Subgroups — #14723021

Order 2816.

634 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13077582	C₂	1	1	yes	maximal, characteristic
2	#13077281	C₂	1	1	yes	maximal, characteristic
3	#13077181	C₂	1	1	yes	maximal, characteristic
4	#13067403	C₂	1	2	yes	maximal, complemented
5	#13067398	C₂	1	2	yes	maximal, complemented
6	#13067390	C₂	1	1	yes	maximal, characteristic, complemented
7	#13067386	C₂	1	1	yes	maximal, characteristic, complemented
8	#13067380	C₂	1	2	yes	maximal, complemented
9	#13067375	C₂	1	1	yes	maximal, characteristic, complemented
10	#13067365	C₂	1	2	yes	maximal, complemented
11	C₂×C₁₁×#334	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#66954	—	2	1	no	—
13	C₄×#4339	C₂²	1	1	yes	characteristic
14	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
17	#10622724	C₄	1	2	yes	—
18	#10622724	C₄	1	2	yes	—
19	#10622723	—	2	1	no	—
20	#10622715	—	2	1	no	—
21	#10622714	—	2	1	no	—
22	#10622538	C₂²	1	1	yes	characteristic
23	#10622537	C₂²	1	1	yes	characteristic
24	#10622537	C₂²	1	1	yes	characteristic
25	#10622453	—	2	2	no	—
26	#10622452	—	2	2	no	—
27	#10622450	C₂²	1	2	yes	—
28	#10622448	C₂²	1	2	yes	—
29	#10622446	C₂²	1	2	yes	—
30	D₁₁×C₄⋊C₈	C₂²	1	2	yes	—
31	#10622301	C₄	1	1	yes	characteristic
32	#10622301	C₄	1	1	yes	characteristic
33	C₄×#4313	C₂²	1	2	yes	—
34	#10622298	C₂²	1	2	yes	—
35	#10622292	C₄	1	1	yes	characteristic
36	#10622292	C₄	1	1	yes	characteristic
37	C₁₁×#334	C₂²	1	1	yes	characteristic
38	C₁₁×#334	C₂²	1	1	yes	characteristic
39	C₁₁×#334	C₂²	1	1	yes	characteristic
40	C₁₁×#334	C₂²	1	1	yes	characteristic
41	#10622118	C₂²	1	2	yes	—
42	#10622118	C₂²	1	2	yes	—
43	#10622117	C₂²	1	2	yes	—
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	C₂²×C₈×C₁₁	—	2	1	no	—
49	C₂²×C₈×C₁₁	—	2	1	no	—
50	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
51	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
53	C₄×C₂²⋊D₁₁	C₂×C₄	1	2	yes	—
54	C₄×C₂²⋊D₁₁	Q₈	1	2	yes	—
55	#66979	D₄	1	1	yes	characteristic
56	C₂×#4318	—	2	1	no	—
57	C₂×#4318	—	2	1	no	—
58	#66954	—	4	4	no	—
59	C₂×#4313	—	2	2	no	—
60	C₂×#4313	C₂×C₄	1	2	yes	—
61	C₂×#4313	C₂×C₄	1	2	yes	—
62	C₂×C₈×D₁₁	—	2	2	no	—
63	C₄×D₄₄	C₂×C₄	1	1	yes	characteristic
64	C₄×D₄₄	Q₈	1	1	yes	characteristic
65	#66925	D₄	1	2	yes	—
66	C₄²×D₁₁	C₂³	1	2	yes	—
67	C₄×Dic₂₂	C₂×C₄	1	1	yes	characteristic
68	C₄×Dic₂₂	Q₈	1	1	yes	characteristic
69	C₁₁×C₄⋊C₈	—	2	1	no	—
70	C₁₁×C₄⋊C₈	—	2	1	no	—
71	C₁₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
72	C₁₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
73	C₁₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
74	C₁₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
75	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
76	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
77	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
78	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
79	C₂²⋊(C₁₁⋊C₈)	C₂×C₄	1	2	yes	—
80	(C₂×D₁₁)⋊C₈	—	2	2	no	—
81	(C₂×D₁₁)⋊C₈	—	2	2	no	—
82	(C₂×D₁₁)⋊C₈	C₂×C₄	1	2	yes	—
83	(C₂×D₁₁)⋊C₈	C₂×C₄	1	2	yes	—
84	#66879	—	2	2	no	—
85	#66879	C₂×C₄	1	2	yes	—
86	#66879	C₂×C₄	1	2	yes	—
87	Dic₁₁⋊C₈	—	2	2	no	—
88	Dic₁₁⋊C₈	—	2	2	no	—
89	Dic₁₁⋊C₈	C₂×C₄	1	2	yes	—
90	Dic₁₁⋊C₈	C₂×C₄	1	2	yes	—
91	C₈×Dic₁₁	—	2	2	no	—
92	C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
93	C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
94	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
95	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
96	C₄⋊(C₁₁⋊C₈)	C₂³	1	2	yes	—
97	C₄⋊(C₁₁⋊C₈)	C₂³	1	2	yes	—
98	C₄×C₁₁⋊C₈	C₂³	1	2	yes	—
99	#17830	—	11	1	no	maximal, Sylow
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	C₂×C₂²⋊D₁₁	C₄⋊C₄	1	2	yes	—
104	#4339	—	2	2	no	—
105	#4339	—	2	2	no	—
106	C₂×D₄₄	C₄⋊C₄	1	1	yes	characteristic
107	C₂×C₄×D₁₁	C₂²×C₄	1	2	yes	—
108	C₂×C₄×D₁₁	C₂×D₄	1	2	yes	—
109	C₂×C₄×D₁₁	C₂×Q₈	1	2	yes	—
110	C₂×Dic₂₂	C₄⋊C₄	1	1	yes	characteristic
111	C₂×C₈×C₁₁	—	2	2	no	—
112	C₂×C₈×C₁₁	—	2	1	no	—
113	C₂×C₈×C₁₁	—	2	1	no	—
114	C₂×C₈×C₁₁	—	2	1	no	—
115	C₂×C₈×C₁₁	—	2	1	no	—
116	C₂×C₈×C₁₁	—	4	1	no	—
117	C₂×C₈×C₁₁	—	4	2	no	—
118	C₂×C₈×C₁₁	—	4	2	no	—
119	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
123	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
124	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
125	C₄²×C₁₁	C₂×Q₈	1	1	yes	characteristic
126	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
127	C₂²⋊Dic₁₁	C₄⋊C₄	1	2	yes	—
128	(C₂×D₁₁)⋊C₄	C₄⋊C₄	1	2	yes	—
129	(C₂×D₁₁)⋊C₄	C₄⋊C₄	1	2	yes	—
130	C₄⋊Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
131	C₄⋊Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
132	Dic₁₁⋊C₄	C₄⋊C₄	1	2	yes	—
133	Dic₁₁⋊C₄	C₄⋊C₄	1	2	yes	—
134	C₄×Dic₁₁	C₂²×C₄	1	2	yes	—
135	C₄×Dic₁₁	C₂×D₄	1	2	yes	—
136	C₄×Dic₁₁	C₂×Q₈	1	2	yes	—
137	#4318	—	4	2	no	—
138	#4318	—	4	2	no	—
139	C₂×C₁₁⋊C₈	—	2	2	no	—
140	C₂×C₁₁⋊C₈	—	2	2	no	—
141	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
142	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
143	#4313	—	2	4	no	—
144	#4313	—	4	2	no	—
145	#4313	—	4	4	no	—
146	C₈×D₁₁	—	4	4	no	—
147	#2965	—	11	1	no	—
148	#2925	—	11	1	no	—
149	#2906	—	11	1	no	—
150	#1574	—	11	2	no	—
151	#1573	—	11	2	no	—
152	#1571	—	11	1	no	—
153	#1570	—	11	1	no	—
154	#1569	—	11	2	no	—
155	#1567	—	11	1	no	—
156	#1565	—	11	2	no	—
157	C₂×#334	D₁₁	1	1	yes	characteristic, complemented
158	C₂³×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
159	C₂²×D₁₁	C₂×C₄⋊C₄	1	2	yes	—
160	C₂×C₄×C₁₁	—	2	1	no	—
161	C₂×C₄×C₁₁	—	2	1	no	—
162	C₂×C₄×C₁₁	—	4	1	no	—
163	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
164	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
165	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
166	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	2	yes	—
167	C₂×C₄×C₁₁	#137	1	2	yes	—
168	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
169	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₁₁	C₂²×Q₈	1	1	yes	characteristic
171	C₂²⋊D₁₁	—	2	4	no	—
172	C₂×Dic₁₁	C₂×C₄⋊C₄	1	2	yes	—
173	C₂×Dic₁₁	C₂×C₄⋊C₄	1	2	yes	—
174	C₂×Dic₁₁	C₂×C₄⋊C₄	1	2	yes	—
175	D₄₄	—	2	2	no	—
176	C₄×D₁₁	—	2	2	no	—
177	C₄×D₁₁	—	2	2	no	—
178	C₄×D₁₁	—	2	2	no	—
179	C₄×D₁₁	—	2	2	no	—
180	C₄×D₁₁	—	4	2	no	—
181	Dic₂₂	—	2	2	no	—
182	C₈×C₁₁	—	2	1	no	—
183	C₈×C₁₁	—	2	1	no	—
184	C₈×C₁₁	—	2	1	no	—
185	C₈×C₁₁	—	4	1	no	—
186	C₈×C₁₁	—	4	1	no	—
187	C₈×C₁₁	—	4	1	no	—
188	C₈×C₁₁	—	4	1	no	—
189	C₈×C₁₁	#131	1	2	yes	complemented
190	C₁₁⋊C₈	—	2	2	no	—
191	C₁₁⋊C₈	—	2	2	no	—
192	C₁₁⋊C₈	—	4	2	no	—
193	C₁₁⋊C₈	—	4	2	no	—
194	C₂×#131	—	22	1	no	—
195	C₄×#41	—	11	1	no	—
196	#446	—	11	1	no	—
197	#446	—	11	1	no	—
198	#436	—	11	1	no	—
199	#436	—	11	1	no	—
200	#435	—	11	2	no	—
201	#435	—	11	2	no	—
202	#433	—	22	2	no	—
203	#432	—	11	2	no	—
204	#431	—	11	1	no	—
205	#431	—	11	2	no	—
206	#431	—	11	2	no	—
207	#424	—	22	2	no	—
208	#424	—	22	1	no	—
209	#423	—	11	1	no	—
210	#423	—	11	1	no	—
211	#423	—	11	2	no	—
212	C₂×C₄⋊C₈	—	11	2	no	—
213	C₂×C₄⋊C₈	C₂×D₁₁	1	1	yes	characteristic
214	C₂×C₄⋊C₈	C₂×D₁₁	1	1	yes	characteristic
215	#408	—	22	1	no	—
216	#405	—	22	1	no	—
217	C₄×M₁₆	—	11	2	no	—
218	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
219	#335	—	11	2	no	—
220	#335	—	11	2	no	—
221	#335	—	11	2	no	—
222	#335	—	11	2	no	—
223	#334	—	11	2	no	—
224	#334	—	11	2	no	—
225	#334	C₂×D₁₁	1	1	yes	characteristic
226	#334	C₂×D₁₁	1	1	yes	characteristic
227	#334	C₂×D₁₁	1	1	yes	characteristic
228	#334	C₂×D₁₁	1	1	yes	characteristic
229	C₂²×C₁₁	—	2	1	no	—
230	C₂²×C₁₁	—	2	1	no	—
231	C₂²×C₁₁	#428	1	2	yes	—
232	C₂²×C₁₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
233	C₂×D₁₁	—	2	2	no	—
234	C₂×D₁₁	—	2	2	no	—
235	C₂×D₁₁	—	2	2	no	—
236	C₄×C₁₁	—	2	1	no	—
237	C₄×C₁₁	—	2	1	no	—
238	C₄×C₁₁	—	2	1	no	—
239	C₄×C₁₁	#428	1	2	yes	—
240	C₄×C₁₁	C₂×#131	1	1	yes	characteristic
241	C₄×C₁₁	#568	1	1	yes	characteristic
242	C₄×C₁₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
243	C₄×C₁₁	C₂×#137	1	1	yes	characteristic
244	Dic₁₁	—	2	2	no	—
245	Dic₁₁	—	2	2	no	—
246	Dic₁₁	—	2	2	no	—
247	C₂×#41	—	11	1	no	—
248	#131	—	44	4	no	—
249	C₂×M₁₆	—	11	2	no	—
250	C₂×M₁₆	—	11	2	no	—
251	C₂×M₁₆	—	22	2	no	—
252	C₂×M₁₆	—	22	1	no	—
253	C₂×M₁₆	—	22	1	no	—
254	C₂²×C₈	—	2	1	no	—
255	C₂²×C₈	—	2	1	no	—
256	C₂²×C₈	—	22	2	no	—
257	C₂²×C₈	C₄×D₁₁	1	1	yes	characteristic
258	C₂²×C₈	C₄×D₁₁	1	1	yes	characteristic
259	C₄×Q₈	—	11	1	no	—
260	C₄×Q₈	—	11	1	no	—
261	C₄×D₄	—	11	2	no	—
262	C₄×D₄	—	11	2	no	—
263	C₄×D₄	—	11	1	no	—
264	C₄×D₄	—	11	1	no	—
265	#117	—	11	1	no	—
266	#117	—	11	2	no	—
267	C₂×C₄²	—	11	2	no	—
268	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
269	C₄⋊C₈	—	2	1	no	—
270	C₄⋊C₈	—	2	1	no	—
271	C₄⋊C₈	—	11	2	no	—
272	C₄⋊C₈	—	11	2	no	—
273	C₄⋊C₈	—	11	1	no	—
274	C₄⋊C₈	—	11	1	no	—
275	C₄⋊C₈	—	11	2	no	—
276	C₄⋊C₈	—	11	2	no	—
277	C₄⋊C₈	—	22	2	no	—
278	C₄⋊C₈	—	22	2	no	—
279	C₄⋊C₈	—	22	1	no	—
280	C₄⋊C₈	—	22	1	no	—
281	C₄⋊C₈	C₂²×D₁₁	1	1	yes	characteristic
282	C₄⋊C₈	C₂²×D₁₁	1	1	yes	characteristic
283	C₄⋊C₈	C₂²×D₁₁	1	1	yes	characteristic
284	C₄⋊C₈	C₂²×D₁₁	1	1	yes	characteristic
285	C₂²⋊C₈	—	11	2	no	—
286	C₂²⋊C₈	—	11	2	no	—
287	C₂²⋊C₈	—	11	2	no	—
288	C₂²⋊C₈	—	22	2	no	—
289	C₂²⋊C₈	—	22	2	no	—
290	#97	—	11	2	no	—
291	#97	—	11	2	no	—
292	#97	—	22	2	no	—
293	C₄×C₈	—	11	2	no	—
294	C₄×C₈	—	22	2	no	—
295	C₄×C₈	C₄×D₁₁	1	1	yes	characteristic
296	C₄×C₈	C₄×D₁₁	1	1	yes	characteristic
297	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
298	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
299	C₂×C₁₁	—	2	2	no	—
300	C₂×C₁₁	#2906	1	1	yes	characteristic
301	C₂×C₁₁	C₂×#428	1	1	yes	characteristic
302	C₂×C₁₁	#2916	1	1	yes	characteristic
303	D₁₁	—	4	2	no	—
304	#41	—	22	2	no	—
305	#41	—	22	2	no	—
306	C₂×Q₈	—	11	1	no	—
307	C₂×D₄	—	11	2	no	—
308	C₂×D₄	—	11	1	no	—
309	C₂²×C₄	—	11	2	no	—
310	C₂²×C₄	—	11	2	no	—
311	C₂²×C₄	—	11	2	no	—
312	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
313	C₂²×C₄	D₄×D₁₁	1	1	yes	characteristic
314	C₂²×C₄	Q₈×D₁₁	1	1	yes	characteristic
315	M₁₆	—	22	4	no	—
316	M₁₆	—	44	2	no	—
317	M₁₆	—	44	4	no	—
318	M₁₆	—	44	2	no	—
319	M₁₆	—	44	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	1	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	4	1	no	—
326	C₂×C₈	—	4	2	no	—
327	C₂×C₈	—	4	2	no	—
328	C₂×C₈	—	11	2	no	—
329	C₂×C₈	—	11	2	no	—
330	C₂×C₈	—	22	2	no	—
331	C₂×C₈	—	22	2	no	—
332	C₂×C₈	—	44	4	no	—
333	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
334	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
335	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
336	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
337	C₄⋊C₄	—	11	2	no	—
338	C₄⋊C₄	—	11	2	no	—
339	C₄⋊C₄	—	11	1	no	—
340	C₄⋊C₄	—	11	1	no	—
341	C₂²⋊C₄	—	11	2	no	—
342	C₂²⋊C₄	—	11	2	no	—
343	C₂²⋊C₄	—	11	2	no	—
344	C₄²	—	11	2	no	—
345	C₄²	—	11	2	no	—
346	C₄²	—	11	2	no	—
347	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
348	C₄²	D₄×D₁₁	1	1	yes	characteristic
349	C₄²	Q₈×D₁₁	1	1	yes	characteristic
350	C₄²	C₂³×D₁₁	1	1	yes	characteristic
351	C₁₁	#17830	1	1	yes	characteristic, complemented, Sylow
352	C₂³	—	11	2	no	—
353	C₂³	C₄⋊C₄×D₁₁	1	1	yes	characteristic
354	Q₈	—	22	2	no	—
355	D₄	—	22	4	no	—
356	D₄	—	22	2	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	11	2	no	—
361	C₂×C₄	—	11	2	no	—
362	C₂×C₄	—	11	2	no	—
363	C₂×C₄	—	22	2	no	—
364	C₂×C₄	—	22	2	no	—
365	C₂×C₄	—	22	2	no	—
366	C₂×C₄	—	22	2	no	—
367	C₂×C₄	—	44	2	no	—
368	C₂×C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
369	C₂×C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
370	C₂×C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
371	C₂×C₄	#66967	1	2	yes	—
372	C₂×C₄	#66968	1	2	yes	—
373	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
374	C₂×C₄	C₂×D₄×D₁₁	1	1	yes	characteristic
375	C₂×C₄	C₂×Q₈×D₁₁	1	1	yes	characteristic
376	C₈	—	2	1	no	—
377	C₈	—	2	1	no	—
378	C₈	—	2	1	no	—
379	C₈	—	4	1	no	—
380	C₈	—	4	1	no	—
381	C₈	—	4	1	no	—
382	C₈	—	4	1	no	—
383	C₈	—	22	2	no	—
384	C₈	—	22	2	no	—
385	C₈	—	44	2	no	—
386	C₈	—	44	2	no	—
387	C₈	#66954	1	2	yes	complemented
388	C₂²	—	2	1	no	—
389	C₂²	—	2	1	no	—
390	C₂²	—	22	2	no	—
391	C₂²	—	22	2	no	—
392	C₂²	—	22	2	no	—
393	C₂²	#10622474	1	2	yes	—
394	C₂²	C₂×C₄⋊C₄×D₁₁	1	1	yes	characteristic
395	C₄	—	2	1	no	—
396	C₄	—	2	1	no	—
397	C₄	—	2	1	no	—
398	C₄	—	22	2	no	—
399	C₄	—	22	2	no	—
400	C₄	—	22	2	no	—
401	C₄	#10622474	1	2	yes	—
402	C₄	C₂×#66954	1	1	yes	characteristic
403	C₄	#10623276	1	1	yes	characteristic
404	C₄	C₂×#66967	1	1	yes	characteristic
405	C₄	C₂×#66968	1	1	yes	characteristic
406	C₂	—	2	2	no	—
407	C₂	—	44	2	no	—
408	C₂	#13077181	1	1	yes	characteristic
409	C₂	C₂×#10622474	1	1	yes	characteristic
410	C₂	#13077224	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₁
commutator	C₂×C₄×C₁₁	C₂³×C₄
Frattini	C₄²	C₂³×D₁₁
Fitting	C₂×C₁₁×#334	C₂
socle	C₂²×C₁₁	C₂²×C₄⋊C₄
prime radical	C₂×#4339	D₄
cosocle	C₄²×C₁₁	C₂⁴
hypercenter	C₂×#334	D₁₁
hypocenter	C₁₁	#17830
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×#334

Complements

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

N	H ≅ G/N	type
4. #13067403	C₂	semidirect
5. #13067398	C₂	semidirect
6. #13067390	C₂	semidirect
7. #13067386	C₂	semidirect
8. #13067380	C₂	semidirect
9. #13067375	C₂	semidirect
10. #13067365	C₂	semidirect
11. C₂×C₁₁×#334	C₂	semidirect
157. C₂×#334	D₁₁	semidirect
189. C₈×C₁₁	#131	semidirect
351. C₁₁	#17830	semidirect
387. C₈	#66954	semidirect

Maximal subgroups

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

subgroup	index
#13077582	2
#13077281	2
#13077181	2
#13067403	2
#13067398	2
#13067390	2
#13067386	2
#13067380	2
#13067375	2
#13067365	2
C₂×C₁₁×#334	2
#17830	11