Finite Group Databasebeta

← #14675882

Subgroups — #14675882

Order 2816.

1602 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622264C211yesmaximal, characteristic, complemented
2C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic
3C2×#10622279C211yesmaximal, characteristic
4#13066864C212yesmaximal
5#13066862C212yesmaximal
6#13066850C212yesmaximal, complemented
7#13066846C211yesmaximal, characteristic, complemented
8#13066840C212yesmaximal, complemented
9#13066840C211yesmaximal, characteristic, complemented
10(C2×D11)⋊#95C211yesmaximal, characteristic
11C11×#1434C211yesmaximal, characteristic, complemented
12C23×C4×D11C2211yescharacteristic
13C22×C42×C11C2211yescharacteristic
14C22×(C2×D11)⋊C4C2212yes—
15C22×(C2×D11)⋊C4C2211yescharacteristic
16C22×(C2×D11)⋊C4C2211yescharacteristic
17C22×(C2×D11)⋊C4C2212yes—
18C22×C4⋊Dic11C2212yes—
19C22×C4×Dic11C2212yes—
20C22×C4×Dic11C2211yescharacteristic
21C2×C11×#95C2211yescharacteristic
22C2×C11×#95C2212yes—
23C2×C11×#95C2212yes—
24C2×C11×#95C2211yescharacteristic
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2211yescharacteristic
27C2×C11⋊#95C2211yescharacteristic
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2211yescharacteristic
34C2×C11⋊#95C2211yescharacteristic
35C4×(C2×D11)⋊C4C418yescomplemented
36#10622279—24no—
37#10622264—24no—
38C24×D11C2311yescharacteristic
39C23×C4×C11C2312yes—
40C23×C4×C11C2311yescharacteristic
41C23×C4×C11C2312yes—
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2311yescharacteristic
44C23×Dic11C2312yes—
45C23×Dic11C2311yescharacteristic
46C23×Dic11C2311yescharacteristic
47C23×Dic11C2312yes—
48C23×Dic11C2311yescharacteristic
49C22×C4×D11—22no—
50C22×C4×D11—22no—
51C22×C4×D11—24no—
52C22×C4×D11—42no—
53C22×C4×D11C2×C414yes—
54C2×C42×C11—42no—
55C2×C42×C11C2×C414yes—
56C2×(C2×D11)⋊C4—24no—
57C2×(C2×D11)⋊C4—24no—
58C2×(C2×D11)⋊C4—24no—
59C2×(C2×D11)⋊C4—22no—
60C2×(C2×D11)⋊C4—22no—
61C2×(C2×D11)⋊C4—24no—
62C2×(C2×D11)⋊C4—24no—
63C2×(C2×D11)⋊C4—42no—
64C2×(C2×D11)⋊C4—42no—
65C2×(C2×D11)⋊C4C2×C414yes—
66C2×(C2×D11)⋊C4C2×C414yes—
67C2×C4⋊Dic11—24no—
68C2×C4⋊Dic11—24no—
69C2×C4⋊Dic11—42no—
70C2×C4×Dic11—22no—
71C2×C4×Dic11—22no—
72C2×C4×Dic11—24no—
73C2×C4×Dic11—24no—
74C2×C4×Dic11—42no—
75C2×C4×Dic11C2×C414yes—
76C11×#95—22no—
77C11×#95—24no—
78C11×#95—42no—
79C11×#95D414yes—
80C11⋊#95—24no—
81C11⋊#95—24no—
82C11⋊#95—22no—
83C11⋊#95—22no—
84C11⋊#95—24no—
85C11⋊#95—24no—
86C11⋊#95—42no—
87C11⋊#95—42no—
88C11⋊#95C2×C414yes—
89C11⋊#95C2×C414yes—
90#13892—111nomaximal, Sylow
91C24×C11C2411yescharacteristic
92C23×D11—21no—
93C23×D11—21no—
94C23×D11—21no—
95C23×D11—22no—
96C23×D11—22no—
97C23×D11—21no—
98C23×D11—21no—
99C23×D11—22no—
100C23×D11—21no—
101C23×D11C22×C412yes—
102C23×D11#4114yes—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—21no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—21no—
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×C11C22×C412yes—
125C22×C4×C11C22×C412yes—
126C22×C4×C11C22×C412yes—
127C22×C4×C11C2×D414yes—
128C22×C4×C11C2×D412yes—
129C22×C4×C11#4112yes—
130C22×C4×C11#4112yes—
131C22×C4×C11#4112yes—
132C22×Dic11—21no—
133C22×Dic11—21no—
134C22×Dic11—21no—
135C22×Dic11—22no—
136C22×Dic11—22no—
137C22×Dic11—21no—
138C22×Dic11—22no—
139C22×Dic11—21no—
140C22×Dic11—21no—
141C22×Dic11—22no—
142C22×Dic11—22no—
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11—22no—
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11—22no—
150C22×Dic11—22no—
151C22×Dic11—22no—
152C22×Dic11—21no—
153C22×Dic11—22no—
154C22×Dic11—22no—
155C22×Dic11—22no—
156C22×Dic11—22no—
157C22×Dic11—21no—
158C22×Dic11C22×C412yes—
159C22×Dic11C22×C412yes—
160C22×Dic11C22×C412yes—
161C22×Dic11#4114yes—
162C22×Dic11#4114yes—
163C2×C4×D11—28no—
164C2×C4×D11—28no—
165C2×C4×D11—44no—
166C2×C4×D11—48no—
167C2×C4×D11—48no—
168C42×C11—44no—
169(C2×D11)⋊C4—216no—
170(C2×D11)⋊C4—28no—
171(C2×D11)⋊C4—28no—
172(C2×D11)⋊C4—48no—
173C4⋊Dic11—48no—
174C4×Dic11—28no—
175C4×Dic11—48no—
176C2×#383—111no—
177C2×C4×C22⋊C4—111no—
178C2×C4×C22⋊C4—111no—
179#1440—112no—
180#1439—112no—
181#1436—112no—
182C4⋊#95—111no—
183#1434—112no—
184#1434—111no—
185#1434D1111yescharacteristic, complemented
186C22⋊#95—111no—
187C23×C11C23×C411yescharacteristic
188C23×C11C22×D411yescharacteristic
189C23×C11C2×#4111yescharacteristic
190C23×C11C2×#4111yescharacteristic
191C23×C11C2×#4111yescharacteristic
192C23×C11C2×#4112yes—
193C23×C11C2×#4112yes—
194C23×C11C2×#4112yes—
195C23×C11H(5,𝔽2)12yes—
196C23×C11H(5,𝔽2)11yescharacteristic
197C23×C112−1+411yescharacteristic
198C22×D11—22no—
199C22×D11—22no—
200C22×D11—22no—
201C22×D11—22no—
202C22×D11—22no—
203C22×D11—22no—
204C22×D11—24no—
205C22×D11—24no—
206C22×D11—24no—
207C22×D11—24no—
208C22×D11—24no—
209C22×D11—24no—
210C22×D11—42no—
211C22×D11—41no—
212C22×D11—41no—
213C22×D11—42no—
214C22×D11—42no—
215C22×D11—42no—
216C22×D11—42no—
217C22×D11—41no—
218C22×D11—42no—
219C22×D11—41no—
220C22×D11#11714yes—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—24no—
226C2×C4×C11—24no—
227C2×C4×C11—24no—
228C2×C4×C11—24no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—24no—
233C2×C4×C11—24no—
234C2×C4×C11—24no—
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×C4×C11#11714yes—
249C2×C4×C11C4×D414yes—
250C2×Dic11—22no—
251C2×Dic11—22no—
252C2×Dic11—24no—
253C2×Dic11—24no—
254C2×Dic11—22no—
255C2×Dic11—22no—
256C2×Dic11—22no—
257C2×Dic11—22no—
258C2×Dic11—22no—
259C2×Dic11—22no—
260C2×Dic11—24no—
261C2×Dic11—24no—
262C2×Dic11—24no—
263C2×Dic11—42no—
264C2×Dic11—42no—
265C2×Dic11—42no—
266C2×Dic11—42no—
267C2×Dic11—42no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—42no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—42no—
274C2×Dic11—42no—
275C2×Dic11—42no—
276C2×Dic11—42no—
277C2×Dic11—42no—
278C2×Dic11—42no—
279C2×Dic11—42no—
280C2×Dic11#11714yes—
281C4×D11—416no—
282C24×C4—111no—
283C22×C4⋊C4—112no—
284C22×C22⋊C4—111no—
285C22×C22⋊C4—111no—
286C22×C22⋊C4—112no—
287C22×C22⋊C4—112no—
288C22×C42—111no—
289C22×C42—112no—
290C22×C42C2×D1111yescharacteristic
291#383—224no—
292C4×C22⋊C4—118no—
293C4×C22⋊C4—224no—
294C2×#95—111no—
295C2×#95—111no—
296C2×#95—112no—
297C2×#95—111no—
298C2×#95—111no—
299C2×#95—112no—
300C2×#95—112no—
301C2×#95—112no—
302C2×#95—112no—
303C2×#95—112no—
304C2×#95C2×D1111yescharacteristic
305C2×#95C2×D1112yes—
306C2×#95C2×D1112yes—
307C2×#95C2×D1111yescharacteristic
308C22×C11C2×#11711yescharacteristic
309C22×C11C2×#11711yescharacteristic
310C22×C11C2×#11711yescharacteristic
311C22×C11C2×C4×D411yescharacteristic
312C22×C11C4×#4111yescharacteristic
313C22×C11#51811yescharacteristic
314C22×C11#52011yescharacteristic
315C22×C11#52512yes—
316C22×C11#52912yes—
317C22×C11#52912yes—
318C22×C11#52912yes—
319C22×C11#53812yes—
320C22×C11#53912yes—
321C22×C11#54612yes—
322C22×C11#54711yescharacteristic
323C22×C11#55011yescharacteristic
324C22×C11#55112yes—
325C22×C11#55112yes—
326C22×C11#55312yes—
327C22×C11#55312yes—
328C22×C11#55511yescharacteristic
329C22×C11#55612yes—
330C22×C11#55611yescharacteristic
331C2×D11—24no—
332C2×D11—24no—
333C2×D11—24no—
334C2×D11—42no—
335C2×D11—42no—
336C2×D11—42no—
337C2×D11—42no—
338C2×D11—44no—
339C2×D11—44no—
340C2×D11—44no—
341C2×D11—44no—
342C4×C11—24no—
343C4×C11—24no—
344C4×C11—42no—
345C4×C11—44no—
346C4×C11—82no—
347Dic11—24no—
348Dic11—42no—
349Dic11—44no—
350Dic11—42no—
351Dic11—82no—
352C25—111no—
353C23×C4—111no—
354C23×C4—112no—
355C23×C4—111no—
356C23×C4—111no—
357C23×C4—114no—
358C23×C4—112no—
359C23×C4—224no—
360C23×C4—222no—
361C23×C4—222no—
362C23×C4—442no—
363C23×C4C22×D1112yes—
364C23×C4C22×D1111yescharacteristic
365C23×C4C22×D1112yes—
366C23×C4C22×D1111yescharacteristic
367C23×C4C22×D1111yescharacteristic
368C2×C4⋊C4—224no—
369C2×C4⋊C4—224no—
370C2×C4⋊C4—442no—
371C2×C22⋊C4—114no—
372C2×C22⋊C4—114no—
373C2×C22⋊C4—224no—
374C2×C22⋊C4—224no—
375C2×C22⋊C4—224no—
376C2×C22⋊C4—224no—
377C2×C22⋊C4—222no—
378C2×C22⋊C4—222no—
379C2×C22⋊C4—224no—
380C2×C22⋊C4—442no—
381C2×C22⋊C4—442no—
382C2×C42—42no—
383C2×C42—114no—
384C2×C42—222no—
385C2×C42—222no—
386C2×C42—224no—
387C2×C42—224no—
388C2×C42—442no—
389C2×C42C4×D1114yes—
390#95—22no—
391#95—24no—
392#95—42no—
393#95—114no—
394#95—114no—
395#95—224no—
396#95—224no—
397#95—222no—
398#95—224no—
399#95—224no—
400#95—222no—
401#95—442no—
402#95—442no—
403#95D4414yes—
404C2×C11#228311yescharacteristic
405C2×C11#229011yescharacteristic
406C2×C11#231811yescharacteristic
407C2×C11#234211yescharacteristic
408C2×C11#234711yescharacteristic
409C2×C11#235311yescharacteristic
410C2×C11#235411yescharacteristic
411C2×C11#246612yes—
412C2×C11#246712yes—
413C2×C11#251812yes—
414C2×C11#252312yes—
415D11—44no—
416C24—112no—
417C24—114no—
418C24—221no—
419C24—221no—
420C24—221no—
421C24—222no—
422C24—221no—
423C24—222no—
424C24—222no—
425C24—221no—
426C24—221no—
427C24C23×D1111yescharacteristic
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—21no—
440C22×C4—21no—
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—112no—
450C22×C4—114no—
451C22×C4—112no—
452C22×C4—112no—
453C22×C4—114no—
454C22×C4—228no—
455C22×C4—221no—
456C22×C4—221no—
457C22×C4—222no—
458C22×C4—221no—
459C22×C4—221no—
460C22×C4—222no—
461C22×C4—221no—
462C22×C4—221no—
463C22×C4—221no—
464C22×C4—222no—
465C22×C4—221no—
466C22×C4—222no—
467C22×C4—222no—
468C22×C4—222no—
469C22×C4—222no—
470C22×C4—222no—
471C22×C4—222no—
472C22×C4—221no—
473C22×C4—221no—
474C22×C4—228no—
475C22×C4—222no—
476C22×C4—222no—
477C22×C4—222no—
478C22×C4—222no—
479C22×C4—222no—
480C22×C4—222no—
481C22×C4—222no—
482C22×C4—444no—
483C22×C4—448no—
484C22×C4—448no—
485C22×C4C2×C4×D1112yes—
486C22×C4C2×C4×D1112yes—
487C22×C4C2×C4×D1112yes—
488C22×C4C2×D4414yes—
489C22×C4C2×D4412yes—
490C22×C4#433912yes—
491C22×C4#434112yes—
492C22×C4#434312yes—
493C4⋊C4—448no—
494C22⋊C4—228no—
495C22⋊C4—2216no—
496C22⋊C4—228no—
497C22⋊C4—448no—
498C42—44no—
499C42—228no—
500C42—448no—
501C11#1389211yescharacteristic, complemented, Sylow
502C23—114no—
503C23—222no—
504C23—222no—
505C23—222no—
506C23—222no—
507C23—222no—
508C23—222no—
509C23—224no—
510C23—224no—
511C23—224no—
512C23—224no—
513C23—224no—
514C23—224no—
515C23—442no—
516C23—442no—
517C23—442no—
518C23—441no—
519C23—442no—
520C23—441no—
521C23—441no—
522C23—441no—
523C23—442no—
524C23—442no—
525C23C22×C4×D1111yescharacteristic
526C23C22×D4411yescharacteristic
527C23C2×#433911yescharacteristic
528C23C2×#434111yescharacteristic
529C23#6703712yes—
530C23C2×#434311yescharacteristic
531C23#41×D1112yes—
532C23#41×D1112yes—
533C23#41×D1112yes—
534C23#6704211yescharacteristic
535C23#6704311yescharacteristic
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—24no—
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—24no—
548C2×C4—24no—
549C2×C4—24no—
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—114no—
564C2×C4—222no—
565C2×C4—222no—
566C2×C4—224no—
567C2×C4—224no—
568C2×C4—224no—
569C2×C4—222no—
570C2×C4—222no—
571C2×C4—222no—
572C2×C4—222no—
573C2×C4—222no—
574C2×C4—222no—
575C2×C4—224no—
576C2×C4—224no—
577C2×C4—4416no—
578C2×C4—442no—
579C2×C4—442no—
580C2×C4—442no—
581C2×C4—441no—
582C2×C4—441no—
583C2×C4—442no—
584C2×C4—441no—
585C2×C4—441no—
586C2×C4—442no—
587C2×C4—442no—
588C2×C4—442no—
589C2×C4—442no—
590C2×C4—442no—
591C2×C4—442no—
592C2×C4—442no—
593C2×C4—442no—
594C2×C4—442no—
595C2×C4C4×D4414yes—
596C2×C4#6694514yes—
597C22—224no—
598C22—224no—
599C22—224no—
600C22—444no—
601C22—444no—
602C22—442no—
603C22—444no—
604C22—442no—
605C22—444no—
606C22—442no—
607C22—442no—
608C22C2×C4×D4411yescharacteristic
609C22#1062301711yescharacteristic
610C22C2×#6694511yescharacteristic
611C22D11×#11711yescharacteristic
612C22D11×#11711yescharacteristic
613C22#1062305311yescharacteristic
614C22#1062305411yescharacteristic
615C22#1062305512yes—
616C22#1062305912yes—
617C22#1062308512yes—
618C22#1062308611yescharacteristic
619C22#1062308712yes—
620C22#1062309411yescharacteristic
621C22#1062310811yescharacteristic
622C22#1062311511yescharacteristic
623C22#1062313212yes—
624C22#1062316812yes—
625C22#1062318812yes—
626C22#1062319112yes—
627C22#1062321112yes—
628C22#1062322212yes—
629C22#1062323312yes—
630C22#1062324012yes—
631C4—24no—
632C4—24no—
633C4—44no—
634C4—42no—
635C4—82no—
636C4—224no—
637C4—444no—
638C4—442no—
639C4—442no—
640C4—882no—
641C2—444no—
642C2#1307100911yescharacteristic
643C2#1307106011yescharacteristic
644C2#1307124511yescharacteristic
645C2#1307146811yescharacteristic
646C2#1307150411yescharacteristic
647C2#1307155811yescharacteristic
648C2#1307156311yescharacteristic
649C2#1307265012yes—
650C2#1307266512yes—
651C2#1307327112yes—
652C2#1307334712yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1434C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenter#1434D11
hypocenterC11#13892
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
1. C2×#10622264C2semidirect
6. #13066850C2semidirect
7. #13066846C2semidirect
8. #13066840C2semidirect
9. #13066840C2semidirect
11. C11×#1434C2semidirect
35. C4×(C2×D11)⋊C4C4semidirect
185. #1434D11semidirect
501. C11#13892semidirect

Maximal subgroups

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

subgroupindex
C2×#106222642
C2×C4×(C2×D11)⋊C42
C2×#106222792
#130668642
#130668622
#130668502
#130668462
#130668402
(C2×D11)⋊#952
C11×#14342
#1389211