Subgroups — C₁₁×#23152 #14600345

Order 2816.

752 conjugacy classes of subgroups.

The subgroup lattice has 396 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×#1940	C₂	1	2	yes	maximal
5	C₁₁×#1917	C₂	1	2	yes	maximal
6	C₁₁×#1916	C₂	1	2	yes	maximal
7	C₁₁×#1771	C₂	1	2	yes	maximal
8	C₁₁×#1767	C₂	1	1	yes	maximal, characteristic
9	C₁₁×#1767	C₂	1	1	yes	maximal, characteristic
10	C₂×C₁₁×C₄⋊Q₈	C₄	1	1	yes	characteristic
11	C₂×C₄×Q₈×C₁₁	C₂²	1	2	yes	—
12	C₁₁×#446	—	2	8	no	—
13	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
14	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
15	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₁×#97	C₂²	1	2	yes	—
20	C₂×C₁₁×#97	C₂²	1	2	yes	—
21	C₂×C₁₁×#97	C₂²	1	2	yes	—
22	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
23	C₁₁×#391	C₄	1	2	yes	—
24	C₁₁×#389	C₄	1	2	yes	—
25	C₁₁×#389	C₄	1	1	yes	characteristic
26	C₁₁×#389	C₄	1	1	yes	characteristic
27	C₁₁×#384	C₄	1	1	yes	characteristic
28	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
31	C₄³×C₁₁	C₂²	1	1	yes	characteristic
32	C₁₁×#336	C₂²	1	2	yes	—
33	C₁₁×#336	C₂²	1	2	yes	—
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	C₂²×Q₈×C₁₁	C₂×C₄	1	2	yes	—
39	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
40	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
41	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
42	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
43	C₁₁×C₄⋊Q₈	—	2	4	no	—
44	C₄×Q₈×C₁₁	—	2	4	no	—
45	C₄×Q₈×C₁₁	—	2	4	no	—
46	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
47	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
48	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
49	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
50	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
51	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
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	1	yes	characteristic
55	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
60	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
61	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
62	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
63	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
64	C₁₁×C₄⋊C₈	—	2	4	no	—
65	C₁₁×C₄⋊C₈	—	2	4	no	—
66	C₁₁×C₄⋊C₈	—	2	2	no	—
67	C₁₁×C₄⋊C₈	—	2	2	no	—
68	C₁₁×C₄⋊C₈	D₄	1	4	yes	—
69	C₁₁×C₄⋊C₈	Q₈	1	4	yes	complemented
70	C₁₁×#97	—	2	4	no	—
71	C₁₁×#97	—	2	4	no	—
72	C₁₁×#97	—	2	4	no	—
73	C₄×C₈×C₁₁	—	2	4	no	—
74	C₁₁×#95	C₂×C₄	1	2	yes	—
75	C₁₁×#95	C₂×C₄	1	2	yes	—
76	C₁₁×#95	C₂×C₄	1	2	yes	—
77	C₁₁×#95	C₂×C₄	1	2	yes	—
78	#23152	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
79	C₂×Q₈×C₁₁	—	2	4	no	—
80	C₂×Q₈×C₁₁	—	2	4	no	—
81	C₂×Q₈×C₁₁	—	4	2	no	—
82	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
84	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
85	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
86	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
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	1	yes	characteristic
92	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
93	C₂×C₈×C₁₁	—	2	2	no	—
94	C₂×C₈×C₁₁	—	2	2	no	—
95	C₂×C₈×C₁₁	—	2	2	no	—
96	C₂×C₈×C₁₁	—	2	2	no	—
97	C₂×C₈×C₁₁	—	2	2	no	—
98	C₂×C₈×C₁₁	—	2	2	no	—
99	C₂×C₈×C₁₁	—	2	2	no	—
100	C₂×C₈×C₁₁	—	2	2	no	—
101	C₂×C₈×C₁₁	—	2	2	no	—
102	C₂×C₈×C₁₁	—	2	2	no	—
103	C₂×C₈×C₁₁	C₂×D₄	1	4	yes	—
104	C₂×C₈×C₁₁	C₂×Q₈	1	4	yes	—
105	C₁₁×C₄⋊C₄	—	2	4	no	—
106	C₁₁×C₄⋊C₄	—	2	4	no	—
107	C₁₁×C₄⋊C₄	—	2	4	no	—
108	C₁₁×C₄⋊C₄	—	2	4	no	—
109	C₁₁×C₄⋊C₄	—	2	2	no	—
110	C₁₁×C₄⋊C₄	—	4	2	no	—
111	C₁₁×C₄⋊C₄	—	4	1	no	—
112	C₁₁×C₄⋊C₄	—	4	1	no	—
113	C₁₁×C₄⋊C₄	M₁₆	1	4	yes	—
114	C₄²×C₁₁	—	2	2	no	—
115	C₄²×C₁₁	—	2	2	no	—
116	C₄²×C₁₁	—	2	2	no	—
117	C₄²×C₁₁	—	2	2	no	—
118	C₄²×C₁₁	—	2	2	no	—
119	C₄²×C₁₁	—	2	1	no	—
120	C₄²×C₁₁	—	2	1	no	—
121	C₄²×C₁₁	—	4	1	no	—
122	C₄²×C₁₁	—	4	1	no	—
123	C₄²×C₁₁	—	4	1	no	—
124	C₄²×C₁₁	C₂×D₄	1	2	yes	—
125	C₄²×C₁₁	C₂×Q₈	1	2	yes	—
126	C₄²×C₁₁	#41	1	2	yes	—
127	C₄²×C₁₁	#41	1	2	yes	—
128	C₂×#446	C₂×C₁₁	1	2	yes	—
129	C₄×C₄⋊Q₈	C₂×C₁₁	1	1	yes	characteristic
130	#1985	C₂×C₁₁	1	2	yes	—
131	#1940	C₂×C₁₁	1	2	yes	—
132	#1917	C₂×C₁₁	1	2	yes	—
133	#1916	C₂×C₁₁	1	2	yes	—
134	#1771	C₂×C₁₁	1	2	yes	—
135	#1767	C₂×C₁₁	1	1	yes	characteristic
136	#1767	C₂×C₁₁	1	1	yes	characteristic
137	C₂³×C₁₁	C₂³×C₄	1	1	yes	characteristic
138	Q₈×C₁₁	—	4	8	no	—
139	C₂×C₄×C₁₁	—	2	2	no	—
140	C₂×C₄×C₁₁	—	2	1	no	—
141	C₂×C₄×C₁₁	—	2	1	no	—
142	C₂×C₄×C₁₁	—	2	1	no	—
143	C₂×C₄×C₁₁	—	2	1	no	—
144	C₂×C₄×C₁₁	—	2	1	no	—
145	C₂×C₄×C₁₁	—	2	1	no	—
146	C₂×C₄×C₁₁	—	2	1	no	—
147	C₂×C₄×C₁₁	—	2	1	no	—
148	C₂×C₄×C₁₁	—	2	1	no	—
149	C₂×C₄×C₁₁	—	2	1	no	—
150	C₂×C₄×C₁₁	—	2	2	no	—
151	C₂×C₄×C₁₁	—	2	2	no	—
152	C₂×C₄×C₁₁	—	2	2	no	—
153	C₂×C₄×C₁₁	—	2	2	no	—
154	C₂×C₄×C₁₁	—	2	1	no	—
155	C₂×C₄×C₁₁	—	2	2	no	—
156	C₂×C₄×C₁₁	—	2	1	no	—
157	C₂×C₄×C₁₁	—	2	1	no	—
158	C₂×C₄×C₁₁	—	2	2	no	—
159	C₂×C₄×C₁₁	—	2	2	no	—
160	C₂×C₄×C₁₁	—	2	2	no	—
161	C₂×C₄×C₁₁	—	2	2	no	—
162	C₂×C₄×C₁₁	—	2	2	no	—
163	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
164	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
165	C₂×C₄×C₁₁	C₄×Q₈	1	2	yes	—
166	C₂×C₄×C₁₁	C₄×Q₈	1	2	yes	—
167	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
168	C₂×C₄×C₁₁	C₂×M₁₆	1	4	yes	—
169	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₁₁	C₂²×Q₈	1	1	yes	characteristic
171	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
172	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
173	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
174	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
175	C₈×C₁₁	—	2	4	no	—
176	C₈×C₁₁	—	2	4	no	—
177	C₈×C₁₁	—	4	2	no	—
178	C₈×C₁₁	—	4	2	no	—
179	C₂×C₄⋊Q₈	C₄×C₁₁	1	1	yes	characteristic
180	C₂×C₄×Q₈	C₂²×C₁₁	1	2	yes	—
181	#446	—	2	8	no	—
182	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
183	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
184	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
185	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
186	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
187	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
188	C₂×#97	C₂²×C₁₁	1	2	yes	—
189	C₂×#97	C₂²×C₁₁	1	2	yes	—
190	C₂×#97	C₂²×C₁₁	1	2	yes	—
191	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	—
192	#391	C₄×C₁₁	1	2	yes	—
193	#389	C₄×C₁₁	1	2	yes	—
194	#389	C₄×C₁₁	1	1	yes	characteristic
195	#389	C₄×C₁₁	1	1	yes	characteristic
196	#384	C₄×C₁₁	1	1	yes	characteristic
197	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
198	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
199	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
200	C₄³	C₂²×C₁₁	1	1	yes	characteristic
201	#336	C₂²×C₁₁	1	2	yes	—
202	#336	C₂²×C₁₁	1	2	yes	—
203	#336	C₂²×C₁₁	1	2	yes	—
204	#336	C₂²×C₁₁	1	2	yes	—
205	#336	C₂²×C₁₁	1	2	yes	—
206	#336	C₂²×C₁₁	1	2	yes	—
207	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
208	C₂²×C₁₁	C₂×C₄×Q₈	1	1	yes	characteristic
209	C₂²×C₁₁	#519	1	1	yes	characteristic
210	C₂²×C₁₁	C₂²×M₁₆	1	1	yes	characteristic
211	C₂²×C₁₁	#568	1	1	yes	characteristic
212	C₂²×C₁₁	#568	1	1	yes	characteristic
213	C₂²×C₁₁	#568	1	1	yes	characteristic
214	C₄×C₁₁	—	2	2	no	—
215	C₄×C₁₁	—	2	2	no	—
216	C₄×C₁₁	—	2	4	no	—
217	C₄×C₁₁	—	2	2	no	—
218	C₄×C₁₁	—	2	2	no	—
219	C₄×C₁₁	—	2	2	no	—
220	C₄×C₁₁	—	4	2	no	—
221	C₄×C₁₁	—	4	2	no	—
222	C₄×C₁₁	—	4	2	no	—
223	C₄×C₁₁	—	4	1	no	—
224	C₄×C₁₁	#547	1	1	yes	characteristic
225	C₄×C₁₁	D₄×Q₈	1	1	yes	characteristic
226	C₄×C₁₁	#556	1	1	yes	characteristic
227	C₄×C₁₁	#557	1	1	yes	characteristic
228	C₂²×Q₈	C₂×C₄×C₁₁	1	2	yes	—
229	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
230	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
231	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
232	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
233	C₄⋊Q₈	—	2	4	no	—
234	C₄×Q₈	—	2	4	no	—
235	C₄×Q₈	—	2	4	no	—
236	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
237	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
238	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
239	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
240	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
241	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
242	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
243	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
244	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
245	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
246	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
247	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
248	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
249	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
250	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
251	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
252	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
253	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
254	C₄⋊C₈	—	2	4	no	—
255	C₄⋊C₈	—	2	4	no	—
256	C₄⋊C₈	—	2	2	no	—
257	C₄⋊C₈	—	2	2	no	—
258	C₄⋊C₈	D₄×C₁₁	1	4	yes	—
259	C₄⋊C₈	Q₈×C₁₁	1	4	yes	complemented
260	#97	—	2	4	no	—
261	#97	—	2	4	no	—
262	#97	—	2	4	no	—
263	C₄×C₈	—	2	4	no	—
264	#95	C₂×C₄×C₁₁	1	2	yes	—
265	#95	C₂×C₄×C₁₁	1	2	yes	—
266	#95	C₂×C₄×C₁₁	1	2	yes	—
267	#95	C₂×C₄×C₁₁	1	2	yes	—
268	C₂×C₁₁	#2365	1	1	yes	characteristic
269	C₂×C₁₁	#2932	1	1	yes	characteristic
270	C₂×C₁₁	D₄×M₁₆	1	1	yes	characteristic
271	C₂×C₁₁	#2961	1	1	yes	characteristic
272	C₂×C₁₁	Q₈×M₁₆	1	1	yes	characteristic
273	C₂×C₁₁	#2983	1	1	yes	characteristic
274	C₂×C₁₁	#2987	1	1	yes	characteristic
275	C₂×Q₈	—	2	4	no	—
276	C₂×Q₈	—	2	4	no	—
277	C₂×Q₈	—	4	2	no	—
278	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
279	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
280	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
281	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
282	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
283	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
284	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
285	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
286	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
287	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
288	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	2	2	no	—
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	2	2	no	—
299	C₂×C₈	C₂×D₄×C₁₁	1	4	yes	—
300	C₂×C₈	C₂×Q₈×C₁₁	1	4	yes	—
301	C₄⋊C₄	—	2	4	no	—
302	C₄⋊C₄	—	2	4	no	—
303	C₄⋊C₄	—	2	4	no	—
304	C₄⋊C₄	—	2	4	no	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	4	2	no	—
307	C₄⋊C₄	—	4	1	no	—
308	C₄⋊C₄	—	4	1	no	—
309	C₄⋊C₄	C₁₁×M₁₆	1	4	yes	—
310	C₄²	—	2	2	no	—
311	C₄²	—	2	2	no	—
312	C₄²	—	2	2	no	—
313	C₄²	—	2	2	no	—
314	C₄²	—	2	2	no	—
315	C₄²	—	2	1	no	—
316	C₄²	—	2	1	no	—
317	C₄²	—	4	1	no	—
318	C₄²	—	4	1	no	—
319	C₄²	—	4	1	no	—
320	C₄²	C₂×D₄×C₁₁	1	2	yes	—
321	C₄²	C₂×Q₈×C₁₁	1	2	yes	—
322	C₄²	C₁₁×#41	1	2	yes	—
323	C₄²	C₁₁×#41	1	2	yes	—
324	C₁₁	#23152	1	1	yes	characteristic, direct product factor, Sylow
325	C₂³	C₂³×C₄×C₁₁	1	1	yes	characteristic
326	Q₈	—	4	8	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
352	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
353	C₂×C₄	C₄×Q₈×C₁₁	1	2	yes	—
354	C₂×C₄	C₄×Q₈×C₁₁	1	2	yes	—
355	C₂×C₄	C₂×C₁₁×M₁₆	1	2	yes	—
356	C₂×C₄	C₂×C₁₁×M₁₆	1	4	yes	—
357	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
358	C₂×C₄	C₂²×Q₈×C₁₁	1	1	yes	characteristic
359	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
360	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
361	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
362	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
363	C₈	—	2	4	no	—
364	C₈	—	2	4	no	—
365	C₈	—	4	2	no	—
366	C₈	—	4	2	no	—
367	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
368	C₂²	C₂×C₄×Q₈×C₁₁	1	1	yes	characteristic
369	C₂²	C₁₁×#519	1	1	yes	characteristic
370	C₂²	C₂²×C₁₁×M₁₆	1	1	yes	characteristic
371	C₂²	C₁₁×#568	1	1	yes	characteristic
372	C₂²	C₁₁×#568	1	1	yes	characteristic
373	C₂²	C₁₁×#568	1	1	yes	characteristic
374	C₄	—	2	2	no	—
375	C₄	—	2	2	no	—
376	C₄	—	2	4	no	—
377	C₄	—	2	2	no	—
378	C₄	—	2	2	no	—
379	C₄	—	2	2	no	—
380	C₄	—	4	2	no	—
381	C₄	—	4	2	no	—
382	C₄	—	4	2	no	—
383	C₄	—	4	1	no	—
384	C₄	C₁₁×#547	1	1	yes	characteristic
385	C₄	D₄×Q₈×C₁₁	1	1	yes	characteristic
386	C₄	C₁₁×#556	1	1	yes	characteristic
387	C₄	C₁₁×#557	1	1	yes	characteristic
388	C₂	C₁₁×#2365	1	1	yes	characteristic
389	C₂	C₁₁×#2932	1	1	yes	characteristic
390	C₂	D₄×C₁₁×M₁₆	1	1	yes	characteristic
391	C₂	C₁₁×#2961	1	1	yes	characteristic
392	C₂	Q₈×C₁₁×M₁₆	1	1	yes	characteristic
393	C₂	C₁₁×#2983	1	1	yes	characteristic
394	C₂	C₁₁×#2987	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
69. C₁₁×C₄⋊C₈	Q₈	semidirect
78. #23152	C₁₁	direct (N × H)
259. C₄⋊C₈	Q₈×C₁₁	semidirect
324. C₁₁	#23152	direct (N × H)

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×#1940	2
C₁₁×#1917	2
C₁₁×#1916	2
C₁₁×#1771	2
C₁₁×#1767	2
#23152	11

Subgroups — C11×#23152 #14600345

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#23152 #14600345