Subgroups — C₁₁×#23343 #14600536

Order 2816.

700 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₁×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#1984	C₂	1	2	yes	maximal, complemented
3	C₁₁×#1940	C₂	1	2	yes	maximal, complemented
4	C₁₁×#1924	C₂	1	2	yes	maximal
5	C₁₁×#1923	C₂	1	2	yes	maximal
6	C₁₁×#1917	C₂	1	2	yes	maximal, complemented
7	C₁₁×#1916	C₂	1	2	yes	maximal, complemented
8	C₁₁×#1817	C₂	1	1	yes	maximal, characteristic
9	C₁₁×#1797	C₂	1	1	yes	maximal, characteristic
10	C₂×C₁₁×C₂²⋊Q₈	C₄	1	1	yes	characteristic
11	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
12	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
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	2	yes	—
16	C₂×C₁₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₁×C₂²⋊C₈	C₂²	1	2	yes	—
18	C₂×C₁₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₁×#97	C₂²	1	2	yes	—
20	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
21	C₁₁×#391	C₄	1	1	yes	characteristic
22	C₁₁×#389	C₄	1	1	yes	characteristic
23	C₁₁×#387	C₄	1	2	yes	—
24	C₁₁×#385	C₄	1	2	yes	—
25	C₁₁×#380	C₄	1	1	yes	characteristic
26	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
27	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₄×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	—
29	C₁₁×#336	C₂²	1	1	yes	characteristic
30	C₁₁×#336	C₂²	1	2	yes	—
31	C₁₁×#336	C₂²	1	2	yes	—
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	1	yes	characteristic
37	C₂²×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
38	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
39	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
40	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
41	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
42	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
43	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
44	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
45	C₁₁×C₂²⋊Q₈	—	2	4	no	—
46	C₄×Q₈×C₁₁	—	4	2	no	—
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	1	yes	characteristic
50	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
51	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
52	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
53	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
54	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
55	C₂×C₄²×C₁₁	—	4	2	no	—
56	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄²×C₁₁	C₂³	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	C₁₁×C₄⋊C₈	—	4	2	no	—
63	C₁₁×C₄⋊C₈	—	4	2	no	—
64	C₁₁×C₄⋊C₈	—	4	2	no	—
65	C₁₁×C₂²⋊C₈	—	4	2	no	—
66	C₁₁×C₂²⋊C₈	—	4	1	no	—
67	C₁₁×C₂²⋊C₈	—	4	1	no	—
68	C₁₁×#97	—	4	2	no	—
69	C₄×C₈×C₁₁	—	4	2	no	—
70	C₁₁×#95	C₂×C₄	1	2	yes	—
71	C₁₁×#95	C₂×C₄	1	2	yes	—
72	C₁₁×#95	C₂×C₄	1	2	yes	—
73	C₁₁×#95	C₂×C₄	1	2	yes	—
74	C₁₁×#95	C₂×C₄	1	2	yes	—
75	#23343	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
76	C₂⁴×C₁₁	C₂²×C₄	1	1	yes	characteristic
77	C₂×Q₈×C₁₁	—	4	1	no	—
78	C₂×Q₈×C₁₁	—	4	1	no	—
79	C₂×Q₈×C₁₁	M₁₆	1	4	yes	—
80	C₂²×C₄×C₁₁	—	2	2	no	—
81	C₂²×C₄×C₁₁	—	2	2	no	—
82	C₂²×C₄×C₁₁	—	2	2	no	—
83	C₂²×C₄×C₁₁	—	2	1	no	—
84	C₂²×C₄×C₁₁	—	2	2	no	—
85	C₂²×C₄×C₁₁	—	2	2	no	—
86	C₂²×C₄×C₁₁	—	2	1	no	—
87	C₂²×C₄×C₁₁	—	4	1	no	—
88	C₂²×C₄×C₁₁	—	4	1	no	—
89	C₂²×C₄×C₁₁	—	4	1	no	—
90	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
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	2	yes	—
95	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
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	2	no	—
103	C₂×C₈×C₁₁	—	2	2	no	—
104	C₂×C₈×C₁₁	—	2	2	no	—
105	C₂×C₈×C₁₁	—	2	2	no	—
106	C₂×C₈×C₁₁	—	2	2	no	—
107	C₂×C₈×C₁₁	—	2	2	no	—
108	C₂×C₈×C₁₁	—	2	2	no	—
109	C₂×C₈×C₁₁	—	2	2	no	—
110	C₂×C₈×C₁₁	—	2	2	no	—
111	C₂×C₈×C₁₁	—	2	2	no	—
112	C₁₁×C₄⋊C₄	—	2	2	no	—
113	C₁₁×C₄⋊C₄	—	2	4	no	—
114	C₁₁×C₄⋊C₄	—	2	4	no	—
115	C₁₁×C₄⋊C₄	—	4	1	no	—
116	C₁₁×C₄⋊C₄	—	4	1	no	—
117	C₁₁×C₄⋊C₄	—	4	2	no	—
118	C₁₁×C₂²⋊C₄	—	2	4	no	—
119	C₁₁×C₂²⋊C₄	—	2	4	no	—
120	C₄²×C₁₁	—	2	2	no	—
121	C₄²×C₁₁	—	2	2	no	—
122	C₄²×C₁₁	—	2	2	no	—
123	C₄²×C₁₁	—	2	2	no	—
124	C₄²×C₁₁	—	2	2	no	—
125	C₄²×C₁₁	—	2	2	no	—
126	C₄²×C₁₁	—	4	1	no	—
127	C₄²×C₁₁	—	4	1	no	—
128	C₄×C₂²⋊Q₈	C₂×C₁₁	1	1	yes	characteristic
129	#1984	C₂×C₁₁	1	2	yes	complemented
130	#1940	C₂×C₁₁	1	2	yes	complemented
131	#1924	C₂×C₁₁	1	2	yes	—
132	#1923	C₂×C₁₁	1	2	yes	—
133	#1917	C₂×C₁₁	1	2	yes	complemented
134	#1916	C₂×C₁₁	1	2	yes	complemented
135	#1817	C₂×C₁₁	1	1	yes	characteristic
136	#1797	C₂×C₁₁	1	1	yes	characteristic
137	C₂³×C₁₁	—	2	1	no	—
138	C₂³×C₁₁	—	2	1	no	—
139	C₂³×C₁₁	—	2	1	no	—
140	C₂³×C₁₁	—	2	1	no	—
141	C₂³×C₁₁	—	2	1	no	—
142	C₂³×C₁₁	—	2	1	no	—
143	C₂³×C₁₁	#131	1	2	yes	—
144	C₂³×C₁₁	C₂³×C₄	1	1	yes	characteristic
145	Q₈×C₁₁	—	4	4	no	—
146	C₂×C₄×C₁₁	—	2	1	no	—
147	C₂×C₄×C₁₁	—	2	1	no	—
148	C₂×C₄×C₁₁	—	2	2	no	—
149	C₂×C₄×C₁₁	—	2	1	no	—
150	C₂×C₄×C₁₁	—	2	1	no	—
151	C₂×C₄×C₁₁	—	2	2	no	—
152	C₂×C₄×C₁₁	—	2	1	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	2	no	—
158	C₂×C₄×C₁₁	—	2	2	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	2	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	1	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	—	4	4	no	—
171	C₂×C₄×C₁₁	—	4	4	no	—
172	C₂×C₄×C₁₁	—	4	2	no	—
173	C₂×C₄×C₁₁	—	4	2	no	—
174	C₂×C₄×C₁₁	C₂×M₁₆	1	4	yes	—
175	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
176	C₂×C₄×C₁₁	#131	1	2	yes	—
177	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
178	C₂×C₄×C₁₁	H(5,𝔽₂)	1	2	yes	—
179	C₂×C₄×C₁₁	2₋¹⁺⁴	1	2	yes	—
180	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
181	C₈×C₁₁	—	4	2	no	—
182	C₈×C₁₁	—	4	2	no	—
183	C₈×C₁₁	—	4	2	no	—
184	C₈×C₁₁	—	4	2	no	—
185	C₂×C₂²⋊Q₈	C₄×C₁₁	1	1	yes	characteristic
186	C₂×C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
187	C₂²×C₄²	C₂²×C₁₁	1	1	yes	characteristic
188	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
189	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
190	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
191	C₂×C₂²⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
192	C₂×C₂²⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
193	C₂×C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
194	C₂×#97	C₂²×C₁₁	1	2	yes	—
195	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	—
196	#391	C₄×C₁₁	1	1	yes	characteristic
197	#389	C₄×C₁₁	1	1	yes	characteristic
198	#387	C₄×C₁₁	1	2	yes	—
199	#385	C₄×C₁₁	1	2	yes	—
200	#380	C₄×C₁₁	1	1	yes	characteristic
201	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
202	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
203	C₄×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	—
204	#336	C₂²×C₁₁	1	2	yes	—
205	#336	C₂²×C₁₁	1	1	yes	characteristic
206	#336	C₂²×C₁₁	1	2	yes	—
207	#336	C₂²×C₁₁	1	1	yes	characteristic
208	#336	C₂²×C₁₁	1	2	yes	—
209	#336	C₂²×C₁₁	1	2	yes	—
210	#336	C₂²×C₁₁	1	2	yes	—
211	#336	C₂²×C₁₁	1	2	yes	—
212	C₂²×C₁₁	—	2	2	no	—
213	C₂²×C₁₁	—	2	2	no	—
214	C₂²×C₁₁	—	2	2	no	—
215	C₂²×C₁₁	—	4	1	no	—
216	C₂²×C₁₁	—	4	1	no	—
217	C₂²×C₁₁	—	4	1	no	—
218	C₂²×C₁₁	—	4	1	no	—
219	C₂²×C₁₁	#518	1	1	yes	characteristic
220	C₂²×C₁₁	#519	1	1	yes	characteristic
221	C₂²×C₁₁	#520	1	1	yes	characteristic
222	C₂²×C₁₁	C₂²×M₁₆	1	1	yes	characteristic
223	C₂²×C₁₁	C₂×#131	1	1	yes	characteristic
224	C₂²×C₁₁	C₂×#131	1	1	yes	characteristic
225	C₂²×C₁₁	#568	1	1	yes	characteristic
226	C₄×C₁₁	—	2	2	no	—
227	C₄×C₁₁	—	2	4	no	—
228	C₄×C₁₁	—	2	2	no	—
229	C₄×C₁₁	—	4	1	no	—
230	C₄×C₁₁	—	4	1	no	—
231	C₄×C₁₁	—	4	2	no	—
232	C₄×C₁₁	—	4	1	no	—
233	C₄×C₁₁	—	4	2	no	—
234	C₄×C₁₁	—	4	2	no	—
235	C₄×C₁₁	#562	1	2	yes	—
236	C₄×C₁₁	#563	1	2	yes	—
237	C₂²×Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
238	C₂³×C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
239	C₂³×C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
240	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
241	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
242	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
243	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
244	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
245	C₂²⋊Q₈	—	2	4	no	—
246	C₄×Q₈	—	4	2	no	—
247	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
248	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
249	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
250	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
251	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
252	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
253	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
254	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
255	C₂×C₄²	—	4	2	no	—
256	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
257	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
258	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
259	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
260	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
261	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
262	C₄⋊C₈	—	4	2	no	—
263	C₄⋊C₈	—	4	2	no	—
264	C₄⋊C₈	—	4	2	no	—
265	C₂²⋊C₈	—	4	2	no	—
266	C₂²⋊C₈	—	4	1	no	—
267	C₂²⋊C₈	—	4	1	no	—
268	#97	—	4	2	no	—
269	C₄×C₈	—	4	2	no	—
270	#95	C₂×C₄×C₁₁	1	2	yes	—
271	#95	C₂×C₄×C₁₁	1	2	yes	—
272	#95	C₂×C₄×C₁₁	1	2	yes	—
273	#95	C₂×C₄×C₁₁	1	2	yes	—
274	#95	C₂×C₄×C₁₁	1	2	yes	—
275	C₂×C₁₁	—	4	2	no	—
276	C₂×C₁₁	#2378	1	1	yes	characteristic
277	C₂×C₁₁	#2973	1	1	yes	characteristic
278	C₂×C₁₁	#2977	1	1	yes	characteristic
279	C₂×C₁₁	#2984	1	1	yes	characteristic
280	C₂×C₁₁	#2985	1	1	yes	characteristic
281	C₂×C₁₁	#2991	1	1	yes	characteristic
282	C₂×C₁₁	#2992	1	1	yes	characteristic
283	C₂⁴	C₂²×C₄×C₁₁	1	1	yes	characteristic
284	C₂×Q₈	—	4	1	no	—
285	C₂×Q₈	—	4	1	no	—
286	C₂×Q₈	C₁₁×M₁₆	1	4	yes	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	1	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	2	1	no	—
294	C₂²×C₄	—	4	1	no	—
295	C₂²×C₄	—	4	1	no	—
296	C₂²×C₄	—	4	1	no	—
297	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
298	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
299	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
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	C₂⁴×C₁₁	1	1	yes	characteristic
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	2	2	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	2	4	no	—
321	C₄⋊C₄	—	2	4	no	—
322	C₄⋊C₄	—	4	1	no	—
323	C₄⋊C₄	—	4	2	no	—
324	C₄⋊C₄	—	4	1	no	—
325	C₂²⋊C₄	—	2	4	no	—
326	C₂²⋊C₄	—	2	4	no	—
327	C₄²	—	2	2	no	—
328	C₄²	—	2	2	no	—
329	C₄²	—	2	2	no	—
330	C₄²	—	2	2	no	—
331	C₄²	—	2	2	no	—
332	C₄²	—	2	2	no	—
333	C₄²	—	4	1	no	—
334	C₄²	—	4	1	no	—
335	C₁₁	#23343	1	1	yes	characteristic, direct product factor, Sylow
336	C₂³	—	2	1	no	—
337	C₂³	—	2	1	no	—
338	C₂³	—	2	1	no	—
339	C₂³	—	2	1	no	—
340	C₂³	—	2	1	no	—
341	C₂³	—	2	1	no	—
342	C₂³	C₁₁×#131	1	2	yes	—
343	C₂³	C₂³×C₄×C₁₁	1	1	yes	characteristic
344	Q₈	—	4	4	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	4	4	no	—
370	C₂×C₄	—	4	4	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	C₂×C₁₁×M₁₆	1	4	yes	—
374	C₂×C₄	C₂×C₁₁×M₁₆	1	2	yes	—
375	C₂×C₄	C₁₁×#131	1	2	yes	—
376	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
377	C₂×C₄	C₁₁×H(5,𝔽₂)	1	2	yes	—
378	C₂×C₄	C₁₁×2₋¹⁺⁴	1	2	yes	—
379	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
380	C₈	—	4	2	no	—
381	C₈	—	4	2	no	—
382	C₈	—	4	2	no	—
383	C₈	—	4	2	no	—
384	C₂²	—	2	2	no	—
385	C₂²	—	2	2	no	—
386	C₂²	—	2	2	no	—
387	C₂²	—	4	1	no	—
388	C₂²	—	4	1	no	—
389	C₂²	—	4	1	no	—
390	C₂²	—	4	1	no	—
391	C₂²	C₁₁×#518	1	1	yes	characteristic
392	C₂²	C₁₁×#519	1	1	yes	characteristic
393	C₂²	C₁₁×#520	1	1	yes	characteristic
394	C₂²	C₂²×C₁₁×M₁₆	1	1	yes	characteristic
395	C₂²	C₂×C₁₁×#131	1	1	yes	characteristic
396	C₂²	C₂×C₁₁×#131	1	1	yes	characteristic
397	C₂²	C₁₁×#568	1	1	yes	characteristic
398	C₄	—	2	2	no	—
399	C₄	—	2	4	no	—
400	C₄	—	2	2	no	—
401	C₄	—	4	1	no	—
402	C₄	—	4	1	no	—
403	C₄	—	4	1	no	—
404	C₄	—	4	2	no	—
405	C₄	—	4	2	no	—
406	C₄	—	4	2	no	—
407	C₄	C₁₁×#562	1	2	yes	—
408	C₄	C₁₁×#563	1	2	yes	—
409	C₂	—	4	2	no	—
410	C₂	C₁₁×#2378	1	1	yes	characteristic
411	C₂	C₁₁×#2973	1	1	yes	characteristic
412	C₂	C₁₁×#2977	1	1	yes	characteristic
413	C₂	C₁₁×#2984	1	1	yes	characteristic
414	C₂	C₁₁×#2985	1	1	yes	characteristic
415	C₂	C₁₁×#2991	1	1	yes	characteristic
416	C₂	C₁₁×#2992	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₁	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
socle	C₂³×C₁₁	C₂³×C₄
prime radical	C₂⁴×C₁₁	C₂²×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
2. C₁₁×#1984	C₂	semidirect
3. C₁₁×#1940	C₂	semidirect
6. C₁₁×#1917	C₂	semidirect
7. C₁₁×#1916	C₂	semidirect
75. #23343	C₁₁	direct (N × H)
129. #1984	C₂×C₁₁	semidirect
130. #1940	C₂×C₁₁	semidirect
133. #1917	C₂×C₁₁	semidirect
134. #1916	C₂×C₁₁	semidirect
335. C₁₁	#23343	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×C₂²⋊Q₈	2
C₁₁×#1984	2
C₁₁×#1940	2
C₁₁×#1924	2
C₁₁×#1923	2
C₁₁×#1917	2
C₁₁×#1916	2
C₁₁×#1817	2
C₁₁×#1797	2
#23343	11

Subgroups — C11×#23343 #14600536

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#23343 #14600536