Subgroups — #14722929

Order 2816.

640 conjugacy classes of subgroups.

The subgroup lattice has 444 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×#10622298	C₂	1	1	yes	maximal, characteristic
4	#13067395	C₂	1	2	yes	maximal, complemented
5	#13067393	C₂	1	2	yes	maximal, complemented
6	#13067389	C₂	1	2	yes	maximal, complemented
7	#13067385	C₂	1	2	yes	maximal, complemented
8	#13067379	C₂	1	1	yes	maximal, characteristic, complemented
9	#13067377	C₂	1	1	yes	maximal, characteristic, complemented
10	#13067377	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₁×#1568	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄²×D₁₁	C₂²	1	1	yes	characteristic
13	C₁₁×#432	C₂²	1	1	yes	characteristic
14	C₁₁×#432	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
16	C₂×(C₂×D₁₁)⋊C₈	C₄	1	2	yes	—
17	C₂×Dic₁₁⋊C₈	C₄	1	2	yes	—
18	#10622539	C₂²	1	1	yes	characteristic
19	#10622539	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
21	#10622450	C₂²	1	2	yes	—
22	#10622448	C₂²	1	2	yes	—
23	#10622446	C₂²	1	2	yes	—
24	D₁₁×C₄⋊C₈	C₂²	1	2	yes	—
25	#10622339	—	2	1	no	—
26	D₁₁×C₂²⋊C₈	—	2	1	no	—
27	#10622332	—	2	1	no	—
28	#10622331	—	2	1	no	—
29	#10622320	—	2	1	no	—
30	#10622318	—	2	1	no	—
31	#10622318	—	2	1	no	—
32	D₁₁×#97	—	2	1	no	—
33	#10622298	C₄	1	2	yes	—
34	#10622298	C₄	1	2	yes	—
35	#10622298	C₂²	1	1	yes	characteristic
36	#10622298	C₂²	1	1	yes	characteristic
37	#10622298	C₂²	1	1	yes	characteristic
38	#10622298	C₂²	1	1	yes	characteristic
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	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
51	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
52	C₂×C₄×Dic₁₁	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄×Dic₁₁	D₄	1	1	yes	characteristic
54	C₂×C₄×Dic₁₁	Q₈	1	1	yes	characteristic
55	C₂²×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
56	C₂×#4313	—	2	2	no	—
57	C₂×C₈×D₁₁	—	2	2	no	—
58	C₄²×D₁₁	C₂×C₄	1	1	yes	characteristic
59	C₄²×D₁₁	C₂×C₄	1	1	yes	characteristic
60	C₄²×D₁₁	D₄	1	1	yes	characteristic
61	C₄²×D₁₁	D₄	1	1	yes	characteristic
62	C₄²×D₁₁	Q₈	1	1	yes	characteristic
63	C₄²×D₁₁	Q₈	1	1	yes	characteristic
64	C₄²×D₁₁	C₂³	1	1	yes	characteristic
65	C₄²×D₁₁	C₂³	1	1	yes	characteristic
66	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
67	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
68	C₁₁×C₂²⋊C₈	—	2	1	no	—
69	C₁₁×C₂²⋊C₈	—	2	1	no	—
70	C₁₁×#97	—	2	1	no	—
71	C₁₁×#97	—	2	1	no	—
72	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
73	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
74	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
75	C₂²⋊(C₁₁⋊C₈)	—	2	1	no	—
76	C₂²⋊(C₁₁⋊C₈)	—	2	1	no	—
77	(C₂×D₁₁)⋊C₈	—	2	2	no	—
78	(C₂×D₁₁)⋊C₈	—	2	2	no	—
79	(C₂×D₁₁)⋊C₈	C₂×C₄	1	2	yes	—
80	(C₂×D₁₁)⋊C₈	C₂×C₄	1	2	yes	—
81	(C₂×D₁₁)⋊C₈	C₂×C₄	1	2	yes	—
82	(C₂×D₁₁)⋊C₈	C₂×C₄	1	2	yes	—
83	#66879	—	2	2	no	—
84	Dic₁₁⋊C₈	—	2	2	no	—
85	Dic₁₁⋊C₈	—	2	2	no	—
86	Dic₁₁⋊C₈	C₂×C₄	1	2	yes	—
87	Dic₁₁⋊C₈	C₂×C₄	1	2	yes	—
88	Dic₁₁⋊C₈	C₂×C₄	1	2	yes	—
89	Dic₁₁⋊C₈	C₂×C₄	1	2	yes	—
90	C₈×Dic₁₁	—	2	2	no	—
91	C₄⋊(C₁₁⋊C₈)	C₂³	1	2	yes	—
92	C₄⋊(C₁₁⋊C₈)	C₂³	1	2	yes	—
93	#66867	—	2	1	no	—
94	#66867	—	2	1	no	—
95	C₄×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
96	C₄×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
97	C₄×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
98	#17816	—	11	1	no	maximal, Sylow
99	C₂³×D₁₁	C₄⋊C₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
103	C₂²×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
104	C₂²×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
105	C₂²×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
106	C₂×C₄×D₁₁	—	2	4	no	—
107	C₂×C₄×D₁₁	—	4	2	no	—
108	C₂×C₄×D₁₁	—	4	2	no	—
109	C₂×C₄×D₁₁	C₄⋊C₄	1	1	yes	characteristic
110	C₂×C₄×D₁₁	C₄⋊C₄	1	1	yes	characteristic
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	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₄×D₁₁	C₂×D₄	1	1	yes	characteristic
118	C₂×C₄×D₁₁	C₂×D₄	1	1	yes	characteristic
119	C₂×C₄×D₁₁	C₂×Q₈	1	1	yes	characteristic
120	C₂×C₄×D₁₁	C₂×Q₈	1	1	yes	characteristic
121	C₂×C₈×C₁₁	—	2	2	no	—
122	C₂×C₈×C₁₁	—	2	2	no	—
123	C₂×C₈×C₁₁	—	4	2	no	—
124	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
125	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
126	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
127	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
128	C₄²×C₁₁	C₂×Q₈	1	1	yes	characteristic
129	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
130	C₄×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
131	C₄×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
132	C₄×Dic₁₁	C₄⋊C₄	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	C₂²×C₄	1	1	yes	characteristic
137	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
138	C₄×Dic₁₁	C₂×D₄	1	1	yes	characteristic
139	C₄×Dic₁₁	C₂×D₄	1	1	yes	characteristic
140	C₄×Dic₁₁	C₂×Q₈	1	1	yes	characteristic
141	C₄×Dic₁₁	C₂×Q₈	1	1	yes	characteristic
142	C₂×C₁₁⋊C₈	—	2	2	no	—
143	C₂×C₁₁⋊C₈	—	2	2	no	—
144	C₂×C₁₁⋊C₈	—	4	2	no	—
145	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
146	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
147	#4313	—	4	4	no	—
148	C₈×D₁₁	—	4	4	no	—
149	#2920	—	11	1	no	—
150	C₂×#432	—	11	1	no	—
151	C₂×#431	—	11	1	no	—
152	#1572	—	11	2	no	—
153	#1572	—	11	2	no	—
154	#1571	—	11	2	no	—
155	#1570	—	11	2	no	—
156	#1568	—	11	1	no	—
157	#1568	—	11	1	no	—
158	#1568	—	11	1	no	—
159	#1568	D₁₁	1	1	yes	characteristic, complemented
160	C₂³×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
161	C₂²×D₁₁	—	2	2	no	—
162	C₂²×D₁₁	—	2	2	no	—
163	C₂²×D₁₁	—	4	1	no	—
164	C₂²×D₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
165	C₂²×D₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
166	C₂×C₄×C₁₁	—	2	2	no	—
167	C₂×C₄×C₁₁	—	2	2	no	—
168	C₂×C₄×C₁₁	—	2	2	no	—
169	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
170	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
171	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
172	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
173	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₁₁	C₂²×Q₈	1	1	yes	characteristic
175	C₂×Dic₁₁	—	2	2	no	—
176	C₂×Dic₁₁	—	2	2	no	—
177	C₂×Dic₁₁	—	4	1	no	—
178	C₂×Dic₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
179	C₂×Dic₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
180	C₂×Dic₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
181	C₂×Dic₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
182	C₂×Dic₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
183	C₂×Dic₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
184	C₄×D₁₁	—	2	2	no	—
185	C₄×D₁₁	—	2	2	no	—
186	C₄×D₁₁	—	2	2	no	—
187	C₄×D₁₁	—	2	2	no	—
188	C₄×D₁₁	—	2	2	no	—
189	C₄×D₁₁	—	4	1	no	—
190	C₄×D₁₁	—	4	1	no	—
191	C₄×D₁₁	—	4	1	no	—
192	C₄×D₁₁	—	4	1	no	—
193	C₄×D₁₁	—	4	1	no	—
194	C₄×D₁₁	—	4	1	no	—
195	C₄×D₁₁	#135	1	4	yes	—
196	C₈×C₁₁	—	2	2	no	—
197	C₈×C₁₁	—	2	2	no	—
198	C₈×C₁₁	—	4	2	no	—
199	C₈×C₁₁	—	4	2	no	—
200	C₁₁⋊C₈	—	2	2	no	—
201	C₁₁⋊C₈	—	2	2	no	—
202	C₁₁⋊C₈	—	4	2	no	—
203	C₁₁⋊C₈	—	4	2	no	—
204	C₂²×C₄²	—	11	1	no	—
205	#432	—	11	1	no	—
206	#432	—	11	1	no	—
207	#432	—	11	2	no	—
208	#432	—	22	1	no	—
209	#432	—	22	1	no	—
210	#432	—	22	1	no	—
211	#432	C₂×D₁₁	1	1	yes	characteristic
212	#432	C₂×D₁₁	1	1	yes	characteristic
213	#431	—	11	1	no	—
214	#431	—	11	1	no	—
215	#431	—	11	1	no	—
216	#431	—	11	1	no	—
217	#431	—	11	2	no	—
218	#431	—	11	2	no	—
219	#431	—	11	2	no	—
220	#431	—	22	1	no	—
221	#423	—	11	2	no	—
222	C₂×C₄⋊C₈	—	11	2	no	—
223	C₂×C₄⋊C₈	—	11	2	no	—
224	#407	—	22	1	no	—
225	C₂×C₂²⋊C₈	—	11	2	no	—
226	C₂×C₂²⋊C₈	—	22	1	no	—
227	C₄×M₁₆	—	22	1	no	—
228	C₂×#97	—	22	1	no	—
229	C₂×C₄×C₈	—	11	1	no	—
230	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
231	#335	—	11	2	no	—
232	#335	—	11	2	no	—
233	#335	—	11	2	no	—
234	#335	C₂×D₁₁	1	2	yes	complemented
235	#334	—	11	2	no	—
236	#334	—	11	2	no	—
237	#334	—	11	2	no	—
238	#334	C₂×D₁₁	1	2	yes	complemented
239	C₂²×C₁₁	—	2	1	no	—
240	C₂²×C₁₁	—	2	1	no	—
241	C₂²×C₁₁	#430	1	2	yes	—
242	C₂²×C₁₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
243	C₂×D₁₁	—	2	1	no	—
244	C₂×D₁₁	—	2	1	no	—
245	C₂×D₁₁	—	2	1	no	—
246	C₂×D₁₁	—	2	1	no	—
247	C₂×D₁₁	—	2	1	no	—
248	C₂×D₁₁	—	4	4	no	—
249	C₂×D₁₁	#427	1	2	yes	—
250	C₄×C₁₁	—	2	1	no	—
251	C₄×C₁₁	—	2	1	no	—
252	C₄×C₁₁	—	2	1	no	—
253	C₄×C₁₁	—	2	1	no	—
254	C₄×C₁₁	#568	1	2	yes	—
255	C₄×C₁₁	C₂×#135	1	2	yes	—
256	Dic₁₁	—	2	1	no	—
257	Dic₁₁	—	2	1	no	—
258	Dic₁₁	—	2	1	no	—
259	Dic₁₁	—	2	1	no	—
260	Dic₁₁	—	2	1	no	—
261	Dic₁₁	#427	1	2	yes	—
262	C₂³×C₄	—	11	1	no	—
263	C₂³×C₄	—	11	1	no	—
264	C₂³×C₄	—	11	1	no	—
265	C₂×M₁₆	—	22	2	no	—
266	C₂²×C₈	—	11	2	no	—
267	C₂²×C₈	—	22	2	no	—
268	C₂²×C₈	C₄×D₁₁	1	2	yes	—
269	C₂×C₄²	—	11	1	no	—
270	C₂×C₄²	—	11	1	no	—
271	C₂×C₄²	—	11	1	no	—
272	C₂×C₄²	—	11	1	no	—
273	C₂×C₄²	—	11	1	no	—
274	C₂×C₄²	—	11	1	no	—
275	C₂×C₄²	—	11	1	no	—
276	C₂×C₄²	—	11	1	no	—
277	C₂×C₄²	—	11	1	no	—
278	C₂×C₄²	—	11	1	no	—
279	C₂×C₄²	—	11	1	no	—
280	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
281	C₄⋊C₈	—	11	2	no	—
282	C₄⋊C₈	—	11	2	no	—
283	C₄⋊C₈	—	11	2	no	—
284	C₄⋊C₈	—	11	2	no	—
285	C₄⋊C₈	—	11	2	no	—
286	C₄⋊C₈	—	11	2	no	—
287	C₄⋊C₈	—	22	2	no	—
288	C₄⋊C₈	—	22	2	no	—
289	C₄⋊C₈	C₂²×D₁₁	1	2	yes	—
290	C₄⋊C₈	C₂²×D₁₁	1	2	yes	—
291	C₂²⋊C₈	—	2	1	no	—
292	C₂²⋊C₈	—	2	1	no	—
293	C₂²⋊C₈	—	11	2	no	—
294	C₂²⋊C₈	—	11	2	no	—
295	C₂²⋊C₈	—	11	2	no	—
296	C₂²⋊C₈	—	11	2	no	—
297	C₂²⋊C₈	—	22	2	no	—
298	C₂²⋊C₈	—	22	2	no	—
299	C₂²⋊C₈	—	22	1	no	—
300	C₂²⋊C₈	—	22	1	no	—
301	#97	—	2	1	no	—
302	#97	—	2	1	no	—
303	#97	—	22	2	no	—
304	#97	—	22	1	no	—
305	#97	—	22	1	no	—
306	C₄×C₈	—	11	2	no	—
307	C₄×C₈	—	11	1	no	—
308	C₄×C₈	—	11	1	no	—
309	C₄×C₈	—	22	2	no	—
310	C₄×C₈	C₄×D₁₁	1	2	yes	—
311	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
312	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
313	C₂×C₁₁	—	2	2	no	—
314	C₂×C₁₁	#2905	1	1	yes	characteristic
315	C₂×C₁₁	C₂×#427	1	1	yes	characteristic
316	C₂×C₁₁	C₂×#430	1	1	yes	characteristic
317	D₁₁	—	2	2	no	—
318	D₁₁	—	4	1	no	—
319	C₂⁴	—	11	1	no	—
320	C₂²×C₄	—	11	1	no	—
321	C₂²×C₄	—	11	1	no	—
322	C₂²×C₄	—	11	1	no	—
323	C₂²×C₄	—	11	1	no	—
324	C₂²×C₄	—	11	1	no	—
325	C₂²×C₄	—	11	1	no	—
326	C₂²×C₄	—	11	1	no	—
327	C₂²×C₄	—	11	1	no	—
328	C₂²×C₄	—	11	1	no	—
329	C₂²×C₄	—	11	1	no	—
330	C₂²×C₄	—	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	—	22	4	no	—
336	C₂²×C₄	—	44	2	no	—
337	C₂²×C₄	—	44	2	no	—
338	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
339	C₂²×C₄	D₄×D₁₁	1	1	yes	characteristic
340	C₂²×C₄	Q₈×D₁₁	1	1	yes	characteristic
341	M₁₆	—	44	4	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	4	2	no	—
345	C₂×C₈	—	11	2	no	—
346	C₂×C₈	—	11	2	no	—
347	C₂×C₈	—	22	2	no	—
348	C₂×C₈	—	22	2	no	—
349	C₂×C₈	—	44	4	no	—
350	C₂×C₈	—	44	2	no	—
351	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
352	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
353	C₄²	—	11	1	no	—
354	C₄²	—	11	1	no	—
355	C₄²	—	11	1	no	—
356	C₄²	—	11	1	no	—
357	C₄²	—	11	1	no	—
358	C₄²	—	11	1	no	—
359	C₄²	—	11	1	no	—
360	C₄²	—	11	1	no	—
361	C₄²	—	11	1	no	—
362	C₄²	—	11	1	no	—
363	C₄²	—	11	1	no	—
364	C₄²	—	11	1	no	—
365	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
366	C₄²	D₄×D₁₁	1	1	yes	characteristic
367	C₄²	Q₈×D₁₁	1	1	yes	characteristic
368	C₄²	C₂³×D₁₁	1	1	yes	characteristic
369	C₁₁	#17816	1	1	yes	characteristic, complemented, Sylow
370	C₂³	—	11	1	no	—
371	C₂³	—	11	1	no	—
372	C₂³	—	22	2	no	—
373	C₂³	—	22	2	no	—
374	C₂³	—	44	1	no	—
375	C₂³	C₄⋊C₄×D₁₁	1	1	yes	characteristic
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	11	1	no	—
380	C₂×C₄	—	11	4	no	—
381	C₂×C₄	—	11	1	no	—
382	C₂×C₄	—	11	1	no	—
383	C₂×C₄	—	11	1	no	—
384	C₂×C₄	—	11	1	no	—
385	C₂×C₄	—	11	1	no	—
386	C₂×C₄	—	22	2	no	—
387	C₂×C₄	—	22	2	no	—
388	C₂×C₄	—	22	2	no	—
389	C₂×C₄	—	22	2	no	—
390	C₂×C₄	—	22	2	no	—
391	C₂×C₄	—	22	2	no	—
392	C₂×C₄	—	22	2	no	—
393	C₂×C₄	—	44	1	no	—
394	C₂×C₄	—	44	1	no	—
395	C₂×C₄	—	44	1	no	—
396	C₂×C₄	—	44	1	no	—
397	C₂×C₄	—	44	1	no	—
398	C₂×C₄	—	44	1	no	—
399	C₂×C₄	—	44	1	no	—
400	C₂×C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
401	C₂×C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
402	C₂×C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
403	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
404	C₂×C₄	C₂×D₄×D₁₁	1	1	yes	characteristic
405	C₂×C₄	C₂×Q₈×D₁₁	1	1	yes	characteristic
406	C₈	—	2	2	no	—
407	C₈	—	2	2	no	—
408	C₈	—	4	2	no	—
409	C₈	—	4	2	no	—
410	C₈	—	22	2	no	—
411	C₈	—	22	2	no	—
412	C₈	—	44	2	no	—
413	C₈	—	44	2	no	—
414	C₂²	—	2	1	no	—
415	C₂²	—	2	1	no	—
416	C₂²	—	11	2	no	—
417	C₂²	—	22	1	no	—
418	C₂²	—	22	1	no	—
419	C₂²	—	22	1	no	—
420	C₂²	—	22	1	no	—
421	C₂²	—	22	1	no	—
422	C₂²	—	44	4	no	—
423	C₂²	#10622506	1	2	yes	—
424	C₂²	C₂×C₄⋊C₄×D₁₁	1	1	yes	characteristic
425	C₄	—	2	1	no	—
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	11	2	no	—
430	C₄	—	22	1	no	—
431	C₄	—	22	1	no	—
432	C₄	—	22	1	no	—
433	C₄	—	22	1	no	—
434	C₄	—	22	1	no	—
435	C₄	#10623276	1	2	yes	—
436	C₄	D₁₁×#135	1	2	yes	—
437	C₂	—	2	2	no	—
438	C₂	—	22	2	no	—
439	C₂	—	44	1	no	—
440	C₂	#13077178	1	1	yes	characteristic
441	C₂	D₁₁×#427	1	1	yes	characteristic
442	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	#17816
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. #13067395	C₂	semidirect
5. #13067393	C₂	semidirect
6. #13067389	C₂	semidirect
7. #13067385	C₂	semidirect
8. #13067379	C₂	semidirect
9. #13067377	C₂	semidirect
10. #13067377	C₂	semidirect
11. C₁₁×#1568	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
159. #1568	D₁₁	semidirect
234. #335	C₂×D₁₁	semidirect
238. #334	C₂×D₁₁	semidirect
369. C₁₁	#17816	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×#10622298	2
#13067395	2
#13067393	2
#13067389	2
#13067385	2
#13067379	2
#13067377	2
C₁₁×#1568	2
#17816	11