁×#97	C₂²	1	2	yes	—
22	C₂×C₁₁×#97	C₂²	1	2	yes	—
23	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
24	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
26	C₁₁×#391	C₄	1	2	yes	—
27	C₁₁×#389	C₄	1	1	yes	characteristic
28	C₁₁×#389	C₄	1	2	yes	—
29	C₁₁×#389	C₄	1	1	yes	characteristic
30	C₁₁×#384	C₄	1	1	yes	characteristic
31	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
32	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₄³×C₁₁	C₂²	1	1	yes	characteristic
35	C₁₁×#336	C₂²	1	1	yes	characteristic
36	C₁₁×#336	C₂²	1	2	yes	—
37	C₁₁×#336	C₂²	1	2	yes	—
38	C₁₁×#336	C₂²	1	2	yes	—
39	C₁₁×#336	C₂²	1	1	yes	characteristic
40	C₁₁×#336	C₂²	1	2	yes	—
41	C₁₁×#336	C₂²	1	2	yes	—
42	C₂²×Q₈×C₁₁	C₂×C₄	1	2	yes	—
43	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
46	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
49	C₁₁×C₄⋊Q₈	—	2	4	no	—
50	C₄×Q₈×C₁₁	—	2	4	no	—
51	C₄×Q₈×C₁₁	—	2	4	no	—
52	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
53	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
54	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
55	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
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	2	yes	—
60	C₂×C₁₁×C₄⋊C₄	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	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
66	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
67	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
68	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
70	C₁₁×C₄⋊C₈	—	2	4	no	—
71	C₁₁×C₄⋊C₈	—	2	4	no	—
72	C₁₁×C₄⋊C₈	—	2	2	no	—
73	C₁₁×C₄⋊C₈	—	2	2	no	—
74	C₁₁×C₄⋊C₈	D₄	1	4	yes	—
75	C₁₁×C₄⋊C₈	Q₈	1	4	yes	complemented
76	C₁₁×#97	—	2	4	no	—
77	C₁₁×#97	—	2	4	no	—
78	C₄×C₈×C₁₁	—	2	4	no	—
79	C₄×C₈×C₁₁	—	2	2	no	—
80	C₄×C₈×C₁₁	—	2	2	no	—
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	C₁₁×#95	C₂×C₄	1	2	yes	—
85	#23151	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
86	C₂×Q₈×C₁₁	—	2	4	no	—
87	C₂×Q₈×C₁₁	—	2	4	no	—
88	C₂×Q₈×C₁₁	—	4	2	no	—
89	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
91	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
92	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
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	1	yes	characteristic
96	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
100	C₂×C₈×C₁₁	—	2	2	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	1	no	—
105	C₂×C₈×C₁₁	—	2	1	no	—
106	C₂×C₈×C₁₁	—	2	2	no	—
107	C₂×C₈×C₁₁	—	2	1	no	—
108	C₂×C₈×C₁₁	—	2	1	no	—
109	C₂×C₈×C₁₁	—	2	1	no	—
110	C₂×C₈×C₁₁	—	2	1	no	—
111	C₂×C₈×C₁₁	—	2	2	no	—
112	C₂×C₈×C₁₁	—	2	2	no	—
113	C₂×C₈×C₁₁	—	2	1	no	—
114	C₂×C₈×C₁₁	—	2	1	no	—
115	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
116	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
117	C₂×C₈×C₁₁	C₂×Q₈	1	4	yes	—
118	C₁₁×C₄⋊C₄	—	2	4	no	—
119	C₁₁×C₄⋊C₄	—	2	4	no	—
120	C₁₁×C₄⋊C₄	—	2	4	no	—
121	C₁₁×C₄⋊C₄	—	2	4	no	—
122	C₁₁×C₄⋊C₄	—	2	2	no	—
123	C₁₁×C₄⋊C₄	—	2	4	no	—
124	C₁₁×C₄⋊C₄	—	2	2	no	—
125	C₁₁×C₄⋊C₄	—	2	2	no	—
126	C₁₁×C₄⋊C₄	M₁₆	1	4	yes	—
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	2	no	—
134	C₄²×C₁₁	—	2	1	no	—
135	C₄²×C₁₁	—	2	1	no	—
136	C₄²×C₁₁	—	4	1	no	—
137	C₄²×C₁₁	C₂×D₄	1	2	yes	—
138	C₄²×C₁₁	C₂×Q₈	1	2	yes	—
139	C₄²×C₁₁	#41	1	2	yes	—
140	C₄²×C₁₁	#41	1	2	yes	—
141	C₂×#446	C₂×C₁₁	1	2	yes	—
142	C₄×C₄⋊Q₈	C₂×C₁₁	1	1	yes	characteristic
143	#1985	C₂×C₁₁	1	2	yes	—
144	#1939	C₂×C₁₁	1	1	yes	characteristic
145	#1939	C₂×C₁₁	1	1	yes	characteristic
146	#1917	C₂×C₁₁	1	2	yes	—
147	#1916	C₂×C₁₁	1	2	yes	—
148	#1770	C₂×C₁₁	1	1	yes	characteristic
149	C₈×C₄⋊C₄	C₂×C₁₁	1	1	yes	characteristic
150	#1767	C₂×C₁₁	1	1	yes	characteristic
151	C₄×C₄⋊C₈	C₂×C₁₁	1	1	yes	characteristic
152	C₂³×C₁₁	C₂³×C₄	1	1	yes	characteristic
153	Q₈×C₁₁	—	4	8	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	1	no	—
161	C₂×C₄×C₁₁	—	2	1	no	—
162	C₂×C₄×C₁₁	—	2	1	no	—
163	C₂×C₄×C₁₁	—	2	2	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	1	no	—
168	C₂×C₄×C₁₁	—	2	2	no	—
169	C₂×C₄×C₁₁	—	2	1	no	—
170	C₂×C₄×C₁₁	—	2	2	no	—
171	C₂×C₄×C₁₁	—	2	2	no	—
172	C₂×C₄×C₁₁	—	2	2	no	—
173	C₂×C₄×C₁₁	—	2	2	no	—
174	C₂×C₄×C₁₁	—	2	1	no	—
175	C₂×C₄×C₁₁	—	2	2	no	—
176	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
177	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
178	C₂×C₄×C₁₁	C₄×Q₈	1	2	yes	—
179	C₂×C₄×C₁₁	C₄×Q₈	1	2	yes	—
180	C₂×C₄×C₁₁	C₂×M₁₆	1	4	yes	—
181	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
182	C₂×C₄×C₁₁	#131	1	2	yes	—
183	C₂×C₄×C₁₁	#131	1	2	yes	—
184	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₄×C₁₁	C₂²×Q₈	1	1	yes	characteristic
186	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
187	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
188	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
189	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
190	C₈×C₁₁	—	2	2	no	—
191	C₈×C₁₁	—	2	2	no	—
192	C₈×C₁₁	—	2	4	no	—
193	C₈×C₁₁	—	4	2	no	—
194	C₈×C₁₁	—	4	1	no	—
195	C₈×C₁₁	—	4	1	no	—
196	C₂×C₄⋊Q₈	C₄×C₁₁	1	1	yes	characteristic
197	C₂×C₄×Q₈	C₂²×C₁₁	1	2	yes	—
198	#446	—	2	8	no	—
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×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
204	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
205	C₂×#97	C₂²×C₁₁	1	2	yes	—
206	C₂×#97	C₂²×C₁₁	1	2	yes	—
207	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	—
208	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
209	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
210	#391	C₄×C₁₁	1	2	yes	—
211	#389	C₄×C₁₁	1	1	yes	characteristic
212	#389	C₄×C₁₁	1	2	yes	—
213	#389	C₄×C₁₁	1	1	yes	characteristic
214	#384	C₄×C₁₁	1	1	yes	characteristic
215	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
216	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
217	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
218	C₄³	C₂²×C₁₁	1	1	yes	characteristic
219	#336	C₂²×C₁₁	1	1	yes	characteristic
220	#336	C₂²×C₁₁	1	2	yes	—
221	#336	C₂²×C₁₁	1	2	yes	—
222	#336	C₂²×C₁₁	1	2	yes	—
223	#336	C₂²×C₁₁	1	1	yes	characteristic
224	#336	C₂²×C₁₁	1	2	yes	—
225	#336	C₂²×C₁₁	1	2	yes	—
226	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
227	C₂²×C₁₁	C₂×C₄×Q₈	1	1	yes	characteristic
228	C₂²×C₁₁	#519	1	1	yes	characteristic
229	C₂²×C₁₁	C₂²×M₁₆	1	1	yes	characteristic
230	C₂²×C₁₁	C₂×#131	1	1	yes	characteristic
231	C₂²×C₁₁	C₂×#131	1	1	yes	characteristic
232	C₂²×C₁₁	#568	1	1	yes	characteristic
233	C₄×C₁₁	—	2	2	no	—
234	C₄×C₁₁	—	2	2	no	—
235	C₄×C₁₁	—	2	4	no	—
236	C₄×C₁₁	—	2	2	no	—
237	C₄×C₁₁	—	2	2	no	—
238	C₄×C₁₁	—	4	2	no	—
239	C₄×C₁₁	—	4	2	no	—
240	C₄×C₁₁	—	4	2	no	—
241	C₄×C₁₁	—	4	1	no	—
242	C₄×C₁₁	#446	1	4	yes	complemented
243	C₄×C₁₁	#547	1	1	yes	characteristic
244	C₄×C₁₁	D₄×Q₈	1	1	yes	characteristic
245	C₄×C₁₁	#556	1	1	yes	characteristic
246	C₄×C₁₁	#557	1	1	yes	characteristic
247	C₂²×Q₈	C₂×C₄×C₁₁	1	2	yes	—
248	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
249	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
250	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
251	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
252	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
253	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
254	C₄⋊Q₈	—	2	4	no	—
255	C₄×Q₈	—	2	4	no	—
256	C₄×Q₈	—	2	4	no	—
257	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
258	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
259	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
260	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
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×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
265	C₂×C₄⋊C₄	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	C₂×C₄×C₁₁	1	1	yes	characteristic
269	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
270	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
271	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
272	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
273	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
274	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
275	C₄⋊C₈	—	2	4	no	—
276	C₄⋊C₈	—	2	4	no	—
277	C₄⋊C₈	—	2	2	no	—
278	C₄⋊C₈	—	2	2	no	—
279	C₄⋊C₈	D₄×C₁₁	1	4	yes	—
280	C₄⋊C₈	Q₈×C₁₁	1	4	yes	complemented
281	#97	—	2	4	no	—
282	#97	—	2	4	no	—
283	C₄×C₈	—	2	4	no	—
284	C₄×C₈	—	2	2	no	—
285	C₄×C₈	—	2	2	no	—
286	#95	C₂×C₄×C₁₁	1	2	yes	—
287	#95	C₂×C₄×C₁₁	1	2	yes	—
288	#95	C₂×C₄×C₁₁	1	2	yes	—
289	#95	C₂×C₄×C₁₁	1	2	yes	—
290	C₂×C₁₁	#2365	1	1	yes	characteristic
291	C₂×C₁₁	#2931	1	1	yes	characteristic
292	C₂×C₁₁	D₄×M₁₆	1	1	yes	characteristic
293	C₂×C₁₁	C₂×#446	1	1	yes	characteristic
294	C₂×C₁₁	#2962	1	1	yes	characteristic
295	C₂×C₁₁	#2984	1	1	yes	characteristic
296	C₂×C₁₁	#2985	1	1	yes	characteristic
297	C₂×Q₈	—	2	4	no	—
298	C₂×Q₈	—	2	4	no	—
299	C₂×Q₈	—	4	2	no	—
300	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
301	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
302	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
303	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
304	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
305	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
306	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
307	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
308	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
309	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
310	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	1	no	—
313	C₂×C₈	—	2	1	no	—
314	C₂×C₈	—	2	1	no	—
315	C₂×C₈	—	2	1	no	—
316	C₂×C₈	—	2	2	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	—	2	1	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
327	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
328	C₂×C₈	C₂×Q₈×C₁₁	1	4	yes	—
329	C₄⋊C₄	—	2	4	no	—
330	C₄⋊C₄	—	2	4	no	—
331	C₄⋊C₄	—	2	4	no	—
332	C₄⋊C₄	—	2	4	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	2	4	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	C₁₁×M₁₆	1	4	yes	—
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	2	no	—
344	C₄²	—	2	2	no	—
345	C₄²	—	2	1	no	—
346	C₄²	—	2	1	no	—
347	C₄²	—	4	1	no	—
348	C₄²	C₂×D₄×C₁₁	1	2	yes	—
349	C₄²	C₂×Q₈×C₁₁	1	2	yes	—
350	C₄²	C₁₁×#41	1	2	yes	—
351	C₄²	C₁₁×#41	1	2	yes	—
352	C₁₁	#23151	1	1	yes	characteristic, direct product factor, Sylow
353	C₂³	C₂³×C₄×C₁₁	1	1	yes	characteristic
354	Q₈	—	4	8	no	—
355	C₂×C₄	—	2	2	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	1	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	1	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
378	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
379	C₂×C₄	C₄×Q₈×C₁₁	1	2	yes	—
380	C₂×C₄	C₄×Q₈×C₁₁	1	2	yes	—
381	C₂×C₄	C₂×C₁₁×M₁₆	1	4	yes	—
382	C₂×C₄	C₂×C₁₁×M₁₆	1	2	yes	—
383	C₂×C₄	C₁₁×#131	1	2	yes	—
384	C₂×C₄	C₁₁×#131	1	2	yes	—
385	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
386	C₂×C₄	C₂²×Q₈×C₁₁	1	1	yes	characteristic
387	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
388	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
389	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
390	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
391	C₈	—	2	2	no	—
392	C₈	—	2	2	no	—
393	C₈	—	2	4	no	—
394	C₈	—	4	2	no	—
395	C₈	—	4	1	no	—
396	C₈	—	4	1	no	—
397	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
398	C₂²	C₂×C₄×Q₈×C₁₁	1	1	yes	characteristic
399	C₂²	C₁₁×#519	1	1	yes	characteristic
400	C₂²	C₂²×C₁₁×M₁₆	1	1	yes	characteristic
401	C₂²	C₂×C₁₁×#131	1	1	yes	characteristic
402	C₂²	C₂×C₁₁×#131	1	1	yes	characteristic
403	C₂²	C₁₁×#568	1	1	yes	characteristic
404	C₄	—	2	2	no	—
405	C₄	—	2	2	no	—
406	C₄	—	2	4	no	—
407	C₄	—	2	2	no	—
408	C₄	—	2	2	no	—
409	C₄	—	4	2	no	—
410	C₄	—	4	2	no	—
411	C₄	—	4	2	no	—
412	C₄	—	4	1	no	—
413	C₄	C₁₁×#446	1	4	yes	complemented
414	C₄	C₁₁×#547	1	1	yes	characteristic
415	C₄	D₄×Q₈×C₁₁	1	1	yes	characteristic
416	C₄	C₁₁×#556	1	1	yes	characteristic
417	C₄	C₁₁×#557	1	1	yes	characteristic
418	C₂	C₁₁×#2365	1	1	yes	characteristic
419	C₂	C₁₁×#2931	1	1	yes	characteristic
420	C₂	D₄×C₁₁×M₁₆	1	1	yes	characteristic
421	C₂	C₂×C₁₁×#446	1	1	yes	characteristic
422	C₂	C₁₁×#2962	1	1	yes	characteristic
423	C₂	C₁₁×#2984	1	1	yes	characteristic
424	C₂	C₁₁×#2985	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
75. C₁₁×C₄⋊C₈	Q₈	semidirect
85. #23151	C₁₁	direct (N × H)
242. C₄×C₁₁	#446	semidirect
280. C₄⋊C₈	Q₈×C₁₁	semidirect
352. C₁₁	#23151	direct (N × H)
413. C₄	C₁₁×#446	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₁×#446	2
C₄×C₁₁×C₄⋊Q₈	2
C₁₁×#1985	2
C₁₁×#1939	2
C₁₁×#1917	2
C₁₁×#1916	2
C₁₁×#1770	2
C₈×C₁₁×C₄⋊C₄	2
C₁₁×#1767	2
C₄×C₁₁×C₄⋊C₈	2
#23151	11

Subgroups — C11×#23151 #14600344

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#23151 #14600344