Subgroups — #14722951

Order 2816.

662 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13077247	C₂	1	1	yes	maximal, characteristic
2	#13077246	C₂	1	1	yes	maximal, characteristic
3	D₁₁×#423	C₂	1	1	yes	maximal, characteristic
4	#13067406	C₂	1	2	yes	maximal, complemented
5	#13067403	C₂	1	2	yes	maximal, complemented
6	#13067389	C₂	1	2	yes	maximal, complemented
7	#13067385	C₂	1	2	yes	maximal, complemented
8	#13067384	C₂	1	1	yes	maximal, characteristic, complemented
9	#13067383	C₂	1	1	yes	maximal, characteristic, complemented
10	#13067381	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₁×#1569	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×M₁₆×D₁₁	—	2	1	no	—
13	C₂×C₄²×D₁₁	C₂²	1	1	yes	characteristic
14	C₁₁×#432	C₂²	1	1	yes	characteristic
15	C₁₁×#423	C₂²	1	1	yes	characteristic
16	C₄×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
17	#10622739	C₄	1	2	yes	—
18	#10622731	—	2	1	no	—
19	#10622731	C₄	1	2	yes	—
20	#10622539	C₂²	1	1	yes	characteristic
21	#10622537	C₂²	1	1	yes	characteristic
22	C₄×#4318	C₂²	1	1	yes	characteristic
23	#10622450	—	2	1	no	—
24	#10622450	C₂²	1	1	yes	characteristic
25	#10622450	C₂²	1	1	yes	characteristic
26	#10622450	C₂²	1	2	yes	—
27	#10622446	C₂²	1	1	yes	characteristic
28	#10622446	C₂²	1	1	yes	characteristic
29	D₁₁×C₄⋊C₈	—	2	1	no	—
30	D₁₁×C₄⋊C₈	C₂²	1	2	yes	—
31	#10622339	—	2	1	no	—
32	#10622331	—	2	1	no	—
33	#10622320	—	2	1	no	—
34	#10622318	—	2	1	no	—
35	#10622318	C₄	1	2	yes	—
36	#10622318	C₄	1	2	yes	—
37	#10622298	C₂²	1	2	yes	—
38	#10622298	C₂²	1	2	yes	—
39	C₁₁×#335	C₂²	1	2	yes	complemented
40	C₁₁×#334	C₂²	1	2	yes	complemented
41	#10622118	C₂²	1	2	yes	complemented
42	#10622118	C₂²	1	2	yes	complemented
43	#10622117	C₂²	1	2	yes	complemented
44	#10622117	C₂²	1	2	yes	complemented
45	#10622096	C₂²	1	2	yes	complemented
46	#10622095	C₂²	1	2	yes	complemented
47	C₂²×C₄×D₁₁	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₄×D₁₁	D₄	1	1	yes	characteristic
49	C₂²×C₄×D₁₁	Q₈	1	1	yes	characteristic
50	C₂×C₁₁×M₁₆	—	2	1	no	—
51	C₂×C₁₁×M₁₆	C₂×C₄	1	2	yes	—
52	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
53	C₂×C₄×Dic₁₁	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄×Dic₁₁	D₄	1	1	yes	characteristic
55	C₂×C₄×Dic₁₁	Q₈	1	1	yes	characteristic
56	C₂×#4318	—	2	1	no	—
57	C₂×#4318	C₂×C₄	1	2	yes	—
58	M₁₆×D₁₁	—	4	4	no	—
59	C₂×#4313	—	2	2	no	—
60	C₂×#4313	—	2	1	no	—
61	C₂×#4313	—	2	1	no	—
62	C₂×C₈×D₁₁	—	2	2	no	—
63	C₄²×D₁₁	C₂×C₄	1	1	yes	characteristic
64	C₄²×D₁₁	C₂×C₄	1	1	yes	characteristic
65	C₄²×D₁₁	D₄	1	1	yes	characteristic
66	C₄²×D₁₁	D₄	1	1	yes	characteristic
67	C₄²×D₁₁	Q₈	1	1	yes	characteristic
68	C₄²×D₁₁	Q₈	1	1	yes	characteristic
69	C₄²×D₁₁	C₂³	1	1	yes	characteristic
70	C₄²×D₁₁	C₂³	1	1	yes	characteristic
71	C₁₁×C₄⋊C₈	—	2	1	no	—
72	C₁₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
73	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
74	C₁₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
75	C₁₁×C₂²⋊C₈	—	2	1	no	—
76	C₁₁×#97	—	2	1	no	—
77	C₁₁×#97	C₂×C₄	1	2	yes	—
78	C₄×C₈×C₁₁	C₂³	1	2	yes	—
79	C₂²⋊(C₁₁⋊C₈)	—	2	1	no	—
80	(C₂×D₁₁)⋊C₈	—	2	1	no	—
81	(C₂×D₁₁)⋊C₈	—	2	1	no	—
82	(C₂×D₁₁)⋊C₈	C₂×C₄	1	4	yes	—
83	(C₂×D₁₁)⋊C₈	C₂×C₄	1	4	yes	—
84	Dic₁₁⋊C₈	—	2	2	no	—
85	Dic₁₁⋊C₈	—	2	2	no	—
86	Dic₁₁⋊C₈	—	2	1	no	—
87	Dic₁₁⋊C₈	—	2	1	no	—
88	Dic₁₁⋊C₈	C₂×C₄	1	4	yes	—
89	Dic₁₁⋊C₈	C₂×C₄	1	4	yes	—
90	C₈×Dic₁₁	—	2	1	no	—
91	C₈×Dic₁₁	—	2	1	no	—
92	C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
93	C₄⋊(C₁₁⋊C₈)	C₂³	1	2	yes	—
94	C₄⋊(C₁₁⋊C₈)	C₂³	1	1	yes	characteristic
95	C₄⋊(C₁₁⋊C₈)	C₂³	1	1	yes	characteristic
96	#66867	—	2	1	no	—
97	#66867	C₂×C₄	1	2	yes	—
98	C₄×C₁₁⋊C₈	C₂³	1	2	yes	—
99	#17820	—	11	1	no	maximal, Sylow
100	C₂³×D₁₁	C₄⋊C₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
104	C₂²×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
105	C₂²×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
106	C₂²×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
107	C₂×C₄×D₁₁	—	2	2	no	—
108	C₂×C₄×D₁₁	—	2	2	no	—
109	C₂×C₄×D₁₁	—	4	2	no	—
110	C₂×C₄×D₁₁	—	4	2	no	—
111	C₂×C₄×D₁₁	C₄⋊C₄	1	1	yes	characteristic
112	C₂×C₄×D₁₁	C₄⋊C₄	1	1	yes	characteristic
113	C₂×C₄×D₁₁	C₄⋊C₄	1	1	yes	characteristic
114	C₂×C₄×D₁₁	C₄⋊C₄	1	1	yes	characteristic
115	C₂×C₄×D₁₁	C₄⋊C₄	1	1	yes	characteristic
116	C₂×C₄×D₁₁	C₄⋊C₄	1	1	yes	characteristic
117	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₄×D₁₁	C₂×D₄	1	1	yes	characteristic
120	C₂×C₄×D₁₁	C₂×D₄	1	1	yes	characteristic
121	C₂×C₄×D₁₁	C₂×Q₈	1	1	yes	characteristic
122	C₂×C₄×D₁₁	C₂×Q₈	1	1	yes	characteristic
123	C₁₁×M₁₆	—	4	2	no	—
124	C₁₁×M₁₆	—	4	2	no	—
125	C₂×C₈×C₁₁	—	2	1	no	—
126	C₂×C₈×C₁₁	—	2	1	no	—
127	C₂×C₈×C₁₁	—	2	2	no	—
128	C₂×C₈×C₁₁	C₂²×C₄	1	4	yes	—
129	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
130	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₁₁	C₂×Q₈	1	1	yes	characteristic
132	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
133	C₄×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
134	C₄×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
135	C₄×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
136	C₄×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
137	C₄×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
138	C₄×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
139	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
140	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
141	C₄×Dic₁₁	C₂×D₄	1	1	yes	characteristic
142	C₄×Dic₁₁	C₂×D₄	1	1	yes	characteristic
143	C₄×Dic₁₁	C₂×Q₈	1	1	yes	characteristic
144	C₄×Dic₁₁	C₂×Q₈	1	1	yes	characteristic
145	#4318	—	4	2	no	—
146	#4318	—	4	2	no	—
147	C₂×C₁₁⋊C₈	—	2	1	no	—
148	C₂×C₁₁⋊C₈	—	2	1	no	—
149	C₂×C₁₁⋊C₈	—	2	2	no	—
150	C₂×C₁₁⋊C₈	C₂²×C₄	1	4	yes	—
151	#4313	—	4	4	no	—
152	#4313	—	4	2	no	—
153	#4313	—	4	2	no	—
154	C₈×D₁₁	—	4	4	no	—
155	#2920	—	11	1	no	—
156	#2920	—	11	1	no	—
157	C₂×#423	—	11	1	no	—
158	#1574	—	11	2	no	—
159	#1574	—	11	2	no	—
160	#1571	—	11	2	no	—
161	#1570	—	11	2	no	—
162	#1569	—	11	1	no	—
163	#1569	—	11	1	no	—
164	#1569	—	11	1	no	—
165	#1569	D₁₁	1	1	yes	characteristic, complemented
166	C₂³×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
167	C₂²×D₁₁	—	2	2	no	—
168	C₂²×D₁₁	—	4	1	no	—
169	C₂²×D₁₁	—	4	1	no	—
170	C₂²×D₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
171	C₂²×D₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
172	C₂×C₄×C₁₁	—	2	2	no	—
173	C₂×C₄×C₁₁	—	2	1	no	—
174	C₂×C₄×C₁₁	—	2	1	no	—
175	C₂×C₄×C₁₁	—	4	1	no	—
176	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
177	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
178	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
179	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
180	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₁₁	C₂²×Q₈	1	1	yes	characteristic
182	C₂×Dic₁₁	—	2	2	no	—
183	C₂×Dic₁₁	—	2	2	no	—
184	C₂×Dic₁₁	—	4	1	no	—
185	C₂×Dic₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
186	C₂×Dic₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
187	C₂×Dic₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
188	C₂×Dic₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
189	C₂×Dic₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
190	C₂×Dic₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
191	C₄×D₁₁	—	2	2	no	—
192	C₄×D₁₁	—	2	2	no	—
193	C₄×D₁₁	—	2	2	no	—
194	C₄×D₁₁	—	2	1	no	—
195	C₄×D₁₁	—	2	1	no	—
196	C₄×D₁₁	—	2	2	no	—
197	C₄×D₁₁	—	2	2	no	—
198	C₄×D₁₁	—	2	2	no	—
199	C₄×D₁₁	—	4	1	no	—
200	C₄×D₁₁	—	4	1	no	—
201	C₄×D₁₁	—	4	1	no	—
202	C₄×D₁₁	—	4	1	no	—
203	C₄×D₁₁	AGL(1,ℤ/8)	1	2	yes	—
204	C₄×D₁₁	#137	1	2	yes	—
205	C₈×C₁₁	—	2	4	no	—
206	C₈×C₁₁	—	4	2	no	—
207	C₈×C₁₁	—	4	1	no	—
208	C₈×C₁₁	—	4	1	no	—
209	C₁₁⋊C₈	—	2	4	no	—
210	C₁₁⋊C₈	—	4	2	no	—
211	C₁₁⋊C₈	—	4	1	no	—
212	C₁₁⋊C₈	—	4	1	no	—
213	C₂²×M₁₆	—	22	1	no	—
214	C₂²×C₄²	—	11	1	no	—
215	#432	—	11	2	no	—
216	#432	—	11	2	no	—
217	#432	—	11	1	no	—
218	#432	—	22	1	no	—
219	#432	C₂×D₁₁	1	1	yes	characteristic
220	#431	—	11	2	no	—
221	#431	—	11	2	no	—
222	#431	—	11	1	no	—
223	#431	—	11	1	no	—
224	#431	—	22	1	no	—
225	#423	—	11	2	no	—
226	#423	—	11	1	no	—
227	#423	—	11	1	no	—
228	#423	—	11	1	no	—
229	#423	—	11	2	no	—
230	#423	—	22	1	no	—
231	#423	—	22	1	no	—
232	#423	C₂×D₁₁	1	1	yes	characteristic
233	C₂×C₄⋊C₈	—	11	2	no	—
234	C₂×C₄⋊C₈	—	22	1	no	—
235	#407	—	11	2	no	—
236	#407	—	22	1	no	—
237	C₄×M₁₆	—	11	1	no	—
238	C₄×M₁₆	—	22	1	no	—
239	C₄×M₁₆	C₂×D₁₁	1	1	yes	characteristic
240	#335	—	11	2	no	—
241	#335	—	11	2	no	—
242	#335	—	11	2	no	—
243	#335	C₂×D₁₁	1	2	yes	complemented
244	#334	—	11	2	no	—
245	#334	—	11	2	no	—
246	#334	—	11	2	no	—
247	#334	C₂×D₁₁	1	2	yes	complemented
248	C₂²×C₁₁	—	2	1	no	—
249	C₂²×C₁₁	—	2	1	no	—
250	C₂²×C₁₁	—	2	1	no	—
251	C₂²×C₁₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
252	C₂×D₁₁	—	2	1	no	—
253	C₂×D₁₁	—	2	1	no	—
254	C₂×D₁₁	—	2	1	no	—
255	C₂×D₁₁	—	2	1	no	—
256	C₂×D₁₁	—	2	1	no	—
257	C₂×D₁₁	—	4	4	no	—
258	C₂×D₁₁	#428	1	2	yes	—
259	C₄×C₁₁	—	2	1	no	—
260	C₄×C₁₁	—	2	1	no	—
261	C₄×C₁₁	—	2	1	no	—
262	C₄×C₁₁	—	2	1	no	—
263	C₄×C₁₁	#568	1	2	yes	—
264	C₄×C₁₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
265	C₄×C₁₁	C₂×#137	1	1	yes	characteristic
266	Dic₁₁	—	2	1	no	—
267	Dic₁₁	—	2	1	no	—
268	Dic₁₁	—	2	1	no	—
269	Dic₁₁	—	2	1	no	—
270	Dic₁₁	#428	1	2	yes	—
271	Dic₁₁	#430	1	2	yes	—
272	C₂³×C₄	—	11	1	no	—
273	C₂³×C₄	—	11	1	no	—
274	C₂³×C₄	—	11	1	no	—
275	C₂×M₁₆	—	2	1	no	—
276	C₂×M₁₆	—	11	2	no	—
277	C₂×M₁₆	—	22	2	no	—
278	C₂×M₁₆	—	22	1	no	—
279	C₂×M₁₆	—	22	1	no	—
280	C₂×M₁₆	—	22	1	no	—
281	C₂×M₁₆	—	44	4	no	—
282	C₂×M₁₆	C₄×D₁₁	1	2	yes	—
283	C₂²×C₈	—	22	2	no	—
284	C₂×C₄²	—	11	1	no	—
285	C₂×C₄²	—	11	1	no	—
286	C₂×C₄²	—	11	1	no	—
287	C₂×C₄²	—	11	1	no	—
288	C₂×C₄²	—	11	1	no	—
289	C₂×C₄²	—	11	1	no	—
290	C₂×C₄²	—	11	1	no	—
291	C₂×C₄²	—	11	1	no	—
292	C₂×C₄²	—	11	1	no	—
293	C₂×C₄²	—	11	1	no	—
294	C₂×C₄²	—	11	1	no	—
295	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
296	C₄⋊C₈	—	2	1	no	—
297	C₄⋊C₈	—	11	4	no	—
298	C₄⋊C₈	—	11	4	no	—
299	C₄⋊C₈	—	11	1	no	—
300	C₄⋊C₈	—	11	2	no	—
301	C₄⋊C₈	—	11	1	no	—
302	C₄⋊C₈	—	22	2	no	—
303	C₄⋊C₈	—	22	2	no	—
304	C₄⋊C₈	—	22	1	no	—
305	C₄⋊C₈	—	22	1	no	—
306	C₄⋊C₈	—	22	1	no	—
307	C₄⋊C₈	C₂²×D₁₁	1	1	yes	characteristic
308	C₄⋊C₈	C₂²×D₁₁	1	2	yes	—
309	C₄⋊C₈	C₂²×D₁₁	1	1	yes	characteristic
310	C₂²⋊C₈	—	2	1	no	—
311	C₂²⋊C₈	—	11	4	no	—
312	C₂²⋊C₈	—	11	4	no	—
313	C₂²⋊C₈	—	22	1	no	—
314	C₂²⋊C₈	—	22	1	no	—
315	C₂²⋊C₈	—	22	1	no	—
316	#97	—	2	1	no	—
317	#97	—	11	2	no	—
318	#97	—	22	1	no	—
319	#97	C₄×D₁₁	1	2	yes	—
320	C₄×C₈	—	11	2	no	—
321	C₄×C₈	—	22	1	no	—
322	C₄×C₈	—	22	1	no	—
323	C₄×C₈	C₂²×D₁₁	1	2	yes	—
324	C₂×C₁₁	—	4	1	no	—
325	C₂×C₁₁	#2905	1	1	yes	characteristic
326	C₂×C₁₁	C₂×#428	1	1	yes	characteristic
327	C₂×C₁₁	C₂×#430	1	1	yes	characteristic
328	D₁₁	—	2	2	no	—
329	D₁₁	—	4	1	no	—
330	C₂⁴	—	11	1	no	—
331	C₂²×C₄	—	11	1	no	—
332	C₂²×C₄	—	11	1	no	—
333	C₂²×C₄	—	11	1	no	—
334	C₂²×C₄	—	11	1	no	—
335	C₂²×C₄	—	11	1	no	—
336	C₂²×C₄	—	11	1	no	—
337	C₂²×C₄	—	11	1	no	—
338	C₂²×C₄	—	11	1	no	—
339	C₂²×C₄	—	11	1	no	—
340	C₂²×C₄	—	11	1	no	—
341	C₂²×C₄	—	11	1	no	—
342	C₂²×C₄	—	11	1	no	—
343	C₂²×C₄	—	11	1	no	—
344	C₂²×C₄	—	11	1	no	—
345	C₂²×C₄	—	11	1	no	—
346	C₂²×C₄	—	22	2	no	—
347	C₂²×C₄	—	22	2	no	—
348	C₂²×C₄	—	44	2	no	—
349	C₂²×C₄	—	44	2	no	—
350	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
351	C₂²×C₄	D₄×D₁₁	1	1	yes	characteristic
352	C₂²×C₄	Q₈×D₁₁	1	1	yes	characteristic
353	M₁₆	—	4	2	no	—
354	M₁₆	—	4	2	no	—
355	M₁₆	—	44	2	no	—
356	M₁₆	—	44	2	no	—
357	M₁₆	—	44	4	no	—
358	M₁₆	—	44	2	no	—
359	M₁₆	—	44	2	no	—
360	C₂×C₈	—	2	1	no	—
361	C₂×C₈	—	2	1	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	11	4	no	—
364	C₂×C₈	—	22	1	no	—
365	C₂×C₈	—	22	1	no	—
366	C₂×C₈	—	22	2	no	—
367	C₂×C₈	—	44	4	no	—
368	C₂×C₈	C₂×C₄×D₁₁	1	4	yes	—
369	C₄²	—	11	1	no	—
370	C₄²	—	11	1	no	—
371	C₄²	—	11	1	no	—
372	C₄²	—	11	1	no	—
373	C₄²	—	11	1	no	—
374	C₄²	—	11	1	no	—
375	C₄²	—	11	1	no	—
376	C₄²	—	11	1	no	—
377	C₄²	—	11	1	no	—
378	C₄²	—	11	1	no	—
379	C₄²	—	11	1	no	—
380	C₄²	—	11	1	no	—
381	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
382	C₄²	D₄×D₁₁	1	1	yes	characteristic
383	C₄²	Q₈×D₁₁	1	1	yes	characteristic
384	C₄²	C₂³×D₁₁	1	1	yes	characteristic
385	C₁₁	#17820	1	1	yes	characteristic, complemented, Sylow
386	C₂³	—	11	1	no	—
387	C₂³	—	11	1	no	—
388	C₂³	—	22	2	no	—
389	C₂³	—	44	1	no	—
390	C₂³	—	44	1	no	—
391	C₂³	C₄⋊C₄×D₁₁	1	1	yes	characteristic
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	11	1	no	—
397	C₂×C₄	—	11	1	no	—
398	C₂×C₄	—	11	2	no	—
399	C₂×C₄	—	11	2	no	—
400	C₂×C₄	—	11	1	no	—
401	C₂×C₄	—	11	1	no	—
402	C₂×C₄	—	11	1	no	—
403	C₂×C₄	—	11	1	no	—
404	C₂×C₄	—	22	2	no	—
405	C₂×C₄	—	22	2	no	—
406	C₂×C₄	—	22	2	no	—
407	C₂×C₄	—	22	2	no	—
408	C₂×C₄	—	22	2	no	—
409	C₂×C₄	—	22	2	no	—
410	C₂×C₄	—	22	2	no	—
411	C₂×C₄	—	22	2	no	—
412	C₂×C₄	—	22	1	no	—
413	C₂×C₄	—	22	1	no	—
414	C₂×C₄	—	44	1	no	—
415	C₂×C₄	—	44	1	no	—
416	C₂×C₄	—	44	1	no	—
417	C₂×C₄	—	44	1	no	—
418	C₂×C₄	—	44	1	no	—
419	C₂×C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
420	C₂×C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
421	C₂×C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
422	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
423	C₂×C₄	C₂×D₄×D₁₁	1	1	yes	characteristic
424	C₂×C₄	C₂×Q₈×D₁₁	1	1	yes	characteristic
425	C₈	—	2	4	no	—
426	C₈	—	4	2	no	—
427	C₈	—	4	1	no	—
428	C₈	—	4	1	no	—
429	C₈	—	22	4	no	—
430	C₈	—	44	2	no	—
431	C₈	—	44	1	no	—
432	C₈	—	44	1	no	—
433	C₂²	—	2	1	no	—
434	C₂²	—	2	1	no	—
435	C₂²	—	2	1	no	—
436	C₂²	—	11	2	no	—
437	C₂²	—	22	1	no	—
438	C₂²	—	22	1	no	—
439	C₂²	—	22	1	no	—
440	C₂²	—	22	1	no	—
441	C₂²	—	22	1	no	—
442	C₂²	—	44	4	no	—
443	C₂²	C₂×C₄⋊C₄×D₁₁	1	1	yes	characteristic
444	C₄	—	2	1	no	—
445	C₄	—	2	1	no	—
446	C₄	—	2	1	no	—
447	C₄	—	2	1	no	—
448	C₄	—	11	2	no	—
449	C₄	—	11	2	no	—
450	C₄	—	22	1	no	—
451	C₄	—	22	1	no	—
452	C₄	—	22	1	no	—
453	C₄	—	22	1	no	—
454	C₄	#10623276	1	2	yes	—
455	C₄	D₁₁×AGL(1,ℤ/8)	1	1	yes	characteristic
456	C₄	D₁₁×#137	1	1	yes	characteristic
457	C₂	—	4	1	no	—
458	C₂	—	22	2	no	—
459	C₂	—	44	1	no	—
460	C₂	#13077178	1	1	yes	characteristic
461	C₂	D₁₁×#428	1	1	yes	characteristic
462	C₂	D₁₁×#430	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×#1569	C₂
socle	C₂²×C₁₁	C₂²×C₄⋊C₄
prime radical	C₂³×D₁₁	C₄⋊C₄
cosocle	C₄²×C₁₁	C₂⁴
hypercenter	#1569	D₁₁
hypocenter	C₁₁	#17820
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1569

Complements

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

N	H ≅ G/N	type
4. #13067406	C₂	semidirect
5. #13067403	C₂	semidirect
6. #13067389	C₂	semidirect
7. #13067385	C₂	semidirect
8. #13067384	C₂	semidirect
9. #13067383	C₂	semidirect
10. #13067381	C₂	semidirect
11. C₁₁×#1569	C₂	semidirect
39. C₁₁×#335	C₂²	semidirect
40. C₁₁×#334	C₂²	semidirect
41. #10622118	C₂²	semidirect
42. #10622118	C₂²	semidirect
43. #10622117	C₂²	semidirect
44. #10622117	C₂²	semidirect
45. #10622096	C₂²	semidirect
46. #10622095	C₂²	semidirect
165. #1569	D₁₁	semidirect
243. #335	C₂×D₁₁	semidirect
247. #334	C₂×D₁₁	semidirect
385. C₁₁	#17820	semidirect

Maximal subgroups

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

subgroup	index
#13077247	2
#13077246	2
D₁₁×#423	2
#13067406	2
#13067403	2
#13067389	2
#13067385	2
#13067384	2
#13067383	2
#13067381	2
C₁₁×#1569	2
#17820	11