Finite Group Databasebeta

← #14682722

Subgroups — #14682722

Order 2816.

1918 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622552C211yesmaximal, characteristic
2C2×#10622278C212yesmaximal
3#13066868C212yesmaximal, complemented
4#13066860C212yesmaximal, complemented
5#13066860C212yesmaximal, complemented
6#13066843C211yesmaximal, characteristic, complemented
7(C2×D11)⋊#95C212yesmaximal, complemented
8(C2×D11)⋊#95C212yesmaximal, complemented
9C11×#1434C211yesmaximal, characteristic, complemented
10C23×D44C2211yescharacteristic
11C23×C4×D11C2212yes—
12C22×C42×C11C2211yescharacteristic
13C22×(C2×D11)⋊C4C2212yes—
14C22×(C2×D11)⋊C4C2212yes—
15C22×(C2×D11)⋊C4C2212yes—
16C22×(C2×D11)⋊C4C2212yes—
17C22×(C2×D11)⋊C4C2212yes—
18C22×C4⋊Dic11C2211yescharacteristic
19C22×Dic11⋊C4C2212yes—
20C2×C11×#95C2212yes—
21C2×C11×#95C2212yes—
22C2×C11×#95C2211yescharacteristic
23C2×C11×#95C2211yescharacteristic
24C2×C11⋊#95C2212yes—
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2211yescharacteristic
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2211yescharacteristic
31#10622552C418yescomplemented
32#10622278—28no—
33C24×D11C2312yes—
34C23×C4×C11C2312yes—
35C23×C4×C11C2311yescharacteristic
36C23×C4×C11C2311yescharacteristic
37C23×C4×C11C2312yes—
38C23×C4×C11C2311yescharacteristic
39C23×Dic11C2312yes—
40C23×Dic11C2312yes—
41C23×Dic11C2312yes—
42C22×D44—41no—
43C22×D44—41no—
44C22×D44—41no—
45C22×D44—41no—
46C22×D44C2×C414yes—
47C22×D44D414yes—
48C22×D44Q814yes—
49C22×C4×D11—24no—
50C22×C4×D11—24no—
51C22×C4×D11—24no—
52C22×C4×D11—42no—
53C22×C4×D11—42no—
54C22×C4×D11—42no—
55C22×C4×D11—42no—
56C2×C42×C11—41no—
57C2×C42×C11—41no—
58C2×C42×C11C2×C414yescomplemented
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×C418yescomplemented
73C2×(C2×D11)⋊C4C2×C418yescomplemented
74C2×C4⋊Dic11—41no—
75C2×C4⋊Dic11—41no—
76C2×C4⋊Dic11C2×C414yescomplemented
77C2×Dic11⋊C4—42no—
78C2×Dic11⋊C4—42no—
79C2×Dic11⋊C4—42no—
80C11×#95—24no—
81C11×#95—24no—
82C11×#95—41no—
83C11×#95—41no—
84C11⋊#95—24no—
85C11⋊#95—24no—
86C11⋊#95—42no—
87C11⋊#95—42no—
88C11⋊#95—42no—
89C11⋊#95—41no—
90C11⋊#95—41no—
91#14486—111nomaximal, Sylow
92C24×C11C2411yescharacteristic
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×D11—22no—
105C23×D11C22×C414yes—
106C23×D11C2×D414yes—
107C23×D11C2×Q814yes—
108C22×C4×C11—21no—
109C22×C4×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11—21no—
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—21no—
121C22×C4×C11—21no—
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×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11C22×C412yes—
134C22×C4×C11C22×C412yes—
135C22×C4×C11C22×C412yes—
136C22×C4×C11C2×D412yes—
137C22×C4×C11C2×Q812yes—
138C22×C4×C11#4114yes—
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×Dic11—22no—
156C22×Dic11—22no—
157C22×Dic11—22no—
158C22×Dic11C22×C414yes—
159C22×Dic11#4114yes—
160C2×D44—44no—
161C2×D44—44no—
162C2×D44—44no—
163C2×D44—44no—
164C2×D44—44no—
165C2×D44—44no—
166C2×D44C4⋊C4116yescomplemented
167C2×C4×D11—48no—
168C2×C4×D11—48no—
169C2×C4×D11—48no—
170C2×C4×D11—48no—
171C2×C4×D11—48no—
172C2×C4×D11—48no—
173C2×C4×D11—48no—
174C42×C11—44no—
175(C2×D11)⋊C4—48no—
176(C2×D11)⋊C4—48no—
177(C2×D11)⋊C4—48no—
178(C2×D11)⋊C4—48no—
179(C2×D11)⋊C4—48no—
180C4⋊Dic11—44no—
181Dic11⋊C4—48no—
182C2×#390—111no—
183C2×#386—112no—
184#1441—112no—
185#1439—112no—
186#1439—112no—
187#1434—111no—
188#1434D1111yescharacteristic, complemented
189C22⋊#95—112no—
190C22⋊#95—112no—
191C23×C11C23×C411yescharacteristic
192C23×C11C22×D411yescharacteristic
193C23×C11C22×Q811yescharacteristic
194C23×C11C2×#4112yes—
195C23×C11C2×#4112yes—
196C23×C11H(5,𝔽2)11yescharacteristic
197C23×C11H(5,𝔽2)11yescharacteristic
198C23×C11H(5,𝔽2)11yescharacteristic
199C23×C11H(5,𝔽2)11yescharacteristic
200C23×C11H(5,𝔽2)12yes—
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×C4⋊C418yes—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
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—22no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—24no—
250C2×C4×C11—24no—
251C2×C4×C11—24no—
252C2×C4×C11—42no—
253C2×C4×C11—42no—
254C2×C4×C11—42no—
255C2×C4×C11—42no—
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—42no—
263C2×C4×C11—42no—
264C2×C4×C11—42no—
265C2×C4×C11—42no—
266C2×C4×C11—42no—
267C2×C4×C11C2×C4⋊C414yes—
268C2×Dic11—24no—
269C2×Dic11—24no—
270C2×Dic11—24no—
271C2×Dic11—24no—
272C2×Dic11—24no—
273C2×Dic11—24no—
274C2×Dic11—42no—
275C2×Dic11—42no—
276C2×Dic11—42no—
277C2×Dic11—42no—
278C2×Dic11—42no—
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×Dic11—42no—
288C2×Dic11—42no—
289D44—416no—
290C4×D11—432no—
291C23×D4—111no—
292C24×C4—112no—
293C22×C4⋊C4—111no—
294C22×C4⋊C4—112no—
295C22×C22⋊C4—112no—
296C22×C22⋊C4—112no—
297C22×C22⋊C4—112no—
298C22×C22⋊C4—112no—
299C22×C22⋊C4—112no—
300C22×C42C2×D1111yescharacteristic
301#390—118no—
302#386—228no—
303C2×#95—112no—
304C2×#95—112no—
305C2×#95—111no—
306C2×#95—112no—
307C2×#95—112no—
308C2×#95—112no—
309C2×#95—111no—
310C2×#95C2×D1112yes—
311C2×#95C2×D1112yes—
312C2×#95C2×D1111yescharacteristic
313C2×#95C2×D1111yescharacteristic
314C22×C11C22×C4⋊C411yescharacteristic
315C22×C11C4×#4111yescharacteristic
316C22×C11C4×#4111yescharacteristic
317C22×C11#51811yescharacteristic
318C22×C11#51811yescharacteristic
319C22×C11#51811yescharacteristic
320C22×C11#51811yescharacteristic
321C22×C11#53411yescharacteristic
322C22×C11#53411yescharacteristic
323C22×C11#53812yes—
324C22×C11#53812yes—
325C22×C11#54012yes—
326C22×C11#54012yes—
327C22×C11#54311yescharacteristic
328C22×C11#54311yescharacteristic
329C22×C11#54612yes—
330C22×C11#54612yes—
331C22×C11#55112yes—
332C22×C11#55412yes—
333C22×C11#55412yes—
334C22×C11#55512yes—
335C22×C11#56012yes—
336C22×C11#56012yes—
337C2×D11—28no—
338C2×D11—28no—
339C2×D11—28no—
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—
350C2×D11—44no—
351C2×D11—44no—
352C4×C11—24no—
353C4×C11—42no—
354C4×C11—42no—
355C4×C11—44no—
356C4×C11—82no—
357Dic11—44no—
358Dic11—44no—
359Dic11—82no—
360C25—112no—
361C22×D4—114no—
362C22×D4—114no—
363C22×D4—114no—
364C22×D4—441no—
365C22×D4—441no—
366C22×D4—441no—
367C22×D4—441no—
368C23×C4—112no—
369C23×C4—112no—
370C23×C4—112no—
371C23×C4—224no—
372C23×C4—224no—
373C23×C4—224no—
374C23×C4—442no—
375C23×C4—442no—
376C23×C4—442no—
377C23×C4—442no—
378C23×C4C22×D1112yes—
379C23×C4C22×D1111yescharacteristic
380C23×C4C22×D1111yescharacteristic
381C23×C4C22×D1112yes—
382C23×C4C22×D1111yescharacteristic
383C2×C4⋊C4—114no—
384C2×C4⋊C4—442no—
385C2×C4⋊C4—442no—
386C2×C4⋊C4—442no—
387C2×C4⋊C4—441no—
388C2×C4⋊C4—441no—
389C2×C22⋊C4—118no—
390C2×C22⋊C4—118no—
391C2×C22⋊C4—224no—
392C2×C22⋊C4—224no—
393C2×C22⋊C4—224no—
394C2×C22⋊C4—224no—
395C2×C22⋊C4—224no—
396C2×C22⋊C4—442no—
397C2×C22⋊C4—442no—
398C2×C22⋊C4—442no—
399C2×C22⋊C4—442no—
400C2×C22⋊C4—442no—
401C2×C22⋊C4—442no—
402C2×C22⋊C4—442no—
403C2×C22⋊C4—442no—
404C2×C42—41no—
405C2×C42—41no—
406C2×C42C4×D1114yescomplemented
407#95—24no—
408#95—24no—
409#95—41no—
410#95—41no—
411#95—224no—
412#95—224no—
413#95—441no—
414#95—441no—
415#95—442no—
416#95—442no—
417#95—442no—
418C2×C11#231511yescharacteristic
419C2×C11#233311yescharacteristic
420C2×C11#233311yescharacteristic
421C2×C11#234911yescharacteristic
422C2×C11#234911yescharacteristic
423C2×C11#237211yescharacteristic
424C2×C11#238011yescharacteristic
425C2×C11#269712yes—
426C2×C11#269912yes—
427C2×C11#274812yes—
428C2×C11#278412yes—
429D11—48no—
430C24—114no—
431C24—114no—
432C24—114no—
433C24—222no—
434C24—222no—
435C24—222no—
436C24—222no—
437C24—222no—
438C24—222no—
439C24—222no—
440C24—222no—
441C24—222no—
442C24—222no—
443C24—222no—
444C24—222no—
445C24C23×D1111yescharacteristic
446C2×D4—1116no—
447C2×D4—444no—
448C2×D4—444no—
449C2×D4—444no—
450C2×D4—444no—
451C2×D4—444no—
452C2×D4—444no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—21no—
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—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—114no—
479C22×C4—114no—
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—222no—
493C22×C4—222no—
494C22×C4—222no—
495C22×C4—222no—
496C22×C4—222no—
497C22×C4—222no—
498C22×C4—222no—
499C22×C4—448no—
500C22×C4—448no—
501C22×C4—448no—
502C22×C4—448no—
503C22×C4—448no—
504C22×C4—448no—
505C22×C4—448no—
506C22×C4C2×C4×D1112yes—
507C22×C4C2×C4×D1112yes—
508C22×C4C2×C4×D1112yes—
509C22×C4#433914yes—
510C22×C4D4×D1112yes—
511C22×C4Q8×D1112yes—
512C4⋊C4—444no—
513C4⋊C4—448no—
514C22⋊C4—448no—
515C22⋊C4—448no—
516C22⋊C4—448no—
517C22⋊C4—448no—
518C22⋊C4—448no—
519C42—44no—
520C11#1448611yescharacteristic, 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
557C23C2×#433912yes—
558C23C2×D4×D1111yescharacteristic
559C23#6703711yescharacteristic
560C23#6703711yescharacteristic
561C23C2×Q8×D1111yescharacteristic
562C23#41×D1112yes—
563C23#6704211yescharacteristic
564C23#6704211yescharacteristic
565C23#6704212yes—
566C23#6704212yes—
567D4—4416no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—24no—
581C2×C4—24no—
582C2×C4—24no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—224no—
599C2×C4—224no—
600C2×C4—224no—
601C2×C4—224no—
602C2×C4—224no—
603C2×C4—224no—
604C2×C4—4432no—
605C2×C4—442no—
606C2×C4—442no—
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×C4—442no—
616C2×C4—442no—
617C2×C4—442no—
618C2×C4—442no—
619C2×C4—442no—
620C2×C4C4⋊C4×D1114yes—
621C22—228no—
622C22—228no—
623C22—228no—
624C22—444no—
625C22—444no—
626C22—444no—
627C22—444no—
628C22—444no—
629C22—444no—
630C22—444no—
631C22—444no—
632C22—444no—
633C22—444no—
634C22—444no—
635C22—444no—
636C22C4×#433911yescharacteristic
637C22#1062301711yescharacteristic
638C22C2×C4⋊C4×D1111yescharacteristic
639C22#1062305211yescharacteristic
640C22#1062305211yescharacteristic
641C22#1062305211yescharacteristic
642C22#1062305311yescharacteristic
643C22#1062305812yes—
644C22#1062306312yes—
645C22#1062308112yes—
646C22#1062309112yes—
647C22#1062309312yes—
648C22#1062311012yes—
649C22#1062313611yescharacteristic
650C22#1062313611yescharacteristic
651C22#1062316511yescharacteristic
652C22#1062316511yescharacteristic
653C22#1062318812yes—
654C22#1062319412yes—
655C22#1062320712yes—
656C22#1062322112yes—
657C22#1062324212yes—
658C22#1062324212yes—
659C4—24no—
660C4—42no—
661C4—42no—
662C4—44no—
663C4—82no—
664C4—444no—
665C4—444no—
666C4—882no—
667C2—448no—
668C2#1307122911yescharacteristic
669C2#1307137811yescharacteristic
670C2#1307138111yescharacteristic
671C2#1307152411yescharacteristic
672C2#1307152711yescharacteristic
673C2#1307172611yescharacteristic
674C2#1307179211yescharacteristic
675C2#1307517612yes—
676C2#1307520012yes—
677C2#1307582412yes—
678C2#1307631212yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1434C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenter#1434D11
hypocenterC11#14486
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
3. #13066868C2semidirect
4. #13066860C2semidirect
5. #13066860C2semidirect
6. #13066843C2semidirect
7. (C2×D11)⋊#95C2semidirect
8. (C2×D11)⋊#95C2semidirect
9. C11×#1434C2semidirect
31. #10622552C4semidirect
58. C2×C42×C11C2×C4semidirect
72. C2×(C2×D11)⋊C4C2×C4semidirect
73. C2×(C2×D11)⋊C4C2×C4semidirect
76. C2×C4⋊Dic11C2×C4semidirect
166. C2×D44C4⋊C4semidirect
188. #1434D11semidirect
406. C2×C42C4×D11semidirect
520. C11#14486semidirect

Maximal subgroups

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

subgroupindex
C2×#106225522
C2×#106222782
#130668682
#130668602
#130668432
(C2×D11)⋊#952
C11×#14342
#1448611