Finite Group Databasebeta

← #14684055

Subgroups — #14684055

Order 2816.

1650 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622564C212yesmaximal, complemented
2#13066869C211yesmaximal, characteristic, complemented
3#13066861C212yesmaximal, complemented
4#13066857C212yesmaximal
5#13066853C212yesmaximal, complemented
6#13066853C212yesmaximal, complemented
7#13066845C211yesmaximal, characteristic, complemented
8#13066841C212yesmaximal, complemented
9C2×C11×#394C211yesmaximal, characteristic
10C23×D4×C11C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12C22×C11×C22⋊C4C2212yes—
13C22×C11×C22⋊C4C2212yes—
14C22×C22⋊Dic11C2212yes—
15C22×C22⋊Dic11C2212yes—
16C22×C22⋊Dic11C2212yes—
17C22×C22⋊Dic11C2212yes—
18C22×C4⋊Dic11C2211yescharacteristic
19C22×C4⋊Dic11C2211yescharacteristic
20C22×C4×Dic11C2212yes—
21C22×C4×Dic11C2211yescharacteristic
22C11×#394C418yescomplemented
23C2×C11×#95C2211yescharacteristic
24C2×C11⋊#95C2212yes—
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2211yescharacteristic
32#10622564—28no—
33C25×C11C2312yes—
34C22×D4×C11—42no—
35C22×D4×C11—42no—
36C22×D4×C11—41no—
37C22×D4×C11—41no—
38C22×D4×C11C2×C414yes—
39C23×C4×C11C2312yes—
40C23×C4×C11C2311yescharacteristic
41C23×C4×C11C2311yescharacteristic
42C23×C4×C11C2311yescharacteristic
43C23×Dic11C2312yes—
44C23×Dic11C2312yes—
45C23×Dic11C2312yes—
46C23×Dic11C2312yes—
47C2×C11×C4⋊C4—41no—
48C2×C11×C4⋊C4—41no—
49C2×C11×C4⋊C4C2×C414yes—
50C2×C11×C22⋊C4—24no—
51C2×C11×C22⋊C4—24no—
52C2×C11×C22⋊C4—42no—
53C2×C11×C22⋊C4—42no—
54C2×C11×C22⋊C4C2×C418yes—
55C2×C11×C22⋊C4C2×C418yes—
56C2×C22⋊Dic11—24no—
57C2×C22⋊Dic11—24no—
58C2×C22⋊Dic11—24no—
59C2×C22⋊Dic11—24no—
60C2×C22⋊Dic11—24no—
61C2×C22⋊Dic11—24no—
62C2×C22⋊Dic11—42no—
63C2×C22⋊Dic11—42no—
64C2×C22⋊Dic11—42no—
65C2×C22⋊Dic11—42no—
66C2×C22⋊Dic11—42no—
67C2×C22⋊Dic11—42no—
68C2×C4⋊Dic11—41no—
69C2×C4⋊Dic11—41no—
70C2×C4⋊Dic11—42no—
71C2×C4⋊Dic11—41no—
72C2×C4⋊Dic11D414yescomplemented
73C2×C4×Dic11—22no—
74C2×C4×Dic11—24no—
75C2×C4×Dic11—24no—
76C2×C4×Dic11—41no—
77C2×C4×Dic11—41no—
78C2×C4×Dic11—42no—
79C11×#95C2×C414yes—
80C11⋊#95—24no—
81C11⋊#95—24no—
82C11⋊#95—24no—
83C11⋊#95—42no—
84C11⋊#95—42no—
85C11⋊#95—42no—
86C11⋊#95—42no—
87C11⋊#95—41no—
88#14589—111nomaximal, Sylow
89C24×C11—22no—
90C24×C11—22no—
91C24×C11—22no—
92C24×C11—22no—
93C24×C11—22no—
94C24×C11—22no—
95C24×C11—22no—
96C24×C11—22no—
97C24×C11—22no—
98C24×C11—22no—
99C24×C11—22no—
100C24×C11—22no—
101C24×C11—22no—
102C24×C11—22no—
103C24×C11C22×C414yes—
104C24×C11C2411yescharacteristic
105C2×D4×C11—44no—
106C2×D4×C11—48no—
107C2×D4×C11—44no—
108C2×D4×C11—48no—
109C2×D4×C11—44no—
110C22×C4×C11—21no—
111C22×C4×C11—21no—
112C22×C4×C11—21no—
113C22×C4×C11—21no—
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—21no—
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—21no—
128C22×C4×C11C22×C414yes—
129C22×C4×C11C22×C412yes—
130C22×C4×C11C22×C412yes—
131C22×C4×C11C22×C412yes—
132C22×C4×C11C2×D412yes—
133C22×C4×C11#4112yes—
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×Dic11—22no—
153C22×Dic11—22no—
154C22×Dic11—22no—
155C22×Dic11—22no—
156C22×Dic11—22no—
157C22×Dic11—22no—
158C22×Dic11—22no—
159C22×Dic11C2×D414yes—
160C22×Dic11#4114yes—
161C22×Dic11#4114yes—
162C11×C4⋊C4—44no—
163C11×C22⋊C4—216no—
164C11×C22⋊C4—48no—
165C22⋊Dic11—48no—
166C22⋊Dic11—48no—
167C22⋊Dic11—48no—
168C22⋊Dic11—48no—
169C4⋊Dic11—44no—
170C4⋊Dic11—44no—
171C4×Dic11—44no—
172C4×Dic11—48no—
173C2×#394D1111yescharacteristic
174C2×#388—112no—
175#1441—111no—
176#1439—112no—
177#1438—112no—
178#1437—112no—
179#1437—112no—
180C4⋊#95—111no—
181#1434—112no—
182C23×C11—24no—
183C23×C11—24no—
184C23×C11—24no—
185C23×C11—24no—
186C23×C11—24no—
187C23×C11—24no—
188C23×C11—24no—
189C23×C11—42no—
190C23×C11—42no—
191C23×C11—42no—
192C23×C11—42no—
193C23×C11—42no—
194C23×C11—42no—
195C23×C11—42no—
196C23×C11—42no—
197C23×C11—42no—
198C23×C11—42no—
199C23×C11—42no—
200C23×C11—42no—
201C23×C11—42no—
202C23×C11—42no—
203C23×C11—42no—
204C23×C11—42no—
205C23×C11—42no—
206C23×C11—42no—
207C23×C11—42no—
208C23×C11—42no—
209C23×C11—42no—
210C23×C11—42no—
211C23×C11—42no—
212C23×C11—42no—
213C23×C11—42no—
214C23×C11—42no—
215C23×C11—42no—
216C23×C11—42no—
217C23×C11C23×C411yescharacteristic
218C23×C11C22×D411yescharacteristic
219C23×C11C2×#4111yescharacteristic
220C23×C11C2×#4112yes—
221C23×C11C2×#4112yes—
222C23×C11H(5,𝔽2)11yescharacteristic
223C23×C11H(5,𝔽2)11yescharacteristic
224C23×C11H(5,𝔽2)12yes—
225C23×C11H(5,𝔽2)12yes—
226C23×C11H(5,𝔽2)11yescharacteristic
227C23×C112−1+411yescharacteristic
228D4×C11—416no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—24no—
236C2×C4×C11—24no—
237C2×C4×C11—24no—
238C2×C4×C11—24no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—24no—
242C2×C4×C11—42no—
243C2×C4×C11—42no—
244C2×C4×C11—42no—
245C2×C4×C11—42no—
246C2×C4×C11—41no—
247C2×C4×C11—42no—
248C2×C4×C11—41no—
249C2×C4×C11—42no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11C4×D414yes—
253C2×Dic11—24no—
254C2×Dic11—24no—
255C2×Dic11—24no—
256C2×Dic11—24no—
257C2×Dic11—24no—
258C2×Dic11—24no—
259C2×Dic11—24no—
260C2×Dic11—24no—
261C2×Dic11—24no—
262C2×Dic11—42no—
263C2×Dic11—42no—
264C2×Dic11—42no—
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—42no—
274C2×Dic11—42no—
275C2×Dic11—42no—
276C2×Dic11—42no—
277C2×Dic11—42no—
278C2×Dic11—42no—
279C2×Dic11—42no—
280C2×Dic11—42no—
281C23×D4C2×D1111yescharacteristic
282C22×C4⋊C4—111no—
283C22×C4⋊C4—111no—
284C22×C4⋊C4C2×D1111yescharacteristic
285C22×C22⋊C4—112no—
286C22×C22⋊C4—112no—
287C22×C22⋊C4—112no—
288C22×C22⋊C4—112no—
289C22×C22⋊C4C2×D1112yes—
290C22×C22⋊C4C2×D1112yes—
291C22×C42—112no—
292C22×C42—111no—
293#394Dic1118yescomplemented
294#388—228no—
295C2×#95—112no—
296C2×#95—112no—
297C2×#95—112no—
298C2×#95—112no—
299C2×#95—112no—
300C2×#95—112no—
301C2×#95—112no—
302C2×#95—111no—
303C2×#95C2×D1111yescharacteristic
304C22×C11—44no—
305C22×C11—44no—
306C22×C11—44no—
307C22×C11—44no—
308C22×C11—44no—
309C22×C11—44no—
310C22×C11—44no—
311C22×C11—82no—
312C22×C11—82no—
313C22×C11—82no—
314C22×C11—82no—
315C22×C11—82no—
316C22×C11—82no—
317C22×C11—82no—
318C22×C11—82no—
319C22×C11C2×C4×D411yescharacteristic
320C22×C11C4×#4112yes—
321C22×C11#51811yescharacteristic
322C22×C11#51812yes—
323C22×C11#52011yescharacteristic
324C22×C11#53411yescharacteristic
325C22×C11#53711yescharacteristic
326C22×C11#53811yescharacteristic
327C22×C11#53812yes—
328C22×C11#53911yescharacteristic
329C22×C11#53912yes—
330C22×C11#54012yes—
331C22×C11#54212yes—
332C22×C11#54612yes—
333C22×C11#55012yes—
334C22×C11#55112yes—
335C22×C11#55312yes—
336C22×C11#55512yes—
337C22×C11#55511yescharacteristic
338C22×C11#55511yescharacteristic
339C22×C11#56011yescharacteristic
340C22×C11#56012yes—
341C22×C11H(3,𝔽4)11yescharacteristic
342C4×C11—24no—
343C4×C11—44no—
344C4×C11—42no—
345C4×C11—42no—
346Dic11—44no—
347Dic11—44no—
348Dic11—44no—
349Dic11—82no—
350C25C22×D1112yes—
351C22×D4—42no—
352C22×D4—42no—
353C22×D4—41no—
354C22×D4—41no—
355C22×D4C2×Dic1114yes—
356C23×C4—112no—
357C23×C4—112no—
358C23×C4—112no—
359C23×C4—112no—
360C23×C4C22×D1111yescharacteristic
361C23×C4C22×D1112yes—
362C23×C4C22×D1111yescharacteristic
363C23×C4C22×D1111yescharacteristic
364C2×C4⋊C4—41no—
365C2×C4⋊C4—41no—
366C2×C4⋊C4—114no—
367C2×C4⋊C4—441no—
368C2×C4⋊C4—441no—
369C2×C4⋊C4—442no—
370C2×C4⋊C4—441no—
371C2×C4⋊C4C2×Dic1114yes—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—42no—
375C2×C22⋊C4—42no—
376C2×C22⋊C4—224no—
377C2×C22⋊C4—224no—
378C2×C22⋊C4—224no—
379C2×C22⋊C4—224no—
380C2×C22⋊C4—224no—
381C2×C22⋊C4—224no—
382C2×C22⋊C4—442no—
383C2×C22⋊C4—442no—
384C2×C22⋊C4—442no—
385C2×C22⋊C4—442no—
386C2×C22⋊C4—442no—
387C2×C22⋊C4—442no—
388C2×C22⋊C4C2×Dic1118yes—
389C2×C22⋊C4C2×Dic1118yes—
390C2×C42—224no—
391C2×C42—224no—
392C2×C42—222no—
393C2×C42—441no—
394C2×C42—441no—
395C2×C42—442no—
396#95—224no—
397#95—224no—
398#95—224no—
399#95—442no—
400#95—442no—
401#95—441no—
402#95—442no—
403#95—442no—
404#95C2×Dic1114yes—
405C2×C11—84no—
406C2×C11#232511yescharacteristic
407C2×C11#233512yes—
408C2×C11#236312yes—
409C2×C11#237211yescharacteristic
410C2×C11#237511yescharacteristic
411C2×C11#269911yescharacteristic
412C2×C11#270512yes—
413C2×C11#273311yescharacteristic
414C2×C11#275612yes—
415C2×C11#278511yescharacteristic
416C2×C11#279511yescharacteristic
417C24—22no—
418C24—22no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24C22×Dic1114yes—
432C24C23×D1111yescharacteristic
433C2×D4—44no—
434C2×D4—48no—
435C2×D4—44no—
436C2×D4—48no—
437C2×D4—44no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—114no—
457C22×C4—114no—
458C22×C4—114no—
459C22×C4—222no—
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—222no—
479C22×C4—222no—
480C22×C4—222no—
481C22×C4—222no—
482C22×C4—222no—
483C22×C4—222no—
484C22×C4D4×D1112yes—
485C22×C4#434112yes—
486C22×C4C22×Dic1114yes—
487C22×C4C22×Dic1112yes—
488C22×C4C22×Dic1112yes—
489C22×C4C22×Dic1112yes—
490C4⋊C4—44no—
491C4⋊C4—444no—
492C4⋊C4—444no—
493C22⋊C4—216no—
494C22⋊C4—48no—
495C22⋊C4—448no—
496C22⋊C4—448no—
497C22⋊C4—448no—
498C22⋊C4—448no—
499C42—444no—
500C42—448no—
501C11#1458911yescharacteristic, complemented, Sylow
502C23—24no—
503C23—24no—
504C23—24no—
505C23—24no—
506C23—24no—
507C23—24no—
508C23—24no—
509C23—42no—
510C23—42no—
511C23—42no—
512C23—42no—
513C23—42no—
514C23—42no—
515C23—42no—
516C23—42no—
517C23—42no—
518C23—42no—
519C23—42no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23—42no—
524C23—42no—
525C23—42no—
526C23—42no—
527C23—42no—
528C23—42no—
529C23—42no—
530C23—42no—
531C23—42no—
532C23—42no—
533C23—42no—
534C23—42no—
535C23—42no—
536C23—42no—
537C23C2×D4×D1111yescharacteristic
538C23C2×#434111yescharacteristic
539C23#6703712yes—
540C23#6703711yescharacteristic
541C23#6703711yescharacteristic
542C23#6703712yes—
543C23#41×D1112yes—
544C23#41×D1112yes—
545C23#6704211yescharacteristic
546C23#6704311yescharacteristic
547C23C23×Dic1111yescharacteristic
548D4—416no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—42no—
565C2×C4—41no—
566C2×C4—42no—
567C2×C4—41no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—224no—
573C2×C4—224no—
574C2×C4—224no—
575C2×C4—224no—
576C2×C4—224no—
577C2×C4—224no—
578C2×C4—224no—
579C2×C4—224no—
580C2×C4—224no—
581C2×C4—442no—
582C2×C4—442no—
583C2×C4—442no—
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×C4—442no—
597C2×C4—442no—
598C2×C4—442no—
599C2×C4—442no—
600C2×C4D4×Dic1114yes—
601C22—44no—
602C22—44no—
603C22—44no—
604C22—44no—
605C22—44no—
606C22—44no—
607C22—44no—
608C22—82no—
609C22—82no—
610C22—82no—
611C22—82no—
612C22—82no—
613C22—82no—
614C22—82no—
615C22—82no—
616C22#1062312511yescharacteristic
617C22#1062312612yes—
618C22#1062312611yescharacteristic
619C22#1062312811yescharacteristic
620C22#1062313012yes—
621C22#1062313311yescharacteristic
622C22#1062313611yescharacteristic
623C22#1062314312yes—
624C22#1062314512yes—
625C22#1062314712yes—
626C22#1062314811yescharacteristic
627C22#1062318812yes—
628C22#1062319112yes—
629C22#1062319312yes—
630C22#1062319412yes—
631C22#1062320111yescharacteristic
632C22#1062320111yescharacteristic
633C22#1062321012yes—
634C22C2×D4×Dic1111yescharacteristic
635C22#1062332912yes—
636C22#1062332911yescharacteristic
637C22#41×Dic1112yes—
638C22#1062335811yescharacteristic
639C4—24no—
640C4—44no—
641C4—42no—
642C4—42no—
643C4—444no—
644C4—444no—
645C4—444no—
646C4—882no—
647C2—84no—
648C2#1307132111yescharacteristic
649C2#1307141012yes—
650C2#1307165812yes—
651C2#1307172811yescharacteristic
652C2#1307175711yescharacteristic
653C2#1307519811yescharacteristic
654C2#1307528212yes—
655C2#1307563911yescharacteristic
656C2#1307593712yes—
657C2#1307632311yescharacteristic
658C2#1307644911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#394C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC2×#394D11
hypocenterC11#14589
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. C2×#10622564C2semidirect
2. #13066869C2semidirect
3. #13066861C2semidirect
5. #13066853C2semidirect
6. #13066853C2semidirect
7. #13066845C2semidirect
8. #13066841C2semidirect
22. C11×#394C4semidirect
72. C2×C4⋊Dic11D4semidirect
293. #394Dic11semidirect
501. C11#14589semidirect

Maximal subgroups

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

subgroupindex
C2×#106225642
#130668692
#130668612
#130668572
#130668532
#130668452
#130668412
C2×C11×#3942
#1458911