Subgroups — C₁₁×#24268 #14601461

Order 2816.

1410 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₁₁×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₁×#467	C₂	1	2	yes	maximal, complemented
3	C₂×C₈×D₄×C₁₁	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#2409	C₂	1	2	yes	maximal
5	C₁₁×#2056	C₂	1	2	yes	maximal, complemented
6	C₁₁×#2001	C₂	1	2	yes	maximal, complemented
7	C₁₁×#1969	C₂	1	2	yes	maximal, complemented
8	C₁₁×#1808	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁×#1787	C₂	1	2	yes	maximal, complemented
10	C₂³×Q₈×C₁₁	C₂²	1	2	yes	—
11	C₂²×C₁₁×Q₁₆	—	2	8	no	—
12	C₂²×C₁₁×Q₁₆	—	2	4	no	—
13	C₂²×C₁₁×Q₁₆	C₂²	1	2	yes	—
14	C₂²×C₁₁×Q₁₆	C₂²	1	2	yes	—
15	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
16	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
17	C₂×C₁₁×C₂²⋊Q₈	C₂²	1	4	yes	—
18	C₂×C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
19	C₁₁×#467	—	2	8	no	—
20	C₈×D₄×C₁₁	—	2	4	no	—
21	C₂×C₁₁×#107	C₂²	1	2	yes	—
22	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₁×#103	C₂²	1	4	yes	—
24	C₂×C₁₁×#103	C₂²	1	4	yes	—
25	C₂×C₁₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
28	C₁₁×#395	—	2	2	no	—
29	C₁₁×#393	—	2	2	no	—
30	C₁₁×#391	C₂²	1	4	yes	—
31	C₁₁×#386	—	2	2	no	—
32	C₁₁×#385	—	2	2	no	—
33	C₁₁×#380	C₂²	1	2	yes	—
34	C₁₁×#340	C₂²	1	2	yes	—
35	C₂²×Q₈×C₁₁	—	2	2	no	—
36	C₂²×Q₈×C₁₁	—	2	8	no	—
37	C₂²×Q₈×C₁₁	—	2	4	no	—
38	C₂²×Q₈×C₁₁	—	2	4	no	—
39	C₂²×Q₈×C₁₁	—	4	4	no	—
40	C₂²×Q₈×C₁₁	C₂³	1	4	yes	—
41	C₂²×D₄×C₁₁	D₄	1	1	yes	characteristic
42	C₂³×C₄×C₁₁	—	2	2	no	—
43	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
45	C₂×C₁₁×Q₁₆	—	2	32	no	—
46	C₂×C₁₁×Q₁₆	—	2	8	no	—
47	C₂×C₁₁×Q₁₆	—	2	4	no	—
48	C₂×C₁₁×Q₁₆	—	2	4	no	—
49	C₂×C₁₁×Q₁₆	—	2	4	no	—
50	C₂×C₁₁×Q₁₆	D₄	1	8	yes	complemented
51	C₂²×C₈×C₁₁	—	2	4	no	—
52	C₂²×C₈×C₁₁	—	2	2	no	—
53	C₂²×C₈×C₁₁	—	2	4	no	—
54	C₂²×C₈×C₁₁	D₄	1	4	yes	—
55	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
59	C₁₁×C₂²⋊Q₈	—	2	8	no	—
60	C₁₁×C₂²⋊Q₈	—	4	4	no	—
61	C₄×D₄×C₁₁	—	2	2	no	—
62	C₄×D₄×C₁₁	—	2	2	no	—
63	C₂×C₁₁×C₄⋊C₄	—	2	4	no	—
64	C₂×C₁₁×C₄⋊C₄	D₄	1	1	yes	characteristic
65	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
66	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
67	C₂×C₁₁×C₂²⋊C₄	—	2	4	no	—
68	C₂×C₁₁×C₂²⋊C₄	D₄	1	1	yes	characteristic
69	C₂×C₁₁×C₂²⋊C₄	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
71	C₁₁×#107	—	2	4	no	—
72	C₁₁×C₄⋊C₈	—	2	2	no	—
73	C₁₁×#103	—	2	8	no	—
74	C₁₁×#103	—	4	4	no	—
75	C₁₁×C₂²⋊C₈	—	2	2	no	—
76	C₁₁×C₂²⋊C₈	—	2	2	no	—
77	C₄×C₈×C₁₁	—	2	2	no	—
78	C₁₁×#95	—	2	2	no	—
79	C₁₁×#95	—	2	4	no	—
80	C₁₁×#95	—	2	4	no	—
81	#24268	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
82	C₂⁴×C₁₁	C₂×D₄	1	1	yes	characteristic
83	C₂⁴×C₁₁	C₂×D₄	1	1	yes	characteristic
84	C₂×Q₈×C₁₁	—	2	4	no	—
85	C₂×Q₈×C₁₁	—	2	16	no	—
86	C₂×Q₈×C₁₁	—	2	4	no	—
87	C₂×Q₈×C₁₁	—	2	4	no	—
88	C₂×Q₈×C₁₁	—	2	4	no	—
89	C₂×Q₈×C₁₁	—	2	4	no	—
90	C₂×Q₈×C₁₁	—	4	8	no	—
91	C₂×Q₈×C₁₁	—	4	16	no	—
92	C₂×Q₈×C₁₁	—	4	8	no	—
93	C₂×Q₈×C₁₁	—	4	4	no	—
94	C₂×Q₈×C₁₁	C₂×D₄	1	8	yes	—
95	C₂×D₄×C₁₁	—	2	2	no	—
96	C₂×D₄×C₁₁	—	2	2	no	—
97	C₂×D₄×C₁₁	Q₁₆	1	4	yes	complemented
98	C₂²×C₄×C₁₁	—	2	2	no	—
99	C₂²×C₄×C₁₁	—	2	2	no	—
100	C₂²×C₄×C₁₁	—	2	4	no	—
101	C₂²×C₄×C₁₁	—	2	1	no	—
102	C₂²×C₄×C₁₁	—	2	2	no	—
103	C₂²×C₄×C₁₁	—	2	1	no	—
104	C₂²×C₄×C₁₁	—	2	2	no	—
105	C₂²×C₄×C₁₁	—	2	4	no	—
106	C₂²×C₄×C₁₁	—	4	8	no	—
107	C₂²×C₄×C₁₁	—	4	4	no	—
108	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₁	#41	1	2	yes	—
114	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
115	C₁₁×Q₁₆	—	2	16	no	—
116	C₁₁×Q₁₆	—	2	16	no	—
117	C₂×C₈×C₁₁	—	2	8	no	—
118	C₂×C₈×C₁₁	—	2	2	no	—
119	C₂×C₈×C₁₁	—	2	1	no	—
120	C₂×C₈×C₁₁	—	2	1	no	—
121	C₂×C₈×C₁₁	—	2	2	no	—
122	C₂×C₈×C₁₁	—	2	2	no	—
123	C₂×C₈×C₁₁	—	4	4	no	—
124	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
125	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
126	C₂×C₈×C₁₁	C₂×D₄	1	4	yes	—
127	C₁₁×C₄⋊C₄	—	2	2	no	—
128	C₁₁×C₄⋊C₄	—	2	4	no	—
129	C₁₁×C₄⋊C₄	—	2	4	no	—
130	C₁₁×C₄⋊C₄	—	4	8	no	—
131	C₁₁×C₂²⋊C₄	—	2	2	no	—
132	C₁₁×C₂²⋊C₄	—	2	2	no	—
133	C₁₁×C₂²⋊C₄	—	4	8	no	—
134	C₁₁×C₂²⋊C₄	—	4	4	no	—
135	C₄²×C₁₁	—	2	1	no	—
136	C₄²×C₁₁	—	2	1	no	—
137	C₂³×Q₁₆	C₂×C₁₁	1	1	yes	characteristic, complemented
138	C₂×#467	C₂×C₁₁	1	2	yes	complemented
139	C₂×C₈×D₄	C₂×C₁₁	1	1	yes	characteristic
140	#2409	C₂×C₁₁	1	2	yes	—
141	#2056	C₂×C₁₁	1	2	yes	complemented
142	#2001	C₂×C₁₁	1	2	yes	complemented
143	#1969	C₂×C₁₁	1	2	yes	complemented
144	#1808	C₂×C₁₁	1	1	yes	characteristic, complemented
145	#1787	C₂×C₁₁	1	2	yes	complemented
146	C₂³×C₁₁	—	2	2	no	—
147	C₂³×C₁₁	—	2	2	no	—
148	C₂³×C₁₁	—	2	1	no	—
149	C₂³×C₁₁	—	2	2	no	—
150	C₂³×C₁₁	—	2	1	no	—
151	C₂³×C₁₁	—	2	2	no	—
152	C₂³×C₁₁	#121	1	2	yes	—
153	C₂³×C₁₁	C₂×Q₁₆	1	2	yes	—
154	C₂³×C₁₁	C₂×Q₁₆	1	2	yes	complemented
155	C₂³×C₁₁	#135	1	2	yes	—
156	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
157	Q₈×C₁₁	—	2	8	no	—
158	Q₈×C₁₁	—	2	8	no	—
159	Q₈×C₁₁	—	4	16	no	—
160	Q₈×C₁₁	—	4	4	no	—
161	Q₈×C₁₁	—	4	4	no	—
162	D₄×C₁₁	—	2	8	no	—
163	C₂×C₄×C₁₁	—	2	1	no	—
164	C₂×C₄×C₁₁	—	2	2	no	—
165	C₂×C₄×C₁₁	—	2	1	no	—
166	C₂×C₄×C₁₁	—	2	2	no	—
167	C₂×C₄×C₁₁	—	2	2	no	—
168	C₂×C₄×C₁₁	—	2	4	no	—
169	C₂×C₄×C₁₁	—	2	1	no	—
170	C₂×C₄×C₁₁	—	2	1	no	—
171	C₂×C₄×C₁₁	—	2	8	no	—
172	C₂×C₄×C₁₁	—	2	2	no	—
173	C₂×C₄×C₁₁	—	2	2	no	—
174	C₂×C₄×C₁₁	—	4	16	no	—
175	C₂×C₄×C₁₁	—	4	4	no	—
176	C₂×C₄×C₁₁	—	4	4	no	—
177	C₂×C₄×C₁₁	—	4	1	no	—
178	C₂×C₄×C₁₁	—	4	1	no	—
179	C₂×C₄×C₁₁	—	4	2	no	—
180	C₂×C₄×C₁₁	—	4	4	no	—
181	C₂×C₄×C₁₁	—	4	4	no	—
182	C₂×C₄×C₁₁	—	4	4	no	—
183	C₂×C₄×C₁₁	#121	1	2	yes	—
184	C₂×C₄×C₁₁	C₂×Q₁₆	1	2	yes	complemented
185	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
187	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
188	C₂×C₄×C₁₁	H(5,𝔽₂)	1	2	yes	—
189	C₈×C₁₁	—	2	2	no	—
190	C₈×C₁₁	—	4	1	no	—
191	C₈×C₁₁	—	4	1	no	—
192	C₈×C₁₁	#120	1	4	yes	—
193	C₂³×Q₈	C₂²×C₁₁	1	2	yes	—
194	C₂²×Q₁₆	—	2	8	no	—
195	C₂²×Q₁₆	—	2	4	no	—
196	C₂²×Q₁₆	C₂²×C₁₁	1	2	yes	—
197	C₂²×Q₁₆	C₂²×C₁₁	1	2	yes	—
198	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
199	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
200	C₂×C₂²⋊Q₈	C₂²×C₁₁	1	4	yes	—
201	C₂×C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic
202	#467	—	2	8	no	—
203	C₈×D₄	—	2	4	no	—
204	C₂×#107	C₂²×C₁₁	1	2	yes	—
205	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
206	C₂×#103	C₂²×C₁₁	1	4	yes	—
207	C₂×#103	C₂²×C₁₁	1	4	yes	—
208	C₂×C₂²⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
209	C₂×C₂²⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
210	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
211	#395	—	2	2	no	—
212	#393	—	2	2	no	—
213	#391	C₂²×C₁₁	1	4	yes	—
214	#386	—	2	2	no	—
215	#385	—	2	2	no	—
216	#380	C₂²×C₁₁	1	2	yes	—
217	#340	C₂²×C₁₁	1	2	yes	—
218	C₂²×C₁₁	—	2	2	no	—
219	C₂²×C₁₁	—	2	4	no	—
220	C₂²×C₁₁	—	2	4	no	—
221	C₂²×C₁₁	—	2	2	no	—
222	C₂²×C₁₁	—	2	4	no	—
223	C₂²×C₁₁	—	2	2	no	—
224	C₂²×C₁₁	—	4	1	no	—
225	C₂²×C₁₁	—	4	2	no	—
226	C₂²×C₁₁	—	4	1	no	—
227	C₂²×C₁₁	#467	1	4	yes	complemented
228	C₂²×C₁₁	C₂×#121	1	1	yes	characteristic
229	C₂²×C₁₁	D₄²	1	2	yes	—
230	C₂²×C₁₁	C₂²×Q₁₆	1	1	yes	characteristic
231	C₂²×C₁₁	C₂×#135	1	1	yes	characteristic
232	C₂²×C₁₁	#578	1	2	yes	—
233	C₄×C₁₁	—	2	2	no	—
234	C₄×C₁₁	—	2	2	no	—
235	C₄×C₁₁	—	4	1	no	—
236	C₄×C₁₁	—	4	8	no	—
237	C₄×C₁₁	—	4	1	no	—
238	C₄×C₁₁	—	8	4	no	—
239	C₄×C₁₁	C₂×#120	1	1	yes	characteristic
240	C₄×C₁₁	#535	1	1	yes	characteristic
241	C₄×C₁₁	#546	1	2	yes	—
242	C₂²×Q₈	—	2	2	no	—
243	C₂²×Q₈	—	2	8	no	—
244	C₂²×Q₈	—	2	4	no	—
245	C₂²×Q₈	—	2	4	no	—
246	C₂²×Q₈	—	4	4	no	—
247	C₂²×Q₈	C₂³×C₁₁	1	4	yes	—
248	C₂²×D₄	D₄×C₁₁	1	1	yes	characteristic
249	C₂³×C₄	—	2	2	no	—
250	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
251	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
252	C₂×Q₁₆	—	2	32	no	—
253	C₂×Q₁₆	—	2	8	no	—
254	C₂×Q₁₆	—	2	4	no	—
255	C₂×Q₁₆	—	2	4	no	—
256	C₂×Q₁₆	—	2	4	no	—
257	C₂×Q₁₆	D₄×C₁₁	1	8	yes	complemented
258	C₂²×C₈	—	2	4	no	—
259	C₂²×C₈	—	2	2	no	—
260	C₂²×C₈	—	2	4	no	—
261	C₂²×C₈	D₄×C₁₁	1	4	yes	—
262	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
263	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
264	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
265	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
266	C₂²⋊Q₈	—	2	8	no	—
267	C₂²⋊Q₈	—	4	4	no	—
268	C₄×D₄	—	2	2	no	—
269	C₄×D₄	—	2	2	no	—
270	C₂×C₄⋊C₄	—	2	4	no	—
271	C₂×C₄⋊C₄	D₄×C₁₁	1	1	yes	characteristic
272	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
273	C₂×C₂²⋊C₄	—	2	4	no	—
274	C₂×C₂²⋊C₄	—	2	2	no	—
275	C₂×C₂²⋊C₄	D₄×C₁₁	1	1	yes	characteristic
276	C₂×C₂²⋊C₄	D₄×C₁₁	1	1	yes	characteristic
277	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
278	#107	—	2	4	no	—
279	C₄⋊C₈	—	2	2	no	—
280	#103	—	2	8	no	—
281	#103	—	4	4	no	—
282	C₂²⋊C₈	—	2	2	no	—
283	C₂²⋊C₈	—	2	2	no	—
284	C₄×C₈	—	2	2	no	—
285	#95	—	2	2	no	—
286	#95	—	2	4	no	—
287	#95	—	2	4	no	—
288	C₂×C₁₁	—	2	4	no	—
289	C₂×C₁₁	—	4	2	no	—
290	C₂×C₁₁	#2408	1	1	yes	characteristic
291	C₂×C₁₁	C₂×#467	1	1	yes	characteristic
292	C₂×C₁₁	#3059	1	1	yes	characteristic
293	C₂×C₁₁	#3285	1	2	yes	—
294	C₂×C₁₁	D₄×Q₁₆	1	2	yes	—
295	C₂⁴	C₂×D₄×C₁₁	1	1	yes	characteristic
296	C₂⁴	C₂×D₄×C₁₁	1	1	yes	characteristic
297	C₂×Q₈	—	2	4	no	—
298	C₂×Q₈	—	2	16	no	—
299	C₂×Q₈	—	2	4	no	—
300	C₂×Q₈	—	2	4	no	—
301	C₂×Q₈	—	2	4	no	—
302	C₂×Q₈	—	2	4	no	—
303	C₂×Q₈	—	4	8	no	—
304	C₂×Q₈	—	4	16	no	—
305	C₂×Q₈	—	4	8	no	—
306	C₂×Q₈	—	4	4	no	—
307	C₂×Q₈	C₂×D₄×C₁₁	1	8	yes	—
308	C₂×D₄	—	2	2	no	—
309	C₂×D₄	—	2	2	no	—
310	C₂×D₄	C₁₁×Q₁₆	1	4	yes	complemented
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	4	no	—
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	2	4	no	—
319	C₂²×C₄	—	4	8	no	—
320	C₂²×C₄	—	4	4	no	—
321	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
322	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
323	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
324	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
325	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
326	C₂²×C₄	C₁₁×#41	1	2	yes	—
327	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
328	Q₁₆	—	2	16	no	—
329	Q₁₆	—	2	16	no	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	2	8	no	—
332	C₂×C₈	—	2	1	no	—
333	C₂×C₈	—	2	1	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	4	4	no	—
337	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
338	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
339	C₂×C₈	C₂×D₄×C₁₁	1	4	yes	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	2	4	no	—
342	C₄⋊C₄	—	2	4	no	—
343	C₄⋊C₄	—	4	8	no	—
344	C₂²⋊C₄	—	2	2	no	—
345	C₂²⋊C₄	—	2	2	no	—
346	C₂²⋊C₄	—	4	8	no	—
347	C₂²⋊C₄	—	4	4	no	—
348	C₄²	—	2	1	no	—
349	C₄²	—	2	1	no	—
350	C₁₁	#24268	1	1	yes	characteristic, direct product factor, Sylow
351	C₂³	—	2	2	no	—
352	C₂³	—	2	2	no	—
353	C₂³	—	2	1	no	—
354	C₂³	—	2	2	no	—
355	C₂³	—	2	1	no	—
356	C₂³	—	2	2	no	—
357	C₂³	C₁₁×#121	1	2	yes	—
358	C₂³	C₂×C₁₁×Q₁₆	1	2	yes	—
359	C₂³	C₂×C₁₁×Q₁₆	1	2	yes	complemented
360	C₂³	C₁₁×#135	1	2	yes	—
361	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
362	Q₈	—	2	8	no	—
363	Q₈	—	2	8	no	—
364	Q₈	—	4	16	no	—
365	Q₈	—	4	4	no	—
366	Q₈	—	4	4	no	—
367	D₄	—	2	8	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	4	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	8	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	4	16	no	—
380	C₂×C₄	—	4	4	no	—
381	C₂×C₄	—	4	4	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	4	no	—
386	C₂×C₄	—	4	4	no	—
387	C₂×C₄	—	4	4	no	—
388	C₂×C₄	C₁₁×#121	1	2	yes	—
389	C₂×C₄	C₂×C₁₁×Q₁₆	1	2	yes	complemented
390	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
391	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
392	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
393	C₂×C₄	C₁₁×H(5,𝔽₂)	1	2	yes	—
394	C₈	—	2	2	no	—
395	C₈	—	4	1	no	—
396	C₈	—	4	1	no	—
397	C₈	C₁₁×#120	1	4	yes	—
398	C₂²	—	2	2	no	—
399	C₂²	—	2	4	no	—
400	C₂²	—	2	4	no	—
401	C₂²	—	2	2	no	—
402	C₂²	—	2	4	no	—
403	C₂²	—	2	2	no	—
404	C₂²	—	4	1	no	—
405	C₂²	—	4	2	no	—
406	C₂²	—	4	1	no	—
407	C₂²	C₁₁×#467	1	4	yes	complemented
408	C₂²	C₂×C₁₁×#121	1	1	yes	characteristic
409	C₂²	D₄²×C₁₁	1	2	yes	—
410	C₂²	C₂²×C₁₁×Q₁₆	1	1	yes	characteristic
411	C₂²	C₂×C₁₁×#135	1	1	yes	characteristic
412	C₂²	C₁₁×#578	1	2	yes	—
413	C₄	—	2	2	no	—
414	C₄	—	2	2	no	—
415	C₄	—	4	1	no	—
416	C₄	—	4	8	no	—
417	C₄	—	4	1	no	—
418	C₄	—	8	4	no	—
419	C₄	C₂×C₁₁×#120	1	1	yes	characteristic
420	C₄	C₁₁×#535	1	1	yes	characteristic
421	C₄	C₁₁×#546	1	2	yes	—
422	C₂	—	2	4	no	—
423	C₂	—	4	2	no	—
424	C₂	C₁₁×#2408	1	1	yes	characteristic
425	C₂	C₂×C₁₁×#467	1	1	yes	characteristic
426	C₂	C₁₁×#3059	1	1	yes	characteristic
427	C₂	C₁₁×#3285	1	2	yes	—
428	C₂	D₄×C₁₁×Q₁₆	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂³×C₁₁×Q₁₆	C₂	semidirect
2. C₂×C₁₁×#467	C₂	semidirect
5. C₁₁×#2056	C₂	semidirect
6. C₁₁×#2001	C₂	semidirect
7. C₁₁×#1969	C₂	semidirect
8. C₁₁×#1808	C₂	semidirect
9. C₁₁×#1787	C₂	semidirect
50. C₂×C₁₁×Q₁₆	D₄	semidirect
81. #24268	C₁₁	direct (N × H)
97. C₂×D₄×C₁₁	Q₁₆	semidirect
137. C₂³×Q₁₆	C₂×C₁₁	semidirect
138. C₂×#467	C₂×C₁₁	semidirect
141. #2056	C₂×C₁₁	semidirect
142. #2001	C₂×C₁₁	semidirect
143. #1969	C₂×C₁₁	semidirect
144. #1808	C₂×C₁₁	semidirect
145. #1787	C₂×C₁₁	semidirect
154. C₂³×C₁₁	C₂×Q₁₆	semidirect
184. C₂×C₄×C₁₁	C₂×Q₁₆	semidirect
227. C₂²×C₁₁	#467	semidirect
257. C₂×Q₁₆	D₄×C₁₁	semidirect
310. C₂×D₄	C₁₁×Q₁₆	semidirect
350. C₁₁	#24268	direct (N × H)
359. C₂³	C₂×C₁₁×Q₁₆	semidirect
389. C₂×C₄	C₂×C₁₁×Q₁₆	semidirect
407. C₂²	C₁₁×#467	semidirect

Maximal subgroups

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

subgroup	index
C₂³×C₁₁×Q₁₆	2
C₂×C₁₁×#467	2
C₂×C₈×D₄×C₁₁	2
C₁₁×#2409	2
C₁₁×#2056	2
C₁₁×#2001	2
C₁₁×#1969	2
C₁₁×#1808	2
C₁₁×#1787	2
#24268	11

Subgroups — C11×#24268 #14601461

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#24268 #14601461