Subgroups — C₁₁×#23191 #14600384

Order 2816.

1026 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#495	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₁×#440	C₂	1	2	yes	maximal, complemented
3	C₁₁×#2367	C₂	1	2	yes	maximal, complemented
4	C₁₁×#1983	C₂	1	2	yes	maximal, complemented
5	C₁₁×#1973	C₂	1	2	yes	maximal, complemented
6	C₁₁×#1879	C₂	1	2	yes	maximal
7	C₁₁×#1878	C₂	1	2	yes	maximal, complemented
8	C₄×C₁₁×#107	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁×#1770	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₁₁×Q₁₆	C₂²	1	1	yes	characteristic
11	C₂²×C₁₁×SD₁₆	C₂²	1	2	yes	—
12	C₂²×C₁₁×D₈	C₂²	1	1	yes	characteristic
13	C₂×C₁₁×#124	C₂²	1	2	yes	—
14	C₂×C₄×Q₈×C₁₁	C₂²	1	2	yes	—
15	C₂×C₄×D₄×C₁₁	C₂²	1	2	yes	—
16	C₁₁×#495	C₄	1	8	yes	complemented
17	C₁₁×#440	—	2	8	no	—
18	C₂×C₁₁×#107	C₂²	1	1	yes	characteristic
19	C₂×C₁₁×#107	C₂²	1	1	yes	characteristic
20	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₁×#103	C₂²	1	2	yes	—
22	C₂×C₁₁×#103	C₂²	1	2	yes	—
23	C₂×C₁₁×#102	C₂²	1	2	yes	—
24	C₂×C₁₁×#102	C₂²	1	2	yes	—
25	C₂×C₁₁×#97	C₂²	1	2	yes	—
26	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
27	C₁₁×#391	C₂²	1	2	yes	—
28	C₁₁×#390	C₂²	1	2	yes	—
29	C₁₁×#388	—	2	2	no	—
30	C₁₁×#388	—	2	2	no	—
31	C₁₁×#385	—	2	2	no	—
32	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
33	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₄×C₁₁×C₂²⋊C₄	—	2	2	no	—
35	C₁₁×#340	C₂²	1	2	yes	—
36	C₁₁×#336	C₂²	1	2	yes	—
37	C₂²×Q₈×C₁₁	C₂³	1	2	yes	—
38	C₂²×D₄×C₁₁	C₂³	1	2	yes	—
39	C₂³×C₄×C₁₁	—	2	2	no	—
40	C₂×C₁₁×Q₁₆	—	4	1	no	—
41	C₂×C₁₁×Q₁₆	—	4	1	no	—
42	C₂×C₁₁×Q₁₆	C₂×C₄	1	4	yes	complemented
43	C₂×C₁₁×SD₁₆	—	2	4	no	—
44	C₂×C₁₁×SD₁₆	—	2	4	no	—
45	C₂×C₁₁×SD₁₆	C₂×C₄	1	8	yes	complemented
46	C₂×C₁₁×D₈	—	4	1	no	—
47	C₂×C₁₁×D₈	—	4	1	no	—
48	C₂×C₁₁×D₈	C₂×C₄	1	4	yes	—
49	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
50	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
52	C₁₁×#124	—	2	4	no	—
53	C₁₁×#124	C₂×C₄	1	8	yes	complemented
54	C₄×Q₈×C₁₁	—	2	4	no	—
55	C₄×Q₈×C₁₁	—	4	2	no	—
56	C₄×D₄×C₁₁	—	2	4	no	—
57	C₄×D₄×C₁₁	—	4	2	no	—
58	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
59	C₂×C₁₁×C₄⋊C₄	D₄	1	1	yes	characteristic
60	C₂×C₁₁×C₄⋊C₄	D₄	1	1	yes	characteristic
61	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
62	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
63	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
64	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
65	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
66	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
67	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
68	C₂×C₄²×C₁₁	—	2	2	no	—
69	C₂×C₄²×C₁₁	—	2	2	no	—
70	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
71	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
72	C₁₁×#107	—	2	2	no	—
73	C₁₁×#107	D₄	1	4	yes	—
74	C₁₁×C₄⋊C₈	—	2	2	no	—
75	C₁₁×#103	—	2	4	no	—
76	C₁₁×#103	—	4	2	no	—
77	C₁₁×#102	—	2	4	no	—
78	C₁₁×#102	—	4	2	no	—
79	C₁₁×#97	—	2	4	no	—
80	C₄×C₈×C₁₁	C₂×C₄	1	4	yes	complemented
81	C₁₁×#95	—	2	2	no	—
82	C₁₁×#95	—	2	2	no	—
83	C₁₁×#95	—	2	2	no	—
84	C₁₁×#95	D₄	1	2	yes	—
85	#23191	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
86	C₂⁴×C₁₁	—	2	2	no	—
87	C₂×Q₈×C₁₁	—	2	2	no	—
88	C₂×Q₈×C₁₁	—	2	2	no	—
89	C₂×Q₈×C₁₁	—	2	2	no	—
90	C₂×Q₈×C₁₁	—	2	2	no	—
91	C₂×Q₈×C₁₁	—	2	2	no	—
92	C₂×Q₈×C₁₁	C₂²×C₄	1	4	yes	—
93	C₂×D₄×C₁₁	—	2	2	no	—
94	C₂×D₄×C₁₁	—	2	2	no	—
95	C₂×D₄×C₁₁	—	2	2	no	—
96	C₂×D₄×C₁₁	—	2	2	no	—
97	C₂×D₄×C₁₁	—	2	2	no	—
98	C₂×D₄×C₁₁	C₂²×C₄	1	4	yes	—
99	C₂²×C₄×C₁₁	—	2	2	no	—
100	C₂²×C₄×C₁₁	—	2	2	no	—
101	C₂²×C₄×C₁₁	—	2	2	no	—
102	C₂²×C₄×C₁₁	—	4	4	no	—
103	C₂²×C₄×C₁₁	—	4	4	no	—
104	C₂²×C₄×C₁₁	—	8	2	no	—
105	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
110	C₁₁×Q₁₆	—	4	4	no	—
111	C₁₁×SD₁₆	—	2	16	no	—
112	C₁₁×D₈	—	4	4	no	—
113	C₂×C₈×C₁₁	—	2	2	no	—
114	C₂×C₈×C₁₁	—	2	2	no	—
115	C₂×C₈×C₁₁	—	2	1	no	—
116	C₂×C₈×C₁₁	—	2	1	no	—
117	C₂×C₈×C₁₁	—	2	2	no	—
118	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
119	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
120	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
121	C₂×C₈×C₁₁	#41	1	2	yes	—
122	C₁₁×C₄⋊C₄	—	2	2	no	—
123	C₁₁×C₄⋊C₄	—	2	2	no	—
124	C₁₁×C₄⋊C₄	—	2	2	no	—
125	C₁₁×C₄⋊C₄	—	4	1	no	—
126	C₁₁×C₄⋊C₄	—	4	1	no	—
127	C₁₁×C₄⋊C₄	—	4	4	no	—
128	C₁₁×C₄⋊C₄	C₂×D₄	1	4	yes	—
129	C₁₁×C₂²⋊C₄	—	2	8	no	—
130	C₁₁×C₂²⋊C₄	—	2	8	no	—
131	C₁₁×C₂²⋊C₄	—	4	4	no	—
132	C₁₁×C₂²⋊C₄	—	4	4	no	—
133	C₁₁×C₂²⋊C₄	—	8	2	no	—
134	C₄²×C₁₁	—	2	2	no	—
135	C₄²×C₁₁	—	2	2	no	—
136	C₄²×C₁₁	—	4	4	no	—
137	C₄²×C₁₁	—	8	2	no	—
138	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
139	C₄²×C₁₁	#41	1	2	yes	—
140	C₂×#495	C₂×C₁₁	1	1	yes	characteristic
141	C₂×#440	C₂×C₁₁	1	2	yes	complemented
142	#2367	C₂×C₁₁	1	2	yes	complemented
143	#1983	C₂×C₁₁	1	2	yes	complemented
144	#1973	C₂×C₁₁	1	2	yes	complemented
145	#1879	C₂×C₁₁	1	2	yes	—
146	#1878	C₂×C₁₁	1	2	yes	complemented
147	C₄×#107	C₂×C₁₁	1	1	yes	characteristic, complemented
148	#1770	C₂×C₁₁	1	1	yes	characteristic, complemented
149	C₂³×C₁₁	—	2	4	no	—
150	C₂³×C₁₁	—	4	2	no	—
151	C₂³×C₁₁	—	4	2	no	—
152	C₂³×C₁₁	—	4	2	no	—
153	C₂³×C₁₁	—	4	2	no	—
154	C₂³×C₁₁	—	4	2	no	—
155	C₂³×C₁₁	—	4	2	no	—
156	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
157	Q₈×C₁₁	—	2	4	no	—
158	Q₈×C₁₁	—	2	4	no	—
159	Q₈×C₁₁	—	4	2	no	—
160	Q₈×C₁₁	—	4	2	no	—
161	D₄×C₁₁	—	2	4	no	—
162	D₄×C₁₁	—	2	4	no	—
163	D₄×C₁₁	—	4	2	no	—
164	D₄×C₁₁	—	4	2	no	—
165	C₂×C₄×C₁₁	—	2	1	no	—
166	C₂×C₄×C₁₁	—	2	1	no	—
167	C₂×C₄×C₁₁	—	2	1	no	—
168	C₂×C₄×C₁₁	—	2	1	no	—
169	C₂×C₄×C₁₁	—	2	4	no	—
170	C₂×C₄×C₁₁	—	2	2	no	—
171	C₂×C₄×C₁₁	—	2	2	no	—
172	C₂×C₄×C₁₁	—	2	4	no	—
173	C₂×C₄×C₁₁	—	2	2	no	—
174	C₂×C₄×C₁₁	—	2	2	no	—
175	C₂×C₄×C₁₁	—	2	2	no	—
176	C₂×C₄×C₁₁	—	2	2	no	—
177	C₂×C₄×C₁₁	—	4	2	no	—
178	C₂×C₄×C₁₁	—	4	2	no	—
179	C₂×C₄×C₁₁	—	4	2	no	—
180	C₂×C₄×C₁₁	—	4	2	no	—
181	C₂×C₄×C₁₁	—	4	2	no	—
182	C₂×C₄×C₁₁	—	4	2	no	—
183	C₂×C₄×C₁₁	—	4	2	no	—
184	C₂×C₄×C₁₁	—	8	8	no	—
185	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
186	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
187	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
188	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
189	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
190	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
191	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
192	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
193	C₈×C₁₁	—	2	2	no	—
194	C₈×C₁₁	—	4	2	no	—
195	C₈×C₁₁	C₄×D₄	1	4	yes	—
196	C₂²×Q₁₆	C₂²×C₁₁	1	1	yes	characteristic
197	C₂²×SD₁₆	C₂²×C₁₁	1	2	yes	—
198	C₂²×D₈	C₂²×C₁₁	1	1	yes	characteristic
199	C₂×#124	C₂²×C₁₁	1	2	yes	—
200	C₂×C₄×Q₈	C₂²×C₁₁	1	2	yes	—
201	C₂×C₄×D₄	C₂²×C₁₁	1	2	yes	—
202	#495	C₄×C₁₁	1	8	yes	complemented
203	#440	—	2	8	no	—
204	C₂×#107	C₂²×C₁₁	1	1	yes	characteristic
205	C₂×#107	C₂²×C₁₁	1	1	yes	characteristic
206	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
207	C₂×#103	C₂²×C₁₁	1	2	yes	—
208	C₂×#103	C₂²×C₁₁	1	2	yes	—
209	C₂×#102	C₂²×C₁₁	1	2	yes	—
210	C₂×#102	C₂²×C₁₁	1	2	yes	—
211	C₂×#97	C₂²×C₁₁	1	2	yes	—
212	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
213	#391	C₂²×C₁₁	1	2	yes	—
214	#390	C₂²×C₁₁	1	2	yes	—
215	#388	—	2	2	no	—
216	#388	—	2	2	no	—
217	#385	—	2	2	no	—
218	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
219	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
220	C₄×C₂²⋊C₄	—	2	2	no	—
221	#340	C₂²×C₁₁	1	2	yes	—
222	#336	C₂²×C₁₁	1	2	yes	—
223	C₂²×C₁₁	—	4	4	no	—
224	C₂²×C₁₁	—	4	4	no	—
225	C₂²×C₁₁	—	4	4	no	—
226	C₂²×C₁₁	—	8	2	no	—
227	C₂²×C₁₁	—	8	2	no	—
228	C₂²×C₁₁	—	8	2	no	—
229	C₂²×C₁₁	—	8	2	no	—
230	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
231	C₂²×C₁₁	D₄²	1	1	yes	characteristic
232	C₂²×C₁₁	#550	1	1	yes	characteristic
233	C₂²×C₁₁	#575	1	1	yes	characteristic
234	C₂²×C₁₁	#575	1	1	yes	characteristic
235	C₂²×C₁₁	#576	1	1	yes	characteristic
236	C₂²×C₁₁	#578	1	1	yes	characteristic
237	C₄×C₁₁	—	2	2	no	—
238	C₄×C₁₁	—	2	2	no	—
239	C₄×C₁₁	—	4	4	no	—
240	C₄×C₁₁	—	4	2	no	—
241	C₄×C₁₁	—	4	4	no	—
242	C₄×C₁₁	—	4	2	no	—
243	C₄×C₁₁	—	8	2	no	—
244	C₄×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
245	C₄×C₁₁	#518	1	1	yes	characteristic
246	C₄×C₁₁	#550	1	1	yes	characteristic
247	C₄×C₁₁	#559	1	1	yes	characteristic
248	C₂²×Q₈	C₂³×C₁₁	1	2	yes	—
249	C₂²×D₄	C₂³×C₁₁	1	2	yes	—
250	C₂³×C₄	—	2	2	no	—
251	C₂×Q₁₆	—	4	1	no	—
252	C₂×Q₁₆	—	4	1	no	—
253	C₂×Q₁₆	C₂×C₄×C₁₁	1	4	yes	complemented
254	C₂×SD₁₆	—	2	4	no	—
255	C₂×SD₁₆	—	2	4	no	—
256	C₂×SD₁₆	C₂×C₄×C₁₁	1	8	yes	complemented
257	C₂×D₈	—	4	1	no	—
258	C₂×D₈	—	4	1	no	—
259	C₂×D₈	C₂×C₄×C₁₁	1	4	yes	—
260	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
261	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
262	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
263	#124	—	2	4	no	—
264	#124	C₂×C₄×C₁₁	1	8	yes	complemented
265	C₄×Q₈	—	2	4	no	—
266	C₄×Q₈	—	4	2	no	—
267	C₄×D₄	—	2	4	no	—
268	C₄×D₄	—	4	2	no	—
269	C₂×C₄⋊C₄	—	2	2	no	—
270	C₂×C₄⋊C₄	D₄×C₁₁	1	1	yes	characteristic
271	C₂×C₄⋊C₄	D₄×C₁₁	1	1	yes	characteristic
272	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
273	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
274	C₂×C₂²⋊C₄	—	2	2	no	—
275	C₂×C₂²⋊C₄	—	2	2	no	—
276	C₂×C₂²⋊C₄	—	2	2	no	—
277	C₂×C₂²⋊C₄	—	2	2	no	—
278	C₂×C₂²⋊C₄	—	2	2	no	—
279	C₂×C₄²	—	2	2	no	—
280	C₂×C₄²	—	2	2	no	—
281	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
282	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
283	#107	—	2	2	no	—
284	#107	D₄×C₁₁	1	4	yes	—
285	C₄⋊C₈	—	2	2	no	—
286	#103	—	2	4	no	—
287	#103	—	4	2	no	—
288	#102	—	2	4	no	—
289	#102	—	4	2	no	—
290	#97	—	2	4	no	—
291	C₄×C₈	C₂×C₄×C₁₁	1	4	yes	complemented
292	#95	—	2	2	no	—
293	#95	—	2	2	no	—
294	#95	—	2	2	no	—
295	#95	D₄×C₁₁	1	2	yes	—
296	C₂×C₁₁	—	8	4	no	—
297	C₂×C₁₁	#2366	1	1	yes	characteristic
298	C₂×C₁₁	#2943	1	1	yes	characteristic
299	C₂×C₁₁	#2951	1	1	yes	characteristic
300	C₂×C₁₁	#3273	1	1	yes	characteristic
301	C₂×C₁₁	#3277	1	1	yes	characteristic
302	C₂×C₁₁	#3402	1	1	yes	characteristic
303	C₂×C₁₁	#3403	1	1	yes	characteristic
304	C₂⁴	—	2	2	no	—
305	C₂×Q₈	—	2	2	no	—
306	C₂×Q₈	—	2	2	no	—
307	C₂×Q₈	—	2	2	no	—
308	C₂×Q₈	—	2	2	no	—
309	C₂×Q₈	—	2	2	no	—
310	C₂×Q₈	C₂²×C₄×C₁₁	1	4	yes	—
311	C₂×D₄	—	2	2	no	—
312	C₂×D₄	—	2	2	no	—
313	C₂×D₄	—	2	2	no	—
314	C₂×D₄	—	2	2	no	—
315	C₂×D₄	—	2	2	no	—
316	C₂×D₄	C₂²×C₄×C₁₁	1	4	yes	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	4	4	no	—
321	C₂²×C₄	—	4	4	no	—
322	C₂²×C₄	—	8	2	no	—
323	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
324	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
325	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
326	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
327	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
328	Q₁₆	—	4	4	no	—
329	SD₁₆	—	2	16	no	—
330	D₈	—	4	4	no	—
331	C₂×C₈	—	2	1	no	—
332	C₂×C₈	—	2	1	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
337	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
338	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
339	C₂×C₈	C₁₁×#41	1	2	yes	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	4	1	no	—
344	C₄⋊C₄	—	4	1	no	—
345	C₄⋊C₄	—	4	4	no	—
346	C₄⋊C₄	C₂×D₄×C₁₁	1	4	yes	—
347	C₂²⋊C₄	—	2	8	no	—
348	C₂²⋊C₄	—	2	8	no	—
349	C₂²⋊C₄	—	4	4	no	—
350	C₂²⋊C₄	—	4	4	no	—
351	C₂²⋊C₄	—	8	2	no	—
352	C₄²	—	2	2	no	—
353	C₄²	—	2	2	no	—
354	C₄²	—	4	4	no	—
355	C₄²	—	8	2	no	—
356	C₄²	C₂²×C₄×C₁₁	1	2	yes	—
357	C₄²	C₁₁×#41	1	2	yes	—
358	C₁₁	#23191	1	1	yes	characteristic, direct product factor, Sylow
359	C₂³	—	2	4	no	—
360	C₂³	—	4	2	no	—
361	C₂³	—	4	2	no	—
362	C₂³	—	4	2	no	—
363	C₂³	—	4	2	no	—
364	C₂³	—	4	2	no	—
365	C₂³	—	4	2	no	—
366	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
367	Q₈	—	2	4	no	—
368	Q₈	—	2	4	no	—
369	Q₈	—	4	2	no	—
370	Q₈	—	4	2	no	—
371	D₄	—	2	4	no	—
372	D₄	—	2	4	no	—
373	D₄	—	4	2	no	—
374	D₄	—	4	2	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	4	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	8	8	no	—
395	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
396	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
397	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
398	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
399	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
400	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
401	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
402	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
403	C₈	—	2	2	no	—
404	C₈	—	4	2	no	—
405	C₈	C₄×D₄×C₁₁	1	4	yes	—
406	C₂²	—	4	4	no	—
407	C₂²	—	4	4	no	—
408	C₂²	—	4	4	no	—
409	C₂²	—	8	2	no	—
410	C₂²	—	8	2	no	—
411	C₂²	—	8	2	no	—
412	C₂²	—	8	2	no	—
413	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
414	C₂²	D₄²×C₁₁	1	1	yes	characteristic
415	C₂²	C₁₁×#550	1	1	yes	characteristic
416	C₂²	C₁₁×#575	1	1	yes	characteristic
417	C₂²	C₁₁×#575	1	1	yes	characteristic
418	C₂²	C₁₁×#576	1	1	yes	characteristic
419	C₂²	C₁₁×#578	1	1	yes	characteristic
420	C₄	—	2	2	no	—
421	C₄	—	2	2	no	—
422	C₄	—	4	2	no	—
423	C₄	—	4	4	no	—
424	C₄	—	4	2	no	—
425	C₄	—	4	4	no	—
426	C₄	—	8	2	no	—
427	C₄	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
428	C₄	C₁₁×#518	1	1	yes	characteristic
429	C₄	C₁₁×#550	1	1	yes	characteristic
430	C₄	C₁₁×#559	1	1	yes	characteristic
431	C₂	—	8	4	no	—
432	C₂	C₁₁×#2366	1	1	yes	characteristic
433	C₂	C₁₁×#2943	1	1	yes	characteristic
434	C₂	C₁₁×#2951	1	1	yes	characteristic
435	C₂	C₁₁×#3273	1	1	yes	characteristic
436	C₂	C₁₁×#3277	1	1	yes	characteristic
437	C₂	C₁₁×#3402	1	1	yes	characteristic
438	C₂	C₁₁×#3403	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
prime radical	C₂²×C₁₁×D₈	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ C₄×C₁₁×C₄⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₁×#440	C₂	semidirect
3. C₁₁×#2367	C₂	semidirect
4. C₁₁×#1983	C₂	semidirect
5. C₁₁×#1973	C₂	semidirect
7. C₁₁×#1878	C₂	semidirect
8. C₄×C₁₁×#107	C₂	semidirect
9. C₁₁×#1770	C₂	semidirect
16. C₁₁×#495	C₄	semidirect
42. C₂×C₁₁×Q₁₆	C₂×C₄	semidirect
45. C₂×C₁₁×SD₁₆	C₂×C₄	semidirect
53. C₁₁×#124	C₂×C₄	semidirect
80. C₄×C₈×C₁₁	C₂×C₄	semidirect
85. #23191	C₁₁	direct (N × H)
141. C₂×#440	C₂×C₁₁	semidirect
142. #2367	C₂×C₁₁	semidirect
143. #1983	C₂×C₁₁	semidirect
144. #1973	C₂×C₁₁	semidirect
146. #1878	C₂×C₁₁	semidirect
147. C₄×#107	C₂×C₁₁	semidirect
148. #1770	C₂×C₁₁	semidirect
202. #495	C₄×C₁₁	semidirect
253. C₂×Q₁₆	C₂×C₄×C₁₁	semidirect
256. C₂×SD₁₆	C₂×C₄×C₁₁	semidirect
264. #124	C₂×C₄×C₁₁	semidirect
291. C₄×C₈	C₂×C₄×C₁₁	semidirect
358. C₁₁	#23191	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×#495	2
C₂×C₁₁×#440	2
C₁₁×#2367	2
C₁₁×#1983	2
C₁₁×#1973	2
C₁₁×#1879	2
C₁₁×#1878	2
C₄×C₁₁×#107	2
C₁₁×#1770	2
#23191	11

Subgroups — C11×#23191 #14600384

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#23191 #14600384