Finite Group Databasebeta

← #14926354

Subgroups — #14926354

Order 2816.

3690 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623024C211yesmaximal, characteristic, complemented
2C2×#10623335C212yesmaximal, complemented
3#13076947C212yesmaximal, complemented
4#13076898C212yesmaximal, complemented
5#13074358C212yesmaximal, complemented
6#13074350C212yesmaximal, complemented
7#13072161C218yesmaximal, complemented
8#13072146C218yesmaximal, complemented
9#13071230C211yesmaximal, characteristic, complemented
10C2×#10622826C212yesmaximal, complemented
11C22×C4×D4×C11C211yesmaximal, characteristic, complemented
12C23×D4×C11C2211yescharacteristic
13C24×C4×C11C2211yescharacteristic
14C24×C4×C11C2211yescharacteristic, complemented
15C23×C22⋊D11C2212yes—
16C2×C4×D4×C11—28no—
17C2×C4×D4×C11C2218yescomplemented
18C22×C11×C4⋊C4C2211yescharacteristic, complemented
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic, complemented
21C22×C42×C11C2211yescharacteristic, complemented
22C2×#67006C2214yescomplemented
23C22×C22⋊Dic11C2212yes—
24#10623335—216no—
25C2×#66992C2218yes—
26C2×#66990C2214yescomplemented
27C2×#66988C2214yescomplemented
28C2×#66983C2212yes—
29C2×#66983C2212yes—
30C2×#66983C2214yescomplemented
31C2×#66982C2214yescomplemented
32C22×(C2×D11)⋊C4C2214yescomplemented
33#10623024—28no—
34C2×#66939C2214yescomplemented
35C2×#66935C2214yescomplemented
36#10622826C2218yescomplemented
37#10622826C2218yescomplemented
38#10622826C2214yescomplemented
39#10622826C2214yescomplemented
40#10622825C2214yescomplemented
41#10622825C2212yescomplemented
42#10622825C2212yescomplemented
43C2×C11⋊#95C2214yescomplemented
44#10622607C2218yescomplemented
45#10622604C2214yescomplemented
46#10622596C2214yescomplemented
47#10622574C2218yescomplemented
48#10622573C2214yescomplemented
49#10622566C2214yescomplemented
50#10622563C2218yescomplemented
51#10622553C2218yescomplemented
52#10622552C2214yescomplemented
53#10622541C2214yescomplemented
54C25×C11C2311yescharacteristic
55C25×C11C2311yescharacteristic
56C24×D11C2312yes—
57C22×D4×C11—24no—
58C22×D4×C11—24no—
59C22×D4×C11D418yescomplemented
60C22×D4×C11C2314yes—
61C23×C4×C11—24no—
62C23×C4×C11—24no—
63C23×C4×C11—44no—
64C23×C4×C11—44no—
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2314yes—
67C23×C4×C11C2314yes—
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C22×C22⋊D11—28no—
73C22×C22⋊D11—28no—
74C22×C22⋊D11—28no—
75C22×C22⋊D11C2314yes—
76C22×C22⋊D11C2314yes—
77C22×C22⋊D11C2318yes—
78C23×Dic11C2312yes—
79C23×Dic11C2314yes—
80C22×D44C2312yes—
81C22×D44C2312yes—
82C4×D4×C11—232no—
83C2×C11×C4⋊C4—24no—
84C2×C11×C4⋊C4C2314yes—
85C2×C11×C22⋊C4—24no—
86C2×C11×C22⋊C4D418yescomplemented
87C2×C11×C22⋊C4C2314yes—
88C2×C11×C22⋊C4C2314yes—
89C2×C42×C11—24no—
90C2×C42×C11C2314yes—
91#67006—216no—
92C2×C22⋊Dic11—28no—
93C2×C22⋊Dic11C2314yes—
94C2×C22⋊Dic11C2314yes—
95C2×C22⋊Dic11C2318yes—
96#66992—232no—
97#66990—216no—
98#66988—216no—
99#66983—28no—
100#66983—28no—
101#66983—48no—
102#66982—216no—
103C2×(C2×D11)⋊C4—48no—
104C2×(C2×D11)⋊C4C2314yes—
105C2×(C2×D11)⋊C4C2314yes—
106C2×(C2×D11)⋊C4C2318yes—
107C2×(C2×D11)⋊C4C2318yes—
108C2×(C2×D11)⋊C4C2318yes—
109C2×C4⋊Dic11C2312yes—
110C2×C4⋊Dic11C2312yes—
111C2×C4⋊Dic11C2314yes—
112C2×C4⋊Dic11C2314yes—
113C2×Dic11⋊C4C2318yes—
114#66939—216no—
115#66935—216no—
116C11⋊#95C2318yes—
117C11⋊#95C2314yes—
118C11⋊#95C2314yes—
119C11⋊#95C2318yes—
120#34984—111nomaximal, Sylow
121C24×C11—22no—
122C24×C11—22no—
123C24×C11—42no—
124C24×C11—42no—
125C24×C11—42no—
126C24×C11—42no—
127C24×C11C2×D414yes—
128C24×C11C2×D414yes—
129C24×C11C2×D414yes—
130C24×C11#4114yes—
131C24×C11C2412yes—
132C24×C11C2411yescharacteristic
133C24×C11C2412yes—
134C23×D11—24no—
135C23×D11—24no—
136C23×D11—24no—
137C23×D11—44no—
138C23×D11—44no—
139C23×D11C2414yes—
140C2×D4×C11—232no—
141C2×D4×C11—28no—
142C2×D4×C11—28no—
143C2×D4×C11C2×D4116yes—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—24no—
148C22×C4×C11—22no—
149C22×C4×C11—28no—
150C22×C4×C11—28no—
151C22×C4×C11—28no—
152C22×C4×C11—28no—
153C22×C4×C11—42no—
154C22×C4×C11—44no—
155C22×C4×C11—44no—
156C22×C4×C11—42no—
157C22×C4×C11—42no—
158C22×C4×C11—416no—
159C22×C4×C11—416no—
160C22×C4×C11C2×D414yes—
161C22×C4×C11C2×D414yes—
162C22×C4×C11C2×D414yes—
163C22×C4×C11C2412yes—
164C22×C4×C11C2412yes—
165C22×C4×C11C2412yes—
166C22×C4×C11C2412yes—
167C22×C4×C11C2412yes—
168C2×C22⋊D11—28no—
169C2×C22⋊D11—28no—
170C2×C22⋊D11—28no—
171C2×C22⋊D11—28no—
172C2×C22⋊D11—216no—
173C2×C22⋊D11—28no—
174C2×C22⋊D11—28no—
175C2×C22⋊D11—48no—
176C2×C22⋊D11—48no—
177C2×C22⋊D11—432no—
178C22×Dic11—24no—
179C22×Dic11—24no—
180C22×Dic11—28no—
181C22×Dic11—24no—
182C22×Dic11—44no—
183C22×Dic11—44no—
184C22×Dic11C2414yes—
185C22×Dic11C2418yes—
186C2×D44—24no—
187C2×D44—24no—
188C2×D44—44no—
189C2×D44—44no—
190C11×C4⋊C4—28no—
191C11×C22⋊C4—28no—
192C11×C22⋊C4C2×D4116yes—
193C42×C11—28no—
194C22⋊Dic11—28no—
195C22⋊Dic11—28no—
196C22⋊Dic11—216no—
197(C2×D11)⋊C4—28no—
198(C2×D11)⋊C4—28no—
199(C2×D11)⋊C4—216no—
200(C2×D11)⋊C4—216no—
201(C2×D11)⋊C4—48no—
202C4⋊Dic11—24no—
203C4⋊Dic11—24no—
204C4⋊Dic11—44no—
205C4⋊Dic11—44no—
206Dic11⋊C4—216no—
207C2×#534—112no—
208C2×#534—111no—
209C22×C4×D4D1111yescharacteristic, complemented
210#2854—112no—
211#2847—112no—
212#2618—112no—
213#2617—112no—
214#2425—118no—
215#2424—118no—
216#2315—111no—
217C2×#386—112no—
218C23×C11—24no—
219C23×C11—22no—
220C23×C11—24no—
221C23×C11—22no—
222C23×C11—28no—
223C23×C11—22no—
224C23×C11—22no—
225C23×C11—24no—
226C23×C11—24no—
227C23×C11—44no—
228C23×C11—48no—
229C23×C11—48no—
230C23×C11—44no—
231C23×C11—48no—
232C23×C11—44no—
233C23×C11—48no—
234C23×C11—44no—
235C23×C11#121116yescomplemented
236C23×C11C22×D414yes—
237C23×C11C22×D412yes—
238C23×C11C22×D414yes—
239C23×C11C22×D414yes—
240C23×C11C22×D412yes—
241C23×C11C2×#4114yes—
242C23×C11C2×#4112yes—
243C23×C11C2511yescharacteristic
244C22×D11—24no—
245C22×D11—24no—
246C22×D11—24no—
247C22×D11—28no—
248C22×D11—28no—
249C22×D11—416no—
250C22×D11—48no—
251C22×D11—84no—
252C22×D11—84no—
253C22×D11—88no—
254D4×C11—232no—
255C2×C4×C11—28no—
256C2×C4×C11—28no—
257C2×C4×C11—22no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—24no—
261C2×C4×C11—22no—
262C2×C4×C11—24no—
263C2×C4×C11—22no—
264C2×C4×C11—24no—
265C2×C4×C11—44no—
266C2×C4×C11—44no—
267C2×C4×C11—416no—
268C2×C4×C11—416no—
269C2×C4×C11—44no—
270C2×C4×C11C22×D414yes—
271C2×C4×C11C22×D414yes—
272C2×C4×C11C22×D414yes—
273C2×C4×C11H(5,𝔽2)14yes—
274C22⋊D11—416no—
275C22⋊D11—416no—
276C22⋊D11—816no—
277C2×Dic11—24no—
278C2×Dic11—28no—
279C2×Dic11—24no—
280C2×Dic11—24no—
281C2×Dic11—28no—
282C2×Dic11—28no—
283C2×Dic11—48no—
284C2×Dic11—88no—
285D44—84no—
286D44—84no—
287C23×D4—112no—
288C23×D4C2×D1111yescharacteristic
289C24×C4C2×D1111yescharacteristic
290C24×C4C2×D1111yescharacteristic, complemented
291#534—2216no—
292#534—228no—
293C2×#123—114no—
294C2×#123—114no—
295C2×#123—114no—
296C2×#121—118no—
297C2×#121—112no—
298C2×#121—112no—
299C2×#121—114no—
300C2×#120—114no—
301C2×#120—114no—
302C2×#120—114no—
303C2×C4×D4—28no—
304C2×C4×D4C2×D1118yescomplemented
305C22×C4⋊C4C2×D1111yescharacteristic, complemented
306C22×C22⋊C4—112no—
307C22×C22⋊C4—114no—
308C22×C22⋊C4C2×D1111yescharacteristic
309C22×C22⋊C4C2×D1111yescharacteristic, complemented
310C22×C42C2×D1111yescharacteristic, complemented
311#398—114no—
312#397—114no—
313#396—118no—
314#394—114no—
315#394—118no—
316#392—114no—
317#390—114no—
318#389—114no—
319#388—118no—
320#386—114no—
321#386—118no—
322#386—114no—
323#386—118no—
324#385—118no—
325#380—112no—
326#380—112no—
327#380—114no—
328C2×#95—114no—
329C22×C11—28no—
330C22×C11—24no—
331C22×C11—22no—
332C22×C11—24no—
333C22×C11—22no—
334C22×C11—24no—
335C22×C11—28no—
336C22×C11—24no—
337C22×C11—24no—
338C22×C11—28no—
339C22×C11—416no—
340C22×C11—416no—
341C22×C11—44no—
342C22×C11—42no—
343C22×C11—42no—
344C22×C11C2×#12114yes—
345C22×C11C2×#12118yes—
346C22×C11C23×D411yescharacteristic
347C22×C11C23×D411yescharacteristic
348C22×C11C22×#4111yescharacteristic
349C22×C11C2×H(5,𝔽2)12yes—
350C22×C11#58512yes—
351C2×D11—44no—
352C2×D11—48no—
353C2×D11—44no—
354C2×D11—44no—
355C2×D11—48no—
356C2×D11—816no—
357C4×C11—24no—
358C4×C11—24no—
359C4×C11—24no—
360C4×C11—24no—
361C4×C11—42no—
362Dic11—44no—
363Dic11—48no—
364C25—112no—
365C25C22×D1111yescharacteristic
366C25C22×D1111yescharacteristic
367C22×D4—24no—
368C22×D4—24no—
369C22×D4—114no—
370C22×D4—114no—
371C22×D4—118no—
372C22×D4—112no—
373C22×D4—112no—
374C22×D4—228no—
375C22×D4—228no—
376C22×D4—228no—
377C22×D4D4418yescomplemented
378C22×D4C22×D1114yes—
379C23×C4—24no—
380C23×C4—24no—
381C23×C4—44no—
382C23×C4—44no—
383C23×C4—112no—
384C23×C4—114no—
385C23×C4C22×D1111yescharacteristic
386C23×C4C22×D1114yes—
387C23×C4C22×D1114yes—
388C23×C4C22×D1111yescharacteristic
389C23×C4C22×D1111yescharacteristic
390C23×C4C22×D1111yescharacteristic
391C23×C4C22×D1111yescharacteristic
392#123—2216no—
393#123—2216no—
394#123—2216no—
395#121—2232no—
396#121—228no—
397#121—228no—
398#121—448no—
399#120—2216no—
400#120—2216no—
401#120—2216no—
402C4×D4—232no—
403C2×C4⋊C4—24no—
404C2×C4⋊C4—112no—
405C2×C4⋊C4—118no—
406C2×C4⋊C4—112no—
407C2×C4⋊C4—114no—
408C2×C4⋊C4—114no—
409C2×C4⋊C4C22×D1114yes—
410C2×C22⋊C4—24no—
411C2×C22⋊C4—114no—
412C2×C22⋊C4—114no—
413C2×C22⋊C4—118no—
414C2×C22⋊C4—118no—
415C2×C22⋊C4—114no—
416C2×C22⋊C4—114no—
417C2×C22⋊C4—118no—
418C2×C22⋊C4—118no—
419C2×C22⋊C4—228no—
420C2×C22⋊C4—448no—
421C2×C22⋊C4C22⋊D1118yescomplemented
422C2×C22⋊C4C22×D1114yes—
423C2×C22⋊C4C22×D1114yes—
424C2×C42—24no—
425C2×C42C22×D1114yes—
426#95—118no—
427#95—118no—
428#95—114no—
429#95—114no—
430C2×C11—28no—
431C2×C11—24no—
432C2×C11—44no—
433C2×C11C22×#12111yescharacteristic
434C2×C11#345912yes—
435C2×C11#348411yescharacteristic
436C2×C11#348511yescharacteristic
437C2×C11#349612yes—
438D11—84no—
439C24—22no—
440C24—22no—
441C24—42no—
442C24—42no—
443C24—42no—
444C24—42no—
445C24—114no—
446C24—224no—
447C24—224no—
448C24—224no—
449C24—444no—
450C24—444no—
451C24C2×D4414yes—
452C24C2×D4414yes—
453C24#433914yes—
454C24C2×C22⋊D1114yes—
455C24C23×D1112yes—
456C24C23×D1111yescharacteristic
457C24C23×D1112yes—
458C2×D4—232no—
459C2×D4—28no—
460C2×D4—28no—
461C2×D4—228no—
462C2×D4—228no—
463C2×D4—228no—
464C2×D4—228no—
465C2×D4—228no—
466C2×D4—228no—
467C2×D4—2216no—
468C2×D4—224no—
469C2×D4—224no—
470C2×D4—444no—
471C2×D4—444no—
472C2×D4—448no—
473C2×D4—448no—
474C2×D4—4432no—
475C2×D4C2×D44116yes—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—24no—
480C22×C4—22no—
481C22×C4—28no—
482C22×C4—28no—
483C22×C4—28no—
484C22×C4—28no—
485C22×C4—42no—
486C22×C4—44no—
487C22×C4—44no—
488C22×C4—42no—
489C22×C4—42no—
490C22×C4—416no—
491C22×C4—416no—
492C22×C4—118no—
493C22×C4—114no—
494C22×C4—224no—
495C22×C4—224no—
496C22×C4—224no—
497C22×C4—228no—
498C22×C4—444no—
499C22×C4—444no—
500C22×C4C2×D4414yes—
501C22×C4C2×C22⋊D1114yes—
502C22×C4C2×C22⋊D1114yes—
503C22×C4C23×D1112yes—
504C22×C4C23×D1112yes—
505C22×C4C23×D1112yes—
506C22×C4C23×D1112yes—
507C22×C4C23×D1112yes—
508C4⋊C4—28no—
509C4⋊C4—2216no—
510C4⋊C4—224no—
511C4⋊C4—224no—
512C4⋊C4—444no—
513C4⋊C4—444no—
514C22⋊C4—28no—
515C22⋊C4—228no—
516C22⋊C4—228no—
517C22⋊C4—2216no—
518C22⋊C4—2216no—
519C22⋊C4—2216no—
520C22⋊C4—228no—
521C22⋊C4—228no—
522C22⋊C4—448no—
523C22⋊C4C2×C22⋊D11116yes—
524C42—28no—
525C11#3498411yescharacteristic, complemented, Sylow
526C23—22no—
527C23—24no—
528C23—22no—
529C23—24no—
530C23—28no—
531C23—22no—
532C23—24no—
533C23—24no—
534C23—22no—
535C23—44no—
536C23—48no—
537C23—48no—
538C23—48no—
539C23—44no—
540C23—44no—
541C23—44no—
542C23—48no—
543C23—224no—
544C23—224no—
545C23—228no—
546C23—228no—
547C23—224no—
548C23—4416no—
549C23—448no—
550C23—888no—
551C23—884no—
552C23—884no—
553C23#66983116yescomplemented
554C23C22×D4414yes—
555C23C22×D4412yes—
556C23C22×D4414yes—
557C23C2×#433912yes—
558C23C2×#433914yes—
559C23C22×C22⋊D1114yes—
560C23C22×C22⋊D1112yes—
561C23C24×D1111yescharacteristic
562D4—232no—
563D4—4416no—
564D4—4416no—
565D4—884no—
566D4—884no—
567D4—8816no—
568C2×C4—28no—
569C2×C4—28no—
570C2×C4—22no—
571C2×C4—24no—
572C2×C4—22no—
573C2×C4—24no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—24no—
577C2×C4—22no—
578C2×C4—44no—
579C2×C4—44no—
580C2×C4—416no—
581C2×C4—416no—
582C2×C4—44no—
583C2×C4—228no—
584C2×C4—224no—
585C2×C4—224no—
586C2×C4—228no—
587C2×C4—228no—
588C2×C4—224no—
589C2×C4—448no—
590C2×C4—888no—
591C2×C4C22×D4414yes—
592C2×C4#6703714yes—
593C2×C4C22×C22⋊D1114yes—
594C2×C4C22×C22⋊D1114yes—
595C22—28no—
596C22—24no—
597C22—22no—
598C22—24no—
599C22—22no—
600C22—24no—
601C22—24no—
602C22—28no—
603C22—28no—
604C22—24no—
605C22—416no—
606C22—416no—
607C22—42no—
608C22—42no—
609C22—44no—
610C22—448no—
611C22—444no—
612C22—444no—
613C22—448no—
614C22—444no—
615C22—8816no—
616C22C2×#6698314yes—
617C22C2×#6698318yes—
618C22C23×D4411yescharacteristic
619C22C22×#433911yescharacteristic
620C22C2×#6703712yes—
621C22#1062345312yes—
622C22C23×C22⋊D1111yescharacteristic
623C4—24no—
624C4—24no—
625C4—24no—
626C4—24no—
627C4—42no—
628C4—448no—
629C4—444no—
630C2—24no—
631C2—28no—
632C2—44no—
633C2—884no—
634C2C22×#6698311yescharacteristic
635C2#1308202512yes—
636C2#1308225111yescharacteristic
637C2#1308226011yescharacteristic
638C2#1308238012yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC22×C4×D4×C11C2
hypercenterC22×C4×D4D11
hypocenterC11#34984
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#10623024C2semidirect
2. C2×#10623335C2semidirect
3. #13076947C2semidirect
4. #13076898C2semidirect
5. #13074358C2semidirect
6. #13074350C2semidirect
7. #13072161C2semidirect
8. #13072146C2semidirect
9. #13071230C2semidirect
10. C2×#10622826C2semidirect
11. C22×C4×D4×C11C2semidirect
14. C24×C4×C11C22semidirect
17. C2×C4×D4×C11C22semidirect
18. C22×C11×C4⋊C4C22semidirect
20. C22×C11×C22⋊C4C22semidirect
21. C22×C42×C11C22semidirect
22. C2×#67006C22semidirect
26. C2×#66990C22semidirect
27. C2×#66988C22semidirect
30. C2×#66983C22semidirect
31. C2×#66982C22semidirect
32. C22×(C2×D11)⋊C4C22semidirect
34. C2×#66939C22semidirect
35. C2×#66935C22semidirect
36. #10622826C22semidirect
37. #10622826C22semidirect
38. #10622826C22semidirect
39. #10622826C22semidirect
40. #10622825C22semidirect
41. #10622825C22semidirect
42. #10622825C22semidirect
43. C2×C11⋊#95C22semidirect
44. #10622607C22semidirect
45. #10622604C22semidirect
46. #10622596C22semidirect
47. #10622574C22semidirect
48. #10622573C22semidirect
49. #10622566C22semidirect
50. #10622563C22semidirect
51. #10622553C22semidirect
52. #10622552C22semidirect
53. #10622541C22semidirect
59. C22×D4×C11D4semidirect
86. C2×C11×C22⋊C4D4semidirect
209. C22×C4×D4D11semidirect
235. C23×C11#121semidirect
290. C24×C4C2×D11semidirect
304. C2×C4×D4C2×D11semidirect
305. C22×C4⋊C4C2×D11semidirect
309. C22×C22⋊C4C2×D11semidirect
310. C22×C42C2×D11semidirect
377. C22×D4D44semidirect
421. C2×C22⋊C4C22⋊D11semidirect
525. C11#34984semidirect
553. C23#66983semidirect

Maximal subgroups

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

subgroupindex
C2×#106230242
C2×#106233352
#130769472
#130768982
#130743582
#130743502
#130721612
#130721462
#130712302
C2×#106228262
C22×C4×D4×C112
#3498411