Subgroups — C₁₁×#23174 #14600367

Order 2816.

1144 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#436	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₁×#435	C₂	1	2	yes	maximal, complemented
3	C₂×C₈×D₄×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₁₁×#127	C₂	1	1	yes	maximal, characteristic
5	C₁₁×#1955	C₂	1	2	yes	maximal, complemented
6	C₁₁×#1954	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#1954	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₁×#1870	C₂	1	2	yes	maximal, complemented
9	C₁₁×#1869	C₂	1	2	yes	maximal, complemented
10	C₁₁×#1767	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₁₁×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₁×M₁₆	C₂²	1	2	yes	—
13	C₂³×C₈×C₁₁	C₂²	1	2	yes	—
14	C₂×C₁₁×#127	C₄	1	1	yes	characteristic
15	C₂×C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₄×C₁₁	C₂²	1	2	yes	—
17	C₂×C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₄×C₁₁	C₂²	1	2	yes	—
19	C₁₁×#436	—	2	4	no	—
20	C₁₁×#435	—	2	8	no	—
21	C₈×D₄×C₁₁	—	2	4	no	—
22	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₁×C₂²⋊C₈	C₂²	1	2	yes	—
27	C₂×C₁₁×C₂²⋊C₈	C₂²	1	2	yes	—
28	C₂×C₁₁×C₂²⋊C₈	C₂²	1	2	yes	—
29	C₂×C₁₁×C₂²⋊C₈	C₂²	1	2	yes	—
30	C₂×C₁₁×C₂²⋊C₈	C₂²	1	2	yes	—
31	C₂×C₁₁×C₂²⋊C₈	C₂²	1	2	yes	—
32	C₂×C₁₁×#97	C₂²	1	2	yes	—
33	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
35	C₁₁×#390	C₄	1	2	yes	—
36	C₁₁×#390	C₄	1	1	yes	characteristic
37	C₁₁×#390	C₄	1	1	yes	characteristic
38	C₁₁×#390	C₄	1	2	yes	—
39	C₁₁×#384	C₄	1	1	yes	characteristic
40	C₄³×C₁₁	C₂²	1	1	yes	characteristic
41	C₁₁×#336	C₂²	1	1	yes	characteristic
42	C₁₁×#336	C₂²	1	2	yes	—
43	C₁₁×#336	C₂²	1	1	yes	characteristic
44	C₂²×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
45	C₂²×D₄×C₁₁	C₂×C₄	1	2	yes	—
46	C₂²×D₄×C₁₁	C₂×C₄	1	2	yes	—
47	C₂²×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
48	C₂³×C₄×C₁₁	C₂³	1	2	yes	—
49	C₂³×C₄×C₁₁	C₂³	1	2	yes	—
50	C₂×C₁₁×M₁₆	—	2	4	no	—
51	C₂×C₁₁×M₁₆	—	2	4	no	—
52	C₂×C₁₁×M₁₆	—	4	2	no	—
53	C₂²×C₈×C₁₁	—	2	4	no	—
54	C₂²×C₈×C₁₁	—	2	4	no	—
55	C₂²×C₈×C₁₁	—	4	2	no	—
56	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
59	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
60	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
61	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
62	C₁₁×#127	—	2	4	no	—
63	C₄×D₄×C₁₁	—	2	2	no	—
64	C₄×D₄×C₁₁	—	2	4	no	—
65	C₄×D₄×C₁₁	—	2	2	no	—
66	C₄×D₄×C₁₁	—	2	2	no	—
67	C₄×D₄×C₁₁	—	2	4	no	—
68	C₄×D₄×C₁₁	—	2	2	no	—
69	C₄×D₄×C₁₁	—	4	2	no	—
70	C₄×D₄×C₁₁	—	4	2	no	—
71	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
72	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
73	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
74	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
75	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
76	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
77	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
78	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
79	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
80	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
81	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
82	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
83	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
84	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
85	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
86	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
88	C₁₁×C₄⋊C₈	—	2	2	no	—
89	C₁₁×C₄⋊C₈	—	2	2	no	—
90	C₁₁×C₄⋊C₈	D₄	1	4	yes	complemented
91	C₁₁×C₄⋊C₈	D₄	1	4	yes	complemented
92	C₁₁×C₂²⋊C₈	—	2	4	no	—
93	C₁₁×C₂²⋊C₈	—	2	4	no	—
94	C₁₁×C₂²⋊C₈	—	2	4	no	—
95	C₁₁×C₂²⋊C₈	—	2	4	no	—
96	C₁₁×C₂²⋊C₈	—	4	2	no	—
97	C₁₁×C₂²⋊C₈	—	4	2	no	—
98	C₁₁×#97	—	2	4	no	—
99	C₄×C₈×C₁₁	—	2	2	no	—
100	C₄×C₈×C₁₁	—	2	2	no	—
101	#23174	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
102	C₂⁴×C₁₁	C₂²×C₄	1	2	yes	—
103	C₂⁴×C₁₁	C₂²×C₄	1	2	yes	—
104	C₂×D₄×C₁₁	—	2	4	no	—
105	C₂×D₄×C₁₁	—	2	4	no	—
106	C₂×D₄×C₁₁	—	2	2	no	—
107	C₂×D₄×C₁₁	—	2	4	no	—
108	C₂×D₄×C₁₁	—	2	2	no	—
109	C₂×D₄×C₁₁	—	2	2	no	—
110	C₂×D₄×C₁₁	—	2	2	no	—
111	C₂×D₄×C₁₁	—	2	4	no	—
112	C₂×D₄×C₁₁	—	2	2	no	—
113	C₂×D₄×C₁₁	—	4	2	no	—
114	C₂×D₄×C₁₁	—	4	2	no	—
115	C₂×D₄×C₁₁	M₁₆	1	4	yes	complemented
116	C₂²×C₄×C₁₁	—	2	2	no	—
117	C₂²×C₄×C₁₁	—	2	2	no	—
118	C₂²×C₄×C₁₁	—	2	2	no	—
119	C₂²×C₄×C₁₁	—	2	2	no	—
120	C₂²×C₄×C₁₁	—	2	2	no	—
121	C₂²×C₄×C₁₁	—	2	2	no	—
122	C₂²×C₄×C₁₁	—	2	2	no	—
123	C₂²×C₄×C₁₁	—	2	2	no	—
124	C₂²×C₄×C₁₁	—	2	2	no	—
125	C₂²×C₄×C₁₁	—	2	2	no	—
126	C₂²×C₄×C₁₁	—	2	2	no	—
127	C₂²×C₄×C₁₁	—	2	2	no	—
128	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
130	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
131	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
137	C₁₁×M₁₆	—	4	8	no	—
138	C₂×C₈×C₁₁	—	2	1	no	—
139	C₂×C₈×C₁₁	—	2	1	no	—
140	C₂×C₈×C₁₁	—	2	2	no	—
141	C₂×C₈×C₁₁	—	2	1	no	—
142	C₂×C₈×C₁₁	—	2	1	no	—
143	C₂×C₈×C₁₁	—	2	2	no	—
144	C₂×C₈×C₁₁	—	2	1	no	—
145	C₂×C₈×C₁₁	—	2	1	no	—
146	C₂×C₈×C₁₁	—	2	2	no	—
147	C₂×C₈×C₁₁	—	2	1	no	—
148	C₂×C₈×C₁₁	—	2	2	no	—
149	C₂×C₈×C₁₁	—	2	1	no	—
150	C₂×C₈×C₁₁	—	2	1	no	—
151	C₂×C₈×C₁₁	—	2	1	no	—
152	C₂×C₈×C₁₁	—	2	2	no	—
153	C₂×C₈×C₁₁	—	4	8	no	—
154	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
155	C₂×C₈×C₁₁	C₂×D₄	1	4	yes	—
156	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
157	C₁₁×C₄⋊C₄	—	2	4	no	—
158	C₁₁×C₄⋊C₄	—	2	2	no	—
159	C₁₁×C₄⋊C₄	—	2	2	no	—
160	C₁₁×C₄⋊C₄	—	4	2	no	—
161	C₁₁×C₂²⋊C₄	—	2	4	no	—
162	C₁₁×C₂²⋊C₄	—	2	4	no	—
163	C₁₁×C₂²⋊C₄	—	2	4	no	—
164	C₁₁×C₂²⋊C₄	—	2	4	no	—
165	C₁₁×C₂²⋊C₄	—	4	2	no	—
166	C₁₁×C₂²⋊C₄	—	4	2	no	—
167	C₄²×C₁₁	—	2	2	no	—
168	C₄²×C₁₁	—	2	2	no	—
169	C₄²×C₁₁	—	2	2	no	—
170	C₄²×C₁₁	—	2	1	no	—
171	C₄²×C₁₁	—	2	1	no	—
172	C₄²×C₁₁	—	4	1	no	—
173	C₄²×C₁₁	C₂×D₄	1	2	yes	—
174	C₄²×C₁₁	C₂×D₄	1	2	yes	—
175	C₄²×C₁₁	#41	1	2	yes	—
176	C₄²×C₁₁	#41	1	2	yes	—
177	C₂×#436	C₂×C₁₁	1	1	yes	characteristic, complemented
178	C₂×#435	C₂×C₁₁	1	2	yes	complemented
179	C₂×C₈×D₄	C₂×C₁₁	1	1	yes	characteristic, complemented
180	C₄×#127	C₂×C₁₁	1	1	yes	characteristic
181	#1955	C₂×C₁₁	1	2	yes	complemented
182	#1954	C₂×C₁₁	1	1	yes	characteristic, complemented
183	#1954	C₂×C₁₁	1	1	yes	characteristic, complemented
184	#1870	C₂×C₁₁	1	2	yes	complemented
185	#1869	C₂×C₁₁	1	2	yes	complemented
186	#1767	C₂×C₁₁	1	1	yes	characteristic, complemented
187	C₄×C₄⋊C₈	C₂×C₁₁	1	1	yes	characteristic, complemented
188	C₂³×C₁₁	—	2	2	no	—
189	C₂³×C₁₁	—	2	2	no	—
190	C₂³×C₁₁	—	2	2	no	—
191	C₂³×C₁₁	—	2	2	no	—
192	C₂³×C₁₁	—	2	2	no	—
193	C₂³×C₁₁	—	2	2	no	—
194	C₂³×C₁₁	—	2	2	no	—
195	C₂³×C₁₁	—	2	2	no	—
196	C₂³×C₁₁	—	2	2	no	—
197	C₂³×C₁₁	—	2	2	no	—
198	C₂³×C₁₁	—	2	2	no	—
199	C₂³×C₁₁	—	2	2	no	—
200	C₂³×C₁₁	—	2	2	no	—
201	C₂³×C₁₁	C₂×M₁₆	1	4	yes	—
202	C₂³×C₁₁	C₂³×C₄	1	1	yes	characteristic
203	D₄×C₁₁	—	2	8	no	—
204	D₄×C₁₁	—	4	8	no	—
205	D₄×C₁₁	—	4	8	no	—
206	D₄×C₁₁	—	4	4	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	2	no	—
216	C₂×C₄×C₁₁	—	2	2	no	—
217	C₂×C₄×C₁₁	—	2	2	no	—
218	C₂×C₄×C₁₁	—	2	2	no	—
219	C₂×C₄×C₁₁	—	2	1	no	—
220	C₂×C₄×C₁₁	—	2	2	no	—
221	C₂×C₄×C₁₁	—	2	2	no	—
222	C₂×C₄×C₁₁	—	2	1	no	—
223	C₂×C₄×C₁₁	—	2	1	no	—
224	C₂×C₄×C₁₁	—	4	2	no	—
225	C₂×C₄×C₁₁	—	4	2	no	—
226	C₂×C₄×C₁₁	—	4	2	no	—
227	C₂×C₄×C₁₁	—	4	2	no	—
228	C₂×C₄×C₁₁	—	4	2	no	—
229	C₂×C₄×C₁₁	—	4	2	no	—
230	C₂×C₄×C₁₁	—	4	2	no	—
231	C₂×C₄×C₁₁	—	4	2	no	—
232	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
233	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
234	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
235	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
236	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
237	C₂×C₄×C₁₁	#131	1	2	yes	—
238	C₂×C₄×C₁₁	#131	1	2	yes	—
239	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
240	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
241	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
242	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
243	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
244	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
245	C₈×C₁₁	—	2	2	no	—
246	C₈×C₁₁	—	2	4	no	—
247	C₈×C₁₁	—	2	2	no	—
248	C₈×C₁₁	—	4	1	no	—
249	C₈×C₁₁	—	4	1	no	—
250	C₈×C₁₁	—	4	2	no	—
251	C₂²×M₁₆	C₂²×C₁₁	1	2	yes	—
252	C₂³×C₈	C₂²×C₁₁	1	2	yes	—
253	C₂×#127	C₄×C₁₁	1	1	yes	characteristic
254	C₂×C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic
255	C₂×C₄×D₄	C₂²×C₁₁	1	2	yes	—
256	C₂×C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic
257	C₂×C₄×D₄	C₂²×C₁₁	1	2	yes	—
258	#436	—	2	4	no	—
259	#435	—	2	8	no	—
260	C₈×D₄	—	2	4	no	—
261	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
262	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
263	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
264	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
265	C₂×C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
266	C₂×C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
267	C₂×C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
268	C₂×C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
269	C₂×C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
270	C₂×C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
271	C₂×#97	C₂²×C₁₁	1	2	yes	—
272	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
273	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
274	#390	C₄×C₁₁	1	2	yes	—
275	#390	C₄×C₁₁	1	1	yes	characteristic
276	#390	C₄×C₁₁	1	1	yes	characteristic
277	#390	C₄×C₁₁	1	2	yes	—
278	#384	C₄×C₁₁	1	1	yes	characteristic
279	C₄³	C₂²×C₁₁	1	1	yes	characteristic
280	#336	C₂²×C₁₁	1	1	yes	characteristic
281	#336	C₂²×C₁₁	1	2	yes	—
282	#336	C₂²×C₁₁	1	1	yes	characteristic
283	C₂²×C₁₁	—	2	4	no	—
284	C₂²×C₁₁	—	2	4	no	—
285	C₂²×C₁₁	—	2	4	no	—
286	C₂²×C₁₁	—	4	2	no	—
287	C₂²×C₁₁	—	4	2	no	—
288	C₂²×C₁₁	—	4	2	no	—
289	C₂²×C₁₁	—	4	2	no	—
290	C₂²×C₁₁	—	4	2	no	—
291	C₂²×C₁₁	—	4	2	no	—
292	C₂²×C₁₁	—	4	2	no	—
293	C₂²×C₁₁	—	4	2	no	—
294	C₂²×C₁₁	—	4	2	no	—
295	C₂²×C₁₁	—	4	2	no	—
296	C₂²×C₁₁	—	4	2	no	—
297	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
298	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
299	C₂²×C₁₁	#518	1	1	yes	characteristic
300	C₂²×C₁₁	C₂²×M₁₆	1	1	yes	characteristic
301	C₂²×C₁₁	C₂×#131	1	1	yes	characteristic
302	C₂²×C₁₁	C₂×#131	1	1	yes	characteristic
303	C₂²×C₁₁	#568	1	1	yes	characteristic
304	C₄×C₁₁	—	2	2	no	—
305	C₄×C₁₁	—	2	2	no	—
306	C₄×C₁₁	—	2	2	no	—
307	C₄×C₁₁	—	2	2	no	—
308	C₄×C₁₁	—	4	2	no	—
309	C₄×C₁₁	—	4	2	no	—
310	C₄×C₁₁	—	4	1	no	—
311	C₄×C₁₁	#435	1	4	yes	complemented
312	C₄×C₁₁	D₄²	1	1	yes	characteristic
313	C₄×C₁₁	#550	1	1	yes	characteristic
314	C₄×C₁₁	#550	1	1	yes	characteristic
315	C₄×C₁₁	#559	1	1	yes	characteristic
316	C₂²×D₄	C₂×C₄×C₁₁	1	1	yes	characteristic
317	C₂²×D₄	C₂×C₄×C₁₁	1	2	yes	—
318	C₂²×D₄	C₂×C₄×C₁₁	1	2	yes	—
319	C₂²×D₄	C₂×C₄×C₁₁	1	1	yes	characteristic
320	C₂³×C₄	C₂³×C₁₁	1	2	yes	—
321	C₂³×C₄	C₂³×C₁₁	1	2	yes	—
322	C₂×M₁₆	—	2	4	no	—
323	C₂×M₁₆	—	2	4	no	—
324	C₂×M₁₆	—	4	2	no	—
325	C₂²×C₈	—	2	4	no	—
326	C₂²×C₈	—	2	4	no	—
327	C₂²×C₈	—	4	2	no	—
328	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
329	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
330	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
331	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
332	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
333	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
334	#127	—	2	4	no	—
335	C₄×D₄	—	2	2	no	—
336	C₄×D₄	—	2	4	no	—
337	C₄×D₄	—	2	2	no	—
338	C₄×D₄	—	2	2	no	—
339	C₄×D₄	—	2	4	no	—
340	C₄×D₄	—	2	2	no	—
341	C₄×D₄	—	4	2	no	—
342	C₄×D₄	—	4	2	no	—
343	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
344	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
345	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
346	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
347	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
348	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
349	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
350	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
351	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
352	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
353	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
354	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
355	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
356	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
357	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
358	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
359	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
360	C₄⋊C₈	—	2	2	no	—
361	C₄⋊C₈	—	2	2	no	—
362	C₄⋊C₈	D₄×C₁₁	1	4	yes	complemented
363	C₄⋊C₈	D₄×C₁₁	1	4	yes	complemented
364	C₂²⋊C₈	—	2	4	no	—
365	C₂²⋊C₈	—	2	4	no	—
366	C₂²⋊C₈	—	2	4	no	—
367	C₂²⋊C₈	—	2	4	no	—
368	C₂²⋊C₈	—	4	2	no	—
369	C₂²⋊C₈	—	4	2	no	—
370	#97	—	2	4	no	—
371	C₄×C₈	—	2	2	no	—
372	C₄×C₈	—	2	2	no	—
373	C₂×C₁₁	—	4	4	no	—
374	C₂×C₁₁	—	8	2	no	—
375	C₂×C₁₁	#2366	1	1	yes	characteristic
376	C₂×C₁₁	C₂×#435	1	1	yes	characteristic
377	C₂×C₁₁	#2931	1	1	yes	characteristic
378	C₂×C₁₁	D₄×M₁₆	1	1	yes	characteristic
379	C₂×C₁₁	#2935	1	1	yes	characteristic
380	C₂×C₁₁	#2974	1	1	yes	characteristic
381	C₂×C₁₁	#2981	1	1	yes	characteristic
382	C₂⁴	C₂²×C₄×C₁₁	1	2	yes	—
383	C₂⁴	C₂²×C₄×C₁₁	1	2	yes	—
384	C₂×D₄	—	2	4	no	—
385	C₂×D₄	—	2	4	no	—
386	C₂×D₄	—	2	2	no	—
387	C₂×D₄	—	2	4	no	—
388	C₂×D₄	—	2	2	no	—
389	C₂×D₄	—	2	2	no	—
390	C₂×D₄	—	2	2	no	—
391	C₂×D₄	—	2	4	no	—
392	C₂×D₄	—	2	2	no	—
393	C₂×D₄	—	4	2	no	—
394	C₂×D₄	—	4	2	no	—
395	C₂×D₄	C₁₁×M₁₆	1	4	yes	complemented
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	2	2	no	—
398	C₂²×C₄	—	2	2	no	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	2	2	no	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
409	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
410	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
411	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
412	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
413	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
414	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
415	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
416	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
417	M₁₆	—	4	8	no	—
418	C₂×C₈	—	2	1	no	—
419	C₂×C₈	—	2	1	no	—
420	C₂×C₈	—	2	2	no	—
421	C₂×C₈	—	2	1	no	—
422	C₂×C₈	—	2	2	no	—
423	C₂×C₈	—	2	1	no	—
424	C₂×C₈	—	2	1	no	—
425	C₂×C₈	—	2	1	no	—
426	C₂×C₈	—	2	2	no	—
427	C₂×C₈	—	2	1	no	—
428	C₂×C₈	—	2	1	no	—
429	C₂×C₈	—	2	2	no	—
430	C₂×C₈	—	2	1	no	—
431	C₂×C₈	—	2	1	no	—
432	C₂×C₈	—	2	2	no	—
433	C₂×C₈	—	4	8	no	—
434	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
435	C₂×C₈	C₂×D₄×C₁₁	1	4	yes	—
436	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
437	C₄⋊C₄	—	2	4	no	—
438	C₄⋊C₄	—	2	2	no	—
439	C₄⋊C₄	—	2	2	no	—
440	C₄⋊C₄	—	4	2	no	—
441	C₂²⋊C₄	—	2	4	no	—
442	C₂²⋊C₄	—	2	4	no	—
443	C₂²⋊C₄	—	2	4	no	—
444	C₂²⋊C₄	—	2	4	no	—
445	C₂²⋊C₄	—	4	2	no	—
446	C₂²⋊C₄	—	4	2	no	—
447	C₄²	—	2	2	no	—
448	C₄²	—	2	2	no	—
449	C₄²	—	2	2	no	—
450	C₄²	—	2	1	no	—
451	C₄²	—	2	1	no	—
452	C₄²	—	4	1	no	—
453	C₄²	C₂×D₄×C₁₁	1	2	yes	—
454	C₄²	C₂×D₄×C₁₁	1	2	yes	—
455	C₄²	C₁₁×#41	1	2	yes	—
456	C₄²	C₁₁×#41	1	2	yes	—
457	C₁₁	#23174	1	1	yes	characteristic, direct product factor, Sylow
458	C₂³	—	2	2	no	—
459	C₂³	—	2	2	no	—
460	C₂³	—	2	2	no	—
461	C₂³	—	2	2	no	—
462	C₂³	—	2	2	no	—
463	C₂³	—	2	2	no	—
464	C₂³	—	2	2	no	—
465	C₂³	—	2	2	no	—
466	C₂³	—	2	2	no	—
467	C₂³	—	2	2	no	—
468	C₂³	—	2	2	no	—
469	C₂³	—	2	2	no	—
470	C₂³	—	2	2	no	—
471	C₂³	C₂×C₁₁×M₁₆	1	4	yes	—
472	C₂³	C₂³×C₄×C₁₁	1	1	yes	characteristic
473	D₄	—	2	8	no	—
474	D₄	—	4	8	no	—
475	D₄	—	4	8	no	—
476	D₄	—	4	4	no	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	1	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	4	2	no	—
495	C₂×C₄	—	4	2	no	—
496	C₂×C₄	—	4	2	no	—
497	C₂×C₄	—	4	2	no	—
498	C₂×C₄	—	4	2	no	—
499	C₂×C₄	—	4	2	no	—
500	C₂×C₄	—	4	2	no	—
501	C₂×C₄	—	4	2	no	—
502	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
503	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
504	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
505	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
506	C₂×C₄	C₂×C₁₁×M₁₆	1	2	yes	—
507	C₂×C₄	C₁₁×#131	1	2	yes	—
508	C₂×C₄	C₁₁×#131	1	2	yes	—
509	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
510	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
511	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
512	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
513	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
514	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
515	C₈	—	2	2	no	—
516	C₈	—	2	4	no	—
517	C₈	—	2	2	no	—
518	C₈	—	4	1	no	—
519	C₈	—	4	1	no	—
520	C₈	—	4	2	no	—
521	C₂²	—	2	4	no	—
522	C₂²	—	2	4	no	—
523	C₂²	—	2	4	no	—
524	C₂²	—	4	2	no	—
525	C₂²	—	4	2	no	—
526	C₂²	—	4	2	no	—
527	C₂²	—	4	2	no	—
528	C₂²	—	4	2	no	—
529	C₂²	—	4	2	no	—
530	C₂²	—	4	2	no	—
531	C₂²	—	4	2	no	—
532	C₂²	—	4	2	no	—
533	C₂²	—	4	2	no	—
534	C₂²	—	4	2	no	—
535	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
536	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
537	C₂²	C₁₁×#518	1	1	yes	characteristic
538	C₂²	C₂²×C₁₁×M₁₆	1	1	yes	characteristic
539	C₂²	C₂×C₁₁×#131	1	1	yes	characteristic
540	C₂²	C₂×C₁₁×#131	1	1	yes	characteristic
541	C₂²	C₁₁×#568	1	1	yes	characteristic
542	C₄	—	2	2	no	—
543	C₄	—	2	2	no	—
544	C₄	—	2	2	no	—
545	C₄	—	2	2	no	—
546	C₄	—	4	1	no	—
547	C₄	—	4	2	no	—
548	C₄	—	4	2	no	—
549	C₄	C₁₁×#435	1	4	yes	complemented
550	C₄	D₄²×C₁₁	1	1	yes	characteristic
551	C₄	C₁₁×#550	1	1	yes	characteristic
552	C₄	C₁₁×#550	1	1	yes	characteristic
553	C₄	C₁₁×#559	1	1	yes	characteristic
554	C₂	—	4	4	no	—
555	C₂	—	8	2	no	—
556	C₂	C₁₁×#2366	1	1	yes	characteristic
557	C₂	C₂×C₁₁×#435	1	1	yes	characteristic
558	C₂	C₁₁×#2931	1	1	yes	characteristic
559	C₂	D₄×C₁₁×M₁₆	1	1	yes	characteristic
560	C₂	C₁₁×#2935	1	1	yes	characteristic
561	C₂	C₁₁×#2974	1	1	yes	characteristic
562	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	C₂×C₁₁×#127	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×#436	C₂	semidirect
2. C₂×C₁₁×#435	C₂	semidirect
3. C₂×C₈×D₄×C₁₁	C₂	semidirect
5. C₁₁×#1955	C₂	semidirect
6. C₁₁×#1954	C₂	semidirect
7. C₁₁×#1954	C₂	semidirect
8. C₁₁×#1870	C₂	semidirect
9. C₁₁×#1869	C₂	semidirect
10. C₁₁×#1767	C₂	semidirect
11. C₄×C₁₁×C₄⋊C₈	C₂	semidirect
90. C₁₁×C₄⋊C₈	D₄	semidirect
91. C₁₁×C₄⋊C₈	D₄	semidirect
101. #23174	C₁₁	direct (N × H)
115. C₂×D₄×C₁₁	M₁₆	semidirect
177. C₂×#436	C₂×C₁₁	semidirect
178. C₂×#435	C₂×C₁₁	semidirect
179. C₂×C₈×D₄	C₂×C₁₁	semidirect
181. #1955	C₂×C₁₁	semidirect
182. #1954	C₂×C₁₁	semidirect
183. #1954	C₂×C₁₁	semidirect
184. #1870	C₂×C₁₁	semidirect
185. #1869	C₂×C₁₁	semidirect
186. #1767	C₂×C₁₁	semidirect
187. C₄×C₄⋊C₈	C₂×C₁₁	semidirect
311. C₄×C₁₁	#435	semidirect
362. C₄⋊C₈	D₄×C₁₁	semidirect
363. C₄⋊C₈	D₄×C₁₁	semidirect
395. C₂×D₄	C₁₁×M₁₆	semidirect
457. C₁₁	#23174	direct (N × H)
549. C₄	C₁₁×#435	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₁×#436	2
C₂×C₁₁×#435	2
C₂×C₈×D₄×C₁₁	2
C₄×C₁₁×#127	2
C₁₁×#1955	2
C₁₁×#1954	2
C₁₁×#1870	2
C₁₁×#1869	2
C₁₁×#1767	2
C₄×C₁₁×C₄⋊C₈	2
#23174	11

Subgroups — C11×#23174 #14600367

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#23174 #14600367