Finite Group Databasebeta

← #14771507

Subgroups — #14771507

Order 2816.

782 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
1C2×#10622474C211yesmaximal, characteristic
2#13071497C211yesmaximal, characteristic
3#13071489C211yesmaximal, characteristic
4#13069354C211yesmaximal, characteristic, complemented
5#13069347C211yesmaximal, characteristic, complemented
6#13069206C211yesmaximal, characteristic, complemented
7#13069199C211yesmaximal, characteristic, complemented
8#13069194C211yesmaximal, characteristic, complemented
9#13069187C211yesmaximal, characteristic, complemented
10#13068710C211yesmaximal, characteristic
11#13068701C211yesmaximal, characteristic
12#13068650C211yesmaximal, characteristic
13#106×Dic11C211yesmaximal, characteristic, complemented
14#13068401C211yesmaximal, characteristic
15C11×#1776C211yesmaximal, characteristic, complemented
16C22×#4313C2211yescharacteristic
17C2×#66945C2211yescharacteristic
18C2×C4⋊C4×D11C2211yescharacteristic
19C2×C11×#107C2211yescharacteristic
20C2×C11×#106C2211yescharacteristic
21C2×C11×#97C2211yescharacteristic
22C4×C11×C4⋊C4C2211yescharacteristic
23C4×C11×C4⋊C4C2211yescharacteristic
24C2×(C2×D11)⋊C8C2211yescharacteristic
25C2×#66882C2211yescharacteristic
26C2×#66881C2211yescharacteristic
27C2×C8×Dic11C2211yescharacteristic
28#10622600C2211yescharacteristic
29#10622600C2211yescharacteristic
30C4⋊C4×Dic11C2211yescharacteristic
31C4⋊C4×Dic11C2211yescharacteristic
32#10622586C2211yescharacteristic
33#10622586C2211yescharacteristic
34C2×#66872C2211yescharacteristic
35C2×#66871C2211yescharacteristic
36#10622553—21no—
37C4×(C2×D11)⋊C4—21no—
38C4×(C2×D11)⋊C4C2211yescharacteristic
39#10622546—21no—
40#10622545—21no—
41#10622541C2211yescharacteristic
42#10622541C2211yescharacteristic
43#10622474C418yescomplemented
44#10622282—21no—
45#10622280—21no—
46#10622265—21no—
47#10622263—21no—
48C11×#340C2211yescharacteristic
49C11×#340C2211yescharacteristic
50#10622189C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60C22×C4×D11—21no—
61C22×C4×D11C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C42×C11—21no—
69C2×C42×C11—21no—
70C2×C42×C11C2311yescharacteristic
71C2×(C2×D11)⋊C4—21no—
72C2×(C2×D11)⋊C4—21no—
73C2×(C2×D11)⋊C4—21no—
74C2×(C2×D11)⋊C4D411yescharacteristic
75C2×(C2×D11)⋊C4D411yescharacteristic
76C2×C4⋊Dic11C2311yescharacteristic
77C2×C4⋊Dic11C2311yescharacteristic
78C2×C4⋊Dic11C2311yescharacteristic
79C2×C4⋊Dic11C2311yescharacteristic
80C2×Dic11⋊C4—21no—
81C2×Dic11⋊C4—21no—
82C2×Dic11⋊C4—21no—
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—21no—
85C2×C4×Dic11—21no—
86C2×C4×Dic11—21no—
87C2×C4×Dic11—21no—
88C2×C4×Dic11C2311yescharacteristic
89C22×C11⋊C8C2311yescharacteristic
90C22×C11⋊C8C2311yescharacteristic
91C2×#4313—22no—
92C2×#4313—22no—
93C2×#4313C2×C414yes—
94#66945—22no—
95#66945C2×C414yes—
96C4⋊C4×D11—22no—
97C4⋊C4×D11C2×C414yes—
98C11×#107—22no—
99C11×#106C2×C414yes—
100C11×#97—22no—
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⋊#95D411yescharacteristic
112C11⋊#95D411yescharacteristic
113(C2×D11)⋊C8—22no—
114#66882C2×C414yes—
115#66881—22no—
116C8×Dic11—22no—
117#66872C2×C414yes—
118#66871C2×C414yes—
119#22621—111nomaximal, Sylow
120C23×D11C2×D411yescharacteristic
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2411yescharacteristic
128C22×Dic11—21no—
129C22×Dic11—21no—
130C22×Dic11—21no—
131C22×Dic11—21no—
132C22×Dic11C2×D411yescharacteristic
133C22×Dic11C2×D411yescharacteristic
134C22×Dic11C2×D411yescharacteristic
135C2×C4×D11—24no—
136C2×C4×D11—21no—
137C2×C4×D11—21no—
138C2×C4×D11—21no—
139C2×C4×D11—21no—
140C2×C4×D11—81no—
141C2×C4×D11—81no—
142C2×C4×D11C22×C412yes—
143C2×C4×D11#4112yes—
144C2×C8×C11—21no—
145C2×C8×C11—21no—
146C2×C8×C11—21no—
147C2×C8×C11C22×C412yes—
148C2×C8×C11#4112yes—
149C2×C8×C11#4112yes—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4C22×C412yes—
157C11×C4⋊C4C22×C412yes—
158C42×C11—21no—
159C42×C11—21no—
160C42×C11—42no—
161C42×C11—81no—
162(C2×D11)⋊C4—22no—
163(C2×D11)⋊C4—24no—
164(C2×D11)⋊C4—41no—
165(C2×D11)⋊C4—42no—
166(C2×D11)⋊C4—81no—
167C4⋊Dic11—21no—
168C4⋊Dic11—21no—
169C4⋊Dic11—21no—
170C4⋊Dic11—21no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11C22×C412yes—
174C4⋊Dic11C22×C412yes—
175Dic11⋊C4—24no—
176Dic11⋊C4—81no—
177Dic11⋊C4—81no—
178Dic11⋊C4—81no—
179Dic11⋊C4—81no—
180C4×Dic11—24no—
181C4×Dic11—21no—
182C4×Dic11—21no—
183C4×Dic11—42no—
184C4×Dic11—81no—
185C2×C11⋊C8—21no—
186C2×C11⋊C8—21no—
187C2×C11⋊C8—21no—
188C2×C11⋊C8—21no—
189C2×C11⋊C8—21no—
190C2×C11⋊C8C22×C412yes—
191#4313—28no—
192C2×#428—111no—
193#2346—111no—
194#2345—111no—
195#1943—111no—
196#1942—111no—
197#1921—111no—
198#1920—111no—
199#1919—111no—
200#1918—111no—
201#1825—111no—
202#1823—111no—
203#1809—111no—
204#1776D1111yescharacteristic, complemented
205C4×#106—111no—
206#1753—111no—
207C23×C11C22×D411yescharacteristic
208C22×D11—21no—
209C22×D11—21no—
210C22×D11—21no—
211C22×D11—21no—
212C22×D11—21no—
213C22×D11—21no—
214C22×D11C4×D412yes—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—21no—
218C2×C4×C11—21no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—41no—
224C2×C4×C11—41no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11C23×C411yescharacteristic
234C2×C4×C11C2×#4111yescharacteristic
235C2×C4×C11C2×#4111yescharacteristic
236C2×C4×C11C2×#4111yescharacteristic
237C2×C4×C112−1+411yescharacteristic
238C2×C4×C112−1+411yescharacteristic
239C2×Dic11—21no—
240C2×Dic11—21no—
241C2×Dic11—21no—
242C2×Dic11—21no—
243C2×Dic11—22no—
244C2×Dic11—22no—
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—21no—
248C2×Dic11—41no—
249C2×Dic11—41no—
250C2×Dic11—41no—
251C2×Dic11—41no—
252C2×Dic11—41no—
253C2×Dic11—41no—
254C2×Dic11—41no—
255C2×Dic11—41no—
256C2×Dic11—41no—
257C2×Dic11—41no—
258C2×Dic11C4×D412yes—
259C2×Dic11#13712yes—
260C4×D11—22no—
261C4×D11—22no—
262C4×D11—22no—
263C4×D11—22no—
264C4×D11—84no—
265C8×C11—41no—
266C8×C11#11714yes—
267C11⋊C8—22no—
268C11⋊C8—41no—
269C22×M16—111no—
270C2×#117—111no—
271C22×C4⋊C4—111no—
272#428—118no—
273C2×#107—111no—
274C2×#107—111no—
275C2×#107C2×D1111yescharacteristic
276C2×#106—111no—
277C2×#106—111no—
278C2×#106C2×D1111yescharacteristic
279C2×C22⋊C8—111no—
280C2×#97C2×D1111yescharacteristic
281C2×C4×C8—111no—
282#389—111no—
283#389—111no—
284#389—111no—
285#389—111no—
286#388—221no—
287#388—221no—
288#387—221no—
289#387—221no—
290#382—221no—
291#380—111no—
292#380—111no—
293#380—221no—
294C4×C4⋊C4—111no—
295C4×C4⋊C4—111no—
296C4×C4⋊C4C2×D1111yescharacteristic
297C4×C4⋊C4C2×D1111yescharacteristic
298C4×C22⋊C4—111no—
299C4×C22⋊C4—221no—
300#376—221no—
301#340—111no—
302#340—111no—
303#340—111no—
304#340—111no—
305#340—111no—
306#340—111no—
307#340—111no—
308#340—111no—
309#340C2×D1111yescharacteristic
310#340C2×D1111yescharacteristic
311#336—111no—
312#336—111no—
313C22×C11C2×C4×D411yescharacteristic
314C22×C11#54711yescharacteristic
315C22×C11#54711yescharacteristic
316C22×C11C2×#13711yescharacteristic
317C22×C11#57511yescharacteristic
318C22×C11#57611yescharacteristic
319C22×C11#57711yescharacteristic
320C2×D11—22no—
321C2×D11—22no—
322C2×D11—22no—
323C2×D11—41no—
324C2×D11—41no—
325C2×D11—41no—
326C2×D11—41no—
327C4×C11—41no—
328C4×C11—41no—
329C4×C11—42no—
330C4×C11—42no—
331C4×C11—81no—
332C4×C11—81no—
333C4×C11C2×#11711yescharacteristic
334C4×C11#51911yescharacteristic
335C4×C11#55211yescharacteristic
336C4×C11#55211yescharacteristic
337Dic11—22no—
338Dic11—22no—
339Dic11—41no—
340Dic11—42no—
341Dic11—42no—
342Dic11—81no—
343Dic11—81no—
344C23×C4—111no—
345C23×C4—221no—
346C2×M16—114no—
347C2×M16—222no—
348C2×M16—222no—
349C22×C8—111no—
350C22×C8—111no—
351C22×C8C22×D1111yescharacteristic
352C22×C8C22×D1111yescharacteristic
353#117—114no—
354#117—222no—
355C2×C4⋊C4—111no—
356C2×C4⋊C4—111no—
357C2×C4⋊C4—114no—
358C2×C4⋊C4—111no—
359C2×C4⋊C4—111no—
360C2×C4⋊C4—222no—
361C2×C4⋊C4—221no—
362C2×C4⋊C4—221no—
363C2×C4⋊C4—221no—
364C2×C4⋊C4—221no—
365C2×C4⋊C4—221no—
366C2×C4⋊C4C22×D1111yescharacteristic
367C2×C4⋊C4C22×D1111yescharacteristic
368C2×C4⋊C4C22×D1111yescharacteristic
369C2×C4⋊C4C22×D1111yescharacteristic
370C2×C22⋊C4—111no—
371C2×C22⋊C4—111no—
372C2×C22⋊C4—221no—
373C2×C22⋊C4—221no—
374C2×C22⋊C4—221no—
375C2×C42—21no—
376C2×C42—21no—
377C2×C42—111no—
378C2×C42—221no—
379C2×C42—221no—
380C2×C42—221no—
381C2×C42C22×D1111yescharacteristic
382#107—22no—
383#107—114no—
384#107—114no—
385#106—114no—
386#106—222no—
387#106C4×D1114yes—
388C22⋊C8—222no—
389#97—22no—
390C4×C8—222no—
391#95—21no—
392#95—21no—
393#95—111no—
394#95—111no—
395#95—221no—
396#95—221no—
397#95—221no—
398#95—221no—
399#95—221no—
400#95—221no—
401#95—221no—
402#95—221no—
403C2×C11#234411yescharacteristic
404C2×C11C4×#13711yescharacteristic
405C2×C11#294611yescharacteristic
406C2×C11#334411yescharacteristic
407C2×C11#334711yescharacteristic
408C2×C11#335111yescharacteristic
409C2×C11#335711yescharacteristic
410D11—42no—
411C24—111no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—111no—
417C22×C4—111no—
418C22×C4—112no—
419C22×C4—112no—
420C22×C4—111no—
421C22×C4—224no—
422C22×C4—221no—
423C22×C4—221no—
424C22×C4—221no—
425C22×C4—221no—
426C22×C4—221no—
427C22×C4—221no—
428C22×C4—221no—
429C22×C4—221no—
430C22×C4—881no—
431C22×C4—881no—
432C22×C4D4×D1111yescharacteristic
433C22×C4D4×D1111yescharacteristic
434C22×C4C23×D1111yescharacteristic
435M16—228no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—112no—
440C2×C8—221no—
441C2×C8—221no—
442C2×C8—221no—
443C2×C8—221no—
444C2×C8—221no—
445C2×C8C2×C4×D1112yes—
446C2×C8#433912yes—
447C2×C8#433912yes—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—112no—
455C4⋊C4—112no—
456C4⋊C4—224no—
457C4⋊C4—221no—
458C4⋊C4—221no—
459C4⋊C4—221no—
460C4⋊C4—221no—
461C4⋊C4—221no—
462C4⋊C4—221no—
463C4⋊C4—881no—
464C4⋊C4—881no—
465C4⋊C4—881no—
466C4⋊C4—881no—
467C4⋊C4C2×C4×D1112yes—
468C4⋊C4C2×C4×D1112yes—
469C22⋊C4—222no—
470C22⋊C4—224no—
471C22⋊C4—441no—
472C22⋊C4—442no—
473C22⋊C4—881no—
474C42—21no—
475C42—21no—
476C42—42no—
477C42—81no—
478C42—224no—
479C42—221no—
480C42—221no—
481C42—442no—
482C42—881no—
483C11#2262111yescharacteristic, complemented, Sylow
484C23—112no—
485C23—221no—
486C23—221no—
487C23—221no—
488C23—221no—
489C23—221no—
490C23—221no—
491C23C2×D4×D1111yescharacteristic
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—112no—
511C2×C4—112no—
512C2×C4—221no—
513C2×C4—221no—
514C2×C4—221no—
515C2×C4—221no—
516C2×C4—222no—
517C2×C4—222no—
518C2×C4—222no—
519C2×C4—222no—
520C2×C4—221no—
521C2×C4—221no—
522C2×C4—222no—
523C2×C4—222no—
524C2×C4—221no—
525C2×C4—441no—
526C2×C4—441no—
527C2×C4—441no—
528C2×C4—441no—
529C2×C4—441no—
530C2×C4—441no—
531C2×C4—441no—
532C2×C4—441no—
533C2×C4—441no—
534C2×C4—441no—
535C2×C4—884no—
536C2×C4C22×C4×D1111yescharacteristic
537C2×C4C2×#433911yescharacteristic
538C2×C4C2×#433911yescharacteristic
539C2×C4#6704011yescharacteristic
540C2×C4#41×D1111yescharacteristic
541C2×C4#6704311yescharacteristic
542C8—41no—
543C8—222no—
544C8—441no—
545C8#6692514yes—
546C22—222no—
547C22—222no—
548C22—222no—
549C22—441no—
550C22—441no—
551C22—441no—
552C22—441no—
553C22#1062303811yescharacteristic
554C22C4×D4×D1111yescharacteristic
555C22#1062308211yescharacteristic
556C22#1062330411yescharacteristic
557C22#1062330511yescharacteristic
558C22D11×#13711yescharacteristic
559C22#1062330911yescharacteristic
560C4—41no—
561C4—41no—
562C4—42no—
563C4—42no—
564C4—81no—
565C4—81no—
566C4—222no—
567C4—222no—
568C4—441no—
569C4—442no—
570C4—442no—
571C4—881no—
572C4—881no—
573C4C2×#6692511yescharacteristic
574C4#1062306011yescharacteristic
575C4#1062310311yescharacteristic
576C4#1062311211yescharacteristic
577C2—442no—
578C2#1307148111yescharacteristic
579C2#1307743811yescharacteristic
580C2#1307744711yescharacteristic
581C2#1308107611yescharacteristic
582C2#1308112111yescharacteristic
583C2#1308117211yescharacteristic
584C2#1308123811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1776C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1776D11
hypocenterC11#22621
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1776

Complements

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

NH ≅ G/Ntype
4. #13069354C2semidirect
5. #13069347C2semidirect
6. #13069206C2semidirect
7. #13069199C2semidirect
8. #13069194C2semidirect
9. #13069187C2semidirect
13. #106×Dic11C2semidirect
15. C11×#1776C2semidirect
43. #10622474C4semidirect
204. #1776D11semidirect
483. C11#22621semidirect

Maximal subgroups

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

subgroupindex
C2×#106224742
#130714972
#130714892
#130693542
#130693472
#130692062
#130691992
#130691942
#130691872
#130687102
#130687012
#130686502
#106×Dic112
#130684012
C11×#17762
#2262111