Subgroups — C₁₁×#23147 #14600340

Order 2816.

808 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3050	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2933	C₂	1	2	yes	maximal, complemented
3	C₁₁×#1938	C₂	1	2	yes	maximal, complemented
4	C₁₁×#1922	C₂	1	2	yes	maximal, complemented
5	C₁₁×#1876	C₂	1	2	yes	maximal, complemented
6	C₁₁×#1871	C₂	1	2	yes	maximal, complemented
7	C₁₁×#1765	C₂	1	2	yes	maximal, complemented
8	C₁₁×#1752	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₁×#341	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₁×#135	C₂²	1	1	yes	characteristic
11	C₂×C₁₁×#131	C₂²	1	2	yes	—
12	C₂²×C₁₁×M₁₆	C₂²	1	2	yes	—
13	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
14	C₁₁×#525	C₂²	1	2	yes	—
15	C₁₁×#467	C₄	1	1	yes	characteristic, complemented
16	C₁₁×#467	C₄	1	1	yes	characteristic, complemented
17	C₁₁×#466	C₄	1	1	yes	characteristic, complemented
18	C₁₁×#466	C₄	1	1	yes	characteristic, complemented
19	C₁₁×#465	C₄	1	2	yes	complemented
20	C₁₁×#465	C₄	1	2	yes	complemented
21	C₁₁×#436	—	2	2	no	—
22	C₁₁×#435	—	2	2	no	—
23	C₁₁×#435	—	2	2	no	—
24	C₈×D₄×C₁₁	—	2	2	no	—
25	C₁₁×#427	C₂²	1	1	yes	characteristic
26	C₁₁×#424	C₂²	1	2	yes	—
27	C₂×C₁₁×#104	C₂²	1	2	yes	—
28	C₂×C₁₁×#104	C₂²	1	2	yes	—
29	C₁₁×#416	C₂²	1	2	yes	—
30	C₁₁×#408	C₂²	1	2	yes	—
31	C₂×C₁₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
32	C₁₁×#405	C₂²	1	2	yes	—
33	C₂×C₁₁×#97	C₂²	1	2	yes	—
34	C₄×C₁₁×C₂²⋊C₄	C₂²	1	1	yes	characteristic
35	C₁₁×#341	C₂²	1	2	yes	—
36	C₁₁×#341	C₂²	1	1	yes	characteristic
37	C₁₁×#341	C₂²	1	1	yes	characteristic
38	C₁₁×#339	C₂²	1	2	yes	—
39	C₁₁×#339	C₂²	1	2	yes	—
40	C₁₁×#336	C₂²	1	2	yes	—
41	C₂×C₁₁×#41	C₂³	1	2	yes	—
42	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
43	C₁₁×#135	—	4	2	no	—
44	C₂×C₁₁×Q₁₆	C₂×C₄	1	1	yes	characteristic
45	C₂×C₁₁×SD₁₆	C₂×C₄	1	2	yes	—
46	C₂×C₁₁×D₈	C₂×C₄	1	1	yes	characteristic
47	C₁₁×#131	—	2	4	no	—
48	C₁₁×#131	—	4	2	no	—
49	C₂×C₁₁×M₁₆	—	2	2	no	—
50	C₂×C₁₁×M₁₆	—	2	2	no	—
51	C₂×C₁₁×M₁₆	—	2	4	no	—
52	C₂×C₁₁×M₁₆	—	4	2	no	—
53	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
54	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
55	C₂²×C₈×C₁₁	—	2	2	no	—
56	C₂²×C₈×C₁₁	—	2	2	no	—
57	C₂²×C₈×C₁₁	—	4	2	no	—
58	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
59	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
60	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
61	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
62	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
65	C₁₁×#123	—	2	2	no	—
66	C₁₁×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
67	C₁₁×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
68	C₁₁×#121	C₂×C₄	1	2	yes	—
69	C₁₁×#121	C₂×C₄	1	2	yes	—
70	C₁₁×#120	—	2	2	no	—
71	C₄×D₄×C₁₁	—	2	2	no	—
72	C₄×D₄×C₁₁	—	2	2	no	—
73	C₁₁×#117	C₂³	1	2	yes	—
74	C₂×C₁₁×C₂²⋊C₄	—	2	1	no	—
75	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
76	C₁₁×#107	C₂×C₄	1	1	yes	characteristic
77	C₁₁×#107	C₂×C₄	1	1	yes	characteristic
78	C₁₁×#106	C₂×C₄	1	2	yes	—
79	C₁₁×C₄⋊C₈	—	2	2	no	—
80	C₁₁×C₄⋊C₈	—	2	2	no	—
81	C₁₁×#104	—	2	4	no	—
82	C₁₁×#104	—	4	2	no	—
83	C₁₁×#103	C₂×C₄	1	2	yes	—
84	C₁₁×#103	C₂×C₄	1	2	yes	—
85	C₁₁×#102	C₂×C₄	1	2	yes	—
86	C₁₁×#102	C₂×C₄	1	2	yes	—
87	C₁₁×C₂²⋊C₈	—	2	2	no	—
88	C₁₁×C₂²⋊C₈	—	2	2	no	—
89	C₁₁×C₂²⋊C₈	D₄	1	2	yes	—
90	C₁₁×C₂²⋊C₈	D₄	1	1	yes	characteristic
91	C₁₁×C₂²⋊C₈	D₄	1	1	yes	characteristic
92	C₁₁×#97	—	2	2	no	—
93	C₁₁×#97	—	4	2	no	—
94	C₄×C₈×C₁₁	—	2	2	no	—
95	C₁₁×#95	—	2	1	no	—
96	#23147	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
97	C₂⁴×C₁₁	#41	1	1	yes	characteristic
98	C₁₁×#41	—	2	2	no	—
99	C₁₁×#41	—	2	2	no	—
100	C₁₁×#41	—	2	2	no	—
101	C₁₁×#41	—	2	2	no	—
102	C₂×Q₈×C₁₁	C₂²×C₄	1	2	yes	—
103	C₂×D₄×C₁₁	—	2	2	no	—
104	C₂×D₄×C₁₁	—	2	2	no	—
105	C₂×D₄×C₁₁	—	2	2	no	—
106	C₂×D₄×C₁₁	C₂²×C₄	1	2	yes	—
107	C₂²×C₄×C₁₁	—	2	2	no	—
108	C₂²×C₄×C₁₁	—	2	2	no	—
109	C₂²×C₄×C₁₁	—	2	2	no	—
110	C₂²×C₄×C₁₁	—	2	2	no	—
111	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
116	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
117	C₁₁×Q₁₆	—	4	1	no	—
118	C₁₁×SD₁₆	—	4	2	no	—
119	C₁₁×D₈	—	4	1	no	—
120	C₁₁×M₁₆	—	2	2	no	—
121	C₁₁×M₁₆	—	2	2	no	—
122	C₁₁×M₁₆	—	2	2	no	—
123	C₁₁×M₁₆	—	4	4	no	—
124	C₁₁×M₁₆	—	4	4	no	—
125	C₁₁×M₁₆	#41	1	4	yes	—
126	C₂×C₈×C₁₁	—	2	2	no	—
127	C₂×C₈×C₁₁	—	2	2	no	—
128	C₂×C₈×C₁₁	—	2	2	no	—
129	C₂×C₈×C₁₁	—	2	2	no	—
130	C₂×C₈×C₁₁	—	2	2	no	—
131	C₂×C₈×C₁₁	—	2	2	no	—
132	C₂×C₈×C₁₁	—	4	1	no	—
133	C₂×C₈×C₁₁	—	4	1	no	—
134	C₂×C₈×C₁₁	—	4	1	no	—
135	C₂×C₈×C₁₁	—	4	1	no	—
136	C₂×C₈×C₁₁	—	4	4	no	—
137	C₂×C₈×C₁₁	—	4	4	no	—
138	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
141	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
142	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
143	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
144	C₁₁×C₄⋊C₄	—	2	2	no	—
145	C₁₁×C₄⋊C₄	—	2	2	no	—
146	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
147	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
148	C₁₁×C₂²⋊C₄	—	2	2	no	—
149	C₁₁×C₂²⋊C₄	—	2	2	no	—
150	C₁₁×C₂²⋊C₄	—	2	2	no	—
151	C₁₁×C₂²⋊C₄	—	2	2	no	—
152	C₁₁×C₂²⋊C₄	—	2	2	no	—
153	C₁₁×C₂²⋊C₄	—	4	2	no	—
154	C₄²×C₁₁	—	2	2	no	—
155	C₄²×C₁₁	—	2	2	no	—
156	C₄²×C₁₁	—	2	2	no	—
157	#3050	C₂×C₁₁	1	1	yes	characteristic
158	#2933	C₂×C₁₁	1	2	yes	complemented
159	#1938	C₂×C₁₁	1	2	yes	complemented
160	#1922	C₂×C₁₁	1	2	yes	complemented
161	#1876	C₂×C₁₁	1	2	yes	complemented
162	#1871	C₂×C₁₁	1	2	yes	complemented
163	#1765	C₂×C₁₁	1	2	yes	complemented
164	#1752	C₂×C₁₁	1	1	yes	characteristic, complemented
165	C₂×#341	C₂×C₁₁	1	1	yes	characteristic, complemented
166	C₂³×C₁₁	—	2	2	no	—
167	C₂³×C₁₁	—	2	2	no	—
168	C₂³×C₁₁	—	2	2	no	—
169	C₂³×C₁₁	—	4	1	no	—
170	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
171	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
172	C₂³×C₁₁	C₂×#41	1	1	yes	characteristic
173	Q₈×C₁₁	—	2	2	no	—
174	Q₈×C₁₁	—	2	2	no	—
175	D₄×C₁₁	—	2	2	no	—
176	D₄×C₁₁	—	2	2	no	—
177	D₄×C₁₁	—	4	2	no	—
178	D₄×C₁₁	—	4	2	no	—
179	D₄×C₁₁	—	4	4	no	—
180	D₄×C₁₁	—	8	2	no	—
181	C₂×C₄×C₁₁	—	2	2	no	—
182	C₂×C₄×C₁₁	—	2	1	no	—
183	C₂×C₄×C₁₁	—	2	1	no	—
184	C₂×C₄×C₁₁	—	2	1	no	—
185	C₂×C₄×C₁₁	—	2	1	no	—
186	C₂×C₄×C₁₁	—	2	2	no	—
187	C₂×C₄×C₁₁	—	2	2	no	—
188	C₂×C₄×C₁₁	—	2	2	no	—
189	C₂×C₄×C₁₁	—	2	2	no	—
190	C₂×C₄×C₁₁	—	2	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	—	4	2	no	—
196	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
197	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
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	2	yes	—
201	C₂×C₄×C₁₁	H(5,𝔽₂)	1	2	yes	—
202	C₈×C₁₁	—	2	1	no	—
203	C₈×C₁₁	—	2	1	no	—
204	C₈×C₁₁	—	2	1	no	—
205	C₈×C₁₁	—	2	1	no	—
206	C₈×C₁₁	—	2	2	no	—
207	C₈×C₁₁	—	2	2	no	—
208	C₈×C₁₁	—	2	4	no	—
209	C₈×C₁₁	—	4	2	no	—
210	C₂×#135	C₂²×C₁₁	1	1	yes	characteristic
211	C₂×#131	C₂²×C₁₁	1	2	yes	—
212	C₂²×M₁₆	C₂²×C₁₁	1	2	yes	—
213	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
214	#525	C₂²×C₁₁	1	2	yes	—
215	#467	C₄×C₁₁	1	1	yes	characteristic, complemented
216	#467	C₄×C₁₁	1	1	yes	characteristic, complemented
217	#466	C₄×C₁₁	1	1	yes	characteristic, complemented
218	#466	C₄×C₁₁	1	1	yes	characteristic, complemented
219	#465	C₄×C₁₁	1	2	yes	complemented
220	#465	C₄×C₁₁	1	2	yes	complemented
221	#436	—	2	2	no	—
222	#435	—	2	2	no	—
223	#435	—	2	2	no	—
224	C₈×D₄	—	2	2	no	—
225	#427	C₂²×C₁₁	1	1	yes	characteristic
226	#424	C₂²×C₁₁	1	2	yes	—
227	C₂×#104	C₂²×C₁₁	1	2	yes	—
228	C₂×#104	C₂²×C₁₁	1	2	yes	—
229	#416	C₂²×C₁₁	1	2	yes	—
230	#408	C₂²×C₁₁	1	2	yes	—
231	C₂×C₂²⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
232	#405	C₂²×C₁₁	1	2	yes	—
233	C₂×#97	C₂²×C₁₁	1	2	yes	—
234	C₄×C₂²⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
235	#341	C₂²×C₁₁	1	2	yes	—
236	#341	C₂²×C₁₁	1	1	yes	characteristic
237	#341	C₂²×C₁₁	1	1	yes	characteristic
238	#339	C₂²×C₁₁	1	2	yes	—
239	#339	C₂²×C₁₁	1	2	yes	—
240	#336	C₂²×C₁₁	1	2	yes	—
241	C₂²×C₁₁	—	2	1	no	—
242	C₂²×C₁₁	—	2	1	no	—
243	C₂²×C₁₁	—	2	1	no	—
244	C₂²×C₁₁	—	2	1	no	—
245	C₂²×C₁₁	—	2	1	no	—
246	C₂²×C₁₁	—	2	1	no	—
247	C₂²×C₁₁	—	2	1	no	—
248	C₂²×C₁₁	—	4	4	no	—
249	C₂²×C₁₁	—	4	2	no	—
250	C₂²×C₁₁	—	4	2	no	—
251	C₂²×C₁₁	—	4	2	no	—
252	C₂²×C₁₁	#444	1	2	yes	—
253	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
254	C₂²×C₁₁	#553	1	2	yes	—
255	C₄×C₁₁	—	2	1	no	—
256	C₄×C₁₁	—	2	1	no	—
257	C₄×C₁₁	—	4	2	no	—
258	C₄×C₁₁	—	4	2	no	—
259	C₄×C₁₁	—	4	2	no	—
260	C₄×C₁₁	—	8	2	no	—
261	C₄×C₁₁	C₄×#41	1	1	yes	characteristic
262	C₄×C₁₁	#518	1	1	yes	characteristic
263	C₄×C₁₁	#546	1	2	yes	—
264	C₂×#41	C₂³×C₁₁	1	2	yes	—
265	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
266	#135	—	4	2	no	—
267	C₂×Q₁₆	C₂×C₄×C₁₁	1	1	yes	characteristic
268	C₂×SD₁₆	C₂×C₄×C₁₁	1	2	yes	—
269	C₂×D₈	C₂×C₄×C₁₁	1	1	yes	characteristic
270	#131	—	2	4	no	—
271	#131	—	4	2	no	—
272	C₂×M₁₆	—	2	2	no	—
273	C₂×M₁₆	—	2	2	no	—
274	C₂×M₁₆	—	2	4	no	—
275	C₂×M₁₆	—	4	2	no	—
276	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
277	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
278	C₂²×C₈	—	2	2	no	—
279	C₂²×C₈	—	2	2	no	—
280	C₂²×C₈	—	4	2	no	—
281	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
282	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
283	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
284	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
285	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
286	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
287	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
288	#123	—	2	2	no	—
289	C₂²⋊Q₈	C₂×C₄×C₁₁	1	2	yes	—
290	C₂²⋊Q₈	C₂×C₄×C₁₁	1	2	yes	—
291	#121	C₂×C₄×C₁₁	1	2	yes	—
292	#121	C₂×C₄×C₁₁	1	2	yes	—
293	#120	—	2	2	no	—
294	C₄×D₄	—	2	2	no	—
295	C₄×D₄	—	2	2	no	—
296	#117	C₂³×C₁₁	1	2	yes	—
297	C₂×C₂²⋊C₄	—	2	1	no	—
298	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
299	#107	C₂×C₄×C₁₁	1	1	yes	characteristic
300	#107	C₂×C₄×C₁₁	1	1	yes	characteristic
301	#106	C₂×C₄×C₁₁	1	2	yes	—
302	C₄⋊C₈	—	2	2	no	—
303	C₄⋊C₈	—	2	2	no	—
304	#104	—	2	4	no	—
305	#104	—	4	2	no	—
306	#103	C₂×C₄×C₁₁	1	2	yes	—
307	#103	C₂×C₄×C₁₁	1	2	yes	—
308	#102	C₂×C₄×C₁₁	1	2	yes	—
309	#102	C₂×C₄×C₁₁	1	2	yes	—
310	C₂²⋊C₈	—	2	2	no	—
311	C₂²⋊C₈	—	2	2	no	—
312	C₂²⋊C₈	D₄×C₁₁	1	2	yes	—
313	C₂²⋊C₈	D₄×C₁₁	1	1	yes	characteristic
314	C₂²⋊C₈	D₄×C₁₁	1	1	yes	characteristic
315	#97	—	2	2	no	—
316	#97	—	4	2	no	—
317	C₄×C₈	—	2	2	no	—
318	#95	—	2	1	no	—
319	C₂×C₁₁	—	2	2	no	—
320	C₂×C₁₁	—	2	2	no	—
321	C₂×C₁₁	—	4	1	no	—
322	C₂×C₁₁	—	8	2	no	—
323	C₂×C₁₁	#2364	1	1	yes	characteristic
324	C₂×C₁₁	C₂×#444	1	1	yes	characteristic
325	C₂×C₁₁	#2957	1	1	yes	characteristic
326	C₂⁴	C₁₁×#41	1	1	yes	characteristic
327	#41	—	2	2	no	—
328	#41	—	2	2	no	—
329	#41	—	2	2	no	—
330	#41	—	2	2	no	—
331	C₂×Q₈	C₂²×C₄×C₁₁	1	2	yes	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	C₂²×C₄×C₁₁	1	2	yes	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
341	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
342	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
343	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
344	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
345	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
346	Q₁₆	—	4	1	no	—
347	SD₁₆	—	4	2	no	—
348	D₈	—	4	1	no	—
349	M₁₆	—	2	2	no	—
350	M₁₆	—	2	2	no	—
351	M₁₆	—	2	2	no	—
352	M₁₆	—	4	4	no	—
353	M₁₆	—	4	4	no	—
354	M₁₆	C₁₁×#41	1	4	yes	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	4	1	no	—
362	C₂×C₈	—	4	1	no	—
363	C₂×C₈	—	4	1	no	—
364	C₂×C₈	—	4	1	no	—
365	C₂×C₈	—	4	4	no	—
366	C₂×C₈	—	4	4	no	—
367	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
368	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
369	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
370	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
371	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
372	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	C₂²×C₄×C₁₁	1	2	yes	—
376	C₄⋊C₄	C₂²×C₄×C₁₁	1	2	yes	—
377	C₂²⋊C₄	—	2	2	no	—
378	C₂²⋊C₄	—	2	2	no	—
379	C₂²⋊C₄	—	2	2	no	—
380	C₂²⋊C₄	—	2	2	no	—
381	C₂²⋊C₄	—	2	2	no	—
382	C₂²⋊C₄	—	4	2	no	—
383	C₄²	—	2	2	no	—
384	C₄²	—	2	2	no	—
385	C₄²	—	2	2	no	—
386	C₁₁	#23147	1	1	yes	characteristic, direct product factor, Sylow
387	C₂³	—	2	2	no	—
388	C₂³	—	2	2	no	—
389	C₂³	—	2	2	no	—
390	C₂³	—	4	1	no	—
391	C₂³	C₄×D₄×C₁₁	1	1	yes	characteristic
392	C₂³	C₄×D₄×C₁₁	1	1	yes	characteristic
393	C₂³	C₂×C₁₁×#41	1	1	yes	characteristic
394	Q₈	—	2	2	no	—
395	Q₈	—	2	2	no	—
396	D₄	—	2	2	no	—
397	D₄	—	2	2	no	—
398	D₄	—	4	2	no	—
399	D₄	—	4	2	no	—
400	D₄	—	4	4	no	—
401	D₄	—	8	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
418	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
419	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
420	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
421	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
422	C₂×C₄	C₁₁×H(5,𝔽₂)	1	2	yes	—
423	C₈	—	2	1	no	—
424	C₈	—	2	1	no	—
425	C₈	—	2	1	no	—
426	C₈	—	2	1	no	—
427	C₈	—	2	2	no	—
428	C₈	—	2	2	no	—
429	C₈	—	2	4	no	—
430	C₈	—	4	2	no	—
431	C₂²	—	2	1	no	—
432	C₂²	—	2	1	no	—
433	C₂²	—	2	1	no	—
434	C₂²	—	2	1	no	—
435	C₂²	—	2	1	no	—
436	C₂²	—	2	1	no	—
437	C₂²	—	2	1	no	—
438	C₂²	—	4	4	no	—
439	C₂²	—	4	2	no	—
440	C₂²	—	4	2	no	—
441	C₂²	—	4	2	no	—
442	C₂²	C₁₁×#444	1	2	yes	—
443	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
444	C₂²	C₁₁×#553	1	2	yes	—
445	C₄	—	2	1	no	—
446	C₄	—	2	1	no	—
447	C₄	—	4	2	no	—
448	C₄	—	4	2	no	—
449	C₄	—	4	2	no	—
450	C₄	—	8	2	no	—
451	C₄	C₄×C₁₁×#41	1	1	yes	characteristic
452	C₄	C₁₁×#518	1	1	yes	characteristic
453	C₄	C₁₁×#546	1	2	yes	—
454	C₂	—	2	2	no	—
455	C₂	—	2	2	no	—
456	C₂	—	4	1	no	—
457	C₂	—	8	2	no	—
458	C₂	C₁₁×#2364	1	1	yes	characteristic
459	C₂	C₂×C₁₁×#444	1	1	yes	characteristic
460	C₂	C₁₁×#2957	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	C₁₁×#3050	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₁₁×C₂²⋊C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₁×#2933	C₂	semidirect
3. C₁₁×#1938	C₂	semidirect
4. C₁₁×#1922	C₂	semidirect
5. C₁₁×#1876	C₂	semidirect
6. C₁₁×#1871	C₂	semidirect
7. C₁₁×#1765	C₂	semidirect
8. C₁₁×#1752	C₂	semidirect
9. C₂×C₁₁×#341	C₂	semidirect
15. C₁₁×#467	C₄	semidirect
16. C₁₁×#467	C₄	semidirect
17. C₁₁×#466	C₄	semidirect
18. C₁₁×#466	C₄	semidirect
19. C₁₁×#465	C₄	semidirect
20. C₁₁×#465	C₄	semidirect
96. #23147	C₁₁	direct (N × H)
158. #2933	C₂×C₁₁	semidirect
159. #1938	C₂×C₁₁	semidirect
160. #1922	C₂×C₁₁	semidirect
161. #1876	C₂×C₁₁	semidirect
162. #1871	C₂×C₁₁	semidirect
163. #1765	C₂×C₁₁	semidirect
164. #1752	C₂×C₁₁	semidirect
165. C₂×#341	C₂×C₁₁	semidirect
215. #467	C₄×C₁₁	semidirect
216. #467	C₄×C₁₁	semidirect
217. #466	C₄×C₁₁	semidirect
218. #466	C₄×C₁₁	semidirect
219. #465	C₄×C₁₁	semidirect
220. #465	C₄×C₁₁	semidirect
386. C₁₁	#23147	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×#3050	2
C₁₁×#2933	2
C₁₁×#1938	2
C₁₁×#1922	2
C₁₁×#1876	2
C₁₁×#1871	2
C₁₁×#1765	2
C₁₁×#1752	2
C₂×C₁₁×#341	2
#23147	11

Subgroups — C11×#23147 #14600340

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#23147 #14600340