Finite Group Databasebeta

← #14676850

Subgroups — #14676850

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×#10622824C211yesmaximal, characteristic
3C2×#10622824C211yesmaximal, characteristic
4C2×C4×C22⋊Dic11C211yesmaximal, characteristic
5#13066877C212yesmaximal, complemented
6#13066871C212yesmaximal, complemented
7#13066847C212yesmaximal, complemented
8#13066840C212yesmaximal, complemented
9#13066839C211yesmaximal, characteristic
10#13066839C211yesmaximal, characteristic
11C22×C11×#95C211yesmaximal, characteristic
12C24×C4×C11C2211yescharacteristic
13C24×C4×C11C2211yescharacteristic
14C24×C4×C11C2211yescharacteristic
15C22×C22⋊Dic11C2211yescharacteristic
16C22×C22⋊Dic11C2211yescharacteristic
17C22×C22⋊Dic11C2211yescharacteristic
18C22×C22⋊Dic11C2211yescharacteristic
19C22×Dic11⋊C4C2212yes—
20C22×C4×Dic11C2211yescharacteristic
21C22×C4×Dic11C2211yescharacteristic
22C2×C11×#95—24no—
23C2×C11×#95C2212yes—
24C2×C11×#95C2212yes—
25#10622824—24no—
26#10622824C418yescomplemented
27#10622823—24no—
28C4×C22⋊Dic11—24no—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2211yescharacteristic
35C2×C11⋊#95C2211yescharacteristic
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40C25×C11C2311yescharacteristic
41C23×C4×C11—22no—
42C23×C4×C11—22no—
43C23×C4×C11—22no—
44C23×C4×C11—22no—
45C23×C4×C11—22no—
46C23×C4×C11—22no—
47C23×C4×C11—22no—
48C23×C4×C11—22no—
49C23×C4×C11—22no—
50C23×C4×C11—24no—
51C23×C4×C11—24no—
52C23×C4×C11—22no—
53C23×C4×C11—22no—
54C23×C4×C11—42no—
55C23×C4×C11—42no—
56C23×C4×C11C2×C414yes—
57C23×C4×C11D414yes—
58C23×C4×C11C2312yes—
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2312yes—
61C23×C4×C11C2311yescharacteristic
62C23×Dic11C2312yes—
63C23×Dic11C2311yescharacteristic
64C23×Dic11C2311yescharacteristic
65C23×Dic11C2312yes—
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C2×C22⋊Dic11—22no—
69C2×C22⋊Dic11—22no—
70C2×C22⋊Dic11—22no—
71C2×C22⋊Dic11—22no—
72C2×C22⋊Dic11—22no—
73C2×C22⋊Dic11—22no—
74C2×C22⋊Dic11—22no—
75C2×C22⋊Dic11—22no—
76C2×C22⋊Dic11—22no—
77C2×C22⋊Dic11C2×C414yes—
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—24no—
89C11⋊#95—22no—
90C11⋊#95—22no—
91C11⋊#95—24no—
92C11⋊#95—24no—
93C11⋊#95—24no—
94C11⋊#95—24no—
95C11⋊#95—24no—
96C11⋊#95—42no—
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—21no—
114C22×C4×C11—21no—
115C22×C4×C11—22no—
116C22×C4×C11—28no—
117C22×C4×C11—28no—
118C22×C4×C11—28no—
119C22×C4×C11—28no—
120C22×C4×C11—28no—
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×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—28no—
138C22×C4×C11—44no—
139C22×C4×C11—48no—
140C22×C4×C11—48no—
141C22×C4×C11—48no—
142C22×C4×C11—48no—
143C22×C4×C11—44no—
144C22×C4×C11—44no—
145C22×C4×C11—44no—
146C22×C4×C11—44no—
147C22×C4×C11—44no—
148C22×C4×C11—44no—
149C22×C4×C11C22×C414yes—
150C22×C4×C11C2×D412yes—
151C22×C4×C11C2×D412yes—
152C22×C4×C11#4114yes—
153C22×C4×C11#4114yes—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11—22no—
159C22×Dic11—22no—
160C22×Dic11—22no—
161C22×Dic11—22no—
162C22×Dic11—22no—
163C22×Dic11—22no—
164C22×Dic11—22no—
165C22×Dic11—22no—
166C22×Dic11—21no—
167C22×Dic11—21no—
168C22×Dic11—21no—
169C22×Dic11—21no—
170C22×Dic11—22no—
171C22×Dic11—22no—
172C22×Dic11—22no—
173C22×Dic11—22no—
174C22×Dic11—22no—
175C22×Dic11—22no—
176C22×Dic11—22no—
177C22×Dic11—22no—
178C22×Dic11—22no—
179C22×Dic11—22no—
180C22×Dic11—22no—
181C22×Dic11—22no—
182C22×Dic11—22no—
183C22×Dic11C22×C412yes—
184C22×Dic11C22×C414yes—
185C22×Dic11C22×C412yes—
186C22×Dic11C2×D412yes—
187C22×Dic11C2×D412yes—
188C22⋊Dic11—28no—
189C22⋊Dic11—28no—
190C22⋊Dic11—28no—
191C22⋊Dic11—44no—
192Dic11⋊C4—48no—
193C4×Dic11—44no—
194C4×Dic11—44no—
195C2×#385—111no—
196C2×#381—111no—
197C2×#381—111no—
198C2×C4×C22⋊C4—111no—
199C22×#95D1111yescharacteristic
200#1443—112no—
201#1442—112no—
202#1436—112no—
203#1434—112no—
204C22⋊#95—111no—
205C22⋊#95—111no—
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×#4112yes—
234C23×C11C2×#4112yes—
235C23×C11C2×#4111yescharacteristic
236C23×C11C2×#4111yescharacteristic
237C23×C11C2×#4111yescharacteristic
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—22no—
248C2×C4×C11—22no—
249C2×C4×C11—24no—
250C2×C4×C11—22no—
251C2×C4×C11—24no—
252C2×C4×C11—24no—
253C2×C4×C11—416no—
254C2×C4×C11—416no—
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×C4×C11—416no—
266C2×C4×C11#12314yes—
267C2×Dic11—24no—
268C2×Dic11—22no—
269C2×Dic11—22no—
270C2×Dic11—24no—
271C2×Dic11—24no—
272C2×Dic11—24no—
273C2×Dic11—24no—
274C2×Dic11—22no—
275C2×Dic11—22no—
276C2×Dic11—24no—
277C2×Dic11—24no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—42no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—42no—
288C2×Dic11—42no—
289C2×Dic11—42no—
290C2×Dic11—42no—
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—42no—
300C2×Dic11—42no—
301C24×C4C2×D1111yescharacteristic
302C24×C4C2×D1111yescharacteristic
303C24×C4C2×D1111yescharacteristic
304C22×C4⋊C4—112no—
305C22×C22⋊C4—111no—
306C22×C22⋊C4—111no—
307C22×C22⋊C4—111no—
308C22×C22⋊C4—111no—
309C22×C42—111no—
310C22×C42—111no—
311#385—224no—
312#381—118no—
313#381—224no—
314C4×C22⋊C4—224no—
315C2×#95—24no—
316C2×#95—112no—
317C2×#95—112no—
318C2×#95—112no—
319C2×#95—112no—
320C2×#95—112no—
321C2×#95—112no—
322C2×#95—112no—
323C2×#95—111no—
324C2×#95—111no—
325C2×#95—112no—
326C2×#95—112no—
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—24no—
364C4×C11—42no—
365C4×C11—44no—
366C4×C11—44no—
367Dic11—42no—
368Dic11—44no—
369Dic11—42no—
370Dic11—42no—
371Dic11—42no—
372Dic11—82no—
373C25C22×D1111yescharacteristic
374C23×C4—22no—
375C23×C4—22no—
376C23×C4—22no—
377C23×C4—22no—
378C23×C4—22no—
379C23×C4—22no—
380C23×C4—22no—
381C23×C4—22no—
382C23×C4—22no—
383C23×C4—24no—
384C23×C4—24no—
385C23×C4—22no—
386C23×C4—22no—
387C23×C4—42no—
388C23×C4—42no—
389C23×C4—111no—
390C23×C4—112no—
391C23×C4—111no—
392C23×C4—111no—
393C23×C4—111no—
394C23×C4—112no—
395C23×C4C4×D1114yes—
396C23×C4C22⋊D1114yes—
397C23×C4C22×D1112yes—
398C23×C4C22×D1112yes—
399C23×C4C22×D1111yescharacteristic
400C23×C4C22×D1111yescharacteristic
401C2×C4⋊C4—224no—
402C2×C4⋊C4—224no—
403C2×C4⋊C4—442no—
404C2×C22⋊C4—114no—
405C2×C22⋊C4—114no—
406C2×C22⋊C4—114no—
407C2×C22⋊C4—222no—
408C2×C22⋊C4—222no—
409C2×C22⋊C4—222no—
410C2×C22⋊C4—222no—
411C2×C22⋊C4—222no—
412C2×C22⋊C4—222no—
413C2×C22⋊C4—222no—
414C2×C22⋊C4—222no—
415C2×C22⋊C4—222no—
416C2×C42—224no—
417C2×C42—222no—
418C2×C42—222no—
419C2×C42—442no—
420#95—24no—
421#95—24no—
422#95—118no—
423#95—118no—
424#95—224no—
425#95—224no—
426#95—224no—
427#95—224no—
428#95—224no—
429#95—222no—
430#95—222no—
431#95—442no—
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—
451C24D4×D1112yes—
452C24#434112yes—
453C24#434112yes—
454C24#434112yes—
455C24C2×C22⋊D1112yes—
456C24C23×D1111yescharacteristic
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—28no—
461C22×C4—28no—
462C22×C4—28no—
463C22×C4—28no—
464C22×C4—28no—
465C22×C4—22no—
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—21no—
475C22×C4—21no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—28no—
482C22×C4—44no—
483C22×C4—48no—
484C22×C4—48no—
485C22×C4—48no—
486C22×C4—48no—
487C22×C4—44no—
488C22×C4—44no—
489C22×C4—44no—
490C22×C4—44no—
491C22×C4—44no—
492C22×C4—44no—
493C22×C4—112no—
494C22×C4—114no—
495C22×C4—112no—
496C22×C4—112no—
497C22×C4—112no—
498C22×C4—222no—
499C22×C4—222no—
500C22×C4—222no—
501C22×C4—222no—
502C22×C4—221no—
503C22×C4—221no—
504C22×C4—222no—
505C22×C4—222no—
506C22×C4—222no—
507C22×C4—222no—
508C22×C4—221no—
509C22×C4—221no—
510C22×C4—222no—
511C22×C4—222no—
512C22×C4—222no—
513C22×C4—222no—
514C22×C4—222no—
515C22×C4—222no—
516C22×C4—221no—
517C22×C4—221no—
518C22×C4—221no—
519C22×C4—221no—
520C22×C4—222no—
521C22×C4—222no—
522C22×C4—222no—
523C22×C4—222no—
524C22×C4—222no—
525C22×C4—222no—
526C22×C4—222no—
527C22×C4C2×C4×D1114yes—
528C22×C4#433914yes—
529C22×C4#433914yes—
530C22×C4C2×C22⋊D1112yes—
531C22×C4C2×C22⋊D1112yes—
532C4⋊C4—448no—
533C22⋊C4—228no—
534C22⋊C4—228no—
535C22⋊C4—228no—
536C22⋊C4—444no—
537C42—444no—
538C42—444no—
539C11#1399211yescharacteristic, complemented, Sylow
540C23—24no—
541C23—24no—
542C23—24no—
543C23—24no—
544C23—24no—
545C23—24no—
546C23—24no—
547C23—24no—
548C23—24no—
549C23—24no—
550C23—24no—
551C23—24no—
552C23—22no—
553C23—22no—
554C23—22no—
555C23—22no—
556C23#6693014yes—
557C23#6693214yes—
558C23(C22⋊D11)⋊C414yes—
559C23#6693814yes—
560C23C4×C22⋊D1114yes—
561C23#6698814yes—
562C23#6699114yes—
563C23C22×C4×D1111yescharacteristic
564C23C2×#433912yes—
565C23C2×#433912yes—
566C23C2×#433911yescharacteristic
567C23C2×D4×D1111yescharacteristic
568C23C2×#434111yescharacteristic
569C23C2×#434111yescharacteristic
570C23C2×#434111yescharacteristic
571C23#6703712yes—
572C23#6704012yes—
573C23C22×C22⋊D1111yescharacteristic
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—24no—
579C2×C4—24no—
580C2×C4—24no—
581C2×C4—24no—
582C2×C4—24no—
583C2×C4—22no—
584C2×C4—24no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—416no—
588C2×C4—416no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—416no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—224no—
601C2×C4—224no—
602C2×C4—224no—
603C2×C4—224no—
604C2×C4—224no—
605C2×C4—224no—
606C2×C4—224no—
607C2×C4—222no—
608C2×C4—222no—
609C2×C4—222no—
610C2×C4—222no—
611C2×C4—442no—
612C2×C4—442no—
613C2×C4—442no—
614C2×C4—442no—
615C2×C4—442no—
616C2×C4—442no—
617C2×C4—442no—
618C2×C4—442no—
619C2×C4—441no—
620C2×C4—441no—
621C2×C4—441no—
622C2×C4—441no—
623C2×C4—441no—
624C2×C4—441no—
625C2×C4—441no—
626C2×C4—441no—
627C2×C4—442no—
628C2×C4—442no—
629C2×C4—442no—
630C2×C4—442no—
631C2×C4—442no—
632C2×C4—442no—
633C2×C4—442no—
634C2×C4#6698214yes—
635C22—24no—
636C22—24no—
637C22—24no—
638C22—28no—
639C22—24no—
640C22—28no—
641C22—28no—
642C22—24no—
643C22—28no—
644C22—24no—
645C22#1062255718yes—
646C22C4×#433912yes—
647C22#1062301012yes—
648C22C2×#6693011yescharacteristic
649C22C2×#6693211yescharacteristic
650C22C2×(C22⋊D11)⋊C411yescharacteristic
651C22#1062302112yes—
652C22C2×#6693811yescharacteristic
653C22#1062302612yes—
654C22#1062302612yes—
655C22#1062302612yes—
656C22#1062303512yes—
657C22#1062303812yes—
658C22#1062304412yes—
659C22#1062304412yes—
660C22#1062304412yes—
661C22#1062304612yes—
662C22C2×C4×C22⋊D1111yescharacteristic
663C22C2×#6698211yescharacteristic
664C22#1062332211yescharacteristic
665C22C2×#6698811yescharacteristic
666C22C2×#6699111yescharacteristic
667C22#1062333511yescharacteristic
668C22#1062334711yescharacteristic
669C4—24no—
670C4—44no—
671C4—44no—
672C4—42no—
673C4—442no—
674C4—442no—
675C4—442no—
676C4—442no—
677C4—444no—
678C4—882no—
679C2—28no—
680C2C2×#1062255711yescharacteristic
681C2C4×#6698211yescharacteristic
682C2#1307128511yescharacteristic
683C2#1307147212yes—
684C2#1307160412yes—
685C2#1307289411yescharacteristic
686C2#1307290311yescharacteristic
687C2#1307291811yescharacteristic
688C2#1307294212yes—
689C2#1307300112yes—
690C2#1307350611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC22×C11×#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
5. #13066877C2semidirect
6. #13066871C2semidirect
7. #13066847C2semidirect
8. #13066840C2semidirect
26. #10622824C4semidirect
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×#106228242
C2×C4×C22⋊Dic112
#130668772
#130668712
#130668472
#130668402
#130668392
C22×C11×#952
#1399211