Finite Group Databasebeta

← #14680203

Subgroups — #14680203

Order 2816.

1926 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
1C22×#66945C211yesmaximal, characteristic
2C2×#10622260C212yesmaximal, complemented
3C2×#10622280C211yesmaximal, characteristic
4C2×#10622280C211yesmaximal, characteristic
5#13066881C211yesmaximal, characteristic, complemented
6#13066880C211yesmaximal, characteristic, complemented
7#13066875C211yesmaximal, characteristic, complemented
8#13066862C212yesmaximal
9#13066860C212yesmaximal
10Dic11⋊#95C212yesmaximal, complemented
11C11×#1442C211yesmaximal, characteristic, complemented
12C23×C4×D11C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×(C2×D11)⋊C4C2212yes—
15C22×(C2×D11)⋊C4C2211yescharacteristic
16C22×(C2×D11)⋊C4C2211yescharacteristic
17C22×(C2×D11)⋊C4C2212yes—
18C22×C4⋊Dic11C2211yescharacteristic
19C22×C4⋊Dic11C2212yes—
20C22×Dic11⋊C4C2211yescharacteristic
21C22×Dic11⋊C4C2211yescharacteristic
22C22×Dic11⋊C4C2212yes—
23C22×Dic11⋊C4C2212yes—
24C22×C4×Dic11C2212yes—
25C2×#66945—24no—
26C2×#66945—28no—
27C2×C11×#95C2212yes—
28C2×C11×#95C2211yescharacteristic
29C2×C11×#95C2212yes—
30C2×C11×#95C2211yescharacteristic
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2211yescharacteristic
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2211yescharacteristic
37#10622280—24no—
38#10622280C418yescomplemented
39#10622260—28no—
40C24×D11C2311yescharacteristic
41C23×C4×C11C2311yescharacteristic
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2312yes—
44C23×C4×C11C2312yes—
45C23×C4×C11C2311yescharacteristic
46C23×Dic11C2311yescharacteristic
47C23×Dic11C2311yescharacteristic
48C23×Dic11C2312yes—
49C23×Dic11C2312yes—
50C23×Dic11C2311yescharacteristic
51C22×C4×D11—24no—
52C22×C4×D11—24no—
53C22×C4×D11C2×C414yes—
54C22×C4×D11D414yes—
55C22×C4×D11Q814yes—
56C2×C11×C4⋊C4—24no—
57C2×C11×C4⋊C4—22no—
58C2×(C2×D11)⋊C4—24no—
59C2×(C2×D11)⋊C4—24no—
60C2×(C2×D11)⋊C4—24no—
61C2×(C2×D11)⋊C4—22no—
62C2×(C2×D11)⋊C4—22no—
63C2×(C2×D11)⋊C4—42no—
64C2×(C2×D11)⋊C4—42no—
65C2×(C2×D11)⋊C4—42no—
66C2×(C2×D11)⋊C4—42no—
67C2×(C2×D11)⋊C4C2×C418yes—
68C2×C4⋊Dic11—22no—
69C2×C4⋊Dic11—24no—
70C2×C4⋊Dic11—24no—
71C2×C4⋊Dic11—42no—
72C2×C4⋊Dic11—42no—
73C2×Dic11⋊C4—24no—
74C2×Dic11⋊C4—24no—
75C2×Dic11⋊C4—24no—
76C2×Dic11⋊C4—24no—
77C2×Dic11⋊C4—22no—
78C2×Dic11⋊C4—22no—
79C2×Dic11⋊C4—24no—
80C2×Dic11⋊C4—42no—
81C2×Dic11⋊C4—42no—
82C2×Dic11⋊C4C2×C418yes—
83C2×C4×Dic11—24no—
84C2×C4×Dic11—24no—
85C2×C4×Dic11D418yes—
86#66945—232no—
87C11×#95—24no—
88C11×#95—22no—
89C11×#95—42no—
90C11×#95C2×C414yes—
91C11⋊#95—24no—
92C11⋊#95—22no—
93C11⋊#95—42no—
94C11⋊#95—42no—
95C11⋊#95—42no—
96C11⋊#95C2×C414yes—
97#14264—111nomaximal, Sylow
98C24×C11C2411yescharacteristic
99C23×D11—22no—
100C23×D11—22no—
101C23×D11—21no—
102C23×D11—21no—
103C23×D11—22no—
104C23×D11—21no—
105C23×D11—21no—
106C23×D11—22no—
107C23×D11C22×C412yes—
108C23×D11C2×D412yes—
109C23×D11C2×Q812yes—
110C22×C4×C11—22no—
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—22no—
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—21no—
126C22×C4×C11—21no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—22no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11C22×C414yes—
135C22×C4×C11C22×C412yes—
136C22×C4×C11C2×D414yes—
137C22×C4×C11C2×D412yes—
138C22×C4×C11C2×Q812yes—
139C22×Dic11—22no—
140C22×Dic11—22no—
141C22×Dic11—22no—
142C22×Dic11—22no—
143C22×Dic11—21no—
144C22×Dic11—21no—
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—21no—
154C22×Dic11—22no—
155C22×Dic11—21no—
156C22×Dic11—22no—
157C22×Dic11—22no—
158C22×Dic11—22no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11C22×C414yes—
162C22×Dic11C22×C412yes—
163C22×Dic11C2×D414yes—
164C22×Dic11C2×D412yes—
165C22×Dic11C2×D414yes—
166C22×Dic11C2×Q812yes—
167C22×Dic11#4114yes—
168C2×C4×D11—216no—
169C2×C4×D11—28no—
170C2×C4×D11—216no—
171C2×C4×D11—28no—
172C2×C4×D11C4⋊C4116yescomplemented
173C11×C4⋊C4—28no—
174(C2×D11)⋊C4—216no—
175(C2×D11)⋊C4—48no—
176(C2×D11)⋊C4—44no—
177(C2×D11)⋊C4—44no—
178C4⋊Dic11—28no—
179C4⋊Dic11—48no—
180Dic11⋊C4—216no—
181Dic11⋊C4—48no—
182Dic11⋊C4—44no—
183Dic11⋊C4—44no—
184C4×Dic11—216no—
185C22×#117—111no—
186C2×#389—112no—
187C2×#380—111no—
188C2×#380—111no—
189#1444—111no—
190#1444—111no—
191#1442—111no—
192#1442D1111yescharacteristic, complemented
193#1439—112no—
194#1439—112no—
195C4⋊#95—112no—
196C23×C11C23×C411yescharacteristic
197C23×C11C22×D411yescharacteristic
198C23×C11C22×D412yes—
199C23×C11C22×Q811yescharacteristic
200C23×C11C2×#4112yes—
201C23×C11H(5,𝔽2)11yescharacteristic
202C23×C11H(5,𝔽2)11yescharacteristic
203C23×C11H(5,𝔽2)12yes—
204C23×C112−1+411yescharacteristic
205C23×C112−1+411yescharacteristic
206C23×C112−1+412yes—
207C22×D11—24no—
208C22×D11—22no—
209C22×D11—22no—
210C22×D11—24no—
211C22×D11—22no—
212C22×D11—24no—
213C22×D11—22no—
214C22×D11—22no—
215C22×D11—22no—
216C22×D11—22no—
217C22×D11—22no—
218C22×D11—22no—
219C22×D11—22no—
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×D11C2×C4⋊C414yes—
230C2×C4×C11—24no—
231C2×C4×C11—22no—
232C2×C4×C11—24no—
233C2×C4×C11—22no—
234C2×C4×C11—24no—
235C2×C4×C11—24no—
236C2×C4×C11—24no—
237C2×C4×C11—24no—
238C2×C4×C11—24no—
239C2×C4×C11—24no—
240C2×C4×C11—42no—
241C2×C4×C11—42no—
242C2×C4×C11—42no—
243C2×C4×C11—42no—
244C2×C4×C11—42no—
245C2×C4×C11—42no—
246C2×C4×C11—42no—
247C2×C4×C11—42no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—42no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—42no—
256C2×C4×C11—42no—
257C2×C4×C11—42no—
258C2×C4×C11C2×C4⋊C414yes—
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—41no—
274C2×Dic11—41no—
275C2×Dic11—42no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—42no—
281C2×Dic11—42no—
282C2×Dic11—42no—
283C2×Dic11C2×C4⋊C414yes—
284C2×Dic11C4×D418yes—
285C2×Dic11#12014yes—
286C2×Dic11C22⋊Q818yes—
287C2×Dic11#12314yes—
288C4×D11—232no—
289C24×C4—111no—
290C2×#117—228no—
291C2×#117—224no—
292C22×C4⋊C4—112no—
293C22×C4⋊C4—111no—
294C22×C4⋊C4—111no—
295C22×C4⋊C4—111no—
296C22×C4⋊C4—112no—
297C22×C4⋊C4—112no—
298C22×C4⋊C4C2×D1111yescharacteristic
299C22×C22⋊C4—112no—
300C22×C22⋊C4—112no—
301C22×C22⋊C4—111no—
302C22×C22⋊C4—111no—
303C22×C42—112no—
304#389—228no—
305#380—118no—
306#380—224no—
307C2×#95—111no—
308C2×#95—112no—
309C2×#95—111no—
310C2×#95—112no—
311C2×#95—112no—
312C2×#95—112no—
313C2×#95C2×D1112yes—
314C2×#95C2×D1111yescharacteristic
315C2×#95C2×D1112yes—
316C2×#95C2×D1111yescharacteristic
317C22×C11C22×C4⋊C411yescharacteristic
318C22×C11C2×C4×D412yes—
319C22×C11#51811yescharacteristic
320C22×C11#51911yescharacteristic
321C22×C11#52012yes—
322C22×C11C2×#12011yescharacteristic
323C22×C11C2×C22⋊Q812yes—
324C22×C11C2×#12311yescharacteristic
325C22×C11#53511yescharacteristic
326C22×C11#53512yes—
327C22×C11#53612yes—
328C22×C11#53611yescharacteristic
329C22×C11#53712yes—
330C22×C11#53711yescharacteristic
331C22×C11#53711yescharacteristic
332C22×C11#53712yes—
333C22×C11#54012yes—
334C22×C11#54112yes—
335C22×C11#54212yes—
336C22×C11#54212yes—
337C22×C11#54411yescharacteristic
338C22×C11#54411yescharacteristic
339C22×C11#54412yes—
340C2×D11—24no—
341C2×D11—24no—
342C2×D11—24no—
343C2×D11—44no—
344C2×D11—44no—
345C2×D11—42no—
346C2×D11—42no—
347C2×D11—42no—
348C2×D11—42no—
349C2×D11—44no—
350C2×D11—44no—
351C4×C11—24no—
352C4×C11—44no—
353C4×C11—44no—
354C4×C11—81no—
355C4×C11—81no—
356Dic11—44no—
357Dic11—44no—
358Dic11—81no—
359Dic11—81no—
360Dic11#38518yes—
361C25—111no—
362C23×C4—111no—
363C23×C4—114no—
364C23×C4—114no—
365C23×C4—114no—
366C23×C4—112no—
367C23×C4—112no—
368C23×C4—111no—
369C23×C4—111no—
370C23×C4—224no—
371C23×C4—224no—
372C23×C4C22×D1111yescharacteristic
373C23×C4C22×D1111yescharacteristic
374C23×C4C22×D1112yes—
375C23×C4C22×D1112yes—
376C23×C4C22×D1111yescharacteristic
377#117—2232no—
378C2×C4⋊C4—24no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—118no—
381C2×C4⋊C4—224no—
382C2×C4⋊C4—224no—
383C2×C4⋊C4—224no—
384C2×C4⋊C4—222no—
385C2×C4⋊C4—222no—
386C2×C4⋊C4—222no—
387C2×C4⋊C4—224no—
388C2×C4⋊C4—224no—
389C2×C4⋊C4—224no—
390C2×C4⋊C4—224no—
391C2×C4⋊C4—442no—
392C2×C4⋊C4—442no—
393C2×C4⋊C4—442no—
394C2×C4⋊C4—442no—
395C2×C22⋊C4—118no—
396C2×C22⋊C4—224no—
397C2×C22⋊C4—224no—
398C2×C22⋊C4—224no—
399C2×C22⋊C4—222no—
400C2×C22⋊C4—222no—
401C2×C22⋊C4—442no—
402C2×C22⋊C4—442no—
403C2×C22⋊C4—442no—
404C2×C22⋊C4—442no—
405C2×C42—118no—
406C2×C42—224no—
407C2×C42—224no—
408#95—22no—
409#95—24no—
410#95—42no—
411#95—114no—
412#95—222no—
413#95—224no—
414#95—442no—
415#95—442no—
416#95—442no—
417#95C4×D1114yes—
418C2×C11C2×#38511yescharacteristic
419C2×C11#231611yescharacteristic
420C2×C11#231711yescharacteristic
421C2×C11#232312yes—
422C2×C11#232412yes—
423C2×C11#261511yescharacteristic
424C2×C11#261611yescharacteristic
425C2×C11#262411yescharacteristic
426C2×C11#262511yescharacteristic
427C2×C11#262812yes—
428C2×C11#262912yes—
429D11—44no—
430C24—112no—
431C24—112no—
432C24—112no—
433C24—222no—
434C24—221no—
435C24—221no—
436C24—222no—
437C24—222no—
438C24—221no—
439C24—222no—
440C24—221no—
441C24C23×D1111yescharacteristic
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—112no—
467C22×C4—114no—
468C22×C4—112no—
469C22×C4—112no—
470C22×C4—114no—
471C22×C4—1116no—
472C22×C4—114no—
473C22×C4—114no—
474C22×C4—228no—
475C22×C4—2216no—
476C22×C4—2216no—
477C22×C4—228no—
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—221no—
491C22×C4—221no—
492C22×C4—222no—
493C22×C4—221no—
494C22×C4—221no—
495C22×C4—222no—
496C22×C4—222no—
497C22×C4—222no—
498C22×C4—221no—
499C22×C4—221no—
500C22×C4C2×C4×D1114yes—
501C22×C4C2×C4×D1112yes—
502C22×C4D4×D1114yes—
503C22×C4D4×D1112yes—
504C22×C4Q8×D1112yes—
505C4⋊C4—28no—
506C4⋊C4—2216no—
507C4⋊C4—228no—
508C4⋊C4—444no—
509C4⋊C4—444no—
510C4⋊C4—448no—
511C4⋊C4—448no—
512C22⋊C4—2216no—
513C22⋊C4—448no—
514C22⋊C4—444no—
515C22⋊C4—444no—
516C42—2216no—
517C11#1426411yescharacteristic, complemented, Sylow
518C23—114no—
519C23—222no—
520C23—224no—
521C23—224no—
522C23—222no—
523C23—222no—
524C23—222no—
525C23—222no—
526C23—224no—
527C23—222no—
528C23—222no—
529C23—222no—
530C23—222no—
531C23—222no—
532C23—224no—
533C23—442no—
534C23—442no—
535C23—442no—
536C23—442no—
537C23—442no—
538C23—442no—
539C23—442no—
540C23—442no—
541C23C22×C4×D1111yescharacteristic
542C23C2×D4×D1111yescharacteristic
543C23C2×D4×D1112yes—
544C23#6703711yescharacteristic
545C23C2×Q8×D1111yescharacteristic
546C23#6704011yescharacteristic
547C23#41×D1112yes—
548C23#6704211yescharacteristic
549C23#6704212yes—
550C23#6704311yescharacteristic
551C23#6704312yes—
552C2×C4—24no—
553C2×C4—22no—
554C2×C4—24no—
555C2×C4—22no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—42no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—42no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—42no—
580C2×C4—114no—
581C2×C4—118no—
582C2×C4—114no—
583C2×C4—118no—
584C2×C4—114no—
585C2×C4—2232no—
586C2×C4—224no—
587C2×C4—224no—
588C2×C4—224no—
589C2×C4—224no—
590C2×C4—224no—
591C2×C4—224no—
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—442no—
601C2×C4—441no—
602C2×C4—441no—
603C2×C4—442no—
604C2×C4—441no—
605C2×C4—441no—
606C2×C4—442no—
607C2×C4—441no—
608C2×C4—441no—
609C2×C4—442no—
610C2×C4C4⋊C4×D1114yes—
611C22—224no—
612C22—224no—
613C22—224no—
614C22—444no—
615C22—444no—
616C22—442no—
617C22—442no—
618C22—444no—
619C22—444no—
620C22—442no—
621C22—442no—
622C22C2×C4⋊C4×D1111yescharacteristic
623C22#1062305412yes—
624C22C4×D4×D1112yes—
625C22#1062307611yescharacteristic
626C22#1062310311yescharacteristic
627C22D11×#12011yescharacteristic
628C22#1062312812yes—
629C22#1062313911yescharacteristic
630C22D11×C22⋊Q812yes—
631C22#1062316012yes—
632C22#1062316011yescharacteristic
633C22#1062317912yes—
634C22D11×#12311yescharacteristic
635C22#1062319412yes—
636C22#1062320512yes—
637C22#1062320511yescharacteristic
638C22#1062320611yescharacteristic
639C22#1062322011yescharacteristic
640C22#1062322012yes—
641C22#1062322712yes—
642C22#1062324112yes—
643C22#1062324112yes—
644C22#1062326011yescharacteristic
645C4—24no—
646C4—44no—
647C4—44no—
648C4—81no—
649C4—81no—
650C4—118no—
651C4—444no—
652C4—444no—
653C4—881no—
654C4—881no—
655C2—444no—
656C2D11×#38511yescharacteristic
657C2#1307123111yescharacteristic
658C2#1307124111yescharacteristic
659C2#1307129712yes—
660C2#1307130412yes—
661C2#1307434311yescharacteristic
662C2#1307434411yescharacteristic
663C2#1307441111yescharacteristic
664C2#1307441711yescharacteristic
665C2#1307444412yes—
666C2#1307444812yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1442C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenter#1442D11
hypocenterC11#14264
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1442

Complements

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

NH ≅ G/Ntype
2. C2×#10622260C2semidirect
5. #13066881C2semidirect
6. #13066880C2semidirect
7. #13066875C2semidirect
10. Dic11⋊#95C2semidirect
11. C11×#1442C2semidirect
38. #10622280C4semidirect
172. C2×C4×D11C4⋊C4semidirect
192. #1442D11semidirect
517. C11#14264semidirect

Maximal subgroups

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

subgroupindex
C22×#669452
C2×#106222602
C2×#106222802
#130668812
#130668802
#130668752
#130668622
#130668602
Dic11⋊#952
C11×#14422
#1426411