Finite Group Databasebeta

← #14684051

Subgroups — #14684051

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×#10622603C212yesmaximal, complemented
3#13066869C211yesmaximal, characteristic, complemented
4#13066862C212yesmaximal, complemented
5#13066856C212yesmaximal
6#13066854C212yesmaximal, complemented
7#13066852C212yesmaximal, complemented
8#13066840C212yesmaximal, complemented
9C11×C4⋊#95C211yesmaximal, characteristic, complemented
10C23×D44C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C42×C11C2211yescharacteristic
14C22×(C2×D11)⋊C4C2212yes—
15C22×(C2×D11)⋊C4C2212yes—
16C22×(C2×D11)⋊C4C2212yes—
17C22×(C2×D11)⋊C4C2212yes—
18C22×(C2×D11)⋊C4C2212yes—
19C22×(C2×D11)⋊C4C2212yes—
20C22×C4⋊Dic11C2211yescharacteristic
21C22×C4×Dic11C2212yes—
22C2×C11×#95C2212yes—
23C2×C11×#95C2212yes—
24C2×C11⋊#95C2212yes—
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2211yescharacteristic
30C2×C11⋊#95C2211yescharacteristic
31#10622604C418yescomplemented
32#10622603—28no—
33C24×D11C2312yes—
34C23×C4×C11C2311yescharacteristic
35C23×C4×C11C2311yescharacteristic
36C23×C4×C11C2312yes—
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—41no—
50C2×C11×C4⋊C4—41no—
51C2×C11×C4⋊C4C2×C414yes—
52C2×C11×C4⋊C4D414yescomplemented
53C2×C42×C11—22no—
54C2×C42×C11—41no—
55C2×C42×C11—41no—
56C2×(C2×D11)⋊C4—24no—
57C2×(C2×D11)⋊C4—24no—
58C2×(C2×D11)⋊C4—24no—
59C2×(C2×D11)⋊C4—24no—
60C2×(C2×D11)⋊C4—24no—
61C2×(C2×D11)⋊C4—24no—
62C2×(C2×D11)⋊C4—24no—
63C2×(C2×D11)⋊C4—24no—
64C2×(C2×D11)⋊C4—42no—
65C2×(C2×D11)⋊C4—42no—
66C2×(C2×D11)⋊C4—42no—
67C2×(C2×D11)⋊C4—42no—
68C2×(C2×D11)⋊C4—42no—
69C2×(C2×D11)⋊C4—42no—
70C2×(C2×D11)⋊C4—42no—
71C2×(C2×D11)⋊C4—42no—
72C2×(C2×D11)⋊C4C2×C418yes—
73C2×(C2×D11)⋊C4C2×C418yes—
74C2×C4⋊Dic11—42no—
75C2×C4⋊Dic11—41no—
76C2×C4×Dic11—24no—
77C2×C4×Dic11—24no—
78C2×C4×Dic11—42no—
79C11×#95—42no—
80C11×#95—42no—
81C11⋊#95—24no—
82C11⋊#95—24no—
83C11⋊#95—24no—
84C11⋊#95—42no—
85C11⋊#95—42no—
86C11⋊#95—41no—
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—21no—
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—21no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11C22×C412yes—
130C22×C4×C11C22×C412yes—
131C22×C4×C11C22×C412yes—
132C22×C4×C11C2×D414yes—
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×Dic11—22no—
155C22×Dic11C22×C414yes—
156C22×Dic11#4114yes—
157C2×D44—44no—
158C2×D44—48no—
159C2×D44—44no—
160C2×D44—48no—
161C2×D44—44no—
162C11×C4⋊C4—44no—
163C11×C4⋊C4—44no—
164C42×C11—44no—
165(C2×D11)⋊C4—216no—
166(C2×D11)⋊C4—48no—
167(C2×D11)⋊C4—48no—
168(C2×D11)⋊C4—48no—
169(C2×D11)⋊C4—48no—
170(C2×D11)⋊C4—48no—
171C4⋊Dic11—44no—
172C4×Dic11—48no—
173C2×#394—111no—
174C2×#388—112no—
175#1441—111no—
176#1439—112no—
177#1438—112no—
178#1437—112no—
179#1437—112no—
180C4⋊#95D1111yescharacteristic, complemented
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)11yescharacteristic
191C23×C11H(5,𝔽2)12yes—
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—24no—
242C2×C4×C11—24no—
243C2×C4×C11—24no—
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—41no—
251C2×C4×C11—42no—
252C2×C4×C11—41no—
253C2×C4×C11—42no—
254C2×C4×C11—42no—
255C2×C4×C11—42no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11C4×D414yes—
259C2×Dic11—24no—
260C2×Dic11—24no—
261C2×Dic11—24no—
262C2×Dic11—24no—
263C2×Dic11—24no—
264C2×Dic11—24no—
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—
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×C42C2×D1111yescharacteristic
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×#95—111no—
302C2×#95C2×D1112yes—
303C2×#95C2×D1112yes—
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#55511yescharacteristic
322C22×C11#55512yes—
323C22×C11#55511yescharacteristic
324C22×C11#56011yescharacteristic
325C22×C11#56012yes—
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—44no—
347Dic11—44no—
348Dic11—44no—
349Dic11—82no—
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×D1111yescharacteristic
360C23×C4C22×D1111yescharacteristic
361C23×C4C22×D1112yes—
362C23×C4C22×D1112yes—
363C23×C4C22×D1111yescharacteristic
364C2×C4⋊C4—41no—
365C2×C4⋊C4—41no—
366C2×C4⋊C4—41no—
367C2×C4⋊C4—41no—
368C2×C4⋊C4—441no—
369C2×C4⋊C4—442no—
370C2×C4⋊C4C4×D1114yes—
371C2×C4⋊C4D4414yescomplemented
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—22no—
391C2×C42—41no—
392C2×C42—41no—
393C2×C42—224no—
394C2×C42—224no—
395C2×C42—442no—
396#95—42no—
397#95—42no—
398#95—114no—
399#95—224no—
400#95—224no—
401#95—224no—
402#95—441no—
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—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—114no—
463C22×C4—114no—
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×C4—222no—
480C22×C4—222no—
481C22×C4—222no—
482C22×C4—222no—
483C22×C4C2×C4×D1112yes—
484C22×C4C2×C4×D1112yes—
485C22×C4C2×C4×D1112yes—
486C22×C4C2×D4414yes—
487C22×C4C2×D4412yes—
488C22×C4#433912yes—
489C22×C4#434314yes—
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—44no—
500C42—448no—
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
538C23C22×D4411yescharacteristic
539C23C2×#433911yescharacteristic
540C23#6703712yes—
541C23#6703711yescharacteristic
542C23#6703711yescharacteristic
543C23#6703711yescharacteristic
544C23C2×#434312yes—
545C23#6704011yescharacteristic
546C23#41×D1112yes—
547C23#6704212yes—
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—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—42no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—224no—
580C2×C4—224no—
581C2×C4—224no—
582C2×C4—224no—
583C2×C4—224no—
584C2×C4—224no—
585C2×C4—442no—
586C2×C4—442no—
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—442no—
599C2×C4—442no—
600C2×C4C4×D4414yes—
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—
616C22C2×C4×D4411yescharacteristic
617C22#1062301711yescharacteristic
618C22#1062302411yescharacteristic
619C22#1062302511yescharacteristic
620C22#1062303511yescharacteristic
621C22#1062304111yescharacteristic
622C22#1062304512yes—
623C22#1062304611yescharacteristic
624C22#1062306312yes—
625C22#1062307612yes—
626C22#1062308512yes—
627C22C4×#434312yes—
628C22#1062310812yes—
629C22#1062314612yes—
630C22#1062315112yes—
631C22#1062316812yes—
632C22#1062317512yes—
633C22#1062320111yescharacteristic
634C22#1062321411yescharacteristic
635C22#1062322312yes—
636C22#1062325111yescharacteristic
637C22#1062326412yes—
638C22#1062326511yescharacteristic
639C4—24no—
640C4—44no—
641C4—42no—
642C4—42no—
643C4—44no—
644C4—444no—
645C4—444no—
646C4—882no—
647C2—884no—
648C2#1307131911yescharacteristic
649C2#1307140912yes—
650C2#1307165612yes—
651C2#1307172711yescharacteristic
652C2#1307175311yescharacteristic
653C2#1307520111yescharacteristic
654C2#1307528712yes—
655C2#1307564211yescharacteristic
656C2#1307593912yes—
657C2#1307632211yescharacteristic
658C2#1307644511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C4⋊#95C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenterC4⋊#95D11
hypocenterC11#14589
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
2. C2×#10622603C2semidirect
3. #13066869C2semidirect
4. #13066862C2semidirect
6. #13066854C2semidirect
7. #13066852C2semidirect
8. #13066840C2semidirect
9. C11×C4⋊#95C2semidirect
31. #10622604C4semidirect
52. C2×C11×C4⋊C4D4semidirect
180. C4⋊#95D11semidirect
371. C2×C4⋊C4D44semidirect
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×#106226032
#130668692
#130668622
#130668562
#130668542
#130668522
#130668402
C11×C4⋊#952
#1458911