Finite Group Databasebeta

← #14685017

Subgroups — #14685017

Order 2816.

2574 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622541C212yesmaximal, complemented
2C2×#10622823C212yesmaximal
3C2×#10622825C211yesmaximal, characteristic
4C2×#10622825C211yesmaximal, characteristic
5#13066849C214yesmaximal, complemented
6#13066846C212yesmaximal, complemented
7#13066839C212yesmaximal
8C23×C42×C11C211yesmaximal, characteristic
9C24×C4×C11C2211yescharacteristic
10C24×C4×C11C2211yescharacteristic
11C24×C4×C11C2211yescharacteristic
12C22×C42×C11—24no—
13C22×C42×C11—28no—
14C22×C42×C11C2212yes—
15C22×C42×C11C2212yes—
16C22×C22⋊Dic11C2212yes—
17C22×C22⋊Dic11C2212yes—
18C22×C4⋊Dic11C2211yescharacteristic
19C22×C4⋊Dic11C2211yescharacteristic
20C22×C4⋊Dic11C2212yes—
21C22×Dic11⋊C4C2214yes—
22#10622825—24no—
23#10622825C418yescomplemented
24#10622823—28no—
25C2×C11⋊#95C2214yes—
26C2×C11⋊#95C2214yes—
27C2×C11⋊#95C2214yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30#10622541—28no—
31C25×C11C2311yescharacteristic
32C23×C4×C11—22no—
33C23×C4×C11—22no—
34C23×C4×C11—22no—
35C23×C4×C11—22no—
36C23×C4×C11—24no—
37C23×C4×C11—24no—
38C23×C4×C11—24no—
39C23×C4×C11—24no—
40C23×C4×C11—24no—
41C23×C4×C11—24no—
42C23×C4×C11C2×C414yes—
43C23×C4×C11D414yes—
44C23×C4×C11D414yes—
45C23×C4×C11Q814yes—
46C23×C4×C11Q814yes—
47C23×C4×C11C2311yescharacteristic
48C23×C4×C11C2312yes—
49C23×C4×C11C2312yes—
50C23×C4×C11C2311yescharacteristic
51C23×Dic11C2312yes—
52C23×Dic11C2312yes—
53C23×Dic11C2314yes—
54C2×C42×C11—232no—
55C2×C42×C11—24no—
56C2×C42×C11—24no—
57C2×C42×C11—24no—
58C2×C42×C11—24no—
59C2×C42×C11—24no—
60C2×C42×C11D418yes—
61C2×C22⋊Dic11—24no—
62C2×C22⋊Dic11—24no—
63C2×C22⋊Dic11—24no—
64C2×C22⋊Dic11—24no—
65C2×C22⋊Dic11—24no—
66C2×C22⋊Dic11C2×C418yes—
67C2×C4⋊Dic11—24no—
68C2×C4⋊Dic11—24no—
69C2×C4⋊Dic11—24no—
70C2×C4⋊Dic11—22no—
71C2×C4⋊Dic11—22no—
72C2×C4⋊Dic11—24no—
73C2×C4⋊Dic11C2×C418yescomplemented
74C2×Dic11⋊C4—28no—
75C2×Dic11⋊C4—28no—
76C2×Dic11⋊C4—28no—
77C11⋊#95—28no—
78C11⋊#95—28no—
79C11⋊#95—24no—
80C11⋊#95—28no—
81C11⋊#95C2×C418yescomplemented
82#14697—111nomaximal, Sylow
83C24×C11—22no—
84C24×C11—22no—
85C24×C11—22no—
86C24×C11—22no—
87C24×C11C22×C412yes—
88C24×C11C2×D412yes—
89C24×C11C2×D412yes—
90C24×C11C2×Q812yes—
91C24×C11C2×Q812yes—
92C24×C11#4112yes—
93C24×C11#4112yes—
94C24×C11C2411yescharacteristic
95C22×C4×C11—28no—
96C22×C4×C11—28no—
97C22×C4×C11—216no—
98C22×C4×C11—216no—
99C22×C4×C11—28no—
100C22×C4×C11—28no—
101C22×C4×C11—28no—
102C22×C4×C11—28no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
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—22no—
113C22×C4×C11—216no—
114C22×C4×C11—28no—
115C22×C4×C11—216no—
116C22×C4×C11—216no—
117C22×C4×C11—216no—
118C22×C4×C11—28no—
119C22×C4×C11C4⋊C4116yescomplemented
120C22×C4×C11C22×C412yes—
121C22×C4×C11C22×C412yes—
122C22×C4×C11C2×D412yes—
123C22×C4×C11C2×D414yes—
124C22×C4×C11C2×D414yes—
125C22×C4×C11C2×D414yes—
126C22×C4×C11C2×D412yes—
127C22×C4×C11C2×D414yes—
128C22×C4×C11C2×Q812yes—
129C22×C4×C11C2×Q814yes—
130C22×C4×C11C2×Q812yes—
131C22×C4×C11#4114yes—
132C22×C4×C11#4114yes—
133C22×C4×C11#4114yes—
134C22×Dic11—24no—
135C22×Dic11—24no—
136C22×Dic11—22no—
137C22×Dic11—24no—
138C22×Dic11—22no—
139C22×Dic11—22no—
140C22×Dic11—22no—
141C22×Dic11—24no—
142C22×Dic11—24no—
143C22×Dic11—24no—
144C22×Dic11—24no—
145C22×Dic11—24no—
146C22×Dic11—24no—
147C22×Dic11—24no—
148C22×Dic11—22no—
149C22×Dic11—22no—
150C22×Dic11C22×C418yes—
151C42×C11—216no—
152C42×C11—216no—
153C22⋊Dic11—216no—
154C22⋊Dic11—48no—
155C4⋊Dic11—216no—
156C4⋊Dic11—44no—
157C4⋊Dic11—44no—
158Dic11⋊C4—416no—
159C23×C42D1111yescharacteristic
160C2×#389—112no—
161C2×#385—112no—
162C2×#380—111no—
163C2×#380—111no—
164#1436—114no—
165C4⋊#95—112no—
166C22⋊#95—112no—
167C23×C11—24no—
168C23×C11—24no—
169C23×C11—22no—
170C23×C11—24no—
171C23×C11—24no—
172C23×C11—24no—
173C23×C11—22no—
174C23×C11—22no—
175C23×C11—22no—
176C23×C11—24no—
177C23×C11—24no—
178C23×C11—24no—
179C23×C11—24no—
180C23×C11—24no—
181C23×C11—24no—
182C23×C11—24no—
183C23×C11C2×C4⋊C414yes—
184C23×C11C4×D414yes—
185C23×C11C4×Q814yes—
186C23×C11#12114yes—
187C23×C11C22⋊Q814yes—
188C23×C11#12514yes—
189C23×C11C4⋊Q814yes—
190C23×C11C23×C411yescharacteristic
191C23×C11C22×D411yescharacteristic
192C23×C11C22×D411yescharacteristic
193C23×C11C22×D412yes—
194C23×C11C22×Q811yescharacteristic
195C23×C11C22×Q811yescharacteristic
196C23×C11C2×#4112yes—
197C23×C11C2×#4111yescharacteristic
198C23×C11C2×#4111yescharacteristic
199C23×C11C2×#4112yes—
200C23×C11C2×#4112yes—
201C2×C4×C11—232no—
202C2×C4×C11—232no—
203C2×C4×C11—24no—
204C2×C4×C11—24no—
205C2×C4×C11—24no—
206C2×C4×C11—22no—
207C2×C4×C11—24no—
208C2×C4×C11—24no—
209C2×C4×C11—24no—
210C2×C4×C11—24no—
211C2×C4×C11—24no—
212C2×C4×C11—22no—
213C2×C4×C11—24no—
214C2×C4×C11—24no—
215C2×C4×C11—24no—
216C2×C4×C11—24no—
217C2×C4×C11—24no—
218C2×C4×C11—24no—
219C2×C4×C11—232no—
220C2×C4×C11C2×C4⋊C414yes—
221C2×C4×C11C2×C4⋊C414yes—
222C2×C4×C11C4×D418yes—
223C2×C4×C11#12014yes—
224C2×C4×C11#12118yes—
225C2×C4×C11C22⋊Q818yes—
226C2×C4×C11C22⋊Q818yes—
227C2×C4×C11#12314yes—
228C2×Dic11—28no—
229C2×Dic11—28no—
230C2×Dic11—28no—
231C2×Dic11—44no—
232C2×Dic11—44no—
233C2×Dic11—44no—
234C2×Dic11—44no—
235C2×Dic11—42no—
236C2×Dic11—44no—
237C2×Dic11—42no—
238C2×Dic11—42no—
239C2×Dic11—42no—
240C2×Dic11—44no—
241C2×Dic11—42no—
242C2×Dic11—42no—
243C2×Dic11—44no—
244C2×Dic11—44no—
245C24×C4C2×D1111yescharacteristic
246C24×C4C2×D1111yescharacteristic
247C24×C4C2×D1111yescharacteristic
248C22×C4⋊C4—112no—
249C22×C4⋊C4—114no—
250C22×C4⋊C4—111no—
251C22×C4⋊C4—111no—
252C22×C22⋊C4—112no—
253C22×C22⋊C4—112no—
254C22×C42—24no—
255C22×C42—28no—
256C22×C42C2×D1112yes—
257C22×C42C2×D1112yes—
258#389—228no—
259#385—228no—
260#380—118no—
261#380—224no—
262C2×#95—112no—
263C2×#95—114no—
264C2×#95—114no—
265C2×#95—114no—
266C2×#95—112no—
267C22×C11—24no—
268C22×C11—24no—
269C22×C11—28no—
270C22×C11—24no—
271C22×C11—24no—
272C22×C11—28no—
273C22×C11—24no—
274C22×C11—24no—
275C22×C11—28no—
276C22×C11—28no—
277C22×C11#38918yescomplemented
278C22×C11C22×C4⋊C411yescharacteristic
279C22×C11C2×C4×D411yescharacteristic
280C22×C11C2×C4×D412yes—
281C22×C11C2×C4×Q811yescharacteristic
282C22×C11C4×#4112yes—
283C22×C11C2×#12011yescharacteristic
284C22×C11C2×#12111yescharacteristic
285C22×C11C2×#12112yes—
286C22×C11C2×C22⋊Q811yescharacteristic
287C22×C11C2×C22⋊Q812yes—
288C22×C11C2×C22⋊Q812yes—
289C22×C11C2×#12311yescharacteristic
290C22×C11#52512yes—
291C22×C11#52511yescharacteristic
292C22×C11#52512yes—
293C22×C11#52511yescharacteristic
294C22×C11C2×#12511yescharacteristic
295C22×C11#52912yes—
296C22×C11#52912yes—
297C22×C11C2×C4⋊Q811yescharacteristic
298C22×C11#53212yes—
299C22×C11#53312yes—
300C22×C11#53312yes—
301C4×C11—28no—
302C4×C11—28no—
303C4×C11—24no—
304C4×C11#38518yescomplemented
305Dic11—48no—
306Dic11—82no—
307Dic11—82no—
308C25C22×D1111yescharacteristic
309C23×C4—22no—
310C23×C4—22no—
311C23×C4—22no—
312C23×C4—22no—
313C23×C4—24no—
314C23×C4—24no—
315C23×C4—24no—
316C23×C4—24no—
317C23×C4—24no—
318C23×C4—24no—
319C23×C4—114no—
320C23×C4—112no—
321C23×C4—112no—
322C23×C4Dic2214yes—
323C23×C4Dic2214yes—
324C23×C4C4×D1114yes—
325C23×C4D4414yes—
326C23×C4C22⋊D1114yes—
327C23×C4C22×D1111yescharacteristic
328C23×C4C22×D1112yes—
329C23×C4C22×D1112yes—
330C23×C4C22×D1111yescharacteristic
331C2×C4⋊C4—118no—
332C2×C4⋊C4—224no—
333C2×C4⋊C4—224no—
334C2×C4⋊C4—228no—
335C2×C4⋊C4—228no—
336C2×C4⋊C4—224no—
337C2×C4⋊C4—222no—
338C2×C4⋊C4—222no—
339C2×C4⋊C4—228no—
340C2×C4⋊C4—224no—
341C2×C22⋊C4—118no—
342C2×C22⋊C4—224no—
343C2×C22⋊C4—224no—
344C2×C22⋊C4—224no—
345C2×C22⋊C4—224no—
346C2×C22⋊C4—224no—
347C2×C42—232no—
348C2×C42—24no—
349C2×C42—24no—
350C2×C42—24no—
351C2×C42—24no—
352C2×C42—24no—
353C2×C42C22⋊D1118yes—
354#95—118no—
355#95—228no—
356#95—228no—
357#95—224no—
358#95—228no—
359C2×C11—28no—
360C2×C11C2×#38511yescharacteristic
361C2×C11C2×#38911yescharacteristic
362C2×C11#229611yescharacteristic
363C2×C11C4×#12112yes—
364C2×C11C4×C22⋊Q812yes—
365C2×C11#284711yescharacteristic
366C2×C11#284811yescharacteristic
367C2×C11#285112yes—
368C2×C11#285411yescharacteristic
369C2×C11#285511yescharacteristic
370C2×C11#285712yes—
371C24—22no—
372C24—22no—
373C24—22no—
374C24—22no—
375C24C2×Dic2212yes—
376C24C2×Dic2212yes—
377C24C2×C4×D1112yes—
378C24C2×D4412yes—
379C24#433912yes—
380C24#433912yes—
381C24C2×C22⋊D1112yes—
382C24C23×D1111yescharacteristic
383C22×C4—28no—
384C22×C4—28no—
385C22×C4—28no—
386C22×C4—28no—
387C22×C4—216no—
388C22×C4—216no—
389C22×C4—28no—
390C22×C4—28no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—216no—
402C22×C4—216no—
403C22×C4—216no—
404C22×C4—28no—
405C22×C4—216no—
406C22×C4—28no—
407C22×C4—118no—
408C22×C4—224no—
409C22×C4—224no—
410C22×C4—224no—
411C22×C4—224no—
412C22×C4—224no—
413C22×C4—224no—
414C22×C4—222no—
415C22×C4—222no—
416C22×C4—224no—
417C22×C4—222no—
418C22×C4—222no—
419C22×C4—224no—
420C22×C4—224no—
421C22×C4—222no—
422C22×C4—222no—
423C22×C4—224no—
424C22×C4Dic11⋊C4116yescomplemented
425C22×C4C2×Dic2212yes—
426C22×C4C2×Dic2214yes—
427C22×C4C2×Dic2212yes—
428C22×C4C2×C4×D1112yes—
429C22×C4C2×C4×D1112yes—
430C22×C4C2×D4414yes—
431C22×C4#433914yes—
432C22×C4#433914yes—
433C22×C4#433914yes—
434C22×C4C2×C22⋊D1112yes—
435C22×C4C2×C22⋊D1114yes—
436C22×C4C2×C22⋊D1114yes—
437C22×C4C2×C22⋊D1112yes—
438C22×C4C2×C22⋊D1114yes—
439C4⋊C4—2216no—
440C4⋊C4—444no—
441C4⋊C4—4416no—
442C4⋊C4—444no—
443C22⋊C4—2216no—
444C22⋊C4—448no—
445C42—216no—
446C42—216no—
447C11#1469711yescharacteristic, complemented, Sylow
448C23—24no—
449C23—24no—
450C23—24no—
451C23—24no—
452C23—24no—
453C23—24no—
454C23—24no—
455C23—24no—
456C23—24no—
457C23—22no—
458C23—24no—
459C23—24no—
460C23—24no—
461C23—22no—
462C23—22no—
463C23—22no—
464C23C4×Dic2214yes—
465C23#6692214yes—
466C23#6692314yes—
467C23C4×D4414yes—
468C23C2×Dic11⋊C414yes—
469C23#6697714yes—
470C23#6698314yes—
471C23C22×Dic2211yescharacteristic
472C23C22×Dic2211yescharacteristic
473C23C22×C4×D1111yescharacteristic
474C23C22×D4411yescharacteristic
475C23C2×#433911yescharacteristic
476C23C2×#433911yescharacteristic
477C23C2×#433912yes—
478C23C2×#433912yes—
479C23C2×#433912yes—
480C23C22×C22⋊D1111yescharacteristic
481C23C22×C22⋊D1112yes—
482C2×C4—232no—
483C2×C4—232no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—22no—
489C2×C4—24no—
490C2×C4—24no—
491C2×C4—24no—
492C2×C4—24no—
493C2×C4—24no—
494C2×C4—24no—
495C2×C4—24no—
496C2×C4—24no—
497C2×C4—24no—
498C2×C4—24no—
499C2×C4—22no—
500C2×C4—232no—
501C2×C4—228no—
502C2×C4—228no—
503C2×C4—228no—
504C2×C4—444no—
505C2×C4—444no—
506C2×C4—444no—
507C2×C4—444no—
508C2×C4—444no—
509C2×C4—444no—
510C2×C4—442no—
511C2×C4—442no—
512C2×C4—442no—
513C2×C4—444no—
514C2×C4—444no—
515C2×C4—442no—
516C2×C4—442no—
517C2×C4—442no—
518C2×C4C2×Dic11⋊C414yes—
519C2×C4C2×Dic11⋊C414yes—
520C2×C4#6697718yes—
521C2×C4#6697718yes—
522C2×C4C4×C22⋊D1118yes—
523C2×C4#6698214yes—
524C2×C4#6698318yes—
525C2×C4#6700614yes—
526C22—28no—
527C22—28no—
528C22—24no—
529C22—24no—
530C22—24no—
531C22—28no—
532C22—24no—
533C22—24no—
534C22—28no—
535C22—24no—
536C22#1062254118yescomplemented
537C22C2×C4×Dic2211yescharacteristic
538C22C2×#6692211yescharacteristic
539C22C2×#6692311yescharacteristic
540C22#1062300112yes—
541C22#1062300112yes—
542C22C2×C4×D4411yescharacteristic
543C22C4×#433912yes—
544C22#1062300812yes—
545C22#1062301012yes—
546C22#1062301012yes—
547C22C22×Dic11⋊C411yescharacteristic
548C22C2×#6697712yes—
549C22C2×#6697711yescharacteristic
550C22C2×#6697712yes—
551C22C2×C4×C22⋊D1112yes—
552C22C2×#6698211yescharacteristic
553C22C2×#6698312yes—
554C22C2×#6698311yescharacteristic
555C22#1062332212yes—
556C22#1062332212yes—
557C22#1062332211yescharacteristic
558C22#1062332211yescharacteristic
559C22C2×#6700611yescharacteristic
560C4—28no—
561C4—28no—
562C4—24no—
563C4—448no—
564C4—882no—
565C4—882no—
566C4#1062282318yescomplemented
567C2—28no—
568C2C2×#1062282311yescharacteristic
569C2C2×#1062254111yescharacteristic
570C2#1307109911yescharacteristic
571C2C4×#6698312yes—
572C2C4×#6697712yes—
573C2#1307689811yescharacteristic
574C2#1307690311yescharacteristic
575C2#1307692612yes—
576C2#1307694711yescharacteristic
577C2#1307695511yescharacteristic
578C2#1307696812yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC23×C42×C11C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC23×C42D11
hypocenterC11#14697
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C23×C42

Complements

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

NH ≅ G/Ntype
1. C2×#10622541C2semidirect
5. #13066849C2semidirect
6. #13066846C2semidirect
23. #10622825C4semidirect
73. C2×C4⋊Dic11C2×C4semidirect
81. C11⋊#95C2×C4semidirect
119. C22×C4×C11C4⋊C4semidirect
277. C22×C11#389semidirect
304. C4×C11#385semidirect
424. C22×C4Dic11⋊C4semidirect
447. C11#14697semidirect
536. C22#10622541semidirect
566. C4#10622823semidirect

Maximal subgroups

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

subgroupindex
C2×#106225412
C2×#106228232
C2×#106228252
#130668492
#130668462
#130668392
C23×C42×C112
#1469711