Subgroups — C₁₁×#22799 #14599992

Order 2816.

952 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#432	C₂	1	2	yes	maximal, complemented
2	C₄²×D₄×C₁₁	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#1954	C₂	1	2	yes	maximal
4	C₁₁×#1924	C₂	1	4	yes	maximal, complemented
5	C₁₁×#1842	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁×#1797	C₂	1	2	yes	maximal, complemented
7	C₁₁×#1770	C₂	1	2	yes	maximal, complemented
8	C₄×C₁₁×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄×D₄×C₁₁	C₄	1	1	yes	characteristic
10	C₂×C₄×D₄×C₁₁	C₄	1	1	yes	characteristic
11	C₂×C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
12	C₂²×C₄²×C₁₁	C₂²	1	2	yes	—
13	C₁₁×#432	—	2	8	no	—
14	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
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	2	yes	—
18	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₁×C₂²⋊C₈	C₂²	1	4	yes	—
20	C₂×C₁₁×C₂²⋊C₈	C₂²	1	4	yes	—
21	C₂×C₁₁×#97	C₂²	1	4	yes	—
22	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
23	C₄×C₁₁×C₄⋊C₄	C₄	1	1	yes	characteristic
24	C₄×C₁₁×C₄⋊C₄	C₄	1	1	yes	characteristic
25	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₄×C₁₁×C₂²⋊C₄	C₄	1	2	yes	—
27	C₄×C₁₁×C₂²⋊C₄	C₄	1	2	yes	—
28	C₄×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	—
29	C₄³×C₁₁	C₂²	1	1	yes	characteristic
30	C₁₁×#336	C₂²	1	2	yes	—
31	C₁₁×#336	C₂²	1	4	yes	—
32	C₂²×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₄×C₁₁	C₂×C₄	1	2	yes	—
34	C₂³×C₄×C₁₁	C₂×C₄	1	2	yes	—
35	C₂³×C₄×C₁₁	C₂³	1	2	yes	—
36	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
37	C₂²×C₈×C₁₁	C₂³	1	4	yes	—
38	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
39	C₄×D₄×C₁₁	—	2	4	no	—
40	C₄×D₄×C₁₁	—	2	4	no	—
41	C₄×D₄×C₁₁	—	2	2	no	—
42	C₄×D₄×C₁₁	—	2	2	no	—
43	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
44	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
45	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
46	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
47	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
48	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
49	C₂×C₄²×C₁₁	—	2	4	no	—
50	C₂×C₄²×C₁₁	—	2	4	no	—
51	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
52	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
53	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
58	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
59	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
60	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
61	C₁₁×C₄⋊C₈	—	2	4	no	—
62	C₁₁×C₄⋊C₈	—	2	4	no	—
63	C₁₁×C₄⋊C₈	—	2	2	no	—
64	C₁₁×C₄⋊C₈	—	4	2	no	—
65	C₁₁×C₄⋊C₈	D₄	1	4	yes	complemented
66	C₁₁×C₂²⋊C₈	—	2	8	no	—
67	C₁₁×C₂²⋊C₈	—	4	4	no	—
68	C₁₁×#97	—	2	8	no	—
69	C₄×C₈×C₁₁	—	2	4	no	—
70	C₁₁×#95	C₂×C₄	1	2	yes	—
71	C₁₁×#95	C₂×C₄	1	2	yes	—
72	C₁₁×#95	C₂×C₄	1	2	yes	—
73	#22799	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
74	C₂⁴×C₁₁	C₂²×C₄	1	2	yes	—
75	C₂×D₄×C₁₁	—	2	2	no	—
76	C₂×D₄×C₁₁	—	2	2	no	—
77	C₂×D₄×C₁₁	M₁₆	1	4	yes	—
78	C₂²×C₄×C₁₁	—	2	4	no	—
79	C₂²×C₄×C₁₁	—	2	4	no	—
80	C₂²×C₄×C₁₁	—	2	4	no	—
81	C₂²×C₄×C₁₁	—	2	4	no	—
82	C₂²×C₄×C₁₁	—	2	4	no	—
83	C₂²×C₄×C₁₁	—	2	2	no	—
84	C₂²×C₄×C₁₁	—	2	2	no	—
85	C₂²×C₄×C₁₁	—	2	2	no	—
86	C₂²×C₄×C₁₁	—	2	2	no	—
87	C₂²×C₄×C₁₁	—	2	2	no	—
88	C₂²×C₄×C₁₁	—	2	2	no	—
89	C₂²×C₄×C₁₁	—	4	2	no	—
90	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
92	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
93	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
94	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
100	C₂×C₈×C₁₁	—	2	4	no	—
101	C₂×C₈×C₁₁	—	2	2	no	—
102	C₂×C₈×C₁₁	—	2	2	no	—
103	C₂×C₈×C₁₁	—	2	4	no	—
104	C₂×C₈×C₁₁	—	2	2	no	—
105	C₂×C₈×C₁₁	—	2	2	no	—
106	C₂×C₈×C₁₁	—	2	4	no	—
107	C₂×C₈×C₁₁	—	2	2	no	—
108	C₂×C₈×C₁₁	C₂×D₄	1	4	yes	—
109	C₁₁×C₄⋊C₄	—	2	2	no	—
110	C₁₁×C₄⋊C₄	—	2	2	no	—
111	C₁₁×C₄⋊C₄	—	2	2	no	—
112	C₁₁×C₂²⋊C₄	—	2	4	no	—
113	C₁₁×C₂²⋊C₄	—	2	4	no	—
114	C₁₁×C₂²⋊C₄	—	2	4	no	—
115	C₄²×C₁₁	—	2	4	no	—
116	C₄²×C₁₁	—	2	4	no	—
117	C₄²×C₁₁	—	2	2	no	—
118	C₄²×C₁₁	—	2	2	no	—
119	C₄²×C₁₁	—	2	2	no	—
120	C₄²×C₁₁	—	2	2	no	—
121	C₄²×C₁₁	—	2	1	no	—
122	C₄²×C₁₁	—	2	1	no	—
123	C₄²×C₁₁	—	4	1	no	—
124	C₄²×C₁₁	M₁₆	1	4	yes	—
125	C₄²×C₁₁	C₂×D₄	1	2	yes	—
126	C₄²×C₁₁	#41	1	2	yes	—
127	C₄²×C₁₁	#41	1	2	yes	—
128	C₄²×C₁₁	#41	1	2	yes	—
129	C₂×#432	C₂×C₁₁	1	2	yes	complemented
130	C₄²×D₄	C₂×C₁₁	1	1	yes	characteristic
131	#1954	C₂×C₁₁	1	2	yes	—
132	#1924	C₂×C₁₁	1	4	yes	complemented
133	#1842	C₂×C₁₁	1	1	yes	characteristic, complemented
134	#1797	C₂×C₁₁	1	2	yes	complemented
135	#1770	C₂×C₁₁	1	2	yes	complemented
136	C₄×C₄⋊C₈	C₂×C₁₁	1	1	yes	characteristic, complemented
137	C₂³×C₁₁	—	2	2	no	—
138	C₂³×C₁₁	—	2	2	no	—
139	C₂³×C₁₁	—	2	2	no	—
140	C₂³×C₁₁	—	2	2	no	—
141	C₂³×C₁₁	—	2	2	no	—
142	C₂³×C₁₁	—	2	2	no	—
143	C₂³×C₁₁	C₂×M₁₆	1	4	yes	—
144	C₂³×C₁₁	C₂³×C₄	1	1	yes	characteristic
145	D₄×C₁₁	—	2	8	no	—
146	C₂×C₄×C₁₁	—	2	1	no	—
147	C₂×C₄×C₁₁	—	2	1	no	—
148	C₂×C₄×C₁₁	—	2	1	no	—
149	C₂×C₄×C₁₁	—	2	1	no	—
150	C₂×C₄×C₁₁	—	2	1	no	—
151	C₂×C₄×C₁₁	—	2	1	no	—
152	C₂×C₄×C₁₁	—	2	2	no	—
153	C₂×C₄×C₁₁	—	2	2	no	—
154	C₂×C₄×C₁₁	—	2	2	no	—
155	C₂×C₄×C₁₁	—	2	2	no	—
156	C₂×C₄×C₁₁	—	2	1	no	—
157	C₂×C₄×C₁₁	—	2	2	no	—
158	C₂×C₄×C₁₁	—	2	1	no	—
159	C₂×C₄×C₁₁	—	2	2	no	—
160	C₂×C₄×C₁₁	—	2	2	no	—
161	C₂×C₄×C₁₁	—	2	1	no	—
162	C₂×C₄×C₁₁	—	2	2	no	—
163	C₂×C₄×C₁₁	—	2	2	no	—
164	C₂×C₄×C₁₁	—	4	8	no	—
165	C₂×C₄×C₁₁	—	4	2	no	—
166	C₂×C₄×C₁₁	—	4	2	no	—
167	C₂×C₄×C₁₁	—	4	2	no	—
168	C₂×C₄×C₁₁	—	4	2	no	—
169	C₂×C₄×C₁₁	—	4	8	no	—
170	C₂×C₄×C₁₁	#117	1	2	yes	—
171	C₂×C₄×C₁₁	#117	1	2	yes	—
172	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
173	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
174	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
175	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
176	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
177	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
178	C₂×C₄×C₁₁	#131	1	2	yes	—
179	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
180	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
181	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
182	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
183	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
184	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
185	C₈×C₁₁	—	2	4	no	—
186	C₈×C₁₁	—	4	4	no	—
187	C₈×C₁₁	—	4	2	no	—
188	C₂×C₄×D₄	C₄×C₁₁	1	1	yes	characteristic
189	C₂×C₄×D₄	C₄×C₁₁	1	1	yes	characteristic
190	C₂×C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic
191	C₂²×C₄²	C₂²×C₁₁	1	2	yes	—
192	#432	—	2	8	no	—
193	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
194	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
195	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
196	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
197	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
198	C₂×C₂²⋊C₈	C₂²×C₁₁	1	4	yes	—
199	C₂×C₂²⋊C₈	C₂²×C₁₁	1	4	yes	—
200	C₂×#97	C₂²×C₁₁	1	4	yes	—
201	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	—
202	C₄×C₄⋊C₄	C₄×C₁₁	1	1	yes	characteristic
203	C₄×C₄⋊C₄	C₄×C₁₁	1	1	yes	characteristic
204	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
205	C₄×C₂²⋊C₄	C₄×C₁₁	1	2	yes	—
206	C₄×C₂²⋊C₄	C₄×C₁₁	1	2	yes	—
207	C₄×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	—
208	C₄³	C₂²×C₁₁	1	1	yes	characteristic
209	#336	C₂²×C₁₁	1	4	yes	—
210	#336	C₂²×C₁₁	1	2	yes	—
211	C₂²×C₁₁	—	2	4	no	—
212	C₂²×C₁₁	—	2	4	no	—
213	C₂²×C₁₁	—	2	4	no	—
214	C₂²×C₁₁	—	4	2	no	—
215	C₂²×C₁₁	—	4	2	no	—
216	C₂²×C₁₁	—	4	2	no	—
217	C₂²×C₁₁	—	4	2	no	—
218	C₂²×C₁₁	C₂×#117	1	1	yes	characteristic
219	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
220	C₂²×C₁₁	#520	1	1	yes	characteristic
221	C₂²×C₁₁	C₂²×M₁₆	1	1	yes	characteristic
222	C₂²×C₁₁	C₂²×M₁₆	1	1	yes	characteristic
223	C₂²×C₁₁	C₂×#131	1	1	yes	characteristic
224	C₂²×C₁₁	#568	1	1	yes	characteristic
225	C₄×C₁₁	—	2	2	no	—
226	C₄×C₁₁	—	2	2	no	—
227	C₄×C₁₁	—	2	2	no	—
228	C₄×C₁₁	—	4	2	no	—
229	C₄×C₁₁	—	4	2	no	—
230	C₄×C₁₁	—	4	2	no	—
231	C₄×C₁₁	—	4	1	no	—
232	C₄×C₁₁	#432	1	4	yes	complemented
233	C₄×C₁₁	#436	1	4	yes	—
234	C₄×C₁₁	#547	1	1	yes	characteristic
235	C₄×C₁₁	#550	1	1	yes	characteristic
236	C₄×C₁₁	#555	1	1	yes	characteristic
237	C₄×C₁₁	#556	1	1	yes	characteristic
238	C₂²×D₄	C₂×C₄×C₁₁	1	1	yes	characteristic
239	C₂³×C₄	C₂×C₄×C₁₁	1	2	yes	—
240	C₂³×C₄	C₂×C₄×C₁₁	1	2	yes	—
241	C₂³×C₄	C₂³×C₁₁	1	2	yes	—
242	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
243	C₂²×C₈	C₂³×C₁₁	1	4	yes	—
244	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
245	C₄×D₄	—	2	4	no	—
246	C₄×D₄	—	2	4	no	—
247	C₄×D₄	—	2	2	no	—
248	C₄×D₄	—	2	2	no	—
249	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
250	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
251	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
252	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
253	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
254	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
255	C₂×C₄²	—	2	4	no	—
256	C₂×C₄²	—	2	4	no	—
257	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
258	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
259	C₂×C₄²	C₂×C₄×C₁₁	1	2	yes	—
260	C₂×C₄²	C₂×C₄×C₁₁	1	2	yes	—
261	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
262	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
263	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
264	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
265	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
266	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
267	C₄⋊C₈	—	2	4	no	—
268	C₄⋊C₈	—	2	4	no	—
269	C₄⋊C₈	—	2	2	no	—
270	C₄⋊C₈	—	4	2	no	—
271	C₄⋊C₈	D₄×C₁₁	1	4	yes	complemented
272	C₂²⋊C₈	—	2	8	no	—
273	C₂²⋊C₈	—	4	4	no	—
274	#97	—	2	8	no	—
275	C₄×C₈	—	2	4	no	—
276	#95	C₂×C₄×C₁₁	1	2	yes	—
277	#95	C₂×C₄×C₁₁	1	2	yes	—
278	#95	C₂×C₄×C₁₁	1	2	yes	—
279	C₂×C₁₁	—	4	4	no	—
280	C₂×C₁₁	#2354	1	1	yes	characteristic
281	C₂×C₁₁	C₂×#432	1	1	yes	characteristic
282	C₂×C₁₁	#2925	1	1	yes	characteristic
283	C₂×C₁₁	C₂×#436	1	1	yes	characteristic
284	C₂×C₁₁	D₄×M₁₆	1	1	yes	characteristic
285	C₂×C₁₁	#2989	1	1	yes	characteristic
286	C₂×C₁₁	#2990	1	1	yes	characteristic
287	C₂⁴	C₂²×C₄×C₁₁	1	2	yes	—
288	C₂×D₄	—	2	2	no	—
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	C₁₁×M₁₆	1	4	yes	—
291	C₂²×C₄	—	2	4	no	—
292	C₂²×C₄	—	2	4	no	—
293	C₂²×C₄	—	2	4	no	—
294	C₂²×C₄	—	2	4	no	—
295	C₂²×C₄	—	2	4	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	4	2	no	—
303	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
304	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
305	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
306	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
307	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
308	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
309	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
310	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
311	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
312	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	4	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	2	4	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	4	no	—
321	C₂×C₈	C₂×D₄×C₁₁	1	4	yes	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₂²⋊C₄	—	2	4	no	—
326	C₂²⋊C₄	—	2	4	no	—
327	C₂²⋊C₄	—	2	4	no	—
328	C₄²	—	2	4	no	—
329	C₄²	—	2	4	no	—
330	C₄²	—	2	2	no	—
331	C₄²	—	2	2	no	—
332	C₄²	—	2	2	no	—
333	C₄²	—	2	2	no	—
334	C₄²	—	2	1	no	—
335	C₄²	—	2	1	no	—
336	C₄²	—	4	1	no	—
337	C₄²	C₁₁×M₁₆	1	4	yes	—
338	C₄²	C₂×D₄×C₁₁	1	2	yes	—
339	C₄²	C₁₁×#41	1	2	yes	—
340	C₄²	C₁₁×#41	1	2	yes	—
341	C₄²	C₁₁×#41	1	2	yes	—
342	C₁₁	#22799	1	1	yes	characteristic, direct product factor, Sylow
343	C₂³	—	2	2	no	—
344	C₂³	—	2	2	no	—
345	C₂³	—	2	2	no	—
346	C₂³	—	2	2	no	—
347	C₂³	—	2	2	no	—
348	C₂³	—	2	2	no	—
349	C₂³	C₂×C₁₁×M₁₆	1	4	yes	—
350	C₂³	C₂³×C₄×C₁₁	1	1	yes	characteristic
351	D₄	—	2	8	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	4	8	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	8	no	—
376	C₂×C₄	C₁₁×#117	1	2	yes	—
377	C₂×C₄	C₁₁×#117	1	2	yes	—
378	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
379	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
380	C₂×C₄	C₂×C₁₁×M₁₆	1	2	yes	—
381	C₂×C₄	C₂×C₁₁×M₁₆	1	2	yes	—
382	C₂×C₄	C₂×C₁₁×M₁₆	1	2	yes	—
383	C₂×C₄	C₂×C₁₁×M₁₆	1	2	yes	—
384	C₂×C₄	C₁₁×#131	1	2	yes	—
385	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
386	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
387	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
388	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
389	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
390	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
391	C₈	—	2	4	no	—
392	C₈	—	4	4	no	—
393	C₈	—	4	2	no	—
394	C₂²	—	2	4	no	—
395	C₂²	—	2	4	no	—
396	C₂²	—	2	4	no	—
397	C₂²	—	4	2	no	—
398	C₂²	—	4	2	no	—
399	C₂²	—	4	2	no	—
400	C₂²	—	4	2	no	—
401	C₂²	C₂×C₁₁×#117	1	1	yes	characteristic
402	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
403	C₂²	C₁₁×#520	1	1	yes	characteristic
404	C₂²	C₂²×C₁₁×M₁₆	1	1	yes	characteristic
405	C₂²	C₂²×C₁₁×M₁₆	1	1	yes	characteristic
406	C₂²	C₂×C₁₁×#131	1	1	yes	characteristic
407	C₂²	C₁₁×#568	1	1	yes	characteristic
408	C₄	—	2	2	no	—
409	C₄	—	2	2	no	—
410	C₄	—	2	2	no	—
411	C₄	—	4	2	no	—
412	C₄	—	4	2	no	—
413	C₄	—	4	1	no	—
414	C₄	—	4	2	no	—
415	C₄	C₁₁×#432	1	4	yes	complemented
416	C₄	C₁₁×#436	1	4	yes	—
417	C₄	C₁₁×#547	1	1	yes	characteristic
418	C₄	C₁₁×#550	1	1	yes	characteristic
419	C₄	C₁₁×#555	1	1	yes	characteristic
420	C₄	C₁₁×#556	1	1	yes	characteristic
421	C₂	—	4	4	no	—
422	C₂	C₁₁×#2354	1	1	yes	characteristic
423	C₂	C₂×C₁₁×#432	1	1	yes	characteristic
424	C₂	C₁₁×#2925	1	1	yes	characteristic
425	C₂	C₂×C₁₁×#436	1	1	yes	characteristic
426	C₂	D₄×C₁₁×M₁₆	1	1	yes	characteristic
427	C₂	C₁₁×#2989	1	1	yes	characteristic
428	C₂	C₁₁×#2990	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×#432	C₂	semidirect
4. C₁₁×#1924	C₂	semidirect
5. C₁₁×#1842	C₂	semidirect
6. C₁₁×#1797	C₂	semidirect
7. C₁₁×#1770	C₂	semidirect
8. C₄×C₁₁×C₄⋊C₈	C₂	semidirect
65. C₁₁×C₄⋊C₈	D₄	semidirect
73. #22799	C₁₁	direct (N × H)
129. C₂×#432	C₂×C₁₁	semidirect
132. #1924	C₂×C₁₁	semidirect
133. #1842	C₂×C₁₁	semidirect
134. #1797	C₂×C₁₁	semidirect
135. #1770	C₂×C₁₁	semidirect
136. C₄×C₄⋊C₈	C₂×C₁₁	semidirect
232. C₄×C₁₁	#432	semidirect
271. C₄⋊C₈	D₄×C₁₁	semidirect
342. C₁₁	#22799	direct (N × H)
415. C₄	C₁₁×#432	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₁×#432	2
C₄²×D₄×C₁₁	2
C₁₁×#1954	2
C₁₁×#1924	2
C₁₁×#1842	2
C₁₁×#1797	2
C₁₁×#1770	2
C₄×C₁₁×C₄⋊C₈	2
#22799	11

Subgroups — C11×#22799 #14599992

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#22799 #14599992