Subgroups — C₁₁×#23081 #14600274

Order 2816.

662 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3076	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2962	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#2925	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#1994	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁×#1950	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁×#1938	C₂	1	2	yes	maximal
7	C₁₁×#1929	C₂	1	2	yes	maximal
8	C₁₁×#1922	C₂	1	2	yes	maximal, complemented
9	C₁₁×#1773	C₂	1	2	yes	maximal, complemented
10	C₁₁×#1767	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₁₁×#104	C₂	1	1	yes	maximal, characteristic
12	C₁₁×#533	C₂²	1	1	yes	characteristic
13	C₄×C₁₁×#41	C₂²	1	1	yes	characteristic
14	C₁₁×#479	C₄	1	2	yes	complemented
15	C₁₁×#478	C₄	1	2	yes	complemented
16	C₁₁×#477	C₄	1	1	yes	characteristic, complemented
17	C₁₁×#476	C₄	1	1	yes	characteristic, complemented
18	C₁₁×#475	C₄	1	1	yes	characteristic, complemented
19	C₁₁×#474	C₄	1	1	yes	characteristic, complemented
20	C₁₁×#446	—	2	2	no	—
21	C₁₁×#446	—	2	1	no	—
22	C₈×Q₈×C₁₁	—	2	1	no	—
23	C₁₁×#433	—	2	2	no	—
24	C₁₁×#432	—	2	1	no	—
25	C₁₁×#431	—	2	1	no	—
26	C₂×C₁₁×#108	C₂²	1	2	yes	—
27	C₁₁×#427	C₂²	1	2	yes	—
28	C₁₁×#424	C₂²	1	2	yes	—
29	C₁₁×#423	C₂²	1	1	yes	characteristic
30	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₁₁×#104	C₂²	1	1	yes	characteristic
33	C₂×C₁₁×#104	C₂²	1	1	yes	characteristic
34	C₁₁×#416	C₂²	1	2	yes	—
35	C₁₁×#408	C₂²	1	2	yes	—
36	C₁₁×#405	C₂²	1	2	yes	—
37	C₁₁×#405	C₂²	1	2	yes	—
38	C₄×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
39	C₂×C₁₁×#97	C₂²	1	2	yes	—
40	C₄³×C₁₁	C₂²	1	1	yes	characteristic
41	C₁₁×#341	C₂²	1	2	yes	—
42	C₁₁×#339	C₂²	1	1	yes	characteristic
43	C₁₁×#339	C₂²	1	2	yes	—
44	C₁₁×#339	C₂²	1	2	yes	—
45	C₁₁×#339	C₂²	1	1	yes	characteristic
46	C₁₁×#336	C₂²	1	2	yes	—
47	C₂×C₁₁×#41	C₂³	1	1	yes	characteristic
48	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
49	C₂×C₁₁×M₁₆	C₂³	1	1	yes	characteristic
50	C₂×C₁₁×M₁₆	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
52	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
53	C₁₁×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
54	C₁₁×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
55	C₁₁×#125	C₂×C₄	1	2	yes	—
56	C₁₁×C₂²⋊Q₈	—	2	1	no	—
57	C₁₁×C₂²⋊Q₈	—	2	1	no	—
58	C₄×Q₈×C₁₁	—	2	1	no	—
59	C₄×Q₈×C₁₁	—	2	1	no	—
60	C₄×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
61	C₄×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
62	C₄×D₄×C₁₁	—	2	1	no	—
63	C₄×D₄×C₁₁	—	2	1	no	—
64	C₄×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
65	C₄×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
66	C₁₁×#117	—	2	1	no	—
67	C₁₁×#117	C₂³	1	1	yes	characteristic
68	C₁₁×#117	C₂³	1	2	yes	—
69	C₂×C₄²×C₁₁	—	2	1	no	—
70	C₂×C₄²×C₁₁	—	2	1	no	—
71	C₂×C₄²×C₁₁	—	2	1	no	—
72	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
75	C₁₁×#108	—	2	4	no	—
76	C₁₁×#107	C₂×C₄	1	2	yes	—
77	C₁₁×#107	C₂×C₄	1	2	yes	—
78	C₁₁×#106	C₂×C₄	1	2	yes	—
79	C₁₁×#106	C₂×C₄	1	2	yes	—
80	C₁₁×C₄⋊C₈	—	2	2	no	—
81	C₁₁×C₄⋊C₈	—	2	2	no	—
82	C₁₁×C₄⋊C₈	—	2	1	no	—
83	C₁₁×C₄⋊C₈	—	2	1	no	—
84	C₁₁×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
85	C₁₁×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
86	C₁₁×C₄⋊C₈	C₂×C₄	1	2	yes	—
87	C₁₁×C₄⋊C₈	D₄	1	1	yes	characteristic
88	C₁₁×C₄⋊C₈	D₄	1	1	yes	characteristic
89	C₁₁×C₄⋊C₈	D₄	1	2	yes	—
90	C₁₁×#104	—	2	2	no	—
91	C₁₁×#104	—	2	2	no	—
92	C₁₁×#103	C₂×C₄	1	2	yes	—
93	C₁₁×#103	C₂×C₄	1	2	yes	—
94	C₁₁×#102	C₂×C₄	1	2	yes	—
95	C₁₁×#102	C₂×C₄	1	2	yes	—
96	C₁₁×C₂²⋊C₈	—	2	2	no	—
97	C₁₁×C₂²⋊C₈	—	2	2	no	—
98	C₁₁×#97	—	2	2	no	—
99	C₁₁×#97	—	2	2	no	—
100	C₁₁×#97	—	2	1	no	—
101	C₁₁×#97	—	2	4	no	—
102	C₄×C₈×C₁₁	—	2	2	no	—
103	C₄×C₈×C₁₁	—	2	2	no	—
104	C₄×C₈×C₁₁	—	2	1	no	—
105	#23081	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
106	C₁₁×#41	—	2	1	no	—
107	C₁₁×#41	—	2	1	no	—
108	C₁₁×#41	—	2	1	no	—
109	C₁₁×#41	—	2	1	no	—
110	C₂×Q₈×C₁₁	—	2	1	no	—
111	C₂×Q₈×C₁₁	—	2	1	no	—
112	C₂×Q₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
113	C₂×D₄×C₁₁	—	2	1	no	—
114	C₂×D₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₁	—	2	1	no	—
116	C₂²×C₄×C₁₁	—	2	1	no	—
117	C₂²×C₄×C₁₁	—	2	1	no	—
118	C₂²×C₄×C₁₁	—	2	1	no	—
119	C₂²×C₄×C₁₁	—	2	1	no	—
120	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
121	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
122	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
123	C₁₁×M₁₆	—	2	1	no	—
124	C₁₁×M₁₆	—	2	2	no	—
125	C₁₁×M₁₆	—	2	1	no	—
126	C₁₁×M₁₆	—	2	1	no	—
127	C₁₁×M₁₆	—	2	2	no	—
128	C₁₁×M₁₆	#41	1	2	yes	—
129	C₂×C₈×C₁₁	—	2	1	no	—
130	C₂×C₈×C₁₁	—	2	2	no	—
131	C₂×C₈×C₁₁	—	2	1	no	—
132	C₂×C₈×C₁₁	—	2	2	no	—
133	C₂×C₈×C₁₁	—	2	2	no	—
134	C₂×C₈×C₁₁	—	2	2	no	—
135	C₂×C₈×C₁₁	—	2	2	no	—
136	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
137	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
138	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
139	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
140	C₁₁×C₄⋊C₄	—	2	1	no	—
141	C₁₁×C₄⋊C₄	—	2	1	no	—
142	C₁₁×C₄⋊C₄	—	2	2	no	—
143	C₁₁×C₄⋊C₄	—	2	2	no	—
144	C₁₁×C₄⋊C₄	—	2	1	no	—
145	C₁₁×C₄⋊C₄	—	2	1	no	—
146	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
147	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
148	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
149	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
150	C₁₁×C₂²⋊C₄	—	2	1	no	—
151	C₁₁×C₂²⋊C₄	—	2	2	no	—
152	C₁₁×C₂²⋊C₄	—	2	1	no	—
153	C₁₁×C₂²⋊C₄	—	2	1	no	—
154	C₄²×C₁₁	—	2	1	no	—
155	C₄²×C₁₁	—	2	1	no	—
156	C₄²×C₁₁	—	2	1	no	—
157	C₄²×C₁₁	—	2	2	no	—
158	C₄²×C₁₁	—	2	1	no	—
159	C₄²×C₁₁	—	2	1	no	—
160	C₄²×C₁₁	—	2	1	no	—
161	C₄²×C₁₁	—	4	2	no	—
162	C₄²×C₁₁	—	4	2	no	—
163	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
164	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
165	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
166	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
167	C₄²×C₁₁	#41	1	2	yes	—
168	#3076	C₂×C₁₁	1	1	yes	characteristic
169	#2962	C₂×C₁₁	1	1	yes	characteristic, complemented
170	#2925	C₂×C₁₁	1	1	yes	characteristic
171	#1994	C₂×C₁₁	1	1	yes	characteristic, complemented
172	#1950	C₂×C₁₁	1	1	yes	characteristic, complemented
173	#1938	C₂×C₁₁	1	2	yes	—
174	#1929	C₂×C₁₁	1	2	yes	—
175	#1922	C₂×C₁₁	1	2	yes	complemented
176	#1773	C₂×C₁₁	1	2	yes	complemented
177	#1767	C₂×C₁₁	1	1	yes	characteristic, complemented
178	C₄×#104	C₂×C₁₁	1	1	yes	characteristic
179	C₂³×C₁₁	—	2	1	no	—
180	C₂³×C₁₁	C₂×#41	1	1	yes	characteristic
181	Q₈×C₁₁	—	2	1	no	—
182	Q₈×C₁₁	—	2	1	no	—
183	Q₈×C₁₁	—	4	2	no	—
184	Q₈×C₁₁	—	8	1	no	—
185	D₄×C₁₁	—	2	1	no	—
186	D₄×C₁₁	—	2	1	no	—
187	D₄×C₁₁	—	4	1	no	—
188	D₄×C₁₁	—	4	1	no	—
189	C₂×C₄×C₁₁	—	2	2	no	—
190	C₂×C₄×C₁₁	—	2	2	no	—
191	C₂×C₄×C₁₁	—	2	1	no	—
192	C₂×C₄×C₁₁	—	2	1	no	—
193	C₂×C₄×C₁₁	—	2	1	no	—
194	C₂×C₄×C₁₁	—	2	2	no	—
195	C₂×C₄×C₁₁	—	2	2	no	—
196	C₂×C₄×C₁₁	—	2	2	no	—
197	C₂×C₄×C₁₁	—	4	1	no	—
198	C₂×C₄×C₁₁	—	4	1	no	—
199	C₂×C₄×C₁₁	—	4	1	no	—
200	C₂×C₄×C₁₁	—	4	1	no	—
201	C₂×C₄×C₁₁	—	4	1	no	—
202	C₂×C₄×C₁₁	—	4	1	no	—
203	C₂×C₄×C₁₁	—	4	1	no	—
204	C₂×C₄×C₁₁	—	4	2	no	—
205	C₂×C₄×C₁₁	—	8	1	no	—
206	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
207	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
208	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
209	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
210	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
211	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
213	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
214	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
215	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
216	C₈×C₁₁	—	2	2	no	—
217	C₈×C₁₁	—	2	2	no	—
218	C₈×C₁₁	—	2	2	no	—
219	C₈×C₁₁	—	2	2	no	—
220	C₈×C₁₁	—	2	2	no	—
221	C₈×C₁₁	—	4	1	no	—
222	C₈×C₁₁	—	4	2	no	—
223	#533	C₂²×C₁₁	1	1	yes	characteristic
224	C₄×#41	C₂²×C₁₁	1	1	yes	characteristic
225	#479	C₄×C₁₁	1	2	yes	complemented
226	#478	C₄×C₁₁	1	2	yes	complemented
227	#477	C₄×C₁₁	1	1	yes	characteristic, complemented
228	#476	C₄×C₁₁	1	1	yes	characteristic, complemented
229	#475	C₄×C₁₁	1	1	yes	characteristic, complemented
230	#474	C₄×C₁₁	1	1	yes	characteristic, complemented
231	#446	—	2	2	no	—
232	#446	—	2	1	no	—
233	C₈×Q₈	—	2	1	no	—
234	#433	—	2	2	no	—
235	#432	—	2	1	no	—
236	#431	—	2	1	no	—
237	C₂×#108	C₂²×C₁₁	1	2	yes	—
238	#427	C₂²×C₁₁	1	2	yes	—
239	#424	C₂²×C₁₁	1	2	yes	—
240	#423	C₂²×C₁₁	1	1	yes	characteristic
241	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
242	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
243	C₂×#104	C₂²×C₁₁	1	1	yes	characteristic
244	C₂×#104	C₂²×C₁₁	1	1	yes	characteristic
245	#416	C₂²×C₁₁	1	2	yes	—
246	#408	C₂²×C₁₁	1	2	yes	—
247	#405	C₂²×C₁₁	1	2	yes	—
248	#405	C₂²×C₁₁	1	2	yes	—
249	C₄×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
250	C₂×#97	C₂²×C₁₁	1	2	yes	—
251	C₄³	C₂²×C₁₁	1	1	yes	characteristic
252	#341	C₂²×C₁₁	1	2	yes	—
253	#339	C₂²×C₁₁	1	1	yes	characteristic
254	#339	C₂²×C₁₁	1	2	yes	—
255	#339	C₂²×C₁₁	1	2	yes	—
256	#339	C₂²×C₁₁	1	1	yes	characteristic
257	#336	C₂²×C₁₁	1	2	yes	—
258	C₂²×C₁₁	—	2	1	no	—
259	C₂²×C₁₁	—	2	1	no	—
260	C₂²×C₁₁	—	4	1	no	—
261	C₂²×C₁₁	—	4	1	no	—
262	C₂²×C₁₁	—	4	1	no	—
263	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
264	C₂²×C₁₁	#552	1	1	yes	characteristic
265	C₂²×C₁₁	#556	1	1	yes	characteristic
266	C₄×C₁₁	—	2	1	no	—
267	C₄×C₁₁	—	2	1	no	—
268	C₄×C₁₁	—	2	1	no	—
269	C₄×C₁₁	—	4	2	no	—
270	C₄×C₁₁	—	4	2	no	—
271	C₄×C₁₁	—	4	1	no	—
272	C₄×C₁₁	—	4	1	no	—
273	C₄×C₁₁	—	4	2	no	—
274	C₄×C₁₁	—	4	1	no	—
275	C₄×C₁₁	—	4	2	no	—
276	C₄×C₁₁	#444	1	2	yes	—
277	C₄×C₁₁	C₄×#41	1	1	yes	characteristic
278	C₄×C₁₁	#519	1	1	yes	characteristic
279	C₄×C₁₁	#547	1	1	yes	characteristic
280	C₄×C₁₁	#548	1	1	yes	characteristic
281	C₂×#41	C₂³×C₁₁	1	1	yes	characteristic
282	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
283	C₂×M₁₆	C₂³×C₁₁	1	1	yes	characteristic
284	C₂×M₁₆	C₂³×C₁₁	1	1	yes	characteristic
285	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
286	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
287	C₄⋊Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
288	C₄⋊Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
289	#125	C₂×C₄×C₁₁	1	2	yes	—
290	C₂²⋊Q₈	—	2	1	no	—
291	C₂²⋊Q₈	—	2	1	no	—
292	C₄×Q₈	—	2	1	no	—
293	C₄×Q₈	—	2	1	no	—
294	C₄×Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
295	C₄×Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
296	C₄×D₄	—	2	1	no	—
297	C₄×D₄	—	2	1	no	—
298	C₄×D₄	C₂×C₄×C₁₁	1	1	yes	characteristic
299	C₄×D₄	C₂×C₄×C₁₁	1	1	yes	characteristic
300	#117	—	2	1	no	—
301	#117	C₂³×C₁₁	1	1	yes	characteristic
302	#117	C₂³×C₁₁	1	2	yes	—
303	C₂×C₄²	—	2	1	no	—
304	C₂×C₄²	—	2	1	no	—
305	C₂×C₄²	—	2	1	no	—
306	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
307	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
308	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
309	#108	—	2	4	no	—
310	#107	C₂×C₄×C₁₁	1	2	yes	—
311	#107	C₂×C₄×C₁₁	1	2	yes	—
312	#106	C₂×C₄×C₁₁	1	2	yes	—
313	#106	C₂×C₄×C₁₁	1	2	yes	—
314	C₄⋊C₈	—	2	2	no	—
315	C₄⋊C₈	—	2	2	no	—
316	C₄⋊C₈	—	2	1	no	—
317	C₄⋊C₈	—	2	1	no	—
318	C₄⋊C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
319	C₄⋊C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
320	C₄⋊C₈	C₂×C₄×C₁₁	1	2	yes	—
321	C₄⋊C₈	D₄×C₁₁	1	1	yes	characteristic
322	C₄⋊C₈	D₄×C₁₁	1	1	yes	characteristic
323	C₄⋊C₈	D₄×C₁₁	1	2	yes	—
324	#104	—	2	2	no	—
325	#104	—	2	2	no	—
326	#103	C₂×C₄×C₁₁	1	2	yes	—
327	#103	C₂×C₄×C₁₁	1	2	yes	—
328	#102	C₂×C₄×C₁₁	1	2	yes	—
329	#102	C₂×C₄×C₁₁	1	2	yes	—
330	C₂²⋊C₈	—	2	2	no	—
331	C₂²⋊C₈	—	2	2	no	—
332	#97	—	2	2	no	—
333	#97	—	2	2	no	—
334	#97	—	2	1	no	—
335	#97	—	2	4	no	—
336	C₄×C₈	—	2	2	no	—
337	C₄×C₈	—	2	2	no	—
338	C₄×C₈	—	2	1	no	—
339	C₂×C₁₁	—	2	1	no	—
340	C₂×C₁₁	—	2	1	no	—
341	C₂×C₁₁	—	8	1	no	—
342	C₂×C₁₁	#2362	1	1	yes	characteristic
343	C₂×C₁₁	C₂×#444	1	1	yes	characteristic
344	C₂×C₁₁	#2956	1	1	yes	characteristic
345	#41	—	2	1	no	—
346	#41	—	2	1	no	—
347	#41	—	2	1	no	—
348	#41	—	2	1	no	—
349	C₂×Q₈	—	2	1	no	—
350	C₂×Q₈	—	2	1	no	—
351	C₂×Q₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
352	C₂×D₄	—	2	1	no	—
353	C₂×D₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
360	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
361	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
362	M₁₆	—	2	1	no	—
363	M₁₆	—	2	1	no	—
364	M₁₆	—	2	2	no	—
365	M₁₆	—	2	1	no	—
366	M₁₆	—	2	2	no	—
367	M₁₆	C₁₁×#41	1	2	yes	—
368	C₂×C₈	—	2	1	no	—
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	2	1	no	—
375	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
376	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
377	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
378	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
379	C₄⋊C₄	—	2	1	no	—
380	C₄⋊C₄	—	2	1	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	2	1	no	—
384	C₄⋊C₄	—	2	1	no	—
385	C₄⋊C₄	C₂²×C₄×C₁₁	1	2	yes	—
386	C₄⋊C₄	C₂²×C₄×C₁₁	1	2	yes	—
387	C₄⋊C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
388	C₄⋊C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
389	C₂²⋊C₄	—	2	1	no	—
390	C₂²⋊C₄	—	2	2	no	—
391	C₂²⋊C₄	—	2	1	no	—
392	C₂²⋊C₄	—	2	1	no	—
393	C₄²	—	2	1	no	—
394	C₄²	—	2	1	no	—
395	C₄²	—	2	1	no	—
396	C₄²	—	2	2	no	—
397	C₄²	—	2	1	no	—
398	C₄²	—	2	1	no	—
399	C₄²	—	2	1	no	—
400	C₄²	—	4	2	no	—
401	C₄²	—	4	2	no	—
402	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
403	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
404	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
405	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
406	C₄²	C₁₁×#41	1	2	yes	—
407	C₁₁	#23081	1	1	yes	characteristic, direct product factor, Sylow
408	C₂³	—	2	1	no	—
409	C₂³	C₂×C₁₁×#41	1	1	yes	characteristic
410	Q₈	—	2	1	no	—
411	Q₈	—	2	1	no	—
412	Q₈	—	4	2	no	—
413	Q₈	—	8	1	no	—
414	D₄	—	2	1	no	—
415	D₄	—	2	1	no	—
416	D₄	—	4	1	no	—
417	D₄	—	4	1	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	8	1	no	—
435	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
436	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
437	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
438	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
439	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
440	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
441	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
442	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
443	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
444	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
445	C₈	—	2	2	no	—
446	C₈	—	2	2	no	—
447	C₈	—	2	2	no	—
448	C₈	—	2	2	no	—
449	C₈	—	2	2	no	—
450	C₈	—	4	1	no	—
451	C₈	—	4	2	no	—
452	C₂²	—	2	1	no	—
453	C₂²	—	2	1	no	—
454	C₂²	—	4	1	no	—
455	C₂²	—	4	1	no	—
456	C₂²	—	4	1	no	—
457	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
458	C₂²	C₁₁×#552	1	1	yes	characteristic
459	C₂²	C₁₁×#556	1	1	yes	characteristic
460	C₄	—	2	1	no	—
461	C₄	—	2	1	no	—
462	C₄	—	2	1	no	—
463	C₄	—	4	2	no	—
464	C₄	—	4	2	no	—
465	C₄	—	4	1	no	—
466	C₄	—	4	2	no	—
467	C₄	—	4	1	no	—
468	C₄	—	4	2	no	—
469	C₄	—	4	1	no	—
470	C₄	C₁₁×#444	1	2	yes	—
471	C₄	C₄×C₁₁×#41	1	1	yes	characteristic
472	C₄	C₁₁×#519	1	1	yes	characteristic
473	C₄	C₁₁×#547	1	1	yes	characteristic
474	C₄	C₁₁×#548	1	1	yes	characteristic
475	C₂	—	2	1	no	—
476	C₂	—	2	1	no	—
477	C₂	—	8	1	no	—
478	C₂	C₁₁×#2362	1	1	yes	characteristic
479	C₂	C₂×C₁₁×#444	1	1	yes	characteristic
480	C₂	C₁₁×#2956	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
socle	C₂²×C₁₁	C₂×C₄×D₄
prime radical	C₂×C₁₁×#41	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₁₁×C₄⋊C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₁×#2962	C₂	semidirect
4. C₁₁×#1994	C₂	semidirect
5. C₁₁×#1950	C₂	semidirect
8. C₁₁×#1922	C₂	semidirect
9. C₁₁×#1773	C₂	semidirect
10. C₁₁×#1767	C₂	semidirect
14. C₁₁×#479	C₄	semidirect
15. C₁₁×#478	C₄	semidirect
16. C₁₁×#477	C₄	semidirect
17. C₁₁×#476	C₄	semidirect
18. C₁₁×#475	C₄	semidirect
19. C₁₁×#474	C₄	semidirect
105. #23081	C₁₁	direct (N × H)
169. #2962	C₂×C₁₁	semidirect
171. #1994	C₂×C₁₁	semidirect
172. #1950	C₂×C₁₁	semidirect
175. #1922	C₂×C₁₁	semidirect
176. #1773	C₂×C₁₁	semidirect
177. #1767	C₂×C₁₁	semidirect
225. #479	C₄×C₁₁	semidirect
226. #478	C₄×C₁₁	semidirect
227. #477	C₄×C₁₁	semidirect
228. #476	C₄×C₁₁	semidirect
229. #475	C₄×C₁₁	semidirect
230. #474	C₄×C₁₁	semidirect
407. C₁₁	#23081	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×#3076	2
C₁₁×#2962	2
C₁₁×#2925	2
C₁₁×#1994	2
C₁₁×#1950	2
C₁₁×#1938	2
C₁₁×#1929	2
C₁₁×#1922	2
C₁₁×#1773	2
C₁₁×#1767	2
C₄×C₁₁×#104	2
#23081	11

Subgroups — C11×#23081 #14600274

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#23081 #14600274