Finite Group Databasebeta

← #14960475

Subgroups — #14960475

Order 2816.

1958 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623219C211yesmaximal, characteristic, complemented
2C2×#10623222C211yesmaximal, characteristic
3#13076683C211yesmaximal, characteristic, complemented
4#13076681C212yesmaximal, complemented
5#13076676C212yesmaximal, complemented
6#13076668C211yesmaximal, characteristic, complemented
7#13076666C211yesmaximal, characteristic, complemented
8#13076652C212yesmaximal, complemented
9#13076649C212yesmaximal
10#13076636C214yesmaximal, complemented
11#13071908C212yesmaximal, complemented
12#13071905C212yesmaximal, complemented
13#13071893C214yesmaximal, complemented
14#13071882C212yesmaximal, complemented
15#13071880C212yesmaximal, complemented
16#13071009C211yesmaximal, characteristic, complemented
17C11×#2822C211yesmaximal, characteristic, complemented
18C2×C11×#125C2211yescharacteristic
19C2×C11×#125C2211yescharacteristic
20#10623222—28no—
21#10623219—28no—
22C2×#66951C2212yes—
23C2×#66950C2211yescharacteristic
24C2×#66949C2212yes—
25C2×#66949C2212yes—
26C2×#66948C2211yescharacteristic
27C2×#66947C2212yes—
28C2×#66946C2212yes—
29C2×#66946C2211yescharacteristic
30C2×#66945C2211yescharacteristic
31C2×#66945C2211yescharacteristic
32C2×#66945C2212yes—
33C2×#66941C2211yescharacteristic
34C2×#66941C2211yescharacteristic
35C2×#66940C2212yes—
36C2×#66940C2211yescharacteristic
37C2×#66940C2212yes—
38C2×#66928C2211yescharacteristic
39C2×C42×D11C2211yescharacteristic
40C2×#66923C2211yescharacteristic
41C11×#400C2212yes—
42C11×#400C2212yes—
43C11×#398C2212yes—
44C11×#398C2214yes—
45C11×#398C2212yes—
46C11×#382C2211yescharacteristic
47#10622607C2214yes—
48#10622607C2214yes—
49#10622606C2212yes—
50#10622605C2212yes—
51#10622605C2214yes—
52#10622604C2214yes—
53#10622604C2212yes—
54#10622600C2212yes—
55#10622599C2212yes—
56#10622597C2214yes—
57#10622596C2212yes—
58#10622595C2212yes—
59#10622593C2212yes—
60#10622592C2214yes—
61#10622592C2212yes—
62C4⋊C4×Dic11C2214yes—
63C4⋊C4×Dic11C2212yes—
64#10622549C2211yescharacteristic
65#10622290C2212yes—
66#10622288C2214yes—
67#10622288C2214yes—
68#10622287C2214yes—
69#10622287C2212yes—
70#10622286C2214yes—
71#10622286C2214yes—
72#10622285C2214yes—
73#10622285C2212yes—
74#10622279C2212yes—
75#10622279C2214yes—
76#10622279C2214yes—
77#10622277C2212yes—
78#10622273C2214yes—
79#10622270C2214yes—
80#10622269C2214yes—
81#10622269C2212yes—
82#10622264C2212yes—
83#10622262C2214yes—
84#10622261C2212yes—
85C22×D44C2311yescharacteristic
86C22×D44C2312yes—
87C22×C4×D11C2312yes—
88C22×C4×D11C2311yescharacteristic
89C22×C4×D11C2311yescharacteristic
90C22×C4×D11C2311yescharacteristic
91C22×Dic22C2311yescharacteristic
92C22×Dic22C2312yes—
93C22×Dic22C2312yes—
94C11×#125—24no—
95C11×#125—24no—
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C4⋊C4C2312yes—
98C2×C11×C4⋊C4C2312yes—
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C11×C4⋊C4C2312yes—
102C2×C11×C4⋊C4C2311yescharacteristic
103C2×C11×C4⋊C4C2312yes—
104C2×C11×C4⋊C4C2314yes—
105C2×C11×C4⋊C4C2312yes—
106C2×C42×C11C2311yescharacteristic
107C2×(C2×D11)⋊C4C2312yes—
108C2×(C2×D11)⋊C4C2312yes—
109C2×(C2×D11)⋊C4C2312yes—
110C2×(C2×D11)⋊C4C2312yes—
111C2×(C2×D11)⋊C4C2312yes—
112C2×(C2×D11)⋊C4C2312yes—
113C2×(C2×D11)⋊C4C2312yes—
114C2×(C2×D11)⋊C4C2314yes—
115C2×(C2×D11)⋊C4C2314yes—
116C2×(C2×D11)⋊C4C2314yes—
117C2×(C2×D11)⋊C4C2314yes—
118C2×(C2×D11)⋊C4C2314yes—
119C2×C4⋊Dic11C2311yescharacteristic
120C2×C4⋊Dic11C2311yescharacteristic
121C2×C4⋊Dic11C2312yes—
122C2×C4⋊Dic11C2314yes—
123C2×C4⋊Dic11C2312yes—
124C2×Dic11⋊C4C2312yes—
125C2×Dic11⋊C4C2312yes—
126C2×Dic11⋊C4C2312yes—
127C2×Dic11⋊C4C2312yes—
128C2×Dic11⋊C4C2312yes—
129C2×Dic11⋊C4C2314yes—
130C2×Dic11⋊C4C2314yes—
131C2×C4×Dic11C2312yes—
132C2×C4×Dic11C2312yes—
133C2×C4×Dic11C2312yes—
134C2×C4×Dic11C2314yes—
135C2×C4×Dic11C2311yescharacteristic
136C2×C4×Dic11C2311yescharacteristic
137C2×C4×Dic11C2311yescharacteristic
138#66951—28no—
139#66950—24no—
140#66949—28no—
141#66949—28no—
142#66948—24no—
143#66947—28no—
144#66946—28no—
145#66946—24no—
146#66945—24no—
147#66945—24no—
148#66945—28no—
149#66941—24no—
150#66941—24no—
151#66940—28no—
152#66940—28no—
153#66940—24no—
154#66928—24no—
155C42×D11D418yes—
156#66923—24no—
157C11×#95C2312yes—
158C11×#95C2314yes—
159C11×#95C2312yes—
160C11×#95C2314yes—
161C11×#95C2314yes—
162C11⋊#95C2314yes—
163C11⋊#95C2312yes—
164C11⋊#95C2314yes—
165C11⋊#95C2314yes—
166C11⋊#95C2312yes—
167C11⋊#95C2314yes—
168C11⋊#95C2314yes—
169C11⋊#95C2314yes—
170C11⋊#95C2314yes—
171#36699—111nomaximal, Sylow
172C23×D11C2412yes—
173C23×D11C2411yescharacteristic
174C22×C4×C11C2412yes—
175C22×C4×C11C2414yes—
176C22×C4×C11C2412yes—
177C22×C4×C11C2412yes—
178C22×C4×C11C2412yes—
179C22×C4×C11C2411yescharacteristic
180C22×C4×C11C2411yescharacteristic
181C22×C4×C11C2411yescharacteristic
182C22×Dic11C2414yes—
183C22×Dic11C2412yes—
184C22×Dic11C2412yes—
185C22×Dic11C2412yes—
186C22×Dic11C2411yescharacteristic
187C22×Dic11C2411yescharacteristic
188C22×Dic11C2411yescharacteristic
189C2×D44—24no—
190C2×D44—22no—
191C2×D44—42no—
192C2×D44—42no—
193C2×D44—42no—
194C2×C4×D11—24no—
195C2×C4×D11—24no—
196C2×C4×D11—28no—
197C2×C4×D11—41no—
198C2×C4×D11—41no—
199C2×C4×D11—42no—
200C2×C4×D11C2×D414yes—
201C2×C4×D11C2×D414yes—
202C2×C4×D11C2×D414yes—
203C2×Dic22—24no—
204C2×Dic22—24no—
205C2×Dic22—22no—
206C2×Dic22—42no—
207C2×Dic22—44no—
208C2×Dic22—42no—
209C2×Dic22—42no—
210C11×C4⋊C4—22no—
211C11×C4⋊C4—24no—
212C11×C4⋊C4—24no—
213C11×C4⋊C4—22no—
214C11×C4⋊C4—22no—
215C11×C4⋊C4—24no—
216C11×C4⋊C4—22no—
217C11×C4⋊C4—24no—
218C11×C4⋊C4—42no—
219C11×C4⋊C4—44no—
220C42×C11C2×D414yes—
221(C2×D11)⋊C4—24no—
222(C2×D11)⋊C4—24no—
223(C2×D11)⋊C4—24no—
224(C2×D11)⋊C4—24no—
225(C2×D11)⋊C4—24no—
226(C2×D11)⋊C4—24no—
227(C2×D11)⋊C4—24no—
228(C2×D11)⋊C4—44no—
229(C2×D11)⋊C4—44no—
230(C2×D11)⋊C4—44no—
231(C2×D11)⋊C4—44no—
232(C2×D11)⋊C4—44no—
233C4⋊Dic11—24no—
234C4⋊Dic11—22no—
235C4⋊Dic11—22no—
236C4⋊Dic11—42no—
237C4⋊Dic11—44no—
238Dic11⋊C4—24no—
239Dic11⋊C4—24no—
240Dic11⋊C4—24no—
241Dic11⋊C4—24no—
242Dic11⋊C4—24no—
243Dic11⋊C4—44no—
244Dic11⋊C4—44no—
245C4×Dic11—24no—
246C4×Dic11—24no—
247C4×Dic11—24no—
248C4×Dic11—28no—
249C4×Dic11C2×D414yes—
250C4×Dic11C2×D414yes—
251C4×Dic11C2×D414yes—
252C2×#533—111no—
253C2×#529—111no—
254#2822—111no—
255#2822D1111yescharacteristic, complemented
256#2821—112no—
257#2821—112no—
258#2820—111no—
259#2820—111no—
260#2817—112no—
261#2816—112no—
262#2814—114no—
263#2399—112no—
264#2398—112no—
265#2396—114no—
266#2395—112no—
267#2395—112no—
268#2283—111no—
269C23×C11C2511yescharacteristic
270C22×D11—22no—
271C22×D11—22no—
272C22×D11—21no—
273C22×D11—21no—
274C22×D11—22no—
275C22×D11—24no—
276C22×D11—22no—
277C22×D11—22no—
278C22×D11—24no—
279C22×D11C22×D412yes—
280C2×C4×C11—22no—
281C2×C4×C11—21no—
282C2×C4×C11—21no—
283C2×C4×C11—22no—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—24no—
289C2×C4×C11—24no—
290C2×C4×C11—22no—
291C2×C4×C11—24no—
292C2×C4×C11—24no—
293C2×C4×C11—22no—
294C2×C4×C11—24no—
295C2×C4×C11—22no—
296C2×C4×C11—22no—
297C2×C4×C11C22×D412yes—
298C2×C4×C11C22×D412yes—
299C2×C4×C11C22×D412yes—
300C2×Dic11—21no—
301C2×Dic11—21no—
302C2×Dic11—22no—
303C2×Dic11—22no—
304C2×Dic11—22no—
305C2×Dic11—22no—
306C2×Dic11—24no—
307C2×Dic11—22no—
308C2×Dic11—24no—
309C2×Dic11—24no—
310C2×Dic11—24no—
311C2×Dic11—24no—
312C2×Dic11—22no—
313C2×Dic11C22×D412yes—
314C2×Dic11C22×D412yes—
315C2×Dic11C22×D412yes—
316C2×Dic112−1+414yes—
317D44—44no—
318D44—48no—
319C4×D11—28no—
320C4×D11—44no—
321C4×D11—44no—
322C4×D11—48no—
323Dic22—48no—
324Dic22—48no—
325Dic22—44no—
326#533—228no—
327C2×C4⋊Q8—111no—
328C2×C4⋊Q8—111no—
329#529—228no—
330C2×#126—112no—
331C2×#125—111no—
332C2×#125C2×D1111yescharacteristic
333C2×#125C2×D1111yescharacteristic
334C2×#124—111no—
335C2×#123—112no—
336C2×C22⋊Q8—112no—
337C2×C22⋊Q8—111no—
338C2×C22⋊Q8—112no—
339C2×#121—111no—
340C2×C4×Q8—112no—
341C2×C4×Q8—112no—
342C2×C4×Q8—111no—
343C2×C4×D4—112no—
344C2×C4×D4—111no—
345C2×#117—111no—
346C2×#117—111no—
347C2×#117—112no—
348C22×C42—111no—
349#400—112no—
350#400—112no—
351#400—114no—
352#400C2×D1112yes—
353#400C2×D1112yes—
354#399—114no—
355#399—112no—
356#399—112no—
357#398—112no—
358#398—112no—
359#398—114no—
360#398—114no—
361#398C2×D1112yes—
362#398C2×D1112yes—
363#398C2×D1114yes—
364#397—112no—
365#397—114no—
366#397—114no—
367#397—112no—
368#397—114no—
369#396—114no—
370#396—114no—
371#395—112no—
372#395—114no—
373#395—112no—
374#395—114no—
375#394—112no—
376#394—114no—
377#394—112no—
378#394—114no—
379#393—114no—
380#393—114no—
381#383—112no—
382#382—111no—
383#382C2×D1111yescharacteristic
384#381—112no—
385#380—112no—
386C4×C4⋊C4—114no—
387C4×C4⋊C4—112no—
388C4×C4⋊C4—114no—
389C4×C22⋊C4—112no—
390C4×C22⋊C4—114no—
391C4×C22⋊C4—114no—
392#376—112no—
393C22×C11C23×D411yescharacteristic
394C22×C11C2×2−1+412yes—
395C22×C11#58511yescharacteristic
396C22×C11#58511yescharacteristic
397C22×C11#58512yes—
398C2×D11—22no—
399C2×D11—22no—
400C2×D11—22no—
401C2×D11—42no—
402C2×D11—42no—
403C2×D11—42no—
404C2×D11—42no—
405C2×D11—42no—
406C2×D11—44no—
407C2×D11—44no—
408C4×C11—22no—
409C4×C11—22no—
410C4×C11—22no—
411C4×C11—42no—
412C4×C11—42no—
413C4×C11—42no—
414C4×C11—42no—
415C4×C11—44no—
416Dic11—22no—
417Dic11—22no—
418Dic11—42no—
419Dic11—42no—
420Dic11—42no—
421Dic11—44no—
422Dic11#53614yes—
423C22×Q8—111no—
424C22×Q8—112no—
425C22×Q8—112no—
426C22×D4—112no—
427C22×D4—111no—
428C23×C4—111no—
429C23×C4—111no—
430C23×C4—111no—
431C23×C4—112no—
432C4⋊Q8—224no—
433C4⋊Q8—224no—
434#126—228no—
435#125—24no—
436#125—24no—
437#125—224no—
438#124—224no—
439#123—228no—
440C22⋊Q8—224no—
441C22⋊Q8—228no—
442C22⋊Q8—228no—
443#121—224no—
444C4×Q8—224no—
445C4×Q8—228no—
446C4×Q8—228no—
447C4×D4—224no—
448C4×D4—228no—
449#117—228no—
450#117—224no—
451#117—224no—
452C2×C4⋊C4—112no—
453C2×C4⋊C4—111no—
454C2×C4⋊C4—111no—
455C2×C4⋊C4—112no—
456C2×C4⋊C4—112no—
457C2×C4⋊C4—112no—
458C2×C4⋊C4—112no—
459C2×C4⋊C4—112no—
460C2×C4⋊C4—112no—
461C2×C4⋊C4—114no—
462C2×C4⋊C4—114no—
463C2×C4⋊C4—114no—
464C2×C4⋊C4C22×D1112yes—
465C2×C4⋊C4C22×D1111yescharacteristic
466C2×C4⋊C4C22×D1111yescharacteristic
467C2×C4⋊C4C22×D1111yescharacteristic
468C2×C4⋊C4C22×D1112yes—
469C2×C4⋊C4C22×D1111yescharacteristic
470C2×C4⋊C4C22×D1112yes—
471C2×C4⋊C4C22×D1112yes—
472C2×C4⋊C4C22×D1112yes—
473C2×C4⋊C4C22×D1114yes—
474C2×C22⋊C4—112no—
475C2×C22⋊C4—112no—
476C2×C22⋊C4—112no—
477C2×C22⋊C4—112no—
478C2×C22⋊C4—112no—
479C2×C22⋊C4—112no—
480C2×C22⋊C4—112no—
481C2×C22⋊C4—114no—
482C2×C22⋊C4—114no—
483C2×C22⋊C4—114no—
484C2×C22⋊C4—114no—
485C2×C22⋊C4—114no—
486C2×C42—111no—
487C2×C42—111no—
488C2×C42—111no—
489C2×C42—118no—
490C2×C42—112no—
491C2×C42—112no—
492C2×C42—112no—
493C2×C42—114no—
494C2×C42C22×D1111yescharacteristic
495#95—114no—
496#95—112no—
497#95—112no—
498#95—114no—
499#95—114no—
500#95—114no—
501#95—114no—
502#95—114no—
503#95—114no—
504#95C22×D1112yes—
505#95C22×D1112yes—
506#95C22×D1114yes—
507#95C22×D1114yes—
508#95C22×D1114yes—
509C2×C11C2×#53611yescharacteristic
510C2×C11#344911yescharacteristic
511C2×C11#344911yescharacteristic
512C2×C11#353112yes—
513C2×C11#353112yes—
514D11—42no—
515D11—82no—
516C24—111no—
517C24—112no—
518C2×Q8—224no—
519C2×Q8—224no—
520C2×Q8—222no—
521C2×Q8—442no—
522C2×Q8—442no—
523C2×Q8—442no—
524C2×Q8—444no—
525C2×D4—224no—
526C2×D4—222no—
527C2×D4—442no—
528C2×D4—442no—
529C2×D4—442no—
530C22×C4—111no—
531C22×C4—111no—
532C22×C4—111no—
533C22×C4—114no—
534C22×C4—114no—
535C22×C4—114no—
536C22×C4—114no—
537C22×C4—112no—
538C22×C4—112no—
539C22×C4—112no—
540C22×C4—224no—
541C22×C4—224no—
542C22×C4—228no—
543C22×C4—441no—
544C22×C4—441no—
545C22×C4—442no—
546C22×C4C23×D1112yes—
547C22×C4C23×D1114yes—
548C22×C4C23×D1112yes—
549C22×C4C23×D1112yes—
550C22×C4C23×D1112yes—
551C22×C4C23×D1111yescharacteristic
552C22×C4C23×D1111yescharacteristic
553C22×C4C23×D1111yescharacteristic
554C4⋊C4—24no—
555C4⋊C4—22no—
556C4⋊C4—22no—
557C4⋊C4—22no—
558C4⋊C4—24no—
559C4⋊C4—22no—
560C4⋊C4—24no—
561C4⋊C4—24no—
562C4⋊C4—42no—
563C4⋊C4—44no—
564C4⋊C4—224no—
565C4⋊C4—224no—
566C4⋊C4—224no—
567C4⋊C4—224no—
568C4⋊C4—222no—
569C4⋊C4—222no—
570C4⋊C4—224no—
571C4⋊C4—224no—
572C4⋊C4—444no—
573C4⋊C4—444no—
574C4⋊C4—442no—
575C4⋊C4—444no—
576C22⋊C4—224no—
577C22⋊C4—224no—
578C22⋊C4—224no—
579C22⋊C4—224no—
580C22⋊C4—224no—
581C22⋊C4—224no—
582C22⋊C4—224no—
583C22⋊C4—444no—
584C22⋊C4—444no—
585C22⋊C4—444no—
586C22⋊C4—444no—
587C22⋊C4—444no—
588C42—114no—
589C42—114no—
590C42—114no—
591C42—224no—
592C42—224no—
593C42—224no—
594C42—228no—
595C42D4×D1114yes—
596C11#3669911yescharacteristic, complemented, Sylow
597C23—112no—
598C23—221no—
599C23—222no—
600C23—222no—
601C23—221no—
602C23—222no—
603C23—222no—
604C23—224no—
605C23—222no—
606C23—224no—
607C23C24×D1111yescharacteristic
608Q8—444no—
609Q8—448no—
610Q8—448no—
611D4—444no—
612D4—448no—
613C2×C4—21no—
614C2×C4—22no—
615C2×C4—21no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—24no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—24no—
625C2×C4—24no—
626C2×C4—24no—
627C2×C4—22no—
628C2×C4—24no—
629C2×C4—22no—
630C2×C4—112no—
631C2×C4—114no—
632C2×C4—112no—
633C2×C4—112no—
634C2×C4—228no—
635C2×C4—221no—
636C2×C4—221no—
637C2×C4—222no—
638C2×C4—222no—
639C2×C4—222no—
640C2×C4—222no—
641C2×C4—222no—
642C2×C4—224no—
643C2×C4—224no—
644C2×C4—224no—
645C2×C4—224no—
646C2×C4—222no—
647C2×C4—224no—
648C2×C4—444no—
649C2×C4—444no—
650C2×C4—448no—
651C2×C4C2×D4×D1112yes—
652C2×C4C2×D4×D1112yes—
653C2×C4C2×D4×D1112yes—
654C22—222no—
655C22—222no—
656C22—222no—
657C22—442no—
658C22—442no—
659C22—442no—
660C22—442no—
661C22—442no—
662C22—444no—
663C22—444no—
664C22C22×D4×D1111yescharacteristic
665C22#1062345511yescharacteristic
666C22D11×2−1+412yes—
667C22#1062345711yescharacteristic
668C22#1062345712yes—
669C4—22no—
670C4—22no—
671C4—22no—
672C4—42no—
673C4—42no—
674C4—42no—
675C4—42no—
676C4—44no—
677C4—114no—
678C4—222no—
679C4—222no—
680C4—442no—
681C4—442no—
682C4—442no—
683C4—444no—
684C2—442no—
685C2—882no—
686C2D11×#53611yescharacteristic
687C2#1308194411yescharacteristic
688C2#1308194811yescharacteristic
689C2#1308276212yes—
690C2#1308276412yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2822C2
prime radicalC2×#66948C22
hypercenter#2822D11
hypocenterC11#36699
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2822

Complements

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

NH ≅ G/Ntype
1. C2×#10623219C2semidirect
3. #13076683C2semidirect
4. #13076681C2semidirect
5. #13076676C2semidirect
6. #13076668C2semidirect
7. #13076666C2semidirect
8. #13076652C2semidirect
10. #13076636C2semidirect
11. #13071908C2semidirect
12. #13071905C2semidirect
13. #13071893C2semidirect
14. #13071882C2semidirect
15. #13071880C2semidirect
16. #13071009C2semidirect
17. C11×#2822C2semidirect
255. #2822D11semidirect
596. C11#36699semidirect

Maximal subgroups

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

subgroupindex
C2×#106232192
C2×#106232222
#130766832
#130766812
#130766762
#130766682
#130766662
#130766522
#130766492
#130766362
#130719082
#130719052
#130718932
#130718822
#130718802
#130710092
C11×#28222
#3669911