Subgroups — #14907376

Order 2816.

574 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13077308	C₂	1	1	yes	maximal, characteristic
2	#13070446	C₂	1	1	yes	maximal, characteristic, complemented
3	#13070445	C₂	1	1	yes	maximal, characteristic, complemented
4	#13070444	C₂	1	1	yes	maximal, characteristic, complemented
5	#13070441	C₂	1	1	yes	maximal, characteristic, complemented
6	#13070439	C₂	1	1	yes	maximal, characteristic, complemented
7	#13070438	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₆×C₂²⋊D₁₁	C₂	1	1	yes	maximal, characteristic, complemented
9	(C₂²⋊D₁₁)⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
10	#13070420	C₂	1	1	yes	maximal, characteristic, complemented
11	#13070420	C₂	1	1	yes	maximal, characteristic, complemented
12	#13070230	C₂	1	1	yes	maximal, characteristic, complemented
13	#13070225	C₂	1	1	yes	maximal, characteristic, complemented
14	D₁₁×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₁×#2113	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₁×#131	C₂²	1	1	yes	characteristic
17	#10623359	C₄	1	1	yes	characteristic
18	C₂²×C₈×D₁₁	C₂²	1	1	yes	characteristic
19	C₂×C₁₁×M₃₂	C₂²	1	1	yes	characteristic, complemented
20	C₂²×C₁₁×C₁₆	C₂²	1	1	yes	characteristic, complemented
21	#10622847	C₄	1	1	yes	characteristic
22	#10622740	C₄	1	1	yes	characteristic
23	#10622740	C₄	1	1	yes	characteristic
24	#10622740	C₄	1	1	yes	characteristic
25	#10622740	C₄	1	1	yes	characteristic
26	#10622739	C₄	1	1	yes	characteristic
27	#10622732	C₄	1	1	yes	characteristic
28	C₈×C₂²⋊D₁₁	C₂²	1	1	yes	characteristic
29	C₈×C₂²⋊D₁₁	C₂²	1	1	yes	characteristic
30	C₈×C₂²⋊D₁₁	C₂²	1	1	yes	characteristic
31	C₈×C₂²⋊D₁₁	C₂²	1	1	yes	characteristic
32	#10622714	C₂²	1	1	yes	characteristic
33	C₂×#66876	C₂²	1	1	yes	characteristic, complemented
34	C₂²×C₁₁⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
35	C₂×#66862	C₂²	1	1	yes	characteristic
36	C₂×#66862	C₂²	1	1	yes	characteristic
37	C₂×C₁₆×D₁₁	C₂²	1	1	yes	characteristic
38	C₂×C₁₆×D₁₁	C₂²	1	1	yes	characteristic
39	C₁₁×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
40	C₁₁×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
41	C₁₁×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
42	C₁₁×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
43	C₂²⋊(C₁₁⋊C₁₆)	C₂²	1	1	yes	characteristic
44	C₂²⋊(C₁₁⋊C₁₆)	C₂²	1	1	yes	characteristic
45	C₂²⋊(C₁₁⋊C₁₆)	C₂²	1	1	yes	characteristic, complemented
46	C₂²⋊(C₁₁⋊C₁₆)	C₂²	1	1	yes	characteristic, complemented
47	(C₂×D₁₁)⋊C₁₆	C₂²	1	1	yes	characteristic
48	(C₂×D₁₁)⋊C₁₆	C₂²	1	1	yes	characteristic
49	(C₂×D₁₁)⋊C₁₆	C₂²	1	1	yes	characteristic
50	(C₂×D₁₁)⋊C₁₆	C₂²	1	1	yes	characteristic
51	#10622140	C₂²	1	1	yes	characteristic, complemented
52	#10622140	C₂²	1	1	yes	characteristic, complemented
53	Dic₁₁⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
54	Dic₁₁⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
55	Dic₁₁⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
56	Dic₁₁⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
57	C₁₆×Dic₁₁	C₂²	1	1	yes	characteristic, complemented
58	C₁₆×Dic₁₁	C₂²	1	1	yes	characteristic, complemented
59	C₂×C₁₁×#41	C₂×C₄	1	1	yes	characteristic
60	C₂²×C₄×D₁₁	C₂×C₄	1	1	yes	characteristic
61	C₁₁×#131	—	4	1	no	—
62	C₁₁×#131	—	4	1	no	—
63	C₂×C₁₁×M₁₆	C₂×C₄	1	1	yes	characteristic
64	C₂×C₁₁×M₁₆	C₂×C₄	1	1	yes	characteristic
65	C₂×C₁₁×M₁₆	C₂×C₄	1	1	yes	characteristic
66	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
67	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
69	#66999	C₈	1	1	yes	characteristic
70	#66999	C₈	1	1	yes	characteristic
71	#66991	C₈	1	1	yes	characteristic
72	#66991	C₈	1	1	yes	characteristic
73	#66990	C₈	1	1	yes	characteristic
74	#66990	C₈	1	1	yes	characteristic
75	#66988	C₈	1	1	yes	characteristic
76	#66988	C₈	1	1	yes	characteristic
77	C₄×C₂²⋊D₁₁	C₂×C₄	1	1	yes	characteristic
78	C₄×C₂²⋊D₁₁	C₂×C₄	1	1	yes	characteristic
79	C₄×C₂²⋊D₁₁	C₂×C₄	1	1	yes	characteristic
80	C₄×C₂²⋊D₁₁	C₂×C₄	1	1	yes	characteristic
81	#66979	C₂×C₄	1	1	yes	characteristic
82	C₂×#4318	C₂×C₄	1	1	yes	characteristic
83	C₂²×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
84	C₂×C₈×D₁₁	—	4	1	no	—
85	C₂×C₈×D₁₁	—	4	1	no	—
86	C₂×C₈×D₁₁	C₂×C₄	1	1	yes	characteristic
87	C₂×C₈×D₁₁	C₂×C₄	1	1	yes	characteristic
88	C₂×C₈×D₁₁	C₂³	1	1	yes	characteristic
89	C₂×C₈×D₁₁	C₂³	1	1	yes	characteristic
90	C₁₁×M₃₂	—	4	1	no	—
91	C₂×C₁₁×C₁₆	—	4	1	no	—
92	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
93	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
94	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
95	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
96	C₂²⋊(C₁₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
97	C₂²⋊(C₁₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
98	C₂²⋊(C₁₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
99	C₂²⋊(C₁₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
100	(C₂×D₁₁)⋊C₈	C₂×C₄	1	1	yes	characteristic
101	(C₂×D₁₁)⋊C₈	C₂×C₄	1	1	yes	characteristic
102	(C₂×D₁₁)⋊C₈	C₂×C₄	1	1	yes	characteristic
103	(C₂×D₁₁)⋊C₈	C₂×C₄	1	1	yes	characteristic
104	#66879	C₂×C₄	1	1	yes	characteristic
105	#66879	C₂×C₄	1	1	yes	characteristic
106	Dic₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
107	Dic₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
108	Dic₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
109	Dic₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
110	C₈×Dic₁₁	C₂³	1	1	yes	characteristic
111	C₈×Dic₁₁	C₂³	1	1	yes	characteristic
112	#66876	—	4	1	no	—
113	C₂×C₁₁⋊C₁₆	—	4	1	no	—
114	C₂×C₁₁⋊C₁₆	C₂³	1	1	yes	characteristic
115	C₂×C₁₁⋊C₁₆	C₂³	1	1	yes	characteristic
116	C₂×C₁₁⋊C₁₆	C₂³	1	1	yes	characteristic
117	C₂×C₁₁⋊C₁₆	C₂³	1	1	yes	characteristic
118	#66862	—	4	1	no	—
119	#66862	—	4	1	no	—
120	C₁₆×D₁₁	—	4	1	no	—
121	C₁₆×D₁₁	—	4	1	no	—
122	#33490	—	11	1	no	maximal, Sylow
123	C₂³×D₁₁	C₂×C₈	1	1	yes	characteristic
124	C₁₁×#41	—	4	1	no	—
125	C₁₁×#41	—	4	1	no	—
126	C₂×Q₈×C₁₁	C₂×C₈	1	1	yes	characteristic
127	C₂×D₄×C₁₁	C₂×C₈	1	1	yes	characteristic
128	C₂×D₄×C₁₁	C₂×C₈	1	1	yes	characteristic
129	C₂×D₄×C₁₁	C₂×C₈	1	1	yes	characteristic
130	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₂²⋊D₁₁	C₂×C₈	1	1	yes	characteristic
134	C₂×C₂²⋊D₁₁	C₂×C₈	1	1	yes	characteristic
135	C₂×C₂²⋊D₁₁	C₂×C₈	1	1	yes	characteristic
136	C₂×C₂²⋊D₁₁	C₂×C₈	1	1	yes	characteristic
137	C₂²×Dic₁₁	C₂×C₈	1	1	yes	characteristic
138	C₂×C₄×D₁₁	—	4	1	no	—
139	C₂×C₄×D₁₁	—	4	1	no	—
140	C₂×C₄×D₁₁	C₂×C₈	1	1	yes	characteristic
141	C₂×C₄×D₁₁	C₂×C₈	1	1	yes	characteristic
142	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
143	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
144	C₁₁×M₁₆	—	4	1	no	—
145	C₁₁×M₁₆	—	4	1	no	—
146	C₁₁×M₁₆	—	4	1	no	—
147	C₂×C₈×C₁₁	—	2	1	no	—
148	C₂×C₈×C₁₁	—	2	1	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	1	no	—
153	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
154	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
155	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
156	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
157	C₂²⋊Dic₁₁	C₂×C₈	1	1	yes	characteristic
158	C₂²⋊Dic₁₁	C₂×C₈	1	1	yes	characteristic
159	C₂²⋊Dic₁₁	C₂×C₈	1	1	yes	characteristic
160	C₂²⋊Dic₁₁	C₂×C₈	1	1	yes	characteristic
161	C₂²⋊Dic₁₁	C₂×C₈	1	1	yes	characteristic
162	C₂²⋊Dic₁₁	C₂×C₈	1	1	yes	characteristic
163	(C₂×D₁₁)⋊C₄	C₂×C₈	1	1	yes	characteristic
164	(C₂×D₁₁)⋊C₄	C₂×C₈	1	1	yes	characteristic
165	(C₂×D₁₁)⋊C₄	C₂×C₈	1	1	yes	characteristic
166	(C₂×D₁₁)⋊C₄	C₂×C₈	1	1	yes	characteristic
167	C₄⋊Dic₁₁	C₂×C₈	1	1	yes	characteristic
168	C₄⋊Dic₁₁	C₂×C₈	1	1	yes	characteristic
169	Dic₁₁⋊C₄	C₂×C₈	1	1	yes	characteristic
170	Dic₁₁⋊C₄	C₂×C₈	1	1	yes	characteristic
171	Dic₁₁⋊C₄	C₂×C₈	1	1	yes	characteristic
172	Dic₁₁⋊C₄	C₂×C₈	1	1	yes	characteristic
173	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
174	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
175	#4318	—	4	1	no	—
176	C₂×C₁₁⋊C₈	—	4	1	no	—
177	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
178	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
179	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
180	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
181	C₈×D₁₁	—	2	1	no	—
182	C₈×D₁₁	—	2	1	no	—
183	C₈×D₁₁	—	2	1	no	—
184	C₈×D₁₁	—	2	1	no	—
185	C₈×D₁₁	—	4	1	no	—
186	C₈×D₁₁	—	4	1	no	—
187	C₁₁×C₁₆	—	2	1	no	—
188	C₁₁×C₁₆	—	2	1	no	—
189	C₁₁×C₁₆	—	2	1	no	—
190	C₁₁×C₁₆	—	2	1	no	—
191	C₁₁⋊C₁₆	—	2	1	no	—
192	C₁₁⋊C₁₆	—	2	1	no	—
193	C₁₁⋊C₁₆	—	2	1	no	—
194	C₁₁⋊C₁₆	—	2	1	no	—
195	#2929	—	11	1	no	—
196	#2169	—	11	1	no	—
197	#2169	—	11	1	no	—
198	#2168	—	11	1	no	—
199	#2168	—	11	1	no	—
200	#2168	—	11	1	no	—
201	#2168	—	11	1	no	—
202	D₄×C₁₆	—	11	1	no	—
203	D₄×C₁₆	—	11	1	no	—
204	#2164	—	11	1	no	—
205	#2164	—	11	1	no	—
206	#2113	—	11	1	no	—
207	#2113	D₁₁	1	1	yes	characteristic, complemented
208	#2112	—	11	1	no	—
209	C₂×C₂²⋊C₁₆	—	11	1	no	—
210	C₂³×C₁₁	C₂²×C₈	1	1	yes	characteristic
211	C₂³×C₁₁	C₂²×C₈	1	1	yes	characteristic
212	C₂³×C₁₁	C₂²×C₈	1	1	yes	characteristic
213	C₂²×D₁₁	—	2	2	no	—
214	C₂²×D₁₁	—	4	1	no	—
215	C₂²×D₁₁	—	4	1	no	—
216	C₂²×D₁₁	C₂²×C₈	1	1	yes	characteristic
217	C₂²×D₁₁	C₂²×C₈	1	1	yes	characteristic
218	Q₈×C₁₁	—	4	1	no	—
219	D₄×C₁₁	—	4	1	no	—
220	D₄×C₁₁	—	4	1	no	—
221	D₄×C₁₁	—	4	1	no	—
222	C₂×C₄×C₁₁	—	2	1	no	—
223	C₂×C₄×C₁₁	—	2	1	no	—
224	C₂×C₄×C₁₁	—	2	1	no	—
225	C₂×C₄×C₁₁	—	2	1	no	—
226	C₂×C₄×C₁₁	—	2	1	no	—
227	C₂×C₄×C₁₁	—	2	1	no	—
228	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
229	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
230	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
231	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
232	C₂²⋊D₁₁	—	2	2	no	—
233	C₂²⋊D₁₁	—	2	2	no	—
234	C₂²⋊D₁₁	—	4	1	no	—
235	C₂²⋊D₁₁	—	4	1	no	—
236	C₂×Dic₁₁	—	4	1	no	—
237	C₂×Dic₁₁	C₂²×C₈	1	1	yes	characteristic
238	C₂×Dic₁₁	C₂²×C₈	1	1	yes	characteristic
239	C₂×Dic₁₁	C₂²×C₈	1	1	yes	characteristic
240	C₂×Dic₁₁	C₂²×C₈	1	1	yes	characteristic
241	C₂×Dic₁₁	C₂²×C₈	1	1	yes	characteristic
242	C₂×Dic₁₁	C₂²×C₈	1	1	yes	characteristic
243	C₄×D₁₁	—	2	1	no	—
244	C₄×D₁₁	—	2	1	no	—
245	C₄×D₁₁	—	2	1	no	—
246	C₄×D₁₁	—	2	1	no	—
247	C₄×D₁₁	—	4	1	no	—
248	C₄×D₁₁	—	4	1	no	—
249	C₈×C₁₁	—	2	1	no	—
250	C₈×C₁₁	—	2	1	no	—
251	C₈×C₁₁	—	2	1	no	—
252	C₈×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
253	C₈×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
254	C₁₁⋊C₈	—	2	1	no	—
255	C₁₁⋊C₈	—	2	1	no	—
256	C₁₁⋊C₈	—	2	1	no	—
257	C₁₁⋊C₈	—	2	1	no	—
258	C₂×#131	C₂×D₁₁	1	1	yes	characteristic
259	C₂³×C₈	—	11	1	no	—
260	#525	—	11	1	no	—
261	C₂×M₃₂	—	11	1	no	—
262	C₂×M₃₂	—	11	1	no	—
263	C₂×M₃₂	—	11	1	no	—
264	C₂×M₃₂	C₂×D₁₁	1	1	yes	characteristic, complemented
265	C₂²×C₁₆	—	11	1	no	—
266	C₂²×C₁₆	—	11	1	no	—
267	C₂²×C₁₆	—	11	1	no	—
268	C₂²×C₁₆	C₂×D₁₁	1	1	yes	characteristic, complemented
269	#435	—	11	1	no	—
270	#435	—	11	1	no	—
271	#435	—	11	1	no	—
272	#435	—	11	1	no	—
273	C₈×D₄	—	11	1	no	—
274	C₈×D₄	—	11	1	no	—
275	C₈×D₄	—	11	1	no	—
276	C₈×D₄	—	11	1	no	—
277	#424	—	11	1	no	—
278	#408	—	11	1	no	—
279	#407	—	11	1	no	—
280	#405	—	11	1	no	—
281	C₄⋊C₁₆	—	11	1	no	—
282	C₄⋊C₁₆	—	11	1	no	—
283	C₄⋊C₁₆	—	11	1	no	—
284	C₄⋊C₁₆	—	11	1	no	—
285	C₂²⋊C₁₆	—	11	1	no	—
286	C₂²⋊C₁₆	—	11	1	no	—
287	C₂²⋊C₁₆	—	11	1	no	—
288	C₂²⋊C₁₆	—	11	1	no	—
289	C₂²⋊C₁₆	—	11	1	no	—
290	C₂²⋊C₁₆	—	11	1	no	—
291	C₂²⋊C₁₆	—	11	1	no	—
292	C₂²⋊C₁₆	—	11	1	no	—
293	C₂²⋊C₁₆	C₂×D₁₁	1	1	yes	characteristic
294	C₂²⋊C₁₆	C₂×D₁₁	1	1	yes	characteristic
295	C₂²⋊C₁₆	C₂×D₁₁	1	1	yes	characteristic, complemented
296	C₂²⋊C₁₆	C₂×D₁₁	1	1	yes	characteristic, complemented
297	#346	—	11	1	no	—
298	#346	—	11	1	no	—
299	C₄×C₁₆	—	11	1	no	—
300	C₄×C₁₆	—	11	1	no	—
301	C₂²×C₁₁	—	2	1	no	—
302	C₂²×C₁₁	—	2	1	no	—
303	C₂²×C₁₁	—	2	1	no	—
304	C₂²×C₁₁	—	2	1	no	—
305	C₂²×C₁₁	—	2	1	no	—
306	C₂²×C₁₁	—	2	1	no	—
307	C₂²×C₁₁	—	2	1	no	—
308	C₂²×C₁₁	—	2	1	no	—
309	C₂²×C₁₁	—	2	1	no	—
310	C₂²×C₁₁	C₂³×C₈	1	1	yes	characteristic
311	C₂×D₁₁	—	2	1	no	—
312	C₂×D₁₁	—	2	1	no	—
313	C₂×D₁₁	—	2	1	no	—
314	C₂×D₁₁	—	2	1	no	—
315	C₂×D₁₁	—	2	1	no	—
316	C₂×D₁₁	—	4	4	no	—
317	C₂×D₁₁	#504	1	2	yes	—
318	C₄×C₁₁	—	2	1	no	—
319	C₄×C₁₁	—	2	1	no	—
320	C₄×C₁₁	—	2	1	no	—
321	C₄×C₁₁	#518	1	1	yes	characteristic
322	C₄×C₁₁	#568	1	1	yes	characteristic
323	Dic₁₁	—	2	1	no	—
324	Dic₁₁	—	2	1	no	—
325	Dic₁₁	—	2	1	no	—
326	Dic₁₁	—	2	1	no	—
327	Dic₁₁	—	2	1	no	—
328	Dic₁₁	—	2	1	no	—
329	C₂×#41	C₄×D₁₁	1	1	yes	characteristic
330	C₂³×C₄	—	11	1	no	—
331	#131	—	4	1	no	—
332	#131	—	4	1	no	—
333	C₂×M₁₆	—	11	1	no	—
334	C₂×M₁₆	C₄×D₁₁	1	1	yes	characteristic
335	C₂×M₁₆	C₄×D₁₁	1	1	yes	characteristic
336	C₂×M₁₆	C₄×D₁₁	1	1	yes	characteristic
337	C₂²×C₈	—	11	1	no	—
338	C₂²×C₈	—	11	1	no	—
339	C₂²×C₈	—	11	1	no	—
340	C₂²×C₈	—	11	1	no	—
341	C₂²×C₈	—	11	1	no	—
342	C₂²×C₈	—	44	1	no	—
343	C₂²×C₈	—	44	1	no	—
344	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
345	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
346	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
347	#123	—	11	1	no	—
348	#123	—	11	1	no	—
349	C₂²⋊Q₈	—	11	1	no	—
350	C₂²⋊Q₈	—	11	1	no	—
351	#121	—	11	1	no	—
352	#121	—	11	1	no	—
353	#120	—	11	1	no	—
354	#120	—	11	1	no	—
355	C₄×D₄	—	11	1	no	—
356	C₄×D₄	—	11	1	no	—
357	C₄×D₄	—	11	1	no	—
358	C₄×D₄	—	11	1	no	—
359	#117	—	11	1	no	—
360	M₃₂	—	4	1	no	—
361	M₃₂	—	44	1	no	—
362	M₃₂	—	44	1	no	—
363	M₃₂	—	44	1	no	—
364	C₂×C₁₆	—	4	1	no	—
365	C₂×C₁₆	—	11	1	no	—
366	C₂×C₁₆	—	11	1	no	—
367	C₂×C₁₆	—	11	1	no	—
368	C₂×C₁₆	—	11	1	no	—
369	C₂×C₁₆	—	44	1	no	—
370	C₂×C₁₆	—	44	1	no	—
371	C₂×C₁₆	—	44	1	no	—
372	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
373	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
374	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
375	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
376	C₄⋊C₈	—	11	1	no	—
377	C₄⋊C₈	—	11	1	no	—
378	C₄⋊C₈	—	11	1	no	—
379	C₄⋊C₈	—	11	1	no	—
380	C₂²⋊C₈	—	11	1	no	—
381	C₂²⋊C₈	—	11	1	no	—
382	C₂²⋊C₈	—	11	1	no	—
383	C₂²⋊C₈	—	11	1	no	—
384	C₂²⋊C₈	—	11	1	no	—
385	C₂²⋊C₈	—	11	1	no	—
386	C₂²⋊C₈	—	11	1	no	—
387	C₂²⋊C₈	—	11	1	no	—
388	#97	—	11	1	no	—
389	#97	—	11	1	no	—
390	C₄×C₈	—	11	1	no	—
391	C₄×C₈	—	11	1	no	—
392	C₂×C₁₁	—	4	1	no	—
393	C₂×C₁₁	—	4	1	no	—
394	C₂×C₁₁	—	4	1	no	—
395	C₂×C₁₁	#2972	1	1	yes	characteristic
396	C₂×C₁₁	C₂×#504	1	1	yes	characteristic
397	C₂×C₁₁	#3407	1	1	yes	characteristic
398	D₁₁	—	2	2	no	—
399	D₁₁	—	4	1	no	—
400	C₂⁴	—	11	1	no	—
401	#41	—	4	1	no	—
402	#41	—	4	1	no	—
403	C₂×Q₈	C₈×D₁₁	1	1	yes	characteristic
404	C₂×D₄	—	11	1	no	—
405	C₂×D₄	—	11	1	no	—
406	C₂×D₄	—	11	1	no	—
407	C₂×D₄	—	11	1	no	—
408	C₂×D₄	C₈×D₁₁	1	1	yes	characteristic
409	C₂×D₄	C₈×D₁₁	1	1	yes	characteristic
410	C₂×D₄	C₈×D₁₁	1	1	yes	characteristic
411	C₂²×C₄	—	11	1	no	—
412	C₂²×C₄	—	11	1	no	—
413	C₂²×C₄	—	11	1	no	—
414	C₂²×C₄	—	11	1	no	—
415	C₂²×C₄	—	11	1	no	—
416	C₂²×C₄	—	44	1	no	—
417	C₂²×C₄	—	44	1	no	—
418	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
419	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
420	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
421	M₁₆	—	4	1	no	—
422	M₁₆	—	4	1	no	—
423	M₁₆	—	4	1	no	—
424	M₁₆	—	44	1	no	—
425	C₂×C₈	—	2	1	no	—
426	C₂×C₈	—	2	1	no	—
427	C₂×C₈	—	2	1	no	—
428	C₂×C₈	—	2	1	no	—
429	C₂×C₈	—	2	1	no	—
430	C₂×C₈	—	2	1	no	—
431	C₂×C₈	—	11	1	no	—
432	C₂×C₈	—	11	1	no	—
433	C₂×C₈	—	11	1	no	—
434	C₂×C₈	—	11	1	no	—
435	C₂×C₈	—	22	1	no	—
436	C₂×C₈	—	22	1	no	—
437	C₂×C₈	—	22	1	no	—
438	C₂×C₈	—	22	1	no	—
439	C₂×C₈	—	44	1	no	—
440	C₂×C₈	—	44	1	no	—
441	C₂×C₈	—	44	1	no	—
442	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
443	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
444	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
445	C₂×C₈	C₂³×D₁₁	1	1	yes	characteristic
446	C₄⋊C₄	—	11	1	no	—
447	C₄⋊C₄	—	11	1	no	—
448	C₄⋊C₄	—	11	1	no	—
449	C₄⋊C₄	—	11	1	no	—
450	C₄⋊C₄	—	11	1	no	—
451	C₄⋊C₄	—	11	1	no	—
452	C₂²⋊C₄	—	11	1	no	—
453	C₂²⋊C₄	—	11	1	no	—
454	C₂²⋊C₄	—	11	1	no	—
455	C₂²⋊C₄	—	11	1	no	—
456	C₂²⋊C₄	—	11	1	no	—
457	C₂²⋊C₄	—	11	1	no	—
458	C₂²⋊C₄	—	11	1	no	—
459	C₂²⋊C₄	—	11	1	no	—
460	C₂²⋊C₄	—	11	1	no	—
461	C₂²⋊C₄	—	11	1	no	—
462	C₄²	—	11	1	no	—
463	C₄²	—	11	1	no	—
464	C₁₆	—	2	1	no	—
465	C₁₆	—	2	1	no	—
466	C₁₆	—	2	1	no	—
467	C₁₆	—	2	1	no	—
468	C₁₆	—	22	1	no	—
469	C₁₆	—	22	1	no	—
470	C₁₆	—	22	1	no	—
471	C₁₆	—	22	1	no	—
472	C₁₁	#33490	1	1	yes	characteristic, complemented, Sylow
473	C₂³	—	11	1	no	—
474	C₂³	—	11	1	no	—
475	C₂³	—	22	2	no	—
476	C₂³	—	44	1	no	—
477	C₂³	—	44	1	no	—
478	C₂³	C₂×C₈×D₁₁	1	1	yes	characteristic
479	C₂³	C₂×C₈×D₁₁	1	1	yes	characteristic
480	C₂³	C₂×C₈×D₁₁	1	1	yes	characteristic
481	Q₈	—	4	1	no	—
482	D₄	—	4	1	no	—
483	D₄	—	4	1	no	—
484	D₄	—	4	1	no	—
485	D₄	—	22	2	no	—
486	D₄	—	22	2	no	—
487	D₄	—	44	1	no	—
488	D₄	—	44	1	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	11	1	no	—
496	C₂×C₄	—	11	1	no	—
497	C₂×C₄	—	11	1	no	—
498	C₂×C₄	—	11	1	no	—
499	C₂×C₄	—	11	1	no	—
500	C₂×C₄	—	11	1	no	—
501	C₂×C₄	—	22	1	no	—
502	C₂×C₄	—	22	1	no	—
503	C₂×C₄	—	22	1	no	—
504	C₂×C₄	—	22	1	no	—
505	C₂×C₄	—	44	1	no	—
506	C₂×C₄	—	44	1	no	—
507	C₂×C₄	—	44	1	no	—
508	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
509	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
510	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
511	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
512	C₈	—	2	1	no	—
513	C₈	—	2	1	no	—
514	C₈	—	2	1	no	—
515	C₈	—	22	1	no	—
516	C₈	—	22	1	no	—
517	C₈	—	22	1	no	—
518	C₈	—	22	1	no	—
519	C₈	#67037	1	1	yes	characteristic
520	C₈	#67037	1	1	yes	characteristic
521	C₂²	—	2	1	no	—
522	C₂²	—	2	1	no	—
523	C₂²	—	2	1	no	—
524	C₂²	—	2	1	no	—
525	C₂²	—	2	1	no	—
526	C₂²	—	2	1	no	—
527	C₂²	—	2	1	no	—
528	C₂²	—	2	1	no	—
529	C₂²	—	2	1	no	—
530	C₂²	—	11	2	no	—
531	C₂²	—	22	1	no	—
532	C₂²	—	22	1	no	—
533	C₂²	—	22	1	no	—
534	C₂²	—	22	1	no	—
535	C₂²	—	22	1	no	—
536	C₂²	—	44	4	no	—
537	C₂²	C₂²×C₈×D₁₁	1	1	yes	characteristic
538	C₄	—	2	1	no	—
539	C₄	—	2	1	no	—
540	C₄	—	2	1	no	—
541	C₄	—	22	1	no	—
542	C₄	—	22	1	no	—
543	C₄	—	22	1	no	—
544	C₄	—	22	1	no	—
545	C₄	—	22	1	no	—
546	C₄	—	22	1	no	—
547	C₄	#10623017	1	1	yes	characteristic
548	C₄	#10623276	1	1	yes	characteristic
549	C₂	—	4	1	no	—
550	C₂	—	4	1	no	—
551	C₂	—	4	1	no	—
552	C₂	—	22	2	no	—
553	C₂	—	44	1	no	—
554	C₂	#13077638	1	1	yes	characteristic
555	C₂	D₁₁×#504	1	1	yes	characteristic
556	C₂	#13081717	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₁₁
commutator, socle	C₂²×C₁₁	C₂³×C₈
Fitting	C₁₁×#2113	C₂
prime radical	#10623359	C₄
cosocle	C₂×C₈×C₁₁	C₂⁴
hypercenter	#2113	D₁₁
hypocenter	C₁₁	#33490
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₈ ◁ #2113

Complements

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

N	H ≅ G/N	type
2. #13070446	C₂	semidirect
3. #13070445	C₂	semidirect
4. #13070444	C₂	semidirect
5. #13070441	C₂	semidirect
6. #13070439	C₂	semidirect
7. #13070438	C₂	semidirect
8. C₁₆×C₂²⋊D₁₁	C₂	semidirect
9. (C₂²⋊D₁₁)⋊C₁₆	C₂	semidirect
10. #13070420	C₂	semidirect
11. #13070420	C₂	semidirect
12. #13070230	C₂	semidirect
13. #13070225	C₂	semidirect
14. D₁₁×C₂²⋊C₁₆	C₂	semidirect
15. C₁₁×#2113	C₂	semidirect
19. C₂×C₁₁×M₃₂	C₂²	semidirect
20. C₂²×C₁₁×C₁₆	C₂²	semidirect
33. C₂×#66876	C₂²	semidirect
34. C₂²×C₁₁⋊C₁₆	C₂²	semidirect
41. C₁₁×C₂²⋊C₁₆	C₂²	semidirect
42. C₁₁×C₂²⋊C₁₆	C₂²	semidirect
45. C₂²⋊(C₁₁⋊C₁₆)	C₂²	semidirect
46. C₂²⋊(C₁₁⋊C₁₆)	C₂²	semidirect
51. #10622140	C₂²	semidirect
52. #10622140	C₂²	semidirect
53. Dic₁₁⋊C₁₆	C₂²	semidirect
54. Dic₁₁⋊C₁₆	C₂²	semidirect
55. Dic₁₁⋊C₁₆	C₂²	semidirect
56. Dic₁₁⋊C₁₆	C₂²	semidirect
57. C₁₆×Dic₁₁	C₂²	semidirect
58. C₁₆×Dic₁₁	C₂²	semidirect
207. #2113	D₁₁	semidirect
264. C₂×M₃₂	C₂×D₁₁	semidirect
268. C₂²×C₁₆	C₂×D₁₁	semidirect
295. C₂²⋊C₁₆	C₂×D₁₁	semidirect
296. C₂²⋊C₁₆	C₂×D₁₁	semidirect
472. C₁₁	#33490	semidirect

Maximal subgroups

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

subgroup	index
#13077308	2
#13070446	2
#13070445	2
#13070444	2
#13070441	2
#13070439	2
#13070438	2
C₁₆×C₂²⋊D₁₁	2
(C₂²⋊D₁₁)⋊C₁₆	2
#13070420	2
#13070230	2
#13070225	2
D₁₁×C₂²⋊C₁₆	2
C₁₁×#2113	2
#33490	11