Subgroups — C₁₁×#22796 #14599989

Order 2816.

828 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#433	C₂	1	2	yes	maximal, complemented
2	C₁₁×#2293	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#1954	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#1954	C₂	1	1	yes	maximal, characteristic
5	C₁₁×#1924	C₂	1	2	yes	maximal, complemented
6	C₁₁×#1923	C₂	1	2	yes	maximal, complemented
7	C₁₁×#1842	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₁×#1798	C₂	1	2	yes	maximal, complemented
9	C₁₁×#1770	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×C₁₁×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₁₁×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
13	C₂×C₁₁×#117	C₂²	1	2	yes	—
14	C₁₁×#433	—	2	8	no	—
15	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
16	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
20	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₁×C₂²⋊C₈	C₂²	1	2	yes	—
22	C₂×C₁₁×C₂²⋊C₈	C₂²	1	2	yes	—
23	C₂×C₁₁×C₂²⋊C₈	C₂²	1	2	yes	—
24	C₂×C₁₁×C₂²⋊C₈	C₂²	1	2	yes	—
25	C₂×C₁₁×#97	C₂²	1	2	yes	—
26	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
27	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
29	C₁₁×#390	C₄	1	1	yes	characteristic
30	C₁₁×#390	C₄	1	1	yes	characteristic
31	C₁₁×#389	C₄	1	1	yes	characteristic
32	C₁₁×#389	C₄	1	1	yes	characteristic
33	C₁₁×#388	C₄	1	2	yes	—
34	C₁₁×#388	C₄	1	2	yes	—
35	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
36	C₄×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	—
37	C₄³×C₁₁	C₂²	1	1	yes	characteristic
38	C₁₁×#336	C₂²	1	1	yes	characteristic
39	C₁₁×#336	C₂²	1	2	yes	—
40	C₁₁×#336	C₂²	1	1	yes	characteristic
41	C₁₁×#336	C₂²	1	2	yes	—
42	C₂²×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
43	C₂³×C₄×C₁₁	C₂³	1	2	yes	—
44	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
47	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
48	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
50	C₄×D₄×C₁₁	—	2	2	no	—
51	C₄×D₄×C₁₁	—	2	2	no	—
52	C₁₁×#117	—	2	4	no	—
53	C₁₁×#117	—	2	4	no	—
54	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
55	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
56	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
57	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
58	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
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×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
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	C₂×C₄	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	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
72	C₁₁×C₄⋊C₈	—	2	4	no	—
73	C₁₁×C₄⋊C₈	—	2	2	no	—
74	C₁₁×C₄⋊C₈	—	2	2	no	—
75	C₁₁×C₄⋊C₈	—	2	2	no	—
76	C₁₁×C₄⋊C₈	—	4	2	no	—
77	C₁₁×C₄⋊C₈	D₄	1	4	yes	complemented
78	C₁₁×C₂²⋊C₈	—	2	4	no	—
79	C₁₁×C₂²⋊C₈	—	2	4	no	—
80	C₁₁×C₂²⋊C₈	—	4	2	no	—
81	C₁₁×C₂²⋊C₈	—	4	2	no	—
82	C₁₁×#97	—	2	4	no	—
83	C₄×C₈×C₁₁	—	2	4	no	—
84	C₄×C₈×C₁₁	—	2	2	no	—
85	C₄×C₈×C₁₁	—	2	2	no	—
86	C₁₁×#95	C₂×C₄	1	2	yes	—
87	C₁₁×#95	C₂×C₄	1	2	yes	—
88	C₁₁×#95	C₂×C₄	1	2	yes	—
89	#22796	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
90	C₂⁴×C₁₁	C₂²×C₄	1	2	yes	—
91	C₂×D₄×C₁₁	—	2	2	no	—
92	C₂×D₄×C₁₁	—	2	2	no	—
93	C₂×D₄×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	—	2	2	no	—
98	C₂²×C₄×C₁₁	—	2	2	no	—
99	C₂²×C₄×C₁₁	—	2	2	no	—
100	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
102	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
103	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
110	C₂×C₈×C₁₁	—	2	2	no	—
111	C₂×C₈×C₁₁	—	2	2	no	—
112	C₂×C₈×C₁₁	—	2	1	no	—
113	C₂×C₈×C₁₁	—	2	1	no	—
114	C₂×C₈×C₁₁	—	2	1	no	—
115	C₂×C₈×C₁₁	—	2	1	no	—
116	C₂×C₈×C₁₁	—	2	2	no	—
117	C₂×C₈×C₁₁	—	2	2	no	—
118	C₂×C₈×C₁₁	—	2	1	no	—
119	C₂×C₈×C₁₁	—	2	1	no	—
120	C₂×C₈×C₁₁	—	2	1	no	—
121	C₂×C₈×C₁₁	—	2	1	no	—
122	C₂×C₈×C₁₁	—	2	2	no	—
123	C₂×C₈×C₁₁	—	2	2	no	—
124	C₂×C₈×C₁₁	—	2	1	no	—
125	C₂×C₈×C₁₁	—	2	1	no	—
126	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
127	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
128	C₁₁×C₄⋊C₄	—	2	2	no	—
129	C₁₁×C₄⋊C₄	—	2	4	no	—
130	C₁₁×C₄⋊C₄	—	2	4	no	—
131	C₁₁×C₄⋊C₄	—	2	2	no	—
132	C₁₁×C₄⋊C₄	—	2	2	no	—
133	C₁₁×C₂²⋊C₄	—	2	4	no	—
134	C₁₁×C₂²⋊C₄	—	2	4	no	—
135	C₁₁×C₂²⋊C₄	—	2	4	no	—
136	C₁₁×C₂²⋊C₄	—	2	4	no	—
137	C₁₁×C₂²⋊C₄	—	4	2	no	—
138	C₄²×C₁₁	—	2	2	no	—
139	C₄²×C₁₁	—	2	2	no	—
140	C₄²×C₁₁	—	2	2	no	—
141	C₄²×C₁₁	—	2	2	no	—
142	C₄²×C₁₁	—	2	2	no	—
143	C₄²×C₁₁	—	2	1	no	—
144	C₄²×C₁₁	—	2	1	no	—
145	C₄²×C₁₁	—	4	1	no	—
146	C₄²×C₁₁	C₂×D₄	1	2	yes	—
147	C₄²×C₁₁	#41	1	2	yes	—
148	C₄²×C₁₁	#41	1	2	yes	—
149	C₄²×C₁₁	#41	1	2	yes	—
150	C₂×#433	C₂×C₁₁	1	2	yes	complemented
151	#2293	C₂×C₁₁	1	1	yes	characteristic
152	#1954	C₂×C₁₁	1	1	yes	characteristic
153	#1954	C₂×C₁₁	1	1	yes	characteristic
154	#1924	C₂×C₁₁	1	2	yes	complemented
155	#1923	C₂×C₁₁	1	2	yes	complemented
156	#1842	C₂×C₁₁	1	1	yes	characteristic, complemented
157	#1798	C₂×C₁₁	1	2	yes	complemented
158	#1770	C₂×C₁₁	1	1	yes	characteristic, complemented
159	C₈×C₄⋊C₄	C₂×C₁₁	1	1	yes	characteristic, complemented
160	C₄×C₄⋊C₈	C₂×C₁₁	1	1	yes	characteristic, complemented
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	—	2	2	no	—
166	C₂³×C₁₁	—	2	2	no	—
167	C₂³×C₁₁	—	2	2	no	—
168	C₂³×C₁₁	C₂³×C₄	1	1	yes	characteristic
169	D₄×C₁₁	—	4	4	no	—
170	C₂×C₄×C₁₁	—	2	1	no	—
171	C₂×C₄×C₁₁	—	2	1	no	—
172	C₂×C₄×C₁₁	—	2	1	no	—
173	C₂×C₄×C₁₁	—	2	1	no	—
174	C₂×C₄×C₁₁	—	2	1	no	—
175	C₂×C₄×C₁₁	—	2	1	no	—
176	C₂×C₄×C₁₁	—	2	1	no	—
177	C₂×C₄×C₁₁	—	2	1	no	—
178	C₂×C₄×C₁₁	—	2	2	no	—
179	C₂×C₄×C₁₁	—	2	2	no	—
180	C₂×C₄×C₁₁	—	2	2	no	—
181	C₂×C₄×C₁₁	—	2	2	no	—
182	C₂×C₄×C₁₁	—	2	1	no	—
183	C₂×C₄×C₁₁	—	2	2	no	—
184	C₂×C₄×C₁₁	—	2	1	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	—	2	1	no	—
189	C₂×C₄×C₁₁	—	2	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	#117	1	2	yes	—
195	C₂×C₄×C₁₁	#117	1	2	yes	—
196	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
197	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
198	C₂×C₄×C₁₁	#131	1	2	yes	—
199	C₂×C₄×C₁₁	#131	1	2	yes	—
200	C₂×C₄×C₁₁	#131	1	2	yes	—
201	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
203	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
204	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
205	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
206	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
207	C₈×C₁₁	—	2	2	no	—
208	C₈×C₁₁	—	2	2	no	—
209	C₈×C₁₁	—	4	2	no	—
210	C₈×C₁₁	—	4	2	no	—
211	C₈×C₁₁	—	4	1	no	—
212	C₈×C₁₁	—	4	1	no	—
213	C₂×C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic
214	C₂×#117	C₂²×C₁₁	1	2	yes	—
215	#433	—	2	8	no	—
216	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
217	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
218	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
219	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
220	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
221	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
222	C₂×C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
223	C₂×C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
224	C₂×C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
225	C₂×C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
226	C₂×#97	C₂²×C₁₁	1	2	yes	—
227	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	—
228	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
229	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
230	#390	C₄×C₁₁	1	1	yes	characteristic
231	#390	C₄×C₁₁	1	1	yes	characteristic
232	#389	C₄×C₁₁	1	1	yes	characteristic
233	#389	C₄×C₁₁	1	1	yes	characteristic
234	#388	C₄×C₁₁	1	2	yes	—
235	#388	C₄×C₁₁	1	2	yes	—
236	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
237	C₄×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	—
238	C₄³	C₂²×C₁₁	1	1	yes	characteristic
239	#336	C₂²×C₁₁	1	2	yes	—
240	#336	C₂²×C₁₁	1	2	yes	—
241	#336	C₂²×C₁₁	1	1	yes	characteristic
242	#336	C₂²×C₁₁	1	1	yes	characteristic
243	C₂²×C₁₁	—	4	2	no	—
244	C₂²×C₁₁	—	4	2	no	—
245	C₂²×C₁₁	—	4	2	no	—
246	C₂²×C₁₁	—	4	2	no	—
247	C₂²×C₁₁	—	4	2	no	—
248	C₂²×C₁₁	—	4	2	no	—
249	C₂²×C₁₁	—	4	2	no	—
250	C₂²×C₁₁	C₂×#117	1	1	yes	characteristic
251	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
252	C₂²×C₁₁	#520	1	1	yes	characteristic
253	C₂²×C₁₁	C₂×#131	1	1	yes	characteristic
254	C₂²×C₁₁	C₂×#131	1	1	yes	characteristic
255	C₂²×C₁₁	C₂×#131	1	1	yes	characteristic
256	C₂²×C₁₁	#568	1	1	yes	characteristic
257	C₄×C₁₁	—	2	2	no	—
258	C₄×C₁₁	—	2	2	no	—
259	C₄×C₁₁	—	2	2	no	—
260	C₄×C₁₁	—	2	2	no	—
261	C₄×C₁₁	—	4	2	no	—
262	C₄×C₁₁	—	4	2	no	—
263	C₄×C₁₁	—	4	2	no	—
264	C₄×C₁₁	—	4	1	no	—
265	C₄×C₁₁	#433	1	4	yes	complemented
266	C₄×C₁₁	#547	1	1	yes	characteristic
267	C₄×C₁₁	#550	1	1	yes	characteristic
268	C₄×C₁₁	#555	1	1	yes	characteristic
269	C₄×C₁₁	#556	1	1	yes	characteristic
270	C₂²×D₄	C₂×C₄×C₁₁	1	1	yes	characteristic
271	C₂³×C₄	C₂³×C₁₁	1	2	yes	—
272	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
273	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
274	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
275	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
276	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
277	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
278	C₄×D₄	—	2	2	no	—
279	C₄×D₄	—	2	2	no	—
280	#117	—	2	4	no	—
281	#117	—	2	4	no	—
282	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
283	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
284	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
285	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
286	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
287	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
288	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
289	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
290	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
291	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
292	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
293	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
294	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
295	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
296	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
297	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
298	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
299	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
300	C₄⋊C₈	—	2	4	no	—
301	C₄⋊C₈	—	2	2	no	—
302	C₄⋊C₈	—	2	2	no	—
303	C₄⋊C₈	—	2	2	no	—
304	C₄⋊C₈	—	4	2	no	—
305	C₄⋊C₈	D₄×C₁₁	1	4	yes	complemented
306	C₂²⋊C₈	—	2	4	no	—
307	C₂²⋊C₈	—	2	4	no	—
308	C₂²⋊C₈	—	4	2	no	—
309	C₂²⋊C₈	—	4	2	no	—
310	#97	—	2	4	no	—
311	C₄×C₈	—	2	4	no	—
312	C₄×C₈	—	2	2	no	—
313	C₄×C₈	—	2	2	no	—
314	#95	C₂×C₄×C₁₁	1	2	yes	—
315	#95	C₂×C₄×C₁₁	1	2	yes	—
316	#95	C₂×C₄×C₁₁	1	2	yes	—
317	C₂×C₁₁	—	8	2	no	—
318	C₂×C₁₁	#2354	1	1	yes	characteristic
319	C₂×C₁₁	C₂×#433	1	1	yes	characteristic
320	C₂×C₁₁	#2925	1	1	yes	characteristic
321	C₂×C₁₁	#2931	1	1	yes	characteristic
322	C₂×C₁₁	#2935	1	1	yes	characteristic
323	C₂×C₁₁	#2993	1	1	yes	characteristic
324	C₂×C₁₁	#2994	1	1	yes	characteristic
325	C₂⁴	C₂²×C₄×C₁₁	1	2	yes	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
336	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
337	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
338	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
339	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
340	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
341	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
342	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
343	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
344	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
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	2	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	1	no	—
357	C₂×C₈	—	2	1	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
362	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	4	no	—
365	C₄⋊C₄	—	2	4	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₂²⋊C₄	—	2	4	no	—
369	C₂²⋊C₄	—	2	4	no	—
370	C₂²⋊C₄	—	2	4	no	—
371	C₂²⋊C₄	—	2	4	no	—
372	C₂²⋊C₄	—	4	2	no	—
373	C₄²	—	2	2	no	—
374	C₄²	—	2	2	no	—
375	C₄²	—	2	2	no	—
376	C₄²	—	2	2	no	—
377	C₄²	—	2	2	no	—
378	C₄²	—	2	1	no	—
379	C₄²	—	2	1	no	—
380	C₄²	—	4	1	no	—
381	C₄²	C₂×D₄×C₁₁	1	2	yes	—
382	C₄²	C₁₁×#41	1	2	yes	—
383	C₄²	C₁₁×#41	1	2	yes	—
384	C₄²	C₁₁×#41	1	2	yes	—
385	C₁₁	#22796	1	1	yes	characteristic, direct product factor, Sylow
386	C₂³	—	2	2	no	—
387	C₂³	—	2	2	no	—
388	C₂³	—	2	2	no	—
389	C₂³	—	2	2	no	—
390	C₂³	—	2	2	no	—
391	C₂³	—	2	2	no	—
392	C₂³	—	2	2	no	—
393	C₂³	C₂³×C₄×C₁₁	1	1	yes	characteristic
394	D₄	—	4	4	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	C₁₁×#117	1	2	yes	—
420	C₂×C₄	C₁₁×#117	1	2	yes	—
421	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
422	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
423	C₂×C₄	C₁₁×#131	1	2	yes	—
424	C₂×C₄	C₁₁×#131	1	2	yes	—
425	C₂×C₄	C₁₁×#131	1	2	yes	—
426	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
427	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
428	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
429	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
430	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
431	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
432	C₈	—	2	2	no	—
433	C₈	—	2	2	no	—
434	C₈	—	4	2	no	—
435	C₈	—	4	2	no	—
436	C₈	—	4	1	no	—
437	C₈	—	4	1	no	—
438	C₂²	—	4	2	no	—
439	C₂²	—	4	2	no	—
440	C₂²	—	4	2	no	—
441	C₂²	—	4	2	no	—
442	C₂²	—	4	2	no	—
443	C₂²	—	4	2	no	—
444	C₂²	—	4	2	no	—
445	C₂²	C₂×C₁₁×#117	1	1	yes	characteristic
446	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
447	C₂²	C₁₁×#520	1	1	yes	characteristic
448	C₂²	C₂×C₁₁×#131	1	1	yes	characteristic
449	C₂²	C₂×C₁₁×#131	1	1	yes	characteristic
450	C₂²	C₂×C₁₁×#131	1	1	yes	characteristic
451	C₂²	C₁₁×#568	1	1	yes	characteristic
452	C₄	—	2	2	no	—
453	C₄	—	2	2	no	—
454	C₄	—	2	2	no	—
455	C₄	—	2	2	no	—
456	C₄	—	4	2	no	—
457	C₄	—	4	2	no	—
458	C₄	—	4	1	no	—
459	C₄	—	4	2	no	—
460	C₄	C₁₁×#433	1	4	yes	complemented
461	C₄	C₁₁×#547	1	1	yes	characteristic
462	C₄	C₁₁×#550	1	1	yes	characteristic
463	C₄	C₁₁×#555	1	1	yes	characteristic
464	C₄	C₁₁×#556	1	1	yes	characteristic
465	C₂	—	8	2	no	—
466	C₂	C₁₁×#2354	1	1	yes	characteristic
467	C₂	C₂×C₁₁×#433	1	1	yes	characteristic
468	C₂	C₁₁×#2925	1	1	yes	characteristic
469	C₂	C₁₁×#2931	1	1	yes	characteristic
470	C₂	C₁₁×#2935	1	1	yes	characteristic
471	C₂	C₁₁×#2993	1	1	yes	characteristic
472	C₂	C₁₁×#2994	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
1. C₂×C₁₁×#433	C₂	semidirect
5. C₁₁×#1924	C₂	semidirect
6. C₁₁×#1923	C₂	semidirect
7. C₁₁×#1842	C₂	semidirect
8. C₁₁×#1798	C₂	semidirect
9. C₁₁×#1770	C₂	semidirect
10. C₈×C₁₁×C₄⋊C₄	C₂	semidirect
11. C₄×C₁₁×C₄⋊C₈	C₂	semidirect
77. C₁₁×C₄⋊C₈	D₄	semidirect
89. #22796	C₁₁	direct (N × H)
150. C₂×#433	C₂×C₁₁	semidirect
154. #1924	C₂×C₁₁	semidirect
155. #1923	C₂×C₁₁	semidirect
156. #1842	C₂×C₁₁	semidirect
157. #1798	C₂×C₁₁	semidirect
158. #1770	C₂×C₁₁	semidirect
159. C₈×C₄⋊C₄	C₂×C₁₁	semidirect
160. C₄×C₄⋊C₈	C₂×C₁₁	semidirect
265. C₄×C₁₁	#433	semidirect
305. C₄⋊C₈	D₄×C₁₁	semidirect
385. C₁₁	#22796	direct (N × H)
460. C₄	C₁₁×#433	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₁×#433	2
C₁₁×#2293	2
C₁₁×#1954	2
C₁₁×#1924	2
C₁₁×#1923	2
C₁₁×#1842	2
C₁₁×#1798	2
C₁₁×#1770	2
C₈×C₁₁×C₄⋊C₄	2
C₄×C₁₁×C₄⋊C₈	2
#22796	11

Subgroups — C11×#22796 #14599989

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#22796 #14599989