Subgroups — C₁₁×#22836 #14600029

Order 2816.

752 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#2293	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#1954	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#1954	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#1924	C₂	1	2	yes	maximal, complemented
5	C₁₁×#1923	C₂	1	2	yes	maximal, complemented
6	C₁₁×#1831	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#1818	C₂	1	2	yes	maximal, complemented
8	C₁₁×#1770	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈×C₁₁×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₁₁×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₁×#1750	C₂	1	2	yes	maximal, complemented
12	C₂×C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
13	C₂×C₁₁×#117	C₂²	1	2	yes	—
14	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₁×C₂²⋊C₈	C₂²	1	2	yes	—
19	C₂×C₁₁×C₂²⋊C₈	C₂²	1	2	yes	—
20	C₂×C₁₁×C₂²⋊C₈	C₂²	1	2	yes	—
21	C₂×C₁₁×C₂²⋊C₈	C₂²	1	2	yes	—
22	C₂×C₁₁×#97	C₂²	1	2	yes	—
23	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
26	C₁₁×#390	C₄	1	1	yes	characteristic
27	C₁₁×#390	C₄	1	1	yes	characteristic
28	C₁₁×#389	C₄	1	1	yes	characteristic
29	C₁₁×#389	C₄	1	1	yes	characteristic
30	C₁₁×#388	C₄	1	2	yes	—
31	C₁₁×#388	C₄	1	2	yes	—
32	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₄×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	—
34	C₄³×C₁₁	C₂²	1	1	yes	characteristic
35	C₁₁×#336	C₂²	1	2	yes	—
36	C₁₁×#336	C₂²	1	2	yes	—
37	C₁₁×#336	C₂²	1	2	yes	—
38	C₁₁×#336	C₂²	1	1	yes	characteristic
39	C₁₁×#336	C₂²	1	2	yes	—
40	C₁₁×#336	C₂²	1	1	yes	characteristic
41	C₂²×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
42	C₂³×C₄×C₁₁	C₂³	1	2	yes	—
43	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
46	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
47	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
49	C₄×D₄×C₁₁	—	2	2	no	—
50	C₄×D₄×C₁₁	—	2	2	no	—
51	C₁₁×#117	—	4	2	no	—
52	C₁₁×#117	—	4	2	no	—
53	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
54	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
55	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
56	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
57	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
58	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
59	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
60	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
61	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
62	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
63	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
70	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
71	C₁₁×C₄⋊C₈	—	2	2	no	—
72	C₁₁×C₄⋊C₈	—	2	2	no	—
73	C₁₁×C₄⋊C₈	—	2	2	no	—
74	C₁₁×C₄⋊C₈	—	2	2	no	—
75	C₁₁×C₂²⋊C₈	—	2	4	no	—
76	C₁₁×C₂²⋊C₈	—	2	4	no	—
77	C₁₁×C₂²⋊C₈	—	4	2	no	—
78	C₁₁×C₂²⋊C₈	—	4	2	no	—
79	C₁₁×#97	—	4	2	no	—
80	C₄×C₈×C₁₁	—	2	2	no	—
81	C₄×C₈×C₁₁	—	2	2	no	—
82	C₄×C₈×C₁₁	—	4	2	no	—
83	C₁₁×#95	C₂×C₄	1	2	yes	—
84	C₁₁×#95	C₂×C₄	1	2	yes	—
85	C₁₁×#95	C₂×C₄	1	2	yes	—
86	#22836	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
87	C₂⁴×C₁₁	C₂²×C₄	1	2	yes	—
88	C₂×D₄×C₁₁	—	2	2	no	—
89	C₂×D₄×C₁₁	—	2	2	no	—
90	C₂×D₄×C₁₁	—	2	2	no	—
91	C₂²×C₄×C₁₁	—	2	2	no	—
92	C₂²×C₄×C₁₁	—	2	2	no	—
93	C₂²×C₄×C₁₁	—	2	2	no	—
94	C₂²×C₄×C₁₁	—	2	2	no	—
95	C₂²×C₄×C₁₁	—	2	2	no	—
96	C₂²×C₄×C₁₁	—	2	2	no	—
97	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
100	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
101	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
107	C₂×C₈×C₁₁	—	2	1	no	—
108	C₂×C₈×C₁₁	—	2	1	no	—
109	C₂×C₈×C₁₁	—	2	1	no	—
110	C₂×C₈×C₁₁	—	2	1	no	—
111	C₂×C₈×C₁₁	—	2	2	no	—
112	C₂×C₈×C₁₁	—	2	2	no	—
113	C₂×C₈×C₁₁	—	2	1	no	—
114	C₂×C₈×C₁₁	—	2	1	no	—
115	C₂×C₈×C₁₁	—	2	2	no	—
116	C₂×C₈×C₁₁	—	2	2	no	—
117	C₂×C₈×C₁₁	—	2	1	no	—
118	C₂×C₈×C₁₁	—	2	1	no	—
119	C₂×C₈×C₁₁	—	2	2	no	—
120	C₂×C₈×C₁₁	—	2	2	no	—
121	C₂×C₈×C₁₁	—	2	1	no	—
122	C₂×C₈×C₁₁	—	2	1	no	—
123	C₂×C₈×C₁₁	#41	1	2	yes	—
124	C₂×C₈×C₁₁	#41	1	2	yes	—
125	C₁₁×C₄⋊C₄	—	2	2	no	—
126	C₁₁×C₄⋊C₄	—	2	2	no	—
127	C₁₁×C₄⋊C₄	—	2	2	no	—
128	C₁₁×C₄⋊C₄	—	4	2	no	—
129	C₁₁×C₄⋊C₄	—	4	2	no	—
130	C₁₁×C₂²⋊C₄	—	2	4	no	—
131	C₁₁×C₂²⋊C₄	—	2	4	no	—
132	C₁₁×C₂²⋊C₄	—	4	2	no	—
133	C₁₁×C₂²⋊C₄	—	4	2	no	—
134	C₁₁×C₂²⋊C₄	—	4	2	no	—
135	C₄²×C₁₁	—	2	2	no	—
136	C₄²×C₁₁	—	2	2	no	—
137	C₄²×C₁₁	—	2	2	no	—
138	C₄²×C₁₁	—	2	1	no	—
139	C₄²×C₁₁	—	2	1	no	—
140	C₄²×C₁₁	—	2	2	no	—
141	C₄²×C₁₁	—	2	2	no	—
142	C₄²×C₁₁	—	2	1	no	—
143	C₄²×C₁₁	—	2	1	no	—
144	C₄²×C₁₁	—	4	1	no	—
145	C₄²×C₁₁	#41	1	2	yes	—
146	C₄²×C₁₁	#41	1	2	yes	—
147	#2293	C₂×C₁₁	1	1	yes	characteristic
148	#1954	C₂×C₁₁	1	1	yes	characteristic
149	#1954	C₂×C₁₁	1	1	yes	characteristic
150	#1924	C₂×C₁₁	1	2	yes	complemented
151	#1923	C₂×C₁₁	1	2	yes	complemented
152	#1831	C₂×C₁₁	1	1	yes	characteristic, complemented
153	#1818	C₂×C₁₁	1	2	yes	complemented
154	#1770	C₂×C₁₁	1	1	yes	characteristic, complemented
155	C₈×C₄⋊C₄	C₂×C₁₁	1	1	yes	characteristic, complemented
156	C₄×C₄⋊C₈	C₂×C₁₁	1	1	yes	characteristic, complemented
157	#1750	C₂×C₁₁	1	2	yes	complemented
158	C₂³×C₁₁	—	2	2	no	—
159	C₂³×C₁₁	—	2	2	no	—
160	C₂³×C₁₁	—	2	2	no	—
161	C₂³×C₁₁	—	2	2	no	—
162	C₂³×C₁₁	—	2	2	no	—
163	C₂³×C₁₁	—	2	2	no	—
164	C₂³×C₁₁	—	2	2	no	—
165	C₂³×C₁₁	C₂³×C₄	1	1	yes	characteristic
166	D₄×C₁₁	—	4	4	no	—
167	C₂×C₄×C₁₁	—	2	1	no	—
168	C₂×C₄×C₁₁	—	2	1	no	—
169	C₂×C₄×C₁₁	—	2	1	no	—
170	C₂×C₄×C₁₁	—	2	1	no	—
171	C₂×C₄×C₁₁	—	2	2	no	—
172	C₂×C₄×C₁₁	—	2	1	no	—
173	C₂×C₄×C₁₁	—	2	2	no	—
174	C₂×C₄×C₁₁	—	2	1	no	—
175	C₂×C₄×C₁₁	—	2	1	no	—
176	C₂×C₄×C₁₁	—	2	2	no	—
177	C₂×C₄×C₁₁	—	2	2	no	—
178	C₂×C₄×C₁₁	—	2	2	no	—
179	C₂×C₄×C₁₁	—	2	1	no	—
180	C₂×C₄×C₁₁	—	2	1	no	—
181	C₂×C₄×C₁₁	—	2	1	no	—
182	C₂×C₄×C₁₁	—	2	1	no	—
183	C₂×C₄×C₁₁	—	2	2	no	—
184	C₂×C₄×C₁₁	—	2	2	no	—
185	C₂×C₄×C₁₁	—	2	2	no	—
186	C₂×C₄×C₁₁	—	2	1	no	—
187	C₂×C₄×C₁₁	—	2	1	no	—
188	C₂×C₄×C₁₁	—	2	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	#117	1	2	yes	—
194	C₂×C₄×C₁₁	#117	1	2	yes	—
195	C₂×C₄×C₁₁	#131	1	2	yes	—
196	C₂×C₄×C₁₁	#131	1	2	yes	—
197	C₂×C₄×C₁₁	#131	1	2	yes	—
198	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
199	C₂×C₄×C₁₁	C₂×#41	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	—	2	2	no	—
206	C₈×C₁₁	—	4	1	no	—
207	C₈×C₁₁	—	4	1	no	—
208	C₈×C₁₁	—	4	2	no	—
209	C₈×C₁₁	—	4	2	no	—
210	C₂×C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic
211	C₂×#117	C₂²×C₁₁	1	2	yes	—
212	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
213	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
214	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
215	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
216	C₂×C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
217	C₂×C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
218	C₂×C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
219	C₂×C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
220	C₂×#97	C₂²×C₁₁	1	2	yes	—
221	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
222	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
223	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	—
224	#390	C₄×C₁₁	1	1	yes	characteristic
225	#390	C₄×C₁₁	1	1	yes	characteristic
226	#389	C₄×C₁₁	1	1	yes	characteristic
227	#389	C₄×C₁₁	1	1	yes	characteristic
228	#388	C₄×C₁₁	1	2	yes	—
229	#388	C₄×C₁₁	1	2	yes	—
230	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
231	C₄×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	—
232	C₄³	C₂²×C₁₁	1	1	yes	characteristic
233	#336	C₂²×C₁₁	1	1	yes	characteristic
234	#336	C₂²×C₁₁	1	2	yes	—
235	#336	C₂²×C₁₁	1	2	yes	—
236	#336	C₂²×C₁₁	1	2	yes	—
237	#336	C₂²×C₁₁	1	2	yes	—
238	#336	C₂²×C₁₁	1	1	yes	characteristic
239	C₂²×C₁₁	—	4	2	no	—
240	C₂²×C₁₁	—	4	2	no	—
241	C₂²×C₁₁	—	4	2	no	—
242	C₂²×C₁₁	—	4	2	no	—
243	C₂²×C₁₁	—	4	2	no	—
244	C₂²×C₁₁	—	4	2	no	—
245	C₂²×C₁₁	—	4	2	no	—
246	C₂²×C₁₁	C₂×#117	1	1	yes	characteristic
247	C₂²×C₁₁	C₄×#41	1	1	yes	characteristic
248	C₂²×C₁₁	#518	1	1	yes	characteristic
249	C₂²×C₁₁	C₂×#131	1	1	yes	characteristic
250	C₂²×C₁₁	C₂×#131	1	1	yes	characteristic
251	C₂²×C₁₁	C₂×#131	1	1	yes	characteristic
252	C₂²×C₁₁	#568	1	1	yes	characteristic
253	C₄×C₁₁	—	2	2	no	—
254	C₄×C₁₁	—	2	2	no	—
255	C₄×C₁₁	—	4	2	no	—
256	C₄×C₁₁	—	4	1	no	—
257	C₄×C₁₁	—	4	1	no	—
258	C₄×C₁₁	—	4	2	no	—
259	C₄×C₁₁	—	4	1	no	—
260	C₄×C₁₁	—	4	2	no	—
261	C₄×C₁₁	#433	1	4	yes	—
262	C₄×C₁₁	#553	1	1	yes	characteristic
263	C₄×C₁₁	#553	1	1	yes	characteristic
264	C₄×C₁₁	#559	1	1	yes	characteristic
265	C₄×C₁₁	#559	1	1	yes	characteristic
266	C₂²×D₄	C₂×C₄×C₁₁	1	1	yes	characteristic
267	C₂³×C₄	C₂³×C₁₁	1	2	yes	—
268	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
269	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
270	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
271	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
272	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
273	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
274	C₄×D₄	—	2	2	no	—
275	C₄×D₄	—	2	2	no	—
276	#117	—	4	2	no	—
277	#117	—	4	2	no	—
278	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
279	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
280	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
281	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
282	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
283	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
284	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
285	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
286	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
287	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
288	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
289	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
290	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
291	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
292	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
293	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
294	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
295	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
296	C₄⋊C₈	—	2	2	no	—
297	C₄⋊C₈	—	2	2	no	—
298	C₄⋊C₈	—	2	2	no	—
299	C₄⋊C₈	—	2	2	no	—
300	C₂²⋊C₈	—	2	4	no	—
301	C₂²⋊C₈	—	2	4	no	—
302	C₂²⋊C₈	—	4	2	no	—
303	C₂²⋊C₈	—	4	2	no	—
304	#97	—	4	2	no	—
305	C₄×C₈	—	2	2	no	—
306	C₄×C₈	—	2	2	no	—
307	C₄×C₈	—	4	2	no	—
308	#95	C₂×C₄×C₁₁	1	2	yes	—
309	#95	C₂×C₄×C₁₁	1	2	yes	—
310	#95	C₂×C₄×C₁₁	1	2	yes	—
311	C₂×C₁₁	—	8	2	no	—
312	C₂×C₁₁	#2357	1	1	yes	characteristic
313	C₂×C₁₁	C₂×#433	1	1	yes	characteristic
314	C₂×C₁₁	#2925	1	1	yes	characteristic
315	C₂×C₁₁	#2966	1	1	yes	characteristic
316	C₂×C₁₁	#2969	1	1	yes	characteristic
317	C₂×C₁₁	#2979	1	1	yes	characteristic
318	C₂×C₁₁	#2981	1	1	yes	characteristic
319	C₂⁴	C₂²×C₄×C₁₁	1	2	yes	—
320	C₂×D₄	—	2	2	no	—
321	C₂×D₄	—	2	2	no	—
322	C₂×D₄	—	2	2	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
330	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
331	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
332	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
333	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
334	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
335	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
336	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
337	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
338	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
339	C₂×C₈	—	2	1	no	—
340	C₂×C₈	—	2	1	no	—
341	C₂×C₈	—	2	1	no	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	C₁₁×#41	1	2	yes	—
356	C₂×C₈	C₁₁×#41	1	2	yes	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	4	2	no	—
361	C₄⋊C₄	—	4	2	no	—
362	C₂²⋊C₄	—	2	4	no	—
363	C₂²⋊C₄	—	2	4	no	—
364	C₂²⋊C₄	—	4	2	no	—
365	C₂²⋊C₄	—	4	2	no	—
366	C₂²⋊C₄	—	4	2	no	—
367	C₄²	—	2	2	no	—
368	C₄²	—	2	2	no	—
369	C₄²	—	2	2	no	—
370	C₄²	—	2	1	no	—
371	C₄²	—	2	1	no	—
372	C₄²	—	2	2	no	—
373	C₄²	—	2	2	no	—
374	C₄²	—	2	1	no	—
375	C₄²	—	2	1	no	—
376	C₄²	—	4	1	no	—
377	C₄²	C₁₁×#41	1	2	yes	—
378	C₄²	C₁₁×#41	1	2	yes	—
379	C₁₁	#22836	1	1	yes	characteristic, direct product factor, Sylow
380	C₂³	—	2	2	no	—
381	C₂³	—	2	2	no	—
382	C₂³	—	2	2	no	—
383	C₂³	—	2	2	no	—
384	C₂³	—	2	2	no	—
385	C₂³	—	2	2	no	—
386	C₂³	—	2	2	no	—
387	C₂³	C₂³×C₄×C₁₁	1	1	yes	characteristic
388	D₄	—	4	4	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	C₁₁×#117	1	2	yes	—
416	C₂×C₄	C₁₁×#117	1	2	yes	—
417	C₂×C₄	C₁₁×#131	1	2	yes	—
418	C₂×C₄	C₁₁×#131	1	2	yes	—
419	C₂×C₄	C₁₁×#131	1	2	yes	—
420	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
421	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
422	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
423	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
424	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
425	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
426	C₈	—	2	2	no	—
427	C₈	—	2	2	no	—
428	C₈	—	4	1	no	—
429	C₈	—	4	1	no	—
430	C₈	—	4	2	no	—
431	C₈	—	4	2	no	—
432	C₂²	—	4	2	no	—
433	C₂²	—	4	2	no	—
434	C₂²	—	4	2	no	—
435	C₂²	—	4	2	no	—
436	C₂²	—	4	2	no	—
437	C₂²	—	4	2	no	—
438	C₂²	—	4	2	no	—
439	C₂²	C₂×C₁₁×#117	1	1	yes	characteristic
440	C₂²	C₄×C₁₁×#41	1	1	yes	characteristic
441	C₂²	C₁₁×#518	1	1	yes	characteristic
442	C₂²	C₂×C₁₁×#131	1	1	yes	characteristic
443	C₂²	C₂×C₁₁×#131	1	1	yes	characteristic
444	C₂²	C₂×C₁₁×#131	1	1	yes	characteristic
445	C₂²	C₁₁×#568	1	1	yes	characteristic
446	C₄	—	2	2	no	—
447	C₄	—	2	2	no	—
448	C₄	—	4	1	no	—
449	C₄	—	4	1	no	—
450	C₄	—	4	2	no	—
451	C₄	—	4	1	no	—
452	C₄	—	4	2	no	—
453	C₄	—	4	2	no	—
454	C₄	C₁₁×#433	1	4	yes	—
455	C₄	C₁₁×#553	1	1	yes	characteristic
456	C₄	C₁₁×#553	1	1	yes	characteristic
457	C₄	C₁₁×#559	1	1	yes	characteristic
458	C₄	C₁₁×#559	1	1	yes	characteristic
459	C₂	—	8	2	no	—
460	C₂	C₁₁×#2357	1	1	yes	characteristic
461	C₂	C₂×C₁₁×#433	1	1	yes	characteristic
462	C₂	C₁₁×#2925	1	1	yes	characteristic
463	C₂	C₁₁×#2966	1	1	yes	characteristic
464	C₂	C₁₁×#2969	1	1	yes	characteristic
465	C₂	C₁₁×#2979	1	1	yes	characteristic
466	C₂	C₁₁×#2981	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
4. C₁₁×#1924	C₂	semidirect
5. C₁₁×#1923	C₂	semidirect
6. C₁₁×#1831	C₂	semidirect
7. C₁₁×#1818	C₂	semidirect
8. C₁₁×#1770	C₂	semidirect
9. C₈×C₁₁×C₄⋊C₄	C₂	semidirect
10. C₄×C₁₁×C₄⋊C₈	C₂	semidirect
11. C₁₁×#1750	C₂	semidirect
86. #22836	C₁₁	direct (N × H)
150. #1924	C₂×C₁₁	semidirect
151. #1923	C₂×C₁₁	semidirect
152. #1831	C₂×C₁₁	semidirect
153. #1818	C₂×C₁₁	semidirect
154. #1770	C₂×C₁₁	semidirect
155. C₈×C₄⋊C₄	C₂×C₁₁	semidirect
156. C₄×C₄⋊C₈	C₂×C₁₁	semidirect
157. #1750	C₂×C₁₁	semidirect
379. C₁₁	#22836	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×#2293	2
C₁₁×#1954	2
C₁₁×#1924	2
C₁₁×#1923	2
C₁₁×#1831	2
C₁₁×#1818	2
C₁₁×#1770	2
C₈×C₁₁×C₄⋊C₄	2
C₄×C₁₁×C₄⋊C₈	2
C₁₁×#1750	2
#22836	11

Subgroups — C11×#22836 #14600029

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#22836 #14600029