Subgroups — C₁₁×#21924 #14599117

Order 2816.

770 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₁×#117	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#1924	C₂	1	2	yes	maximal
3	C₁₁×#1923	C₂	1	2	yes	maximal
4	C₁₁×#1917	C₂	1	2	yes	maximal, complemented
5	C₁₁×#1916	C₂	1	2	yes	maximal, complemented
6	C₁₁×#1842	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#1831	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₁×#1797	C₂	1	1	yes	maximal, characteristic
9	C₁₁×#1797	C₂	1	1	yes	maximal, characteristic
10	C₁₁×#1767	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₁₁×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₁×#117	C₄	1	1	yes	characteristic
13	C₂×C₁₁×#117	C₄	1	1	yes	characteristic
14	C₂²×C₄²×C₁₁	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×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
20	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
21	C₂×C₁₁×C₂²⋊C₈	C₂²	1	2	yes	—
22	C₂×C₁₁×C₂²⋊C₈	C₂²	1	2	yes	—
23	C₂×C₁₁×#97	C₂²	1	2	yes	—
24	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
25	C₄×C₁₁×C₄⋊C₄	C₄	1	1	yes	characteristic
26	C₄×C₁₁×C₄⋊C₄	C₄	1	1	yes	characteristic
27	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₄×C₁₁×C₂²⋊C₄	C₄	1	1	yes	characteristic
30	C₄×C₁₁×C₂²⋊C₄	C₄	1	1	yes	characteristic
31	C₄×C₁₁×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₄×C₁₁×C₂²⋊C₄	C₂²	1	1	yes	characteristic
33	C₁₁×#376	C₄	1	1	yes	characteristic
34	C₁₁×#376	C₄	1	1	yes	characteristic
35	C₄³×C₁₁	C₂²	1	1	yes	characteristic
36	C₄³×C₁₁	C₂²	1	1	yes	characteristic
37	C₁₁×#336	C₂²	1	2	yes	—
38	C₁₁×#336	C₂²	1	2	yes	—
39	C₁₁×#336	C₂²	1	2	yes	—
40	C₁₁×#336	C₂²	1	2	yes	—
41	C₁₁×#336	C₂²	1	2	yes	—
42	C₁₁×#336	C₂²	1	2	yes	—
43	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
45	C₂³×C₄×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	2	yes	—
49	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
50	C₁₁×#117	—	2	4	no	—
51	C₁₁×#117	—	2	4	no	—
52	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
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×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
57	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
58	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
59	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄²×C₁₁	—	2	2	no	—
61	C₂×C₄²×C₁₁	—	2	2	no	—
62	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
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	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
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×C₄⋊C₈	—	2	2	no	—
79	C₁₁×C₄⋊C₈	—	2	2	no	—
80	C₁₁×C₄⋊C₈	—	2	2	no	—
81	C₁₁×C₄⋊C₈	—	2	2	no	—
82	C₁₁×C₄⋊C₈	—	4	2	no	—
83	C₁₁×C₄⋊C₈	—	4	2	no	—
84	C₁₁×C₂²⋊C₈	—	4	2	no	—
85	C₁₁×C₂²⋊C₈	—	4	2	no	—
86	C₁₁×#97	—	4	2	no	—
87	C₄×C₈×C₁₁	—	4	2	no	—
88	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
89	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
90	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
91	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
92	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
93	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
94	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
95	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
96	#21924	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
97	C₂⁴×C₁₁	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₁	—	2	2	no	—
99	C₂²×C₄×C₁₁	—	2	2	no	—
100	C₂²×C₄×C₁₁	—	2	2	no	—
101	C₂²×C₄×C₁₁	—	2	2	no	—
102	C₂²×C₄×C₁₁	—	2	2	no	—
103	C₂²×C₄×C₁₁	—	2	2	no	—
104	C₂²×C₄×C₁₁	—	2	1	no	—
105	C₂²×C₄×C₁₁	—	2	1	no	—
106	C₂²×C₄×C₁₁	—	2	1	no	—
107	C₂²×C₄×C₁₁	—	2	1	no	—
108	C₂²×C₄×C₁₁	—	2	1	no	—
109	C₂²×C₄×C₁₁	—	2	1	no	—
110	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
124	C₂×C₈×C₁₁	—	2	2	no	—
125	C₂×C₈×C₁₁	—	2	2	no	—
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	—	2	2	no	—
133	C₂×C₈×C₁₁	—	2	2	no	—
134	C₂×C₈×C₁₁	—	2	2	no	—
135	C₂×C₈×C₁₁	—	2	2	no	—
136	C₁₁×C₄⋊C₄	—	2	2	no	—
137	C₁₁×C₄⋊C₄	—	2	2	no	—
138	C₁₁×C₄⋊C₄	—	2	2	no	—
139	C₁₁×C₄⋊C₄	M₁₆	1	4	yes	—
140	C₁₁×C₂²⋊C₄	—	2	2	no	—
141	C₁₁×C₂²⋊C₄	—	2	2	no	—
142	C₁₁×C₂²⋊C₄	—	2	2	no	—
143	C₁₁×C₂²⋊C₄	M₁₆	1	4	yes	—
144	C₄²×C₁₁	—	2	2	no	—
145	C₄²×C₁₁	—	2	2	no	—
146	C₄²×C₁₁	—	2	2	no	—
147	C₄²×C₁₁	—	2	2	no	—
148	C₄²×C₁₁	—	2	2	no	—
149	C₄²×C₁₁	—	2	2	no	—
150	C₄²×C₁₁	—	2	2	no	—
151	C₄²×C₁₁	—	2	2	no	—
152	C₄²×C₁₁	—	2	2	no	—
153	C₄²×C₁₁	—	2	2	no	—
154	C₄²×C₁₁	—	2	1	no	—
155	C₄²×C₁₁	—	2	1	no	—
156	C₄²×C₁₁	—	2	1	no	—
157	C₄²×C₁₁	—	2	1	no	—
158	C₄²×C₁₁	—	2	1	no	—
159	C₄²×C₁₁	—	2	1	no	—
160	C₄²×C₁₁	—	2	1	no	—
161	C₄²×C₁₁	—	2	1	no	—
162	C₄²×C₁₁	—	2	1	no	—
163	C₄²×C₁₁	—	2	1	no	—
164	C₄²×C₁₁	#41	1	2	yes	—
165	C₄²×C₁₁	#41	1	2	yes	—
166	C₄×#117	C₂×C₁₁	1	1	yes	characteristic
167	#1924	C₂×C₁₁	1	2	yes	—
168	#1923	C₂×C₁₁	1	2	yes	—
169	#1917	C₂×C₁₁	1	2	yes	complemented
170	#1916	C₂×C₁₁	1	2	yes	complemented
171	#1842	C₂×C₁₁	1	1	yes	characteristic, complemented
172	#1831	C₂×C₁₁	1	1	yes	characteristic, complemented
173	#1797	C₂×C₁₁	1	1	yes	characteristic
174	#1797	C₂×C₁₁	1	1	yes	characteristic
175	#1767	C₂×C₁₁	1	1	yes	characteristic, complemented
176	C₄×C₄⋊C₈	C₂×C₁₁	1	1	yes	characteristic, complemented
177	C₂³×C₁₁	—	2	1	no	—
178	C₂³×C₁₁	—	2	1	no	—
179	C₂³×C₁₁	—	2	1	no	—
180	C₂³×C₁₁	—	2	1	no	—
181	C₂³×C₁₁	—	2	1	no	—
182	C₂³×C₁₁	—	2	1	no	—
183	C₂³×C₁₁	C₂×M₁₆	1	2	yes	—
184	C₂³×C₁₁	C₂³×C₄	1	1	yes	characteristic
185	C₂×C₄×C₁₁	—	2	8	no	—
186	C₂×C₄×C₁₁	—	2	1	no	—
187	C₂×C₄×C₁₁	—	2	1	no	—
188	C₂×C₄×C₁₁	—	2	1	no	—
189	C₂×C₄×C₁₁	—	2	1	no	—
190	C₂×C₄×C₁₁	—	2	1	no	—
191	C₂×C₄×C₁₁	—	2	1	no	—
192	C₂×C₄×C₁₁	—	2	1	no	—
193	C₂×C₄×C₁₁	—	2	1	no	—
194	C₂×C₄×C₁₁	—	2	1	no	—
195	C₂×C₄×C₁₁	—	2	1	no	—
196	C₂×C₄×C₁₁	—	2	1	no	—
197	C₂×C₄×C₁₁	—	2	1	no	—
198	C₂×C₄×C₁₁	—	2	1	no	—
199	C₂×C₄×C₁₁	—	2	1	no	—
200	C₂×C₄×C₁₁	—	2	1	no	—
201	C₂×C₄×C₁₁	—	2	1	no	—
202	C₂×C₄×C₁₁	—	2	1	no	—
203	C₂×C₄×C₁₁	—	2	1	no	—
204	C₂×C₄×C₁₁	—	2	1	no	—
205	C₂×C₄×C₁₁	—	2	1	no	—
206	C₂×C₄×C₁₁	—	2	1	no	—
207	C₂×C₄×C₁₁	—	2	1	no	—
208	C₂×C₄×C₁₁	—	2	1	no	—
209	C₂×C₄×C₁₁	—	2	1	no	—
210	C₂×C₄×C₁₁	—	2	1	no	—
211	C₂×C₄×C₁₁	—	2	1	no	—
212	C₂×C₄×C₁₁	—	2	1	no	—
213	C₂×C₄×C₁₁	—	2	1	no	—
214	C₂×C₄×C₁₁	—	2	1	no	—
215	C₂×C₄×C₁₁	—	2	1	no	—
216	C₂×C₄×C₁₁	—	4	1	no	—
217	C₂×C₄×C₁₁	—	4	1	no	—
218	C₂×C₄×C₁₁	—	4	1	no	—
219	C₂×C₄×C₁₁	—	4	1	no	—
220	C₂×C₄×C₁₁	—	4	4	no	—
221	C₂×C₄×C₁₁	#117	1	2	yes	—
222	C₂×C₄×C₁₁	#117	1	2	yes	—
223	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
224	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
225	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
226	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
227	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
228	C₂×C₄×C₁₁	#131	1	2	yes	—
229	C₂×C₄×C₁₁	#131	1	2	yes	—
230	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
231	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
232	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
233	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
234	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
235	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
236	C₈×C₁₁	—	4	2	no	—
237	C₈×C₁₁	—	4	2	no	—
238	C₈×C₁₁	—	4	2	no	—
239	C₈×C₁₁	—	4	2	no	—
240	C₂×#117	C₄×C₁₁	1	1	yes	characteristic
241	C₂×#117	C₄×C₁₁	1	1	yes	characteristic
242	C₂²×C₄²	C₂²×C₁₁	1	1	yes	characteristic
243	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
244	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
245	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
246	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
247	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
248	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
249	C₂×C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
250	C₂×C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
251	C₂×#97	C₂²×C₁₁	1	2	yes	—
252	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	—
253	C₄×C₄⋊C₄	C₄×C₁₁	1	1	yes	characteristic
254	C₄×C₄⋊C₄	C₄×C₁₁	1	1	yes	characteristic
255	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
256	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
257	C₄×C₂²⋊C₄	C₄×C₁₁	1	1	yes	characteristic
258	C₄×C₂²⋊C₄	C₄×C₁₁	1	1	yes	characteristic
259	C₄×C₂²⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
260	C₄×C₂²⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
261	#376	C₄×C₁₁	1	1	yes	characteristic
262	#376	C₄×C₁₁	1	1	yes	characteristic
263	C₄³	C₂²×C₁₁	1	1	yes	characteristic
264	C₄³	C₂²×C₁₁	1	1	yes	characteristic
265	#336	C₂²×C₁₁	1	2	yes	—
266	#336	C₂²×C₁₁	1	2	yes	—
267	#336	C₂²×C₁₁	1	2	yes	—
268	#336	C₂²×C₁₁	1	2	yes	—
269	#336	C₂²×C₁₁	1	2	yes	—
270	#336	C₂²×C₁₁	1	2	yes	—
271	C₂²×C₁₁	—	2	2	no	—
272	C₂²×C₁₁	—	2	2	no	—
273	C₂²×C₁₁	—	2	2	no	—
274	C₂²×C₁₁	—	4	1	no	—
275	C₂²×C₁₁	—	4	1	no	—
276	C₂²×C₁₁	—	4	1	no	—
277	C₂²×C₁₁	—	4	1	no	—
278	C₂²×C₁₁	C₂×#117	1	1	yes	characteristic
279	C₂²×C₁₁	#520	1	1	yes	characteristic
280	C₂²×C₁₁	#520	1	1	yes	characteristic
281	C₂²×C₁₁	C₂²×M₁₆	1	1	yes	characteristic
282	C₂²×C₁₁	C₂²×M₁₆	1	1	yes	characteristic
283	C₂²×C₁₁	C₂×#131	1	1	yes	characteristic
284	C₂²×C₁₁	C₂×#131	1	1	yes	characteristic
285	C₄×C₁₁	—	2	2	no	—
286	C₄×C₁₁	—	2	2	no	—
287	C₄×C₁₁	—	2	2	no	—
288	C₄×C₁₁	—	2	2	no	—
289	C₄×C₁₁	—	2	2	no	—
290	C₄×C₁₁	—	2	2	no	—
291	C₄×C₁₁	—	4	1	no	—
292	C₄×C₁₁	—	4	1	no	—
293	C₄×C₁₁	—	4	1	no	—
294	C₄×C₁₁	—	4	1	no	—
295	C₄×C₁₁	—	4	1	no	—
296	C₄×C₁₁	—	4	1	no	—
297	C₄×C₁₁	#433	1	4	yes	—
298	C₄×C₁₁	#540	1	1	yes	characteristic
299	C₄×C₁₁	#541	1	1	yes	characteristic
300	C₄×C₁₁	#542	1	1	yes	characteristic
301	C₄×C₁₁	#542	1	1	yes	characteristic
302	C₂³×C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
303	C₂³×C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
304	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
305	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
306	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
307	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
308	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
309	#117	—	2	4	no	—
310	#117	—	2	4	no	—
311	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
312	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
313	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
314	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
315	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
316	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
317	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
318	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
319	C₂×C₄²	—	2	2	no	—
320	C₂×C₄²	—	2	2	no	—
321	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
322	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
323	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
324	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
325	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
326	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
327	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
328	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
329	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
330	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
331	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
332	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
333	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
334	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
335	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
336	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
337	C₄⋊C₈	—	2	2	no	—
338	C₄⋊C₈	—	2	2	no	—
339	C₄⋊C₈	—	2	2	no	—
340	C₄⋊C₈	—	2	2	no	—
341	C₄⋊C₈	—	4	2	no	—
342	C₄⋊C₈	—	4	2	no	—
343	C₂²⋊C₈	—	4	2	no	—
344	C₂²⋊C₈	—	4	2	no	—
345	#97	—	4	2	no	—
346	C₄×C₈	—	4	2	no	—
347	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
348	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
349	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
350	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
351	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
352	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
353	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
354	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
355	C₂×C₁₁	—	4	2	no	—
356	C₂×C₁₁	#2314	1	1	yes	characteristic
357	C₂×C₁₁	C₂×#433	1	1	yes	characteristic
358	C₂×C₁₁	#2920	1	1	yes	characteristic
359	C₂×C₁₁	#2990	1	1	yes	characteristic
360	C₂×C₁₁	#2990	1	1	yes	characteristic
361	C₂×C₁₁	#2990	1	1	yes	characteristic
362	C₂×C₁₁	#2991	1	1	yes	characteristic
363	C₂⁴	C₂²×C₄×C₁₁	1	1	yes	characteristic
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	2	1	no	—
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
377	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
378	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
379	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
380	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
381	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
382	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
383	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
384	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
385	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
386	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
387	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
388	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
389	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	2	2	no	—
394	C₂×C₈	—	2	2	no	—
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	—	2	2	no	—
398	C₂×C₈	—	2	2	no	—
399	C₂×C₈	—	2	2	no	—
400	C₂×C₈	—	2	2	no	—
401	C₂×C₈	—	2	2	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	C₁₁×M₁₆	1	4	yes	—
406	C₂²⋊C₄	—	2	2	no	—
407	C₂²⋊C₄	—	2	2	no	—
408	C₂²⋊C₄	—	2	2	no	—
409	C₂²⋊C₄	C₁₁×M₁₆	1	4	yes	—
410	C₄²	—	2	2	no	—
411	C₄²	—	2	2	no	—
412	C₄²	—	2	2	no	—
413	C₄²	—	2	2	no	—
414	C₄²	—	2	2	no	—
415	C₄²	—	2	2	no	—
416	C₄²	—	2	2	no	—
417	C₄²	—	2	2	no	—
418	C₄²	—	2	2	no	—
419	C₄²	—	2	2	no	—
420	C₄²	—	2	1	no	—
421	C₄²	—	2	1	no	—
422	C₄²	—	2	1	no	—
423	C₄²	—	2	1	no	—
424	C₄²	—	2	1	no	—
425	C₄²	—	2	1	no	—
426	C₄²	—	2	1	no	—
427	C₄²	—	2	1	no	—
428	C₄²	—	2	1	no	—
429	C₄²	—	2	1	no	—
430	C₄²	C₁₁×#41	1	2	yes	—
431	C₄²	C₁₁×#41	1	2	yes	—
432	C₁₁	#21924	1	1	yes	characteristic, direct product factor, Sylow
433	C₂³	—	2	1	no	—
434	C₂³	—	2	1	no	—
435	C₂³	—	2	1	no	—
436	C₂³	—	2	1	no	—
437	C₂³	—	2	1	no	—
438	C₂³	—	2	1	no	—
439	C₂³	C₂×C₁₁×M₁₆	1	2	yes	—
440	C₂³	C₂³×C₄×C₁₁	1	1	yes	characteristic
441	C₂×C₄	—	2	8	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	1	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	1	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	4	1	no	—
473	C₂×C₄	—	4	1	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	4	1	no	—
476	C₂×C₄	—	4	4	no	—
477	C₂×C₄	C₁₁×#117	1	2	yes	—
478	C₂×C₄	C₁₁×#117	1	2	yes	—
479	C₂×C₄	C₂×C₁₁×M₁₆	1	2	yes	—
480	C₂×C₄	C₂×C₁₁×M₁₆	1	2	yes	—
481	C₂×C₄	C₂×C₁₁×M₁₆	1	2	yes	—
482	C₂×C₄	C₂×C₁₁×M₁₆	1	2	yes	—
483	C₂×C₄	C₂×C₁₁×M₁₆	1	2	yes	—
484	C₂×C₄	C₁₁×#131	1	2	yes	—
485	C₂×C₄	C₁₁×#131	1	2	yes	—
486	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
487	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
488	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
489	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
490	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
491	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
492	C₈	—	4	2	no	—
493	C₈	—	4	2	no	—
494	C₈	—	4	2	no	—
495	C₈	—	4	2	no	—
496	C₂²	—	2	2	no	—
497	C₂²	—	2	2	no	—
498	C₂²	—	2	2	no	—
499	C₂²	—	4	1	no	—
500	C₂²	—	4	1	no	—
501	C₂²	—	4	1	no	—
502	C₂²	—	4	1	no	—
503	C₂²	C₂×C₁₁×#117	1	1	yes	characteristic
504	C₂²	C₁₁×#520	1	1	yes	characteristic
505	C₂²	C₁₁×#520	1	1	yes	characteristic
506	C₂²	C₂²×C₁₁×M₁₆	1	1	yes	characteristic
507	C₂²	C₂²×C₁₁×M₁₆	1	1	yes	characteristic
508	C₂²	C₂×C₁₁×#131	1	1	yes	characteristic
509	C₂²	C₂×C₁₁×#131	1	1	yes	characteristic
510	C₄	—	2	2	no	—
511	C₄	—	2	2	no	—
512	C₄	—	2	2	no	—
513	C₄	—	2	2	no	—
514	C₄	—	2	2	no	—
515	C₄	—	2	2	no	—
516	C₄	—	4	1	no	—
517	C₄	—	4	1	no	—
518	C₄	—	4	1	no	—
519	C₄	—	4	1	no	—
520	C₄	—	4	1	no	—
521	C₄	—	4	1	no	—
522	C₄	C₁₁×#433	1	4	yes	—
523	C₄	C₁₁×#540	1	1	yes	characteristic
524	C₄	C₁₁×#541	1	1	yes	characteristic
525	C₄	C₁₁×#542	1	1	yes	characteristic
526	C₄	C₁₁×#542	1	1	yes	characteristic
527	C₂	—	4	2	no	—
528	C₂	C₁₁×#2314	1	1	yes	characteristic
529	C₂	C₂×C₁₁×#433	1	1	yes	characteristic
530	C₂	C₁₁×#2920	1	1	yes	characteristic
531	C₂	C₁₁×#2990	1	1	yes	characteristic
532	C₂	C₁₁×#2990	1	1	yes	characteristic
533	C₂	C₁₁×#2990	1	1	yes	characteristic
534	C₂	C₁₁×#2991	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	C₂⁴×C₁₁	C₂²×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×#1917	C₂	semidirect
5. C₁₁×#1916	C₂	semidirect
6. C₁₁×#1842	C₂	semidirect
7. C₁₁×#1831	C₂	semidirect
10. C₁₁×#1767	C₂	semidirect
11. C₄×C₁₁×C₄⋊C₈	C₂	semidirect
96. #21924	C₁₁	direct (N × H)
169. #1917	C₂×C₁₁	semidirect
170. #1916	C₂×C₁₁	semidirect
171. #1842	C₂×C₁₁	semidirect
172. #1831	C₂×C₁₁	semidirect
175. #1767	C₂×C₁₁	semidirect
176. C₄×C₄⋊C₈	C₂×C₁₁	semidirect
432. C₁₁	#21924	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₁₁×#117	2
C₁₁×#1924	2
C₁₁×#1923	2
C₁₁×#1917	2
C₁₁×#1916	2
C₁₁×#1842	2
C₁₁×#1831	2
C₁₁×#1797	2
C₁₁×#1767	2
C₄×C₁₁×C₄⋊C₈	2
#21924	11

Subgroups — C11×#21924 #14599117

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#21924 #14599117