Finite Group Databasebeta

← #14680678

Subgroups — #14680678

Order 2816.

1766 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622835C211yesmaximal, characteristic
2C2×#10622834C211yesmaximal, characteristic
3C2×#10622558C212yesmaximal, complemented
4C2×#10622262C211yesmaximal, characteristic, complemented
5#13066880C211yesmaximal, characteristic, complemented
6#13066870C211yesmaximal, characteristic, complemented
7#13066859C212yesmaximal, complemented
8#13066859C212yesmaximal, complemented
9#13066853C212yesmaximal, complemented
10#13066841C211yesmaximal, 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×Dic11⋊C4C2212yes—
23C22×C4×Dic11C2211yescharacteristic
24C22×C4×Dic11C2211yescharacteristic
25C22×C4×Dic11C2211yescharacteristic
26C2×C11×#95C2211yescharacteristic
27C2×C11×#95C2211yescharacteristic
28#10622835C418yescomplemented
29#10622834—24no—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2211yescharacteristic
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2211yescharacteristic
37#10622558—28no—
38#10622262—24no—
39C25×C11C2312yes—
40C22×D4×C11—22no—
41C22×D4×C11—22no—
42C22×D4×C11—42no—
43C22×D4×C11—42no—
44C22×D4×C11C2×C414yes—
45C23×C4×C11C2312yes—
46C23×C4×C11C2311yescharacteristic
47C23×C4×C11C2311yescharacteristic
48C23×C4×C11C2311yescharacteristic
49C23×Dic11C2312yes—
50C23×Dic11C2311yescharacteristic
51C23×Dic11C2312yes—
52C23×Dic11C2311yescharacteristic
53C23×Dic11C2311yescharacteristic
54C23×Dic11C2311yescharacteristic
55C2×C11×C22⋊C4—24no—
56C2×C11×C22⋊C4—24no—
57C2×C11×C22⋊C4—42no—
58C2×C11×C22⋊C4—42no—
59C2×C11×C22⋊C4—42no—
60C2×C11×C22⋊C4—42no—
61C2×C22⋊Dic11—24no—
62C2×C22⋊Dic11—24no—
63C2×C22⋊Dic11—24no—
64C2×C22⋊Dic11—24no—
65C2×C22⋊Dic11—24no—
66C2×C22⋊Dic11—24no—
67C2×C22⋊Dic11—42no—
68C2×C22⋊Dic11—42no—
69C2×C22⋊Dic11—42no—
70C2×C22⋊Dic11—42no—
71C2×C22⋊Dic11C2×C418yes—
72C2×C22⋊Dic11C2×C418yes—
73C2×C4⋊Dic11—22no—
74C2×C4⋊Dic11—42no—
75C2×Dic11⋊C4—22no—
76C2×Dic11⋊C4—22no—
77C2×Dic11⋊C4—22no—
78C2×Dic11⋊C4—22no—
79C2×Dic11⋊C4—22no—
80C2×Dic11⋊C4—24no—
81C2×Dic11⋊C4—42no—
82C2×Dic11⋊C4—42no—
83C2×Dic11⋊C4C2×C414yes—
84C2×C4×Dic11—22no—
85C2×C4×Dic11—22no—
86C2×C4×Dic11—22no—
87C2×C4×Dic11—42no—
88C2×C4×Dic11—42no—
89C2×C4×Dic11D414yes—
90C2×C4×Dic11D414yescomplemented
91C11×#95—22no—
92C11×#95—22no—
93C11⋊#95—22no—
94C11⋊#95—24no—
95C11⋊#95—24no—
96C11⋊#95—42no—
97C11⋊#95—42no—
98C11⋊#95—42no—
99C11⋊#95C2×C414yes—
100#14312—111nomaximal, Sylow
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×C11—22no—
111C24×C11—22no—
112C24×C11—22no—
113C24×C11—22no—
114C24×C11—22no—
115C24×C11C22×C414yes—
116C24×C11C2411yescharacteristic
117C2×D4×C11—28no—
118C2×D4×C11—48no—
119C2×D4×C11—44no—
120C2×D4×C11—44no—
121C2×D4×C11—48no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
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—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11C22×C412yes—
140C22×C4×C11C2×D412yes—
141C22×C4×C11C2×D412yes—
142C22×C4×C11#4112yes—
143C22×C4×C11#4112yes—
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—22no—
156C22×Dic11—22no—
157C22×Dic11—22no—
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—22no—
167C22×Dic11—22no—
168C22×Dic11—22no—
169C22×Dic11—22no—
170C22×Dic11—22no—
171C22×Dic11C22×C414yes—
172C22×Dic11C22×C412yes—
173C22×Dic11C22×C412yes—
174C22×Dic11C2×D412yes—
175C22×Dic11C2×D412yes—
176C22×Dic11C2×D412yes—
177C22×Dic11C2×D412yes—
178C22×Dic11#4112yes—
179C22×Dic11#4112yes—
180C11×C22⋊C4—48no—
181C11×C22⋊C4—48no—
182C22⋊Dic11—216no—
183C22⋊Dic11—48no—
184C22⋊Dic11—48no—
185C22⋊Dic11—48no—
186C4⋊Dic11—44no—
187Dic11⋊C4—28no—
188Dic11⋊C4—28no—
189Dic11⋊C4—48no—
190C4×Dic11—28no—
191C4×Dic11—44no—
192C4×Dic11—44no—
193C2×#394—111no—
194C2×#390—111no—
195C2×#388—112no—
196C2×C4×C4⋊C4—111no—
197#1444—111no—
198#1441—111no—
199#1439—112no—
200#1439—112no—
201#1438D1111yescharacteristic
202#1437—112no—
203#1434—111no—
204C23×C11—24no—
205C23×C11—24no—
206C23×C11—24no—
207C23×C11—24no—
208C23×C11—24no—
209C23×C11—24no—
210C23×C11—24no—
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×C11—42no—
233C23×C11—42no—
234C23×C11—42no—
235C23×C11—42no—
236C23×C11—42no—
237C23×C11—42no—
238C23×C11—42no—
239C23×C11C23×C411yescharacteristic
240C23×C11C22×D411yescharacteristic
241C23×C11C22×D411yescharacteristic
242C23×C11C2×#4111yescharacteristic
243C23×C11C2×#4111yescharacteristic
244C23×C11C2×#4111yescharacteristic
245C23×C11C2×#4111yescharacteristic
246C23×C11H(5,𝔽2)12yes—
247C23×C11H(5,𝔽2)12yes—
248C23×C11H(5,𝔽2)12yes—
249C23×C112−1+412yes—
250D4×C11—416no—
251C2×C4×C11—24no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—24no—
255C2×C4×C11—22no—
256C2×C4×C11—22no—
257C2×C4×C11—24no—
258C2×C4×C11—24no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—42no—
264C2×C4×C11—42no—
265C2×C4×C11—42no—
266C2×C4×C11—42no—
267C2×C4×C11—42no—
268C2×C4×C11—42no—
269C2×C4×C11—42no—
270C2×C4×C11—42no—
271C2×C4×C11—42no—
272C2×C4×C11C4×D414yes—
273C2×Dic11—22no—
274C2×Dic11—22no—
275C2×Dic11—22no—
276C2×Dic11—22no—
277C2×Dic11—22no—
278C2×Dic11—22no—
279C2×Dic11—22no—
280C2×Dic11—22no—
281C2×Dic11—24no—
282C2×Dic11—24no—
283C2×Dic11—22no—
284C2×Dic11—24no—
285C2×Dic11—24no—
286C2×Dic11—24no—
287C2×Dic11—24no—
288C2×Dic11—22no—
289C2×Dic11—22no—
290C2×Dic11—22no—
291C2×Dic11—41no—
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—42no—
302C2×Dic11—42no—
303C2×Dic11—42no—
304C2×Dic11—42no—
305C2×Dic11—42no—
306C2×Dic11—42no—
307C2×Dic11C4×D414yes—
308C2×Dic11#12114yes—
309C23×D4C2×D1111yescharacteristic
310C22×C4⋊C4—111no—
311C22×C4⋊C4—111no—
312C22×C4⋊C4—112no—
313C22×C4⋊C4—111no—
314C22×C22⋊C4—112no—
315C22×C22⋊C4—112no—
316C22×C22⋊C4—112no—
317C22×C22⋊C4—112no—
318C22×C22⋊C4C2×D1112yes—
319C22×C22⋊C4C2×D1112yes—
320C22×C42—111no—
321C22×C42—111no—
322C22×C42—111no—
323#394—118no—
324#390—224no—
325#388—228no—
326C4×C4⋊C4—224no—
327C2×#95—111no—
328C2×#95—112no—
329C2×#95—111no—
330C2×#95—112no—
331C2×#95—112no—
332C2×#95—112no—
333C2×#95—112no—
334C2×#95C2×D1111yescharacteristic
335C2×#95C2×D1111yescharacteristic
336C22×C11—44no—
337C22×C11—44no—
338C22×C11—44no—
339C22×C11—44no—
340C22×C11—44no—
341C22×C11—44no—
342C22×C11—44no—
343C22×C11—82no—
344C22×C11—82no—
345C22×C11—82no—
346C22×C11—82no—
347C22×C11—82no—
348C22×C11—82no—
349C22×C11—82no—
350C22×C11—82no—
351C22×C11C2×C4×D411yescharacteristic
352C22×C11C2×C4×D411yescharacteristic
353C22×C11C4×#4111yescharacteristic
354C22×C11#51812yes—
355C22×C11#52012yes—
356C22×C11C2×#12111yescharacteristic
357C22×C11#52511yescharacteristic
358C22×C11#52911yescharacteristic
359C22×C11#53211yescharacteristic
360C22×C11#53411yescharacteristic
361C22×C11#53511yescharacteristic
362C22×C11#53511yescharacteristic
363C22×C11#53512yes—
364C22×C11#53611yescharacteristic
365C22×C11#53712yes—
366C22×C11#53812yes—
367C22×C11#53812yes—
368C22×C11#53912yes—
369C22×C11#54012yes—
370C22×C11#54012yes—
371C22×C11#54212yes—
372C22×C11#54212yes—
373C22×C11#54212yes—
374C4×C11—24no—
375C4×C11—42no—
376C4×C11—42no—
377C4×C11—82no—
378Dic11—24no—
379Dic11—24no—
380Dic11—42no—
381Dic11—44no—
382Dic11—42no—
383Dic11—82no—
384C25C22×D1112yes—
385C22×D4—22no—
386C22×D4—22no—
387C22×D4—42no—
388C22×D4—42no—
389C22×D4C4×D1114yes—
390C23×C4—111no—
391C23×C4—111no—
392C23×C4—112no—
393C23×C4—111no—
394C23×C4—111no—
395C23×C4—112no—
396C23×C4C22×D1112yes—
397C23×C4C22×D1111yescharacteristic
398C23×C4C22×D1111yescharacteristic
399C23×C4C22×D1111yescharacteristic
400C2×C4⋊C4—114no—
401C2×C4⋊C4—222no—
402C2×C4⋊C4—222no—
403C2×C4⋊C4—222no—
404C2×C4⋊C4—222no—
405C2×C4⋊C4—222no—
406C2×C4⋊C4—224no—
407C2×C4⋊C4—222no—
408C2×C4⋊C4—442no—
409C2×C4⋊C4—442no—
410C2×C4⋊C4—442no—
411C2×C22⋊C4—24no—
412C2×C22⋊C4—24no—
413C2×C22⋊C4—42no—
414C2×C22⋊C4—42no—
415C2×C22⋊C4—42no—
416C2×C22⋊C4—42no—
417C2×C22⋊C4—118no—
418C2×C22⋊C4—118no—
419C2×C22⋊C4—224no—
420C2×C22⋊C4—224no—
421C2×C22⋊C4—224no—
422C2×C22⋊C4—224no—
423C2×C22⋊C4—224no—
424C2×C22⋊C4—224no—
425C2×C22⋊C4—442no—
426C2×C22⋊C4—442no—
427C2×C22⋊C4—442no—
428C2×C22⋊C4—442no—
429C2×C42—114no—
430C2×C42—114no—
431C2×C42—222no—
432C2×C42—222no—
433C2×C42—222no—
434C2×C42—442no—
435C2×C42—442no—
436#95—22no—
437#95—22no—
438#95—114no—
439#95—222no—
440#95—224no—
441#95—224no—
442#95—442no—
443#95—442no—
444#95—442no—
445C2×C11—84no—
446C2×C11C4×#12111yescharacteristic
447C2×C11#232111yescharacteristic
448C2×C11#232412yes—
449C2×C11#232611yescharacteristic
450C2×C11#233512yes—
451C2×C11#261811yescharacteristic
452C2×C11#261911yescharacteristic
453C2×C11#263211yescharacteristic
454C2×C11#263511yescharacteristic
455C2×C11#265112yes—
456C2×C11#266212yes—
457C24—22no—
458C24—22no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24—22no—
465C24—22no—
466C24—22no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24—22no—
471C24C2×C4×D1114yes—
472C24C23×D1111yescharacteristic
473C2×D4—28no—
474C2×D4—48no—
475C2×D4—44no—
476C2×D4—44no—
477C2×D4—48no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—112no—
496C22×C4—112no—
497C22×C4—112no—
498C22×C4—112no—
499C22×C4—112no—
500C22×C4—112no—
501C22×C4—114no—
502C22×C4—112no—
503C22×C4—112no—
504C22×C4—221no—
505C22×C4—221no—
506C22×C4—221no—
507C22×C4—222no—
508C22×C4—221no—
509C22×C4—222no—
510C22×C4—221no—
511C22×C4—222no—
512C22×C4—221no—
513C22×C4—221no—
514C22×C4—222no—
515C22×C4—222no—
516C22×C4—222no—
517C22×C4—222no—
518C22×C4—222no—
519C22×C4—222no—
520C22×C4—222no—
521C22×C4—222no—
522C22×C4—221no—
523C22×C4—222no—
524C22×C4—222no—
525C22×C4—222no—
526C22×C4—222no—
527C22×C4—222no—
528C22×C4—222no—
529C22×C4—222no—
530C22×C4—222no—
531C22×C4C2×C4×D1112yes—
532C22×C4D4×D1112yes—
533C22×C4D4×D1112yes—
534C22×C4#434112yes—
535C22×C4#434112yes—
536C4⋊C4—228no—
537C4⋊C4—228no—
538C4⋊C4—448no—
539C4⋊C4—444no—
540C22⋊C4—48no—
541C22⋊C4—48no—
542C22⋊C4—2216no—
543C22⋊C4—448no—
544C22⋊C4—448no—
545C22⋊C4—448no—
546C42—228no—
547C42—444no—
548C42—444no—
549C11#1431211yescharacteristic, complemented, Sylow
550C23—24no—
551C23—24no—
552C23—24no—
553C23—24no—
554C23—24no—
555C23—24no—
556C23—24no—
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—
571C23—42no—
572C23—42no—
573C23—42no—
574C23—42no—
575C23—42no—
576C23—42no—
577C23—42no—
578C23—42no—
579C23—42no—
580C23—42no—
581C23—42no—
582C23—42no—
583C23—42no—
584C23—42no—
585C23C22×C4×D1111yescharacteristic
586C23C2×D4×D1111yescharacteristic
587C23C2×D4×D1111yescharacteristic
588C23C2×#434111yescharacteristic
589C23C2×#434111yescharacteristic
590C23#6703712yes—
591C23#6703712yes—
592C23#6703712yes—
593C23#41×D1111yescharacteristic
594C23#41×D1111yescharacteristic
595C23#6704312yes—
596D4—416no—
597C2×C4—24no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—24no—
601C2×C4—24no—
602C2×C4—24no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—42no—
610C2×C4—42no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—42no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4—114no—
619C2×C4—114no—
620C2×C4—222no—
621C2×C4—222no—
622C2×C4—222no—
623C2×C4—222no—
624C2×C4—222no—
625C2×C4—222no—
626C2×C4—224no—
627C2×C4—224no—
628C2×C4—222no—
629C2×C4—222no—
630C2×C4—222no—
631C2×C4—222no—
632C2×C4—224no—
633C2×C4—224no—
634C2×C4—224no—
635C2×C4—224no—
636C2×C4—222no—
637C2×C4—222no—
638C2×C4—441no—
639C2×C4—442no—
640C2×C4—441no—
641C2×C4—442no—
642C2×C4—442no—
643C2×C4—442no—
644C2×C4—442no—
645C2×C4—442no—
646C2×C4—442no—
647C2×C4—442no—
648C2×C4—442no—
649C2×C4—442no—
650C2×C4—442no—
651C2×C4—442no—
652C2×C4—442no—
653C2×C4—442no—
654C2×C4(C22⋊D11)⋊C414yes—
655C22—44no—
656C22—44no—
657C22—44no—
658C22—44no—
659C22—44no—
660C22—44no—
661C22—44no—
662C22—82no—
663C22—82no—
664C22—82no—
665C22—82no—
666C22—82no—
667C22—82no—
668C22—82no—
669C22—82no—
670C22C2×(C22⋊D11)⋊C411yescharacteristic
671C22#1062301712yes—
672C22C4×#434111yescharacteristic
673C22C4×D4×D1111yescharacteristic
674C22#1062307712yes—
675C22#1062312011yescharacteristic
676C22#1062312311yescharacteristic
677C22#1062312312yes—
678C22#1062312412yes—
679C22#1062312412yes—
680C22#1062313412yes—
681C22#1062313412yes—
682C22D11×#12111yescharacteristic
683C22#1062313711yescharacteristic
684C22#1062313912yes—
685C22#1062314612yes—
686C22#1062314612yes—
687C22#1062319112yes—
688C22#1062319312yes—
689C22#1062320611yescharacteristic
690C22#1062321111yescharacteristic
691C22#1062324611yescharacteristic
692C22#1062324711yescharacteristic
693C4—24no—
694C4—42no—
695C4—42no—
696C4—82no—
697C4—224no—
698C4—224no—
699C4—442no—
700C4—442no—
701C4—444no—
702C4—882no—
703C2—84no—
704C2#1307113211yescharacteristic
705C2#1307127111yescharacteristic
706C2#1307130612yes—
707C2#1307132611yescharacteristic
708C2#1307140712yes—
709C2#1307435711yescharacteristic
710C2#1307436511yescharacteristic
711C2#1307448111yescharacteristic
712C2#1307450511yescharacteristic
713C2#1307464612yes—
714C2#1307475812yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1438C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenter#1438D11
hypocenterC11#14312
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1438

Complements

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

NH ≅ G/Ntype
3. C2×#10622558C2semidirect
4. C2×#10622262C2semidirect
5. #13066880C2semidirect
6. #13066870C2semidirect
7. #13066859C2semidirect
8. #13066859C2semidirect
9. #13066853C2semidirect
10. #13066841C2semidirect
28. #10622835C4semidirect
90. C2×C4×Dic11D4semidirect
549. C11#14312semidirect

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×#106225582
C2×#106222622
#130668802
#130668702
#130668592
#130668532
#130668412
C11×#14382
#1431211