Finite Group Databasebeta

← #14826898

Subgroups — #14826898

Order 2816.

672 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073014C211yesmaximal, characteristic
2#13071648C211yesmaximal, characteristic
3#13070034C211yesmaximal, characteristic, complemented
4#13069818C211yesmaximal, characteristic
5#13069811C211yesmaximal, characteristic
6#13069386C211yesmaximal, characteristic, complemented
7#13069352C211yesmaximal, characteristic, complemented
8#13069228C211yesmaximal, characteristic
9#13069205C211yesmaximal, characteristic, complemented
10#13069200C211yesmaximal, characteristic, complemented
11#13068868C211yesmaximal, characteristic, complemented
12#13068814C211yesmaximal, characteristic
13#13068710C211yesmaximal, characteristic
14#13068448C211yesmaximal, characteristic, complemented
15C11×#2066C211yesmaximal, characteristic, complemented
16C2×#66999C2211yescharacteristic
17C2×Q8×Dic11C2211yescharacteristic
18C2×#66945C2211yescharacteristic
19C2×C11×#106C2211yescharacteristic
20C2×C11×C4⋊C8C2211yescharacteristic
21C2×C11×#103C2211yescharacteristic
22C2×C11×#103C2211yescharacteristic
23C11×#391C2211yescharacteristic
24C11×#389C2211yescharacteristic
25C2×#66899C2211yescharacteristic
26C2×#66899C2211yescharacteristic
27C2×(C2×D11)⋊C8C2211yescharacteristic
28C2×(C2×D11)⋊C8C2211yescharacteristic
29C2×#66882C2211yescharacteristic
30C2×#66881C2211yescharacteristic
31C2×#66879C2211yescharacteristic
32#10622606—21no—
33#10622600C2211yescharacteristic
34#10622600C2211yescharacteristic
35#10622591—21no—
36C4⋊C4×Dic11C2211yescharacteristic
37#10622586C2211yescharacteristic
38#10622586C2211yescharacteristic
39C2×#66871C2211yescharacteristic
40C4×(C2×D11)⋊C4C2211yescharacteristic
41#10622549C2211yescharacteristic
42C4×C4⋊Dic11C2211yescharacteristic
43#10622283—21no—
44#10622282—21no—
45#10622282—21no—
46C11⋊#401—21no—
47#10622268—21no—
48#10622262—21no—
49C11×#340C2211yescharacteristic
50#10622189C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×Q8×C11C2311yescharacteristic
60C22×C4×D11C2311yescharacteristic
61C22×C8×C11C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C42×C11C2311yescharacteristic
68#66999—22no—
69#66999—22no—
70Q8×Dic11—22no—
71Q8×Dic11—41no—
72C2×(C2×D11)⋊C4—21no—
73C2×(C2×D11)⋊C4—21no—
74C2×(C2×D11)⋊C4—21no—
75C2×(C2×D11)⋊C4—21no—
76C2×(C2×D11)⋊C4D411yescharacteristic
77C2×(C2×D11)⋊C4D411yescharacteristic
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11C2311yescharacteristic
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2311yescharacteristic
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—21no—
86C2×C4×Dic11—21no—
87C2×C4×Dic11—21no—
88C2×C4×Dic11—21no—
89C2×C4×Dic11—21no—
90C2×C4×Dic11C2311yescharacteristic
91C22×C11⋊C8C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93#66945—22no—
94#66945—41no—
95C11×#106—41no—
96C11×C4⋊C8—22no—
97C11×#103—22no—
98C11×#103—41no—
99C11×#95—21no—
100C11×#95—21no—
101C11×#95—21no—
102#66899—22no—
103#66899—22no—
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(C2×D11)⋊C8—41no—
116#66882—22no—
117#66881—22no—
118#66879—41no—
119#66871—22no—
120#27061—111nomaximal, Sylow
121C23×D11C2×D411yescharacteristic
122C2×Q8×C11—21no—
123C2×Q8×C11—21no—
124C2×Q8×C11—21no—
125C2×Q8×C11—21no—
126C2×Q8×C11—21no—
127C2×Q8×C11#4112yes—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2411yescharacteristic
135C22×Dic11—21no—
136C22×Dic11—21no—
137C22×Dic11—21no—
138C22×Dic11—21no—
139C22×Dic11C2×D411yescharacteristic
140C22×Dic11C2×D411yescharacteristic
141C22×Dic11C2×D411yescharacteristic
142C2×C4×D11—21no—
143C2×C4×D11—21no—
144C2×C4×D11—21no—
145C2×C4×D11—21no—
146C2×C4×D11—21no—
147C2×C4×D11—21no—
148C2×C8×C11—21no—
149C2×C8×C11—21no—
150C2×C8×C11—21no—
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11#4112yes—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—81no—
161C42×C11—21no—
162C42×C11—21no—
163(C2×D11)⋊C4—24no—
164(C2×D11)⋊C4—41no—
165(C2×D11)⋊C4—41no—
166(C2×D11)⋊C4—42no—
167(C2×D11)⋊C4—42no—
168(C2×D11)⋊C4—81no—
169C4⋊Dic11—21no—
170C4⋊Dic11—21no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11—42no—
176C4⋊Dic11#4112yes—
177C4⋊Dic11#4112yes—
178Dic11⋊C4—24no—
179Dic11⋊C4—42no—
180Dic11⋊C4—42no—
181C4×Dic11—21no—
182C4×Dic11—21no—
183C4×Dic11—42no—
184C4×Dic11—42no—
185C4×Dic11—42no—
186C4×Dic11—81no—
187C2×C11⋊C8—21no—
188C2×C11⋊C8—21no—
189C2×C11⋊C8—21no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—21no—
192C2×C11⋊C8—21no—
193#2494—111no—
194#2362—111no—
195#2074—111no—
196#2066D1111yescharacteristic, complemented
197#2036—111no—
198#2035—111no—
199#1949—111no—
200#1943—111no—
201#1924—111no—
202#1921—111no—
203#1920—111no—
204#1863—111no—
205#1854—111no—
206#1825—111no—
207#1763—111no—
208C23×C11C22×D411yescharacteristic
209C22×D11—21no—
210C22×D11—21no—
211C22×D11—21no—
212C22×D11—21no—
213C22×D11—21no—
214C22×D11—21no—
215C22×D11—21no—
216Q8×C11—22no—
217Q8×C11—22no—
218Q8×C11—41no—
219Q8×C11—41no—
220C2×C4×C11—22no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
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×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11C2×#4111yescharacteristic
239C2×C4×C11C2×#4111yescharacteristic
240C2×C4×C11C2×#4111yescharacteristic
241C2×C4×C11C2×#4111yescharacteristic
242C2×C4×C11H(5,𝔽2)11yescharacteristic
243C2×C4×C112−1+411yescharacteristic
244C2×Dic11—21no—
245C2×Dic11—22no—
246C2×Dic11—21no—
247C2×Dic11—21no—
248C2×Dic11—22no—
249C2×Dic11—21no—
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11—21no—
254C2×Dic11—21no—
255C2×Dic11—41no—
256C2×Dic11—41no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265C4×D11—41no—
266C4×D11—41no—
267C4×D11—41no—
268C4×D11—41no—
269C8×C11—22no—
270C8×C11—41no—
271C11⋊C8—41no—
272C11⋊C8—41no—
273C2×C22⋊Q8—111no—
274C2×C4×Q8—111no—
275C2×#117—111no—
276C2×#107—111no—
277C2×#107—111no—
278C2×#106—111no—
279C2×#106C2×D1111yescharacteristic
280C2×C4⋊C8C2×D1111yescharacteristic
281C2×#103—111no—
282C2×#103—111no—
283C2×#103C2×D1111yescharacteristic
284C2×#103C2×D1111yescharacteristic
285C2×C22⋊C8—111no—
286C2×C22⋊C8—111no—
287C2×#97—111no—
288#401—221no—
289#397—221no—
290#391C2×D1111yescharacteristic
291#389—111no—
292#389—111no—
293#389C2×D1111yescharacteristic
294#388—221no—
295#388—221no—
296#388—221no—
297#387—221no—
298#387—221no—
299#382—111no—
300#380—111no—
301#380—111no—
302C4×C4⋊C4—111no—
303C4×C4⋊C4—111no—
304C4×C4⋊C4—221no—
305C4×C22⋊C4—111no—
306#340—111no—
307#340—111no—
308#340—111no—
309#340—111no—
310#340—111no—
311#340—111no—
312#340—111no—
313#340C2×D1111yescharacteristic
314#336—111no—
315#336—111no—
316C22×C11#52511yescharacteristic
317C22×C11#54611yescharacteristic
318C22×C11#54711yescharacteristic
319C22×C11#57511yescharacteristic
320C22×C11#57511yescharacteristic
321C22×C11#57711yescharacteristic
322C22×C11#57811yescharacteristic
323C2×D11—41no—
324C2×D11—41no—
325C2×D11—41no—
326C2×D11—41no—
327C2×D11—41no—
328C2×D11—41no—
329C2×D11—41no—
330C4×C11—41no—
331C4×C11—41no—
332C4×C11—42no—
333C4×C11—81no—
334C4×C11—81no—
335C4×C11—81no—
336C4×C11#52911yescharacteristic
337C4×C11#53911yescharacteristic
338C4×C11#55311yescharacteristic
339C4×C11#55611yescharacteristic
340Dic11—42no—
341Dic11—41no—
342Dic11—41no—
343Dic11—42no—
344Dic11—41no—
345Dic11—81no—
346Dic11—81no—
347C22×Q8C22×D1111yescharacteristic
348C23×C4—111no—
349C22×C8—111no—
350C22×C8—111no—
351C22×C8C22×D1111yescharacteristic
352C22×C8C22×D1111yescharacteristic
353C22⋊Q8—222no—
354C22⋊Q8—222no—
355C4×Q8—222no—
356C4×Q8—441no—
357#117—222no—
358#117—441no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—111no—
361C2×C4⋊C4—111no—
362C2×C4⋊C4—111no—
363C2×C4⋊C4—111no—
364C2×C4⋊C4—221no—
365C2×C4⋊C4—221no—
366C2×C4⋊C4—221no—
367C2×C4⋊C4—221no—
368C2×C4⋊C4C22×D1111yescharacteristic
369C2×C4⋊C4C22×D1111yescharacteristic
370C2×C4⋊C4C22×D1111yescharacteristic
371C2×C22⋊C4—111no—
372C2×C22⋊C4—111no—
373C2×C22⋊C4—221no—
374C2×C22⋊C4—221no—
375C2×C22⋊C4—221no—
376C2×C22⋊C4—221no—
377C2×C42—111no—
378C2×C42—221no—
379C2×C42—221no—
380C2×C42—221no—
381C2×C42—221no—
382C2×C42C22×D1111yescharacteristic
383#107—222no—
384#107—222no—
385#106—41no—
386#106—222no—
387C4⋊C8—22no—
388#103—22no—
389#103—41no—
390#103—222no—
391#103—222no—
392C22⋊C8—222no—
393C22⋊C8—441no—
394#97—441no—
395#95—21no—
396#95—21no—
397#95—21no—
398#95—111no—
399#95—111no—
400#95—221no—
401#95—221no—
402#95—221no—
403#95—221no—
404#95—221no—
405#95—221no—
406#95—221no—
407#95—221no—
408C2×C11#246611yescharacteristic
409C2×C11#311111yescharacteristic
410C2×C11#312111yescharacteristic
411C2×C11#330711yescharacteristic
412C2×C11#332711yescharacteristic
413C2×C11#334911yescharacteristic
414C2×C11#335011yescharacteristic
415D11—81no—
416C24—111no—
417C2×Q8—21no—
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8#434312yes—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—111no—
428C22×C4—111no—
429C22×C4—111no—
430C22×C4—221no—
431C22×C4—221no—
432C22×C4—221no—
433C22×C4—221no—
434C22×C4—221no—
435C22×C4—221no—
436C22×C4—221no—
437C22×C4—221no—
438C22×C4—221no—
439C22×C4—221no—
440C22×C4D4×D1111yescharacteristic
441C22×C4D4×D1111yescharacteristic
442C22×C4C23×D1111yescharacteristic
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—221no—
449C2×C8—221no—
450C2×C8—221no—
451C2×C8—221no—
452C2×C8—221no—
453C2×C8—221no—
454C2×C8#434112yes—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—81no—
462C4⋊C4—112no—
463C4⋊C4—112no—
464C4⋊C4—224no—
465C4⋊C4—221no—
466C4⋊C4—221no—
467C4⋊C4—221no—
468C4⋊C4—221no—
469C4⋊C4—221no—
470C4⋊C4—221no—
471C4⋊C4—442no—
472C4⋊C4—442no—
473C4⋊C4—442no—
474C22⋊C4—224no—
475C22⋊C4—441no—
476C22⋊C4—441no—
477C22⋊C4—442no—
478C22⋊C4—442no—
479C22⋊C4—881no—
480C42—21no—
481C42—21no—
482C42—221no—
483C42—221no—
484C42—442no—
485C42—442no—
486C42—442no—
487C42—881no—
488C11#2706111yescharacteristic, complemented, Sylow
489C23—221no—
490C23—221no—
491C23—221no—
492C23—221no—
493C23—221no—
494C23—221no—
495C23—221no—
496C23C2×D4×D1111yescharacteristic
497Q8—22no—
498Q8—22no—
499Q8—41no—
500Q8—41no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—22no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—221no—
520C2×C4—221no—
521C2×C4—221no—
522C2×C4—221no—
523C2×C4—221no—
524C2×C4—221no—
525C2×C4—221no—
526C2×C4—222no—
527C2×C4—221no—
528C2×C4—222no—
529C2×C4—221no—
530C2×C4—441no—
531C2×C4—441no—
532C2×C4—441no—
533C2×C4—441no—
534C2×C4—441no—
535C2×C4—441no—
536C2×C4—441no—
537C2×C4—441no—
538C2×C4—441no—
539C2×C4—441no—
540C2×C4—441no—
541C2×C4—441no—
542C2×C4—441no—
543C2×C4—441no—
544C2×C4C2×#434111yescharacteristic
545C2×C4#6703711yescharacteristic
546C2×C4C2×#434311yescharacteristic
547C2×C4#41×D1111yescharacteristic
548C2×C4#41×D1111yescharacteristic
549C2×C4#6704311yescharacteristic
550C8—22no—
551C8—41no—
552C8—441no—
553C8—441no—
554C22—441no—
555C22—441no—
556C22—441no—
557C22—441no—
558C22—441no—
559C22—441no—
560C22—441no—
561C22#1062314211yescharacteristic
562C22#1062314311yescharacteristic
563C22#1062315811yescharacteristic
564C22#1062329311yescharacteristic
565C22#1062329911yescharacteristic
566C22#1062330811yescharacteristic
567C22#1062331011yescharacteristic
568C4—42no—
569C4—41no—
570C4—41no—
571C4—81no—
572C4—81no—
573C4—81no—
574C4—441no—
575C4—441no—
576C4—442no—
577C4—441no—
578C4—442no—
579C4—881no—
580C4—881no—
581C4#1062313211yescharacteristic
582C4#1062315511yescharacteristic
583C4#1062317611yescharacteristic
584C4#1062323311yescharacteristic
585C2—881no—
586C2#1307265511yescharacteristic
587C2#1307873211yescharacteristic
588C2#1307885211yescharacteristic
589C2#1308059911yescharacteristic
590C2#1308089111yescharacteristic
591C2#1308114111yescharacteristic
592C2#1308116711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2066C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenter#2066D11
hypocenterC11#27061
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2066

Complements

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

NH ≅ G/Ntype
3. #13070034C2semidirect
6. #13069386C2semidirect
7. #13069352C2semidirect
9. #13069205C2semidirect
10. #13069200C2semidirect
11. #13068868C2semidirect
14. #13068448C2semidirect
15. C11×#2066C2semidirect
196. #2066D11semidirect
488. C11#27061semidirect

Maximal subgroups

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

subgroupindex
#130730142
#130716482
#130700342
#130698182
#130698112
#130693862
#130693522
#130692282
#130692052
#130692002
#130688682
#130688142
#130687102
#130684482
C11×#20662
#2706111