Finite Group Databasebeta

← #14683831

Subgroups — #14683831

Order 2816.

1966 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×#10622564C212yesmaximal, complemented
2C2×#10622833C212yesmaximal
3#13066884C211yesmaximal, characteristic, complemented
4#13066873C212yesmaximal, complemented
5#13066861C212yesmaximal, complemented
6#13066848C211yesmaximal, characteristic, complemented
7#13066838C212yesmaximal, complemented
8#13066838C212yesmaximal, complemented
9C2×C11×#394C211yesmaximal, characteristic
10C23×D4×C11C2211yescharacteristic
11C24×Dic11C2212yes—
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C11×C22⋊C4C2212yes—
14C22×C11×C22⋊C4C2212yes—
15C22×C22⋊Dic11C2212yes—
16C22×C22⋊Dic11C2212yes—
17C22×C22⋊Dic11C2212yes—
18C22×C4⋊Dic11C2212yes—
19C22×C4×Dic11C2211yescharacteristic
20C11×#394C418yescomplemented
21C2×C11×#95C2211yescharacteristic
22#10622833—28no—
23C2×C11⋊#95C2212yes—
24C2×C11⋊#95C2212yes—
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2211yescharacteristic
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2211yescharacteristic
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2211yescharacteristic
33#10622564—28no—
34C25×C11C2312yes—
35C22×D4×C11—24no—
36C22×D4×C11—24no—
37C22×D4×C11—41no—
38C22×D4×C11—41no—
39C22×D4×C11C2×C414yes—
40C23×C4×C11C2311yescharacteristic
41C23×C4×C11C2312yes—
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2311yescharacteristic
44C23×Dic11—24no—
45C23×Dic11—24no—
46C23×Dic11—24no—
47C23×Dic11—42no—
48C23×Dic11—42no—
49C23×Dic11—42no—
50C23×Dic11—42no—
51C23×Dic11C2312yes—
52C23×Dic11C2312yes—
53C23×Dic11C2312yes—
54C23×Dic11C2312yes—
55C2×C11×C4⋊C4—41no—
56C2×C11×C4⋊C4—41no—
57C2×C11×C4⋊C4C2×C414yescomplemented
58C2×C11×C22⋊C4—24no—
59C2×C11×C22⋊C4—24no—
60C2×C11×C22⋊C4—42no—
61C2×C11×C22⋊C4—42no—
62C2×C11×C22⋊C4C2×C418yescomplemented
63C2×C11×C22⋊C4C2×C418yescomplemented
64C2×C22⋊Dic11—24no—
65C2×C22⋊Dic11—24no—
66C2×C22⋊Dic11—24no—
67C2×C22⋊Dic11—24no—
68C2×C22⋊Dic11—42no—
69C2×C22⋊Dic11—42no—
70C2×C22⋊Dic11—42no—
71C2×C22⋊Dic11—42no—
72C2×C22⋊Dic11D418yes—
73C2×C4⋊Dic11—24no—
74C2×C4⋊Dic11—42no—
75C2×C4⋊Dic11—42no—
76C2×C4×Dic11—24no—
77C2×C4×Dic11—41no—
78C11×#95C2×C414yescomplemented
79C11⋊#95—24no—
80C11⋊#95—24no—
81C11⋊#95—24no—
82C11⋊#95—24no—
83C11⋊#95—24no—
84C11⋊#95—42no—
85C11⋊#95—41no—
86C11⋊#95—41no—
87C11⋊#95—42no—
88C11⋊#95—41no—
89#14571—111nomaximal, Sylow
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×C11C22×C414yes—
103C24×C11C2×D414yes—
104C24×C11#4114yes—
105C24×C11C2411yescharacteristic
106C2×D4×C11—216no—
107C2×D4×C11—44no—
108C2×D4×C11—44no—
109C2×D4×C11—48no—
110C2×D4×C11—44no—
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—21no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—22no—
129C22×C4×C11C22×C414yes—
130C22×C4×C11C22×C412yes—
131C22×C4×C11C22×C412yes—
132C22×C4×C11C22×C412yes—
133C22×Dic11—22no—
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—48no—
159C22×Dic11—48no—
160C22×Dic11—48no—
161C22×Dic11—48no—
162C22×Dic11—48no—
163C22×Dic11—48no—
164C22×Dic11—48no—
165C22×Dic11C2×D414yes—
166C22×Dic11C2×D414yes—
167C22×Dic11#4114yes—
168C11×C4⋊C4—44no—
169C11×C22⋊C4—216no—
170C11×C22⋊C4—48no—
171C22⋊Dic11—48no—
172C22⋊Dic11—48no—
173C22⋊Dic11—48no—
174C4⋊Dic11—48no—
175C4×Dic11—44no—
176C2×#394D1111yescharacteristic
177C2×#388—112no—
178C2×#386—112no—
179#1445—111no—
180#1442—112no—
181#1439—112no—
182#1436—111no—
183C22⋊#95—112no—
184C22⋊#95—112no—
185C23×C11—24no—
186C23×C11—24no—
187C23×C11—24no—
188C23×C11—24no—
189C23×C11—24no—
190C23×C11—24no—
191C23×C11—24no—
192C23×C11—24no—
193C23×C11—24no—
194C23×C11—24no—
195C23×C11—24no—
196C23×C11—24no—
197C23×C11—24no—
198C23×C11—24no—
199C23×C11—24no—
200C23×C11—24no—
201C23×C11—24no—
202C23×C11—24no—
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×C11—42no—
218C23×C11—42no—
219C23×C11C4×D418yes—
220C23×C11C23×C411yescharacteristic
221C23×C11C22×D412yes—
222C23×C11C2×#4112yes—
223C23×C11C2×#4112yes—
224C23×C11H(5,𝔽2)12yes—
225C23×C11H(5,𝔽2)11yescharacteristic
226C23×C11H(5,𝔽2)11yescharacteristic
227C23×C11H(5,𝔽2)12yes—
228C23×C112−1+412yes—
229D4×C11—416no—
230C2×C4×C11—24no—
231C2×C4×C11—24no—
232C2×C4×C11—24no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—24no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
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—41no—
247C2×C4×C11—41no—
248C2×C4×C11—42no—
249C2×C4×C11—42no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×Dic11—24no—
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—432no—
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
282C24×C4—112no—
283C22×C4⋊C4—112no—
284C22×C4⋊C4C2×D1111yescharacteristic
285C22×C22⋊C4—112no—
286C22×C22⋊C4—112no—
287C22×C22⋊C4—112no—
288C22×C22⋊C4C2×D1112yes—
289C22×C22⋊C4C2×D1112yes—
290C22×C42—111no—
291#394Dic1118yescomplemented
292#388—228no—
293#386—228no—
294C2×#95—112no—
295C2×#95—112no—
296C2×#95—112no—
297C2×#95—112no—
298C2×#95—112no—
299C2×#95—111no—
300C2×#95—112no—
301C2×#95—111no—
302C2×#95—112no—
303C2×#95—111no—
304C2×#95C2×D1111yescharacteristic
305C22×C11—28no—
306C22×C11—28no—
307C22×C11—28no—
308C22×C11—44no—
309C22×C11—44no—
310C22×C11—44no—
311C22×C11—44no—
312C22×C11—44no—
313C22×C11—44no—
314C22×C11—44no—
315C22×C11—44no—
316C22×C11—44no—
317C22×C11—44no—
318C22×C11—44no—
319C22×C11—44no—
320C22×C11C2×C4×D412yes—
321C22×C11C4×#4111yescharacteristic
322C22×C11#51811yescharacteristic
323C22×C11#51811yescharacteristic
324C22×C11#52012yes—
325C22×C11#53412yes—
326C22×C11#53712yes—
327C22×C11#53812yes—
328C22×C11#53812yes—
329C22×C11#53912yes—
330C22×C11#54012yes—
331C22×C11D4211yescharacteristic
332C22×C11#54612yes—
333C22×C11#54612yes—
334C22×C11#54712yes—
335C22×C11#55111yescharacteristic
336C22×C11#55112yes—
337C22×C11#55212yes—
338C22×C11H(3,𝔽4)11yescharacteristic
339C22×C11#56212yes—
340C22×C11#56311yescharacteristic
341C4×C11—44no—
342C4×C11—42no—
343C4×C11—42no—
344C4×C11—42no—
345Dic11—44no—
346Dic11—44no—
347Dic11—44no—
348Dic11—82no—
349C25C22×D1112yes—
350C22×D4—24no—
351C22×D4—24no—
352C22×D4—41no—
353C22×D4—41no—
354C22×D4C2×Dic1114yes—
355C23×C4—112no—
356C23×C4—112no—
357C23×C4—112no—
358C23×C4—112no—
359C23×C4—224no—
360C23×C4—224no—
361C23×C4—224no—
362C23×C4—442no—
363C23×C4—442no—
364C23×C4—442no—
365C23×C4—442no—
366C23×C4C22×D1112yes—
367C23×C4C22×D1111yescharacteristic
368C23×C4C22×D1111yescharacteristic
369C23×C4C22×D1111yescharacteristic
370C2×C4⋊C4—41no—
371C2×C4⋊C4—41no—
372C2×C4⋊C4—224no—
373C2×C4⋊C4—442no—
374C2×C4⋊C4—442no—
375C2×C4⋊C4C2×Dic1114yescomplemented
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—42no—
379C2×C22⋊C4—42no—
380C2×C22⋊C4—118no—
381C2×C22⋊C4—224no—
382C2×C22⋊C4—224no—
383C2×C22⋊C4—224no—
384C2×C22⋊C4—224no—
385C2×C22⋊C4—442no—
386C2×C22⋊C4—442no—
387C2×C22⋊C4—442no—
388C2×C22⋊C4—442no—
389C2×C22⋊C4C2×Dic1118yescomplemented
390C2×C22⋊C4C2×Dic1118yescomplemented
391C2×C42—224no—
392C2×C42—441no—
393#95—224no—
394#95—224no—
395#95—224no—
396#95—224no—
397#95—224no—
398#95—442no—
399#95—441no—
400#95—441no—
401#95—441no—
402#95—442no—
403#95C2×Dic1114yescomplemented
404C2×C11—48no—
405C2×C11#232512yes—
406C2×C11#233311yescharacteristic
407C2×C11#235811yescharacteristic
408C2×C11#235912yes—
409C2×C11#237911yescharacteristic
410C2×C11#267112yes—
411C2×C11#268412yes—
412C2×C11#269512yes—
413C2×C11#274312yes—
414C24—22no—
415C24—22no—
416C24—22no—
417C24—22no—
418C24—22no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24D4×D1114yes—
427C24#434114yes—
428C24C22×Dic1114yes—
429C24C23×D1111yescharacteristic
430C2×D4—216no—
431C2×D4—44no—
432C2×D4—44no—
433C2×D4—44no—
434C2×D4—48no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—114no—
454C22×C4—114no—
455C22×C4—114no—
456C22×C4—222no—
457C22×C4—222no—
458C22×C4—222no—
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—448no—
482C22×C4—448no—
483C22×C4—448no—
484C22×C4—448no—
485C22×C4—448no—
486C22×C4—448no—
487C22×C4—448no—
488C22×C4C22×Dic1114yes—
489C22×C4C22×Dic1112yes—
490C22×C4C22×Dic1112yes—
491C22×C4C22×Dic1112yes—
492C4⋊C4—44no—
493C4⋊C4—448no—
494C22⋊C4—216no—
495C22⋊C4—48no—
496C22⋊C4—448no—
497C22⋊C4—448no—
498C22⋊C4—448no—
499C42—444no—
500C11#1457111yescharacteristic, complemented, Sylow
501C23—24no—
502C23—24no—
503C23—24no—
504C23—24no—
505C23—24no—
506C23—24no—
507C23—24no—
508C23—24no—
509C23—24no—
510C23—24no—
511C23—24no—
512C23—24no—
513C23—24no—
514C23—24no—
515C23—24no—
516C23—24no—
517C23—24no—
518C23—24no—
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—
535C23D4×Dic1118yes—
536C23C2×D4×D1112yes—
537C23C2×#434112yes—
538C23#6703711yescharacteristic
539C23#6703711yescharacteristic
540C23#6703712yes—
541C23#41×D1112yes—
542C23#6704212yes—
543C23#6704312yes—
544C23C23×Dic1111yescharacteristic
545D4—416no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—24no—
549C2×C4—22no—
550C2×C4—24no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—24no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—224no—
569C2×C4—224no—
570C2×C4—224no—
571C2×C4—224no—
572C2×C4—224no—
573C2×C4—224no—
574C2×C4—224no—
575C2×C4—224no—
576C2×C4—224no—
577C2×C4—4432no—
578C2×C4—442no—
579C2×C4—442no—
580C2×C4—442no—
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—
597C22—28no—
598C22—28no—
599C22—28no—
600C22—44no—
601C22—44no—
602C22—44no—
603C22—44no—
604C22—44no—
605C22—44no—
606C22—44no—
607C22—44no—
608C22—44no—
609C22—44no—
610C22—44no—
611C22—44no—
612C22#1062311811yescharacteristic
613C22#1062312111yescharacteristic
614C22#1062312212yes—
615C22#1062312812yes—
616C22#1062313312yes—
617C22#1062313612yes—
618C22#1062314412yes—
619C22#1062314612yes—
620C22#1062314812yes—
621C22#1062318112yes—
622C22#1062318512yes—
623C22#1062318612yes—
624C22#1062318912yes—
625C22#1062320311yescharacteristic
626C22#1062321411yescharacteristic
627C22#1062321512yes—
628C22C2×D4×Dic1112yes—
629C22#1062332911yescharacteristic
630C22#1062332911yescharacteristic
631C22#41×Dic1111yescharacteristic
632C22#1062335812yes—
633C4—42no—
634C4—44no—
635C4—42no—
636C4—42no—
637C4—444no—
638C4—444no—
639C4—444no—
640C4—882no—
641C2—48no—
642C2#1307132112yes—
643C2#1307138311yescharacteristic
644C2#1307160011yescharacteristic
645C2#1307161212yes—
646C2#1307179011yescharacteristic
647C2#1307484512yes—
648C2#1307499112yes—
649C2#1307515012yes—
650C2#1307575712yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#394C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC2×#394D11
hypocenterC11#14571
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
3. #13066884C2semidirect
4. #13066873C2semidirect
5. #13066861C2semidirect
6. #13066848C2semidirect
7. #13066838C2semidirect
8. #13066838C2semidirect
20. C11×#394C4semidirect
57. C2×C11×C4⋊C4C2×C4semidirect
62. C2×C11×C22⋊C4C2×C4semidirect
63. C2×C11×C22⋊C4C2×C4semidirect
78. C11×#95C2×C4semidirect
291. #394Dic11semidirect
375. C2×C4⋊C4C2×Dic11semidirect
389. C2×C22⋊C4C2×Dic11semidirect
390. C2×C22⋊C4C2×Dic11semidirect
403. #95C2×Dic11semidirect
500. C11#14571semidirect

Maximal subgroups

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

subgroupindex
C2×#106225642
C2×#106228332
#130668842
#130668732
#130668612
#130668482
#130668382
C2×C11×#3942
#1457111