Finite Group Databasebeta

← #14926513

Subgroups — #14926513

Order 2816.

2042 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076922C214yesmaximal, complemented
2#13074588C214yesmaximal, complemented
3#13073119C214yesmaximal, complemented
4#13073117C214yesmaximal, complemented
5#13072759C214yesmaximal, complemented
6#13072751C214yesmaximal, complemented
7#13071230C211yesmaximal, characteristic
8#13071228C211yesmaximal, characteristic
9#13071228C211yesmaximal, characteristic
10#13071228C211yesmaximal, characteristic
11C2×#10622823C211yesmaximal, characteristic
12C2×C4×C22⋊Dic11C211yesmaximal, characteristic
13C2×C11×#385C211yesmaximal, characteristic
14C24×C4×C11C2211yescharacteristic
15C22×C11×C4⋊C4C2212yes—
16C22×C11×C22⋊C4C2211yescharacteristic
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C22⋊Dic11C2211yescharacteristic
19C22×C22⋊Dic11C2211yescharacteristic
20C22×C22⋊Dic11C2211yescharacteristic
21C22×C22⋊Dic11C2211yescharacteristic
22C22×Dic11⋊C4C2212yes—
23C22×C4×Dic11C2212yes—
24C2×#66942C2214yescomplemented
25C11×#385C2214yes—
26C11×#385C2212yes—
27C11×#385C2212yes—
28C2×C11×#95C2212yes—
29#10622825C2212yes—
30#10622825C2212yes—
31#10622823C2212yes—
32#10622823C2214yes—
33#10622823C2214yes—
34#10622823C2214yes—
35#10622823C2212yes—
36#10622823C2212yes—
37#10622823C2212yes—
38C4×C22⋊Dic11C2214yes—
39C4×C22⋊Dic11C2214yes—
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42#10622597C2214yescomplemented
43#10622596C2214yescomplemented
44#10622595C2214yescomplemented
45#10622594C2214yescomplemented
46#10622593C2214yescomplemented
47#10622591C2214yescomplemented
48#10622585C2214yescomplemented
49#10622563C2214yes—
50#10622563C2214yes—
51#10622559C2212yes—
52#10622559C2214yes—
53#10622559C2214yes—
54#10622559C2212yes—
55#10622555C2212yes—
56#10622555C2214yes—
57#10622555C2214yes—
58#10622555C2212yes—
59#10622272C2214yescomplemented
60#10622271C2214yescomplemented
61#10622271C2214yescomplemented
62#10622270C2214yescomplemented
63#10622266C2214yescomplemented
64#10622265C2214yescomplemented
65#10622263C2214yescomplemented
66#10622260C2214yescomplemented
67C25×C11C2311yescharacteristic
68C23×C4×C11—24no—
69C23×C4×C11—44no—
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2312yes—
72C23×C4×C11C2312yes—
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2312yes—
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×Dic11C2312yes—
78C23×Dic11C2311yescharacteristic
79C23×Dic11C2312yes—
80C23×Dic11C2311yescharacteristic
81C23×Dic11C2312yes—
82C2×C11×C4⋊C4—44no—
83C2×C11×C4⋊C4C2314yes—
84C2×C11×C4⋊C4C2314yes—
85C2×C11×C22⋊C4—24no—
86C2×C11×C22⋊C4—24no—
87C2×C11×C22⋊C4C2312yes—
88C2×C11×C22⋊C4C2312yes—
89C2×C11×C22⋊C4C2312yes—
90C2×C11×C22⋊C4C2312yes—
91C2×C22⋊Dic11—24no—
92C2×C22⋊Dic11—24no—
93C2×C22⋊Dic11—24no—
94C2×C22⋊Dic11Q818yes—
95C2×C22⋊Dic11C2312yes—
96C2×C22⋊Dic11C2312yes—
97C2×C22⋊Dic11C2312yes—
98C2×C22⋊Dic11C2312yes—
99C2×C22⋊Dic11C2312yes—
100C2×C22⋊Dic11C2312yes—
101C2×C22⋊Dic11C2312yes—
102C2×C22⋊Dic11C2312yes—
103C2×C4⋊Dic11C2314yes—
104C2×C4⋊Dic11C2314yes—
105C2×Dic11⋊C4—44no—
106C2×Dic11⋊C4C2314yes—
107C2×Dic11⋊C4C2314yes—
108C2×Dic11⋊C4C2314yes—
109C2×Dic11⋊C4C2314yes—
110C2×Dic11⋊C4C2314yes—
111C2×Dic11⋊C4C2314yes—
112C2×Dic11⋊C4C2314yes—
113C2×Dic11⋊C4C2314yes—
114C2×C4×Dic11—44no—
115C2×C4×Dic11C2314yes—
116C2×C4×Dic11C2314yes—
117#66942—48no—
118C11×#95C2314yes—
119C11×#95C2314yes—
120C11⋊#95C2314yes—
121C11⋊#95C2314yes—
122C11⋊#95C2314yes—
123C11⋊#95C2314yes—
124C11⋊#95C2314yes—
125C11⋊#95C2314yes—
126C11⋊#95C2314yes—
127C11⋊#95C2314yes—
128C11⋊#95C2314yes—
129C11⋊#95C2314yes—
130C11⋊#95C2314yes—
131C11⋊#95C2314yes—
132#34994—111nomaximal, Sylow
133C24×C11—42no—
134C24×C11—42no—
135C24×C11C2×Q814yes—
136C24×C11#4114yes—
137C24×C11#4114yes—
138C24×C11C2411yescharacteristic
139C24×C11C2411yescharacteristic
140C24×C11C2411yescharacteristic
141C22×C4×C11—22no—
142C22×C4×C11—24no—
143C22×C4×C11—24no—
144C22×C4×C11—24no—
145C22×C4×C11—24no—
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11—24no—
150C22×C4×C11—24no—
151C22×C4×C11—42no—
152C22×C4×C11—42no—
153C22×C4×C11—42no—
154C22×C4×C11—42no—
155C22×C4×C11—42no—
156C22×C4×C11—42no—
157C22×C4×C11—42no—
158C22×C4×C11—416no—
159C22×C4×C11C2412yes—
160C22×C4×C11C2412yes—
161C22×C4×C11C2414yes—
162C22×C4×C11C2412yes—
163C22×C4×C11C2412yes—
164C22×Dic11—24no—
165C22×Dic11—24no—
166C22×Dic11—22no—
167C22×Dic11—22no—
168C22×Dic11—42no—
169C22×Dic11—42no—
170C22×Dic11—42no—
171C22×Dic11—42no—
172C22×Dic11—42no—
173C22×Dic11—42no—
174C22×Dic11—42no—
175C22×Dic11—42no—
176C22×Dic11C2×Q818yes—
177C22×Dic11C2412yes—
178C22×Dic11C2414yes—
179C22×Dic11C2414yes—
180C22×Dic11C2412yes—
181C22×Dic11C2414yes—
182C11×C4⋊C4—28no—
183C11×C4⋊C4—44no—
184C11×C22⋊C4—24no—
185C11×C22⋊C4—24no—
186C11×C22⋊C4—24no—
187C11×C22⋊C4—24no—
188C22⋊Dic11—24no—
189C22⋊Dic11—24no—
190C22⋊Dic11—24no—
191C22⋊Dic11—24no—
192C22⋊Dic11—24no—
193C22⋊Dic11—24no—
194C22⋊Dic11C2×Q818yes—
195C22⋊Dic11C2×Q818yes—
196C4⋊Dic11—44no—
197C4⋊Dic11—44no—
198Dic11⋊C4—28no—
199Dic11⋊C4—44no—
200Dic11⋊C4—44no—
201Dic11⋊C4—44no—
202Dic11⋊C4—44no—
203Dic11⋊C4—44no—
204Dic11⋊C4—44no—
205Dic11⋊C4—44no—
206C4×Dic11—28no—
207C4×Dic11—44no—
208#2851—114no—
209#2646—114no—
210#2505—114no—
211#2505—114no—
212#2473—114no—
213#2473—114no—
214#2315—111no—
215#2315—111no—
216#2315—111no—
217#2315—111no—
218C2×#385—111no—
219C2×#385D1111yescharacteristic
220C2×C4×C22⋊C4—111no—
221C23×C11—22no—
222C23×C11—22no—
223C23×C11—22no—
224C23×C11—22no—
225C23×C11—22no—
226C23×C11—22no—
227C23×C11—44no—
228C23×C11—48no—
229C23×C11—48no—
230C23×C11—44no—
231C23×C11#125116yescomplemented
232C23×C11C22×Q812yes—
233C23×C11C22×Q812yes—
234C23×C11C22×Q812yes—
235C23×C11C2×#4112yes—
236C23×C11C2×#4112yes—
237C23×C11C2×#4112yes—
238C23×C11C2×#4112yes—
239C23×C11C2×#4112yes—
240C23×C11C2×#4112yes—
241C23×C11C2511yescharacteristic
242C2×C4×C11—28no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—24no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—24no—
250C2×C4×C11—22no—
251C2×C4×C11—24no—
252C2×C4×C11—22no—
253C2×C4×C11—24no—
254C2×C4×C11—24no—
255C2×C4×C11—48no—
256C2×C4×C11—48no—
257C2×C4×C11—48no—
258C2×C4×C11—44no—
259C2×C4×C11—82no—
260C2×C4×C11—82no—
261C2×C4×C11H(5,𝔽2)14yes—
262C2×Dic11—24no—
263C2×Dic11—24no—
264C2×Dic11—24no—
265C2×Dic11—24no—
266C2×Dic11—22no—
267C2×Dic11—22no—
268C2×Dic11—24no—
269C2×Dic11—24no—
270C2×Dic11—24no—
271C2×Dic11—24no—
272C2×Dic11—24no—
273C2×Dic11—24no—
274C2×Dic11—48no—
275C2×Dic11—48no—
276C2×Dic11—48no—
277C2×Dic11—82no—
278C2×Dic11—82no—
279C2×Dic11C22×Q818yes—
280C24×C4C2×D1111yescharacteristic
281C2×#125—114no—
282C22×C4⋊C4—112no—
283C22×C4⋊C4C2×D1112yes—
284C22×C22⋊C4—111no—
285C22×C22⋊C4—111no—
286C22×C22⋊C4—111no—
287C22×C22⋊C4—111no—
288C22×C22⋊C4C2×D1111yescharacteristic
289C22×C22⋊C4C2×D1111yescharacteristic
290C22×C42—112no—
291#400—114no—
292#400—114no—
293#400—114no—
294#400—114no—
295#398—114no—
296#398—114no—
297#398—114no—
298#398—114no—
299#389—114no—
300#389—114no—
301#387—114no—
302#387—114no—
303#387—114no—
304#387—114no—
305#385—112no—
306#385—114no—
307#385—114no—
308#385—112no—
309#385—112no—
310#385—112no—
311#385—114no—
312#385—114no—
313#385—114no—
314#385—112no—
315#385—114no—
316#385—112no—
317#385—114no—
318#385C2×D1112yes—
319#385C2×D1112yes—
320#385C2×D1114yes—
321#382—114no—
322#380—112no—
323#380—112no—
324#380—114no—
325#380—114no—
326#380—112no—
327#380—112no—
328C4×C22⋊C4—114no—
329C4×C22⋊C4—114no—
330C2×#95—112no—
331C2×#95—112no—
332C2×#95C2×D1112yes—
333C22×C11—24no—
334C22×C11—24no—
335C22×C11—24no—
336C22×C11—22no—
337C22×C11—22no—
338C22×C11—22no—
339C22×C11—22no—
340C22×C11—22no—
341C22×C11—22no—
342C22×C11—24no—
343C22×C11—24no—
344C22×C11—24no—
345C22×C11—416no—
346C22×C11C2×#12514yes—
347C22×C11C2×#12514yes—
348C22×C11C2×#12514yes—
349C22×C11C23×Q811yescharacteristic
350C22×C11C22×#4111yescharacteristic
351C22×C11C22×#4111yescharacteristic
352C22×C11C2×H(5,𝔽2)12yes—
353C22×C11#58512yes—
354C4×C11—24no—
355C4×C11—44no—
356C4×C11—42no—
357C4×C11—42no—
358C4×C11—42no—
359Dic11—28no—
360Dic11—44no—
361Dic11—44no—
362Dic11—42no—
363Dic11—42no—
364C25C22×D1111yescharacteristic
365C23×C4—24no—
366C23×C4—44no—
367C23×C4—112no—
368C23×C4—111no—
369C23×C4—112no—
370C23×C4—111no—
371C23×C4—112no—
372C23×C4C22×D1111yescharacteristic
373C23×C4C22×D1112yes—
374C23×C4C22×D1112yes—
375C23×C4C22×D1111yescharacteristic
376C23×C4C22×D1112yes—
377C23×C4C22×D1111yescharacteristic
378C23×C4C22×D1111yescharacteristic
379#125—448no—
380C2×C4⋊C4—44no—
381C2×C4⋊C4—114no—
382C2×C4⋊C4—114no—
383C2×C4⋊C4—114no—
384C2×C4⋊C4—114no—
385C2×C4⋊C4—114no—
386C2×C4⋊C4—114no—
387C2×C4⋊C4—114no—
388C2×C4⋊C4—114no—
389C2×C4⋊C4—114no—
390C2×C4⋊C4—114no—
391C2×C4⋊C4—444no—
392C2×C4⋊C4C22×D1114yes—
393C2×C4⋊C4C22×D1114yes—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—118no—
397C2×C22⋊C4—112no—
398C2×C22⋊C4—112no—
399C2×C22⋊C4—112no—
400C2×C22⋊C4—112no—
401C2×C22⋊C4—112no—
402C2×C22⋊C4—112no—
403C2×C22⋊C4—112no—
404C2×C22⋊C4—112no—
405C2×C22⋊C4—224no—
406C2×C22⋊C4—224no—
407C2×C22⋊C4—224no—
408C2×C22⋊C4C22×D1112yes—
409C2×C22⋊C4C22×D1112yes—
410C2×C22⋊C4C22×D1112yes—
411C2×C22⋊C4C22×D1112yes—
412C2×C42—114no—
413C2×C42—114no—
414C2×C42—444no—
415#95—114no—
416#95—114no—
417#95—114no—
418#95—114no—
419#95—114no—
420#95—114no—
421#95—114no—
422#95—114no—
423#95—114no—
424#95—114no—
425#95—114no—
426#95—114no—
427#95C22×D1114yes—
428#95C22×D1114yes—
429C2×C11—24no—
430C2×C11—24no—
431C2×C11—24no—
432C2×C11C22×#12511yescharacteristic
433C2×C11#345912yes—
434C2×C11#349011yescharacteristic
435C2×C11#349111yescharacteristic
436C2×C11#350112yes—
437C24—42no—
438C24—42no—
439C24#433914yes—
440C24#434114yes—
441C24Q8×D1114yes—
442C24C23×D1111yescharacteristic
443C24C23×D1111yescharacteristic
444C24C23×D1111yescharacteristic
445C22×C4—22no—
446C22×C4—24no—
447C22×C4—24no—
448C22×C4—24no—
449C22×C4—24no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—24no—
454C22×C4—24no—
455C22×C4—42no—
456C22×C4—42no—
457C22×C4—42no—
458C22×C4—42no—
459C22×C4—42no—
460C22×C4—42no—
461C22×C4—42no—
462C22×C4—416no—
463C22×C4—114no—
464C22×C4—118no—
465C22×C4—112no—
466C22×C4—114no—
467C22×C4—114no—
468C22×C4—112no—
469C22×C4—224no—
470C22×C4—224no—
471C22×C4—222no—
472C22×C4—222no—
473C22×C4—442no—
474C22×C4—442no—
475C22×C4—442no—
476C22×C4—442no—
477C22×C4—442no—
478C22×C4—442no—
479C22×C4—442no—
480C22×C4—442no—
481C22×C4C23×D1112yes—
482C22×C4C23×D1112yes—
483C22×C4C23×D1114yes—
484C22×C4C23×D1112yes—
485C22×C4C23×D1112yes—
486C4⋊C4—28no—
487C4⋊C4—44no—
488C4⋊C4—228no—
489C4⋊C4—444no—
490C4⋊C4—444no—
491C4⋊C4—444no—
492C4⋊C4—444no—
493C4⋊C4—444no—
494C4⋊C4—444no—
495C4⋊C4—444no—
496C4⋊C4—444no—
497C4⋊C4—444no—
498C22⋊C4—24no—
499C22⋊C4—24no—
500C22⋊C4—24no—
501C22⋊C4—24no—
502C22⋊C4—118no—
503C22⋊C4—118no—
504C22⋊C4—224no—
505C22⋊C4—224no—
506C22⋊C4—224no—
507C22⋊C4—224no—
508C22⋊C4—224no—
509C22⋊C4—224no—
510C42—228no—
511C42—444no—
512C11#3499411yescharacteristic, complemented, Sylow
513C23—22no—
514C23—22no—
515C23—22no—
516C23—22no—
517C23—22no—
518C23—22no—
519C23—44no—
520C23—48no—
521C23—44no—
522C23—48no—
523C23#66942116yescomplemented
524C23C2×#433912yes—
525C23C2×#433912yes—
526C23C2×#433912yes—
527C23C2×#434112yes—
528C23C2×#434112yes—
529C23C2×#434112yes—
530C23C2×Q8×D1112yes—
531C23C2×Q8×D1112yes—
532C23C2×Q8×D1112yes—
533C23C24×D1111yescharacteristic
534C2×C4—28no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—24no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—48no—
548C2×C4—48no—
549C2×C4—48no—
550C2×C4—44no—
551C2×C4—82no—
552C2×C4—82no—
553C2×C4—118no—
554C2×C4—224no—
555C2×C4—224no—
556C2×C4—224no—
557C2×C4—224no—
558C2×C4—222no—
559C2×C4—222no—
560C2×C4—224no—
561C2×C4—224no—
562C2×C4—224no—
563C2×C4—224no—
564C2×C4—224no—
565C2×C4—224no—
566C2×C4—448no—
567C2×C4—448no—
568C2×C4—448no—
569C2×C4—882no—
570C2×C4—882no—
571C2×C4#6703714yes—
572C22—24no—
573C22—24no—
574C22—24no—
575C22—24no—
576C22—24no—
577C22—24no—
578C22—22no—
579C22—22no—
580C22—22no—
581C22—22no—
582C22—22no—
583C22—22no—
584C22—416no—
585C22C2×#6694214yes—
586C22C2×#6694214yes—
587C22C2×#6694214yes—
588C22C22×#433911yescharacteristic
589C22C22×#434111yescharacteristic
590C22C2×#6703712yes—
591C22C22×Q8×D1111yescharacteristic
592C22#1062345312yes—
593C4—24no—
594C4—44no—
595C4—42no—
596C4—42no—
597C4—42no—
598C4—228no—
599C4—444no—
600C4—444no—
601C4—442no—
602C4—442no—
603C2—24no—
604C2—24no—
605C2—24no—
606C2C22×#6694211yescharacteristic
607C2#1308202512yes—
608C2#1308230311yescharacteristic
609C2#1308231211yescharacteristic
610C2#1308241212yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC2×C11×#385C2
prime radicalC25×C11C23
hypercenterC2×#385D11
hypocenterC11#34994
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. #13076922C2semidirect
2. #13074588C2semidirect
3. #13073119C2semidirect
4. #13073117C2semidirect
5. #13072759C2semidirect
6. #13072751C2semidirect
24. C2×#66942C22semidirect
42. #10622597C22semidirect
43. #10622596C22semidirect
44. #10622595C22semidirect
45. #10622594C22semidirect
46. #10622593C22semidirect
47. #10622591C22semidirect
48. #10622585C22semidirect
59. #10622272C22semidirect
60. #10622271C22semidirect
61. #10622271C22semidirect
62. #10622270C22semidirect
63. #10622266C22semidirect
64. #10622265C22semidirect
65. #10622263C22semidirect
66. #10622260C22semidirect
231. C23×C11#125semidirect
512. C11#34994semidirect
523. C23#66942semidirect

Maximal subgroups

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

subgroupindex
#130769222
#130745882
#130731192
#130731172
#130727592
#130727512
#130712302
#130712282
C2×#106228232
C2×C4×C22⋊Dic112
C2×C11×#3852
#3499411