Finite Group Databasebeta

← #14690492

Subgroups — #14690492

Order 2816.

2214 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66941C211yesmaximal, characteristic, complemented
2C2×#10622286C214yesmaximal, complemented
3C2×#10622552C211yesmaximal, characteristic
4C2×#10622601C211yesmaximal, characteristic
5C2×#10622601C211yesmaximal, characteristic
6#13066860C214yesmaximal, complemented
7#13066845C211yesmaximal, characteristic, complemented
8C4×C11⋊#95C211yesmaximal, characteristic, complemented
9C11×C4⋊#95C211yesmaximal, characteristic, complemented
10C23×D44C2211yescharacteristic
11C23×Dic22C2212yes—
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C42×C11C2211yescharacteristic
15C22×(C2×D11)⋊C4C2212yes—
16C22×(C2×D11)⋊C4C2212yes—
17C22×(C2×D11)⋊C4C2214yes—
18C22×(C2×D11)⋊C4C2214yes—
19C22×C4⋊Dic11C2211yescharacteristic
20C22×Dic11⋊C4C2212yes—
21C22×C4×Dic11C2211yescharacteristic
22C22×C4×Dic11C2211yescharacteristic
23C2×#66941—24no—
24C2×#66941—24no—
25C2×#66941—24no—
26C2×C11×#95C2214yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2214yes—
29C2×C11⋊#95C2212yes—
30#10622601—24no—
31#10622601—24no—
32#10622552—24no—
33#10622286—216no—
34C24×D11C2312yes—
35C23×C4×C11C2312yes—
36C23×C4×C11C2312yes—
37C23×C4×C11C2312yes—
38C23×C4×C11C2311yescharacteristic
39C23×Dic11C2312yes—
40C23×Dic11C2312yes—
41C23×Dic11C2311yescharacteristic
42C23×Dic11C2311yescharacteristic
43C22×D44—22no—
44C22×D44—22no—
45C22×D44—22no—
46C22×D44—22no—
47C22×D44—22no—
48C22×D44—22no—
49C22×D44Q814yescomplemented
50C22×Dic22—24no—
51C22×Dic22—24no—
52C22×Dic22—24no—
53C22×Dic22—28no—
54C22×Dic22—44no—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4—22no—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4D414yes—
61C2×C42×C11—22no—
62C2×C42×C11—22no—
63C2×C42×C11—22no—
64C2×(C2×D11)⋊C4—28no—
65C2×(C2×D11)⋊C4—28no—
66C2×(C2×D11)⋊C4—28no—
67C2×(C2×D11)⋊C4—28no—
68C2×(C2×D11)⋊C4—28no—
69C2×(C2×D11)⋊C4—24no—
70C2×(C2×D11)⋊C4—24no—
71C2×(C2×D11)⋊C4—28no—
72C2×(C2×D11)⋊C4—44no—
73C2×(C2×D11)⋊C4—44no—
74C2×C4⋊Dic11—22no—
75C2×C4⋊Dic11—22no—
76C2×C4⋊Dic11D414yes—
77C2×Dic11⋊C4—24no—
78C2×Dic11⋊C4—24no—
79C2×Dic11⋊C4—24no—
80C2×C4×Dic11—22no—
81C2×C4×Dic11—22no—
82C2×C4×Dic11—22no—
83C2×C4×Dic11—22no—
84C2×C4×Dic11—22no—
85C2×C4×Dic11D414yes—
86#66941—232no—
87C11×#95—28no—
88C11⋊#95—28no—
89C11⋊#95—24no—
90C11⋊#95D418yescomplemented
91#15144—111nomaximal, Sylow
92C24×C11C2411yescharacteristic
93C23×D11—24no—
94C23×D11—22no—
95C23×D11—22no—
96C23×D11—22no—
97C23×D11—24no—
98C23×D11—22no—
99C23×D11—22no—
100C23×D11—22no—
101C23×D11—24no—
102C23×D11—24no—
103C23×D11C2×Q814yes—
104C22×C4×C11—24no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—24no—
113C22×C4×C11—22no—
114C22×C4×C11—24no—
115C22×C4×C11—22no—
116C22×C4×C11—24no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11C2×D414yes—
120C22×C4×C11C2×D414yes—
121C22×C4×C11C2×D412yes—
122C22×C4×C11C2×D412yes—
123C22×C4×C11C2×D412yes—
124C22×C4×C11C2×Q812yes—
125C22×C4×C11#4112yes—
126C22×C4×C11#4112yes—
127C22×C4×C11#4112yes—
128C22×Dic11—21no—
129C22×Dic11—21no—
130C22×Dic11—21no—
131C22×Dic11—21no—
132C22×Dic11—24no—
133C22×Dic11—22no—
134C22×Dic11—22no—
135C22×Dic11—22no—
136C22×Dic11—22no—
137C22×Dic11—22no—
138C22×Dic11—22no—
139C22×Dic11—22no—
140C22×Dic11—22no—
141C22×Dic11—24no—
142C22×Dic11—22no—
143C22×Dic11—22no—
144C22×Dic11C2×D414yes—
145C22×Dic11C2×D414yes—
146C22×Dic11C2×D412yes—
147C22×Dic11C2×D414yes—
148C22×Dic11C2×D412yes—
149C22×Dic11#4114yes—
150C2×D44—28no—
151C2×D44—28no—
152C2×D44—28no—
153C2×D44—44no—
154C2×D44—44no—
155C2×D44—44no—
156C2×D44—44no—
157C2×Dic22—216no—
158C2×Dic22—416no—
159C2×Dic22—416no—
160C2×Dic22—48no—
161C2×Dic22—48no—
162C11×C4⋊C4—28no—
163C11×C4⋊C4—44no—
164C42×C11—44no—
165(C2×D11)⋊C4—416no—
166(C2×D11)⋊C4—416no—
167(C2×D11)⋊C4—48no—
168(C2×D11)⋊C4—48no—
169C4⋊Dic11—28no—
170Dic11⋊C4—216no—
171C4×Dic11—28no—
172C4×Dic11—44no—
173C22×C4⋊Q8—111no—
174C2×#393—114no—
175C2×#390—111no—
176C2×#390—111no—
177C2×#390—111no—
178#1439—114no—
179C4⋊#95—111no—
180C4⋊#95D1111yescharacteristic, complemented
181C4×#95—111no—
182C23×C11C22×D411yescharacteristic
183C23×C11C22×D411yescharacteristic
184C23×C11C22×D411yescharacteristic
185C23×C11C22×D412yes—
186C23×C11C22×Q811yescharacteristic
187C23×C11C2×#4111yescharacteristic
188C23×C11C2×#4111yescharacteristic
189C23×C11C2×#4111yescharacteristic
190C23×C11C2×#4112yes—
191C23×C11H(5,𝔽2)12yes—
192C23×C112−1+412yes—
193C22×D11—24no—
194C22×D11—24no—
195C22×D11—24no—
196C22×D11—28no—
197C22×D11—28no—
198C22×D11—42no—
199C22×D11—42no—
200C22×D11—42no—
201C22×D11—42no—
202C22×D11—42no—
203C22×D11—42no—
204C22×D11—44no—
205C22×D11—44no—
206C22×D11—42no—
207C22×D11—42no—
208C22×D11—44no—
209C22×D11—44no—
210C22×D11—44no—
211C22×D11—44no—
212C22×D11—44no—
213C22×D11—44no—
214C22×D11—44no—
215C22×D11—44no—
216C2×C4×C11—24no—
217C2×C4×C11—24no—
218C2×C4×C11—24no—
219C2×C4×C11—28no—
220C2×C4×C11—24no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11—44no—
226C2×C4×C11—42no—
227C2×C4×C11—42no—
228C2×C4×C11—42no—
229C2×C4×C11—42no—
230C2×C4×C11—42no—
231C2×C4×C11—44no—
232C2×C4×C11—44no—
233C2×C4×C11#12014yes—
234C2×C4×C11C22⋊Q814yes—
235C2×C4×C11C22⋊Q814yes—
236C2×C4×C11C22⋊Q814yes—
237C2×C4×C11#12414yes—
238C2×C4×C11#12414yes—
239C2×C4×C11#12414yes—
240C2×Dic11—22no—
241C2×Dic11—22no—
242C2×Dic11—22no—
243C2×Dic11—22no—
244C2×Dic11—24no—
245C2×Dic11—24no—
246C2×Dic11—24no—
247C2×Dic11—24no—
248C2×Dic11—24no—
249C2×Dic11—24no—
250C2×Dic11—24no—
251C2×Dic11—28no—
252C2×Dic11—24no—
253C2×Dic11—42no—
254C2×Dic11—42no—
255C2×Dic11—42no—
256C2×Dic11—42no—
257C2×Dic11—44no—
258C2×Dic11—42no—
259C2×Dic11—42no—
260C2×Dic11#12414yes—
261C2×Dic11#12714yes—
262D44—416no—
263Dic22—432no—
264C23×Q8—112no—
265C23×D4—111no—
266C2×C4⋊Q8—224no—
267C2×C4⋊Q8—224no—
268C2×C4⋊Q8—224no—
269C22×C4⋊C4—111no—
270C22×C4⋊C4—112no—
271C22×C4⋊C4C2×D1111yescharacteristic
272C22×C4⋊C4C2×D1111yescharacteristic
273C22×C22⋊C4—112no—
274C22×C22⋊C4—112no—
275C22×C22⋊C4—114no—
276C22×C22⋊C4—114no—
277C22×C42—111no—
278C22×C42—111no—
279C22×C42C2×D1111yescharacteristic
280#393—2216no—
281#390—224no—
282#390—224no—
283#390—224no—
284C2×#95—112no—
285C2×#95—114no—
286C2×#95—112no—
287C2×#95C2×D1114yes—
288C22×C11C2×#12011yescharacteristic
289C22×C11C2×C22⋊Q811yescharacteristic
290C22×C11C2×C22⋊Q811yescharacteristic
291C22×C11C2×C22⋊Q811yescharacteristic
292C22×C11C2×#12411yescharacteristic
293C22×C11C2×#12411yescharacteristic
294C22×C11C2×#12411yescharacteristic
295C22×C11C2×#12411yescharacteristic
296C22×C11C2×#12711yescharacteristic
297C22×C11#53212yes—
298C22×C11#53212yes—
299C22×C11#53511yescharacteristic
300C22×C11#53611yescharacteristic
301C22×C11#54212yes—
302C22×C11#54212yes—
303C22×C11D4212yes—
304C22×C11D4212yes—
305C22×C11#54712yes—
306C22×C11#54812yes—
307C22×C11#54812yes—
308C22×C11D4×Q812yes—
309C22×C11#55412yes—
310C22×C11#55512yes—
311C2×D11—44no—
312C2×D11—44no—
313C2×D11—48no—
314C2×D11—48no—
315C2×D11—44no—
316C2×D11—82no—
317C2×D11—82no—
318C2×D11—82no—
319C2×D11—82no—
320C2×D11—84no—
321C2×D11—84no—
322C4×C11—44no—
323C4×C11—44no—
324C4×C11—82no—
325C4×C11#39318yescomplemented
326Dic11—24no—
327Dic11—24no—
328Dic11—44no—
329Dic11—44no—
330C25—112no—
331C22×Q8—224no—
332C22×Q8—224no—
333C22×Q8—228no—
334C22×Q8—224no—
335C22×Q8—444no—
336C22×D4—114no—
337C22×D4—222no—
338C22×D4—222no—
339C22×D4—222no—
340C22×D4—222no—
341C22×D4—222no—
342C22×D4—222no—
343C23×C4—111no—
344C23×C4—111no—
345C23×C4—112no—
346C23×C4—112no—
347C23×C4C22×D1112yes—
348C23×C4C22×D1112yes—
349C23×C4C22×D1112yes—
350C23×C4C22×D1111yescharacteristic
351C4⋊Q8—2232no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—114no—
358C2×C4⋊C4—224no—
359C2×C4⋊C4—224no—
360C2×C4⋊C4—224no—
361C2×C4⋊C4—222no—
362C2×C4⋊C4—222no—
363C2×C4⋊C4D4414yes—
364C2×C22⋊C4—228no—
365C2×C22⋊C4—224no—
366C2×C22⋊C4—224no—
367C2×C22⋊C4—228no—
368C2×C22⋊C4—228no—
369C2×C22⋊C4—228no—
370C2×C22⋊C4—228no—
371C2×C22⋊C4—228no—
372C2×C22⋊C4—444no—
373C2×C22⋊C4—444no—
374C2×C42—22no—
375C2×C42—22no—
376C2×C42—22no—
377C2×C42—114no—
378C2×C42—222no—
379C2×C42—222no—
380C2×C42—222no—
381C2×C42—222no—
382C2×C42—222no—
383#95—28no—
384#95—118no—
385#95—224no—
386#95—228no—
387C2×C11C2×#39311yescharacteristic
388C2×C11#243311yescharacteristic
389C2×C11#243611yescharacteristic
390C2×C11#245212yes—
391C2×C11#245212yes—
392C2×C11#249112yes—
393C2×C11#249112yes—
394C2×C11#254211yescharacteristic
395C2×C11#256311yescharacteristic
396C2×C11#264011yescharacteristic
397C2×C11#285811yescharacteristic
398D11—84no—
399C24—114no—
400C24—222no—
401C24—222no—
402C24—222no—
403C24—224no—
404C24—222no—
405C24—222no—
406C24—222no—
407C24—224no—
408C24—224no—
409C24—224no—
410C24C23×D1111yescharacteristic
411C2×Q8—2216no—
412C2×Q8—4416no—
413C2×Q8—448no—
414C2×Q8—4416no—
415C2×Q8—448no—
416C2×D4—228no—
417C2×D4—228no—
418C2×D4—228no—
419C2×D4—444no—
420C2×D4—444no—
421C2×D4—444no—
422C2×D4—444no—
423C22×C4—22no—
424C22×C4—24no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—24no—
433C22×C4—22no—
434C22×C4—24no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—24no—
438C22×C4—114no—
439C22×C4—112no—
440C22×C4—112no—
441C22×C4—114no—
442C22×C4—114no—
443C22×C4—114no—
444C22×C4—221no—
445C22×C4—221no—
446C22×C4—221no—
447C22×C4—221no—
448C22×C4—222no—
449C22×C4—222no—
450C22×C4—222no—
451C22×C4—222no—
452C22×C4—222no—
453C22×C4—222no—
454C22×C4—224no—
455C22×C4—222no—
456C22×C4—222no—
457C22×C4—222no—
458C22×C4—222no—
459C22×C4—224no—
460C22×C4C2×D4414yes—
461C22×C4C2×D4412yes—
462C22×C4#433912yes—
463C22×C4#433912yes—
464C22×C4D4×D1114yes—
465C22×C4D4×D1112yes—
466C22×C4D4×D1112yes—
467C22×C4#434112yes—
468C22×C4Q8×D1112yes—
469C4⋊C4—28no—
470C4⋊C4—44no—
471C4⋊C4—2216no—
472C4⋊C4—228no—
473C22⋊C4—4416no—
474C22⋊C4—4416no—
475C22⋊C4—448no—
476C22⋊C4—448no—
477C42—44no—
478C42—228no—
479C42—444no—
480C11#1514411yescharacteristic, complemented, Sylow
481C23—228no—
482C23—224no—
483C23—224no—
484C23—224no—
485C23—228no—
486C23—442no—
487C23—442no—
488C23—442no—
489C23—442no—
490C23—442no—
491C23—442no—
492C23—444no—
493C23—444no—
494C23—444no—
495C23—444no—
496C23—444no—
497C23—444no—
498C23—444no—
499C23—444no—
500C23—444no—
501C23—444no—
502C23—442no—
503C23—442no—
504C23C22×D4411yescharacteristic
505C23C2×#433911yescharacteristic
506C23C2×#433911yescharacteristic
507C23C2×D4×D1111yescharacteristic
508C23C2×D4×D1112yes—
509C23C2×D4×D1111yescharacteristic
510C23C2×#434111yescharacteristic
511C23C2×Q8×D1111yescharacteristic
512C23#6704012yes—
513C23#41×D1112yes—
514C23#6704212yes—
515Q8—4432no—
516D4—4416no—
517C2×C4—24no—
518C2×C4—24no—
519C2×C4—28no—
520C2×C4—24no—
521C2×C4—24no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—44no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—44no—
532C2×C4—44no—
533C2×C4—42no—
534C2×C4—114no—
535C2×C4—114no—
536C2×C4—222no—
537C2×C4—222no—
538C2×C4—222no—
539C2×C4—224no—
540C2×C4—224no—
541C2×C4—224no—
542C2×C4—224no—
543C2×C4—222no—
544C2×C4—224no—
545C2×C4—224no—
546C2×C4—224no—
547C2×C4—224no—
548C2×C4—228no—
549C2×C4—442no—
550C2×C4—442no—
551C2×C4—442no—
552C2×C4—444no—
553C2×C4—442no—
554C2×C4—442no—
555C2×C4—442no—
556C2×C4#6692814yes—
557C2×C4#6693514yes—
558C2×C4#6693814yes—
559C2×C4#6693814yes—
560C2×C4#6694914yes—
561C2×C4#6694914yes—
562C2×C4#6695014yes—
563C22—448no—
564C22—448no—
565C22—444no—
566C22—444no—
567C22—444no—
568C22—884no—
569C22—884no—
570C22—882no—
571C22—882no—
572C22—882no—
573C22—882no—
574C22C2×#6692811yescharacteristic
575C22C2×#6693511yescharacteristic
576C22C2×#6693811yescharacteristic
577C22C2×#6693811yescharacteristic
578C22#1062303812yes—
579C22C2×#6694911yescharacteristic
580C22C2×#6694911yescharacteristic
581C22C2×#6695011yescharacteristic
582C22#1062306312yes—
583C22#1062307912yes—
584C22D4×D4412yes—
585C22#1062310712yes—
586C22#1062311312yes—
587C22#1062312712yes—
588C22#1062314012yes—
589C22#1062316412yes—
590C22#1062317412yes—
591C22D11×#12411yescharacteristic
592C22#1062320511yescharacteristic
593C22#1062322112yes—
594C22D11×#12711yescharacteristic
595C22#1062325511yescharacteristic
596C22#1062325812yes—
597C4—44no—
598C4—44no—
599C4—82no—
600C4—224no—
601C4—224no—
602C4—444no—
603C4—444no—
604C4#1062228618yescomplemented
605C2—884no—
606C2C2×#1062228611yescharacteristic
607C2#1307225211yescharacteristic
608C2#1307227311yescharacteristic
609C2#1307246412yes—
610C2#1307246712yes—
611C2#1307297312yes—
612C2#1307297512yes—
613C2#1307356811yescharacteristic
614C2#1307378811yescharacteristic
615C2#1307455511yescharacteristic
616C2#1307697011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutator, socle, cosocleC24×C11C24
FittingC11×C4⋊#95C2
prime radicalC23×D44C22
hypercenterC4⋊#95D11
hypocenterC11#15144
LCSG ▷ C24×C11 ▷ C11
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
1. C22×#66941C2semidirect
2. C2×#10622286C2semidirect
6. #13066860C2semidirect
7. #13066845C2semidirect
8. C4×C11⋊#95C2semidirect
9. C11×C4⋊#95C2semidirect
49. C22×D44Q8semidirect
90. C11⋊#95D4semidirect
180. C4⋊#95D11semidirect
325. C4×C11#393semidirect
480. C11#15144semidirect
604. C4#10622286semidirect

Maximal subgroups

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

subgroupindex
C22×#669412
C2×#106222862
C2×#106225522
C2×#106226012
#130668602
#130668452
C4×C11⋊#952
C11×C4⋊#952
#1514411