Finite Group Databasebeta

← #14680742

Subgroups — #14680742

Order 2816.

1558 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622290C211yesmaximal, characteristic
2C2×#10622586C211yesmaximal, characteristic, complemented
3C2×#10622279C211yesmaximal, characteristic
4#13066885C211yesmaximal, characteristic, complemented
5#13066868C212yesmaximal, complemented
6#13066860C212yesmaximal
7#13066858C211yesmaximal, characteristic
8#13066850C212yesmaximal, complemented
9#13066841C211yesmaximal, characteristic, complemented
10(C2×D11)⋊#95C212yesmaximal
11C11×#1442C211yesmaximal, characteristic, complemented
12C23×C4×D11C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×(C2×D11)⋊C4C2211yescharacteristic
15C22×(C2×D11)⋊C4C2211yescharacteristic
16C22×(C2×D11)⋊C4C2212yes—
17C22×(C2×D11)⋊C4C2212yes—
18C22×C4⋊Dic11C2211yescharacteristic
19C22×C4⋊Dic11C2212yes—
20C22×Dic11⋊C4C2212yes—
21C22×C4×Dic11C2211yescharacteristic
22C22×C4×Dic11C2211yescharacteristic
23C2×C11×#95C2211yescharacteristic
24C2×C11×#95C2212yes—
25C2×C11×#95C2212yes—
26C2×C11×#95C2211yescharacteristic
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2211yescharacteristic
30C2×C11⋊#95C2211yescharacteristic
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35#10622586—24no—
36#10622290C418yescomplemented
37#10622279—24no—
38C24×D11C2311yescharacteristic
39C23×C4×C11C2312yes—
40C23×C4×C11C2312yes—
41C23×C4×C11C2311yescharacteristic
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2311yescharacteristic
44C23×Dic11C2312yes—
45C23×Dic11C2311yescharacteristic
46C23×Dic11C2312yes—
47C23×Dic11C2311yescharacteristic
48C23×Dic11C2311yescharacteristic
49C22×C4×D11—22no—
50C22×C4×D11—22no—
51C22×C4×D11—42no—
52C22×C4×D11—42no—
53C22×C4×D11Q814yes—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4—42no—
56C2×(C2×D11)⋊C4—22no—
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—42no—
63C2×(C2×D11)⋊C4—42no—
64C2×(C2×D11)⋊C4—42no—
65C2×(C2×D11)⋊C4—42no—
66C2×(C2×D11)⋊C4C2×C414yes—
67C2×(C2×D11)⋊C4C2×C418yes—
68C2×C4⋊Dic11—22no—
69C2×C4⋊Dic11—22no—
70C2×C4⋊Dic11—42no—
71C2×C4⋊Dic11—42no—
72C2×C4⋊Dic11C2×C414yescomplemented
73C2×C4⋊Dic11C2×C418yescomplemented
74C2×Dic11⋊C4—24no—
75C2×Dic11⋊C4—42no—
76C2×Dic11⋊C4—42no—
77C2×C4×Dic11—22no—
78C2×C4×Dic11—42no—
79C2×C4×Dic11—42no—
80C2×C4×Dic11D414yes—
81C11×#95—22no—
82C11×#95—24no—
83C11×#95—42no—
84C11×#95C2×C414yescomplemented
85C11⋊#95—22no—
86C11⋊#95—22no—
87C11⋊#95—24no—
88C11⋊#95—24no—
89C11⋊#95—42no—
90C11⋊#95—42no—
91C11⋊#95—42no—
92C11⋊#95—42no—
93#14317—111nomaximal, Sylow
94C24×C11C2411yescharacteristic
95C23×D11—21no—
96C23×D11—21no—
97C23×D11—21no—
98C23×D11—21no—
99C23×D11—22no—
100C23×D11—22no—
101C23×D11—22no—
102C23×D11—22no—
103C23×D11C22×C412yes—
104C23×D11C2×Q812yes—
105C23×D11#4112yes—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—21no—
109C22×C4×C11—21no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—21no—
113C22×C4×C11—21no—
114C22×C4×C11—22no—
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×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11C22×C414yes—
130C22×C4×C11C22×C412yes—
131C22×C4×C11C2×D412yes—
132C22×C4×C11C2×Q812yes—
133C22×C4×C11#4112yes—
134C22×C4×C11#4112yes—
135C22×Dic11—21no—
136C22×Dic11—22no—
137C22×Dic11—22no—
138C22×Dic11—21no—
139C22×Dic11—21no—
140C22×Dic11—21no—
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×Dic11—22no—
158C22×Dic11C22×C414yes—
159C22×Dic11C22×C412yes—
160C22×Dic11C2×D412yes—
161C22×Dic11C2×D412yes—
162C22×Dic11C2×Q812yes—
163C22×Dic11#4112yes—
164C2×C4×D11—28no—
165C2×C4×D11—48no—
166C2×C4×D11—44no—
167C2×C4×D11—44no—
168C2×C4×D11—48no—
169C11×C4⋊C4—44no—
170(C2×D11)⋊C4—28no—
171(C2×D11)⋊C4—28no—
172(C2×D11)⋊C4—48no—
173(C2×D11)⋊C4—48no—
174C4⋊Dic11—28no—
175C4⋊Dic11—48no—
176Dic11⋊C4—48no—
177C4×Dic11—44no—
178C4×Dic11—44no—
179C2×#399—111no—
180C2×#389—111no—
181C2×C4×C22⋊C4—111no—
182#1445—111no—
183#1442D1111yescharacteristic, complemented
184#1441—112no—
185#1439—112no—
186#1439—111no—
187#1436—112no—
188#1434—111no—
189C22⋊#95—112no—
190C23×C11C23×C411yescharacteristic
191C23×C11C22×D411yescharacteristic
192C23×C11C22×Q811yescharacteristic
193C23×C11C2×#4111yescharacteristic
194C23×C11C2×#4111yescharacteristic
195C23×C11C2×#4111yescharacteristic
196C23×C11C2×#4111yescharacteristic
197C23×C11H(5,𝔽2)12yes—
198C23×C11H(5,𝔽2)12yes—
199C23×C11H(5,𝔽2)12yes—
200C23×C112−1+412yes—
201C22×D11—22no—
202C22×D11—22no—
203C22×D11—24no—
204C22×D11—24no—
205C22×D11—22no—
206C22×D11—22no—
207C22×D11—22no—
208C22×D11—22no—
209C22×D11—24no—
210C22×D11—24no—
211C22×D11—24no—
212C22×D11—24no—
213C22×D11—41no—
214C22×D11—41no—
215C22×D11—41no—
216C22×D11—41no—
217C22×D11—42no—
218C22×D11—42no—
219C22×D11—42no—
220C22×D11—42no—
221C22×D11—42no—
222C22×D11—42no—
223C22×D11C4×Q814yes—
224C2×C4×C11—24no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—24no—
228C2×C4×C11—24no—
229C2×C4×C11—24no—
230C2×C4×C11—24no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—24no—
234C2×C4×C11—24no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
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—42no—
250C2×C4×C11—42no—
251C2×C4×C11—42no—
252C2×C4×C11C4×D414yes—
253C2×Dic11—22no—
254C2×Dic11—22no—
255C2×Dic11—24no—
256C2×Dic11—24no—
257C2×Dic11—24no—
258C2×Dic11—22no—
259C2×Dic11—24no—
260C2×Dic11—24no—
261C2×Dic11—24no—
262C2×Dic11—22no—
263C2×Dic11—22no—
264C2×Dic11—22no—
265C2×Dic11—41no—
266C2×Dic11—42no—
267C2×Dic11—42no—
268C2×Dic11—41no—
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—42no—
278C2×Dic11—42no—
279C2×Dic11—42no—
280C2×Dic11—42no—
281C2×Dic11C22⋊Q814yes—
282C4×D11—416no—
283C24×C4—111no—
284C22×C4⋊C4—111no—
285C22×C4⋊C4—112no—
286C22×C4⋊C4—112no—
287C22×C4⋊C4C2×D1111yescharacteristic
288C22×C22⋊C4—111no—
289C22×C22⋊C4—112no—
290C22×C22⋊C4—111no—
291C22×C22⋊C4—112no—
292C22×C42—111no—
293C22×C42—111no—
294#399—118no—
295#389—224no—
296C4×C22⋊C4—224no—
297C2×#95—112no—
298C2×#95—112no—
299C2×#95—111no—
300C2×#95—111no—
301C2×#95—112no—
302C2×#95—112no—
303C2×#95—112no—
304C2×#95—112no—
305C2×#95C2×D1112yes—
306C2×#95C2×D1111yescharacteristic
307C2×#95C2×D1112yes—
308C2×#95C2×D1111yescharacteristic
309C22×C11C2×C4×D411yescharacteristic
310C22×C11C2×C4×Q811yescharacteristic
311C22×C11C4×#4111yescharacteristic
312C22×C11#51812yes—
313C22×C11#52012yes—
314C22×C11C2×C22⋊Q811yescharacteristic
315C22×C11#52511yescharacteristic
316C22×C11#52911yescharacteristic
317C22×C11#53311yescharacteristic
318C22×C11#53411yescharacteristic
319C22×C11#53511yescharacteristic
320C22×C11#53511yescharacteristic
321C22×C11#53611yescharacteristic
322C22×C11#53812yes—
323C22×C11#53812yes—
324C22×C11#53912yes—
325C22×C11#53912yes—
326C22×C11#53912yes—
327C22×C11#54012yes—
328C22×C11#54012yes—
329C22×C11#54212yes—
330C22×C11#54312yes—
331C22×C11#54412yes—
332C2×D11—28no—
333C2×D11—24no—
334C2×D11—42no—
335C2×D11—42no—
336C2×D11—44no—
337C2×D11—42no—
338C2×D11—42no—
339C2×D11—42no—
340C2×D11—42no—
341C2×D11—44no—
342C2×D11—44no—
343C4×C11—24no—
344C4×C11—44no—
345C4×C11—42no—
346C4×C11—42no—
347C4×C11—82no—
348Dic11—24no—
349Dic11—44no—
350Dic11—42no—
351Dic11—42no—
352Dic11—82no—
353C25—111no—
354C23×C4—111no—
355C23×C4—112no—
356C23×C4—111no—
357C23×C4—111no—
358C23×C4—114no—
359C23×C4—112no—
360C23×C4—222no—
361C23×C4—222no—
362C23×C4—442no—
363C23×C4—442no—
364C23×C4C22×D1112yes—
365C23×C4C22×D1112yes—
366C23×C4C22×D1111yescharacteristic
367C23×C4C22×D1111yescharacteristic
368C23×C4C22×D1111yescharacteristic
369C2×C4⋊C4—22no—
370C2×C4⋊C4—42no—
371C2×C4⋊C4—114no—
372C2×C4⋊C4—118no—
373C2×C4⋊C4—222no—
374C2×C4⋊C4—222no—
375C2×C4⋊C4—224no—
376C2×C4⋊C4—442no—
377C2×C4⋊C4—442no—
378C2×C4⋊C4—442no—
379C2×C4⋊C4—442no—
380C2×C22⋊C4—114no—
381C2×C22⋊C4—118no—
382C2×C22⋊C4—222no—
383C2×C22⋊C4—222no—
384C2×C22⋊C4—222no—
385C2×C22⋊C4—222no—
386C2×C22⋊C4—222no—
387C2×C22⋊C4—224no—
388C2×C22⋊C4—442no—
389C2×C22⋊C4—442no—
390C2×C22⋊C4—442no—
391C2×C22⋊C4—442no—
392C2×C42—114no—
393C2×C42—222no—
394C2×C42—442no—
395C2×C42—442no—
396#95—22no—
397#95—24no—
398#95—42no—
399#95—224no—
400#95—222no—
401#95—224no—
402#95—222no—
403#95—442no—
404#95—442no—
405#95—442no—
406#95—442no—
407#95C4×D1114yescomplemented
408C2×C11C4×C22⋊Q811yescharacteristic
409C2×C11#232211yescharacteristic
410C2×C11#232811yescharacteristic
411C2×C11#232912yes—
412C2×C11#233512yes—
413C2×C11#262611yescharacteristic
414C2×C11#262811yescharacteristic
415C2×C11#263311yescharacteristic
416C2×C11#263511yescharacteristic
417C2×C11#264912yes—
418C2×C11#266712yes—
419D11—44no—
420C24—112no—
421C24—112no—
422C24—112no—
423C24—221no—
424C24—221no—
425C24—222no—
426C24—221no—
427C24—221no—
428C24—222no—
429C24—222no—
430C24—222no—
431C24C23×D1111yescharacteristic
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—112no—
456C22×C4—112no—
457C22×C4—112no—
458C22×C4—112no—
459C22×C4—114no—
460C22×C4—112no—
461C22×C4—228no—
462C22×C4—222no—
463C22×C4—222no—
464C22×C4—221no—
465C22×C4—222no—
466C22×C4—221no—
467C22×C4—222no—
468C22×C4—221no—
469C22×C4—222no—
470C22×C4—221no—
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×C4—222no—
480C22×C4—222no—
481C22×C4—222no—
482C22×C4—222no—
483C22×C4—222no—
484C22×C4—222no—
485C22×C4—448no—
486C22×C4—444no—
487C22×C4—444no—
488C22×C4—448no—
489C22×C4C2×C4×D1114yes—
490C22×C4C2×C4×D1112yes—
491C22×C4D4×D1112yes—
492C22×C4#434112yes—
493C22×C4Q8×D1112yes—
494C22×C4#434312yes—
495C4⋊C4—44no—
496C4⋊C4—228no—
497C4⋊C4—448no—
498C4⋊C4—448no—
499C22⋊C4—228no—
500C22⋊C4—228no—
501C22⋊C4—448no—
502C22⋊C4—448no—
503C42—444no—
504C42—444no—
505C11#1431711yescharacteristic, complemented, Sylow
506C23—114no—
507C23—224no—
508C23—222no—
509C23—222no—
510C23—224no—
511C23—222no—
512C23—224no—
513C23—222no—
514C23—222no—
515C23—224no—
516C23—224no—
517C23—224no—
518C23—222no—
519C23—442no—
520C23—441no—
521C23—442no—
522C23—442no—
523C23—441no—
524C23—442no—
525C23—441no—
526C23—441no—
527C23—442no—
528C23—442no—
529C23C22×C4×D1111yescharacteristic
530C23C2×D4×D1111yescharacteristic
531C23C2×#434111yescharacteristic
532C23#6703712yes—
533C23C2×Q8×D1111yescharacteristic
534C23C2×#434311yescharacteristic
535C23#41×D1111yescharacteristic
536C23#41×D1111yescharacteristic
537C23#6704212yes—
538C23#6704212yes—
539C23#6704312yes—
540C2×C4—24no—
541C2×C4—22no—
542C2×C4—24no—
543C2×C4—22no—
544C2×C4—24no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—24no—
550C2×C4—24no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—41no—
554C2×C4—42no—
555C2×C4—41no—
556C2×C4—42no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—114no—
569C2×C4—222no—
570C2×C4—224no—
571C2×C4—222no—
572C2×C4—224no—
573C2×C4—222no—
574C2×C4—224no—
575C2×C4—224no—
576C2×C4—224no—
577C2×C4—224no—
578C2×C4—222no—
579C2×C4—222no—
580C2×C4—222no—
581C2×C4—4416no—
582C2×C4—442no—
583C2×C4—442no—
584C2×C4—441no—
585C2×C4—442no—
586C2×C4—441no—
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×C4—442no—
596C2×C4—442no—
597C2×C4—442no—
598C2×C4#6694614yes—
599C22—224no—
600C22—228no—
601C22—442no—
602C22—444no—
603C22—442no—
604C22—442no—
605C22—444no—
606C22—442no—
607C22—444no—
608C22—442no—
609C22—442no—
610C22C2×#6694611yescharacteristic
611C22#1062305212yes—
612C22C4×#434111yescharacteristic
613C22#1062307712yes—
614C22C4×Q8×D1111yescharacteristic
615C22#1062312011yescharacteristic
616C22#1062313711yescharacteristic
617C22#1062315012yes—
618C22D11×C22⋊Q811yescharacteristic
619C22#1062316512yes—
620C22#1062317612yes—
621C22#1062317911yescharacteristic
622C22#1062318812yes—
623C22#1062319612yes—
624C22#1062320511yescharacteristic
625C22#1062320511yescharacteristic
626C22#1062320912yes—
627C22#1062322012yes—
628C22#1062322211yescharacteristic
629C22#1062322912yes—
630C22#1062323812yes—
631C22#1062324112yes—
632C22#1062325911yescharacteristic
633C4—24no—
634C4—44no—
635C4—42no—
636C4—42no—
637C4—82no—
638C4—224no—
639C4—442no—
640C4—442no—
641C4—444no—
642C4—882no—
643C2—444no—
644C2#1307114611yescharacteristic
645C2#1307128411yescharacteristic
646C2#1307133911yescharacteristic
647C2#1307134512yes—
648C2#1307141112yes—
649C2#1307442011yescharacteristic
650C2#1307444411yescharacteristic
651C2#1307448911yescharacteristic
652C2#1307450811yescharacteristic
653C2#1307461812yes—
654C2#1307481512yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1442C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenter#1442D11
hypocenterC11#14317
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1442

Complements

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

NH ≅ G/Ntype
2. C2×#10622586C2semidirect
4. #13066885C2semidirect
5. #13066868C2semidirect
8. #13066850C2semidirect
9. #13066841C2semidirect
11. C11×#1442C2semidirect
36. #10622290C4semidirect
72. C2×C4⋊Dic11C2×C4semidirect
73. C2×C4⋊Dic11C2×C4semidirect
84. C11×#95C2×C4semidirect
183. #1442D11semidirect
407. #95C4×D11semidirect
505. C11#14317semidirect

Maximal subgroups

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

subgroupindex
C2×#106222902
C2×#106225862
C2×#106222792
#130668852
#130668682
#130668602
#130668582
#130668502
#130668412
(C2×D11)⋊#952
C11×#14422
#1431711