Finite Group Databasebeta

← #14685168

Subgroups — #14685168

Order 2816.

3654 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66977C211yesmaximal, characteristic, complemented
2C23×(C2×D11)⋊C4C211yesmaximal, characteristic
3C2×#10622286C212yesmaximal, complemented
4C2×#10622568C212yesmaximal
5#13066862C212yesmaximal, complemented
6#13066860C214yesmaximal, complemented
7#13066838C212yesmaximal, complemented
8C11×C22⋊#95C211yesmaximal, characteristic, complemented
9C25×D11C2211yescharacteristic
10C24×C4×C11C2211yescharacteristic
11C24×Dic11C2211yescharacteristic
12C23×Dic22C2211yescharacteristic, complemented
13C22×C11×C22⋊C4C2212yes—
14C22×C22⋊Dic11C2212yes—
15C22×(C2×D11)⋊C4—24no—
16C22×(C2×D11)⋊C4—28no—
17C22×(C2×D11)⋊C4C2212yes—
18C22×(C2×D11)⋊C4C2214yes—
19C22×(C2×D11)⋊C4C2214yes—
20C22×(C2×D11)⋊C4C2212yes—
21C22×C4⋊Dic11C2211yescharacteristic, complemented
22C2×#66977—24no—
23C2×#66977—28no—
24C22×Dic11⋊C4C2212yescomplemented
25C2×C11×#95C2212yescomplemented
26C2×C11×#95C2212yescomplemented
27C2×C11⋊#95C2214yescomplemented
28C2×C11⋊#95C2214yescomplemented
29#10622568—28no—
30#10622286—28no—
31C25×C11C2311yescharacteristic
32C24×D11—22no—
33C24×D11—22no—
34C24×D11—24no—
35C24×D11—24no—
36C24×D11—24no—
37C24×D11—24no—
38C24×D11—42no—
39C24×D11—42no—
40C24×D11Q814yescomplemented
41C24×D11C2312yes—
42C23×C4×C11—24no—
43C23×C4×C11—24no—
44C23×C4×C11—42no—
45C23×C4×C11D414yes—
46C23×C4×C11C2314yes—
47C23×C4×C11C2311yescharacteristic
48C23×C4×C11C2311yescharacteristic
49C23×Dic11—22no—
50C23×Dic11—24no—
51C23×Dic11—24no—
52C23×Dic11—42no—
53C23×Dic11C2312yes—
54C23×Dic11C2312yes—
55C23×Dic11C2312yes—
56C22×Dic22—22no—
57C22×Dic22—24no—
58C22×Dic22—24no—
59C22×Dic22—42no—
60C2×C11×C22⋊C4—24no—
61C2×C11×C22⋊C4—24no—
62C2×C11×C22⋊C4—24no—
63C2×C22⋊Dic11—24no—
64C2×C22⋊Dic11—24no—
65C2×C22⋊Dic11D418yes—
66C2×(C2×D11)⋊C4—232no—
67C2×(C2×D11)⋊C4—24no—
68C2×(C2×D11)⋊C4—24no—
69C2×(C2×D11)⋊C4—24no—
70C2×(C2×D11)⋊C4—24no—
71C2×(C2×D11)⋊C4—24no—
72C2×(C2×D11)⋊C4—28no—
73C2×(C2×D11)⋊C4—28no—
74C2×(C2×D11)⋊C4—28no—
75C2×(C2×D11)⋊C4—28no—
76C2×(C2×D11)⋊C4—44no—
77C2×(C2×D11)⋊C4—44no—
78C2×(C2×D11)⋊C4D418yes—
79C2×C4⋊Dic11—22no—
80C2×C4⋊Dic11—24no—
81#66977—232no—
82C2×Dic11⋊C4—24no—
83C2×Dic11⋊C4—24no—
84C2×Dic11⋊C4—24no—
85C11×#95—24no—
86C11×#95—42no—
87C11⋊#95—28no—
88C11⋊#95—44no—
89#14717—111nomaximal, Sylow
90C24×C11—22no—
91C24×C11—22no—
92C24×C11—22no—
93C24×C11—22no—
94C24×C11C2×D412yes—
95C24×C11C2×D414yes—
96C24×C11C2×Q812yes—
97C24×C11#4114yes—
98C24×C11#4112yes—
99C24×C11C2411yescharacteristic
100C23×D11—28no—
101C23×D11—216no—
102C23×D11—28no—
103C23×D11—28no—
104C23×D11—22no—
105C23×D11—22no—
106C23×D11—24no—
107C23×D11—22no—
108C23×D11—22no—
109C23×D11—24no—
110C23×D11—24no—
111C23×D11—24no—
112C23×D11—216no—
113C23×D11—216no—
114C23×D11—48no—
115C23×D11—416no—
116C23×D11—416no—
117C23×D11—416no—
118C23×D11—416no—
119C23×D11—44no—
120C23×D11—44no—
121C23×D11—48no—
122C23×D11—44no—
123C23×D11—44no—
124C23×D11—48no—
125C23×D11C2×D414yes—
126C23×D11C2×Q814yes—
127C23×D11#4114yes—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—28no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—28no—
135C22×C4×C11—24no—
136C22×C4×C11—24no—
137C22×C4×C11—24no—
138C22×C4×C11—24no—
139C22×C4×C11—24no—
140C22×C4×C11—24no—
141C22×C4×C11—24no—
142C22×C4×C11—44no—
143C22×C4×C11—416no—
144C22×C4×C11C2×D412yes—
145C22×C4×C11C2×D412yes—
146C22×C4×C11C2×D414yes—
147C22×Dic11—28no—
148C22×Dic11—24no—
149C22×Dic11—22no—
150C22×Dic11—22no—
151C22×Dic11—22no—
152C22×Dic11—22no—
153C22×Dic11—22no—
154C22×Dic11—22no—
155C22×Dic11—24no—
156C22×Dic11—24no—
157C22×Dic11—24no—
158C22×Dic11—24no—
159C22×Dic11—24no—
160C22×Dic11—416no—
161C22×Dic11—44no—
162C22×Dic11—44no—
163C22×Dic11C2×D414yes—
164C22×Dic11C2×D414yes—
165C22×Dic11C2×D414yes—
166C2×Dic22—28no—
167C2×Dic22—416no—
168C2×Dic22—44no—
169C2×Dic22—44no—
170C11×C22⋊C4—48no—
171C22⋊Dic11—216no—
172(C2×D11)⋊C4—216no—
173(C2×D11)⋊C4—216no—
174(C2×D11)⋊C4—416no—
175(C2×D11)⋊C4—416no—
176C4⋊Dic11—28no—
177Dic11⋊C4—216no—
178C22×C22⋊Q8—111no—
179C23×C22⋊C4—111no—
180C2×#393—112no—
181C2×#379—112no—
182#1439—114no—
183#1439—112no—
184C22⋊#95—112no—
185C22⋊#95D1111yescharacteristic, complemented
186C23×C11—22no—
187C23×C11—24no—
188C23×C11—22no—
189C23×C11—24no—
190C23×C11—22no—
191C23×C11—22no—
192C23×C11—24no—
193C23×C11—24no—
194C23×C11—28no—
195C23×C11—28no—
196C23×C11—28no—
197C23×C11—28no—
198C23×C11#12014yes—
199C23×C11C22⋊Q818yes—
200C23×C11C22⋊Q814yes—
201C23×C11#12414yes—
202C23×C11#12418yes—
203C23×C11C22×D411yescharacteristic
204C23×C11C22×D412yes—
205C23×C11C22×D412yes—
206C23×C11C22×Q811yescharacteristic
207C23×C11C2×#4112yes—
208C23×C11C2×#4111yescharacteristic
209C23×C11C2×#4112yes—
210C23×C11H(5,𝔽2)12yes—
211C23×C11H(5,𝔽2)12yes—
212C22×D11—232no—
213C22×D11—24no—
214C22×D11—28no—
215C22×D11—24no—
216C22×D11—24no—
217C22×D11—24no—
218C22×D11—24no—
219C22×D11—24no—
220C22×D11—28no—
221C22×D11—28no—
222C22×D11—28no—
223C22×D11—28no—
224C22×D11—28no—
225C22×D11—464no—
226C22×D11—416no—
227C22×D11—416no—
228C22×D11—416no—
229C22×D11—416no—
230C22×D11—416no—
231C22×D11—464no—
232C22×D11—42no—
233C22×D11—42no—
234C22×D11—44no—
235C22×D11—42no—
236C22×D11—42no—
237C22×D11—44no—
238C22×D11—44no—
239C22×D11—44no—
240C22×D11—44no—
241C22×D11—44no—
242C22×D11—416no—
243C22×D11C22⋊Q818yescomplemented
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—28no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—416no—
251C2×C4×C11—44no—
252C2×C4×C11—44no—
253C2×C4×C11—44no—
254C2×C4×C11—44no—
255C2×C4×C11—44no—
256C2×C4×C11—44no—
257C2×C4×C11—44no—
258C2×C4×C11—44no—
259C2×C4×C11#12014yes—
260C2×Dic11—24no—
261C2×Dic11—24no—
262C2×Dic11—24no—
263C2×Dic11—28no—
264C2×Dic11—28no—
265C2×Dic11—28no—
266C2×Dic11—416no—
267C2×Dic11—42no—
268C2×Dic11—42no—
269C2×Dic11—42no—
270C2×Dic11—42no—
271C2×Dic11—42no—
272C2×Dic11—42no—
273C2×Dic11—44no—
274C2×Dic11—44no—
275C2×Dic11—44no—
276Dic22—416no—
277C26—111no—
278C23×Q8—111no—
279C24×C4—111no—
280C24×C4C2×D1111yescharacteristic
281C2×C22⋊Q8—228no—
282C2×C22⋊Q8—224no—
283C22×C4⋊C4—112no—
284C22×C4⋊C4—111no—
285C22×C22⋊C4—112no—
286C22×C22⋊C4—112no—
287C22×C22⋊C4—112no—
288C22×C22⋊C4—114no—
289C22×C22⋊C4—114no—
290C22×C22⋊C4—228no—
291C22×C22⋊C4—224no—
292C22×C22⋊C4C2×D1112yes—
293#393—228no—
294#379—228no—
295C2×#95—114no—
296C2×#95—114no—
297C2×#95C2×D1112yescomplemented
298C2×#95C2×D1112yescomplemented
299C22×C11—24no—
300C22×C11—24no—
301C22×C11—24no—
302C22×C11—24no—
303C22×C11—24no—
304C22×C11—24no—
305C22×C11—216no—
306C22×C11—216no—
307C22×C11#39318yescomplemented
308C22×C11C2×#12011yescharacteristic
309C22×C11C2×#12011yescharacteristic
310C22×C11C2×C22⋊Q812yes—
311C22×C11C2×C22⋊Q811yescharacteristic
312C22×C11C2×C22⋊Q812yes—
313C22×C11#52511yescharacteristic
314C22×C11#52512yes—
315C22×C11C2×#12411yescharacteristic
316C22×C11C2×#12412yes—
317C22×C11#53411yescharacteristic
318C22×C11#53511yescharacteristic
319C22×C11#53812yes—
320C22×C11#54312yes—
321C22×C11D4214yes—
322C22×C11#54614yes—
323C22×C11#54614yes—
324C22×C11#55114yes—
325C2×D11—28no—
326C2×D11—216no—
327C2×D11—464no—
328C2×D11—44no—
329C2×D11—44no—
330C2×D11—44no—
331C2×D11—44no—
332C2×D11—44no—
333C2×D11—44no—
334C2×D11—48no—
335C2×D11—48no—
336C2×D11—48no—
337C4×C11—24no—
338C4×C11—42no—
339C4×C11—84no—
340Dic11—44no—
341Dic11—44no—
342Dic11—44no—
343C25—112no—
344C25—114no—
345C25—224no—
346C25—224no—
347C25—222no—
348C25—222no—
349C25—224no—
350C25—224no—
351C25—442no—
352C25—442no—
353C25C22×D1111yescharacteristic
354C22×Q8—224no—
355C22×Q8—222no—
356C22×Q8—224no—
357C22×Q8—442no—
358C23×C4—24no—
359C23×C4—24no—
360C23×C4—42no—
361C23×C4—112no—
362C23×C4—112no—
363C23×C4—112no—
364C23×C4—224no—
365C23×C4—222no—
366C23×C4—224no—
367C23×C4—442no—
368C23×C4D4414yes—
369C23×C4C22×D1114yes—
370C23×C4C22×D1111yescharacteristic
371C23×C4C22×D1111yescharacteristic
372C22⋊Q8—2232no—
373C2×C4⋊C4—224no—
374C2×C4⋊C4—224no—
375C2×C4⋊C4—224no—
376C2×C4⋊C4—224no—
377C2×C4⋊C4—222no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—118no—
382C2×C22⋊C4—118no—
383C2×C22⋊C4—224no—
384C2×C22⋊C4—224no—
385C2×C22⋊C4—2232no—
386C2×C22⋊C4—224no—
387C2×C22⋊C4—224no—
388C2×C22⋊C4—224no—
389C2×C22⋊C4—224no—
390C2×C22⋊C4—224no—
391C2×C22⋊C4—228no—
392C2×C22⋊C4—228no—
393C2×C22⋊C4—228no—
394C2×C22⋊C4—228no—
395C2×C22⋊C4—444no—
396C2×C22⋊C4—444no—
397#95—24no—
398#95—42no—
399#95—228no—
400#95—444no—
401C2×C11—28no—
402C2×C11C2×#39311yescharacteristic
403C2×C11#240311yescharacteristic
404C2×C11#240411yescharacteristic
405C2×C11#243511yescharacteristic
406C2×C11#243714yes—
407C2×C11#247214yes—
408C2×C11#256111yescharacteristic
409C2×C11#262611yescharacteristic
410C2×C11#284811yescharacteristic
411D11—48no—
412C24—22no—
413C24—22no—
414C24—22no—
415C24—22no—
416C24—114no—
417C24—114no—
418C24—114no—
419C24—2216no—
420C24—228no—
421C24—228no—
422C24—2216no—
423C24—228no—
424C24—222no—
425C24—224no—
426C24—222no—
427C24—224no—
428C24—222no—
429C24—224no—
430C24—222no—
431C24—224no—
432C24—2216no—
433C24—448no—
434C24—4416no—
435C24—4416no—
436C24—4416no—
437C24—4416no—
438C24—444no—
439C24—444no—
440C24—448no—
441C24—444no—
442C24—444no—
443C24—448no—
444C24C2×D4412yes—
445C24#433914yes—
446C24D4×D1114yes—
447C24#434112yes—
448C24Q8×D1112yes—
449C24C23×D1111yescharacteristic
450C2×Q8—228no—
451C2×Q8—4416no—
452C2×Q8—444no—
453C2×Q8—444no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—28no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—28no—
461C22×C4—24no—
462C22×C4—24no—
463C22×C4—24no—
464C22×C4—24no—
465C22×C4—24no—
466C22×C4—24no—
467C22×C4—24no—
468C22×C4—44no—
469C22×C4—416no—
470C22×C4—114no—
471C22×C4—114no—
472C22×C4—114no—
473C22×C4—228no—
474C22×C4—222no—
475C22×C4—222no—
476C22×C4—222no—
477C22×C4—224no—
478C22×C4—224no—
479C22×C4—222no—
480C22×C4—222no—
481C22×C4—222no—
482C22×C4—224no—
483C22×C4—224no—
484C22×C4—224no—
485C22×C4—224no—
486C22×C4—4416no—
487C22×C4—444no—
488C22×C4—444no—
489C22×C4C2×D4412yes—
490C22×C4C2×D4412yes—
491C22×C4D4×D1114yes—
492C4⋊C4—2216no—
493C4⋊C4—228no—
494C22⋊C4—48no—
495C22⋊C4—2216no—
496C22⋊C4—2216no—
497C22⋊C4—2216no—
498C22⋊C4—4416no—
499C22⋊C4—4416no—
500C11#1471711yescharacteristic, complemented, Sylow
501C23—22no—
502C23—22no—
503C23—22no—
504C23—22no—
505C23—28no—
506C23—28no—
507C23—28no—
508C23—24no—
509C23—24no—
510C23—24no—
511C23—24no—
512C23—28no—
513C23—118no—
514C23—2232no—
515C23—224no—
516C23—228no—
517C23—224no—
518C23—224no—
519C23—228no—
520C23—228no—
521C23—228no—
522C23—224no—
523C23—224no—
524C23—224no—
525C23—228no—
526C23—228no—
527C23—4464no—
528C23—4416no—
529C23—4416no—
530C23—4416no—
531C23—4464no—
532C23—4416no—
533C23—4416no—
534C23—442no—
535C23—442no—
536C23—444no—
537C23—442no—
538C23—4416no—
539C23—442no—
540C23—444no—
541C23—444no—
542C23—444no—
543C23—444no—
544C23—444no—
545C23#6692814yes—
546C23#6693514yes—
547C23#6693818yes—
548C23#6694918yes—
549C23#6695014yes—
550C23C22×D4411yescharacteristic
551C23C2×#433912yes—
552C23C2×D4×D1112yes—
553C23C2×D4×D1112yes—
554C23C2×#434111yescharacteristic
555C23#6703712yes—
556C23C2×Q8×D1111yescharacteristic
557C23#41×D1112yes—
558C23#6704212yes—
559Q8—4416no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—28no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—416no—
567C2×C4—44no—
568C2×C4—44no—
569C2×C4—44no—
570C2×C4—44no—
571C2×C4—44no—
572C2×C4—44no—
573C2×C4—44no—
574C2×C4—44no—
575C2×C4—224no—
576C2×C4—224no—
577C2×C4—224no—
578C2×C4—228no—
579C2×C4—228no—
580C2×C4—228no—
581C2×C4—4416no—
582C2×C4—442no—
583C2×C4—442no—
584C2×C4—442no—
585C2×C4—442no—
586C2×C4—442no—
587C2×C4—442no—
588C2×C4—444no—
589C2×C4—444no—
590C2×C4—444no—
591C2×C4#6693514yes—
592C22—24no—
593C22—24no—
594C22—24no—
595C22—216no—
596C22—24no—
597C22—216no—
598C22—24no—
599C22—24no—
600C22—2216no—
601C22—228no—
602C22—4464no—
603C22—444no—
604C22—444no—
605C22—444no—
606C22—448no—
607C22—448no—
608C22—444no—
609C22—448no—
610C22—444no—
611C22—444no—
612C22#1062228618yescomplemented
613C22C2×#6692811yescharacteristic
614C22C2×#6693511yescharacteristic
615C22C2×#6693511yescharacteristic
616C22C2×#6693812yes—
617C22#1062302411yescharacteristic
618C22C2×#6694912yes—
619C22C2×#6695011yescharacteristic
620C22#1062305511yescharacteristic
621C22#1062305611yescharacteristic
622C22#1062308114yes—
623C22#1062308714yes—
624C22#1062312114yes—
625C22#1062313712yes—
626C22#1062314812yes—
627C22D11×C22⋊Q812yes—
628C22#1062316512yes—
629C22#1062318514yes—
630C4—24no—
631C4—42no—
632C4—84no—
633C4—444no—
634C4—444no—
635C4—444no—
636C2—28no—
637C2—448no—
638C2C2×#1062228611yescharacteristic
639C2#1307192911yescharacteristic
640C2#1307193711yescharacteristic
641C2#1307226711yescharacteristic
642C2#1307228114yes—
643C2#1307274714yes—
644C2#1307376911yescharacteristic
645C2#1307442411yescharacteristic
646C2#1307690411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutator, socle, cosocleC24×C11C24
FittingC11×C22⋊#95C2
prime radicalC25×D11C22
hypercenterC22⋊#95D11
hypocenterC11#14717
LCSG ▷ C24×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
1. C22×#66977C2semidirect
3. C2×#10622286C2semidirect
5. #13066862C2semidirect
6. #13066860C2semidirect
7. #13066838C2semidirect
8. C11×C22⋊#95C2semidirect
12. C23×Dic22C22semidirect
21. C22×C4⋊Dic11C22semidirect
24. C22×Dic11⋊C4C22semidirect
25. C2×C11×#95C22semidirect
26. C2×C11×#95C22semidirect
27. C2×C11⋊#95C22semidirect
28. C2×C11⋊#95C22semidirect
40. C24×D11Q8semidirect
185. C22⋊#95D11semidirect
243. C22×D11C22⋊Q8semidirect
297. C2×#95C2×D11semidirect
298. C2×#95C2×D11semidirect
307. C22×C11#393semidirect
500. C11#14717semidirect
612. C22#10622286semidirect

Maximal subgroups

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

subgroupindex
C22×#669772
C23×(C2×D11)⋊C42
C2×#106222862
C2×#106225682
#130668622
#130668602
#130668382
C11×C22⋊#952
#1471711