Subgroups — #14723009

Order 2816.

702 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13077572	C₂	1	1	yes	maximal, characteristic
2	#13077185	C₂	1	1	yes	maximal, characteristic
3	#13077181	C₂	1	1	yes	maximal, characteristic
4	#13067391	C₂	1	1	yes	maximal, characteristic, complemented
5	#13067389	C₂	1	2	yes	maximal, complemented
6	#13067389	C₂	1	2	yes	maximal, complemented
7	#13067374	C₂	1	1	yes	maximal, characteristic, complemented
8	#13067373	C₂	1	2	yes	maximal, complemented
9	C₂×#10622117	C₂	1	1	yes	maximal, characteristic, complemented
10	D₁₁×#335	C₂	1	2	yes	maximal, complemented
11	C₁₁×#1571	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#66960	—	2	1	no	—
13	C₂×#66954	—	2	1	no	—
14	C₄×#4339	C₂²	1	1	yes	characteristic
15	C₁₁×#431	C₂²	1	1	yes	characteristic
16	C₁₁×#423	C₂²	1	1	yes	characteristic
17	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	#10622732	—	2	1	no	—
19	#10622715	—	2	1	no	—
20	#10622537	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
23	#10622452	—	2	2	no	—
24	#10622452	—	2	2	no	—
25	#10622450	C₂²	1	2	yes	—
26	#10622450	C₂²	1	2	yes	—
27	#10622447	C₄	1	1	yes	characteristic
28	#10622447	C₄	1	1	yes	characteristic
29	D₁₁×C₄⋊C₈	C₂²	1	2	yes	—
30	D₁₁×C₄⋊C₈	C₂²	1	2	yes	—
31	#10622443	C₄	1	1	yes	characteristic
32	#10622443	C₄	1	1	yes	characteristic
33	(C₂²⋊D₁₁)⋊C₈	C₄	1	2	yes	—
34	(C₂²⋊D₁₁)⋊C₈	C₄	1	2	yes	—
35	#10622298	C₂²	1	2	yes	—
36	C₄×C₈×D₁₁	C₂²	1	2	yes	—
37	C₁₁×#335	C₂²	1	2	yes	—
38	C₁₁×#335	C₂²	1	2	yes	—
39	#10622117	C₂²	1	1	yes	characteristic
40	#10622117	C₂²	1	2	yes	—
41	#10622117	C₂²	1	1	yes	characteristic
42	#10622117	C₂²	1	1	yes	characteristic
43	#10622117	C₂²	1	1	yes	characteristic
44	#10622117	C₂²	1	2	yes	—
45	#10622096	C₂²	1	2	yes	—
46	#10622096	C₂²	1	2	yes	—
47	C₂×#4339	D₄	1	1	yes	characteristic
48	C₂×C₁₁×M₁₆	—	2	1	no	—
49	C₂²×C₈×C₁₁	—	2	1	no	—
50	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
51	C₄×C₂²⋊D₁₁	C₂×C₄	1	2	yes	—
52	C₄×C₂²⋊D₁₁	Q₈	1	2	yes	—
53	#66979	D₄	1	1	yes	characteristic
54	C₂×#4318	—	2	1	no	—
55	C₂²×C₁₁⋊C₈	—	2	1	no	—
56	C₂²×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
57	C₂²×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
58	#66960	—	4	4	no	—
59	#66954	—	4	4	no	—
60	C₂×#4313	—	2	2	no	—
61	C₂×#4313	—	2	2	no	—
62	C₂×C₈×D₁₁	—	2	2	no	—
63	C₂×C₈×D₁₁	—	2	2	no	—
64	C₂×C₈×D₁₁	C₂×C₄	1	2	yes	—
65	C₂×C₈×D₁₁	C₂×C₄	1	2	yes	—
66	C₄×D₄₄	C₂×C₄	1	1	yes	characteristic
67	C₄×D₄₄	Q₈	1	1	yes	characteristic
68	#66925	D₄	1	2	yes	—
69	C₄²×D₁₁	C₂³	1	2	yes	—
70	C₄×Dic₂₂	C₂×C₄	1	1	yes	characteristic
71	C₄×Dic₂₂	Q₈	1	1	yes	characteristic
72	C₁₁×C₄⋊C₈	—	2	1	no	—
73	C₁₁×C₄⋊C₈	—	2	1	no	—
74	C₁₁×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
75	C₁₁×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
76	C₁₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
77	C₁₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
78	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
79	C₁₁×C₂²⋊C₈	C₂×C₄	1	2	yes	—
80	C₄×C₈×C₁₁	C₂³	1	2	yes	—
81	(C₂×D₁₁)⋊C₈	C₂×C₄	1	2	yes	—
82	(C₂×D₁₁)⋊C₈	C₂×C₄	1	2	yes	—
83	Dic₁₁⋊C₈	—	2	2	no	—
84	Dic₁₁⋊C₈	—	2	2	no	—
85	Dic₁₁⋊C₈	—	2	2	no	—
86	Dic₁₁⋊C₈	—	2	2	no	—
87	Dic₁₁⋊C₈	C₂×C₄	1	2	yes	—
88	Dic₁₁⋊C₈	C₂×C₄	1	2	yes	—
89	C₈×Dic₁₁	C₂×C₄	1	2	yes	—
90	C₈×Dic₁₁	C₂×C₄	1	2	yes	—
91	C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
92	C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
93	C₄⋊(C₁₁⋊C₈)	C₂³	1	1	yes	characteristic
94	C₄⋊(C₁₁⋊C₈)	C₂³	1	1	yes	characteristic
95	C₄⋊(C₁₁⋊C₈)	C₂³	1	2	yes	—
96	C₄×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
97	C₄×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
98	C₄×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
99	C₄×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
100	#17828	—	11	1	no	maximal, Sylow
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	C₂×C₂²⋊D₁₁	C₄⋊C₄	1	2	yes	—
105	#4339	D₈	1	4	yes	—
106	#4339	Q₁₆	1	4	yes	—
107	C₂×D₄₄	C₄⋊C₄	1	1	yes	characteristic
108	C₂×C₄×D₁₁	C₂²×C₄	1	2	yes	—
109	C₂×C₄×D₁₁	C₂×D₄	1	2	yes	—
110	C₂×C₄×D₁₁	C₂×Q₈	1	2	yes	—
111	C₂×Dic₂₂	C₄⋊C₄	1	1	yes	characteristic
112	C₁₁×M₁₆	—	4	2	no	—
113	C₂×C₈×C₁₁	—	2	1	no	—
114	C₂×C₈×C₁₁	—	2	2	no	—
115	C₂×C₈×C₁₁	—	2	1	no	—
116	C₂×C₈×C₁₁	—	4	2	no	—
117	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
118	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
119	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
120	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
121	C₄²×C₁₁	C₂×Q₈	1	1	yes	characteristic
122	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
123	C₂²⋊Dic₁₁	C₄⋊C₄	1	2	yes	—
124	(C₂×D₁₁)⋊C₄	C₄⋊C₄	1	2	yes	—
125	(C₂×D₁₁)⋊C₄	C₄⋊C₄	1	2	yes	—
126	C₄⋊Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
127	C₄⋊Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
128	Dic₁₁⋊C₄	C₄⋊C₄	1	2	yes	—
129	Dic₁₁⋊C₄	C₄⋊C₄	1	2	yes	—
130	C₄×Dic₁₁	C₂²×C₄	1	2	yes	—
131	C₄×Dic₁₁	C₂×D₄	1	2	yes	—
132	C₄×Dic₁₁	C₂×Q₈	1	2	yes	—
133	#4318	—	4	2	no	—
134	C₂×C₁₁⋊C₈	—	2	2	no	—
135	C₂×C₁₁⋊C₈	—	2	1	no	—
136	C₂×C₁₁⋊C₈	—	2	2	no	—
137	C₂×C₁₁⋊C₈	—	2	1	no	—
138	C₂×C₁₁⋊C₈	—	4	1	no	—
139	C₂×C₁₁⋊C₈	—	4	2	no	—
140	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
141	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
142	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
143	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
144	#4313	—	4	4	no	—
145	#4313	—	4	4	no	—
146	C₈×D₁₁	—	2	4	no	—
147	C₈×D₁₁	—	4	2	no	—
148	C₈×D₁₁	—	4	4	no	—
149	C₈×D₁₁	—	4	4	no	—
150	C₈×#41	—	11	1	no	—
151	#2906	—	11	1	no	—
152	#2906	—	11	1	no	—
153	#1571	—	11	1	no	—
154	#1571	—	11	2	no	—
155	#1571	—	11	2	no	—
156	#1571	D₁₁	1	1	yes	characteristic, complemented
157	#1567	—	11	1	no	—
158	#1567	—	11	2	no	—
159	C₂×#335	—	11	1	no	—
160	C₂×#335	—	11	2	no	—
161	C₂³×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
162	C₂²×D₁₁	C₂×C₄⋊C₄	1	2	yes	—
163	C₂×C₄×C₁₁	—	2	1	no	—
164	C₂×C₄×C₁₁	—	2	1	no	—
165	C₂×C₄×C₁₁	—	4	1	no	—
166	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
167	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
168	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
169	C₂×C₄×C₁₁	C₂×D₈	1	2	yes	—
170	C₂×C₄×C₁₁	C₂×Q₁₆	1	2	yes	—
171	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
172	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₁₁	C₂²×Q₈	1	1	yes	characteristic
174	C₂²⋊D₁₁	#107	1	8	yes	—
175	C₂×Dic₁₁	C₂×C₄⋊C₄	1	2	yes	—
176	C₂×Dic₁₁	C₂×C₄⋊C₄	1	2	yes	—
177	C₂×Dic₁₁	C₂×C₄⋊C₄	1	2	yes	—
178	D₄₄	#107	1	4	yes	—
179	C₄×D₁₁	—	2	2	no	—
180	C₄×D₁₁	—	2	2	no	—
181	C₄×D₁₁	—	4	2	no	—
182	C₄×D₁₁	C₂×D₈	1	4	yes	—
183	C₄×D₁₁	C₂×Q₁₆	1	4	yes	—
184	Dic₂₂	#107	1	4	yes	—
185	C₈×C₁₁	—	2	2	no	—
186	C₈×C₁₁	—	2	2	no	—
187	C₈×C₁₁	—	4	1	no	—
188	C₈×C₁₁	—	4	2	no	—
189	C₈×C₁₁	—	4	1	no	—
190	C₁₁⋊C₈	—	2	1	no	—
191	C₁₁⋊C₈	—	2	1	no	—
192	C₁₁⋊C₈	—	2	1	no	—
193	C₁₁⋊C₈	—	4	1	no	—
194	C₁₁⋊C₈	—	4	2	no	—
195	C₁₁⋊C₈	—	4	1	no	—
196	C₁₁⋊C₈	#131	1	2	yes	complemented
197	C₂×#131	—	22	1	no	—
198	C₂×#131	—	22	1	no	—
199	C₄×#41	—	11	1	no	—
200	C₈×Q₈	—	11	1	no	—
201	C₈×Q₈	—	11	1	no	—
202	C₈×D₄	—	11	1	no	—
203	C₈×D₄	—	11	1	no	—
204	C₈×D₄	—	11	2	no	—
205	C₈×D₄	—	11	2	no	—
206	#431	—	11	2	no	—
207	#431	C₂×D₁₁	1	1	yes	characteristic
208	#424	—	22	2	no	—
209	#424	—	22	2	no	—
210	#424	—	22	1	no	—
211	#424	—	22	1	no	—
212	#423	—	11	1	no	—
213	#423	—	11	2	no	—
214	#423	—	11	2	no	—
215	#423	C₂×D₁₁	1	1	yes	characteristic
216	C₂×C₄⋊C₈	—	11	1	no	—
217	C₂×C₄⋊C₈	—	11	2	no	—
218	C₂×C₄⋊C₈	—	11	2	no	—
219	C₂×C₄⋊C₈	C₂×D₁₁	1	1	yes	characteristic
220	C₂×C₄×C₈	—	11	1	no	—
221	C₂×C₄×C₈	—	11	2	no	—
222	#335	—	11	1	no	—
223	#335	—	11	2	no	—
224	#335	—	11	1	no	—
225	#335	—	11	1	no	—
226	#335	—	11	1	no	—
227	#335	—	11	2	no	—
228	#335	—	11	2	no	—
229	#335	—	11	2	no	—
230	#335	C₂×D₁₁	1	2	yes	—
231	#335	C₂×D₁₁	1	2	yes	—
232	C₂²×C₁₁	—	2	1	no	—
233	C₂²×C₁₁	—	2	1	no	—
234	C₂²×C₁₁	C₂×#107	1	2	yes	—
235	C₂²×C₁₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
236	C₂×D₁₁	—	2	2	no	—
237	C₂×D₁₁	—	2	2	no	—
238	C₂×D₁₁	C₂×#107	1	4	yes	—
239	C₄×C₁₁	—	2	1	no	—
240	C₄×C₁₁	—	2	1	no	—
241	C₄×C₁₁	—	2	1	no	—
242	C₄×C₁₁	C₂×#107	1	2	yes	—
243	C₄×C₁₁	C₂×#131	1	1	yes	characteristic
244	C₄×C₁₁	#568	1	1	yes	characteristic
245	C₄×C₁₁	C₂²×D₈	1	1	yes	characteristic
246	C₄×C₁₁	C₂²×Q₁₆	1	1	yes	characteristic
247	Dic₁₁	—	2	2	no	—
248	Dic₁₁	—	2	2	no	—
249	Dic₁₁	C₂×#107	1	4	yes	—
250	C₂×#41	—	11	1	no	—
251	#131	—	44	4	no	—
252	#131	—	44	4	no	—
253	C₂×M₁₆	—	2	1	no	—
254	C₂×M₁₆	—	22	2	no	—
255	C₂×M₁₆	—	22	2	no	—
256	C₂×M₁₆	—	22	1	no	—
257	C₂²×C₈	—	2	1	no	—
258	C₂²×C₈	—	11	1	no	—
259	C₂²×C₈	—	11	1	no	—
260	C₂²×C₈	—	11	2	no	—
261	C₂²×C₈	—	11	2	no	—
262	C₂²×C₈	—	22	2	no	—
263	C₂²×C₈	—	22	2	no	—
264	C₂²×C₈	—	22	1	no	—
265	C₄×Q₈	—	11	1	no	—
266	C₄×Q₈	—	11	1	no	—
267	C₄×D₄	—	11	2	no	—
268	C₄×D₄	—	11	2	no	—
269	C₄×D₄	—	11	1	no	—
270	C₄×D₄	—	11	1	no	—
271	#117	—	11	1	no	—
272	#117	—	11	2	no	—
273	C₂×C₄²	—	11	2	no	—
274	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
275	C₄⋊C₈	—	2	1	no	—
276	C₄⋊C₈	—	2	1	no	—
277	C₄⋊C₈	—	11	2	no	—
278	C₄⋊C₈	—	11	2	no	—
279	C₄⋊C₈	—	11	1	no	—
280	C₄⋊C₈	—	11	1	no	—
281	C₄⋊C₈	—	11	2	no	—
282	C₄⋊C₈	—	22	2	no	—
283	C₄⋊C₈	—	22	2	no	—
284	C₄⋊C₈	—	22	2	no	—
285	C₄⋊C₈	—	22	2	no	—
286	C₄⋊C₈	—	22	1	no	—
287	C₄⋊C₈	—	22	1	no	—
288	C₄⋊C₈	C₄×D₁₁	1	1	yes	characteristic
289	C₄⋊C₈	C₄×D₁₁	1	1	yes	characteristic
290	C₄⋊C₈	C₂²×D₁₁	1	1	yes	characteristic
291	C₄⋊C₈	C₂²×D₁₁	1	2	yes	—
292	C₄⋊C₈	C₂²×D₁₁	1	1	yes	characteristic
293	C₂²⋊C₈	—	11	2	no	—
294	C₂²⋊C₈	—	11	2	no	—
295	C₂²⋊C₈	C₄×D₁₁	1	2	yes	—
296	C₄×C₈	—	11	2	no	—
297	C₄×C₈	—	11	2	no	—
298	C₄×C₈	—	11	1	no	—
299	C₄×C₈	—	11	1	no	—
300	C₄×C₈	—	11	1	no	—
301	C₄×C₈	—	11	1	no	—
302	C₄×C₈	C₂²×D₁₁	1	2	yes	—
303	C₂×C₁₁	—	2	2	no	—
304	C₂×C₁₁	#2906	1	1	yes	characteristic
305	C₂×C₁₁	C₂²×#107	1	1	yes	characteristic
306	C₂×C₁₁	#2916	1	1	yes	characteristic
307	D₁₁	—	2	4	no	—
308	#41	—	11	4	no	—
309	#41	—	11	4	no	—
310	C₂×Q₈	—	11	1	no	—
311	C₂×D₄	—	11	2	no	—
312	C₂×D₄	—	11	1	no	—
313	C₂²×C₄	—	11	2	no	—
314	C₂²×C₄	—	11	2	no	—
315	C₂²×C₄	—	11	2	no	—
316	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
317	C₂²×C₄	D₄×D₁₁	1	1	yes	characteristic
318	C₂²×C₄	Q₈×D₁₁	1	1	yes	characteristic
319	M₁₆	—	4	2	no	—
320	M₁₆	—	44	4	no	—
321	M₁₆	—	44	4	no	—
322	M₁₆	—	44	2	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	4	2	no	—
327	C₂×C₈	—	11	1	no	—
328	C₂×C₈	—	11	1	no	—
329	C₂×C₈	—	11	1	no	—
330	C₂×C₈	—	11	1	no	—
331	C₂×C₈	—	22	4	no	—
332	C₂×C₈	—	22	2	no	—
333	C₂×C₈	—	22	1	no	—
334	C₂×C₈	—	22	2	no	—
335	C₂×C₈	—	22	1	no	—
336	C₂×C₈	—	44	2	no	—
337	C₂×C₈	—	44	4	no	—
338	C₂×C₈	—	44	4	no	—
339	C₂×C₈	—	44	1	no	—
340	C₂×C₈	—	44	2	no	—
341	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
342	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
343	C₄⋊C₄	—	11	2	no	—
344	C₄⋊C₄	—	11	2	no	—
345	C₄⋊C₄	—	11	1	no	—
346	C₄⋊C₄	—	11	1	no	—
347	C₂²⋊C₄	—	11	2	no	—
348	C₂²⋊C₄	—	11	2	no	—
349	C₂²⋊C₄	—	11	2	no	—
350	C₄²	—	11	2	no	—
351	C₄²	—	11	2	no	—
352	C₄²	—	11	2	no	—
353	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
354	C₄²	D₄×D₁₁	1	1	yes	characteristic
355	C₄²	Q₈×D₁₁	1	1	yes	characteristic
356	C₄²	C₂³×D₁₁	1	1	yes	characteristic
357	C₁₁	#17828	1	1	yes	characteristic, complemented, Sylow
358	C₂³	—	11	2	no	—
359	C₂³	C₄⋊C₄×D₁₁	1	1	yes	characteristic
360	Q₈	—	11	4	no	—
361	D₄	—	11	8	no	—
362	D₄	—	11	4	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	11	2	no	—
367	C₂×C₄	—	11	4	no	—
368	C₂×C₄	—	11	4	no	—
369	C₂×C₄	—	11	2	no	—
370	C₂×C₄	—	11	2	no	—
371	C₂×C₄	—	22	2	no	—
372	C₂×C₄	—	22	2	no	—
373	C₂×C₄	—	44	2	no	—
374	C₂×C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
375	C₂×C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
376	C₂×C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
377	C₂×C₄	D₈×D₁₁	1	2	yes	—
378	C₂×C₄	Q₁₆×D₁₁	1	2	yes	—
379	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
380	C₂×C₄	C₂×D₄×D₁₁	1	1	yes	characteristic
381	C₂×C₄	C₂×Q₈×D₁₁	1	1	yes	characteristic
382	C₈	—	2	2	no	—
383	C₈	—	2	2	no	—
384	C₈	—	4	1	no	—
385	C₈	—	4	1	no	—
386	C₈	—	4	2	no	—
387	C₈	—	11	2	no	—
388	C₈	—	22	1	no	—
389	C₈	—	22	1	no	—
390	C₈	—	22	1	no	—
391	C₈	—	44	1	no	—
392	C₈	—	44	2	no	—
393	C₈	—	44	1	no	—
394	C₂²	—	2	1	no	—
395	C₂²	—	2	1	no	—
396	C₂²	—	11	4	no	—
397	C₂²	—	22	2	no	—
398	C₂²	—	22	2	no	—
399	C₂²	D₁₁×#107	1	2	yes	—
400	C₂²	C₂×C₄⋊C₄×D₁₁	1	1	yes	characteristic
401	C₄	—	2	1	no	—
402	C₄	—	2	1	no	—
403	C₄	—	2	1	no	—
404	C₄	—	11	4	no	—
405	C₄	—	22	2	no	—
406	C₄	—	22	2	no	—
407	C₄	D₁₁×#107	1	2	yes	—
408	C₄	D₁₁×#131	1	1	yes	characteristic
409	C₄	#10623281	1	1	yes	characteristic
410	C₄	C₂×D₈×D₁₁	1	1	yes	characteristic
411	C₄	C₂×Q₁₆×D₁₁	1	1	yes	characteristic
412	C₂	—	2	2	no	—
413	C₂	—	22	4	no	—
414	C₂	#13077183	1	1	yes	characteristic
415	C₂	C₂×D₁₁×#107	1	1	yes	characteristic
416	C₂	#13077226	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	C₂×#4339	D₄
cosocle	C₄²×C₁₁	C₂⁴
hypercenter	#1571	D₁₁
hypocenter	C₁₁	#17828
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. #13067391	C₂	semidirect
5. #13067389	C₂	semidirect
6. #13067389	C₂	semidirect
7. #13067374	C₂	semidirect
8. #13067373	C₂	semidirect
9. C₂×#10622117	C₂	semidirect
10. D₁₁×#335	C₂	semidirect
11. C₁₁×#1571	C₂	semidirect
156. #1571	D₁₁	semidirect
196. C₁₁⋊C₈	#131	semidirect
357. C₁₁	#17828	semidirect

Maximal subgroups

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

subgroup	index
#13077572	2
#13077185	2
#13077181	2
#13067391	2
#13067389	2
#13067374	2
#13067373	2
C₂×#10622117	2
D₁₁×#335	2
C₁₁×#1571	2
#17828	11