Finite Group Databasebeta

← #14682953

Subgroups — #14682953

Order 2816.

1962 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622564C212yesmaximal, complemented
2#13066884C212yesmaximal, complemented
3#13066861C212yesmaximal, complemented
4#13066857C211yesmaximal, characteristic
5#13066857C211yesmaximal, characteristic
6#13066853C212yesmaximal, complemented
7#13066845C212yesmaximal, complemented
8#13066839C212yesmaximal, complemented
9C22×C11×#123C211yesmaximal, characteristic
10C23×D4×C11C2211yescharacteristic
11C24×C4×C11C2211yescharacteristic
12C2×C11×#123—28no—
13C2×C11×#123C418yescomplemented
14C22×C11×C4⋊C4C2212yes—
15C22×C11×C22⋊C4C2212yes—
16C22×C11×C22⋊C4C2211yescharacteristic
17C22×C22⋊Dic11C2212yes—
18C22×C22⋊Dic11C2212yes—
19C22×C22⋊Dic11C2211yescharacteristic
20C22×C22⋊Dic11C2212yes—
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C4⋊Dic11C2212yes—
23C22×C4×Dic11C2212yes—
24C2×C11⋊#95C2212yes—
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2211yescharacteristic
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2211yescharacteristic
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—42no—
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—
53C11×#123—232no—
54C2×C11×C4⋊C4—24no—
55C2×C11×C4⋊C4—24no—
56C2×C11×C4⋊C4C2×C418yes—
57C2×C11×C22⋊C4—24no—
58C2×C11×C22⋊C4—24no—
59C2×C11×C22⋊C4C2×C418yes—
60C2×C11×C22⋊C4C2×C414yes—
61C2×C11×C22⋊C4D418yes—
62C2×C22⋊Dic11—24no—
63C2×C22⋊Dic11—24no—
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—41no—
71C2×C22⋊Dic11—42no—
72C2×C22⋊Dic11—42no—
73C2×C22⋊Dic11—41no—
74C2×C22⋊Dic11—42no—
75C2×C4⋊Dic11—24no—
76C2×C4⋊Dic11—24no—
77C2×C4⋊Dic11—42no—
78C2×C4×Dic11—24no—
79C2×C4×Dic11—24no—
80C2×C4×Dic11—42no—
81C11⋊#95—24no—
82C11⋊#95—24no—
83C11⋊#95—41no—
84C11⋊#95—42no—
85C11⋊#95—42no—
86C11⋊#95—42no—
87C11⋊#95—42no—
88C11⋊#95—41no—
89C11⋊#95—42no—
90#14506—111nomaximal, Sylow
91C24×C11—22no—
92C24×C11—22no—
93C24×C11—22no—
94C24×C11—22no—
95C24×C11—21no—
96C24×C11—21no—
97C24×C11—22no—
98C24×C11—22no—
99C24×C11—22no—
100C24×C11—22no—
101C24×C11—22no—
102C24×C11—22no—
103C24×C11—21no—
104C24×C11—21no—
105C24×C11—22no—
106C24×C11C22×C412yes—
107C24×C11C22×C412yes—
108C24×C11C2×D414yes—
109C24×C11C2411yescharacteristic
110C2×D4×C11—28no—
111C2×D4×C11—44no—
112C2×D4×C11—44no—
113C2×D4×C11—48no—
114C2×D4×C11—48no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—28no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—44no—
131C22×C4×C11—44no—
132C22×C4×C11—48no—
133C22×C4×C11—48no—
134C22×C4×C11C22×C414yes—
135C22×C4×C11C22×C412yes—
136C22×C4×C11C22×C414yes—
137C22×C4×C11C2×D414yes—
138C22×C4×C11C2×D414yes—
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×Dic11—22no—
165C22×Dic11#4114yes—
166C22×Dic11#4114yes—
167C11×C4⋊C4—216no—
168C11×C22⋊C4—216no—
169C11×C22⋊C4C22⋊C4116yescomplemented
170C22⋊Dic11—48no—
171C22⋊Dic11—48no—
172C22⋊Dic11—44no—
173C22⋊Dic11—48no—
174C22⋊Dic11—44no—
175C4⋊Dic11—48no—
176C4×Dic11—48no—
177C22×#123D1111yescharacteristic
178C2×#388—112no—
179#1445—112no—
180#1439—112no—
181#1438—111no—
182#1438—111no—
183#1437—112no—
184C4⋊#95—112no—
185C22⋊#95—112no—
186C23×C11—24no—
187C23×C11—22no—
188C23×C11—22no—
189C23×C11—24no—
190C23×C11—24no—
191C23×C11—24no—
192C23×C11—24no—
193C23×C11—24no—
194C23×C11—24no—
195C23×C11—24no—
196C23×C11—22no—
197C23×C11—24no—
198C23×C11—22no—
199C23×C11—22no—
200C23×C11—24no—
201C23×C11—42no—
202C23×C11—42no—
203C23×C11—42no—
204C23×C11—42no—
205C23×C11—41no—
206C23×C11—42no—
207C23×C11—41no—
208C23×C11—41no—
209C23×C11—42no—
210C23×C11—41no—
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×C11—42no—
220C23×C11—42no—
221C23×C11—41no—
222C23×C11—42no—
223C23×C11—41no—
224C23×C11—41no—
225C23×C11—42no—
226C23×C11—41no—
227C23×C11C2×C22⋊C414yes—
228C23×C11C23×C411yescharacteristic
229C23×C11C22×D412yes—
230C23×C11C2×#4112yes—
231C23×C11C2×#4112yes—
232C23×C11H(5,𝔽2)12yes—
233C23×C11H(5,𝔽2)11yescharacteristic
234C23×C11H(5,𝔽2)11yescharacteristic
235C23×C11H(5,𝔽2)12yes—
236C23×C112−1+412yes—
237D4×C11—416no—
238C2×C4×C11—24no—
239C2×C4×C11—24no—
240C2×C4×C11—24no—
241C2×C4×C11—24no—
242C2×C4×C11—24no—
243C2×C4×C11—24no—
244C2×C4×C11—24no—
245C2×C4×C11—22no—
246C2×C4×C11—24no—
247C2×C4×C11—24no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—416no—
251C2×C4×C11—42no—
252C2×C4×C11—42no—
253C2×C4×C11—42no—
254C2×C4×C11—42no—
255C2×C4×C11—42no—
256C2×C4×C11—42no—
257C2×C4×C11C2×C22⋊C418yes—
258C2×Dic11—24no—
259C2×Dic11—24no—
260C2×Dic11—24no—
261C2×Dic11—24no—
262C2×Dic11—24no—
263C2×Dic11—24no—
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—
285C2×Dic11—42no—
286C23×D4C2×D1111yescharacteristic
287C24×C4C2×D1111yescharacteristic
288C2×#123—28no—
289C2×#123Dic1118yescomplemented
290C22×C4⋊C4—112no—
291C22×C4⋊C4C2×D1112yes—
292C22×C22⋊C4—112no—
293C22×C22⋊C4—112no—
294C22×C22⋊C4—111no—
295C22×C22⋊C4—112no—
296C22×C22⋊C4—111no—
297C22×C22⋊C4C2×D1112yes—
298C22×C22⋊C4C2×D1111yescharacteristic
299C22×C42—112no—
300#388—228no—
301C2×#95—112no—
302C2×#95—112no—
303C2×#95—112no—
304C2×#95—112no—
305C2×#95—112no—
306C2×#95—112no—
307C2×#95—111no—
308C2×#95—112no—
309C2×#95—111no—
310C22×C11—24no—
311C22×C11—28no—
312C22×C11—44no—
313C22×C11—42no—
314C22×C11—42no—
315C22×C11—44no—
316C22×C11—44no—
317C22×C11—44no—
318C22×C11—44no—
319C22×C11—42no—
320C22×C11—44no—
321C22×C11—44no—
322C22×C11—42no—
323C22×C11—42no—
324C22×C11—82no—
325C22×C11—82no—
326C22×C11—82no—
327C22×C11—82no—
328C22×C11C22×C22⋊C411yescharacteristic
329C22×C11C4×#4112yes—
330C22×C11#51811yescharacteristic
331C22×C11#51811yescharacteristic
332C22×C11#52012yes—
333C22×C11#53512yes—
334C22×C11#53512yes—
335C22×C11#53812yes—
336C22×C11#53912yes—
337C22×C11#54012yes—
338C22×C11#54212yes—
339C22×C11#54612yes—
340C22×C11#54612yes—
341C22×C11#54712yes—
342C22×C11#54712yes—
343C22×C11#55111yescharacteristic
344C22×C11#55312yes—
345C22×C11#55911yescharacteristic
346C22×C11#56011yescharacteristic
347C22×C11#56212yes—
348C22×C11#56311yescharacteristic
349C4×C11—28no—
350C4×C11—44no—
351C4×C11—42no—
352Dic11—44no—
353Dic11—44no—
354Dic11—82no—
355Dic11—82no—
356C25C22×D1111yescharacteristic
357C25C22×D1111yescharacteristic
358C22×D4—24no—
359C22×D4—41no—
360C22×D4—42no—
361C22×D4—41no—
362C22×D4C2×Dic1114yes—
363C23×C4—24no—
364C23×C4—41no—
365C23×C4—42no—
366C23×C4—41no—
367C23×C4—112no—
368C23×C4—112no—
369C23×C4—112no—
370C23×C4—112no—
371C23×C4C2×Dic1114yes—
372C23×C4C22×D1112yes—
373C23×C4C22×D1111yescharacteristic
374C23×C4C22×D1112yes—
375#123—232no—
376C2×C4⋊C4—24no—
377C2×C4⋊C4—24no—
378C2×C4⋊C4—224no—
379C2×C4⋊C4—224no—
380C2×C4⋊C4—442no—
381C2×C4⋊C4C2×Dic1118yes—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—224no—
385C2×C22⋊C4—224no—
386C2×C22⋊C4—224no—
387C2×C22⋊C4—224no—
388C2×C22⋊C4—224no—
389C2×C22⋊C4—224no—
390C2×C22⋊C4—441no—
391C2×C22⋊C4—442no—
392C2×C22⋊C4—442no—
393C2×C22⋊C4—442no—
394C2×C22⋊C4—442no—
395C2×C22⋊C4—441no—
396C2×C22⋊C4—442no—
397C2×C22⋊C4C2×Dic1118yes—
398C2×C22⋊C4C2×Dic1114yes—
399C2×C22⋊C4C22⋊D1118yes—
400C2×C42—224no—
401C2×C42—224no—
402C2×C42—442no—
403#95—224no—
404#95—224no—
405#95—442no—
406#95—442no—
407#95—442no—
408#95—442no—
409#95—441no—
410#95—442no—
411#95—441no—
412C2×C11—44no—
413C2×C11—82no—
414C2×C11#230911yescharacteristic
415C2×C11#233512yes—
416C2×C11#233912yes—
417C2×C11#237411yescharacteristic
418C2×C11#237611yescharacteristic
419C2×C11#270312yes—
420C2×C11#270612yes—
421C2×C11#271012yes—
422C2×C11#271812yes—
423C24—21no—
424C24—22no—
425C24—21no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—21no—
431C24—22no—
432C24—21no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24C22×Dic1112yes—
439C24C22×Dic1112yes—
440C24C2×C22⋊D1114yes—
441C24C23×D1111yescharacteristic
442C2×D4—28no—
443C2×D4—44no—
444C2×D4—44no—
445C2×D4—48no—
446C2×D4—48no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—28no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—44no—
463C22×C4—44no—
464C22×C4—48no—
465C22×C4—48no—
466C22×C4—114no—
467C22×C4—114no—
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×C4—222no—
493C22×C4—222no—
494C22×C4C22×Dic1114yes—
495C22×C4C22×Dic1112yes—
496C22×C4C22×Dic1114yes—
497C22×C4C2×C22⋊D1114yes—
498C22×C4C2×C22⋊D1114yes—
499C4⋊C4—216no—
500C4⋊C4—448no—
501C22⋊C4—216no—
502C22⋊C4—444no—
503C22⋊C4—448no—
504C22⋊C4—448no—
505C22⋊C4—448no—
506C22⋊C4—444no—
507C22⋊C4C22⋊Dic11116yescomplemented
508C42—448no—
509C11#1450611yescharacteristic, complemented, Sylow
510C23—22no—
511C23—22no—
512C23—24no—
513C23—24no—
514C23—24no—
515C23—24no—
516C23—24no—
517C23—24no—
518C23—24no—
519C23—24no—
520C23—22no—
521C23—22no—
522C23—24no—
523C23—24no—
524C23—22no—
525C23—41no—
526C23—42no—
527C23—41no—
528C23—42no—
529C23—42no—
530C23—42no—
531C23—42no—
532C23—41no—
533C23—41no—
534C23—42no—
535C23—42no—
536C23—42no—
537C23—42no—
538C23—42no—
539C23—42no—
540C23—42no—
541C23—41no—
542C23—42no—
543C23—41no—
544C23—42no—
545C23—42no—
546C23—42no—
547C23—42no—
548C23—41no—
549C23—41no—
550C23—42no—
551C23C2×C22⋊Dic1114yes—
552C23#6703711yescharacteristic
553C23#6703712yes—
554C23#6703711yescharacteristic
555C23#41×D1112yes—
556C23#41×D1112yes—
557C23#6704212yes—
558C23#6704312yes—
559C23C23×Dic1111yescharacteristic
560C23C22×C22⋊D1112yes—
561D4—416no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—24no—
573C2×C4—22no—
574C2×C4—416no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—224no—
582C2×C4—224no—
583C2×C4—224no—
584C2×C4—224no—
585C2×C4—224no—
586C2×C4—224no—
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×C4—442no—
608C2×C4—442no—
609C2×C4C2×C22⋊Dic1118yes—
610C22—28no—
611C22—24no—
612C22—44no—
613C22—44no—
614C22—44no—
615C22—44no—
616C22—42no—
617C22—42no—
618C22—44no—
619C22—44no—
620C22—44no—
621C22—42no—
622C22—42no—
623C22—42no—
624C22—82no—
625C22—82no—
626C22—82no—
627C22—82no—
628C22#1062318211yescharacteristic
629C22#1062318812yes—
630C22#1062319011yescharacteristic
631C22#1062319112yes—
632C22#1062319212yes—
633C22#1062319312yes—
634C22#1062319412yes—
635C22#1062319511yescharacteristic
636C22#1062319711yescharacteristic
637C22#1062319812yes—
638C22#1062332911yescharacteristic
639C22#1062332911yescharacteristic
640C22#1062333612yes—
641C22#1062333612yes—
642C22#1062335512yes—
643C22#1062335512yes—
644C22#41×Dic1112yes—
645C22#1062335812yes—
646C22#1062336012yes—
647C22#1062336012yes—
648C22C22×C22⋊Dic1111yescharacteristic
649C4—28no—
650C4—44no—
651C4—42no—
652C4—444no—
653C4—444no—
654C4—882no—
655C4—882no—
656C2—44no—
657C2—82no—
658C2#1307119811yescharacteristic
659C2#1307141012yes—
660C2#1307144612yes—
661C2#1307175211yescharacteristic
662C2#1307176411yescharacteristic
663C2#1307525312yes—
664C2#1307529812yes—
665C2#1307535412yes—
666C2#1307546212yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC22×C11×#123C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC22×#123D11
hypocenterC11#14506
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
1. C2×#10622564C2semidirect
2. #13066884C2semidirect
3. #13066861C2semidirect
6. #13066853C2semidirect
7. #13066845C2semidirect
8. #13066839C2semidirect
13. C2×C11×#123C4semidirect
169. C11×C22⋊C4C22⋊C4semidirect
289. C2×#123Dic11semidirect
507. C22⋊C4C22⋊Dic11semidirect
509. C11#14506semidirect

Maximal subgroups

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

subgroupindex
C2×#106225642
#130668842
#130668612
#130668572
#130668532
#130668452
#130668392
C22×C11×#1232
#1450611