Finite Group Databasebeta

← #14780339

Subgroups — #14780339

Order 2816.

688 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079071C211yesmaximal, characteristic
2#13069113C211yesmaximal, characteristic, complemented
3#13069111C211yesmaximal, characteristic, complemented
4#13069110C211yesmaximal, characteristic, complemented
5#13069091C211yesmaximal, characteristic, complemented
6#13069088C211yesmaximal, characteristic, complemented
7#13069087C211yesmaximal, characteristic, complemented
8#13069086C211yesmaximal, characteristic, complemented
9#13069009C211yesmaximal, characteristic, complemented
10#13069006C211yesmaximal, characteristic, complemented
11#13068997C211yesmaximal, characteristic
12#13068996C211yesmaximal, characteristic
13#13068764C211yesmaximal, characteristic, complemented
14#13068763C211yesmaximal, characteristic, complemented
15C11×#1905C211yesmaximal, characteristic, complemented
16C2×C11×#137C2211yescharacteristic
17C11×#519C2211yescharacteristic
18#10623363C2211yescharacteristic
19C2×#67004C2211yescharacteristic
20#10623350C2211yescharacteristic
21C2×#66997C2211yescharacteristic
22C2×#66995C2211yescharacteristic
23C2×#66962C2211yescharacteristic
24#10623276C2211yescharacteristic
25#10623047C2211yescharacteristic
26C11×#421C2211yescharacteristic
27C11×#419C2211yescharacteristic
28C11×#410C2211yescharacteristic
29#10622849C2211yescharacteristic
30C2×#66900C2211yescharacteristic
31#10622838C2211yescharacteristic
32#10622803C412yescomplemented
33#10622794C412yescomplemented
34#10622788C412yescomplemented
35#10622780C412yescomplemented
36C2×#66888C2211yescharacteristic
37M16×Dic11C2211yescharacteristic
38#10622619C2211yescharacteristic
39#10622618C2211yescharacteristic
40#10622618C2211yescharacteristic
41#10622617C2211yescharacteristic
42#10622617C2211yescharacteristic
43C11×#344C2211yescharacteristic
44C11×H(3,ℤ/4)C2211yescharacteristic
45C11⋊#338C2211yescharacteristic
46C11⋊#338C2211yescharacteristic
47#10622194C2211yescharacteristic
48#10622193C2211yescharacteristic
49#10622171C2211yescharacteristic
50#10622171C2211yescharacteristic
51#10622170C2211yescharacteristic
52#10622170C2211yescharacteristic
53#10622170C2211yescharacteristic
54#10622169C2211yescharacteristic
55C2×C11×#41C2311yescharacteristic
56C22×Q8×C11C2311yescharacteristic
57C2×#4339C2311yescharacteristic
58C22×Dic22C2311yescharacteristic
59C11×#137—41no—
60C11×#137—41no—
61C2×C11×Q16C2×C412yes—
62C2×C11×SD16C2×C412yes—
63C2×C11×M16C2311yescharacteristic
64C2×C11×M16C2311yescharacteristic
65C4×Q8×C11—41no—
66C4×Q8×C11—41no—
67C11×#117—41no—
68C11×#117C2311yescharacteristic
69C11×#117C2311yescharacteristic
70C11×#117C2311yescharacteristic
71#67004—41no—
72#67004—41no—
73#67001—41no—
74#67001—41no—
75#67000C2×C411yescharacteristic
76#66997—41no—
77#66997C2×C412yes—
78#66997C2×C412yes—
79#66997C2×C411yescharacteristic
80C2×#4326C2×C412yes—
81C2×#4326C2×C412yes—
82#66995—41no—
83#66995—41no—
84C2×#4325C2×C412yes—
85#66993C2×C411yescharacteristic
86#66992—41no—
87#66989C2×C411yescharacteristic
88C2×#4324C2×C412yes—
89C4×C22⋊D11—41no—
90#66979C2311yescharacteristic
91C2×Dic11⋊C4—41no—
92C2×C4×Dic11C2311yescharacteristic
93C2×#4318—41no—
94C2×#4318C2311yescharacteristic
95C2×#4318C2311yescharacteristic
96C2×#4318C2311yescharacteristic
97C2×#4318C2311yescharacteristic
98#66962—41no—
99#66962—41no—
100#66960—41no—
101M16×D11—41no—
102C2×Dic44C2×C412yes—
103C2×#4314C2×C412yes—
104#66954—41no—
105#66940—41no—
106#66930—41no—
107C4×Dic22—41no—
108C11×#104—41no—
109C11×#103—41no—
110C11×#99—41no—
111#66901—41no—
112#66900—41no—
113#66899—41no—
114#66888—41no—
115#66879C2×C412yes—
116C8×Dic11C2×C412yes—
117#66874—41no—
118#66874—41no—
119#66870—41no—
120#66869—41no—
121#66869—41no—
122#23360—111nomaximal, Sylow
123C11×#41—21no—
124C11×#41—21no—
125C11×#41—21no—
126C11×#41—21no—
127C2×Q8×C11—21no—
128C2×Q8×C11—21no—
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11C22×C412yes—
133C2×Q8×C11C22×C411yescharacteristic
134C2×D4×C11—21no—
135C2×D4×C11C22×C411yescharacteristic
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11C2411yescharacteristic
139C2×C22⋊D11—21no—
140C2×C22⋊D11—41no—
141C22×Dic11—21no—
142C22×Dic11—21no—
143#4339—21no—
144#4339—21no—
145#4339—21no—
146#4339—21no—
147C2×D44C22×C411yescharacteristic
148C2×C4×D11—21no—
149C2×Dic22—21no—
150C2×Dic22—21no—
151C2×Dic22—21no—
152C2×Dic22—21no—
153C2×Dic22—21no—
154C2×Dic22C22×C412yes—
155C2×Dic22C22×C411yescharacteristic
156C11×Q16—42no—
157C11×SD16—42no—
158C11×M16—21no—
159C11×M16—21no—
160C11×M16—21no—
161C11×M16—21no—
162C2×C8×C11—21no—
163C2×C8×C11C22×C412yes—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—42no—
168C11×C22⋊C4—21no—
169C11×C22⋊C4—21no—
170C11×C22⋊C4—21no—
171C42×C11—21no—
172C42×C11—21no—
173C42×C11—21no—
174C42×C11—42no—
175C22⋊Dic11—21no—
176C22⋊Dic11—41no—
177#4326—42no—
178#4326—42no—
179#4325—42no—
180#4324—42no—
181(C2×D11)⋊C4—41no—
182C4⋊Dic11—21no—
183Dic11⋊C4—42no—
184Dic11⋊C4—42no—
185Dic11⋊C4—41no—
186Dic11⋊C4—42no—
187C4×Dic11—21no—
188C4×Dic11—21no—
189C4×Dic11—42no—
190C4×Dic11C22×C411yescharacteristic
191C4×Dic11C22×C411yescharacteristic
192#4318—21no—
193#4318—21no—
194#4318—21no—
195#4318—21no—
196#4318—21no—
197#4318—21no—
198#4318—21no—
199#4318—21no—
200#4318—42no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—42no—
205C2×C11⋊C8C22×C412yes—
206Dic44—42no—
207#4314—42no—
208#4313—42no—
209C8×D11—42no—
210#3152—111no—
211#1905—111no—
212#1905—111no—
213#1905—111no—
214#1905D1111yescharacteristic, complemented
215#1902—111no—
216#1902—111no—
217#1902—111no—
218#1902—111no—
219#1886—111no—
220#1886—111no—
221#1884—111no—
222#1884—111no—
223#1841—111no—
224#1841—111no—
225C23×C11—21no—
226C23×C11H(5,𝔽2)11yescharacteristic
227C22×D11—21no—
228Q8×C11—22no—
229Q8×C11—21no—
230Q8×C11—22no—
231Q8×C11—21no—
232Q8×C11—41no—
233Q8×C11—41no—
234D4×C11—21no—
235D4×C11—21no—
236D4×C11—41no—
237D4×C11—41no—
238C2×C4×C11—22no—
239C2×C4×C11—21no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11C23×C411yescharacteristic
248C2×C4×C11H(5,𝔽2)11yescharacteristic
249C2×C4×C11H(5,𝔽2)11yescharacteristic
250C2×C4×C11H(5,𝔽2)11yescharacteristic
251C2×C4×C11H(5,𝔽2)11yescharacteristic
252C2×C4×C11H(5,𝔽2)11yescharacteristic
253C22⋊D11—41no—
254C22⋊D11—41no—
255C22⋊D11—82no—
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11—22no—
259C2×Dic11—21no—
260C2×Dic11—42no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264D44—21no—
265D44—21no—
266C4×D11—41no—
267C4×D11—41no—
268Dic22—22no—
269Dic22—21no—
270Dic22—22no—
271Dic22—21no—
272Dic22—41no—
273Dic22—41no—
274C8×C11—22no—
275C8×C11—41no—
276C11⋊C8—22no—
277C11⋊C8—41no—
278C11⋊C8—41no—
279C11⋊C8—41no—
280C2×#137—111no—
281C2×#137—111no—
282C2×#137—111no—
283C2×#137C2×D1111yescharacteristic
284#568—111no—
285#568—111no—
286#532—111no—
287C2×C4⋊Q8—111no—
288#519—111no—
289#519C2×D1111yescharacteristic
290#497—112no—
291#497—112no—
292#494—112no—
293#492—112no—
294#421—111no—
295#421—111no—
296#421—111no—
297#421C2×D1111yescharacteristic
298#419—111no—
299#419—111no—
300#419—111no—
301#419C2×D1111yescharacteristic
302C2×#101—111no—
303C2×#101—111no—
304#410—111no—
305#410C2×D1111yescharacteristic
306C4×M16—111no—
307#344—111no—
308#344—111no—
309#344—111no—
310#344C2×D1111yescharacteristic
311#339—111no—
312#339—111no—
313#339—111no—
314#339—111no—
315#338—111no—
316#338—111no—
317H(3,ℤ/4)—111no—
318H(3,ℤ/4)C2×D1111yescharacteristic
319C22×C11—41no—
320C22×C11—41no—
321C22×C11—81no—
322C22×C11#51811yescharacteristic
323C22×C11#56011yescharacteristic
324C22×C11#56011yescharacteristic
325C2×D11—41no—
326C2×D11—81no—
327C4×C11—41no—
328C4×C11—42no—
329C4×C11—81no—
330C4×C11—81no—
331C4×C11—81no—
332C4×C11#51811yescharacteristic
333C4×C11#51811yescharacteristic
334C4×C11#56011yescharacteristic
335C4×C11#56011yescharacteristic
336Dic11—22no—
337Dic11—41no—
338Dic11—42no—
339Dic11—41no—
340Dic11—81no—
341C2×#41—111no—
342C2×#41C22×D1111yescharacteristic
343C22×Q8—111no—
344C22×Q8C22×D1111yescharacteristic
345#137—41no—
346#137—41no—
347#137—441no—
348#137—441no—
349#137—441no—
350#137—441no—
351#137—441no—
352#137—441no—
353C2×Q16—112no—
354C2×Q16—112no—
355C2×Q16—112no—
356C2×Q16C4×D1112yes—
357C2×SD16—112no—
358C2×SD16—112no—
359C2×SD16—112no—
360C2×SD16C4×D1112yes—
361#131—441no—
362#131—441no—
363#131—441no—
364#131—441no—
365C2×M16—111no—
366C2×M16—111no—
367C2×M16—111no—
368C2×M16—111no—
369C2×M16—441no—
370C2×M16—441no—
371C2×M16C22×D1111yescharacteristic
372C2×M16C22×D1111yescharacteristic
373C4⋊Q8—112no—
374C4⋊Q8—112no—
375C4⋊Q8—111no—
376C4⋊Q8—441no—
377#127—111no—
378#124—111no—
379#124—111no—
380#121—441no—
381C4×Q8—41no—
382C4×Q8—41no—
383C4×Q8—441no—
384C4×Q8—441no—
385C4×D4—441no—
386#117—41no—
387#117—111no—
388#117—441no—
389#117C22×D1111yescharacteristic
390#117C22×D1111yescharacteristic
391#117C22×D1111yescharacteristic
392C2×C4⋊C4—441no—
393C2×C42—111no—
394#104—41no—
395#104—441no—
396#104—441no—
397#104—441no—
398#103—41no—
399#103—441no—
400#103—441no—
401#103—441no—
402#101—441no—
403#101—441no—
404#99—41no—
405#99—441no—
406#97—112no—
407C4×C8—112no—
408C2×C11—21no—
409C2×C11—21no—
410C2×C11—21no—
411C2×C11—81no—
412C2×C11#238011yescharacteristic
413D11—81no—
414#41—21no—
415#41—21no—
416#41—21no—
417#41—21no—
418#41—221no—
419#41—221no—
420#41—221no—
421#41—221no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—111no—
428C2×Q8—112no—
429C2×Q8—221no—
430C2×Q8—221no—
431C2×Q8—221no—
432C2×Q8—221no—
433C2×Q8—221no—
434C2×Q8C2×C4×D1111yescharacteristic
435C2×Q8C2×C4×D1112yes—
436C2×D4—21no—
437C2×D4—111no—
438C2×D4—221no—
439C2×D4—441no—
440C2×D4C2×C4×D1111yescharacteristic
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—221no—
444C22×C4—221no—
445C22×C4—221no—
446C22×C4C23×D1111yescharacteristic
447Q16—42no—
448Q16—442no—
449Q16—442no—
450Q16—442no—
451SD16—42no—
452SD16—442no—
453SD16—442no—
454SD16—442no—
455M16—21no—
456M16—21no—
457M16—21no—
458M16—21no—
459M16—221no—
460M16—221no—
461M16—221no—
462M16—221no—
463M16—221no—
464M16—221no—
465M16—221no—
466M16—221no—
467M16—442no—
468M16—442no—
469C2×C8—21no—
470C2×C8—112no—
471C2×C8—221no—
472C2×C8—221no—
473C2×C8—221no—
474C2×C8—442no—
475C2×C8—442no—
476C2×C8C2×C4×D1112yes—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—42no—
481C4⋊C4—221no—
482C4⋊C4—442no—
483C4⋊C4—442no—
484C4⋊C4—441no—
485C4⋊C4—442no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—21no—
489C22⋊C4—221no—
490C22⋊C4—441no—
491C22⋊C4—441no—
492C42—21no—
493C42—21no—
494C42—21no—
495C42—42no—
496C42—111no—
497C42—111no—
498C42—221no—
499C42—221no—
500C42—442no—
501C11#2336011yescharacteristic, complemented, Sylow
502C23—21no—
503C23—221no—
504C23#6703711yescharacteristic
505Q8—22no—
506Q8—21no—
507Q8—22no—
508Q8—21no—
509Q8—41no—
510Q8—41no—
511Q8—222no—
512Q8—221no—
513Q8—222no—
514Q8—221no—
515Q8—441no—
516Q8—441no—
517D4—21no—
518D4—21no—
519D4—41no—
520D4—41no—
521D4—221no—
522D4—221no—
523D4—441no—
524D4—441no—
525D4—882no—
526C2×C4—21no—
527C2×C4—22no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—221no—
536C2×C4—221no—
537C2×C4—221no—
538C2×C4—222no—
539C2×C4—442no—
540C2×C4—441no—
541C2×C4—441no—
542C2×C4—441no—
543C2×C4—441no—
544C2×C4—441no—
545C2×C4C22×C4×D1111yescharacteristic
546C2×C4#6703711yescharacteristic
547C2×C4#6703711yescharacteristic
548C2×C4#6703711yescharacteristic
549C2×C4#6704211yescharacteristic
550C2×C4#6704211yescharacteristic
551C8—22no—
552C8—41no—
553C8—222no—
554C8—441no—
555C8—441no—
556C8—441no—
557C22—41no—
558C22—41no—
559C22—81no—
560C22—441no—
561C22—881no—
562C22#1062307611yescharacteristic
563C22#1062312611yescharacteristic
564C22#1062315111yescharacteristic
565C4—41no—
566C4—42no—
567C4—81no—
568C4—81no—
569C4—81no—
570C4—222no—
571C4—441no—
572C4—441no—
573C4—442no—
574C4—881no—
575C4#1062301711yescharacteristic
576C4#1062307611yescharacteristic
577C4#1062315111yescharacteristic
578C4#1062319711yescharacteristic
579C2—21no—
580C2—21no—
581C2—21no—
582C2—81no—
583C2—881no—
584C2#1307179111yescharacteristic
subgroupG/H
centerC2#13071791
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1905C2
socleC2×C11#2380
prime radical#10623363C22
cosocleC22×C4×C11C24
hypercenter#1905D11
hypocenterC11#23360
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22×C4 ◁ #1905

Complements

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

NH ≅ G/Ntype
2. #13069113C2semidirect
3. #13069111C2semidirect
4. #13069110C2semidirect
5. #13069091C2semidirect
6. #13069088C2semidirect
7. #13069087C2semidirect
8. #13069086C2semidirect
9. #13069009C2semidirect
10. #13069006C2semidirect
13. #13068764C2semidirect
14. #13068763C2semidirect
15. C11×#1905C2semidirect
32. #10622803C4semidirect
33. #10622794C4semidirect
34. #10622788C4semidirect
35. #10622780C4semidirect
214. #1905D11semidirect
501. C11#23360semidirect

Maximal subgroups

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

subgroupindex
#130790712
#130691132
#130691112
#130691102
#130690912
#130690882
#130690872
#130690862
#130690092
#130690062
#130689972
#130689962
#130687642
#130687632
C11×#19052
#2336011