Subgroups — #14722804

Order 2816.

712 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13077246	C₂	1	1	yes	maximal, characteristic
2	D₁₁×#432	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×#4313	C₂	1	1	yes	maximal, characteristic
4	#13067382	C₂	1	2	yes	maximal, complemented
5	#13067380	C₂	1	2	yes	maximal, complemented
6	#13067379	C₂	1	1	yes	maximal, characteristic, complemented
7	#13067377	C₂	1	1	yes	maximal, characteristic, complemented
8	#13067377	C₂	1	1	yes	maximal, characteristic, complemented
9	#13067367	C₂	1	2	yes	maximal, complemented
10	#13067365	C₂	1	2	yes	maximal, complemented
11	C₁₁×#1568	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#4313	C₄	1	1	yes	characteristic
13	C₂²×#4313	C₄	1	1	yes	characteristic
14	C₂×C₄²×D₁₁	C₂²	1	1	yes	characteristic
15	C₁₁×#432	C₂²	1	1	yes	characteristic
16	C₁₁×#432	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
18	C₂×#66879	C₄	1	1	yes	characteristic
19	C₂×#66879	C₄	1	1	yes	characteristic
20	#10622539	C₂²	1	1	yes	characteristic
21	#10622539	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
23	#10622450	C₂²	1	2	yes	—
24	#10622448	C₂²	1	2	yes	—
25	#10622446	C₂²	1	2	yes	—
26	D₁₁×C₄⋊C₈	C₂²	1	2	yes	—
27	#10622339	—	2	1	no	—
28	D₁₁×C₂²⋊C₈	—	2	1	no	—
29	#10622332	—	2	1	no	—
30	#10622331	—	2	1	no	—
31	#10622320	—	2	1	no	—
32	#10622318	—	2	1	no	—
33	#10622318	—	2	1	no	—
34	D₁₁×#97	—	2	1	no	—
35	C₄×#4313	C₄	1	1	yes	characteristic
36	C₄×#4313	C₄	1	1	yes	characteristic
37	C₄×#4313	C₄	1	1	yes	characteristic
38	C₄×#4313	C₄	1	1	yes	characteristic
39	C₄×#4313	C₂²	1	1	yes	characteristic
40	C₄×#4313	C₂²	1	1	yes	characteristic
41	C₄×#4313	C₂²	1	1	yes	characteristic
42	C₄×#4313	C₂²	1	1	yes	characteristic
43	C₁₁×#335	C₂²	1	2	yes	complemented
44	C₁₁×#334	C₂²	1	2	yes	complemented
45	#10622118	C₂²	1	2	yes	complemented
46	#10622118	C₂²	1	2	yes	complemented
47	#10622117	C₂²	1	2	yes	complemented
48	#10622117	C₂²	1	2	yes	complemented
49	#10622096	C₂²	1	2	yes	complemented
50	#10622095	C₂²	1	2	yes	complemented
51	C₂²×C₄×D₁₁	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₄×D₁₁	D₄	1	1	yes	characteristic
53	C₂²×C₄×D₁₁	Q₈	1	1	yes	characteristic
54	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
55	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
57	C₂×C₄×Dic₁₁	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄×Dic₁₁	D₄	1	1	yes	characteristic
59	C₂×C₄×Dic₁₁	Q₈	1	1	yes	characteristic
60	C₂²×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
61	C₂²×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
62	C₂×#4313	—	2	4	no	—
63	C₂×#4313	—	2	4	no	—
64	C₂×#4313	—	2	2	no	—
65	C₂×#4313	C₂×C₄	1	1	yes	characteristic
66	C₂×#4313	C₂×C₄	1	1	yes	characteristic
67	C₂×#4313	C₂×C₄	1	1	yes	characteristic
68	C₂×#4313	C₂×C₄	1	1	yes	characteristic
69	C₂×#4313	C₂×C₄	1	1	yes	characteristic
70	C₂×#4313	C₂×C₄	1	1	yes	characteristic
71	C₂×#4313	C₂×C₄	1	1	yes	characteristic
72	C₂×#4313	C₂×C₄	1	1	yes	characteristic
73	C₂×C₈×D₁₁	—	2	2	no	—
74	C₄²×D₁₁	C₂×C₄	1	1	yes	characteristic
75	C₄²×D₁₁	C₂×C₄	1	1	yes	characteristic
76	C₄²×D₁₁	D₄	1	1	yes	characteristic
77	C₄²×D₁₁	D₄	1	1	yes	characteristic
78	C₄²×D₁₁	Q₈	1	1	yes	characteristic
79	C₄²×D₁₁	Q₈	1	1	yes	characteristic
80	C₄²×D₁₁	C₂³	1	1	yes	characteristic
81	C₄²×D₁₁	C₂³	1	1	yes	characteristic
82	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
83	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
84	C₁₁×C₂²⋊C₈	—	2	1	no	—
85	C₁₁×C₂²⋊C₈	—	2	1	no	—
86	C₁₁×#97	—	2	1	no	—
87	C₁₁×#97	—	2	1	no	—
88	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
89	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
90	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
91	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
92	C₂²⋊(C₁₁⋊C₈)	—	2	1	no	—
93	C₂²⋊(C₁₁⋊C₈)	—	2	1	no	—
94	(C₂×D₁₁)⋊C₈	—	2	2	no	—
95	(C₂×D₁₁)⋊C₈	—	2	2	no	—
96	#66879	—	2	2	no	—
97	#66879	C₂×C₄	1	1	yes	characteristic
98	#66879	C₂×C₄	1	1	yes	characteristic
99	#66879	C₂×C₄	1	1	yes	characteristic
100	#66879	C₂×C₄	1	1	yes	characteristic
101	#66879	C₂×C₄	1	1	yes	characteristic
102	#66879	C₂×C₄	1	1	yes	characteristic
103	#66879	C₂×C₄	1	1	yes	characteristic
104	#66879	C₂×C₄	1	1	yes	characteristic
105	Dic₁₁⋊C₈	—	2	2	no	—
106	Dic₁₁⋊C₈	—	2	2	no	—
107	C₈×Dic₁₁	—	2	2	no	—
108	C₄⋊(C₁₁⋊C₈)	C₂³	1	2	yes	—
109	C₄⋊(C₁₁⋊C₈)	C₂³	1	2	yes	—
110	#66867	—	2	1	no	—
111	#66867	—	2	1	no	—
112	C₄×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
113	C₄×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
114	C₄×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
115	C₄×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
116	#17797	—	11	1	no	maximal, Sylow
117	C₂³×D₁₁	C₄⋊C₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
121	C₂²×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
122	C₂²×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
123	C₂²×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
124	C₂×C₄×D₁₁	—	2	2	no	—
125	C₂×C₄×D₁₁	—	2	2	no	—
126	C₂×C₄×D₁₁	—	4	2	no	—
127	C₂×C₄×D₁₁	—	4	2	no	—
128	C₂×C₄×D₁₁	C₄⋊C₄	1	1	yes	characteristic
129	C₂×C₄×D₁₁	C₄⋊C₄	1	1	yes	characteristic
130	C₂×C₄×D₁₁	C₄⋊C₄	1	1	yes	characteristic
131	C₂×C₄×D₁₁	C₄⋊C₄	1	1	yes	characteristic
132	C₂×C₄×D₁₁	C₄⋊C₄	1	1	yes	characteristic
133	C₂×C₄×D₁₁	C₄⋊C₄	1	1	yes	characteristic
134	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₄×D₁₁	C₂×D₄	1	1	yes	characteristic
137	C₂×C₄×D₁₁	C₂×D₄	1	1	yes	characteristic
138	C₂×C₄×D₁₁	C₂×Q₈	1	1	yes	characteristic
139	C₂×C₄×D₁₁	C₂×Q₈	1	1	yes	characteristic
140	C₂×C₈×C₁₁	—	2	2	no	—
141	C₂×C₈×C₁₁	—	2	2	no	—
142	C₂×C₈×C₁₁	—	2	2	no	—
143	C₂×C₈×C₁₁	—	2	2	no	—
144	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
145	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
146	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
148	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
149	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
150	C₄²×C₁₁	C₂×Q₈	1	1	yes	characteristic
151	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
152	C₄×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
153	C₄×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
154	C₄×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
155	C₄×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
156	C₄×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
157	C₄×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
158	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
159	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
160	C₄×Dic₁₁	C₂×D₄	1	1	yes	characteristic
161	C₄×Dic₁₁	C₂×D₄	1	1	yes	characteristic
162	C₄×Dic₁₁	C₂×Q₈	1	1	yes	characteristic
163	C₄×Dic₁₁	C₂×Q₈	1	1	yes	characteristic
164	C₂×C₁₁⋊C₈	—	2	2	no	—
165	C₂×C₁₁⋊C₈	—	2	2	no	—
166	C₂×C₁₁⋊C₈	—	2	2	no	—
167	C₂×C₁₁⋊C₈	—	2	2	no	—
168	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
169	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
170	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
171	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
172	#4313	—	2	2	no	—
173	#4313	—	2	2	no	—
174	#4313	—	2	2	no	—
175	#4313	—	2	2	no	—
176	#4313	—	2	2	no	—
177	#4313	—	2	2	no	—
178	#4313	—	4	4	no	—
179	#4313	M₁₆	1	4	yes	complemented
180	#4313	M₁₆	1	4	yes	complemented
181	C₈×D₁₁	—	4	4	no	—
182	#2920	—	11	1	no	—
183	C₂×#432	—	11	1	no	—
184	C₂×C₄×M₁₆	—	11	1	no	—
185	#1569	—	11	2	no	—
186	#1569	—	11	2	no	—
187	#1568	—	11	1	no	—
188	#1568	—	11	1	no	—
189	#1568	—	11	1	no	—
190	#1568	D₁₁	1	1	yes	characteristic, complemented
191	#1565	—	11	2	no	—
192	#1565	—	11	2	no	—
193	C₂³×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
194	C₂²×D₁₁	—	2	2	no	—
195	C₂²×D₁₁	—	2	2	no	—
196	C₂²×D₁₁	—	4	1	no	—
197	C₂²×D₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
198	C₂²×D₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
199	C₂×C₄×C₁₁	—	2	2	no	—
200	C₂×C₄×C₁₁	—	2	1	no	—
201	C₂×C₄×C₁₁	—	2	1	no	—
202	C₂×C₄×C₁₁	—	2	2	no	—
203	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
204	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
205	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
206	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
207	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
208	C₂×C₄×C₁₁	C₂²×Q₈	1	1	yes	characteristic
209	C₂×Dic₁₁	—	2	2	no	—
210	C₂×Dic₁₁	—	2	2	no	—
211	C₂×Dic₁₁	—	4	1	no	—
212	C₂×Dic₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
213	C₂×Dic₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
214	C₂×Dic₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
215	C₂×Dic₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
216	C₂×Dic₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
217	C₂×Dic₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
218	C₄×D₁₁	—	2	2	no	—
219	C₄×D₁₁	—	2	1	no	—
220	C₄×D₁₁	—	2	1	no	—
221	C₄×D₁₁	—	2	2	no	—
222	C₄×D₁₁	—	2	2	no	—
223	C₄×D₁₁	—	2	2	no	—
224	C₄×D₁₁	—	4	1	no	—
225	C₄×D₁₁	—	4	1	no	—
226	C₄×D₁₁	—	4	1	no	—
227	C₄×D₁₁	—	4	1	no	—
228	C₄×D₁₁	—	4	1	no	—
229	C₄×D₁₁	—	4	1	no	—
230	C₄×D₁₁	C₂×M₁₆	1	2	yes	—
231	C₄×D₁₁	C₂×M₁₆	1	2	yes	—
232	C₈×C₁₁	—	2	1	no	—
233	C₈×C₁₁	—	2	1	no	—
234	C₈×C₁₁	—	4	2	no	—
235	C₈×C₁₁	—	4	2	no	—
236	C₈×C₁₁	C₂×M₁₆	1	2	yes	—
237	C₈×C₁₁	C₂×M₁₆	1	2	yes	—
238	C₁₁⋊C₈	—	2	1	no	—
239	C₁₁⋊C₈	—	2	1	no	—
240	C₁₁⋊C₈	—	4	2	no	—
241	C₁₁⋊C₈	—	4	2	no	—
242	C₁₁⋊C₈	C₂×M₁₆	1	2	yes	—
243	C₁₁⋊C₈	C₂×M₁₆	1	2	yes	—
244	C₂²×M₁₆	—	11	1	no	—
245	C₂²×M₁₆	—	11	1	no	—
246	C₂²×C₄²	—	11	1	no	—
247	#432	—	11	1	no	—
248	#432	—	11	1	no	—
249	#432	—	11	2	no	—
250	#432	—	22	1	no	—
251	#432	—	22	1	no	—
252	#432	—	22	1	no	—
253	#432	C₂×D₁₁	1	1	yes	characteristic
254	#432	C₂×D₁₁	1	1	yes	characteristic
255	#431	—	11	2	no	—
256	#431	—	22	1	no	—
257	#423	—	11	2	no	—
258	C₂×C₄⋊C₈	—	11	2	no	—
259	#407	—	22	1	no	—
260	C₂×C₂²⋊C₈	—	22	1	no	—
261	C₄×M₁₆	—	11	1	no	—
262	C₄×M₁₆	—	11	1	no	—
263	C₄×M₁₆	—	11	1	no	—
264	C₄×M₁₆	—	11	1	no	—
265	C₄×M₁₆	—	11	1	no	—
266	C₄×M₁₆	—	11	1	no	—
267	C₄×M₁₆	—	11	1	no	—
268	C₄×M₁₆	—	11	1	no	—
269	C₄×M₁₆	—	22	1	no	—
270	C₂×#97	—	11	1	no	—
271	C₂×#97	—	11	1	no	—
272	C₂×#97	—	22	1	no	—
273	C₂×C₄×C₈	—	11	1	no	—
274	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
275	#335	—	11	2	no	—
276	#335	—	11	2	no	—
277	#335	—	11	2	no	—
278	#335	C₂×D₁₁	1	2	yes	complemented
279	#334	—	11	2	no	—
280	#334	—	11	2	no	—
281	#334	—	11	2	no	—
282	#334	C₂×D₁₁	1	2	yes	complemented
283	C₂²×C₁₁	—	2	1	no	—
284	C₂²×C₁₁	—	2	1	no	—
285	C₂²×C₁₁	#430	1	2	yes	—
286	C₂²×C₁₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
287	C₂×D₁₁	—	2	1	no	—
288	C₂×D₁₁	—	2	1	no	—
289	C₂×D₁₁	—	2	1	no	—
290	C₂×D₁₁	—	2	1	no	—
291	C₂×D₁₁	—	2	1	no	—
292	C₂×D₁₁	—	4	4	no	—
293	C₂×D₁₁	#423	1	2	yes	—
294	C₄×C₁₁	—	2	1	no	—
295	C₄×C₁₁	—	2	1	no	—
296	C₄×C₁₁	—	2	1	no	—
297	C₄×C₁₁	—	2	1	no	—
298	C₄×C₁₁	C₂²×M₁₆	1	1	yes	characteristic
299	C₄×C₁₁	C₂²×M₁₆	1	1	yes	characteristic
300	C₄×C₁₁	#575	1	2	yes	—
301	Dic₁₁	—	2	1	no	—
302	Dic₁₁	—	2	1	no	—
303	Dic₁₁	—	2	1	no	—
304	Dic₁₁	—	2	1	no	—
305	Dic₁₁	—	2	1	no	—
306	Dic₁₁	#423	1	2	yes	—
307	C₂³×C₄	—	11	1	no	—
308	C₂³×C₄	—	11	1	no	—
309	C₂³×C₄	—	11	1	no	—
310	C₂×M₁₆	—	11	1	no	—
311	C₂×M₁₆	—	11	1	no	—
312	C₂×M₁₆	—	11	1	no	—
313	C₂×M₁₆	—	11	1	no	—
314	C₂×M₁₆	—	11	1	no	—
315	C₂×M₁₆	—	11	1	no	—
316	C₂×M₁₆	—	11	1	no	—
317	C₂×M₁₆	—	11	1	no	—
318	C₂×M₁₆	—	22	4	no	—
319	C₂×M₁₆	—	22	4	no	—
320	C₂×M₁₆	—	22	2	no	—
321	C₂²×C₈	—	11	1	no	—
322	C₂²×C₈	—	11	1	no	—
323	C₂²×C₈	—	22	2	no	—
324	C₂²×C₈	C₄×D₁₁	1	1	yes	characteristic
325	C₂²×C₈	C₄×D₁₁	1	1	yes	characteristic
326	C₂×C₄²	—	11	1	no	—
327	C₂×C₄²	—	11	1	no	—
328	C₂×C₄²	—	11	1	no	—
329	C₂×C₄²	—	11	1	no	—
330	C₂×C₄²	—	11	1	no	—
331	C₂×C₄²	—	11	1	no	—
332	C₂×C₄²	—	11	1	no	—
333	C₂×C₄²	—	11	1	no	—
334	C₂×C₄²	—	11	1	no	—
335	C₂×C₄²	—	11	1	no	—
336	C₂×C₄²	—	11	1	no	—
337	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
338	C₄⋊C₈	—	11	2	no	—
339	C₄⋊C₈	—	11	2	no	—
340	C₄⋊C₈	—	22	2	no	—
341	C₄⋊C₈	—	22	2	no	—
342	C₄⋊C₈	C₂²×D₁₁	1	2	yes	—
343	C₄⋊C₈	C₂²×D₁₁	1	2	yes	—
344	C₂²⋊C₈	—	2	1	no	—
345	C₂²⋊C₈	—	2	1	no	—
346	C₂²⋊C₈	—	22	2	no	—
347	C₂²⋊C₈	—	22	2	no	—
348	C₂²⋊C₈	—	22	1	no	—
349	C₂²⋊C₈	—	22	1	no	—
350	#97	—	2	1	no	—
351	#97	—	2	1	no	—
352	#97	—	11	1	no	—
353	#97	—	11	1	no	—
354	#97	—	11	1	no	—
355	#97	—	11	1	no	—
356	#97	—	11	1	no	—
357	#97	—	11	1	no	—
358	#97	—	11	1	no	—
359	#97	—	11	1	no	—
360	#97	—	22	2	no	—
361	#97	—	22	1	no	—
362	#97	—	22	1	no	—
363	C₄×C₈	—	11	1	no	—
364	C₄×C₈	—	11	1	no	—
365	C₄×C₈	—	11	1	no	—
366	C₄×C₈	—	11	1	no	—
367	C₄×C₈	—	22	2	no	—
368	C₄×C₈	C₄×D₁₁	1	1	yes	characteristic
369	C₄×C₈	C₄×D₁₁	1	1	yes	characteristic
370	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
371	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
372	C₂×C₁₁	—	2	2	no	—
373	C₂×C₁₁	C₂×#423	1	1	yes	characteristic
374	C₂×C₁₁	#2911	1	1	yes	characteristic
375	C₂×C₁₁	C₂×#430	1	1	yes	characteristic
376	D₁₁	—	2	2	no	—
377	D₁₁	—	4	1	no	—
378	C₂⁴	—	11	1	no	—
379	C₂²×C₄	—	11	1	no	—
380	C₂²×C₄	—	11	1	no	—
381	C₂²×C₄	—	11	1	no	—
382	C₂²×C₄	—	11	1	no	—
383	C₂²×C₄	—	11	1	no	—
384	C₂²×C₄	—	11	1	no	—
385	C₂²×C₄	—	11	1	no	—
386	C₂²×C₄	—	11	1	no	—
387	C₂²×C₄	—	11	1	no	—
388	C₂²×C₄	—	11	1	no	—
389	C₂²×C₄	—	11	1	no	—
390	C₂²×C₄	—	11	1	no	—
391	C₂²×C₄	—	11	1	no	—
392	C₂²×C₄	—	11	1	no	—
393	C₂²×C₄	—	11	1	no	—
394	C₂²×C₄	—	22	2	no	—
395	C₂²×C₄	—	22	2	no	—
396	C₂²×C₄	—	44	2	no	—
397	C₂²×C₄	—	44	2	no	—
398	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
399	C₂²×C₄	D₄×D₁₁	1	1	yes	characteristic
400	C₂²×C₄	Q₈×D₁₁	1	1	yes	characteristic
401	M₁₆	—	11	4	no	—
402	M₁₆	—	11	4	no	—
403	M₁₆	—	22	2	no	—
404	M₁₆	—	22	2	no	—
405	M₁₆	—	22	2	no	—
406	M₁₆	—	22	2	no	—
407	M₁₆	—	22	2	no	—
408	M₁₆	—	22	2	no	—
409	M₁₆	—	44	4	no	—
410	C₂×C₈	—	2	2	no	—
411	C₂×C₈	—	2	2	no	—
412	C₂×C₈	—	2	2	no	—
413	C₂×C₈	—	2	2	no	—
414	C₂×C₈	—	11	1	no	—
415	C₂×C₈	—	11	1	no	—
416	C₂×C₈	—	11	1	no	—
417	C₂×C₈	—	11	1	no	—
418	C₂×C₈	—	22	2	no	—
419	C₂×C₈	—	22	2	no	—
420	C₂×C₈	—	22	2	no	—
421	C₂×C₈	—	22	2	no	—
422	C₂×C₈	—	44	4	no	—
423	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
424	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
425	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
426	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
427	C₄²	—	11	1	no	—
428	C₄²	—	11	1	no	—
429	C₄²	—	11	1	no	—
430	C₄²	—	11	1	no	—
431	C₄²	—	11	1	no	—
432	C₄²	—	11	1	no	—
433	C₄²	—	11	1	no	—
434	C₄²	—	11	1	no	—
435	C₄²	—	11	1	no	—
436	C₄²	—	11	1	no	—
437	C₄²	—	11	1	no	—
438	C₄²	—	11	1	no	—
439	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
440	C₄²	D₄×D₁₁	1	1	yes	characteristic
441	C₄²	Q₈×D₁₁	1	1	yes	characteristic
442	C₄²	C₂³×D₁₁	1	1	yes	characteristic
443	C₁₁	#17797	1	1	yes	characteristic, complemented, Sylow
444	C₂³	—	11	1	no	—
445	C₂³	—	11	1	no	—
446	C₂³	—	22	2	no	—
447	C₂³	—	22	2	no	—
448	C₂³	—	44	1	no	—
449	C₂³	C₄⋊C₄×D₁₁	1	1	yes	characteristic
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	11	1	no	—
455	C₂×C₄	—	11	2	no	—
456	C₂×C₄	—	11	2	no	—
457	C₂×C₄	—	11	1	no	—
458	C₂×C₄	—	11	1	no	—
459	C₂×C₄	—	11	1	no	—
460	C₂×C₄	—	11	1	no	—
461	C₂×C₄	—	11	1	no	—
462	C₂×C₄	—	22	2	no	—
463	C₂×C₄	—	22	2	no	—
464	C₂×C₄	—	22	2	no	—
465	C₂×C₄	—	22	2	no	—
466	C₂×C₄	—	22	1	no	—
467	C₂×C₄	—	22	1	no	—
468	C₂×C₄	—	22	2	no	—
469	C₂×C₄	—	22	2	no	—
470	C₂×C₄	—	44	1	no	—
471	C₂×C₄	—	44	1	no	—
472	C₂×C₄	—	44	1	no	—
473	C₂×C₄	—	44	1	no	—
474	C₂×C₄	—	44	1	no	—
475	C₂×C₄	—	44	1	no	—
476	C₂×C₄	—	44	1	no	—
477	C₂×C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
478	C₂×C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
479	C₂×C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
480	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
481	C₂×C₄	C₂×D₄×D₁₁	1	1	yes	characteristic
482	C₂×C₄	C₂×Q₈×D₁₁	1	1	yes	characteristic
483	C₈	—	2	1	no	—
484	C₈	—	2	1	no	—
485	C₈	—	4	2	no	—
486	C₈	—	4	2	no	—
487	C₈	—	11	2	no	—
488	C₈	—	11	2	no	—
489	C₈	—	22	1	no	—
490	C₈	—	22	1	no	—
491	C₈	—	44	2	no	—
492	C₈	—	44	2	no	—
493	C₈	M₁₆×D₁₁	1	2	yes	—
494	C₈	M₁₆×D₁₁	1	2	yes	—
495	C₂²	—	2	1	no	—
496	C₂²	—	2	1	no	—
497	C₂²	—	11	2	no	—
498	C₂²	—	22	1	no	—
499	C₂²	—	22	1	no	—
500	C₂²	—	22	1	no	—
501	C₂²	—	22	1	no	—
502	C₂²	—	22	1	no	—
503	C₂²	—	44	4	no	—
504	C₂²	#10622506	1	2	yes	—
505	C₂²	C₂×C₄⋊C₄×D₁₁	1	1	yes	characteristic
506	C₄	—	2	1	no	—
507	C₄	—	2	1	no	—
508	C₄	—	2	1	no	—
509	C₄	—	2	1	no	—
510	C₄	—	11	2	no	—
511	C₄	—	22	1	no	—
512	C₄	—	22	1	no	—
513	C₄	—	22	1	no	—
514	C₄	—	22	1	no	—
515	C₄	—	22	1	no	—
516	C₄	C₂×M₁₆×D₁₁	1	1	yes	characteristic
517	C₄	C₂×M₁₆×D₁₁	1	1	yes	characteristic
518	C₄	#10623299	1	2	yes	—
519	C₂	—	2	2	no	—
520	C₂	—	22	2	no	—
521	C₂	—	44	1	no	—
522	C₂	D₁₁×#423	1	1	yes	characteristic
523	C₂	#13077204	1	1	yes	characteristic
524	C₂	C₂×#10622506	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₁
commutator	C₂×C₄×C₁₁	C₂³×C₄
Frattini	C₄²	C₂³×D₁₁
Fitting	C₁₁×#1568	C₂
socle	C₂²×C₁₁	C₂²×C₄⋊C₄
prime radical	C₂³×D₁₁	C₄⋊C₄
cosocle	C₄²×C₁₁	C₂⁴
hypercenter	#1568	D₁₁
hypocenter	C₁₁	#17797
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1568

Complements

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

N	H ≅ G/N	type
4. #13067382	C₂	semidirect
5. #13067380	C₂	semidirect
6. #13067379	C₂	semidirect
7. #13067377	C₂	semidirect
8. #13067377	C₂	semidirect
9. #13067367	C₂	semidirect
10. #13067365	C₂	semidirect
11. C₁₁×#1568	C₂	semidirect
43. C₁₁×#335	C₂²	semidirect
44. C₁₁×#334	C₂²	semidirect
45. #10622118	C₂²	semidirect
46. #10622118	C₂²	semidirect
47. #10622117	C₂²	semidirect
48. #10622117	C₂²	semidirect
49. #10622096	C₂²	semidirect
50. #10622095	C₂²	semidirect
179. #4313	M₁₆	semidirect
180. #4313	M₁₆	semidirect
190. #1568	D₁₁	semidirect
278. #335	C₂×D₁₁	semidirect
282. #334	C₂×D₁₁	semidirect
443. C₁₁	#17797	semidirect

Maximal subgroups

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

subgroup	index
#13077246	2
D₁₁×#432	2
C₂×C₄×#4313	2
#13067382	2
#13067380	2
#13067379	2
#13067377	2
#13067367	2
#13067365	2
C₁₁×#1568	2
#17797	11