Finite Group Databasebeta

← #14773559

Subgroups — #14773559

Order 2816.

802 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622371C211yesmaximal, characteristic
2#13071588C211yesmaximal, characteristic
3#13071577C211yesmaximal, characteristic, complemented
4#13069498C211yesmaximal, characteristic
5#13069496C211yesmaximal, characteristic
6#13069251C211yesmaximal, characteristic, complemented
7#13069249C211yesmaximal, characteristic, complemented
8#13069245C211yesmaximal, characteristic
9#13068777C211yesmaximal, characteristic, complemented
10#13068630C211yesmaximal, characteristic, complemented
11#13068624C211yesmaximal, characteristic
12#13068514C211yesmaximal, characteristic, complemented
13#13068512C211yesmaximal, characteristic, complemented
14#13068482C211yesmaximal, characteristic, complemented
15C11×#1926C211yesmaximal, characteristic
16C2×D4×Dic11C2211yescharacteristic
17C22×#4324C2211yescharacteristic
18C2×#66940C2211yescharacteristic
19C2×C11×#106C2211yescharacteristic
20C2×C11×#102C2211yescharacteristic
21C2×C11×#102C2211yescharacteristic
22C11×#390C2211yescharacteristic
23C4×C11×C4⋊C4C2211yescharacteristic
24#10622834C2211yescharacteristic
25C2×#66896C2211yescharacteristic
26C2×#66881C2211yescharacteristic
27C2×#66880C2211yescharacteristic
28C2×#66880C2211yescharacteristic
29C2×#66879C2211yescharacteristic
30C2×Dic11⋊C8C2211yescharacteristic
31C2×C8×Dic11C2211yescharacteristic
32#10622590C2211yescharacteristic
33#10622590C2211yescharacteristic
34C4⋊C4×Dic11C2211yescharacteristic
35C4⋊C4×Dic11C2211yescharacteristic
36#10622587C2211yescharacteristic
37C2×#66874C2211yescharacteristic
38C2×#66872C2211yescharacteristic
39C2×#66871C2211yescharacteristic
40C2×#66871C2211yescharacteristic
41#10622558—21no—
42#10622557—21no—
43#10622556—21no—
44C22⋊C4×Dic11—21no—
45C4×C4⋊Dic11C2211yescharacteristic
46#10622546—21no—
47#10622545—21no—
48C4×Dic11⋊C4C2211yescharacteristic
49#10622542C2211yescharacteristic
50C2×#66867C2211yescharacteristic
51#10622371C418yescomplemented
52#10622265—21no—
53#10622264—21no—
54C11×#340C2211yescharacteristic
55C11×#336C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C22×D4×C11C2311yescharacteristic
61C23×Dic11—21no—
62C22×Dic22C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C22⋊C4—21no—
69C2×C11×C22⋊C4—21no—
70C2×C42×C11—21no—
71C2×C42×C11C2311yescharacteristic
72C2×C22⋊Dic11—21no—
73C2×C22⋊Dic11—21no—
74C2×C22⋊Dic11—21no—
75D4×Dic11—22no—
76D4×Dic11C2×C414yes—
77C2×#4324—22no—
78C2×#4324—22no—
79C2×#4324C2×C414yes—
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2311yescharacteristic
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4D411yescharacteristic
85C2×Dic11⋊C4D411yescharacteristic
86C2×C4×Dic11—21no—
87C2×C4×Dic11—21no—
88C2×C4×Dic11—21no—
89C2×C4×Dic11—21no—
90C2×C4×Dic11C2311yescharacteristic
91C2×C4×Dic11C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94#66940—22no—
95#66940C2×C414yes—
96C11×#106—41no—
97C11×#102—41no—
98C11×#102C2×C414yes—
99C11×#95—21no—
100#66896—41no—
101C11⋊#95—21no—
102C11⋊#95—21no—
103C11⋊#95—21no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95D411yescharacteristic
113C11⋊#95D411yescharacteristic
114#66881—41no—
115#66880—41no—
116#66880C2×C414yes—
117#66879—22no—
118Dic11⋊C8—22no—
119C8×Dic11C2×C414yes—
120#66874—41no—
121#66872C2×C414yes—
122#66871—22no—
123#66871—22no—
124#66867—22no—
125#22812—111nomaximal, Sylow
126C24×C11—21no—
127C2×D4×C11—21no—
128C2×D4×C11—21no—
129C2×D4×C11—21no—
130C2×D4×C11—21no—
131C2×D4×C11—21no—
132C2×D4×C11C22×C412yes—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2411yescharacteristic
139C22×Dic11—24no—
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11—81no—
145C22×Dic11—81no—
146C22×Dic11C2×D411yescharacteristic
147C22×Dic11C2×D411yescharacteristic
148C22×Dic11C2×D411yescharacteristic
149C22×Dic11C2×D411yescharacteristic
150C2×Dic22—21no—
151C2×Dic22—21no—
152C2×Dic22—21no—
153C2×Dic22—21no—
154C2×Dic22—21no—
155C2×Dic22C22×C412yes—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11C22×C412yes—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4C22×C412yes—
168C11×C22⋊C4—42no—
169C11×C22⋊C4—81no—
170C42×C11—21no—
171C42×C11—21no—
172C42×C11—42no—
173C22⋊Dic11—24no—
174C22⋊Dic11—42no—
175C22⋊Dic11—81no—
176#4324—28no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11C22×C412yes—
183Dic11⋊C4—24no—
184Dic11⋊C4—41no—
185Dic11⋊C4—41no—
186C4×Dic11—24no—
187C4×Dic11—21no—
188C4×Dic11—21no—
189C4×Dic11—42no—
190C4×Dic11—81no—
191C4×Dic11—81no—
192C4×Dic11C22×C412yes—
193C4×Dic11#4112yes—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8C22×C412yes—
198C2×C11⋊C8#4112yes—
199C2×C11⋊C8#4112yes—
200C2×C4×SD16—111no—
201#2357—111no—
202#2356—111no—
203#1973—111no—
204#1973—111no—
205#1927—111no—
206#1927—111no—
207#1926—111no—
208#1926D1111yescharacteristic
209#1846—111no—
210#1805—111no—
211#1804—111no—
212#1776—111no—
213#1776—111no—
214#1770—111no—
215C23×C11—22no—
216C23×C11—41no—
217C23×C11—41no—
218C23×C11—41no—
219C23×C11—41no—
220C23×C11—41no—
221C23×C11—41no—
222C23×C11C22×D411yescharacteristic
223D4×C11—22no—
224D4×C11—22no—
225D4×C11—41no—
226D4×C11—41no—
227C2×C4×C11—22no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11C23×C411yescharacteristic
243C2×C4×C11C2×#4111yescharacteristic
244C2×C4×C11C2×#4111yescharacteristic
245C2×C4×C11C2×#4111yescharacteristic
246C2×C4×C11H(5,𝔽2)11yescharacteristic
247C2×C4×C112−1+411yescharacteristic
248C2×Dic11—21no—
249C2×Dic11—21no—
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—22no—
253C2×Dic11—22no—
254C2×Dic11—21no—
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11—21no—
259C2×Dic11—21no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—84no—
271C2×Dic11C4×D412yes—
272C2×Dic11C4×D412yes—
273Dic22—22no—
274Dic22—22no—
275Dic22—41no—
276Dic22—41no—
277C8×C11—22no—
278C8×C11—41no—
279C11⋊C8—41no—
280C11⋊C8#11714yes—
281C22×SD16—111no—
282C2×C4×Q8—111no—
283C2×C4×D4—111no—
284C4×SD16—118no—
285C2×#107—111no—
286C2×#107—111no—
287C2×#106—111no—
288C2×#106—111no—
289C2×#106C2×D1111yescharacteristic
290C2×C4⋊C8—111no—
291C2×#103—111no—
292C2×#103—111no—
293C2×#103—111no—
294C2×#102—111no—
295C2×#102C2×D1111yescharacteristic
296C2×#102C2×D1111yescharacteristic
297C2×#97—111no—
298C2×#97—111no—
299C2×C4×C8—111no—
300#391—111no—
301#391—111no—
302#390—111no—
303#390C2×D1111yescharacteristic
304#388—221no—
305#388—221no—
306#387—221no—
307#387—221no—
308#383—221no—
309#382—111no—
310#382—111no—
311#381—221no—
312C4×C4⋊C4—111no—
313C4×C4⋊C4—111no—
314C4×C4⋊C4—111no—
315C4×C4⋊C4—111no—
316C4×C4⋊C4C2×D1111yescharacteristic
317C4×C22⋊C4—221no—
318#376—221no—
319#340—111no—
320#340—111no—
321#340—111no—
322#340C2×D1111yescharacteristic
323#336—111no—
324#336C2×D1111yescharacteristic
325C22×C11—42no—
326C22×C11—42no—
327C22×C11—42no—
328C22×C11—81no—
329C22×C11—81no—
330C22×C11—81no—
331C22×C11—81no—
332C22×C11C2×C4×D411yescharacteristic
333C22×C11#54711yescharacteristic
334C22×C11#55011yescharacteristic
335C22×C11#57511yescharacteristic
336C22×C11#57511yescharacteristic
337C22×C11#57711yescharacteristic
338C22×C11#57711yescharacteristic
339C4×C11—41no—
340C4×C11—41no—
341C4×C11—42no—
342C4×C11—81no—
343C4×C11—81no—
344C4×C11C2×#11711yescharacteristic
345C4×C11#52011yescharacteristic
346C4×C11#55511yescharacteristic
347C4×C11#55611yescharacteristic
348Dic11—22no—
349Dic11—22no—
350Dic11—41no—
351Dic11—41no—
352Dic11—42no—
353Dic11—42no—
354Dic11—81no—
355Dic11—81no—
356C22×Q8—111no—
357C22×D4C22×D1111yescharacteristic
358C23×C4—221no—
359C2×SD16—114no—
360C2×SD16—222no—
361C2×SD16—222no—
362C22×C8—111no—
363C22×C8—111no—
364C22×C8C22×D1111yescharacteristic
365C22×C8C22×D1111yescharacteristic
366C4×Q8—114no—
367C4×Q8—222no—
368C4×D4—114no—
369C4×D4—222no—
370C2×C4⋊C4—111no—
371C2×C4⋊C4—111no—
372C2×C4⋊C4—111no—
373C2×C4⋊C4—111no—
374C2×C4⋊C4—111no—
375C2×C4⋊C4—221no—
376C2×C4⋊C4C22×D1111yescharacteristic
377C2×C4⋊C4C22×D1111yescharacteristic
378C2×C4⋊C4C22×D1111yescharacteristic
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—221no—
382C2×C22⋊C4—221no—
383C2×C22⋊C4—221no—
384C2×C42—21no—
385C2×C42—111no—
386C2×C42—111no—
387C2×C42—221no—
388C2×C42—221no—
389C2×C42—221no—
390C2×C42—221no—
391C2×C42C22×D1111yescharacteristic
392#107—222no—
393#107—222no—
394#106—41no—
395#106—114no—
396#106—441no—
397C4⋊C8—222no—
398#103—114no—
399#103—441no—
400#103—441no—
401#102—41no—
402#102—441no—
403#102C4×D1114yes—
404#97—222no—
405#97—222no—
406C4×C8—114no—
407#95—21no—
408#95—111no—
409#95—111no—
410#95—221no—
411#95—221no—
412#95—221no—
413#95—221no—
414#95—221no—
415#95—221no—
416#95—221no—
417#95—221no—
418#95—221no—
419#95—221no—
420#95—221no—
421C2×C11—82no—
422C2×C11#235411yescharacteristic
423C2×C11#294311yescharacteristic
424C2×C11#294911yescharacteristic
425C2×C11#335111yescharacteristic
426C2×C11#335111yescharacteristic
427C2×C11#340111yescharacteristic
428C2×C11#340111yescharacteristic
429C24—21no—
430C2×Q8—112no—
431C2×Q8—221no—
432C2×Q8—221no—
433C2×Q8—221no—
434C2×Q8—221no—
435C2×Q8—221no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4C2×C4×D1112yes—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—111no—
446C22×C4—111no—
447C22×C4—111no—
448C22×C4—111no—
449C22×C4—224no—
450C22×C4—221no—
451C22×C4—221no—
452C22×C4—221no—
453C22×C4—221no—
454C22×C4—881no—
455C22×C4—881no—
456C22×C4D4×D1111yescharacteristic
457C22×C4D4×D1111yescharacteristic
458C22×C4C23×D1111yescharacteristic
459SD16—228no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—112no—
466C2×C8—112no—
467C2×C8—112no—
468C2×C8—221no—
469C2×C8—221no—
470C2×C8—221no—
471C2×C8C2×C4×D1112yes—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—112no—
478C4⋊C4—224no—
479C4⋊C4—221no—
480C4⋊C4—221no—
481C4⋊C4—221no—
482C4⋊C4—221no—
483C4⋊C4—221no—
484C4⋊C4—441no—
485C4⋊C4—441no—
486C4⋊C4C2×C4×D1112yes—
487C22⋊C4—42no—
488C22⋊C4—81no—
489C22⋊C4—224no—
490C22⋊C4—442no—
491C22⋊C4—881no—
492C42—21no—
493C42—21no—
494C42—42no—
495C42—112no—
496C42—112no—
497C42—224no—
498C42—221no—
499C42—221no—
500C42—442no—
501C42—881no—
502C42—881no—
503C11#2281211yescharacteristic, complemented, Sylow
504C23—22no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23—41no—
511C23C2×D4×D1111yescharacteristic
512Q8—222no—
513Q8—222no—
514Q8—441no—
515Q8—441no—
516D4—22no—
517D4—22no—
518D4—41no—
519D4—41no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—22no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—112no—
536C2×C4—112no—
537C2×C4—221no—
538C2×C4—221no—
539C2×C4—221no—
540C2×C4—221no—
541C2×C4—221no—
542C2×C4—221no—
543C2×C4—221no—
544C2×C4—221no—
545C2×C4—222no—
546C2×C4—222no—
547C2×C4—221no—
548C2×C4—221no—
549C2×C4—441no—
550C2×C4—441no—
551C2×C4—441no—
552C2×C4—441no—
553C2×C4—441no—
554C2×C4—441no—
555C2×C4—441no—
556C2×C4—441no—
557C2×C4—441no—
558C2×C4—441no—
559C2×C4—884no—
560C2×C4C22×C4×D1111yescharacteristic
561C2×C4#6703711yescharacteristic
562C2×C4#41×D1111yescharacteristic
563C2×C4#41×D1111yescharacteristic
564C2×C4#41×D1111yescharacteristic
565C2×C4#6704311yescharacteristic
566C8—22no—
567C8—41no—
568C8—114no—
569C8—441no—
570C22—42no—
571C22—42no—
572C22—42no—
573C22—81no—
574C22—81no—
575C22—81no—
576C22—81no—
577C22C4×D4×D1111yescharacteristic
578C22#1062313011yescharacteristic
579C22#1062318611yescharacteristic
580C22#1062329311yescharacteristic
581C22#1062330111yescharacteristic
582C22#1062330411yescharacteristic
583C22#1062330411yescharacteristic
584C4—41no—
585C4—41no—
586C4—42no—
587C4—81no—
588C4—81no—
589C4—222no—
590C4—222no—
591C4—441no—
592C4—441no—
593C4—442no—
594C4—442no—
595C4—881no—
596C4—881no—
597C4D11×#11711yescharacteristic
598C4#1062307711yescharacteristic
599C4#1062320111yescharacteristic
600C4#1062323311yescharacteristic
601C2—82no—
602C2#1307156211yescharacteristic
603C2#1307741311yescharacteristic
604C2#1307747011yescharacteristic
605C2#1308116911yescharacteristic
606C2#1308118011yescharacteristic
607C2#1308167511yescharacteristic
608C2#1308167911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1926C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
cosocleC22×C4×C11C24
hypercenter#1926D11
hypocenterC11#22812
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1926

Complements

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

NH ≅ G/Ntype
3. #13071577C2semidirect
6. #13069251C2semidirect
7. #13069249C2semidirect
9. #13068777C2semidirect
10. #13068630C2semidirect
12. #13068514C2semidirect
13. #13068512C2semidirect
14. #13068482C2semidirect
51. #10622371C4semidirect
503. C11#22812semidirect

Maximal subgroups

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

subgroupindex
C2×#106223712
#130715882
#130715772
#130694982
#130694962
#130692512
#130692492
#130692452
#130687772
#130686302
#130686242
#130685142
#130685122
#130684822
C11×#19262
#2281211