Finite Group Databasebeta

← #14920620

Subgroups — #14920620

Order 2816.

2934 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623010C211yesmaximal, characteristic, complemented
2#13074511C214yesmaximal, complemented
3#13074484C212yesmaximal, complemented
4#13074468C212yesmaximal, complemented
5#13074421C212yesmaximal, complemented
6#13074396C212yesmaximal, complemented
7#13074350C212yesmaximal, complemented
8#13074328C212yesmaximal, complemented
9#13071900C212yesmaximal, complemented
10#13071895C212yesmaximal, complemented
11#13071854C214yesmaximal, complemented
12C4×#67006C214yesmaximal, complemented
13#13071014C211yesmaximal, characteristic, complemented
14C22×C4×D4×C11C211yesmaximal, characteristic, complemented
15C23×D4×C11C2211yescharacteristic
16C24×C4×C11C2212yes—
17C2×C4×D4×C11—28no—
18C2×C4×D4×C11C2212yes—
19C2×C4×D4×C11C2212yes—
20C2×C4×D4×C11C2212yes—
21C2×C4×D4×C11C2212yes—
22C22×C11×C4⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2212yes—
24C22×C42×C11C2211yescharacteristic
25C2×#67006C2214yes—
26C2×#66983C2211yescharacteristic
27C2×#66982C2212yes—
28C2×C4×C22⋊D11C2212yes—
29C2×C4×C22⋊D11C2218yescomplemented
30C2×#66977C2211yescharacteristic
31#10623010—28no—
32C2×#66929C2212yescomplemented
33C2×#66928C2211yescharacteristic, complemented
34C2×C4×D44C2211yescharacteristic, complemented
35C2×#66925C2212yescomplemented
36C2×#66923C2211yescharacteristic, complemented
37C2×C4×Dic22C2211yescharacteristic, complemented
38#10622860C2214yes—
39#10622836C2214yes—
40#10622836C2214yes—
41#10622835C2214yes—
42#10622835C2214yes—
43#10622826C2214yes—
44#10622826C2218yescomplemented
45#10622825C2212yes—
46#10622824C2212yes—
47#10622823C2214yes—
48#10622823C2218yescomplemented
49C4×C22⋊Dic11C2212yes—
50C4×C22⋊Dic11C2218yescomplemented
51#10622606C2214yescomplemented
52#10622605C2214yescomplemented
53#10622595C2214yescomplemented
54#10622593C2214yescomplemented
55#10622574C2218yescomplemented
56#10622573C2214yescomplemented
57#10622566C2214yescomplemented
58#10622562C2214yescomplemented
59#10622561C2218yescomplemented
60#10622560C2214yescomplemented
61#10622550C2212yescomplemented
62#10622549C2212yescomplemented
63C4×C4⋊Dic11C2212yescomplemented
64#10622545C2212yescomplemented
65C25×C11C2312yes—
66C22×D4×C11—28no—
67C22×D4×C11—24no—
68C22×D4×C11C2312yes—
69C22×D4×C11C2312yes—
70C23×C4×C11—28no—
71C23×C4×C11—48no—
72C23×C4×C11C2314yes—
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2312yes—
76C23×C4×C11C2314yes—
77C23×C4×C11C2311yescharacteristic
78C22×C22⋊D11C2312yes—
79C22×C22⋊D11C2318yes—
80C22×D44C2311yescharacteristic
81C22×C4×D11C2312yes—
82C22×Dic22C2311yescharacteristic
83C4×D4×C11—28no—
84C4×D4×C11—28no—
85C4×D4×C11—28no—
86C4×D4×C11—28no—
87C2×C11×C4⋊C4—24no—
88C2×C11×C4⋊C4C2312yes—
89C2×C11×C4⋊C4C2312yes—
90C2×C11×C22⋊C4—28no—
91C2×C11×C22⋊C4C2314yes—
92C2×C11×C22⋊C4C2314yes—
93C2×C42×C11D418yescomplemented
94C2×C42×C11C2311yescharacteristic
95C2×C42×C11C2311yescharacteristic
96C2×C42×C11C2311yescharacteristic
97C2×C42×C11C2311yescharacteristic
98#67006—216no—
99C2×C22⋊Dic11C2312yes—
100C2×C22⋊Dic11C2318yes—
101C2×C22⋊Dic11C2314yes—
102C2×C22⋊Dic11C2318yes—
103C2×C22⋊Dic11C2318yes—
104#66983—24no—
105#66982—28no—
106C4×C22⋊D11—28no—
107C4×C22⋊D11—416no—
108C2×(C2×D11)⋊C4C2312yes—
109C2×(C2×D11)⋊C4C2312yes—
110C2×(C2×D11)⋊C4C2312yes—
111C2×(C2×D11)⋊C4C2312yes—
112C2×(C2×D11)⋊C4C2318yes—
113C2×C4⋊Dic11C2311yescharacteristic
114C2×C4⋊Dic11C2311yescharacteristic
115C2×C4⋊Dic11C2314yes—
116#66977—24no—
117C2×Dic11⋊C4C2312yes—
118C2×Dic11⋊C4C2312yes—
119C2×Dic11⋊C4C2312yes—
120C2×Dic11⋊C4C2312yes—
121C2×Dic11⋊C4C2318yes—
122C2×C4×Dic11C2312yes—
123C2×C4×Dic11C2314yes—
124#66929—28no—
125#66928—24no—
126C4×D44—24no—
127#66925—28no—
128#66923—24no—
129C4×Dic22—24no—
130C11⋊#95C2314yes—
131C11⋊#95C2314yes—
132C11⋊#95C2314yes—
133C11⋊#95C2314yes—
134C11⋊#95C2318yes—
135C11⋊#95C2318yes—
136#34593—111nomaximal, Sylow
137C24×C11—24no—
138C24×C11—24no—
139C24×C11—44no—
140C24×C11—44no—
141C24×C11#4118yes—
142C24×C11C2414yes—
143C24×C11C2411yescharacteristic
144C23×D11C2412yes—
145C2×D4×C11—232no—
146C2×D4×C11—28no—
147C2×D4×C11—28no—
148C2×D4×C11—24no—
149C2×D4×C11—24no—
150C22×C4×C11—24no—
151C22×C4×C11—24no—
152C22×C4×C11—24no—
153C22×C4×C11—28no—
154C22×C4×C11—28no—
155C22×C4×C11—216no—
156C22×C4×C11—48no—
157C22×C4×C11—44no—
158C22×C4×C11—42no—
159C22×C4×C11—432no—
160C22×C4×C11C2×D414yes—
161C22×C4×C11C2×D414yes—
162C22×C4×C11C2×D414yes—
163C22×C4×C11C2414yes—
164C22×C4×C11C2411yescharacteristic
165C22×C4×C11C2411yescharacteristic
166C22×C4×C11C2411yescharacteristic
167C22×C4×C11C2411yescharacteristic
168C22×C4×C11C2411yescharacteristic
169C22×C4×C11C2411yescharacteristic
170C2×C22⋊D11—24no—
171C2×C22⋊D11—216no—
172C2×C22⋊D11—28no—
173C2×C22⋊D11—48no—
174C2×C22⋊D11—48no—
175C22×Dic11C2418yes—
176C22×Dic11C2412yes—
177C22×Dic11C2412yes—
178C22×Dic11C2412yes—
179C2×D44—22no—
180C2×D44—42no—
181C2×C4×D11—24no—
182C2×C4×D11—28no—
183C2×Dic22—22no—
184C2×Dic22—42no—
185C11×C4⋊C4—24no—
186C11×C4⋊C4—24no—
187C11×C22⋊C4—28no—
188C11×C22⋊C4—28no—
189C42×C11C2×D414yes—
190C42×C11C2×D414yes—
191C42×C11C2×D414yes—
192C42×C11C2×D414yes—
193C22⋊Dic11—24no—
194C22⋊Dic11—216no—
195C22⋊Dic11—28no—
196C22⋊Dic11—48no—
197C22⋊Dic11—48no—
198(C2×D11)⋊C4—24no—
199(C2×D11)⋊C4—24no—
200(C2×D11)⋊C4—24no—
201(C2×D11)⋊C4—24no—
202(C2×D11)⋊C4—48no—
203C4⋊Dic11—22no—
204C4⋊Dic11—22no—
205C4⋊Dic11—44no—
206Dic11⋊C4—24no—
207Dic11⋊C4—24no—
208Dic11⋊C4—24no—
209Dic11⋊C4—24no—
210Dic11⋊C4—48no—
211C4×Dic11—24no—
212C4×Dic11—28no—
213C2×#529—111no—
214C22×C4×D4D1111yescharacteristic, complemented
215#2636—114no—
216#2633—112no—
217#2631—112no—
218#2626—112no—
219#2623—112no—
220#2617—112no—
221#2613—112no—
222#2398—112no—
223#2397—112no—
224#2392—114no—
225C4×#120—114no—
226#2283—111no—
227C23×C11—22no—
228C23×C11—22no—
229C23×C11—216no—
230C23×C11—24no—
231C23×C11—24no—
232C23×C11—28no—
233C23×C11—28no—
234C23×C11—416no—
235C23×C11—48no—
236C23×C11—48no—
237C23×C11—416no—
238C23×C11C22×D412yes—
239C23×C11C2×#4118yes—
240C23×C11C2×#4114yes—
241C23×C11C2511yescharacteristic
242C22×D11—22no—
243C22×D11—24no—
244C22×D11—24no—
245C22×D11—24no—
246D4×C11—216no—
247D4×C11—216no—
248C2×C4×C11—28no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—28no—
255C2×C4×C11—24no—
256C2×C4×C11—28no—
257C2×C4×C11—44no—
258C2×C4×C11—416no—
259C2×C4×C11—48no—
260C2×C4×C11—416no—
261C2×C4×C11C22×D412yes—
262C2×C4×C11C22×D412yes—
263C2×C4×C11C22×D412yes—
264C2×C4×C11C22×D412yes—
265C2×C4×C11C22×D412yes—
266C2×C4×C11C22×D412yes—
267C2×C4×C11H(5,𝔽2)14yes—
268C22⋊D11—432no—
269C22⋊D11—48no—
270C2×Dic11—22no—
271C2×Dic11—22no—
272C2×Dic11—22no—
273C2×Dic11—24no—
274C2×Dic11—28no—
275C2×Dic11—28no—
276C2×Dic11—24no—
277C2×Dic11—28no—
278C2×Dic11—24no—
279D44—44no—
280C4×D11—48no—
281Dic22—44no—
282C23×D4C2×D1111yescharacteristic
283C24×C4C2×D1112yes—
284#529—228no—
285C2×#126—112no—
286C2×#125—111no—
287C2×#124—111no—
288C2×#123—112no—
289C2×C22⋊Q8—111no—
290C2×#121—111no—
291C2×#120—114no—
292C2×C4×Q8—111no—
293C2×C4×D4—28no—
294C2×C4×D4—112no—
295C2×C4×D4—118no—
296C2×C4×D4—111no—
297C2×C4×D4C2×D1112yes—
298C2×C4×D4C2×D1112yes—
299C2×C4×D4C2×D1112yes—
300C2×C4×D4C2×D1112yes—
301C2×#117—112no—
302C22×C4⋊C4C2×D1111yescharacteristic
303C22×C22⋊C4C2×D1112yes—
304C22×C42C2×D1111yescharacteristic
305#400—114no—
306#399—114no—
307#399—114no—
308#398—114no—
309#397—114no—
310#397—114no—
311#396—118no—
312#394—114no—
313#394—114no—
314#394—118no—
315#393—114no—
316#392—114no—
317#392—114no—
318#392—114no—
319#386—114no—
320#386—118no—
321#385—114no—
322#385—118no—
323#383—112no—
324#382—112no—
325#381—112no—
326#380—112no—
327#379—114no—
328C4×C4⋊C4—112no—
329C4×C22⋊C4—118no—
330C4×C22⋊C4—112no—
331#376—112no—
332C22×C11—22no—
333C22×C11—22no—
334C22×C11—28no—
335C22×C11—28no—
336C22×C11—216no—
337C22×C11—432no—
338C22×C11—44no—
339C22×C11—44no—
340C22×C11—48no—
341C22×C11#52514yes—
342C22×C11C23×D411yescharacteristic
343C22×C11C22×#4112yes—
344C22×C11C2×H(5,𝔽2)12yes—
345C22×C11#58512yes—
346C2×D11—42no—
347C2×D11—42no—
348C2×D11—42no—
349C2×D11—48no—
350C4×C11—22no—
351C4×C11—22no—
352C4×C11—22no—
353C4×C11—22no—
354C4×C11—22no—
355C4×C11—44no—
356C4×C11#53514yes—
357Dic11—42no—
358Dic11—42no—
359Dic11—42no—
360Dic11—48no—
361C25C22×D1112yes—
362C22×Q8—111no—
363C22×D4—28no—
364C22×D4—24no—
365C22×D4—112no—
366C22×D4—118no—
367C22×D4—111no—
368C22×D4C22×D1112yes—
369C22×D4C22×D1112yes—
370C23×C4—28no—
371C23×C4—48no—
372C23×C4—112no—
373C23×C4C22×D1114yes—
374C23×C4C22×D1111yescharacteristic
375C23×C4C22×D1111yescharacteristic
376C23×C4C22×D1112yes—
377C23×C4C22×D1114yes—
378C23×C4C22×D1111yescharacteristic
379#126—228no—
380#125—224no—
381#124—224no—
382#123—228no—
383C22⋊Q8—224no—
384#121—224no—
385#120—2216no—
386C4×Q8—224no—
387C4×D4—28no—
388C4×D4—28no—
389C4×D4—28no—
390C4×D4—28no—
391C4×D4—228no—
392C4×D4—224no—
393C4×D4—4416no—
394#117—228no—
395C2×C4⋊C4—24no—
396C2×C4⋊C4—112no—
397C2×C4⋊C4—112no—
398C2×C4⋊C4—111no—
399C2×C4⋊C4—112no—
400C2×C4⋊C4—111no—
401C2×C4⋊C4—112no—
402C2×C4⋊C4—118no—
403C2×C4⋊C4—114no—
404C2×C4⋊C4C22×D1112yes—
405C2×C4⋊C4C22×D1112yes—
406C2×C22⋊C4—28no—
407C2×C22⋊C4—112no—
408C2×C22⋊C4—114no—
409C2×C22⋊C4—118no—
410C2×C22⋊C4—112no—
411C2×C22⋊C4—112no—
412C2×C22⋊C4—112no—
413C2×C22⋊C4—112no—
414C2×C22⋊C4—118no—
415C2×C22⋊C4—118no—
416C2×C22⋊C4—118no—
417C2×C22⋊C4C22×D1114yes—
418C2×C22⋊C4C22×D1114yes—
419C2×C42—112no—
420C2×C42—114no—
421C2×C42C22⋊D1118yescomplemented
422C2×C42C22×D1111yescharacteristic
423C2×C42C22×D1111yescharacteristic
424C2×C42C22×D1111yescharacteristic
425C2×C42C22×D1111yescharacteristic
426#95—114no—
427#95—114no—
428#95—114no—
429#95—118no—
430#95—118no—
431#95—114no—
432C2×C11—24no—
433C2×C11—48no—
434C2×C11C2×#52511yescharacteristic
435C2×C11C2×#53511yescharacteristic
436C2×C11#344911yescharacteristic
437C2×C11#345914yes—
438D11—82no—
439C24—24no—
440C24—24no—
441C24—44no—
442C24—44no—
443C24—112no—
444C24#433918yes—
445C24C23×D1114yes—
446C24C23×D1111yescharacteristic
447C2×Q8—222no—
448C2×Q8—442no—
449C2×D4—232no—
450C2×D4—28no—
451C2×D4—28no—
452C2×D4—24no—
453C2×D4—24no—
454C2×D4—2216no—
455C2×D4—228no—
456C2×D4—224no—
457C2×D4—222no—
458C2×D4—442no—
459C2×D4—448no—
460C2×D4—448no—
461C22×C4—24no—
462C22×C4—24no—
463C22×C4—24no—
464C22×C4—216no—
465C22×C4—28no—
466C22×C4—28no—
467C22×C4—48no—
468C22×C4—44no—
469C22×C4—42no—
470C22×C4—432no—
471C22×C4—118no—
472C22×C4—112no—
473C22×C4—112no—
474C22×C4—112no—
475C22×C4—228no—
476C22×C4—224no—
477C22×C4C2×C22⋊D1114yes—
478C22×C4C2×C22⋊D1114yes—
479C22×C4C2×C22⋊D1114yes—
480C22×C4C23×D1114yes—
481C22×C4C23×D1111yescharacteristic
482C22×C4C23×D1111yescharacteristic
483C22×C4C23×D1111yescharacteristic
484C22×C4C23×D1111yescharacteristic
485C22×C4C23×D1111yescharacteristic
486C22×C4C23×D1111yescharacteristic
487C4⋊C4—24no—
488C4⋊C4—24no—
489C4⋊C4—224no—
490C4⋊C4—224no—
491C4⋊C4—222no—
492C4⋊C4—224no—
493C4⋊C4—222no—
494C4⋊C4—224no—
495C4⋊C4—448no—
496C4⋊C4—444no—
497C22⋊C4—28no—
498C22⋊C4—28no—
499C22⋊C4—2216no—
500C22⋊C4—228no—
501C22⋊C4—224no—
502C22⋊C4—224no—
503C22⋊C4—224no—
504C22⋊C4—224no—
505C22⋊C4—224no—
506C22⋊C4—448no—
507C22⋊C4—448no—
508C22⋊C4—448no—
509C42—228no—
510C42—224no—
511C42C2×C22⋊D1114yes—
512C42C2×C22⋊D1114yes—
513C42C2×C22⋊D1114yes—
514C42C2×C22⋊D1114yes—
515C11#3459311yescharacteristic, complemented, Sylow
516C23—22no—
517C23—22no—
518C23—216no—
519C23—24no—
520C23—28no—
521C23—28no—
522C23—24no—
523C23—416no—
524C23—48no—
525C23—48no—
526C23—416no—
527C23—224no—
528C23—224no—
529C23—224no—
530C23—222no—
531C23C2×#433918yes—
532C23C2×#433914yes—
533C23C22×C22⋊D1112yes—
534C23C24×D1111yescharacteristic
535Q8—444no—
536D4—216no—
537D4—216no—
538D4—444no—
539D4—4432no—
540D4—448no—
541C2×C4—28no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—28no—
548C2×C4—28no—
549C2×C4—24no—
550C2×C4—44no—
551C2×C4—416no—
552C2×C4—48no—
553C2×C4—416no—
554C2×C4—224no—
555C2×C4—228no—
556C2×C4—228no—
557C2×C4—224no—
558C2×C4—224no—
559C2×C4—228no—
560C2×C4—222no—
561C2×C4—222no—
562C2×C4—222no—
563C2×C4—448no—
564C2×C4#6703714yes—
565C2×C4C22×C22⋊D1112yes—
566C2×C4C22×C22⋊D1112yes—
567C2×C4C22×C22⋊D1112yes—
568C2×C4C22×C22⋊D1112yes—
569C2×C4C22×C22⋊D1112yes—
570C2×C4C22×C22⋊D1112yes—
571C22—22no—
572C22—22no—
573C22—28no—
574C22—28no—
575C22—216no—
576C22—432no—
577C22—44no—
578C22—44no—
579C22—48no—
580C22—442no—
581C22—442no—
582C22—442no—
583C22—448no—
584C22#1062332214yes—
585C22C22×#433912yes—
586C22C2×#6703712yes—
587C22#1062345312yes—
588C22C23×C22⋊D1111yescharacteristic
589C4—22no—
590C4—22no—
591C4—22no—
592C4—22no—
593C4—22no—
594C4—44no—
595C4—442no—
596C4—442no—
597C4—442no—
598C4—448no—
599C4#1062333614yes—
600C2—24no—
601C2—48no—
602C2—882no—
603C2C2×#1062332211yescharacteristic
604C2C2×#1062333611yescharacteristic
605C2#1308194511yescharacteristic
606C2#1308202514yes—
subgroupG/H
centerC22×C4C23×D11
commutator, socle, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C4×D4×C11C2
hypercenterC22×C4×D4D11
hypocenterC11#34593
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#10623010C2semidirect
2. #13074511C2semidirect
3. #13074484C2semidirect
4. #13074468C2semidirect
5. #13074421C2semidirect
6. #13074396C2semidirect
7. #13074350C2semidirect
8. #13074328C2semidirect
9. #13071900C2semidirect
10. #13071895C2semidirect
11. #13071854C2semidirect
12. C4×#67006C2semidirect
13. #13071014C2semidirect
14. C22×C4×D4×C11C2semidirect
29. C2×C4×C22⋊D11C22semidirect
32. C2×#66929C22semidirect
33. C2×#66928C22semidirect
34. C2×C4×D44C22semidirect
35. C2×#66925C22semidirect
36. C2×#66923C22semidirect
37. C2×C4×Dic22C22semidirect
44. #10622826C22semidirect
48. #10622823C22semidirect
50. C4×C22⋊Dic11C22semidirect
51. #10622606C22semidirect
52. #10622605C22semidirect
53. #10622595C22semidirect
54. #10622593C22semidirect
55. #10622574C22semidirect
56. #10622573C22semidirect
57. #10622566C22semidirect
58. #10622562C22semidirect
59. #10622561C22semidirect
60. #10622560C22semidirect
61. #10622550C22semidirect
62. #10622549C22semidirect
63. C4×C4⋊Dic11C22semidirect
64. #10622545C22semidirect
93. C2×C42×C11D4semidirect
214. C22×C4×D4D11semidirect
421. C2×C42C22⋊D11semidirect
515. C11#34593semidirect

Maximal subgroups

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

subgroupindex
C2×#106230102
#130745112
#130744842
#130744682
#130744212
#130743962
#130743502
#130743282
#130719002
#130718952
#130718542
C4×#670062
#130710142
C22×C4×D4×C112
#3459311