Finite Group Databasebeta

← #14682227

Subgroups — #14682227

Order 2816.

1658 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622552C211yesmaximal, characteristic
2C2×#10622283C212yesmaximal, complemented
3#13066864C212yesmaximal, complemented
4#13066862C212yesmaximal, complemented
5#13066856C212yesmaximal
6#13066852C212yesmaximal, complemented
7#13066850C212yesmaximal, complemented
8#13066846C211yesmaximal, characteristic, complemented
9C11×#1434C211yesmaximal, characteristic, complemented
10C23×D44C2211yescharacteristic
11C22×C42×C11C2211yescharacteristic
12C22×(C2×D11)⋊C4C2212yes—
13C22×(C2×D11)⋊C4C2212yes—
14C22×(C2×D11)⋊C4C2212yes—
15C22×(C2×D11)⋊C4C2212yes—
16C22×(C2×D11)⋊C4C2212yes—
17C22×(C2×D11)⋊C4C2212yes—
18C22×C4⋊Dic11C2212yes—
19C22×C4⋊Dic11C2211yescharacteristic
20C22×C4×Dic11C2212yes—
21C2×C11×#95C2212yes—
22C2×C11×#95C2211yescharacteristic
23C2×C11×#95C2212yes—
24C2×C11×#95C2211yescharacteristic
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2211yescharacteristic
28C2×C11⋊#95C2211yescharacteristic
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31#10622552C418yescomplemented
32#10622283—28no—
33C24×D11C2312yes—
34C23×C4×C11C2312yes—
35C23×C4×C11C2311yescharacteristic
36C23×C4×C11C2312yes—
37C23×C4×C11C2311yescharacteristic
38C23×C4×C11C2311yescharacteristic
39C23×Dic11C2312yes—
40C23×Dic11C2312yes—
41C23×Dic11C2312yes—
42C22×D44—22no—
43C22×D44—22no—
44C22×D44—42no—
45C22×D44—42no—
46C22×D44C2×C414yes—
47C2×C42×C11—42no—
48C2×C42×C11C2×C414yes—
49C2×(C2×D11)⋊C4—24no—
50C2×(C2×D11)⋊C4—24no—
51C2×(C2×D11)⋊C4—24no—
52C2×(C2×D11)⋊C4—24no—
53C2×(C2×D11)⋊C4—24no—
54C2×(C2×D11)⋊C4—24no—
55C2×(C2×D11)⋊C4—42no—
56C2×(C2×D11)⋊C4—42no—
57C2×(C2×D11)⋊C4—42no—
58C2×(C2×D11)⋊C4—42no—
59C2×(C2×D11)⋊C4—42no—
60C2×(C2×D11)⋊C4—42no—
61C2×(C2×D11)⋊C4—42no—
62C2×(C2×D11)⋊C4—42no—
63C2×(C2×D11)⋊C4—42no—
64C2×(C2×D11)⋊C4—42no—
65C2×(C2×D11)⋊C4C2×C418yes—
66C2×(C2×D11)⋊C4C2×C418yes—
67C2×C4⋊Dic11—24no—
68C2×C4⋊Dic11—24no—
69C2×C4⋊Dic11—42no—
70C2×C4⋊Dic11—42no—
71C2×C4⋊Dic11C2×C414yes—
72C2×C4×Dic11—24no—
73C2×C4×Dic11—42no—
74C2×C4×Dic11—42no—
75C11×#95—22no—
76C11×#95—24no—
77C11×#95—42no—
78C11×#95D414yescomplemented
79C11⋊#95—24no—
80C11⋊#95—24no—
81C11⋊#95—42no—
82C11⋊#95—42no—
83C11⋊#95—41no—
84C11⋊#95—41no—
85#14444—111nomaximal, Sylow
86C24×C11C2411yescharacteristic
87C23×D11—22no—
88C23×D11—22no—
89C23×D11—22no—
90C23×D11—22no—
91C23×D11—22no—
92C23×D11—22no—
93C23×D11—22no—
94C23×D11—22no—
95C23×D11—22no—
96C23×D11—22no—
97C23×D11—22no—
98C23×D11—22no—
99C23×D11—22no—
100C23×D11—22no—
101C23×D11C22×C414yes—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—21no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—21no—
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×C11C22×C412yes—
124C22×C4×C11C22×C412yes—
125C22×C4×C11C22×C412yes—
126C22×C4×C11C2×D414yes—
127C22×C4×C11C2×D412yes—
128C22×C4×C11#4112yes—
129C22×C4×C11#4112yes—
130C22×C4×C11#4112yes—
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×Dic11C22×C414yes—
151C22×Dic11#4114yes—
152C2×D44—28no—
153C2×D44—44no—
154C2×D44—44no—
155C2×D44—48no—
156C2×D44—48no—
157C42×C11—44no—
158(C2×D11)⋊C4—216no—
159(C2×D11)⋊C4—48no—
160(C2×D11)⋊C4—48no—
161(C2×D11)⋊C4—48no—
162(C2×D11)⋊C4—48no—
163(C2×D11)⋊C4—48no—
164C4⋊Dic11—44no—
165C4⋊Dic11—48no—
166C4×Dic11—48no—
167C2×#390—111no—
168C2×#388—112no—
169#1440—112no—
170#1439—112no—
171#1438—112no—
172#1437—112no—
173#1436—112no—
174C4⋊#95—111no—
175#1434D1111yescharacteristic, complemented
176C23×C11C23×C411yescharacteristic
177C23×C11C22×D411yescharacteristic
178C23×C11C2×#4111yescharacteristic
179C23×C11C2×#4111yescharacteristic
180C23×C11C2×#4111yescharacteristic
181C23×C11C2×#4112yes—
182C23×C11H(5,𝔽2)12yes—
183C23×C11H(5,𝔽2)12yes—
184C23×C11H(5,𝔽2)12yes—
185C23×C11H(5,𝔽2)11yescharacteristic
186C23×C112−1+411yescharacteristic
187C22×D11—24no—
188C22×D11—24no—
189C22×D11—24no—
190C22×D11—24no—
191C22×D11—24no—
192C22×D11—24no—
193C22×D11—24no—
194C22×D11—42no—
195C22×D11—42no—
196C22×D11—42no—
197C22×D11—42no—
198C22×D11—42no—
199C22×D11—42no—
200C22×D11—42no—
201C22×D11—42no—
202C22×D11—42no—
203C22×D11—42no—
204C22×D11—42no—
205C22×D11—42no—
206C22×D11—42no—
207C22×D11—42no—
208C22×D11—42no—
209C22×D11—42no—
210C22×D11—42no—
211C22×D11—42no—
212C22×D11—42no—
213C22×D11—42no—
214C22×D11—42no—
215C22×D11—42no—
216C22×D11—42no—
217C22×D11—42no—
218C22×D11—42no—
219C22×D11—42no—
220C22×D11—42no—
221C22×D11—42no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—24no—
227C2×C4×C11—24no—
228C2×C4×C11—24no—
229C2×C4×C11—24no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—24no—
234C2×C4×C11—24no—
235C2×C4×C11—24no—
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×C4×C11—42no—
249C2×C4×C11#11714yes—
250C2×C4×C11C4×D414yes—
251C2×Dic11—24no—
252C2×Dic11—24no—
253C2×Dic11—24no—
254C2×Dic11—24no—
255C2×Dic11—24no—
256C2×Dic11—24no—
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—
272D44—416no—
273C23×D4—111no—
274C22×C4⋊C4—111no—
275C22×C4⋊C4—112no—
276C22×C22⋊C4—112no—
277C22×C22⋊C4—112no—
278C22×C22⋊C4—112no—
279C22×C22⋊C4—112no—
280C22×C22⋊C4—112no—
281C22×C22⋊C4—112no—
282C22×C42—112no—
283C22×C42C2×D1111yescharacteristic
284#390—118no—
285#388—228no—
286C2×#95—112no—
287C2×#95—112no—
288C2×#95—111no—
289C2×#95—111no—
290C2×#95—112no—
291C2×#95—112no—
292C2×#95C2×D1112yes—
293C2×#95C2×D1111yescharacteristic
294C2×#95C2×D1112yes—
295C2×#95C2×D1111yescharacteristic
296C22×C11C2×#11711yescharacteristic
297C22×C11C2×C4×D411yescharacteristic
298C22×C11C4×#4111yescharacteristic
299C22×C11#51811yescharacteristic
300C22×C11#51811yescharacteristic
301C22×C11#51811yescharacteristic
302C22×C11#52011yescharacteristic
303C22×C11#53512yes—
304C22×C11#53812yes—
305C22×C11#53812yes—
306C22×C11#53812yes—
307C22×C11#54012yes—
308C22×C11#54212yes—
309C22×C11#54612yes—
310C22×C11#54711yescharacteristic
311C22×C11#55011yescharacteristic
312C22×C11#55312yes—
313C22×C11#55312yes—
314C22×C11#55511yescharacteristic
315C22×C11#55611yescharacteristic
316C22×C11#55912yes—
317C22×C11#56012yes—
318C22×C11#56212yes—
319C2×D11—44no—
320C2×D11—44no—
321C2×D11—44no—
322C2×D11—44no—
323C2×D11—44no—
324C2×D11—44no—
325C2×D11—44no—
326C2×D11—82no—
327C2×D11—82no—
328C2×D11—82no—
329C2×D11—82no—
330C2×D11—82no—
331C2×D11—82no—
332C2×D11—82no—
333C2×D11—82no—
334C4×C11—24no—
335C4×C11—24no—
336C4×C11—42no—
337C4×C11—44no—
338C4×C11—82no—
339Dic11—44no—
340Dic11—44no—
341Dic11—82no—
342C25—112no—
343C22×D4—114no—
344C22×D4—222no—
345C22×D4—222no—
346C22×D4—442no—
347C22×D4—442no—
348C23×C4—112no—
349C23×C4—112no—
350C23×C4—112no—
351C23×C4C22×D1112yes—
352C23×C4C22×D1111yescharacteristic
353C23×C4C22×D1112yes—
354C23×C4C22×D1111yescharacteristic
355C23×C4C22×D1111yescharacteristic
356C2×C4⋊C4—114no—
357C2×C4⋊C4—224no—
358C2×C4⋊C4—224no—
359C2×C4⋊C4—442no—
360C2×C4⋊C4—442no—
361C2×C22⋊C4—118no—
362C2×C22⋊C4—118no—
363C2×C22⋊C4—224no—
364C2×C22⋊C4—224no—
365C2×C22⋊C4—224no—
366C2×C22⋊C4—224no—
367C2×C22⋊C4—224no—
368C2×C22⋊C4—224no—
369C2×C22⋊C4—442no—
370C2×C22⋊C4—442no—
371C2×C22⋊C4—442no—
372C2×C22⋊C4—442no—
373C2×C22⋊C4—442no—
374C2×C22⋊C4—442no—
375C2×C22⋊C4—442no—
376C2×C22⋊C4—442no—
377C2×C22⋊C4—442no—
378C2×C22⋊C4—442no—
379C2×C42—42no—
380C2×C42—224no—
381C2×C42—442no—
382C2×C42—442no—
383C2×C42C4×D1114yes—
384#95—22no—
385#95—24no—
386#95—42no—
387#95—224no—
388#95—224no—
389#95—441no—
390#95—441no—
391#95—442no—
392#95—442no—
393#95D4414yescomplemented
394C2×C11#231211yescharacteristic
395C2×C11#232811yescharacteristic
396C2×C11#233711yescharacteristic
397C2×C11#235411yescharacteristic
398C2×C11#235711yescharacteristic
399C2×C11#236411yescharacteristic
400C2×C11#237711yescharacteristic
401C2×C11#271012yes—
402C2×C11#271412yes—
403C2×C11#280012yes—
404C2×C11#280312yes—
405D11—84no—
406C24—114no—
407C24—222no—
408C24—222no—
409C24—222no—
410C24—222no—
411C24—222no—
412C24—222no—
413C24—222no—
414C24—222no—
415C24—222no—
416C24—222no—
417C24—222no—
418C24—222no—
419C24—222no—
420C24—222no—
421C24C23×D1111yescharacteristic
422C2×D4—228no—
423C2×D4—444no—
424C2×D4—444no—
425C2×D4—448no—
426C2×D4—448no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—21no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—21no—
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—114no—
449C22×C4—114no—
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×C4—222no—
463C22×C4—222no—
464C22×C4—222no—
465C22×C4—222no—
466C22×C4—222no—
467C22×C4—222no—
468C22×C4—222no—
469C22×C4C2×C4×D1112yes—
470C22×C4C2×C4×D1112yes—
471C22×C4C2×C4×D1112yes—
472C22×C4C2×D4414yes—
473C22×C4C2×D4412yes—
474C22×C4#433912yes—
475C22×C4#434112yes—
476C22×C4#434312yes—
477C4⋊C4—444no—
478C4⋊C4—448no—
479C22⋊C4—2216no—
480C22⋊C4—448no—
481C22⋊C4—448no—
482C22⋊C4—448no—
483C22⋊C4—448no—
484C22⋊C4—448no—
485C42—44no—
486C42—448no—
487C11#1444411yescharacteristic, complemented, Sylow
488C23—224no—
489C23—224no—
490C23—224no—
491C23—224no—
492C23—224no—
493C23—224no—
494C23—224no—
495C23—442no—
496C23—442no—
497C23—442no—
498C23—442no—
499C23—442no—
500C23—442no—
501C23—442no—
502C23—442no—
503C23—442no—
504C23—442no—
505C23—442no—
506C23—442no—
507C23—442no—
508C23—442no—
509C23—442no—
510C23—442no—
511C23—442no—
512C23—442no—
513C23—442no—
514C23—442no—
515C23—442no—
516C23—442no—
517C23—442no—
518C23—442no—
519C23—442no—
520C23—442no—
521C23—442no—
522C23—442no—
523C23C22×C4×D1111yescharacteristic
524C23C22×D4411yescharacteristic
525C23C2×#433911yescharacteristic
526C23C2×#434111yescharacteristic
527C23#6703712yes—
528C23C2×#434311yescharacteristic
529C23#41×D1112yes—
530C23#6704211yescharacteristic
531C23#6704212yes—
532C23#6704212yes—
533C23#6704311yescharacteristic
534D4—4416no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—24no—
540C2×C4—24no—
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—24no—
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—224no—
563C2×C4—224no—
564C2×C4—224no—
565C2×C4—224no—
566C2×C4—224no—
567C2×C4—224no—
568C2×C4—442no—
569C2×C4—442no—
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×C4C4×D4414yes—
584C2×C4#6694514yes—
585C22—444no—
586C22—444no—
587C22—444no—
588C22—444no—
589C22—444no—
590C22—444no—
591C22—444no—
592C22—882no—
593C22—882no—
594C22—882no—
595C22—882no—
596C22—882no—
597C22—882no—
598C22—882no—
599C22—882no—
600C22C2×C4×D4411yescharacteristic
601C22#1062301711yescharacteristic
602C22C2×#6694511yescharacteristic
603C22#1062305211yescharacteristic
604C22#1062305211yescharacteristic
605C22#1062305311yescharacteristic
606C22#1062305411yescharacteristic
607C22#1062305612yes—
608C22#1062306612yes—
609C22#1062307112yes—
610C22#1062308512yes—
611C22#1062308611yescharacteristic
612C22#1062309411yescharacteristic
613C22#1062310811yescharacteristic
614C22#1062311511yescharacteristic
615C22#1062314812yes—
616C22#1062317512yes—
617C22#1062319712yes—
618C22#1062319812yes—
619C22#1062321212yes—
620C22#1062322612yes—
621C22#1062323512yes—
622C22#1062324112yes—
623C4—24no—
624C4—24no—
625C4—44no—
626C4—42no—
627C4—82no—
628C4—444no—
629C4—444no—
630C4—882no—
631C2—884no—
632C2#1307121311yescharacteristic
633C2#1307134111yescharacteristic
634C2#1307142611yescharacteristic
635C2#1307156311yescharacteristic
636C2#1307159111yescharacteristic
637C2#1307166611yescharacteristic
638C2#1307177511yescharacteristic
639C2#1307535612yes—
640C2#1307541012yes—
641C2#1307651512yes—
642C2#1307655212yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1434C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenter#1434D11
hypocenterC11#14444
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
2. C2×#10622283C2semidirect
3. #13066864C2semidirect
4. #13066862C2semidirect
6. #13066852C2semidirect
7. #13066850C2semidirect
8. #13066846C2semidirect
9. C11×#1434C2semidirect
31. #10622552C4semidirect
78. C11×#95D4semidirect
175. #1434D11semidirect
393. #95D44semidirect
487. C11#14444semidirect

Maximal subgroups

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

subgroupindex
C2×#106225522
C2×#106222832
#130668642
#130668622
#130668562
#130668522
#130668502
#130668462
C11×#14342
#1444411