Subgroups — C₁₁×#23189 #14600382

Order 2816.

1026 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#495	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₁×#442	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₁×#441	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#2367	C₂	1	2	yes	maximal, complemented
5	C₁₁×#1983	C₂	1	2	yes	maximal, complemented
6	C₁₁×#1972	C₂	1	1	yes	maximal, characteristic
7	C₁₁×#1971	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₁×#1880	C₂	1	2	yes	maximal, complemented
9	C₁₁×#1877	C₂	1	2	yes	maximal, complemented
10	C₄×C₁₁×#106	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₁×#1770	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₁×Q₁₆	C₂²	1	1	yes	characteristic
13	C₂²×C₁₁×SD₁₆	C₂²	1	2	yes	—
14	C₂²×C₁₁×D₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₁×#124	C₂²	1	2	yes	—
16	C₂×C₄×Q₈×C₁₁	C₂²	1	2	yes	—
17	C₂×C₄×D₄×C₁₁	C₂²	1	2	yes	—
18	C₁₁×#495	C₄	1	8	yes	complemented
19	C₁₁×#442	—	2	4	no	—
20	C₁₁×#441	—	2	4	no	—
21	C₂×C₁₁×#106	C₂²	1	1	yes	characteristic
22	C₂×C₁₁×#106	C₂²	1	1	yes	characteristic
23	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₁×#103	C₂²	1	2	yes	—
25	C₂×C₁₁×#103	C₂²	1	2	yes	—
26	C₂×C₁₁×#102	C₂²	1	2	yes	—
27	C₂×C₁₁×#102	C₂²	1	2	yes	—
28	C₂×C₁₁×#97	C₂²	1	1	yes	characteristic
29	C₂×C₁₁×#97	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
31	C₁₁×#391	C₂²	1	2	yes	—
32	C₁₁×#390	C₂²	1	2	yes	—
33	C₁₁×#388	—	2	2	no	—
34	C₁₁×#388	—	2	2	no	—
35	C₁₁×#385	—	2	2	no	—
36	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
37	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
38	C₄×C₁₁×C₂²⋊C₄	—	2	2	no	—
39	C₁₁×#340	C₂²	1	2	yes	—
40	C₁₁×#336	C₂²	1	1	yes	characteristic
41	C₁₁×#336	C₂²	1	1	yes	characteristic
42	C₂²×Q₈×C₁₁	C₂³	1	2	yes	—
43	C₂²×D₄×C₁₁	C₂³	1	2	yes	—
44	C₂³×C₄×C₁₁	—	2	2	no	—
45	C₂×C₁₁×Q₁₆	—	2	2	no	—
46	C₂×C₁₁×Q₁₆	—	2	2	no	—
47	C₂×C₁₁×Q₁₆	C₂×C₄	1	4	yes	complemented
48	C₂×C₁₁×SD₁₆	—	4	2	no	—
49	C₂×C₁₁×SD₁₆	—	4	2	no	—
50	C₂×C₁₁×SD₁₆	C₂×C₄	1	8	yes	complemented
51	C₂×C₁₁×D₈	—	2	2	no	—
52	C₂×C₁₁×D₈	—	2	2	no	—
53	C₂×C₁₁×D₈	C₂×C₄	1	4	yes	—
54	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
58	C₁₁×#124	—	2	4	no	—
59	C₁₁×#124	C₂×C₄	1	8	yes	complemented
60	C₄×Q₈×C₁₁	—	2	4	no	—
61	C₄×Q₈×C₁₁	—	4	2	no	—
62	C₄×D₄×C₁₁	—	2	4	no	—
63	C₄×D₄×C₁₁	—	4	2	no	—
64	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
65	C₂×C₁₁×C₄⋊C₄	D₄	1	2	yes	—
66	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
67	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
68	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
69	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
70	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
71	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
72	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
73	C₂×C₄²×C₁₁	—	2	2	no	—
74	C₂×C₄²×C₁₁	—	2	2	no	—
75	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
78	C₁₁×#106	—	2	2	no	—
79	C₁₁×#106	D₄	1	4	yes	—
80	C₁₁×C₄⋊C₈	—	2	2	no	—
81	C₁₁×#103	—	2	4	no	—
82	C₁₁×#103	—	4	2	no	—
83	C₁₁×#102	—	2	4	no	—
84	C₁₁×#102	—	4	2	no	—
85	C₁₁×#97	—	2	2	no	—
86	C₁₁×#97	—	2	2	no	—
87	C₄×C₈×C₁₁	C₂×C₄	1	4	yes	complemented
88	C₁₁×#95	—	2	2	no	—
89	C₁₁×#95	—	2	2	no	—
90	C₁₁×#95	—	2	2	no	—
91	C₁₁×#95	D₄	1	2	yes	—
92	#23189	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
93	C₂⁴×C₁₁	—	2	2	no	—
94	C₂×Q₈×C₁₁	—	2	2	no	—
95	C₂×Q₈×C₁₁	—	2	2	no	—
96	C₂×Q₈×C₁₁	—	2	2	no	—
97	C₂×Q₈×C₁₁	—	2	2	no	—
98	C₂×Q₈×C₁₁	—	2	2	no	—
99	C₂×Q₈×C₁₁	C₂²×C₄	1	4	yes	—
100	C₂×D₄×C₁₁	—	2	2	no	—
101	C₂×D₄×C₁₁	—	2	2	no	—
102	C₂×D₄×C₁₁	—	2	2	no	—
103	C₂×D₄×C₁₁	—	2	2	no	—
104	C₂×D₄×C₁₁	—	2	2	no	—
105	C₂×D₄×C₁₁	C₂²×C₄	1	4	yes	—
106	C₂²×C₄×C₁₁	—	2	2	no	—
107	C₂²×C₄×C₁₁	—	2	2	no	—
108	C₂²×C₄×C₁₁	—	2	2	no	—
109	C₂²×C₄×C₁₁	—	4	4	no	—
110	C₂²×C₄×C₁₁	—	4	4	no	—
111	C₂²×C₄×C₁₁	—	8	2	no	—
112	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
117	C₁₁×Q₁₆	—	2	8	no	—
118	C₁₁×SD₁₆	—	4	8	no	—
119	C₁₁×D₈	—	2	8	no	—
120	C₂×C₈×C₁₁	—	2	1	no	—
121	C₂×C₈×C₁₁	—	2	1	no	—
122	C₂×C₈×C₁₁	—	2	1	no	—
123	C₂×C₈×C₁₁	—	2	1	no	—
124	C₂×C₈×C₁₁	—	2	1	no	—
125	C₂×C₈×C₁₁	—	2	1	no	—
126	C₂×C₈×C₁₁	—	2	1	no	—
127	C₂×C₈×C₁₁	—	2	1	no	—
128	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
129	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
130	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
131	C₂×C₈×C₁₁	#41	1	2	yes	—
132	C₁₁×C₄⋊C₄	—	2	2	no	—
133	C₁₁×C₄⋊C₄	—	2	2	no	—
134	C₁₁×C₄⋊C₄	—	2	2	no	—
135	C₁₁×C₄⋊C₄	—	4	2	no	—
136	C₁₁×C₄⋊C₄	—	4	4	no	—
137	C₁₁×C₄⋊C₄	C₂×D₄	1	4	yes	—
138	C₁₁×C₂²⋊C₄	—	2	8	no	—
139	C₁₁×C₂²⋊C₄	—	2	8	no	—
140	C₁₁×C₂²⋊C₄	—	4	4	no	—
141	C₁₁×C₂²⋊C₄	—	4	4	no	—
142	C₁₁×C₂²⋊C₄	—	8	2	no	—
143	C₄²×C₁₁	—	2	1	no	—
144	C₄²×C₁₁	—	2	1	no	—
145	C₄²×C₁₁	—	2	1	no	—
146	C₄²×C₁₁	—	2	1	no	—
147	C₄²×C₁₁	—	4	4	no	—
148	C₄²×C₁₁	—	8	2	no	—
149	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
150	C₄²×C₁₁	#41	1	2	yes	—
151	C₂×#495	C₂×C₁₁	1	1	yes	characteristic
152	C₂×#442	C₂×C₁₁	1	1	yes	characteristic
153	C₂×#441	C₂×C₁₁	1	1	yes	characteristic, complemented
154	#2367	C₂×C₁₁	1	2	yes	complemented
155	#1983	C₂×C₁₁	1	2	yes	complemented
156	#1972	C₂×C₁₁	1	1	yes	characteristic
157	#1971	C₂×C₁₁	1	1	yes	characteristic, complemented
158	#1880	C₂×C₁₁	1	2	yes	complemented
159	#1877	C₂×C₁₁	1	2	yes	complemented
160	C₄×#106	C₂×C₁₁	1	1	yes	characteristic, complemented
161	#1770	C₂×C₁₁	1	1	yes	characteristic, complemented
162	C₂³×C₁₁	—	2	4	no	—
163	C₂³×C₁₁	—	4	2	no	—
164	C₂³×C₁₁	—	4	2	no	—
165	C₂³×C₁₁	—	4	2	no	—
166	C₂³×C₁₁	—	4	2	no	—
167	C₂³×C₁₁	—	4	2	no	—
168	C₂³×C₁₁	—	4	2	no	—
169	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
170	Q₈×C₁₁	—	2	4	no	—
171	Q₈×C₁₁	—	2	4	no	—
172	Q₈×C₁₁	—	4	2	no	—
173	Q₈×C₁₁	—	4	2	no	—
174	D₄×C₁₁	—	2	4	no	—
175	D₄×C₁₁	—	2	4	no	—
176	D₄×C₁₁	—	4	2	no	—
177	D₄×C₁₁	—	4	2	no	—
178	C₂×C₄×C₁₁	—	2	2	no	—
179	C₂×C₄×C₁₁	—	2	2	no	—
180	C₂×C₄×C₁₁	—	2	4	no	—
181	C₂×C₄×C₁₁	—	2	2	no	—
182	C₂×C₄×C₁₁	—	2	2	no	—
183	C₂×C₄×C₁₁	—	2	4	no	—
184	C₂×C₄×C₁₁	—	2	2	no	—
185	C₂×C₄×C₁₁	—	2	2	no	—
186	C₂×C₄×C₁₁	—	2	2	no	—
187	C₂×C₄×C₁₁	—	2	2	no	—
188	C₂×C₄×C₁₁	—	4	2	no	—
189	C₂×C₄×C₁₁	—	4	2	no	—
190	C₂×C₄×C₁₁	—	4	2	no	—
191	C₂×C₄×C₁₁	—	4	2	no	—
192	C₂×C₄×C₁₁	—	4	2	no	—
193	C₂×C₄×C₁₁	—	4	2	no	—
194	C₂×C₄×C₁₁	—	4	2	no	—
195	C₂×C₄×C₁₁	—	8	8	no	—
196	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
197	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
198	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
199	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
201	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
202	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
203	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
204	C₈×C₁₁	—	2	2	no	—
205	C₈×C₁₁	—	4	1	no	—
206	C₈×C₁₁	—	4	1	no	—
207	C₈×C₁₁	C₄×D₄	1	4	yes	—
208	C₂²×Q₁₆	C₂²×C₁₁	1	1	yes	characteristic
209	C₂²×SD₁₆	C₂²×C₁₁	1	2	yes	—
210	C₂²×D₈	C₂²×C₁₁	1	1	yes	characteristic
211	C₂×#124	C₂²×C₁₁	1	2	yes	—
212	C₂×C₄×Q₈	C₂²×C₁₁	1	2	yes	—
213	C₂×C₄×D₄	C₂²×C₁₁	1	2	yes	—
214	#495	C₄×C₁₁	1	8	yes	complemented
215	#442	—	2	4	no	—
216	#441	—	2	4	no	—
217	C₂×#106	C₂²×C₁₁	1	1	yes	characteristic
218	C₂×#106	C₂²×C₁₁	1	1	yes	characteristic
219	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
220	C₂×#103	C₂²×C₁₁	1	2	yes	—
221	C₂×#103	C₂²×C₁₁	1	2	yes	—
222	C₂×#102	C₂²×C₁₁	1	2	yes	—
223	C₂×#102	C₂²×C₁₁	1	2	yes	—
224	C₂×#97	C₂²×C₁₁	1	1	yes	characteristic
225	C₂×#97	C₂²×C₁₁	1	1	yes	characteristic
226	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
227	#391	C₂²×C₁₁	1	2	yes	—
228	#390	C₂²×C₁₁	1	2	yes	—
229	#388	—	2	2	no	—
230	#388	—	2	2	no	—
231	#385	—	2	2	no	—
232	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
233	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
234	C₄×C₂²⋊C₄	—	2	2	no	—
235	#340	C₂²×C₁₁	1	2	yes	—
236	#336	C₂²×C₁₁	1	1	yes	characteristic
237	#336	C₂²×C₁₁	1	1	yes	characteristic
238	C₂²×C₁₁	—	4	4	no	—
239	C₂²×C₁₁	—	4	4	no	—
240	C₂²×C₁₁	—	4	4	no	—
241	C₂²×C₁₁	—	8	2	no	—
242	C₂²×C₁₁	—	8	2	no	—
243	C₂²×C₁₁	—	8	2	no	—
244	C₂²×C₁₁	—	8	2	no	—
245	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
246	C₂²×C₁₁	D₄²	1	1	yes	characteristic
247	C₂²×C₁₁	#550	1	1	yes	characteristic
248	C₂²×C₁₁	#575	1	2	yes	—
249	C₂²×C₁₁	#577	1	2	yes	—
250	C₄×C₁₁	—	2	2	no	—
251	C₄×C₁₁	—	2	2	no	—
252	C₄×C₁₁	—	4	4	no	—
253	C₄×C₁₁	—	4	2	no	—
254	C₄×C₁₁	—	4	2	no	—
255	C₄×C₁₁	—	4	4	no	—
256	C₄×C₁₁	—	8	2	no	—
257	C₄×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
258	C₄×C₁₁	#518	1	1	yes	characteristic
259	C₄×C₁₁	#550	1	1	yes	characteristic
260	C₄×C₁₁	#559	1	1	yes	characteristic
261	C₂²×Q₈	C₂³×C₁₁	1	2	yes	—
262	C₂²×D₄	C₂³×C₁₁	1	2	yes	—
263	C₂³×C₄	—	2	2	no	—
264	C₂×Q₁₆	—	2	2	no	—
265	C₂×Q₁₆	—	2	2	no	—
266	C₂×Q₁₆	C₂×C₄×C₁₁	1	4	yes	complemented
267	C₂×SD₁₆	—	4	2	no	—
268	C₂×SD₁₆	—	4	2	no	—
269	C₂×SD₁₆	C₂×C₄×C₁₁	1	8	yes	complemented
270	C₂×D₈	—	2	2	no	—
271	C₂×D₈	—	2	2	no	—
272	C₂×D₈	C₂×C₄×C₁₁	1	4	yes	—
273	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
274	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
275	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
276	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
277	#124	—	2	4	no	—
278	#124	C₂×C₄×C₁₁	1	8	yes	complemented
279	C₄×Q₈	—	2	4	no	—
280	C₄×Q₈	—	4	2	no	—
281	C₄×D₄	—	2	4	no	—
282	C₄×D₄	—	4	2	no	—
283	C₂×C₄⋊C₄	—	2	2	no	—
284	C₂×C₄⋊C₄	D₄×C₁₁	1	2	yes	—
285	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
286	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
287	C₂×C₂²⋊C₄	—	2	2	no	—
288	C₂×C₂²⋊C₄	—	2	2	no	—
289	C₂×C₂²⋊C₄	—	2	2	no	—
290	C₂×C₂²⋊C₄	—	2	2	no	—
291	C₂×C₂²⋊C₄	—	2	2	no	—
292	C₂×C₄²	—	2	2	no	—
293	C₂×C₄²	—	2	2	no	—
294	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
295	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
296	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
297	#106	—	2	2	no	—
298	#106	D₄×C₁₁	1	4	yes	—
299	C₄⋊C₈	—	2	2	no	—
300	#103	—	2	4	no	—
301	#103	—	4	2	no	—
302	#102	—	2	4	no	—
303	#102	—	4	2	no	—
304	#97	—	2	2	no	—
305	#97	—	2	2	no	—
306	C₄×C₈	C₂×C₄×C₁₁	1	4	yes	complemented
307	#95	—	2	2	no	—
308	#95	—	2	2	no	—
309	#95	—	2	2	no	—
310	#95	D₄×C₁₁	1	2	yes	—
311	C₂×C₁₁	—	8	4	no	—
312	C₂×C₁₁	#2366	1	1	yes	characteristic
313	C₂×C₁₁	#2943	1	1	yes	characteristic
314	C₂×C₁₁	#2952	1	1	yes	characteristic
315	C₂×C₁₁	#3275	1	2	yes	—
316	C₂×C₁₁	#3401	1	2	yes	—
317	C₂⁴	—	2	2	no	—
318	C₂×Q₈	—	2	2	no	—
319	C₂×Q₈	—	2	2	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	C₂²×C₄×C₁₁	1	4	yes	—
324	C₂×D₄	—	2	2	no	—
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	C₂²×C₄×C₁₁	1	4	yes	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	4	4	no	—
334	C₂²×C₄	—	4	4	no	—
335	C₂²×C₄	—	8	2	no	—
336	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
337	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
338	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
339	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
340	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
341	Q₁₆	—	2	8	no	—
342	SD₁₆	—	4	8	no	—
343	D₈	—	2	8	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	2	1	no	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
353	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
354	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
355	C₂×C₈	C₁₁×#41	1	2	yes	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	4	2	no	—
360	C₄⋊C₄	—	4	4	no	—
361	C₄⋊C₄	C₂×D₄×C₁₁	1	4	yes	—
362	C₂²⋊C₄	—	2	8	no	—
363	C₂²⋊C₄	—	2	8	no	—
364	C₂²⋊C₄	—	4	4	no	—
365	C₂²⋊C₄	—	4	4	no	—
366	C₂²⋊C₄	—	8	2	no	—
367	C₄²	—	2	1	no	—
368	C₄²	—	2	1	no	—
369	C₄²	—	2	1	no	—
370	C₄²	—	2	1	no	—
371	C₄²	—	4	4	no	—
372	C₄²	—	8	2	no	—
373	C₄²	C₂²×C₄×C₁₁	1	2	yes	—
374	C₄²	C₁₁×#41	1	2	yes	—
375	C₁₁	#23189	1	1	yes	characteristic, direct product factor, Sylow
376	C₂³	—	2	4	no	—
377	C₂³	—	4	2	no	—
378	C₂³	—	4	2	no	—
379	C₂³	—	4	2	no	—
380	C₂³	—	4	2	no	—
381	C₂³	—	4	2	no	—
382	C₂³	—	4	2	no	—
383	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
384	Q₈	—	2	4	no	—
385	Q₈	—	2	4	no	—
386	Q₈	—	4	2	no	—
387	Q₈	—	4	2	no	—
388	D₄	—	2	4	no	—
389	D₄	—	2	4	no	—
390	D₄	—	4	2	no	—
391	D₄	—	4	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	4	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	8	8	no	—
410	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
411	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
412	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
413	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
414	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
415	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
416	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
417	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
418	C₈	—	2	2	no	—
419	C₈	—	4	1	no	—
420	C₈	—	4	1	no	—
421	C₈	C₄×D₄×C₁₁	1	4	yes	—
422	C₂²	—	4	4	no	—
423	C₂²	—	4	4	no	—
424	C₂²	—	4	4	no	—
425	C₂²	—	8	2	no	—
426	C₂²	—	8	2	no	—
427	C₂²	—	8	2	no	—
428	C₂²	—	8	2	no	—
429	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
430	C₂²	D₄²×C₁₁	1	1	yes	characteristic
431	C₂²	C₁₁×#550	1	1	yes	characteristic
432	C₂²	C₁₁×#575	1	2	yes	—
433	C₂²	C₁₁×#577	1	2	yes	—
434	C₄	—	2	2	no	—
435	C₄	—	2	2	no	—
436	C₄	—	4	2	no	—
437	C₄	—	4	2	no	—
438	C₄	—	4	4	no	—
439	C₄	—	4	4	no	—
440	C₄	—	8	2	no	—
441	C₄	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
442	C₄	C₁₁×#518	1	1	yes	characteristic
443	C₄	C₁₁×#550	1	1	yes	characteristic
444	C₄	C₁₁×#559	1	1	yes	characteristic
445	C₂	—	8	4	no	—
446	C₂	C₁₁×#2366	1	1	yes	characteristic
447	C₂	C₁₁×#2943	1	1	yes	characteristic
448	C₂	C₁₁×#2952	1	1	yes	characteristic
449	C₂	C₁₁×#3275	1	2	yes	—
450	C₂	C₁₁×#3401	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
prime radical	C₂²×C₁₁×D₈	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ C₄×C₁₁×C₄⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₁₁×#441	C₂	semidirect
4. C₁₁×#2367	C₂	semidirect
5. C₁₁×#1983	C₂	semidirect
7. C₁₁×#1971	C₂	semidirect
8. C₁₁×#1880	C₂	semidirect
9. C₁₁×#1877	C₂	semidirect
10. C₄×C₁₁×#106	C₂	semidirect
11. C₁₁×#1770	C₂	semidirect
18. C₁₁×#495	C₄	semidirect
47. C₂×C₁₁×Q₁₆	C₂×C₄	semidirect
50. C₂×C₁₁×SD₁₆	C₂×C₄	semidirect
59. C₁₁×#124	C₂×C₄	semidirect
87. C₄×C₈×C₁₁	C₂×C₄	semidirect
92. #23189	C₁₁	direct (N × H)
153. C₂×#441	C₂×C₁₁	semidirect
154. #2367	C₂×C₁₁	semidirect
155. #1983	C₂×C₁₁	semidirect
157. #1971	C₂×C₁₁	semidirect
158. #1880	C₂×C₁₁	semidirect
159. #1877	C₂×C₁₁	semidirect
160. C₄×#106	C₂×C₁₁	semidirect
161. #1770	C₂×C₁₁	semidirect
214. #495	C₄×C₁₁	semidirect
266. C₂×Q₁₆	C₂×C₄×C₁₁	semidirect
269. C₂×SD₁₆	C₂×C₄×C₁₁	semidirect
278. #124	C₂×C₄×C₁₁	semidirect
306. C₄×C₈	C₂×C₄×C₁₁	semidirect
375. C₁₁	#23189	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₁×#495	2
C₂×C₁₁×#442	2
C₂×C₁₁×#441	2
C₁₁×#2367	2
C₁₁×#1983	2
C₁₁×#1972	2
C₁₁×#1971	2
C₁₁×#1880	2
C₁₁×#1877	2
C₄×C₁₁×#106	2
C₁₁×#1770	2
#23189	11

Subgroups — C11×#23189 #14600382

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#23189 #14600382