Finite Group Databasebeta

← #14676855

Subgroups — #14676855

Order 2816.

1918 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622823C211yesmaximal, characteristic
2C2×#10622556C211yesmaximal, characteristic
3C2×#10622556C211yesmaximal, characteristic
4C2×C22⋊C4×Dic11C211yesmaximal, characteristic
5C22×C11⋊#95C211yesmaximal, characteristic
6#13066877C212yesmaximal, complemented
7#13066874C212yesmaximal, complemented
8#13066847C212yesmaximal, complemented
9#13066841C212yesmaximal, complemented
10#13066838C211yesmaximal, characteristic
11C11×C22⋊#95C211yesmaximal, characteristic
12C24×C4×C11C2211yescharacteristic
13C24×Dic11C2211yescharacteristic
14C24×Dic11C2211yescharacteristic
15C22×C11×C22⋊C4C2211yescharacteristic
16C22×C11×C22⋊C4C2211yescharacteristic
17C22×C22⋊Dic11C2211yescharacteristic
18C22×C22⋊Dic11C2211yescharacteristic
19C22×Dic11⋊C4C2212yes—
20C22×C4×Dic11C2211yescharacteristic
21C22×C4×Dic11C2211yescharacteristic
22C2×C11×#95C2212yes—
23C2×C11×#95C2212yes—
24#10622823—24no—
25C2×C11⋊#95—24no—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2211yescharacteristic
33C2×C11⋊#95C2211yescharacteristic
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37#10622556—24no—
38#10622556C418yescomplemented
39C22⋊C4×Dic11—24no—
40C25×C11C2311yescharacteristic
41C23×C4×C11—22no—
42C23×C4×C11—24no—
43C23×C4×C11—22no—
44C23×C4×C11—22no—
45C23×C4×C11—42no—
46C23×C4×C11C2312yes—
47C23×C4×C11C2311yescharacteristic
48C23×C4×C11C2311yescharacteristic
49C23×C4×C11C2312yes—
50C23×Dic11—22no—
51C23×Dic11—22no—
52C23×Dic11—22no—
53C23×Dic11—22no—
54C23×Dic11—22no—
55C23×Dic11—22no—
56C23×Dic11—22no—
57C23×Dic11—22no—
58C23×Dic11—24no—
59C23×Dic11—42no—
60C23×Dic11C2×C414yes—
61C23×Dic11D414yes—
62C23×Dic11C2312yes—
63C23×Dic11C2312yes—
64C23×Dic11C2311yescharacteristic
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C2×C11×C22⋊C4—22no—
69C2×C11×C22⋊C4—22no—
70C2×C11×C22⋊C4—22no—
71C2×C11×C22⋊C4—22no—
72C2×C11×C22⋊C4—22no—
73C2×C11×C22⋊C4C2×C414yes—
74C2×C22⋊Dic11—22no—
75C2×C22⋊Dic11—22no—
76C2×C22⋊Dic11—22no—
77C2×C22⋊Dic11—22no—
78C2×C22⋊Dic11C2×C414yes—
79C2×C22⋊Dic11D414yes—
80C2×Dic11⋊C4—24no—
81C2×Dic11⋊C4—24no—
82C2×Dic11⋊C4—42no—
83C2×C4×Dic11—22no—
84C2×C4×Dic11—22no—
85C2×C4×Dic11—24no—
86C2×C4×Dic11—42no—
87C11×#95—24no—
88C11×#95—42no—
89C11⋊#95—22no—
90C11⋊#95—22no—
91C11⋊#95—24no—
92C11⋊#95—24no—
93C11⋊#95—24no—
94C11⋊#95—24no—
95C11⋊#95—24no—
96C11⋊#95—24no—
97C11⋊#95—42no—
98C11⋊#95C2×C418yescomplemented
99C11⋊#95C2×C418yescomplemented
100#13992—111nomaximal, Sylow
101C24×C11—22no—
102C24×C11—22no—
103C24×C11—22no—
104C24×C11—22no—
105C24×C11C22×C412yes—
106C24×C11C2×D412yes—
107C24×C11C2×D412yes—
108C24×C11#4112yes—
109C24×C11#4112yes—
110C24×C11#4112yes—
111C24×C11#4112yes—
112C24×C11C2411yescharacteristic
113C22×C4×C11—28no—
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—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×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—48no—
136C22×C4×C11—48no—
137C22×C4×C11—44no—
138C22×C4×C11—44no—
139C22×C4×C11C22×C412yes—
140C22×C4×C11C22×C412yes—
141C22×C4×C11#4114yes—
142C22×Dic11—28no—
143C22×Dic11—28no—
144C22×Dic11—28no—
145C22×Dic11—28no—
146C22×Dic11—28no—
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—22no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—22no—
155C22×Dic11—22no—
156C22×Dic11—22no—
157C22×Dic11—22no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—22no—
161C22×Dic11—22no—
162C22×Dic11—22no—
163C22×Dic11—21no—
164C22×Dic11—22no—
165C22×Dic11—22no—
166C22×Dic11—21no—
167C22×Dic11—22no—
168C22×Dic11—22no—
169C22×Dic11—22no—
170C22×Dic11—22no—
171C22×Dic11—22no—
172C22×Dic11—22no—
173C22×Dic11—22no—
174C22×Dic11—44no—
175C22×Dic11—48no—
176C22×Dic11—48no—
177C22×Dic11—44no—
178C22×Dic11—44no—
179C22×Dic11—44no—
180C22×Dic11—44no—
181C22×Dic11C22×C414yes—
182C22×Dic11C22×C414yes—
183C22×Dic11C2×D412yes—
184C22×Dic11C2×D412yes—
185C22×Dic11C2×D412yes—
186C22×Dic11C2×D412yes—
187C22×Dic11#4114yes—
188C11×C22⋊C4—28no—
189C11×C22⋊C4—44no—
190C22⋊Dic11—28no—
191C22⋊Dic11—28no—
192Dic11⋊C4—48no—
193C4×Dic11—44no—
194C4×Dic11—44no—
195C2×#385—111no—
196C2×#381—111no—
197C2×#381—111no—
198C2×C4×C22⋊C4—111no—
199C22×#95—111no—
200#1443—112no—
201#1442—112no—
202#1436—112no—
203#1434—112no—
204C22⋊#95—111no—
205C22⋊#95D1111yescharacteristic
206C23×C11—24no—
207C23×C11—24no—
208C23×C11—22no—
209C23×C11—22no—
210C23×C11—24no—
211C23×C11—22no—
212C23×C11—22no—
213C23×C11—24no—
214C23×C11—24no—
215C23×C11—24no—
216C23×C11—24no—
217C23×C11—24no—
218C23×C11—24no—
219C23×C11—24no—
220C23×C11—24no—
221C23×C11—24no—
222C23×C11#11714yes—
223C23×C11C4×D414yes—
224C23×C11C4×D414yes—
225C23×C11#12114yes—
226C23×C11#12314yes—
227C23×C11#12414yes—
228C23×C11#12614yes—
229C23×C11C23×C411yescharacteristic
230C23×C11C22×D411yescharacteristic
231C23×C11C22×D411yescharacteristic
232C23×C11C2×#4111yescharacteristic
233C23×C11C2×#4111yescharacteristic
234C23×C11C2×#4111yescharacteristic
235C23×C11C2×#4112yes—
236C23×C11C2×#4111yescharacteristic
237C23×C11C2×#4112yes—
238C23×C11H(5,𝔽2)12yes—
239C23×C112−1+412yes—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—24no—
243C2×C4×C11—24no—
244C2×C4×C11—24no—
245C2×C4×C11—24no—
246C2×C4×C11—24no—
247C2×C4×C11—416no—
248C2×C4×C11—42no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—42no—
252C2×C4×C11—41no—
253C2×C4×C11—42no—
254C2×C4×C11—41no—
255C2×C4×C11—42no—
256C2×C4×C11—42no—
257C2×C4×C11—42no—
258C2×C4×C11—42no—
259C2×C4×C11—42no—
260C2×C4×C11—42no—
261C2×C4×C11—42no—
262C2×C4×C11—42no—
263C2×C4×C11—42no—
264C2×C4×C11—42no—
265C2×Dic11—22no—
266C2×Dic11—22no—
267C2×Dic11—24no—
268C2×Dic11—24no—
269C2×Dic11—24no—
270C2×Dic11—24no—
271C2×Dic11—24no—
272C2×Dic11—24no—
273C2×Dic11—24no—
274C2×Dic11—24no—
275C2×Dic11—22no—
276C2×Dic11—22no—
277C2×Dic11—22no—
278C2×Dic11—22no—
279C2×Dic11—22no—
280C2×Dic11—24no—
281C2×Dic11—24no—
282C2×Dic11—416no—
283C2×Dic11—42no—
284C2×Dic11—41no—
285C2×Dic11—42no—
286C2×Dic11—41no—
287C2×Dic11—42no—
288C2×Dic11—42no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—42no—
292C2×Dic11—42no—
293C2×Dic11—42no—
294C2×Dic11—42no—
295C2×Dic11—42no—
296C2×Dic11—42no—
297C2×Dic11—42no—
298C2×Dic11—42no—
299C2×Dic11—416no—
300C2×Dic11#12314yes—
301C24×C4—111no—
302C24×C4—111no—
303C24×C4C2×D1111yescharacteristic
304C22×C4⋊C4—112no—
305C22×C22⋊C4—111no—
306C22×C22⋊C4—111no—
307C22×C22⋊C4C2×D1111yescharacteristic
308C22×C22⋊C4C2×D1111yescharacteristic
309C22×C42—111no—
310C22×C42—111no—
311#385—224no—
312#381—118no—
313#381—224no—
314C4×C22⋊C4—224no—
315C2×#95—112no—
316C2×#95—112no—
317C2×#95—112no—
318C2×#95—112no—
319C2×#95—112no—
320C2×#95—112no—
321C2×#95—112no—
322C2×#95—111no—
323C2×#95—112no—
324C2×#95—111no—
325C2×#95—112no—
326C2×#95—224no—
327C2×#95C2×D1112yes—
328C2×#95C2×D1112yes—
329C22×C11—24no—
330C22×C11—28no—
331C22×C11—28no—
332C22×C11—24no—
333C22×C11—24no—
334C22×C11—24no—
335C22×C11—28no—
336C22×C11—28no—
337C22×C11—24no—
338C22×C11—24no—
339C22×C11#38818yes—
340C22×C11C2×#11711yescharacteristic
341C22×C11C2×C4×D411yescharacteristic
342C22×C11C2×C4×D411yescharacteristic
343C22×C11C4×#4112yes—
344C22×C11#52012yes—
345C22×C11C2×#12111yescharacteristic
346C22×C11C2×#12311yescharacteristic
347C22×C11C2×#12311yescharacteristic
348C22×C11#52511yescharacteristic
349C22×C11C2×#12411yescharacteristic
350C22×C11C2×#12611yescharacteristic
351C22×C11#52912yes—
352C22×C11#53411yescharacteristic
353C22×C11#53611yescharacteristic
354C22×C11#53912yes—
355C22×C11#54612yes—
356C22×C11#54712yes—
357C22×C11#55112yes—
358C22×C11#55112yes—
359C22×C11#55112yes—
360C22×C11#55212yes—
361C22×C11#55212yes—
362C22×C11#55212yes—
363C4×C11—42no—
364C4×C11—44no—
365C4×C11—42no—
366C4×C11—82no—
367Dic11—24no—
368Dic11—44no—
369Dic11—42no—
370Dic11—42no—
371Dic11—42no—
372Dic11—44no—
373C25C22×D1111yescharacteristic
374C23×C4—22no—
375C23×C4—24no—
376C23×C4—22no—
377C23×C4—22no—
378C23×C4—42no—
379C23×C4—111no—
380C23×C4—114no—
381C23×C4—111no—
382C23×C4—112no—
383C23×C4—111no—
384C23×C4—112no—
385C23×C4—111no—
386C23×C4—114no—
387C23×C4—224no—
388C23×C4—222no—
389C23×C4—222no—
390C23×C4—222no—
391C23×C4—222no—
392C23×C4—222no—
393C23×C4—222no—
394C23×C4—222no—
395C23×C4—222no—
396C23×C4—442no—
397C23×C4C22×D1112yes—
398C23×C4C22×D1111yescharacteristic
399C23×C4C22×D1111yescharacteristic
400C23×C4C22×D1112yes—
401C2×C4⋊C4—224no—
402C2×C4⋊C4—224no—
403C2×C4⋊C4—442no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—22no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—114no—
410C2×C22⋊C4—114no—
411C2×C22⋊C4—222no—
412C2×C22⋊C4—222no—
413C2×C22⋊C4—222no—
414C2×C22⋊C4—222no—
415C2×C22⋊C4C4×D1114yes—
416C2×C42—222no—
417C2×C42—222no—
418C2×C42—224no—
419C2×C42—442no—
420#95—24no—
421#95—42no—
422#95—118no—
423#95—118no—
424#95—224no—
425#95—224no—
426#95—224no—
427#95—222no—
428#95—222no—
429#95—224no—
430#95—224no—
431#95—224no—
432#95—442no—
433C2×C11—28no—
434C2×C11C2×#38811yescharacteristic
435C2×C11C4×#12311yescharacteristic
436C2×C11#232211yescharacteristic
437C2×C11#234312yes—
438C2×C11#235912yes—
439C2×C11#248311yescharacteristic
440C2×C11#248411yescharacteristic
441C2×C11#248611yescharacteristic
442C2×C11#248812yes—
443C2×C11#249312yes—
444C2×C11#253411yescharacteristic
445C24—22no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24C2×C4×D1112yes—
450C24#433912yes—
451C24#433912yes—
452C24D4×D1112yes—
453C24D4×D1112yes—
454C24#434112yes—
455C24#434312yes—
456C24C23×D1111yescharacteristic
457C22×C4—28no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—48no—
480C22×C4—48no—
481C22×C4—44no—
482C22×C4—44no—
483C22×C4—112no—
484C22×C4—114no—
485C22×C4—114no—
486C22×C4—114no—
487C22×C4—112no—
488C22×C4—112no—
489C22×C4—112no—
490C22×C4—228no—
491C22×C4—221no—
492C22×C4—222no—
493C22×C4—221no—
494C22×C4—228no—
495C22×C4—228no—
496C22×C4—228no—
497C22×C4—228no—
498C22×C4—221no—
499C22×C4—221no—
500C22×C4—222no—
501C22×C4—222no—
502C22×C4—221no—
503C22×C4—222no—
504C22×C4—222no—
505C22×C4—221no—
506C22×C4—221no—
507C22×C4—222no—
508C22×C4—222no—
509C22×C4—222no—
510C22×C4—222no—
511C22×C4—222no—
512C22×C4—222no—
513C22×C4—222no—
514C22×C4—222no—
515C22×C4—222no—
516C22×C4—221no—
517C22×C4—222no—
518C22×C4—222no—
519C22×C4—222no—
520C22×C4—222no—
521C22×C4—222no—
522C22×C4—444no—
523C22×C4—448no—
524C22×C4—448no—
525C22×C4—444no—
526C22×C4—444no—
527C22×C4—444no—
528C22×C4—444no—
529C22×C4C2×C4×D1112yes—
530C22×C4C2×C4×D1112yes—
531C22×C4#434114yes—
532C4⋊C4—448no—
533C22⋊C4—28no—
534C22⋊C4—44no—
535C22⋊C4—228no—
536C22⋊C4—228no—
537C42—444no—
538C42—444no—
539C11#1399211yescharacteristic, complemented, Sylow
540C23—24no—
541C23—24no—
542C23—24no—
543C23—24no—
544C23—24no—
545C23—24no—
546C23—22no—
547C23—22no—
548C23—24no—
549C23—24no—
550C23—24no—
551C23—24no—
552C23—24no—
553C23—22no—
554C23—22no—
555C23—24no—
556C23#6692514yes—
557C23(C22⋊D11)⋊C414yes—
558C23#6693714yes—
559C23#6693814yes—
560C23#6694614yes—
561C23#6694714yes—
562C23#6695114yes—
563C23C22×C4×D1111yescharacteristic
564C23C2×#433911yescharacteristic
565C23C2×#433911yescharacteristic
566C23C2×D4×D1111yescharacteristic
567C23C2×D4×D1111yescharacteristic
568C23C2×#434111yescharacteristic
569C23C2×#434112yes—
570C23#6703712yes—
571C23C2×#434311yescharacteristic
572C23#41×D1112yes—
573C23#6704312yes—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—24no—
580C2×C4—24no—
581C2×C4—416no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—114no—
600C2×C4—222no—
601C2×C4—224no—
602C2×C4—222no—
603C2×C4—224no—
604C2×C4—224no—
605C2×C4—224no—
606C2×C4—222no—
607C2×C4—222no—
608C2×C4—224no—
609C2×C4—224no—
610C2×C4—222no—
611C2×C4—224no—
612C2×C4—224no—
613C2×C4—222no—
614C2×C4—224no—
615C2×C4—222no—
616C2×C4—224no—
617C2×C4—4416no—
618C2×C4—442no—
619C2×C4—442no—
620C2×C4—442no—
621C2×C4—442no—
622C2×C4—442no—
623C2×C4—4416no—
624C2×C4—442no—
625C2×C4—442no—
626C2×C4—441no—
627C2×C4—441no—
628C2×C4—442no—
629C2×C4—442no—
630C2×C4—442no—
631C2×C4—442no—
632C2×C4—441no—
633C2×C4—441no—
634C2×C4—442no—
635C22—24no—
636C22—24no—
637C22—24no—
638C22—24no—
639C22—28no—
640C22—24no—
641C22—28no—
642C22—28no—
643C22—24no—
644C22—28no—
645C22#1062228218yes—
646C22C2×#6692511yescharacteristic
647C22C2×(C22⋊D11)⋊C411yescharacteristic
648C22C2×#6693711yescharacteristic
649C22C2×#6693811yescharacteristic
650C22#1062302612yes—
651C22C2×#6694611yescharacteristic
652C22C2×#6694711yescharacteristic
653C22C2×#6695111yescharacteristic
654C22#1062306212yes—
655C22C4×#434112yes—
656C22#1062307212yes—
657C22#1062307712yes—
658C22#1062308712yes—
659C22#1062311711yescharacteristic
660C22#1062312011yescharacteristic
661C22#1062312212yes—
662C22#1062313112yes—
663C22#1062313312yes—
664C22#1062316812yes—
665C22#1062317312yes—
666C22#1062317911yescharacteristic
667C22D11×#12311yescharacteristic
668C22#1062318612yes—
669C4—42no—
670C4—44no—
671C4—42no—
672C4—82no—
673C4—224no—
674C4—442no—
675C4—442no—
676C4—442no—
677C4—444no—
678C4—444no—
679C2—28no—
680C2C2×#1062228211yescharacteristic
681C2#1307114111yescharacteristic
682C2#1307129011yescharacteristic
683C2#1307147012yes—
684C2#1307160612yes—
685C2#1307289611yescharacteristic
686C2#1307290211yescharacteristic
687C2#1307292311yescharacteristic
688C2#1307294012yes—
689C2#1307300712yes—
690C2#1307350911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C22⋊#95C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC22⋊#95D11
hypocenterC11#13992
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
6. #13066877C2semidirect
7. #13066874C2semidirect
8. #13066847C2semidirect
9. #13066841C2semidirect
38. #10622556C4semidirect
98. C11⋊#95C2×C4semidirect
99. C11⋊#95C2×C4semidirect
539. C11#13992semidirect

Maximal subgroups

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

subgroupindex
C2×#106228232
C2×#106225562
C2×C22⋊C4×Dic112
C22×C11⋊#952
#130668772
#130668742
#130668472
#130668412
#130668382
C11×C22⋊#952
#1399211