Finite Group Databasebeta

← #14675745

Subgroups — #14675745

Order 2816.

2006 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622589C211yesmaximal, characteristic, complemented
2C2×#10622590C211yesmaximal, characteristic, complemented
3C2×#10622825C211yesmaximal, characteristic
4C2×C4×C22⋊Dic11C211yesmaximal, characteristic
5#13066859C214yesmaximal
6#13066849C214yesmaximal, complemented
7#13066845C211yesmaximal, characteristic, complemented
8#13066845C211yesmaximal, characteristic, complemented
9C22×C11×#117C211yesmaximal, characteristic
10C24×C4×C11C2211yescharacteristic
11C2×C11×#117—24no—
12C2×C11×#117—24no—
13C2×C11×#117—24no—
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C11×C22⋊C4C2212yes—
17C22×C42×C11C2212yes—
18C22×C22⋊Dic11C2212yes—
19C22×C22⋊Dic11C2212yes—
20C22×C4⋊Dic11C2211yescharacteristic
21C22×C4⋊Dic11C2211yescharacteristic
22C22×Dic11⋊C4C2214yes—
23C22×C4×Dic11C2211yescharacteristic
24C22×C4×Dic11C2211yescharacteristic
25#10622825—24no—
26C4×C22⋊Dic11C418yescomplemented
27C2×C11⋊#95C2214yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2214yes—
30C2×C11⋊#95C2214yes—
31C2×C11⋊#95C2212yes—
32#10622590—24no—
33#10622589—24no—
34C25×C11C2311yescharacteristic
35C23×C4×C11—22no—
36C23×C4×C11—22no—
37C23×C4×C11—22no—
38C23×C4×C11—22no—
39C23×C4×C11C2×C414yes—
40C23×C4×C11D414yes—
41C23×C4×C11Q814yes—
42C23×C4×C11C2312yes—
43C23×C4×C11C2312yes—
44C23×C4×C11C2311yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C23×Dic11C2312yes—
47C23×Dic11C2312yes—
48C23×Dic11C2312yes—
49C23×Dic11C2312yes—
50C11×#117—232no—
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4D414yes—
56C2×C11×C4⋊C4D414yes—
57C2×C11×C22⋊C4—24no—
58C2×C11×C22⋊C4—24no—
59C2×C11×C22⋊C4—24no—
60C2×C42×C11—24no—
61C2×C42×C11—24no—
62C2×C42×C11—24no—
63C2×C22⋊Dic11—24no—
64C2×C22⋊Dic11—24no—
65C2×C22⋊Dic11—24no—
66C2×C22⋊Dic11—44no—
67C2×C22⋊Dic11C2×C418yes—
68C2×C4⋊Dic11—22no—
69C2×C4⋊Dic11—22no—
70C2×C4⋊Dic11—22no—
71C2×C4⋊Dic11—22no—
72C2×C4⋊Dic11—22no—
73C2×C4⋊Dic11—22no—
74C2×Dic11⋊C4—28no—
75C2×Dic11⋊C4—28no—
76C2×Dic11⋊C4—44no—
77C2×C4×Dic11—22no—
78C2×C4×Dic11—22no—
79C2×C4×Dic11—22no—
80C2×C4×Dic11—22no—
81C2×C4×Dic11C2×C414yes—
82C2×C4×Dic11C2×C414yes—
83C11⋊#95—24no—
84C11⋊#95—28no—
85C11⋊#95—28no—
86C11⋊#95—44no—
87C11⋊#95C2×C418yes—
88#13879—111nomaximal, Sylow
89C24×C11—21no—
90C24×C11—21no—
91C24×C11—22no—
92C24×C11—22no—
93C24×C11—21no—
94C24×C11—21no—
95C24×C11—22no—
96C24×C11—22no—
97C24×C11C22×C412yes—
98C24×C11C2×D412yes—
99C24×C11C2×Q812yes—
100C24×C11C2411yescharacteristic
101C22×C4×C11—21no—
102C22×C4×C11—21no—
103C22×C4×C11—21no—
104C22×C4×C11—21no—
105C22×C4×C11—28no—
106C22×C4×C11—28no—
107C22×C4×C11—28no—
108C22×C4×C11—28no—
109C22×C4×C11—28no—
110C22×C4×C11—28no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—24no—
116C22×C4×C11—24no—
117C22×C4×C11—24no—
118C22×C4×C11—24no—
119C22×C4×C11C4⋊C4116yescomplemented
120C22×C4×C11C22×C412yes—
121C22×C4×C11C22×C412yes—
122C22×C4×C11C2×D414yes—
123C22×C4×C11C2×D414yes—
124C22×C4×C11C2×D412yes—
125C22×C4×C11C2×D412yes—
126C22×C4×C11C2×D412yes—
127C22×C4×C11C2×D412yes—
128C22×C4×C11C2×Q812yes—
129C22×C4×C11C2×Q812yes—
130C22×C4×C11#4112yes—
131C22×C4×C11#4112yes—
132C22×Dic11—22no—
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—24no—
143C22×Dic11—24no—
144C22×Dic11—22no—
145C22×Dic11—22no—
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11—24no—
149C22×Dic11—24no—
150C22×Dic11—22no—
151C22×Dic11—22no—
152C22×Dic11C22×C414yes—
153C22×Dic11C22×C414yes—
154C22×Dic11#4114yes—
155C22×Dic11#4114yes—
156C11×C4⋊C4—28no—
157C11×C4⋊C4—28no—
158C11×C22⋊C4—216no—
159C42×C11—216no—
160C22⋊Dic11—216no—
161C22⋊Dic11—48no—
162C4⋊Dic11—44no—
163C4⋊Dic11—44no—
164Dic11⋊C4—416no—
165C4×Dic11—28no—
166C4×Dic11—28no—
167C22×#117D1111yescharacteristic
168C2×#384—111no—
169C2×#382—111no—
170C2×#380—111no—
171C2×C4×C22⋊C4—111no—
172#1439—114no—
173#1436—114no—
174C4⋊#95—111no—
175C4⋊#95—111no—
176C23×C11—24no—
177C23×C11—22no—
178C23×C11—22no—
179C23×C11—24no—
180C23×C11—22no—
181C23×C11—22no—
182C23×C11—22no—
183C23×C11—22no—
184C23×C11—22no—
185C23×C11—22no—
186C23×C11—24no—
187C23×C11—22no—
188C23×C11—22no—
189C23×C11—24no—
190C23×C11—42no—
191C23×C11—42no—
192C23×C11—42no—
193C23×C11—42no—
194C23×C11—42no—
195C23×C11—42no—
196C23×C11—42no—
197C23×C11—42no—
198C23×C11C2×C4⋊C414yes—
199C23×C11C23×C411yescharacteristic
200C23×C11C22×D411yescharacteristic
201C23×C11C22×D411yescharacteristic
202C23×C11C22×D411yescharacteristic
203C23×C11C22×Q811yescharacteristic
204C23×C11C2×#4111yescharacteristic
205C23×C11C2×#4111yescharacteristic
206C23×C11C2×#4112yes—
207C23×C11C2×#4112yes—
208C23×C11H(5,𝔽2)12yes—
209C23×C112−1+412yes—
210C2×C4×C11—22no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—232no—
217C2×C4×C11—24no—
218C2×C4×C11—24no—
219C2×C4×C11—28no—
220C2×C4×C11—28no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11—44no—
226C2×C4×C11—44no—
227C2×C4×C11C2×C4⋊C414yes—
228C2×C4×C11C2×C4⋊C414yes—
229C2×C4×C11C4×D414yes—
230C2×C4×C11C4×D414yes—
231C2×C4×C11#12014yes—
232C2×C4×C11C22⋊Q814yes—
233C2×C4×C11C22⋊Q814yes—
234C2×C4×C11#12314yes—
235C2×Dic11—24no—
236C2×Dic11—24no—
237C2×Dic11—24no—
238C2×Dic11—24no—
239C2×Dic11—24no—
240C2×Dic11—24no—
241C2×Dic11—24no—
242C2×Dic11—24no—
243C2×Dic11—24no—
244C2×Dic11—42no—
245C2×Dic11—42no—
246C2×Dic11—42no—
247C2×Dic11—42no—
248C2×Dic11—42no—
249C2×Dic11—42no—
250C2×Dic11—42no—
251C2×Dic11—42no—
252C2×Dic11—42no—
253C2×Dic11—42no—
254C2×Dic11—44no—
255C2×Dic11—44no—
256C2×Dic11—44no—
257C2×Dic11—44no—
258C2×Dic11#11718yescomplemented
259C24×C4C2×D1111yescharacteristic
260C2×#117—24no—
261C2×#117—24no—
262C2×#117—24no—
263C22×C4⋊C4—111no—
264C22×C4⋊C4—111no—
265C22×C4⋊C4—114no—
266C22×C4⋊C4C2×D1111yescharacteristic
267C22×C4⋊C4C2×D1111yescharacteristic
268C22×C22⋊C4—112no—
269C22×C22⋊C4—112no—
270C22×C22⋊C4C2×D1112yes—
271C22×C42—111no—
272C22×C42—111no—
273C22×C42C2×D1112yes—
274#384—224no—
275#382—224no—
276#380—224no—
277C4×C22⋊C4—118no—
278C2×#95—112no—
279C2×#95—114no—
280C2×#95—112no—
281C2×#95—114no—
282C2×#95—114no—
283C22×C11—24no—
284C22×C11—24no—
285C22×C11—24no—
286C22×C11—44no—
287C22×C11—44no—
288C22×C11—42no—
289C22×C11—42no—
290C22×C11—44no—
291C22×C11—44no—
292C22×C11—42no—
293C22×C11—42no—
294C22×C11C22×C4⋊C411yescharacteristic
295C22×C11C2×#11712yes—
296C22×C11C2×C4×D411yescharacteristic
297C22×C11C2×C4×D411yescharacteristic
298C22×C11#52012yes—
299C22×C11C2×#12011yescharacteristic
300C22×C11C2×C22⋊Q811yescharacteristic
301C22×C11C2×C22⋊Q811yescharacteristic
302C22×C11C2×#12311yescharacteristic
303C22×C11#53211yescharacteristic
304C22×C11#53211yescharacteristic
305C22×C11#53312yes—
306C22×C11#53511yescharacteristic
307C22×C11#53611yescharacteristic
308C22×C11#54412yes—
309C22×C11#54612yes—
310C22×C11#54712yes—
311C22×C11#54812yes—
312C22×C11#55012yes—
313C22×C11#55212yes—
314C22×C11#55312yes—
315C22×C11#55512yes—
316C22×C11#55612yes—
317C4×C11—24no—
318C4×C11—44no—
319C4×C11—44no—
320C4×C11#38518yes—
321Dic11—28no—
322Dic11—44no—
323Dic11—82no—
324Dic11—82no—
325C25C22×D1111yescharacteristic
326C23×C4—22no—
327C23×C4—22no—
328C23×C4—22no—
329C23×C4—22no—
330C23×C4—112no—
331C23×C4—112no—
332C23×C4—112no—
333C23×C4—112no—
334C23×C4Dic2214yes—
335C23×C4C4×D1114yes—
336C23×C4C22⋊D1114yes—
337C23×C4C22×D1112yes—
338C23×C4C22×D1112yes—
339C23×C4C22×D1111yescharacteristic
340C23×C4C22×D1111yescharacteristic
341#117—232no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—228no—
347C2×C4⋊C4—222no—
348C2×C4⋊C4—222no—
349C2×C4⋊C4—222no—
350C2×C4⋊C4—222no—
351C2×C4⋊C4—222no—
352C2×C4⋊C4—228no—
353C2×C4⋊C4—222no—
354C2×C4⋊C4—444no—
355C2×C4⋊C4C22⋊D1114yes—
356C2×C4⋊C4C22⋊D1114yes—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—118no—
361C2×C22⋊C4—224no—
362C2×C22⋊C4—224no—
363C2×C22⋊C4—224no—
364C2×C22⋊C4—444no—
365C2×C42—24no—
366C2×C42—24no—
367C2×C42—24no—
368C2×C42—114no—
369C2×C42—114no—
370C2×C42—222no—
371C2×C42—222no—
372C2×C42—222no—
373C2×C42—222no—
374#95—118no—
375#95—228no—
376#95—224no—
377#95—228no—
378#95—444no—
379C2×C11—44no—
380C2×C11#228511yescharacteristic
381C2×C11C2×#38511yescharacteristic
382C2×C11#231711yescharacteristic
383C2×C11#235212yes—
384C2×C11#235412yes—
385C2×C11#243111yescharacteristic
386C2×C11#243211yescharacteristic
387C2×C11#243912yes—
388C2×C11#244112yes—
389C2×C11#249911yescharacteristic
390C2×C11#250011yescharacteristic
391C24—21no—
392C24—21no—
393C24—22no—
394C24—22no—
395C24—22no—
396C24—22no—
397C24—21no—
398C24—21no—
399C24C2×Dic2212yes—
400C24C2×C4×D1112yes—
401C24C2×C22⋊D1112yes—
402C24C23×D1111yescharacteristic
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—28no—
408C22×C4—28no—
409C22×C4—28no—
410C22×C4—28no—
411C22×C4—28no—
412C22×C4—28no—
413C22×C4—24no—
414C22×C4—24no—
415C22×C4—24no—
416C22×C4—24no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—114no—
422C22×C4—114no—
423C22×C4—114no—
424C22×C4—114no—
425C22×C4—222no—
426C22×C4—222no—
427C22×C4—222no—
428C22×C4—222no—
429C22×C4—222no—
430C22×C4—222no—
431C22×C4—222no—
432C22×C4—222no—
433C22×C4—222no—
434C22×C4—222no—
435C22×C4—222no—
436C22×C4—222no—
437C22×C4—224no—
438C22×C4—224no—
439C22×C4—224no—
440C22×C4—224no—
441C22×C4—222no—
442C22×C4—222no—
443C22×C4—222no—
444C22×C4—222no—
445C22×C4Dic11⋊C4116yescomplemented
446C22×C4C2×Dic2212yes—
447C22×C4C2×Dic2212yes—
448C22×C4C2×C4×D1112yes—
449C22×C4C2×C4×D1112yes—
450C22×C4#433912yes—
451C22×C4#433912yes—
452C22×C4C2×C22⋊D1114yes—
453C22×C4C2×C22⋊D1114yes—
454C22×C4C2×C22⋊D1112yes—
455C22×C4C2×C22⋊D1112yes—
456C22×C4C2×C22⋊D1112yes—
457C22×C4C2×C22⋊D1112yes—
458C4⋊C4—28no—
459C4⋊C4—28no—
460C4⋊C4—4416no—
461C4⋊C4—444no—
462C4⋊C4—444no—
463C22⋊C4—216no—
464C22⋊C4—2216no—
465C22⋊C4—448no—
466C42—216no—
467C42—228no—
468C42—228no—
469C11#1387911yescharacteristic, complemented, Sylow
470C23—24no—
471C23—24no—
472C23—24no—
473C23—24no—
474C23—22no—
475C23—22no—
476C23—22no—
477C23—22no—
478C23—22no—
479C23—22no—
480C23—22no—
481C23—22no—
482C23—22no—
483C23—22no—
484C23—42no—
485C23—42no—
486C23—42no—
487C23—42no—
488C23—42no—
489C23—42no—
490C23—42no—
491C23—42no—
492C23C2×Dic11⋊C414yes—
493C23C22×Dic2211yescharacteristic
494C23C22×C4×D1111yescharacteristic
495C23C2×#433911yescharacteristic
496C23C2×#433911yescharacteristic
497C23#41×D1112yes—
498C23#41×D1112yes—
499C23#6704212yes—
500C23#6704312yes—
501C23C22×C22⋊D1111yescharacteristic
502C23C22×C22⋊D1111yescharacteristic
503C23C22×C22⋊D1111yescharacteristic
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—232no—
511C2×C4—28no—
512C2×C4—28no—
513C2×C4—24no—
514C2×C4—24no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—44no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—44no—
521C2×C4—118no—
522C2×C4—224no—
523C2×C4—224no—
524C2×C4—224no—
525C2×C4—224no—
526C2×C4—224no—
527C2×C4—224no—
528C2×C4—224no—
529C2×C4—224no—
530C2×C4—224no—
531C2×C4—442no—
532C2×C4—442no—
533C2×C4—442no—
534C2×C4—442no—
535C2×C4—444no—
536C2×C4—444no—
537C2×C4—442no—
538C2×C4—444no—
539C2×C4—442no—
540C2×C4—442no—
541C2×C4—442no—
542C2×C4—442no—
543C2×C4—444no—
544C2×C4—442no—
545C2×C4C2×Dic11⋊C414yes—
546C2×C4C2×Dic11⋊C414yes—
547C2×C4#6697714yes—
548C2×C4#6697714yes—
549C2×C4C4×C22⋊D1114yes—
550C2×C4C4×C22⋊D1114yes—
551C2×C4#6698214yes—
552C2×C4#6700614yes—
553C22—24no—
554C22—24no—
555C22—24no—
556C22—42no—
557C22—42no—
558C22—42no—
559C22—44no—
560C22—42no—
561C22—44no—
562C22—44no—
563C22—44no—
564C22#1062304812yes—
565C22#1062305012yes—
566C22D11×#11712yes—
567C22#1062305412yes—
568C22#1062306012yes—
569C22#1062306112yes—
570C22#1062306312yes—
571C22#1062306412yes—
572C22C22×Dic11⋊C411yescharacteristic
573C22C2×#6697711yescharacteristic
574C22C2×#6697711yescharacteristic
575C22C2×C4×C22⋊D1111yescharacteristic
576C22C2×C4×C22⋊D1111yescharacteristic
577C22C2×#6698211yescharacteristic
578C22#1062335512yes—
579C22#1062335611yescharacteristic
580C22#1062336012yes—
581C22#1062336111yescharacteristic
582C22#1062336212yes—
583C22#1062336311yescharacteristic
584C22#1062336311yescharacteristic
585C22#1062336512yes—
586C22C2×#6700611yescharacteristic
587C4—24no—
588C4—44no—
589C4—44no—
590C4—228no—
591C4—444no—
592C4—882no—
593C4—882no—
594C4#1062282318yes—
595C2—44no—
596C2#1307101911yescharacteristic
597C2C2×#1062282311yescharacteristic
598C2#1307123611yescharacteristic
599C2#1307154612yes—
600C2#1307156612yes—
601C2#1307223111yescharacteristic
602C2#1307224011yescharacteristic
603C2#1307230112yes—
604C2#1307232312yes—
605C2#1307306511yescharacteristic
606C2#1307307411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC22×C11×#117C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC22×#117D11
hypocenterC11#13879
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#117

Complements

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

NH ≅ G/Ntype
1. C2×#10622589C2semidirect
2. C2×#10622590C2semidirect
6. #13066849C2semidirect
7. #13066845C2semidirect
8. #13066845C2semidirect
26. C4×C22⋊Dic11C4semidirect
119. C22×C4×C11C4⋊C4semidirect
258. C2×Dic11#117semidirect
445. C22×C4Dic11⋊C4semidirect
469. C11#13879semidirect

Maximal subgroups

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

subgroupindex
C2×#106225892
C2×#106225902
C2×#106228252
C2×C4×C22⋊Dic112
#130668592
#130668492
#130668452
C22×C11×#1172
#1387911