Finite Group Databasebeta

← #14757330

Subgroups — #14757330

Order 2816.

882 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622506C211yesmaximal, characteristic
2#13077203C211yesmaximal, characteristic
3C2×#10622494C211yesmaximal, characteristic
4D11×#428C211yesmaximal, characteristic
5#13077032C211yesmaximal, characteristic
6#13069400C211yesmaximal, characteristic, complemented
7#13069399C211yesmaximal, characteristic, complemented
8#13069398C211yesmaximal, characteristic, complemented
9#13069397C211yesmaximal, characteristic, complemented
10#13069396C211yesmaximal, characteristic, complemented
11#13069395C211yesmaximal, characteristic, complemented
12#13069393C211yesmaximal, characteristic, complemented
13#13068353C211yesmaximal, characteristic
14D11×#343C211yesmaximal, characteristic
15C11×#1952C211yesmaximal, characteristic, complemented
16C2×M16×D11C2211yescharacteristic
17C2×M16×D11C2211yescharacteristic
18C2×M16×D11C2211yescharacteristic
19C22×#4313C2211yescharacteristic
20D11×#117C2211yescharacteristic
21C2×#66945C2211yescharacteristic
22C2×C4⋊C4×D11C2211yescharacteristic
23C2×C11×#108C2211yescharacteristic
24C11×#428C2211yescharacteristic
25C11×#428C2211yescharacteristic
26C2×C11×#107C2211yescharacteristic
27C11×#405C2211yescharacteristic
28C2×#66886C2211yescharacteristic
29C2×#66886C2211yescharacteristic
30#10622735C2211yescharacteristic
31#10622734C2211yescharacteristic
32#10622734C2211yescharacteristic
33C2×#66883C2211yescharacteristic
34C2×#66881C2211yescharacteristic
35#10622714C2211yescharacteristic
36#10622610C2211yescharacteristic
37#10622608C2211yescharacteristic
38#10622608C2211yescharacteristic
39#10622577C2211yescharacteristic
40#10622577C2211yescharacteristic
41C2×#66872C2211yescharacteristic
42C2×#66871C2211yescharacteristic
43#10622506C418yescomplemented
44#10622494—21no—
45#10622494—21no—
46#10622494—21no—
47#10622494—21no—
48#10622494—21no—
49#10622494—21no—
50#10622493—21no—
51D11×#107—21no—
52#10622474—21no—
53#10622474—21no—
54#10622473—21no—
55D11×#106—21no—
56#10622321—21no—
57#10622320—21no—
58#10622302—21no—
59C4×#4313—21no—
60C11×#343C2211yescharacteristic
61C11×#343C2211yescharacteristic
62#10622192C2211yescharacteristic
63#10622192C2211yescharacteristic
64#10622192C2211yescharacteristic
65#10622192C2211yescharacteristic
66#10622168C2211yescharacteristic
67#10622168C2211yescharacteristic
68C22×C4×D11—21no—
69C22×C4×D11C2311yescharacteristic
70C2×C11×M16C2311yescharacteristic
71C2×C11×M16C2311yescharacteristic
72C2×C11×M16C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C11×#117C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×(C2×D11)⋊C4—21no—
78#66979C2311yescharacteristic
79C2×C4⋊Dic11C2311yescharacteristic
80C2×C4⋊Dic11C2311yescharacteristic
81C2×Dic11⋊C4—21no—
82C2×C4×Dic11—21no—
83C2×#4318C2311yescharacteristic
84C2×#4318C2311yescharacteristic
85C2×#4318C2311yescharacteristic
86C22×C11⋊C8C2311yescharacteristic
87M16×D11—22no—
88M16×D11—22no—
89M16×D11—22no—
90M16×D11C2×C414yes—
91M16×D11C2×C414yes—
92M16×D11Q814yes—
93C2×#4313—21no—
94C2×#4313—21no—
95C2×#4313—21no—
96C2×#4313C2×C414yes—
97C2×#4313D411yescharacteristic
98C2×#4313D411yescharacteristic
99C2×#4313D411yescharacteristic
100C2×#4313D411yescharacteristic
101C2×#4313Q814yes—
102C2×C8×D11—21no—
103C2×C8×D11—21no—
104C2×C8×D11—21no—
105#66945—21no—
106#66945—21no—
107#66945—21no—
108#66945—21no—
109#66945D411yescharacteristic
110#66945D411yescharacteristic
111C4⋊C4×D11—21no—
112C4⋊C4×D11—21no—
113C4⋊C4×D11—21no—
114C4⋊C4×D11—21no—
115C4⋊C4×D11D411yescharacteristic
116C4⋊C4×D11D411yescharacteristic
117C22⋊C4×D11—21no—
118#66930—21no—
119#66925—21no—
120C42×D11—21no—
121C11×#108C2×C414yescomplemented
122C11×#107—21no—
123C11×#107—21no—
124C11×#107—21no—
125C11×#107—21no—
126C11×#106—21no—
127C11×#106—21no—
128C11×#97—21no—
129C4×C8×C11—21no—
130#66886C2×C414yescomplemented
131#66886C2×C414yescomplemented
132#66883C2×C414yescomplemented
133#66882—21no—
134#66882—21no—
135#66881—21no—
136#66881—21no—
137#66881—21no—
138#66881—21no—
139#66879—21no—
140#66879—21no—
141C8×Dic11—21no—
142C8×Dic11—21no—
143#66872—21no—
144#66872—21no—
145#66872—21no—
146#66872—21no—
147#66872—21no—
148#66872—21no—
149#66871—21no—
150#66871—21no—
151#66871—21no—
152#66871—21no—
153#66871—21no—
154#66871—21no—
155#66867—21no—
156C4×C11⋊C8—21no—
157#21182—111nomaximal, Sylow
158C23×D11#4111yescharacteristic
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11C2411yescharacteristic
162C22×Dic11—21no—
163C22×Dic11—21no—
164C22×Dic11#4111yescharacteristic
165C2×C4×D11—21no—
166C2×C4×D11—21no—
167C2×C4×D11—41no—
168C2×C4×D11—41no—
169C2×C4×D11—82no—
170C2×C4×D11C22×C412yes—
171C2×C4×D11C2×D411yescharacteristic
172C2×C4×D11C2×D411yescharacteristic
173C2×C4×D11C2×D411yescharacteristic
174C2×C4×D11C2×D411yescharacteristic
175C2×C4×D11C2×Q812yes—
176C2×C4×D11C2×Q812yes—
177C2×C4×D11#4112yes—
178C11×M16—21no—
179C11×M16—21no—
180C11×M16—21no—
181C11×M16C22×C412yes—
182C11×M16C22×C412yes—
183C11×M16C2×Q812yes—
184C2×C8×C11—21no—
185C2×C8×C11—21no—
186C2×C8×C11—21no—
187C2×C8×C11C22×C412yes—
188C2×C8×C11C2×D411yescharacteristic
189C2×C8×C11C2×D411yescharacteristic
190C2×C8×C11C2×Q812yes—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4—21no—
194C11×C4⋊C4—21no—
195C11×C4⋊C4C2×D411yescharacteristic
196C11×C4⋊C4C2×D411yescharacteristic
197C11×C22⋊C4—21no—
198C42×C11—21no—
199C22⋊Dic11—21no—
200(C2×D11)⋊C4—21no—
201(C2×D11)⋊C4—21no—
202(C2×D11)⋊C4—41no—
203(C2×D11)⋊C4—41no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11—21no—
208C4⋊Dic11C2×D411yescharacteristic
209C4⋊Dic11C2×D411yescharacteristic
210Dic11⋊C4—21no—
211Dic11⋊C4—21no—
212Dic11⋊C4—41no—
213Dic11⋊C4—41no—
214C4×Dic11—21no—
215C4×Dic11—21no—
216C4×Dic11—21no—
217C4×Dic11—41no—
218C4×Dic11—41no—
219#4318—21no—
220#4318—21no—
221#4318—21no—
222#4318C22×C412yes—
223#4318C22×C412yes—
224#4318C2×Q812yes—
225C2×C11⋊C8—21no—
226C2×C11⋊C8—21no—
227C2×C11⋊C8—21no—
228C2×C11⋊C8C22×C412yes—
229C2×C11⋊C8C2×D411yescharacteristic
230C2×C11⋊C8C2×D411yescharacteristic
231C2×C11⋊C8C2×Q812yes—
232#4313—24no—
233#4313—24no—
234#4313—24no—
235#4313C4⋊C414yes—
236#4313C4⋊C414yes—
237#4313C4⋊C414yes—
238#4313C4⋊C414yes—
239C8×D11—24no—
240C8×D11—24no—
241C8×D11—24no—
242C2×#430—111no—
243#2911—111no—
244C2×#428—111no—
245C2×#428—111no—
246#2873—111no—
247#1952—111no—
248#1952—111no—
249#1952—111no—
250#1952D1111yescharacteristic, complemented
251#1951—111no—
252#1951—111no—
253#1951—111no—
254#1951—111no—
255#1742—111no—
256C2×#343—111no—
257C23×C11C2×#4111yescharacteristic
258C22×D11—41no—
259C22×D11—41no—
260C22×D11C4×Q812yes—
261C22×D11#12111yescharacteristic
262C22×D11#12111yescharacteristic
263C22×D11#12512yes—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—81no—
269C2×C4×C11—81no—
270C2×C4×C11C23×C411yescharacteristic
271C2×C4×C11C22×D411yescharacteristic
272C2×C4×C11C22×D411yescharacteristic
273C2×C4×C11C22×Q811yescharacteristic
274C2×C4×C11C22×Q811yescharacteristic
275C2×C4×C11C2×#4111yescharacteristic
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—81no—
281C2×Dic11—81no—
282C2×Dic11C4×Q812yes—
283C2×Dic11#12111yescharacteristic
284C2×Dic11#12111yescharacteristic
285C2×Dic11#12512yes—
286C4×D11—81no—
287C4×D11—81no—
288C4×D11—82no—
289C4×D11—82no—
290C4×D11C2×C4⋊C412yes—
291C4×D11C2×C4⋊C412yes—
292C4×D11C4×D412yes—
293C4×D11C4×D412yes—
294C4×D11C22⋊Q812yes—
295C4×D11C22⋊Q812yes—
296C4×D11C4⋊Q812yes—
297C4×D11C4⋊Q812yes—
298C8×C11—22no—
299C8×C11—22no—
300C8×C11—22no—
301C8×C11C2×C4⋊C412yes—
302C8×C11C2×C4⋊C412yes—
303C11⋊C8—22no—
304C11⋊C8—22no—
305C11⋊C8—22no—
306C11⋊C8C2×C4⋊C412yes—
307C11⋊C8C2×C4⋊C412yes—
308C22×M16—111no—
309C22×M16—111no—
310C22×M16—111no—
311C22×M16—111no—
312C2×#117—111no—
313C2×#117—111no—
314C22×C4⋊C4—111no—
315#430—118no—
316C2×#108—111no—
317C2×#108—111no—
318C2×#108—111no—
319C2×#108C2×D1111yescharacteristic
320#428—111no—
321#428—111no—
322#428—111no—
323#428—111no—
324#428—111no—
325#428—111no—
326#428—221no—
327#428—221no—
328#428—221no—
329#428—221no—
330#428—221no—
331#428—221no—
332#428—221no—
333#428—221no—
334#428C2×D1111yescharacteristic
335#428C2×D1111yescharacteristic
336#427—221no—
337#427—221no—
338C2×#107—111no—
339C2×#107—221no—
340C2×#107C2×D1111yescharacteristic
341C2×#106—111no—
342C2×#106—111no—
343C2×#106—221no—
344#405—111no—
345#405—111no—
346#405—111no—
347#405—221no—
348#405—221no—
349#405C2×D1111yescharacteristic
350C4×M16—221no—
351C4×M16—221no—
352#343—111no—
353#343—111no—
354#343—111no—
355#343—111no—
356#343—111no—
357#343—111no—
358#343C2×D1111yescharacteristic
359#343C2×D1111yescharacteristic
360C22×C11—21no—
361C22×C11—21no—
362C22×C11C2×C4×Q811yescharacteristic
363C22×C11C2×#12111yescharacteristic
364C22×C11C2×#12511yescharacteristic
365C2×D11—21no—
366C2×D11—21no—
367C2×D11—21no—
368C2×D11—21no—
369C2×D11—42no—
370C2×D11—42no—
371C2×D11#38912yes—
372C2×D11#38912yes—
373C4×C11—41no—
374C4×C11—41no—
375C4×C11—81no—
376C4×C11—81no—
377C4×C11C22×C4⋊C411yescharacteristic
378C4×C11C2×C4×D411yescharacteristic
379C4×C11C2×C22⋊Q811yescharacteristic
380C4×C11C2×C4⋊Q811yescharacteristic
381Dic11—41no—
382Dic11—41no—
383Dic11—81no—
384Dic11—81no—
385Dic11#38912yes—
386Dic11#38912yes—
387C23×C4—111no—
388C23×C4—221no—
389C2×M16—114no—
390C2×M16—111no—
391C2×M16—111no—
392C2×M16—111no—
393C2×M16—111no—
394C2×M16—114no—
395C2×M16—111no—
396C2×M16—111no—
397C2×M16—111no—
398C2×M16—114no—
399C2×M16—114no—
400C2×M16—114no—
401C2×M16—221no—
402C2×M16—221no—
403C2×M16—221no—
404C2×M16—222no—
405C2×M16—222no—
406C2×M16—222no—
407C2×M16C22×D1111yescharacteristic
408C2×M16C22×D1111yescharacteristic
409C2×M16C22×D1111yescharacteristic
410C22×C8—111no—
411C22×C8—221no—
412C22×C8—221no—
413C22×C8—221no—
414C22×C8C22×D1111yescharacteristic
415#117—111no—
416#117—111no—
417#117—111no—
418#117—221no—
419#117—221no—
420#117—221no—
421#117—221no—
422#117—221no—
423#117—221no—
424#117C22×D1111yescharacteristic
425C2×C4⋊C4—111no—
426C2×C4⋊C4—111no—
427C2×C4⋊C4—111no—
428C2×C4⋊C4—111no—
429C2×C4⋊C4—221no—
430C2×C4⋊C4—221no—
431C2×C4⋊C4—221no—
432C2×C4⋊C4—221no—
433C2×C4⋊C4—221no—
434C2×C4⋊C4C22×D1111yescharacteristic
435C2×C4⋊C4C22×D1111yescharacteristic
436C2×C22⋊C4—221no—
437C2×C22⋊C4—221no—
438C2×C42—221no—
439C2×C42—221no—
440#108—114no—
441#108—114no—
442#108—114no—
443#108C4×D1114yescomplemented
444#107—21no—
445#107—21no—
446#107—21no—
447#107—21no—
448#107—221no—
449#107—221no—
450#107—221no—
451#107—221no—
452#107—221no—
453#107—221no—
454#107—221no—
455#107—221no—
456#106—21no—
457#106—21no—
458#106—221no—
459#106—221no—
460#106—221no—
461#106—221no—
462#106—221no—
463#106—221no—
464#106—221no—
465#106—221no—
466#106—221no—
467#106—221no—
468#97—21no—
469#97—221no—
470#97—221no—
471#97—221no—
472C4×C8—21no—
473C4×C8—221no—
474C4×C8—221no—
475C4×C8—221no—
476C2×C11—21no—
477C2×C11—21no—
478C2×C11C2×#38911yescharacteristic
479C2×C11#306811yescharacteristic
480C2×C11#306911yescharacteristic
481D11—22no—
482D11—22no—
483C24—111no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—111no—
487C22×C4—112no—
488C22×C4—111no—
489C22×C4—111no—
490C22×C4—111no—
491C22×C4—111no—
492C22×C4—112no—
493C22×C4—112no—
494C22×C4—112no—
495C22×C4—221no—
496C22×C4—221no—
497C22×C4—221no—
498C22×C4—221no—
499C22×C4—441no—
500C22×C4—441no—
501C22×C4—882no—
502C22×C4C23×D1111yescharacteristic
503M16—21no—
504M16—21no—
505M16—21no—
506M16—114no—
507M16—114no—
508M16—114no—
509M16—114no—
510M16—112no—
511M16—112no—
512M16—112no—
513M16—224no—
514M16—224no—
515M16—224no—
516M16—221no—
517M16—221no—
518M16—221no—
519M16C2×C4×D1112yes—
520M16C2×C4×D1112yes—
521M16Q8×D1112yes—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—112no—
526C2×C8—111no—
527C2×C8—111no—
528C2×C8—112no—
529C2×C8—224no—
530C2×C8—224no—
531C2×C8—224no—
532C2×C8—221no—
533C2×C8—221no—
534C2×C8—221no—
535C2×C8C2×C4×D1112yes—
536C2×C8D4×D1111yescharacteristic
537C2×C8D4×D1111yescharacteristic
538C2×C8Q8×D1112yes—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—111no—
544C4⋊C4—111no—
545C4⋊C4—221no—
546C4⋊C4—221no—
547C4⋊C4—221no—
548C4⋊C4—221no—
549C4⋊C4—221no—
550C4⋊C4—221no—
551C4⋊C4—441no—
552C4⋊C4—441no—
553C4⋊C4D4×D1111yescharacteristic
554C4⋊C4D4×D1111yescharacteristic
555C22⋊C4—21no—
556C22⋊C4—221no—
557C22⋊C4—221no—
558C22⋊C4—221no—
559C22⋊C4—441no—
560C22⋊C4—441no—
561C42—21no—
562C42—221no—
563C42—221no—
564C42—221no—
565C42—441no—
566C42—441no—
567C11#2118211yescharacteristic, complemented, Sylow
568C23—111no—
569C23—111no—
570C23—112no—
571C23—112no—
572C23—441no—
573C23—441no—
574C23#41×D1111yescharacteristic
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—81no—
580C2×C4—81no—
581C2×C4—112no—
582C2×C4—111no—
583C2×C4—111no—
584C2×C4—112no—
585C2×C4—112no—
586C2×C4—112no—
587C2×C4—112no—
588C2×C4—112no—
589C2×C4—112no—
590C2×C4—112no—
591C2×C4—112no—
592C2×C4—112no—
593C2×C4—221no—
594C2×C4—221no—
595C2×C4—441no—
596C2×C4—441no—
597C2×C4—881no—
598C2×C4—881no—
599C2×C4—882no—
600C2×C4—882no—
601C2×C4—881no—
602C2×C4—881no—
603C2×C4C22×C4×D1111yescharacteristic
604C2×C4C2×D4×D1111yescharacteristic
605C2×C4C2×D4×D1111yescharacteristic
606C2×C4C2×Q8×D1111yescharacteristic
607C2×C4C2×Q8×D1111yescharacteristic
608C2×C4#41×D1111yescharacteristic
609C8—22no—
610C8—22no—
611C8—22no—
612C8—112no—
613C8—112no—
614C8—222no—
615C8—222no—
616C8—222no—
617C8C4⋊C4×D1112yes—
618C8C4⋊C4×D1112yes—
619C22—21no—
620C22—21no—
621C22—112no—
622C22—112no—
623C22—221no—
624C22—221no—
625C22—221no—
626C22—221no—
627C22—442no—
628C22—442no—
629C22C4×Q8×D1111yescharacteristic
630C22D11×#12111yescharacteristic
631C22D11×#12511yescharacteristic
632C4—41no—
633C4—41no—
634C4—81no—
635C4—81no—
636C4—112no—
637C4—112no—
638C4—441no—
639C4—441no—
640C4—881no—
641C4—881no—
642C4C2×C4⋊C4×D1111yescharacteristic
643C4C4×D4×D1111yescharacteristic
644C4D11×C22⋊Q811yescharacteristic
645C4D11×C4⋊Q811yescharacteristic
646C2—21no—
647C2—21no—
648C2—222no—
649C2—222no—
650C2D11×#38911yescharacteristic
651C2#1307834211yescharacteristic
652C2#1307835111yescharacteristic
subgroupG/H
centerC22D11×#121
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1952C2
socleC22×C11C2×#121
prime radicalC23×D11#41
cosocleC22×C4×C11C24
hypercenter#1952D11
hypocenterC11#21182
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1952

Complements

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

NH ≅ G/Ntype
6. #13069400C2semidirect
7. #13069399C2semidirect
8. #13069398C2semidirect
9. #13069397C2semidirect
10. #13069396C2semidirect
11. #13069395C2semidirect
12. #13069393C2semidirect
15. C11×#1952C2semidirect
43. #10622506C4semidirect
121. C11×#108C2×C4semidirect
130. #66886C2×C4semidirect
131. #66886C2×C4semidirect
132. #66883C2×C4semidirect
250. #1952D11semidirect
443. #108C4×D11semidirect
567. C11#21182semidirect

Maximal subgroups

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

subgroupindex
C2×#106225062
#130772032
C2×#106224942
D11×#4282
#130770322
#130694002
#130693992
#130693982
#130693972
#130693962
#130693952
#130693932
#130683532
D11×#3432
C11×#19522
#2118211