Subgroups — C₁₁×#21419 #14598612

Order 2816.

1122 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3455	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2921	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₁₁×#117	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#1995	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁×#1994	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁×#1963	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#1962	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₁×#1897	C₂	1	2	yes	maximal, complemented
9	C₁₁×#1896	C₂	1	2	yes	maximal, complemented
10	C₁₁×#1759	C₂	1	2	yes	maximal, complemented
11	C₄×C₁₁×#104	C₂	1	2	yes	maximal, complemented
12	C₁₁×#542	C₄	1	4	yes	complemented
13	C₁₁×#541	C₄	1	2	yes	complemented
14	C₁₁×#540	C₄	1	2	yes	complemented
15	C₁₁×#539	—	2	2	no	—
16	C₁₁×#538	—	2	2	no	—
17	C₁₁×#533	C₂²	1	1	yes	characteristic
18	C₁₁×#532	C₂²	1	1	yes	characteristic
19	C₁₁×#529	—	2	4	no	—
20	C₁₁×#525	C₂²	1	2	yes	—
21	C₄×C₁₁×#41	C₂²	1	2	yes	—
22	C₂×C₁₁×#117	C₂²	1	1	yes	characteristic
23	C₂×C₁₁×#117	C₂²	1	1	yes	characteristic
24	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
25	C₁₁×#433	—	2	4	no	—
26	C₁₁×#423	C₂²	1	1	yes	characteristic
27	C₁₁×#423	C₂²	1	1	yes	characteristic
28	C₂×C₁₁×#104	C₂²	1	2	yes	—
29	C₂×C₁₁×#104	C₂²	1	2	yes	—
30	C₂×C₁₁×#104	C₂²	1	2	yes	—
31	C₂×C₁₁×#104	C₂²	1	2	yes	—
32	C₁₁×#407	C₂²	1	2	yes	—
33	C₄×C₁₁×M₁₆	C₂²	1	2	yes	—
34	C₄×C₁₁×C₄⋊C₄	—	2	2	no	—
35	C₄×C₁₁×C₂²⋊C₄	—	2	2	no	—
36	C₁₁×#376	C₂²	1	1	yes	characteristic
37	C₁₁×#376	C₂²	1	1	yes	characteristic
38	C₄³×C₁₁	C₂²	1	1	yes	characteristic
39	C₄³×C₁₁	C₂²	1	1	yes	characteristic
40	C₁₁×#339	C₂²	1	2	yes	—
41	C₁₁×#339	C₂²	1	2	yes	—
42	C₁₁×#339	C₂²	1	2	yes	—
43	C₁₁×#339	C₂²	1	2	yes	—
44	C₂×C₁₁×#41	C₂³	1	2	yes	—
45	C₂³×C₄×C₁₁	—	2	1	no	—
46	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
47	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
48	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
49	C₁₁×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic, complemented
50	C₁₁×C₄⋊Q₈	C₂×C₄	1	2	yes	complemented
51	C₁₁×#127	C₂×C₄	1	1	yes	characteristic, complemented
52	C₁₁×#126	—	2	4	no	—
53	C₁₁×#126	—	2	4	no	—
54	C₁₁×#125	—	2	4	no	—
55	C₁₁×#125	C₂×C₄	1	2	yes	complemented
56	C₁₁×#124	—	2	4	no	—
57	C₁₁×#124	C₂×C₄	1	2	yes	complemented
58	C₁₁×#123	—	2	2	no	—
59	C₁₁×#123	—	2	4	no	—
60	C₁₁×#123	—	2	4	no	—
61	C₁₁×C₂²⋊Q₈	—	2	2	no	—
62	C₁₁×C₂²⋊Q₈	—	2	4	no	—
63	C₁₁×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
64	C₁₁×#121	—	2	2	no	—
65	C₁₁×#121	—	2	4	no	—
66	C₁₁×#121	C₂×C₄	1	4	yes	—
67	C₁₁×#120	—	2	2	no	—
68	C₄×Q₈×C₁₁	—	2	2	no	—
69	C₄×Q₈×C₁₁	C₂×C₄	1	4	yes	complemented
70	C₄×D₄×C₁₁	—	2	4	no	—
71	C₄×D₄×C₁₁	—	2	4	no	—
72	C₄×D₄×C₁₁	—	2	2	no	—
73	C₄×D₄×C₁₁	C₂×C₄	1	4	yes	complemented
74	C₁₁×#117	—	2	2	no	—
75	C₁₁×#117	—	2	2	no	—
76	C₁₁×#117	—	2	2	no	—
77	C₁₁×#117	C₂×C₄	1	2	yes	—
78	C₁₁×#117	C₂×C₄	1	2	yes	—
79	C₁₁×#117	D₄	1	4	yes	—
80	C₁₁×#117	C₂³	1	2	yes	—
81	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
82	C₂×C₁₁×C₄⋊C₄	D₄	1	2	yes	—
83	C₂×C₁₁×C₂²⋊C₄	—	2	1	no	—
84	C₂×C₁₁×C₂²⋊C₄	D₄	1	2	yes	—
85	C₂×C₄²×C₁₁	—	2	1	no	—
86	C₂×C₄²×C₁₁	—	2	2	no	—
87	C₂×C₄²×C₁₁	—	2	2	no	—
88	C₂×C₄²×C₁₁	—	2	2	no	—
89	C₂×C₄²×C₁₁	—	2	2	no	—
90	C₂×C₄²×C₁₁	—	2	2	no	—
91	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
92	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
93	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
94	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
95	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
96	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
97	C₁₁×C₄⋊C₈	—	2	2	no	—
98	C₁₁×C₄⋊C₈	—	2	2	no	—
99	C₁₁×#104	—	2	4	no	—
100	C₁₁×#104	—	2	4	no	—
101	C₁₁×#104	—	2	4	no	—
102	C₁₁×#104	—	2	4	no	—
103	C₁₁×C₂²⋊C₈	—	2	4	no	—
104	C₁₁×#97	—	2	2	no	—
105	C₄×C₈×C₁₁	—	2	2	no	—
106	C₁₁×#95	—	2	2	no	—
107	C₁₁×#95	—	2	2	no	—
108	#21419	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
109	C₂⁴×C₁₁	C₂×D₄	1	1	yes	characteristic
110	C₁₁×#41	—	2	2	no	—
111	C₁₁×#41	—	2	2	no	—
112	C₁₁×#41	—	2	2	no	—
113	C₁₁×#41	—	2	2	no	—
114	C₂×Q₈×C₁₁	—	2	2	no	—
115	C₂×Q₈×C₁₁	C₂²×C₄	1	2	yes	—
116	C₂×D₄×C₁₁	—	2	2	no	—
117	C₂×D₄×C₁₁	—	2	4	no	—
118	C₂×D₄×C₁₁	—	2	2	no	—
119	C₂×D₄×C₁₁	C₂²×C₄	1	2	yes	—
120	C₂²×C₄×C₁₁	—	2	1	no	—
121	C₂²×C₄×C₁₁	—	2	1	no	—
122	C₂²×C₄×C₁₁	—	2	1	no	—
123	C₂²×C₄×C₁₁	—	2	1	no	—
124	C₂²×C₄×C₁₁	—	2	1	no	—
125	C₂²×C₄×C₁₁	—	2	4	no	—
126	C₂²×C₄×C₁₁	—	2	1	no	—
127	C₂²×C₄×C₁₁	—	2	1	no	—
128	C₂²×C₄×C₁₁	—	2	1	no	—
129	C₂²×C₄×C₁₁	—	2	2	no	—
130	C₂²×C₄×C₁₁	—	2	4	no	—
131	C₂²×C₄×C₁₁	—	4	4	no	—
132	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
133	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
136	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
137	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
138	C₁₁×M₁₆	—	2	2	no	—
139	C₁₁×M₁₆	—	2	2	no	—
140	C₁₁×M₁₆	—	2	2	no	—
141	C₁₁×M₁₆	—	2	2	no	—
142	C₂×C₈×C₁₁	—	2	2	no	—
143	C₂×C₈×C₁₁	—	2	2	no	—
144	C₁₁×C₄⋊C₄	—	2	4	no	—
145	C₁₁×C₄⋊C₄	—	2	4	no	—
146	C₁₁×C₄⋊C₄	—	2	2	no	—
147	C₁₁×C₄⋊C₄	—	2	4	no	—
148	C₁₁×C₄⋊C₄	—	2	4	no	—
149	C₁₁×C₄⋊C₄	—	2	2	no	—
150	C₁₁×C₄⋊C₄	C₂²⋊C₄	1	4	yes	—
151	C₁₁×C₄⋊C₄	C₂²⋊C₄	1	4	yes	—
152	C₁₁×C₄⋊C₄	C₂²×C₄	1	4	yes	—
153	C₁₁×C₂²⋊C₄	—	2	4	no	—
154	C₁₁×C₂²⋊C₄	—	2	4	no	—
155	C₁₁×C₂²⋊C₄	—	2	2	no	—
156	C₁₁×C₂²⋊C₄	—	2	4	no	—
157	C₁₁×C₂²⋊C₄	—	2	4	no	—
158	C₁₁×C₂²⋊C₄	—	2	4	no	—
159	C₁₁×C₂²⋊C₄	C₂²⋊C₄	1	4	yes	—
160	C₁₁×C₂²⋊C₄	C₂²⋊C₄	1	4	yes	—
161	C₄²×C₁₁	—	2	4	no	—
162	C₄²×C₁₁	—	2	4	no	—
163	C₄²×C₁₁	—	2	2	no	—
164	C₄²×C₁₁	—	2	1	no	—
165	C₄²×C₁₁	—	2	1	no	—
166	C₄²×C₁₁	—	2	1	no	—
167	C₄²×C₁₁	—	2	1	no	—
168	C₄²×C₁₁	—	4	4	no	—
169	C₄²×C₁₁	—	4	4	no	—
170	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
171	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
172	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
173	C₄²×C₁₁	C₂×D₄	1	2	yes	—
174	C₄²×C₁₁	C₂×D₄	1	2	yes	—
175	C₄²×C₁₁	#41	1	2	yes	—
176	C₄²×C₁₁	#41	1	2	yes	—
177	C₄²×C₁₁	#41	1	2	yes	—
178	C₄²×C₁₁	#41	1	2	yes	—
179	#3455	C₂×C₁₁	1	1	yes	characteristic
180	#2921	C₂×C₁₁	1	1	yes	characteristic, complemented
181	C₄×#117	C₂×C₁₁	1	1	yes	characteristic, complemented
182	#1995	C₂×C₁₁	1	1	yes	characteristic, complemented
183	#1994	C₂×C₁₁	1	1	yes	characteristic, complemented
184	#1963	C₂×C₁₁	1	1	yes	characteristic, complemented
185	#1962	C₂×C₁₁	1	1	yes	characteristic, complemented
186	#1897	C₂×C₁₁	1	2	yes	complemented
187	#1896	C₂×C₁₁	1	2	yes	complemented
188	#1759	C₂×C₁₁	1	2	yes	complemented
189	C₄×#104	C₂×C₁₁	1	2	yes	complemented
190	C₂³×C₁₁	—	2	1	no	—
191	C₂³×C₁₁	—	2	1	no	—
192	C₂³×C₁₁	—	2	2	no	—
193	C₂³×C₁₁	—	4	2	no	—
194	C₂³×C₁₁	C₂×C₂²⋊C₄	1	2	yes	—
195	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
196	Q₈×C₁₁	—	2	2	no	—
197	Q₈×C₁₁	—	2	2	no	—
198	Q₈×C₁₁	—	8	2	no	—
199	D₄×C₁₁	—	2	2	no	—
200	D₄×C₁₁	—	2	2	no	—
201	D₄×C₁₁	—	4	2	no	—
202	D₄×C₁₁	—	4	2	no	—
203	D₄×C₁₁	—	8	2	no	—
204	D₄×C₁₁	—	8	4	no	—
205	C₂×C₄×C₁₁	—	2	4	no	—
206	C₂×C₄×C₁₁	—	2	1	no	—
207	C₂×C₄×C₁₁	—	2	2	no	—
208	C₂×C₄×C₁₁	—	2	1	no	—
209	C₂×C₄×C₁₁	—	2	2	no	—
210	C₂×C₄×C₁₁	—	2	2	no	—
211	C₂×C₄×C₁₁	—	2	2	no	—
212	C₂×C₄×C₁₁	—	2	2	no	—
213	C₂×C₄×C₁₁	—	2	2	no	—
214	C₂×C₄×C₁₁	—	2	4	no	—
215	C₂×C₄×C₁₁	—	2	2	no	—
216	C₂×C₄×C₁₁	—	2	2	no	—
217	C₂×C₄×C₁₁	—	2	2	no	—
218	C₂×C₄×C₁₁	—	4	2	no	—
219	C₂×C₄×C₁₁	—	4	2	no	—
220	C₂×C₄×C₁₁	—	4	8	no	—
221	C₂×C₄×C₁₁	—	4	2	no	—
222	C₂×C₄×C₁₁	—	4	2	no	—
223	C₂×C₄×C₁₁	—	4	2	no	—
224	C₂×C₄×C₁₁	—	4	2	no	—
225	C₂×C₄×C₁₁	—	4	2	no	—
226	C₂×C₄×C₁₁	—	8	4	no	—
227	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	4	yes	—
228	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	2	yes	—
229	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	2	yes	—
230	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	2	yes	—
231	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
232	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
233	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
234	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
235	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
236	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
237	C₈×C₁₁	—	4	2	no	—
238	C₈×C₁₁	—	4	2	no	—
239	#542	C₄×C₁₁	1	4	yes	complemented
240	#541	C₄×C₁₁	1	2	yes	complemented
241	#540	C₄×C₁₁	1	2	yes	complemented
242	#539	—	2	2	no	—
243	#538	—	2	2	no	—
244	#533	C₂²×C₁₁	1	1	yes	characteristic
245	#532	C₂²×C₁₁	1	1	yes	characteristic
246	#529	—	2	4	no	—
247	#525	C₂²×C₁₁	1	2	yes	—
248	C₄×#41	C₂²×C₁₁	1	2	yes	—
249	C₂×#117	C₂²×C₁₁	1	1	yes	characteristic
250	C₂×#117	C₂²×C₁₁	1	1	yes	characteristic
251	C₂²×C₄²	C₂²×C₁₁	1	1	yes	characteristic
252	#433	—	2	4	no	—
253	#423	C₂²×C₁₁	1	1	yes	characteristic
254	#423	C₂²×C₁₁	1	1	yes	characteristic
255	C₂×#104	C₂²×C₁₁	1	2	yes	—
256	C₂×#104	C₂²×C₁₁	1	2	yes	—
257	C₂×#104	C₂²×C₁₁	1	2	yes	—
258	C₂×#104	C₂²×C₁₁	1	2	yes	—
259	#407	C₂²×C₁₁	1	2	yes	—
260	C₄×M₁₆	C₂²×C₁₁	1	2	yes	—
261	C₄×C₄⋊C₄	—	2	2	no	—
262	C₄×C₂²⋊C₄	—	2	2	no	—
263	#376	C₂²×C₁₁	1	1	yes	characteristic
264	#376	C₂²×C₁₁	1	1	yes	characteristic
265	C₄³	C₂²×C₁₁	1	1	yes	characteristic
266	C₄³	C₂²×C₁₁	1	1	yes	characteristic
267	#339	C₂²×C₁₁	1	2	yes	—
268	#339	C₂²×C₁₁	1	2	yes	—
269	#339	C₂²×C₁₁	1	2	yes	—
270	#339	C₂²×C₁₁	1	2	yes	—
271	C₂²×C₁₁	—	2	2	no	—
272	C₂²×C₁₁	—	2	4	no	—
273	C₂²×C₁₁	—	2	2	no	—
274	C₂²×C₁₁	—	4	2	no	—
275	C₂²×C₁₁	—	4	2	no	—
276	C₂²×C₁₁	—	4	4	no	—
277	C₂²×C₁₁	—	4	2	no	—
278	C₂²×C₁₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
279	C₂²×C₁₁	#525	1	1	yes	characteristic
280	C₂²×C₁₁	#525	1	1	yes	characteristic
281	C₄×C₁₁	—	2	4	no	—
282	C₄×C₁₁	—	2	4	no	—
283	C₄×C₁₁	—	2	2	no	—
284	C₄×C₁₁	—	2	2	no	—
285	C₄×C₁₁	—	2	2	no	—
286	C₄×C₁₁	—	4	2	no	—
287	C₄×C₁₁	—	4	2	no	—
288	C₄×C₁₁	—	4	2	no	—
289	C₄×C₁₁	—	4	4	no	—
290	C₄×C₁₁	—	4	2	no	—
291	C₄×C₁₁	C₄×#41	1	1	yes	characteristic
292	C₄×C₁₁	C₄×#41	1	1	yes	characteristic
293	C₄×C₁₁	#532	1	1	yes	characteristic
294	C₄×C₁₁	#532	1	1	yes	characteristic
295	C₂×#41	C₂³×C₁₁	1	2	yes	—
296	C₂³×C₄	—	2	1	no	—
297	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
298	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
299	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
300	C₄⋊Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic, complemented
301	C₄⋊Q₈	C₂×C₄×C₁₁	1	2	yes	complemented
302	#127	C₂×C₄×C₁₁	1	1	yes	characteristic, complemented
303	#126	—	2	4	no	—
304	#126	—	2	4	no	—
305	#125	—	2	4	no	—
306	#125	C₂×C₄×C₁₁	1	2	yes	complemented
307	#124	—	2	4	no	—
308	#124	C₂×C₄×C₁₁	1	2	yes	complemented
309	#123	—	2	2	no	—
310	#123	—	2	4	no	—
311	#123	—	2	4	no	—
312	C₂²⋊Q₈	—	2	2	no	—
313	C₂²⋊Q₈	—	2	4	no	—
314	C₂²⋊Q₈	C₂×C₄×C₁₁	1	4	yes	—
315	#121	—	2	2	no	—
316	#121	—	2	4	no	—
317	#121	C₂×C₄×C₁₁	1	4	yes	—
318	#120	—	2	2	no	—
319	C₄×Q₈	—	2	2	no	—
320	C₄×Q₈	C₂×C₄×C₁₁	1	4	yes	complemented
321	C₄×D₄	—	2	4	no	—
322	C₄×D₄	—	2	4	no	—
323	C₄×D₄	—	2	2	no	—
324	C₄×D₄	C₂×C₄×C₁₁	1	4	yes	complemented
325	#117	—	2	2	no	—
326	#117	—	2	2	no	—
327	#117	—	2	2	no	—
328	#117	C₂×C₄×C₁₁	1	2	yes	—
329	#117	C₂×C₄×C₁₁	1	2	yes	—
330	#117	D₄×C₁₁	1	4	yes	—
331	#117	C₂³×C₁₁	1	2	yes	—
332	C₂×C₄⋊C₄	—	2	1	no	—
333	C₂×C₄⋊C₄	D₄×C₁₁	1	2	yes	—
334	C₂×C₂²⋊C₄	—	2	1	no	—
335	C₂×C₂²⋊C₄	D₄×C₁₁	1	2	yes	—
336	C₂×C₄²	—	2	1	no	—
337	C₂×C₄²	—	2	2	no	—
338	C₂×C₄²	—	2	2	no	—
339	C₂×C₄²	—	2	2	no	—
340	C₂×C₄²	—	2	2	no	—
341	C₂×C₄²	—	2	2	no	—
342	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
343	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
344	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
345	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
346	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
347	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
348	C₄⋊C₈	—	2	2	no	—
349	C₄⋊C₈	—	2	2	no	—
350	#104	—	2	4	no	—
351	#104	—	2	4	no	—
352	#104	—	2	4	no	—
353	#104	—	2	4	no	—
354	C₂²⋊C₈	—	2	4	no	—
355	#97	—	2	2	no	—
356	C₄×C₈	—	2	2	no	—
357	#95	—	2	2	no	—
358	#95	—	2	2	no	—
359	C₂×C₁₁	—	2	1	no	—
360	C₂×C₁₁	—	2	1	no	—
361	C₂×C₁₁	—	4	2	no	—
362	C₂×C₁₁	—	8	2	no	—
363	C₂×C₁₁	#2297	1	1	yes	characteristic
364	C₂×C₁₁	#2901	1	2	yes	—
365	C₂⁴	C₂×D₄×C₁₁	1	1	yes	characteristic
366	#41	—	2	2	no	—
367	#41	—	2	2	no	—
368	#41	—	2	2	no	—
369	#41	—	2	2	no	—
370	C₂×Q₈	—	2	2	no	—
371	C₂×Q₈	C₂²×C₄×C₁₁	1	2	yes	—
372	C₂×D₄	—	2	2	no	—
373	C₂×D₄	—	2	4	no	—
374	C₂×D₄	—	2	2	no	—
375	C₂×D₄	C₂²×C₄×C₁₁	1	2	yes	—
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	2	4	no	—
382	C₂²×C₄	—	2	1	no	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	2	1	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	2	4	no	—
387	C₂²×C₄	—	4	4	no	—
388	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
389	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
390	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
391	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
392	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
393	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
394	M₁₆	—	2	2	no	—
395	M₁₆	—	2	2	no	—
396	M₁₆	—	2	2	no	—
397	M₁₆	—	2	2	no	—
398	C₂×C₈	—	2	2	no	—
399	C₂×C₈	—	2	2	no	—
400	C₄⋊C₄	—	2	4	no	—
401	C₄⋊C₄	—	2	4	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	2	4	no	—
404	C₄⋊C₄	—	2	4	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	C₁₁×C₂²⋊C₄	1	4	yes	—
407	C₄⋊C₄	C₁₁×C₂²⋊C₄	1	4	yes	—
408	C₄⋊C₄	C₂²×C₄×C₁₁	1	4	yes	—
409	C₂²⋊C₄	—	2	4	no	—
410	C₂²⋊C₄	—	2	4	no	—
411	C₂²⋊C₄	—	2	2	no	—
412	C₂²⋊C₄	—	2	4	no	—
413	C₂²⋊C₄	—	2	4	no	—
414	C₂²⋊C₄	—	2	4	no	—
415	C₂²⋊C₄	C₁₁×C₂²⋊C₄	1	4	yes	—
416	C₂²⋊C₄	C₁₁×C₂²⋊C₄	1	4	yes	—
417	C₄²	—	2	4	no	—
418	C₄²	—	2	4	no	—
419	C₄²	—	2	2	no	—
420	C₄²	—	2	1	no	—
421	C₄²	—	2	1	no	—
422	C₄²	—	2	1	no	—
423	C₄²	—	2	1	no	—
424	C₄²	—	4	4	no	—
425	C₄²	—	4	4	no	—
426	C₄²	C₂²×C₄×C₁₁	1	2	yes	—
427	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
428	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
429	C₄²	C₂×D₄×C₁₁	1	2	yes	—
430	C₄²	C₂×D₄×C₁₁	1	2	yes	—
431	C₄²	C₁₁×#41	1	2	yes	—
432	C₄²	C₁₁×#41	1	2	yes	—
433	C₄²	C₁₁×#41	1	2	yes	—
434	C₄²	C₁₁×#41	1	2	yes	—
435	C₁₁	#21419	1	1	yes	characteristic, direct product factor, Sylow
436	C₂³	—	2	1	no	—
437	C₂³	—	2	1	no	—
438	C₂³	—	2	2	no	—
439	C₂³	—	4	2	no	—
440	C₂³	C₂×C₁₁×C₂²⋊C₄	1	2	yes	—
441	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
442	Q₈	—	2	2	no	—
443	Q₈	—	2	2	no	—
444	Q₈	—	8	2	no	—
445	D₄	—	2	2	no	—
446	D₄	—	2	2	no	—
447	D₄	—	4	2	no	—
448	D₄	—	4	2	no	—
449	D₄	—	8	2	no	—
450	D₄	—	8	4	no	—
451	C₂×C₄	—	2	4	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	4	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	8	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	—	8	4	no	—
473	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	4	yes	—
474	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	2	yes	—
475	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	2	yes	—
476	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	2	yes	—
477	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
478	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
479	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
480	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
481	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
482	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
483	C₈	—	4	2	no	—
484	C₈	—	4	2	no	—
485	C₂²	—	2	2	no	—
486	C₂²	—	2	4	no	—
487	C₂²	—	2	2	no	—
488	C₂²	—	4	2	no	—
489	C₂²	—	4	2	no	—
490	C₂²	—	4	4	no	—
491	C₂²	—	4	2	no	—
492	C₂²	C₂²×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
493	C₂²	C₁₁×#525	1	1	yes	characteristic
494	C₂²	C₁₁×#525	1	1	yes	characteristic
495	C₄	—	2	4	no	—
496	C₄	—	2	4	no	—
497	C₄	—	2	2	no	—
498	C₄	—	2	2	no	—
499	C₄	—	2	2	no	—
500	C₄	—	4	2	no	—
501	C₄	—	4	2	no	—
502	C₄	—	4	2	no	—
503	C₄	—	4	4	no	—
504	C₄	—	4	2	no	—
505	C₄	C₄×C₁₁×#41	1	1	yes	characteristic
506	C₄	C₄×C₁₁×#41	1	1	yes	characteristic
507	C₄	C₁₁×#532	1	1	yes	characteristic
508	C₄	C₁₁×#532	1	1	yes	characteristic
509	C₂	—	2	1	no	—
510	C₂	—	2	1	no	—
511	C₂	—	4	2	no	—
512	C₂	—	8	2	no	—
513	C₂	C₁₁×#2297	1	1	yes	characteristic
514	C₂	C₁₁×#2901	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
socle	C₂²×C₁₁	C₂²×C₂²⋊C₄
prime radical	C₁₁×#3455	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₁₁×#117 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₁×#2921	C₂	semidirect
3. C₄×C₁₁×#117	C₂	semidirect
4. C₁₁×#1995	C₂	semidirect
5. C₁₁×#1994	C₂	semidirect
6. C₁₁×#1963	C₂	semidirect
7. C₁₁×#1962	C₂	semidirect
8. C₁₁×#1897	C₂	semidirect
9. C₁₁×#1896	C₂	semidirect
10. C₁₁×#1759	C₂	semidirect
11. C₄×C₁₁×#104	C₂	semidirect
12. C₁₁×#542	C₄	semidirect
13. C₁₁×#541	C₄	semidirect
14. C₁₁×#540	C₄	semidirect
49. C₁₁×C₄⋊Q₈	C₂×C₄	semidirect
50. C₁₁×C₄⋊Q₈	C₂×C₄	semidirect
51. C₁₁×#127	C₂×C₄	semidirect
55. C₁₁×#125	C₂×C₄	semidirect
57. C₁₁×#124	C₂×C₄	semidirect
69. C₄×Q₈×C₁₁	C₂×C₄	semidirect
73. C₄×D₄×C₁₁	C₂×C₄	semidirect
108. #21419	C₁₁	direct (N × H)
180. #2921	C₂×C₁₁	semidirect
181. C₄×#117	C₂×C₁₁	semidirect
182. #1995	C₂×C₁₁	semidirect
183. #1994	C₂×C₁₁	semidirect
184. #1963	C₂×C₁₁	semidirect
185. #1962	C₂×C₁₁	semidirect
186. #1897	C₂×C₁₁	semidirect
187. #1896	C₂×C₁₁	semidirect
188. #1759	C₂×C₁₁	semidirect
189. C₄×#104	C₂×C₁₁	semidirect
239. #542	C₄×C₁₁	semidirect
240. #541	C₄×C₁₁	semidirect
241. #540	C₄×C₁₁	semidirect
300. C₄⋊Q₈	C₂×C₄×C₁₁	semidirect
301. C₄⋊Q₈	C₂×C₄×C₁₁	semidirect
302. #127	C₂×C₄×C₁₁	semidirect
306. #125	C₂×C₄×C₁₁	semidirect
308. #124	C₂×C₄×C₁₁	semidirect
320. C₄×Q₈	C₂×C₄×C₁₁	semidirect
324. C₄×D₄	C₂×C₄×C₁₁	semidirect
435. C₁₁	#21419	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₁×#3455	2
C₁₁×#2921	2
C₄×C₁₁×#117	2
C₁₁×#1995	2
C₁₁×#1994	2
C₁₁×#1963	2
C₁₁×#1962	2
C₁₁×#1897	2
C₁₁×#1896	2
C₁₁×#1759	2
C₄×C₁₁×#104	2
#21419	11

Subgroups — C11×#21419 #14598612

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#21419 #14598612