Finite Group Databasebeta

← #14925776

Subgroups — #14925776

Order 2816.

2834 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×#10623153C211yesmaximal, characteristic, complemented
2C22×#66946C211yesmaximal, characteristic
3#13073788C212yesmaximal, complemented
4#13073778C214yesmaximal, complemented
5#13073773C214yesmaximal, complemented
6#13073613C212yesmaximal, complemented
7#13073097C211yesmaximal, characteristic, complemented
8#13072268C211yesmaximal, characteristic
9#13072267C211yesmaximal, characteristic
10#13071905C214yesmaximal, complemented
11#13071159C212yesmaximal, complemented
12#13071155C212yesmaximal, complemented
13#13070996C214yesmaximal, complemented
14C4×#66930C211yesmaximal, characteristic, complemented
15C11×#2503C211yesmaximal, characteristic, complemented
16C23×D44C2211yescharacteristic
17C23×C4×D11C2212yes—
18C2×C11×C22⋊Q8C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C2×#67000C2212yes—
21C2×Q8×Dic11C2211yescharacteristic, complemented
22C2×#66997C2211yescharacteristic, complemented
23C22×(C2×D11)⋊C4C2212yes—
24C2×#66977C2211yescharacteristic
25C22×C4×Dic11C2211yescharacteristic
26#10623153—28no—
27C2×#66946—28no—
28C2×#66946C2212yes—
29C2×#66946C2212yes—
30C2×#66946C2212yes—
31C2×#66946C2212yes—
32C2×#66942C2212yescomplemented
33C2×#66941C2211yescharacteristic, complemented
34C2×#66940C2212yescomplemented
35C2×#66940C2211yescharacteristic, complemented
36C2×#66931C2212yes—
37C2×#66930C2212yes—
38C2×#66930C2212yes—
39C2×#66928C2212yes—
40C11×#400C2214yescomplemented
41C11×#391C2212yescomplemented
42C11×#382C2212yescomplemented
43C11×#381C2214yes—
44C4×C11×C22⋊C4C2211yescharacteristic
45#10622824C2214yes—
46C4×C22⋊Dic11C2211yescharacteristic
47#10622604C2214yes—
48#10622601C2212yes—
49#10622595C2214yescomplemented
50#10622590C2212yescomplemented
51#10622587C2212yescomplemented
52#10622568C2214yes—
53#10622568C2214yes—
54C22⋊C4×Dic11C2212yes—
55#10622552C2212yes—
56C4×Dic11⋊C4C2212yescomplemented
57C42×Dic11C2212yescomplemented
58#10622288C2218yescomplemented
59#10622286C2218yescomplemented
60#10622285C2214yes—
61#10622283C2218yescomplemented
62#10622282C2218yescomplemented
63#10622280C2218yescomplemented
64#10622280C2218yescomplemented
65#10622279C2218yescomplemented
66#10622279C2218yescomplemented
67#10622262C2212yescomplemented
68#10622261C2212yescomplemented
69C24×D11C2312yes—
70C22×Q8×C11C2311yescharacteristic
71C23×C4×C11C2312yes—
72C23×C4×C11C2311yescharacteristic
73C23×Dic11C2311yescharacteristic
74C23×Dic11C2311yescharacteristic
75C22×D44—24no—
76C22×D44—28no—
77C22×D44C2312yes—
78C22×D44C2312yes—
79C22×C4×D11—28no—
80C22×C4×D11—216no—
81C22×C4×D11C2314yes—
82C22×C4×D11C2314yes—
83C22×Dic22C2311yescharacteristic
84C22×Dic22C2312yes—
85C11×C22⋊Q8—24no—
86C2×C11×C4⋊C4—24no—
87C2×C11×C4⋊C4C2311yescharacteristic
88C2×C11×C4⋊C4C2312yes—
89C2×C11×C4⋊C4C2312yes—
90C2×C11×C4⋊C4C2312yes—
91C2×C11×C22⋊C4C2312yes—
92C2×C11×C22⋊C4C2312yes—
93C2×C42×C11C2312yes—
94C2×C22⋊Dic11C2312yes—
95C2×C22⋊Dic11C2312yes—
96#67000—28no—
97Q8×Dic11—24no—
98#66997—24no—
99C2×(C2×D11)⋊C4—28no—
100C2×(C2×D11)⋊C4C2318yes—
101C2×(C2×D11)⋊C4C2314yes—
102C2×(C2×D11)⋊C4C2314yes—
103C2×(C2×D11)⋊C4C2318yes—
104C2×(C2×D11)⋊C4C2318yes—
105C2×(C2×D11)⋊C4C2318yes—
106C2×C4⋊Dic11C2312yes—
107C2×C4⋊Dic11C2311yescharacteristic
108#66977—24no—
109C2×Dic11⋊C4C2312yes—
110C2×Dic11⋊C4C2312yes—
111C2×Dic11⋊C4C2314yes—
112C2×Dic11⋊C4C2312yes—
113C2×Dic11⋊C4C2312yes—
114C2×Dic11⋊C4C2312yes—
115C2×C4×Dic11D418yes—
116C2×C4×Dic11C2312yes—
117C2×C4×Dic11C2312yes—
118C2×C4×Dic11C2314yes—
119C2×C4×Dic11C2312yes—
120C2×C4×Dic11C2314yes—
121C2×C4×Dic11C2311yescharacteristic
122C2×C4×Dic11C2311yescharacteristic
123C2×C4×Dic11C2311yescharacteristic
124C2×C4×Dic11C2311yescharacteristic
125#66946—28no—
126#66946—28no—
127#66946—28no—
128#66946—28no—
129#66942—28no—
130#66941—24no—
131#66940—24no—
132#66940—28no—
133#66931—28no—
134#66930—28no—
135#66930—28no—
136#66928—28no—
137C11×#95C2312yes—
138C11×#95C2318yes—
139C11×#95C2318yes—
140C11⋊#95C2312yes—
141C11⋊#95C2314yes—
142C11⋊#95C2318yes—
143C11⋊#95C2318yes—
144#34946—111nomaximal, Sylow
145C24×C11C2411yescharacteristic
146C23×D11—24no—
147C23×D11—28no—
148C23×D11—28no—
149C23×D11—44no—
150C23×D11C2414yes—
151C2×Q8×C11—22no—
152C2×Q8×C11—24no—
153C22×C4×C11—24no—
154C22×C4×C11—24no—
155C22×C4×C11—28no—
156C22×C4×C11C2×D414yes—
157C22×C4×C11C2414yes—
158C22×C4×C11C2414yes—
159C22×C4×C11C2412yes—
160C22×C4×C11C2412yes—
161C22×C4×C11C2411yescharacteristic
162C22×C4×C11C2411yescharacteristic
163C22×Dic11—42no—
164C22×Dic11C2×D414yes—
165C22×Dic11C2×D414yes—
166C22×Dic11#4118yes—
167C22×Dic11C2414yes—
168C22×Dic11C2412yes—
169C22×Dic11C2412yes—
170C22×Dic11C2411yescharacteristic
171C22×Dic11C2411yescharacteristic
172C22×Dic11C2411yescharacteristic
173C22×Dic11C2411yescharacteristic
174C2×D44—232no—
175C2×D44—28no—
176C2×D44—24no—
177C2×D44—24no—
178C2×D44—24no—
179C2×D44#4118yes—
180C2×C4×D11—28no—
181C2×C4×D11—28no—
182C2×C4×D11—216no—
183C2×C4×D11—216no—
184C2×C4×D11—432no—
185C2×Dic22—24no—
186C2×Dic22—22no—
187C2×Dic22—24no—
188C2×Dic22—44no—
189C11×C4⋊C4—22no—
190C11×C4⋊C4—24no—
191C11×C4⋊C4—24no—
192C11×C4⋊C4—24no—
193C11×C22⋊C4—24no—
194C11×C22⋊C4—24no—
195C42×C11—24no—
196C22⋊Dic11—24no—
197C22⋊Dic11—24no—
198(C2×D11)⋊C4—28no—
199(C2×D11)⋊C4—28no—
200(C2×D11)⋊C4—216no—
201(C2×D11)⋊C4—216no—
202(C2×D11)⋊C4—48no—
203(C2×D11)⋊C4—48no—
204C4⋊Dic11—24no—
205C4⋊Dic11—22no—
206Dic11⋊C4—24no—
207Dic11⋊C4—24no—
208Dic11⋊C4—24no—
209Dic11⋊C4—24no—
210Dic11⋊C4—28no—
211Dic11⋊C4—24no—
212C4×Dic11—24no—
213C4×Dic11—24no—
214C4×Dic11—28no—
215C4×Dic11—24no—
216C4×Dic11—44no—
217C4×Dic11C2×D414yes—
218C4×Dic11C2×D414yes—
219C4×Dic11C2×D414yes—
220C4×Dic11C2×D414yes—
221C2×#533—111no—
222C22×C4×D4—111no—
223#2563—112no—
224#2562—114no—
225#2561—114no—
226#2547—112no—
227#2503—111no—
228#2503D1111yescharacteristic, complemented
229#2435—111no—
230#2435—111no—
231#2398—114no—
232C4×#124—112no—
233C4×#124—112no—
234#2280—114no—
235C4×#117—111no—
236C23×C11—22no—
237C23×C11—22no—
238C23×C11C22×D412yes—
239C23×C11C2×#4114yes—
240C23×C11C2511yescharacteristic
241C22×D11—216no—
242C22×D11—24no—
243C22×D11—28no—
244C22×D11—24no—
245C22×D11—28no—
246C22×D11—432no—
247C22×D11—48no—
248C22×D11—48no—
249C22×D11C2×#4118yes—
250Q8×C11—44no—
251C2×C4×C11—22no—
252C2×C4×C11—28no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—24no—
256C2×C4×C11—24no—
257C2×C4×C11—24no—
258C2×C4×C11—24no—
259C2×C4×C11—28no—
260C2×C4×C11—24no—
261C2×C4×C11—24no—
262C2×C4×C11—48no—
263C2×C4×C11C22×D412yes—
264C2×C4×C11C22×D412yes—
265C2×C4×C11C2×#4114yes—
266C2×Dic11—22no—
267C2×Dic11—22no—
268C2×Dic11—22no—
269C2×Dic11—22no—
270C2×Dic11—24no—
271C2×Dic11—24no—
272C2×Dic11—24no—
273C2×Dic11—24no—
274C2×Dic11—24no—
275C2×Dic11—44no—
276C2×Dic11#124116yescomplemented
277C2×Dic11C22×D412yes—
278C2×Dic11C22×D412yes—
279C2×Dic11C22×D412yes—
280C2×Dic11C22×D412yes—
281C2×Dic11C2×#4114yes—
282C2×Dic11C2×#4114yes—
283D44—216no—
284D44—216no—
285C4×D11—416no—
286C4×D11—416no—
287Dic22—48no—
288Dic22—44no—
289C23×D4—111no—
290C24×C4—112no—
291#533—228no—
292C2×C4⋊Q8—111no—
293C2×C4⋊Q8—111no—
294C2×#125—112no—
295C2×#124—112no—
296C2×#124—112no—
297C2×C22⋊Q8—111no—
298C2×C22⋊Q8—112no—
299C2×C22⋊Q8C2×D1111yescharacteristic
300C2×C4×Q8—111no—
301C2×C4×Q8—112no—
302C2×C4×Q8—111no—
303C2×C4×D4—112no—
304C2×C4×D4—112no—
305C2×C4×D4—112no—
306C2×C4×D4—112no—
307C2×C4×D4—228no—
308C2×#117—112no—
309C2×#117—112no—
310C22×C4⋊C4C2×D1111yescharacteristic
311C22×C22⋊C4—112no—
312C22×C42—111no—
313#400—114no—
314#400C2×D1114yescomplemented
315#397—118no—
316#394—114no—
317#394—114no—
318#393—118no—
319#391—112no—
320#391C2×D1112yescomplemented
321#390—112no—
322#390—112no—
323#388—118no—
324#388—118no—
325#382—112no—
326#382C2×D1112yescomplemented
327#381—114no—
328#381C2×D1114yes—
329#380—118no—
330#380—118no—
331#379—114no—
332#379—114no—
333C4×C4⋊C4—112no—
334C4×C4⋊C4—112no—
335C4×C22⋊C4—111no—
336C4×C22⋊C4—112no—
337C4×C22⋊C4—118no—
338C4×C22⋊C4—118no—
339C4×C22⋊C4C2×D1111yescharacteristic
340#376—112no—
341C43—112no—
342C22×C11—22no—
343C22×C11—22no—
344C22×C11—28no—
345C22×C11C2×#12414yes—
346C22×C11C23×D411yescharacteristic
347C22×C11C22×#4112yes—
348C22×C11C22×#4112yes—
349C22×C11#58512yes—
350C2×D11—28no—
351C2×D11—216no—
352C2×D11—432no—
353C2×D11—44no—
354C2×D11—44no—
355C2×D11—48no—
356C4×C11—22no—
357C4×C11—42no—
358C4×C11—44no—
359C4×C11—42no—
360C4×C11—44no—
361C4×C11#52514yes—
362Dic11—22no—
363Dic11—22no—
364Dic11—42no—
365Dic11—42no—
366Dic11—44no—
367Dic11C2×#12414yes—
368Dic11C2×#12414yes—
369C25—112no—
370C22×Q8—111no—
371C22×Q8—112no—
372C22×Q8C22×D1111yescharacteristic
373C22×D4—112no—
374C22×D4—112no—
375C22×D4—228no—
376C22×D4—224no—
377C23×C4—111no—
378C23×C4—111no—
379C23×C4—114no—
380C23×C4—114no—
381C23×C4—228no—
382C23×C4—2216no—
383C23×C4C22×D1112yes—
384C23×C4C22×D1111yescharacteristic
385C4⋊Q8—224no—
386C4⋊Q8—224no—
387#125—228no—
388#124—228no—
389#124—228no—
390C22⋊Q8—24no—
391C22⋊Q8—228no—
392C22⋊Q8—224no—
393C4×Q8—228no—
394C4×Q8—224no—
395C4×Q8—224no—
396C4×D4—228no—
397C4×D4—228no—
398C4×D4—228no—
399C4×D4—228no—
400#117—228no—
401#117—228no—
402C2×C4⋊C4—24no—
403C2×C4⋊C4—112no—
404C2×C4⋊C4—112no—
405C2×C4⋊C4—114no—
406C2×C4⋊C4—112no—
407C2×C4⋊C4—112no—
408C2×C4⋊C4—112no—
409C2×C4⋊C4—111no—
410C2×C4⋊C4—112no—
411C2×C4⋊C4C22×D1112yes—
412C2×C4⋊C4C22×D1112yes—
413C2×C4⋊C4C22×D1112yes—
414C2×C4⋊C4C22×D1111yescharacteristic
415C2×C22⋊C4—112no—
416C2×C22⋊C4—112no—
417C2×C22⋊C4—114no—
418C2×C22⋊C4—114no—
419C2×C22⋊C4—118no—
420C2×C22⋊C4—118no—
421C2×C22⋊C4—118no—
422C2×C22⋊C4—118no—
423C2×C22⋊C4—228no—
424C2×C22⋊C4C22×D1112yes—
425C2×C22⋊C4C22×D1112yes—
426C2×C42—118no—
427C2×C42—111no—
428C2×C42—111no—
429C2×C42—111no—
430C2×C42—111no—
431C2×C42—112no—
432C2×C42—112no—
433C2×C42—114no—
434C2×C42—112no—
435C2×C42—114no—
436C2×C42C22×D1112yes—
437#95—114no—
438#95—112no—
439#95—118no—
440#95—118no—
441#95C22×D1112yes—
442#95C22×D1118yes—
443#95C22×D1118yes—
444C2×C11—24no—
445C2×C11C2×#52511yescharacteristic
446C2×C11C22×#12411yescharacteristic
447C2×C11#344911yescharacteristic
448C2×C11#347514yes—
449D11—48no—
450C24—114no—
451C24—228no—
452C24—224no—
453C24—228no—
454C24—444no—
455C24C23×D1111yescharacteristic
456C2×Q8—22no—
457C2×Q8—24no—
458C2×Q8—224no—
459C2×Q8—222no—
460C2×Q8—224no—
461C2×Q8—444no—
462C2×D4—118no—
463C2×D4—228no—
464C2×D4—2232no—
465C2×D4—224no—
466C2×D4—224no—
467C2×D4—224no—
468C22×C4—24no—
469C22×C4—24no—
470C22×C4—28no—
471C22×C4—114no—
472C22×C4—118no—
473C22×C4—111no—
474C22×C4—111no—
475C22×C4—111no—
476C22×C4—111no—
477C22×C4—114no—
478C22×C4—114no—
479C22×C4—112no—
480C22×C4—112no—
481C22×C4—228no—
482C22×C4—228no—
483C22×C4—2216no—
484C22×C4—2216no—
485C22×C4—4432no—
486C22×C4—442no—
487C22×C4D4×D1114yes—
488C22×C4C23×D1114yes—
489C22×C4C23×D1114yes—
490C22×C4C23×D1112yes—
491C22×C4C23×D1112yes—
492C22×C4C23×D1111yescharacteristic
493C22×C4C23×D1111yescharacteristic
494C4⋊C4—24no—
495C4⋊C4—24no—
496C4⋊C4—24no—
497C4⋊C4—22no—
498C4⋊C4—224no—
499C4⋊C4—224no—
500C4⋊C4—228no—
501C4⋊C4—224no—
502C4⋊C4—224no—
503C4⋊C4—224no—
504C4⋊C4—224no—
505C4⋊C4—222no—
506C22⋊C4—24no—
507C22⋊C4—24no—
508C22⋊C4—228no—
509C22⋊C4—228no—
510C22⋊C4—2216no—
511C22⋊C4—2216no—
512C22⋊C4—224no—
513C22⋊C4—224no—
514C22⋊C4—448no—
515C22⋊C4—448no—
516C42—24no—
517C42—114no—
518C42—114no—
519C42—114no—
520C42—114no—
521C42—224no—
522C42—224no—
523C42—228no—
524C42—224no—
525C42—444no—
526C11#3494611yescharacteristic, complemented, Sylow
527C23—22no—
528C23—22no—
529C23—118no—
530C23—2216no—
531C23—224no—
532C23—228no—
533C23—224no—
534C23—228no—
535C23—4432no—
536C23—448no—
537C23—448no—
538C23C2×D4×D1112yes—
539C23#41×D1114yes—
540C23C24×D1111yescharacteristic
541Q8—44no—
542Q8—448no—
543Q8—444no—
544D4—2216no—
545D4—2216no—
546C2×C4—22no—
547C2×C4—28no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—28no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—48no—
558C2×C4—112no—
559C2×C4—112no—
560C2×C4—114no—
561C2×C4—114no—
562C2×C4—1116no—
563C2×C4—112no—
564C2×C4—112no—
565C2×C4—222no—
566C2×C4—222no—
567C2×C4—222no—
568C2×C4—222no—
569C2×C4—224no—
570C2×C4—224no—
571C2×C4—224no—
572C2×C4—224no—
573C2×C4—224no—
574C2×C4—4416no—
575C2×C4—4416no—
576C2×C4—444no—
577C2×C4C2×D4×D1112yes—
578C2×C4C2×D4×D1112yes—
579C2×C4#41×D1114yes—
580C22—28no—
581C22—22no—
582C22—22no—
583C22—2216no—
584C22—228no—
585C22—4432no—
586C22—444no—
587C22—448no—
588C22—444no—
589C22D11×#12414yes—
590C22C22×D4×D1111yescharacteristic
591C22C2×#41×D1112yes—
592C22C2×#41×D1112yes—
593C22#1062345712yes—
594C4—22no—
595C4—44no—
596C4—44no—
597C4—42no—
598C4—42no—
599C4—114no—
600C4—114no—
601C4—222no—
602C4—222no—
603C4—444no—
604C4—442no—
605C4—442no—
606C4#1062318714yes—
607C2—24no—
608C2—448no—
609C2C2×#1062318711yescharacteristic
610C2C2×D11×#12411yescharacteristic
611C2#1308194811yescharacteristic
612C2#1308218114yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2503C2
prime radicalC23×D44C22
hypercenter#2503D11
hypocenterC11#34946
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2503

Complements

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

NH ≅ G/Ntype
1. C2×#10623153C2semidirect
3. #13073788C2semidirect
4. #13073778C2semidirect
5. #13073773C2semidirect
6. #13073613C2semidirect
7. #13073097C2semidirect
10. #13071905C2semidirect
11. #13071159C2semidirect
12. #13071155C2semidirect
13. #13070996C2semidirect
14. C4×#66930C2semidirect
15. C11×#2503C2semidirect
21. C2×Q8×Dic11C22semidirect
22. C2×#66997C22semidirect
32. C2×#66942C22semidirect
33. C2×#66941C22semidirect
34. C2×#66940C22semidirect
35. C2×#66940C22semidirect
40. C11×#400C22semidirect
41. C11×#391C22semidirect
42. C11×#382C22semidirect
49. #10622595C22semidirect
50. #10622590C22semidirect
51. #10622587C22semidirect
56. C4×Dic11⋊C4C22semidirect
57. C42×Dic11C22semidirect
58. #10622288C22semidirect
59. #10622286C22semidirect
61. #10622283C22semidirect
62. #10622282C22semidirect
63. #10622280C22semidirect
64. #10622280C22semidirect
65. #10622279C22semidirect
66. #10622279C22semidirect
67. #10622262C22semidirect
68. #10622261C22semidirect
228. #2503D11semidirect
276. C2×Dic11#124semidirect
314. #400C2×D11semidirect
320. #391C2×D11semidirect
326. #382C2×D11semidirect
526. C11#34946semidirect

Maximal subgroups

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

subgroupindex
C2×#106231532
C22×#669462
#130737882
#130737782
#130737732
#130736132
#130730972
#130722682
#130722672
#130719052
#130711592
#130711552
#130709962
C4×#669302
C11×#25032
#3494611