Finite Group Databasebeta

← #14675375

Subgroups — #14675375

Order 2816.

2390 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622552C211yesmaximal, characteristic
2C2×#10622278C212yesmaximal
3C2×C4×(C2×D11)⋊C4C212yesmaximal, complemented
4C2×#10622279C212yesmaximal, complemented
5#13066854C212yesmaximal, complemented
6#13066852C212yesmaximal, complemented
7#13066850C212yesmaximal, complemented
8C4×C11⋊#95C211yesmaximal, characteristic, complemented
9C4×C11×#95C211yesmaximal, characteristic, complemented
10C23×D44C2211yescharacteristic
11C23×C4×D11C2212yes—
12C22×C42×C11C2212yes—
13C22×C42×C11C2211yescharacteristic
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×Dic11C2212yes—
22C2×C11×#95C2211yescharacteristic
23C2×C11×#95C2212yes—
24C2×C11×#95C2211yescharacteristic
25C2×C11⋊#95C2211yescharacteristic
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2211yescharacteristic
31#10622552C418yescomplemented
32C4×(C2×D11)⋊C4—28no—
33#10622279—28no—
34#10622278C4116yescomplemented
35C24×D11C2312yes—
36C23×C4×C11C2312yes—
37C23×C4×C11C2311yescharacteristic
38C23×C4×C11C2311yescharacteristic
39C23×C4×C11C2312yes—
40C23×C4×C11C2311yescharacteristic
41C23×Dic11C2312yes—
42C23×Dic11C2312yes—
43C23×Dic11C2312yes—
44C22×D44—41no—
45C22×D44—41no—
46C22×D44—42no—
47C22×D44C2×C418yes—
48C22×D44C2×C414yes—
49C22×C4×D11—24no—
50C22×C4×D11—24no—
51C22×C4×D11—24no—
52C22×C4×D11—24no—
53C22×C4×D11—42no—
54C22×C4×D11—42no—
55C22×C4×D11C2×C418yescomplemented
56C2×C42×C11—24no—
57C2×C42×C11—24no—
58C2×C42×C11—42no—
59C2×C42×C11—42no—
60C2×C42×C11C2×C414yescomplemented
61C2×(C2×D11)⋊C4—24no—
62C2×(C2×D11)⋊C4—24no—
63C2×(C2×D11)⋊C4—24no—
64C2×(C2×D11)⋊C4—24no—
65C2×(C2×D11)⋊C4—24no—
66C2×(C2×D11)⋊C4—24no—
67C2×(C2×D11)⋊C4—24no—
68C2×(C2×D11)⋊C4—24no—
69C2×(C2×D11)⋊C4—42no—
70C2×(C2×D11)⋊C4—42no—
71C2×(C2×D11)⋊C4C2×C418yes—
72C2×(C2×D11)⋊C4C2×C418yes—
73C2×(C2×D11)⋊C4C2×C418yescomplemented
74C2×(C2×D11)⋊C4C2×C418yescomplemented
75C2×(C2×D11)⋊C4C2×C418yescomplemented
76C2×C4⋊Dic11—41no—
77C2×C4⋊Dic11—41no—
78C2×C4⋊Dic11C2×C414yescomplemented
79C2×C4×Dic11—24no—
80C2×C4×Dic11—24no—
81C2×C4×Dic11—24no—
82C2×C4×Dic11—24no—
83C2×C4×Dic11—42no—
84C2×C4×Dic11—42no—
85C11×#95—22no—
86C11×#95C2×C418yescomplemented
87C11×#95D414yescomplemented
88C11⋊#95—24no—
89C11⋊#95—22no—
90C11⋊#95—24no—
91C11⋊#95—42no—
92C11⋊#95C2×C418yescomplemented
93C11⋊#95D414yescomplemented
94#13824—111nomaximal, Sylow
95C24×C11C2411yescharacteristic
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×D11—22no—
105C23×D11—22no—
106C23×D11—22no—
107C23×D11—22no—
108C23×D11C22×C414yes—
109C23×D11C22×C414yes—
110C23×D11C22×C414yes—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—21no—
118C22×C4×C11—21no—
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×C11C22×C414yes—
129C22×C4×C11C22×C414yes—
130C22×C4×C11C22×C412yes—
131C22×C4×C11C22×C414yes—
132C22×C4×C11C22×C412yes—
133C22×C4×C11C22×C412yes—
134C22×C4×C11C2×D414yes—
135C22×C4×C11C2×D412yes—
136C22×C4×C11C2×D412yes—
137C22×C4×C11#4112yes—
138C22×C4×C11#4114yes—
139C22×C4×C11#4112yes—
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×Dic11C22×C414yes—
157C22×Dic11C22×C414yes—
158C22×Dic11C22×C414yes—
159C22×Dic11C2×D414yes—
160C22×Dic11#4114yes—
161C2×D44—44no—
162C2×D44—44no—
163C2×D44—48no—
164C2×D44—48no—
165C2×D44C42116yescomplemented
166C2×C4×D11—216no—
167C2×C4×D11—216no—
168C2×C4×D11—48no—
169C2×C4×D11—48no—
170C2×C4×D11—48no—
171C2×C4×D11—48no—
172C2×C4×D11—48no—
173C42×C11—44no—
174C42×C11—48no—
175(C2×D11)⋊C4—216no—
176(C2×D11)⋊C4—216no—
177(C2×D11)⋊C4—216no—
178(C2×D11)⋊C4—216no—
179(C2×D11)⋊C4—48no—
180C4⋊Dic11—44no—
181C4×Dic11—48no—
182C4×Dic11—48no—
183C2×#390—111no—
184C2×#386—112no—
185C2×C4×C22⋊C4—112no—
186C2×C4×C22⋊C4—112no—
187#1437—112no—
188#1437—112no—
189#1436—112no—
190C4×#95—111no—
191C4×#95D1111yescharacteristic, complemented
192C23×C11C23×C411yescharacteristic
193C23×C11C23×C412yes—
194C23×C11C22×D411yescharacteristic
195C23×C11C22×D411yescharacteristic
196C23×C11C2×#4112yes—
197C23×C11C2×#4111yescharacteristic
198C23×C11C2×#4111yescharacteristic
199C23×C11C2×#4112yes—
200C23×C11H(5,𝔽2)12yes—
201C23×C11H(5,𝔽2)11yescharacteristic
202C23×C11H(5,𝔽2)11yescharacteristic
203C22×D11—24no—
204C22×D11—24no—
205C22×D11—24no—
206C22×D11—24no—
207C22×D11—24no—
208C22×D11—24no—
209C22×D11—24no—
210C22×D11—24no—
211C22×D11—24no—
212C22×D11—24no—
213C22×D11—24no—
214C22×D11—24no—
215C22×D11—24no—
216C22×D11—24no—
217C22×D11—24no—
218C22×D11—24no—
219C22×D11—24no—
220C22×D11—24no—
221C22×D11—42no—
222C22×D11—42no—
223C22×D11—42no—
224C22×D11—42no—
225C22×D11—42no—
226C22×D11—42no—
227C22×D11—42no—
228C22×D11—42no—
229C22×D11—42no—
230C22×D11—42no—
231C22×D11—42no—
232C22×D11—42no—
233C22×D11—42no—
234C22×D11—42no—
235C22×D11—42no—
236C22×D11—42no—
237C22×D11C2×C4218yes—
238C2×C4×C11—24no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—24no—
246C2×C4×C11—24no—
247C2×C4×C11—24no—
248C2×C4×C11—24no—
249C2×C4×C11—24no—
250C2×C4×C11—24no—
251C2×C4×C11—24no—
252C2×C4×C11—24no—
253C2×C4×C11—24no—
254C2×C4×C11—24no—
255C2×C4×C11—24no—
256C2×C4×C11—24no—
257C2×C4×C11—24no—
258C2×C4×C11—24no—
259C2×C4×C11—42no—
260C2×C4×C11—42no—
261C2×C4×C11—42no—
262C2×C4×C11—42no—
263C2×C4×C11C2×C4214yes—
264C2×C4×C11C4×D414yes—
265C2×C4×C11C4×D418yes—
266C2×C4×C11C4×D414yes—
267C2×Dic11—24no—
268C2×Dic11—24no—
269C2×Dic11—24no—
270C2×Dic11—24no—
271C2×Dic11—24no—
272C2×Dic11—24no—
273C2×Dic11—24no—
274C2×Dic11—24no—
275C2×Dic11—24no—
276C2×Dic11—24no—
277C2×Dic11—24no—
278C2×Dic11—24no—
279C2×Dic11—42no—
280C2×Dic11—42no—
281C2×Dic11—42no—
282C2×Dic11—42no—
283C2×Dic11—42no—
284C2×Dic11—42no—
285C2×Dic11—42no—
286C2×Dic11—42no—
287C2×Dic11C4×D418yes—
288D44—416no—
289C4×D11—432no—
290C23×D4—111no—
291C24×C4—112no—
292C22×C4⋊C4—111no—
293C22×C22⋊C4—112no—
294C22×C22⋊C4—112no—
295C22×C22⋊C4—112no—
296C22×C22⋊C4—112no—
297C22×C22⋊C4—112no—
298C22×C42—112no—
299C22×C42—112no—
300C22×C42C2×D1112yes—
301C22×C42C2×D1111yescharacteristic
302#390—118no—
303#386—1116no—
304C4×C22⋊C4—228no—
305C4×C22⋊C4—228no—
306C2×#95—112no—
307C2×#95—111no—
308C2×#95—111no—
309C2×#95—112no—
310C2×#95—112no—
311C2×#95—112no—
312C2×#95C2×D1111yescharacteristic
313C2×#95C2×D1112yes—
314C2×#95C2×D1111yescharacteristic
315C22×C11C22×C4211yescharacteristic
316C22×C11C2×C4×D412yes—
317C22×C11C2×C4×D411yescharacteristic
318C22×C11C2×C4×D411yescharacteristic
319C22×C11C2×C4×D412yes—
320C22×C11C4×#4112yes—
321C22×C11C4×#4111yescharacteristic
322C22×C11C4×#4111yescharacteristic
323C22×C11C4×#4112yes—
324C22×C11#51811yescharacteristic
325C22×C11#51811yescharacteristic
326C22×C11#51812yes—
327C22×C11#51812yes—
328C22×C11D4211yescharacteristic
329C22×C11#54612yes—
330C22×C11#54612yes—
331C22×C11#55011yescharacteristic
332C22×C11#55011yescharacteristic
333C22×C11#55112yes—
334C22×C11#55312yes—
335C22×C11#55312yes—
336C22×C11#55512yes—
337C22×C11#55911yescharacteristic
338C2×D11—28no—
339C2×D11—28no—
340C2×D11—28no—
341C2×D11—44no—
342C2×D11—44no—
343C2×D11—44no—
344C2×D11—44no—
345C2×D11—44no—
346C2×D11—44no—
347C2×D11—44no—
348C2×D11—44no—
349C2×D11—44no—
350C2×D11—44no—
351C2×D11—44no—
352C2×D11—44no—
353C4×C11—28no—
354C4×C11—24no—
355C4×C11—24no—
356C4×C11—24no—
357C4×C11—44no—
358Dic11—28no—
359Dic11—44no—
360Dic11—44no—
361C25—112no—
362C22×D4—118no—
363C22×D4—114no—
364C22×D4—442no—
365C22×D4—441no—
366C22×D4—441no—
367C23×C4—112no—
368C23×C4—112no—
369C23×C4—112no—
370C23×C4—118no—
371C23×C4—224no—
372C23×C4—224no—
373C23×C4—224no—
374C23×C4—224no—
375C23×C4—442no—
376C23×C4—442no—
377C23×C4C22×D1112yes—
378C23×C4C22×D1111yescharacteristic
379C23×C4C22×D1111yescharacteristic
380C23×C4C22×D1112yes—
381C23×C4C22×D1111yescharacteristic
382C2×C4⋊C4—114no—
383C2×C4⋊C4—441no—
384C2×C4⋊C4—441no—
385C2×C22⋊C4—118no—
386C2×C22⋊C4—118no—
387C2×C22⋊C4—118no—
388C2×C22⋊C4—118no—
389C2×C22⋊C4—118no—
390C2×C22⋊C4—224no—
391C2×C22⋊C4—224no—
392C2×C22⋊C4—224no—
393C2×C22⋊C4—224no—
394C2×C22⋊C4—224no—
395C2×C22⋊C4—224no—
396C2×C22⋊C4—224no—
397C2×C22⋊C4—224no—
398C2×C22⋊C4—442no—
399C2×C22⋊C4—442no—
400C2×C42—24no—
401C2×C42—24no—
402C2×C42—42no—
403C2×C42—42no—
404C2×C42—224no—
405C2×C42—224no—
406C2×C42—224no—
407C2×C42—224no—
408C2×C42—442no—
409C2×C42—442no—
410C2×C42C4×D1114yescomplemented
411#95—22no—
412#95—118no—
413#95—114no—
414#95—224no—
415#95—224no—
416#95—222no—
417#95—442no—
418#95C4×D1118yescomplemented
419#95D4414yescomplemented
420C2×C11C42×D411yescharacteristic
421C2×C11C42×D411yescharacteristic
422C2×C11#227311yescharacteristic
423C2×C11#235812yes—
424C2×C11#236312yes—
425C2×C11#236312yes—
426C2×C11#236411yescharacteristic
427C2×C11#236411yescharacteristic
428C2×C11#236611yescharacteristic
429C2×C11#237211yescharacteristic
430C2×C11#237412yes—
431D11—48no—
432C24—114no—
433C24—114no—
434C24—114no—
435C24—222no—
436C24—222no—
437C24—222no—
438C24—222no—
439C24—222no—
440C24—222no—
441C24—222no—
442C24—222no—
443C24—222no—
444C24—222no—
445C24—222no—
446C24—222no—
447C24C23×D1111yescharacteristic
448C2×D4—1116no—
449C2×D4—444no—
450C2×D4—444no—
451C2×D4—448no—
452C2×D4—448no—
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—21no—
463C22×C4—21no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—114no—
471C22×C4—114no—
472C22×C4—114no—
473C22×C4—114no—
474C22×C4—114no—
475C22×C4—2216no—
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—222no—
486C22×C4—222no—
487C22×C4—222no—
488C22×C4—222no—
489C22×C4—222no—
490C22×C4—222no—
491C22×C4—222no—
492C22×C4—2216no—
493C22×C4—448no—
494C22×C4—448no—
495C22×C4—448no—
496C22×C4—448no—
497C22×C4—448no—
498C22×C4C2×C4×D1114yes—
499C22×C4C2×C4×D1114yes—
500C22×C4C2×C4×D1112yes—
501C22×C4C2×C4×D1114yes—
502C22×C4C2×C4×D1112yes—
503C22×C4C2×C4×D1112yes—
504C22×C4C2×D4414yes—
505C22×C4C2×D4412yes—
506C22×C4#433912yes—
507C22×C4#433914yes—
508C22×C4D4×D1112yes—
509C22×C4#434312yes—
510C4⋊C4—444no—
511C22⋊C4—2216no—
512C22⋊C4—2216no—
513C22⋊C4—2216no—
514C22⋊C4—2216no—
515C22⋊C4—448no—
516C42—44no—
517C42—48no—
518C42—448no—
519C42—448no—
520C11#1382411yescharacteristic, complemented, Sylow
521C23—118no—
522C23—224no—
523C23—224no—
524C23—224no—
525C23—224no—
526C23—224no—
527C23—224no—
528C23—224no—
529C23—224no—
530C23—224no—
531C23—224no—
532C23—224no—
533C23—224no—
534C23—224no—
535C23—224no—
536C23—224no—
537C23—224no—
538C23—224no—
539C23—224no—
540C23—442no—
541C23—442no—
542C23—442no—
543C23—442no—
544C23—442no—
545C23—442no—
546C23—442no—
547C23—442no—
548C23—442no—
549C23—442no—
550C23—442no—
551C23—442no—
552C23—442no—
553C23—442no—
554C23—442no—
555C23—442no—
556C23C22×C4×D1111yescharacteristic
557C23C22×C4×D1112yes—
558C23C22×D4411yescharacteristic
559C23C2×#433912yes—
560C23C2×#433911yescharacteristic
561C23C2×D4×D1111yescharacteristic
562C23#6703712yes—
563C23C2×#434311yescharacteristic
564C23#41×D1112yes—
565C23#6704211yescharacteristic
566C23#6704211yescharacteristic
567D4—4416no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—24no—
573C2×C4—24no—
574C2×C4—24no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—24no—
580C2×C4—24no—
581C2×C4—24no—
582C2×C4—24no—
583C2×C4—24no—
584C2×C4—24no—
585C2×C4—24no—
586C2×C4—24no—
587C2×C4—24no—
588C2×C4—24no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—118no—
594C2×C4—224no—
595C2×C4—224no—
596C2×C4—224no—
597C2×C4—224no—
598C2×C4—224no—
599C2×C4—224no—
600C2×C4—224no—
601C2×C4—224no—
602C2×C4—224no—
603C2×C4—224no—
604C2×C4—224no—
605C2×C4—224no—
606C2×C4—4432no—
607C2×C4—442no—
608C2×C4—442no—
609C2×C4—442no—
610C2×C4—442no—
611C2×C4—442no—
612C2×C4—442no—
613C2×C4—442no—
614C2×C4—442no—
615C2×C4C42×D1114yes—
616C2×C4C4×D4414yes—
617C2×C4C4×D4418yes—
618C2×C4#6694614yes—
619C22—228no—
620C22—228no—
621C22—228no—
622C22—444no—
623C22—444no—
624C22—444no—
625C22—444no—
626C22—444no—
627C22—444no—
628C22—444no—
629C22—444no—
630C22—444no—
631C22—444no—
632C22—444no—
633C22—444no—
634C22C2×C42×D1111yescharacteristic
635C22C2×C4×D4412yes—
636C22C2×C4×D4411yescharacteristic
637C22C4×#433912yes—
638C22C4×#433911yescharacteristic
639C22#1062301711yescharacteristic
640C22#1062302112yes—
641C22C2×#6694611yescharacteristic
642C22#1062304512yes—
643C22#1062305211yescharacteristic
644C22#1062305311yescharacteristic
645C22#1062305812yes—
646C22#1062306312yes—
647C22#1062307112yes—
648C22C4×D4×D1112yes—
649C22#1062307612yes—
650C22#1062307612yes—
651C22D4×D4411yescharacteristic
652C22#1062308411yescharacteristic
653C22#1062308512yes—
654C22C4×#434312yes—
655C22#1062310811yescharacteristic
656C22#1062311611yescharacteristic
657C4—24no—
658C4—24no—
659C4—24no—
660C4—28no—
661C4—44no—
662C4—228no—
663C4—444no—
664C4—444no—
665C2—448no—
666C2C4×#6694611yescharacteristic
667C2C42×D4411yescharacteristic
668C2#1307096811yescharacteristic
669C2#1307159812yes—
670C2#1307165512yes—
671C2#1307165612yes—
672C2#1307166311yescharacteristic
673C2#1307166611yescharacteristic
674C2#1307168011yescharacteristic
675C2#1307172611yescharacteristic
676C2#1307174512yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC22×C11C22×C42
FittingC4×C11×#95C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenterC4×#95D11
hypocenterC11#13824
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
3. C2×C4×(C2×D11)⋊C4C2semidirect
4. C2×#10622279C2semidirect
5. #13066854C2semidirect
6. #13066852C2semidirect
7. #13066850C2semidirect
8. C4×C11⋊#95C2semidirect
9. C4×C11×#95C2semidirect
31. #10622552C4semidirect
34. #10622278C4semidirect
55. C22×C4×D11C2×C4semidirect
60. C2×C42×C11C2×C4semidirect
73. C2×(C2×D11)⋊C4C2×C4semidirect
74. C2×(C2×D11)⋊C4C2×C4semidirect
75. C2×(C2×D11)⋊C4C2×C4semidirect
78. C2×C4⋊Dic11C2×C4semidirect
86. C11×#95C2×C4semidirect
87. C11×#95D4semidirect
92. C11⋊#95C2×C4semidirect
93. C11⋊#95D4semidirect
165. C2×D44C42semidirect
191. C4×#95D11semidirect
410. C2×C42C4×D11semidirect
418. #95C4×D11semidirect
419. #95D44semidirect
520. C11#13824semidirect

Maximal subgroups

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

subgroupindex
C2×#106225522
C2×#106222782
C2×C4×(C2×D11)⋊C42
C2×#106222792
#130668542
#130668522
#130668502
C4×C11⋊#952
C4×C11×#952
#1382411