Finite Group Databasebeta

← #14684056

Subgroups — #14684056

Order 2816.

1650 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622604C211yesmaximal, characteristic
2C2×#10622283C212yesmaximal, complemented
3#13066858C212yesmaximal, complemented
4#13066856C212yesmaximal
5#13066852C212yesmaximal, complemented
6#13066852C212yesmaximal, complemented
7#13066845C211yesmaximal, characteristic, complemented
8#13066842C212yesmaximal, complemented
9C11×#1441C211yesmaximal, characteristic, complemented
10C23×D44C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×(C2×D11)⋊C4C2212yes—
14C22×(C2×D11)⋊C4C2212yes—
15C22×(C2×D11)⋊C4C2212yes—
16C22×(C2×D11)⋊C4C2212yes—
17C22×(C2×D11)⋊C4C2212yes—
18C22×(C2×D11)⋊C4C2212yes—
19C22×C4⋊Dic11C2211yescharacteristic
20C22×C4×Dic11C2212yes—
21C22×C4×Dic11C2211yescharacteristic
22C2×C11×#95C2212yes—
23C2×C11×#95C2212yes—
24C2×C11×#95C2211yescharacteristic
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2211yescharacteristic
31#10622604C418yescomplemented
32#10622283—28no—
33C24×D11C2312yes—
34C23×C4×C11C2312yes—
35C23×C4×C11C2311yescharacteristic
36C23×C4×C11C2311yescharacteristic
37C23×C4×C11C2312yes—
38C23×C4×C11C2311yescharacteristic
39C23×Dic11C2312yes—
40C23×Dic11C2312yes—
41C23×Dic11C2312yes—
42C22×D44—42no—
43C22×D44—42no—
44C22×D44—41no—
45C22×D44—41no—
46C22×D44C2×C414yes—
47C2×C11×C4⋊C4—41no—
48C2×C11×C4⋊C4—41no—
49C2×C11×C4⋊C4—42no—
50C2×C11×C4⋊C4—41no—
51C2×C11×C4⋊C4C2×C414yes—
52C2×(C2×D11)⋊C4—24no—
53C2×(C2×D11)⋊C4—24no—
54C2×(C2×D11)⋊C4—24no—
55C2×(C2×D11)⋊C4—24no—
56C2×(C2×D11)⋊C4—24no—
57C2×(C2×D11)⋊C4—24no—
58C2×(C2×D11)⋊C4—24no—
59C2×(C2×D11)⋊C4—24no—
60C2×(C2×D11)⋊C4—42no—
61C2×(C2×D11)⋊C4—42no—
62C2×(C2×D11)⋊C4—42no—
63C2×(C2×D11)⋊C4—42no—
64C2×(C2×D11)⋊C4—42no—
65C2×(C2×D11)⋊C4—42no—
66C2×(C2×D11)⋊C4—42no—
67C2×(C2×D11)⋊C4—42no—
68C2×(C2×D11)⋊C4C2×C418yes—
69C2×(C2×D11)⋊C4C2×C418yes—
70C2×C4⋊Dic11—41no—
71C2×C4⋊Dic11—41no—
72C2×C4⋊Dic11D414yescomplemented
73C2×C4×Dic11—24no—
74C2×C4×Dic11—22no—
75C2×C4×Dic11—24no—
76C2×C4×Dic11—42no—
77C2×C4×Dic11—41no—
78C2×C4×Dic11—41no—
79C11×#95—24no—
80C11×#95—42no—
81C11×#95—41no—
82C11⋊#95—24no—
83C11⋊#95—24no—
84C11⋊#95—42no—
85C11⋊#95—42no—
86C11⋊#95—42no—
87C11⋊#95C2×C414yes—
88#14589—111nomaximal, Sylow
89C24×C11C2411yescharacteristic
90C23×D11—22no—
91C23×D11—22no—
92C23×D11—22no—
93C23×D11—22no—
94C23×D11—22no—
95C23×D11—22no—
96C23×D11—22no—
97C23×D11—22no—
98C23×D11—22no—
99C23×D11—22no—
100C23×D11—22no—
101C23×D11—22no—
102C23×D11—22no—
103C23×D11—22no—
104C23×D11C22×C414yes—
105C22×C4×C11—21no—
106C22×C4×C11—21no—
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—21no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—21no—
120C22×C4×C11—21no—
121C22×C4×C11—21no—
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×C11—22no—
130C22×C4×C11C22×C412yes—
131C22×C4×C11C22×C412yes—
132C22×C4×C11C22×C412yes—
133C22×C4×C11C2×D412yes—
134C22×C4×C11#4114yes—
135C22×C4×C11#4112yes—
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×C414yes—
155C22×Dic11C2×D414yes—
156C22×Dic11#4114yes—
157C2×D44—44no—
158C2×D44—48no—
159C2×D44—48no—
160C2×D44—44no—
161C2×D44—44no—
162C11×C4⋊C4—44no—
163C11×C4⋊C4—44no—
164(C2×D11)⋊C4—216no—
165(C2×D11)⋊C4—48no—
166(C2×D11)⋊C4—48no—
167(C2×D11)⋊C4—48no—
168(C2×D11)⋊C4—48no—
169(C2×D11)⋊C4—48no—
170C4⋊Dic11—44no—
171C4×Dic11—48no—
172C4×Dic11—44no—
173C2×#394—111no—
174C2×#388—112no—
175#1441D1111yescharacteristic, complemented
176#1439—112no—
177#1438—112no—
178#1437—112no—
179#1437—112no—
180C4⋊#95—111no—
181#1434—112no—
182C23×C11C23×C411yescharacteristic
183C23×C11C22×D411yescharacteristic
184C23×C11C2×#4111yescharacteristic
185C23×C11C2×#4112yes—
186C23×C11C2×#4112yes—
187C23×C11H(5,𝔽2)11yescharacteristic
188C23×C11H(5,𝔽2)11yescharacteristic
189C23×C11H(5,𝔽2)12yes—
190C23×C11H(5,𝔽2)12yes—
191C23×C11H(5,𝔽2)11yescharacteristic
192C23×C112−1+411yescharacteristic
193C22×D11—24no—
194C22×D11—24no—
195C22×D11—24no—
196C22×D11—24no—
197C22×D11—24no—
198C22×D11—24no—
199C22×D11—24no—
200C22×D11—42no—
201C22×D11—42no—
202C22×D11—42no—
203C22×D11—42no—
204C22×D11—42no—
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—42no—
214C22×D11—42no—
215C22×D11—42no—
216C22×D11—42no—
217C22×D11—42no—
218C22×D11—42no—
219C22×D11—42no—
220C22×D11—42no—
221C22×D11—42no—
222C22×D11—42no—
223C22×D11—42no—
224C22×D11—42no—
225C22×D11—42no—
226C22×D11—42no—
227C22×D11—42no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—24no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—24no—
238C2×C4×C11—24no—
239C2×C4×C11—24no—
240C2×C4×C11—24no—
241C2×C4×C11—42no—
242C2×C4×C11—42no—
243C2×C4×C11—42no—
244C2×C4×C11—42no—
245C2×C4×C11—41no—
246C2×C4×C11—42no—
247C2×C4×C11—42no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—42no—
252C2×C4×C11—42no—
253C2×C4×C11—42no—
254C2×C4×C11—42no—
255C2×C4×C11—42no—
256C2×C4×C11—42no—
257C2×C4×C11—42no—
258C2×C4×C11C4×D414yes—
259C2×Dic11—24no—
260C2×Dic11—24no—
261C2×Dic11—24no—
262C2×Dic11—24no—
263C2×Dic11—24no—
264C2×Dic11—24no—
265C2×Dic11—24no—
266C2×Dic11—24no—
267C2×Dic11—24no—
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—42no—
278C2×Dic11—42no—
279C2×Dic11—42no—
280D44—416no—
281C23×D4—111no—
282C22×C4⋊C4—111no—
283C22×C4⋊C4C2×D1111yescharacteristic
284C22×C4⋊C4C2×D1111yescharacteristic
285C22×C22⋊C4—112no—
286C22×C22⋊C4—112no—
287C22×C22⋊C4—112no—
288C22×C22⋊C4—112no—
289C22×C22⋊C4—112no—
290C22×C22⋊C4—112no—
291C22×C42—112no—
292C22×C42—111no—
293#394—118no—
294#388—228no—
295C2×#95—111no—
296C2×#95—112no—
297C2×#95—112no—
298C2×#95—112no—
299C2×#95—112no—
300C2×#95—112no—
301C2×#95C2×D1112yes—
302C2×#95C2×D1112yes—
303C2×#95C2×D1111yescharacteristic
304C22×C11C2×C4×D411yescharacteristic
305C22×C11C4×#4112yes—
306C22×C11#51811yescharacteristic
307C22×C11#51812yes—
308C22×C11#52011yescharacteristic
309C22×C11#53411yescharacteristic
310C22×C11#53711yescharacteristic
311C22×C11#53811yescharacteristic
312C22×C11#53812yes—
313C22×C11#53911yescharacteristic
314C22×C11#53912yes—
315C22×C11#54012yes—
316C22×C11#54212yes—
317C22×C11#54612yes—
318C22×C11#55012yes—
319C22×C11#55112yes—
320C22×C11#55312yes—
321C22×C11#55512yes—
322C22×C11#55511yescharacteristic
323C22×C11#55511yescharacteristic
324C22×C11#56012yes—
325C22×C11#56011yescharacteristic
326C22×C11H(3,𝔽4)11yescharacteristic
327C2×D11—44no—
328C2×D11—44no—
329C2×D11—44no—
330C2×D11—44no—
331C2×D11—44no—
332C2×D11—44no—
333C2×D11—44no—
334C2×D11—82no—
335C2×D11—82no—
336C2×D11—82no—
337C2×D11—82no—
338C2×D11—82no—
339C2×D11—82no—
340C2×D11—82no—
341C2×D11—82no—
342C4×C11—24no—
343C4×C11—42no—
344C4×C11—42no—
345C4×C11—44no—
346C4×C11—82no—
347Dic11—44no—
348Dic11—44no—
349Dic11—44no—
350C25—112no—
351C22×D4—114no—
352C22×D4—442no—
353C22×D4—441no—
354C22×D4—441no—
355C22×D4—442no—
356C23×C4—112no—
357C23×C4—112no—
358C23×C4—112no—
359C23×C4C22×D1112yes—
360C23×C4C22×D1111yescharacteristic
361C23×C4C22×D1111yescharacteristic
362C23×C4C22×D1112yes—
363C23×C4C22×D1111yescharacteristic
364C2×C4⋊C4—41no—
365C2×C4⋊C4—41no—
366C2×C4⋊C4—42no—
367C2×C4⋊C4—41no—
368C2×C4⋊C4—114no—
369C2×C4⋊C4—441no—
370C2×C4⋊C4—441no—
371C2×C4⋊C4C4×D1114yes—
372C2×C22⋊C4—118no—
373C2×C22⋊C4—118no—
374C2×C22⋊C4—224no—
375C2×C22⋊C4—224no—
376C2×C22⋊C4—224no—
377C2×C22⋊C4—224no—
378C2×C22⋊C4—224no—
379C2×C22⋊C4—224no—
380C2×C22⋊C4—224no—
381C2×C22⋊C4—224no—
382C2×C22⋊C4—442no—
383C2×C22⋊C4—442no—
384C2×C22⋊C4—442no—
385C2×C22⋊C4—442no—
386C2×C22⋊C4—442no—
387C2×C22⋊C4—442no—
388C2×C22⋊C4—442no—
389C2×C22⋊C4—442no—
390C2×C42—224no—
391C2×C42—224no—
392C2×C42—222no—
393C2×C42—442no—
394C2×C42—441no—
395C2×C42—441no—
396#95—24no—
397#95—42no—
398#95—41no—
399#95—114no—
400#95—224no—
401#95—224no—
402#95—442no—
403#95—442no—
404#95—442no—
405C2×C11#232511yescharacteristic
406C2×C11#233512yes—
407C2×C11#236312yes—
408C2×C11#237211yescharacteristic
409C2×C11#237511yescharacteristic
410C2×C11#269911yescharacteristic
411C2×C11#270512yes—
412C2×C11#273311yescharacteristic
413C2×C11#275612yes—
414C2×C11#278511yescharacteristic
415C2×C11#279511yescharacteristic
416D11—84no—
417C24—114no—
418C24—222no—
419C24—222no—
420C24—222no—
421C24—222no—
422C24—222no—
423C24—222no—
424C24—222no—
425C24—222no—
426C24—222no—
427C24—222no—
428C24—222no—
429C24—222no—
430C24—222no—
431C24—222no—
432C24C23×D1111yescharacteristic
433C2×D4—444no—
434C2×D4—448no—
435C2×D4—444no—
436C2×D4—448no—
437C2×D4—444no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—114no—
464C22×C4—114no—
465C22×C4—114no—
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×C4—222no—
480C22×C4—222no—
481C22×C4—222no—
482C22×C4—222no—
483C22×C4—222no—
484C22×C4C2×C4×D1112yes—
485C22×C4C2×C4×D1112yes—
486C22×C4C2×C4×D1112yes—
487C22×C4D4×D1112yes—
488C22×C4#434314yes—
489C22×C4#434312yes—
490C4⋊C4—44no—
491C4⋊C4—44no—
492C4⋊C4—444no—
493C22⋊C4—2216no—
494C22⋊C4—448no—
495C22⋊C4—448no—
496C22⋊C4—448no—
497C22⋊C4—448no—
498C22⋊C4—448no—
499C42—448no—
500C42—444no—
501C11#1458911yescharacteristic, complemented, Sylow
502C23—224no—
503C23—224no—
504C23—224no—
505C23—224no—
506C23—224no—
507C23—224no—
508C23—224no—
509C23—442no—
510C23—442no—
511C23—442no—
512C23—442no—
513C23—442no—
514C23—442no—
515C23—442no—
516C23—442no—
517C23—442no—
518C23—442no—
519C23—442no—
520C23—442no—
521C23—442no—
522C23—442no—
523C23—442no—
524C23—442no—
525C23—442no—
526C23—442no—
527C23—442no—
528C23—442no—
529C23—442no—
530C23—442no—
531C23—442no—
532C23—442no—
533C23—442no—
534C23—442no—
535C23—442no—
536C23—442no—
537C23C22×C4×D1111yescharacteristic
538C23C2×D4×D1111yescharacteristic
539C23#6703711yescharacteristic
540C23#6703712yes—
541C23#6703711yescharacteristic
542C23C2×#434311yescharacteristic
543C23C2×#434312yes—
544C23#41×D1112yes—
545C23#6704212yes—
546C23#6704211yescharacteristic
547C23#6704311yescharacteristic
548D4—4416no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—42no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—224no—
580C2×C4—224no—
581C2×C4—224no—
582C2×C4—224no—
583C2×C4—224no—
584C2×C4—224no—
585C2×C4—224no—
586C2×C4—224no—
587C2×C4—224no—
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—442no—
599C2×C4—442no—
600C2×C4#6694614yes—
601C22—444no—
602C22—444no—
603C22—444no—
604C22—444no—
605C22—444no—
606C22—444no—
607C22—444no—
608C22—882no—
609C22—882no—
610C22—882no—
611C22—882no—
612C22—882no—
613C22—882no—
614C22—882no—
615C22—882no—
616C22#1062301711yescharacteristic
617C22C2×#6694611yescharacteristic
618C22#1062305411yescharacteristic
619C22#1062307612yes—
620C22C4×#434312yes—
621C22#1062312511yescharacteristic
622C22#1062312811yescharacteristic
623C22#1062313012yes—
624C22#1062313611yescharacteristic
625C22#1062315112yes—
626C22#1062316112yes—
627C22#1062316812yes—
628C22#1062317511yescharacteristic
629C22#1062317612yes—
630C22#1062317611yescharacteristic
631C22#1062318812yes—
632C22#1062319711yescharacteristic
633C22#1062320111yescharacteristic
634C22#1062322612yes—
635C22#1062322912yes—
636C22#1062324112yes—
637C22#1062326511yescharacteristic
638C22#1062326512yes—
639C4—24no—
640C4—44no—
641C4—42no—
642C4—42no—
643C4—82no—
644C4—444no—
645C4—444no—
646C4—444no—
647C2—884no—
648C2#1307131611yescharacteristic
649C2#1307140512yes—
650C2#1307165312yes—
651C2#1307172711yescharacteristic
652C2#1307175411yescharacteristic
653C2#1307520211yescharacteristic
654C2#1307528812yes—
655C2#1307563911yescharacteristic
656C2#1307594412yes—
657C2#1307632411yescharacteristic
658C2#1307645011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1441C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenter#1441D11
hypocenterC11#14589
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
2. C2×#10622283C2semidirect
3. #13066858C2semidirect
5. #13066852C2semidirect
6. #13066852C2semidirect
7. #13066845C2semidirect
8. #13066842C2semidirect
9. C11×#1441C2semidirect
31. #10622604C4semidirect
72. C2×C4⋊Dic11D4semidirect
175. #1441D11semidirect
501. C11#14589semidirect

Maximal subgroups

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

subgroupindex
C2×#106226042
C2×#106222832
#130668582
#130668562
#130668522
#130668452
#130668422
C11×#14412
#1458911