Finite Group Databasebeta

← #14680821

Subgroups — #14680821

Order 2816.

1650 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622835C211yesmaximal, characteristic
2C2×#10622834C211yesmaximal, characteristic
3C2×#10622265C211yesmaximal, characteristic, complemented
4#13066872C211yesmaximal, characteristic, complemented
5#13066870C211yesmaximal, characteristic, complemented
6#13066863C212yesmaximal, complemented
7#13066859C212yesmaximal, complemented
8#13066853C212yesmaximal, complemented
9#13066853C212yesmaximal, complemented
10#95×Dic11C211yesmaximal, characteristic, complemented
11C11×#1438C211yesmaximal, characteristic
12C23×D4×C11C2211yescharacteristic
13C22×C11×C22⋊C4C2212yes—
14C22×C11×C22⋊C4C2212yes—
15C22×C22⋊Dic11C2212yes—
16C22×C22⋊Dic11C2212yes—
17C22×C22⋊Dic11C2212yes—
18C22×C22⋊Dic11C2212yes—
19C22×C4⋊Dic11C2211yescharacteristic
20C22×Dic11⋊C4C2211yescharacteristic
21C22×Dic11⋊C4C2211yescharacteristic
22C22×C4×Dic11C2212yes—
23C22×C4×Dic11C2211yescharacteristic
24C2×C11×#95C2211yescharacteristic
25C2×C11×#95C2211yescharacteristic
26#10622835C418yescomplemented
27#10622834—24no—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2211yescharacteristic
30C2×C11⋊#95C2211yescharacteristic
31C2×C11⋊#95C2211yescharacteristic
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2211yescharacteristic
37#10622265—24no—
38C25×C11C2312yes—
39C22×D4×C11—22no—
40C22×D4×C11—22no—
41C22×D4×C11—42no—
42C22×D4×C11—42no—
43C22×D4×C11C2×C414yes—
44C23×C4×C11C2311yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C23×C4×C11C2312yes—
47C23×C4×C11C2311yescharacteristic
48C23×Dic11C2312yes—
49C23×Dic11C2312yes—
50C23×Dic11C2311yescharacteristic
51C23×Dic11C2311yescharacteristic
52C23×Dic11C2311yescharacteristic
53C23×Dic11C2311yescharacteristic
54C2×C11×C22⋊C4—24no—
55C2×C11×C22⋊C4—24no—
56C2×C11×C22⋊C4—42no—
57C2×C11×C22⋊C4—42no—
58C2×C11×C22⋊C4—42no—
59C2×C11×C22⋊C4—42no—
60C2×C22⋊Dic11—24no—
61C2×C22⋊Dic11—24no—
62C2×C22⋊Dic11—24no—
63C2×C22⋊Dic11—24no—
64C2×C22⋊Dic11—42no—
65C2×C22⋊Dic11—42no—
66C2×C22⋊Dic11—42no—
67C2×C22⋊Dic11—42no—
68C2×C22⋊Dic11—42no—
69C2×C22⋊Dic11—42no—
70C2×C22⋊Dic11C2×C418yes—
71C2×C22⋊Dic11C2×C418yes—
72C2×C4⋊Dic11—22no—
73C2×C4⋊Dic11—42no—
74C2×Dic11⋊C4—22no—
75C2×Dic11⋊C4—22no—
76C2×Dic11⋊C4—22no—
77C2×Dic11⋊C4—42no—
78C2×Dic11⋊C4C2×C414yes—
79C2×C4×Dic11—24no—
80C2×C4×Dic11—42no—
81C2×C4×Dic11—42no—
82C2×C4×Dic11—42no—
83C2×C4×Dic11D414yes—
84C11×#95—22no—
85C11×#95—22no—
86C11⋊#95—24no—
87C11⋊#95—22no—
88C11⋊#95—22no—
89C11⋊#95—22no—
90C11⋊#95—42no—
91C11⋊#95—42no—
92C11⋊#95—42no—
93C11⋊#95—42no—
94C11⋊#95C2×C414yes—
95#14325—111nomaximal, Sylow
96C24×C11—22no—
97C24×C11—22no—
98C24×C11—22no—
99C24×C11—22no—
100C24×C11—22no—
101C24×C11—22no—
102C24×C11—22no—
103C24×C11—22no—
104C24×C11—22no—
105C24×C11—22no—
106C24×C11—22no—
107C24×C11—22no—
108C24×C11—22no—
109C24×C11—22no—
110C24×C11C22×C414yes—
111C24×C11C2411yescharacteristic
112C2×D4×C11—28no—
113C2×D4×C11—48no—
114C2×D4×C11—44no—
115C2×D4×C11—44no—
116C2×D4×C11—48no—
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—21no—
126C22×C4×C11—21no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—21no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11C22×C412yes—
136C22×C4×C11C2×D412yes—
137C22×C4×C11#4114yes—
138C22×C4×C11#4112yes—
139C22×Dic11—21no—
140C22×Dic11—21no—
141C22×Dic11—22no—
142C22×Dic11—22no—
143C22×Dic11—22no—
144C22×Dic11—22no—
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11—22no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—22no—
153C22×Dic11—22no—
154C22×Dic11—22no—
155C22×Dic11—22no—
156C22×Dic11—22no—
157C22×Dic11—22no—
158C22×Dic11—22no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11—22no—
164C22×Dic11—22no—
165C22×Dic11—22no—
166C22×Dic11—22no—
167C22×Dic11—21no—
168C22×Dic11—21no—
169C22×Dic11C22×C414yes—
170C22×Dic11C22×C412yes—
171C22×Dic11C22×C412yes—
172C22×Dic11C2×D412yes—
173C22×Dic11C2×D412yes—
174C22×Dic11#4114yes—
175C11×C22⋊C4—48no—
176C11×C22⋊C4—48no—
177C22⋊Dic11—48no—
178C22⋊Dic11—48no—
179C22⋊Dic11—48no—
180C22⋊Dic11—48no—
181C4⋊Dic11—44no—
182Dic11⋊C4—28no—
183Dic11⋊C4—44no—
184C4×Dic11—44no—
185C4×Dic11—48no—
186C2×#394—111no—
187C2×#390—111no—
188C2×#387—111no—
189#1442—111no—
190#1441—111no—
191#1440—112no—
192#1439—112no—
193#1438D1111yescharacteristic
194#1437—112no—
195#1437—112no—
196C4×#95—111no—
197C23×C11—24no—
198C23×C11—24no—
199C23×C11—24no—
200C23×C11—24no—
201C23×C11—24no—
202C23×C11—24no—
203C23×C11—24no—
204C23×C11—42no—
205C23×C11—42no—
206C23×C11—42no—
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—42no—
218C23×C11—42no—
219C23×C11—42no—
220C23×C11—42no—
221C23×C11—42no—
222C23×C11—42no—
223C23×C11—42no—
224C23×C11—42no—
225C23×C11—42no—
226C23×C11—42no—
227C23×C11—42no—
228C23×C11—42no—
229C23×C11—42no—
230C23×C11—42no—
231C23×C11—42no—
232C23×C11C23×C411yescharacteristic
233C23×C11C22×D411yescharacteristic
234C23×C11C2×#4111yescharacteristic
235C23×C11C2×#4112yes—
236C23×C11C2×#4112yes—
237C23×C11H(5,𝔽2)12yes—
238C23×C11H(5,𝔽2)12yes—
239C23×C11H(5,𝔽2)11yescharacteristic
240C23×C11H(5,𝔽2)11yescharacteristic
241C23×C11H(5,𝔽2)11yescharacteristic
242C23×C112−1+411yescharacteristic
243D4×C11—416no—
244C2×C4×C11—24no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—24no—
248C2×C4×C11—24no—
249C2×C4×C11—24no—
250C2×C4×C11—24no—
251C2×C4×C11—42no—
252C2×C4×C11—42no—
253C2×C4×C11—42no—
254C2×C4×C11—42no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—42no—
262C2×C4×C11—42no—
263C2×C4×C11—42no—
264C2×C4×C11—42no—
265C2×C4×C11C4×D414yes—
266C2×Dic11—22no—
267C2×Dic11—22no—
268C2×Dic11—24no—
269C2×Dic11—24no—
270C2×Dic11—22no—
271C2×Dic11—22no—
272C2×Dic11—24no—
273C2×Dic11—22no—
274C2×Dic11—24no—
275C2×Dic11—24no—
276C2×Dic11—24no—
277C2×Dic11—22no—
278C2×Dic11—22no—
279C2×Dic11—22no—
280C2×Dic11—22no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—42no—
286C2×Dic11—42no—
287C2×Dic11—42no—
288C2×Dic11—42no—
289C2×Dic11—41no—
290C2×Dic11—42no—
291C2×Dic11—42no—
292C2×Dic11—42no—
293C2×Dic11—41no—
294C2×Dic11—42no—
295C2×Dic11—42no—
296C2×Dic11—42no—
297C2×Dic11—42no—
298C2×Dic11—42no—
299C2×Dic11—42no—
300C2×Dic11—42no—
301C2×Dic11#12414yes—
302C23×D4C2×D1111yescharacteristic
303C22×C4⋊C4—111no—
304C22×C4⋊C4—111no—
305C22×C4⋊C4—111no—
306C22×C22⋊C4—112no—
307C22×C22⋊C4—112no—
308C22×C22⋊C4—112no—
309C22×C22⋊C4—112no—
310C22×C22⋊C4C2×D1112yes—
311C22×C22⋊C4C2×D1112yes—
312C22×C42—111no—
313C22×C42—112no—
314#394—118no—
315#390—224no—
316#387—224no—
317C2×#95—111no—
318C2×#95—112no—
319C2×#95—111no—
320C2×#95—111no—
321C2×#95—111no—
322C2×#95—112no—
323C2×#95—112no—
324C2×#95—112no—
325C2×#95—112no—
326C2×#95C2×D1111yescharacteristic
327C2×#95C2×D1111yescharacteristic
328C22×C11—44no—
329C22×C11—44no—
330C22×C11—44no—
331C22×C11—44no—
332C22×C11—44no—
333C22×C11—44no—
334C22×C11—44no—
335C22×C11—82no—
336C22×C11—82no—
337C22×C11—82no—
338C22×C11—82no—
339C22×C11—82no—
340C22×C11—82no—
341C22×C11—82no—
342C22×C11—82no—
343C22×C11C2×C4×D411yescharacteristic
344C22×C11C4×#4112yes—
345C22×C11#51812yes—
346C22×C11#51811yescharacteristic
347C22×C11#52011yescharacteristic
348C22×C11C2×#12411yescharacteristic
349C22×C11#52912yes—
350C22×C11#53211yescharacteristic
351C22×C11#53411yescharacteristic
352C22×C11#53511yescharacteristic
353C22×C11#53511yescharacteristic
354C22×C11#53711yescharacteristic
355C22×C11#53812yes—
356C22×C11#53812yes—
357C22×C11#53812yes—
358C22×C11#53812yes—
359C22×C11#53912yes—
360C22×C11#54011yescharacteristic
361C22×C11#54012yes—
362C22×C11#54012yes—
363C22×C11#54012yes—
364C22×C11#54212yes—
365C22×C11#54211yescharacteristic
366C4×C11—24no—
367C4×C11—44no—
368C4×C11—81no—
369C4×C11—81no—
370Dic11—24no—
371Dic11—42no—
372Dic11—42no—
373Dic11—44no—
374Dic11—42no—
375Dic11—82no—
376C25C22×D1112yes—
377C22×D4—22no—
378C22×D4—22no—
379C22×D4—42no—
380C22×D4—42no—
381C22×D4C4×D1114yes—
382C23×C4—111no—
383C23×C4—111no—
384C23×C4—111no—
385C23×C4—111no—
386C23×C4—112no—
387C23×C4—112no—
388C23×C4C22×D1111yescharacteristic
389C23×C4C22×D1111yescharacteristic
390C23×C4C22×D1112yes—
391C23×C4C22×D1111yescharacteristic
392C2×C4⋊C4—114no—
393C2×C4⋊C4—222no—
394C2×C4⋊C4—222no—
395C2×C4⋊C4—222no—
396C2×C4⋊C4—222no—
397C2×C4⋊C4—442no—
398C2×C4⋊C4—442no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—42no—
402C2×C22⋊C4—42no—
403C2×C22⋊C4—42no—
404C2×C22⋊C4—42no—
405C2×C22⋊C4—118no—
406C2×C22⋊C4—118no—
407C2×C22⋊C4—224no—
408C2×C22⋊C4—224no—
409C2×C22⋊C4—224no—
410C2×C22⋊C4—224no—
411C2×C22⋊C4—442no—
412C2×C22⋊C4—442no—
413C2×C22⋊C4—442no—
414C2×C22⋊C4—442no—
415C2×C22⋊C4—442no—
416C2×C22⋊C4—442no—
417C2×C42—114no—
418C2×C42—224no—
419C2×C42—442no—
420C2×C42—442no—
421C2×C42—442no—
422#95—22no—
423#95—22no—
424#95—114no—
425#95—222no—
426#95—222no—
427#95—222no—
428#95—224no—
429#95—442no—
430#95—442no—
431#95—442no—
432#95—442no—
433C2×C11—84no—
434C2×C11C4×#12411yescharacteristic
435C2×C11#232111yescharacteristic
436C2×C11#232411yescharacteristic
437C2×C11#233312yes—
438C2×C11#233512yes—
439C2×C11#263911yescharacteristic
440C2×C11#264111yescharacteristic
441C2×C11#264812yes—
442C2×C11#265112yes—
443C2×C11#266111yescharacteristic
444C2×C11#266211yescharacteristic
445C24—22no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24C2×C4×D1114yes—
460C24C23×D1111yescharacteristic
461C2×D4—28no—
462C2×D4—48no—
463C2×D4—44no—
464C2×D4—44no—
465C2×D4—48no—
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—21no—
480C22×C4—21no—
481C22×C4—22no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—112no—
485C22×C4—114no—
486C22×C4—114no—
487C22×C4—112no—
488C22×C4—112no—
489C22×C4—112no—
490C22×C4—222no—
491C22×C4—221no—
492C22×C4—221no—
493C22×C4—221no—
494C22×C4—221no—
495C22×C4—222no—
496C22×C4—222no—
497C22×C4—221no—
498C22×C4—221no—
499C22×C4—221no—
500C22×C4—222no—
501C22×C4—222no—
502C22×C4—222no—
503C22×C4—222no—
504C22×C4—222no—
505C22×C4—221no—
506C22×C4—221no—
507C22×C4—222no—
508C22×C4—222no—
509C22×C4—222no—
510C22×C4—221no—
511C22×C4—221no—
512C22×C4—221no—
513C22×C4—222no—
514C22×C4—222no—
515C22×C4—222no—
516C22×C4—222no—
517C22×C4—222no—
518C22×C4—222no—
519C22×C4—222no—
520C22×C4C2×C4×D1112yes—
521C22×C4D4×D1112yes—
522C22×C4#434114yes—
523C22×C4#434112yes—
524C4⋊C4—228no—
525C4⋊C4—444no—
526C4⋊C4—444no—
527C22⋊C4—48no—
528C22⋊C4—48no—
529C22⋊C4—448no—
530C22⋊C4—448no—
531C22⋊C4—448no—
532C22⋊C4—448no—
533C42—444no—
534C42—448no—
535C11#1432511yescharacteristic, complemented, Sylow
536C23—24no—
537C23—24no—
538C23—24no—
539C23—24no—
540C23—24no—
541C23—24no—
542C23—24no—
543C23—42no—
544C23—42no—
545C23—42no—
546C23—42no—
547C23—42no—
548C23—42no—
549C23—42no—
550C23—42no—
551C23—42no—
552C23—42no—
553C23—42no—
554C23—42no—
555C23—42no—
556C23—42no—
557C23—42no—
558C23—42no—
559C23—42no—
560C23—42no—
561C23—42no—
562C23—42no—
563C23—42no—
564C23—42no—
565C23—42no—
566C23—42no—
567C23—42no—
568C23—42no—
569C23—42no—
570C23—42no—
571C23C22×C4×D1111yescharacteristic
572C23C2×D4×D1111yescharacteristic
573C23C2×#434112yes—
574C23C2×#434111yescharacteristic
575C23#6703711yescharacteristic
576C23#6703711yescharacteristic
577C23#6703712yes—
578C23#6703712yes—
579C23#41×D1112yes—
580C23#6704211yescharacteristic
581C23#6704311yescharacteristic
582D4—416no—
583C2×C4—24no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—24no—
587C2×C4—24no—
588C2×C4—24no—
589C2×C4—24no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—42no—
604C2×C4—114no—
605C2×C4—222no—
606C2×C4—222no—
607C2×C4—224no—
608C2×C4—224no—
609C2×C4—222no—
610C2×C4—222no—
611C2×C4—222no—
612C2×C4—224no—
613C2×C4—224no—
614C2×C4—224no—
615C2×C4—222no—
616C2×C4—224no—
617C2×C4—222no—
618C2×C4—222no—
619C2×C4—222no—
620C2×C4—441no—
621C2×C4—441no—
622C2×C4—441no—
623C2×C4—442no—
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—442no—
634C2×C4—442no—
635C2×C4—442no—
636C2×C4—442no—
637C2×C4—442no—
638C2×C4—442no—
639C2×C4—442no—
640C2×C4(C22⋊D11)⋊C414yes—
641C22—44no—
642C22—44no—
643C22—44no—
644C22—44no—
645C22—44no—
646C22—44no—
647C22—44no—
648C22—82no—
649C22—82no—
650C22—82no—
651C22—82no—
652C22—82no—
653C22—82no—
654C22—82no—
655C22—82no—
656C22C2×(C22⋊D11)⋊C411yescharacteristic
657C22#1062301712yes—
658C22C4×#434112yes—
659C22#1062307611yescharacteristic
660C22#1062307711yescharacteristic
661C22#1062312011yescharacteristic
662C22#1062312311yescharacteristic
663C22#1062312412yes—
664C22#1062312412yes—
665C22#1062312412yes—
666C22#1062313112yes—
667C22#1062313412yes—
668C22#1062313811yescharacteristic
669C22#1062313911yescharacteristic
670C22#1062314412yes—
671C22#1062314612yes—
672C22#1062315012yes—
673C22#1062319112yes—
674C22#1062319412yes—
675C22D11×#12411yescharacteristic
676C22#1062321311yescharacteristic
677C22#1062324711yescharacteristic
678C22#1062325011yescharacteristic
679C4—24no—
680C4—44no—
681C4—81no—
682C4—81no—
683C4—224no—
684C4—444no—
685C4—442no—
686C4—442no—
687C4—442no—
688C4—882no—
689C2—84no—
690C2#1307116311yescharacteristic
691C2#1307127111yescharacteristic
692C2#1307131211yescharacteristic
693C2#1307138212yes—
694C2#1307140712yes—
695C2#1307454711yescharacteristic
696C2#1307455811yescharacteristic
697C2#1307460512yes—
698C2#1307465012yes—
699C2#1307474711yescharacteristic
700C2#1307475811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1438C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenter#1438D11
hypocenterC11#14325
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1438

Complements

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

NH ≅ G/Ntype
3. C2×#10622265C2semidirect
4. #13066872C2semidirect
5. #13066870C2semidirect
6. #13066863C2semidirect
7. #13066859C2semidirect
8. #13066853C2semidirect
9. #13066853C2semidirect
10. #95×Dic11C2semidirect
26. #10622835C4semidirect
535. C11#14325semidirect

Maximal subgroups

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

subgroupindex
C2×#106228352
C2×#106228342
C2×#106222652
#130668722
#130668702
#130668632
#130668592
#130668532
#95×Dic112
C11×#14382
#1432511