Finite Group Databasebeta

← #14720944

Subgroups — #14720944

Order 2816.

1108 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622539C211yesmaximal, characteristic, complemented
2C4×#66979C211yesmaximal, characteristic, complemented
3#13067141C214yesmaximal, complemented
4#13067128C212yesmaximal, complemented
5#13067124C212yesmaximal, complemented
6#13067107C214yesmaximal, complemented
7C11×#3444C211yesmaximal, characteristic
8C11×#533C411yescharacteristic, complemented
9C11×#533C411yescharacteristic, complemented
10C11×#533C2211yescharacteristic
11C11×#532C411yescharacteristic, complemented
12C11×#532C411yescharacteristic, complemented
13C11×#532C2211yescharacteristic
14C11×#529—21no—
15C11×#529—21no—
16C11×#529—21no—
17C11×#529—21no—
18C11×#529C412yescomplemented
19C11×#529C2212yes—
20C11×#525—21no—
21C11×#525—21no—
22C11×#525C2212yes—
23C4×C11×#41—21no—
24C4×C11×#41—21no—
25C4×C11×#41C412yescomplemented
26C22×C42×C11C2211yescharacteristic
27C2×#66979—21no—
28C4×C22⋊Dic11—21no—
29C4×C22⋊Dic11C2212yes—
30C2×C22⋊(C11⋊C8)C2212yes—
31C4×C4⋊Dic11—21no—
32C4×C4⋊Dic11C2212yes—
33#10622545C2212yes—
34C42×Dic11—21no—
35#10622539—21no—
36#10622539—21no—
37#10622539C2212yes—
38#10622539C2212yes—
39C2×C4⋊(C11⋊C8)—21no—
40C2×#66867—21no—
41#10622176C2218yes—
42#10622175C2218yes—
43C2×C11×#41—21no—
44C2×C11×#41—21no—
45C2×C11×#41C2×C412yes—
46C23×C4×C11D411yescharacteristic
47C23×C4×C11D411yescharacteristic
48C23×C4×C11C2311yescharacteristic
49C11×C4⋊Q8C2×C411yescharacteristic
50C11×C4⋊Q8C2×C411yescharacteristic
51C11×C4⋊Q8C2×C411yescharacteristic
52C11×#127C2×C411yescharacteristic
53C11×#126—22no—
54C11×#126—22no—
55C11×#125—21no—
56C11×#125—21no—
57C11×#125C2×C412yes—
58C11×#124—21no—
59C11×#124—21no—
60C11×#124C2×C412yes—
61C11×#123—22no—
62C11×#123—22no—
63C11×#123—22no—
64C11×C22⋊Q8—21no—
65C11×C22⋊Q8—21no—
66C11×C22⋊Q8—21no—
67C11×C22⋊Q8—21no—
68C11×C22⋊Q8C2×C412yes—
69C11×C22⋊Q8C2312yes—
70C11×#121—21no—
71C11×#121—21no—
72C11×#121—21no—
73C11×#121—21no—
74C11×#121C2×C412yes—
75C11×#121C2312yes—
76C11×#120—22no—
77C4×Q8×C11—21no—
78C4×Q8×C11—21no—
79C4×Q8×C11—21no—
80C4×Q8×C11—21no—
81C4×Q8×C11C2×C412yes—
82C4×Q8×C11C2×C412yes—
83C4×D4×C11—22no—
84C4×D4×C11—22no—
85C4×D4×C11—22no—
86C4×D4×C11—22no—
87C4×D4×C11—22no—
88C4×D4×C11—22no—
89C4×D4×C11—21no—
90C4×D4×C11—21no—
91C4×D4×C11—21no—
92C4×D4×C11—21no—
93C4×D4×C11C2×C412yes—
94C4×D4×C11C2×C412yes—
95C11×#117—21no—
96C11×#117—21no—
97C11×#117—22no—
98C11×#117—22no—
99C11×#117—22no—
100C11×#117C2×C412yes—
101C2×C42×C11—22no—
102C2×C42×C11C2×C411yescharacteristic
103C2×C42×C11C2×C411yescharacteristic
104C2×C42×C11C2×C411yescharacteristic
105C2×C42×C11C2×C411yescharacteristic
106C2×C42×C11D411yescharacteristic
107C2×C42×C11D411yescharacteristic
108C2×C42×C11D411yescharacteristic
109C2×C42×C11D411yescharacteristic
110C2×C42×C11D411yescharacteristic
111C2×C42×C11D411yescharacteristic
112C2×C42×C11C2311yescharacteristic
113C2×C42×C11C2311yescharacteristic
114C2×C22⋊Dic11—22no—
115#66979—28no—
116C2×C4⋊Dic11—22no—
117C2×C4×Dic11—22no—
118C2×C4×Dic11—22no—
119C2×C4×Dic11—22no—
120C22×C11⋊C8—22no—
121C11⋊#95—22no—
122C11⋊#95C2314yes—
123C22⋊(C11⋊C8)—22no—
124C22⋊(C11⋊C8)C2314yes—
125C4⋊(C11⋊C8)—22no—
126C4⋊(C11⋊C8)—22no—
127#66867—22no—
128#66867—22no—
129#17543—111nomaximal, Sylow
130C24×C11C2×D411yescharacteristic
131C11×#41—44no—
132C11×#41—44no—
133C11×#41—44no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11C22×C412yes—
137C2×D4×C11—22no—
138C2×D4×C11—22no—
139C2×D4×C11—22no—
140C2×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11C22×C412yes—
143C22×C4×C11—24no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—42no—
148C22×C4×C11—42no—
149C22×C4×C11C22⋊C411yescharacteristic
150C22×C4×C11C22⋊C411yescharacteristic
151C22×C4×C11C22⋊C411yescharacteristic
152C22×C4×C11C22⋊C411yescharacteristic
153C22×C4×C11C22⋊C411yescharacteristic
154C22×C4×C11C22⋊C411yescharacteristic
155C22×C4×C11C22⋊C411yescharacteristic
156C22×C4×C11C22⋊C411yescharacteristic
157C22×C4×C11C22×C411yescharacteristic
158C22×C4×C11C22×C411yescharacteristic
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2411yescharacteristic
167C22×Dic11—24no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—22no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—22no—
178C11×C4⋊C4C22×C412yes—
179C11×C4⋊C4C22×C412yes—
180C11×C22⋊C4—22no—
181C11×C22⋊C4—22no—
182C11×C22⋊C4—22no—
183C11×C22⋊C4—22no—
184C11×C22⋊C4—22no—
185C11×C22⋊C4—22no—
186C11×C22⋊C4—22no—
187C11×C22⋊C4—22no—
188C11×C22⋊C4—22no—
189C42×C11—22no—
190C42×C11—22no—
191C42×C11—22no—
192C42×C11C22⋊C411yescharacteristic
193C42×C11C22⋊C411yescharacteristic
194C42×C11C22⋊C411yescharacteristic
195C42×C11C22⋊C411yescharacteristic
196C42×C11C22⋊C411yescharacteristic
197C42×C11C22⋊C411yescharacteristic
198C42×C11C22⋊C411yescharacteristic
199C42×C11C22⋊C411yescharacteristic
200C42×C11C22×C411yescharacteristic
201C42×C11C22×C411yescharacteristic
202C42×C11C22×C411yescharacteristic
203C42×C11C22×C411yescharacteristic
204C42×C11C2×D411yescharacteristic
205C42×C11C2×D411yescharacteristic
206C42×C11C2×D411yescharacteristic
207C42×C11C2×D411yescharacteristic
208C22⋊Dic11—28no—
209C4⋊Dic11—28no—
210C4×Dic11—28no—
211C4×Dic11—44no—
212C4×Dic11—44no—
213C2×C11⋊C8—24no—
214C2×C11⋊C8—44no—
215#3444D1111yescharacteristic
216C2×#432—111no—
217C4×#117—111no—
218#1509—114no—
219#1506—112no—
220#1505—112no—
221#1501—114no—
222C23×C11—22no—
223C23×C11—22no—
224C23×C11—22no—
225C23×C11—41no—
226C23×C11C2×C22⋊C411yescharacteristic
227C23×C11C2×C22⋊C411yescharacteristic
228C23×C11C22×D411yescharacteristic
229Q8×C11—42no—
230Q8×C11—42no—
231Q8×C11—42no—
232D4×C11—42no—
233D4×C11—42no—
234D4×C11—44no—
235D4×C11—44no—
236D4×C11—44no—
237D4×C11—42no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—44no—
259C2×C4×C11—44no—
260C2×C4×C11—44no—
261C2×C4×C11#10414yes—
262C2×C4×C11C2×C22⋊C411yescharacteristic
263C2×C4×C11C2×C22⋊C411yescharacteristic
264C2×C4×C11C2×C22⋊C411yescharacteristic
265C2×C4×C11C2×C22⋊C411yescharacteristic
266C2×C4×C11C2×C22⋊C411yescharacteristic
267C2×C4×C11C2×C22⋊C411yescharacteristic
268C2×C4×C11C2×C22⋊C411yescharacteristic
269C2×C4×C11C2×C22⋊C411yescharacteristic
270C2×C4×C11C2×C22⋊C411yescharacteristic
271C2×C4×C11C2×C22⋊C411yescharacteristic
272C2×C4×C11C23×C411yescharacteristic
273C2×C4×C11C22×D411yescharacteristic
274C2×Dic11—28no—
275C2×Dic11—44no—
276C2×Dic11—44no—
277C11⋊C8—44no—
278#533Dic1111yescharacteristic, complemented
279#533Dic1111yescharacteristic, complemented
280#533C2×D1111yescharacteristic
281#532Dic1111yescharacteristic, complemented
282#532Dic1111yescharacteristic, complemented
283#532C2×D1111yescharacteristic
284#529—21no—
285#529—21no—
286#529—21no—
287#529—21no—
288#529Dic1112yescomplemented
289#529C2×D1112yes—
290#525—21no—
291#525—21no—
292#525C2×D1112yes—
293C4×#41—21no—
294C4×#41—21no—
295C4×#41Dic1112yescomplemented
296C2×#117—221no—
297C22×C42C2×D1111yescharacteristic
298#432—112no—
299#432—112no—
300#432—221no—
301#432—221no—
302C2×C4⋊C8—221no—
303C2×C22⋊C8—112no—
304C2×#97—221no—
305C4×C4⋊C4—112no—
306C4×C4⋊C4—221no—
307C4×C22⋊C4—112no—
308C4×C22⋊C4—221no—
309#376—112no—
310C43—221no—
311#328—118no—
312#327—118no—
313C22×C11—21no—
314C22×C11—21no—
315C22×C11—21no—
316C22×C11—21no—
317C22×C11—21no—
318C22×C11—21no—
319C22×C11—21no—
320C22×C11—44no—
321C22×C11—42no—
322C22×C11—42no—
323C22×C11—42no—
324C22×C11C2×#10412yes—
325C22×C11C22×C22⋊C411yescharacteristic
326C22×C11#57512yes—
327C4×C11—21no—
328C4×C11—21no—
329C4×C11—21no—
330C4×C11—21no—
331C4×C11—21no—
332C4×C11—21no—
333C4×C11—21no—
334C4×C11—21no—
335C4×C11—21no—
336C4×C11—42no—
337C4×C11—42no—
338C4×C11—42no—
339C4×C11#41012yes—
340C4×C11C2×#10412yes—
341C4×C11C2×#10412yes—
342Dic11—48no—
343C2×#41—21no—
344C2×#41—21no—
345C2×#41C2×Dic1112yes—
346C23×C4C22⋊D1111yescharacteristic
347C23×C4C22⋊D1111yescharacteristic
348C23×C4C22×D1111yescharacteristic
349C22×C8—222no—
350C4⋊Q8C2×Dic1111yescharacteristic
351C4⋊Q8C2×Dic1111yescharacteristic
352C4⋊Q8C2×Dic1111yescharacteristic
353#127C2×Dic1111yescharacteristic
354#126—22no—
355#126—22no—
356#125—21no—
357#125—21no—
358#125C2×Dic1112yes—
359#124—21no—
360#124—21no—
361#124C2×Dic1112yes—
362#123—22no—
363#123—22no—
364#123—22no—
365C22⋊Q8—21no—
366C22⋊Q8—21no—
367C22⋊Q8—21no—
368C22⋊Q8—21no—
369C22⋊Q8C2×Dic1112yes—
370C22⋊Q8C22×D1112yes—
371#121—21no—
372#121—21no—
373#121—21no—
374#121—21no—
375#121C2×Dic1112yes—
376#121C22×D1112yes—
377#120—22no—
378C4×Q8—21no—
379C4×Q8—21no—
380C4×Q8—21no—
381C4×Q8—21no—
382C4×Q8C2×Dic1112yes—
383C4×Q8C2×Dic1112yes—
384C4×D4—22no—
385C4×D4—22no—
386C4×D4—22no—
387C4×D4—22no—
388C4×D4—22no—
389C4×D4—22no—
390C4×D4—21no—
391C4×D4—21no—
392C4×D4—21no—
393C4×D4—21no—
394C4×D4C2×Dic1112yes—
395C4×D4C2×Dic1112yes—
396#117—21no—
397#117—21no—
398#117—22no—
399#117—22no—
400#117—22no—
401#117—228no—
402#117C2×Dic1112yes—
403C2×C4⋊C4—222no—
404C2×C22⋊C4—222no—
405C2×C42—22no—
406C2×C42—222no—
407C2×C42—222no—
408C2×C42—222no—
409C2×C42C2×Dic1111yescharacteristic
410C2×C42C2×Dic1111yescharacteristic
411C2×C42C2×Dic1111yescharacteristic
412C2×C42C2×Dic1111yescharacteristic
413C2×C42C22⋊D1111yescharacteristic
414C2×C42C22⋊D1111yescharacteristic
415C2×C42C22⋊D1111yescharacteristic
416C2×C42C22⋊D1111yescharacteristic
417C2×C42C22⋊D1111yescharacteristic
418C2×C42C22⋊D1111yescharacteristic
419C2×C42C22×D1111yescharacteristic
420C2×C42C22×D1111yescharacteristic
421C4⋊C8—222no—
422C4⋊C8—222no—
423C22⋊C8—114no—
424C22⋊C8—222no—
425#97—222no—
426#97—222no—
427#95—114no—
428#95—222no—
429C2×C11—22no—
430C2×C11—22no—
431C2×C11—41no—
432C2×C11—82no—
433C2×C11C2×#41011yescharacteristic
434C2×C11#289611yescharacteristic
435C2×C11C22×#10411yescharacteristic
436C24C2×C22⋊D1111yescharacteristic
437#41—44no—
438#41—44no—
439#41—44no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8C22×Dic1112yes—
443C2×D4—22no—
444C2×D4—22no—
445C2×D4—22no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4C22×Dic1112yes—
449C22×C4—24no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—42no—
454C22×C4—42no—
455C22×C4—224no—
456C22×C4C22⋊Dic1111yescharacteristic
457C22×C4C22⋊Dic1111yescharacteristic
458C22×C4C22⋊Dic1111yescharacteristic
459C22×C4C22⋊Dic1111yescharacteristic
460C22×C4C22⋊Dic1111yescharacteristic
461C22×C4C22⋊Dic1111yescharacteristic
462C22×C4C22⋊Dic1111yescharacteristic
463C22×C4C22⋊Dic1111yescharacteristic
464C22×C4C22×Dic1111yescharacteristic
465C22×C4C22×Dic1111yescharacteristic
466C22×C4C2×C22⋊D1111yescharacteristic
467C22×C4C2×C22⋊D1111yescharacteristic
468C22×C4C2×C22⋊D1111yescharacteristic
469C22×C4C2×C22⋊D1111yescharacteristic
470C22×C4C2×C22⋊D1111yescharacteristic
471C22×C4C2×C22⋊D1111yescharacteristic
472C22×C4C2×C22⋊D1111yescharacteristic
473C22×C4C23×D1111yescharacteristic
474C2×C8—224no—
475C2×C8—444no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—228no—
487C4⋊C4C22×Dic1112yes—
488C4⋊C4C22×Dic1112yes—
489C22⋊C4—22no—
490C22⋊C4—22no—
491C22⋊C4—22no—
492C22⋊C4—22no—
493C22⋊C4—22no—
494C22⋊C4—22no—
495C22⋊C4—22no—
496C22⋊C4—22no—
497C22⋊C4—22no—
498C22⋊C4—228no—
499C42—22no—
500C42—22no—
501C42—22no—
502C42—228no—
503C42—444no—
504C42—444no—
505C42C22⋊Dic1111yescharacteristic
506C42C22⋊Dic1111yescharacteristic
507C42C22⋊Dic1111yescharacteristic
508C42C22⋊Dic1111yescharacteristic
509C42C22⋊Dic1111yescharacteristic
510C42C22⋊Dic1111yescharacteristic
511C42C22⋊Dic1111yescharacteristic
512C42C22⋊Dic1111yescharacteristic
513C42C22×Dic1111yescharacteristic
514C42C22×Dic1111yescharacteristic
515C42C22×Dic1111yescharacteristic
516C42C22×Dic1111yescharacteristic
517C42C2×C22⋊D1111yescharacteristic
518C42C2×C22⋊D1111yescharacteristic
519C42C2×C22⋊D1111yescharacteristic
520C42C2×C22⋊D1111yescharacteristic
521C11#1754311yescharacteristic, complemented, Sylow
522C23—22no—
523C23—22no—
524C23—22no—
525C23—41no—
526C23C2×C22⋊Dic1111yescharacteristic
527C23C2×C22⋊Dic1111yescharacteristic
528C23C22×C22⋊D1111yescharacteristic
529Q8—42no—
530Q8—42no—
531Q8—42no—
532D4—42no—
533D4—42no—
534D4—44no—
535D4—44no—
536D4—44no—
537D4—42no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—44no—
559C2×C4—44no—
560C2×C4—44no—
561C2×C4—228no—
562C2×C4—444no—
563C2×C4—444no—
564C2×C4#6690114yes—
565C2×C4C2×C22⋊Dic1111yescharacteristic
566C2×C4C2×C22⋊Dic1111yescharacteristic
567C2×C4C2×C22⋊Dic1111yescharacteristic
568C2×C4C2×C22⋊Dic1111yescharacteristic
569C2×C4C2×C22⋊Dic1111yescharacteristic
570C2×C4C2×C22⋊Dic1111yescharacteristic
571C2×C4C2×C22⋊Dic1111yescharacteristic
572C2×C4C2×C22⋊Dic1111yescharacteristic
573C2×C4C2×C22⋊Dic1111yescharacteristic
574C2×C4C2×C22⋊Dic1111yescharacteristic
575C2×C4C23×Dic1111yescharacteristic
576C2×C4C22×C22⋊D1111yescharacteristic
577C8—444no—
578C22—21no—
579C22—21no—
580C22—21no—
581C22—21no—
582C22—21no—
583C22—21no—
584C22—21no—
585C22—44no—
586C22—42no—
587C22—42no—
588C22—42no—
589C22C2×#6690112yes—
590C22#1062335312yes—
591C22C22×C22⋊Dic1111yescharacteristic
592C4—21no—
593C4—21no—
594C4—21no—
595C4—21no—
596C4—21no—
597C4—21no—
598C4—21no—
599C4—21no—
600C4—21no—
601C4—42no—
602C4—42no—
603C4—42no—
604C4—448no—
605C4C2×#6690112yes—
606C4C2×#6690112yes—
607C4#1062285312yes—
608C2—22no—
609C2—22no—
610C2—41no—
611C2—82no—
612C2C2×#1062285311yescharacteristic
613C2#1307713511yescharacteristic
614C2C22×#6690111yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊Dic11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#3444C2
socleC22×C11C22×C22⋊C4
cosocleC22×C4×C11C24
hypercenter#3444D11
hypocenterC11#17543
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ #3444

Complements

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

NH ≅ G/Ntype
1. C2×#10622539C2semidirect
2. C4×#66979C2semidirect
3. #13067141C2semidirect
4. #13067128C2semidirect
5. #13067124C2semidirect
6. #13067107C2semidirect
8. C11×#533C4semidirect
9. C11×#533C4semidirect
11. C11×#532C4semidirect
12. C11×#532C4semidirect
18. C11×#529C4semidirect
25. C4×C11×#41C4semidirect
278. #533Dic11semidirect
279. #533Dic11semidirect
281. #532Dic11semidirect
282. #532Dic11semidirect
288. #529Dic11semidirect
295. C4×#41Dic11semidirect
521. C11#17543semidirect

Maximal subgroups

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

subgroupindex
C2×#106225392
C4×#669792
#130671412
#130671282
#130671242
#130671072
C11×#34442
#1754311