Finite Group Databasebeta

← #14660740

Subgroups — #14660740

Order 2816.

1022 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66899C211yesmaximal, characteristic
2C2×#10622843C211yesmaximal, characteristic
3C2×#10622590C211yesmaximal, characteristic
4C2×#10622189C211yesmaximal, characteristic
5C2×#10622167C211yesmaximal, characteristic
6C2×#10622188C211yesmaximal, characteristic
7C22×C11×#103C211yesmaximal, characteristic
8C23×Q8×C11C2211yescharacteristic
9C23×C8×C11C2211yescharacteristic
10C22×C11×C4⋊C4C2211yescharacteristic
11C22×C4⋊Dic11C2211yescharacteristic
12C22×C4⋊Dic11C2211yescharacteristic
13C22×C4×Dic11C2211yescharacteristic
14C23×C11⋊C8C2211yescharacteristic
15C2×C11×#103—22no—
16C2×C11×#103—22no—
17C2×C11×#103—22no—
18#10622843—22no—
19#10622843C414yescomplemented
20C2×#66899—22no—
21C2×#66899—22no—
22C2×#66899—22no—
23C2×C11⋊#95—22no—
24C2×C11⋊#95—22no—
25#10622590—22no—
26#10622590—22no—
27#10622189—22no—
28#10622188—22no—
29#10622167—22no—
30C22×Q8×C11—21no—
31C22×Q8×C11—21no—
32C22×Q8×C11—21no—
33C22×Q8×C11—21no—
34C22×Q8×C11—21no—
35C22×Q8×C11—21no—
36C22×Q8×C11—21no—
37C22×Q8×C11—21no—
38C22×Q8×C11—21no—
39C22×Q8×C11—21no—
40C22×Q8×C11—21no—
41C22×Q8×C11C2×C412yes—
42C22×Q8×C11D412yes—
43C22×Q8×C11Q812yes—
44C23×C4×C11—21no—
45C23×C4×C11—21no—
46C23×C4×C11C2311yescharacteristic
47C23×Dic11—21no—
48C23×Dic11—21no—
49C23×Dic11D412yes—
50C22×C8×C11—21no—
51C22×C8×C11—21no—
52C22×C8×C11—21no—
53C22×C8×C11—21no—
54C22×C8×C11—21no—
55C22×C8×C11—21no—
56C22×C8×C11D412yes—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4D412yes—
63C2×C4⋊Dic11—21no—
64C2×C4⋊Dic11—21no—
65C2×C4⋊Dic11—21no—
66C2×C4⋊Dic11—21no—
67C2×C4⋊Dic11—21no—
68C2×C4⋊Dic11—21no—
69C2×C4⋊Dic11—21no—
70C2×C4⋊Dic11—21no—
71C2×C4⋊Dic11—21no—
72C2×C4⋊Dic11—21no—
73C2×C4⋊Dic11C2×C412yes—
74C2×C4⋊Dic11D412yes—
75C2×C4×Dic11—21no—
76C2×C4×Dic11—21no—
77C2×C4×Dic11—21no—
78C2×C4×Dic11—21no—
79C2×C4×Dic11C2×C412yes—
80C2×C4×Dic11D412yes—
81C22×C11⋊C8—21no—
82C22×C11⋊C8—21no—
83C22×C11⋊C8—21no—
84C22×C11⋊C8—21no—
85C22×C11⋊C8—21no—
86C22×C11⋊C8—21no—
87C22×C11⋊C8D412yes—
88C11×#103—28no—
89#66899—28no—
90C11⋊#95—28no—
91C11⋊#95—28no—
92#11052—111nomaximal, Sylow
93C24×C11C2×D411yescharacteristic
94C2×Q8×C11—22no—
95C2×Q8×C11—22no—
96C2×Q8×C11—22no—
97C2×Q8×C11—22no—
98C2×Q8×C11—22no—
99C2×Q8×C11—22no—
100C2×Q8×C11—22no—
101C2×Q8×C11—22no—
102C2×Q8×C11—22no—
103C2×Q8×C11—22no—
104C2×Q8×C11—22no—
105C2×Q8×C11—22no—
106C2×Q8×C11—22no—
107C2×Q8×C11—22no—
108C2×Q8×C11—22no—
109C2×Q8×C11—41no—
110C2×Q8×C11—41no—
111C2×Q8×C11—41no—
112C2×Q8×C11—41no—
113C2×Q8×C11—41no—
114C2×Q8×C11—41no—
115C2×Q8×C11—41no—
116C2×Q8×C11—41no—
117C2×Q8×C11—41no—
118C2×Q8×C11—41no—
119C2×Q8×C11—41no—
120C2×Q8×C11—41no—
121C2×Q8×C11C4⋊C414yes—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—41no—
127C22×C4×C11—41no—
128C22×C4×C11—41no—
129C22×C4×C11—41no—
130C22×C4×C11—41no—
131C22×C4×C11—41no—
132C22×C4×C11—42no—
133C22×C4×C11—42no—
134C22×C4×C11C22×C411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×Q811yescharacteristic
142C22×C4×C11#4111yescharacteristic
143C22×C4×C11#4111yescharacteristic
144C22×C4×C11#4111yescharacteristic
145C22×C4×C11#4111yescharacteristic
146C22×C4×C11#4111yescharacteristic
147C22×C4×C11#4111yescharacteristic
148C22×Dic11—22no—
149C22×Dic11—22no—
150C22×Dic11—22no—
151C22×Dic11—22no—
152C22×Dic11—22no—
153C22×Dic11—22no—
154C22×Dic11—22no—
155C22×Dic11—22no—
156C22×Dic11—41no—
157C22×Dic11—41no—
158C22×Dic11—41no—
159C22×Dic11—41no—
160C22×Dic11—42no—
161C22×Dic11—42no—
162C22×Dic11—42no—
163C22×Dic11—42no—
164C22×Dic11C22⋊C414yes—
165C2×C8×C11—22no—
166C2×C8×C11—22no—
167C2×C8×C11—22no—
168C2×C8×C11—41no—
169C2×C8×C11—41no—
170C2×C8×C11—41no—
171C2×C8×C11—41no—
172C11×C4⋊C4—22no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—41no—
175C11×C4⋊C4—41no—
176C4⋊Dic11—22no—
177C4⋊Dic11—22no—
178C4⋊Dic11—22no—
179C4⋊Dic11—22no—
180C4⋊Dic11—41no—
181C4⋊Dic11—41no—
182C4⋊Dic11—41no—
183C4⋊Dic11—41no—
184C4×Dic11—22no—
185C4×Dic11—22no—
186C4×Dic11—22no—
187C4×Dic11—22no—
188C2×C11⋊C8—22no—
189C2×C11⋊C8—22no—
190C2×C11⋊C8—22no—
191C2×C11⋊C8—41no—
192C2×C11⋊C8—41no—
193C2×C11⋊C8—41no—
194C2×C11⋊C8—41no—
195C22×#103—111no—
196C22×#103D1111yescharacteristic
197C2×#391—111no—
198C2×#382—111no—
199C2×#340—111no—
200C2×#340—111no—
201C2×#336—111no—
202C23×C11C2×C22⋊C411yescharacteristic
203C23×C11#12011yescharacteristic
204C23×C11#12111yescharacteristic
205C23×C11C22⋊Q811yescharacteristic
206C23×C11#12311yescharacteristic
207C23×C11#12411yescharacteristic
208C23×C11#12711yescharacteristic
209C23×C11#13512yes—
210C23×C11#13512yes—
211C23×C11#13712yes—
212C23×C11#13712yes—
213Q8×C11—24no—
214Q8×C11—24no—
215Q8×C11—42no—
216Q8×C11—42no—
217Q8×C11—42no—
218Q8×C11—42no—
219Q8×C11—42no—
220Q8×C11—42no—
221C2×C4×C11—24no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11—42no—
228C2×C4×C11—42no—
229C2×C4×C11—44no—
230C2×C4×C11—82no—
231C2×C4×C11—81no—
232C2×C4×C11—81no—
233C2×C4×C11C2×C4⋊C411yescharacteristic
234C2×C4×C11#11711yescharacteristic
235C2×C4×C11C4×D411yescharacteristic
236C2×C4×C11C4×D411yescharacteristic
237C2×C4×C11C4×D411yescharacteristic
238C2×C4×C11C4×D411yescharacteristic
239C2×C4×C11#12011yescharacteristic
240C2×C4×C11#12011yescharacteristic
241C2×C4×C11#12111yescharacteristic
242C2×C4×C11#12111yescharacteristic
243C2×C4×C11#12111yescharacteristic
244C2×C4×C11#12111yescharacteristic
245C2×C4×C11#12111yescharacteristic
246C2×C4×C11#12111yescharacteristic
247C2×C4×C11#12111yescharacteristic
248C2×C4×C11C22⋊Q811yescharacteristic
249C2×C4×C11C22⋊Q811yescharacteristic
250C2×C4×C11C22⋊Q811yescharacteristic
251C2×C4×C11C22⋊Q811yescharacteristic
252C2×C4×C11C22⋊Q811yescharacteristic
253C2×C4×C11#12311yescharacteristic
254C2×C4×C11#12311yescharacteristic
255C2×C4×C11#12311yescharacteristic
256C2×C4×C11#12311yescharacteristic
257C2×C4×C11#12411yescharacteristic
258C2×C4×C11#12411yescharacteristic
259C2×C4×C11#12611yescharacteristic
260C2×C4×C11#12611yescharacteristic
261C2×Dic11—24no—
262C2×Dic11—24no—
263C2×Dic11—24no—
264C2×Dic11—42no—
265C2×Dic11—42no—
266C2×Dic11—42no—
267C2×Dic11—42no—
268C2×Dic11—42no—
269C2×Dic11—42no—
270C2×Dic11—44no—
271C2×Dic11—44no—
272C2×Dic11—82no—
273C2×Dic11—82no—
274C2×Dic11—81no—
275C2×Dic11—81no—
276C2×Dic11—81no—
277C2×Dic11—81no—
278C8×C11—42no—
279C11⋊C8—42no—
280C23×Q8C2×D1111yescharacteristic
281C23×C8—111no—
282C23×C8C2×D1111yescharacteristic
283C22×C4⋊C4—111no—
284C22×C4⋊C4—111no—
285C22×C4⋊C4C2×D1111yescharacteristic
286C22×C42—111no—
287C2×#103—22no—
288C2×#103—22no—
289C2×#103—22no—
290C2×#103—222no—
291C2×#103—222no—
292C2×#103—222no—
293#391—114no—
294#391—222no—
295#382—222no—
296#382—222no—
297C2×#95—222no—
298C2×#95—222no—
299#340—222no—
300#340—222no—
301#336—222no—
302C22×C11#38011yescharacteristic
303C22×C11#38611yescharacteristic
304C22×C11#39011yescharacteristic
305C22×C11#39211yescharacteristic
306C22×C11#39311yescharacteristic
307C22×C11#39711yescharacteristic
308C22×C11#39911yescharacteristic
309C22×C11#41612yes—
310C22×C11#41912yes—
311C22×C11#45212yes—
312C22×C11#45212yes—
313C22×C11#46412yes—
314C22×C11#46412yes—
315C22×C11#47912yes—
316C22×C11#47912yes—
317C22×C11#48512yes—
318C22×C11#48512yes—
319C22×C11#48812yes—
320C22×C11#49112yes—
321C22×C11#49511yescharacteristic
322C22×C11#49511yescharacteristic
323C22×C11#49711yescharacteristic
324C22×C11#49711yescharacteristic
325C4×C11—44no—
326C4×C11—82no—
327C4×C11#38511yescharacteristic
328C4×C11#38511yescharacteristic
329C4×C11#38811yescharacteristic
330C4×C11#38811yescharacteristic
331C4×C11#39411yescharacteristic
332C4×C11#39411yescharacteristic
333C4×C11#39611yescharacteristic
334C4×C11#39611yescharacteristic
335Dic11—44no—
336Dic11—82no—
337Dic11—82no—
338C22×Q8—21no—
339C22×Q8—21no—
340C22×Q8—21no—
341C22×Q8—21no—
342C22×Q8—21no—
343C22×Q8—21no—
344C22×Q8—21no—
345C22×Q8—21no—
346C22×Q8—21no—
347C22×Q8—21no—
348C22×Q8—21no—
349C22×Q8Dic2212yes—
350C22×Q8C4×D1112yes—
351C22×Q8C22⋊D1112yes—
352C23×C4—21no—
353C23×C4—21no—
354C23×C4—112no—
355C23×C4—221no—
356C23×C4—221no—
357C23×C4C22×D1111yescharacteristic
358C22×C8—21no—
359C22×C8—21no—
360C22×C8—21no—
361C22×C8—21no—
362C22×C8—21no—
363C22×C8—21no—
364C22×C8—112no—
365C22×C8—221no—
366C22×C8—221no—
367C22×C8—221no—
368C22×C8—221no—
369C22×C8—221no—
370C22×C8—221no—
371C22×C8C22⋊D1112yes—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—112no—
378C2×C4⋊C4—112no—
379C2×C4⋊C4—221no—
380C2×C4⋊C4—221no—
381C2×C4⋊C4—221no—
382C2×C4⋊C4—221no—
383C2×C4⋊C4—221no—
384C2×C4⋊C4—221no—
385C2×C4⋊C4—221no—
386C2×C4⋊C4—221no—
387C2×C4⋊C4—221no—
388C2×C4⋊C4—221no—
389C2×C4⋊C4C22⋊D1112yes—
390C2×C42—112no—
391C2×C42—112no—
392C2×C42—221no—
393C2×C42—221no—
394C2×C42—221no—
395C2×C42—221no—
396#103—28no—
397#103—228no—
398#95—228no—
399#95—228no—
400C2×C11#143911yescharacteristic
401C2×C11#180512yes—
402C2×C11#187312yes—
403C2×C11#195811yescharacteristic
404C2×C11#196011yescharacteristic
405C2×C11#201511yescharacteristic
406C2×C11#201511yescharacteristic
407C2×C11#202612yes—
408C2×C11#207412yes—
409C2×C11#209711yescharacteristic
410C2×C11#209711yescharacteristic
411C24D4×D1111yescharacteristic
412C2×Q8—22no—
413C2×Q8—22no—
414C2×Q8—22no—
415C2×Q8—22no—
416C2×Q8—22no—
417C2×Q8—22no—
418C2×Q8—22no—
419C2×Q8—22no—
420C2×Q8—22no—
421C2×Q8—22no—
422C2×Q8—22no—
423C2×Q8—22no—
424C2×Q8—22no—
425C2×Q8—22no—
426C2×Q8—22no—
427C2×Q8—41no—
428C2×Q8—41no—
429C2×Q8—41no—
430C2×Q8—41no—
431C2×Q8—41no—
432C2×Q8—41no—
433C2×Q8—41no—
434C2×Q8—41no—
435C2×Q8—41no—
436C2×Q8—41no—
437C2×Q8—41no—
438C2×Q8—41no—
439C2×Q8Dic11⋊C414yes—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—42no—
449C22×C4—42no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—114no—
453C22×C4—222no—
454C22×C4—222no—
455C22×C4—222no—
456C22×C4—222no—
457C22×C4—222no—
458C22×C4—222no—
459C22×C4—222no—
460C22×C4—222no—
461C22×C4—441no—
462C22×C4—442no—
463C22×C4—442no—
464C22×C4—442no—
465C22×C4—442no—
466C22×C4—441no—
467C22×C4—441no—
468C22×C4—441no—
469C22×C4C2×Dic2211yescharacteristic
470C22×C4C2×C4×D1111yescharacteristic
471C22×C4#433911yescharacteristic
472C22×C4#433911yescharacteristic
473C22×C4D4×D1111yescharacteristic
474C22×C4D4×D1111yescharacteristic
475C22×C4D4×D1111yescharacteristic
476C22×C4#434111yescharacteristic
477C22×C4#434111yescharacteristic
478C22×C4#434111yescharacteristic
479C22×C4#434111yescharacteristic
480C22×C4C2×C22⋊D1111yescharacteristic
481C22×C4C2×C22⋊D1111yescharacteristic
482C22×C4C2×C22⋊D1111yescharacteristic
483C2×C8—22no—
484C2×C8—22no—
485C2×C8—22no—
486C2×C8—41no—
487C2×C8—41no—
488C2×C8—41no—
489C2×C8—41no—
490C2×C8—222no—
491C2×C8—222no—
492C2×C8—222no—
493C2×C8—441no—
494C2×C8—441no—
495C2×C8—441no—
496C2×C8—441no—
497C4⋊C4—22no—
498C4⋊C4—22no—
499C4⋊C4—41no—
500C4⋊C4—41no—
501C4⋊C4—222no—
502C4⋊C4—222no—
503C4⋊C4—222no—
504C4⋊C4—222no—
505C4⋊C4—441no—
506C4⋊C4—441no—
507C4⋊C4—441no—
508C4⋊C4—441no—
509C42—222no—
510C42—222no—
511C42—222no—
512C42—222no—
513C11#1105211yescharacteristic, complemented, Sylow
514C23#6693111yescharacteristic
515C23C22⋊C4×D1111yescharacteristic
516C23#6693611yescharacteristic
517C23#6693811yescharacteristic
518C23#6696812yes—
519C23#6696912yes—
520C23#6697112yes—
521C23#6697212yes—
522C23#6699011yescharacteristic
523C23#6699211yescharacteristic
524C23#6699311yescharacteristic
525Q8—24no—
526Q8—24no—
527Q8—42no—
528Q8—42no—
529Q8—42no—
530Q8—42no—
531Q8—42no—
532Q8—42no—
533C2×C4—24no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—44no—
541C2×C4—42no—
542C2×C4—82no—
543C2×C4—81no—
544C2×C4—81no—
545C2×C4—224no—
546C2×C4—224no—
547C2×C4—224no—
548C2×C4—442no—
549C2×C4—442no—
550C2×C4—442no—
551C2×C4—442no—
552C2×C4—444no—
553C2×C4—442no—
554C2×C4—442no—
555C2×C4—444no—
556C2×C4—881no—
557C2×C4—882no—
558C2×C4—881no—
559C2×C4—881no—
560C2×C4—881no—
561C2×C4—882no—
562C2×C4#6693011yescharacteristic
563C2×C4#6693111yescharacteristic
564C2×C4#6693111yescharacteristic
565C2×C4#6693111yescharacteristic
566C2×C4#6693211yescharacteristic
567C2×C4#6693211yescharacteristic
568C2×C4(C22⋊D11)⋊C411yescharacteristic
569C2×C4(C22⋊D11)⋊C411yescharacteristic
570C2×C4#6693611yescharacteristic
571C2×C4#6693711yescharacteristic
572C2×C4#6693711yescharacteristic
573C2×C4#6693811yescharacteristic
574C2×C4C2×Dic11⋊C411yescharacteristic
575C2×C4#6697711yescharacteristic
576C2×C4#6697711yescharacteristic
577C2×C4C4×C22⋊D1111yescharacteristic
578C2×C4C4×C22⋊D1111yescharacteristic
579C2×C4#6698211yescharacteristic
580C2×C4#6698811yescharacteristic
581C2×C4#6698811yescharacteristic
582C2×C4#6698911yescharacteristic
583C2×C4#6699011yescharacteristic
584C2×C4#6699111yescharacteristic
585C2×C4#6699111yescharacteristic
586C2×C4#6699211yescharacteristic
587C2×C4#6699211yescharacteristic
588C2×C4#6699211yescharacteristic
589C2×C4#6700611yescharacteristic
590C8—42no—
591C8—442no—
592C22#1062240912yes—
593C22#1062241012yes—
594C22#1062241212yes—
595C22#1062241312yes—
596C22#1062241512yes—
597C22#1062241712yes—
598C22#1062242712yes—
599C22#1062242812yes—
600C22#1062255511yescharacteristic
601C22#1062256011yescharacteristic
602C22#1062256211yescharacteristic
603C22#1062256511yescharacteristic
604C22#1062256911yescharacteristic
605C22#1062257011yescharacteristic
606C22#1062277912yes—
607C22#1062278011yescharacteristic
608C22#1062278111yescharacteristic
609C22#1062278612yes—
610C22#1062279812yes—
611C22#1062280012yes—
612C22#1062280311yescharacteristic
613C22#1062280411yescharacteristic
614C22#1062283611yescharacteristic
615C4—44no—
616C4—82no—
617C4—444no—
618C4—882no—
619C4—882no—
620C4#1062255711yescharacteristic
621C4#1062255811yescharacteristic
622C4#1062255911yescharacteristic
623C4#1062256111yescharacteristic
624C4#1062256111yescharacteristic
625C4#1062257211yescharacteristic
626C4#1062282311yescharacteristic
627C4#1062283511yescharacteristic
628C2#1306685911yescharacteristic
629C2#1306862912yes—
630C2#1306892512yes—
631C2#1306942411yescharacteristic
632C2#1306943411yescharacteristic
633C2#1306970711yescharacteristic
634C2#1306970811yescharacteristic
635C2#1306976512yes—
636C2#1307003712yes—
637C2#1307016211yescharacteristic
638C2#1307016611yescharacteristic
subgroupG/H
centerC24D4×D11
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC22×C11×#103C2
socle, prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenterC22×#103D11
hypocenterC11#11052
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#103

Complements

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

NH ≅ G/Ntype
19. #10622843C4semidirect
513. C11#11052semidirect

Maximal subgroups

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

subgroupindex
C22×#668992
C2×#106228432
C2×#106225902
C2×#106221892
C2×#106221672
C2×#106221882
C22×C11×#1032
#1105211