Finite Group Databasebeta

← #14811848

Subgroups — #14811848

Order 2816.

696 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13072343C211yesmaximal, characteristic
2#13071497C211yesmaximal, characteristic
3#13070183C211yesmaximal, characteristic, complemented
4#13070115C211yesmaximal, characteristic, complemented
5#13070114C211yesmaximal, characteristic, complemented
6#13069952C211yesmaximal, characteristic, complemented
7#13069572C211yesmaximal, characteristic, complemented
8#13069194C211yesmaximal, characteristic, complemented
9#13069193C211yesmaximal, characteristic, complemented
10#13068807C211yesmaximal, characteristic
11#13068797C211yesmaximal, characteristic
12#13068710C211yesmaximal, characteristic
13#13068650C211yesmaximal, characteristic
14#13068334C211yesmaximal, characteristic
15C11×#1949C211yesmaximal, characteristic, complemented
16C22×#4313C2211yescharacteristic
17C2×#66945C2211yescharacteristic
18C2×C4⋊C4×D11C2211yescharacteristic
19C2×#66943C2211yescharacteristic
20C2×C11×#107C2211yescharacteristic
21C2×C11×#106C2211yescharacteristic
22C2×C11×C4⋊C8C2211yescharacteristic
23C11×#382C2211yescharacteristic
24C4×C11×C4⋊C4C2211yescharacteristic
25C2×(C2×D11)⋊C8C2211yescharacteristic
26C2×#66881C2211yescharacteristic
27C2×Dic11⋊C8C2211yescharacteristic
28#10622600C2211yescharacteristic
29#10622600C2211yescharacteristic
30C4⋊C4×Dic11C2211yescharacteristic
31#10622586C2211yescharacteristic
32#10622586C2211yescharacteristic
33C2×#66872C2211yescharacteristic
34#10622553—21no—
35C4×(C2×D11)⋊C4C2211yescharacteristic
36#10622545—21no—
37#10622541C2211yescharacteristic
38#10622541C2211yescharacteristic
39#10622282—21no—
40#10622281—21no—
41#10622280—21no—
42#10622271—21no—
43#10622270—21no—
44#10622263—21no—
45C11×#340C2211yescharacteristic
46C11×#340C2211yescharacteristic
47#10622189C2211yescharacteristic
48#10622189C2211yescharacteristic
49#10622189C2211yescharacteristic
50#10622188C2211yescharacteristic
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×C4×D11—21no—
60C22×C4×D11C2311yescharacteristic
61C22×C8×C11C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C2×C11×C4⋊C4C2311yescharacteristic
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C42×C11—21no—
68C2×C42×C11C2311yescharacteristic
69C2×(C2×D11)⋊C4—21no—
70C2×(C2×D11)⋊C4—21no—
71C2×(C2×D11)⋊C4—21no—
72C2×(C2×D11)⋊C4D411yescharacteristic
73C2×(C2×D11)⋊C4D411yescharacteristic
74C2×C4⋊Dic11—21no—
75C2×C4⋊Dic11C2311yescharacteristic
76C2×C4⋊Dic11C2311yescharacteristic
77C2×C4⋊Dic11C2311yescharacteristic
78C2×C4⋊Dic11C2311yescharacteristic
79C2×Dic11⋊C4—21no—
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×Dic11C2311yescharacteristic
88C22×C11⋊C8C2311yescharacteristic
89C22×C11⋊C8C2311yescharacteristic
90C2×#4313—22no—
91C2×#4313—22no—
92C2×#4313—41no—
93#66945—22no—
94#66945Q814yes—
95C4⋊C4×D11—22no—
96C4⋊C4×D11—41no—
97#66943—22no—
98#66943—41no—
99C11×#107—41no—
100C11×#106—41no—
101C11×C4⋊C8—22no—
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(C2×D11)⋊C8—22no—
115#66881—22no—
116Dic11⋊C8—41no—
117#66872—22no—
118#26019—111nomaximal, Sylow
119C23×D11C2×D411yescharacteristic
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2411yescharacteristic
127C22×Dic11—21no—
128C22×Dic11—21no—
129C22×Dic11—21no—
130C22×Dic11—21no—
131C22×Dic11C2×D411yescharacteristic
132C22×Dic11C2×D411yescharacteristic
133C22×Dic11C2×D411yescharacteristic
134C2×C4×D11—21no—
135C2×C4×D11—21no—
136C2×C4×D11—21no—
137C2×C4×D11—21no—
138C2×C4×D11—42no—
139C2×C4×D11—42no—
140C2×C4×D11—81no—
141C2×C4×D11C2×Q812yes—
142C2×C4×D11#4112yes—
143C2×C8×C11—21no—
144C2×C8×C11—21no—
145C2×C8×C11—21no—
146C2×C8×C11—21no—
147C2×C8×C11—21no—
148C2×C8×C11#4112yes—
149C11×C4⋊C4—21no—
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⋊C4C2×Q812yes—
157C42×C11—21no—
158C42×C11—21no—
159C42×C11—42no—
160(C2×D11)⋊C4—24no—
161(C2×D11)⋊C4—41no—
162(C2×D11)⋊C4—41no—
163(C2×D11)⋊C4—42no—
164(C2×D11)⋊C4—81no—
165C4⋊Dic11—21no—
166C4⋊Dic11—21no—
167C4⋊Dic11—21no—
168C4⋊Dic11—21no—
169C4⋊Dic11—21no—
170C4⋊Dic11—21no—
171C4⋊Dic11—42no—
172C4⋊Dic11C2×Q812yes—
173C4⋊Dic11#4112yes—
174Dic11⋊C4—42no—
175Dic11⋊C4—42no—
176Dic11⋊C4—81no—
177Dic11⋊C4—81no—
178Dic11⋊C4—81no—
179Dic11⋊C4—81no—
180C4×Dic11—24no—
181C4×Dic11—21no—
182C4×Dic11—21no—
183C4×Dic11—42no—
184C2×C11⋊C8—21no—
185C2×C11⋊C8—21no—
186C2×C11⋊C8—21no—
187C2×C11⋊C8—21no—
188C2×C11⋊C8—21no—
189C2×C11⋊C8—21no—
190#4313—44no—
191#2442—111no—
192#2346—111no—
193#2101—111no—
194#2088—111no—
195#2088—111no—
196#2059—111no—
197#1989—111no—
198#1949D1111yescharacteristic, complemented
199#1919—111no—
200#1919—111no—
201#1853—111no—
202#1851—111no—
203#1825—111no—
204#1809—111no—
205#1736—111no—
206C23×C11C22×D411yescharacteristic
207C22×D11—21no—
208C22×D11—21no—
209C22×D11—21no—
210C22×D11—21no—
211C22×D11—21no—
212C22×D11—21no—
213C22×D11C22⋊Q812yes—
214C2×C4×C11—22no—
215C2×C4×C11—21no—
216C2×C4×C11—21no—
217C2×C4×C11—21no—
218C2×C4×C11—21no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—41no—
222C2×C4×C11—41no—
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×C11C22×Q811yescharacteristic
233C2×C4×C11C2×#4111yescharacteristic
234C2×C4×C11C2×#4111yescharacteristic
235C2×C4×C11C2×#4111yescharacteristic
236C2×C4×C11H(5,𝔽2)11yescharacteristic
237C2×C4×C112−1+411yescharacteristic
238C2×Dic11—21no—
239C2×Dic11—21no—
240C2×Dic11—22no—
241C2×Dic11—21no—
242C2×Dic11—21no—
243C2×Dic11—22no—
244C2×Dic11—21no—
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×Dic11C22⋊Q812yes—
259C4×D11—22no—
260C4×D11—22no—
261C4×D11—22no—
262C4×D11—22no—
263C4×D11—84no—
264C8×C11—22no—
265C8×C11—41no—
266C11⋊C8—41no—
267C11⋊C8—41no—
268C22×M16—111no—
269C2×#125—111no—
270C2×#117—111no—
271C22×C4⋊C4—111no—
272C2×#107C2×D1111yescharacteristic
273C2×#106—111no—
274C2×#106—111no—
275C2×#106C2×D1111yescharacteristic
276C2×C4⋊C8—111no—
277C2×C4⋊C8C2×D1111yescharacteristic
278C2×C22⋊C8—111no—
279#400—221no—
280#398—221no—
281#389—111no—
282#389—111no—
283#389—111no—
284#389—111no—
285#388—221no—
286#388—221no—
287#385—221no—
288#382—221no—
289#382C2×D1111yescharacteristic
290#380—111no—
291#380—111no—
292#380—221no—
293C4×C4⋊C4—111no—
294C4×C4⋊C4C2×D1111yescharacteristic
295C4×C22⋊C4—111no—
296#376—221no—
297#340—111no—
298#340—111no—
299#340—111no—
300#340—111no—
301#340—111no—
302#340—111no—
303#340—111no—
304#340—111no—
305#340—111no—
306#340—111no—
307#340C2×D1111yescharacteristic
308#340C2×D1111yescharacteristic
309#336—111no—
310#336—111no—
311C22×C11C2×C22⋊Q811yescharacteristic
312C22×C11#54611yescharacteristic
313C22×C11#54711yescharacteristic
314C22×C11#57511yescharacteristic
315C22×C11#57511yescharacteristic
316C22×C11#57711yescharacteristic
317C22×C11#57711yescharacteristic
318C2×D11—22no—
319C2×D11—22no—
320C2×D11—22no—
321C2×D11—41no—
322C2×D11—41no—
323C2×D11—41no—
324C2×D11—41no—
325C4×C11—42no—
326C4×C11—41no—
327C4×C11—41no—
328C4×C11—81no—
329C4×C11—81no—
330C4×C11—81no—
331C4×C11#53311yescharacteristic
332C4×C11#54411yescharacteristic
333C4×C11#55111yescharacteristic
334C4×C11#55211yescharacteristic
335Dic11—22no—
336Dic11—42no—
337Dic11—41no—
338Dic11—42no—
339Dic11—41no—
340Dic11—81no—
341Dic11—81no—
342C23×C4—111no—
343C23×C4—221no—
344C2×M16—222no—
345C2×M16—222no—
346C2×M16—441no—
347C22×C8—111no—
348C22×C8—111no—
349C22×C8C22×D1111yescharacteristic
350C22×C8C22×D1111yescharacteristic
351#125—222no—
352#125—441no—
353#117—114no—
354#117—222no—
355C2×C4⋊C4—111no—
356C2×C4⋊C4—111no—
357C2×C4⋊C4—111no—
358C2×C4⋊C4—111no—
359C2×C4⋊C4—222no—
360C2×C4⋊C4—221no—
361C2×C4⋊C4—221no—
362C2×C4⋊C4—221no—
363C2×C4⋊C4—221no—
364C2×C4⋊C4—221no—
365C2×C4⋊C4—221no—
366C2×C4⋊C4—221no—
367C2×C4⋊C4—441no—
368C2×C4⋊C4C22×D1111yescharacteristic
369C2×C4⋊C4C22×D1111yescharacteristic
370C2×C4⋊C4C22×D1111yescharacteristic
371C2×C4⋊C4C22×D1111yescharacteristic
372C2×C22⋊C4—111no—
373C2×C22⋊C4—111no—
374C2×C22⋊C4—221no—
375C2×C22⋊C4—221no—
376C2×C22⋊C4—221no—
377C2×C42—21no—
378C2×C42—111no—
379C2×C42—221no—
380C2×C42—221no—
381C2×C42C22×D1111yescharacteristic
382#107—41no—
383#106—41no—
384#106—222no—
385#106—222no—
386C4⋊C8—22no—
387C4⋊C8—441no—
388C22⋊C8—222no—
389#95—21no—
390#95—21no—
391#95—21no—
392#95—111no—
393#95—111no—
394#95—221no—
395#95—221no—
396#95—221no—
397#95—221no—
398#95—221no—
399#95—221no—
400#95—221no—
401C2×C11#243811yescharacteristic
402C2×C11#308011yescharacteristic
403C2×C11#308411yescharacteristic
404C2×C11#332111yescharacteristic
405C2×C11#332311yescharacteristic
406C2×C11#334811yescharacteristic
407C2×C11#335111yescharacteristic
408D11—42no—
409C24—111no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—111no—
415C22×C4—112no—
416C22×C4—112no—
417C22×C4—111no—
418C22×C4—111no—
419C22×C4—221no—
420C22×C4—221no—
421C22×C4—221no—
422C22×C4—221no—
423C22×C4—221no—
424C22×C4—221no—
425C22×C4—221no—
426C22×C4—221no—
427C22×C4—442no—
428C22×C4—442no—
429C22×C4—881no—
430C22×C4D4×D1111yescharacteristic
431C22×C4D4×D1111yescharacteristic
432C22×C4C23×D1111yescharacteristic
433M16—444no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—221no—
440C2×C8—221no—
441C2×C8—221no—
442C2×C8—221no—
443C2×C8—221no—
444C2×C8—221no—
445C2×C8#433912yes—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—112no—
454C4⋊C4—112no—
455C4⋊C4—221no—
456C4⋊C4—221no—
457C4⋊C4—221no—
458C4⋊C4—221no—
459C4⋊C4—221no—
460C4⋊C4—221no—
461C4⋊C4—442no—
462C4⋊C4—442no—
463C4⋊C4—442no—
464C4⋊C4—881no—
465C4⋊C4—881no—
466C4⋊C4—881no—
467C4⋊C4—881no—
468C4⋊C4Q8×D1112yes—
469C22⋊C4—224no—
470C22⋊C4—441no—
471C22⋊C4—441no—
472C22⋊C4—442no—
473C22⋊C4—881no—
474C42—21no—
475C42—21no—
476C42—42no—
477C42—224no—
478C42—221no—
479C42—221no—
480C42—442no—
481C11#2601911yescharacteristic, complemented, Sylow
482C23—112no—
483C23—221no—
484C23—221no—
485C23—221no—
486C23—221no—
487C23—221no—
488C23—221no—
489C23C2×D4×D1111yescharacteristic
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—22no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
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—112no—
509C2×C4—221no—
510C2×C4—221no—
511C2×C4—222no—
512C2×C4—222no—
513C2×C4—222no—
514C2×C4—222no—
515C2×C4—221no—
516C2×C4—221no—
517C2×C4—221no—
518C2×C4—221no—
519C2×C4—221no—
520C2×C4—221no—
521C2×C4—222no—
522C2×C4—222no—
523C2×C4—441no—
524C2×C4—441no—
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—884no—
534C2×C4C2×#433911yescharacteristic
535C2×C4#6703711yescharacteristic
536C2×C4C2×Q8×D1111yescharacteristic
537C2×C4#6704011yescharacteristic
538C2×C4#41×D1111yescharacteristic
539C2×C4#41×D1111yescharacteristic
540C8—22no—
541C8—41no—
542C8—441no—
543C8—441no—
544C22—222no—
545C22—222no—
546C22—222no—
547C22—441no—
548C22—441no—
549C22—441no—
550C22—441no—
551C22#1062303811yescharacteristic
552C22#1062314311yescharacteristic
553C22D11×C22⋊Q811yescharacteristic
554C22#1062329911yescharacteristic
555C22#1062330111yescharacteristic
556C22#1062330411yescharacteristic
557C22#1062330911yescharacteristic
558C4—41no—
559C4—41no—
560C4—42no—
561C4—81no—
562C4—81no—
563C4—81no—
564C4—222no—
565C4—441no—
566C4—442no—
567C4—442no—
568C4—441no—
569C4—881no—
570C4—881no—
571C4#1062308711yescharacteristic
572C4#1062310911yescharacteristic
573C4#1062322411yescharacteristic
574C4#1062326011yescharacteristic
575C2—442no—
576C2#1307229911yescharacteristic
577C2#1307843311yescharacteristic
578C2#1307848111yescharacteristic
579C2#1308080911yescharacteristic
580C2#1308083911yescharacteristic
581C2#1308112711yescharacteristic
582C2#1308117211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1949C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenter#1949D11
hypocenterC11#26019
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1949

Complements

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

NH ≅ G/Ntype
3. #13070183C2semidirect
4. #13070115C2semidirect
5. #13070114C2semidirect
6. #13069952C2semidirect
7. #13069572C2semidirect
8. #13069194C2semidirect
9. #13069193C2semidirect
15. C11×#1949C2semidirect
198. #1949D11semidirect
481. C11#26019semidirect

Maximal subgroups

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

subgroupindex
#130723432
#130714972
#130701832
#130701152
#130701142
#130699522
#130695722
#130691942
#130691932
#130688072
#130687972
#130687102
#130686502
#130683342
C11×#19492
#2601911