Subgroups — #14723413

Order 2816.

648 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	#13077729	C₂	1	1	yes	maximal, characteristic
2	C₄×#66995	C₂	1	1	yes	maximal, characteristic
3	#13067494	C₂	1	2	yes	maximal, complemented
4	#13067487	C₂	1	2	yes	maximal, complemented
5	#13067466	C₂	1	2	yes	maximal, complemented
6	#13067459	C₂	1	2	yes	maximal, complemented
7	#13067369	C₂	1	1	yes	maximal, characteristic, complemented
8	#13066996	C₂	1	1	yes	maximal, characteristic
9	C₂×Q₈⋊(C₁₁⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
10	#13066906	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₁×#2982	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
13	C₂×#66995	C₄	1	1	yes	characteristic
14	C₄×#4339	C₂²	1	1	yes	characteristic
15	C₈×Q₈×C₁₁	—	2	1	no	—
16	C₈×Q₈×C₁₁	—	2	1	no	—
17	C₈×Q₈×C₁₁	C₂²	1	2	yes	—
18	C₈×Q₈×C₁₁	C₂²	1	2	yes	—
19	C₁₁×#431	—	2	2	no	—
20	C₁₁×#431	C₂²	1	1	yes	characteristic
21	C₁₁×#431	C₂²	1	1	yes	characteristic
22	#10622838	C₄	1	1	yes	characteristic
23	#10622643	C₄	1	2	yes	—
24	C₄×#4326	C₂²	1	2	yes	—
25	#10622639	C₄	1	2	yes	—
26	C₄×#4325	C₂²	1	2	yes	—
27	#10622579	C₄	1	1	yes	characteristic
28	#10622577	C₄	1	1	yes	characteristic
29	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	1	yes	characteristic
30	C₄×#4318	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
32	#10622450	—	2	1	no	—
33	#10622448	—	2	1	no	—
34	#10622343	—	2	2	no	—
35	#10622301	C₂²	1	2	yes	—
36	#10622292	C₂²	1	2	yes	—
37	Q₈⋊(C₁₁⋊C₈)	C₂²	1	2	yes	—
38	Q₈⋊(C₁₁⋊C₈)	C₂²	1	2	yes	—
39	#10622122	C₂²	1	1	yes	characteristic
40	#10622122	C₂²	1	1	yes	characteristic
41	#10622121	C₂²	1	1	yes	characteristic
42	#10622121	C₂²	1	1	yes	characteristic
43	#10622118	C₂²	1	2	yes	—
44	#10622117	C₂²	1	2	yes	—
45	#10622093	C₂²	1	2	yes	—
46	#10622092	C₂²	1	2	yes	—
47	C₂²×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
48	C₂×#4339	C₂×C₄	1	1	yes	characteristic
49	C₄×Q₈×C₁₁	—	2	1	no	—
50	C₄×Q₈×C₁₁	—	2	1	no	—
51	C₄×Q₈×C₁₁	C₂×C₄	1	2	yes	—
52	C₄×Q₈×C₁₁	C₂³	1	2	yes	—
53	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
54	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄²×C₁₁	—	2	1	no	—
56	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
57	C₂×#4326	C₂×C₄	1	2	yes	—
58	#66995	—	2	4	no	—
59	C₂×#4325	C₂×C₄	1	2	yes	—
60	C₄×C₂²⋊D₁₁	—	2	1	no	—
61	C₄×C₂²⋊D₁₁	—	2	1	no	—
62	#66979	C₂×C₄	1	1	yes	characteristic
63	C₂×#4318	C₂×C₄	1	1	yes	characteristic
64	C₂×#4318	C₂×C₄	1	1	yes	characteristic
65	C₂²×C₁₁⋊C₈	—	2	1	no	—
66	C₂²×C₁₁⋊C₈	—	2	1	no	—
67	C₂×#4313	—	2	2	no	—
68	C₄×D₄₄	C₂×C₄	1	1	yes	characteristic
69	C₄×D₄₄	C₂³	1	1	yes	characteristic
70	#66925	—	2	1	no	—
71	C₄²×D₁₁	—	2	1	no	—
72	C₄×Dic₂₂	C₂×C₄	1	1	yes	characteristic
73	C₄×Dic₂₂	C₂³	1	1	yes	characteristic
74	C₁₁×C₄⋊C₈	—	2	2	no	—
75	C₁₁×C₄⋊C₈	—	2	2	no	—
76	C₁₁×C₄⋊C₈	D₄	1	1	yes	characteristic
77	C₁₁×C₄⋊C₈	D₄	1	1	yes	characteristic
78	C₁₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
79	C₁₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
80	C₁₁×C₂²⋊C₈	—	2	1	no	—
81	C₁₁×C₂²⋊C₈	D₄	1	2	yes	—
82	C₄×C₈×C₁₁	—	2	2	no	—
83	C₄×C₈×C₁₁	—	2	2	no	—
84	C₄×C₈×C₁₁	—	2	1	no	—
85	C₄×C₈×C₁₁	C₂³	1	2	yes	—
86	#66899	C₂×C₄	1	2	yes	—
87	#66899	C₂×C₄	1	2	yes	—
88	(C₂×D₁₁)⋊C₈	—	2	2	no	—
89	#66879	—	2	2	no	—
90	Dic₁₁⋊C₈	—	2	2	no	—
91	#66874	C₂×C₄	1	2	yes	—
92	#66873	C₂×C₄	1	2	yes	—
93	#66872	C₂×C₄	1	2	yes	—
94	#66871	C₂×C₄	1	2	yes	—
95	C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
96	C₄⋊(C₁₁⋊C₈)	C₂³	1	2	yes	—
97	#66867	C₂×C₄	1	2	yes	—
98	C₄×C₁₁⋊C₈	—	2	1	no	—
99	C₄×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
100	C₄×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
101	C₄×C₁₁⋊C₈	C₂³	1	2	yes	—
102	#17874	—	11	1	no	maximal, Sylow
103	C₂×Q₈×C₁₁	—	2	1	no	—
104	C₂×Q₈×C₁₁	—	2	2	no	—
105	C₂×Q₈×C₁₁	M₁₆	1	4	yes	complemented
106	C₂×Q₈×C₁₁	C₂²×C₄	1	2	yes	—
107	C₂²×C₄×C₁₁	—	2	1	no	—
108	C₂²×C₄×C₁₁	—	2	1	no	—
109	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
112	C₂×C₂²⋊D₁₁	—	2	1	no	—
113	#4339	—	2	2	no	—
114	#4339	—	2	2	no	—
115	C₂×D₄₄	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₄×D₁₁	—	2	1	no	—
117	C₂×C₄×D₁₁	—	2	1	no	—
118	C₂×C₄×D₁₁	—	2	1	no	—
119	C₂×Dic₂₂	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₈×C₁₁	—	2	1	no	—
121	C₂×C₈×C₁₁	—	2	1	no	—
122	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
123	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
124	C₁₁×C₄⋊C₄	—	2	2	no	—
125	C₁₁×C₄⋊C₄	—	2	1	no	—
126	C₁₁×C₄⋊C₄	—	2	2	no	—
127	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
128	C₄²×C₁₁	—	2	2	no	—
129	C₄²×C₁₁	—	2	2	no	—
130	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
131	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
132	C₄²×C₁₁	#41	1	1	yes	characteristic
133	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
134	C₂²⋊Dic₁₁	—	2	1	no	—
135	#4326	—	2	4	no	—
136	#4325	—	2	4	no	—
137	(C₂×D₁₁)⋊C₄	—	2	1	no	—
138	(C₂×D₁₁)⋊C₄	—	2	1	no	—
139	C₄⋊Dic₁₁	C₂²×C₄	1	1	yes	characteristic
140	C₄⋊Dic₁₁	C₂²×C₄	1	1	yes	characteristic
141	Dic₁₁⋊C₄	—	2	1	no	—
142	Dic₁₁⋊C₄	—	2	1	no	—
143	C₄×Dic₁₁	—	2	1	no	—
144	C₄×Dic₁₁	—	2	1	no	—
145	C₄×Dic₁₁	—	2	1	no	—
146	#4318	—	2	2	no	—
147	#4318	—	2	2	no	—
148	C₂×C₁₁⋊C₈	—	2	2	no	—
149	C₂×C₁₁⋊C₈	—	2	1	no	—
150	C₂×C₁₁⋊C₈	—	2	1	no	—
151	C₂×C₁₁⋊C₈	—	4	2	no	—
152	C₂×C₁₁⋊C₈	—	8	1	no	—
153	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
154	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
155	#4313	—	8	2	no	—
156	#2989	—	11	1	no	—
157	#2982	D₁₁	1	1	yes	characteristic, complemented
158	C₄×#137	—	11	1	no	—
159	#1588	—	11	2	no	—
160	#1587	—	11	2	no	—
161	#1584	—	11	2	no	—
162	#1583	—	11	2	no	—
163	#1565	—	11	1	no	—
164	#1476	—	11	1	no	—
165	C₂×Q₈⋊C₈	—	11	1	no	—
166	#1451	—	11	1	no	—
167	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
168	C₂²×D₁₁	—	2	1	no	—
169	Q₈×C₁₁	—	2	2	no	—
170	Q₈×C₁₁	—	2	4	no	—
171	Q₈×C₁₁	C₂×M₁₆	1	4	yes	—
172	C₂×C₄×C₁₁	—	2	2	no	—
173	C₂×C₄×C₁₁	—	2	4	no	—
174	C₂×C₄×C₁₁	—	2	1	no	—
175	C₂×C₄×C₁₁	—	2	1	no	—
176	C₂×C₄×C₁₁	—	2	2	no	—
177	C₂×C₄×C₁₁	—	4	1	no	—
178	C₂×C₄×C₁₁	—	8	1	no	—
179	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
180	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
181	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
182	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
183	C₂×C₄×C₁₁	#131	1	2	yes	—
184	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
185	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
187	C₂²⋊D₁₁	—	4	2	no	—
188	C₂×Dic₁₁	—	2	1	no	—
189	C₂×Dic₁₁	—	2	1	no	—
190	C₂×Dic₁₁	—	2	1	no	—
191	D₄₄	—	2	1	no	—
192	D₄₄	—	2	1	no	—
193	C₄×D₁₁	—	4	1	no	—
194	C₄×D₁₁	—	4	1	no	—
195	C₄×D₁₁	—	4	2	no	—
196	C₄×D₁₁	—	8	1	no	—
197	Dic₂₂	—	2	1	no	—
198	Dic₂₂	—	2	1	no	—
199	C₈×C₁₁	—	2	2	no	—
200	C₈×C₁₁	—	2	2	no	—
201	C₈×C₁₁	—	4	1	no	—
202	C₈×C₁₁	—	4	1	no	—
203	C₁₁⋊C₈	—	2	2	no	—
204	C₁₁⋊C₈	—	2	2	no	—
205	C₁₁⋊C₈	—	2	2	no	—
206	C₁₁⋊C₈	—	4	1	no	—
207	C₁₁⋊C₈	—	4	2	no	—
208	C₂×#137	—	11	1	no	—
209	C₄×#41	—	11	1	no	—
210	C₂×C₄×Q₈	C₂×D₁₁	1	1	yes	characteristic
211	#446	—	11	2	no	—
212	C₈×Q₈	—	2	1	no	—
213	C₈×Q₈	—	2	1	no	—
214	C₈×Q₈	C₂×D₁₁	1	2	yes	—
215	C₈×Q₈	C₂×D₁₁	1	2	yes	—
216	#441	—	11	2	no	—
217	#440	—	11	2	no	—
218	C₄×Q₁₆	—	11	2	no	—
219	C₄×SD₁₆	—	11	2	no	—
220	#436	—	11	2	no	—
221	#435	—	22	2	no	—
222	#432	—	22	1	no	—
223	#431	—	2	2	no	—
224	#431	C₂×D₁₁	1	1	yes	characteristic
225	#431	C₂×D₁₁	1	1	yes	characteristic
226	#428	—	11	1	no	—
227	#423	—	22	1	no	—
228	C₂×C₄⋊C₈	—	11	1	no	—
229	#419	—	11	1	no	—
230	#417	—	11	1	no	—
231	C₄×M₁₆	—	11	1	no	—
232	C₂×C₄×C₈	—	11	1	no	—
233	#335	—	11	2	no	—
234	#334	—	11	2	no	—
235	Q₈⋊C₈	—	11	2	no	—
236	Q₈⋊C₈	—	11	2	no	—
237	Q₈⋊C₈	—	11	1	no	—
238	Q₈⋊C₈	—	11	1	no	—
239	D₄⋊C₈	—	11	1	no	—
240	D₄⋊C₈	—	11	1	no	—
241	#322	—	11	2	no	—
242	#322	—	11	2	no	—
243	C₂²×C₁₁	—	2	1	no	—
244	C₂²×C₁₁	—	2	1	no	—
245	C₂²×C₁₁	#435	1	2	yes	—
246	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
247	C₂×D₁₁	—	4	1	no	—
248	C₂×D₁₁	—	4	1	no	—
249	C₂×D₁₁	—	4	1	no	—
250	C₄×C₁₁	—	2	4	no	—
251	C₄×C₁₁	—	2	1	no	—
252	C₄×C₁₁	—	2	1	no	—
253	C₄×C₁₁	—	2	1	no	—
254	C₄×C₁₁	—	4	2	no	—
255	C₄×C₁₁	#435	1	2	yes	—
256	C₄×C₁₁	C₂²×M₁₆	1	1	yes	characteristic
257	C₄×C₁₁	C₂×#131	1	1	yes	characteristic
258	C₄×C₁₁	#577	1	1	yes	characteristic
259	C₄×C₁₁	#578	1	1	yes	characteristic
260	Dic₁₁	—	4	1	no	—
261	Dic₁₁	—	4	1	no	—
262	Dic₁₁	—	4	1	no	—
263	C₂×#41	—	11	1	no	—
264	C₂²×Q₈	C₄×D₁₁	1	1	yes	characteristic
265	#137	—	22	4	no	—
266	C₂×Q₁₆	—	11	2	no	—
267	C₂×SD₁₆	—	11	2	no	—
268	C₂×M₁₆	—	11	1	no	—
269	C₂×M₁₆	—	11	1	no	—
270	C₂×M₁₆	—	22	2	no	—
271	C₂²×C₈	—	22	1	no	—
272	C₂²×C₈	—	22	1	no	—
273	C₄×Q₈	—	2	1	no	—
274	C₄×Q₈	—	2	1	no	—
275	C₄×Q₈	—	11	1	no	—
276	C₄×Q₈	—	11	1	no	—
277	C₄×Q₈	C₄×D₁₁	1	2	yes	—
278	C₄×Q₈	C₂²×D₁₁	1	2	yes	—
279	C₄×D₄	—	11	1	no	—
280	C₄×D₄	—	11	1	no	—
281	C₄×D₄	—	22	1	no	—
282	C₄×D₄	—	22	1	no	—
283	#117	—	11	1	no	—
284	#117	—	22	1	no	—
285	C₂×C₄⋊C₄	—	2	1	no	—
286	C₂×C₄⋊C₄	C₄×D₁₁	1	1	yes	characteristic
287	C₂×C₄²	—	2	1	no	—
288	C₂×C₄²	—	22	1	no	—
289	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
290	#107	—	11	2	no	—
291	#106	—	11	2	no	—
292	C₄⋊C₈	—	2	2	no	—
293	C₄⋊C₈	—	2	2	no	—
294	C₄⋊C₈	—	11	2	no	—
295	C₄⋊C₈	—	22	2	no	—
296	C₄⋊C₈	—	22	1	no	—
297	C₄⋊C₈	C₂²⋊D₁₁	1	1	yes	characteristic
298	C₄⋊C₈	C₂²⋊D₁₁	1	1	yes	characteristic
299	C₄⋊C₈	C₂²×D₁₁	1	1	yes	characteristic
300	C₄⋊C₈	C₂²×D₁₁	1	1	yes	characteristic
301	#103	—	11	2	no	—
302	#103	—	11	2	no	—
303	#103	—	11	2	no	—
304	#102	—	11	2	no	—
305	C₂²⋊C₈	—	2	1	no	—
306	C₂²⋊C₈	—	22	2	no	—
307	C₂²⋊C₈	C₂²⋊D₁₁	1	2	yes	—
308	#97	—	11	2	no	—
309	#97	—	22	2	no	—
310	C₄×C₈	—	2	2	no	—
311	C₄×C₈	—	2	2	no	—
312	C₄×C₈	—	2	1	no	—
313	C₄×C₈	—	11	2	no	—
314	C₄×C₈	—	11	1	no	—
315	C₄×C₈	—	11	1	no	—
316	C₄×C₈	—	22	1	no	—
317	C₄×C₈	C₂²×D₁₁	1	2	yes	—
318	C₂×C₁₁	—	2	2	no	—
319	C₂×C₁₁	C₂×#435	1	1	yes	characteristic
320	C₂×C₁₁	#2947	1	1	yes	characteristic
321	C₂×C₁₁	#2956	1	1	yes	characteristic
322	D₁₁	—	8	1	no	—
323	#41	—	22	2	no	—
324	#41	—	22	2	no	—
325	C₂×Q₈	—	2	2	no	—
326	C₂×Q₈	—	2	1	no	—
327	C₂×Q₈	—	11	1	no	—
328	C₂×Q₈	#4313	1	4	yes	complemented
329	C₂×Q₈	C₂×C₄×D₁₁	1	2	yes	—
330	C₂×D₄	—	11	1	no	—
331	C₂×D₄	—	22	1	no	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	22	1	no	—
335	C₂²×C₄	—	22	1	no	—
336	C₂²×C₄	—	22	1	no	—
337	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
338	C₂²×C₄	#4339	1	1	yes	characteristic
339	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
340	Q₁₆	—	22	4	no	—
341	SD₁₆	—	22	4	no	—
342	M₁₆	—	22	2	no	—
343	M₁₆	—	22	2	no	—
344	M₁₆	—	88	2	no	—
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	11	2	no	—
348	C₂×C₈	—	11	2	no	—
349	C₂×C₈	—	22	1	no	—
350	C₂×C₈	—	22	1	no	—
351	C₂×C₈	—	22	2	no	—
352	C₂×C₈	—	44	2	no	—
353	C₂×C₈	—	88	1	no	—
354	C₂×C₈	C₂×C₂²⋊D₁₁	1	2	yes	—
355	C₂×C₈	C₂×C₂²⋊D₁₁	1	2	yes	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	11	1	no	—
360	C₄⋊C₄	—	11	1	no	—
361	C₄⋊C₄	—	22	1	no	—
362	C₄⋊C₄	—	22	1	no	—
363	C₄⋊C₄	C₂×C₄×D₁₁	1	2	yes	—
364	C₂²⋊C₄	—	22	1	no	—
365	C₂²⋊C₄	—	22	1	no	—
366	C₂²⋊C₄	—	22	1	no	—
367	C₄²	—	2	2	no	—
368	C₄²	—	2	2	no	—
369	C₄²	—	22	1	no	—
370	C₄²	—	22	1	no	—
371	C₄²	—	22	1	no	—
372	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
373	C₄²	#4339	1	1	yes	characteristic
374	C₄²	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
375	C₄²	C₂³×D₁₁	1	1	yes	characteristic
376	C₁₁	#17874	1	1	yes	characteristic, complemented, Sylow
377	C₂³	—	22	1	no	—
378	C₂³	C₄×C₂²⋊D₁₁	1	1	yes	characteristic
379	Q₈	—	2	4	no	—
380	Q₈	—	2	2	no	—
381	Q₈	—	22	1	no	—
382	Q₈	—	22	1	no	—
383	Q₈	C₂×#4313	1	4	yes	—
384	D₄	—	22	1	no	—
385	D₄	—	22	1	no	—
386	D₄	—	44	2	no	—
387	C₂×C₄	—	2	4	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	8	1	no	—
394	C₂×C₄	—	22	1	no	—
395	C₂×C₄	—	22	1	no	—
396	C₂×C₄	—	22	1	no	—
397	C₂×C₄	—	44	2	no	—
398	C₂×C₄	—	44	1	no	—
399	C₂×C₄	—	44	1	no	—
400	C₂×C₄	—	88	1	no	—
401	C₂×C₄	C₂×#4313	1	2	yes	—
402	C₂×C₄	#66954	1	2	yes	—
403	C₂×C₄	C₄×C₂²⋊D₁₁	1	1	yes	characteristic
404	C₂×C₄	C₄×C₂²⋊D₁₁	1	1	yes	characteristic
405	C₂×C₄	C₄×C₂²⋊D₁₁	1	1	yes	characteristic
406	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
407	C₂×C₄	C₂×#4339	1	1	yes	characteristic
408	C₂×C₄	C₂²×C₂²⋊D₁₁	1	1	yes	characteristic
409	C₈	—	2	2	no	—
410	C₈	—	2	2	no	—
411	C₈	—	4	1	no	—
412	C₈	—	4	1	no	—
413	C₈	—	22	2	no	—
414	C₈	—	22	2	no	—
415	C₈	—	22	2	no	—
416	C₈	—	44	1	no	—
417	C₈	—	44	2	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	44	1	no	—
421	C₂²	—	44	1	no	—
422	C₂²	—	44	1	no	—
423	C₂²	#10622724	1	2	yes	—
424	C₂²	C₂×C₄×C₂²⋊D₁₁	1	1	yes	characteristic
425	C₄	—	2	1	no	—
426	C₄	—	2	1	no	—
427	C₄	—	2	4	no	—
428	C₄	—	2	1	no	—
429	C₄	—	4	2	no	—
430	C₄	—	44	1	no	—
431	C₄	—	44	1	no	—
432	C₄	—	44	1	no	—
433	C₄	#10622724	1	2	yes	—
434	C₄	C₂²×#4313	1	1	yes	characteristic
435	C₄	C₂×#66954	1	1	yes	characteristic
436	C₄	#10623368	1	1	yes	characteristic
437	C₄	#10623369	1	1	yes	characteristic
438	C₂	—	2	2	no	—
439	C₂	—	88	1	no	—
440	C₂	C₂×#10622724	1	1	yes	characteristic
441	C₂	#13077459	1	1	yes	characteristic
442	C₂	#13077523	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₁₁
commutator	C₂×C₄×C₁₁	C₂³×C₄
Frattini	C₄²	C₂³×D₁₁
Fitting	C₁₁×#2982	C₂
socle	C₂²×C₁₁	C₂×C₄×D₄
prime radical	C₂×#4339	C₂×C₄
cosocle	C₄²×C₁₁	C₂⁴
hypercenter	#2982	D₁₁
hypocenter	C₁₁	#17874
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ #431 ◁ #2982

Complements

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

N	H ≅ G/N	type
3. #13067494	C₂	semidirect
4. #13067487	C₂	semidirect
5. #13067466	C₂	semidirect
6. #13067459	C₂	semidirect
7. #13067369	C₂	semidirect
9. C₂×Q₈⋊(C₁₁⋊C₈)	C₂	semidirect
10. #13066906	C₂	semidirect
11. C₁₁×#2982	C₂	semidirect
105. C₂×Q₈×C₁₁	M₁₆	semidirect
157. #2982	D₁₁	semidirect
328. C₂×Q₈	#4313	semidirect
376. C₁₁	#17874	semidirect

Maximal subgroups

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

subgroup	index
#13077729	2
C₄×#66995	2
#13067494	2
#13067487	2
#13067466	2
#13067459	2
#13067369	2
#13066996	2
C₂×Q₈⋊(C₁₁⋊C₈)	2
#13066906	2
C₁₁×#2982	2
#17874	11