Finite Group Databasebeta

← #14660730

Subgroups — #14660730

Order 2816.

1110 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66899C211yesmaximal, characteristic
2C2×#10622843C211yesmaximal, characteristic
3C2×#10622589C211yesmaximal, 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×Dic11⋊C4—22no—
14C22×C4×Dic11C2211yescharacteristic
15C23×C11⋊C8C2211yescharacteristic
16C2×C11×#103—22no—
17C2×C11×#103—22no—
18C2×C11×#103—22no—
19#10622843—22no—
20#10622843C414yescomplemented
21C2×#66899—22no—
22C2×#66899—22no—
23C2×#66899—22no—
24C2×C11⋊#95—22no—
25#10622589—22no—
26#10622589—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×Dic11⋊C4—28no—
76C2×Dic11⋊C4—44no—
77C2×Dic11⋊C4—44no—
78C2×C4×Dic11—21no—
79C2×C4×Dic11—21no—
80C2×C4×Dic11—21no—
81C2×C4×Dic11—21no—
82C2×C4×Dic11C2×C412yes—
83C2×C4×Dic11D412yes—
84C22×C11⋊C8—21no—
85C22×C11⋊C8—21no—
86C22×C11⋊C8—21no—
87C22×C11⋊C8—21no—
88C22×C11⋊C8—21no—
89C22×C11⋊C8—21no—
90C22×C11⋊C8D412yes—
91C11×#103—28no—
92#66899—28no—
93C11⋊#95—28no—
94#11050—111nomaximal, Sylow
95C24×C11C2×D411yescharacteristic
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—22no—
110C2×Q8×C11—22no—
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×C11—41no—
122C2×Q8×C11—41no—
123C2×Q8×C11C4⋊C414yescomplemented
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—41no—
129C22×C4×C11—41no—
130C22×C4×C11—41no—
131C22×C4×C11—41no—
132C22×C4×C11—41no—
133C22×C4×C11—41no—
134C22×C4×C11—42no—
135C22×C4×C11—42no—
136C22×C4×C11C22×C411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×Q811yescharacteristic
144C22×C4×C11#4111yescharacteristic
145C22×C4×C11#4111yescharacteristic
146C22×C4×C11#4111yescharacteristic
147C22×C4×C11#4111yescharacteristic
148C22×C4×C11#4111yescharacteristic
149C22×C4×C11#4111yescharacteristic
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—
165C22×Dic11SD1614yes—
166C22×Dic11Q1614yes—
167C2×C8×C11—22no—
168C2×C8×C11—22no—
169C2×C8×C11—22no—
170C2×C8×C11—41no—
171C2×C8×C11—41no—
172C2×C8×C11—41no—
173C2×C8×C11—41no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—41no—
177C11×C4⋊C4—41no—
178C4⋊Dic11—22no—
179C4⋊Dic11—22no—
180C4⋊Dic11—22no—
181C4⋊Dic11—22no—
182C4⋊Dic11—41no—
183C4⋊Dic11—41no—
184C4⋊Dic11—41no—
185C4⋊Dic11—41no—
186Dic11⋊C4—416no—
187C4×Dic11—22no—
188C4×Dic11—22no—
189C4×Dic11—22no—
190C4×Dic11—22no—
191C2×C11⋊C8—22no—
192C2×C11⋊C8—22no—
193C2×C11⋊C8—22no—
194C2×C11⋊C8—41no—
195C2×C11⋊C8—41no—
196C2×C11⋊C8—41no—
197C2×C11⋊C8—41no—
198C22×#103—111no—
199C22×#103D1111yescharacteristic
200C2×#391—111no—
201C2×#384—111no—
202C2×#340—111no—
203C2×#340—111no—
204C2×#336—111no—
205C23×C11C2×C22⋊C411yescharacteristic
206C23×C11#12011yescharacteristic
207C23×C11#12111yescharacteristic
208C23×C11C22⋊Q811yescharacteristic
209C23×C11#12311yescharacteristic
210C23×C11#12411yescharacteristic
211C23×C11#12711yescharacteristic
212C23×C11C2×SD1612yes—
213C23×C11C2×Q1612yes—
214C23×C11AGL(1,ℤ/8)12yes—
215C23×C11#13712yes—
216Q8×C11—24no—
217Q8×C11—24no—
218Q8×C11—42no—
219Q8×C11—42no—
220Q8×C11—42no—
221Q8×C11—42no—
222Q8×C11—42no—
223Q8×C11—42no—
224C2×C4×C11—24no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11—42no—
228C2×C4×C11—42no—
229C2×C4×C11—42no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11—44no—
233C2×C4×C11—82no—
234C2×C4×C11—81no—
235C2×C4×C11—81no—
236C2×C4×C11C2×C4⋊C411yescharacteristic
237C2×C4×C11#11711yescharacteristic
238C2×C4×C11C4×D411yescharacteristic
239C2×C4×C11C4×D411yescharacteristic
240C2×C4×C11C4×D411yescharacteristic
241C2×C4×C11C4×D411yescharacteristic
242C2×C4×C11#12011yescharacteristic
243C2×C4×C11#12011yescharacteristic
244C2×C4×C11#12111yescharacteristic
245C2×C4×C11#12111yescharacteristic
246C2×C4×C11#12111yescharacteristic
247C2×C4×C11#12111yescharacteristic
248C2×C4×C11#12111yescharacteristic
249C2×C4×C11#12111yescharacteristic
250C2×C4×C11#12111yescharacteristic
251C2×C4×C11C22⋊Q811yescharacteristic
252C2×C4×C11C22⋊Q811yescharacteristic
253C2×C4×C11C22⋊Q811yescharacteristic
254C2×C4×C11C22⋊Q811yescharacteristic
255C2×C4×C11C22⋊Q811yescharacteristic
256C2×C4×C11#12311yescharacteristic
257C2×C4×C11#12311yescharacteristic
258C2×C4×C11#12311yescharacteristic
259C2×C4×C11#12311yescharacteristic
260C2×C4×C11#12411yescharacteristic
261C2×C4×C11#12411yescharacteristic
262C2×C4×C11#12611yescharacteristic
263C2×C4×C11#12611yescharacteristic
264C2×Dic11—24no—
265C2×Dic11—24no—
266C2×Dic11—24no—
267C2×Dic11—24no—
268C2×Dic11—24no—
269C2×Dic11—24no—
270C2×Dic11—42no—
271C2×Dic11—42no—
272C2×Dic11—44no—
273C2×Dic11—44no—
274C2×Dic11—82no—
275C2×Dic11—82no—
276C2×Dic11—81no—
277C2×Dic11—81no—
278C2×Dic11—81no—
279C2×Dic11—81no—
280C2×Dic11#10318yescomplemented
281C8×C11—42no—
282C11⋊C8—42no—
283C23×Q8C2×D1111yescharacteristic
284C23×C8—111no—
285C23×C8C2×D1111yescharacteristic
286C22×C4⋊C4—111no—
287C22×C4⋊C4—111no—
288C22×C4⋊C4—222no—
289C22×C4⋊C4C2×D1111yescharacteristic
290C22×C42—111no—
291C2×#103—22no—
292C2×#103—22no—
293C2×#103—22no—
294C2×#103—222no—
295C2×#103—222no—
296C2×#103—222no—
297#391—114no—
298#391—222no—
299#384—222no—
300#384—222no—
301C2×#95—222no—
302#340—222no—
303#340—222no—
304#336—222no—
305C22×C11#38011yescharacteristic
306C22×C11#38611yescharacteristic
307C22×C11#39011yescharacteristic
308C22×C11#39211yescharacteristic
309C22×C11#39311yescharacteristic
310C22×C11#39711yescharacteristic
311C22×C11#39911yescharacteristic
312C22×C11C2×#10312yes—
313C22×C11#41712yes—
314C22×C11#45012yes—
315C22×C11#45112yes—
316C22×C11#46012yes—
317C22×C11#46212yes—
318C22×C11#47512yes—
319C22×C11#47712yes—
320C22×C11#48312yes—
321C22×C11#48412yes—
322C22×C11#48712yes—
323C22×C11#48912yes—
324C22×C11#49211yescharacteristic
325C22×C11#49411yescharacteristic
326C22×C11#49611yescharacteristic
327C22×C11#49711yescharacteristic
328C4×C11—44no—
329C4×C11—82no—
330C4×C11#38511yescharacteristic
331C4×C11#38511yescharacteristic
332C4×C11#38811yescharacteristic
333C4×C11#38811yescharacteristic
334C4×C11#39411yescharacteristic
335C4×C11#39411yescharacteristic
336C4×C11#39611yescharacteristic
337C4×C11#39611yescharacteristic
338Dic11—28no—
339Dic11—82no—
340Dic11—82no—
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×Q8—21no—
350C22×Q8—21no—
351C22×Q8—21no—
352C22×Q8Dic2212yes—
353C22×Q8C4×D1112yes—
354C22×Q8C22⋊D1112yes—
355C23×C4—21no—
356C23×C4—21no—
357C23×C4—112no—
358C23×C4—221no—
359C23×C4—221no—
360C23×C4C22×D1111yescharacteristic
361C22×C8—21no—
362C22×C8—21no—
363C22×C8—21no—
364C22×C8—21no—
365C22×C8—21no—
366C22×C8—21no—
367C22×C8—112no—
368C22×C8—221no—
369C22×C8—221no—
370C22×C8—221no—
371C22×C8—221no—
372C22×C8—221no—
373C22×C8—221no—
374C22×C8C22⋊D1112yes—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—112no—
381C2×C4⋊C4—112no—
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⋊C4—221no—
390C2×C4⋊C4—228no—
391C2×C4⋊C4—221no—
392C2×C4⋊C4—221no—
393C2×C4⋊C4—444no—
394C2×C4⋊C4—444no—
395C2×C4⋊C4C22⋊D1112yes—
396C2×C42—112no—
397C2×C42—112no—
398C2×C42—221no—
399C2×C42—221no—
400C2×C42—221no—
401C2×C42—221no—
402#103—28no—
403#103—228no—
404#95—228no—
405C2×C11#143911yescharacteristic
406C2×C11#180312yes—
407C2×C11#187212yes—
408C2×C11#195611yescharacteristic
409C2×C11#195911yescharacteristic
410C2×C11#201411yescharacteristic
411C2×C11#201611yescharacteristic
412C2×C11#202412yes—
413C2×C11#207212yes—
414C2×C11#209511yescharacteristic
415C2×C11#209611yescharacteristic
416C24D4×D1111yescharacteristic
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—22no—
428C2×Q8—22no—
429C2×Q8—22no—
430C2×Q8—22no—
431C2×Q8—22no—
432C2×Q8—41no—
433C2×Q8—41no—
434C2×Q8—41no—
435C2×Q8—41no—
436C2×Q8—41no—
437C2×Q8—41no—
438C2×Q8—41no—
439C2×Q8—41no—
440C2×Q8—41no—
441C2×Q8—41no—
442C2×Q8—41no—
443C2×Q8—41no—
444C2×Q8Dic11⋊C414yescomplemented
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4—42no—
454C22×C4—42no—
455C22×C4—41no—
456C22×C4—41no—
457C22×C4—114no—
458C22×C4—114no—
459C22×C4—114no—
460C22×C4—222no—
461C22×C4—222no—
462C22×C4—222no—
463C22×C4—222no—
464C22×C4—222no—
465C22×C4—222no—
466C22×C4—441no—
467C22×C4—442no—
468C22×C4—442no—
469C22×C4—442no—
470C22×C4—442no—
471C22×C4—441no—
472C22×C4—441no—
473C22×C4—441no—
474C22×C4C2×Dic2211yescharacteristic
475C22×C4C2×C4×D1111yescharacteristic
476C22×C4#433911yescharacteristic
477C22×C4#433911yescharacteristic
478C22×C4D4×D1111yescharacteristic
479C22×C4D4×D1111yescharacteristic
480C22×C4D4×D1111yescharacteristic
481C22×C4#434111yescharacteristic
482C22×C4#434111yescharacteristic
483C22×C4#434111yescharacteristic
484C22×C4#434111yescharacteristic
485C22×C4C2×C22⋊D1111yescharacteristic
486C22×C4C2×C22⋊D1111yescharacteristic
487C22×C4C2×C22⋊D1111yescharacteristic
488C2×C8—22no—
489C2×C8—22no—
490C2×C8—22no—
491C2×C8—41no—
492C2×C8—41no—
493C2×C8—41no—
494C2×C8—41no—
495C2×C8—222no—
496C2×C8—222no—
497C2×C8—222no—
498C2×C8—441no—
499C2×C8—441no—
500C2×C8—441no—
501C2×C8—441no—
502C4⋊C4—22no—
503C4⋊C4—22no—
504C4⋊C4—41no—
505C4⋊C4—41no—
506C4⋊C4—222no—
507C4⋊C4—222no—
508C4⋊C4—222no—
509C4⋊C4—222no—
510C4⋊C4—4416no—
511C4⋊C4—441no—
512C4⋊C4—441no—
513C4⋊C4—441no—
514C4⋊C4—441no—
515C42—222no—
516C42—222no—
517C42—222no—
518C42—222no—
519C11#1105011yescharacteristic, complemented, Sylow
520C23#6693111yescharacteristic
521C23C22⋊C4×D1111yescharacteristic
522C23#6693611yescharacteristic
523C23#6693811yescharacteristic
524C23SD16×D1112yes—
525C23#6696712yes—
526C23Q16×D1112yes—
527C23#6697112yes—
528C23#6699011yescharacteristic
529C23#6699211yescharacteristic
530C23#6699311yescharacteristic
531Q8—24no—
532Q8—24no—
533Q8—42no—
534Q8—42no—
535Q8—42no—
536Q8—42no—
537Q8—42no—
538Q8—42no—
539C2×C4—24no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—44no—
547C2×C4—42no—
548C2×C4—82no—
549C2×C4—81no—
550C2×C4—81no—
551C2×C4—118no—
552C2×C4—224no—
553C2×C4—224no—
554C2×C4—224no—
555C2×C4—224no—
556C2×C4—224no—
557C2×C4—224no—
558C2×C4—444no—
559C2×C4—442no—
560C2×C4—442no—
561C2×C4—444no—
562C2×C4—882no—
563C2×C4—881no—
564C2×C4—881no—
565C2×C4—881no—
566C2×C4—881no—
567C2×C4—882no—
568C2×C4#6693011yescharacteristic
569C2×C4#6693111yescharacteristic
570C2×C4#6693111yescharacteristic
571C2×C4#6693111yescharacteristic
572C2×C4#6693211yescharacteristic
573C2×C4#6693211yescharacteristic
574C2×C4(C22⋊D11)⋊C411yescharacteristic
575C2×C4(C22⋊D11)⋊C411yescharacteristic
576C2×C4#6693611yescharacteristic
577C2×C4#6693711yescharacteristic
578C2×C4#6693711yescharacteristic
579C2×C4#6693811yescharacteristic
580C2×C4C2×Dic11⋊C411yescharacteristic
581C2×C4#6697711yescharacteristic
582C2×C4#6697711yescharacteristic
583C2×C4C4×C22⋊D1111yescharacteristic
584C2×C4C4×C22⋊D1111yescharacteristic
585C2×C4#6698211yescharacteristic
586C2×C4#6698811yescharacteristic
587C2×C4#6698811yescharacteristic
588C2×C4#6698911yescharacteristic
589C2×C4#6699011yescharacteristic
590C2×C4#6699111yescharacteristic
591C2×C4#6699111yescharacteristic
592C2×C4#6699211yescharacteristic
593C2×C4#6699211yescharacteristic
594C2×C4#6699211yescharacteristic
595C2×C4#6700611yescharacteristic
596C8—42no—
597C8—442no—
598C22#1062240412yes—
599C22#1062240512yes—
600C22#1062240712yes—
601C22#1062240812yes—
602C22D11×#10312yes—
603C22#1062241612yes—
604C22#1062241812yes—
605C22#1062242212yes—
606C22#1062255511yescharacteristic
607C22#1062256011yescharacteristic
608C22#1062256211yescharacteristic
609C22#1062256511yescharacteristic
610C22#1062256911yescharacteristic
611C22#1062257011yescharacteristic
612C22#1062277612yes—
613C22#1062278212yes—
614C22#1062278811yescharacteristic
615C22#1062278911yescharacteristic
616C22#1062279411yescharacteristic
617C22#1062279512yes—
618C22#1062279912yes—
619C22#1062280311yescharacteristic
620C22#1062283611yescharacteristic
621C4—44no—
622C4—82no—
623C4—228no—
624C4—882no—
625C4—882no—
626C4#1062255711yescharacteristic
627C4#1062255811yescharacteristic
628C4#1062255911yescharacteristic
629C4#1062256111yescharacteristic
630C4#1062256111yescharacteristic
631C4#1062257211yescharacteristic
632C4#1062282311yescharacteristic
633C4#1062283511yescharacteristic
634C2#1306685911yescharacteristic
635C2#1306861912yes—
636C2#1306892012yes—
637C2#1306941611yescharacteristic
638C2#1306942911yescharacteristic
639C2#1306970211yescharacteristic
640C2#1306971411yescharacteristic
641C2#1306975512yes—
642C2#1307002712yes—
643C2#1307015211yescharacteristic
644C2#1307015711yescharacteristic
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#11050
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
20. #10622843C4semidirect
123. C2×Q8×C11C4⋊C4semidirect
280. C2×Dic11#103semidirect
444. C2×Q8Dic11⋊C4semidirect
519. C11#11050semidirect

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×#106225892
C2×#106221892
C2×#106221672
C2×#106221882
C22×C11×#1032
#1105011