Finite Group Databasebeta

← #14680796

Subgroups — #14680796

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×#10622843C211yesmaximal, characteristic, complemented
2C2×#10622564C211yesmaximal, characteristic
3#13066887C211yesmaximal, characteristic, complemented
4#13066878C212yesmaximal, complemented
5#13066873C211yesmaximal, characteristic, complemented
6#13066865C212yesmaximal
7#13066861C211yesmaximal, characteristic
8#13066853C212yesmaximal
9#13066850C212yesmaximal, complemented
10#95×Dic11C211yesmaximal, characteristic, complemented
11C2×C11×#393C211yesmaximal, characteristic
12C23×Q8×C11C2211yescharacteristic
13C22×C11×C22⋊C4C2211yescharacteristic
14C22×C11×C22⋊C4C2212yes—
15C22×C22⋊Dic11C2211yescharacteristic
16C22×C22⋊Dic11C2212yes—
17C22×C22⋊Dic11C2211yescharacteristic
18C22×C4⋊Dic11C2211yescharacteristic
19C22×C4⋊Dic11C2211yescharacteristic
20C22×C4×Dic11C2212yes—
21C22×C4×Dic11C2211yescharacteristic
22C11×#393C418yescomplemented
23C2×C11×#95C2211yescharacteristic
24C2×C11×#95C2212yes—
25#10622843—24no—
26C2×C11⋊#95C2211yescharacteristic
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2211yescharacteristic
32C2×C11⋊#95C2211yescharacteristic
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37#10622564—24no—
38C25×C11C2311yescharacteristic
39C22×Q8×C11—22no—
40C22×Q8×C11—22no—
41C22×Q8×C11—42no—
42C22×Q8×C11—42no—
43C22×Q8×C11C2×C414yes—
44C23×C4×C11C2312yes—
45C23×C4×C11C2311yescharacteristic
46C23×C4×C11C2312yes—
47C23×C4×C11C2311yescharacteristic
48C23×Dic11C2312yes—
49C23×Dic11C2311yescharacteristic
50C23×Dic11C2311yescharacteristic
51C23×Dic11C2311yescharacteristic
52C23×Dic11C2312yes—
53C23×Dic11C2311yescharacteristic
54C2×C11×C22⋊C4—22no—
55C2×C11×C22⋊C4—22no—
56C2×C11×C22⋊C4—42no—
57C2×C11×C22⋊C4—42no—
58C2×C11×C22⋊C4C2×C414yes—
59C2×C11×C22⋊C4C2×C418yes—
60C2×C22⋊Dic11—22no—
61C2×C22⋊Dic11—22no—
62C2×C22⋊Dic11—24no—
63C2×C22⋊Dic11—24no—
64C2×C22⋊Dic11—42no—
65C2×C22⋊Dic11—42no—
66C2×C22⋊Dic11—42no—
67C2×C4⋊Dic11—22no—
68C2×C4⋊Dic11—22no—
69C2×C4⋊Dic11—24no—
70C2×C4⋊Dic11—42no—
71C2×C4×Dic11—24no—
72C2×C4×Dic11—42no—
73C2×C4×Dic11—42no—
74C2×C4×Dic11—42no—
75C2×C4×Dic11D414yes—
76C11×#95C2×C418yes—
77C11×#95C2×C414yes—
78C11⋊#95—22no—
79C11⋊#95—22no—
80C11⋊#95—22no—
81C11⋊#95—24no—
82C11⋊#95—24no—
83C11⋊#95—24no—
84C11⋊#95—24no—
85C11⋊#95—42no—
86C11⋊#95—42no—
87C11⋊#95—42no—
88C11⋊#95—42no—
89#14323—111nomaximal, Sylow
90C24×C11—21no—
91C24×C11—22no—
92C24×C11—22no—
93C24×C11—21no—
94C24×C11—21no—
95C24×C11—22no—
96C24×C11—22no—
97C24×C11—21no—
98C24×C11—21no—
99C24×C11—21no—
100C24×C11C22×C412yes—
101C24×C11C2411yescharacteristic
102C2×Q8×C11—28no—
103C2×Q8×C11—48no—
104C2×Q8×C11—44no—
105C2×Q8×C11—44no—
106C2×Q8×C11—48no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—21no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
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×C11—22no—
125C22×C4×C11C22×C412yes—
126C22×C4×C11C22×C414yes—
127C22×C4×C11C22×C414yes—
128C22×C4×C11C22×C412yes—
129C22×C4×C11C2×D412yes—
130C22×C4×C11#4112yes—
131C22×Dic11—22no—
132C22×Dic11—21no—
133C22×Dic11—21no—
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—21no—
143C22×Dic11—22no—
144C22×Dic11—22no—
145C22×Dic11—22no—
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11—21no—
149C22×Dic11—22no—
150C22×Dic11—22no—
151C22×Dic11—22no—
152C22×Dic11—22no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—22no—
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11—22no—
160C22×Dic11—21no—
161C22×Dic11C2×D412yes—
162C22×Dic11C2×D412yes—
163C22×Dic11#4114yes—
164C22×Dic11#4114yes—
165C11×C22⋊C4—28no—
166C11×C22⋊C4—48no—
167C22⋊Dic11—44no—
168C22⋊Dic11—48no—
169C22⋊Dic11—44no—
170C4⋊Dic11—44no—
171C4⋊Dic11—44no—
172C4×Dic11—44no—
173C4×Dic11—48no—
174C2×#393D1111yescharacteristic
175C2×#391—111no—
176C2×#388—111no—
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—42no—
205C23×C11—41no—
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
219Q8×C11—416no—
220C2×C4×C11—24no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—24no—
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—24no—
232C2×C4×C11—41no—
233C2×C4×C11—42no—
234C2×C4×C11—41no—
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×C11C4×D414yes—
244C2×Dic11—22no—
245C2×Dic11—22no—
246C2×Dic11—24no—
247C2×Dic11—24no—
248C2×Dic11—24no—
249C2×Dic11—22no—
250C2×Dic11—22no—
251C2×Dic11—22no—
252C2×Dic11—24no—
253C2×Dic11—24no—
254C2×Dic11—42no—
255C2×Dic11—42no—
256C2×Dic11—42no—
257C2×Dic11—42no—
258C2×Dic11—42no—
259C2×Dic11—42no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—42no—
263C2×Dic11—41no—
264C2×Dic11—42no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—41no—
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—
277C2×Dic11#12414yes—
278C23×Q8C2×D1111yescharacteristic
279C22×C4⋊C4—111no—
280C22×C4⋊C4—111no—
281C22×C22⋊C4—111no—
282C22×C22⋊C4—112no—
283C22×C22⋊C4—111no—
284C22×C22⋊C4C2×D1111yescharacteristic
285C22×C22⋊C4C2×D1112yes—
286C22×C42—111no—
287C22×C42—112no—
288#393Dic1118yescomplemented
289#391—224no—
290#388—224no—
291C2×#95—111no—
292C2×#95—112no—
293C2×#95—112no—
294C2×#95—112no—
295C2×#95—112no—
296C2×#95—111no—
297C2×#95—111no—
298C2×#95—112no—
299C2×#95—112no—
300C2×#95—112no—
301C2×#95—112no—
302C2×#95C2×D1111yescharacteristic
303C2×#95C2×D1112yes—
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#54212yes—
335C22×C11#54211yescharacteristic
336C22×C11#54212yes—
337C22×C11#54212yes—
338C4×C11—24no—
339C4×C11—44no—
340C4×C11—44no—
341C4×C11—42no—
342Dic11—24no—
343Dic11—44no—
344Dic11—42no—
345Dic11—81no—
346Dic11—81no—
347Dic11—82no—
348C25C22×D1111yescharacteristic
349C22×Q8—22no—
350C22×Q8—22no—
351C22×Q8—42no—
352C22×Q8—42no—
353C22×Q8C2×Dic1114yes—
354C23×C4—111no—
355C23×C4—111no—
356C23×C4—112no—
357C23×C4—112no—
358C23×C4—111no—
359C23×C4—111no—
360C23×C4C22×D1111yescharacteristic
361C23×C4C22×D1112yes—
362C23×C4C22×D1112yes—
363C23×C4C22×D1111yescharacteristic
364C2×C4⋊C4—222no—
365C2×C4⋊C4—224no—
366C2×C4⋊C4—222no—
367C2×C4⋊C4—442no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—42no—
371C2×C22⋊C4—42no—
372C2×C22⋊C4—222no—
373C2×C22⋊C4—222no—
374C2×C22⋊C4—224no—
375C2×C22⋊C4—224no—
376C2×C22⋊C4—442no—
377C2×C22⋊C4—442no—
378C2×C22⋊C4—442no—
379C2×C22⋊C4C2×Dic1114yes—
380C2×C22⋊C4C2×Dic1118yes—
381C2×C42—114no—
382C2×C42—224no—
383C2×C42—442no—
384C2×C42—442no—
385C2×C42—442no—
386#95—224no—
387#95—224no—
388#95—222no—
389#95—224no—
390#95—224no—
391#95—222no—
392#95—222no—
393#95—442no—
394#95—442no—
395#95—442no—
396#95—442no—
397#95C2×Dic1118yes—
398#95C2×Dic1114yes—
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—21no—
413C24—22no—
414C24—22no—
415C24—21no—
416C24—21no—
417C24—22no—
418C24—22no—
419C24—21no—
420C24—21no—
421C24C22×Dic1112yes—
422C24C23×D1111yescharacteristic
423C2×Q8—28no—
424C2×Q8—48no—
425C2×Q8—44no—
426C2×Q8—44no—
427C2×Q8—48no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—22no—
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—112no—
447C22×C4—114no—
448C22×C4—112no—
449C22×C4—114no—
450C22×C4—222no—
451C22×C4—221no—
452C22×C4—221no—
453C22×C4—222no—
454C22×C4—222no—
455C22×C4—222no—
456C22×C4—222no—
457C22×C4—221no—
458C22×C4—222no—
459C22×C4—222no—
460C22×C4—222no—
461C22×C4—222no—
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—221no—
471C22×C4—221no—
472C22×C4—222no—
473C22×C4—222no—
474C22×C4—222no—
475C22×C4—222no—
476C22×C4—222no—
477C22×C4—221no—
478C22×C4—222no—
479C22×C4—221no—
480C22×C4D4×D1112yes—
481C22×C4#434112yes—
482C22×C4C22×Dic1112yes—
483C22×C4C22×Dic1114yes—
484C22×C4C22×Dic1114yes—
485C22×C4C22×Dic1112yes—
486C4⋊C4—444no—
487C4⋊C4—444no—
488C22⋊C4—28no—
489C22⋊C4—48no—
490C22⋊C4—444no—
491C22⋊C4—444no—
492C22⋊C4—448no—
493C42—444no—
494C42—448no—
495C11#1432311yescharacteristic, complemented, Sylow
496C23—22no—
497C23—24no—
498C23—22no—
499C23—24no—
500C23—22no—
501C23—41no—
502C23—41no—
503C23—42no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—42no—
508C23—42no—
509C23—42no—
510C23—42no—
511C23—41no—
512C23—41no—
513C23—42no—
514C23—42no—
515C23—41no—
516C23—42no—
517C23—42no—
518C23—42no—
519C23C2×D4×D1111yescharacteristic
520C23C2×#434111yescharacteristic
521C23#6703712yes—
522C23#6703712yes—
523C23#6704011yescharacteristic
524C23#6704011yescharacteristic
525C23#41×D1112yes—
526C23#41×D1112yes—
527C23#6704211yescharacteristic
528C23#6704311yescharacteristic
529C23C23×Dic1111yescharacteristic
530Q8—416no—
531C2×C4—24no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—24no—
535C2×C4—22no—
536C2×C4—24no—
537C2×C4—24no—
538C2×C4—24no—
539C2×C4—24no—
540C2×C4—24no—
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—41no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—41no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—114no—
555C2×C4—222no—
556C2×C4—222no—
557C2×C4—224no—
558C2×C4—224no—
559C2×C4—222no—
560C2×C4—222no—
561C2×C4—224no—
562C2×C4—222no—
563C2×C4—224no—
564C2×C4—224no—
565C2×C4—442no—
566C2×C4—442no—
567C2×C4—442no—
568C2×C4—442no—
569C2×C4—442no—
570C2×C4—442no—
571C2×C4—441no—
572C2×C4—442no—
573C2×C4—441no—
574C2×C4—441no—
575C2×C4—442no—
576C2×C4—441no—
577C2×C4—442no—
578C2×C4—442no—
579C2×C4—442no—
580C2×C4—442no—
581C2×C4—442no—
582C2×C4—442no—
583C2×C4—441no—
584C2×C4—441no—
585C2×C4—442no—
586C2×C4—442no—
587C2×C4—442no—
588C2×C4D4×Dic1114yes—
589C22—44no—
590C22—42no—
591C22—44no—
592C22—42no—
593C22—42no—
594C22—81no—
595C22—81no—
596C22—81no—
597C22—81no—
598C22—82no—
599C22—82no—
600C22#1062312011yescharacteristic
601C22#1062312311yescharacteristic
602C22#1062312412yes—
603C22#1062315611yescharacteristic
604C22#1062315911yescharacteristic
605C22#1062316011yescharacteristic
606C22#1062316912yes—
607C22#1062316912yes—
608C22#1062317112yes—
609C22#1062317112yes—
610C22#1062317411yescharacteristic
611C22#1062319911yescharacteristic
612C22#1062320012yes—
613C22#1062320012yes—
614C22D11×#12411yescharacteristic
615C22#1062320912yes—
616C22#1062320912yes—
617C22#1062321112yes—
618C22C2×D4×Dic1111yescharacteristic
619C22#1062332912yes—
620C22#1062334311yescharacteristic
621C22#41×Dic1112yes—
622C22#1062335811yescharacteristic
623C4—24no—
624C4—42no—
625C4—44no—
626C4—44no—
627C4—224no—
628C4—442no—
629C4—444no—
630C4—882no—
631C4—881no—
632C4—881no—
633C2—82no—
634C2#124×Dic1111yescharacteristic
635C2#1307127711yescharacteristic
636C2#1307130011yescharacteristic
637C2#1307137412yes—
638C2#1307143112yes—
639C2#1307454511yescharacteristic
640C2#1307455411yescharacteristic
641C2#1307463112yes—
642C2#1307467612yes—
643C2#1307476211yescharacteristic
644C2#1307477211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#393C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×#393D11
hypocenterC11#14323
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#393

Complements

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

NH ≅ G/Ntype
1. C2×#10622843C2semidirect
3. #13066887C2semidirect
4. #13066878C2semidirect
5. #13066873C2semidirect
9. #13066850C2semidirect
10. #95×Dic11C2semidirect
22. C11×#393C4semidirect
288. #393Dic11semidirect
495. C11#14323semidirect

Maximal subgroups

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

subgroupindex
C2×#106228432
C2×#106225642
#130668872
#130668782
#130668732
#130668652
#130668612
#130668532
#130668502
#95×Dic112
C2×C11×#3932
#1432311