Subgroups — #14722932

Order 2816.

640 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13077248	C₂	1	1	yes	maximal, characteristic
2	C₂×#10622448	C₂	1	1	yes	maximal, characteristic
3	D₁₁×#431	C₂	1	1	yes	maximal, characteristic
4	#13067395	C₂	1	4	yes	maximal, complemented
5	#13067391	C₂	1	1	yes	maximal, characteristic, complemented
6	#13067388	C₂	1	1	yes	maximal, characteristic, complemented
7	#13067386	C₂	1	1	yes	maximal, characteristic, complemented
8	#13067378	C₂	1	4	yes	maximal, complemented
9	C₁₁×#1571	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₄²×D₁₁	C₂²	1	1	yes	characteristic
11	C₁₁×#431	C₂²	1	1	yes	characteristic
12	C₁₁×#423	C₂²	1	1	yes	characteristic
13	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
14	#10622739	—	2	1	no	—
15	M₁₆×Dic₁₁	—	2	1	no	—
16	C₂×(C₂×D₁₁)⋊C₈	—	2	1	no	—
17	C₂×#66879	—	2	1	no	—
18	#10622538	C₂²	1	1	yes	characteristic
19	#10622537	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	1	yes	characteristic
21	#10622448	—	2	1	no	—
22	#10622448	—	2	1	no	—
23	#10622448	—	2	1	no	—
24	#10622448	C₂²	1	2	yes	—
25	#10622448	C₂²	1	2	yes	—
26	#10622448	C₂²	1	2	yes	—
27	#10622446	—	2	1	no	—
28	#10622446	C₄	1	2	yes	—
29	#10622446	C₂²	1	2	yes	—
30	D₁₁×C₄⋊C₈	C₄	1	2	yes	—
31	D₁₁×C₂²⋊C₈	C₄	1	2	yes	—
32	#10622331	C₄	1	2	yes	—
33	#10622298	C₂²	1	2	yes	—
34	C₄×C₈×D₁₁	C₂²	1	2	yes	—
35	C₁₁×#335	C₂²	1	4	yes	complemented
36	#10622118	C₂²	1	4	yes	complemented
37	#10622118	C₂²	1	4	yes	complemented
38	#10622096	C₂²	1	4	yes	complemented
39	C₂²×C₄×D₁₁	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₄×D₁₁	D₄	1	1	yes	characteristic
41	C₂²×C₄×D₁₁	Q₈	1	1	yes	characteristic
42	C₂×C₁₁×M₁₆	—	2	1	no	—
43	C₂²×C₈×C₁₁	—	2	1	no	—
44	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
45	C₂×C₄×Dic₁₁	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄×Dic₁₁	D₄	1	1	yes	characteristic
47	C₂×C₄×Dic₁₁	Q₈	1	1	yes	characteristic
48	C₂×#4318	—	2	1	no	—
49	C₂²×C₁₁⋊C₈	—	2	1	no	—
50	C₂×C₈×D₁₁	C₂×C₄	1	4	yes	—
51	C₄²×D₁₁	C₂×C₄	1	1	yes	characteristic
52	C₄²×D₁₁	C₂×C₄	1	1	yes	characteristic
53	C₄²×D₁₁	D₄	1	1	yes	characteristic
54	C₄²×D₁₁	D₄	1	1	yes	characteristic
55	C₄²×D₁₁	Q₈	1	1	yes	characteristic
56	C₄²×D₁₁	Q₈	1	1	yes	characteristic
57	C₄²×D₁₁	C₂³	1	1	yes	characteristic
58	C₄²×D₁₁	C₂³	1	1	yes	characteristic
59	C₁₁×C₄⋊C₈	—	2	1	no	—
60	C₁₁×C₄⋊C₈	—	2	1	no	—
61	C₁₁×C₄⋊C₈	C₂×C₄	1	2	yes	—
62	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
63	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
64	C₁₁×C₂²⋊C₈	C₂×C₄	1	2	yes	—
65	C₄×C₈×C₁₁	C₂³	1	2	yes	—
66	C₂²⋊(C₁₁⋊C₈)	C₂×C₄	1	2	yes	—
67	(C₂×D₁₁)⋊C₈	—	2	2	no	—
68	(C₂×D₁₁)⋊C₈	—	2	2	no	—
69	(C₂×D₁₁)⋊C₈	—	2	2	no	—
70	(C₂×D₁₁)⋊C₈	—	2	2	no	—
71	(C₂×D₁₁)⋊C₈	C₂×C₄	1	4	yes	—
72	#66879	—	2	2	no	—
73	#66879	—	2	2	no	—
74	#66879	—	2	2	no	—
75	Dic₁₁⋊C₈	C₂×C₄	1	4	yes	—
76	C₈×Dic₁₁	—	2	2	no	—
77	C₈×Dic₁₁	C₂×C₄	1	4	yes	—
78	C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
79	C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
80	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	2	yes	—
81	C₄⋊(C₁₁⋊C₈)	C₂³	1	2	yes	—
82	C₄⋊(C₁₁⋊C₈)	C₂³	1	2	yes	—
83	C₄×C₁₁⋊C₈	C₂³	1	2	yes	—
84	#17816	—	11	1	no	maximal, Sylow
85	C₂³×D₁₁	C₄⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
89	C₂²×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
90	C₂²×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
91	C₂²×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
92	C₂×C₄×D₁₁	—	2	2	no	—
93	C₂×C₄×D₁₁	—	2	2	no	—
94	C₂×C₄×D₁₁	—	4	2	no	—
95	C₂×C₄×D₁₁	—	4	2	no	—
96	C₂×C₄×D₁₁	C₄⋊C₄	1	1	yes	characteristic
97	C₂×C₄×D₁₁	C₄⋊C₄	1	1	yes	characteristic
98	C₂×C₄×D₁₁	C₄⋊C₄	1	1	yes	characteristic
99	C₂×C₄×D₁₁	C₄⋊C₄	1	1	yes	characteristic
100	C₂×C₄×D₁₁	C₄⋊C₄	1	1	yes	characteristic
101	C₂×C₄×D₁₁	C₄⋊C₄	1	1	yes	characteristic
102	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
103	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
104	C₂×C₄×D₁₁	C₂×D₄	1	1	yes	characteristic
105	C₂×C₄×D₁₁	C₂×D₄	1	1	yes	characteristic
106	C₂×C₄×D₁₁	C₂×Q₈	1	1	yes	characteristic
107	C₂×C₄×D₁₁	C₂×Q₈	1	1	yes	characteristic
108	C₁₁×M₁₆	—	4	2	no	—
109	C₂×C₈×C₁₁	—	2	2	no	—
110	C₂×C₈×C₁₁	—	2	2	no	—
111	C₂×C₈×C₁₁	—	4	2	no	—
112	C₂×C₈×C₁₁	C₂²×C₄	1	4	yes	—
113	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
114	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
115	C₄²×C₁₁	C₂×Q₈	1	1	yes	characteristic
116	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
117	C₄×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
118	C₄×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
119	C₄×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
120	C₄×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
121	C₄×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
122	C₄×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
123	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
124	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
125	C₄×Dic₁₁	C₂×D₄	1	1	yes	characteristic
126	C₄×Dic₁₁	C₂×D₄	1	1	yes	characteristic
127	C₄×Dic₁₁	C₂×Q₈	1	1	yes	characteristic
128	C₄×Dic₁₁	C₂×Q₈	1	1	yes	characteristic
129	#4318	—	4	2	no	—
130	C₂×C₁₁⋊C₈	—	2	2	no	—
131	C₂×C₁₁⋊C₈	—	2	2	no	—
132	C₂×C₁₁⋊C₈	—	4	2	no	—
133	C₂×C₁₁⋊C₈	C₂²×C₄	1	4	yes	—
134	C₈×D₁₁	—	4	4	no	—
135	#2920	—	11	1	no	—
136	C₂×#432	—	11	1	no	—
137	C₂×#431	—	11	1	no	—
138	#1572	—	11	4	no	—
139	#1571	—	11	1	no	—
140	#1571	D₁₁	1	1	yes	characteristic, complemented
141	#1570	—	11	1	no	—
142	#1570	—	11	1	no	—
143	#1568	—	11	4	no	—
144	C₂³×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
145	C₂²×D₁₁	—	2	2	no	—
146	C₂²×D₁₁	—	2	2	no	—
147	C₂²×D₁₁	—	4	1	no	—
148	C₂²×D₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
149	C₂²×D₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₁₁	—	2	2	no	—
151	C₂×C₄×C₁₁	—	4	1	no	—
152	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
155	C₂×C₄×C₁₁	#135	1	2	yes	—
156	C₂×C₄×C₁₁	#135	1	2	yes	—
157	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
158	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
159	C₂×C₄×C₁₁	C₂²×Q₈	1	1	yes	characteristic
160	C₂×Dic₁₁	—	2	2	no	—
161	C₂×Dic₁₁	—	4	1	no	—
162	C₂×Dic₁₁	—	4	1	no	—
163	C₂×Dic₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
164	C₂×Dic₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
165	C₂×Dic₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
166	C₂×Dic₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
167	C₂×Dic₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
168	C₂×Dic₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
169	C₄×D₁₁	—	2	2	no	—
170	C₄×D₁₁	—	2	2	no	—
171	C₄×D₁₁	—	2	2	no	—
172	C₄×D₁₁	—	2	2	no	—
173	C₄×D₁₁	—	2	1	no	—
174	C₄×D₁₁	—	2	1	no	—
175	C₄×D₁₁	—	2	1	no	—
176	C₄×D₁₁	—	2	1	no	—
177	C₄×D₁₁	—	2	2	no	—
178	C₄×D₁₁	—	2	2	no	—
179	C₄×D₁₁	—	4	1	no	—
180	C₄×D₁₁	—	4	1	no	—
181	C₄×D₁₁	—	4	1	no	—
182	C₄×D₁₁	—	4	1	no	—
183	C₈×C₁₁	—	2	4	no	—
184	C₈×C₁₁	—	4	2	no	—
185	C₈×C₁₁	—	4	2	no	—
186	C₁₁⋊C₈	—	2	4	no	—
187	C₁₁⋊C₈	—	4	2	no	—
188	C₁₁⋊C₈	—	4	2	no	—
189	C₂²×C₄²	—	11	1	no	—
190	#432	—	11	2	no	—
191	#432	—	11	2	no	—
192	#432	—	11	2	no	—
193	#432	—	22	1	no	—
194	#432	—	22	1	no	—
195	#432	—	22	1	no	—
196	#431	—	11	1	no	—
197	#431	—	11	2	no	—
198	#431	—	11	2	no	—
199	#431	—	11	2	no	—
200	#431	—	11	2	no	—
201	#431	—	22	1	no	—
202	#431	C₂×D₁₁	1	1	yes	characteristic
203	#423	—	11	1	no	—
204	#423	C₂×D₁₁	1	1	yes	characteristic
205	C₂×C₄⋊C₈	—	11	2	no	—
206	C₂×C₄⋊C₈	—	11	1	no	—
207	C₂×C₄⋊C₈	C₂×D₁₁	1	1	yes	characteristic
208	#407	—	22	1	no	—
209	C₂×C₂²⋊C₈	—	11	2	no	—
210	C₂×C₂²⋊C₈	—	22	1	no	—
211	C₄×M₁₆	—	22	1	no	—
212	C₂×#97	—	22	1	no	—
213	C₂×C₄×C₈	—	11	2	no	—
214	#335	—	11	4	no	—
215	#335	C₂×D₁₁	1	4	yes	complemented
216	#334	—	11	4	no	—
217	#334	—	11	4	no	—
218	C₂²×C₁₁	—	2	1	no	—
219	C₂²×C₁₁	—	2	1	no	—
220	C₂²×C₁₁	#427	1	2	yes	—
221	C₂²×C₁₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
222	C₂×D₁₁	—	2	1	no	—
223	C₂×D₁₁	—	2	1	no	—
224	C₂×D₁₁	—	2	1	no	—
225	C₂×D₁₁	—	2	1	no	—
226	C₂×D₁₁	—	2	1	no	—
227	C₂×D₁₁	—	4	4	no	—
228	C₂×D₁₁	#430	1	2	yes	—
229	C₄×C₁₁	—	2	1	no	—
230	C₄×C₁₁	—	2	1	no	—
231	C₄×C₁₁	—	2	1	no	—
232	C₄×C₁₁	#427	1	2	yes	—
233	C₄×C₁₁	#568	1	2	yes	—
234	C₄×C₁₁	C₂×#135	1	1	yes	characteristic
235	C₄×C₁₁	C₂×#135	1	1	yes	characteristic
236	Dic₁₁	—	2	1	no	—
237	Dic₁₁	—	2	1	no	—
238	Dic₁₁	—	2	1	no	—
239	Dic₁₁	—	2	1	no	—
240	Dic₁₁	—	2	1	no	—
241	Dic₁₁	—	2	1	no	—
242	C₂³×C₄	—	11	1	no	—
243	C₂³×C₄	—	11	1	no	—
244	C₂³×C₄	—	11	1	no	—
245	C₂×M₁₆	—	2	1	no	—
246	C₂×M₁₆	—	22	1	no	—
247	C₂²×C₈	—	2	1	no	—
248	C₂²×C₈	—	11	4	no	—
249	C₂²×C₈	—	22	1	no	—
250	C₂×C₄²	—	11	1	no	—
251	C₂×C₄²	—	11	1	no	—
252	C₂×C₄²	—	11	1	no	—
253	C₂×C₄²	—	11	1	no	—
254	C₂×C₄²	—	11	1	no	—
255	C₂×C₄²	—	11	1	no	—
256	C₂×C₄²	—	11	1	no	—
257	C₂×C₄²	—	11	1	no	—
258	C₂×C₄²	—	11	1	no	—
259	C₂×C₄²	—	11	1	no	—
260	C₂×C₄²	—	11	1	no	—
261	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
262	C₄⋊C₈	—	2	1	no	—
263	C₄⋊C₈	—	2	1	no	—
264	C₄⋊C₈	—	11	4	no	—
265	C₄⋊C₈	—	11	2	no	—
266	C₄⋊C₈	—	11	2	no	—
267	C₄⋊C₈	—	11	2	no	—
268	C₄⋊C₈	—	22	1	no	—
269	C₄⋊C₈	—	22	1	no	—
270	C₄⋊C₈	C₄×D₁₁	1	2	yes	—
271	C₄⋊C₈	C₂²×D₁₁	1	2	yes	—
272	C₄⋊C₈	C₂²×D₁₁	1	2	yes	—
273	C₂²⋊C₈	—	11	2	no	—
274	C₂²⋊C₈	—	11	4	no	—
275	C₂²⋊C₈	—	22	2	no	—
276	C₂²⋊C₈	—	22	2	no	—
277	C₂²⋊C₈	—	22	2	no	—
278	C₂²⋊C₈	—	22	2	no	—
279	C₂²⋊C₈	C₄×D₁₁	1	2	yes	—
280	#97	—	22	2	no	—
281	#97	—	22	2	no	—
282	#97	—	22	2	no	—
283	C₄×C₈	—	11	4	no	—
284	C₄×C₈	—	11	2	no	—
285	C₄×C₈	—	22	2	no	—
286	C₄×C₈	C₂²×D₁₁	1	2	yes	—
287	C₂×C₁₁	—	2	2	no	—
288	C₂×C₁₁	#2905	1	1	yes	characteristic
289	C₂×C₁₁	C₂×#427	1	1	yes	characteristic
290	C₂×C₁₁	C₂×#430	1	1	yes	characteristic
291	D₁₁	—	2	2	no	—
292	D₁₁	—	4	1	no	—
293	C₂⁴	—	11	1	no	—
294	C₂²×C₄	—	11	1	no	—
295	C₂²×C₄	—	11	1	no	—
296	C₂²×C₄	—	11	1	no	—
297	C₂²×C₄	—	11	1	no	—
298	C₂²×C₄	—	11	1	no	—
299	C₂²×C₄	—	11	1	no	—
300	C₂²×C₄	—	11	1	no	—
301	C₂²×C₄	—	11	1	no	—
302	C₂²×C₄	—	11	1	no	—
303	C₂²×C₄	—	11	1	no	—
304	C₂²×C₄	—	11	1	no	—
305	C₂²×C₄	—	11	1	no	—
306	C₂²×C₄	—	11	1	no	—
307	C₂²×C₄	—	11	1	no	—
308	C₂²×C₄	—	11	1	no	—
309	C₂²×C₄	—	22	2	no	—
310	C₂²×C₄	—	22	2	no	—
311	C₂²×C₄	—	44	2	no	—
312	C₂²×C₄	—	44	2	no	—
313	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
314	C₂²×C₄	D₄×D₁₁	1	1	yes	characteristic
315	C₂²×C₄	Q₈×D₁₁	1	1	yes	characteristic
316	M₁₆	—	4	2	no	—
317	M₁₆	—	44	2	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	4	2	no	—
321	C₂×C₈	—	11	4	no	—
322	C₂×C₈	—	22	2	no	—
323	C₂×C₈	—	22	2	no	—
324	C₂×C₈	—	44	4	no	—
325	C₂×C₈	—	44	2	no	—
326	C₂×C₈	C₂×C₄×D₁₁	1	4	yes	—
327	C₄²	—	11	1	no	—
328	C₄²	—	11	1	no	—
329	C₄²	—	11	1	no	—
330	C₄²	—	11	1	no	—
331	C₄²	—	11	1	no	—
332	C₄²	—	11	1	no	—
333	C₄²	—	11	1	no	—
334	C₄²	—	11	1	no	—
335	C₄²	—	11	1	no	—
336	C₄²	—	11	1	no	—
337	C₄²	—	11	1	no	—
338	C₄²	—	11	1	no	—
339	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
340	C₄²	D₄×D₁₁	1	1	yes	characteristic
341	C₄²	Q₈×D₁₁	1	1	yes	characteristic
342	C₄²	C₂³×D₁₁	1	1	yes	characteristic
343	C₁₁	#17816	1	1	yes	characteristic, complemented, Sylow
344	C₂³	—	11	1	no	—
345	C₂³	—	11	1	no	—
346	C₂³	—	22	2	no	—
347	C₂³	—	22	2	no	—
348	C₂³	—	44	1	no	—
349	C₂³	C₄⋊C₄×D₁₁	1	1	yes	characteristic
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	4	1	no	—
352	C₂×C₄	—	11	1	no	—
353	C₂×C₄	—	11	1	no	—
354	C₂×C₄	—	11	1	no	—
355	C₂×C₄	—	11	1	no	—
356	C₂×C₄	—	11	1	no	—
357	C₂×C₄	—	11	1	no	—
358	C₂×C₄	—	22	2	no	—
359	C₂×C₄	—	22	2	no	—
360	C₂×C₄	—	22	2	no	—
361	C₂×C₄	—	22	2	no	—
362	C₂×C₄	—	22	2	no	—
363	C₂×C₄	—	22	2	no	—
364	C₂×C₄	—	22	2	no	—
365	C₂×C₄	—	22	1	no	—
366	C₂×C₄	—	22	1	no	—
367	C₂×C₄	—	22	1	no	—
368	C₂×C₄	—	22	1	no	—
369	C₂×C₄	—	44	1	no	—
370	C₂×C₄	—	44	1	no	—
371	C₂×C₄	—	44	1	no	—
372	C₂×C₄	—	44	1	no	—
373	C₂×C₄	—	44	1	no	—
374	C₂×C₄	—	44	1	no	—
375	C₂×C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
376	C₂×C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
377	C₂×C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
378	C₂×C₄	#66965	1	2	yes	—
379	C₂×C₄	#66972	1	2	yes	—
380	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
381	C₂×C₄	C₂×D₄×D₁₁	1	1	yes	characteristic
382	C₂×C₄	C₂×Q₈×D₁₁	1	1	yes	characteristic
383	C₈	—	2	4	no	—
384	C₈	—	4	2	no	—
385	C₈	—	4	2	no	—
386	C₈	—	22	4	no	—
387	C₈	—	44	2	no	—
388	C₈	—	44	2	no	—
389	C₂²	—	2	1	no	—
390	C₂²	—	2	1	no	—
391	C₂²	—	11	2	no	—
392	C₂²	—	22	1	no	—
393	C₂²	—	22	1	no	—
394	C₂²	—	22	1	no	—
395	C₂²	—	22	1	no	—
396	C₂²	—	22	1	no	—
397	C₂²	—	44	4	no	—
398	C₂²	#10622493	1	2	yes	—
399	C₂²	C₂×C₄⋊C₄×D₁₁	1	1	yes	characteristic
400	C₄	—	2	1	no	—
401	C₄	—	2	1	no	—
402	C₄	—	2	1	no	—
403	C₄	—	22	1	no	—
404	C₄	—	22	1	no	—
405	C₄	—	22	1	no	—
406	C₄	—	22	1	no	—
407	C₄	—	22	1	no	—
408	C₄	—	22	1	no	—
409	C₄	#10622493	1	2	yes	—
410	C₄	#10623281	1	2	yes	—
411	C₄	C₂×#66965	1	1	yes	characteristic
412	C₄	C₂×#66972	1	1	yes	characteristic
413	C₂	—	2	2	no	—
414	C₂	—	22	2	no	—
415	C₂	—	44	1	no	—
416	C₂	#13077177	1	1	yes	characteristic
417	C₂	C₂×#10622493	1	1	yes	characteristic
418	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×#1571	C₂
socle	C₂²×C₁₁	C₂²×C₄⋊C₄
prime radical	C₂³×D₁₁	C₄⋊C₄
cosocle	C₄²×C₁₁	C₂⁴
hypercenter	#1571	D₁₁
hypocenter	C₁₁	#17816
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1571

Complements

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

N	H ≅ G/N	type
4. #13067395	C₂	semidirect
5. #13067391	C₂	semidirect
6. #13067388	C₂	semidirect
7. #13067386	C₂	semidirect
8. #13067378	C₂	semidirect
9. C₁₁×#1571	C₂	semidirect
35. C₁₁×#335	C₂²	semidirect
36. #10622118	C₂²	semidirect
37. #10622118	C₂²	semidirect
38. #10622096	C₂²	semidirect
140. #1571	D₁₁	semidirect
215. #335	C₂×D₁₁	semidirect
343. C₁₁	#17816	semidirect

Maximal subgroups

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

subgroup	index
#13077248	2
C₂×#10622448	2
D₁₁×#431	2
#13067395	2
#13067391	2
#13067388	2
#13067386	2
#13067378	2
C₁₁×#1571	2
#17816	11