Finite Group Databasebeta

← #14660296

Subgroups — #14660296

Order 2816.

1634 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66898C211yesmaximal, characteristic, complemented
2C22×#66898C212yesmaximal, complemented
3#13071194C211yesmaximal, characteristic, complemented
4C2×#10622165C212yesmaximal, complemented
5C2×C11×#534C211yesmaximal, characteristic
6C23×D4×C11C2211yescharacteristic
7C23×D4×C11C2211yescharacteristic
8C11×#534—24no—
9C11×#534—24no—
10C2×C11×#123—21no—
11C2×C11×#123C412yescomplemented
12C2×C11×#121—22no—
13C2×C11×#120—21no—
14C2×C11×#120C412yescomplemented
15C22×C11×C22⋊C4C2211yescharacteristic
16C22×C22⋊Dic11C2212yes—
17C22×C22⋊Dic11C2212yes—
18#10622860—21no—
19#10622833—24no—
20C2×#66898—22no—
21C2×#66898—24no—
22C2×#66898—24no—
23C2×#66898—24no—
24C2×#66898—24no—
25#10622824—21no—
26#10622165—24no—
27C25×C11C2×C411yescharacteristic
28C25×C11D411yescharacteristic
29C25×C11C2311yescharacteristic
30C22×D4×C11—22no—
31C22×D4×C11—22no—
32C22×D4×C11—22no—
33C22×D4×C11—22no—
34C22×D4×C11—21no—
35C22×D4×C11—21no—
36C22×D4×C11—22no—
37C22×D4×C11—22no—
38C22×D4×C11—22no—
39C22×D4×C11—22no—
40C22×D4×C11—22no—
41C22×D4×C11—22no—
42C22×D4×C11—22no—
43C22×D4×C11—22no—
44C22×D4×C11C2×C412yes—
45C22×D4×C11D412yes—
46C22×D4×C11D414yes—
47C23×C4×C11—21no—
48C23×C4×C11C2×C411yescharacteristic
49C23×C4×C11D411yescharacteristic
50C23×Dic11—22no—
51C23×Dic11—22no—
52C11×#123—28no—
53C11×#123—24no—
54C11×#123—24no—
55C11×#121—216no—
56C11×#120—28no—
57C11×#120—24no—
58C11×#120—24no—
59C2×C11×C4⋊C4—22no—
60C2×C11×C22⋊C4—22no—
61C2×C11×C22⋊C4—21no—
62C2×C11×C22⋊C4—22no—
63C2×C11×C22⋊C4—22no—
64C2×C11×C22⋊C4C2×C412yes—
65C2×C11×C22⋊C4D414yes—
66C2×C22⋊Dic11—22no—
67C2×C22⋊Dic11—22no—
68C2×C22⋊Dic11—22no—
69C2×C22⋊Dic11—22no—
70C2×C22⋊Dic11—22no—
71C2×C22⋊Dic11—22no—
72C2×C22⋊Dic11—22no—
73C2×C22⋊Dic11—22no—
74C2×C22⋊Dic11—22no—
75C2×C22⋊Dic11—22no—
76C2×C22⋊Dic11—24no—
77C2×C22⋊Dic11D414yescomplemented
78C2×C22⋊Dic11D414yescomplemented
79#66898—28no—
80#66898—216no—
81C11⋊#95—24no—
82#10972—111nomaximal, Sylow
83C24×C11—21no—
84C24×C11—21no—
85C24×C11—21no—
86C24×C11—22no—
87C24×C11—22no—
88C24×C11—22no—
89C24×C11—22no—
90C24×C11—21no—
91C24×C11—82no—
92C24×C11—82no—
93C24×C11—82no—
94C24×C11C22⋊C412yes—
95C24×C11C22⋊C412yescomplemented
96C24×C11C22×C411yescharacteristic
97C24×C11C2×D411yescharacteristic
98C24×C11C2×D411yescharacteristic
99C24×C11C2×D412yes—
100C24×C11C2×D412yes—
101C24×C11C2×D412yes—
102C24×C11C2×D412yes—
103C24×C11#4112yes—
104C24×C11#4112yes—
105C2×D4×C11—22no—
106C2×D4×C11—22no—
107C2×D4×C11—24no—
108C2×D4×C11—24no—
109C2×D4×C11—22no—
110C2×D4×C11—24no—
111C2×D4×C11—24no—
112C2×D4×C11—24no—
113C2×D4×C11—24no—
114C2×D4×C11—24no—
115C2×D4×C11—24no—
116C2×D4×C11—24no—
117C2×D4×C11—22no—
118C2×D4×C11—24no—
119C2×D4×C11—28no—
120C2×D4×C11—41no—
121C2×D4×C11—41no—
122C2×D4×C11—42no—
123C2×D4×C11—42no—
124C2×D4×C11—42no—
125C2×D4×C11—42no—
126C2×D4×C11—42no—
127C2×D4×C11—42no—
128C2×D4×C11—42no—
129C2×D4×C11—42no—
130C2×D4×C11—42no—
131C2×D4×C11—41no—
132C2×D4×C11—41no—
133C2×D4×C11—42no—
134C2×D4×C11—42no—
135C2×D4×C11—42no—
136C2×D4×C11—42no—
137C2×D4×C11—42no—
138C2×D4×C11—84no—
139C22×C4×C11—22no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—21no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—21no—
148C22×C4×C11—24no—
149C22×C4×C11—82no—
150C22×C4×C11C22⋊C412yes—
151C22×C4×C11C22⋊C412yescomplemented
152C22×Dic11—24no—
153C22×Dic11—24no—
154C22×Dic11—42no—
155C22×Dic11—42no—
156C22×Dic11—42no—
157C22×Dic11—42no—
158C22×Dic11—84no—
159C22×Dic11—84no—
160C11×C4⋊C4—28no—
161C11×C22⋊C4—28no—
162C11×C22⋊C4—28no—
163C11×C22⋊C4—22no—
164C11×C22⋊C4—24no—
165C11×C22⋊C4C22⋊C414yescomplemented
166C22⋊Dic11—24no—
167C22⋊Dic11—24no—
168C22⋊Dic11—24no—
169C22⋊Dic11—24no—
170C22⋊Dic11—42no—
171C22⋊Dic11—42no—
172C22⋊Dic11—42no—
173C22⋊Dic11—42no—
174C22⋊Dic11—84no—
175C2×#534D1111yescharacteristic
176C22×#99—112no—
177C22×#99—111no—
178#2308—111no—
179C2×#342—112no—
180C23×C11—22no—
181C23×C11—22no—
182C23×C11—22no—
183C23×C11—22no—
184C23×C11—24no—
185C23×C11—44no—
186C23×C11—44no—
187C23×C11—42no—
188C23×C11—42no—
189C23×C11—42no—
190C23×C11—44no—
191C23×C11—44no—
192C23×C11—44no—
193C23×C11—41no—
194C23×C11—41no—
195C23×C11—42no—
196C23×C11—42no—
197C23×C11—42no—
198C23×C11—82no—
199C23×C11—84no—
200C23×C11—82no—
201C23×C11—82no—
202C23×C11—82no—
203C23×C11—82no—
204C23×C11—82no—
205C23×C11—82no—
206C23×C11—84no—
207C23×C11—84no—
208C23×C11—84no—
209C23×C11C2×C22⋊C411yescharacteristic
210C23×C11C2×C22⋊C411yescharacteristic
211C23×C11C2×C22⋊C411yescharacteristic
212C23×C11C4×D412yes—
213C23×C11C4×D412yes—
214C23×C11#12011yescharacteristic
215C23×C11#12011yescharacteristic
216C23×C11#12012yes—
217C23×C11#12012yes—
218C23×C11#12012yes—
219C23×C11#12112yes—
220C23×C11#12112yes—
221C23×C11#12112yes—
222C23×C11#12112yes—
223C23×C11#12112yes—
224C23×C11#12112yes—
225C23×C11#12311yescharacteristic
226C23×C11#12311yescharacteristic
227C23×C11#12312yes—
228C23×C11#12412yes—
229C23×C11#12712yes—
230D4×C11—44no—
231D4×C11—44no—
232D4×C11—44no—
233D4×C11—44no—
234D4×C11—44no—
235D4×C11—44no—
236D4×C11—44no—
237D4×C11—44no—
238D4×C11—88no—
239C2×C4×C11—24no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—24no—
245C2×C4×C11—44no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—42no—
249C2×C4×C11—42no—
250C2×C4×C11—42no—
251C2×C4×C11—84no—
252C2×Dic11—48no—
253C2×Dic11—44no—
254C2×Dic11—44no—
255C2×Dic11—84no—
256C2×Dic11—84no—
257C2×Dic11—84no—
258C2×Dic11—84no—
259C2×Dic11—84no—
260C23×D4C2×D1111yescharacteristic
261C23×D4C2×D1111yescharacteristic
262#534—24no—
263#534—24no—
264C2×#123—21no—
265C2×#123Dic1112yescomplemented
266C2×#121—22no—
267C2×#120—21no—
268C2×#120Dic1112yescomplemented
269C22×C22⋊C4—112no—
270C22×C22⋊C4—112no—
271C22×C22⋊C4C2×D1111yescharacteristic
272C2×#99—224no—
273C2×#99—224no—
274C2×#99—224no—
275C2×#99—222no—
276C2×#99—224no—
277#386—224no—
278#381—221no—
279#379—221no—
280#342—224no—
281C22×C11—22no—
282C22×C11—22no—
283C22×C11—24no—
284C22×C11—22no—
285C22×C11—24no—
286C22×C11—42no—
287C22×C11—41no—
288C22×C11—41no—
289C22×C11—42no—
290C22×C11—42no—
291C22×C11—42no—
292C22×C11—42no—
293C22×C11—41no—
294C22×C11—42no—
295C22×C11—42no—
296C22×C11—42no—
297C22×C11—42no—
298C22×C11—41no—
299C22×C11—42no—
300C22×C11—42no—
301C22×C11—42no—
302C22×C11—44no—
303C22×C11—44no—
304C22×C11—44no—
305C22×C11—42no—
306C22×C11—42no—
307C22×C11—82no—
308C22×C11—84no—
309C22×C11—84no—
310C22×C11—82no—
311C22×C11—84no—
312C22×C11—84no—
313C22×C11—82no—
314C22×C11#37911yescharacteristic
315C22×C11#38611yescharacteristic
316C22×C11#38612yes—
317C22×C11#38611yescharacteristic
318C22×C11#39012yes—
319C22×C11#39212yes—
320C22×C11#39212yes—
321C22×C11#39412yes—
322C22×C11#39412yes—
323C4×C11—44no—
324C4×C11—42no—
325C4×C11—42no—
326Dic11—84no—
327Dic11—84no—
328C25C2×Dic1111yescharacteristic
329C25C22⋊D1111yescharacteristic
330C25C22×D1111yescharacteristic
331C22×D4—22no—
332C22×D4—22no—
333C22×D4—22no—
334C22×D4—22no—
335C22×D4—22no—
336C22×D4—22no—
337C22×D4—22no—
338C22×D4—22no—
339C22×D4—21no—
340C22×D4—21no—
341C22×D4—22no—
342C22×D4—22no—
343C22×D4—22no—
344C22×D4—22no—
345C22×D4C2×Dic1112yes—
346C22×D4C22⋊D1112yes—
347C22×D4C22⋊D1114yes—
348C23×C4—21no—
349C23×C4—222no—
350C23×C4—222no—
351C23×C4C2×Dic1111yescharacteristic
352C23×C4C22⋊D1111yescharacteristic
353#123—28no—
354#123—24no—
355#123—24no—
356#121—216no—
357#120—28no—
358#120—24no—
359#120—24no—
360C2×C4⋊C4—22no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—114no—
366C2×C22⋊C4—114no—
367C2×C22⋊C4—222no—
368C2×C22⋊C4—222no—
369C2×C22⋊C4—222no—
370C2×C22⋊C4—222no—
371C2×C22⋊C4—222no—
372C2×C22⋊C4—222no—
373C2×C22⋊C4—222no—
374C2×C22⋊C4—222no—
375C2×C22⋊C4—222no—
376C2×C22⋊C4—222no—
377C2×C22⋊C4—224no—
378C2×C22⋊C4C2×Dic1112yes—
379C2×C22⋊C4C22⋊D1114yes—
380#99—2216no—
381#99—228no—
382#95—224no—
383C2×C11—22no—
384C2×C11—22no—
385C2×C11—21no—
386C2×C11—21no—
387C2×C11—22no—
388C2×C11—22no—
389C2×C11—22no—
390C2×C11—22no—
391C2×C11—82no—
392C2×C11—82no—
393C2×C11#143811yescharacteristic
394C2×C11#191312yes—
395C24—21no—
396C24—21no—
397C24—22no—
398C24—22no—
399C24—21no—
400C24—22no—
401C24—21no—
402C24—22no—
403C24—82no—
404C24—82no—
405C24—82no—
406C24C22⋊Dic1112yes—
407C24C22⋊Dic1112yescomplemented
408C24D4×D1112yes—
409C24D4×D1112yes—
410C24#434112yes—
411C24#434112yes—
412C24C22×Dic1111yescharacteristic
413C24C2×C22⋊D1111yescharacteristic
414C24C2×C22⋊D1111yescharacteristic
415C24C2×C22⋊D1112yes—
416C24C2×C22⋊D1112yes—
417C2×D4—24no—
418C2×D4—24no—
419C2×D4—22no—
420C2×D4—24no—
421C2×D4—22no—
422C2×D4—24no—
423C2×D4—24no—
424C2×D4—24no—
425C2×D4—24no—
426C2×D4—22no—
427C2×D4—22no—
428C2×D4—24no—
429C2×D4—24no—
430C2×D4—24no—
431C2×D4—28no—
432C2×D4—41no—
433C2×D4—41no—
434C2×D4—42no—
435C2×D4—42no—
436C2×D4—42no—
437C2×D4—41no—
438C2×D4—41no—
439C2×D4—42no—
440C2×D4—42no—
441C2×D4—42no—
442C2×D4—42no—
443C2×D4—42no—
444C2×D4—42no—
445C2×D4—42no—
446C2×D4—42no—
447C2×D4—42no—
448C2×D4—42no—
449C2×D4—42no—
450C2×D4—84no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—24no—
461C22×C4—82no—
462C22×C4—224no—
463C22×C4—224no—
464C22×C4—442no—
465C22×C4—442no—
466C22×C4—442no—
467C22×C4—442no—
468C22×C4—884no—
469C22×C4—884no—
470C22×C4C22⋊Dic1112yes—
471C22×C4C22⋊Dic1112yescomplemented
472C4⋊C4—28no—
473C22⋊C4—28no—
474C22⋊C4—28no—
475C22⋊C4—22no—
476C22⋊C4—24no—
477C22⋊C4—224no—
478C22⋊C4—224no—
479C22⋊C4—224no—
480C22⋊C4—224no—
481C22⋊C4—442no—
482C22⋊C4—442no—
483C22⋊C4—442no—
484C22⋊C4—442no—
485C22⋊C4—884no—
486C22⋊C4C22⋊Dic1114yescomplemented
487C11#1097211yescharacteristic, complemented, Sylow
488C23—22no—
489C23—22no—
490C23—22no—
491C23—22no—
492C23—24no—
493C23—42no—
494C23—44no—
495C23—44no—
496C23—42no—
497C23—42no—
498C23—44no—
499C23—44no—
500C23—44no—
501C23—41no—
502C23—41no—
503C23—42no—
504C23—42no—
505C23—42no—
506C23—82no—
507C23—84no—
508C23—82no—
509C23—82no—
510C23—82no—
511C23—82no—
512C23—82no—
513C23—82no—
514C23—84no—
515C23—84no—
516C23—84no—
517C23D4×Dic1112yes—
518C23D4×Dic1112yes—
519C23#6698811yescharacteristic
520C23#6698811yescharacteristic
521C23#6698812yes—
522C23#6698912yes—
523C23#6699011yescharacteristic
524C23#6699011yescharacteristic
525C23#6699012yes—
526C23#6699112yes—
527C23#6699112yes—
528C23#6699212yes—
529C23#6699212yes—
530C23#6699212yes—
531C23#6699212yes—
532C23#6699312yes—
533C23C2×C22⋊Dic1111yescharacteristic
534C23C2×C22⋊Dic1111yescharacteristic
535C23C2×C22⋊Dic1111yescharacteristic
536C23#6700612yes—
537C23#6700612yes—
538D4—44no—
539D4—44no—
540D4—44no—
541D4—44no—
542D4—44no—
543D4—44no—
544D4—44no—
545D4—44no—
546D4—88no—
547C2×C4—22no—
548C2×C4—24no—
549C2×C4—22no—
550C2×C4—24no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—44no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—84no—
560C2×C4—448no—
561C2×C4—444no—
562C2×C4—444no—
563C2×C4—884no—
564C2×C4—884no—
565C2×C4—884no—
566C2×C4—884no—
567C2×C4—884no—
568C22—22no—
569C22—22no—
570C22—24no—
571C22—24no—
572C22—22no—
573C22—42no—
574C22—42no—
575C22—42no—
576C22—42no—
577C22—42no—
578C22—42no—
579C22—42no—
580C22—41no—
581C22—41no—
582C22—42no—
583C22—41no—
584C22—42no—
585C22—42no—
586C22—42no—
587C22—41no—
588C22—42no—
589C22—44no—
590C22—44no—
591C22—44no—
592C22—42no—
593C22—42no—
594C22—82no—
595C22—84no—
596C22—84no—
597C22—82no—
598C22—84no—
599C22—84no—
600C22—82no—
601C22#1062283311yescharacteristic
602C22#1062283312yes—
603C22#1062283311yescharacteristic
604C22#1062283412yes—
605C22#1062283512yes—
606C22#1062283512yes—
607C22#1062283612yes—
608C22#1062283612yes—
609C22#1062286011yescharacteristic
610C4—44no—
611C4—42no—
612C4—42no—
613C4—884no—
614C4—884no—
615C2—21no—
616C2—22no—
617C2—22no—
618C2—21no—
619C2—22no—
620C2—22no—
621C2—22no—
622C2—22no—
623C2—82no—
624C2—82no—
625C2#1306685711yescharacteristic
626C2#1306915912yes—
subgroupG/H
centerC22#10622833
commutatorC24×C11C22×C4
FrattiniC25C22×D11
Fitting, prime radicalC2×C11×#534C2
socleC22×C11#386
cosocleC25×C11C23
hypercenterC2×#534D11
hypocenterC11#10972
LCSG ▷ C24×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C25 ◁ C2×#534

Complements

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

NH ≅ G/Ntype
1. C22×#66898C2semidirect
2. C22×#66898C2semidirect
3. #13071194C2semidirect
4. C2×#10622165C2semidirect
11. C2×C11×#123C4semidirect
14. C2×C11×#120C4semidirect
77. C2×C22⋊Dic11D4semidirect
78. C2×C22⋊Dic11D4semidirect
95. C24×C11C22⋊C4semidirect
151. C22×C4×C11C22⋊C4semidirect
165. C11×C22⋊C4C22⋊C4semidirect
265. C2×#123Dic11semidirect
268. C2×#120Dic11semidirect
407. C24C22⋊Dic11semidirect
471. C22×C4C22⋊Dic11semidirect
486. C22⋊C4C22⋊Dic11semidirect
487. C11#10972semidirect

Maximal subgroups

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

subgroupindex
C22×#668982
#130711942
C2×#106221652
C2×C11×#5342
#1097211