Finite Group Databasebeta

← #14682955

Subgroups — #14682955

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
1C22×#66988C211yesmaximal, characteristic
2C2×#10622557C212yesmaximal, complemented
3#13066882C212yesmaximal, complemented
4#13066859C212yesmaximal, complemented
5#13066857C211yesmaximal, characteristic
6#13066853C212yesmaximal, complemented
7Dic11⋊#95C212yesmaximal, complemented
8#13066838C212yesmaximal, complemented
9C11×#1438C211yesmaximal, characteristic
10C23×D4×C11C2211yescharacteristic
11C24×Dic11C2211yescharacteristic
12C22×C11×C22⋊C4C2212yes—
13C22×C11×C22⋊C4C2211yescharacteristic
14C22×C11×C22⋊C4C2211yescharacteristic
15C22×C22⋊Dic11C2212yes—
16C22×C22⋊Dic11C2212yes—
17C22×C22⋊Dic11C2212yes—
18C22×C22⋊Dic11C2211yescharacteristic
19C2×#66988—28no—
20C2×#66988C418yescomplemented
21C22×Dic11⋊C4C2212yes—
22C22×Dic11⋊C4C2212yes—
23C22×C4×Dic11C2212yes—
24C2×C11×#95C2212yes—
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2211yescharacteristic
32C2×C11⋊#95C2211yescharacteristic
33#10622557—28no—
34C25×C11C2311yescharacteristic
35C25×C11C2311yescharacteristic
36C22×D4×C11—24no—
37C22×D4×C11—41no—
38C22×D4×C11—41no—
39C22×D4×C11—42no—
40C22×D4×C11C2×C414yes—
41C23×C4×C11C2312yes—
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2312yes—
44C23×Dic11—24no—
45C23×Dic11—42no—
46C23×Dic11—41no—
47C23×Dic11—41no—
48C23×Dic11C2×C414yes—
49C23×Dic11C2312yes—
50C23×Dic11C2312yes—
51C23×Dic11C2312yes—
52C23×Dic11C2312yes—
53C2×C11×C22⋊C4—24no—
54C2×C11×C22⋊C4—24no—
55C2×C11×C22⋊C4—24no—
56C2×C11×C22⋊C4—41no—
57C2×C11×C22⋊C4—42no—
58C2×C11×C22⋊C4—41no—
59C2×C11×C22⋊C4—42no—
60C2×C22⋊Dic11—24no—
61C2×C22⋊Dic11—24no—
62C2×C22⋊Dic11—24no—
63C2×C22⋊Dic11—24no—
64C2×C22⋊Dic11—24no—
65C2×C22⋊Dic11—42no—
66C2×C22⋊Dic11—42no—
67C2×C22⋊Dic11—42no—
68C2×C22⋊Dic11C2×C418yes—
69C2×C22⋊Dic11C2×C414yes—
70C2×C22⋊Dic11D418yes—
71#66988—232no—
72C2×Dic11⋊C4—24no—
73C2×Dic11⋊C4—24no—
74C2×Dic11⋊C4—24no—
75C2×Dic11⋊C4—24no—
76C2×Dic11⋊C4—42no—
77C2×Dic11⋊C4C2×C418yes—
78C2×C4×Dic11—24no—
79C2×C4×Dic11—24no—
80C2×C4×Dic11—42no—
81C11×#95—42no—
82C11⋊#95—24no—
83C11⋊#95—24no—
84C11⋊#95—41no—
85C11⋊#95—42no—
86C11⋊#95—42no—
87C11⋊#95—42no—
88C11⋊#95—42no—
89C11⋊#95—41no—
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—22no—
120C22×C4×C11—21no—
121C22×C4×C11—21no—
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—22no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11C22×C412yes—
133C22×C4×C11#4114yes—
134C22×Dic11—28no—
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—44no—
159C22×Dic11—44no—
160C22×Dic11—48no—
161C22×Dic11—48no—
162C22×Dic11C22×C414yes—
163C22×Dic11C22×C414yes—
164C22×Dic11C2×D414yes—
165C22×Dic11C2×D414yes—
166C22×Dic11#4114yes—
167C11×C22⋊C4—44no—
168C11×C22⋊C4—48no—
169C11×C22⋊C4—44no—
170C22⋊Dic11—216no—
171C22⋊Dic11—48no—
172C22⋊Dic11—48no—
173C22⋊Dic11C22⋊C4116yescomplemented
174Dic11⋊C4—216no—
175Dic11⋊C4—48no—
176C4×Dic11—48no—
177C22×#123—111no—
178C2×#388—112no—
179#1445—112no—
180#1439—112no—
181#1438—111no—
182#1438D1111yescharacteristic
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—22no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—24no—
242C2×C4×C11—24no—
243C2×C4×C11—24no—
244C2×C4×C11—42no—
245C2×C4×C11—42no—
246C2×C4×C11—42no—
247C2×C4×C11—42no—
248C2×C4×C11—42no—
249C2×C4×C11—42no—
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×C11—42no—
257C2×Dic11—24no—
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—24no—
268C2×Dic11—24no—
269C2×Dic11—416no—
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×Dic11C2×C22⋊C418yes—
286C23×D4C2×D1111yescharacteristic
287C24×C4—111no—
288C2×#123—118no—
289C2×#123—228no—
290C22×C4⋊C4—112no—
291C22×C4⋊C4—112no—
292C22×C22⋊C4—111no—
293C22×C22⋊C4—112no—
294C22×C22⋊C4—112no—
295C22×C22⋊C4—112no—
296C22×C22⋊C4C2×D1112yes—
297C22×C22⋊C4C2×D1111yescharacteristic
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—111no—
309C2×#95C2×D1112yes—
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—42no—
350C4×C11—44no—
351C4×C11—82no—
352Dic11—28no—
353Dic11—44no—
354Dic11—44no—
355Dic11—82no—
356C25C22×D1111yescharacteristic
357C25C22×D1111yescharacteristic
358C22×D4—24no—
359C22×D4—42no—
360C22×D4—41no—
361C22×D4—41no—
362C22×D4C4×D1114yes—
363C23×C4—112no—
364C23×C4—112no—
365C23×C4—112no—
366C23×C4—114no—
367C23×C4—112no—
368C23×C4—224no—
369C23×C4—442no—
370C23×C4—441no—
371C23×C4—441no—
372C23×C4C22×D1112yes—
373C23×C4C22×D1111yescharacteristic
374C23×C4C22×D1112yes—
375#123—2232no—
376C2×C4⋊C4—118no—
377C2×C4⋊C4—224no—
378C2×C4⋊C4—224no—
379C2×C4⋊C4—224no—
380C2×C4⋊C4—224no—
381C2×C4⋊C4—442no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—41no—
386C2×C22⋊C4—42no—
387C2×C22⋊C4—41no—
388C2×C22⋊C4—42no—
389C2×C22⋊C4—114no—
390C2×C22⋊C4—118no—
391C2×C22⋊C4—118no—
392C2×C22⋊C4—224no—
393C2×C22⋊C4—224no—
394C2×C22⋊C4—224no—
395C2×C22⋊C4—224no—
396C2×C22⋊C4—224no—
397C2×C22⋊C4—442no—
398C2×C22⋊C4—442no—
399C2×C22⋊C4—442no—
400C2×C42—224no—
401C2×C42—224no—
402C2×C42—442no—
403#95—42no—
404#95—224no—
405#95—224no—
406#95—442no—
407#95—442no—
408#95—441no—
409#95—441no—
410#95—442no—
411#95—442no—
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—22no—
424C24—22no—
425C24—22no—
426C24—21no—
427C24—21no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—21no—
434C24—21no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24C2×C4×D1112yes—
439C24C2×C4×D1112yes—
440C24D4×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—22no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—114no—
465C22×C4—114no—
466C22×C4—114no—
467C22×C4—114no—
468C22×C4—114no—
469C22×C4—222no—
470C22×C4—222no—
471C22×C4—222no—
472C22×C4—222no—
473C22×C4—228no—
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—444no—
494C22×C4—444no—
495C22×C4—448no—
496C22×C4—448no—
497C22×C4C2×C4×D1112yes—
498C22×C4#434114yes—
499C4⋊C4—2216no—
500C4⋊C4—448no—
501C22⋊C4—44no—
502C22⋊C4—48no—
503C22⋊C4—44no—
504C22⋊C4—1116no—
505C22⋊C4—2216no—
506C22⋊C4—448no—
507C22⋊C4—448no—
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—22no—
523C23—24no—
524C23—24no—
525C23—42no—
526C23—41no—
527C23—41no—
528C23—42no—
529C23—42no—
530C23—42no—
531C23—42no—
532C23—41no—
533C23—41no—
534C23—42no—
535C23—42no—
536C23—41no—
537C23—42no—
538C23—42no—
539C23—42no—
540C23—41no—
541C23—42no—
542C23—42no—
543C23—42no—
544C23—42no—
545C23—42no—
546C23—42no—
547C23—41no—
548C23—42no—
549C23—41no—
550C23—42no—
551C23C22⋊C4×D1114yes—
552C23C22×C4×D1111yescharacteristic
553C23C2×D4×D1112yes—
554C23C2×#434112yes—
555C23#6703712yes—
556C23#6703712yes—
557C23#6703711yescharacteristic
558C23#6703711yescharacteristic
559C23#41×D1112yes—
560C23#6704312yes—
561D4—416no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—118no—
582C2×C4—224no—
583C2×C4—224no—
584C2×C4—224no—
585C2×C4—224no—
586C2×C4—224no—
587C2×C4—224no—
588C2×C4—224no—
589C2×C4—224no—
590C2×C4—224no—
591C2×C4—224no—
592C2×C4—224no—
593C2×C4—224no—
594C2×C4—4416no—
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×C4—442no—
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—
628C22C2×C22⋊C4×D1111yescharacteristic
629C22#1062301711yescharacteristic
630C22#1062301711yescharacteristic
631C22C4×#434112yes—
632C22#1062307712yes—
633C22#1062311811yescharacteristic
634C22#1062312212yes—
635C22#1062312312yes—
636C22#1062312312yes—
637C22#1062312611yescharacteristic
638C22#1062313312yes—
639C22#1062314112yes—
640C22#1062314212yes—
641C22#1062314412yes—
642C22#1062314512yes—
643C22#1062315212yes—
644C22#1062318211yescharacteristic
645C22#1062318612yes—
646C22#1062319511yescharacteristic
647C22#1062320012yes—
648C22#1062325012yes—
649C4—42no—
650C4—44no—
651C4—82no—
652C4—228no—
653C4—444no—
654C4—444no—
655C4—882no—
656C2—44no—
657C2—82no—
658C2#1307119711yescharacteristic
659C2#1307140312yes—
660C2#1307144212yes—
661C2#1307174911yescharacteristic
662C2#1307175911yescharacteristic
663C2#1307526612yes—
664C2#1307531112yes—
665C2#1307536412yes—
666C2#1307547212yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1438C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenter#1438D11
hypocenterC11#14506
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1438

Complements

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

NH ≅ G/Ntype
2. C2×#10622557C2semidirect
3. #13066882C2semidirect
4. #13066859C2semidirect
6. #13066853C2semidirect
7. Dic11⋊#95C2semidirect
8. #13066838C2semidirect
20. C2×#66988C4semidirect
173. C22⋊Dic11C22⋊C4semidirect
509. C11#14506semidirect

Maximal subgroups

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

subgroupindex
C22×#669882
C2×#106225572
#130668822
#130668592
#130668572
#130668532
Dic11⋊#952
#130668382
C11×#14382
#1450611