Subgroups — #14723112

Order 2816.

594 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13077741	C₂	1	2	yes	maximal
2	#13067401	C₂	1	2	yes	maximal, complemented
3	#13067396	C₂	1	2	yes	maximal, complemented
4	#13067391	C₂	1	2	yes	maximal, complemented
5	#13067383	C₂	1	2	yes	maximal, complemented
6	#13067379	C₂	1	1	yes	maximal, characteristic, complemented
7	#13067368	C₂	1	2	yes	maximal, complemented
8	C₂×#10622096	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁×#2965	C₂	1	1	yes	maximal, characteristic
10	C₄×C₁₁×#41	C₂²	1	1	yes	characteristic
11	C₁₁×#446	C₄	1	1	yes	characteristic
12	C₁₁×#446	C₄	1	1	yes	characteristic
13	C₁₁×#436	C₄	1	1	yes	characteristic
14	C₁₁×#436	C₄	1	1	yes	characteristic
15	C₁₁×#435	C₄	1	2	yes	—
16	C₁₁×#435	C₄	1	2	yes	—
17	C₁₁×#431	C₂²	1	2	yes	—
18	C₁₁×#431	C₂²	1	1	yes	characteristic
19	C₄×C₁₁×M₁₆	C₂²	1	2	yes	—
20	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
21	#10622637	—	2	2	no	—
22	#10622624	—	2	2	no	—
23	#10622624	—	2	2	no	—
24	D₄×C₁₁⋊C₈	—	2	2	no	—
25	#10622539	C₂²	1	2	yes	—
26	#10622539	C₂²	1	2	yes	—
27	#10622538	C₂²	1	2	yes	—
28	#10622537	C₂²	1	2	yes	—
29	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	2	yes	—
30	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	2	yes	—
31	#10622096	C₂²	1	1	yes	characteristic
32	#10622096	C₂²	1	1	yes	characteristic
33	#10622096	C₂²	1	2	yes	—
34	#10622096	C₂²	1	2	yes	—
35	#10622096	C₂²	1	1	yes	characteristic
36	#10622096	C₂²	1	1	yes	characteristic
37	#10622096	C₂²	1	2	yes	—
38	#10622095	C₂²	1	2	yes	—
39	#10622095	C₂²	1	2	yes	—
40	#10622095	C₂²	1	2	yes	—
41	C₂×C₁₁×#41	Q₈	1	1	yes	characteristic
42	C₂×C₁₁×M₁₆	C₂×C₄	1	2	yes	—
43	C₂×C₁₁×M₁₆	C₂×C₄	1	2	yes	—
44	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
46	C₄×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
47	C₄×Q₈×C₁₁	D₄	1	1	yes	characteristic
48	C₄×D₄×C₁₁	C₂×C₄	1	2	yes	—
49	C₄×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
50	C₄×D₄×C₁₁	D₄	1	2	yes	—
51	C₄×D₄×C₁₁	D₄	1	1	yes	characteristic
52	C₁₁×#117	Q₈	1	1	yes	characteristic
53	C₁₁×#117	Q₈	1	2	yes	—
54	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
55	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
56	C₂×#4318	—	2	2	no	—
57	C₂²×C₁₁⋊C₈	—	2	2	no	—
58	C₂²×C₁₁⋊C₈	—	2	2	no	—
59	C₁₁×C₄⋊C₈	C₂×C₄	1	2	yes	—
60	C₁₁×C₄⋊C₈	C₂×C₄	1	2	yes	—
61	C₁₁×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
62	C₁₁×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
63	C₁₁×C₂²⋊C₈	C₂×C₄	1	2	yes	—
64	C₁₁×C₂²⋊C₈	C₂×C₄	1	2	yes	—
65	C₁₁×C₂²⋊C₈	C₂×C₄	1	2	yes	—
66	C₁₁×#97	C₂×C₄	1	2	yes	—
67	C₁₁×#97	C₂×C₄	1	2	yes	—
68	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
69	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
70	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
71	C₄×C₈×C₁₁	C₂³	1	2	yes	—
72	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
73	C₂²⋊(C₁₁⋊C₈)	—	2	2	no	—
74	C₂²⋊(C₁₁⋊C₈)	—	2	2	no	—
75	C₂²⋊(C₁₁⋊C₈)	—	2	2	no	—
76	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
77	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
78	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
79	C₄⋊(C₁₁⋊C₈)	C₂³	1	2	yes	—
80	C₄⋊(C₁₁⋊C₈)	C₂³	1	2	yes	—
81	C₄⋊(C₁₁⋊C₈)	C₂³	1	2	yes	—
82	C₄⋊(C₁₁⋊C₈)	C₂³	1	2	yes	—
83	#66867	—	2	2	no	—
84	#66867	—	2	2	no	—
85	C₄×C₁₁⋊C₈	—	2	2	no	—
86	#17840	—	11	1	no	maximal, Sylow
87	C₁₁×#41	—	4	2	no	—
88	C₂×Q₈×C₁₁	C₄⋊C₄	1	1	yes	characteristic
89	C₂×D₄×C₁₁	C₄⋊C₄	1	2	yes	—
90	C₂×D₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
93	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
95	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
96	C₂²×C₄×C₁₁	C₂×Q₈	1	2	yes	—
97	C₁₁×M₁₆	—	2	4	no	—
98	C₁₁×M₁₆	—	4	2	no	—
99	C₂×C₈×C₁₁	—	2	2	no	—
100	C₂×C₈×C₁₁	—	4	1	no	—
101	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
102	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
103	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
104	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
105	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
106	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
107	C₁₁×C₄⋊C₄	C₄⋊C₄	1	2	yes	—
108	C₁₁×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
109	C₁₁×C₄⋊C₄	C₄⋊C₄	1	2	yes	—
110	C₁₁×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
111	C₁₁×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
112	C₁₁×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
113	C₁₁×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
114	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
115	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
116	C₄²×C₁₁	C₂×D₄	1	2	yes	—
117	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
118	C₄²×C₁₁	C₂×Q₈	1	1	yes	characteristic
119	C₄²×C₁₁	C₂×Q₈	1	2	yes	—
120	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
121	#4318	—	8	2	no	—
122	C₂×C₁₁⋊C₈	—	2	2	no	—
123	C₂×C₁₁⋊C₈	—	2	2	no	—
124	C₂×C₁₁⋊C₈	—	2	2	no	—
125	C₂×C₁₁⋊C₈	—	2	2	no	—
126	C₂×C₁₁⋊C₈	—	8	2	no	—
127	C₂×C₁₁⋊C₈	—	8	2	no	—
128	#2990	—	11	2	no	—
129	#2965	D₁₁	1	1	yes	characteristic
130	#1573	—	11	2	no	—
131	#1572	—	11	2	no	—
132	#1571	—	11	2	no	—
133	#1569	—	11	2	no	—
134	#1568	—	11	1	no	—
135	#1565	—	11	2	no	—
136	C₂×#335	—	11	1	no	—
137	C₂³×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
138	C₂³×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
139	Q₈×C₁₁	—	4	1	no	—
140	D₄×C₁₁	—	2	4	no	—
141	D₄×C₁₁	—	4	1	no	—
142	C₂×C₄×C₁₁	—	2	2	no	—
143	C₂×C₄×C₁₁	—	2	1	no	—
144	C₂×C₄×C₁₁	—	2	2	no	—
145	C₂×C₄×C₁₁	—	2	1	no	—
146	C₂×C₄×C₁₁	—	2	2	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	2	no	—
151	C₂×C₄×C₁₁	—	4	2	no	—
152	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
154	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
155	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
156	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
157	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
158	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
159	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
160	C₂×C₄×C₁₁	C₂²×Q₈	1	1	yes	characteristic
161	C₈×C₁₁	—	2	1	no	—
162	C₈×C₁₁	—	2	2	no	—
163	C₈×C₁₁	—	2	1	no	—
164	C₈×C₁₁	—	2	1	no	—
165	C₈×C₁₁	—	2	2	no	—
166	C₈×C₁₁	#131	1	2	yes	—
167	C₁₁⋊C₈	—	4	2	no	—
168	C₁₁⋊C₈	—	4	2	no	—
169	C₁₁⋊C₈	—	4	2	no	—
170	C₁₁⋊C₈	—	4	2	no	—
171	C₄×#41	C₂×D₁₁	1	1	yes	characteristic
172	#446	—	22	2	no	—
173	#446	Dic₁₁	1	1	yes	characteristic
174	#446	Dic₁₁	1	1	yes	characteristic
175	#436	Dic₁₁	1	1	yes	characteristic
176	#436	Dic₁₁	1	1	yes	characteristic
177	#435	—	22	2	no	—
178	#435	—	22	2	no	—
179	#435	Dic₁₁	1	2	yes	—
180	#435	Dic₁₁	1	2	yes	—
181	C₈×D₄	—	22	2	no	—
182	#432	—	11	2	no	—
183	#432	—	11	2	no	—
184	#431	—	11	2	no	—
185	#431	C₂×D₁₁	1	2	yes	—
186	#431	C₂×D₁₁	1	1	yes	characteristic
187	#423	—	11	2	no	—
188	C₂×C₄⋊C₈	—	11	2	no	—
189	C₂×C₄⋊C₈	—	11	2	no	—
190	C₄×M₁₆	C₂×D₁₁	1	2	yes	—
191	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
192	#335	—	11	1	no	—
193	#335	—	11	1	no	—
194	#335	—	11	2	no	—
195	#335	—	11	2	no	—
196	#335	—	11	1	no	—
197	#335	—	11	1	no	—
198	#335	—	11	2	no	—
199	#334	—	11	2	no	—
200	#334	—	11	2	no	—
201	#334	—	11	2	no	—
202	C₂²×C₁₁	—	2	1	no	—
203	C₂²×C₁₁	—	2	1	no	—
204	C₂²×C₁₁	—	2	2	no	—
205	C₂²×C₁₁	—	2	2	no	—
206	C₂²×C₁₁	—	2	2	no	—
207	C₂²×C₁₁	#430	1	2	yes	—
208	C₂²×C₁₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
209	C₄×C₁₁	—	2	1	no	—
210	C₄×C₁₁	—	2	2	no	—
211	C₄×C₁₁	—	2	1	no	—
212	C₄×C₁₁	—	2	2	no	—
213	C₄×C₁₁	—	2	1	no	—
214	C₄×C₁₁	—	2	1	no	—
215	C₄×C₁₁	—	2	2	no	—
216	C₄×C₁₁	C₂×#131	1	1	yes	characteristic
217	C₄×C₁₁	#568	1	1	yes	characteristic
218	C₄×C₁₁	#576	1	1	yes	characteristic
219	C₄×C₁₁	#578	1	1	yes	characteristic
220	C₂×#41	Dic₂₂	1	1	yes	characteristic
221	C₂×M₁₆	—	22	2	no	—
222	C₂×M₁₆	C₂×Dic₁₁	1	2	yes	—
223	C₂×M₁₆	C₂×Dic₁₁	1	2	yes	—
224	C₂²×C₈	—	22	2	no	—
225	C₂²×C₈	—	22	2	no	—
226	C₂²×C₈	C₂×Dic₁₁	1	1	yes	characteristic
227	C₂²×C₈	C₂×Dic₁₁	1	1	yes	characteristic
228	C₄×Q₈	D₄₄	1	1	yes	characteristic
229	C₄×Q₈	C₂×Dic₁₁	1	1	yes	characteristic
230	C₄×D₄	D₄₄	1	2	yes	—
231	C₄×D₄	D₄₄	1	1	yes	characteristic
232	C₄×D₄	C₂×Dic₁₁	1	2	yes	—
233	C₄×D₄	C₂×Dic₁₁	1	1	yes	characteristic
234	#117	Dic₂₂	1	1	yes	characteristic
235	#117	Dic₂₂	1	2	yes	—
236	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
237	C₂×C₄²	C₂²×D₁₁	1	2	yes	—
238	C₄⋊C₈	—	11	2	no	—
239	C₄⋊C₈	—	11	2	no	—
240	C₄⋊C₈	—	11	2	no	—
241	C₄⋊C₈	—	11	2	no	—
242	C₄⋊C₈	—	22	2	no	—
243	C₄⋊C₈	—	22	2	no	—
244	C₄⋊C₈	—	22	2	no	—
245	C₄⋊C₈	C₂×Dic₁₁	1	2	yes	—
246	C₄⋊C₈	C₂×Dic₁₁	1	2	yes	—
247	C₄⋊C₈	C₂×Dic₁₁	1	1	yes	characteristic
248	C₄⋊C₈	C₂×Dic₁₁	1	1	yes	characteristic
249	C₂²⋊C₈	—	22	2	no	—
250	C₂²⋊C₈	—	22	2	no	—
251	C₂²⋊C₈	—	22	2	no	—
252	C₂²⋊C₈	C₂×Dic₁₁	1	2	yes	—
253	C₂²⋊C₈	C₂×Dic₁₁	1	2	yes	—
254	C₂²⋊C₈	C₂×Dic₁₁	1	2	yes	—
255	#97	—	22	2	no	—
256	#97	—	22	2	no	—
257	#97	C₂×Dic₁₁	1	2	yes	—
258	#97	C₂×Dic₁₁	1	2	yes	—
259	C₄×C₈	—	22	2	no	—
260	C₄×C₈	C₂×Dic₁₁	1	1	yes	characteristic
261	C₄×C₈	C₂×Dic₁₁	1	1	yes	characteristic
262	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
263	C₄×C₈	C₂²×D₁₁	1	2	yes	—
264	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
265	C₂×C₁₁	—	2	2	no	—
266	C₂×C₁₁	—	4	2	no	—
267	C₂×C₁₁	#2906	1	1	yes	characteristic
268	C₂×C₁₁	#2913	1	1	yes	characteristic
269	C₂×C₁₁	C₂×#430	1	1	yes	characteristic
270	#41	—	4	2	no	—
271	C₂×Q₈	C₄⋊Dic₁₁	1	1	yes	characteristic
272	C₂×D₄	C₄⋊Dic₁₁	1	2	yes	—
273	C₂×D₄	C₄⋊Dic₁₁	1	1	yes	characteristic
274	C₂²×C₄	C₂×Dic₂₂	1	1	yes	characteristic
275	C₂²×C₄	C₂×Dic₂₂	1	2	yes	—
276	C₂²×C₄	C₂×D₄₄	1	1	yes	characteristic
277	C₂²×C₄	C₂×D₄₄	1	2	yes	—
278	C₂²×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
279	C₂²×C₄	C₂²×Dic₁₁	1	2	yes	—
280	M₁₆	—	2	4	no	—
281	M₁₆	—	4	2	no	—
282	M₁₆	—	88	2	no	—
283	C₂×C₈	—	2	2	no	—
284	C₂×C₈	—	4	1	no	—
285	C₂×C₈	—	22	2	no	—
286	C₂×C₈	—	22	2	no	—
287	C₂×C₈	—	22	2	no	—
288	C₂×C₈	—	22	2	no	—
289	C₂×C₈	—	88	2	no	—
290	C₂×C₈	—	88	2	no	—
291	C₂×C₈	C₂²×Dic₁₁	1	1	yes	characteristic
292	C₂×C₈	C₂²×Dic₁₁	1	1	yes	characteristic
293	C₂×C₈	C₂²×Dic₁₁	1	1	yes	characteristic
294	C₂×C₈	C₂²×Dic₁₁	1	2	yes	—
295	C₂×C₈	C₂²×Dic₁₁	1	2	yes	—
296	C₂×C₈	C₂²×Dic₁₁	1	1	yes	characteristic
297	C₄⋊C₄	C₄⋊Dic₁₁	1	2	yes	—
298	C₄⋊C₄	C₄⋊Dic₁₁	1	1	yes	characteristic
299	C₄⋊C₄	C₄⋊Dic₁₁	1	2	yes	—
300	C₄⋊C₄	C₄⋊Dic₁₁	1	1	yes	characteristic
301	C₂²⋊C₄	C₄⋊Dic₁₁	1	2	yes	—
302	C₂²⋊C₄	C₄⋊Dic₁₁	1	2	yes	—
303	C₂²⋊C₄	C₄⋊Dic₁₁	1	2	yes	—
304	C₄²	C₂×Dic₂₂	1	1	yes	characteristic
305	C₄²	C₂×Dic₂₂	1	2	yes	—
306	C₄²	C₂×D₄₄	1	2	yes	—
307	C₄²	C₂×D₄₄	1	1	yes	characteristic
308	C₄²	C₂²×Dic₁₁	1	1	yes	characteristic
309	C₄²	C₂²×Dic₁₁	1	2	yes	—
310	C₄²	C₂³×D₁₁	1	1	yes	characteristic
311	C₁₁	#17840	1	1	yes	characteristic, complemented, Sylow
312	C₂³	C₂×C₄⋊Dic₁₁	1	2	yes	—
313	C₂³	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
314	Q₈	—	4	1	no	—
315	D₄	—	2	4	no	—
316	D₄	—	4	1	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	C₂×C₄⋊Dic₁₁	1	2	yes	—
328	C₂×C₄	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
329	C₂×C₄	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
330	C₂×C₄	C₂×C₄⋊Dic₁₁	1	2	yes	—
331	C₂×C₄	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
332	C₂×C₄	C₂×C₄⋊Dic₁₁	1	2	yes	—
333	C₂×C₄	C₂²×Dic₂₂	1	1	yes	characteristic
334	C₂×C₄	C₂²×D₄₄	1	1	yes	characteristic
335	C₂×C₄	C₂³×Dic₁₁	1	1	yes	characteristic
336	C₈	—	2	1	no	—
337	C₈	—	2	2	no	—
338	C₈	—	2	1	no	—
339	C₈	—	2	1	no	—
340	C₈	—	2	2	no	—
341	C₈	—	44	2	no	—
342	C₈	—	44	2	no	—
343	C₈	—	44	2	no	—
344	C₈	—	44	2	no	—
345	C₈	#67001	1	2	yes	—
346	C₂²	—	2	1	no	—
347	C₂²	—	2	1	no	—
348	C₂²	—	2	2	no	—
349	C₂²	—	2	2	no	—
350	C₂²	—	2	2	no	—
351	C₂²	#10622738	1	2	yes	—
352	C₂²	C₂²×C₄⋊Dic₁₁	1	1	yes	characteristic
353	C₄	—	2	1	no	—
354	C₄	—	2	2	no	—
355	C₄	—	2	1	no	—
356	C₄	—	2	2	no	—
357	C₄	—	2	1	no	—
358	C₄	—	2	1	no	—
359	C₄	—	2	2	no	—
360	C₄	#10623283	1	1	yes	characteristic
361	C₄	#10623284	1	1	yes	characteristic
362	C₄	C₂×#67001	1	1	yes	characteristic
363	C₄	#10623350	1	1	yes	characteristic
364	C₂	—	2	2	no	—
365	C₂	—	4	2	no	—
366	C₂	#13077184	1	1	yes	characteristic
367	C₂	#13077216	1	1	yes	characteristic
368	C₂	C₂×#10622738	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₄₄
commutator	C₂×C₄×C₁₁	C₂³×C₄
Frattini	C₄²	C₂³×D₁₁
Fitting	C₁₁×#2965	C₂
socle	C₂²×C₁₁	C₂²×C₄⋊C₄
prime radical	C₂×C₁₁×#41	Q₈
cosocle	C₄²×C₁₁	C₂⁴
hypercenter	#2965	D₁₁
hypocenter	C₁₁	#17840
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41 ◁ #2965

Complements

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

N	H ≅ G/N	type
2. #13067401	C₂	semidirect
3. #13067396	C₂	semidirect
4. #13067391	C₂	semidirect
5. #13067383	C₂	semidirect
6. #13067379	C₂	semidirect
7. #13067368	C₂	semidirect
8. C₂×#10622096	C₂	semidirect
311. C₁₁	#17840	semidirect

Maximal subgroups

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

subgroup	index
#13077741	2
#13067401	2
#13067396	2
#13067391	2
#13067383	2
#13067379	2
#13067368	2
C₂×#10622096	2
C₁₁×#2965	2
#17840	11