Finite Group Databasebeta

← #14758740

Subgroups — #14758740

Order 2816.

1226 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623059C211yesmaximal, characteristic
2C2×#10622318C211yesmaximal, characteristic, complemented
3C2×C4×C8×D11C211yesmaximal, characteristic, complemented
4#13069550C212yesmaximal, complemented
5#13069408C212yesmaximal, complemented
6#13068907C212yesmaximal, complemented
7#13068905C212yesmaximal, complemented
8#13068385C211yesmaximal, characteristic, complemented
9#13068383C211yesmaximal, characteristic, complemented
10#13068382C211yesmaximal, characteristic, complemented
11C11×#1750C211yesmaximal, characteristic, complemented
12C2×C11×#117C2211yescharacteristic
13C2×C4×C22⋊D11C2211yescharacteristic
14C2×C4×C22⋊D11C2211yescharacteristic
15C22×C8×D11C2212yes—
16#10623059—24no—
17#10623059—24no—
18C2×#66951C411yescharacteristic
19C2×#66949C411yescharacteristic
20C2×#66947C411yescharacteristic
21C2×#66942C411yescharacteristic
22C2×#66938C411yescharacteristic
23C2×#66937C411yescharacteristic
24C2×#66936C411yescharacteristic
25C2×#66932C411yescharacteristic
26C2×C4×D44C2211yescharacteristic
27C2×#66925C2211yescharacteristic
28C2×C42×D11C2211yescharacteristic
29C2×C4×Dic22C2211yescharacteristic
30C2×C11×C22⋊C8C2212yes—
31C2×C11×#97C2211yescharacteristic
32C2×C4×C8×C11C2211yescharacteristic
33C2×C22⋊(C11⋊C8)C2212yes—
34C2×(C2×D11)⋊C8C2212yes—
35C2×(C2×D11)⋊C8C2212yes—
36C2×(C2×D11)⋊C8C2212yes—
37C2×Dic11⋊C8C2212yes—
38C2×C8×Dic11C2212yes—
39C2×#66867C2211yescharacteristic
40C2×C4×C11⋊C8C2211yescharacteristic
41#10622318—24no—
42C4×C8×D11—24no—
43C11×#336C2212yes—
44#10622188C2212yes—
45#10622188C2212yes—
46#10622162C2212yes—
47C23×C4×C11C2311yescharacteristic
48C22×C22⋊D11C2×C411yescharacteristic
49C22×C22⋊D11C2×C411yescharacteristic
50C22×D44C2×C411yescharacteristic
51C22×C4×D11C2×C411yescharacteristic
52C22×C4×D11C2×C411yescharacteristic
53C22×C4×D11C2311yescharacteristic
54C22×C4×D11C2311yescharacteristic
55C22×Dic22C2×C411yescharacteristic
56C22×C8×C11C2312yes—
57C22×C8×C11C2312yes—
58C11×#117—22no—
59C11×#117—22no—
60C2×C11×C4⋊C4C2×C411yescharacteristic
61C2×C11×C4⋊C4C2×C411yescharacteristic
62C2×C11×C22⋊C4C2×C411yescharacteristic
63C2×C11×C22⋊C4C2×C411yescharacteristic
64C2×C42×C11C2311yescharacteristic
65C2×C42×C11C2311yescharacteristic
66C2×C22⋊Dic11C2×C411yescharacteristic
67C2×C22⋊Dic11C2×C411yescharacteristic
68C4×C22⋊D11—22no—
69C4×C22⋊D11—22no—
70C4×C22⋊D11—22no—
71C4×C22⋊D11—22no—
72C2×(C2×D11)⋊C4C2×C411yescharacteristic
73C2×(C2×D11)⋊C4C2×C411yescharacteristic
74C2×(C2×D11)⋊C4C2×C411yescharacteristic
75C2×(C2×D11)⋊C4C2×C411yescharacteristic
76C2×(C2×D11)⋊C4C2×C411yescharacteristic
77C2×(C2×D11)⋊C4C2×C411yescharacteristic
78C2×C4⋊Dic11C2×C411yescharacteristic
79C2×C4⋊Dic11C2×C411yescharacteristic
80C2×Dic11⋊C4C2×C411yescharacteristic
81C2×Dic11⋊C4C2×C411yescharacteristic
82C2×Dic11⋊C4C2×C411yescharacteristic
83C2×Dic11⋊C4C2×C411yescharacteristic
84C2×Dic11⋊C4C2×C411yescharacteristic
85C2×Dic11⋊C4C2×C411yescharacteristic
86C2×C4×Dic11C2×C411yescharacteristic
87C2×C4×Dic11C2×C411yescharacteristic
88C2×C4×Dic11C2311yescharacteristic
89C2×C4×Dic11C2311yescharacteristic
90C22×C11⋊C8C2312yes—
91C22×C11⋊C8C2312yes—
92C2×C8×D11—24no—
93C2×C8×D11—24no—
94C2×C8×D11—24no—
95#66951—24no—
96#66949—24no—
97#66947—24no—
98#66942—24no—
99#66938—24no—
100#66937—24no—
101#66936—24no—
102#66932—24no—
103C4×D44—22no—
104C4×D44—22no—
105#66925—22no—
106#66925—22no—
107C42×D11D414yes—
108C42×D11D414yes—
109C4×Dic22—22no—
110C4×Dic22—22no—
111C11×C22⋊C8—24no—
112C11×#97—22no—
113C4×C8×C11—22no—
114C22⋊(C11⋊C8)—24no—
115(C2×D11)⋊C8—24no—
116(C2×D11)⋊C8—24no—
117(C2×D11)⋊C8—24no—
118Dic11⋊C8—24no—
119C8×Dic11—24no—
120#66867—22no—
121C4×C11⋊C8—22no—
122#21375—111nomaximal, Sylow
123C24×C11C22×C411yescharacteristic
124C23×D11C22×C411yescharacteristic
125C23×D11C22×C411yescharacteristic
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11C22×C411yescharacteristic
131C22×C4×C11C22×C411yescharacteristic
132C22×C4×C11C22×C411yescharacteristic
133C22×C4×C11C22×C411yescharacteristic
134C22×C4×C11C22×C411yescharacteristic
135C22×C4×C11C2411yescharacteristic
136C2×C22⋊D11—22no—
137C2×C22⋊D11—24no—
138C2×C22⋊D11—22no—
139C2×C22⋊D11—24no—
140C22×Dic11C22×C411yescharacteristic
141C22×Dic11C22×C411yescharacteristic
142C22×Dic11C22×C411yescharacteristic
143C22×Dic11C22×C411yescharacteristic
144C22×Dic11C22×C411yescharacteristic
145C22×Dic11C22×C411yescharacteristic
146C2×D44—22no—
147C2×D44—24no—
148C2×C4×D11—24no—
149C2×C4×D11—24no—
150C2×C4×D11—21no—
151C2×C4×D11—21no—
152C2×C4×D11—22no—
153C2×C4×D11—22no—
154C2×C4×D11—22no—
155C2×C4×D11—22no—
156C2×C4×D11C22⋊C414yes—
157C2×C4×D11C22⋊C414yes—
158C2×C4×D11C2×D412yes—
159C2×C4×D11C2×D412yes—
160C2×Dic22—22no—
161C2×Dic22—24no—
162C2×C8×C11—22no—
163C2×C8×C11—22no—
164C2×C8×C11—22no—
165C2×C8×C11—22no—
166C2×C8×C11—22no—
167C2×C8×C11#4114yes—
168C11×C4⋊C4—22no—
169C11×C4⋊C4—22no—
170C11×C22⋊C4—22no—
171C11×C22⋊C4—22no—
172C42×C11—21no—
173C42×C11—21no—
174C42×C11C2×D412yes—
175C42×C11C2×D412yes—
176C22⋊Dic11—22no—
177C22⋊Dic11—22no—
178(C2×D11)⋊C4—22no—
179(C2×D11)⋊C4—22no—
180(C2×D11)⋊C4—22no—
181(C2×D11)⋊C4—22no—
182(C2×D11)⋊C4—22no—
183(C2×D11)⋊C4—22no—
184C4⋊Dic11—22no—
185C4⋊Dic11—22no—
186Dic11⋊C4—22no—
187Dic11⋊C4—22no—
188Dic11⋊C4—22no—
189Dic11⋊C4—22no—
190Dic11⋊C4—22no—
191Dic11⋊C4—22no—
192C4×Dic11—21no—
193C4×Dic11—21no—
194C4×Dic11C22⋊C414yes—
195C4×Dic11C22⋊C414yes—
196C4×Dic11C2×D412yes—
197C4×Dic11C2×D412yes—
198C2×C11⋊C8—22no—
199C2×C11⋊C8—22no—
200C2×C11⋊C8—22no—
201C2×C11⋊C8—22no—
202C2×C11⋊C8—22no—
203C2×C11⋊C8#4114yes—
204C8×D11—216no—
205C2×#529—111no—
206C2×#432—111no—
207C22×C4×C8—111no—
208#1984—112no—
209#1954—112no—
210#1869—112no—
211#1869—112no—
212#1750—111no—
213#1750—111no—
214#1750—111no—
215#1750D1111yescharacteristic, complemented
216C23×C11—21no—
217C23×C11—21no—
218C23×C11—21no—
219C23×C11—22no—
220C23×C11—22no—
221C23×C11C23×C411yescharacteristic
222C22×D11—21no—
223C22×D11—21no—
224C22×D11—22no—
225C22×D11—21no—
226C22×D11—21no—
227C22×D11—21no—
228C22×D11—22no—
229C22×D11—22no—
230C22×D11C2×C22⋊C412yes—
231C22×D11#13114yes—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—42no—
242C2×C4×C11—42no—
243C2×C4×C11C2×C22⋊C412yes—
244C2×C4×C11C2×C22⋊C412yes—
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C22×D411yescharacteristic
247C2×C4×C11C2×#4112yes—
248C2×C4×C11C2×#4112yes—
249C22⋊D11—44no—
250C22⋊D11—44no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11—22no—
254C2×Dic11—21no—
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11—21no—
259C2×Dic11—22no—
260C2×Dic11—22no—
261C2×Dic11C2×C22⋊C412yes—
262C2×Dic11C2×C22⋊C412yes—
263C2×Dic11C2×C22⋊C412yes—
264C2×Dic11#13114yes—
265D44—44no—
266C4×D11—28no—
267C4×D11—24no—
268C4×D11—24no—
269C4×D11—28no—
270C4×D11—42no—
271C4×D11—42no—
272Dic22—44no—
273C8×C11—24no—
274C8×C11—42no—
275C11⋊C8—24no—
276C11⋊C8—42no—
277C23×C8—112no—
278#529—224no—
279#529—224no—
280C2×#126—111no—
281C2×#126—111no—
282C2×#125—111no—
283C2×#124—111no—
284C2×#123—111no—
285C2×#123—111no—
286C2×C22⋊Q8—111no—
287C2×#121—111no—
288C2×C4×Q8—111no—
289C2×C4×D4—111no—
290C2×C4×D4—111no—
291C2×C4×D4—111no—
292C2×#117—111no—
293C2×#117C2×D1111yescharacteristic
294C22×C42—111no—
295#432—224no—
296C2×C4⋊C8—112no—
297C2×C22⋊C8—112no—
298C2×C22⋊C8—112no—
299C2×C22⋊C8—112no—
300C2×C22⋊C8—112no—
301C2×C22⋊C8C2×D1112yes—
302C2×#97—111no—
303C2×#97C2×D1111yescharacteristic
304C2×C4×C8—112no—
305C2×C4×C8—111no—
306C2×C4×C8—224no—
307C2×C4×C8C2×D1111yescharacteristic
308#336—112no—
309#336—112no—
310#336—112no—
311#336C2×D1112yes—
312C22×C11—41no—
313C22×C11—41no—
314C22×C11—42no—
315C22×C11—42no—
316C22×C11—41no—
317C22×C11C22×C22⋊C411yescharacteristic
318C22×C11C4×#4111yescharacteristic
319C22×C11C4×#4111yescharacteristic
320C22×C11C2×#13112yes—
321C22×C11C2×#13112yes—
322C2×D11—22no—
323C2×D11—24no—
324C2×D11—24no—
325C2×D11—22no—
326C2×D11—41no—
327C2×D11—41no—
328C2×D11—42no—
329C2×D11—42no—
330C2×D11—41no—
331C2×D11#40814yes—
332C4×C11—22no—
333C4×C11—22no—
334C4×C11—41no—
335C4×C11—41no—
336C4×C11—41no—
337C4×C11#52512yes—
338C4×C11#53212yes—
339Dic11—22no—
340Dic11—22no—
341Dic11—41no—
342Dic11—41no—
343Dic11—41no—
344Dic11#40814yes—
345C22×Q8—111no—
346C22×D4—111no—
347C22×D4—111no—
348C22×D4—111no—
349C23×C4—111no—
350C23×C4—111no—
351C23×C4—111no—
352C23×C4—111no—
353C23×C4C22×D1111yescharacteristic
354C22×C8—112no—
355C22×C8—112no—
356C22×C8—224no—
357C22×C8—224no—
358C22×C8—224no—
359C22×C8C22×D1112yes—
360C22×C8C22×D1112yes—
361#126—224no—
362#126—224no—
363#125—224no—
364#124—224no—
365#123—224no—
366#123—224no—
367C22⋊Q8—224no—
368#121—224no—
369C4×Q8—222no—
370C4×Q8—222no—
371C4×D4—222no—
372C4×D4—222no—
373C4×D4—222no—
374C4×D4—222no—
375C4×D4—222no—
376C4×D4—222no—
377#117—22no—
378#117—22no—
379#117—222no—
380#117—222no—
381C2×C4⋊C4—111no—
382C2×C4⋊C4—111no—
383C2×C4⋊C4—111no—
384C2×C4⋊C4—111no—
385C2×C4⋊C4—111no—
386C2×C4⋊C4—111no—
387C2×C4⋊C4—111no—
388C2×C4⋊C4—111no—
389C2×C4⋊C4C4×D1111yescharacteristic
390C2×C4⋊C4C4×D1111yescharacteristic
391C2×C22⋊C4—111no—
392C2×C22⋊C4—111no—
393C2×C22⋊C4—111no—
394C2×C22⋊C4—111no—
395C2×C22⋊C4—111no—
396C2×C22⋊C4—111no—
397C2×C22⋊C4—111no—
398C2×C22⋊C4—111no—
399C2×C22⋊C4C4×D1111yescharacteristic
400C2×C22⋊C4C4×D1111yescharacteristic
401C2×C42—111no—
402C2×C42—111no—
403C2×C42—111no—
404C2×C42—114no—
405C2×C42—114no—
406C2×C42—111no—
407C2×C42C22×D1111yescharacteristic
408C2×C42C22×D1111yescharacteristic
409C4⋊C8—224no—
410C22⋊C8—24no—
411C22⋊C8—224no—
412C22⋊C8—224no—
413C22⋊C8—224no—
414C22⋊C8—224no—
415#97—22no—
416#97—222no—
417C4×C8—22no—
418C4×C8—224no—
419C4×C8—222no—
420C2×C11—81no—
421C2×C11#229711yescharacteristic
422C2×C11C2×#40811yescharacteristic
423C2×C11C2×#40811yescharacteristic
424C2×C11#296612yes—
425C2×C11#296612yes—
426D11—24no—
427D11—81no—
428C24—111no—
429C24—111no—
430C24C2×C4×D1111yescharacteristic
431C2×Q8—222no—
432C2×Q8—224no—
433C2×D4—222no—
434C2×D4—224no—
435C2×D4—222no—
436C2×D4—224no—
437C2×D4—222no—
438C2×D4—224no—
439C22×C4—22no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—111no—
444C22×C4—111no—
445C22×C4—111no—
446C22×C4—114no—
447C22×C4—114no—
448C22×C4—112no—
449C22×C4—112no—
450C22×C4—111no—
451C22×C4—111no—
452C22×C4—111no—
453C22×C4—224no—
454C22×C4—224no—
455C22×C4—222no—
456C22×C4—222no—
457C22×C4—222no—
458C22×C4—221no—
459C22×C4—221no—
460C22×C4—222no—
461C22×C4C2×C4×D1111yescharacteristic
462C22×C4C2×C4×D1111yescharacteristic
463C22×C4C2×C4×D1111yescharacteristic
464C22×C4C2×C4×D1111yescharacteristic
465C22×C4C2×C4×D1111yescharacteristic
466C22×C4C23×D1111yescharacteristic
467C2×C8—22no—
468C2×C8—22no—
469C2×C8—22no—
470C2×C8—22no—
471C2×C8—22no—
472C2×C8—114no—
473C2×C8—2216no—
474C2×C8—222no—
475C2×C8—222no—
476C2×C8—222no—
477C2×C8—222no—
478C2×C8—222no—
479C2×C8#433914yes—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—222no—
483C4⋊C4—222no—
484C4⋊C4—222no—
485C4⋊C4—222no—
486C4⋊C4—222no—
487C4⋊C4—222no—
488C4⋊C4—222no—
489C4⋊C4—222no—
490C22⋊C4—22no—
491C22⋊C4—22no—
492C22⋊C4—222no—
493C22⋊C4—222no—
494C22⋊C4—222no—
495C22⋊C4—222no—
496C22⋊C4—222no—
497C22⋊C4—222no—
498C22⋊C4—222no—
499C22⋊C4—222no—
500C42—21no—
501C42—21no—
502C42—114no—
503C42—114no—
504C42—112no—
505C42—112no—
506C42—221no—
507C42—221no—
508C42D4×D1112yes—
509C42D4×D1112yes—
510C11#2137511yescharacteristic, complemented, Sylow
511C23—21no—
512C23—21no—
513C23—22no—
514C23—22no—
515C23—21no—
516C23—112no—
517C23—114no—
518C23—221no—
519C23—222no—
520C23—221no—
521C23—221no—
522C23—221no—
523C23—222no—
524C23—222no—
525C23—221no—
526C23C22×C4×D1111yescharacteristic
527Q8—444no—
528D4—444no—
529D4—444no—
530D4—444no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—21no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—112no—
543C2×C4—114no—
544C2×C4—112no—
545C2×C4—112no—
546C2×C4—228no—
547C2×C4—228no—
548C2×C4—221no—
549C2×C4—222no—
550C2×C4—221no—
551C2×C4—224no—
552C2×C4—224no—
553C2×C4—221no—
554C2×C4—221no—
555C2×C4—221no—
556C2×C4—221no—
557C2×C4—222no—
558C2×C4—222no—
559C2×C4—221no—
560C2×C4—442no—
561C2×C4—442no—
562C2×C4C22⋊C4×D1112yes—
563C2×C4C22⋊C4×D1112yes—
564C2×C4C2×#433912yes—
565C2×C4C2×D4×D1111yescharacteristic
566C2×C4C2×D4×D1111yescharacteristic
567C2×C4#41×D1112yes—
568C8—24no—
569C8—42no—
570C8—224no—
571C8—442no—
572C22—41no—
573C22—41no—
574C22—42no—
575C22—42no—
576C22—41no—
577C22—114no—
578C22—222no—
579C22—224no—
580C22—224no—
581C22—222no—
582C22—441no—
583C22—441no—
584C22—442no—
585C22—442no—
586C22—441no—
587C22C4×#433911yescharacteristic
588C22C2×C22⋊C4×D1111yescharacteristic
589C22#1062305311yescharacteristic
590C22D11×#13112yes—
591C22D11×#13112yes—
592C4—22no—
593C4—22no—
594C4—41no—
595C4—41no—
596C4—41no—
597C4—114no—
598C4—222no—
599C4—222no—
600C4—441no—
601C4—441no—
602C4—441no—
603C4#1062307812yes—
604C4#1062307912yes—
605C2—81no—
606C2—224no—
607C2—881no—
608C2#1307110211yescharacteristic
609C2D11×#40811yescharacteristic
610C2D11×#40811yescharacteristic
611C2#1307758712yes—
612C2#1307758912yes—
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1750C2
prime radicalC2×#66937C4
cosocleC22×C4×C11C24
hypercenter#1750D11
hypocenterC11#21375
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1750

Complements

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

NH ≅ G/Ntype
2. C2×#10622318C2semidirect
3. C2×C4×C8×D11C2semidirect
4. #13069550C2semidirect
5. #13069408C2semidirect
6. #13068907C2semidirect
7. #13068905C2semidirect
8. #13068385C2semidirect
9. #13068383C2semidirect
10. #13068382C2semidirect
11. C11×#1750C2semidirect
215. #1750D11semidirect
510. C11#21375semidirect

Maximal subgroups

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

subgroupindex
C2×#106230592
C2×#106223182
C2×C4×C8×D112
#130695502
#130694082
#130689072
#130689052
#130683852
#130683832
#130683822
C11×#17502
#2137511