Subgroups — C₁₁×#61365 #14638558

Order 2816.

1766 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×C₁₁×#41	C₂	1	2	yes	maximal, complemented
2	C₁₁×#3390	C₂	1	2	yes	maximal, complemented
3	C₁₁×#3389	C₂	1	2	yes	maximal, complemented
4	C₁₁×#3388	C₂	1	4	yes	maximal, complemented
5	C₁₁×#3387	C₂	1	2	yes	maximal, complemented
6	C₁₁×#3386	C₂	1	2	yes	maximal, complemented
7	C₁₁×#3385	C₂	1	2	yes	maximal, complemented
8	C₁₁×#3384	C₂	1	2	yes	maximal, complemented
9	C₁₁×#3162	C₂	1	2	yes	maximal, complemented
10	C₁₁×#3160	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₁×#3076	C₂	1	2	yes	maximal, complemented
12	C₁₁×#3076	C₂	1	4	yes	maximal, complemented
13	C₂×C₁₁×#446	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₁×#2943	C₂	1	2	yes	maximal
15	C₄×C₁₁×#135	C₂	1	1	yes	maximal, characteristic
16	C₂×C₁₁×#135	C₂²	1	1	yes	characteristic
17	Q₈²×C₁₁	C₂²	1	2	yes	—
18	C₁₁×#557	C₂²	1	2	yes	—
19	C₁₁×#557	C₂²	1	4	yes	—
20	C₁₁×#554	—	2	4	no	—
21	C₁₁×#554	—	2	2	no	—
22	C₁₁×#554	C₂²	1	2	yes	—
23	C₁₁×#554	C₂²	1	4	yes	—
24	D₄×Q₈×C₁₁	—	2	2	no	—
25	D₄×Q₈×C₁₁	C₂²	1	2	yes	—
26	C₁₁×#533	—	2	2	no	—
27	C₁₁×#533	—	2	4	no	—
28	C₁₁×#533	C₂²	1	2	yes	—
29	C₁₁×#533	C₂²	1	4	yes	—
30	C₄×C₁₁×#41	C₂²	1	2	yes	—
31	C₄×C₁₁×#41	C₂²	1	4	yes	—
32	C₂×C₄×Q₈×C₁₁	—	2	2	no	—
33	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
34	C₁₁×#501	C₂²	1	4	yes	—
35	C₁₁×#501	C₂²	1	4	yes	—
36	C₁₁×#501	C₂²	1	4	yes	—
37	C₁₁×#501	C₂²	1	4	yes	—
38	C₁₁×#500	C₂²	1	1	yes	characteristic
39	C₁₁×#500	C₂²	1	1	yes	characteristic
40	C₁₁×#499	C₂²	1	2	yes	—
41	C₁₁×#499	C₂²	1	2	yes	—
42	C₁₁×#498	C₂²	1	2	yes	—
43	C₁₁×#479	C₂²	1	4	yes	—
44	C₁₁×#479	C₂²	1	4	yes	—
45	C₁₁×#479	C₂²	1	4	yes	—
46	C₁₁×#478	C₂²	1	4	yes	—
47	C₁₁×#478	C₂²	1	4	yes	—
48	C₁₁×#478	C₂²	1	4	yes	—
49	C₁₁×#477	C₂²	1	2	yes	—
50	C₁₁×#477	C₂²	1	4	yes	—
51	C₁₁×#476	C₂²	1	2	yes	—
52	C₁₁×#476	C₂²	1	4	yes	—
53	C₁₁×#475	C₂²	1	2	yes	—
54	C₁₁×#475	C₂²	1	4	yes	—
55	C₁₁×#474	C₂²	1	2	yes	—
56	C₁₁×#474	C₂²	1	4	yes	—
57	C₁₁×#446	C₂²	1	2	yes	—
58	C₁₁×#446	C₂²	1	2	yes	—
59	C₁₁×#446	C₂²	1	2	yes	—
60	C₁₁×#446	C₂²	1	2	yes	—
61	C₁₁×#442	C₂²	1	4	yes	—
62	C₁₁×#441	C₂²	1	4	yes	—
63	C₁₁×#440	C₂²	1	4	yes	—
64	C₁₁×#440	C₂²	1	4	yes	—
65	C₄×C₁₁×Q₁₆	C₂²	1	1	yes	characteristic
66	C₄×C₁₁×Q₁₆	C₂²	1	1	yes	characteristic
67	C₄×C₁₁×SD₁₆	C₂²	1	2	yes	—
68	C₄×C₁₁×SD₁₆	C₂²	1	2	yes	—
69	C₄×C₁₁×D₈	C₂²	1	1	yes	characteristic
70	C₄×C₁₁×D₈	C₂²	1	1	yes	characteristic
71	C₁₁×#427	C₂²	1	2	yes	—
72	C₁₁×#427	C₂²	1	2	yes	—
73	C₁₁×#427	C₂²	1	1	yes	characteristic
74	C₁₁×#427	C₂²	1	4	yes	—
75	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
76	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
77	C₁₁×#416	C₂²	1	2	yes	—
78	C₁₁×#416	C₂²	1	4	yes	—
79	C₂×C₁₁×#97	C₂²	1	2	yes	—
80	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
81	C₂×C₁₁×#41	C₂³	1	2	yes	—
82	C₂²×Q₈×C₁₁	—	2	2	no	—
83	C₂²×Q₈×C₁₁	D₄	1	1	yes	characteristic
84	C₁₁×#135	Q₈	1	8	yes	complemented
85	C₂×C₁₁×Q₁₆	C₂³	1	1	yes	characteristic
86	C₂×C₁₁×SD₁₆	C₂³	1	2	yes	—
87	C₂×C₁₁×D₈	C₂³	1	1	yes	characteristic
88	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
89	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
90	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
91	C₁₁×C₄⋊Q₈	—	2	2	no	—
92	C₁₁×C₄⋊Q₈	—	2	4	no	—
93	C₁₁×C₄⋊Q₈	—	2	2	no	—
94	C₁₁×C₄⋊Q₈	—	2	4	no	—
95	C₁₁×C₄⋊Q₈	C₂³	1	2	yes	—
96	C₁₁×C₄⋊Q₈	C₂³	1	2	yes	—
97	C₁₁×C₄⋊Q₈	C₂³	1	4	yes	—
98	C₁₁×C₄⋊Q₈	C₂³	1	4	yes	—
99	C₁₁×#125	—	2	4	no	—
100	C₁₁×#125	—	2	4	no	—
101	C₁₁×#125	—	2	4	no	—
102	C₁₁×#125	C₂³	1	4	yes	—
103	C₁₁×#125	C₂³	1	4	yes	—
104	C₁₁×#125	C₂³	1	4	yes	—
105	C₁₁×C₂²⋊Q₈	—	2	2	no	—
106	C₁₁×C₂²⋊Q₈	—	2	4	no	—
107	C₁₁×C₂²⋊Q₈	—	2	2	no	—
108	C₁₁×C₂²⋊Q₈	—	2	4	no	—
109	C₁₁×C₂²⋊Q₈	—	2	2	no	—
110	C₁₁×C₂²⋊Q₈	—	2	4	no	—
111	C₁₁×C₂²⋊Q₈	—	2	2	no	—
112	C₁₁×C₂²⋊Q₈	—	2	4	no	—
113	C₁₁×C₂²⋊Q₈	—	2	4	no	—
114	C₁₁×C₂²⋊Q₈	—	2	4	no	—
115	C₁₁×C₂²⋊Q₈	—	2	4	no	—
116	C₄×Q₈×C₁₁	—	2	2	no	—
117	C₄×Q₈×C₁₁	—	2	4	no	—
118	C₄×Q₈×C₁₁	—	2	2	no	—
119	C₄×Q₈×C₁₁	—	2	2	no	—
120	C₄×Q₈×C₁₁	—	2	4	no	—
121	C₄×Q₈×C₁₁	—	2	4	no	—
122	C₄×Q₈×C₁₁	—	2	2	no	—
123	C₄×Q₈×C₁₁	D₄	1	2	yes	—
124	C₄×Q₈×C₁₁	D₄	1	2	yes	—
125	C₄×Q₈×C₁₁	C₂³	1	2	yes	—
126	C₄×Q₈×C₁₁	C₂³	1	4	yes	—
127	C₄×Q₈×C₁₁	C₂³	1	2	yes	—
128	C₄×Q₈×C₁₁	C₂³	1	4	yes	—
129	C₄×Q₈×C₁₁	C₂³	1	2	yes	—
130	C₄×Q₈×C₁₁	C₂³	1	2	yes	—
131	C₄×D₄×C₁₁	—	2	2	no	—
132	C₄×D₄×C₁₁	—	2	4	no	—
133	C₄×D₄×C₁₁	—	2	2	no	—
134	C₄×D₄×C₁₁	—	2	4	no	—
135	C₄×D₄×C₁₁	C₂³	1	2	yes	—
136	C₄×D₄×C₁₁	C₂³	1	4	yes	—
137	C₄×D₄×C₁₁	C₂³	1	2	yes	—
138	C₄×D₄×C₁₁	C₂³	1	4	yes	—
139	C₁₁×#117	—	2	4	no	—
140	C₁₁×#117	—	2	2	no	—
141	C₁₁×#117	C₂³	1	2	yes	—
142	C₁₁×#117	C₂³	1	4	yes	—
143	C₂×C₁₁×C₄⋊C₄	—	2	4	no	—
144	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
145	C₂×C₁₁×C₄⋊C₄	D₄	1	2	yes	—
146	C₂×C₁₁×C₄⋊C₄	D₄	1	1	yes	characteristic
147	C₂×C₄²×C₁₁	—	2	2	no	—
148	C₂×C₄²×C₁₁	—	2	4	no	—
149	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
150	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
151	C₁₁×#107	C₂³	1	2	yes	—
152	C₁₁×#107	C₂³	1	2	yes	—
153	C₁₁×#107	C₂³	1	2	yes	—
154	C₁₁×#107	C₂³	1	2	yes	—
155	C₁₁×#107	C₂³	1	1	yes	characteristic
156	C₁₁×#107	C₂³	1	1	yes	characteristic
157	C₁₁×#107	C₂³	1	4	yes	—
158	C₁₁×#107	C₂³	1	4	yes	—
159	C₁₁×#106	C₂³	1	4	yes	—
160	C₁₁×#106	C₂³	1	4	yes	—
161	C₁₁×#106	C₂³	1	2	yes	—
162	C₁₁×#106	C₂³	1	4	yes	—
163	C₁₁×#106	C₂³	1	4	yes	—
164	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
165	C₁₁×C₄⋊C₈	C₂³	1	4	yes	—
166	C₁₁×C₄⋊C₈	C₂³	1	4	yes	—
167	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
168	C₁₁×#103	C₂³	1	2	yes	—
169	C₁₁×#103	C₂³	1	2	yes	—
170	C₁₁×#103	C₂³	1	4	yes	—
171	C₁₁×#103	C₂³	1	4	yes	—
172	C₁₁×#102	C₂³	1	2	yes	—
173	C₁₁×#102	C₂³	1	2	yes	—
174	C₁₁×#102	C₂³	1	4	yes	—
175	C₁₁×#102	C₂³	1	4	yes	—
176	C₁₁×#97	C₂³	1	4	yes	—
177	C₁₁×#97	C₂³	1	4	yes	—
178	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
179	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
180	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
181	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
182	#61365	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
183	C₁₁×#41	—	2	4	no	—
184	C₁₁×#41	C₂×Q₈	1	8	yes	complemented
185	C₂×Q₈×C₁₁	—	2	4	no	—
186	C₂×Q₈×C₁₁	—	2	2	no	—
187	C₂×Q₈×C₁₁	—	2	4	no	—
188	C₂×Q₈×C₁₁	—	2	2	no	—
189	C₂×Q₈×C₁₁	—	4	2	no	—
190	C₂×Q₈×C₁₁	—	4	8	no	—
191	C₂×Q₈×C₁₁	C₂×D₄	1	2	yes	—
192	C₂×Q₈×C₁₁	C₂×D₄	1	2	yes	—
193	C₂×Q₈×C₁₁	C₂⁴	1	2	yes	—
194	C₂×D₄×C₁₁	—	2	2	no	—
195	C₂×D₄×C₁₁	C₂⁴	1	2	yes	—
196	C₂²×C₄×C₁₁	—	2	2	no	—
197	C₂²×C₄×C₁₁	—	2	4	no	—
198	C₂²×C₄×C₁₁	—	2	2	no	—
199	C₂²×C₄×C₁₁	—	2	2	no	—
200	C₂²×C₄×C₁₁	—	2	4	no	—
201	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
202	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
203	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
204	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
205	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
206	C₁₁×Q₁₆	C₂×Q₈	1	4	yes	complemented
207	C₁₁×SD₁₆	C₂×Q₈	1	8	yes	complemented
208	C₁₁×D₈	C₂×Q₈	1	4	yes	complemented
209	C₂×C₈×C₁₁	—	2	2	no	—
210	C₂×C₈×C₁₁	—	2	4	no	—
211	C₂×C₈×C₁₁	C₂×Q₈	1	4	yes	complemented
212	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
213	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
214	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
215	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
216	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
217	C₁₁×C₄⋊C₄	—	2	4	no	—
218	C₁₁×C₄⋊C₄	—	2	4	no	—
219	C₁₁×C₄⋊C₄	—	2	4	no	—
220	C₁₁×C₄⋊C₄	—	2	4	no	—
221	C₁₁×C₄⋊C₄	—	2	2	no	—
222	C₁₁×C₄⋊C₄	—	2	4	no	—
223	C₁₁×C₄⋊C₄	—	2	4	no	—
224	C₁₁×C₄⋊C₄	—	2	2	no	—
225	C₁₁×C₄⋊C₄	—	2	2	no	—
226	C₁₁×C₄⋊C₄	—	2	4	no	—
227	C₁₁×C₄⋊C₄	—	2	2	no	—
228	C₁₁×C₄⋊C₄	—	2	4	no	—
229	C₁₁×C₄⋊C₄	—	2	4	no	—
230	C₁₁×C₄⋊C₄	—	2	4	no	—
231	C₁₁×C₄⋊C₄	C₂×D₄	1	4	yes	—
232	C₁₁×C₄⋊C₄	C₂×D₄	1	2	yes	—
233	C₁₁×C₄⋊C₄	C₂×D₄	1	2	yes	—
234	C₁₁×C₄⋊C₄	C₂×D₄	1	4	yes	—
235	C₁₁×C₄⋊C₄	C₂⁴	1	2	yes	—
236	C₁₁×C₄⋊C₄	C₂⁴	1	2	yes	—
237	C₁₁×C₄⋊C₄	C₂⁴	1	4	yes	—
238	C₁₁×C₄⋊C₄	C₂⁴	1	4	yes	—
239	C₁₁×C₂²⋊C₄	—	2	2	no	—
240	C₁₁×C₂²⋊C₄	—	2	4	no	—
241	C₁₁×C₂²⋊C₄	—	2	4	no	—
242	C₁₁×C₂²⋊C₄	—	2	4	no	—
243	C₁₁×C₂²⋊C₄	—	2	2	no	—
244	C₁₁×C₂²⋊C₄	—	2	2	no	—
245	C₄²×C₁₁	—	2	2	no	—
246	C₄²×C₁₁	—	2	4	no	—
247	C₄²×C₁₁	—	2	4	no	—
248	C₄²×C₁₁	—	2	2	no	—
249	C₄²×C₁₁	—	2	2	no	—
250	C₄²×C₁₁	—	2	4	no	—
251	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
252	C₄²×C₁₁	C₂×D₄	1	4	yes	—
253	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
254	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
255	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
256	C₄²×C₁₁	C₂⁴	1	4	yes	—
257	Q₈×#41	C₂×C₁₁	1	2	yes	complemented
258	#3390	C₂×C₁₁	1	2	yes	complemented
259	#3389	C₂×C₁₁	1	2	yes	complemented
260	#3388	C₂×C₁₁	1	4	yes	complemented
261	#3387	C₂×C₁₁	1	2	yes	complemented
262	#3386	C₂×C₁₁	1	2	yes	complemented
263	#3385	C₂×C₁₁	1	2	yes	complemented
264	#3384	C₂×C₁₁	1	2	yes	complemented
265	#3162	C₂×C₁₁	1	2	yes	complemented
266	#3160	C₂×C₁₁	1	1	yes	characteristic, complemented
267	#3076	C₂×C₁₁	1	2	yes	complemented
268	#3076	C₂×C₁₁	1	4	yes	complemented
269	C₂×#446	C₂×C₁₁	1	1	yes	characteristic, complemented
270	#2943	C₂×C₁₁	1	2	yes	—
271	C₄×#135	C₂×C₁₁	1	1	yes	characteristic
272	C₂³×C₁₁	—	2	2	no	—
273	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
274	Q₈×C₁₁	—	2	4	no	—
275	Q₈×C₁₁	—	2	2	no	—
276	Q₈×C₁₁	—	4	2	no	—
277	Q₈×C₁₁	—	4	8	no	—
278	Q₈×C₁₁	—	4	4	no	—
279	Q₈×C₁₁	—	8	4	no	—
280	Q₈×C₁₁	—	8	2	no	—
281	Q₈×C₁₁	C₂²×Q₈	1	4	yes	—
282	D₄×C₁₁	—	2	8	no	—
283	D₄×C₁₁	—	2	2	no	—
284	D₄×C₁₁	C₂²×Q₈	1	4	yes	—
285	C₂×C₄×C₁₁	—	2	2	no	—
286	C₂×C₄×C₁₁	—	2	8	no	—
287	C₂×C₄×C₁₁	—	2	2	no	—
288	C₂×C₄×C₁₁	—	2	4	no	—
289	C₂×C₄×C₁₁	—	2	2	no	—
290	C₂×C₄×C₁₁	—	2	4	no	—
291	C₂×C₄×C₁₁	—	2	2	no	—
292	C₂×C₄×C₁₁	—	4	1	no	—
293	C₂×C₄×C₁₁	—	4	2	no	—
294	C₂×C₄×C₁₁	—	4	2	no	—
295	C₂×C₄×C₁₁	—	4	8	no	—
296	C₂×C₄×C₁₁	—	4	4	no	—
297	C₂×C₄×C₁₁	—	8	2	no	—
298	C₂×C₄×C₁₁	—	8	4	no	—
299	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
300	C₂×C₄×C₁₁	C₂²×D₄	1	4	yes	—
301	C₂×C₄×C₁₁	C₂²×D₄	1	4	yes	—
302	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
303	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
304	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
305	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
306	C₂×C₄×C₁₁	C₂²×Q₈	1	2	yes	—
307	C₂×C₄×C₁₁	2₋¹⁺⁴	1	2	yes	—
308	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
309	C₈×C₁₁	—	2	1	no	—
310	C₈×C₁₁	—	2	1	no	—
311	C₈×C₁₁	—	2	4	no	—
312	C₈×C₁₁	C₂²×Q₈	1	2	yes	—
313	C₈×C₁₁	C₂²×Q₈	1	2	yes	—
314	C₂×#135	C₂²×C₁₁	1	1	yes	characteristic
315	Q₈²	C₂²×C₁₁	1	2	yes	—
316	#557	C₂²×C₁₁	1	2	yes	—
317	#557	C₂²×C₁₁	1	4	yes	—
318	#554	—	2	4	no	—
319	#554	—	2	2	no	—
320	#554	C₂²×C₁₁	1	2	yes	—
321	#554	C₂²×C₁₁	1	4	yes	—
322	D₄×Q₈	—	2	2	no	—
323	D₄×Q₈	C₂²×C₁₁	1	2	yes	—
324	#533	—	2	2	no	—
325	#533	—	2	4	no	—
326	#533	C₂²×C₁₁	1	2	yes	—
327	#533	C₂²×C₁₁	1	4	yes	—
328	C₄×#41	C₂²×C₁₁	1	2	yes	—
329	C₄×#41	C₂²×C₁₁	1	4	yes	—
330	C₂×C₄×Q₈	—	2	2	no	—
331	C₂×C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
332	#501	C₂²×C₁₁	1	4	yes	—
333	#501	C₂²×C₁₁	1	4	yes	—
334	#501	C₂²×C₁₁	1	4	yes	—
335	#501	C₂²×C₁₁	1	4	yes	—
336	#500	C₂²×C₁₁	1	1	yes	characteristic
337	#500	C₂²×C₁₁	1	1	yes	characteristic
338	#499	C₂²×C₁₁	1	2	yes	—
339	#499	C₂²×C₁₁	1	2	yes	—
340	#498	C₂²×C₁₁	1	2	yes	—
341	#479	C₂²×C₁₁	1	4	yes	—
342	#479	C₂²×C₁₁	1	4	yes	—
343	#479	C₂²×C₁₁	1	4	yes	—
344	#478	C₂²×C₁₁	1	4	yes	—
345	#478	C₂²×C₁₁	1	4	yes	—
346	#478	C₂²×C₁₁	1	4	yes	—
347	#477	C₂²×C₁₁	1	2	yes	—
348	#477	C₂²×C₁₁	1	4	yes	—
349	#476	C₂²×C₁₁	1	2	yes	—
350	#476	C₂²×C₁₁	1	4	yes	—
351	#475	C₂²×C₁₁	1	2	yes	—
352	#475	C₂²×C₁₁	1	4	yes	—
353	#474	C₂²×C₁₁	1	2	yes	—
354	#474	C₂²×C₁₁	1	4	yes	—
355	#446	C₂²×C₁₁	1	2	yes	—
356	#446	C₂²×C₁₁	1	2	yes	—
357	#446	C₂²×C₁₁	1	2	yes	—
358	#446	C₂²×C₁₁	1	2	yes	—
359	#442	C₂²×C₁₁	1	4	yes	—
360	#441	C₂²×C₁₁	1	4	yes	—
361	#440	C₂²×C₁₁	1	4	yes	—
362	#440	C₂²×C₁₁	1	4	yes	—
363	C₄×Q₁₆	C₂²×C₁₁	1	1	yes	characteristic
364	C₄×Q₁₆	C₂²×C₁₁	1	1	yes	characteristic
365	C₄×SD₁₆	C₂²×C₁₁	1	2	yes	—
366	C₄×SD₁₆	C₂²×C₁₁	1	2	yes	—
367	C₄×D₈	C₂²×C₁₁	1	1	yes	characteristic
368	C₄×D₈	C₂²×C₁₁	1	1	yes	characteristic
369	#427	C₂²×C₁₁	1	2	yes	—
370	#427	C₂²×C₁₁	1	4	yes	—
371	#427	C₂²×C₁₁	1	2	yes	—
372	#427	C₂²×C₁₁	1	1	yes	characteristic
373	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
374	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
375	#416	C₂²×C₁₁	1	2	yes	—
376	#416	C₂²×C₁₁	1	4	yes	—
377	C₂×#97	C₂²×C₁₁	1	2	yes	—
378	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
379	C₂²×C₁₁	—	2	1	no	—
380	C₂²×C₁₁	—	2	1	no	—
381	C₂²×C₁₁	—	2	4	no	—
382	C₂²×C₁₁	—	4	2	no	—
383	C₂²×C₁₁	—	4	2	no	—
384	C₂²×C₁₁	D₄×Q₈	1	2	yes	—
385	C₂²×C₁₁	C₂³×D₄	1	1	yes	characteristic
386	C₄×C₁₁	—	2	1	no	—
387	C₄×C₁₁	—	2	4	no	—
388	C₄×C₁₁	—	2	1	no	—
389	C₄×C₁₁	—	2	4	no	—
390	C₄×C₁₁	—	2	1	no	—
391	C₄×C₁₁	—	2	4	no	—
392	C₄×C₁₁	—	4	2	no	—
393	C₄×C₁₁	—	4	4	no	—
394	C₄×C₁₁	—	4	4	no	—
395	C₄×C₁₁	—	4	2	no	—
396	C₄×C₁₁	D₄×Q₈	1	2	yes	—
397	C₄×C₁₁	#575	1	2	yes	—
398	C₄×C₁₁	C₂³×Q₈	1	1	yes	characteristic
399	C₄×C₁₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
400	C₂×#41	C₂³×C₁₁	1	2	yes	—
401	C₂²×Q₈	—	2	2	no	—
402	C₂²×Q₈	D₄×C₁₁	1	1	yes	characteristic
403	#135	Q₈×C₁₁	1	8	yes	complemented
404	C₂×Q₁₆	C₂³×C₁₁	1	1	yes	characteristic
405	C₂×SD₁₆	C₂³×C₁₁	1	2	yes	—
406	C₂×D₈	C₂³×C₁₁	1	1	yes	characteristic
407	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
408	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
409	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
410	C₄⋊Q₈	—	2	2	no	—
411	C₄⋊Q₈	—	2	4	no	—
412	C₄⋊Q₈	—	2	2	no	—
413	C₄⋊Q₈	—	2	4	no	—
414	C₄⋊Q₈	C₂³×C₁₁	1	2	yes	—
415	C₄⋊Q₈	C₂³×C₁₁	1	4	yes	—
416	C₄⋊Q₈	C₂³×C₁₁	1	4	yes	—
417	C₄⋊Q₈	C₂³×C₁₁	1	2	yes	—
418	#125	—	2	4	no	—
419	#125	—	2	4	no	—
420	#125	—	2	4	no	—
421	#125	C₂³×C₁₁	1	4	yes	—
422	#125	C₂³×C₁₁	1	4	yes	—
423	#125	C₂³×C₁₁	1	4	yes	—
424	C₂²⋊Q₈	—	2	2	no	—
425	C₂²⋊Q₈	—	2	4	no	—
426	C₂²⋊Q₈	—	2	2	no	—
427	C₂²⋊Q₈	—	2	4	no	—
428	C₂²⋊Q₈	—	2	2	no	—
429	C₂²⋊Q₈	—	2	4	no	—
430	C₂²⋊Q₈	—	2	2	no	—
431	C₂²⋊Q₈	—	2	4	no	—
432	C₂²⋊Q₈	—	2	4	no	—
433	C₂²⋊Q₈	—	2	4	no	—
434	C₂²⋊Q₈	—	2	4	no	—
435	C₄×Q₈	—	2	2	no	—
436	C₄×Q₈	—	2	4	no	—
437	C₄×Q₈	—	2	2	no	—
438	C₄×Q₈	—	2	2	no	—
439	C₄×Q₈	—	2	4	no	—
440	C₄×Q₈	—	2	4	no	—
441	C₄×Q₈	—	2	2	no	—
442	C₄×Q₈	D₄×C₁₁	1	2	yes	—
443	C₄×Q₈	D₄×C₁₁	1	2	yes	—
444	C₄×Q₈	C₂³×C₁₁	1	2	yes	—
445	C₄×Q₈	C₂³×C₁₁	1	4	yes	—
446	C₄×Q₈	C₂³×C₁₁	1	2	yes	—
447	C₄×Q₈	C₂³×C₁₁	1	4	yes	—
448	C₄×Q₈	C₂³×C₁₁	1	2	yes	—
449	C₄×Q₈	C₂³×C₁₁	1	2	yes	—
450	C₄×D₄	—	2	2	no	—
451	C₄×D₄	—	2	4	no	—
452	C₄×D₄	—	2	2	no	—
453	C₄×D₄	—	2	4	no	—
454	C₄×D₄	C₂³×C₁₁	1	2	yes	—
455	C₄×D₄	C₂³×C₁₁	1	4	yes	—
456	C₄×D₄	C₂³×C₁₁	1	2	yes	—
457	C₄×D₄	C₂³×C₁₁	1	4	yes	—
458	#117	—	2	4	no	—
459	#117	—	2	2	no	—
460	#117	C₂³×C₁₁	1	2	yes	—
461	#117	C₂³×C₁₁	1	4	yes	—
462	C₂×C₄⋊C₄	—	2	4	no	—
463	C₂×C₄⋊C₄	—	2	2	no	—
464	C₂×C₄⋊C₄	D₄×C₁₁	1	2	yes	—
465	C₂×C₄⋊C₄	D₄×C₁₁	1	1	yes	characteristic
466	C₂×C₄²	—	2	2	no	—
467	C₂×C₄²	—	2	4	no	—
468	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
469	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
470	#107	C₂³×C₁₁	1	1	yes	characteristic
471	#107	C₂³×C₁₁	1	1	yes	characteristic
472	#107	C₂³×C₁₁	1	2	yes	—
473	#107	C₂³×C₁₁	1	2	yes	—
474	#107	C₂³×C₁₁	1	2	yes	—
475	#107	C₂³×C₁₁	1	4	yes	—
476	#107	C₂³×C₁₁	1	4	yes	—
477	#107	C₂³×C₁₁	1	2	yes	—
478	#106	C₂³×C₁₁	1	2	yes	—
479	#106	C₂³×C₁₁	1	4	yes	—
480	#106	C₂³×C₁₁	1	4	yes	—
481	#106	C₂³×C₁₁	1	4	yes	—
482	#106	C₂³×C₁₁	1	4	yes	—
483	C₄⋊C₈	C₂³×C₁₁	1	2	yes	—
484	C₄⋊C₈	C₂³×C₁₁	1	4	yes	—
485	C₄⋊C₈	C₂³×C₁₁	1	4	yes	—
486	C₄⋊C₈	C₂³×C₁₁	1	2	yes	—
487	#103	C₂³×C₁₁	1	2	yes	—
488	#103	C₂³×C₁₁	1	2	yes	—
489	#103	C₂³×C₁₁	1	4	yes	—
490	#103	C₂³×C₁₁	1	4	yes	—
491	#102	C₂³×C₁₁	1	2	yes	—
492	#102	C₂³×C₁₁	1	2	yes	—
493	#102	C₂³×C₁₁	1	4	yes	—
494	#102	C₂³×C₁₁	1	4	yes	—
495	#97	C₂³×C₁₁	1	4	yes	—
496	#97	C₂³×C₁₁	1	4	yes	—
497	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
498	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
499	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
500	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
501	C₂×C₁₁	—	2	2	no	—
502	C₂×C₁₁	—	4	4	no	—
503	C₂×C₁₁	C₂×D₄×Q₈	1	1	yes	characteristic
504	C₂×C₁₁	C₂×#575	1	1	yes	characteristic
505	C₂×C₁₁	#3584	1	1	yes	characteristic
506	#41	—	2	4	no	—
507	#41	C₂×Q₈×C₁₁	1	8	yes	complemented
508	C₂×Q₈	—	2	4	no	—
509	C₂×Q₈	—	2	2	no	—
510	C₂×Q₈	—	2	4	no	—
511	C₂×Q₈	—	2	2	no	—
512	C₂×Q₈	—	4	2	no	—
513	C₂×Q₈	—	4	8	no	—
514	C₂×Q₈	C₂×D₄×C₁₁	1	2	yes	—
515	C₂×Q₈	C₂×D₄×C₁₁	1	2	yes	—
516	C₂×Q₈	C₂⁴×C₁₁	1	2	yes	—
517	C₂×D₄	—	2	2	no	—
518	C₂×D₄	C₂⁴×C₁₁	1	2	yes	—
519	C₂²×C₄	—	2	2	no	—
520	C₂²×C₄	—	2	4	no	—
521	C₂²×C₄	—	2	2	no	—
522	C₂²×C₄	—	2	2	no	—
523	C₂²×C₄	—	2	4	no	—
524	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
525	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
526	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
527	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
528	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
529	Q₁₆	C₂×Q₈×C₁₁	1	4	yes	complemented
530	SD₁₆	C₂×Q₈×C₁₁	1	8	yes	complemented
531	D₈	C₂×Q₈×C₁₁	1	4	yes	complemented
532	C₂×C₈	—	2	2	no	—
533	C₂×C₈	—	2	4	no	—
534	C₂×C₈	C₂×Q₈×C₁₁	1	4	yes	complemented
535	C₂×C₈	C₂⁴×C₁₁	1	1	yes	characteristic
536	C₂×C₈	C₂⁴×C₁₁	1	1	yes	characteristic
537	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
538	C₂×C₈	C₂⁴×C₁₁	1	1	yes	characteristic
539	C₂×C₈	C₂⁴×C₁₁	1	1	yes	characteristic
540	C₄⋊C₄	—	2	4	no	—
541	C₄⋊C₄	—	2	4	no	—
542	C₄⋊C₄	—	2	4	no	—
543	C₄⋊C₄	—	2	4	no	—
544	C₄⋊C₄	—	2	2	no	—
545	C₄⋊C₄	—	2	4	no	—
546	C₄⋊C₄	—	2	4	no	—
547	C₄⋊C₄	—	2	2	no	—
548	C₄⋊C₄	—	2	2	no	—
549	C₄⋊C₄	—	2	4	no	—
550	C₄⋊C₄	—	2	2	no	—
551	C₄⋊C₄	—	2	4	no	—
552	C₄⋊C₄	—	2	4	no	—
553	C₄⋊C₄	—	2	4	no	—
554	C₄⋊C₄	C₂×D₄×C₁₁	1	4	yes	—
555	C₄⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
556	C₄⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
557	C₄⋊C₄	C₂×D₄×C₁₁	1	4	yes	—
558	C₄⋊C₄	C₂⁴×C₁₁	1	2	yes	—
559	C₄⋊C₄	C₂⁴×C₁₁	1	2	yes	—
560	C₄⋊C₄	C₂⁴×C₁₁	1	4	yes	—
561	C₄⋊C₄	C₂⁴×C₁₁	1	4	yes	—
562	C₂²⋊C₄	—	2	2	no	—
563	C₂²⋊C₄	—	2	4	no	—
564	C₂²⋊C₄	—	2	4	no	—
565	C₂²⋊C₄	—	2	4	no	—
566	C₂²⋊C₄	—	2	2	no	—
567	C₂²⋊C₄	—	2	2	no	—
568	C₄²	—	2	2	no	—
569	C₄²	—	2	4	no	—
570	C₄²	—	2	2	no	—
571	C₄²	—	2	4	no	—
572	C₄²	—	2	4	no	—
573	C₄²	—	2	2	no	—
574	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
575	C₄²	C₂×D₄×C₁₁	1	4	yes	—
576	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
577	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
578	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
579	C₄²	C₂⁴×C₁₁	1	4	yes	—
580	C₁₁	#61365	1	1	yes	characteristic, direct product factor, Sylow
581	C₂³	—	2	2	no	—
582	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
583	Q₈	—	2	4	no	—
584	Q₈	—	2	2	no	—
585	Q₈	—	4	2	no	—
586	Q₈	—	4	8	no	—
587	Q₈	—	4	4	no	—
588	Q₈	—	8	4	no	—
589	Q₈	—	8	2	no	—
590	Q₈	C₂²×Q₈×C₁₁	1	4	yes	—
591	D₄	—	2	8	no	—
592	D₄	—	2	2	no	—
593	D₄	C₂²×Q₈×C₁₁	1	4	yes	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	2	8	no	—
596	C₂×C₄	—	2	2	no	—
597	C₂×C₄	—	2	4	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	2	4	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	4	1	no	—
602	C₂×C₄	—	4	2	no	—
603	C₂×C₄	—	4	2	no	—
604	C₂×C₄	—	4	8	no	—
605	C₂×C₄	—	4	4	no	—
606	C₂×C₄	—	8	2	no	—
607	C₂×C₄	—	8	4	no	—
608	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
609	C₂×C₄	C₂²×D₄×C₁₁	1	4	yes	—
610	C₂×C₄	C₂²×D₄×C₁₁	1	4	yes	—
611	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
612	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
613	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
614	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
615	C₂×C₄	C₂²×Q₈×C₁₁	1	2	yes	—
616	C₂×C₄	C₁₁×2₋¹⁺⁴	1	2	yes	—
617	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
618	C₈	—	2	1	no	—
619	C₈	—	2	1	no	—
620	C₈	—	2	4	no	—
621	C₈	C₂²×Q₈×C₁₁	1	2	yes	—
622	C₈	C₂²×Q₈×C₁₁	1	2	yes	—
623	C₂²	—	2	1	no	—
624	C₂²	—	2	1	no	—
625	C₂²	—	2	4	no	—
626	C₂²	—	4	2	no	—
627	C₂²	—	4	2	no	—
628	C₂²	D₄×Q₈×C₁₁	1	2	yes	—
629	C₂²	C₂³×D₄×C₁₁	1	1	yes	characteristic
630	C₄	—	2	4	no	—
631	C₄	—	2	1	no	—
632	C₄	—	2	4	no	—
633	C₄	—	2	1	no	—
634	C₄	—	2	4	no	—
635	C₄	—	2	1	no	—
636	C₄	—	4	4	no	—
637	C₄	—	4	2	no	—
638	C₄	—	4	2	no	—
639	C₄	—	4	4	no	—
640	C₄	D₄×Q₈×C₁₁	1	2	yes	—
641	C₄	C₁₁×#575	1	2	yes	—
642	C₄	C₂³×Q₈×C₁₁	1	1	yes	characteristic
643	C₄	C₂×C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
644	C₂	—	2	2	no	—
645	C₂	—	4	4	no	—
646	C₂	C₂×D₄×Q₈×C₁₁	1	1	yes	characteristic
647	C₂	C₂×C₁₁×#575	1	1	yes	characteristic
648	C₂	C₁₁×#3584	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₁
socle	C₂²×C₁₁	C₂³×D₄
prime radical	C₂×C₁₁×#135	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₄×Q₈×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. Q₈×C₁₁×#41	C₂	semidirect
2. C₁₁×#3390	C₂	semidirect
3. C₁₁×#3389	C₂	semidirect
4. C₁₁×#3388	C₂	semidirect
5. C₁₁×#3387	C₂	semidirect
6. C₁₁×#3386	C₂	semidirect
7. C₁₁×#3385	C₂	semidirect
8. C₁₁×#3384	C₂	semidirect
9. C₁₁×#3162	C₂	semidirect
10. C₁₁×#3160	C₂	semidirect
11. C₁₁×#3076	C₂	semidirect
12. C₁₁×#3076	C₂	semidirect
13. C₂×C₁₁×#446	C₂	semidirect
84. C₁₁×#135	Q₈	semidirect
182. #61365	C₁₁	direct (N × H)
184. C₁₁×#41	C₂×Q₈	semidirect
206. C₁₁×Q₁₆	C₂×Q₈	semidirect
207. C₁₁×SD₁₆	C₂×Q₈	semidirect
208. C₁₁×D₈	C₂×Q₈	semidirect
211. C₂×C₈×C₁₁	C₂×Q₈	semidirect
257. Q₈×#41	C₂×C₁₁	semidirect
258. #3390	C₂×C₁₁	semidirect
259. #3389	C₂×C₁₁	semidirect
260. #3388	C₂×C₁₁	semidirect
261. #3387	C₂×C₁₁	semidirect
262. #3386	C₂×C₁₁	semidirect
263. #3385	C₂×C₁₁	semidirect
264. #3384	C₂×C₁₁	semidirect
265. #3162	C₂×C₁₁	semidirect
266. #3160	C₂×C₁₁	semidirect
267. #3076	C₂×C₁₁	semidirect
268. #3076	C₂×C₁₁	semidirect
269. C₂×#446	C₂×C₁₁	semidirect
403. #135	Q₈×C₁₁	semidirect
507. #41	C₂×Q₈×C₁₁	semidirect
529. Q₁₆	C₂×Q₈×C₁₁	semidirect
530. SD₁₆	C₂×Q₈×C₁₁	semidirect
531. D₈	C₂×Q₈×C₁₁	semidirect
534. C₂×C₈	C₂×Q₈×C₁₁	semidirect
580. C₁₁	#61365	direct (N × H)

Maximal subgroups

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

subgroup	index
Q₈×C₁₁×#41	2
C₁₁×#3390	2
C₁₁×#3389	2
C₁₁×#3388	2
C₁₁×#3387	2
C₁₁×#3386	2
C₁₁×#3385	2
C₁₁×#3384	2
C₁₁×#3162	2
C₁₁×#3160	2
C₁₁×#3076	2
C₂×C₁₁×#446	2
C₁₁×#2943	2
C₄×C₁₁×#135	2
#61365	11

Subgroups — C11×#61365 #14638558

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#61365 #14638558