Subgroups — D₁₁×#1568 #14722776

Order 2816.

766 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₁×#432	C₂	1	2	yes	maximal
2	C₂×C₄×C₈×D₁₁	C₂	1	1	yes	maximal, characteristic
3	#13067379	C₂	1	1	yes	maximal, characteristic, complemented
4	#13067378	C₂	1	2	yes	maximal, complemented
5	#13067377	C₂	1	2	yes	maximal, complemented
6	#13067376	C₂	1	2	yes	maximal, complemented
7	D₁₁×#335	C₂	1	2	yes	maximal, complemented
8	D₁₁×#334	C₂	1	2	yes	maximal, complemented
9	C₁₁×#1568	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₈×D₁₁	C₄	1	1	yes	characteristic
11	C₂²×C₈×D₁₁	C₄	1	1	yes	characteristic
12	C₂×C₄²×D₁₁	C₂²	1	1	yes	characteristic
13	C₁₁×#432	C₂²	1	2	yes	—
14	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
15	C₂×C₈×Dic₁₁	C₄	1	1	yes	characteristic
16	C₂×C₈×Dic₁₁	C₄	1	1	yes	characteristic
17	#10622539	C₂²	1	2	yes	—
18	C₂×C₄×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
19	#10622448	C₂²	1	4	yes	—
20	D₁₁×C₄⋊C₈	C₂²	1	4	yes	—
21	D₁₁×C₂²⋊C₈	—	2	2	no	—
22	#10622332	—	2	2	no	—
23	#10622318	—	2	2	no	—
24	D₁₁×#97	—	2	2	no	—
25	C₄×C₈×D₁₁	C₄	1	1	yes	characteristic
26	C₄×C₈×D₁₁	C₄	1	1	yes	characteristic
27	C₄×C₈×D₁₁	C₄	1	1	yes	characteristic
28	C₄×C₈×D₁₁	C₄	1	1	yes	characteristic
29	C₄×C₈×D₁₁	C₂²	1	1	yes	characteristic
30	C₄×C₈×D₁₁	C₂²	1	1	yes	characteristic
31	C₄×C₈×D₁₁	C₂²	1	1	yes	characteristic
32	C₄×C₈×D₁₁	C₂²	1	1	yes	characteristic
33	C₁₁×#335	C₂²	1	2	yes	complemented
34	C₁₁×#334	C₂²	1	2	yes	complemented
35	#10622118	C₂²	1	4	yes	complemented
36	#10622117	C₂²	1	4	yes	complemented
37	#10622096	C₂²	1	2	yes	complemented
38	#10622095	C₂²	1	2	yes	complemented
39	C₂²×C₄×D₁₁	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₄×D₁₁	D₄	1	1	yes	characteristic
41	C₂²×C₄×D₁₁	Q₈	1	1	yes	characteristic
42	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
43	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
45	C₂×C₄×Dic₁₁	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄×Dic₁₁	D₄	1	1	yes	characteristic
47	C₂×C₄×Dic₁₁	Q₈	1	1	yes	characteristic
48	C₂²×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
50	C₂×C₈×D₁₁	—	2	4	no	—
51	C₂×C₈×D₁₁	—	2	4	no	—
52	C₂×C₈×D₁₁	—	2	4	no	—
53	C₂×C₈×D₁₁	C₂×C₄	1	1	yes	characteristic
54	C₂×C₈×D₁₁	C₂×C₄	1	1	yes	characteristic
55	C₂×C₈×D₁₁	C₂×C₄	1	1	yes	characteristic
56	C₂×C₈×D₁₁	C₂×C₄	1	1	yes	characteristic
57	C₂×C₈×D₁₁	C₂×C₄	1	1	yes	characteristic
58	C₂×C₈×D₁₁	C₂×C₄	1	1	yes	characteristic
59	C₂×C₈×D₁₁	C₂×C₄	1	1	yes	characteristic
60	C₂×C₈×D₁₁	C₂×C₄	1	1	yes	characteristic
61	C₄²×D₁₁	C₂×C₄	1	1	yes	characteristic
62	C₄²×D₁₁	C₂×C₄	1	1	yes	characteristic
63	C₄²×D₁₁	D₄	1	1	yes	characteristic
64	C₄²×D₁₁	D₄	1	1	yes	characteristic
65	C₄²×D₁₁	Q₈	1	1	yes	characteristic
66	C₄²×D₁₁	Q₈	1	1	yes	characteristic
67	C₄²×D₁₁	C₂³	1	1	yes	characteristic
68	C₄²×D₁₁	C₂³	1	1	yes	characteristic
69	C₁₁×C₄⋊C₈	C₂³	1	4	yes	—
70	C₁₁×C₂²⋊C₈	—	2	2	no	—
71	C₁₁×#97	—	2	2	no	—
72	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
73	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
74	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
75	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
76	C₂²⋊(C₁₁⋊C₈)	—	2	2	no	—
77	(C₂×D₁₁)⋊C₈	—	2	4	no	—
78	#66879	—	2	4	no	—
79	Dic₁₁⋊C₈	—	2	4	no	—
80	C₈×Dic₁₁	C₂×C₄	1	1	yes	characteristic
81	C₈×Dic₁₁	C₂×C₄	1	1	yes	characteristic
82	C₈×Dic₁₁	C₂×C₄	1	1	yes	characteristic
83	C₈×Dic₁₁	C₂×C₄	1	1	yes	characteristic
84	C₈×Dic₁₁	C₂×C₄	1	1	yes	characteristic
85	C₈×Dic₁₁	C₂×C₄	1	1	yes	characteristic
86	C₈×Dic₁₁	C₂×C₄	1	1	yes	characteristic
87	C₈×Dic₁₁	C₂×C₄	1	1	yes	characteristic
88	C₄⋊(C₁₁⋊C₈)	C₂³	1	4	yes	—
89	#66867	—	2	2	no	—
90	C₄×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
91	C₄×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
92	C₄×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
93	C₄×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
94	C₂×#1568	—	11	1	no	maximal, Sylow
95	C₂³×D₁₁	C₄⋊C₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
99	C₂²×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
100	C₂²×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
101	C₂²×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
102	C₂×C₄×D₁₁	—	2	2	no	—
103	C₂×C₄×D₁₁	—	2	2	no	—
104	C₂×C₄×D₁₁	—	2	4	no	—
105	C₂×C₄×D₁₁	—	2	4	no	—
106	C₂×C₄×D₁₁	C₄⋊C₄	1	1	yes	characteristic
107	C₂×C₄×D₁₁	C₄⋊C₄	1	1	yes	characteristic
108	C₂×C₄×D₁₁	C₄⋊C₄	1	1	yes	characteristic
109	C₂×C₄×D₁₁	C₄⋊C₄	1	1	yes	characteristic
110	C₂×C₄×D₁₁	C₄⋊C₄	1	1	yes	characteristic
111	C₂×C₄×D₁₁	C₄⋊C₄	1	1	yes	characteristic
112	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₄×D₁₁	C₂×D₄	1	1	yes	characteristic
115	C₂×C₄×D₁₁	C₂×D₄	1	1	yes	characteristic
116	C₂×C₄×D₁₁	C₂×Q₈	1	1	yes	characteristic
117	C₂×C₄×D₁₁	C₂×Q₈	1	1	yes	characteristic
118	C₂×C₈×C₁₁	—	2	2	no	—
119	C₂×C₈×C₁₁	—	2	2	no	—
120	C₂×C₈×C₁₁	—	2	4	no	—
121	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
125	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
126	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
127	C₄²×C₁₁	C₂×Q₈	1	1	yes	characteristic
128	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
129	C₄×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
130	C₄×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
131	C₄×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
132	C₄×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
133	C₄×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
134	C₄×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
135	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
136	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
137	C₄×Dic₁₁	C₂×D₄	1	1	yes	characteristic
138	C₄×Dic₁₁	C₂×D₄	1	1	yes	characteristic
139	C₄×Dic₁₁	C₂×Q₈	1	1	yes	characteristic
140	C₄×Dic₁₁	C₂×Q₈	1	1	yes	characteristic
141	C₂×C₁₁⋊C₈	—	2	2	no	—
142	C₂×C₁₁⋊C₈	—	2	2	no	—
143	C₂×C₁₁⋊C₈	—	2	4	no	—
144	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
145	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
146	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
148	C₈×D₁₁	—	2	2	no	—
149	C₈×D₁₁	—	2	2	no	—
150	C₈×D₁₁	—	2	2	no	—
151	C₈×D₁₁	—	2	2	no	—
152	C₈×D₁₁	—	2	2	no	—
153	C₈×D₁₁	—	2	2	no	—
154	C₈×D₁₁	—	4	8	no	—
155	C₈×D₁₁	M₁₆	1	4	yes	—
156	C₈×D₁₁	M₁₆	1	4	yes	—
157	C₂×#432	—	11	2	no	—
158	C₂²×C₄×C₈	—	11	1	no	—
159	#1568	—	11	2	no	—
160	#1568	—	11	1	no	—
161	#1568	—	11	2	no	—
162	#1568	—	11	2	no	—
163	#1568	D₁₁	1	1	yes	characteristic, direct product factor
164	C₂×#335	—	11	2	no	—
165	C₂×#334	—	11	2	no	—
166	C₂³×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
167	C₂²×D₁₁	—	2	2	no	—
168	C₂²×D₁₁	—	2	2	no	—
169	C₂²×D₁₁	#108	1	4	yes	—
170	C₂²×D₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
171	C₂²×D₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
172	C₂×C₄×C₁₁	—	2	2	no	—
173	C₂×C₄×C₁₁	—	2	1	no	—
174	C₂×C₄×C₁₁	—	2	1	no	—
175	C₂×C₄×C₁₁	—	2	2	no	—
176	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
177	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
178	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
179	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
180	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₁₁	C₂²×Q₈	1	1	yes	characteristic
182	C₂×Dic₁₁	—	2	2	no	—
183	C₂×Dic₁₁	—	2	2	no	—
184	C₂×Dic₁₁	—	2	2	no	—
185	C₂×Dic₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
186	C₂×Dic₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
187	C₂×Dic₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
188	C₂×Dic₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
189	C₂×Dic₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
190	C₂×Dic₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
191	C₄×D₁₁	—	2	2	no	—
192	C₄×D₁₁	—	2	2	no	—
193	C₄×D₁₁	—	2	2	no	—
194	C₄×D₁₁	—	2	2	no	—
195	C₄×D₁₁	—	2	2	no	—
196	C₄×D₁₁	—	2	2	no	—
197	C₄×D₁₁	—	2	1	no	—
198	C₄×D₁₁	—	2	1	no	—
199	C₄×D₁₁	—	2	2	no	—
200	C₄×D₁₁	—	2	2	no	—
201	C₄×D₁₁	—	2	2	no	—
202	C₄×D₁₁	C₂×M₁₆	1	2	yes	—
203	C₄×D₁₁	C₂×M₁₆	1	2	yes	—
204	C₄×D₁₁	#135	1	4	yes	—
205	C₈×C₁₁	—	2	1	no	—
206	C₈×C₁₁	—	2	1	no	—
207	C₈×C₁₁	—	4	4	no	—
208	C₈×C₁₁	C₂×M₁₆	1	2	yes	—
209	C₈×C₁₁	C₂×M₁₆	1	2	yes	—
210	C₁₁⋊C₈	—	2	1	no	—
211	C₁₁⋊C₈	—	2	1	no	—
212	C₁₁⋊C₈	—	4	4	no	—
213	C₁₁⋊C₈	C₂×M₁₆	1	2	yes	—
214	C₁₁⋊C₈	C₂×M₁₆	1	2	yes	—
215	C₂³×C₈	—	11	1	no	—
216	C₂³×C₈	—	11	1	no	—
217	C₂²×C₄²	—	11	1	no	—
218	#432	—	11	2	no	—
219	#432	—	11	4	no	—
220	#432	—	22	2	no	—
221	#432	—	22	2	no	—
222	#432	C₂×D₁₁	1	2	yes	—
223	C₂×C₄⋊C₈	—	11	4	no	—
224	C₂×C₂²⋊C₈	—	22	2	no	—
225	C₂×#97	—	22	2	no	—
226	C₂×C₄×C₈	—	11	1	no	—
227	C₂×C₄×C₈	—	11	1	no	—
228	C₂×C₄×C₈	—	11	1	no	—
229	C₂×C₄×C₈	—	11	1	no	—
230	C₂×C₄×C₈	—	11	1	no	—
231	C₂×C₄×C₈	—	11	1	no	—
232	C₂×C₄×C₈	—	11	1	no	—
233	C₂×C₄×C₈	—	11	1	no	—
234	C₂×C₄×C₈	—	11	1	no	—
235	C₂×C₄×C₈	—	11	1	no	—
236	C₂×C₄×C₈	—	11	1	no	—
237	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
238	#335	—	11	4	no	—
239	#335	—	11	2	no	—
240	#335	C₂×D₁₁	1	2	yes	complemented
241	#334	—	11	4	no	—
242	#334	—	11	2	no	—
243	#334	C₂×D₁₁	1	2	yes	complemented
244	C₂²×C₁₁	—	2	1	no	—
245	C₂²×C₁₁	—	2	1	no	—
246	C₂²×C₁₁	C₂×#108	1	2	yes	—
247	C₂²×C₁₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
248	C₂×D₁₁	—	2	1	no	—
249	C₂×D₁₁	—	2	1	no	—
250	C₂×D₁₁	—	2	8	no	—
251	C₂×D₁₁	#423	1	2	yes	—
252	C₂×D₁₁	#427	1	2	yes	—
253	C₂×D₁₁	C₂×#108	1	2	yes	—
254	C₂×D₁₁	C₂×#108	1	2	yes	—
255	C₄×C₁₁	—	2	1	no	—
256	C₄×C₁₁	—	2	1	no	—
257	C₄×C₁₁	—	2	1	no	—
258	C₄×C₁₁	—	2	1	no	—
259	C₄×C₁₁	C₂²×M₁₆	1	1	yes	characteristic
260	C₄×C₁₁	C₂²×M₁₆	1	1	yes	characteristic
261	C₄×C₁₁	C₂×#135	1	2	yes	—
262	Dic₁₁	—	2	1	no	—
263	Dic₁₁	—	2	1	no	—
264	Dic₁₁	—	2	1	no	—
265	Dic₁₁	—	2	1	no	—
266	Dic₁₁	#423	1	2	yes	—
267	Dic₁₁	#427	1	2	yes	—
268	C₂³×C₄	—	11	1	no	—
269	C₂³×C₄	—	11	1	no	—
270	C₂³×C₄	—	11	1	no	—
271	C₂²×C₈	—	11	1	no	—
272	C₂²×C₈	—	11	1	no	—
273	C₂²×C₈	—	11	1	no	—
274	C₂²×C₈	—	11	1	no	—
275	C₂²×C₈	—	11	1	no	—
276	C₂²×C₈	—	11	1	no	—
277	C₂²×C₈	—	11	1	no	—
278	C₂²×C₈	—	11	1	no	—
279	C₂²×C₈	—	11	1	no	—
280	C₂²×C₈	—	11	1	no	—
281	C₂²×C₈	—	22	4	no	—
282	C₂²×C₈	—	22	4	no	—
283	C₂²×C₈	—	22	4	no	—
284	C₂²×C₈	C₄×D₁₁	1	1	yes	characteristic
285	C₂²×C₈	C₄×D₁₁	1	1	yes	characteristic
286	C₂×C₄²	—	11	1	no	—
287	C₂×C₄²	—	11	1	no	—
288	C₂×C₄²	—	11	1	no	—
289	C₂×C₄²	—	11	1	no	—
290	C₂×C₄²	—	11	1	no	—
291	C₂×C₄²	—	11	1	no	—
292	C₂×C₄²	—	11	1	no	—
293	C₂×C₄²	—	11	1	no	—
294	C₂×C₄²	—	11	1	no	—
295	C₂×C₄²	—	11	1	no	—
296	C₂×C₄²	—	11	1	no	—
297	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
298	C₄⋊C₈	—	11	4	no	—
299	C₄⋊C₈	—	22	4	no	—
300	C₄⋊C₈	C₂²×D₁₁	1	4	yes	—
301	C₂²⋊C₈	—	2	2	no	—
302	C₂²⋊C₈	—	22	4	no	—
303	C₂²⋊C₈	—	22	2	no	—
304	#97	—	2	2	no	—
305	#97	—	22	4	no	—
306	#97	—	22	2	no	—
307	C₄×C₈	—	11	1	no	—
308	C₄×C₈	—	11	1	no	—
309	C₄×C₈	—	11	1	no	—
310	C₄×C₈	—	11	1	no	—
311	C₄×C₈	—	11	1	no	—
312	C₄×C₈	—	11	1	no	—
313	C₄×C₈	—	11	1	no	—
314	C₄×C₈	—	11	1	no	—
315	C₄×C₈	—	11	1	no	—
316	C₄×C₈	—	11	1	no	—
317	C₄×C₈	—	11	1	no	—
318	C₄×C₈	—	11	1	no	—
319	C₄×C₈	C₄×D₁₁	1	1	yes	characteristic
320	C₄×C₈	C₄×D₁₁	1	1	yes	characteristic
321	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
322	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
323	C₂×C₁₁	—	2	2	no	—
324	C₂×C₁₁	C₂×#423	1	1	yes	characteristic
325	C₂×C₁₁	C₂×#427	1	1	yes	characteristic
326	C₂×C₁₁	C₂²×#108	1	1	yes	characteristic
327	D₁₁	—	2	2	no	—
328	D₁₁	#1568	1	4	yes	direct product factor
329	C₂⁴	—	11	1	no	—
330	C₂²×C₄	—	11	1	no	—
331	C₂²×C₄	—	11	1	no	—
332	C₂²×C₄	—	11	1	no	—
333	C₂²×C₄	—	11	1	no	—
334	C₂²×C₄	—	11	1	no	—
335	C₂²×C₄	—	11	1	no	—
336	C₂²×C₄	—	11	1	no	—
337	C₂²×C₄	—	11	1	no	—
338	C₂²×C₄	—	11	1	no	—
339	C₂²×C₄	—	11	1	no	—
340	C₂²×C₄	—	11	1	no	—
341	C₂²×C₄	—	11	1	no	—
342	C₂²×C₄	—	11	1	no	—
343	C₂²×C₄	—	11	1	no	—
344	C₂²×C₄	—	11	1	no	—
345	C₂²×C₄	—	22	2	no	—
346	C₂²×C₄	—	22	2	no	—
347	C₂²×C₄	—	22	4	no	—
348	C₂²×C₄	—	22	4	no	—
349	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
350	C₂²×C₄	D₄×D₁₁	1	1	yes	characteristic
351	C₂²×C₄	Q₈×D₁₁	1	1	yes	characteristic
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	2	4	no	—
355	C₂×C₈	—	11	1	no	—
356	C₂×C₈	—	11	1	no	—
357	C₂×C₈	—	11	4	no	—
358	C₂×C₈	—	11	4	no	—
359	C₂×C₈	—	11	1	no	—
360	C₂×C₈	—	11	1	no	—
361	C₂×C₈	—	22	2	no	—
362	C₂×C₈	—	22	2	no	—
363	C₂×C₈	—	22	2	no	—
364	C₂×C₈	—	22	2	no	—
365	C₂×C₈	—	22	2	no	—
366	C₂×C₈	—	22	2	no	—
367	C₂×C₈	—	22	2	no	—
368	C₂×C₈	—	22	2	no	—
369	C₂×C₈	—	22	4	no	—
370	C₂×C₈	—	44	8	no	—
371	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
372	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
373	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
374	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
375	C₄²	—	11	1	no	—
376	C₄²	—	11	1	no	—
377	C₄²	—	11	1	no	—
378	C₄²	—	11	1	no	—
379	C₄²	—	11	1	no	—
380	C₄²	—	11	1	no	—
381	C₄²	—	11	1	no	—
382	C₄²	—	11	1	no	—
383	C₄²	—	11	1	no	—
384	C₄²	—	11	1	no	—
385	C₄²	—	11	1	no	—
386	C₄²	—	11	1	no	—
387	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
388	C₄²	D₄×D₁₁	1	1	yes	characteristic
389	C₄²	Q₈×D₁₁	1	1	yes	characteristic
390	C₄²	C₂³×D₁₁	1	1	yes	characteristic
391	C₁₁	C₂×#1568	1	1	yes	characteristic, complemented, Sylow
392	C₂³	—	11	1	no	—
393	C₂³	—	11	4	no	—
394	C₂³	—	11	1	no	—
395	C₂³	—	22	2	no	—
396	C₂³	—	22	2	no	—
397	C₂³	C₄⋊C₄×D₁₁	1	1	yes	characteristic
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	11	1	no	—
403	C₂×C₄	—	11	1	no	—
404	C₂×C₄	—	11	2	no	—
405	C₂×C₄	—	11	2	no	—
406	C₂×C₄	—	11	4	no	—
407	C₂×C₄	—	11	1	no	—
408	C₂×C₄	—	11	1	no	—
409	C₂×C₄	—	11	1	no	—
410	C₂×C₄	—	11	1	no	—
411	C₂×C₄	—	22	2	no	—
412	C₂×C₄	—	22	2	no	—
413	C₂×C₄	—	22	2	no	—
414	C₂×C₄	—	22	2	no	—
415	C₂×C₄	—	22	2	no	—
416	C₂×C₄	—	22	2	no	—
417	C₂×C₄	—	22	2	no	—
418	C₂×C₄	—	22	2	no	—
419	C₂×C₄	—	22	2	no	—
420	C₂×C₄	—	22	2	no	—
421	C₂×C₄	—	22	2	no	—
422	C₂×C₄	—	22	1	no	—
423	C₂×C₄	—	22	1	no	—
424	C₂×C₄	—	22	2	no	—
425	C₂×C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
426	C₂×C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
427	C₂×C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
428	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
429	C₂×C₄	C₂×D₄×D₁₁	1	1	yes	characteristic
430	C₂×C₄	C₂×Q₈×D₁₁	1	1	yes	characteristic
431	C₈	—	2	1	no	—
432	C₈	—	2	1	no	—
433	C₈	—	4	4	no	—
434	C₈	—	11	2	no	—
435	C₈	—	11	2	no	—
436	C₈	—	22	1	no	—
437	C₈	—	22	1	no	—
438	C₈	—	44	4	no	—
439	C₈	M₁₆×D₁₁	1	2	yes	—
440	C₈	M₁₆×D₁₁	1	2	yes	—
441	C₂²	—	2	1	no	—
442	C₂²	—	2	1	no	—
443	C₂²	—	11	2	no	—
444	C₂²	—	11	2	no	—
445	C₂²	—	11	2	no	—
446	C₂²	—	11	2	no	—
447	C₂²	—	22	8	no	—
448	C₂²	—	22	1	no	—
449	C₂²	—	22	1	no	—
450	C₂²	D₁₁×#108	1	2	yes	—
451	C₂²	C₂×C₄⋊C₄×D₁₁	1	1	yes	characteristic
452	C₄	—	2	1	no	—
453	C₄	—	2	1	no	—
454	C₄	—	2	1	no	—
455	C₄	—	2	1	no	—
456	C₄	—	11	2	no	—
457	C₄	—	11	2	no	—
458	C₄	—	22	1	no	—
459	C₄	—	22	1	no	—
460	C₄	—	22	1	no	—
461	C₄	—	22	1	no	—
462	C₄	C₂×M₁₆×D₁₁	1	1	yes	characteristic
463	C₄	C₂×M₁₆×D₁₁	1	1	yes	characteristic
464	C₄	D₁₁×#135	1	2	yes	—
465	C₂	—	2	2	no	—
466	C₂	—	11	4	no	—
467	C₂	—	22	2	no	—
468	C₂	D₁₁×#423	1	1	yes	characteristic
469	C₂	D₁₁×#427	1	1	yes	characteristic
470	C₂	C₂×D₁₁×#108	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₁
commutator	C₂×C₄×C₁₁	C₂³×C₄
Frattini	C₄²	C₂³×D₁₁
Fitting	C₁₁×#1568	C₂
socle	C₂²×C₁₁	C₂²×C₄⋊C₄
prime radical	C₂³×D₁₁	C₄⋊C₄
cosocle	C₄²×C₁₁	C₂⁴
hypercenter	#1568	D₁₁
hypocenter	C₁₁	C₂×#1568
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1568

Complements

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

N	H ≅ G/N	type
3. #13067379	C₂	semidirect
4. #13067378	C₂	semidirect
5. #13067377	C₂	semidirect
6. #13067376	C₂	semidirect
7. D₁₁×#335	C₂	semidirect
8. D₁₁×#334	C₂	semidirect
9. C₁₁×#1568	C₂	semidirect
33. C₁₁×#335	C₂²	semidirect
34. C₁₁×#334	C₂²	semidirect
35. #10622118	C₂²	semidirect
36. #10622117	C₂²	semidirect
37. #10622096	C₂²	semidirect
38. #10622095	C₂²	semidirect
163. #1568	D₁₁	direct (N × H)
240. #335	C₂×D₁₁	semidirect
243. #334	C₂×D₁₁	semidirect
328. D₁₁	#1568	direct (N × H)
391. C₁₁	C₂×#1568	semidirect

Maximal subgroups

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

subgroup	index
D₁₁×#432	2
C₂×C₄×C₈×D₁₁	2
#13067379	2
#13067378	2
#13067377	2
#13067376	2
D₁₁×#335	2
D₁₁×#334	2
C₁₁×#1568	2
C₂×#1568	11

Subgroups — D11×#1568 #14722776

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₁×#1568 #14722776