Finite Group Databasebeta

← #14684839

Subgroups — #14684839

Order 2816.

1602 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622833C211yesmaximal, characteristic
2#13066877C212yesmaximal, complemented
3#13066871C212yesmaximal, complemented
4#13066863C212yesmaximal, complemented
5#13066859C212yesmaximal, complemented
6#13066859C212yesmaximal, complemented
7#13066857C211yesmaximal, characteristic
8#13066838C212yesmaximal, complemented
9C11×#1438C211yesmaximal, characteristic
10C23×D4×C11C2211yescharacteristic
11C24×Dic11C2211yescharacteristic
12C22×C11×C22⋊C4C2212yes—
13C22×C11×C22⋊C4C2212yes—
14C22×C22⋊Dic11C2212yes—
15C22×C22⋊Dic11C2211yescharacteristic
16C22×C22⋊Dic11C2211yescharacteristic
17C22×C22⋊Dic11C2211yescharacteristic
18C22×C22⋊Dic11C2212yes—
19C22×Dic11⋊C4C2212yes—
20C2×C11×#95C2211yescharacteristic
21C2×C11×#95C2211yescharacteristic
22#10622833C418yescomplemented
23C2×C11⋊#95C2212yes—
24C2×C11⋊#95C2212yes—
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C25×C11C2311yescharacteristic
33C25×C11C2311yescharacteristic
34C22×D4×C11—24no—
35C22×D4×C11—42no—
36C22×D4×C11—41no—
37C22×D4×C11—41no—
38C22×D4×C11C2×C414yes—
39C23×C4×C11C2312yes—
40C23×C4×C11C2312yes—
41C23×C4×C11C2311yescharacteristic
42C23×Dic11—41no—
43C23×Dic11—41no—
44C23×Dic11—42no—
45C23×Dic11—42no—
46C23×Dic11C2×C414yes—
47C23×Dic11C2312yes—
48C23×Dic11C2312yes—
49C23×Dic11C2312yes—
50C23×Dic11C2312yes—
51C2×C11×C22⋊C4—24no—
52C2×C11×C22⋊C4—42no—
53C2×C11×C22⋊C4—42no—
54C2×C11×C22⋊C4—42no—
55C2×C11×C22⋊C4—42no—
56C2×C11×C22⋊C4—42no—
57C2×C22⋊Dic11—24no—
58C2×C22⋊Dic11—42no—
59C2×C22⋊Dic11—42no—
60C2×C22⋊Dic11—42no—
61C2×C22⋊Dic11—42no—
62C2×C22⋊Dic11—42no—
63C2×C22⋊Dic11—41no—
64C2×C22⋊Dic11—41no—
65C2×C22⋊Dic11—42no—
66C2×C22⋊Dic11—42no—
67C2×C22⋊Dic11C2×C414yes—
68C2×C22⋊Dic11C2×C418yes—
69C2×Dic11⋊C4—42no—
70C2×Dic11⋊C4—42no—
71C2×Dic11⋊C4—42no—
72C11×#95—41no—
73C11×#95—41no—
74C11⋊#95—42no—
75C11⋊#95—42no—
76C11⋊#95—42no—
77C11⋊#95—42no—
78C11⋊#95—42no—
79C11⋊#95—42no—
80C11⋊#95—42no—
81C11⋊#95—42no—
82C11⋊#95C2×C418yes—
83#14666—111nomaximal, Sylow
84C24×C11—22no—
85C24×C11—22no—
86C24×C11—22no—
87C24×C11—22no—
88C24×C11—21no—
89C24×C11—21no—
90C24×C11—22no—
91C24×C11—22no—
92C24×C11—22no—
93C24×C11—22no—
94C24×C11—22no—
95C24×C11—21no—
96C24×C11—21no—
97C24×C11—22no—
98C24×C11—22no—
99C24×C11C22×C412yes—
100C24×C11C22×C412yes—
101C24×C11#4114yes—
102C24×C11C2411yescharacteristic
103C2×D4×C11—28no—
104C2×D4×C11—44no—
105C2×D4×C11—44no—
106C2×D4×C11—48no—
107C2×D4×C11—48no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—21no—
111C22×C4×C11—21no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
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—44no—
154C22×Dic11—48no—
155C22×Dic11—44no—
156C22×Dic11—48no—
157C22×Dic11—44no—
158C22×Dic11C22×C414yes—
159C22×Dic11C22×C414yes—
160C11×C22⋊C4—48no—
161C11×C22⋊C4—48no—
162C22⋊Dic11—44no—
163C22⋊Dic11—48no—
164C22⋊Dic11—48no—
165C22⋊Dic11—44no—
166C22⋊Dic11—44no—
167Dic11⋊C4—48no—
168C2×#386—111no—
169#1443—112no—
170#1442—112no—
171#1440—112no—
172#1439—112no—
173#1439—112no—
174#1438—111no—
175#1438D1111yescharacteristic
176C22⋊#95—112no—
177C23×C11—22no—
178C23×C11—22no—
179C23×C11—24no—
180C23×C11—24no—
181C23×C11—24no—
182C23×C11—24no—
183C23×C11—24no—
184C23×C11—24no—
185C23×C11—24no—
186C23×C11—24no—
187C23×C11—22no—
188C23×C11—24no—
189C23×C11—22no—
190C23×C11—22no—
191C23×C11—24no—
192C23×C11—41no—
193C23×C11—42no—
194C23×C11—41no—
195C23×C11—42no—
196C23×C11—42no—
197C23×C11—41no—
198C23×C11—42no—
199C23×C11—42no—
200C23×C11—42no—
201C23×C11—41no—
202C23×C11—42no—
203C23×C11—42no—
204C23×C11—42no—
205C23×C11—42no—
206C23×C11—42no—
207C23×C11—42no—
208C23×C11—41no—
209C23×C11—42no—
210C23×C11—41no—
211C23×C11—42no—
212C23×C11—42no—
213C23×C11—41no—
214C23×C11—42no—
215C23×C11—42no—
216C23×C11—42no—
217C23×C11—41no—
218C23×C11#11714yes—
219C23×C11C23×C411yescharacteristic
220C23×C11C2×#4112yes—
221C23×C11H(5,𝔽2)11yescharacteristic
222C23×C11H(5,𝔽2)12yes—
223C23×C11H(5,𝔽2)11yescharacteristic
224C23×C11H(5,𝔽2)12yes—
225C23×C11H(5,𝔽2)12yes—
226C23×C11H(5,𝔽2)12yes—
227C23×C112−1+412yes—
228D4×C11—416no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—42no—
233C2×C4×C11—42no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11—42no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—42no—
240C2×C4×C11—42no—
241C2×C4×C11—42no—
242C2×C4×C11—42no—
243C2×C4×C11—42no—
244C2×C4×C11—42no—
245C2×C4×C11—42no—
246C2×C4×C11—42no—
247C2×C4×C11—42no—
248C2×Dic11—24no—
249C2×Dic11—24no—
250C2×Dic11—24no—
251C2×Dic11—24no—
252C2×Dic11—24no—
253C2×Dic11—24no—
254C2×Dic11—416no—
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—
268C2×Dic11—42no—
269C2×Dic11—42no—
270C2×Dic11—42no—
271C2×Dic11—42no—
272C2×Dic11—42no—
273C2×Dic11—42no—
274C2×Dic11—42no—
275C2×Dic11—42no—
276C2×Dic11—42no—
277C23×D4C2×D1111yescharacteristic
278C24×C4—111no—
279C22×C4⋊C4—112no—
280C22×C22⋊C4—111no—
281C22×C22⋊C4—112no—
282C22×C22⋊C4—112no—
283C22×C22⋊C4—111no—
284C22×C22⋊C4—111no—
285C22×C22⋊C4C2×D1112yes—
286C22×C22⋊C4C2×D1112yes—
287#386—118no—
288C2×#95—112no—
289C2×#95—112no—
290C2×#95—112no—
291C2×#95—112no—
292C2×#95—112no—
293C2×#95—112no—
294C2×#95—112no—
295C2×#95—112no—
296C2×#95—112no—
297C2×#95C2×D1111yescharacteristic
298C2×#95C2×D1111yescharacteristic
299C22×C11—24no—
300C22×C11—28no—
301C22×C11—44no—
302C22×C11—44no—
303C22×C11—44no—
304C22×C11—44no—
305C22×C11—42no—
306C22×C11—42no—
307C22×C11—44no—
308C22×C11—42no—
309C22×C11—44no—
310C22×C11—42no—
311C22×C11—42no—
312C22×C11—44no—
313C22×C11—82no—
314C22×C11—82no—
315C22×C11—82no—
316C22×C11—82no—
317C22×C11C2×#11711yescharacteristic
318C22×C11#51811yescharacteristic
319C22×C11#51811yescharacteristic
320C22×C11#51812yes—
321C22×C11#52012yes—
322C22×C11#53812yes—
323C22×C11#53812yes—
324C22×C11#53812yes—
325C22×C11#53812yes—
326C22×C11#53912yes—
327C22×C11#53912yes—
328C22×C11#56011yescharacteristic
329C22×C11#56011yescharacteristic
330C22×C11#56012yes—
331C22×C11#56012yes—
332C22×C11#56012yes—
333C22×C11H(3,𝔽4)11yescharacteristic
334C22×C11#56212yes—
335C22×C11#56212yes—
336C22×C11#56212yes—
337C22×C11#56311yescharacteristic
338C4×C11—42no—
339C4×C11—82no—
340C4×C11—82no—
341Dic11—44no—
342Dic11—44no—
343Dic11—82no—
344Dic11—82no—
345C25C22×D1111yescharacteristic
346C25C22×D1111yescharacteristic
347C22×D4—24no—
348C22×D4—41no—
349C22×D4—41no—
350C22×D4—42no—
351C22×D4C4×D1114yes—
352C23×C4—112no—
353C23×C4—112no—
354C23×C4—114no—
355C23×C4—112no—
356C23×C4—112no—
357C23×C4—441no—
358C23×C4—441no—
359C23×C4—442no—
360C23×C4—442no—
361C23×C4C22×D1112yes—
362C23×C4C22×D1112yes—
363C23×C4C22×D1111yescharacteristic
364C2×C4⋊C4—442no—
365C2×C4⋊C4—442no—
366C2×C4⋊C4—442no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—42no—
369C2×C22⋊C4—42no—
370C2×C22⋊C4—42no—
371C2×C22⋊C4—42no—
372C2×C22⋊C4—42no—
373C2×C22⋊C4—114no—
374C2×C22⋊C4—118no—
375C2×C22⋊C4—224no—
376C2×C22⋊C4—442no—
377C2×C22⋊C4—442no—
378C2×C22⋊C4—442no—
379C2×C22⋊C4—442no—
380C2×C22⋊C4—442no—
381C2×C22⋊C4—441no—
382C2×C22⋊C4—441no—
383C2×C22⋊C4—442no—
384C2×C22⋊C4—442no—
385#95—41no—
386#95—41no—
387#95—118no—
388#95—442no—
389#95—442no—
390#95—442no—
391#95—442no—
392#95—442no—
393#95—442no—
394#95—442no—
395#95—442no—
396C2×C11—44no—
397C2×C11—82no—
398C2×C11#231211yescharacteristic
399C2×C11#231812yes—
400C2×C11#237511yescharacteristic
401C2×C11#237611yescharacteristic
402C2×C11#237712yes—
403C2×C11#282412yes—
404C2×C11#282512yes—
405C2×C11#282612yes—
406C2×C11#282712yes—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—21no—
411C24—21no—
412C24—22no—
413C24—22no—
414C24—22no—
415C24—22no—
416C24—22no—
417C24—22no—
418C24—21no—
419C24—21no—
420C24—22no—
421C24—22no—
422C24C2×C4×D1112yes—
423C24C2×C4×D1112yes—
424C24#434114yes—
425C24C23×D1111yescharacteristic
426C2×D4—28no—
427C2×D4—44no—
428C2×D4—44no—
429C2×D4—48no—
430C2×D4—48no—
431C22×C4—22no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—114no—
450C22×C4—114no—
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×C4—222no—
463C22×C4—222no—
464C22×C4—222no—
465C22×C4—222no—
466C22×C4—222no—
467C22×C4—222no—
468C22×C4—222no—
469C22×C4—222no—
470C22×C4—222no—
471C22×C4—222no—
472C22×C4—222no—
473C22×C4—222no—
474C22×C4—222no—
475C22×C4—222no—
476C22×C4—222no—
477C22×C4—444no—
478C22×C4—448no—
479C22×C4—444no—
480C22×C4—448no—
481C22×C4—444no—
482C22×C4C2×C4×D1112yes—
483C4⋊C4—448no—
484C22⋊C4—48no—
485C22⋊C4—48no—
486C22⋊C4—444no—
487C22⋊C4—448no—
488C22⋊C4—448no—
489C22⋊C4—444no—
490C22⋊C4—444no—
491C11#1466611yescharacteristic, complemented, Sylow
492C23—22no—
493C23—22no—
494C23—24no—
495C23—24no—
496C23—24no—
497C23—24no—
498C23—24no—
499C23—24no—
500C23—24no—
501C23—24no—
502C23—22no—
503C23—22no—
504C23—22no—
505C23—24no—
506C23—24no—
507C23—41no—
508C23—41no—
509C23—42no—
510C23—42no—
511C23—42no—
512C23—42no—
513C23—42no—
514C23—42no—
515C23—41no—
516C23—41no—
517C23—41no—
518C23—41no—
519C23—42no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23—42no—
524C23—42no—
525C23—42no—
526C23—42no—
527C23—42no—
528C23—42no—
529C23—42no—
530C23—42no—
531C23—41no—
532C23—41no—
533C23#6693014yes—
534C23C22×C4×D1111yescharacteristic
535C23C2×#434112yes—
536C23#6703711yescharacteristic
537C23#6703711yescharacteristic
538C23#6703712yes—
539C23#6703712yes—
540C23#6703712yes—
541C23#6704212yes—
542C23#6704312yes—
543D4—416no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—224no—
564C2×C4—224no—
565C2×C4—224no—
566C2×C4—224no—
567C2×C4—224no—
568C2×C4—224no—
569C2×C4—4416no—
570C2×C4—442no—
571C2×C4—442no—
572C2×C4—442no—
573C2×C4—442no—
574C2×C4—442no—
575C2×C4—442no—
576C2×C4—442no—
577C2×C4—442no—
578C2×C4—442no—
579C2×C4—442no—
580C2×C4—442no—
581C2×C4—442no—
582C2×C4—442no—
583C2×C4—442no—
584C2×C4—442no—
585C2×C4—442no—
586C2×C4—442no—
587C2×C4—442no—
588C2×C4—442no—
589C2×C4—442no—
590C2×C4—442no—
591C2×C4—442no—
592C22—24no—
593C22—28no—
594C22—42no—
595C22—42no—
596C22—44no—
597C22—44no—
598C22—44no—
599C22—44no—
600C22—44no—
601C22—42no—
602C22—42no—
603C22—44no—
604C22—42no—
605C22—44no—
606C22—82no—
607C22—82no—
608C22—82no—
609C22—82no—
610C22C2×#6693011yescharacteristic
611C22#1062301711yescharacteristic
612C22#1062301711yescharacteristic
613C22#1062307612yes—
614C22#1062307712yes—
615C22#1062312412yes—
616C22#1062312412yes—
617C22#1062312412yes—
618C22#1062312612yes—
619C22#1062313312yes—
620C22#1062314812yes—
621C22#1062315112yes—
622C22#1062315112yes—
623C22#1062315212yes—
624C22#1062315212yes—
625C22#1062319612yes—
626C22#1062319812yes—
627C22#1062320311yescharacteristic
628C22#1062321411yescharacteristic
629C22#1062325111yescharacteristic
630C22#1062325111yescharacteristic
631C4—42no—
632C4—82no—
633C4—82no—
634C4—444no—
635C4—444no—
636C4—882no—
637C4—882no—
638C2—44no—
639C2—82no—
640C2#1307121211yescharacteristic
641C2#1307124212yes—
642C2#1307175311yescharacteristic
643C2#1307176611yescharacteristic
644C2#1307177412yes—
645C2#1307669912yes—
646C2#1307670412yes—
647C2#1307671512yes—
648C2#1307672812yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1438C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenter#1438D11
hypocenterC11#14666
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1438

Complements

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

NH ≅ G/Ntype
2. #13066877C2semidirect
3. #13066871C2semidirect
4. #13066863C2semidirect
5. #13066859C2semidirect
6. #13066859C2semidirect
8. #13066838C2semidirect
22. #10622833C4semidirect
491. C11#14666semidirect

Maximal subgroups

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

subgroupindex
C2×#106228332
#130668772
#130668712
#130668632
#130668592
#130668572
#130668382
C11×#14382
#1466611