Finite Group Databasebeta

← #14675372

Subgroups — #14675372

Order 2816.

2390 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622601C211yesmaximal, characteristic
2C2×#10622278C212yesmaximal
3C2×C4×(C2×D11)⋊C4C212yesmaximal, complemented
4C2×#10622279C212yesmaximal, complemented
5#13066852C212yesmaximal, complemented
6#13066852C212yesmaximal, complemented
7#13066848C211yesmaximal, characteristic, complemented
8#95×Dic11C212yesmaximal, complemented
9C11×#1436C211yesmaximal, characteristic, complemented
10C23×D44C2211yescharacteristic
11C23×C4×D11C2212yes—
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×C4×Dic11C2212yes—
20C22×C4×Dic11C2212yes—
21C22×C4×Dic11C2211yescharacteristic
22C22×C4×Dic11C2211yescharacteristic
23C2×C11×#95C2212yes—
24C2×C11×#95C2211yescharacteristic
25C2×C11×#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2211yescharacteristic
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31#10622601C418yescomplemented
32C4×(C2×D11)⋊C4—28no—
33#10622279—28no—
34#10622278C4116yescomplemented
35C24×D11C2312yes—
36C23×C4×C11C2312yes—
37C23×C4×C11C2311yescharacteristic
38C23×C4×C11C2311yescharacteristic
39C23×C4×C11C2311yescharacteristic
40C23×C4×C11C2312yes—
41C23×Dic11C2312yes—
42C23×Dic11C2312yes—
43C23×Dic11C2312yes—
44C22×D44—42no—
45C22×D44—41no—
46C22×D44—41no—
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×C11×C4⋊C4—41no—
57C2×C11×C4⋊C4—41no—
58C2×C11×C4⋊C4C2×C414yescomplemented
59C2×C42×C11—24no—
60C2×C42×C11—41no—
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—24no—
77C2×C4×Dic11—24no—
78C2×C4×Dic11—24no—
79C2×C4×Dic11—24no—
80C2×C4×Dic11—24no—
81C2×C4×Dic11—42no—
82C2×C4×Dic11—42no—
83C2×C4×Dic11—42no—
84C2×C4×Dic11—41no—
85C2×C4×Dic11C2×C414yescomplemented
86C11×#95—24no—
87C11×#95—41no—
88C11×#95C2×C418yescomplemented
89C11⋊#95—24no—
90C11⋊#95—24no—
91C11⋊#95—41no—
92C11⋊#95C2×C418yescomplemented
93C11⋊#95D418yescomplemented
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—21no—
117C22×C4×C11—21no—
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—21no—
127C22×C4×C11—22no—
128C22×C4×C11—21no—
129C22×C4×C11—22no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11C22×C414yes—
133C22×C4×C11C22×C412yes—
134C22×C4×C11C22×C412yes—
135C22×C4×C11C22×C414yes—
136C22×C4×C11C22×C412yes—
137C22×C4×C11C22×C414yes—
138C22×C4×C11C2×D414yes—
139C22×C4×C11#4114yes—
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×Dic11C22×C414yes—
156C22×Dic11C22×C414yes—
157C22×Dic11C2×D414yes—
158C22×Dic11C2×D414yes—
159C22×Dic11#4114yes—
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—
173C11×C4⋊C4—44no—
174C42×C11—44no—
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—44no—
183C4×Dic11—48no—
184C2×#390—111no—
185C2×#386—112no—
186C2×C4×C22⋊C4—112no—
187C2×C4×C22⋊C4—112no—
188#1437—112no—
189#1437—112no—
190#1436—111no—
191#1436D1111yescharacteristic, complemented
192C4×#95—112no—
193C23×C11C23×C411yescharacteristic
194C23×C11C23×C412yes—
195C23×C11C22×D412yes—
196C23×C11C2×#4112yes—
197C23×C11C2×#4112yes—
198C23×C11C2×#4112yes—
199C23×C11H(5,𝔽2)11yescharacteristic
200C23×C11H(5,𝔽2)11yescharacteristic
201C23×C11H(5,𝔽2)12yes—
202C22×D11—24no—
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—42no—
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×D11C2×C4218yes—
237C2×C4×C11—24no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—24no—
241C2×C4×C11—24no—
242C2×C4×C11—24no—
243C2×C4×C11—24no—
244C2×C4×C11—24no—
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—22no—
253C2×C4×C11—22no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—42no—
257C2×C4×C11—42no—
258C2×C4×C11—42no—
259C2×C4×C11—42no—
260C2×C4×C11—42no—
261C2×C4×C11—42no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11C2×C4214yes—
265C2×C4×C11C4×D418yes—
266C2×Dic11—24no—
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—24no—
280C2×Dic11—24no—
281C2×Dic11—42no—
282C2×Dic11—42no—
283C2×Dic11—42no—
284C2×Dic11—42no—
285C2×Dic11C4×D418yes—
286C2×Dic11C4×D418yes—
287D44—416no—
288C4×D11—432no—
289C23×D4—111no—
290C24×C4—112no—
291C22×C4⋊C4C2×D1111yescharacteristic
292C22×C22⋊C4—112no—
293C22×C22⋊C4—112no—
294C22×C22⋊C4—112no—
295C22×C22⋊C4—112no—
296C22×C22⋊C4—112no—
297C22×C42—111no—
298C22×C42—112no—
299C22×C42—112no—
300C22×C42—111no—
301C22×C42C2×D1111yescharacteristic
302#390—118no—
303#386—1116no—
304C4×C22⋊C4—228no—
305C4×C22⋊C4—228no—
306C2×#95—112no—
307C2×#95—112no—
308C2×#95—112no—
309C2×#95—112no—
310C2×#95—111no—
311C2×#95C2×D1112yes—
312C2×#95C2×D1111yescharacteristic
313C2×#95C2×D1112yes—
314C22×C11C22×C4211yescharacteristic
315C22×C11C2×C4×D412yes—
316C22×C11C2×C4×D412yes—
317C22×C11C2×C4×D412yes—
318C22×C11C4×#4112yes—
319C22×C11C4×#4112yes—
320C22×C11C4×#4112yes—
321C22×C11#51811yescharacteristic
322C22×C11#51811yescharacteristic
323C22×C11#51812yes—
324C22×C11#51812yes—
325C22×C11D4211yescharacteristic
326C22×C11#54612yes—
327C22×C11#54612yes—
328C22×C11#55012yes—
329C22×C11#55112yes—
330C22×C11#55312yes—
331C22×C11#55312yes—
332C22×C11#55511yescharacteristic
333C22×C11#55511yescharacteristic
334C22×C11#55911yescharacteristic
335C2×D11—28no—
336C2×D11—28no—
337C2×D11—28no—
338C2×D11—44no—
339C2×D11—44no—
340C2×D11—44no—
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—
350C4×C11—28no—
351C4×C11—24no—
352C4×C11—44no—
353C4×C11—42no—
354C4×C11—42no—
355Dic11—28no—
356Dic11—28no—
357Dic11—44no—
358C25—112no—
359C22×D4—118no—
360C22×D4—114no—
361C22×D4—441no—
362C22×D4—441no—
363C22×D4—442no—
364C23×C4—112no—
365C23×C4—112no—
366C23×C4—112no—
367C23×C4—118no—
368C23×C4—224no—
369C23×C4—224no—
370C23×C4—224no—
371C23×C4—224no—
372C23×C4—442no—
373C23×C4—442no—
374C23×C4C22×D1111yescharacteristic
375C23×C4C22×D1111yescharacteristic
376C23×C4C22×D1112yes—
377C23×C4C22×D1111yescharacteristic
378C23×C4C22×D1112yes—
379C2×C4⋊C4—41no—
380C2×C4⋊C4—41no—
381C2×C4⋊C4C4×D1114yescomplemented
382C2×C22⋊C4—118no—
383C2×C22⋊C4—118no—
384C2×C22⋊C4—118no—
385C2×C22⋊C4—118no—
386C2×C22⋊C4—118no—
387C2×C22⋊C4—224no—
388C2×C22⋊C4—224no—
389C2×C22⋊C4—224no—
390C2×C22⋊C4—224no—
391C2×C22⋊C4—224no—
392C2×C22⋊C4—224no—
393C2×C22⋊C4—224no—
394C2×C22⋊C4—224no—
395C2×C22⋊C4—442no—
396C2×C22⋊C4—442no—
397C2×C42—24no—
398C2×C42—41no—
399C2×C42—114no—
400C2×C42—224no—
401C2×C42—224no—
402C2×C42—224no—
403C2×C42—224no—
404C2×C42—224no—
405C2×C42—442no—
406C2×C42—442no—
407C2×C42—441no—
408C2×C42—442no—
409#95—24no—
410#95—41no—
411#95—118no—
412#95—118no—
413#95—224no—
414#95—224no—
415#95—441no—
416#95C4×D1118yescomplemented
417C2×C11C42×D412yes—
418C2×C11#227311yescharacteristic
419C2×C11#235812yes—
420C2×C11#236312yes—
421C2×C11#236312yes—
422C2×C11#236412yes—
423C2×C11#236611yescharacteristic
424C2×C11#237211yescharacteristic
425C2×C11#237412yes—
426D11—48no—
427C24—114no—
428C24—114no—
429C24—114no—
430C24—222no—
431C24—222no—
432C24—222no—
433C24—222no—
434C24—222no—
435C24—222no—
436C24—222no—
437C24—222no—
438C24—222no—
439C24—222no—
440C24—222no—
441C24—222no—
442C24C23×D1111yescharacteristic
443C2×D4—1116no—
444C2×D4—444no—
445C2×D4—444no—
446C2×D4—448no—
447C2×D4—448no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—114no—
470C22×C4—114no—
471C22×C4—114no—
472C22×C4—114no—
473C22×C4—114no—
474C22×C4—114no—
475C22×C4—114no—
476C22×C4—2216no—
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—2216no—
492C22×C4—448no—
493C22×C4—448no—
494C22×C4—448no—
495C22×C4—448no—
496C22×C4—448no—
497C22×C4C2×C4×D1114yes—
498C22×C4C2×C4×D1112yes—
499C22×C4C2×C4×D1112yes—
500C22×C4C2×C4×D1114yes—
501C22×C4C2×C4×D1112yes—
502C22×C4C2×C4×D1114yes—
503C22×C4D4×D1114yes—
504C22×C4#434314yes—
505C4⋊C4—44no—
506C22⋊C4—2216no—
507C22⋊C4—2216no—
508C22⋊C4—2216no—
509C22⋊C4—2216no—
510C22⋊C4—448no—
511C42—44no—
512C42—444no—
513C42—448no—
514C42—444no—
515C42—448no—
516C11#1382411yescharacteristic, complemented, Sylow
517C23—118no—
518C23—224no—
519C23—224no—
520C23—224no—
521C23—224no—
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—442no—
537C23—442no—
538C23—442no—
539C23—442no—
540C23—442no—
541C23—442no—
542C23—442no—
543C23—442no—
544C23—442no—
545C23—442no—
546C23—442no—
547C23—442no—
548C23—442no—
549C23—442no—
550C23—442no—
551C23—442no—
552C23C22×C4×D1111yescharacteristic
553C23C22×C4×D1112yes—
554C23C2×D4×D1112yes—
555C23#6703711yescharacteristic
556C23#6703711yescharacteristic
557C23C2×#434312yes—
558C23#41×D1112yes—
559C23#41×D1112yes—
560C23#6704212yes—
561D4—4416no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—42no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—42no—
589C2×C4—118no—
590C2×C4—118no—
591C2×C4—224no—
592C2×C4—224no—
593C2×C4—224no—
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×C4C42×D1114yes—
612C2×C4#6694618yes—
613C22—228no—
614C22—228no—
615C22—228no—
616C22—444no—
617C22—444no—
618C22—444no—
619C22—444no—
620C22—444no—
621C22—444no—
622C22—444no—
623C22—444no—
624C22—444no—
625C22—444no—
626C22—444no—
627C22—444no—
628C22C2×C42×D1111yescharacteristic
629C22#1062301711yescharacteristic
630C22C2×#6694612yes—
631C22#1062305211yescharacteristic
632C22#1062305312yes—
633C22C4×D4×D1112yes—
634C22C4×D4×D1112yes—
635C22#1062307612yes—
636C22#1062307612yes—
637C22C4×#434312yes—
638C22C4×#434312yes—
639C22#1062312111yescharacteristic
640C22#1062313012yes—
641C22#1062316112yes—
642C22#1062316812yes—
643C22#1062318512yes—
644C22#1062319511yescharacteristic
645C22#1062320111yescharacteristic
646C22#1062322612yes—
647C22#1062324012yes—
648C22#1062326511yescharacteristic
649C4—24no—
650C4—28no—
651C4—44no—
652C4—42no—
653C4—42no—
654C4—228no—
655C4—228no—
656C4—444no—
657C2—448no—
658C2C4×#6694612yes—
659C2#1307096811yescharacteristic
660C2#1307159212yes—
661C2#1307164912yes—
662C2#1307165312yes—
663C2#1307166212yes—
664C2#1307167911yescharacteristic
665C2#1307172711yescharacteristic
666C2#1307174812yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC22×C11C22×C42
FittingC11×#1436C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenter#1436D11
hypocenterC11#13824
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
3. C2×C4×(C2×D11)⋊C4C2semidirect
4. C2×#10622279C2semidirect
5. #13066852C2semidirect
6. #13066852C2semidirect
7. #13066848C2semidirect
8. #95×Dic11C2semidirect
9. C11×#1436C2semidirect
31. #10622601C4semidirect
34. #10622278C4semidirect
55. C22×C4×D11C2×C4semidirect
58. C2×C11×C4⋊C4C2×C4semidirect
73. C2×(C2×D11)⋊C4C2×C4semidirect
74. C2×(C2×D11)⋊C4C2×C4semidirect
75. C2×(C2×D11)⋊C4C2×C4semidirect
85. C2×C4×Dic11C2×C4semidirect
88. C11×#95C2×C4semidirect
92. C11⋊#95C2×C4semidirect
93. C11⋊#95D4semidirect
165. C2×D44C42semidirect
191. #1436D11semidirect
381. C2×C4⋊C4C4×D11semidirect
416. #95C4×D11semidirect
516. C11#13824semidirect

Maximal subgroups

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

subgroupindex
C2×#106226012
C2×#106222782
C2×C4×(C2×D11)⋊C42
C2×#106222792
#130668522
#130668482
#95×Dic112
C11×#14362
#1382411