Finite Group Databasebeta

← #14682237

Subgroups — #14682237

Order 2816.

1758 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×#10622834C211yesmaximal, characteristic
2C2×#10622558C212yesmaximal, complemented
3C2×#10622557C212yesmaximal, complemented
4#13066859C212yesmaximal, complemented
5#13066859C212yesmaximal, complemented
6#13066857C211yesmaximal, characteristic
7#13066850C212yesmaximal, complemented
8Dic11⋊#95C212yesmaximal, complemented
9C11×#1438C211yesmaximal, characteristic
10C23×D4×C11C2211yescharacteristic
11C22×C11×C22⋊C4C2211yescharacteristic
12C22×C11×C22⋊C4C2212yes—
13C22×C11×C22⋊C4C2211yescharacteristic
14C22×C22⋊Dic11C2211yescharacteristic
15C22×C22⋊Dic11C2212yes—
16C22×C22⋊Dic11C2212yes—
17C22×C22⋊Dic11C2212yes—
18C22×C22⋊Dic11C2211yescharacteristic
19C22×C4⋊Dic11C2211yescharacteristic
20C22×Dic11⋊C4C2212yes—
21C22×Dic11⋊C4C2212yes—
22C22×C4×Dic11C2212yes—
23C22×C4×Dic11C2211yescharacteristic
24C2×C11×#95C2212yes—
25#10622834C418yescomplemented
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32#10622558—28no—
33#10622557—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×C11C2312yes—
42C23×C4×C11C2312yes—
43C23×C4×C11C2311yescharacteristic
44C23×Dic11C2312yes—
45C23×Dic11C2312yes—
46C23×Dic11C2312yes—
47C23×Dic11C2312yes—
48C2×C11×C22⋊C4—24no—
49C2×C11×C22⋊C4—24no—
50C2×C11×C22⋊C4—41no—
51C2×C11×C22⋊C4—42no—
52C2×C11×C22⋊C4—42no—
53C2×C11×C22⋊C4—41no—
54C2×C11×C22⋊C4—42no—
55C2×C22⋊Dic11—24no—
56C2×C22⋊Dic11—24no—
57C2×C22⋊Dic11—24no—
58C2×C22⋊Dic11—24no—
59C2×C22⋊Dic11—24no—
60C2×C22⋊Dic11—24no—
61C2×C22⋊Dic11—41no—
62C2×C22⋊Dic11—42no—
63C2×C22⋊Dic11—42no—
64C2×C22⋊Dic11—41no—
65C2×C22⋊Dic11—42no—
66C2×C22⋊Dic11C2×C418yes—
67C2×C22⋊Dic11C2×C418yes—
68C2×C4⋊Dic11—41no—
69C2×C4⋊Dic11—41no—
70C2×C4⋊Dic11C2×C414yes—
71C2×Dic11⋊C4—24no—
72C2×Dic11⋊C4—42no—
73C2×Dic11⋊C4—42no—
74C2×Dic11⋊C4—42no—
75C2×Dic11⋊C4—42no—
76C2×Dic11⋊C4D418yescomplemented
77C2×C4×Dic11—24no—
78C2×C4×Dic11—24no—
79C2×C4×Dic11—42no—
80C2×C4×Dic11—42no—
81C2×C4×Dic11C2×C414yes—
82C11×#95—24no—
83C11⋊#95—24no—
84C11⋊#95—24no—
85C11⋊#95—24no—
86C11⋊#95—24no—
87C11⋊#95—24no—
88C11⋊#95—42no—
89#14445—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—21no—
100C24×C11—21no—
101C24×C11—22no—
102C24×C11—21no—
103C24×C11—21no—
104C24×C11—22no—
105C24×C11—22no—
106C24×C11C22×C412yes—
107C24×C11C22×C412yes—
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—21no—
116C22×C4×C11—21no—
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—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11C22×C412yes—
131C22×C4×C11C2×D414yes—
132C22×C4×C11#4114yes—
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×Dic11C22×C414yes—
157C22×Dic11C22×C414yes—
158C22×Dic11C2×D414yes—
159C22×Dic11C2×D414yes—
160C22×Dic11#4114yes—
161C11×C22⋊C4—44no—
162C11×C22⋊C4—48no—
163C11×C22⋊C4—44no—
164C22⋊Dic11—216no—
165C22⋊Dic11—216no—
166C22⋊Dic11—44no—
167C22⋊Dic11—48no—
168C22⋊Dic11—44no—
169C4⋊Dic11—44no—
170Dic11⋊C4—48no—
171Dic11⋊C4—48no—
172C4×Dic11—44no—
173C4×Dic11—48no—
174C2×#390—111no—
175C2×#388—112no—
176C2×#388—112no—
177#1439—112no—
178#1439—112no—
179#1438—111no—
180#1438D1111yescharacteristic
181#1436—112no—
182C4⋊#95—112no—
183C23×C11—22no—
184C23×C11—22no—
185C23×C11—24no—
186C23×C11—24no—
187C23×C11—22no—
188C23×C11—22no—
189C23×C11—22no—
190C23×C11—22no—
191C23×C11—24no—
192C23×C11—24no—
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—41no—
206C23×C11—41no—
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—41no—
218C23×C11—41no—
219C23×C11—41no—
220C23×C11—41no—
221C23×C11—42no—
222C23×C11—42no—
223C23×C11—41no—
224C23×C11—41no—
225C23×C11C23×C411yescharacteristic
226C23×C11C22×D412yes—
227C23×C11C2×#4112yes—
228C23×C11C2×#4112yes—
229C23×C11H(5,𝔽2)12yes—
230C23×C11H(5,𝔽2)11yescharacteristic
231C23×C11H(5,𝔽2)11yescharacteristic
232C23×C11H(5,𝔽2)12yes—
233C23×C112−1+412yes—
234D4×C11—416no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—24no—
238C2×C4×C11—24no—
239C2×C4×C11—24no—
240C2×C4×C11—24no—
241C2×C4×C11—24no—
242C2×C4×C11—42no—
243C2×C4×C11—42no—
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#11714yes—
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—24no—
263C2×Dic11—24no—
264C2×Dic11—24no—
265C2×Dic11—24no—
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×Dic11C4×D418yes—
282C23×D4C2×D1111yescharacteristic
283C22×C4⋊C4—112no—
284C22×C4⋊C4—111no—
285C22×C4⋊C4—112no—
286C22×C22⋊C4—112no—
287C22×C22⋊C4—112no—
288C22×C22⋊C4—111no—
289C22×C22⋊C4—112no—
290C22×C22⋊C4—111no—
291C22×C22⋊C4C2×D1111yescharacteristic
292C22×C22⋊C4C2×D1112yes—
293C22×C22⋊C4C2×D1111yescharacteristic
294C22×C42—111no—
295C22×C42—112no—
296#390—118no—
297#388—228no—
298#388—228no—
299C2×#95—112no—
300C2×#95—112no—
301C2×#95—112no—
302C2×#95—112no—
303C2×#95—112no—
304C2×#95—112no—
305C2×#95C2×D1112yes—
306C22×C11—42no—
307C22×C11—42no—
308C22×C11—44no—
309C22×C11—44no—
310C22×C11—44no—
311C22×C11—44no—
312C22×C11—42no—
313C22×C11—42no—
314C22×C11—42no—
315C22×C11—42no—
316C22×C11—82no—
317C22×C11—82no—
318C22×C11—82no—
319C22×C11—82no—
320C22×C11—82no—
321C22×C11—82no—
322C22×C11—82no—
323C22×C11—82no—
324C22×C11C2×#11711yescharacteristic
325C22×C11C2×C4×D412yes—
326C22×C11#51811yescharacteristic
327C22×C11#51811yescharacteristic
328C22×C11#52012yes—
329C22×C11#53412yes—
330C22×C11#53712yes—
331C22×C11#53812yes—
332C22×C11#53812yes—
333C22×C11#53812yes—
334C22×C11#53912yes—
335C22×C11D4211yescharacteristic
336C22×C11#54712yes—
337C22×C11#55012yes—
338C22×C11#55012yes—
339C22×C11#55512yes—
340C22×C11#55612yes—
341C22×C11#55911yescharacteristic
342C22×C11H(3,𝔽4)11yescharacteristic
343C22×C11#56212yes—
344C22×C11#56311yescharacteristic
345C4×C11—24no—
346C4×C11—44no—
347C4×C11—82no—
348Dic11—28no—
349Dic11—44no—
350Dic11—44no—
351Dic11—82no—
352C25C22×D1111yescharacteristic
353C25C22×D1111yescharacteristic
354C22×D4—24no—
355C22×D4—42no—
356C22×D4—41no—
357C22×D4—41no—
358C22×D4C4×D1114yes—
359C23×C4—112no—
360C23×C4—112no—
361C23×C4—112no—
362C23×C4—112no—
363C23×C4C22×D1112yes—
364C23×C4C22×D1112yes—
365C23×C4C22×D1111yescharacteristic
366C2×C4⋊C4—114no—
367C2×C4⋊C4—118no—
368C2×C4⋊C4—224no—
369C2×C4⋊C4—442no—
370C2×C4⋊C4—442no—
371C2×C4⋊C4—442no—
372C2×C4⋊C4—442no—
373C2×C4⋊C4—441no—
374C2×C4⋊C4—441no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—41no—
378C2×C22⋊C4—42no—
379C2×C22⋊C4—42no—
380C2×C22⋊C4—41no—
381C2×C22⋊C4—42no—
382C2×C22⋊C4—118no—
383C2×C22⋊C4—118no—
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—441no—
394C2×C22⋊C4—442no—
395C2×C42—114no—
396C2×C42—224no—
397C2×C42—224no—
398C2×C42—442no—
399C2×C42—442no—
400#95—24no—
401#95—224no—
402#95—224no—
403#95—224no—
404#95—224no—
405#95—224no—
406#95—442no—
407C2×C11—82no—
408C2×C11—82no—
409C2×C11#231211yescharacteristic
410C2×C11#232512yes—
411C2×C11#235412yes—
412C2×C11#236611yescharacteristic
413C2×C11#237911yescharacteristic
414C2×C11#268212yes—
415C2×C11#272712yes—
416C2×C11#273312yes—
417C2×C11#280812yes—
418C24—22no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—21no—
426C24—21no—
427C24—22no—
428C24—21no—
429C24—21no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24C2×C4×D1112yes—
435C24C2×C4×D1112yes—
436C24C23×D1111yescharacteristic
437C2×D4—28no—
438C2×D4—44no—
439C2×D4—44no—
440C2×D4—48no—
441C2×D4—48no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—21no—
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—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—114no—
459C22×C4—114no—
460C22×C4—114no—
461C22×C4—114no—
462C22×C4—114no—
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×C4—222no—
485C22×C4—222no—
486C22×C4C2×C4×D1112yes—
487C22×C4D4×D1114yes—
488C22×C4#434114yes—
489C4⋊C4—448no—
490C4⋊C4—444no—
491C4⋊C4—448no—
492C22⋊C4—44no—
493C22⋊C4—48no—
494C22⋊C4—44no—
495C22⋊C4—2216no—
496C22⋊C4—2216no—
497C22⋊C4—444no—
498C22⋊C4—448no—
499C22⋊C4—444no—
500C42—444no—
501C42—448no—
502C11#1444511yescharacteristic, complemented, Sylow
503C23—22no—
504C23—22no—
505C23—22no—
506C23—22no—
507C23—22no—
508C23—22no—
509C23—24no—
510C23—24no—
511C23—24no—
512C23—24no—
513C23—42no—
514C23—42no—
515C23—42no—
516C23—42no—
517C23—41no—
518C23—41no—
519C23—42no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23—41no—
524C23—41no—
525C23—42no—
526C23—42no—
527C23—42no—
528C23—42no—
529C23—42no—
530C23—42no—
531C23—42no—
532C23—42no—
533C23—42no—
534C23—42no—
535C23—42no—
536C23—42no—
537C23—41no—
538C23—41no—
539C23—42no—
540C23—42no—
541C23—41no—
542C23—41no—
543C23—42no—
544C23—42no—
545C23C22×C4×D1111yescharacteristic
546C23C2×D4×D1112yes—
547C23C2×#434112yes—
548C23#6703712yes—
549C23#6703712yes—
550C23#6703711yescharacteristic
551C23#6703711yescharacteristic
552C23#41×D1112yes—
553C23#6704312yes—
554D4—416no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—118no—
574C2×C4—224no—
575C2×C4—224no—
576C2×C4—224no—
577C2×C4—224no—
578C2×C4—224no—
579C2×C4—224no—
580C2×C4—224no—
581C2×C4—224no—
582C2×C4—224no—
583C2×C4—224no—
584C2×C4—224no—
585C2×C4—224no—
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#6693014yes—
602C22—42no—
603C22—42no—
604C22—42no—
605C22—42no—
606C22—42no—
607C22—42no—
608C22—44no—
609C22—44no—
610C22—44no—
611C22—44no—
612C22—82no—
613C22—82no—
614C22—82no—
615C22—82no—
616C22—82no—
617C22—82no—
618C22—82no—
619C22—82no—
620C22C2×#6693011yescharacteristic
621C22#1062301711yescharacteristic
622C22#1062301711yescharacteristic
623C22C4×D4×D1112yes—
624C22#1062307712yes—
625C22#1062312012yes—
626C22#1062312111yescharacteristic
627C22#1062312412yes—
628C22#1062312412yes—
629C22#1062312511yescharacteristic
630C22#1062313012yes—
631C22#1062313912yes—
632C22#1062314212yes—
633C22#1062314412yes—
634C22#1062314712yes—
635C22#1062315212yes—
636C22#1062318211yescharacteristic
637C22#1062319112yes—
638C22#1062319511yescharacteristic
639C22#1062320212yes—
640C22#1062324912yes—
641C4—24no—
642C4—44no—
643C4—82no—
644C4—228no—
645C4—444no—
646C4—444no—
647C4—882no—
648C2—82no—
649C2—82no—
650C2#1307121211yescharacteristic
651C2#1307131812yes—
652C2#1307156412yes—
653C2#1307167911yescharacteristic
654C2#1307178611yescharacteristic
655C2#1307498312yes—
656C2#1307558112yes—
657C2#1307564412yes—
658C2#1307659512yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1438C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenter#1438D11
hypocenterC11#14445
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1438

Complements

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

NH ≅ G/Ntype
2. C2×#10622558C2semidirect
3. C2×#10622557C2semidirect
4. #13066859C2semidirect
5. #13066859C2semidirect
7. #13066850C2semidirect
8. Dic11⋊#95C2semidirect
25. #10622834C4semidirect
76. C2×Dic11⋊C4D4semidirect
502. C11#14445semidirect

Maximal subgroups

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

subgroupindex
C2×#106228342
C2×#106225582
C2×#106225572
#130668592
#130668572
#130668502
Dic11⋊#952
C11×#14382
#1444511