Finite Group Databasebeta

← #14681813

Subgroups — #14681813

Order 2816.

1866 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622564C212yesmaximal, complemented
2C2×#10622825C212yesmaximal, complemented
3#13066873C212yesmaximal, complemented
4#13066861C212yesmaximal, complemented
5#13066857C211yesmaximal, characteristic
6#13066857C211yesmaximal, characteristic
7#13066853C212yesmaximal, complemented
8#13066850C212yesmaximal, complemented
9C2×C11×#386C211yesmaximal, characteristic
10C23×D4×C11C2211yescharacteristic
11C24×C4×C11C2211yescharacteristic
12C22×C11×C22⋊C4C2212yes—
13C22×C11×C22⋊C4C2211yescharacteristic
14C22×C22⋊Dic11C2212yes—
15C22×C22⋊Dic11C2212yes—
16C22×C22⋊Dic11C2211yescharacteristic
17C22×C22⋊Dic11C2212yes—
18C22×C22⋊Dic11C2211yescharacteristic
19C22×C4⋊Dic11C2212yes—
20C22×C4⋊Dic11C2212yes—
21C22×C4×Dic11C2212yes—
22C11×#386C418yescomplemented
23C2×C11×#95C2212yes—
24#10622825—28no—
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2211yescharacteristic
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2211yescharacteristic
32C2×C11⋊#95C2212yes—
33#10622564—28no—
34C25×C11C2311yescharacteristic
35C25×C11C2311yescharacteristic
36C22×D4×C11—24no—
37C22×D4×C11—42no—
38C22×D4×C11—41no—
39C22×D4×C11—41no—
40C22×D4×C11C2×C414yes—
41C23×C4×C11—24no—
42C23×C4×C11—24no—
43C23×C4×C11—41no—
44C23×C4×C11—41no—
45C23×C4×C11C2×C414yes—
46C23×C4×C11C2312yes—
47C23×C4×C11C2311yescharacteristic
48C23×C4×C11C2312yes—
49C23×Dic11C2312yes—
50C23×Dic11C2312yes—
51C23×Dic11C2312yes—
52C23×Dic11C2312yes—
53C2×C11×C22⋊C4—24no—
54C2×C11×C22⋊C4—24no—
55C2×C11×C22⋊C4—42no—
56C2×C11×C22⋊C4C2×C418yes—
57C2×C11×C22⋊C4C2×C414yes—
58C2×C22⋊Dic11—24no—
59C2×C22⋊Dic11—24no—
60C2×C22⋊Dic11—24no—
61C2×C22⋊Dic11—24no—
62C2×C22⋊Dic11—24no—
63C2×C22⋊Dic11—24no—
64C2×C22⋊Dic11—42no—
65C2×C22⋊Dic11—42no—
66C2×C22⋊Dic11—41no—
67C2×C22⋊Dic11—42no—
68C2×C22⋊Dic11—42no—
69C2×C22⋊Dic11—42no—
70C2×C22⋊Dic11—41no—
71C2×C4⋊Dic11—24no—
72C2×C4⋊Dic11—24no—
73C2×C4⋊Dic11—24no—
74C2×C4⋊Dic11—24no—
75C2×C4⋊Dic11—42no—
76C2×C4⋊Dic11—42no—
77C2×C4×Dic11—24no—
78C2×C4×Dic11—42no—
79C2×C4×Dic11—42no—
80C11×#95C2×C418yes—
81C11⋊#95—24no—
82C11⋊#95—24no—
83C11⋊#95—42no—
84C11⋊#95—41no—
85C11⋊#95—42no—
86C11⋊#95—42no—
87C11⋊#95—41no—
88C11⋊#95D418yescomplemented
89#14410—111nomaximal, Sylow
90C24×C11—22no—
91C24×C11—22no—
92C24×C11—22no—
93C24×C11—22no—
94C24×C11—21no—
95C24×C11—21no—
96C24×C11—22no—
97C24×C11—22no—
98C24×C11—22no—
99C24×C11—22no—
100C24×C11—22no—
101C24×C11—22no—
102C24×C11—21no—
103C24×C11—21no—
104C24×C11—22no—
105C24×C11C22×C412yes—
106C24×C11C22×C412yes—
107C24×C11#4114yes—
108C24×C11C2411yescharacteristic
109C2×D4×C11—28no—
110C2×D4×C11—44no—
111C2×D4×C11—44no—
112C2×D4×C11—48no—
113C2×D4×C11—48no—
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—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—216no—
129C22×C4×C11—44no—
130C22×C4×C11—44no—
131C22×C4×C11—48no—
132C22×C4×C11—44no—
133C22×C4×C11C22×C412yes—
134C22×C4×C11C22×C414yes—
135C22×C4×C11C22×C414yes—
136C22×C4×C11C2×D414yes—
137C22×C4×C11#4114yes—
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×Dic11—22no—
160C22×Dic11—22no—
161C22×Dic11—22no—
162C22×Dic11—22no—
163C22×Dic11—22no—
164C22×Dic11C2×D414yes—
165C22×Dic11C2×D414yes—
166C11×C22⋊C4—216no—
167C11×C22⋊C4—44no—
168C22⋊Dic11—48no—
169C22⋊Dic11—48no—
170C22⋊Dic11—44no—
171C22⋊Dic11—48no—
172C22⋊Dic11—44no—
173C4⋊Dic11—48no—
174C4⋊Dic11—48no—
175C4×Dic11—48no—
176C2×#388—112no—
177C2×#386D1111yescharacteristic
178C2×#380—112no—
179#1442—112no—
180#1439—112no—
181#1438—111no—
182#1438—111no—
183#1437—112no—
184#1436—112no—
185C23×C11—24no—
186C23×C11—22no—
187C23×C11—22no—
188C23×C11—24no—
189C23×C11—24no—
190C23×C11—24no—
191C23×C11—24no—
192C23×C11—24no—
193C23×C11—24no—
194C23×C11—24no—
195C23×C11—22no—
196C23×C11—24no—
197C23×C11—22no—
198C23×C11—22no—
199C23×C11—24no—
200C23×C11—42no—
201C23×C11—42no—
202C23×C11—42no—
203C23×C11—42no—
204C23×C11—41no—
205C23×C11—42no—
206C23×C11—41no—
207C23×C11—41no—
208C23×C11—42no—
209C23×C11—41no—
210C23×C11—42no—
211C23×C11—42no—
212C23×C11—42no—
213C23×C11—42no—
214C23×C11—42no—
215C23×C11—42no—
216C23×C11—41no—
217C23×C11—42no—
218C23×C11—42no—
219C23×C11—42no—
220C23×C11—41no—
221C23×C11—42no—
222C23×C11—42no—
223C23×C11—41no—
224C23×C11—42no—
225C23×C11—41no—
226C23×C11#11714yes—
227C23×C11C23×C411yescharacteristic
228C23×C11C22×D412yes—
229C23×C11C2×#4112yes—
230C23×C11C2×#4112yes—
231C23×C11H(5,𝔽2)12yes—
232C23×C11H(5,𝔽2)11yescharacteristic
233C23×C11H(5,𝔽2)11yescharacteristic
234C23×C11H(5,𝔽2)12yes—
235C23×C112−1+412yes—
236D4×C11—416no—
237C2×C4×C11—24no—
238C2×C4×C11—24no—
239C2×C4×C11—24no—
240C2×C4×C11—24no—
241C2×C4×C11—24no—
242C2×C4×C11—24no—
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—416no—
250C2×C4×C11—42no—
251C2×C4×C11—42no—
252C2×C4×C11—42no—
253C2×C4×C11—42no—
254C2×C4×C11—42no—
255C2×C4×C11—42no—
256C2×C4×C11C4×D418yes—
257C2×Dic11—24no—
258C2×Dic11—24no—
259C2×Dic11—24no—
260C2×Dic11—24no—
261C2×Dic11—24no—
262C2×Dic11—24no—
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—
281C2×Dic11—42no—
282C2×Dic11—42no—
283C2×Dic11—42no—
284C2×Dic11—42no—
285C23×D4C2×D1111yescharacteristic
286C24×C4C2×D1111yescharacteristic
287C22×C4⋊C4—112no—
288C22×C4⋊C4—112no—
289C22×C22⋊C4—112no—
290C22×C22⋊C4—112no—
291C22×C22⋊C4—111no—
292C22×C22⋊C4—112no—
293C22×C22⋊C4—111no—
294C22×C22⋊C4C2×D1112yes—
295C22×C22⋊C4C2×D1111yescharacteristic
296C22×C42—112no—
297#388—228no—
298#386Dic1118yescomplemented
299#380—228no—
300C2×#95—112no—
301C2×#95—112no—
302C2×#95—112no—
303C2×#95—111no—
304C2×#95—112no—
305C2×#95—112no—
306C2×#95—112no—
307C2×#95—111no—
308C2×#95C2×D1112yes—
309C22×C11—24no—
310C22×C11—28no—
311C22×C11—44no—
312C22×C11—42no—
313C22×C11—42no—
314C22×C11—44no—
315C22×C11—44no—
316C22×C11—44no—
317C22×C11—44no—
318C22×C11—42no—
319C22×C11—44no—
320C22×C11—44no—
321C22×C11—42no—
322C22×C11—42no—
323C22×C11—82no—
324C22×C11—82no—
325C22×C11—82no—
326C22×C11—82no—
327C22×C11C2×#11711yescharacteristic
328C22×C11C2×C4×D412yes—
329C22×C11#51811yescharacteristic
330C22×C11#51811yescharacteristic
331C22×C11#52012yes—
332C22×C11#53512yes—
333C22×C11#53712yes—
334C22×C11#53812yes—
335C22×C11#53812yes—
336C22×C11#54012yes—
337C22×C11#54212yes—
338C22×C11D4211yescharacteristic
339C22×C11#54612yes—
340C22×C11#54612yes—
341C22×C11#54812yes—
342C22×C11#55111yescharacteristic
343C22×C11#55212yes—
344C22×C11#55312yes—
345C22×C11#56011yescharacteristic
346C22×C11#56212yes—
347C22×C11#56311yescharacteristic
348C4×C11—28no—
349C4×C11—42no—
350C4×C11—44no—
351Dic11—44no—
352Dic11—44no—
353Dic11—82no—
354Dic11—82no—
355C25C22×D1111yescharacteristic
356C25C22×D1111yescharacteristic
357C22×D4—24no—
358C22×D4—42no—
359C22×D4—41no—
360C22×D4—41no—
361C22×D4C2×Dic1114yes—
362C23×C4—24no—
363C23×C4—24no—
364C23×C4—41no—
365C23×C4—41no—
366C23×C4—112no—
367C23×C4—112no—
368C23×C4—112no—
369C23×C4—112no—
370C23×C4C2×Dic1114yes—
371C23×C4C22×D1112yes—
372C23×C4C22×D1111yescharacteristic
373C23×C4C22×D1112yes—
374C2×C4⋊C4—224no—
375C2×C4⋊C4—224no—
376C2×C4⋊C4—224no—
377C2×C4⋊C4—224no—
378C2×C4⋊C4—442no—
379C2×C4⋊C4—442no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—42no—
383C2×C22⋊C4—224no—
384C2×C22⋊C4—224no—
385C2×C22⋊C4—224no—
386C2×C22⋊C4—224no—
387C2×C22⋊C4—224no—
388C2×C22⋊C4—224no—
389C2×C22⋊C4—441no—
390C2×C22⋊C4—442no—
391C2×C22⋊C4—442no—
392C2×C22⋊C4—442no—
393C2×C22⋊C4—442no—
394C2×C22⋊C4—441no—
395C2×C22⋊C4—442no—
396C2×C22⋊C4C2×Dic1118yes—
397C2×C22⋊C4C2×Dic1114yes—
398C2×C42—224no—
399C2×C42—442no—
400C2×C42—442no—
401#95—118no—
402#95—224no—
403#95—224no—
404#95—442no—
405#95—442no—
406#95—441no—
407#95—441no—
408#95—442no—
409#95C2×Dic1118yes—
410C2×C11—44no—
411C2×C11—82no—
412C2×C11#231211yescharacteristic
413C2×C11#232412yes—
414C2×C11#235212yes—
415C2×C11#235811yescharacteristic
416C2×C11#237611yescharacteristic
417C2×C11#267612yes—
418C2×C11#270212yes—
419C2×C11#270312yes—
420C2×C11#274112yes—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—21no—
425C24—21no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—21no—
432C24—21no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24#433914yes—
437C24C22×Dic1112yes—
438C24C22×Dic1112yes—
439C24C23×D1111yescharacteristic
440C2×D4—28no—
441C2×D4—44no—
442C2×D4—44no—
443C2×D4—48no—
444C2×D4—48no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—216no—
460C22×C4—44no—
461C22×C4—44no—
462C22×C4—44no—
463C22×C4—48no—
464C22×C4—114no—
465C22×C4—114no—
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×C4—222no—
485C22×C4—222no—
486C22×C4—222no—
487C22×C4—222no—
488C22×C4—222no—
489C22×C4—222no—
490C22×C4—222no—
491C22×C4—222no—
492C22×C4D4×D1114yes—
493C22×C4#434114yes—
494C22×C4C22×Dic1112yes—
495C22×C4C22×Dic1114yes—
496C22×C4C22×Dic1114yes—
497C4⋊C4—448no—
498C4⋊C4—448no—
499C22⋊C4—216no—
500C22⋊C4—44no—
501C22⋊C4—444no—
502C22⋊C4—448no—
503C22⋊C4—448no—
504C22⋊C4—448no—
505C22⋊C4—444no—
506C42—448no—
507C11#1441011yescharacteristic, complemented, Sylow
508C23—24no—
509C23—24no—
510C23—24no—
511C23—24no—
512C23—22no—
513C23—22no—
514C23—24no—
515C23—24no—
516C23—24no—
517C23—24no—
518C23—22no—
519C23—24no—
520C23—22no—
521C23—22no—
522C23—24no—
523C23—41no—
524C23—41no—
525C23—42no—
526C23—42no—
527C23—42no—
528C23—42no—
529C23—42no—
530C23—41no—
531C23—41no—
532C23—42no—
533C23—42no—
534C23—42no—
535C23—42no—
536C23—42no—
537C23—42no—
538C23—42no—
539C23—41no—
540C23—41no—
541C23—42no—
542C23—42no—
543C23—42no—
544C23—42no—
545C23—42no—
546C23—41no—
547C23—41no—
548C23—42no—
549C23#6697914yes—
550C23C2×#433912yes—
551C23C2×D4×D1112yes—
552C23C2×#434112yes—
553C23#6703711yescharacteristic
554C23#6703711yescharacteristic
555C23#6703712yes—
556C23#6704212yes—
557C23#6704312yes—
558C23C23×Dic1111yescharacteristic
559D4—416no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—22no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—24no—
572C2×C4—416no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—224no—
580C2×C4—224no—
581C2×C4—224no—
582C2×C4—224no—
583C2×C4—224no—
584C2×C4—224no—
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×C4—442no—
601C2×C4—442no—
602C2×C4—442no—
603C2×C4—442no—
604C2×C4—442no—
605C2×C4—442no—
606C2×C4—442no—
607C2×C4D4×Dic1118yes—
608C22—24no—
609C22—28no—
610C22—44no—
611C22—44no—
612C22—44no—
613C22—42no—
614C22—44no—
615C22—44no—
616C22—42no—
617C22—42no—
618C22—42no—
619C22—44no—
620C22—44no—
621C22—42no—
622C22—82no—
623C22—82no—
624C22—82no—
625C22—82no—
626C22#1062302512yes—
627C22#1062302512yes—
628C22#1062307212yes—
629C22#1062308112yes—
630C22#1062308312yes—
631C22#1062309612yes—
632C22#1062311811yescharacteristic
633C22#1062312111yescharacteristic
634C22#1062312212yes—
635C22#1062313412yes—
636C22#1062313812yes—
637C22#1062313912yes—
638C22#1062315012yes—
639C22#1062318211yescharacteristic
640C22#1062319711yescharacteristic
641C22#1062319812yes—
642C22C2×#6697911yescharacteristic
643C22C2×D4×Dic1112yes—
644C22#1062332911yescharacteristic
645C22#1062332911yescharacteristic
646C22#1062335812yes—
647C4—28no—
648C4—42no—
649C4—44no—
650C4—444no—
651C4—444no—
652C4—882no—
653C4—882no—
654C2—44no—
655C2—82no—
656C2#1307121411yescharacteristic
657C2#1307131112yes—
658C2#1307154512yes—
659C2#1307160011yescharacteristic
660C2#1307176411yescharacteristic
661C2#1307492112yes—
662C2#1307524812yes—
663C2#1307526312yes—
664C2#1307573512yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#386C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC2×#386D11
hypocenterC11#14410
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. C2×#10622564C2semidirect
2. C2×#10622825C2semidirect
3. #13066873C2semidirect
4. #13066861C2semidirect
7. #13066853C2semidirect
8. #13066850C2semidirect
22. C11×#386C4semidirect
88. C11⋊#95D4semidirect
298. #386Dic11semidirect
507. C11#14410semidirect

Maximal subgroups

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

subgroupindex
C2×#106225642
C2×#106228252
#130668732
#130668612
#130668572
#130668532
#130668502
C2×C11×#3862
#1441011