Subgroups — C₁₁×#61943 #14639136

Order 2816.

1650 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3556	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁×#3510	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#3400	C₂	1	4	yes	maximal, complemented
4	C₁₁×#3398	C₂	1	4	yes	maximal, complemented
5	C₁₁×#3377	C₂	1	4	yes	maximal, complemented
6	C₁₁×#3371	C₂	1	4	yes	maximal, complemented
7	C₁₁×#3223	C₂	1	2	yes	maximal, complemented
8	C₁₁×#3222	C₂	1	2	yes	maximal
9	C₁₁×#3215	C₂	1	2	yes	maximal, complemented
10	C₁₁×#3127	C₂	1	2	yes	maximal, complemented
11	C₁₁×#3123	C₂	1	2	yes	maximal, complemented
12	C₁₁×#3116	C₂	1	2	yes	maximal, complemented
13	C₁₁×#2987	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₁×#564	—	2	2	no	—
15	C₁₁×#559	C₂²	1	4	yes	—
16	C₁₁×#557	—	2	2	no	—
17	C₁₁×#557	C₂²	1	4	yes	complemented
18	C₁₁×#557	C₂²	1	4	yes	complemented
19	C₁₁×#556	C₂²	1	4	yes	—
20	C₁₁×#551	—	2	4	no	—
21	C₁₁×#542	—	2	2	no	—
22	C₁₁×#541	—	2	4	no	—
23	C₁₁×#541	C₂²	1	2	yes	—
24	C₁₁×#541	C₂²	1	2	yes	—
25	C₁₁×#536	C₂²	1	1	yes	characteristic
26	C₁₁×#535	C₂²	1	1	yes	characteristic
27	C₁₁×#533	C₂²	1	2	yes	—
28	C₁₁×#533	C₂²	1	1	yes	characteristic
29	C₁₁×#529	—	2	2	no	—
30	C₂×C₁₁×#124	C₂²	1	1	yes	characteristic
31	C₁₁×#519	C₂²	1	1	yes	characteristic
32	C₁₁×#518	C₂²	1	1	yes	characteristic
33	C₄×C₁₁×#41	C₂²	1	1	yes	characteristic
34	C₁₁×#497	C₂²	1	4	yes	—
35	C₁₁×#497	C₂²	1	2	yes	—
36	C₁₁×#497	C₂²	1	2	yes	complemented
37	C₁₁×#494	C₂²	1	2	yes	complemented
38	C₁₁×#492	C₂²	1	2	yes	—
39	C₁₁×#491	C₂²	1	2	yes	complemented
40	C₁₁×#490	C₂²	1	2	yes	—
41	C₁₁×#489	C₂²	1	4	yes	—
42	C₁₁×#488	C₂²	1	2	yes	—
43	C₁₁×#488	C₂²	1	2	yes	complemented
44	C₁₁×#485	C₂²	1	4	yes	—
45	C₁₁×#479	C₂²	1	4	yes	complemented
46	C₁₁×#478	C₂²	1	4	yes	—
47	C₁₁×#477	C₂²	1	2	yes	complemented
48	C₁₁×#476	C₂²	1	2	yes	complemented
49	C₁₁×#464	C₂²	1	4	yes	—
50	C₁₁×#464	C₂²	1	4	yes	—
51	C₁₁×#464	C₂²	1	4	yes	—
52	C₁₁×#464	C₂²	1	4	yes	complemented
53	C₁₁×#462	C₂²	1	4	yes	complemented
54	C₁₁×#462	C₂²	1	2	yes	complemented
55	C₁₁×#462	C₂²	1	4	yes	complemented
56	C₁₁×#461	C₂²	1	4	yes	—
57	C₁₁×#461	C₂²	1	2	yes	complemented
58	C₁₁×#460	C₂²	1	4	yes	—
59	C₁₁×#452	C₂²	1	4	yes	—
60	C₁₁×#451	C₂²	1	4	yes	—
61	C₁₁×#450	C₂²	1	4	yes	—
62	C₁₁×#446	C₂²	1	4	yes	complemented
63	C₁₁×#446	C₂²	1	4	yes	complemented
64	C₁₁×#441	C₂²	1	4	yes	complemented
65	C₁₁×#441	C₂²	1	4	yes	complemented
66	C₁₁×#440	C₂²	1	4	yes	—
67	C₁₁×#440	C₂²	1	4	yes	complemented
68	C₄×C₁₁×Q₁₆	C₂²	1	4	yes	complemented
69	C₄×C₁₁×SD₁₆	C₂²	1	4	yes	—
70	C₁₁×#433	C₂²	1	2	yes	—
71	C₁₁×#433	C₂²	1	2	yes	—
72	C₁₁×#432	C₂²	1	2	yes	—
73	C₂×C₁₁×#41	C₂³	1	1	yes	characteristic
74	C₂²×Q₈×C₁₁	C₂³	1	1	yes	characteristic
75	C₂²×D₄×C₁₁	C₂³	1	1	yes	characteristic
76	C₂×C₁₁×Q₁₆	C₂³	1	4	yes	—
77	C₂×C₁₁×Q₁₆	C₂³	1	4	yes	—
78	C₂×C₁₁×Q₁₆	C₂³	1	4	yes	—
79	C₂×C₁₁×SD₁₆	C₂³	1	4	yes	—
80	C₂×C₁₁×SD₁₆	C₂³	1	4	yes	—
81	C₂×C₁₁×SD₁₆	C₂³	1	4	yes	—
82	C₁₁×C₄⋊Q₈	—	2	4	no	—
83	C₁₁×C₄⋊Q₈	D₄	1	2	yes	—
84	C₁₁×C₄⋊Q₈	C₂³	1	2	yes	—
85	C₁₁×C₄⋊Q₈	C₂³	1	2	yes	—
86	C₁₁×C₄⋊Q₈	C₂³	1	2	yes	—
87	C₁₁×C₄⋊Q₈	C₂³	1	2	yes	—
88	C₁₁×C₄⋊Q₈	C₂³	1	2	yes	—
89	C₁₁×#127	C₂³	1	2	yes	—
90	C₁₁×#126	—	2	4	no	—
91	C₁₁×#126	—	2	4	no	—
92	C₁₁×#126	—	2	4	no	—
93	C₁₁×#126	—	2	4	no	—
94	C₁₁×#125	—	2	4	no	—
95	C₁₁×#125	—	2	4	no	—
96	C₁₁×#125	—	2	4	no	—
97	C₁₁×#125	—	2	4	no	—
98	C₁₁×#125	—	2	4	no	—
99	C₁₁×#125	—	2	4	no	—
100	C₁₁×#125	—	2	4	no	—
101	C₁₁×#125	—	2	2	no	—
102	C₁₁×#125	D₄	1	2	yes	—
103	C₁₁×#125	C₂³	1	2	yes	—
104	C₁₁×#125	C₂³	1	2	yes	—
105	C₁₁×#124	—	2	4	no	—
106	C₁₁×#124	—	2	1	no	—
107	C₁₁×#124	—	2	1	no	—
108	C₁₁×#124	C₂³	1	4	yes	—
109	C₁₁×#124	C₂³	1	2	yes	—
110	C₁₁×#124	C₂³	1	2	yes	—
111	C₁₁×#123	—	2	4	no	—
112	C₁₁×#123	—	2	4	no	—
113	C₁₁×#123	—	2	2	no	—
114	C₁₁×C₂²⋊Q₈	—	2	4	no	—
115	C₁₁×C₂²⋊Q₈	—	2	2	no	—
116	C₁₁×C₂²⋊Q₈	—	2	2	no	—
117	C₁₁×C₂²⋊Q₈	D₄	1	4	yes	—
118	C₁₁×C₂²⋊Q₈	C₂³	1	4	yes	—
119	C₁₁×#121	—	2	2	no	—
120	C₁₁×#120	—	2	2	no	—
121	C₄×Q₈×C₁₁	—	2	4	no	—
122	C₄×Q₈×C₁₁	—	2	2	no	—
123	C₄×Q₈×C₁₁	—	2	4	no	—
124	C₄×Q₈×C₁₁	—	2	2	no	—
125	C₄×Q₈×C₁₁	C₂³	1	2	yes	—
126	C₄×Q₈×C₁₁	C₂³	1	4	yes	—
127	C₄×Q₈×C₁₁	C₂³	1	4	yes	—
128	C₄×Q₈×C₁₁	C₂³	1	4	yes	—
129	C₄×Q₈×C₁₁	C₂³	1	4	yes	—
130	C₄×Q₈×C₁₁	C₂³	1	4	yes	—
131	C₄×D₄×C₁₁	—	2	2	no	—
132	C₄×D₄×C₁₁	—	2	2	no	—
133	C₄×D₄×C₁₁	—	2	4	no	—
134	C₄×D₄×C₁₁	C₂³	1	2	yes	—
135	C₄×D₄×C₁₁	C₂³	1	4	yes	—
136	C₁₁×#117	—	2	2	no	—
137	C₁₁×#117	—	2	4	no	—
138	C₁₁×#117	—	2	2	no	—
139	C₁₁×#117	—	2	1	no	—
140	C₁₁×#117	C₂³	1	1	yes	characteristic
141	C₁₁×#117	C₂³	1	1	yes	characteristic
142	C₁₁×#117	C₂³	1	1	yes	characteristic
143	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
144	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
145	C₂×C₄²×C₁₁	—	2	1	no	—
146	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
147	C₁₁×#107	C₂³	1	4	yes	—
148	C₁₁×#106	C₂³	1	4	yes	—
149	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
150	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
151	C₁₁×C₄⋊C₈	C₂³	1	4	yes	—
152	C₁₁×C₄⋊C₈	C₂³	1	4	yes	—
153	C₁₁×#103	C₂³	1	4	yes	—
154	C₁₁×#103	C₂³	1	4	yes	—
155	C₁₁×#103	C₂³	1	4	yes	—
156	C₁₁×#103	C₂³	1	4	yes	—
157	C₁₁×#103	C₂³	1	4	yes	—
158	C₁₁×#102	C₂³	1	4	yes	—
159	C₁₁×#102	C₂³	1	4	yes	—
160	C₁₁×#102	C₂³	1	4	yes	—
161	C₁₁×C₂²⋊C₈	C₂³	1	4	yes	—
162	C₁₁×#97	C₂³	1	4	yes	—
163	C₁₁×#97	C₂³	1	2	yes	—
164	C₁₁×#97	C₂³	1	2	yes	—
165	C₄×C₈×C₁₁	C₂³	1	2	yes	—
166	C₄×C₈×C₁₁	C₂³	1	2	yes	—
167	#61943	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
168	C₂⁴×C₁₁	—	2	1	no	—
169	C₁₁×#41	—	4	2	no	—
170	C₂×Q₈×C₁₁	—	2	2	no	—
171	C₂×Q₈×C₁₁	—	2	1	no	—
172	C₂×Q₈×C₁₁	—	4	2	no	—
173	C₂×Q₈×C₁₁	C₂×D₄	1	4	yes	—
174	C₂×Q₈×C₁₁	C₂⁴	1	2	yes	—
175	C₂×Q₈×C₁₁	C₂⁴	1	1	yes	characteristic
176	C₂×Q₈×C₁₁	C₂⁴	1	4	yes	—
177	C₂×D₄×C₁₁	—	2	1	no	—
178	C₂×D₄×C₁₁	—	2	1	no	—
179	C₂×D₄×C₁₁	—	2	4	no	—
180	C₂×D₄×C₁₁	—	4	2	no	—
181	C₂×D₄×C₁₁	C₂⁴	1	2	yes	—
182	C₂×D₄×C₁₁	C₂⁴	1	1	yes	characteristic
183	C₂²×C₄×C₁₁	—	2	1	no	—
184	C₂²×C₄×C₁₁	—	2	1	no	—
185	C₂²×C₄×C₁₁	—	2	2	no	—
186	C₂²×C₄×C₁₁	—	2	4	no	—
187	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
188	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
189	C₁₁×Q₁₆	—	4	4	no	—
190	C₁₁×Q₁₆	—	4	4	no	—
191	C₁₁×Q₁₆	—	4	4	no	—
192	C₁₁×SD₁₆	—	4	4	no	—
193	C₁₁×SD₁₆	—	4	4	no	—
194	C₁₁×SD₁₆	—	4	4	no	—
195	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
196	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
197	C₁₁×C₄⋊C₄	—	2	2	no	—
198	C₁₁×C₄⋊C₄	—	2	4	no	—
199	C₁₁×C₄⋊C₄	—	2	4	no	—
200	C₁₁×C₄⋊C₄	—	2	2	no	—
201	C₁₁×C₄⋊C₄	—	2	2	no	—
202	C₁₁×C₄⋊C₄	—	2	2	no	—
203	C₁₁×C₄⋊C₄	—	2	4	no	—
204	C₁₁×C₄⋊C₄	—	2	4	no	—
205	C₁₁×C₄⋊C₄	—	2	4	no	—
206	C₁₁×C₄⋊C₄	—	2	4	no	—
207	C₁₁×C₄⋊C₄	—	2	4	no	—
208	C₁₁×C₄⋊C₄	—	2	4	no	—
209	C₁₁×C₄⋊C₄	—	2	4	no	—
210	C₁₁×C₄⋊C₄	—	2	4	no	—
211	C₁₁×C₄⋊C₄	C₂×D₄	1	4	yes	—
212	C₁₁×C₄⋊C₄	C₂×D₄	1	2	yes	—
213	C₁₁×C₄⋊C₄	C₂×D₄	1	2	yes	—
214	C₁₁×C₄⋊C₄	C₂×D₄	1	4	yes	—
215	C₁₁×C₄⋊C₄	C₂×D₄	1	4	yes	—
216	C₁₁×C₄⋊C₄	C₂⁴	1	4	yes	—
217	C₁₁×C₄⋊C₄	C₂⁴	1	2	yes	—
218	C₁₁×C₂²⋊C₄	—	2	1	no	—
219	C₁₁×C₂²⋊C₄	—	2	4	no	—
220	C₁₁×C₂²⋊C₄	—	2	4	no	—
221	C₁₁×C₂²⋊C₄	—	2	4	no	—
222	C₁₁×C₂²⋊C₄	—	2	4	no	—
223	C₁₁×C₂²⋊C₄	—	2	2	no	—
224	C₁₁×C₂²⋊C₄	—	2	4	no	—
225	C₁₁×C₂²⋊C₄	—	2	4	no	—
226	C₁₁×C₂²⋊C₄	C₂×D₄	1	2	yes	—
227	C₁₁×C₂²⋊C₄	C₂×D₄	1	2	yes	—
228	C₄²×C₁₁	—	2	2	no	—
229	C₄²×C₁₁	—	2	1	no	—
230	C₄²×C₁₁	—	2	4	no	—
231	C₄²×C₁₁	—	2	4	no	—
232	C₄²×C₁₁	—	2	4	no	—
233	C₄²×C₁₁	—	2	4	no	—
234	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
235	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
236	C₄²×C₁₁	C₂⁴	1	2	yes	—
237	C₄²×C₁₁	C₂⁴	1	2	yes	—
238	C₄²×C₁₁	C₂⁴	1	2	yes	—
239	#3556	C₂×C₁₁	1	1	yes	characteristic, complemented
240	#3510	C₂×C₁₁	1	1	yes	characteristic
241	#3400	C₂×C₁₁	1	4	yes	complemented
242	#3398	C₂×C₁₁	1	4	yes	complemented
243	#3377	C₂×C₁₁	1	4	yes	complemented
244	#3371	C₂×C₁₁	1	4	yes	complemented
245	#3223	C₂×C₁₁	1	2	yes	complemented
246	#3222	C₂×C₁₁	1	2	yes	—
247	#3215	C₂×C₁₁	1	2	yes	complemented
248	#3127	C₂×C₁₁	1	2	yes	complemented
249	#3123	C₂×C₁₁	1	2	yes	complemented
250	#3116	C₂×C₁₁	1	2	yes	complemented
251	#2987	C₂×C₁₁	1	1	yes	characteristic, complemented
252	C₂³×C₁₁	—	2	2	no	—
253	C₂³×C₁₁	—	2	1	no	—
254	C₂³×C₁₁	—	4	2	no	—
255	C₂³×C₁₁	—	8	2	no	—
256	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
257	Q₈×C₁₁	—	2	4	no	—
258	Q₈×C₁₁	—	2	4	no	—
259	Q₈×C₁₁	—	2	4	no	—
260	Q₈×C₁₁	—	2	2	no	—
261	Q₈×C₁₁	—	4	4	no	—
262	Q₈×C₁₁	—	4	4	no	—
263	Q₈×C₁₁	—	4	2	no	—
264	D₄×C₁₁	—	2	4	no	—
265	D₄×C₁₁	—	2	2	no	—
266	D₄×C₁₁	—	4	2	no	—
267	D₄×C₁₁	—	4	2	no	—
268	D₄×C₁₁	—	8	4	no	—
269	C₂×C₄×C₁₁	—	2	2	no	—
270	C₂×C₄×C₁₁	—	2	2	no	—
271	C₂×C₄×C₁₁	—	2	4	no	—
272	C₂×C₄×C₁₁	—	2	4	no	—
273	C₂×C₄×C₁₁	—	2	2	no	—
274	C₂×C₄×C₁₁	—	2	1	no	—
275	C₂×C₄×C₁₁	—	4	2	no	—
276	C₂×C₄×C₁₁	—	4	2	no	—
277	C₂×C₄×C₁₁	—	4	2	no	—
278	C₂×C₄×C₁₁	—	8	2	no	—
279	C₂×C₄×C₁₁	—	8	4	no	—
280	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
281	C₂×C₄×C₁₁	C₂²×D₄	1	4	yes	—
282	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
283	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
284	C₂×C₄×C₁₁	C₂²×D₄	1	4	yes	—
285	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
286	C₈×C₁₁	—	2	4	no	—
287	C₈×C₁₁	—	2	4	no	—
288	#564	—	2	2	no	—
289	#559	C₂²×C₁₁	1	4	yes	—
290	#557	—	2	2	no	—
291	#557	C₂²×C₁₁	1	4	yes	complemented
292	#557	C₂²×C₁₁	1	4	yes	complemented
293	#556	C₂²×C₁₁	1	4	yes	—
294	#551	—	2	4	no	—
295	#542	—	2	2	no	—
296	#541	—	2	4	no	—
297	#541	C₂²×C₁₁	1	2	yes	—
298	#541	C₂²×C₁₁	1	2	yes	—
299	#536	C₂²×C₁₁	1	1	yes	characteristic
300	#535	C₂²×C₁₁	1	1	yes	characteristic
301	#533	C₂²×C₁₁	1	2	yes	—
302	#533	C₂²×C₁₁	1	1	yes	characteristic
303	#529	—	2	2	no	—
304	C₂×#124	C₂²×C₁₁	1	1	yes	characteristic
305	#519	C₂²×C₁₁	1	1	yes	characteristic
306	#518	C₂²×C₁₁	1	1	yes	characteristic
307	C₄×#41	C₂²×C₁₁	1	1	yes	characteristic
308	#497	C₂²×C₁₁	1	2	yes	—
309	#497	C₂²×C₁₁	1	4	yes	—
310	#497	C₂²×C₁₁	1	2	yes	complemented
311	#494	C₂²×C₁₁	1	2	yes	complemented
312	#492	C₂²×C₁₁	1	2	yes	—
313	#491	C₂²×C₁₁	1	2	yes	complemented
314	#490	C₂²×C₁₁	1	2	yes	—
315	#489	C₂²×C₁₁	1	4	yes	—
316	#488	C₂²×C₁₁	1	2	yes	—
317	#488	C₂²×C₁₁	1	2	yes	complemented
318	#485	C₂²×C₁₁	1	4	yes	—
319	#479	C₂²×C₁₁	1	4	yes	complemented
320	#478	C₂²×C₁₁	1	4	yes	—
321	#477	C₂²×C₁₁	1	2	yes	complemented
322	#476	C₂²×C₁₁	1	2	yes	complemented
323	#464	C₂²×C₁₁	1	4	yes	—
324	#464	C₂²×C₁₁	1	4	yes	—
325	#464	C₂²×C₁₁	1	4	yes	—
326	#464	C₂²×C₁₁	1	4	yes	complemented
327	#462	C₂²×C₁₁	1	2	yes	complemented
328	#462	C₂²×C₁₁	1	4	yes	complemented
329	#462	C₂²×C₁₁	1	4	yes	complemented
330	#461	C₂²×C₁₁	1	4	yes	—
331	#461	C₂²×C₁₁	1	2	yes	complemented
332	#460	C₂²×C₁₁	1	4	yes	—
333	#452	C₂²×C₁₁	1	4	yes	—
334	#451	C₂²×C₁₁	1	4	yes	—
335	#450	C₂²×C₁₁	1	4	yes	—
336	#446	C₂²×C₁₁	1	4	yes	complemented
337	#446	C₂²×C₁₁	1	4	yes	complemented
338	#441	C₂²×C₁₁	1	4	yes	complemented
339	#441	C₂²×C₁₁	1	4	yes	complemented
340	#440	C₂²×C₁₁	1	4	yes	—
341	#440	C₂²×C₁₁	1	4	yes	complemented
342	C₄×Q₁₆	C₂²×C₁₁	1	4	yes	complemented
343	C₄×SD₁₆	C₂²×C₁₁	1	4	yes	—
344	#433	C₂²×C₁₁	1	2	yes	—
345	#433	C₂²×C₁₁	1	2	yes	—
346	#432	C₂²×C₁₁	1	2	yes	—
347	C₂²×C₁₁	—	2	2	no	—
348	C₂²×C₁₁	—	2	1	no	—
349	C₂²×C₁₁	—	4	2	no	—
350	C₂²×C₁₁	—	4	4	no	—
351	C₂²×C₁₁	—	4	1	no	—
352	C₂²×C₁₁	—	4	2	no	—
353	C₂²×C₁₁	—	16	2	no	—
354	C₂²×C₁₁	C₂³×D₄	1	1	yes	characteristic
355	C₄×C₁₁	—	2	2	no	—
356	C₄×C₁₁	—	2	2	no	—
357	C₄×C₁₁	—	2	4	no	—
358	C₄×C₁₁	—	2	4	no	—
359	C₄×C₁₁	—	2	1	no	—
360	C₄×C₁₁	—	4	2	no	—
361	C₄×C₁₁	—	4	4	no	—
362	C₄×C₁₁	—	4	1	no	—
363	C₄×C₁₁	—	4	2	no	—
364	C₄×C₁₁	—	4	4	no	—
365	C₄×C₁₁	#585	1	2	yes	—
366	C₂×#41	C₂³×C₁₁	1	1	yes	characteristic
367	C₂²×Q₈	C₂³×C₁₁	1	1	yes	characteristic
368	C₂²×D₄	C₂³×C₁₁	1	1	yes	characteristic
369	C₂×Q₁₆	C₂³×C₁₁	1	4	yes	—
370	C₂×Q₁₆	C₂³×C₁₁	1	4	yes	—
371	C₂×Q₁₆	C₂³×C₁₁	1	4	yes	—
372	C₂×SD₁₆	C₂³×C₁₁	1	4	yes	—
373	C₂×SD₁₆	C₂³×C₁₁	1	4	yes	—
374	C₂×SD₁₆	C₂³×C₁₁	1	4	yes	—
375	C₄⋊Q₈	—	2	4	no	—
376	C₄⋊Q₈	D₄×C₁₁	1	2	yes	—
377	C₄⋊Q₈	C₂³×C₁₁	1	2	yes	—
378	C₄⋊Q₈	C₂³×C₁₁	1	2	yes	—
379	C₄⋊Q₈	C₂³×C₁₁	1	2	yes	—
380	C₄⋊Q₈	C₂³×C₁₁	1	2	yes	—
381	C₄⋊Q₈	C₂³×C₁₁	1	2	yes	—
382	#127	C₂³×C₁₁	1	2	yes	—
383	#126	—	2	4	no	—
384	#126	—	2	4	no	—
385	#126	—	2	4	no	—
386	#126	—	2	4	no	—
387	#125	—	2	4	no	—
388	#125	—	2	4	no	—
389	#125	—	2	4	no	—
390	#125	—	2	4	no	—
391	#125	—	2	4	no	—
392	#125	—	2	4	no	—
393	#125	—	2	4	no	—
394	#125	—	2	2	no	—
395	#125	D₄×C₁₁	1	2	yes	—
396	#125	C₂³×C₁₁	1	2	yes	—
397	#125	C₂³×C₁₁	1	2	yes	—
398	#124	—	2	4	no	—
399	#124	—	2	1	no	—
400	#124	—	2	1	no	—
401	#124	C₂³×C₁₁	1	4	yes	—
402	#124	C₂³×C₁₁	1	2	yes	—
403	#124	C₂³×C₁₁	1	2	yes	—
404	#123	—	2	4	no	—
405	#123	—	2	4	no	—
406	#123	—	2	2	no	—
407	C₂²⋊Q₈	—	2	4	no	—
408	C₂²⋊Q₈	—	2	2	no	—
409	C₂²⋊Q₈	—	2	2	no	—
410	C₂²⋊Q₈	D₄×C₁₁	1	4	yes	—
411	C₂²⋊Q₈	C₂³×C₁₁	1	4	yes	—
412	#121	—	2	2	no	—
413	#120	—	2	2	no	—
414	C₄×Q₈	—	2	4	no	—
415	C₄×Q₈	—	2	2	no	—
416	C₄×Q₈	—	2	4	no	—
417	C₄×Q₈	—	2	2	no	—
418	C₄×Q₈	C₂³×C₁₁	1	2	yes	—
419	C₄×Q₈	C₂³×C₁₁	1	4	yes	—
420	C₄×Q₈	C₂³×C₁₁	1	4	yes	—
421	C₄×Q₈	C₂³×C₁₁	1	4	yes	—
422	C₄×Q₈	C₂³×C₁₁	1	4	yes	—
423	C₄×Q₈	C₂³×C₁₁	1	4	yes	—
424	C₄×D₄	—	2	2	no	—
425	C₄×D₄	—	2	2	no	—
426	C₄×D₄	—	2	4	no	—
427	C₄×D₄	C₂³×C₁₁	1	2	yes	—
428	C₄×D₄	C₂³×C₁₁	1	4	yes	—
429	#117	—	2	2	no	—
430	#117	—	2	4	no	—
431	#117	—	2	2	no	—
432	#117	—	2	1	no	—
433	#117	C₂³×C₁₁	1	1	yes	characteristic
434	#117	C₂³×C₁₁	1	1	yes	characteristic
435	#117	C₂³×C₁₁	1	1	yes	characteristic
436	C₂×C₂²⋊C₄	—	2	2	no	—
437	C₂×C₂²⋊C₄	—	2	2	no	—
438	C₂×C₄²	—	2	1	no	—
439	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
440	#107	C₂³×C₁₁	1	4	yes	—
441	#106	C₂³×C₁₁	1	4	yes	—
442	C₄⋊C₈	C₂³×C₁₁	1	2	yes	—
443	C₄⋊C₈	C₂³×C₁₁	1	2	yes	—
444	C₄⋊C₈	C₂³×C₁₁	1	4	yes	—
445	C₄⋊C₈	C₂³×C₁₁	1	4	yes	—
446	#103	C₂³×C₁₁	1	4	yes	—
447	#103	C₂³×C₁₁	1	4	yes	—
448	#103	C₂³×C₁₁	1	4	yes	—
449	#103	C₂³×C₁₁	1	4	yes	—
450	#103	C₂³×C₁₁	1	4	yes	—
451	#102	C₂³×C₁₁	1	4	yes	—
452	#102	C₂³×C₁₁	1	4	yes	—
453	#102	C₂³×C₁₁	1	4	yes	—
454	C₂²⋊C₈	C₂³×C₁₁	1	4	yes	—
455	#97	C₂³×C₁₁	1	4	yes	—
456	#97	C₂³×C₁₁	1	2	yes	—
457	#97	C₂³×C₁₁	1	2	yes	—
458	C₄×C₈	C₂³×C₁₁	1	2	yes	—
459	C₄×C₈	C₂³×C₁₁	1	2	yes	—
460	C₂×C₁₁	—	4	1	no	—
461	C₂×C₁₁	—	8	1	no	—
462	C₂×C₁₁	—	8	2	no	—
463	C₂×C₁₁	#3487	1	1	yes	characteristic
464	C₂×C₁₁	#3586	1	2	yes	—
465	C₂⁴	—	2	1	no	—
466	#41	—	4	2	no	—
467	C₂×Q₈	—	2	2	no	—
468	C₂×Q₈	—	2	1	no	—
469	C₂×Q₈	—	4	2	no	—
470	C₂×Q₈	C₂×D₄×C₁₁	1	4	yes	—
471	C₂×Q₈	C₂⁴×C₁₁	1	2	yes	—
472	C₂×Q₈	C₂⁴×C₁₁	1	1	yes	characteristic
473	C₂×Q₈	C₂⁴×C₁₁	1	4	yes	—
474	C₂×D₄	—	2	1	no	—
475	C₂×D₄	—	2	1	no	—
476	C₂×D₄	—	2	4	no	—
477	C₂×D₄	—	4	2	no	—
478	C₂×D₄	C₂⁴×C₁₁	1	2	yes	—
479	C₂×D₄	C₂⁴×C₁₁	1	1	yes	characteristic
480	C₂²×C₄	—	2	1	no	—
481	C₂²×C₄	—	2	1	no	—
482	C₂²×C₄	—	2	2	no	—
483	C₂²×C₄	—	2	4	no	—
484	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
485	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
486	Q₁₆	—	4	4	no	—
487	Q₁₆	—	4	4	no	—
488	Q₁₆	—	4	4	no	—
489	SD₁₆	—	4	4	no	—
490	SD₁₆	—	4	4	no	—
491	SD₁₆	—	4	4	no	—
492	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
493	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
494	C₄⋊C₄	—	2	2	no	—
495	C₄⋊C₄	—	2	4	no	—
496	C₄⋊C₄	—	2	4	no	—
497	C₄⋊C₄	—	2	2	no	—
498	C₄⋊C₄	—	2	2	no	—
499	C₄⋊C₄	—	2	2	no	—
500	C₄⋊C₄	—	2	4	no	—
501	C₄⋊C₄	—	2	4	no	—
502	C₄⋊C₄	—	2	4	no	—
503	C₄⋊C₄	—	2	4	no	—
504	C₄⋊C₄	—	2	4	no	—
505	C₄⋊C₄	—	2	4	no	—
506	C₄⋊C₄	—	2	4	no	—
507	C₄⋊C₄	—	2	4	no	—
508	C₄⋊C₄	C₂×D₄×C₁₁	1	4	yes	—
509	C₄⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
510	C₄⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
511	C₄⋊C₄	C₂×D₄×C₁₁	1	4	yes	—
512	C₄⋊C₄	C₂×D₄×C₁₁	1	4	yes	—
513	C₄⋊C₄	C₂⁴×C₁₁	1	4	yes	—
514	C₄⋊C₄	C₂⁴×C₁₁	1	2	yes	—
515	C₂²⋊C₄	—	2	1	no	—
516	C₂²⋊C₄	—	2	4	no	—
517	C₂²⋊C₄	—	2	4	no	—
518	C₂²⋊C₄	—	2	4	no	—
519	C₂²⋊C₄	—	2	4	no	—
520	C₂²⋊C₄	—	2	2	no	—
521	C₂²⋊C₄	—	2	4	no	—
522	C₂²⋊C₄	—	2	4	no	—
523	C₂²⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
524	C₂²⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
525	C₄²	—	2	2	no	—
526	C₄²	—	2	1	no	—
527	C₄²	—	2	4	no	—
528	C₄²	—	2	4	no	—
529	C₄²	—	2	4	no	—
530	C₄²	—	2	4	no	—
531	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
532	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
533	C₄²	C₂⁴×C₁₁	1	2	yes	—
534	C₄²	C₂⁴×C₁₁	1	2	yes	—
535	C₄²	C₂⁴×C₁₁	1	2	yes	—
536	C₁₁	#61943	1	1	yes	characteristic, direct product factor, Sylow
537	C₂³	—	2	2	no	—
538	C₂³	—	2	1	no	—
539	C₂³	—	4	2	no	—
540	C₂³	—	8	2	no	—
541	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
542	Q₈	—	2	4	no	—
543	Q₈	—	2	4	no	—
544	Q₈	—	2	4	no	—
545	Q₈	—	2	2	no	—
546	Q₈	—	4	4	no	—
547	Q₈	—	4	4	no	—
548	Q₈	—	4	2	no	—
549	D₄	—	2	4	no	—
550	D₄	—	2	2	no	—
551	D₄	—	4	2	no	—
552	D₄	—	4	2	no	—
553	D₄	—	8	4	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	2	4	no	—
557	C₂×C₄	—	2	4	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	4	2	no	—
561	C₂×C₄	—	4	2	no	—
562	C₂×C₄	—	4	2	no	—
563	C₂×C₄	—	8	2	no	—
564	C₂×C₄	—	8	4	no	—
565	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
566	C₂×C₄	C₂²×D₄×C₁₁	1	4	yes	—
567	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
568	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
569	C₂×C₄	C₂²×D₄×C₁₁	1	4	yes	—
570	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
571	C₈	—	2	4	no	—
572	C₈	—	2	4	no	—
573	C₂²	—	2	1	no	—
574	C₂²	—	2	2	no	—
575	C₂²	—	4	1	no	—
576	C₂²	—	4	2	no	—
577	C₂²	—	4	2	no	—
578	C₂²	—	4	4	no	—
579	C₂²	—	16	2	no	—
580	C₂²	C₂³×D₄×C₁₁	1	1	yes	characteristic
581	C₄	—	2	1	no	—
582	C₄	—	2	2	no	—
583	C₄	—	2	2	no	—
584	C₄	—	2	4	no	—
585	C₄	—	2	4	no	—
586	C₄	—	4	1	no	—
587	C₄	—	4	2	no	—
588	C₄	—	4	4	no	—
589	C₄	—	4	2	no	—
590	C₄	—	4	4	no	—
591	C₄	C₁₁×#585	1	2	yes	—
592	C₂	—	4	1	no	—
593	C₂	—	8	2	no	—
594	C₂	—	8	1	no	—
595	C₂	C₁₁×#3487	1	1	yes	characteristic
596	C₂	C₁₁×#3586	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₁
prime radical	C₁₁×#535	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₁₁×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₁×#3556	C₂	semidirect
3. C₁₁×#3400	C₂	semidirect
4. C₁₁×#3398	C₂	semidirect
5. C₁₁×#3377	C₂	semidirect
6. C₁₁×#3371	C₂	semidirect
7. C₁₁×#3223	C₂	semidirect
9. C₁₁×#3215	C₂	semidirect
10. C₁₁×#3127	C₂	semidirect
11. C₁₁×#3123	C₂	semidirect
12. C₁₁×#3116	C₂	semidirect
13. C₁₁×#2987	C₂	semidirect
17. C₁₁×#557	C₂²	semidirect
18. C₁₁×#557	C₂²	semidirect
36. C₁₁×#497	C₂²	semidirect
37. C₁₁×#494	C₂²	semidirect
39. C₁₁×#491	C₂²	semidirect
43. C₁₁×#488	C₂²	semidirect
45. C₁₁×#479	C₂²	semidirect
47. C₁₁×#477	C₂²	semidirect
48. C₁₁×#476	C₂²	semidirect
52. C₁₁×#464	C₂²	semidirect
53. C₁₁×#462	C₂²	semidirect
54. C₁₁×#462	C₂²	semidirect
55. C₁₁×#462	C₂²	semidirect
57. C₁₁×#461	C₂²	semidirect
62. C₁₁×#446	C₂²	semidirect
63. C₁₁×#446	C₂²	semidirect
64. C₁₁×#441	C₂²	semidirect
65. C₁₁×#441	C₂²	semidirect
67. C₁₁×#440	C₂²	semidirect
68. C₄×C₁₁×Q₁₆	C₂²	semidirect
167. #61943	C₁₁	direct (N × H)
239. #3556	C₂×C₁₁	semidirect
241. #3400	C₂×C₁₁	semidirect
242. #3398	C₂×C₁₁	semidirect
243. #3377	C₂×C₁₁	semidirect
244. #3371	C₂×C₁₁	semidirect
245. #3223	C₂×C₁₁	semidirect
247. #3215	C₂×C₁₁	semidirect
248. #3127	C₂×C₁₁	semidirect
249. #3123	C₂×C₁₁	semidirect
250. #3116	C₂×C₁₁	semidirect
251. #2987	C₂×C₁₁	semidirect
291. #557	C₂²×C₁₁	semidirect
292. #557	C₂²×C₁₁	semidirect
310. #497	C₂²×C₁₁	semidirect
311. #494	C₂²×C₁₁	semidirect
313. #491	C₂²×C₁₁	semidirect
317. #488	C₂²×C₁₁	semidirect
319. #479	C₂²×C₁₁	semidirect
321. #477	C₂²×C₁₁	semidirect
322. #476	C₂²×C₁₁	semidirect
326. #464	C₂²×C₁₁	semidirect
327. #462	C₂²×C₁₁	semidirect
328. #462	C₂²×C₁₁	semidirect
329. #462	C₂²×C₁₁	semidirect
331. #461	C₂²×C₁₁	semidirect
336. #446	C₂²×C₁₁	semidirect
337. #446	C₂²×C₁₁	semidirect
338. #441	C₂²×C₁₁	semidirect
339. #441	C₂²×C₁₁	semidirect
341. #440	C₂²×C₁₁	semidirect
342. C₄×Q₁₆	C₂²×C₁₁	semidirect
536. C₁₁	#61943	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×#3556	2
C₁₁×#3510	2
C₁₁×#3400	2
C₁₁×#3398	2
C₁₁×#3377	2
C₁₁×#3371	2
C₁₁×#3223	2
C₁₁×#3222	2
C₁₁×#3215	2
C₁₁×#3127	2
C₁₁×#3123	2
C₁₁×#3116	2
C₁₁×#2987	2
#61943	11

Subgroups — C11×#61943 #14639136

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#61943 #14639136