Finite Group Databasebeta

← #14682723

Subgroups — #14682723

Order 2816.

1918 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622601C211yesmaximal, characteristic
2C2×#10622278C212yesmaximal
3#13066869C211yesmaximal, characteristic, complemented
4#13066862C212yesmaximal, complemented
5#13066858C212yesmaximal, complemented
6#13066842C212yesmaximal, complemented
7(C2×D11)⋊#95C212yesmaximal, complemented
8(C2×D11)⋊#95C212yesmaximal, complemented
9C11×#1441C211yesmaximal, characteristic, complemented
10C23×D44C2211yescharacteristic
11C23×C4×D11C2212yes—
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
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×Dic11C2211yescharacteristic
21C2×C11×#95C2212yes—
22C2×C11×#95C2211yescharacteristic
23C2×C11×#95C2212yes—
24C2×C11⋊#95C2212yes—
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2211yescharacteristic
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31#10622601C418yescomplemented
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×C11×C4⋊C4—41no—
57C2×C11×C4⋊C4—41no—
58C2×C11×C4⋊C4—42no—
59C2×C11×C4⋊C4—41no—
60C2×C11×C4⋊C4C2×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—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)⋊C4—42no—
73C2×(C2×D11)⋊C4—42no—
74C2×(C2×D11)⋊C4C2×C418yescomplemented
75C2×(C2×D11)⋊C4C2×C418yescomplemented
76C2×C4⋊Dic11—42no—
77C2×C4⋊Dic11—41no—
78C2×C4×Dic11—41no—
79C2×C4×Dic11—41no—
80C2×C4×Dic11C2×C414yescomplemented
81C11×#95—24no—
82C11×#95—42no—
83C11×#95—41no—
84C11⋊#95—24no—
85C11⋊#95—24no—
86C11⋊#95—24no—
87C11⋊#95—42no—
88C11⋊#95—42no—
89C11⋊#95—41no—
90C11⋊#95—42no—
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—21no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—21no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—21no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—21no—
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—
174C11×C4⋊C4—44no—
175C11×C4⋊C4—44no—
176(C2×D11)⋊C4—48no—
177(C2×D11)⋊C4—48no—
178(C2×D11)⋊C4—48no—
179(C2×D11)⋊C4—48no—
180(C2×D11)⋊C4—48no—
181C4⋊Dic11—44no—
182C4×Dic11—44no—
183C2×#390—111no—
184C2×#386—112no—
185#1441—111no—
186#1441D1111yescharacteristic, complemented
187#1439—112no—
188#1439—112no—
189#1434—112no—
190C22⋊#95—112no—
191C22⋊#95—112no—
192C23×C11C23×C411yescharacteristic
193C23×C11C22×D411yescharacteristic
194C23×C11C22×Q811yescharacteristic
195C23×C11C2×#4112yes—
196C23×C11C2×#4112yes—
197C23×C11H(5,𝔽2)11yescharacteristic
198C23×C11H(5,𝔽2)11yescharacteristic
199C23×C11H(5,𝔽2)12yes—
200C23×C11H(5,𝔽2)11yescharacteristic
201C23×C11H(5,𝔽2)11yescharacteristic
202C23×C11H(5,𝔽2)12yes—
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×C4⋊C418yes—
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—24no—
245C2×C4×C11—24no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—24no—
249C2×C4×C11—24no—
250C2×C4×C11—24no—
251C2×C4×C11—42no—
252C2×C4×C11—42no—
253C2×C4×C11—42no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—42no—
257C2×C4×C11—41no—
258C2×C4×C11—42no—
259C2×C4×C11—42no—
260C2×C4×C11—41no—
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×C11—42no—
268C2×C4×C11C2×C4⋊C414yes—
269C2×Dic11—24no—
270C2×Dic11—24no—
271C2×Dic11—24no—
272C2×Dic11—24no—
273C2×Dic11—24no—
274C2×Dic11—24no—
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—
289C2×Dic11—42no—
290D44—416no—
291C4×D11—432no—
292C23×D4—111no—
293C24×C4—112no—
294C22×C4⋊C4—111no—
295C22×C4⋊C4C2×D1111yescharacteristic
296C22×C4⋊C4C2×D1111yescharacteristic
297C22×C22⋊C4—112no—
298C22×C22⋊C4—112no—
299C22×C22⋊C4—112no—
300C22×C22⋊C4—112no—
301C22×C22⋊C4—112no—
302C22×C42—111no—
303#390—118no—
304#386—228no—
305C2×#95—112no—
306C2×#95—112no—
307C2×#95—112no—
308C2×#95—112no—
309C2×#95—111no—
310C2×#95—112no—
311C2×#95—112no—
312C2×#95C2×D1112yes—
313C2×#95C2×D1111yescharacteristic
314C2×#95C2×D1112yes—
315C22×C11C22×C4⋊C411yescharacteristic
316C22×C11C4×#4112yes—
317C22×C11#51811yescharacteristic
318C22×C11#51811yescharacteristic
319C22×C11#51812yes—
320C22×C11#53411yescharacteristic
321C22×C11#53411yescharacteristic
322C22×C11#53812yes—
323C22×C11#53812yes—
324C22×C11#54012yes—
325C22×C11#54012yes—
326C22×C11#54311yescharacteristic
327C22×C11#54311yescharacteristic
328C22×C11#54612yes—
329C22×C11#54612yes—
330C22×C11#55112yes—
331C22×C11#55412yes—
332C22×C11#55412yes—
333C22×C11#55511yescharacteristic
334C22×C11#55511yescharacteristic
335C22×C11#56011yescharacteristic
336C22×C11#56012yes—
337C22×C11#56011yescharacteristic
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—24no—
354C4×C11—42no—
355C4×C11—42no—
356C4×C11—44no—
357C4×C11—82no—
358Dic11—44no—
359Dic11—44no—
360Dic11—82no—
361C25—112no—
362C22×D4—114no—
363C22×D4—114no—
364C22×D4—114no—
365C22×D4—441no—
366C22×D4—441no—
367C22×D4—441no—
368C22×D4—441no—
369C23×C4—112no—
370C23×C4—112no—
371C23×C4—112no—
372C23×C4—224no—
373C23×C4—224no—
374C23×C4—224no—
375C23×C4—442no—
376C23×C4—442no—
377C23×C4—442no—
378C23×C4—442no—
379C23×C4C22×D1112yes—
380C23×C4C22×D1111yescharacteristic
381C23×C4C22×D1111yescharacteristic
382C23×C4C22×D1112yes—
383C23×C4C22×D1111yescharacteristic
384C2×C4⋊C4—41no—
385C2×C4⋊C4—41no—
386C2×C4⋊C4—42no—
387C2×C4⋊C4—41no—
388C2×C4⋊C4—441no—
389C2×C4⋊C4—442no—
390C2×C4⋊C4C4×D1114yescomplemented
391C2×C22⋊C4—118no—
392C2×C22⋊C4—118no—
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×C22⋊C4—442no—
401C2×C22⋊C4—442no—
402C2×C22⋊C4—442no—
403C2×C22⋊C4—442no—
404C2×C22⋊C4—442no—
405C2×C22⋊C4—442no—
406C2×C42—114no—
407C2×C42—441no—
408C2×C42—441no—
409#95—24no—
410#95—42no—
411#95—41no—
412#95—224no—
413#95—224no—
414#95—224no—
415#95—441no—
416#95—442no—
417#95—442no—
418#95—442no—
419C2×C11#231511yescharacteristic
420C2×C11#233312yes—
421C2×C11#234912yes—
422C2×C11#237211yescharacteristic
423C2×C11#238011yescharacteristic
424C2×C11#269712yes—
425C2×C11#269911yescharacteristic
426C2×C11#269911yescharacteristic
427C2×C11#274812yes—
428C2×C11#278411yescharacteristic
429C2×C11#278411yescharacteristic
430D11—48no—
431C24—114no—
432C24—114no—
433C24—114no—
434C24—222no—
435C24—222no—
436C24—222no—
437C24—222no—
438C24—222no—
439C24—222no—
440C24—222no—
441C24—222no—
442C24—222no—
443C24—222no—
444C24—222no—
445C24—222no—
446C24C23×D1111yescharacteristic
447C2×D4—1116no—
448C2×D4—444no—
449C2×D4—444no—
450C2×D4—444no—
451C2×D4—444no—
452C2×D4—444no—
453C2×D4—444no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—21no—
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—21no—
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—22no—
479C22×C4—114no—
480C22×C4—114no—
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—222no—
500C22×C4—448no—
501C22×C4—448no—
502C22×C4—448no—
503C22×C4—448no—
504C22×C4—448no—
505C22×C4—448no—
506C22×C4—448no—
507C22×C4C2×C4×D1112yes—
508C22×C4C2×C4×D1112yes—
509C22×C4C2×C4×D1112yes—
510C22×C4D4×D1112yes—
511C22×C4Q8×D1112yes—
512C22×C4#434314yes—
513C4⋊C4—44no—
514C4⋊C4—44no—
515C4⋊C4—444no—
516C22⋊C4—448no—
517C22⋊C4—448no—
518C22⋊C4—448no—
519C22⋊C4—448no—
520C22⋊C4—448no—
521C42—444no—
522C11#1448611yescharacteristic, complemented, Sylow
523C23—118no—
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—224no—
541C23—224no—
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—
556C23—442no—
557C23—442no—
558C23C22×C4×D1111yescharacteristic
559C23C2×D4×D1111yescharacteristic
560C23#6703712yes—
561C23#6703711yescharacteristic
562C23#6703711yescharacteristic
563C23C2×Q8×D1111yescharacteristic
564C23C2×#434312yes—
565C23#41×D1112yes—
566C23#6704211yescharacteristic
567C23#6704212yes—
568C23#6704211yescharacteristic
569D4—4416no—
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—24no—
579C2×C4—24no—
580C2×C4—24no—
581C2×C4—24no—
582C2×C4—24no—
583C2×C4—42no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
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×C4—442no—
616C2×C4—442no—
617C2×C4—442no—
618C2×C4—442no—
619C2×C4—442no—
620C2×C4—442no—
621C2×C4—442no—
622C2×C4C4⋊C4×D1114yes—
623C22—228no—
624C22—228no—
625C22—228no—
626C22—444no—
627C22—444no—
628C22—444no—
629C22—444no—
630C22—444no—
631C22—444no—
632C22—444no—
633C22—444no—
634C22—444no—
635C22—444no—
636C22—444no—
637C22—444no—
638C22#1062301711yescharacteristic
639C22C2×C4⋊C4×D1111yescharacteristic
640C22#1062305211yescharacteristic
641C22#1062307612yes—
642C22C4×#434312yes—
643C22#1062312611yescharacteristic
644C22#1062313611yescharacteristic
645C22#1062313611yescharacteristic
646C22#1062314312yes—
647C22#1062315112yes—
648C22#1062316112yes—
649C22#1062316511yescharacteristic
650C22#1062316511yescharacteristic
651C22#1062316812yes—
652C22#1062317512yes—
653C22#1062319412yes—
654C22#1062319711yescharacteristic
655C22#1062320111yescharacteristic
656C22#1062322112yes—
657C22#1062322912yes—
658C22#1062323512yes—
659C22#1062326112yes—
660C22#1062326511yescharacteristic
661C4—24no—
662C4—42no—
663C4—42no—
664C4—44no—
665C4—82no—
666C4—444no—
667C4—444no—
668C4—882no—
669C2—448no—
670C2#1307122911yescharacteristic
671C2#1307138012yes—
672C2#1307152512yes—
673C2#1307172711yescharacteristic
674C2#1307179111yescharacteristic
675C2#1307517412yes—
676C2#1307519811yescharacteristic
677C2#1307520211yescharacteristic
678C2#1307582812yes—
679C2#1307631611yescharacteristic
680C2#1307631911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1441C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenter#1441D11
hypocenterC11#14486
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
3. #13066869C2semidirect
4. #13066862C2semidirect
5. #13066858C2semidirect
6. #13066842C2semidirect
7. (C2×D11)⋊#95C2semidirect
8. (C2×D11)⋊#95C2semidirect
9. C11×#1441C2semidirect
31. #10622601C4semidirect
60. C2×C11×C4⋊C4C2×C4semidirect
74. C2×(C2×D11)⋊C4C2×C4semidirect
75. C2×(C2×D11)⋊C4C2×C4semidirect
80. C2×C4×Dic11C2×C4semidirect
166. C2×D44C4⋊C4semidirect
186. #1441D11semidirect
390. C2×C4⋊C4C4×D11semidirect
522. C11#14486semidirect

Maximal subgroups

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

subgroupindex
C2×#106226012
C2×#106222782
#130668692
#130668622
#130668582
#130668422
(C2×D11)⋊#952
C11×#14412
#1448611