Finite Group Databasebeta

← #14760714

Subgroups — #14760714

Order 2816.

876 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078337C211yesmaximal, characteristic
2#13077520C212yesmaximal, complemented
3C2×#10622313C211yesmaximal, characteristic, complemented
4C4×#66954C211yesmaximal, characteristic, complemented
5#13069512C211yesmaximal, characteristic, complemented
6#13069407C211yesmaximal, characteristic, complemented
7#13069286C212yesmaximal, complemented
8#13069116C212yesmaximal, complemented
9#13068667C211yesmaximal, characteristic, complemented
10#13068417C212yesmaximal, complemented
11C11×#1772C211yesmaximal, characteristic, complemented
12#10623279C2212yes—
13C2×#66957C2211yescharacteristic
14C2×#66954C2212yes—
15C2×#66954C2211yescharacteristic
16C2×#66954C2211yescharacteristic
17C4×#4339C2211yescharacteristic
18C2×C11×#108C2211yescharacteristic
19C11×#427C2211yescharacteristic
20C11×#405C2212yes—
21C2×C4×C8×C11C2211yescharacteristic
22#10622745C2212yes—
23#10622738C2212yes—
24C2×#66883C2211yescharacteristic
25#10622714C2211yescharacteristic
26#10622714C2211yescharacteristic
27#10622619C2212yes—
28#10622618C2212yes—
29#10622618C2212yes—
30C2×#66869C2212yes—
31C4×#4318C2211yescharacteristic
32#10622511C414yescomplemented
33#10622510C412yescomplemented
34#10622509C412yescomplemented
35#10622330—24no—
36#10622313—24no—
37#10622313—21no—
38#10622313—21no—
39#10622313—21no—
40#10622313—21no—
41#10622302—21no—
42#10622302—21no—
43C4×#4313—21no—
44C4×C8×D11—21no—
45C11×#339C2212yes—
46#10622197C2212yes—
47#10622171C2212yes—
48C2×#4339C2312yes—
49C2×#4339C2311yescharacteristic
50C2×C11×M16C2312yes—
51C22×C8×C11C2311yescharacteristic
52C22×C8×C11C2311yescharacteristic
53C11×#117C2312yes—
54C2×C42×C11C2311yescharacteristic
55C4×C22⋊D11—22no—
56#66979C2311yescharacteristic
57C2×#4318C2312yes—
58C2×#4318C2311yescharacteristic
59C2×#4318C2311yescharacteristic
60#66962—22no—
61#66962C2×C414yes—
62#66961—22no—
63#66961C2×C414yes—
64C2×Dic44C2×C411yescharacteristic, complemented
65#66957—24no—
66#66957—21no—
67#66957—21no—
68#66957—21no—
69#66957—21no—
70C2×D88C2×C411yescharacteristic, complemented
71C2×#4314C2×C412yescomplemented
72#66954—21no—
73#66954—21no—
74#66954—21no—
75#66954—21no—
76#66954—22no—
77#66954—22no—
78#66954—22no—
79#66954—22no—
80#66954C2×C412yes—
81#66954C2×C412yes—
82#66954D412yes—
83#66954D412yes—
84C2×#4313—21no—
85C2×#4313—21no—
86C2×#4313—22no—
87C2×C8×D11—21no—
88C2×C8×D11—21no—
89C2×C8×D11—22no—
90C4×D44—21no—
91#66925—21no—
92C42×D11—21no—
93C4×Dic22—21no—
94C11×#108C2×C412yescomplemented
95C11×#108C2×C412yescomplemented
96C11×#107—21no—
97C11×#106—21no—
98C11×#97—22no—
99C4×C8×C11—22no—
100C4×C8×C11D411yescharacteristic
101C4×C8×C11D411yescharacteristic
102C4×C8×C11D411yescharacteristic
103C4×C8×C11D411yescharacteristic
104#66888C2×C414yescomplemented
105#66887C2×C414yescomplemented
106#66883—21no—
107#66883—21no—
108#66883—24no—
109#66879—21no—
110#66879—21no—
111C8×Dic11—21no—
112C8×Dic11—21no—
113#66870—24no—
114#66869—24no—
115#66869—22no—
116#66869—22no—
117#66869—24no—
118#66867—21no—
119C4×C11⋊C8—21no—
120#21558—111nomaximal, Sylow
121C22×C4×C11—21no—
122C22×C4×C11C2411yescharacteristic
123C2×C22⋊D11—21no—
124C2×C22⋊D11—22no—
125#4339—22no—
126#4339—22no—
127#4339—21no—
128#4339—21no—
129#4339—22no—
130#4339—22no—
131#4339C22×C412yes—
132#4339C2×D412yes—
133C2×D44C22×C412yes—
134C2×D44#4111yescharacteristic
135C2×C4×D11—22no—
136C2×C4×D11—21no—
137C2×C4×D11—22no—
138C2×Dic22C22×C412yes—
139C2×Dic22#4111yescharacteristic
140C11×M16—22no—
141C11×M16C22×C414yes—
142C2×C8×C11—22no—
143C2×C8×C11C22×C411yescharacteristic
144C2×C8×C11C22×C411yescharacteristic
145C2×C8×C11C2×D411yescharacteristic
146C2×C8×C11C2×D411yescharacteristic
147C2×C8×C11C2×D411yescharacteristic
148C2×C8×C11C2×D411yescharacteristic
149C2×C8×C11C2×D411yescharacteristic
150C2×C8×C11C2×D411yescharacteristic
151C2×C8×C11#4111yescharacteristic
152C2×C8×C11#4111yescharacteristic
153C2×C8×C11#4111yescharacteristic
154C2×C8×C11#4111yescharacteristic
155C11×C4⋊C4—22no—
156C11×C22⋊C4—22no—
157C42×C11—21no—
158C42×C11—22no—
159C42×C11C2×D411yescharacteristic
160C42×C11C2×D411yescharacteristic
161C22⋊Dic11#4112yes—
162(C2×D11)⋊C4—22no—
163C4⋊Dic11—21no—
164Dic11⋊C4—22no—
165C4×Dic11—22no—
166C4×Dic11—21no—
167#4318—22no—
168#4318—22no—
169#4318—21no—
170#4318—21no—
171#4318C22×C412yes—
172#4318C2×D412yes—
173C2×C11⋊C8—21no—
174C2×C11⋊C8—21no—
175C2×C11⋊C8—22no—
176Dic44—24no—
177Dic44—21no—
178Dic44—21no—
179D88—24no—
180D88—21no—
181D88—21no—
182#4314—24no—
183#4314—24no—
184#4314—22no—
185#4314—22no—
186#4313—22no—
187#4313—22no—
188#4313—22no—
189#4313—22no—
190#4313—42no—
191#4313—42no—
192C8×D11—22no—
193C8×D11—22no—
194C8×D11—22no—
195C8×D11—22no—
196C8×D11—42no—
197C8×D11—42no—
198#3067—111no—
199#2955—112no—
200C2×#443—111no—
201C4×#131—111no—
202#1976—111no—
203#1953—111no—
204#1932—112no—
205#1906—112no—
206#1814—111no—
207#1772D1111yescharacteristic, complemented
208#1757—112no—
209C23×C11C2×#4111yescharacteristic
210C22×D11—21no—
211C22×D11—22no—
212C2×C4×C11—21no—
213C2×C4×C11—21no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11C23×C411yescharacteristic
217C2×C4×C11C22×D411yescharacteristic
218C2×C4×C11C22×D411yescharacteristic
219C2×C4×C11C2×#4111yescharacteristic
220C2×C4×C11C2×#4111yescharacteristic
221C2×C4×C11C2×#4111yescharacteristic
222C22⋊D11—22no—
223C22⋊D11—22no—
224C22⋊D11—42no—
225C22⋊D11—42no—
226C2×Dic11—21no—
227C2×Dic11—22no—
228C2×Dic11—22no—
229D44—22no—
230D44—22no—
231D44—21no—
232D44C4×D412yes—
233C4×D11—22no—
234C4×D11—22no—
235C4×D11—44no—
236C4×D11—42no—
237C4×D11—42no—
238Dic22—21no—
239Dic22—22no—
240Dic22—22no—
241Dic22C4×D412yes—
242C8×C11—24no—
243C8×C11C4×D411yescharacteristic
244C8×C11C4×D411yescharacteristic
245C8×C11C4×D411yescharacteristic
246C8×C11C4×D411yescharacteristic
247C8×C11#12111yescharacteristic
248C8×C11#12111yescharacteristic
249C8×C11#12111yescharacteristic
250C8×C11#12111yescharacteristic
251C11⋊C8—22no—
252C11⋊C8—22no—
253C11⋊C8—42no—
254#575—112no—
255C2×#135—111no—
256C2×#131—111no—
257C2×#131—111no—
258C2×#131—112no—
259C4×#41—111no—
260#473—112no—
261#472—112no—
262#471—114no—
263#444—224no—
264#443—224no—
265#443—221no—
266#443—221no—
267#443—221no—
268#443—221no—
269#430—112no—
270C2×#108—111no—
271C2×#108C2×D1111yescharacteristic
272#427C2×D1111yescharacteristic
273#421—112no—
274#421—112no—
275C2×#104—112no—
276#413—112no—
277#410—112no—
278#405—111no—
279#405—111no—
280#405—221no—
281#405—221no—
282#405C2×D1112yes—
283C4×M16—111no—
284C4×M16—221no—
285C2×C4×C8—221no—
286C2×C4×C8C2×D1111yescharacteristic
287#344—112no—
288#344—112no—
289#339C2×D1112yes—
290C22×C11—41no—
291C22×C11C4×#4111yescharacteristic
292C22×C11#52511yescharacteristic
293C22×C11#53211yescharacteristic
294C2×D11—22no—
295C2×D11—42no—
296C2×D11—42no—
297C2×D11—82no—
298C4×C11—22no—
299C4×C11—41no—
300C4×C11—82no—
301C4×C11C2×C4×D411yescharacteristic
302C4×C11C2×C4×D411yescharacteristic
303C4×C11C2×#12111yescharacteristic
304C4×C11#52911yescharacteristic
305Dic11—22no—
306Dic11—42no—
307Dic11—42no—
308C2×#41—111no—
309C2×#41—112no—
310#137—114no—
311#137—222no—
312AGL(1,ℤ/8)—114no—
313AGL(1,ℤ/8)—222no—
314#135—224no—
315#135—221no—
316#135—221no—
317#135—221no—
318#135—221no—
319C2×Q16—111no—
320C2×SD16—112no—
321C2×D8—111no—
322#131—112no—
323#131—112no—
324#131—112no—
325#131—112no—
326#131—221no—
327#131—221no—
328#131—221no—
329#131—221no—
330#131—222no—
331#131—222no—
332#131—222no—
333#131—222no—
334C2×M16—111no—
335C2×M16—111no—
336C2×M16—112no—
337C2×M16—221no—
338C2×M16—221no—
339C2×M16—222no—
340C2×M16C22×D1112yes—
341C22×C8—221no—
342C22×C8—221no—
343C22×C8—222no—
344C22×C8C22×D1111yescharacteristic
345C22×C8C22×D1111yescharacteristic
346C4×Q8—221no—
347C4×D4—221no—
348C4×D4—222no—
349#117—111no—
350#117—221no—
351#117C22×D1112yes—
352C2×C42—221no—
353C2×C42C22×D1111yescharacteristic
354#108—224no—
355#108—221no—
356#108—221no—
357#108C4×D1112yescomplemented
358#108C4×D1112yescomplemented
359#107—21no—
360#106—21no—
361#104—224no—
362#104—224no—
363#104—222no—
364#104—222no—
365#101—114no—
366#100—114no—
367#99—224no—
368#97—22no—
369#97—221no—
370#97—221no—
371#97—221no—
372C4×C8—22no—
373C4×C8—221no—
374C4×C8—221no—
375C4×C8—221no—
376C4×C8D4411yescharacteristic
377C4×C8D4411yescharacteristic
378C4×C8D4411yescharacteristic
379C4×C8D4411yescharacteristic
380C2×C11—21no—
381C2×C11—21no—
382C2×C11—21no—
383C2×C11C4×#12111yescharacteristic
384D11—42no—
385D11—82no—
386#41—112no—
387#41—112no—
388#41—221no—
389#41—221no—
390#41—222no—
391#41—222no—
392#41—222no—
393#41—222no—
394C2×Q8—112no—
395C2×Q8—111no—
396C2×D4—112no—
397C2×D4—111no—
398C2×D4—221no—
399C2×D4—222no—
400C22×C4—21no—
401C22×C4—222no—
402C22×C4—221no—
403C22×C4—222no—
404C22×C4C23×D1111yescharacteristic
405Q16—224no—
406Q16—221no—
407Q16—221no—
408SD16—224no—
409SD16—224no—
410SD16—222no—
411SD16—222no—
412D8—224no—
413D8—221no—
414D8—221no—
415M16—22no—
416M16—112no—
417M16—112no—
418M16—221no—
419M16—221no—
420M16—222no—
421M16—222no—
422M16—222no—
423M16—222no—
424M16—222no—
425M16—222no—
426M16—442no—
427M16—442no—
428M16C2×C4×D1114yes—
429C2×C8—22no—
430C2×C8—221no—
431C2×C8—221no—
432C2×C8—222no—
433C2×C8—222no—
434C2×C8—222no—
435C2×C8—222no—
436C2×C8—222no—
437C2×C8—442no—
438C2×C8—442no—
439C2×C8C2×C4×D1111yescharacteristic
440C2×C8C2×C4×D1111yescharacteristic
441C2×C8C2×D4411yescharacteristic
442C2×C8C2×D4411yescharacteristic
443C2×C8C2×D4411yescharacteristic
444C2×C8C2×D4411yescharacteristic
445C2×C8#433911yescharacteristic
446C2×C8#433911yescharacteristic
447C2×C8D4×D1111yescharacteristic
448C2×C8D4×D1111yescharacteristic
449C2×C8#434311yescharacteristic
450C2×C8#434311yescharacteristic
451C4⋊C4—22no—
452C4⋊C4—222no—
453C4⋊C4—221no—
454C22⋊C4—22no—
455C22⋊C4—112no—
456C22⋊C4—222no—
457C42—21no—
458C42—22no—
459C42—222no—
460C42—221no—
461C42C2×D4411yescharacteristic
462C42C2×D4411yescharacteristic
463C11#2155811yescharacteristic, complemented, Sylow
464C23—221no—
465C23—222no—
466C23#41×D1111yescharacteristic
467Q8—112no—
468Q8—221no—
469Q8—222no—
470Q8—222no—
471D4—112no—
472D4—222no—
473D4—222no—
474D4—222no—
475D4—222no—
476D4—221no—
477D4—442no—
478D4—442no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—221no—
484C2×C4—222no—
485C2×C4—222no—
486C2×C4—222no—
487C2×C4—222no—
488C2×C4—444no—
489C2×C4—442no—
490C2×C4—442no—
491C2×C4C22×C4×D1111yescharacteristic
492C2×C4C22×D4411yescharacteristic
493C2×C4C2×#433911yescharacteristic
494C2×C4C2×D4×D1111yescharacteristic
495C2×C4C2×#434311yescharacteristic
496C2×C4#41×D1111yescharacteristic
497C8—24no—
498C8—222no—
499C8—222no—
500C8—442no—
501C8C4×D4411yescharacteristic
502C8C4×D4411yescharacteristic
503C8C4×D4411yescharacteristic
504C8C4×D4411yescharacteristic
505C8#6694811yescharacteristic
506C8#6694811yescharacteristic
507C8#6694811yescharacteristic
508C8#6694811yescharacteristic
509C22—41no—
510C22—222no—
511C22—442no—
512C22—442no—
513C22—882no—
514C22#1062305511yescharacteristic
515C22#1062307911yescharacteristic
516C22C4×#434311yescharacteristic
517C4—22no—
518C4—41no—
519C4—82no—
520C4—222no—
521C4—442no—
522C4—442no—
523C4C2×C4×D4411yescharacteristic
524C4C2×#6694811yescharacteristic
525C4C4×D4×D1111yescharacteristic
526C4#1062311111yescharacteristic
527C2—21no—
528C2—21no—
529C2—21no—
530C2—442no—
531C2—882no—
532C2C4×#6694811yescharacteristic
subgroupG/H
centerC8#66948
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1772C2
socleC2×C11C4×#121
prime radical#13078337C2
cosocleC22×C4×C11C24
hypercenter#1772D11
hypocenterC11#21558
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C8 ◁ C22×C8 ◁ #1772

Complements

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

NH ≅ G/Ntype
2. #13077520C2semidirect
3. C2×#10622313C2semidirect
4. C4×#66954C2semidirect
5. #13069512C2semidirect
6. #13069407C2semidirect
7. #13069286C2semidirect
8. #13069116C2semidirect
9. #13068667C2semidirect
10. #13068417C2semidirect
11. C11×#1772C2semidirect
32. #10622511C4semidirect
33. #10622510C4semidirect
34. #10622509C4semidirect
64. C2×Dic44C2×C4semidirect
70. C2×D88C2×C4semidirect
71. C2×#4314C2×C4semidirect
94. C11×#108C2×C4semidirect
95. C11×#108C2×C4semidirect
104. #66888C2×C4semidirect
105. #66887C2×C4semidirect
207. #1772D11semidirect
357. #108C4×D11semidirect
358. #108C4×D11semidirect
463. C11#21558semidirect

Maximal subgroups

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

subgroupindex
#130783372
#130775202
C2×#106223132
C4×#669542
#130695122
#130694072
#130692862
#130691162
#130686672
#130684172
C11×#17722
#2155811