Subgroups — C₁₁×#22130 #14599323

Order 2816.

648 conjugacy classes of subgroups.

The subgroup lattice has 490 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×#2960	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#2922	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#1986	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁×#1950	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁×#1945	C₂	1	2	yes	maximal, complemented
7	C₁₁×#1937	C₂	1	2	yes	maximal
8	C₁₁×#1929	C₂	1	2	yes	maximal
9	C₁₁×#1922	C₂	1	2	yes	maximal, complemented
10	C₁₁×#1806	C₂	1	1	yes	maximal, characteristic
11	C₈×C₁₁×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
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	1	no	—
21	C₁₁×#446	—	2	1	no	—
22	C₈×Q₈×C₁₁	—	2	1	no	—
23	C₈×Q₈×C₁₁	—	2	1	no	—
24	C₁₁×#433	—	2	1	no	—
25	C₁₁×#433	—	2	1	no	—
26	C₁₁×#431	—	2	1	no	—
27	C₁₁×#431	—	2	1	no	—
28	C₂×C₁₁×#108	C₂²	1	2	yes	—
29	C₁₁×#427	C₂²	1	2	yes	—
30	C₁₁×#424	C₂²	1	1	yes	characteristic
31	C₁₁×#424	C₂²	1	1	yes	characteristic
32	C₁₁×#424	C₂²	1	2	yes	—
33	C₁₁×#423	C₂²	1	1	yes	characteristic
34	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
35	C₂×C₁₁×#104	C₂²	1	2	yes	—
36	C₁₁×#416	C₂²	1	2	yes	—
37	C₁₁×#408	C₂²	1	1	yes	characteristic
38	C₁₁×#408	C₂²	1	1	yes	characteristic
39	C₁₁×#405	C₂²	1	2	yes	—
40	C₄×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
42	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
43	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
44	C₁₁×#341	C₂²	1	2	yes	—
45	C₁₁×#339	C₂²	1	2	yes	—
46	C₁₁×#339	C₂²	1	2	yes	—
47	C₁₁×#339	C₂²	1	2	yes	—
48	C₁₁×#336	C₂²	1	2	yes	—
49	C₂×C₁₁×#41	C₂³	1	1	yes	characteristic
50	C₂×C₁₁×M₁₆	C₂³	1	1	yes	characteristic
51	C₂×C₁₁×M₁₆	C₂³	1	1	yes	characteristic
52	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
53	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
54	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
56	C₁₁×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
57	C₁₁×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
58	C₁₁×#125	C₂×C₄	1	2	yes	—
59	C₁₁×C₂²⋊Q₈	—	2	1	no	—
60	C₁₁×C₂²⋊Q₈	—	2	1	no	—
61	C₄×Q₈×C₁₁	—	2	1	no	—
62	C₄×Q₈×C₁₁	—	2	1	no	—
63	C₄×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
64	C₄×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
65	C₄×D₄×C₁₁	—	2	1	no	—
66	C₄×D₄×C₁₁	—	2	1	no	—
67	C₄×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
68	C₄×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
69	C₁₁×#117	—	2	1	no	—
70	C₁₁×#117	C₂³	1	1	yes	characteristic
71	C₁₁×#117	C₂³	1	2	yes	—
72	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
73	C₂×C₄²×C₁₁	—	2	1	no	—
74	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
75	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
76	C₁₁×#108	—	4	2	no	—
77	C₁₁×#107	C₂×C₄	1	2	yes	—
78	C₁₁×#107	C₂×C₄	1	2	yes	—
79	C₁₁×#106	C₂×C₄	1	2	yes	—
80	C₁₁×#106	C₂×C₄	1	2	yes	—
81	C₁₁×C₄⋊C₈	—	2	1	no	—
82	C₁₁×C₄⋊C₈	—	2	1	no	—
83	C₁₁×C₄⋊C₈	—	2	1	no	—
84	C₁₁×C₄⋊C₈	—	2	1	no	—
85	C₁₁×C₄⋊C₈	—	2	2	no	—
86	C₁₁×C₄⋊C₈	—	2	2	no	—
87	C₁₁×C₄⋊C₈	—	2	1	no	—
88	C₁₁×C₄⋊C₈	—	2	1	no	—
89	C₁₁×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
90	C₁₁×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
91	C₁₁×C₄⋊C₈	C₂×C₄	1	2	yes	—
92	C₁₁×#104	—	4	2	no	—
93	C₁₁×#103	C₂×C₄	1	2	yes	—
94	C₁₁×#103	C₂×C₄	1	2	yes	—
95	C₁₁×#102	C₂×C₄	1	2	yes	—
96	C₁₁×#102	C₂×C₄	1	2	yes	—
97	C₁₁×C₂²⋊C₈	—	2	1	no	—
98	C₁₁×C₂²⋊C₈	—	2	1	no	—
99	C₁₁×C₂²⋊C₈	—	2	1	no	—
100	C₁₁×C₂²⋊C₈	—	2	1	no	—
101	C₁₁×#97	—	2	2	no	—
102	C₁₁×#97	—	2	1	no	—
103	C₄×C₈×C₁₁	—	2	2	no	—
104	C₄×C₈×C₁₁	—	2	1	no	—
105	C₄×C₈×C₁₁	—	4	2	no	—
106	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
107	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
108	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
109	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
110	C₁₁×#95	—	2	1	no	—
111	#22130	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
112	C₁₁×#41	—	2	1	no	—
113	C₁₁×#41	—	2	1	no	—
114	C₁₁×#41	—	2	1	no	—
115	C₁₁×#41	—	2	1	no	—
116	C₂×Q₈×C₁₁	—	2	1	no	—
117	C₂×Q₈×C₁₁	—	2	1	no	—
118	C₂×Q₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
119	C₂×D₄×C₁₁	—	2	1	no	—
120	C₂×D₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₁	—	2	2	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	#41	1	1	yes	characteristic
126	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
127	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
128	C₁₁×M₁₆	—	2	2	no	—
129	C₁₁×M₁₆	—	2	1	no	—
130	C₁₁×M₁₆	—	2	1	no	—
131	C₁₁×M₁₆	—	2	1	no	—
132	C₁₁×M₁₆	—	2	2	no	—
133	C₁₁×M₁₆	—	2	1	no	—
134	C₂×C₈×C₁₁	—	2	1	no	—
135	C₂×C₈×C₁₁	—	2	1	no	—
136	C₂×C₈×C₁₁	—	2	2	no	—
137	C₂×C₈×C₁₁	—	2	1	no	—
138	C₂×C₈×C₁₁	—	2	2	no	—
139	C₂×C₈×C₁₁	—	2	1	no	—
140	C₂×C₈×C₁₁	—	2	1	no	—
141	C₂×C₈×C₁₁	—	2	2	no	—
142	C₂×C₈×C₁₁	—	2	1	no	—
143	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
144	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
145	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
146	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
147	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
148	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
149	C₁₁×C₄⋊C₄	—	2	4	no	—
150	C₁₁×C₄⋊C₄	—	2	1	no	—
151	C₁₁×C₄⋊C₄	—	2	1	no	—
152	C₁₁×C₄⋊C₄	—	2	2	no	—
153	C₁₁×C₄⋊C₄	—	2	2	no	—
154	C₁₁×C₄⋊C₄	—	2	1	no	—
155	C₁₁×C₄⋊C₄	—	2	1	no	—
156	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
157	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
158	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
159	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
160	C₁₁×C₂²⋊C₄	—	2	1	no	—
161	C₁₁×C₂²⋊C₄	—	2	2	no	—
162	C₁₁×C₂²⋊C₄	—	2	1	no	—
163	C₁₁×C₂²⋊C₄	—	2	1	no	—
164	C₄²×C₁₁	—	2	1	no	—
165	C₄²×C₁₁	—	2	1	no	—
166	C₄²×C₁₁	—	2	2	no	—
167	C₄²×C₁₁	—	2	1	no	—
168	C₄²×C₁₁	—	2	2	no	—
169	C₄²×C₁₁	—	2	2	no	—
170	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
171	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
172	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
173	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
174	#3076	C₂×C₁₁	1	1	yes	characteristic
175	#2960	C₂×C₁₁	1	1	yes	characteristic, complemented
176	#2922	C₂×C₁₁	1	1	yes	characteristic
177	#1986	C₂×C₁₁	1	1	yes	characteristic, complemented
178	#1950	C₂×C₁₁	1	1	yes	characteristic, complemented
179	#1945	C₂×C₁₁	1	2	yes	complemented
180	#1937	C₂×C₁₁	1	2	yes	—
181	#1929	C₂×C₁₁	1	2	yes	—
182	#1922	C₂×C₁₁	1	2	yes	complemented
183	#1806	C₂×C₁₁	1	1	yes	characteristic
184	C₈×C₄⋊C₄	C₂×C₁₁	1	1	yes	characteristic, complemented
185	C₂³×C₁₁	—	2	1	no	—
186	C₂³×C₁₁	C₂×#41	1	1	yes	characteristic
187	Q₈×C₁₁	—	2	1	no	—
188	Q₈×C₁₁	—	2	1	no	—
189	Q₈×C₁₁	—	4	2	no	—
190	Q₈×C₁₁	—	4	2	no	—
191	D₄×C₁₁	—	2	1	no	—
192	D₄×C₁₁	—	2	1	no	—
193	D₄×C₁₁	—	4	1	no	—
194	D₄×C₁₁	—	4	1	no	—
195	C₂×C₄×C₁₁	—	2	2	no	—
196	C₂×C₄×C₁₁	—	2	4	no	—
197	C₂×C₄×C₁₁	—	2	1	no	—
198	C₂×C₄×C₁₁	—	2	1	no	—
199	C₂×C₄×C₁₁	—	2	1	no	—
200	C₂×C₄×C₁₁	—	2	2	no	—
201	C₂×C₄×C₁₁	—	2	2	no	—
202	C₂×C₄×C₁₁	—	4	1	no	—
203	C₂×C₄×C₁₁	—	4	2	no	—
204	C₂×C₄×C₁₁	—	4	2	no	—
205	C₂×C₄×C₁₁	—	4	2	no	—
206	C₂×C₄×C₁₁	—	4	1	no	—
207	C₂×C₄×C₁₁	—	4	1	no	—
208	C₂×C₄×C₁₁	—	4	2	no	—
209	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
210	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
211	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
212	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
213	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
214	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
215	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
216	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
217	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
218	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
219	C₈×C₁₁	—	2	2	no	—
220	C₈×C₁₁	—	2	2	no	—
221	C₈×C₁₁	—	2	1	no	—
222	C₈×C₁₁	—	2	1	no	—
223	C₈×C₁₁	—	2	1	no	—
224	C₈×C₁₁	—	2	1	no	—
225	C₈×C₁₁	—	4	1	no	—
226	C₈×C₁₁	—	4	1	no	—
227	C₈×C₁₁	—	4	2	no	—
228	#533	C₂²×C₁₁	1	1	yes	characteristic
229	C₄×#41	C₂²×C₁₁	1	1	yes	characteristic
230	#479	C₄×C₁₁	1	2	yes	complemented
231	#478	C₄×C₁₁	1	2	yes	complemented
232	#477	C₄×C₁₁	1	1	yes	characteristic, complemented
233	#476	C₄×C₁₁	1	1	yes	characteristic, complemented
234	#475	C₄×C₁₁	1	1	yes	characteristic, complemented
235	#474	C₄×C₁₁	1	1	yes	characteristic, complemented
236	#446	—	2	1	no	—
237	#446	—	2	1	no	—
238	C₈×Q₈	—	2	1	no	—
239	C₈×Q₈	—	2	1	no	—
240	#433	—	2	1	no	—
241	#433	—	2	1	no	—
242	#431	—	2	1	no	—
243	#431	—	2	1	no	—
244	C₂×#108	C₂²×C₁₁	1	2	yes	—
245	#427	C₂²×C₁₁	1	2	yes	—
246	#424	C₂²×C₁₁	1	1	yes	characteristic
247	#424	C₂²×C₁₁	1	1	yes	characteristic
248	#424	C₂²×C₁₁	1	2	yes	—
249	#423	C₂²×C₁₁	1	1	yes	characteristic
250	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
251	C₂×#104	C₂²×C₁₁	1	2	yes	—
252	#416	C₂²×C₁₁	1	2	yes	—
253	#408	C₂²×C₁₁	1	1	yes	characteristic
254	#408	C₂²×C₁₁	1	1	yes	characteristic
255	#405	C₂²×C₁₁	1	2	yes	—
256	C₄×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
257	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	—
258	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
259	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
260	#341	C₂²×C₁₁	1	2	yes	—
261	#339	C₂²×C₁₁	1	2	yes	—
262	#339	C₂²×C₁₁	1	2	yes	—
263	#339	C₂²×C₁₁	1	2	yes	—
264	#336	C₂²×C₁₁	1	2	yes	—
265	C₂²×C₁₁	—	2	1	no	—
266	C₂²×C₁₁	—	2	1	no	—
267	C₂²×C₁₁	—	4	1	no	—
268	C₂²×C₁₁	—	4	1	no	—
269	C₂²×C₁₁	—	4	1	no	—
270	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
271	C₂²×C₁₁	#541	1	1	yes	characteristic
272	C₂²×C₁₁	#542	1	1	yes	characteristic
273	C₄×C₁₁	—	2	1	no	—
274	C₄×C₁₁	—	2	1	no	—
275	C₄×C₁₁	—	2	1	no	—
276	C₄×C₁₁	—	4	4	no	—
277	C₄×C₁₁	—	4	1	no	—
278	C₄×C₁₁	—	4	1	no	—
279	C₄×C₁₁	—	4	2	no	—
280	C₄×C₁₁	—	4	1	no	—
281	C₄×C₁₁	—	4	2	no	—
282	C₄×C₁₁	#443	1	2	yes	—
283	C₄×C₁₁	#519	1	1	yes	characteristic
284	C₄×C₁₁	#520	1	1	yes	characteristic
285	C₄×C₁₁	#536	1	1	yes	characteristic
286	C₄×C₁₁	#537	1	1	yes	characteristic
287	C₂×#41	C₂³×C₁₁	1	1	yes	characteristic
288	C₂×M₁₆	C₂³×C₁₁	1	1	yes	characteristic
289	C₂×M₁₆	C₂³×C₁₁	1	1	yes	characteristic
290	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
291	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
292	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
293	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
294	C₄⋊Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
295	C₄⋊Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
296	#125	C₂×C₄×C₁₁	1	2	yes	—
297	C₂²⋊Q₈	—	2	1	no	—
298	C₂²⋊Q₈	—	2	1	no	—
299	C₄×Q₈	—	2	1	no	—
300	C₄×Q₈	—	2	1	no	—
301	C₄×Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
302	C₄×Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
303	C₄×D₄	—	2	1	no	—
304	C₄×D₄	—	2	1	no	—
305	C₄×D₄	C₂×C₄×C₁₁	1	1	yes	characteristic
306	C₄×D₄	C₂×C₄×C₁₁	1	1	yes	characteristic
307	#117	—	2	1	no	—
308	#117	C₂³×C₁₁	1	1	yes	characteristic
309	#117	C₂³×C₁₁	1	2	yes	—
310	C₂×C₄⋊C₄	—	2	1	no	—
311	C₂×C₄²	—	2	1	no	—
312	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
313	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
314	#108	—	4	2	no	—
315	#107	C₂×C₄×C₁₁	1	2	yes	—
316	#107	C₂×C₄×C₁₁	1	2	yes	—
317	#106	C₂×C₄×C₁₁	1	2	yes	—
318	#106	C₂×C₄×C₁₁	1	2	yes	—
319	C₄⋊C₈	—	2	1	no	—
320	C₄⋊C₈	—	2	1	no	—
321	C₄⋊C₈	—	2	1	no	—
322	C₄⋊C₈	—	2	1	no	—
323	C₄⋊C₈	—	2	2	no	—
324	C₄⋊C₈	—	2	2	no	—
325	C₄⋊C₈	—	2	1	no	—
326	C₄⋊C₈	—	2	1	no	—
327	C₄⋊C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
328	C₄⋊C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
329	C₄⋊C₈	C₂×C₄×C₁₁	1	2	yes	—
330	#104	—	4	2	no	—
331	#103	C₂×C₄×C₁₁	1	2	yes	—
332	#103	C₂×C₄×C₁₁	1	2	yes	—
333	#102	C₂×C₄×C₁₁	1	2	yes	—
334	#102	C₂×C₄×C₁₁	1	2	yes	—
335	C₂²⋊C₈	—	2	1	no	—
336	C₂²⋊C₈	—	2	1	no	—
337	C₂²⋊C₈	—	2	1	no	—
338	C₂²⋊C₈	—	2	1	no	—
339	#97	—	2	2	no	—
340	#97	—	2	1	no	—
341	C₄×C₈	—	2	2	no	—
342	C₄×C₈	—	2	1	no	—
343	C₄×C₈	—	4	2	no	—
344	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
345	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
346	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
347	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
348	#95	—	2	1	no	—
349	C₂×C₁₁	—	2	1	no	—
350	C₂×C₁₁	—	2	1	no	—
351	C₂×C₁₁	—	8	1	no	—
352	C₂×C₁₁	#2323	1	1	yes	characteristic
353	C₂×C₁₁	C₂×#443	1	1	yes	characteristic
354	C₂×C₁₁	#2955	1	1	yes	characteristic
355	#41	—	2	1	no	—
356	#41	—	2	1	no	—
357	#41	—	2	1	no	—
358	#41	—	2	1	no	—
359	C₂×Q₈	—	2	1	no	—
360	C₂×Q₈	—	2	1	no	—
361	C₂×Q₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
362	C₂×D₄	—	2	1	no	—
363	C₂×D₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
369	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
370	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
371	M₁₆	—	2	2	no	—
372	M₁₆	—	2	1	no	—
373	M₁₆	—	2	1	no	—
374	M₁₆	—	2	1	no	—
375	M₁₆	—	2	1	no	—
376	M₁₆	—	2	2	no	—
377	C₂×C₈	—	2	1	no	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	—	2	2	no	—
380	C₂×C₈	—	2	1	no	—
381	C₂×C₈	—	2	1	no	—
382	C₂×C₈	—	2	1	no	—
383	C₂×C₈	—	2	1	no	—
384	C₂×C₈	—	2	1	no	—
385	C₂×C₈	—	2	2	no	—
386	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
387	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
388	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
389	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
390	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
391	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
392	C₄⋊C₄	—	2	4	no	—
393	C₄⋊C₄	—	2	1	no	—
394	C₄⋊C₄	—	2	1	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	—	2	1	no	—
398	C₄⋊C₄	—	2	1	no	—
399	C₄⋊C₄	C₂²×C₄×C₁₁	1	2	yes	—
400	C₄⋊C₄	C₂²×C₄×C₁₁	1	2	yes	—
401	C₄⋊C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
402	C₄⋊C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
403	C₂²⋊C₄	—	2	1	no	—
404	C₂²⋊C₄	—	2	2	no	—
405	C₂²⋊C₄	—	2	1	no	—
406	C₂²⋊C₄	—	2	1	no	—
407	C₄²	—	2	1	no	—
408	C₄²	—	2	1	no	—
409	C₄²	—	2	2	no	—
410	C₄²	—	2	1	no	—
411	C₄²	—	2	2	no	—
412	C₄²	—	2	2	no	—
413	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
414	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
415	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
416	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
417	C₁₁	#22130	1	1	yes	characteristic, direct product factor, Sylow
418	C₂³	—	2	1	no	—
419	C₂³	C₂×C₁₁×#41	1	1	yes	characteristic
420	Q₈	—	2	1	no	—
421	Q₈	—	2	1	no	—
422	Q₈	—	4	2	no	—
423	Q₈	—	4	2	no	—
424	D₄	—	2	1	no	—
425	D₄	—	2	1	no	—
426	D₄	—	4	1	no	—
427	D₄	—	4	1	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	4	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
443	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
444	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
445	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
446	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
447	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
448	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
449	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
450	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
451	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
452	C₈	—	2	2	no	—
453	C₈	—	2	2	no	—
454	C₈	—	2	1	no	—
455	C₈	—	2	1	no	—
456	C₈	—	2	1	no	—
457	C₈	—	2	1	no	—
458	C₈	—	4	1	no	—
459	C₈	—	4	1	no	—
460	C₈	—	4	2	no	—
461	C₂²	—	2	1	no	—
462	C₂²	—	2	1	no	—
463	C₂²	—	4	1	no	—
464	C₂²	—	4	1	no	—
465	C₂²	—	4	1	no	—
466	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
467	C₂²	C₁₁×#541	1	1	yes	characteristic
468	C₂²	C₁₁×#542	1	1	yes	characteristic
469	C₄	—	2	1	no	—
470	C₄	—	2	1	no	—
471	C₄	—	2	1	no	—
472	C₄	—	4	4	no	—
473	C₄	—	4	1	no	—
474	C₄	—	4	2	no	—
475	C₄	—	4	1	no	—
476	C₄	—	4	2	no	—
477	C₄	—	4	1	no	—
478	C₄	C₁₁×#443	1	2	yes	—
479	C₄	C₁₁×#519	1	1	yes	characteristic
480	C₄	C₁₁×#520	1	1	yes	characteristic
481	C₄	C₁₁×#536	1	1	yes	characteristic
482	C₄	C₁₁×#537	1	1	yes	characteristic
483	C₂	—	2	1	no	—
484	C₂	—	2	1	no	—
485	C₂	—	8	1	no	—
486	C₂	C₁₁×#2323	1	1	yes	characteristic
487	C₂	C₂×C₁₁×#443	1	1	yes	characteristic
488	C₂	C₁₁×#2955	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×C₄×C₈×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₁×#2960	C₂	semidirect
4. C₁₁×#1986	C₂	semidirect
5. C₁₁×#1950	C₂	semidirect
6. C₁₁×#1945	C₂	semidirect
9. C₁₁×#1922	C₂	semidirect
11. C₈×C₁₁×C₄⋊C₄	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
111. #22130	C₁₁	direct (N × H)
175. #2960	C₂×C₁₁	semidirect
177. #1986	C₂×C₁₁	semidirect
178. #1950	C₂×C₁₁	semidirect
179. #1945	C₂×C₁₁	semidirect
182. #1922	C₂×C₁₁	semidirect
184. C₈×C₄⋊C₄	C₂×C₁₁	semidirect
230. #479	C₄×C₁₁	semidirect
231. #478	C₄×C₁₁	semidirect
232. #477	C₄×C₁₁	semidirect
233. #476	C₄×C₁₁	semidirect
234. #475	C₄×C₁₁	semidirect
235. #474	C₄×C₁₁	semidirect
417. C₁₁	#22130	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×#2960	2
C₁₁×#2922	2
C₁₁×#1986	2
C₁₁×#1950	2
C₁₁×#1945	2
C₁₁×#1937	2
C₁₁×#1929	2
C₁₁×#1922	2
C₁₁×#1806	2
C₈×C₁₁×C₄⋊C₄	2
#22130	11

Subgroups — C11×#22130 #14599323

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#22130 #14599323