Finite Group Databasebeta

← #14671293

Subgroups — #14671293

Order 2816.

1040 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 1040 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66898C211yesmaximal, characteristic, complemented
2C2×#10622183C212yesmaximal, complemented
3#13068531C211yesmaximal, characteristic, complemented
4#13066741C212yesmaximal, complemented
5C11×#2433C211yesmaximal, characteristic
6C23×D4×C11C2211yescharacteristic
7C2×C11×#127C411yescharacteristic, complemented
8C2×C11×#127C2211yescharacteristic
9C2×C11×#121C411yescharacteristic, complemented
10C2×C11×#120—21no—
11C2×C11×#120—21no—
12C22×C22⋊Dic11—21no—
13C11×#392—21no—
14C11×#392—21no—
15C11×#390C411yescharacteristic, complemented
16C11×#390C2211yescharacteristic
17C4×C11×C22⋊C4C411yescharacteristic, complemented
18#10622860—21no—
19C2×#66898—21no—
20C2×#66898—24no—
21C2×#66898—21no—
22C2×#66898C2212yes—
23C2×#66898C2212yes—
24#10622183—24no—
25C25×C11D411yescharacteristic
26C25×C11D411yescharacteristic
27C22×D4×C11—22no—
28C22×D4×C11—22no—
29C22×D4×C11—21no—
30C22×D4×C11—21no—
31C22×D4×C11—21no—
32C22×D4×C11—21no—
33C22×D4×C11—21no—
34C22×D4×C11—41no—
35C22×D4×C11—41no—
36C22×D4×C11—42no—
37C22×D4×C11C2×C411yescharacteristic
38C22×D4×C11C2×C411yescharacteristic, complemented
39C22×D4×C11D411yescharacteristic
40C22×D4×C11D411yescharacteristic
41C22×D4×C11C2311yescharacteristic
42C23×C4×C11C2×C411yescharacteristic
43C23×Dic11—41no—
44C11×#127—22no—
45C11×#127—22no—
46C11×#127—42no—
47C11×#121—41no—
48C11×#121—41no—
49C11×#120—44no—
50C11×#120—44no—
51C2×C11×C4⋊C4C2×C411yescharacteristic, complemented
52C2×C11×C22⋊C4—21no—
53C2×C11×C22⋊C4—21no—
54C2×C11×C22⋊C4—21no—
55C2×C11×C22⋊C4—21no—
56C2×C11×C22⋊C4—21no—
57C2×C11×C22⋊C4—21no—
58C2×C42×C11C2×C411yescharacteristic, complemented
59C2×C42×C11C2×C411yescharacteristic, complemented
60C2×C22⋊Dic11—24no—
61C2×C22⋊Dic11—22no—
62C2×C22⋊Dic11—22no—
63C2×C22⋊Dic11—41no—
64C2×C22⋊Dic11—42no—
65C2×C22⋊Dic11—41no—
66C2×C22⋊Dic11—41no—
67C11×#95—21no—
68#66898—24no—
69#66898—22no—
70#66898—22no—
71#66898—22no—
72#66898—42no—
73#66898D414yescomplemented
74#13088—111nomaximal, Sylow
75C24×C11—21no—
76C24×C11—22no—
77C24×C11—21no—
78C24×C11—21no—
79C24×C11—21no—
80C24×C11—21no—
81C24×C11—21no—
82C24×C11—22no—
83C24×C11—21no—
84C24×C11—41no—
85C24×C11—42no—
86C24×C11—42no—
87C24×C11—81no—
88C24×C11—81no—
89C24×C11C22⋊C411yescharacteristic
90C24×C11C22⋊C411yescharacteristic
91C24×C11C22⋊C411yescharacteristic
92C24×C11C2×D411yescharacteristic
93C24×C11C2×D411yescharacteristic
94C2×D4×C11—22no—
95C2×D4×C11—22no—
96C2×D4×C11—21no—
97C2×D4×C11—22no—
98C2×D4×C11—21no—
99C2×D4×C11—22no—
100C2×D4×C11—22no—
101C2×D4×C11—41no—
102C2×D4×C11—41no—
103C2×D4×C11—41no—
104C2×D4×C11—41no—
105C2×D4×C11—41no—
106C2×D4×C11—41no—
107C2×D4×C11—42no—
108C2×D4×C11—42no—
109C2×D4×C11—42no—
110C2×D4×C11—42no—
111C2×D4×C11—41no—
112C2×D4×C11—41no—
113C2×D4×C11—44no—
114C2×D4×C11—44no—
115C2×D4×C11—44no—
116C2×D4×C11—44no—
117C2×D4×C11—42no—
118C2×D4×C11—42no—
119C2×D4×C11—42no—
120C2×D4×C11—41no—
121C2×D4×C11—41no—
122C2×D4×C11—42no—
123C2×D4×C11—41no—
124C2×D4×C11—42no—
125C2×D4×C11—41no—
126C2×D4×C11—81no—
127C2×D4×C11—81no—
128C2×D4×C11—81no—
129C2×D4×C11—81no—
130C2×D4×C11C2×D412yes—
131C2×D4×C11#4112yes—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—22no—
137C22×C4×C11—21no—
138C22×C4×C11—41no—
139C22×C4×C11C22⋊C411yescharacteristic
140C22×C4×C11C22×C411yescharacteristic
141C22×Dic11—44no—
142C22×Dic11—42no—
143C22×Dic11—42no—
144C22×Dic11—82no—
145C22×Dic11—82no—
146C11×C4⋊C4—41no—
147C11×C22⋊C4—24no—
148C11×C22⋊C4—42no—
149C11×C22⋊C4—42no—
150C11×C22⋊C4—42no—
151C11×C22⋊C4—42no—
152C11×C22⋊C4—42no—
153C42×C11—22no—
154C42×C11—41no—
155C22⋊Dic11—24no—
156C22⋊Dic11—44no—
157C22⋊Dic11—42no—
158C22⋊Dic11—42no—
159C22⋊Dic11—42no—
160C22⋊Dic11—82no—
161C22⋊Dic11—82no—
162C22×#99—111no—
163#2433D1111yescharacteristic
164C2×#353—112no—
165#1781—111no—
166#1393—112no—
167C23×C11—22no—
168C23×C11—22no—
169C23×C11—22no—
170C23×C11—22no—
171C23×C11—22no—
172C23×C11—21no—
173C23×C11—21no—
174C23×C11—21no—
175C23×C11—21no—
176C23×C11—21no—
177C23×C11—21no—
178C23×C11—21no—
179C23×C11—21no—
180C23×C11—21no—
181C23×C11—21no—
182C23×C11—21no—
183C23×C11—41no—
184C23×C11—42no—
185C23×C11—42no—
186C23×C11—42no—
187C23×C11—41no—
188C23×C11—41no—
189C23×C11—41no—
190C23×C11—41no—
191C23×C11—41no—
192C23×C11—41no—
193C23×C11—41no—
194C23×C11—41no—
195C23×C11—42no—
196C23×C11—41no—
197C23×C11—41no—
198C23×C11—41no—
199C23×C11—41no—
200C23×C11—42no—
201C23×C11—42no—
202C23×C11—41no—
203C23×C11—41no—
204C23×C11—41no—
205C23×C11—81no—
206C23×C11—81no—
207C23×C11—81no—
208C23×C11—81no—
209C23×C11—84no—
210C23×C11—82no—
211C23×C11—82no—
212C23×C11—84no—
213C23×C11—84no—
214C23×C11#9911yescharacteristic
215C23×C11#9911yescharacteristic
216C23×C11#9912yes—
217C23×C11C2×C22⋊C411yescharacteristic
218C23×C11#12011yescharacteristic
219C23×C11#12112yes—
220C23×C11#12311yescharacteristic
221D4×C11—42no—
222D4×C11—42no—
223D4×C11—44no—
224D4×C11—44no—
225D4×C11—42no—
226D4×C11—42no—
227D4×C11—82no—
228D4×C11—84no—
229D4×C11—82no—
230D4×C11—84no—
231D4×C11—82no—
232D4×C11—84no—
233D4×C11—82no—
234D4×C11—82no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—42no—
243C2×C4×C11—42no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11C4×D412yes—
252C2×Dic11—44no—
253C2×Dic11—88no—
254C2×Dic11—82no—
255C2×Dic11—82no—
256C2×Dic11—82no—
257C2×Dic11—82no—
258C2×Dic11—82no—
259C23×D4C2×D1111yescharacteristic
260C2×#127Dic1111yescharacteristic, complemented
261C2×#127C2×D1111yescharacteristic
262C2×#121Dic1111yescharacteristic, complemented
263C2×#120—21no—
264C2×#120—21no—
265C22×C22⋊C4—221no—
266C2×#99—112no—
267C2×#99—112no—
268C2×#99—224no—
269C2×#99—221no—
270C2×#99—221no—
271#392—21no—
272#392—21no—
273#390Dic1111yescharacteristic, complemented
274#390C2×D1111yescharacteristic
275#379—221no—
276C4×C22⋊C4Dic1111yescharacteristic, complemented
277#353—224no—
278C22×C11—21no—
279C22×C11—21no—
280C22×C11—21no—
281C22×C11—21no—
282C22×C11—21no—
283C22×C11—21no—
284C22×C11—21no—
285C22×C11—22no—
286C22×C11—21no—
287C22×C11—21no—
288C22×C11—22no—
289C22×C11—42no—
290C22×C11—42no—
291C22×C11—42no—
292C22×C11—41no—
293C22×C11—42no—
294C22×C11—41no—
295C22×C11—44no—
296C22×C11—44no—
297C22×C11—42no—
298C22×C11—41no—
299C22×C11—41no—
300C22×C11—41no—
301C22×C11—41no—
302C22×C11—41no—
303C22×C11—41no—
304C22×C11—41no—
305C22×C11—41no—
306C22×C11—41no—
307C22×C11—81no—
308C22×C11—81no—
309C22×C11—81no—
310C22×C11—84no—
311C22×C11—81no—
312C22×C11—81no—
313C22×C11—81no—
314C22×C11—81no—
315C22×C11—81no—
316C22×C11—82no—
317C22×C11—82no—
318C22×C11—84no—
319C22×C11—81no—
320C22×C11—81no—
321C22×C11—81no—
322C22×C11#35312yescomplemented
323C22×C11#38611yescharacteristic
324C22×C11C2×#9911yescharacteristic
325C22×C11C2×#9911yescharacteristic
326C4×C11—22no—
327C4×C11—42no—
328C4×C11—42no—
329C4×C11—41no—
330C4×C11—81no—
331Dic11—84no—
332Dic11—162no—
333C25C22⋊D1111yescharacteristic
334C25C22⋊D1111yescharacteristic
335C22×D4—22no—
336C22×D4—22no—
337C22×D4—21no—
338C22×D4—21no—
339C22×D4—21no—
340C22×D4—21no—
341C22×D4—21no—
342C22×D4—41no—
343C22×D4—41no—
344C22×D4—42no—
345C22×D4C2×Dic1111yescharacteristic
346C22×D4C2×Dic1111yescharacteristic, complemented
347C22×D4C22⋊D1111yescharacteristic
348C22×D4C22⋊D1111yescharacteristic
349C22×D4C22×D1111yescharacteristic
350C23×C4—441no—
351C23×C4C2×Dic1111yescharacteristic
352#127—22no—
353#127—22no—
354#127—42no—
355#121—41no—
356#121—41no—
357#120—44no—
358#120—44no—
359C2×C4⋊C4C2×Dic1111yescharacteristic, complemented
360C2×C22⋊C4—21no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—224no—
367C2×C22⋊C4—222no—
368C2×C22⋊C4—222no—
369C2×C22⋊C4—441no—
370C2×C22⋊C4—442no—
371C2×C22⋊C4—441no—
372C2×C22⋊C4—441no—
373C2×C42C2×Dic1111yescharacteristic, complemented
374C2×C42C2×Dic1111yescharacteristic, complemented
375#99—114no—
376#99—224no—
377#99—222no—
378#99—222no—
379#99—222no—
380#99—442no—
381#95—21no—
382C2×C11—21no—
383C2×C11—21no—
384C2×C11—22no—
385C2×C11—41no—
386C2×C11—42no—
387C2×C11—41no—
388C2×C11—42no—
389C2×C11—41no—
390C2×C11—81no—
391C2×C11—161no—
392C2×C11#189811yescharacteristic
393C2×C11C2×#35311yescharacteristic
394C2×C11#212711yescharacteristic
395C24—21no—
396C24—22no—
397C24—21no—
398C24—21no—
399C24—21no—
400C24—21no—
401C24—21no—
402C24—22no—
403C24—21no—
404C24—41no—
405C24—42no—
406C24—42no—
407C24—81no—
408C24—81no—
409C24C22⋊Dic1111yescharacteristic
410C24C22⋊Dic1111yescharacteristic
411C24C22⋊Dic1111yescharacteristic
412C24C2×C22⋊D1111yescharacteristic
413C24C2×C22⋊D1111yescharacteristic
414C2×D4—22no—
415C2×D4—22no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—22no—
421C2×D4—41no—
422C2×D4—41no—
423C2×D4—41no—
424C2×D4—41no—
425C2×D4—41no—
426C2×D4—41no—
427C2×D4—41no—
428C2×D4—41no—
429C2×D4—42no—
430C2×D4—42no—
431C2×D4—42no—
432C2×D4—42no—
433C2×D4—44no—
434C2×D4—44no—
435C2×D4—44no—
436C2×D4—44no—
437C2×D4—42no—
438C2×D4—42no—
439C2×D4—42no—
440C2×D4—41no—
441C2×D4—41no—
442C2×D4—42no—
443C2×D4—41no—
444C2×D4—41no—
445C2×D4—42no—
446C2×D4—81no—
447C2×D4—81no—
448C2×D4—81no—
449C2×D4—81no—
450C2×D4D4×D1112yes—
451C2×D4#434112yes—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—41no—
459C22×C4—444no—
460C22×C4—442no—
461C22×C4—442no—
462C22×C4—882no—
463C22×C4—882no—
464C22×C4C22⋊Dic1111yescharacteristic
465C22×C4C22×Dic1111yescharacteristic
466C4⋊C4—41no—
467C22⋊C4—24no—
468C22⋊C4—42no—
469C22⋊C4—42no—
470C22⋊C4—42no—
471C22⋊C4—42no—
472C22⋊C4—42no—
473C22⋊C4—224no—
474C22⋊C4—444no—
475C22⋊C4—442no—
476C22⋊C4—442no—
477C22⋊C4—442no—
478C22⋊C4—882no—
479C22⋊C4—882no—
480C42—22no—
481C42—41no—
482C11#1308811yescharacteristic, complemented, Sylow
483C23—22no—
484C23—22no—
485C23—22no—
486C23—22no—
487C23—21no—
488C23—21no—
489C23—21no—
490C23—21no—
491C23—21no—
492C23—22no—
493C23—21no—
494C23—21no—
495C23—21no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23—41no—
500C23—42no—
501C23—42no—
502C23—42no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23—41no—
511C23—42no—
512C23—41no—
513C23—41no—
514C23—41no—
515C23—41no—
516C23—42no—
517C23—42no—
518C23—41no—
519C23—41no—
520C23—41no—
521C23—81no—
522C23—81no—
523C23—81no—
524C23—81no—
525C23—84no—
526C23—82no—
527C23—82no—
528C23—84no—
529C23—84no—
530C23#6689811yescharacteristic
531C23#6689811yescharacteristic
532C23#6689812yes—
533C23#6698811yescharacteristic
534C23#6699011yescharacteristic
535C23#6699212yes—
536C23C2×C22⋊Dic1111yescharacteristic
537D4—42no—
538D4—42no—
539D4—44no—
540D4—44no—
541D4—42no—
542D4—42no—
543D4—82no—
544D4—84no—
545D4—82no—
546D4—82no—
547D4—84no—
548D4—84no—
549D4—82no—
550D4—82no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—444no—
568C2×C4—888no—
569C2×C4—882no—
570C2×C4—882no—
571C2×C4—882no—
572C2×C4—882no—
573C2×C4—882no—
574C2×C4D4×Dic1112yes—
575C22—21no—
576C22—21no—
577C22—21no—
578C22—21no—
579C22—21no—
580C22—21no—
581C22—22no—
582C22—22no—
583C22—21no—
584C22—21no—
585C22—21no—
586C22—42no—
587C22—42no—
588C22—42no—
589C22—41no—
590C22—41no—
591C22—42no—
592C22—44no—
593C22—44no—
594C22—42no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—81no—
605C22—81no—
606C22—81no—
607C22—84no—
608C22—81no—
609C22—81no—
610C22—81no—
611C22—81no—
612C22—81no—
613C22—82no—
614C22—82no—
615C22—84no—
616C22—81no—
617C22—81no—
618C22—81no—
619C22#1062218312yescomplemented
620C22C2×#6689811yescharacteristic
621C22C2×#6689811yescharacteristic
622C22#1062283311yescharacteristic
623C4—22no—
624C4—42no—
625C4—42no—
626C4—41no—
627C4—81no—
628C4—884no—
629C4—1762no—
630C2—21no—
631C2—21no—
632C2—22no—
633C2—41no—
634C2—42no—
635C2—41no—
636C2—42no—
637C2—41no—
638C2—81no—
639C2—161no—
640C2#1306907011yescharacteristic
641C2C2×#1062218311yescharacteristic
642C2#1307028511yescharacteristic
subgroupG/H
centerC22C2×#66898
commutatorC22×C4×C11C22×C4
FrattiniC22×D4C22×D11
Fitting, prime radicalC11×#2433C2
socleC22×C11C2×#99
cosocleC22×D4×C11C23
hypercenter#2433D11
hypocenterC11#13088
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C24 ◁ C23×D4 ◁ #2433

Complements

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

NH ≅ G/Ntype
1. C22×#66898C2semidirect
2. C2×#10622183C2semidirect
3. #13068531C2semidirect
4. #13066741C2semidirect
7. C2×C11×#127C4semidirect
9. C2×C11×#121C4semidirect
15. C11×#390C4semidirect
17. C4×C11×C22⋊C4C4semidirect
38. C22×D4×C11C2×C4semidirect
51. C2×C11×C4⋊C4C2×C4semidirect
58. C2×C42×C11C2×C4semidirect
59. C2×C42×C11C2×C4semidirect
73. #66898D4semidirect
260. C2×#127Dic11semidirect
262. C2×#121Dic11semidirect
273. #390Dic11semidirect
276. C4×C22⋊C4Dic11semidirect
322. C22×C11#353semidirect
346. C22×D4C2×Dic11semidirect
359. C2×C4⋊C4C2×Dic11semidirect
373. C2×C42C2×Dic11semidirect
374. C2×C42C2×Dic11semidirect
482. C11#13088semidirect
619. C22#10622183semidirect

Maximal subgroups

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

subgroupindex
C22×#668982
C2×#106221832
#130685312
#130667412
C11×#24332
#1308811