Subgroups — C₁₁×#23237 #14600430

Order 2816.

844 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×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#1984	C₂	1	2	yes	maximal, complemented
3	C₁₁×#1916	C₂	1	2	yes	maximal, complemented
4	C₁₁×#1916	C₂	1	2	yes	maximal, complemented
5	C₁₁×#1850	C₂	1	2	yes	maximal
6	C₈×C₁₁×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
7	C₈×C₁₁×C₂²⋊C₄	C₂	1	2	yes	maximal
8	C₄×C₁₁×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
9	C₂×C₁₁×#336	C₂	1	1	yes	maximal, characteristic
10	C₂³×C₈×C₁₁	C₂²	1	2	yes	—
11	C₂×C₁₁×C₂²⋊Q₈	C₄	1	1	yes	characteristic
12	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
13	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
18	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
19	C₂×C₄×C₈×C₁₁	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	1	yes	characteristic
27	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
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	1	yes	characteristic
36	C₁₁×#336	C₂²	1	2	yes	—
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	—	2	4	no	—
42	C₂²×C₈×C₁₁	—	2	4	no	—
43	C₂²×C₈×C₁₁	—	4	2	no	—
44	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
45	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
46	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
47	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
48	C₁₁×C₂²⋊Q₈	C₈	1	8	yes	complemented
49	C₄×Q₈×C₁₁	—	4	2	no	—
50	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
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	2	yes	—
54	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
55	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
56	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
57	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
58	C₂×C₄²×C₁₁	—	4	2	no	—
59	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
63	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
64	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
65	C₁₁×C₄⋊C₈	—	2	4	no	—
66	C₁₁×C₄⋊C₈	—	4	2	no	—
67	C₁₁×C₂²⋊C₈	—	2	2	no	—
68	C₁₁×C₂²⋊C₈	Q₈	1	4	yes	complemented
69	C₄×C₈×C₁₁	—	2	4	no	—
70	C₄×C₈×C₁₁	—	4	2	no	—
71	C₄×C₈×C₁₁	—	4	2	no	—
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	C₁₁×#95	C₂×C₄	1	2	yes	—
76	C₁₁×#95	C₂×C₄	1	2	yes	—
77	#23237	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
78	C₂⁴×C₁₁	C₂²×C₄	1	1	yes	characteristic
79	C₂×Q₈×C₁₁	—	4	1	no	—
80	C₂×Q₈×C₁₁	—	4	1	no	—
81	C₂×Q₈×C₁₁	C₂×C₈	1	4	yes	complemented
82	C₂²×C₄×C₁₁	—	2	2	no	—
83	C₂²×C₄×C₁₁	—	2	2	no	—
84	C₂²×C₄×C₁₁	—	2	2	no	—
85	C₂²×C₄×C₁₁	—	2	2	no	—
86	C₂²×C₄×C₁₁	—	4	1	no	—
87	C₂²×C₄×C₁₁	—	4	1	no	—
88	C₂²×C₄×C₁₁	—	4	1	no	—
89	C₂²×C₄×C₁₁	C₂×C₈	1	4	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	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	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	C₂×Q₈	1	2	yes	—
100	C₂²×C₄×C₁₁	#41	1	2	yes	—
101	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
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	C₂×C₈×C₁₁	—	4	8	no	—
113	C₂×C₈×C₁₁	C₂×Q₈	1	4	yes	—
114	C₂×C₈×C₁₁	#41	1	4	yes	—
115	C₁₁×C₄⋊C₄	—	2	4	no	—
116	C₁₁×C₄⋊C₄	—	4	1	no	—
117	C₁₁×C₄⋊C₄	—	4	1	no	—
118	C₁₁×C₄⋊C₄	—	4	2	no	—
119	C₁₁×C₄⋊C₄	C₂×C₈	1	4	yes	complemented
120	C₁₁×C₄⋊C₄	C₂×C₈	1	8	yes	complemented
121	C₁₁×C₂²⋊C₄	—	2	4	no	—
122	C₁₁×C₂²⋊C₄	C₂×C₈	1	8	yes	—
123	C₄²×C₁₁	—	2	2	no	—
124	C₄²×C₁₁	—	2	2	no	—
125	C₄²×C₁₁	—	2	2	no	—
126	C₄²×C₁₁	—	2	2	no	—
127	C₄²×C₁₁	—	2	2	no	—
128	C₄²×C₁₁	—	2	2	no	—
129	C₄²×C₁₁	—	4	1	no	—
130	C₄²×C₁₁	—	4	1	no	—
131	C₄×C₂²⋊Q₈	C₂×C₁₁	1	1	yes	characteristic
132	#1984	C₂×C₁₁	1	2	yes	complemented
133	#1916	C₂×C₁₁	1	2	yes	complemented
134	#1916	C₂×C₁₁	1	2	yes	complemented
135	#1850	C₂×C₁₁	1	2	yes	—
136	C₈×C₄⋊C₄	C₂×C₁₁	1	2	yes	complemented
137	C₈×C₂²⋊C₄	C₂×C₁₁	1	2	yes	—
138	C₄×C₂²⋊C₈	C₂×C₁₁	1	1	yes	characteristic
139	C₂×#336	C₂×C₁₁	1	1	yes	characteristic
140	C₂³×C₁₁	—	2	1	no	—
141	C₂³×C₁₁	—	2	1	no	—
142	C₂³×C₁₁	—	2	1	no	—
143	C₂³×C₁₁	—	2	1	no	—
144	C₂³×C₁₁	C₄×Q₈	1	2	yes	—
145	C₂³×C₁₁	C₂²×C₈	1	2	yes	—
146	C₂³×C₁₁	#131	1	2	yes	—
147	C₂³×C₁₁	C₂³×C₄	1	1	yes	characteristic
148	Q₈×C₁₁	—	4	4	no	—
149	C₂×C₄×C₁₁	—	2	2	no	—
150	C₂×C₄×C₁₁	—	2	1	no	—
151	C₂×C₄×C₁₁	—	2	1	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	2	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	4	no	—
162	C₂×C₄×C₁₁	—	2	4	no	—
163	C₂×C₄×C₁₁	—	2	2	no	—
164	C₂×C₄×C₁₁	—	2	1	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	2	no	—
169	C₂×C₄×C₁₁	—	2	1	no	—
170	C₂×C₄×C₁₁	—	2	1	no	—
171	C₂×C₄×C₁₁	—	2	2	no	—
172	C₂×C₄×C₁₁	—	4	4	no	—
173	C₂×C₄×C₁₁	—	4	4	no	—
174	C₂×C₄×C₁₁	C₄×Q₈	1	2	yes	—
175	C₂×C₄×C₁₁	C₂²×C₈	1	4	yes	—
176	C₂×C₄×C₁₁	C₂²×C₈	1	4	yes	—
177	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
178	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
179	C₂×C₄×C₁₁	#131	1	2	yes	—
180	C₂×C₄×C₁₁	C₂²×Q₈	1	1	yes	characteristic
181	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
182	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
183	C₂×C₄×C₁₁	H(5,𝔽₂)	1	2	yes	—
184	C₈×C₁₁	—	2	4	no	—
185	C₈×C₁₁	—	2	4	no	—
186	C₈×C₁₁	—	4	2	no	—
187	C₈×C₁₁	—	4	2	no	—
188	C₂³×C₈	C₂²×C₁₁	1	2	yes	—
189	C₂×C₂²⋊Q₈	C₄×C₁₁	1	1	yes	characteristic
190	C₂×C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
191	C₂²×C₄²	C₂²×C₁₁	1	1	yes	characteristic
192	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
193	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
194	C₂×C₂²⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
195	C₂×C₂²⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
196	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	—
197	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	—
198	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	—
199	#391	C₄×C₁₁	1	1	yes	characteristic
200	#389	C₄×C₁₁	1	1	yes	characteristic
201	#387	C₄×C₁₁	1	2	yes	—
202	#385	C₄×C₁₁	1	2	yes	—
203	#380	C₄×C₁₁	1	1	yes	characteristic
204	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
205	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
206	C₄×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	—
207	#336	C₂²×C₁₁	1	2	yes	—
208	#336	C₂²×C₁₁	1	2	yes	—
209	#336	C₂²×C₁₁	1	1	yes	characteristic
210	#336	C₂²×C₁₁	1	2	yes	—
211	#336	C₂²×C₁₁	1	2	yes	—
212	#336	C₂²×C₁₁	1	2	yes	—
213	#336	C₂²×C₁₁	1	2	yes	—
214	#336	C₂²×C₁₁	1	1	yes	characteristic
215	C₂²×C₁₁	—	2	2	no	—
216	C₂²×C₁₁	—	2	2	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	C₈×Q₈	1	4	yes	—
222	C₂²×C₁₁	C₂×C₄×Q₈	1	1	yes	characteristic
223	C₂²×C₁₁	C₄×#41	1	1	yes	characteristic
224	C₂²×C₁₁	#518	1	1	yes	characteristic
225	C₂²×C₁₁	C₂³×C₈	1	1	yes	characteristic
226	C₂²×C₁₁	C₂×#131	1	1	yes	characteristic
227	C₂²×C₁₁	C₂×#131	1	1	yes	characteristic
228	C₂²×C₁₁	#568	1	1	yes	characteristic
229	C₄×C₁₁	—	2	2	no	—
230	C₄×C₁₁	—	2	4	no	—
231	C₄×C₁₁	—	2	2	no	—
232	C₄×C₁₁	—	2	2	no	—
233	C₄×C₁₁	—	2	4	no	—
234	C₄×C₁₁	—	2	2	no	—
235	C₄×C₁₁	—	4	2	no	—
236	C₄×C₁₁	—	4	2	no	—
237	C₄×C₁₁	—	4	1	no	—
238	C₄×C₁₁	#551	1	2	yes	—
239	C₄×C₁₁	#554	1	2	yes	—
240	C₂²×Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
241	C₂³×C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
242	C₂³×C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
243	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
244	C₂²×C₈	—	2	4	no	—
245	C₂²×C₈	—	2	4	no	—
246	C₂²×C₈	—	4	2	no	—
247	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
248	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
249	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
250	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
251	C₂²⋊Q₈	C₈×C₁₁	1	8	yes	complemented
252	C₄×Q₈	—	4	2	no	—
253	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
254	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
255	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
256	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
257	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
258	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
259	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
260	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
261	C₂×C₄²	—	4	2	no	—
262	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
263	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
264	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
265	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
266	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
267	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
268	C₄⋊C₈	—	2	4	no	—
269	C₄⋊C₈	—	4	2	no	—
270	C₂²⋊C₈	—	2	2	no	—
271	C₂²⋊C₈	Q₈×C₁₁	1	4	yes	complemented
272	C₄×C₈	—	2	4	no	—
273	C₄×C₈	—	4	2	no	—
274	C₄×C₈	—	4	2	no	—
275	#95	C₂×C₄×C₁₁	1	2	yes	—
276	#95	C₂×C₄×C₁₁	1	2	yes	—
277	#95	C₂×C₄×C₁₁	1	2	yes	—
278	#95	C₂×C₄×C₁₁	1	2	yes	—
279	#95	C₂×C₄×C₁₁	1	2	yes	—
280	C₂×C₁₁	—	2	4	no	—
281	C₂×C₁₁	#2368	1	1	yes	characteristic
282	C₂×C₁₁	C₂×C₈×Q₈	1	1	yes	characteristic
283	C₂×C₁₁	#2962	1	1	yes	characteristic
284	C₂×C₁₁	C₈×#41	1	1	yes	characteristic
285	C₂×C₁₁	#2968	1	1	yes	characteristic
286	C₂×C₁₁	#2972	1	1	yes	characteristic
287	C₂×C₁₁	#2977	1	1	yes	characteristic
288	C₂⁴	C₂²×C₄×C₁₁	1	1	yes	characteristic
289	C₂×Q₈	—	4	1	no	—
290	C₂×Q₈	—	4	1	no	—
291	C₂×Q₈	C₂×C₈×C₁₁	1	4	yes	complemented
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	4	1	no	—
297	C₂²×C₄	—	4	1	no	—
298	C₂²×C₄	—	4	1	no	—
299	C₂²×C₄	C₂×C₈×C₁₁	1	4	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	2	yes	—
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	2	yes	—
307	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
308	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
309	C₂²×C₄	C₂×Q₈×C₁₁	1	2	yes	—
310	C₂²×C₄	C₁₁×#41	1	2	yes	—
311	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
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	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	4	8	no	—
323	C₂×C₈	C₂×Q₈×C₁₁	1	4	yes	—
324	C₂×C₈	C₁₁×#41	1	4	yes	—
325	C₄⋊C₄	—	2	4	no	—
326	C₄⋊C₄	—	4	1	no	—
327	C₄⋊C₄	—	4	2	no	—
328	C₄⋊C₄	—	4	1	no	—
329	C₄⋊C₄	C₂×C₈×C₁₁	1	4	yes	complemented
330	C₄⋊C₄	C₂×C₈×C₁₁	1	8	yes	complemented
331	C₂²⋊C₄	—	2	4	no	—
332	C₂²⋊C₄	C₂×C₈×C₁₁	1	8	yes	—
333	C₄²	—	2	2	no	—
334	C₄²	—	2	2	no	—
335	C₄²	—	2	2	no	—
336	C₄²	—	2	2	no	—
337	C₄²	—	2	2	no	—
338	C₄²	—	2	2	no	—
339	C₄²	—	4	1	no	—
340	C₄²	—	4	1	no	—
341	C₁₁	#23237	1	1	yes	characteristic, direct product factor, Sylow
342	C₂³	—	2	1	no	—
343	C₂³	—	2	1	no	—
344	C₂³	—	2	1	no	—
345	C₂³	—	2	1	no	—
346	C₂³	C₄×Q₈×C₁₁	1	2	yes	—
347	C₂³	C₂²×C₈×C₁₁	1	2	yes	—
348	C₂³	C₁₁×#131	1	2	yes	—
349	C₂³	C₂³×C₄×C₁₁	1	1	yes	characteristic
350	Q₈	—	4	4	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	4	4	no	—
375	C₂×C₄	—	4	4	no	—
376	C₂×C₄	C₄×Q₈×C₁₁	1	2	yes	—
377	C₂×C₄	C₂²×C₈×C₁₁	1	4	yes	—
378	C₂×C₄	C₂²×C₈×C₁₁	1	4	yes	—
379	C₂×C₄	C₂²×C₈×C₁₁	1	2	yes	—
380	C₂×C₄	C₂²×C₈×C₁₁	1	2	yes	—
381	C₂×C₄	C₁₁×#131	1	2	yes	—
382	C₂×C₄	C₂²×Q₈×C₁₁	1	1	yes	characteristic
383	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
384	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
385	C₂×C₄	C₁₁×H(5,𝔽₂)	1	2	yes	—
386	C₈	—	2	4	no	—
387	C₈	—	2	4	no	—
388	C₈	—	4	2	no	—
389	C₈	—	4	2	no	—
390	C₂²	—	2	2	no	—
391	C₂²	—	2	2	no	—
392	C₂²	—	2	2	no	—
393	C₂²	—	2	2	no	—
394	C₂²	—	2	2	no	—
395	C₂²	—	2	2	no	—
396	C₂²	C₈×Q₈×C₁₁	1	4	yes	—
397	C₂²	C₂×C₄×Q₈×C₁₁	1	1	yes	characteristic
398	C₂²	C₄×C₁₁×#41	1	1	yes	characteristic
399	C₂²	C₁₁×#518	1	1	yes	characteristic
400	C₂²	C₂³×C₈×C₁₁	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	4	no	—
405	C₄	—	2	2	no	—
406	C₄	—	2	2	no	—
407	C₄	—	2	4	no	—
408	C₄	—	2	2	no	—
409	C₄	—	2	2	no	—
410	C₄	—	4	2	no	—
411	C₄	—	4	1	no	—
412	C₄	—	4	2	no	—
413	C₄	C₁₁×#551	1	2	yes	—
414	C₄	C₁₁×#554	1	2	yes	—
415	C₂	—	2	4	no	—
416	C₂	C₁₁×#2368	1	1	yes	characteristic
417	C₂	C₂×C₈×Q₈×C₁₁	1	1	yes	characteristic
418	C₂	C₁₁×#2962	1	1	yes	characteristic
419	C₂	C₈×C₁₁×#41	1	1	yes	characteristic
420	C₂	C₁₁×#2968	1	1	yes	characteristic
421	C₂	C₁₁×#2972	1	1	yes	characteristic
422	C₂	C₁₁×#2977	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₁	C₂⁴
commutator	C₂²	C₂³×C₈×C₁₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
socle	C₂³×C₁₁	C₂³×C₄
prime radical	C₂⁴×C₁₁	C₂²×C₄
LCS	G ▷ C₂² ▷ 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×#1916	C₂	semidirect
4. C₁₁×#1916	C₂	semidirect
6. C₈×C₁₁×C₄⋊C₄	C₂	semidirect
48. C₁₁×C₂²⋊Q₈	C₈	semidirect
68. C₁₁×C₂²⋊C₈	Q₈	semidirect
77. #23237	C₁₁	direct (N × H)
81. C₂×Q₈×C₁₁	C₂×C₈	semidirect
119. C₁₁×C₄⋊C₄	C₂×C₈	semidirect
120. C₁₁×C₄⋊C₄	C₂×C₈	semidirect
132. #1984	C₂×C₁₁	semidirect
133. #1916	C₂×C₁₁	semidirect
134. #1916	C₂×C₁₁	semidirect
136. C₈×C₄⋊C₄	C₂×C₁₁	semidirect
251. C₂²⋊Q₈	C₈×C₁₁	semidirect
271. C₂²⋊C₈	Q₈×C₁₁	semidirect
291. C₂×Q₈	C₂×C₈×C₁₁	semidirect
329. C₄⋊C₄	C₂×C₈×C₁₁	semidirect
330. C₄⋊C₄	C₂×C₈×C₁₁	semidirect
341. C₁₁	#23237	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×#1916	2
C₁₁×#1850	2
C₈×C₁₁×C₄⋊C₄	2
C₈×C₁₁×C₂²⋊C₄	2
C₄×C₁₁×C₂²⋊C₈	2
C₂×C₁₁×#336	2
#23237	11

Subgroups — C11×#23237 #14600430

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#23237 #14600430