Finite Group Databasebeta

← #14675413

Subgroups — #14675413

Order 2816.

1998 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622601C211yesmaximal, characteristic
2C2×#10622278C212yesmaximal
3#13066854C212yesmaximal, complemented
4#13066852C212yesmaximal, complemented
5#13066848C211yesmaximal, characteristic, complemented
6#13066841C212yesmaximal, complemented
7(C2×D11)⋊#95C212yesmaximal, complemented
8(C2×D11)⋊#95C212yesmaximal, 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×Dic11C2211yescharacteristic
20C22×C4×Dic11C2211yescharacteristic
21C2×C11×#95C2211yescharacteristic
22C2×C11×#95C2212yes—
23C2×C11×#95C2212yes—
24C2×C11⋊#95C2212yes—
25C2×C11⋊#95C2211yescharacteristic
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31#10622601C418yescomplemented
32#10622278C4116yescomplemented
33C24×D11C2312yes—
34C23×C4×C11C2311yescharacteristic
35C23×C4×C11C2312yes—
36C23×C4×C11C2311yescharacteristic
37C23×C4×C11C2312yes—
38C23×C4×C11C2311yescharacteristic
39C23×Dic11C2312yes—
40C23×Dic11C2312yes—
41C23×Dic11C2312yes—
42C22×D44—42no—
43C22×D44—41no—
44C22×D44—41no—
45C22×D44C2×C418yes—
46C22×D44C2×C414yes—
47C22×C4×D11—42no—
48C22×C4×D11—42no—
49C22×C4×D11—42no—
50C22×C4×D11—42no—
51C22×C4×D11—42no—
52C22×C4×D11—42no—
53C22×C4×D11C2×C418yescomplemented
54C2×C11×C4⋊C4—41no—
55C2×C11×C4⋊C4—41no—
56C2×C11×C4⋊C4C2×C414yescomplemented
57C2×C42×C11—42no—
58C2×C42×C11—41no—
59C2×(C2×D11)⋊C4—42no—
60C2×(C2×D11)⋊C4—42no—
61C2×(C2×D11)⋊C4—42no—
62C2×(C2×D11)⋊C4—42no—
63C2×(C2×D11)⋊C4—42no—
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)⋊C4C2×C418yes—
70C2×(C2×D11)⋊C4C2×C418yes—
71C2×(C2×D11)⋊C4C2×C418yescomplemented
72C2×(C2×D11)⋊C4C2×C418yescomplemented
73C2×(C2×D11)⋊C4C2×C418yescomplemented
74C2×C4×Dic11—42no—
75C2×C4×Dic11—42no—
76C2×C4×Dic11—41no—
77C2×C4×Dic11C2×C414yescomplemented
78C11×#95—42no—
79C11×#95—41no—
80C11×#95C2×C418yescomplemented
81C11⋊#95—42no—
82C11⋊#95—42no—
83C11⋊#95—42no—
84C11⋊#95—42no—
85C11⋊#95—42no—
86C11⋊#95—41no—
87C11⋊#95C2×C418yescomplemented
88#13832—111nomaximal, Sylow
89C24×C11C2411yescharacteristic
90C23×D11—22no—
91C23×D11—22no—
92C23×D11—22no—
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×D11C22×C414yes—
103C23×D11C22×C414yes—
104C23×D11C22×C414yes—
105C22×C4×C11—22no—
106C22×C4×C11—21no—
107C22×C4×C11—21no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
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—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—21no—
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×C11C22×C414yes—
129C22×C4×C11C22×C414yes—
130C22×C4×C11C22×C412yes—
131C22×C4×C11C22×C412yes—
132C22×C4×C11C22×C414yes—
133C22×C4×C11C22×C412yes—
134C22×Dic11—22no—
135C22×Dic11—22no—
136C22×Dic11—22no—
137C22×Dic11—22no—
138C22×Dic11—22no—
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×Dic11C22×C414yes—
153C22×Dic11C22×C414yes—
154C22×Dic11C22×C414yes—
155C2×D44—44no—
156C2×D44—44no—
157C2×D44—48no—
158C2×D44—48no—
159C2×D44C42116yescomplemented
160C2×C4×D11—48no—
161C2×C4×D11—48no—
162C2×C4×D11—48no—
163C2×C4×D11—48no—
164C2×C4×D11—48no—
165C2×C4×D11—48no—
166C2×C4×D11—48no—
167C11×C4⋊C4—44no—
168C42×C11—44no—
169(C2×D11)⋊C4—48no—
170(C2×D11)⋊C4—48no—
171(C2×D11)⋊C4—48no—
172(C2×D11)⋊C4—48no—
173(C2×D11)⋊C4—48no—
174C4×Dic11—44no—
175C4×Dic11—44no—
176C2×#390—111no—
177C2×#386—112no—
178#1437—112no—
179#1437—112no—
180#1436—111no—
181#1436D1111yescharacteristic, complemented
182#1434—112no—
183C22⋊#95—112no—
184C22⋊#95—112no—
185C23×C11C23×C411yescharacteristic
186C23×C11C23×C412yes—
187C23×C11H(5,𝔽2)11yescharacteristic
188C23×C11H(5,𝔽2)11yescharacteristic
189C23×C11H(5,𝔽2)12yes—
190C23×C11H(5,𝔽2)12yes—
191C23×C11H(5,𝔽2)12yes—
192C23×C11H(5,𝔽2)12yes—
193C23×C112−1+412yes—
194C22×D11—24no—
195C22×D11—24no—
196C22×D11—24no—
197C22×D11—24no—
198C22×D11—24no—
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×D11—24no—
208C22×D11—24no—
209C22×D11—24no—
210C22×D11—24no—
211C22×D11—24no—
212C22×D11—42no—
213C22×D11—42no—
214C22×D11—42no—
215C22×D11—42no—
216C22×D11—42no—
217C22×D11—42no—
218C22×D11—42no—
219C22×D11—42no—
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×D11C2×C4218yes—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—24no—
232C2×C4×C11—24no—
233C2×C4×C11—24no—
234C2×C4×C11—24no—
235C2×C4×C11—24no—
236C2×C4×C11—24no—
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—41no—
244C2×C4×C11—42no—
245C2×C4×C11—41no—
246C2×C4×C11—42no—
247C2×C4×C11—42no—
248C2×C4×C11—42no—
249C2×C4×C11—41no—
250C2×C4×C11—42no—
251C2×C4×C11—42no—
252C2×C4×C11—42no—
253C2×C4×C11—41no—
254C2×C4×C11—42no—
255C2×C4×C11—42no—
256C2×C4×C11—42no—
257C2×C4×C11C2×C4214yes—
258C2×Dic11—24no—
259C2×Dic11—24no—
260C2×Dic11—24no—
261C2×Dic11—24no—
262C2×Dic11—24no—
263C2×Dic11—24no—
264C2×Dic11—24no—
265C2×Dic11—24no—
266C2×Dic11—24no—
267C2×Dic11—42no—
268C2×Dic11—42no—
269C2×Dic11—42no—
270C2×Dic11—42no—
271C2×Dic11—42no—
272C2×Dic11—42no—
273C2×Dic11—42no—
274C2×Dic11—42no—
275C2×Dic11—42no—
276C2×Dic11—42no—
277C2×Dic11—42no—
278C2×Dic11—42no—
279D44—416no—
280C4×D11—432no—
281C23×D4—111no—
282C24×C4—112no—
283C22×C4⋊C4C2×D1111yescharacteristic
284C22×C22⋊C4—112no—
285C22×C22⋊C4—112no—
286C22×C22⋊C4—112no—
287C22×C22⋊C4—112no—
288C22×C22⋊C4—112no—
289C22×C42—111no—
290C22×C42—111no—
291C22×C42C2×D1111yescharacteristic
292#390—118no—
293#386—1116no—
294C2×#95—112no—
295C2×#95—112no—
296C2×#95—111no—
297C2×#95—112no—
298C2×#95—112no—
299C2×#95—112no—
300C2×#95—112no—
301C2×#95C2×D1111yescharacteristic
302C2×#95C2×D1112yes—
303C2×#95C2×D1112yes—
304C22×C11C22×C4211yescharacteristic
305C22×C11#51811yescharacteristic
306C22×C11#51812yes—
307C22×C11#51811yescharacteristic
308C22×C11#51812yes—
309C22×C11#51812yes—
310C22×C11#51812yes—
311C22×C11#51812yes—
312C22×C11#52012yes—
313C22×C11#52012yes—
314C22×C11#52012yes—
315C22×C11#56012yes—
316C22×C11#56011yescharacteristic
317C22×C11#56012yes—
318C22×C11#56012yes—
319C22×C11#56011yescharacteristic
320C22×C11H(3,𝔽4)11yescharacteristic
321C22×C11#56212yes—
322C22×C11#56212yes—
323C22×C11#56212yes—
324C22×C11#56311yescharacteristic
325C2×D11—28no—
326C2×D11—28no—
327C2×D11—28no—
328C2×D11—44no—
329C2×D11—44no—
330C2×D11—44no—
331C2×D11—44no—
332C2×D11—44no—
333C2×D11—44no—
334C2×D11—44no—
335C2×D11—44no—
336C2×D11—44no—
337C2×D11—44no—
338C2×D11—44no—
339C2×D11—44no—
340C4×C11—24no—
341C4×C11—44no—
342C4×C11—44no—
343C4×C11—42no—
344C4×C11—42no—
345Dic11—44no—
346Dic11—44no—
347Dic11—44no—
348C25—112no—
349C22×D4—118no—
350C22×D4—114no—
351C22×D4—441no—
352C22×D4—441no—
353C22×D4—442no—
354C23×C4—112no—
355C23×C4—112no—
356C23×C4—112no—
357C23×C4—118no—
358C23×C4—442no—
359C23×C4—442no—
360C23×C4—442no—
361C23×C4—442no—
362C23×C4—442no—
363C23×C4—442no—
364C23×C4C22×D1111yescharacteristic
365C23×C4C22×D1111yescharacteristic
366C23×C4C22×D1112yes—
367C23×C4C22×D1112yes—
368C23×C4C22×D1111yescharacteristic
369C2×C4⋊C4—41no—
370C2×C4⋊C4—41no—
371C2×C4⋊C4C4×D1114yescomplemented
372C2×C22⋊C4—118no—
373C2×C22⋊C4—118no—
374C2×C22⋊C4—118no—
375C2×C22⋊C4—118no—
376C2×C22⋊C4—118no—
377C2×C22⋊C4—442no—
378C2×C22⋊C4—442no—
379C2×C22⋊C4—442no—
380C2×C22⋊C4—442no—
381C2×C22⋊C4—442no—
382C2×C22⋊C4—442no—
383C2×C22⋊C4—442no—
384C2×C22⋊C4—442no—
385C2×C22⋊C4—442no—
386C2×C22⋊C4—442no—
387C2×C42—42no—
388C2×C42—41no—
389C2×C42—114no—
390C2×C42—442no—
391C2×C42—441no—
392C2×C42—442no—
393#95—42no—
394#95—41no—
395#95—118no—
396#95—441no—
397#95—442no—
398#95—442no—
399#95—442no—
400#95—442no—
401#95—442no—
402#95C4×D1118yescomplemented
403C2×C11#227311yescharacteristic
404C2×C11#227512yes—
405C2×C11#237512yes—
406C2×C11#237612yes—
407C2×C11#237712yes—
408C2×C11#237712yes—
409C2×C11#237712yes—
410C2×C11#237911yescharacteristic
411C2×C11#238011yescharacteristic
412D11—48no—
413C24—114no—
414C24—114no—
415C24—114no—
416C24—222no—
417C24—222no—
418C24—222no—
419C24—222no—
420C24—222no—
421C24—222no—
422C24—222no—
423C24—222no—
424C24—222no—
425C24—222no—
426C24—222no—
427C24—222no—
428C24C23×D1111yescharacteristic
429C2×D4—1116no—
430C2×D4—444no—
431C2×D4—444no—
432C2×D4—448no—
433C2×D4—448no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—21no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—21no—
447C22×C4—21no—
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—22no—
457C22×C4—114no—
458C22×C4—114no—
459C22×C4—114no—
460C22×C4—222no—
461C22×C4—222no—
462C22×C4—222no—
463C22×C4—222no—
464C22×C4—222no—
465C22×C4—222no—
466C22×C4—222no—
467C22×C4—222no—
468C22×C4—222no—
469C22×C4—222no—
470C22×C4—222no—
471C22×C4—222no—
472C22×C4—222no—
473C22×C4—222no—
474C22×C4—222no—
475C22×C4—222no—
476C22×C4—222no—
477C22×C4—222no—
478C22×C4—448no—
479C22×C4—448no—
480C22×C4—448no—
481C22×C4—448no—
482C22×C4—448no—
483C22×C4—448no—
484C22×C4—448no—
485C22×C4C2×C4×D1114yes—
486C22×C4C2×C4×D1114yes—
487C22×C4C2×C4×D1112yes—
488C22×C4C2×C4×D1112yes—
489C22×C4C2×C4×D1114yes—
490C22×C4C2×C4×D1112yes—
491C4⋊C4—44no—
492C22⋊C4—448no—
493C22⋊C4—448no—
494C22⋊C4—448no—
495C22⋊C4—448no—
496C22⋊C4—448no—
497C42—44no—
498C42—444no—
499C42—444no—
500C11#1383211yescharacteristic, complemented, Sylow
501C23—118no—
502C23—224no—
503C23—224no—
504C23—224no—
505C23—224no—
506C23—224no—
507C23—224no—
508C23—224no—
509C23—224no—
510C23—224no—
511C23—224no—
512C23—224no—
513C23—224no—
514C23—224no—
515C23—224no—
516C23—224no—
517C23—224no—
518C23—224no—
519C23—224no—
520C23—442no—
521C23—442no—
522C23—442no—
523C23—442no—
524C23—442no—
525C23—442no—
526C23—442no—
527C23—442no—
528C23—442no—
529C23—442no—
530C23—442no—
531C23—442no—
532C23—442no—
533C23—442no—
534C23—442no—
535C23—442no—
536C23C22×C4×D1111yescharacteristic
537C23C22×C4×D1112yes—
538C23#6703711yescharacteristic
539C23#6703711yescharacteristic
540C23#6703712yes—
541C23#6704012yes—
542C23#6704212yes—
543C23#6704212yes—
544C23#6704212yes—
545D4—4416no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—24no—
549C2×C4—24no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—41no—
570C2×C4—42no—
571C2×C4—41no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—224no—
575C2×C4—224no—
576C2×C4—224no—
577C2×C4—224no—
578C2×C4—224no—
579C2×C4—224no—
580C2×C4—224no—
581C2×C4—224no—
582C2×C4—224no—
583C2×C4—4432no—
584C2×C4—442no—
585C2×C4—442no—
586C2×C4—442no—
587C2×C4—442no—
588C2×C4—442no—
589C2×C4—442no—
590C2×C4—442no—
591C2×C4—442no—
592C2×C4—442no—
593C2×C4—442no—
594C2×C4—442no—
595C2×C4—442no—
596C2×C4C42×D1114yes—
597C22—228no—
598C22—228no—
599C22—228no—
600C22—444no—
601C22—444no—
602C22—444no—
603C22—444no—
604C22—444no—
605C22—444no—
606C22—444no—
607C22—444no—
608C22—444no—
609C22—444no—
610C22—444no—
611C22—444no—
612C22C2×C42×D1111yescharacteristic
613C22#1062301711yescharacteristic
614C22#1062303512yes—
615C22#1062305211yescharacteristic
616C22#1062305212yes—
617C22#1062307612yes—
618C22#1062307612yes—
619C22#1062307612yes—
620C22#1062307612yes—
621C22#1062310512yes—
622C22#1062310512yes—
623C22#1062312611yescharacteristic
624C22#1062315112yes—
625C22#1062317812yes—
626C22#1062317812yes—
627C22#1062319712yes—
628C22#1062319711yescharacteristic
629C22#1062321411yescharacteristic
630C22#1062323112yes—
631C22#1062324212yes—
632C22#1062326611yescharacteristic
633C4—24no—
634C4—44no—
635C4—44no—
636C4—42no—
637C4—42no—
638C4—444no—
639C4—444no—
640C4—444no—
641C2—448no—
642C2#1307096811yescharacteristic
643C2#1307097612yes—
644C2#1307175612yes—
645C2#1307176112yes—
646C2#1307177112yes—
647C2#1307177112yes—
648C2#1307177212yes—
649C2#1307178811yescharacteristic
650C2#1307179111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC22×C11C22×C42
FittingC11×#1436C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenter#1436D11
hypocenterC11#13832
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
3. #13066854C2semidirect
4. #13066852C2semidirect
5. #13066848C2semidirect
6. #13066841C2semidirect
7. (C2×D11)⋊#95C2semidirect
8. (C2×D11)⋊#95C2semidirect
9. C11×#1436C2semidirect
31. #10622601C4semidirect
32. #10622278C4semidirect
53. C22×C4×D11C2×C4semidirect
56. C2×C11×C4⋊C4C2×C4semidirect
71. C2×(C2×D11)⋊C4C2×C4semidirect
72. C2×(C2×D11)⋊C4C2×C4semidirect
73. C2×(C2×D11)⋊C4C2×C4semidirect
77. C2×C4×Dic11C2×C4semidirect
80. C11×#95C2×C4semidirect
87. C11⋊#95C2×C4semidirect
159. C2×D44C42semidirect
181. #1436D11semidirect
371. C2×C4⋊C4C4×D11semidirect
402. #95C4×D11semidirect
500. C11#13832semidirect

Maximal subgroups

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

subgroupindex
C2×#106226012
C2×#106222782
#130668542
#130668522
#130668482
#130668412
(C2×D11)⋊#952
C11×#14362
#1383211