Subgroups — C₁₁×#60705 #14637898

Order 2816.

1846 conjugacy classes of subgroups.

The subgroup lattice has 524 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	C₂×C₁₁×#541	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#3178	C₂	1	8	yes	maximal, complemented
4	C₁₁×#3177	C₂	1	4	yes	maximal, complemented
5	C₁₁×#3174	C₂	1	4	yes	maximal, complemented
6	C₁₁×#3166	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#3152	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₁×#3142	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁×#3139	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₁×#3056	C₂	1	4	yes	maximal, complemented
11	C₄×C₁₁×#137	C₂	1	4	yes	maximal, complemented
12	C₁₁×#2873	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₁₁×#137	C₂²	1	4	yes	—
14	C₂²×C₁₁×M₁₆	C₂²	1	2	yes	—
15	C₁₁×#542	C₂²	1	4	yes	—
16	C₁₁×#541	—	2	4	no	—
17	C₁₁×#541	C₂²	1	4	yes	—
18	C₁₁×#541	C₂²	1	2	yes	—
19	C₁₁×#541	C₂²	1	4	yes	—
20	C₁₁×#540	C₂²	1	2	yes	—
21	C₁₁×#539	—	2	2	no	—
22	C₁₁×#538	—	2	2	no	—
23	C₁₁×#533	C₂²	1	1	yes	characteristic
24	C₁₁×#532	C₂²	1	1	yes	characteristic
25	C₂×C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₁₁×#529	—	2	4	no	—
27	C₂×C₁₁×#126	—	2	2	no	—
28	C₂×C₁₁×#125	—	2	2	no	—
29	C₂×C₁₁×#125	C₂²	1	1	yes	characteristic
30	C₁₁×#525	C₂²	1	2	yes	—
31	C₂×C₁₁×C₂²⋊Q₈	C₂²	1	2	yes	—
32	C₄×C₁₁×#41	C₂²	1	2	yes	—
33	C₂×C₄×Q₈×C₁₁	C₂²	1	2	yes	—
34	C₂×C₁₁×#117	C₂²	1	1	yes	characteristic
35	C₁₁×#501	C₂²	1	4	yes	complemented
36	C₁₁×#499	C₂²	1	4	yes	complemented
37	C₁₁×#497	C₂²	1	4	yes	complemented
38	C₁₁×#494	C₂²	1	2	yes	complemented
39	C₁₁×#492	C₂²	1	2	yes	complemented
40	C₁₁×#491	C₂²	1	4	yes	complemented
41	C₁₁×#491	C₂²	1	2	yes	complemented
42	C₁₁×#490	C₂²	1	2	yes	complemented
43	C₁₁×#488	C₂²	1	4	yes	complemented
44	C₁₁×#487	C₂²	1	4	yes	complemented
45	C₁₁×#470	C₂²	1	8	yes	—
46	C₁₁×#468	C₂²	1	8	yes	—
47	C₁₁×#467	C₂²	1	8	yes	—
48	C₁₁×#465	C₂²	1	8	yes	—
49	C₁₁×#441	C₂²	1	8	yes	complemented
50	C₁₁×#440	C₂²	1	8	yes	complemented
51	C₄×C₁₁×Q₁₆	C₂²	1	8	yes	complemented
52	C₄×C₁₁×SD₁₆	C₂²	1	8	yes	complemented
53	C₁₁×#428	C₂²	1	4	yes	—
54	C₁₁×#419	C₂²	1	4	yes	—
55	C₁₁×#417	C₂²	1	4	yes	—
56	C₁₁×#405	C₂²	1	4	yes	—
57	C₁₁×#405	C₂²	1	4	yes	—
58	C₄×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
59	C₄×C₁₁×M₁₆	C₂²	1	2	yes	—
60	C₄×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
61	C₂×C₁₁×#41	C₂³	1	2	yes	—
62	C₂²×Q₈×C₁₁	C₂³	1	2	yes	—
63	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
64	C₁₁×#137	—	2	16	no	—
65	C₂×C₁₁×Q₁₆	C₂³	1	8	yes	—
66	C₂×C₁₁×SD₁₆	C₂³	1	8	yes	—
67	C₂×C₁₁×M₁₆	—	2	8	no	—
68	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
69	C₂×C₁₁×M₁₆	C₂³	1	4	yes	—
70	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
71	C₂²×C₈×C₁₁	C₂³	1	4	yes	—
72	C₁₁×C₄⋊Q₈	—	2	2	no	—
73	C₁₁×C₄⋊Q₈	C₂³	1	2	yes	—
74	C₁₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
75	C₁₁×C₄⋊Q₈	C₂³	1	2	yes	—
76	C₁₁×C₄⋊Q₈	C₂³	1	2	yes	—
77	C₁₁×#127	C₂³	1	1	yes	characteristic
78	C₁₁×#126	—	2	4	no	—
79	C₁₁×#126	—	2	8	no	—
80	C₁₁×#126	—	2	8	no	—
81	C₁₁×#126	—	2	4	no	—
82	C₁₁×#125	—	2	8	no	—
83	C₁₁×#125	—	2	8	no	—
84	C₁₁×#125	—	2	4	no	—
85	C₁₁×#125	—	2	2	no	—
86	C₁₁×#125	C₂³	1	2	yes	—
87	C₁₁×#125	C₂³	1	2	yes	—
88	C₁₁×#125	C₂³	1	2	yes	—
89	C₁₁×#124	—	2	4	no	—
90	C₁₁×#124	C₂³	1	2	yes	—
91	C₁₁×#123	—	2	2	no	—
92	C₁₁×#123	—	2	4	no	—
93	C₁₁×#123	—	2	4	no	—
94	C₁₁×C₂²⋊Q₈	—	2	4	no	—
95	C₁₁×C₂²⋊Q₈	—	2	2	no	—
96	C₁₁×C₂²⋊Q₈	—	2	4	no	—
97	C₁₁×C₂²⋊Q₈	C₂³	1	8	yes	—
98	C₁₁×C₂²⋊Q₈	C₂³	1	4	yes	—
99	C₁₁×#121	—	2	2	no	—
100	C₁₁×#121	—	2	4	no	—
101	C₁₁×#121	C₂³	1	4	yes	—
102	C₁₁×#120	—	2	2	no	—
103	C₄×Q₈×C₁₁	—	2	4	no	—
104	C₄×Q₈×C₁₁	—	2	2	no	—
105	C₄×Q₈×C₁₁	C₂³	1	8	yes	—
106	C₄×Q₈×C₁₁	C₂³	1	4	yes	—
107	C₄×D₄×C₁₁	—	2	4	no	—
108	C₄×D₄×C₁₁	—	2	4	no	—
109	C₄×D₄×C₁₁	—	2	2	no	—
110	C₄×D₄×C₁₁	C₂³	1	4	yes	—
111	C₁₁×#117	—	2	2	no	—
112	C₁₁×#117	D₄	1	4	yes	—
113	C₁₁×#117	C₂³	1	2	yes	—
114	C₁₁×#117	C₂³	1	2	yes	—
115	C₁₁×#117	C₂³	1	2	yes	—
116	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
117	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
118	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
119	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
120	C₂×C₁₁×C₄⋊C₄	D₄	1	2	yes	—
121	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
122	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
123	C₂×C₁₁×C₂²⋊C₄	D₄	1	2	yes	—
124	C₂×C₄²×C₁₁	—	2	2	no	—
125	C₂×C₄²×C₁₁	—	2	2	no	—
126	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
127	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
128	C₁₁×#107	C₂³	1	8	yes	—
129	C₁₁×#106	C₂³	1	8	yes	—
130	C₁₁×#103	C₂³	1	8	yes	—
131	C₁₁×#103	C₂³	1	8	yes	—
132	C₁₁×#103	C₂³	1	8	yes	—
133	C₁₁×#102	C₂³	1	8	yes	—
134	C₁₁×#97	C₂³	1	2	yes	—
135	C₁₁×#97	C₂³	1	2	yes	—
136	C₁₁×#97	C₂³	1	4	yes	—
137	C₄×C₈×C₁₁	C₂³	1	2	yes	—
138	C₄×C₈×C₁₁	C₂³	1	4	yes	—
139	C₄×C₈×C₁₁	C₂³	1	2	yes	—
140	#60705	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
141	C₂⁴×C₁₁	C₂×D₄	1	1	yes	characteristic
142	C₁₁×#41	—	2	8	no	—
143	C₂×Q₈×C₁₁	—	2	2	no	—
144	C₂×Q₈×C₁₁	—	2	2	no	—
145	C₂×Q₈×C₁₁	—	2	8	no	—
146	C₂×Q₈×C₁₁	C₂⁴	1	2	yes	—
147	C₂×Q₈×C₁₁	C₂⁴	1	4	yes	—
148	C₂×D₄×C₁₁	—	2	2	no	—
149	C₂×D₄×C₁₁	—	2	4	no	—
150	C₂×D₄×C₁₁	—	2	2	no	—
151	C₂×D₄×C₁₁	C₂⁴	1	2	yes	—
152	C₂²×C₄×C₁₁	—	2	4	no	—
153	C₂²×C₄×C₁₁	—	2	2	no	—
154	C₂²×C₄×C₁₁	—	2	2	no	—
155	C₂²×C₄×C₁₁	—	2	2	no	—
156	C₂²×C₄×C₁₁	—	2	4	no	—
157	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
159	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
160	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
161	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
162	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
163	C₁₁×Q₁₆	—	2	16	no	—
164	C₁₁×SD₁₆	—	2	16	no	—
165	C₁₁×M₁₆	—	2	8	no	—
166	C₁₁×M₁₆	—	2	4	no	—
167	C₁₁×M₁₆	#41	1	8	yes	—
168	C₂×C₈×C₁₁	—	2	8	no	—
169	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
170	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
171	C₁₁×C₄⋊C₄	—	2	8	no	—
172	C₁₁×C₄⋊C₄	—	2	8	no	—
173	C₁₁×C₄⋊C₄	—	2	4	no	—
174	C₁₁×C₄⋊C₄	—	2	4	no	—
175	C₁₁×C₄⋊C₄	—	2	4	no	—
176	C₁₁×C₄⋊C₄	—	2	4	no	—
177	C₁₁×C₄⋊C₄	—	2	2	no	—
178	C₁₁×C₄⋊C₄	—	2	4	no	—
179	C₁₁×C₄⋊C₄	—	2	2	no	—
180	C₁₁×C₄⋊C₄	—	2	4	no	—
181	C₁₁×C₄⋊C₄	—	2	4	no	—
182	C₁₁×C₄⋊C₄	—	2	2	no	—
183	C₁₁×C₄⋊C₄	C₂×D₄	1	4	yes	—
184	C₁₁×C₄⋊C₄	C₂×D₄	1	4	yes	—
185	C₁₁×C₄⋊C₄	C₂⁴	1	4	yes	—
186	C₁₁×C₄⋊C₄	C₂⁴	1	4	yes	—
187	C₁₁×C₂²⋊C₄	—	2	8	no	—
188	C₁₁×C₂²⋊C₄	—	2	2	no	—
189	C₁₁×C₂²⋊C₄	—	2	4	no	—
190	C₁₁×C₂²⋊C₄	—	2	4	no	—
191	C₁₁×C₂²⋊C₄	—	2	4	no	—
192	C₁₁×C₂²⋊C₄	—	2	4	no	—
193	C₁₁×C₂²⋊C₄	C₂×D₄	1	4	yes	—
194	C₁₁×C₂²⋊C₄	C₂×D₄	1	4	yes	—
195	C₄²×C₁₁	—	2	2	no	—
196	C₄²×C₁₁	—	2	4	no	—
197	C₄²×C₁₁	—	2	8	no	—
198	C₄²×C₁₁	C₂×D₄	1	2	yes	—
199	C₄²×C₁₁	C₂×D₄	1	2	yes	—
200	C₄²×C₁₁	C₂⁴	1	2	yes	—
201	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
202	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
203	#3455	C₂×C₁₁	1	1	yes	characteristic
204	C₂×#541	C₂×C₁₁	1	1	yes	characteristic, complemented
205	#3178	C₂×C₁₁	1	8	yes	complemented
206	#3177	C₂×C₁₁	1	4	yes	complemented
207	#3174	C₂×C₁₁	1	4	yes	complemented
208	#3166	C₂×C₁₁	1	1	yes	characteristic, complemented
209	#3152	C₂×C₁₁	1	1	yes	characteristic, complemented
210	#3142	C₂×C₁₁	1	1	yes	characteristic, complemented
211	#3139	C₂×C₁₁	1	1	yes	characteristic, complemented
212	#3056	C₂×C₁₁	1	4	yes	complemented
213	C₄×#137	C₂×C₁₁	1	4	yes	complemented
214	#2873	C₂×C₁₁	1	1	yes	characteristic, complemented
215	C₂³×C₁₁	—	2	2	no	—
216	C₂³×C₁₁	—	2	2	no	—
217	C₂³×C₁₁	—	4	2	no	—
218	C₂³×C₁₁	C₂²×D₄	1	2	yes	—
219	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
220	Q₈×C₁₁	—	2	8	no	—
221	Q₈×C₁₁	—	2	4	no	—
222	Q₈×C₁₁	—	4	4	no	—
223	Q₈×C₁₁	—	8	2	no	—
224	D₄×C₁₁	—	2	4	no	—
225	D₄×C₁₁	—	4	4	no	—
226	D₄×C₁₁	—	8	2	no	—
227	D₄×C₁₁	—	8	4	no	—
228	C₂×C₄×C₁₁	—	2	2	no	—
229	C₂×C₄×C₁₁	—	2	4	no	—
230	C₂×C₄×C₁₁	—	2	2	no	—
231	C₂×C₄×C₁₁	—	2	2	no	—
232	C₂×C₄×C₁₁	—	2	2	no	—
233	C₂×C₄×C₁₁	—	2	4	no	—
234	C₂×C₄×C₁₁	—	2	4	no	—
235	C₂×C₄×C₁₁	—	2	4	no	—
236	C₂×C₄×C₁₁	—	4	2	no	—
237	C₂×C₄×C₁₁	—	4	2	no	—
238	C₂×C₄×C₁₁	—	4	4	no	—
239	C₂×C₄×C₁₁	—	4	4	no	—
240	C₂×C₄×C₁₁	—	4	4	no	—
241	C₂×C₄×C₁₁	—	8	4	no	—
242	C₂×C₄×C₁₁	C₂²×D₄	1	4	yes	—
243	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
244	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
245	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
246	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
247	C₂×C₄×C₁₁	C₂×#41	1	4	yes	—
248	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
249	C₈×C₁₁	—	2	4	no	—
250	C₈×C₁₁	C₂×#41	1	8	yes	—
251	C₂×#137	C₂²×C₁₁	1	4	yes	—
252	C₂²×M₁₆	C₂²×C₁₁	1	2	yes	—
253	#542	C₂²×C₁₁	1	4	yes	—
254	#541	—	2	4	no	—
255	#541	C₂²×C₁₁	1	4	yes	—
256	#541	C₂²×C₁₁	1	2	yes	—
257	#541	C₂²×C₁₁	1	4	yes	—
258	#540	C₂²×C₁₁	1	2	yes	—
259	#539	—	2	2	no	—
260	#538	—	2	2	no	—
261	#533	C₂²×C₁₁	1	1	yes	characteristic
262	#532	C₂²×C₁₁	1	1	yes	characteristic
263	C₂×C₄⋊Q₈	C₂²×C₁₁	1	1	yes	characteristic
264	#529	—	2	4	no	—
265	C₂×#126	—	2	2	no	—
266	C₂×#125	—	2	2	no	—
267	C₂×#125	C₂²×C₁₁	1	1	yes	characteristic
268	#525	C₂²×C₁₁	1	2	yes	—
269	C₂×C₂²⋊Q₈	C₂²×C₁₁	1	2	yes	—
270	C₄×#41	C₂²×C₁₁	1	2	yes	—
271	C₂×C₄×Q₈	C₂²×C₁₁	1	2	yes	—
272	C₂×#117	C₂²×C₁₁	1	1	yes	characteristic
273	#501	C₂²×C₁₁	1	4	yes	complemented
274	#499	C₂²×C₁₁	1	4	yes	complemented
275	#497	C₂²×C₁₁	1	4	yes	complemented
276	#494	C₂²×C₁₁	1	2	yes	complemented
277	#492	C₂²×C₁₁	1	2	yes	complemented
278	#491	C₂²×C₁₁	1	4	yes	complemented
279	#491	C₂²×C₁₁	1	2	yes	complemented
280	#490	C₂²×C₁₁	1	2	yes	complemented
281	#488	C₂²×C₁₁	1	4	yes	complemented
282	#487	C₂²×C₁₁	1	4	yes	complemented
283	#470	C₂²×C₁₁	1	8	yes	—
284	#468	C₂²×C₁₁	1	8	yes	—
285	#467	C₂²×C₁₁	1	8	yes	—
286	#465	C₂²×C₁₁	1	8	yes	—
287	#441	C₂²×C₁₁	1	8	yes	complemented
288	#440	C₂²×C₁₁	1	8	yes	complemented
289	C₄×Q₁₆	C₂²×C₁₁	1	8	yes	complemented
290	C₄×SD₁₆	C₂²×C₁₁	1	8	yes	complemented
291	#428	C₂²×C₁₁	1	4	yes	—
292	#419	C₂²×C₁₁	1	4	yes	—
293	#417	C₂²×C₁₁	1	4	yes	—
294	#405	C₂²×C₁₁	1	4	yes	—
295	#405	C₂²×C₁₁	1	4	yes	—
296	C₄×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
297	C₄×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
298	C₄×M₁₆	C₂²×C₁₁	1	2	yes	—
299	C₂²×C₁₁	—	2	2	no	—
300	C₂²×C₁₁	—	2	4	no	—
301	C₂²×C₁₁	—	2	2	no	—
302	C₂²×C₁₁	—	4	4	no	—
303	C₂²×C₁₁	—	4	2	no	—
304	C₂²×C₁₁	—	8	2	no	—
305	C₂²×C₁₁	#532	1	2	yes	—
306	C₂²×C₁₁	C₂³×D₄	1	1	yes	characteristic
307	C₄×C₁₁	—	2	4	no	—
308	C₄×C₁₁	—	2	2	no	—
309	C₄×C₁₁	—	2	2	no	—
310	C₄×C₁₁	—	2	2	no	—
311	C₄×C₁₁	—	4	4	no	—
312	C₄×C₁₁	—	4	4	no	—
313	C₄×C₁₁	—	4	2	no	—
314	C₄×C₁₁	—	4	4	no	—
315	C₄×C₁₁	#532	1	2	yes	—
316	C₄×C₁₁	C₂²×#41	1	2	yes	—
317	C₂×#41	C₂³×C₁₁	1	2	yes	—
318	C₂²×Q₈	C₂³×C₁₁	1	2	yes	—
319	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
320	#137	—	2	16	no	—
321	C₂×Q₁₆	C₂³×C₁₁	1	8	yes	—
322	C₂×SD₁₆	C₂³×C₁₁	1	8	yes	—
323	C₂×M₁₆	—	2	8	no	—
324	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
325	C₂×M₁₆	C₂³×C₁₁	1	4	yes	—
326	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
327	C₂²×C₈	C₂³×C₁₁	1	4	yes	—
328	C₄⋊Q₈	—	2	2	no	—
329	C₄⋊Q₈	C₂³×C₁₁	1	2	yes	—
330	C₄⋊Q₈	C₂³×C₁₁	1	2	yes	—
331	C₄⋊Q₈	C₂³×C₁₁	1	1	yes	characteristic
332	C₄⋊Q₈	C₂³×C₁₁	1	2	yes	—
333	#127	C₂³×C₁₁	1	1	yes	characteristic
334	#126	—	2	4	no	—
335	#126	—	2	8	no	—
336	#126	—	2	8	no	—
337	#126	—	2	4	no	—
338	#125	—	2	8	no	—
339	#125	—	2	8	no	—
340	#125	—	2	4	no	—
341	#125	—	2	2	no	—
342	#125	C₂³×C₁₁	1	2	yes	—
343	#125	C₂³×C₁₁	1	2	yes	—
344	#125	C₂³×C₁₁	1	2	yes	—
345	#124	—	2	4	no	—
346	#124	C₂³×C₁₁	1	2	yes	—
347	#123	—	2	2	no	—
348	#123	—	2	4	no	—
349	#123	—	2	4	no	—
350	C₂²⋊Q₈	—	2	4	no	—
351	C₂²⋊Q₈	—	2	2	no	—
352	C₂²⋊Q₈	—	2	4	no	—
353	C₂²⋊Q₈	C₂³×C₁₁	1	8	yes	—
354	C₂²⋊Q₈	C₂³×C₁₁	1	4	yes	—
355	#121	—	2	2	no	—
356	#121	—	2	4	no	—
357	#121	C₂³×C₁₁	1	4	yes	—
358	#120	—	2	2	no	—
359	C₄×Q₈	—	2	4	no	—
360	C₄×Q₈	—	2	2	no	—
361	C₄×Q₈	C₂³×C₁₁	1	8	yes	—
362	C₄×Q₈	C₂³×C₁₁	1	4	yes	—
363	C₄×D₄	—	2	4	no	—
364	C₄×D₄	—	2	4	no	—
365	C₄×D₄	—	2	2	no	—
366	C₄×D₄	C₂³×C₁₁	1	4	yes	—
367	#117	—	2	2	no	—
368	#117	D₄×C₁₁	1	4	yes	—
369	#117	C₂³×C₁₁	1	2	yes	—
370	#117	C₂³×C₁₁	1	2	yes	—
371	#117	C₂³×C₁₁	1	2	yes	—
372	C₂×C₄⋊C₄	—	2	2	no	—
373	C₂×C₄⋊C₄	—	2	2	no	—
374	C₂×C₄⋊C₄	—	2	2	no	—
375	C₂×C₄⋊C₄	—	2	2	no	—
376	C₂×C₄⋊C₄	D₄×C₁₁	1	2	yes	—
377	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
378	C₂×C₂²⋊C₄	—	2	2	no	—
379	C₂×C₂²⋊C₄	D₄×C₁₁	1	2	yes	—
380	C₂×C₄²	—	2	2	no	—
381	C₂×C₄²	—	2	2	no	—
382	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
383	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
384	#107	C₂³×C₁₁	1	8	yes	—
385	#106	C₂³×C₁₁	1	8	yes	—
386	#103	C₂³×C₁₁	1	8	yes	—
387	#103	C₂³×C₁₁	1	8	yes	—
388	#103	C₂³×C₁₁	1	8	yes	—
389	#102	C₂³×C₁₁	1	8	yes	—
390	#97	C₂³×C₁₁	1	4	yes	—
391	#97	C₂³×C₁₁	1	2	yes	—
392	#97	C₂³×C₁₁	1	2	yes	—
393	C₄×C₈	C₂³×C₁₁	1	4	yes	—
394	C₄×C₈	C₂³×C₁₁	1	2	yes	—
395	C₄×C₈	C₂³×C₁₁	1	2	yes	—
396	C₂×C₁₁	—	2	2	no	—
397	C₂×C₁₁	—	4	2	no	—
398	C₂×C₁₁	—	8	2	no	—
399	C₂×C₁₁	C₂×#532	1	1	yes	characteristic
400	C₂×C₁₁	#3586	1	2	yes	—
401	C₂⁴	C₂×D₄×C₁₁	1	1	yes	characteristic
402	#41	—	2	8	no	—
403	C₂×Q₈	—	2	2	no	—
404	C₂×Q₈	—	2	2	no	—
405	C₂×Q₈	—	2	8	no	—
406	C₂×Q₈	C₂⁴×C₁₁	1	2	yes	—
407	C₂×Q₈	C₂⁴×C₁₁	1	4	yes	—
408	C₂×D₄	—	2	2	no	—
409	C₂×D₄	—	2	4	no	—
410	C₂×D₄	—	2	2	no	—
411	C₂×D₄	C₂⁴×C₁₁	1	2	yes	—
412	C₂²×C₄	—	2	4	no	—
413	C₂²×C₄	—	2	2	no	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	2	2	no	—
416	C₂²×C₄	—	2	4	no	—
417	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
418	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
419	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
420	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
421	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
422	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
423	Q₁₆	—	2	16	no	—
424	SD₁₆	—	2	16	no	—
425	M₁₆	—	2	4	no	—
426	M₁₆	—	2	8	no	—
427	M₁₆	C₁₁×#41	1	8	yes	—
428	C₂×C₈	—	2	8	no	—
429	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
430	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
431	C₄⋊C₄	—	2	8	no	—
432	C₄⋊C₄	—	2	8	no	—
433	C₄⋊C₄	—	2	4	no	—
434	C₄⋊C₄	—	2	4	no	—
435	C₄⋊C₄	—	2	4	no	—
436	C₄⋊C₄	—	2	4	no	—
437	C₄⋊C₄	—	2	2	no	—
438	C₄⋊C₄	—	2	4	no	—
439	C₄⋊C₄	—	2	2	no	—
440	C₄⋊C₄	—	2	4	no	—
441	C₄⋊C₄	—	2	4	no	—
442	C₄⋊C₄	—	2	2	no	—
443	C₄⋊C₄	C₂×D₄×C₁₁	1	4	yes	—
444	C₄⋊C₄	C₂×D₄×C₁₁	1	4	yes	—
445	C₄⋊C₄	C₂⁴×C₁₁	1	4	yes	—
446	C₄⋊C₄	C₂⁴×C₁₁	1	4	yes	—
447	C₂²⋊C₄	—	2	8	no	—
448	C₂²⋊C₄	—	2	2	no	—
449	C₂²⋊C₄	—	2	4	no	—
450	C₂²⋊C₄	—	2	4	no	—
451	C₂²⋊C₄	—	2	4	no	—
452	C₂²⋊C₄	—	2	4	no	—
453	C₂²⋊C₄	C₂×D₄×C₁₁	1	4	yes	—
454	C₂²⋊C₄	C₂×D₄×C₁₁	1	4	yes	—
455	C₄²	—	2	2	no	—
456	C₄²	—	2	4	no	—
457	C₄²	—	2	8	no	—
458	C₄²	C₂×D₄×C₁₁	1	2	yes	—
459	C₄²	C₂×D₄×C₁₁	1	2	yes	—
460	C₄²	C₂⁴×C₁₁	1	2	yes	—
461	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
462	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
463	C₁₁	#60705	1	1	yes	characteristic, direct product factor, Sylow
464	C₂³	—	2	2	no	—
465	C₂³	—	2	2	no	—
466	C₂³	—	4	2	no	—
467	C₂³	C₂²×D₄×C₁₁	1	2	yes	—
468	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
469	Q₈	—	2	8	no	—
470	Q₈	—	2	4	no	—
471	Q₈	—	4	4	no	—
472	Q₈	—	8	2	no	—
473	D₄	—	2	4	no	—
474	D₄	—	4	4	no	—
475	D₄	—	8	2	no	—
476	D₄	—	8	4	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	4	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	4	no	—
483	C₂×C₄	—	2	4	no	—
484	C₂×C₄	—	2	4	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	—	4	2	no	—
487	C₂×C₄	—	4	4	no	—
488	C₂×C₄	—	4	4	no	—
489	C₂×C₄	—	4	4	no	—
490	C₂×C₄	—	8	4	no	—
491	C₂×C₄	C₂²×D₄×C₁₁	1	4	yes	—
492	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
493	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
494	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
495	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
496	C₂×C₄	C₂×C₁₁×#41	1	4	yes	—
497	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
498	C₈	—	2	4	no	—
499	C₈	C₂×C₁₁×#41	1	8	yes	—
500	C₂²	—	2	2	no	—
501	C₂²	—	2	2	no	—
502	C₂²	—	2	4	no	—
503	C₂²	—	4	2	no	—
504	C₂²	—	4	4	no	—
505	C₂²	—	8	2	no	—
506	C₂²	C₁₁×#532	1	2	yes	—
507	C₂²	C₂³×D₄×C₁₁	1	1	yes	characteristic
508	C₄	—	2	2	no	—
509	C₄	—	2	4	no	—
510	C₄	—	2	2	no	—
511	C₄	—	2	2	no	—
512	C₄	—	4	2	no	—
513	C₄	—	4	4	no	—
514	C₄	—	4	4	no	—
515	C₄	—	4	4	no	—
516	C₄	C₁₁×#532	1	2	yes	—
517	C₄	C₂²×C₁₁×#41	1	2	yes	—
518	C₂	—	2	2	no	—
519	C₂	—	4	2	no	—
520	C₂	—	8	2	no	—
521	C₂	C₂×C₁₁×#532	1	1	yes	characteristic
522	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×#3455	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂×C₁₁×#117 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₁×#541	C₂	semidirect
3. C₁₁×#3178	C₂	semidirect
4. C₁₁×#3177	C₂	semidirect
5. C₁₁×#3174	C₂	semidirect
6. C₁₁×#3166	C₂	semidirect
7. C₁₁×#3152	C₂	semidirect
8. C₁₁×#3142	C₂	semidirect
9. C₁₁×#3139	C₂	semidirect
10. C₁₁×#3056	C₂	semidirect
11. C₄×C₁₁×#137	C₂	semidirect
12. C₁₁×#2873	C₂	semidirect
35. C₁₁×#501	C₂²	semidirect
36. C₁₁×#499	C₂²	semidirect
37. C₁₁×#497	C₂²	semidirect
38. C₁₁×#494	C₂²	semidirect
39. C₁₁×#492	C₂²	semidirect
40. C₁₁×#491	C₂²	semidirect
41. C₁₁×#491	C₂²	semidirect
42. C₁₁×#490	C₂²	semidirect
43. C₁₁×#488	C₂²	semidirect
44. C₁₁×#487	C₂²	semidirect
49. C₁₁×#441	C₂²	semidirect
50. C₁₁×#440	C₂²	semidirect
51. C₄×C₁₁×Q₁₆	C₂²	semidirect
52. C₄×C₁₁×SD₁₆	C₂²	semidirect
140. #60705	C₁₁	direct (N × H)
204. C₂×#541	C₂×C₁₁	semidirect
205. #3178	C₂×C₁₁	semidirect
206. #3177	C₂×C₁₁	semidirect
207. #3174	C₂×C₁₁	semidirect
208. #3166	C₂×C₁₁	semidirect
209. #3152	C₂×C₁₁	semidirect
210. #3142	C₂×C₁₁	semidirect
211. #3139	C₂×C₁₁	semidirect
212. #3056	C₂×C₁₁	semidirect
213. C₄×#137	C₂×C₁₁	semidirect
214. #2873	C₂×C₁₁	semidirect
273. #501	C₂²×C₁₁	semidirect
274. #499	C₂²×C₁₁	semidirect
275. #497	C₂²×C₁₁	semidirect
276. #494	C₂²×C₁₁	semidirect
277. #492	C₂²×C₁₁	semidirect
278. #491	C₂²×C₁₁	semidirect
279. #491	C₂²×C₁₁	semidirect
280. #490	C₂²×C₁₁	semidirect
281. #488	C₂²×C₁₁	semidirect
282. #487	C₂²×C₁₁	semidirect
287. #441	C₂²×C₁₁	semidirect
288. #440	C₂²×C₁₁	semidirect
289. C₄×Q₁₆	C₂²×C₁₁	semidirect
290. C₄×SD₁₆	C₂²×C₁₁	semidirect
463. C₁₁	#60705	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
C₂×C₁₁×#541	2
C₁₁×#3178	2
C₁₁×#3177	2
C₁₁×#3174	2
C₁₁×#3166	2
C₁₁×#3152	2
C₁₁×#3142	2
C₁₁×#3139	2
C₁₁×#3056	2
C₄×C₁₁×#137	2
C₁₁×#2873	2
#60705	11

Subgroups — C11×#60705 #14637898

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#60705 #14637898