Finite Group Databasebeta

← #14676003

Subgroups — #14676003

Order 2816.

2278 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊C4×D11C211yesmaximal, characteristic
2C2×#10622277C214yesmaximal
3C2×#10622600C211yesmaximal, characteristic
4C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic
5#13066882C214yesmaximal, complemented
6#13066846C211yesmaximal, characteristic, complemented
7#13066845C211yesmaximal, characteristic, complemented
8#13066845C211yesmaximal, characteristic, complemented
9C11×C4⋊#95C211yesmaximal, characteristic, complemented
10C23×C4×D11C2212yes—
11C23×C4×D11C2211yescharacteristic
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C42×C11C2211yescharacteristic
15C22×(C2×D11)⋊C4C2212yes—
16C22×(C2×D11)⋊C4C2212yes—
17C22×C4⋊Dic11C2211yescharacteristic
18C22×C4⋊Dic11C2211yescharacteristic
19C22×Dic11⋊C4C2212yes—
20C22×C4×Dic11C2211yescharacteristic
21C2×C4⋊C4×D11—24no—
22C2×C4⋊C4×D11—24no—
23C2×C4⋊C4×D11C418yescomplemented
24C2×C11×#95C2214yes—
25C2×C11⋊#95C2214yes—
26C2×C11⋊#95C2214yes—
27C2×C11⋊#95C2214yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30#10622600—24no—
31C4×(C2×D11)⋊C4—24no—
32#10622277—216no—
33C24×D11C2311yescharacteristic
34C23×C4×C11C2312yes—
35C23×C4×C11C2312yes—
36C23×C4×C11C2312yes—
37C23×C4×C11C2311yescharacteristic
38C23×Dic11C2312yes—
39C23×Dic11C2312yes—
40C23×Dic11C2312yes—
41C23×Dic11C2311yescharacteristic
42C22×C4×D11—22no—
43C22×C4×D11—22no—
44C22×C4×D11—22no—
45C22×C4×D11—22no—
46C22×C4×D11—24no—
47C22×C4×D11—24no—
48C22×C4×D11—28no—
49C22×C4×D11—28no—
50C22×C4×D11C2×C418yes—
51C22×C4×D11C2×C414yes—
52C22×C4×D11D414yes—
53C22×C4×D11D414yes—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4—22no—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4C2×C414yes—
60C2×C42×C11—22no—
61C2×C42×C11—22no—
62C2×C42×C11—22no—
63C2×(C2×D11)⋊C4—24no—
64C2×(C2×D11)⋊C4—24no—
65C2×(C2×D11)⋊C4—28no—
66C2×(C2×D11)⋊C4—24no—
67C2×(C2×D11)⋊C4D418yes—
68C2×C4⋊Dic11—22no—
69C2×C4⋊Dic11—22no—
70C2×C4⋊Dic11—22no—
71C2×C4⋊Dic11—22no—
72C2×C4⋊Dic11—22no—
73C2×C4⋊Dic11C2×C414yes—
74C2×Dic11⋊C4—24no—
75C2×Dic11⋊C4—24no—
76C2×Dic11⋊C4C2×C418yes—
77C2×C4×Dic11—22no—
78C2×C4×Dic11—22no—
79C2×C4×Dic11—22no—
80C4⋊C4×D11—232no—
81C11×#95—28no—
82C11⋊#95—28no—
83C11⋊#95—28no—
84C11⋊#95—28no—
85C11⋊#95—24no—
86C11⋊#95—24no—
87#13904—111nomaximal, Sylow
88C24×C11C2411yescharacteristic
89C23×D11—21no—
90C23×D11—21no—
91C23×D11—21no—
92C23×D11—21no—
93C23×D11—22no—
94C23×D11—22no—
95C23×D11C22×C412yes—
96C23×D11C2×D412yes—
97C23×D11C2×D412yes—
98C23×D11C2×D414yes—
99C23×D11#4114yes—
100C22×C4×C11—24no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—24no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—24no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—24no—
115C22×C4×C11C22×C414yes—
116C22×C4×C11C22×C412yes—
117C22×C4×C11C2×D414yes—
118C22×C4×C11C2×D412yes—
119C22×C4×C11C2×D412yes—
120C22×C4×C11#4112yes—
121C22×C4×C11#4112yes—
122C22×C4×C11#4112yes—
123C22×C4×C11#4112yes—
124C22×Dic11—24no—
125C22×Dic11—22no—
126C22×Dic11—22no—
127C22×Dic11—22no—
128C22×Dic11—24no—
129C22×Dic11—22no—
130C22×Dic11—21no—
131C22×Dic11—21no—
132C22×Dic11—21no—
133C22×Dic11—21no—
134C22×Dic11—22no—
135C22×Dic11—22no—
136C22×Dic11—22no—
137C22×Dic11—24no—
138C22×Dic11—22no—
139C22×Dic11—22no—
140C22×Dic11—22no—
141C22×Dic11—22no—
142C22×Dic11—24no—
143C22×Dic11C22×C414yes—
144C22×Dic11C22×C412yes—
145C22×Dic11C2×D414yes—
146C22×Dic11C2×D412yes—
147C22×Dic11C2×D412yes—
148C2×C4×D11—216no—
149C2×C4×D11—232no—
150C2×C4×D11—28no—
151C2×C4×D11—28no—
152C2×C4×D11—28no—
153C2×C4×D11—28no—
154C2×C4×D11—28no—
155C2×C4×D11—28no—
156C2×C4×D11—416no—
157C2×C4×D11—48no—
158C2×C4×D11—48no—
159C2×C4×D11C22⋊C4116yes—
160C11×C4⋊C4—28no—
161C11×C4⋊C4—44no—
162C42×C11—44no—
163(C2×D11)⋊C4—216no—
164(C2×D11)⋊C4—48no—
165C4⋊Dic11—28no—
166C4⋊Dic11—44no—
167Dic11⋊C4—216no—
168C4×Dic11—44no—
169C23×C4⋊C4—111no—
170C2×#381—114no—
171C2×#380—111no—
172C2×C4×C22⋊C4—111no—
173#1445—114no—
174C4⋊#95—111no—
175C4⋊#95—111no—
176C4⋊#95—111no—
177C4⋊#95D1111yescharacteristic, complemented
178C23×C11C23×C411yescharacteristic
179C23×C11C22×D411yescharacteristic
180C23×C11C22×D411yescharacteristic
181C23×C11C22×D412yes—
182C23×C11C2×#4111yescharacteristic
183C23×C11C2×#4111yescharacteristic
184C23×C11C2×#4111yescharacteristic
185C23×C11C2×#4111yescharacteristic
186C23×C11C2×#4112yes—
187C23×C112−1+412yes—
188C23×C112−1+412yes—
189C22×D11—22no—
190C22×D11—22no—
191C22×D11—24no—
192C22×D11—22no—
193C22×D11—22no—
194C22×D11—22no—
195C22×D11—22no—
196C22×D11—22no—
197C22×D11—24no—
198C22×D11—22no—
199C22×D11—24no—
200C22×D11—24no—
201C22×D11—24no—
202C22×D11—24no—
203C22×D11—24no—
204C22×D11—24no—
205C22×D11—24no—
206C22×D11—24no—
207C22×D11C2×C22⋊C414yes—
208C22×D11C4×D418yes—
209C22×D11#12118yes—
210C22×D11#12414yes—
211C22×D11#12714yes—
212C2×C4×C11—24no—
213C2×C4×C11—28no—
214C2×C4×C11—24no—
215C2×C4×C11—24no—
216C2×C4×C11—24no—
217C2×C4×C11—44no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11—44no—
228C2×C4×C11—44no—
229C2×C4×C11C2×C22⋊C414yes—
230C2×C4×C11#11714yes—
231C2×C4×C11#11714yes—
232C2×C4×C11#12314yes—
233C2×C4×C11#12314yes—
234C2×C4×C11#12314yes—
235C2×C4×C11#12314yes—
236C2×Dic11—22no—
237C2×Dic11—22no—
238C2×Dic11—22no—
239C2×Dic11—22no—
240C2×Dic11—22no—
241C2×Dic11—22no—
242C2×Dic11—24no—
243C2×Dic11—28no—
244C2×Dic11—24no—
245C2×Dic11—24no—
246C2×Dic11—24no—
247C2×Dic11—44no—
248C2×Dic11—42no—
249C2×Dic11—42no—
250C2×Dic11—42no—
251C2×Dic11—42no—
252C2×Dic11—42no—
253C2×Dic11—42no—
254C2×Dic11—42no—
255C2×Dic11—42no—
256C2×Dic11—42no—
257C2×Dic11—44no—
258C2×Dic11—44no—
259C2×Dic11C2×C22⋊C414yes—
260C4×D11—232no—
261C4×D11—432no—
262C24×C4—111no—
263C24×C4—112no—
264C22×C4⋊C4—112no—
265C22×C4⋊C4—111no—
266C22×C4⋊C4—118no—
267C22×C4⋊C4—111no—
268C22×C4⋊C4—224no—
269C22×C4⋊C4—224no—
270C22×C4⋊C4C2×D1111yescharacteristic
271C22×C4⋊C4C2×D1111yescharacteristic
272C22×C22⋊C4—112no—
273C22×C22⋊C4—112no—
274C22×C42—111no—
275C22×C42C2×D1111yescharacteristic
276#381—2216no—
277#380—224no—
278C4×C22⋊C4—224no—
279C2×#95—114no—
280C2×#95—114no—
281C2×#95—114no—
282C2×#95—112no—
283C2×#95—112no—
284C2×#95C2×D1114yes—
285C22×C11C22×C22⋊C411yescharacteristic
286C22×C11C2×#11711yescharacteristic
287C22×C11C2×#11711yescharacteristic
288C22×C11C2×C4×D412yes—
289C22×C11#51912yes—
290C22×C11C2×#12112yes—
291C22×C11C2×#12311yescharacteristic
292C22×C11C2×#12311yescharacteristic
293C22×C11C2×#12311yescharacteristic
294C22×C11C2×#12311yescharacteristic
295C22×C11C2×#12411yescharacteristic
296C22×C11C2×#12711yescharacteristic
297C22×C11#53611yescharacteristic
298C22×C11#53612yes—
299C22×C11#53611yescharacteristic
300C22×C11#54712yes—
301C22×C11#54712yes—
302C22×C11#54712yes—
303C22×C11#54712yes—
304C22×C11#55212yes—
305C22×C11#55212yes—
306C22×C11#55212yes—
307C22×C11#55212yes—
308C2×D11—24no—
309C2×D11—28no—
310C2×D11—28no—
311C2×D11—28no—
312C2×D11—28no—
313C2×D11—24no—
314C2×D11—24no—
315C2×D11—24no—
316C2×D11—24no—
317C2×D11—24no—
318C2×D11#39018yes—
319C4×C11—44no—
320C4×C11—44no—
321C4×C11—82no—
322C4×C11#38118yescomplemented
323Dic11—24no—
324Dic11—44no—
325Dic11—44no—
326Dic11—82no—
327C25—111no—
328C23×C4—111no—
329C23×C4—114no—
330C23×C4—114no—
331C23×C4—114no—
332C23×C4—112no—
333C23×C4—112no—
334C23×C4—118no—
335C23×C4—112no—
336C23×C4—224no—
337C23×C4—224no—
338C23×C4—228no—
339C23×C4—228no—
340C23×C4—222no—
341C23×C4—222no—
342C23×C4—222no—
343C23×C4—222no—
344C23×C4C22×D1112yes—
345C23×C4C22×D1112yes—
346C23×C4C22×D1112yes—
347C23×C4C22×D1111yescharacteristic
348C2×C4⋊C4—22no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—118no—
354C2×C4⋊C4—114no—
355C2×C4⋊C4—2232no—
356C2×C4⋊C4—224no—
357C2×C4⋊C4—224no—
358C2×C4⋊C4—222no—
359C2×C4⋊C4—222no—
360C2×C4⋊C4—222no—
361C2×C4⋊C4—222no—
362C2×C4⋊C4—222no—
363C2×C4⋊C4C4×D1114yes—
364C2×C22⋊C4—118no—
365C2×C22⋊C4—224no—
366C2×C22⋊C4—224no—
367C2×C22⋊C4—224no—
368C2×C22⋊C4—228no—
369C2×C42—22no—
370C2×C42—22no—
371C2×C42—22no—
372C2×C42—222no—
373C2×C42—222no—
374C2×C42—222no—
375#95—28no—
376#95—224no—
377#95—224no—
378#95—228no—
379#95—228no—
380#95—228no—
381C2×C11C2×#38111yescharacteristic
382C2×C11C2×#39011yescharacteristic
383C2×C11#231011yescharacteristic
384C2×C11#234412yes—
385C2×C11#234412yes—
386C2×C11#248612yes—
387C2×C11#248612yes—
388C2×C11#250111yescharacteristic
389C2×C11#250111yescharacteristic
390C2×C11#250311yescharacteristic
391C2×C11#250311yescharacteristic
392D11—28no—
393C24—112no—
394C24—114no—
395C24—112no—
396C24—112no—
397C24—114no—
398C24—221no—
399C24—221no—
400C24—221no—
401C24—221no—
402C24—222no—
403C24—222no—
404C24C23×D1111yescharacteristic
405C22×C4—22no—
406C22×C4—24no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—24no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—24no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—24no—
420C22×C4—112no—
421C22×C4—112no—
422C22×C4—112no—
423C22×C4—1116no—
424C22×C4—114no—
425C22×C4—114no—
426C22×C4—2216no—
427C22×C4—2232no—
428C22×C4—221no—
429C22×C4—221no—
430C22×C4—221no—
431C22×C4—221no—
432C22×C4—228no—
433C22×C4—228no—
434C22×C4—228no—
435C22×C4—228no—
436C22×C4—228no—
437C22×C4—228no—
438C22×C4—222no—
439C22×C4—224no—
440C22×C4—222no—
441C22×C4—222no—
442C22×C4—222no—
443C22×C4—222no—
444C22×C4—222no—
445C22×C4—222no—
446C22×C4—224no—
447C22×C4—222no—
448C22×C4—222no—
449C22×C4—224no—
450C22×C4—222no—
451C22×C4—222no—
452C22×C4—224no—
453C22×C4—448no—
454C22×C4—4416no—
455C22×C4—448no—
456C22×C4C2×C4×D1114yes—
457C22×C4C2×C4×D1112yes—
458C22×C4#433912yes—
459C22×C4#433912yes—
460C22×C4D4×D1114yes—
461C22×C4D4×D1112yes—
462C22×C4D4×D1112yes—
463C22×C4#434112yes—
464C22×C4#434312yes—
465C4⋊C4—28no—
466C4⋊C4—44no—
467C4⋊C4—2216no—
468C4⋊C4—228no—
469C4⋊C4—444no—
470C22⋊C4—2216no—
471C22⋊C4—448no—
472C42—44no—
473C42—444no—
474C11#1390411yescharacteristic, complemented, Sylow
475C23—114no—
476C23—114no—
477C23—118no—
478C23—118no—
479C23—114no—
480C23—222no—
481C23—224no—
482C23—222no—
483C23—222no—
484C23—222no—
485C23—222no—
486C23—222no—
487C23—222no—
488C23—224no—
489C23—224no—
490C23—224no—
491C23—224no—
492C23—224no—
493C23—224no—
494C23—224no—
495C23—224no—
496C23—222no—
497C23—224no—
498C23C22×C4×D1111yescharacteristic
499C23C2×#433911yescharacteristic
500C23C2×#433911yescharacteristic
501C23C2×D4×D1111yescharacteristic
502C23C2×D4×D1112yes—
503C23C2×D4×D1111yescharacteristic
504C23C2×#434111yescharacteristic
505C23C2×#434311yescharacteristic
506C23#6704012yes—
507C23#41×D1112yes—
508C23#6704312yes—
509C2×C4—24no—
510C2×C4—24no—
511C2×C4—28no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—44no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—44no—
524C2×C4—44no—
525C2×C4—42no—
526C2×C4—114no—
527C2×C4—222no—
528C2×C4—222no—
529C2×C4—222no—
530C2×C4—222no—
531C2×C4—222no—
532C2×C4—222no—
533C2×C4—2232no—
534C2×C4—224no—
535C2×C4—224no—
536C2×C4—228no—
537C2×C4—224no—
538C2×C4—224no—
539C2×C4—4432no—
540C2×C4—442no—
541C2×C4—442no—
542C2×C4—442no—
543C2×C4—444no—
544C2×C4—442no—
545C2×C4—442no—
546C2×C4—442no—
547C2×C4—442no—
548C2×C4—442no—
549C2×C4—444no—
550C2×C4—442no—
551C2×C4—444no—
552C2×C4#6692514yes—
553C2×C4C22⋊C4×D1114yes—
554C2×C4#6693614yes—
555C2×C4#6693614yes—
556C2×C4#6694514yes—
557C2×C4#6694714yes—
558C2×C4#6694714yes—
559C22—118no—
560C22—228no—
561C22—228no—
562C22—224no—
563C22—228no—
564C22—228no—
565C22—224no—
566C22—224no—
567C22—224no—
568C22—224no—
569C22—224no—
570C22C2×#6692511yescharacteristic
571C22C2×C22⋊C4×D1111yescharacteristic
572C22C2×#6693611yescharacteristic
573C22C2×#6693611yescharacteristic
574C22C2×#6694511yescharacteristic
575C22C2×#6694711yescharacteristic
576C22C2×#6694711yescharacteristic
577C22#1062303812yes—
578C22#1062306012yes—
579C22C4×D4×D1112yes—
580C22#1062308212yes—
581C22#1062310312yes—
582C22#1062311212yes—
583C22D11×#12112yes—
584C22#1062314212yes—
585C22#1062315912yes—
586C22#1062317012yes—
587C22D11×#12411yescharacteristic
588C22#1062320611yescharacteristic
589C22#1062322512yes—
590C22D11×#12711yescharacteristic
591C22#1062325511yescharacteristic
592C22#1062325712yes—
593C4—44no—
594C4—44no—
595C4—82no—
596C4—224no—
597C4—444no—
598C4—444no—
599C4—882no—
600C4#1062227718yescomplemented
601C2—228no—
602C2C2×#1062227711yescharacteristic
603C2D11×#39011yescharacteristic
604C2#1307119911yescharacteristic
605C2#1307148112yes—
606C2#1307148412yes—
607C2#1307292012yes—
608C2#1307292212yes—
609C2#1307308411yescharacteristic
610C2#1307308611yescharacteristic
611C2#1307309811yescharacteristic
612C2#1307310011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C4⋊#95C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenterC4⋊#95D11
hypocenterC11#13904
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
5. #13066882C2semidirect
6. #13066846C2semidirect
7. #13066845C2semidirect
8. #13066845C2semidirect
9. C11×C4⋊#95C2semidirect
23. C2×C4⋊C4×D11C4semidirect
177. C4⋊#95D11semidirect
322. C4×C11#381semidirect
474. C11#13904semidirect
600. C4#10622277semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊C4×D112
C2×#106222772
C2×#106226002
C2×C4×(C2×D11)⋊C42
#130668822
#130668462
#130668452
C11×C4⋊#952
#1390411