Finite Group Databasebeta

← #14676379

Subgroups — #14676379

Order 2816.

1486 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic
2#13066877C212yesmaximal, complemented
3#13066864C212yesmaximal
4#13066854C212yesmaximal
5#13066843C211yesmaximal, characteristic, complemented
6#13066843C212yesmaximal, complemented
7#13066842C211yesmaximal, characteristic, complemented
8#13066842C211yesmaximal, characteristic, complemented
9(C2×D11)⋊#95C211yesmaximal, characteristic
10(C2×D11)⋊#95C211yesmaximal, characteristic
11C4×C11×#95C211yesmaximal, characteristic, complemented
12C23×C4×D11C2211yescharacteristic
13C22×C42×C11C2212yes—
14C22×C42×C11C2211yescharacteristic
15C22×(C2×D11)⋊C4C2212yes—
16C22×(C2×D11)⋊C4C2212yes—
17C22×(C2×D11)⋊C4C2211yescharacteristic
18C22×(C2×D11)⋊C4C2211yescharacteristic
19C22×C4×Dic11C2211yescharacteristic
20C2×C11×#95C2211yescharacteristic
21C2×C11×#95C2211yescharacteristic
22C2×C11×#95C2212yes—
23C2×C11⋊#95C2211yescharacteristic
24C2×C11⋊#95C2211yescharacteristic
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
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
36C24×D11C2311yescharacteristic
37C23×C4×C11C2311yescharacteristic
38C23×C4×C11C2312yes—
39C23×C4×C11C2312yes—
40C23×C4×C11C2311yescharacteristic
41C23×C4×C11C2311yescharacteristic
42C23×Dic11C2312yes—
43C23×Dic11C2312yes—
44C23×Dic11C2311yescharacteristic
45C23×Dic11C2311yescharacteristic
46C23×Dic11C2311yescharacteristic
47C22×C4×D11—22no—
48C22×C4×D11—22no—
49C22×C4×D11—42no—
50C22×C4×D11—42no—
51C22×C4×D11C2×C414yes—
52C2×C42×C11—24no—
53C2×C42×C11—24no—
54C2×C42×C11—42no—
55C2×C42×C11—42no—
56C2×C42×C11C2×C414yes—
57C2×(C2×D11)⋊C4—22no—
58C2×(C2×D11)⋊C4—22no—
59C2×(C2×D11)⋊C4—22no—
60C2×(C2×D11)⋊C4—22no—
61C2×(C2×D11)⋊C4—24no—
62C2×(C2×D11)⋊C4—24no—
63C2×(C2×D11)⋊C4—24no—
64C2×(C2×D11)⋊C4—24no—
65C2×(C2×D11)⋊C4—42no—
66C2×(C2×D11)⋊C4—42no—
67C2×(C2×D11)⋊C4C2×C414yes—
68C2×(C2×D11)⋊C4C2×C414yes—
69C2×C4×Dic11—42no—
70C2×C4×Dic11C2×C414yes—
71C11×#95—24no—
72C11×#95—22no—
73C11×#95—22no—
74C11⋊#95—24no—
75C11⋊#95—24no—
76C11⋊#95—22no—
77C11⋊#95—22no—
78C11⋊#95—24no—
79C11⋊#95—42no—
80C11⋊#95—42no—
81C11⋊#95—42no—
82C11⋊#95—42no—
83C11⋊#95—42no—
84C11⋊#95C2×C414yes—
85C11⋊#95C2×C414yes—
86#13947—111nomaximal, Sylow
87C24×C11C2411yescharacteristic
88C23×D11—21no—
89C23×D11—21no—
90C23×D11—22no—
91C23×D11—22no—
92C23×D11—21no—
93C23×D11—21no—
94C23×D11—22no—
95C23×D11—22no—
96C23×D11C22×C412yes—
97C23×D11#4112yes—
98C23×D11#4112yes—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—21no—
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—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11C22×C412yes—
120C22×C4×C11C22×C412yes—
121C22×C4×C11C22×C412yes—
122C22×C4×C11#4114yes—
123C22×C4×C11#4114yes—
124C22×C4×C11#4112yes—
125C22×C4×C11#4112yes—
126C22×C4×C11#4112yes—
127C22×C4×C11#4112yes—
128C22×Dic11—22no—
129C22×Dic11—22no—
130C22×Dic11—21no—
131C22×Dic11—21no—
132C22×Dic11—21no—
133C22×Dic11—21no—
134C22×Dic11—21no—
135C22×Dic11—21no—
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×Dic11C22×C412yes—
155C22×Dic11C22×C412yes—
156C22×Dic11C22×C412yes—
157C2×C4×D11—28no—
158C2×C4×D11—44no—
159C2×C4×D11—44no—
160C2×C4×D11—48no—
161C2×C4×D11—48no—
162C42×C11—44no—
163C42×C11—48no—
164(C2×D11)⋊C4—28no—
165(C2×D11)⋊C4—28no—
166(C2×D11)⋊C4—48no—
167(C2×D11)⋊C4—48no—
168C4×Dic11—44no—
169C2×C4×C22⋊C4—111no—
170#1443—112no—
171#1440—112no—
172#1437—112no—
173#1434—112no—
174#1434—111no—
175#1434—111no—
176#1434—111no—
177C22⋊#95—111no—
178C22⋊#95—111no—
179C4×#95D1111yescharacteristic, complemented
180C23×C11C23×C411yescharacteristic
181C23×C11C2×#4111yescharacteristic
182C23×C11C2×#4111yescharacteristic
183C23×C11C2×#4112yes—
184C23×C11C2×#4112yes—
185C23×C11C2×#4111yescharacteristic
186C23×C11C2×#4111yescharacteristic
187C23×C11C2×#4111yescharacteristic
188C23×C11C2×#4111yescharacteristic
189C23×C11H(5,𝔽2)12yes—
190C23×C11H(5,𝔽2)12yes—
191C22×D11—22no—
192C22×D11—22no—
193C22×D11—22no—
194C22×D11—22no—
195C22×D11—22no—
196C22×D11—22no—
197C22×D11—22no—
198C22×D11—22no—
199C22×D11—22no—
200C22×D11—22no—
201C22×D11—24no—
202C22×D11—24no—
203C22×D11—24no—
204C22×D11—24no—
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#11714yes—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—24no—
219C2×C4×C11—24no—
220C2×C4×C11—24no—
221C2×C4×C11—24no—
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—24no—
230C2×C4×C11—24no—
231C2×C4×C11—42no—
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#11714yes—
242C2×C4×C11#11714yes—
243C2×Dic11—22no—
244C2×Dic11—22no—
245C2×Dic11—22no—
246C2×Dic11—22no—
247C2×Dic11—22no—
248C2×Dic11—22no—
249C2×Dic11—22no—
250C2×Dic11—22no—
251C2×Dic11—22no—
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—
268C2×Dic11—42no—
269C2×Dic11—42no—
270C2×Dic11—42no—
271C2×Dic11—42no—
272C4×D11—416no—
273C24×C4—111no—
274C22×C22⋊C4—111no—
275C22×C22⋊C4—111no—
276C22×C22⋊C4—112no—
277C22×C22⋊C4—112no—
278C22×C42—111no—
279C22×C42C2×D1112yes—
280C22×C42C2×D1111yescharacteristic
281C4×C22⋊C4—118no—
282C2×#95—111no—
283C2×#95—111no—
284C2×#95—111no—
285C2×#95—111no—
286C2×#95—112no—
287C2×#95—112no—
288C2×#95—112no—
289C2×#95—112no—
290C2×#95—112no—
291C2×#95—112no—
292C2×#95—112no—
293C2×#95—112no—
294C2×#95C2×D1111yescharacteristic
295C2×#95C2×D1111yescharacteristic
296C2×#95C2×D1112yes—
297C22×C11C2×#11711yescharacteristic
298C22×C11C2×#11711yescharacteristic
299C22×C11C2×#11711yescharacteristic
300C22×C11C4×#4111yescharacteristic
301C22×C11C4×#4111yescharacteristic
302C22×C11#51811yescharacteristic
303C22×C11#51811yescharacteristic
304C22×C11#52912yes—
305C22×C11#52912yes—
306C22×C11#52911yescharacteristic
307C22×C11#52911yescharacteristic
308C22×C11#52911yescharacteristic
309C22×C11#52911yescharacteristic
310C22×C11#53812yes—
311C22×C11#53812yes—
312C22×C11#55112yes—
313C22×C11#55112yes—
314C22×C11#55112yes—
315C22×C11#55312yes—
316C22×C11#55312yes—
317C22×C11#55312yes—
318C22×C11#55312yes—
319C22×C11#55912yes—
320C2×D11—24no—
321C2×D11—24no—
322C2×D11—24no—
323C2×D11—42no—
324C2×D11—44no—
325C2×D11—44no—
326C2×D11—44no—
327C2×D11—44no—
328C2×D11—42no—
329C2×D11—42no—
330C2×D11—42no—
331C4×C11—24no—
332C4×C11—24no—
333C4×C11—44no—
334C4×C11—44no—
335C4×C11—42no—
336Dic11—42no—
337Dic11—42no—
338Dic11—42no—
339Dic11—82no—
340Dic11—82no—
341C25—111no—
342C23×C4—111no—
343C23×C4—111no—
344C23×C4—111no—
345C23×C4—114no—
346C23×C4—112no—
347C23×C4—112no—
348C23×C4—222no—
349C23×C4—222no—
350C23×C4—442no—
351C23×C4—442no—
352C23×C4C22×D1111yescharacteristic
353C23×C4C22×D1112yes—
354C23×C4C22×D1112yes—
355C23×C4C22×D1111yescharacteristic
356C23×C4C22×D1111yescharacteristic
357C2×C22⋊C4—114no—
358C2×C22⋊C4—114no—
359C2×C22⋊C4—222no—
360C2×C22⋊C4—222no—
361C2×C22⋊C4—222no—
362C2×C22⋊C4—222no—
363C2×C22⋊C4—224no—
364C2×C22⋊C4—224no—
365C2×C22⋊C4—224no—
366C2×C22⋊C4—224no—
367C2×C22⋊C4—442no—
368C2×C22⋊C4—442no—
369C2×C42—24no—
370C2×C42—24no—
371C2×C42—42no—
372C2×C42—42no—
373C2×C42—114no—
374C2×C42—442no—
375C2×C42C4×D1114yes—
376#95—24no—
377#95—22no—
378#95—22no—
379#95—114no—
380#95—114no—
381#95—224no—
382#95—224no—
383#95—222no—
384#95—222no—
385#95—224no—
386#95—442no—
387#95—442no—
388#95—442no—
389#95—442no—
390#95—442no—
391C2×C11#228311yescharacteristic
392C2×C11#229811yescharacteristic
393C2×C11#231211yescharacteristic
394C2×C11#235311yescharacteristic
395C2×C11#235311yescharacteristic
396C2×C11#235311yescharacteristic
397C2×C11#235711yescharacteristic
398C2×C11#257612yes—
399C2×C11#257812yes—
400C2×C11#259512yes—
401C2×C11#259712yes—
402D11—44no—
403C24—112no—
404C24—112no—
405C24—112no—
406C24—222no—
407C24—222no—
408C24—221no—
409C24—221no—
410C24—221no—
411C24—222no—
412C24—221no—
413C24—222no—
414C24C23×D1111yescharacteristic
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
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—22no—
435C22×C4—112no—
436C22×C4—112no—
437C22×C4—112no—
438C22×C4—222no—
439C22×C4—222no—
440C22×C4—221no—
441C22×C4—221no—
442C22×C4—221no—
443C22×C4—222no—
444C22×C4—221no—
445C22×C4—221no—
446C22×C4—221no—
447C22×C4—222no—
448C22×C4—222no—
449C22×C4—222no—
450C22×C4—228no—
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—444no—
466C22×C4—444no—
467C22×C4—448no—
468C22×C4—448no—
469C22×C4C2×C4×D1112yes—
470C22×C4C2×C4×D1112yes—
471C22×C4C2×C4×D1112yes—
472C22×C4#433914yes—
473C22×C4#433914yes—
474C22×C4#433912yes—
475C22×C4#433912yes—
476C22×C4#434112yes—
477C22×C4#434312yes—
478C22⋊C4—228no—
479C22⋊C4—228no—
480C22⋊C4—448no—
481C22⋊C4—448no—
482C42—44no—
483C42—48no—
484C42—444no—
485C11#1394711yescharacteristic, complemented, Sylow
486C23—114no—
487C23—222no—
488C23—222no—
489C23—222no—
490C23—222no—
491C23—222no—
492C23—222no—
493C23—224no—
494C23—224no—
495C23—224no—
496C23—222no—
497C23—222no—
498C23—224no—
499C23—222no—
500C23—222no—
501C23—442no—
502C23—442no—
503C23—442no—
504C23—442no—
505C23—442no—
506C23—442no—
507C23—442no—
508C23—442no—
509C23C22×C4×D1111yescharacteristic
510C23C2×#433911yescharacteristic
511C23C2×#433911yescharacteristic
512C23C2×#433912yes—
513C23C2×#433912yes—
514C23C2×#434111yescharacteristic
515C23#6703712yes—
516C23C2×#434311yescharacteristic
517C23#41×D1111yescharacteristic
518C23#41×D1111yescharacteristic
519C23#6704212yes—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—24no—
524C2×C4—24no—
525C2×C4—22no—
526C2×C4—24no—
527C2×C4—24no—
528C2×C4—22no—
529C2×C4—24no—
530C2×C4—24no—
531C2×C4—22no—
532C2×C4—24no—
533C2×C4—22no—
534C2×C4—24no—
535C2×C4—24no—
536C2×C4—24no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—222no—
548C2×C4—222no—
549C2×C4—222no—
550C2×C4—222no—
551C2×C4—222no—
552C2×C4—222no—
553C2×C4—222no—
554C2×C4—222no—
555C2×C4—222no—
556C2×C4—4416no—
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—
571C2×C4—442no—
572C2×C4—442no—
573C2×C4—442no—
574C2×C4—442no—
575C2×C4—442no—
576C2×C4—442no—
577C2×C4#6692514yes—
578C2×C4#6694514yes—
579C22—224no—
580C22—224no—
581C22—224no—
582C22—444no—
583C22—442no—
584C22—444no—
585C22—442no—
586C22—442no—
587C22—444no—
588C22—442no—
589C22—444no—
590C22C2×#6692511yescharacteristic
591C22C4×#433911yescharacteristic
592C22C4×#433911yescharacteristic
593C22#1062301012yes—
594C22#1062301012yes—
595C22#1062301711yescharacteristic
596C22#1062302612yes—
597C22C2×#6694511yescharacteristic
598C22#1062304512yes—
599C22D11×#11711yescharacteristic
600C22#1062305211yescharacteristic
601C22#1062305812yes—
602C22#1062306112yes—
603C22#1062308712yes—
604C22#1062308811yescharacteristic
605C22#1062308811yescharacteristic
606C22#1062308912yes—
607C22#1062309112yes—
608C22#1062309112yes—
609C22#1062309612yes—
610C22#1062311111yescharacteristic
611C22#1062311111yescharacteristic
612C22#1062311612yes—
613C4—24no—
614C4—24no—
615C4—44no—
616C4—44no—
617C4—42no—
618C4—442no—
619C4—442no—
620C4—442no—
621C4—882no—
622C4—882no—
623C2—444no—
624C2#1307101211yescharacteristic
625C2#1307111311yescharacteristic
626C2#1307121111yescharacteristic
627C2#1307155211yescharacteristic
628C2#1307155711yescharacteristic
629C2#1307155911yescharacteristic
630C2#1307158711yescharacteristic
631C2#1307392012yes—
632C2#1307395012yes—
633C2#1307413712yes—
634C2#1307416712yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC4×C11×#95C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenterC4×#95D11
hypocenterC11#13947
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
2. #13066877C2semidirect
5. #13066843C2semidirect
6. #13066843C2semidirect
7. #13066842C2semidirect
8. #13066842C2semidirect
11. C4×C11×#95C2semidirect
35. C4×(C2×D11)⋊C4C4semidirect
179. C4×#95D11semidirect
485. C11#13947semidirect

Maximal subgroups

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

subgroupindex
C2×C4×(C2×D11)⋊C42
#130668772
#130668642
#130668542
#130668432
#130668422
(C2×D11)⋊#952
C4×C11×#952
#1394711