Finite Group Databasebeta

← #14660207

Subgroups — #14660207

Order 2816.

966 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622849C211yesmaximal, characteristic
2C2×#10622853C211yesmaximal, characteristic
3#13070973C211yesmaximal, characteristic, complemented
4C2×#10622194C211yesmaximal, characteristic, complemented
5#13068335C211yesmaximal, characteristic, complemented
6C2×#10622195C211yesmaximal, characteristic, complemented
7C2×C11×#417C211yesmaximal, characteristic
8C22×C11×#41C2211yescharacteristic
9C22×C11×M16C2211yescharacteristic
10C22×C11×C4⋊C4C2211yescharacteristic
11C2×#66979C2211yescharacteristic
12C2×#66979C2211yescharacteristic
13C2×#66979C2211yescharacteristic
14C22×#4318C2211yescharacteristic
15C11×#417—22no—
16C11×#417—22no—
17C2×C11×#103C412yescomplemented
18C2×C11×#102C412yescomplemented
19#10622853—22no—
20#10622853C414yescomplemented
21#10622849—22no—
22#10622849C414yescomplemented
23C2×#66901—22no—
24C2×#66898—22no—
25C4×C22⋊Dic11—22no—
26C4⋊C4×Dic11—22no—
27C4⋊C4×Dic11—22no—
28#10622195—22no—
29#10622194—22no—
30#10622167—22no—
31C2×C11×#41—21no—
32C2×C11×#41—21no—
33C2×C11×#41—21no—
34C2×C11×#41—21no—
35C2×C11×#41—21no—
36C2×C11×#41—21no—
37C2×C11×#41—21no—
38C2×C11×#41—21no—
39C2×C11×#41—21no—
40C2×C11×#41—21no—
41C2×C11×#41C2×C412yes—
42C2×C11×#41C2×C412yes—
43C22×Q8×C11C2×C411yescharacteristic
44C22×D4×C11—21no—
45C22×D4×C11C2×C411yescharacteristic
46C23×C4×C11—21no—
47C23×C4×C11—21no—
48C23×C4×C11C2311yescharacteristic
49C2×C11×M16—21no—
50C2×C11×M16—21no—
51C2×C11×M16—21no—
52C2×C11×M16—21no—
53C2×C11×M16—21no—
54C2×C11×M16—21no—
55C22×C8×C11C2×C412yes—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4C2×C412yes—
60C2×C11×C4⋊C4D412yes—
61C2×C11×C4⋊C4D412yes—
62C2×C22⋊Dic11—21no—
63C2×C22⋊Dic11—21no—
64C2×C22⋊Dic11D412yes—
65#66979—21no—
66#66979—21no—
67#66979—21no—
68#66979—21no—
69#66979—21no—
70#66979—21no—
71#66979—21no—
72#66979C2×C412yes—
73#66979C2×C412yes—
74#66979C2×C412yes—
75#66979D412yes—
76#66979D412yes—
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×Dic11D412yes—
84C2×#4318—21no—
85C2×#4318—21no—
86C2×#4318—21no—
87C2×#4318—21no—
88C2×#4318—21no—
89C2×#4318C2×C412yes—
90C22×C11⋊C8—21no—
91C11×#103—24no—
92C11×#102—24no—
93#66901—28no—
94#66898—28no—
95C11⋊#95—24no—
96#10954—111nomaximal, Sylow
97C24×C11—21no—
98C24×C11C2×D411yescharacteristic
99C11×#41—22no—
100C11×#41—22no—
101C11×#41—22no—
102C11×#41—22no—
103C11×#41—22no—
104C11×#41—22no—
105C11×#41—22no—
106C11×#41—22no—
107C11×#41—41no—
108C11×#41—41no—
109C11×#41—41no—
110C11×#41—41no—
111C11×#41—41no—
112C11×#41—41no—
113C11×#41—41no—
114C11×#41—41no—
115C2×Q8×C11—21no—
116C2×Q8×C11—21no—
117C2×Q8×C11—21no—
118C2×Q8×C11—21no—
119C2×Q8×C11—21no—
120C2×Q8×C11C4212yescomplemented
121C2×D4×C11—22no—
122C2×D4×C11—22no—
123C2×D4×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11—21no—
127C2×D4×C11—21no—
128C2×D4×C11—41no—
129C2×D4×C11—41no—
130C2×D4×C11—41no—
131C2×D4×C11—41no—
132C2×D4×C11C4212yescomplemented
133C22×C4×C11—21no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—41no—
140C22×C4×C11—41no—
141C22×C4×C11—41no—
142C22×C4×C11—41no—
143C22×C4×C11—82no—
144C22×C4×C11C22×C411yescharacteristic
145C22×C4×C11C22×C411yescharacteristic
146C22×C4×C11C22×C411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11#4111yescharacteristic
153C22×C4×C11#4111yescharacteristic
154C22×C4×C11#4111yescharacteristic
155C22×C4×C11#4111yescharacteristic
156C22×C4×C11#4111yescharacteristic
157C22×C4×C11#4111yescharacteristic
158C22×Dic11—22no—
159C22×Dic11—22no—
160C22×Dic11—41no—
161C11×M16—41no—
162C11×M16—41no—
163C11×M16—41no—
164C11×M16—41no—
165C2×C8×C11—22no—
166C2×C8×C11—22no—
167C2×C8×C11—22no—
168C11×C4⋊C4—22no—
169C11×C4⋊C4—22no—
170C11×C4⋊C4—22no—
171C11×C4⋊C4C22⋊C414yes—
172C22⋊Dic11—22no—
173C22⋊Dic11—22no—
174C22⋊Dic11—22no—
175C22⋊Dic11—22no—
176C22⋊Dic11—41no—
177C22⋊Dic11C22⋊C414yes—
178C4⋊Dic11—22no—
179C4⋊Dic11—22no—
180C4⋊Dic11—22no—
181C4⋊Dic11—22no—
182C4⋊Dic11—22no—
183C4⋊Dic11—41no—
184C4×Dic11—22no—
185C4×Dic11—22no—
186C4×Dic11—22no—
187C4×Dic11—22no—
188C4×Dic11—41no—
189C4×Dic11—84no—
190C4×Dic11C22⋊C414yes—
191#4318—22no—
192#4318—22no—
193#4318—41no—
194#4318—41no—
195C2×C11⋊C8—22no—
196C2×C11⋊C8—41no—
197C2×C11⋊C8—41no—
198C2×#421—111no—
199C2×#417D1111yescharacteristic
200C2×#410—111no—
201#2274—111no—
202C2×#344—111no—
203#1736—111no—
204C2×H(3,ℤ/4)—111no—
205C23×C11—22no—
206C23×C11—41no—
207C23×C11—41no—
208C23×C11—41no—
209C23×C11—41no—
210C23×C11—81no—
211C23×C11—81no—
212C23×C11C2×C22⋊C411yescharacteristic
213C23×C11C4×D411yescharacteristic
214C23×C11C4×D411yescharacteristic
215C23×C11#12011yescharacteristic
216C23×C11#12111yescharacteristic
217C23×C11#12111yescharacteristic
218C23×C11#12311yescharacteristic
219Q8×C11—22no—
220Q8×C11—22no—
221Q8×C11—41no—
222Q8×C11—41no—
223D4×C11—22no—
224D4×C11—22no—
225D4×C11—42no—
226D4×C11—42no—
227D4×C11—42no—
228D4×C11—42no—
229D4×C11—41no—
230D4×C11—41no—
231C2×C4×C11—22no—
232C2×C4×C11—24no—
233C2×C4×C11—44no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—42no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—42no—
240C2×C4×C11—82no—
241C2×C4×C11—82no—
242C2×C4×C11C2×C4211yescharacteristic
243C2×C4×C11C2×C22⋊C411yescharacteristic
244C2×C4×C11C2×C22⋊C411yescharacteristic
245C2×C4×C11#11711yescharacteristic
246C2×C4×C11#11711yescharacteristic
247C2×C4×C11#11711yescharacteristic
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×C11C4×D411yescharacteristic
255C2×C4×C11C4×D411yescharacteristic
256C2×C4×C11C4×D411yescharacteristic
257C2×C4×C11C4×D411yescharacteristic
258C2×C4×C11#12111yescharacteristic
259C2×C4×C11#12111yescharacteristic
260C2×C4×C11#12111yescharacteristic
261C2×C4×C11#12111yescharacteristic
262C2×C4×C11#12311yescharacteristic
263C2×C4×C11#12311yescharacteristic
264C2×C4×C11#12411yescharacteristic
265C2×C4×C11#12411yescharacteristic
266C2×C4×C11#12411yescharacteristic
267C2×C4×C11#12611yescharacteristic
268C2×C4×C11#12611yescharacteristic
269C2×C4×C11#12711yescharacteristic
270C2×Dic11—24no—
271C2×Dic11—24no—
272C2×Dic11—42no—
273C2×Dic11—42no—
274C2×Dic11—42no—
275C2×Dic11—42no—
276C2×Dic11—42no—
277C2×Dic11—81no—
278C2×Dic11—81no—
279C8×C11—42no—
280C11⋊C8—42no—
281C22×#41C2×D1111yescharacteristic
282C22×M16—111no—
283C22×M16C2×D1111yescharacteristic
284C2×#117—111no—
285C2×#117—111no—
286C2×#117—111no—
287C22×C4⋊C4C2×D1111yescharacteristic
288#421—114no—
289#421—222no—
290C2×#104—222no—
291#417—22no—
292#417—22no—
293C2×#103Dic1112yescomplemented
294C2×#102Dic1112yescomplemented
295#410—114no—
296#410—222no—
297C2×#99—222no—
298C4×C4⋊C4—222no—
299C4×C4⋊C4—222no—
300C4×C22⋊C4—222no—
301#344—222no—
302#340—222no—
303H(3,ℤ/4)—222no—
304C22×C11—21no—
305C22×C11—21no—
306C22×C11—21no—
307C22×C11—21no—
308C22×C11—21no—
309C22×C11—21no—
310C22×C11—41no—
311C22×C11—41no—
312C22×C11—41no—
313C22×C11—41no—
314C22×C11—42no—
315C22×C11—82no—
316C22×C11—82no—
317C22×C11—81no—
318C22×C11—81no—
319C22×C11C4×C22⋊C411yescharacteristic
320C22×C11#38611yescharacteristic
321C22×C11#38611yescharacteristic
322C22×C11#38611yescharacteristic
323C22×C11#38811yescharacteristic
324C22×C11#38811yescharacteristic
325C22×C11#39011yescharacteristic
326C4×C11—44no—
327C4×C11—42no—
328C4×C11C4×C22⋊C411yescharacteristic
329C4×C11C4×C22⋊C411yescharacteristic
330C4×C11#38811yescharacteristic
331C4×C11#38811yescharacteristic
332C4×C11#38811yescharacteristic
333C4×C11#38811yescharacteristic
334C4×C11#39011yescharacteristic
335C4×C11#39011yescharacteristic
336Dic11—44no—
337Dic11—44no—
338Dic11—82no—
339C2×#41—21no—
340C2×#41—21no—
341C2×#41—21no—
342C2×#41—21no—
343C2×#41—21no—
344C2×#41—21no—
345C2×#41—21no—
346C2×#41—21no—
347C2×#41—21no—
348C2×#41—21no—
349C2×#41C4×D1112yes—
350C2×#41C4×D1112yes—
351C22×Q8C2×Dic1111yescharacteristic
352C22×D4—21no—
353C22×D4C2×Dic1111yescharacteristic
354C23×C4—21no—
355C23×C4—21no—
356C23×C4C22×D1111yescharacteristic
357C2×M16—21no—
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—
369C22×C8—221no—
370C22×C8C2×Dic1112yes—
371#117—112no—
372#117—112no—
373#117—112no—
374#117—112no—
375#117—112no—
376#117—221no—
377#117—221no—
378#117—221no—
379#117—221no—
380#117—221no—
381#117—221no—
382#117—221no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—221no—
387C2×C4⋊C4—221no—
388C2×C4⋊C4—221no—
389C2×C4⋊C4C2×Dic1112yes—
390C2×C4⋊C4C22⋊D1112yes—
391C2×C4⋊C4C22⋊D1112yes—
392C2×C22⋊C4—112no—
393C2×C22⋊C4—221no—
394C2×C22⋊C4—221no—
395C2×C42—112no—
396C2×C42—221no—
397C2×C42—221no—
398C2×C42—224no—
399#104—228no—
400#103—24no—
401#102—24no—
402#99—228no—
403#95—224no—
404C2×C11—21no—
405C2×C11—21no—
406C2×C11—21no—
407C2×C11—21no—
408C2×C11—21no—
409C2×C11—21no—
410C2×C11—82no—
411C2×C11#143711yescharacteristic
412C2×C11#190411yescharacteristic
413C2×C11#190511yescharacteristic
414C24—21no—
415C24D4×D1111yescharacteristic
416#41—22no—
417#41—22no—
418#41—22no—
419#41—22no—
420#41—22no—
421#41—22no—
422#41—22no—
423#41—22no—
424#41—41no—
425#41—41no—
426#41—41no—
427#41—41no—
428#41—41no—
429#41—41no—
430#41—41no—
431#41—41no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8C4×Dic1112yescomplemented
438C2×D4—22no—
439C2×D4—22no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—41no—
446C2×D4—41no—
447C2×D4—41no—
448C2×D4—41no—
449C2×D4C4×Dic1112yescomplemented
450C22×C4—21no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—41no—
457C22×C4—41no—
458C22×C4—41no—
459C22×C4—41no—
460C22×C4—82no—
461C22×C4—222no—
462C22×C4—222no—
463C22×C4—441no—
464C22×C4C2×C4×D1111yescharacteristic
465C22×C4C2×C4×D1111yescharacteristic
466C22×C4#433911yescharacteristic
467C22×C4#433911yescharacteristic
468C22×C4D4×D1111yescharacteristic
469C22×C4D4×D1111yescharacteristic
470C22×C4D4×D1111yescharacteristic
471C22×C4#434111yescharacteristic
472C22×C4#434111yescharacteristic
473C22×C4#434111yescharacteristic
474C22×C4#434111yescharacteristic
475C22×C4C22×Dic1111yescharacteristic
476C22×C4C2×C22⋊D1111yescharacteristic
477C22×C4C2×C22⋊D1111yescharacteristic
478M16—41no—
479M16—41no—
480M16—41no—
481M16—41no—
482M16—222no—
483M16—222no—
484M16—441no—
485M16—441no—
486C2×C8—22no—
487C2×C8—22no—
488C2×C8—22no—
489C2×C8—222no—
490C2×C8—441no—
491C2×C8—441no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—222no—
496C4⋊C4—222no—
497C4⋊C4—222no—
498C4⋊C4—222no—
499C4⋊C4—222no—
500C4⋊C4—441no—
501C4⋊C4C22⋊Dic1114yes—
502C22⋊C4—114no—
503C22⋊C4—222no—
504C22⋊C4—222no—
505C22⋊C4—222no—
506C22⋊C4—222no—
507C22⋊C4—441no—
508C42—114no—
509C42—222no—
510C42—222no—
511C42—222no—
512C42—222no—
513C42—441no—
514C42—884no—
515C11#1095411yescharacteristic, complemented, Sylow
516C23—22no—
517C23—41no—
518C23—41no—
519C23—41no—
520C23—41no—
521C23—81no—
522C23—81no—
523C23C22⋊C4×D1111yescharacteristic
524C23(C22⋊D11)⋊C411yescharacteristic
525C23#6693611yescharacteristic
526C23#6693711yescharacteristic
527C23D4×Dic1111yescharacteristic
528C23#6699011yescharacteristic
529C23#6699211yescharacteristic
530Q8—22no—
531Q8—22no—
532Q8—41no—
533Q8—41no—
534D4—22no—
535D4—22no—
536D4—42no—
537D4—42no—
538D4—42no—
539D4—42no—
540D4—41no—
541D4—41no—
542C2×C4—22no—
543C2×C4—24no—
544C2×C4—44no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—82no—
552C2×C4—82no—
553C2×C4—224no—
554C2×C4—224no—
555C2×C4—442no—
556C2×C4—442no—
557C2×C4—442no—
558C2×C4—442no—
559C2×C4—442no—
560C2×C4—881no—
561C2×C4—881no—
562C2×C4#6693011yescharacteristic
563C2×C4#6693011yescharacteristic
564C2×C4#6693211yescharacteristic
565C2×C4#6693211yescharacteristic
566C2×C4C22⋊C4×D1111yescharacteristic
567C2×C4(C22⋊D11)⋊C411yescharacteristic
568C2×C4(C22⋊D11)⋊C411yescharacteristic
569C2×C4(C22⋊D11)⋊C411yescharacteristic
570C2×C4#6693611yescharacteristic
571C2×C4#6693711yescharacteristic
572C2×C4#6693811yescharacteristic
573C2×C4#6693811yescharacteristic
574C2×C4C2×C4×Dic1111yescharacteristic
575C2×C4#6697911yescharacteristic
576C2×C4C4×C22⋊D1111yescharacteristic
577C2×C4C4×C22⋊D1111yescharacteristic
578C2×C4C4×C22⋊D1111yescharacteristic
579C2×C4C4×C22⋊D1111yescharacteristic
580C2×C4D4×Dic1111yescharacteristic
581C2×C4D4×Dic1111yescharacteristic
582C2×C4D4×Dic1111yescharacteristic
583C2×C4#6698811yescharacteristic
584C2×C4#6698911yescharacteristic
585C2×C4#6699111yescharacteristic
586C2×C4#6699111yescharacteristic
587C2×C4#6699211yescharacteristic
588C2×C4#6699311yescharacteristic
589C2×C4C2×C22⋊Dic1111yescharacteristic
590C8—42no—
591C8—442no—
592C22—21no—
593C22—21no—
594C22—21no—
595C22—21no—
596C22—21no—
597C22—21no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—42no—
603C22—82no—
604C22—82no—
605C22—81no—
606C22—81no—
607C22C22⋊C4×Dic1111yescharacteristic
608C22#1062255811yescharacteristic
609C22#1062256411yescharacteristic
610C22#1062256911yescharacteristic
611C22#1062256911yescharacteristic
612C22#1062257011yescharacteristic
613C22#1062283311yescharacteristic
614C4—44no—
615C4—42no—
616C4—444no—
617C4—444no—
618C4—882no—
619C4C22⋊C4×Dic1111yescharacteristic
620C4#1062255711yescharacteristic
621C4#1062255711yescharacteristic
622C4#1062255811yescharacteristic
623C4#1062256411yescharacteristic
624C4#1062257011yescharacteristic
625C4C4×C22⋊Dic1111yescharacteristic
626C4#1062283411yescharacteristic
627C2—21no—
628C2—21no—
629C2—21no—
630C2—21no—
631C2—21no—
632C2—21no—
633C2—82no—
634C2#1306685311yescharacteristic
635C2#1306910511yescharacteristic
636C2#1306911211yescharacteristic
subgroupG/H
centerC22#10622833
commutatorC2×C4×C11C2×C42
FrattiniC23×C4C22×D11
FittingC2×C11×#417C2
socleC22×C11#386
prime radicalC22×C11×#41C22
cosocleC23×C4×C11C23
hypercenterC2×#417D11
hypocenterC11#10954
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
3. #13070973C2semidirect
4. C2×#10622194C2semidirect
5. #13068335C2semidirect
6. C2×#10622195C2semidirect
17. C2×C11×#103C4semidirect
18. C2×C11×#102C4semidirect
20. #10622853C4semidirect
22. #10622849C4semidirect
120. C2×Q8×C11C42semidirect
132. C2×D4×C11C42semidirect
293. C2×#103Dic11semidirect
294. C2×#102Dic11semidirect
437. C2×Q8C4×Dic11semidirect
449. C2×D4C4×Dic11semidirect
515. C11#10954semidirect

Maximal subgroups

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

subgroupindex
C2×#106228492
C2×#106228532
#130709732
C2×#106221942
#130683352
C2×#106221952
C2×C11×#4172
#1095411