Finite Group Databasebeta

← #14680793

Subgroups — #14680793

Order 2816.

1454 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622560C211yesmaximal, characteristic
2C2×#10622542C211yesmaximal, characteristic, complemented
3#13066886C211yesmaximal, characteristic, complemented
4#13066876C212yesmaximal, complemented
5#13066872C211yesmaximal, characteristic, complemented
6#13066863C212yesmaximal
7#13066861C211yesmaximal, characteristic
8#13066853C212yesmaximal
9#13066848C212yesmaximal, complemented
10C4×C11⋊#95C211yesmaximal, characteristic, complemented
11C2×C11×#388C211yesmaximal, characteristic
12C23×Dic22C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C11×C22⋊C4C2211yescharacteristic
15C22×C11×C22⋊C4C2211yescharacteristic
16C22×C11×C22⋊C4C2211yescharacteristic
17C22×C42×C11C2211yescharacteristic
18C22×C22⋊Dic11C2212yes—
19C22×C22⋊Dic11C2212yes—
20C22×C4⋊Dic11C2211yescharacteristic
21C22×C4×Dic11C2212yes—
22C11×#388—24no—
23C2×C11×#95C2211yescharacteristic
24C2×C11×#95C2211yescharacteristic
25C2×C11⋊#95C2211yescharacteristic
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2211yescharacteristic
35C2×C11⋊#95C2212yes—
36#10622560C418yescomplemented
37#10622542—24no—
38C25×C11C2311yescharacteristic
39C23×C4×C11C2311yescharacteristic
40C23×C4×C11C2311yescharacteristic
41C23×C4×C11C2311yescharacteristic
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2311yescharacteristic
45C23×Dic11C2312yes—
46C23×Dic11C2312yes—
47C23×Dic11C2312yes—
48C23×Dic11C2312yes—
49C22×Dic22—22no—
50C22×Dic22—22no—
51C22×Dic22—42no—
52C22×Dic22—42no—
53C22×Dic22C2×C414yes—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4—24no—
56C2×C11×C22⋊C4—22no—
57C2×C11×C22⋊C4—22no—
58C2×C11×C22⋊C4—22no—
59C2×C11×C22⋊C4—22no—
60C2×C11×C22⋊C4—24no—
61C2×C11×C22⋊C4—42no—
62C2×C11×C22⋊C4C2×C414yes—
63C2×C42×C11—42no—
64C2×C42×C11D414yes—
65C2×C22⋊Dic11—24no—
66C2×C22⋊Dic11—42no—
67C2×C22⋊Dic11—42no—
68C2×C22⋊Dic11—42no—
69C2×C22⋊Dic11—42no—
70C2×C22⋊Dic11C2×C418yes—
71C2×C4⋊Dic11—22no—
72C2×C4⋊Dic11—42no—
73C2×C4×Dic11—24no—
74C2×C4×Dic11—42no—
75C2×C4×Dic11—42no—
76C11×#95—22no—
77C11×#95—22no—
78C11⋊#95—24no—
79C11⋊#95—24no—
80C11⋊#95—22no—
81C11⋊#95—24no—
82C11⋊#95—24no—
83C11⋊#95—42no—
84C11⋊#95—42no—
85C11⋊#95—42no—
86C11⋊#95—42no—
87C11⋊#95C2×C414yes—
88C11⋊#95C2×C418yes—
89#14323—111nomaximal, Sylow
90C24×C11—21no—
91C24×C11—22no—
92C24×C11—21no—
93C24×C11—22no—
94C24×C11—22no—
95C24×C11—21no—
96C24×C11—22no—
97C24×C11—21no—
98C24×C11—21no—
99C24×C11—21no—
100C24×C11C22×C412yes—
101C24×C11C2411yescharacteristic
102C22×C4×C11—21no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—21no—
107C22×C4×C11—21no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—21no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—21no—
114C22×C4×C11—21no—
115C22×C4×C11—21no—
116C22×C4×C11—21no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—21no—
121C22×C4×C11—22no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11C22×C412yes—
126C22×C4×C11C22×C412yes—
127C22×C4×C11C2×D412yes—
128C22×C4×C11C2×D412yes—
129C22×C4×C11C2×D412yes—
130C22×C4×C11#4112yes—
131C22×C4×C11#4114yes—
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—22no—
155C22×Dic11—22no—
156C22×Dic11—22no—
157C22×Dic11C22×C414yes—
158C22×Dic11C22×C414yes—
159C22×Dic11#4114yes—
160C2×Dic22—28no—
161C2×Dic22—48no—
162C2×Dic22—44no—
163C2×Dic22—44no—
164C2×Dic22—48no—
165C11×C4⋊C4—44no—
166C11×C22⋊C4—28no—
167C11×C22⋊C4—44no—
168C11×C22⋊C4—44no—
169C42×C11—44no—
170C22⋊Dic11—48no—
171C22⋊Dic11—48no—
172C4⋊Dic11—44no—
173C4×Dic11—48no—
174C2×#393—111no—
175C2×#391—111no—
176C2×#388D1111yescharacteristic
177#1446—111no—
178#1443—112no—
179#1442—111no—
180#1440—112no—
181#1439—111no—
182#1437—112no—
183#1436—112no—
184C4×#95—111no—
185C23×C11—22no—
186C23×C11—24no—
187C23×C11—24no—
188C23×C11—22no—
189C23×C11—22no—
190C23×C11—41no—
191C23×C11—42no—
192C23×C11—41no—
193C23×C11—41no—
194C23×C11—41no—
195C23×C11—41no—
196C23×C11—41no—
197C23×C11—42no—
198C23×C11—42no—
199C23×C11—42no—
200C23×C11—42no—
201C23×C11—42no—
202C23×C11—41no—
203C23×C11—42no—
204C23×C11—41no—
205C23×C11—42no—
206C23×C11—42no—
207C23×C11—42no—
208C23×C11C23×C411yescharacteristic
209C23×C11C22×D411yescharacteristic
210C23×C11C2×#4111yescharacteristic
211C23×C11C2×#4112yes—
212C23×C11C2×#4112yes—
213C23×C11H(5,𝔽2)12yes—
214C23×C11H(5,𝔽2)12yes—
215C23×C11H(5,𝔽2)11yescharacteristic
216C23×C112−1+411yescharacteristic
217C23×C112−1+411yescharacteristic
218C23×C112−1+411yescharacteristic
219C2×C4×C11—24no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—24no—
225C2×C4×C11—24no—
226C2×C4×C11—24no—
227C2×C4×C11—22no—
228C2×C4×C11—24no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—41no—
233C2×C4×C11—42no—
234C2×C4×C11—41no—
235C2×C4×C11—42no—
236C2×C4×C11—42no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—42no—
244C2×C4×C11—42no—
245C2×C4×C11—42no—
246C2×C4×C11—42no—
247C2×C4×C11C4×D414yes—
248C2×C4×C11#12414yes—
249C2×Dic11—24no—
250C2×Dic11—24no—
251C2×Dic11—24no—
252C2×Dic11—24no—
253C2×Dic11—24no—
254C2×Dic11—24no—
255C2×Dic11—24no—
256C2×Dic11—24no—
257C2×Dic11—24no—
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—
277Dic22—416no—
278C23×Q8—111no—
279C22×C4⋊C4—111no—
280C22×C4⋊C4C2×D1111yescharacteristic
281C22×C22⋊C4—112no—
282C22×C22⋊C4—112no—
283C22×C22⋊C4C2×D1111yescharacteristic
284C22×C22⋊C4C2×D1111yescharacteristic
285C22×C22⋊C4C2×D1111yescharacteristic
286C22×C42—112no—
287C22×C42C2×D1111yescharacteristic
288#393—118no—
289#391—224no—
290#388—24no—
291C2×#95—111no—
292C2×#95—112no—
293C2×#95—111no—
294C2×#95—112no—
295C2×#95—112no—
296C2×#95—112no—
297C2×#95—112no—
298C2×#95—112no—
299C2×#95—112no—
300C2×#95—112no—
301C2×#95—112no—
302C2×#95C2×D1111yescharacteristic
303C2×#95C2×D1111yescharacteristic
304C22×C11—42no—
305C22×C11—42no—
306C22×C11—44no—
307C22×C11—44no—
308C22×C11—42no—
309C22×C11—81no—
310C22×C11—81no—
311C22×C11—82no—
312C22×C11—82no—
313C22×C11—81no—
314C22×C11—81no—
315C22×C11C2×C4×D411yescharacteristic
316C22×C11C4×#4112yes—
317C22×C11#51812yes—
318C22×C11#51911yescharacteristic
319C22×C11#52011yescharacteristic
320C22×C11C2×#12411yescharacteristic
321C22×C11#52912yes—
322C22×C11#53211yescharacteristic
323C22×C11#53411yescharacteristic
324C22×C11#53511yescharacteristic
325C22×C11#53611yescharacteristic
326C22×C11#53711yescharacteristic
327C22×C11#53812yes—
328C22×C11#53812yes—
329C22×C11#53812yes—
330C22×C11#53912yes—
331C22×C11#53912yes—
332C22×C11#54111yescharacteristic
333C22×C11#54212yes—
334C22×C11#54211yescharacteristic
335C22×C11#54212yes—
336C22×C11#54212yes—
337C22×C11#54212yes—
338C4×C11—24no—
339C4×C11—24no—
340C4×C11—42no—
341C4×C11—42no—
342C4×C11—81no—
343C4×C11—81no—
344Dic11—44no—
345Dic11—44no—
346Dic11—44no—
347Dic11—82no—
348C25C22×D1111yescharacteristic
349C22×Q8—114no—
350C22×Q8—222no—
351C22×Q8—222no—
352C22×Q8—442no—
353C22×Q8—442no—
354C23×C4—112no—
355C23×C4—112no—
356C23×C4—112no—
357C23×C4—112no—
358C23×C4C22×D1111yescharacteristic
359C23×C4C22×D1111yescharacteristic
360C23×C4C22×D1111yescharacteristic
361C23×C4C22×D1111yescharacteristic
362C23×C4C22×D1111yescharacteristic
363C23×C4C22×D1111yescharacteristic
364C2×C4⋊C4—24no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—222no—
367C2×C4⋊C4—442no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—42no—
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⋊C4C4×D1114yes—
381C2×C42—42no—
382C2×C42—224no—
383C2×C42—442no—
384C2×C42—442no—
385C2×C42C22⋊D1114yes—
386#95—22no—
387#95—22no—
388#95—114no—
389#95—118no—
390#95—224no—
391#95—224no—
392#95—222no—
393#95—224no—
394#95—224no—
395#95—442no—
396#95—442no—
397#95—442no—
398#95—442no—
399C2×C11—82no—
400C2×C11C4×#12411yescharacteristic
401C2×C11#232111yescharacteristic
402C2×C11#232311yescharacteristic
403C2×C11#233212yes—
404C2×C11#233712yes—
405C2×C11#263911yescharacteristic
406C2×C11#264011yescharacteristic
407C2×C11#265012yes—
408C2×C11#265312yes—
409C2×C11#266211yescharacteristic
410C2×C11#266311yescharacteristic
411C24—21no—
412C24—22no—
413C24—22no—
414C24—22no—
415C24—21no—
416C24—22no—
417C24—21no—
418C24—21no—
419C24—21no—
420C24—21no—
421C24C2×C4×D1112yes—
422C24C23×D1111yescharacteristic
423C2×Q8—228no—
424C2×Q8—448no—
425C2×Q8—444no—
426C2×Q8—448no—
427C2×Q8—444no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—114no—
452C22×C4—114no—
453C22×C4—114no—
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—222no—
478C22×C4—222no—
479C22×C4C2×C4×D1112yes—
480C22×C4C2×C4×D1112yes—
481C22×C4#433912yes—
482C22×C4#434114yes—
483C22×C4C2×C22⋊D1112yes—
484C22×C4C2×C22⋊D1112yes—
485C22×C4C2×C22⋊D1112yes—
486C4⋊C4—44no—
487C4⋊C4—444no—
488C22⋊C4—28no—
489C22⋊C4—44no—
490C22⋊C4—44no—
491C22⋊C4—448no—
492C22⋊C4—448no—
493C42—44no—
494C42—448no—
495C11#1432311yescharacteristic, complemented, Sylow
496C23—22no—
497C23—22no—
498C23—22no—
499C23—24no—
500C23—24no—
501C23—42no—
502C23—42no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—42no—
508C23—42no—
509C23—41no—
510C23—41no—
511C23—41no—
512C23—41no—
513C23—42no—
514C23—42no—
515C23—42no—
516C23—42no—
517C23—42no—
518C23—42no—
519C23C22×C4×D1111yescharacteristic
520C23C2×#433911yescharacteristic
521C23C2×#434112yes—
522C23#6703712yes—
523C23#41×D1112yes—
524C23#6704211yescharacteristic
525C23#6704212yes—
526C23#6704311yescharacteristic
527C23#6704311yescharacteristic
528C23#6704311yescharacteristic
529C23C22×C22⋊D1111yescharacteristic
530Q8—4416no—
531C2×C4—24no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—24no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—24no—
538C2×C4—24no—
539C2×C4—22no—
540C2×C4—24no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—41no—
545C2×C4—42no—
546C2×C4—41no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—224no—
560C2×C4—224no—
561C2×C4—224no—
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×C4—442no—
584C2×C4—442no—
585C2×C4—442no—
586C2×C4—442no—
587C2×C4C4×C22⋊D1114yes—
588C2×C4#6698914yes—
589C22—44no—
590C22—42no—
591C22—44no—
592C22—42no—
593C22—42no—
594C22—81no—
595C22—81no—
596C22—81no—
597C22—81no—
598C22—82no—
599C22—82no—
600C22#1062304711yescharacteristic
601C22#1062304911yescharacteristic
602C22#1062305411yescharacteristic
603C22#1062306511yescharacteristic
604C22C4×#434112yes—
605C22#1062307612yes—
606C22#1062308812yes—
607C22#1062309112yes—
608C22#1062313312yes—
609C22#1062314812yes—
610C22#1062319112yes—
611C22#1062319312yes—
612C22#1062321312yes—
613C22#1062321312yes—
614C22#1062323512yes—
615C22#1062324112yes—
616C22C2×C4×C22⋊D1111yescharacteristic
617C22C2×#6698911yescharacteristic
618C22#1062333511yescharacteristic
619C22#1062335611yescharacteristic
620C22#1062336111yescharacteristic
621C22#1062336311yescharacteristic
622C22#1062336411yescharacteristic
623C4—24no—
624C4—24no—
625C4—42no—
626C4—42no—
627C4—81no—
628C4—81no—
629C4—444no—
630C4—444no—
631C4—444no—
632C4—882no—
633C2—82no—
634C2C4×#6698911yescharacteristic
635C2#1307127011yescharacteristic
636C2#1307129811yescharacteristic
637C2#1307136612yes—
638C2#1307142312yes—
639C2#1307454911yescharacteristic
640C2#1307455611yescharacteristic
641C2#1307463812yes—
642C2#1307468312yes—
643C2#1307475611yescharacteristic
644C2#1307476611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#388C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×#388D11
hypocenterC11#14323
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C2×#10622542C2semidirect
3. #13066886C2semidirect
4. #13066876C2semidirect
5. #13066872C2semidirect
9. #13066848C2semidirect
10. C4×C11⋊#95C2semidirect
36. #10622560C4semidirect
495. C11#14323semidirect

Maximal subgroups

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

subgroupindex
C2×#106225602
C2×#106225422
#130668862
#130668762
#130668722
#130668632
#130668612
#130668532
#130668482
C4×C11⋊#952
C2×C11×#3882
#1432311