Finite Group Databasebeta

← #14684616

Subgroups — #14684616

Order 2816.

1486 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13066884C211yesmaximal, characteristic, complemented
2#13066873C212yesmaximal, complemented
3#13066865C212yesmaximal, complemented
4#13066861C212yesmaximal, complemented
5#13066861C212yesmaximal, complemented
6#13066857C212yesmaximal
7#13066853C212yesmaximal, complemented
8#13066848C211yesmaximal, characteristic, complemented
9C2×C11×#394C211yesmaximal, characteristic
10C23×D4×C11C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12C22×C11×C22⋊C4C2212yes—
13C22×C11×C22⋊C4C2212yes—
14C22×C22⋊Dic11C2212yes—
15C22×C22⋊Dic11C2212yes—
16C22×C22⋊Dic11C2212yes—
17C22×C22⋊Dic11C2212yes—
18C22×C4⋊Dic11C2212yes—
19C22×C4×Dic11C2211yescharacteristic
20C11×#394C418yescomplemented
21C2×C11×#95C2211yescharacteristic
22C2×C11⋊#95C2212yes—
23C2×C11⋊#95C2212yes—
24C2×C11⋊#95C2211yescharacteristic
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2211yescharacteristic
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2211yescharacteristic
32C25×C11C2312yes—
33C22×D4×C11—42no—
34C22×D4×C11—42no—
35C22×D4×C11—41no—
36C22×D4×C11—41no—
37C22×D4×C11C2×C414yes—
38C23×C4×C11C2311yescharacteristic
39C23×C4×C11C2312yes—
40C23×C4×C11C2311yescharacteristic
41C23×C4×C11C2311yescharacteristic
42C23×Dic11C2312yes—
43C23×Dic11C2312yes—
44C23×Dic11C2312yes—
45C23×Dic11C2312yes—
46C2×C11×C4⋊C4—41no—
47C2×C11×C4⋊C4—41no—
48C2×C11×C4⋊C4C2×C414yes—
49C2×C11×C22⋊C4—42no—
50C2×C11×C22⋊C4—42no—
51C2×C11×C22⋊C4—42no—
52C2×C11×C22⋊C4—42no—
53C2×C11×C22⋊C4C2×C418yes—
54C2×C11×C22⋊C4C2×C418yes—
55C2×C22⋊Dic11—24no—
56C2×C22⋊Dic11—24no—
57C2×C22⋊Dic11—42no—
58C2×C22⋊Dic11—42no—
59C2×C22⋊Dic11—42no—
60C2×C22⋊Dic11—42no—
61C2×C22⋊Dic11—42no—
62C2×C22⋊Dic11—42no—
63C2×C22⋊Dic11—42no—
64C2×C22⋊Dic11—42no—
65C2×C22⋊Dic11—42no—
66C2×C22⋊Dic11—42no—
67C2×C4⋊Dic11—42no—
68C2×C4⋊Dic11—42no—
69C2×C4⋊Dic11—42no—
70C2×C4×Dic11—42no—
71C2×C4×Dic11—41no—
72C11×#95C2×C414yes—
73C11⋊#95—24no—
74C11⋊#95—42no—
75C11⋊#95—42no—
76C11⋊#95—42no—
77C11⋊#95—42no—
78C11⋊#95—42no—
79C11⋊#95—42no—
80C11⋊#95—41no—
81C11⋊#95—41no—
82C11⋊#95—41no—
83#14641—111nomaximal, Sylow
84C24×C11—22no—
85C24×C11—22no—
86C24×C11—22no—
87C24×C11—22no—
88C24×C11—22no—
89C24×C11—22no—
90C24×C11—22no—
91C24×C11—22no—
92C24×C11—22no—
93C24×C11—22no—
94C24×C11—22no—
95C24×C11—22no—
96C24×C11—22no—
97C24×C11—22no—
98C24×C11C22×C414yes—
99C24×C11C2411yescharacteristic
100C2×D4×C11—44no—
101C2×D4×C11—48no—
102C2×D4×C11—48no—
103C2×D4×C11—44no—
104C2×D4×C11—44no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—21no—
111C22×C4×C11—21no—
112C22×C4×C11—21no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—21no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—22no—
123C22×C4×C11C22×C414yes—
124C22×C4×C11C22×C412yes—
125C22×C4×C11C22×C412yes—
126C22×C4×C11C22×C412yes—
127C22×Dic11—22no—
128C22×Dic11—22no—
129C22×Dic11—22no—
130C22×Dic11—22no—
131C22×Dic11—22no—
132C22×Dic11—22no—
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—22no—
142C22×Dic11—22no—
143C22×Dic11—22no—
144C22×Dic11—22no—
145C22×Dic11—22no—
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11—22no—
150C22×Dic11—22no—
151C22×Dic11—22no—
152C22×Dic11—22no—
153C22×Dic11—22no—
154C22×Dic11#4114yes—
155C11×C4⋊C4—44no—
156C11×C22⋊C4—48no—
157C11×C22⋊C4—48no—
158C22⋊Dic11—48no—
159C22⋊Dic11—48no—
160C22⋊Dic11—48no—
161C22⋊Dic11—48no—
162C4⋊Dic11—48no—
163C4×Dic11—44no—
164C2×#394D1111yescharacteristic
165#1445—111no—
166#1442—112no—
167#1440—112no—
168#1439—112no—
169#1439—112no—
170#1438—112no—
171#1437—112no—
172#1436—111no—
173C23×C11—24no—
174C23×C11—24no—
175C23×C11—24no—
176C23×C11—24no—
177C23×C11—24no—
178C23×C11—24no—
179C23×C11—24no—
180C23×C11—42no—
181C23×C11—42no—
182C23×C11—42no—
183C23×C11—42no—
184C23×C11—42no—
185C23×C11—42no—
186C23×C11—42no—
187C23×C11—42no—
188C23×C11—42no—
189C23×C11—42no—
190C23×C11—42no—
191C23×C11—42no—
192C23×C11—42no—
193C23×C11—42no—
194C23×C11—42no—
195C23×C11—42no—
196C23×C11—42no—
197C23×C11—42no—
198C23×C11—42no—
199C23×C11—42no—
200C23×C11—42no—
201C23×C11—42no—
202C23×C11—42no—
203C23×C11—42no—
204C23×C11—42no—
205C23×C11—42no—
206C23×C11—42no—
207C23×C11—42no—
208C23×C11C23×C411yescharacteristic
209C23×C11C2×#4112yes—
210C23×C11H(5,𝔽2)11yescharacteristic
211C23×C11H(5,𝔽2)12yes—
212C23×C11H(5,𝔽2)12yes—
213C23×C11H(5,𝔽2)11yescharacteristic
214C23×C11H(5,𝔽2)12yes—
215C23×C11H(5,𝔽2)12yes—
216C23×C112−1+412yes—
217D4×C11—416no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—24no—
221C2×C4×C11—24no—
222C2×C4×C11—24no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—24no—
227C2×C4×C11—24no—
228C2×C4×C11—42no—
229C2×C4×C11—42no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11—41no—
233C2×C4×C11—42no—
234C2×C4×C11—42no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—42no—
239C2×C4×C11—42no—
240C2×Dic11—24no—
241C2×Dic11—24no—
242C2×Dic11—24no—
243C2×Dic11—42no—
244C2×Dic11—42no—
245C2×Dic11—42no—
246C2×Dic11—42no—
247C2×Dic11—42no—
248C2×Dic11—42no—
249C2×Dic11—42no—
250C2×Dic11—42no—
251C2×Dic11—42no—
252C2×Dic11—42no—
253C2×Dic11—42no—
254C2×Dic11—42no—
255C2×Dic11—42no—
256C2×Dic11—42no—
257C2×Dic11—42no—
258C2×Dic11—42no—
259C2×Dic11—42no—
260C2×Dic11—42no—
261C2×Dic11—42no—
262C2×Dic11—42no—
263C2×Dic11—42no—
264C2×Dic11—42no—
265C2×Dic11—42no—
266C2×Dic11—42no—
267C2×Dic11—42no—
268C23×D4C2×D1111yescharacteristic
269C22×C4⋊C4—112no—
270C22×C4⋊C4C2×D1111yescharacteristic
271C22×C22⋊C4—112no—
272C22×C22⋊C4—112no—
273C22×C22⋊C4—112no—
274C22×C22⋊C4—112no—
275C22×C22⋊C4C2×D1112yes—
276C22×C22⋊C4C2×D1112yes—
277C22×C42—111no—
278#394Dic1118yescomplemented
279C2×#95—112no—
280C2×#95—112no—
281C2×#95—111no—
282C2×#95—112no—
283C2×#95—112no—
284C2×#95—112no—
285C2×#95—112no—
286C2×#95—111no—
287C2×#95—112no—
288C2×#95—111no—
289C2×#95C2×D1111yescharacteristic
290C22×C11—44no—
291C22×C11—44no—
292C22×C11—44no—
293C22×C11—44no—
294C22×C11—44no—
295C22×C11—44no—
296C22×C11—44no—
297C22×C11—82no—
298C22×C11—82no—
299C22×C11—82no—
300C22×C11—82no—
301C22×C11—82no—
302C22×C11—82no—
303C22×C11—82no—
304C22×C11—82no—
305C22×C11C4×#4111yescharacteristic
306C22×C11#51811yescharacteristic
307C22×C11#51811yescharacteristic
308C22×C11#51812yes—
309C22×C11#52012yes—
310C22×C11#53812yes—
311C22×C11#53812yes—
312C22×C11#53912yes—
313C22×C11#54012yes—
314C22×C11#54012yes—
315C22×C11#54212yes—
316C22×C11#56012yes—
317C22×C11#56011yescharacteristic
318C22×C11#56012yes—
319C22×C11#56012yes—
320C22×C11H(3,𝔽4)11yescharacteristic
321C22×C11H(3,𝔽4)11yescharacteristic
322C22×C11#56212yes—
323C22×C11#56212yes—
324C22×C11#56212yes—
325C22×C11#56311yescharacteristic
326C4×C11—42no—
327C4×C11—42no—
328C4×C11—42no—
329C4×C11—44no—
330Dic11—44no—
331Dic11—82no—
332Dic11—82no—
333Dic11—82no—
334C25C22×D1112yes—
335C22×D4—42no—
336C22×D4—42no—
337C22×D4—41no—
338C22×D4—41no—
339C22×D4C2×Dic1114yes—
340C23×C4—112no—
341C23×C4—112no—
342C23×C4—112no—
343C23×C4—112no—
344C23×C4C22×D1112yes—
345C23×C4C22×D1111yescharacteristic
346C23×C4C22×D1111yescharacteristic
347C23×C4C22×D1111yescharacteristic
348C2×C4⋊C4—41no—
349C2×C4⋊C4—41no—
350C2×C4⋊C4—442no—
351C2×C4⋊C4—442no—
352C2×C4⋊C4—442no—
353C2×C4⋊C4C2×Dic1114yes—
354C2×C22⋊C4—42no—
355C2×C22⋊C4—42no—
356C2×C22⋊C4—42no—
357C2×C22⋊C4—42no—
358C2×C22⋊C4—224no—
359C2×C22⋊C4—224no—
360C2×C22⋊C4—442no—
361C2×C22⋊C4—442no—
362C2×C22⋊C4—442no—
363C2×C22⋊C4—442no—
364C2×C22⋊C4—442no—
365C2×C22⋊C4—442no—
366C2×C22⋊C4—442no—
367C2×C22⋊C4—442no—
368C2×C22⋊C4—442no—
369C2×C22⋊C4—442no—
370C2×C22⋊C4C2×Dic1118yes—
371C2×C22⋊C4C2×Dic1118yes—
372C2×C42—442no—
373C2×C42—441no—
374#95—224no—
375#95—442no—
376#95—442no—
377#95—442no—
378#95—441no—
379#95—441no—
380#95—441no—
381#95—442no—
382#95—442no—
383#95—442no—
384#95C2×Dic1114yes—
385C2×C11—84no—
386C2×C11#233311yescharacteristic
387C2×C11#233512yes—
388C2×C11#237511yescharacteristic
389C2×C11#237712yes—
390C2×C11#237911yescharacteristic
391C2×C11#282412yes—
392C2×C11#282812yes—
393C2×C11#282912yes—
394C2×C11#283712yes—
395C24—22no—
396C24—22no—
397C24—22no—
398C24—22no—
399C24—22no—
400C24—22no—
401C24—22no—
402C24—22no—
403C24—22no—
404C24—22no—
405C24—22no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24C22×Dic1114yes—
410C24C23×D1111yescharacteristic
411C2×D4—44no—
412C2×D4—48no—
413C2×D4—44no—
414C2×D4—44no—
415C2×D4—48no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—114no—
435C22×C4—222no—
436C22×C4—222no—
437C22×C4—222no—
438C22×C4—222no—
439C22×C4—222no—
440C22×C4—222no—
441C22×C4—222no—
442C22×C4—222no—
443C22×C4—222no—
444C22×C4—222no—
445C22×C4—222no—
446C22×C4—222no—
447C22×C4—222no—
448C22×C4—222no—
449C22×C4—222no—
450C22×C4—222no—
451C22×C4—222no—
452C22×C4—222no—
453C22×C4—222no—
454C22×C4—222no—
455C22×C4—222no—
456C22×C4—222no—
457C22×C4—222no—
458C22×C4—222no—
459C22×C4—222no—
460C22×C4—222no—
461C22×C4—222no—
462C22×C4C22×Dic1114yes—
463C22×C4C22×Dic1112yes—
464C22×C4C22×Dic1112yes—
465C22×C4C22×Dic1112yes—
466C4⋊C4—44no—
467C4⋊C4—448no—
468C22⋊C4—48no—
469C22⋊C4—48no—
470C22⋊C4—448no—
471C22⋊C4—448no—
472C22⋊C4—448no—
473C22⋊C4—448no—
474C42—444no—
475C11#1464111yescharacteristic, complemented, Sylow
476C23—24no—
477C23—24no—
478C23—24no—
479C23—24no—
480C23—24no—
481C23—24no—
482C23—24no—
483C23—42no—
484C23—42no—
485C23—42no—
486C23—42no—
487C23—42no—
488C23—42no—
489C23—42no—
490C23—42no—
491C23—42no—
492C23—42no—
493C23—42no—
494C23—42no—
495C23—42no—
496C23—42no—
497C23—42no—
498C23—42no—
499C23—42no—
500C23—42no—
501C23—42no—
502C23—42no—
503C23—42no—
504C23—42no—
505C23—42no—
506C23—42no—
507C23—42no—
508C23—42no—
509C23—42no—
510C23—42no—
511C23#6703711yescharacteristic
512C23#6703712yes—
513C23#6703711yescharacteristic
514C23#6703712yes—
515C23#6703712yes—
516C23#41×D1112yes—
517C23#6704212yes—
518C23#6704312yes—
519C23C23×Dic1111yescharacteristic
520D4—416no—
521C2×C4—22no—
522C2×C4—24no—
523C2×C4—24no—
524C2×C4—24no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—24no—
529C2×C4—22no—
530C2×C4—24no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—42no—
535C2×C4—41no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—224no—
544C2×C4—224no—
545C2×C4—224no—
546C2×C4—442no—
547C2×C4—442no—
548C2×C4—442no—
549C2×C4—442no—
550C2×C4—442no—
551C2×C4—442no—
552C2×C4—442no—
553C2×C4—442no—
554C2×C4—442no—
555C2×C4—442no—
556C2×C4—442no—
557C2×C4—442no—
558C2×C4—442no—
559C2×C4—442no—
560C2×C4—442no—
561C2×C4—442no—
562C2×C4—442no—
563C2×C4—442no—
564C2×C4—442no—
565C2×C4—442no—
566C2×C4—442no—
567C2×C4—442no—
568C2×C4—442no—
569C2×C4—442no—
570C2×C4—442no—
571C22—44no—
572C22—44no—
573C22—44no—
574C22—44no—
575C22—44no—
576C22—44no—
577C22—44no—
578C22—82no—
579C22—82no—
580C22—82no—
581C22—82no—
582C22—82no—
583C22—82no—
584C22—82no—
585C22—82no—
586C22#1062312511yescharacteristic
587C22#1062312611yescharacteristic
588C22#1062312612yes—
589C22#1062314412yes—
590C22#1062314612yes—
591C22#1062315112yes—
592C22#1062315112yes—
593C22#1062315212yes—
594C22#1062315212yes—
595C22#1062318812yes—
596C22#1062319112yes—
597C22#1062319312yes—
598C22#1062319412yes—
599C22#1062320311yescharacteristic
600C22#1062321411yescharacteristic
601C22#1062321512yes—
602C22#1062332911yescharacteristic
603C22#1062332911yescharacteristic
604C22#1062332912yes—
605C22#41×Dic1111yescharacteristic
606C22#1062335812yes—
607C4—42no—
608C4—42no—
609C4—42no—
610C4—44no—
611C4—444no—
612C4—882no—
613C4—882no—
614C4—882no—
615C2—84no—
616C2#1307138311yescharacteristic
617C2#1307141012yes—
618C2#1307175711yescharacteristic
619C2#1307177312yes—
620C2#1307179011yescharacteristic
621C2#1307669212yes—
622C2#1307673212yes—
623C2#1307674912yes—
624C2#1307682312yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#394C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC2×#394D11
hypocenterC11#14641
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. #13066884C2semidirect
2. #13066873C2semidirect
3. #13066865C2semidirect
4. #13066861C2semidirect
5. #13066861C2semidirect
7. #13066853C2semidirect
8. #13066848C2semidirect
20. C11×#394C4semidirect
278. #394Dic11semidirect
475. C11#14641semidirect

Maximal subgroups

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

subgroupindex
#130668842
#130668732
#130668652
#130668612
#130668572
#130668532
#130668482
C2×C11×#3942
#1464111