Finite Group Databasebeta

← #14660228

Subgroups — #14660228

Order 2816.

1230 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622828C211yesmaximal, characteristic
2C2×#10622834C211yesmaximal, characteristic
3#13070972C211yesmaximal, characteristic, complemented
4C2×#10622192C211yesmaximal, characteristic, complemented
5C2×#10622193C211yesmaximal, characteristic, complemented
6C2×#10622170C211yesmaximal, characteristic, complemented
7C2×C11×#418C211yesmaximal, characteristic
8C23×D4×C11C2211yescharacteristic
9C22×C11×M16C2211yescharacteristic
10C2×C11×#117C2211yescharacteristic
11C22×C22⋊Dic11—22no—
12C2×#66979C2211yescharacteristic
13C22×C4⋊Dic11C2211yescharacteristic
14C22×C4×Dic11C2211yescharacteristic
15C22×#4318C2211yescharacteristic
16C11×#418—22no—
17C11×#418C414yescomplemented
18C2×C11×#102—22no—
19#10622834—22no—
20#10622834C414yescomplemented
21#10622828—22no—
22#10622828C414yescomplemented
23C2×#66896—22no—
24C4⋊C4×Dic11—22no—
25C22⋊C4×Dic11—22no—
26C4×C4⋊Dic11—22no—
27#10622193—22no—
28#10622192—22no—
29#10622170—22no—
30C25×C11—21no—
31C22×D4×C11—21no—
32C22×D4×C11—21no—
33C22×D4×C11—21no—
34C22×D4×C11—21no—
35C22×D4×C11—21no—
36C22×D4×C11—21no—
37C22×D4×C11—21no—
38C22×D4×C11—21no—
39C22×D4×C11—21no—
40C22×D4×C11—21no—
41C22×D4×C11—21no—
42C22×D4×C11C2×C412yes—
43C22×D4×C11C2×C412yes—
44C22×D4×C11C2×C412yes—
45C23×C4×C11C2311yescharacteristic
46C23×Dic11—21no—
47C23×Dic11D412yes—
48C2×C11×M16—21no—
49C2×C11×M16—21no—
50C2×C11×M16—21no—
51C2×C11×M16—21no—
52C2×C11×M16—21no—
53C2×C11×M16C2×C412yes—
54C22×C8×C11—21no—
55C11×#117—21no—
56C11×#117—21no—
57C11×#117C2×C412yes—
58C11×#117D412yes—
59C2×C11×C4⋊C4D412yes—
60C2×C11×C22⋊C4—21no—
61C2×C42×C11—21no—
62C2×C22⋊Dic11—21no—
63C2×C22⋊Dic11—28no—
64C2×C22⋊Dic11—48no—
65#66979—21no—
66#66979—21no—
67#66979C2×C412yes—
68#66979D412yes—
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⋊Dic11D412yes—
76C2×C4×Dic11—21no—
77C2×C4×Dic11—21no—
78C2×C4×Dic11—21no—
79C2×C4×Dic11—21no—
80C2×C4×Dic11—21no—
81C2×C4×Dic11—21no—
82C2×C4×Dic11—24no—
83C2×C4×Dic11C2×C412yes—
84C2×#4318—21no—
85C2×#4318—21no—
86C2×#4318—21no—
87C2×#4318—21no—
88C2×#4318—21no—
89C2×#4318C2×C412yes—
90C22×C11⋊C8—21no—
91C11×#102—28no—
92#66896—28no—
93C11⋊#95—24no—
94#10958—111nomaximal, Sylow
95C24×C11—22no—
96C24×C11—22no—
97C24×C11—22no—
98C24×C11—44no—
99C24×C11—44no—
100C24×C11—41no—
101C24×C11—41no—
102C24×C11—41no—
103C24×C11—41no—
104C24×C11C2×D411yescharacteristic
105C2×D4×C11—22no—
106C2×D4×C11—22no—
107C2×D4×C11—22no—
108C2×D4×C11—22no—
109C2×D4×C11—22no—
110C2×D4×C11—22no—
111C2×D4×C11—22no—
112C2×D4×C11—22no—
113C2×D4×C11—22no—
114C2×D4×C11—22no—
115C2×D4×C11—22no—
116C2×D4×C11—22no—
117C2×D4×C11—22no—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11—41no—
121C2×D4×C11—41no—
122C2×D4×C11—41no—
123C2×D4×C11—41no—
124C2×D4×C11—41no—
125C2×D4×C11—41no—
126C2×D4×C11—41no—
127C2×D4×C11—41no—
128C2×D4×C11—41no—
129C2×D4×C11—41no—
130C2×D4×C11—41no—
131C2×D4×C11—41no—
132C2×D4×C11C4214yescomplemented
133C22×C4×C11—22no—
134C22×C4×C11C22×C411yescharacteristic
135C22×C4×C11C22×C411yescharacteristic
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×C11#4111yescharacteristic
143C22×C4×C11#4111yescharacteristic
144C22×C4×C11#4111yescharacteristic
145C22×C4×C11#4111yescharacteristic
146C22×C4×C11#4111yescharacteristic
147C22×C4×C11#4111yescharacteristic
148C22×Dic11—24no—
149C22×Dic11—22no—
150C22×Dic11—22no—
151C22×Dic11—22no—
152C22×Dic11—22no—
153C22×Dic11—42no—
154C22×Dic11—44no—
155C22×Dic11—41no—
156C22×Dic11—41no—
157C22×Dic11C22⋊C414yes—
158C11×M16—22no—
159C11×M16—22no—
160C11×M16—41no—
161C11×M16—41no—
162C2×C8×C11—22no—
163C2×C8×C11—41no—
164C2×C8×C11—41no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4C22⋊C414yescomplemented
167C11×C22⋊C4—22no—
168C11×C22⋊C4—22no—
169C42×C11—22no—
170C42×C11—22no—
171C22⋊Dic11—22no—
172C22⋊Dic11—22no—
173C22⋊Dic11—416no—
174C4⋊Dic11—22no—
175C4⋊Dic11—22no—
176C4⋊Dic11—22no—
177C4⋊Dic11—22no—
178C4⋊Dic11—22no—
179C4⋊Dic11C22⋊C414yescomplemented
180C4×Dic11—22no—
181C4×Dic11—22no—
182C4×Dic11—22no—
183C4×Dic11—22no—
184C4×Dic11—41no—
185C4×Dic11—41no—
186C4×Dic11—84no—
187#4318—22no—
188#4318—22no—
189#4318—41no—
190#4318—41no—
191C2×C11⋊C8—22no—
192C2×C11⋊C8—41no—
193C2×C11⋊C8—41no—
194C2×#418—111no—
195C2×#418D1111yescharacteristic
196C2×#390—111no—
197#2274—111no—
198C2×#343—111no—
199C2×#339—111no—
200C2×#339—111no—
201C23×C11—22no—
202C23×C11—22no—
203C23×C11—24no—
204C23×C11—44no—
205C23×C11—48no—
206C23×C11—48no—
207C23×C11—44no—
208C23×C11—42no—
209C23×C11—42no—
210C23×C11—42no—
211C23×C11—42no—
212C23×C11—42no—
213C23×C11—42no—
214C23×C11—84no—
215C23×C11—84no—
216C23×C11—82no—
217C23×C11—82no—
218C23×C11—82no—
219C23×C11—82no—
220C23×C11C2×C22⋊C411yescharacteristic
221C23×C11C4×D411yescharacteristic
222C23×C11C4×D411yescharacteristic
223C23×C11#12011yescharacteristic
224C23×C11#12111yescharacteristic
225C23×C11#12111yescharacteristic
226C23×C11#12311yescharacteristic
227D4×C11—24no—
228D4×C11—24no—
229D4×C11—42no—
230D4×C11—42no—
231D4×C11—42no—
232D4×C11—42no—
233D4×C11—42no—
234D4×C11—42no—
235C2×C4×C11—24no—
236C2×C4×C11—42no—
237C2×C4×C11—42no—
238C2×C4×C11C2×C4211yescharacteristic
239C2×C4×C11C2×C22⋊C411yescharacteristic
240C2×C4×C11C2×C22⋊C411yescharacteristic
241C2×C4×C11#11711yescharacteristic
242C2×C4×C11#11711yescharacteristic
243C2×C4×C11#11711yescharacteristic
244C2×C4×C11C4×D411yescharacteristic
245C2×C4×C11C4×D411yescharacteristic
246C2×C4×C11C4×D411yescharacteristic
247C2×C4×C11C4×D411yescharacteristic
248C2×C4×C11C4×D411yescharacteristic
249C2×C4×C11C4×D411yescharacteristic
250C2×C4×C11C4×D411yescharacteristic
251C2×C4×C11C4×D411yescharacteristic
252C2×C4×C11C4×D411yescharacteristic
253C2×C4×C11C4×D411yescharacteristic
254C2×C4×C11#12111yescharacteristic
255C2×C4×C11#12111yescharacteristic
256C2×C4×C11#12111yescharacteristic
257C2×C4×C11#12111yescharacteristic
258C2×C4×C11#12311yescharacteristic
259C2×C4×C11#12311yescharacteristic
260C2×C4×C11#12411yescharacteristic
261C2×C4×C11#12411yescharacteristic
262C2×C4×C11#12411yescharacteristic
263C2×C4×C11#12611yescharacteristic
264C2×C4×C11#12611yescharacteristic
265C2×C4×C11#12711yescharacteristic
266C2×Dic11—24no—
267C2×Dic11—24no—
268C2×Dic11—24no—
269C2×Dic11—44no—
270C2×Dic11—44no—
271C2×Dic11—42no—
272C2×Dic11—42no—
273C2×Dic11—42no—
274C2×Dic11—44no—
275C2×Dic11—42no—
276C2×Dic11—44no—
277C2×Dic11—82no—
278C8×C11—42no—
279C11⋊C8—42no—
280C23×D4C2×D1111yescharacteristic
281C22×M16—111no—
282C22×M16C2×D1111yescharacteristic
283C2×#117—111no—
284C2×#117C2×D1111yescharacteristic
285C22×C4⋊C4—111no—
286C22×C22⋊C4—222no—
287C22×C42—111no—
288#418—22no—
289#418—114no—
290#418—222no—
291#418Dic1114yescomplemented
292C2×#102—22no—
293C2×#102—222no—
294#390—114no—
295#390—222no—
296C4×C4⋊C4—222no—
297C4×C4⋊C4—222no—
298C4×C22⋊C4—222no—
299#343—222no—
300#339—222no—
301#339—222no—
302C22×C11—22no—
303C22×C11—22no—
304C22×C11—22no—
305C22×C11—22no—
306C22×C11—21no—
307C22×C11—21no—
308C22×C11—21no—
309C22×C11—21no—
310C22×C11—48no—
311C22×C11—44no—
312C22×C11—84no—
313C22×C11—84no—
314C22×C11—84no—
315C22×C11—84no—
316C22×C11—84no—
317C22×C11—82no—
318C22×C11—82no—
319C22×C11C4×C22⋊C411yescharacteristic
320C22×C11#38611yescharacteristic
321C22×C11#38611yescharacteristic
322C22×C11#38611yescharacteristic
323C22×C11#38811yescharacteristic
324C22×C11#38811yescharacteristic
325C22×C11#39011yescharacteristic
326C22×C11#45312yes—
327C22×C11#45412yes—
328C4×C11—44no—
329C4×C11C4×C22⋊C411yescharacteristic
330C4×C11C4×C22⋊C411yescharacteristic
331C4×C11#38811yescharacteristic
332C4×C11#38811yescharacteristic
333C4×C11#38811yescharacteristic
334C4×C11#38811yescharacteristic
335C4×C11#39011yescharacteristic
336C4×C11#39011yescharacteristic
337Dic11—44no—
338Dic11—44no—
339Dic11—44no—
340C25—21no—
341C22×D4—21no—
342C22×D4—21no—
343C22×D4—21no—
344C22×D4—21no—
345C22×D4—21no—
346C22×D4—21no—
347C22×D4—21no—
348C22×D4—21no—
349C22×D4—21no—
350C22×D4—21no—
351C22×D4—21no—
352C22×D4C4×D1112yes—
353C22×D4C4×D1112yes—
354C22×D4C2×Dic1112yes—
355C23×C4—112no—
356C23×C4—221no—
357C23×C4C22×D1111yescharacteristic
358C2×M16—21no—
359C2×M16—21no—
360C2×M16—21no—
361C2×M16—21no—
362C2×M16—21no—
363C2×M16—112no—
364C2×M16—221no—
365C2×M16—221no—
366C2×M16—221no—
367C2×M16—221no—
368C2×M16—221no—
369C2×M16C2×Dic1112yes—
370C22×C8—21no—
371C22×C8—221no—
372#117—21no—
373#117—21no—
374#117—112no—
375#117—112no—
376#117—221no—
377#117—221no—
378#117C2×Dic1112yes—
379#117C22⋊D1112yes—
380C2×C4⋊C4—112no—
381C2×C4⋊C4—112no—
382C2×C4⋊C4—112no—
383C2×C4⋊C4—221no—
384C2×C4⋊C4—221no—
385C2×C4⋊C4—221no—
386C2×C4⋊C4—221no—
387C2×C4⋊C4C22⋊D1112yes—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—221no—
390C2×C22⋊C4—228no—
391C2×C22⋊C4—448no—
392C2×C42—21no—
393C2×C42—112no—
394C2×C42—221no—
395C2×C42—221no—
396C2×C42—221no—
397C2×C42—221no—
398C2×C42—221no—
399C2×C42—221no—
400C2×C42—224no—
401#102—28no—
402#102—228no—
403#95—224no—
404C2×C11—21no—
405C2×C11—21no—
406C2×C11—21no—
407C2×C11—21no—
408C2×C11—84no—
409C2×C11#143711yescharacteristic
410C2×C11#188312yes—
411C2×C11#188312yes—
412C2×C11#188711yescharacteristic
413C2×C11#188811yescharacteristic
414C24—22no—
415C24—22no—
416C24—22no—
417C24—44no—
418C24—44no—
419C24—41no—
420C24—41no—
421C24—41no—
422C24—41no—
423C24D4×D1111yescharacteristic
424C2×D4—22no—
425C2×D4—22no—
426C2×D4—22no—
427C2×D4—22no—
428C2×D4—22no—
429C2×D4—22no—
430C2×D4—22no—
431C2×D4—22no—
432C2×D4—22no—
433C2×D4—22no—
434C2×D4—22no—
435C2×D4—22no—
436C2×D4—22no—
437C2×D4—22no—
438C2×D4—22no—
439C2×D4—41no—
440C2×D4—41no—
441C2×D4—41no—
442C2×D4—41no—
443C2×D4—41no—
444C2×D4—41no—
445C2×D4—41no—
446C2×D4—41no—
447C2×D4—41no—
448C2×D4—41no—
449C2×D4—41no—
450C2×D4—41no—
451C2×D4C4×Dic1114yescomplemented
452C22×C4—22no—
453C22×C4—114no—
454C22×C4—224no—
455C22×C4—222no—
456C22×C4—222no—
457C22×C4—222no—
458C22×C4—222no—
459C22×C4—442no—
460C22×C4—441no—
461C22×C4—441no—
462C22×C4—444no—
463C22×C4C2×C4×D1111yescharacteristic
464C22×C4C2×C4×D1111yescharacteristic
465C22×C4#433911yescharacteristic
466C22×C4#433911yescharacteristic
467C22×C4D4×D1111yescharacteristic
468C22×C4D4×D1111yescharacteristic
469C22×C4D4×D1111yescharacteristic
470C22×C4#434111yescharacteristic
471C22×C4#434111yescharacteristic
472C22×C4#434111yescharacteristic
473C22×C4#434111yescharacteristic
474C22×C4C22×Dic1111yescharacteristic
475C22×C4C2×C22⋊D1111yescharacteristic
476C22×C4C2×C22⋊D1111yescharacteristic
477M16—22no—
478M16—22no—
479M16—41no—
480M16—41no—
481M16—222no—
482M16—222no—
483M16—441no—
484M16—441no—
485C2×C8—22no—
486C2×C8—41no—
487C2×C8—41no—
488C2×C8—222no—
489C2×C8—441no—
490C2×C8—441no—
491C4⋊C4—22no—
492C4⋊C4—114no—
493C4⋊C4—222no—
494C4⋊C4—222no—
495C4⋊C4—222no—
496C4⋊C4—222no—
497C4⋊C4—222no—
498C4⋊C4C22⋊Dic1114yescomplemented
499C22⋊C4—22no—
500C22⋊C4—22no—
501C22⋊C4—222no—
502C22⋊C4—222no—
503C22⋊C4—4416no—
504C42—22no—
505C42—22no—
506C42—222no—
507C42—222no—
508C42—222no—
509C42—222no—
510C42—441no—
511C42—441no—
512C42—884no—
513C11#1095811yescharacteristic, complemented, Sylow
514C23—22no—
515C23—22no—
516C23—24no—
517C23—44no—
518C23—48no—
519C23—48no—
520C23—44no—
521C23—42no—
522C23—42no—
523C23—42no—
524C23—42no—
525C23—42no—
526C23—42no—
527C23—84no—
528C23—84no—
529C23—82no—
530C23—82no—
531C23—82no—
532C23—82no—
533C23C22⋊C4×D1111yescharacteristic
534C23(C22⋊D11)⋊C411yescharacteristic
535C23#6693611yescharacteristic
536C23#6693711yescharacteristic
537C23D4×Dic1111yescharacteristic
538C23#6699011yescharacteristic
539C23#6699211yescharacteristic
540D4—24no—
541D4—24no—
542D4—42no—
543D4—42no—
544D4—42no—
545D4—42no—
546D4—42no—
547D4—42no—
548C2×C4—24no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—224no—
552C2×C4—224no—
553C2×C4—224no—
554C2×C4—444no—
555C2×C4—444no—
556C2×C4—442no—
557C2×C4—442no—
558C2×C4—444no—
559C2×C4—442no—
560C2×C4—442no—
561C2×C4—444no—
562C2×C4—882no—
563C2×C4#6693011yescharacteristic
564C2×C4#6693011yescharacteristic
565C2×C4#6693211yescharacteristic
566C2×C4#6693211yescharacteristic
567C2×C4C22⋊C4×D1111yescharacteristic
568C2×C4(C22⋊D11)⋊C411yescharacteristic
569C2×C4(C22⋊D11)⋊C411yescharacteristic
570C2×C4(C22⋊D11)⋊C411yescharacteristic
571C2×C4#6693611yescharacteristic
572C2×C4#6693711yescharacteristic
573C2×C4#6693811yescharacteristic
574C2×C4#6693811yescharacteristic
575C2×C4C2×C4×Dic1111yescharacteristic
576C2×C4#6697911yescharacteristic
577C2×C4C4×C22⋊D1111yescharacteristic
578C2×C4C4×C22⋊D1111yescharacteristic
579C2×C4C4×C22⋊D1111yescharacteristic
580C2×C4C4×C22⋊D1111yescharacteristic
581C2×C4D4×Dic1111yescharacteristic
582C2×C4D4×Dic1111yescharacteristic
583C2×C4D4×Dic1111yescharacteristic
584C2×C4#6698811yescharacteristic
585C2×C4#6698911yescharacteristic
586C2×C4#6699111yescharacteristic
587C2×C4#6699111yescharacteristic
588C2×C4#6699211yescharacteristic
589C2×C4#6699311yescharacteristic
590C2×C4C2×C22⋊Dic1111yescharacteristic
591C8—42no—
592C8—442no—
593C22—22no—
594C22—22no—
595C22—22no—
596C22—22no—
597C22—21no—
598C22—21no—
599C22—21no—
600C22—21no—
601C22—48no—
602C22—44no—
603C22—84no—
604C22—84no—
605C22—84no—
606C22—84no—
607C22—84no—
608C22—82no—
609C22—82no—
610C22C22⋊C4×Dic1111yescharacteristic
611C22#1062255811yescharacteristic
612C22#1062256411yescharacteristic
613C22#1062256911yescharacteristic
614C22#1062256911yescharacteristic
615C22#1062257011yescharacteristic
616C22#1062281112yes—
617C22#1062281412yes—
618C22#1062283311yescharacteristic
619C4—44no—
620C4—444no—
621C4—444no—
622C4—444no—
623C4C22⋊C4×Dic1111yescharacteristic
624C4#1062255711yescharacteristic
625C4#1062255711yescharacteristic
626C4#1062255811yescharacteristic
627C4#1062256411yescharacteristic
628C4#1062257011yescharacteristic
629C4C4×C22⋊Dic1111yescharacteristic
630C4#1062283411yescharacteristic
631C2—21no—
632C2—21no—
633C2—21no—
634C2—21no—
635C2—84no—
636C2#1306685311yescharacteristic
637C2#1306898912yes—
638C2#1306899412yes—
639C2#1306901111yescharacteristic
640C2#1306901611yescharacteristic
subgroupG/H
centerC23#66990
commutatorC2×C4×C11C2×C42
FrattiniC23×C4C22×D11
FittingC2×C11×#418C2
socleC23×C11#120
prime radicalC23×D4×C11C22
cosocleC23×C4×C11C23
hypercenterC2×#418D11
hypocenterC11#10958
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#418

Complements

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

NH ≅ G/Ntype
3. #13070972C2semidirect
4. C2×#10622192C2semidirect
5. C2×#10622193C2semidirect
6. C2×#10622170C2semidirect
17. C11×#418C4semidirect
20. #10622834C4semidirect
22. #10622828C4semidirect
132. C2×D4×C11C42semidirect
166. C11×C4⋊C4C22⋊C4semidirect
179. C4⋊Dic11C22⋊C4semidirect
291. #418Dic11semidirect
451. C2×D4C4×Dic11semidirect
498. C4⋊C4C22⋊Dic11semidirect
513. C11#10958semidirect

Maximal subgroups

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

subgroupindex
C2×#106228282
C2×#106228342
#130709722
C2×#106221922
C2×#106221932
C2×#106221702
C2×C11×#4182
#1095811