Finite Group Databasebeta

← #14760725

Subgroups — #14760725

Order 2816.

868 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078337C211yesmaximal, characteristic
2#13077520C212yesmaximal, complemented
3C2×#10622330C211yesmaximal, characteristic, complemented
4#13077041C211yesmaximal, characteristic, complemented
5#13069512C211yesmaximal, characteristic, complemented
6#13069407C211yesmaximal, characteristic, complemented
7#13069286C212yesmaximal, complemented
8#13069116C212yesmaximal, complemented
9#13068667C211yesmaximal, characteristic, complemented
10#13068417C212yesmaximal, complemented
11C11×#1773C211yesmaximal, characteristic, complemented
12#10623279C2212yes—
13C2×#66957C2211yescharacteristic
14C2×#66954C2212yes—
15C2×#66954C2211yescharacteristic
16C2×#66954C2211yescharacteristic
17C4×#4339C2211yescharacteristic
18C2×C11×#108C2211yescharacteristic
19C11×#427C2211yescharacteristic
20C11×#405C2212yes—
21C2×C11×#97C2211yescharacteristic
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#10622330—21no—
37#10622330—21no—
38#10622330—21no—
39#10622330—21no—
40#10622321—21no—
41#10622321—21no—
42#10622320—21no—
43D11×#97—21no—
44#10622313—24no—
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—22no—
75#66954—22no—
76#66954—22no—
77#66954—22no—
78#66954—22no—
79#66954C2×C412yes—
80#66954C2×C412yes—
81#66954D414yes—
82C2×#4313—21no—
83C2×#4313—21no—
84C2×#4313—22no—
85C2×C8×D11—21no—
86C2×C8×D11—21no—
87C2×C8×D11—22no—
88C4×D44—21no—
89#66925—21no—
90C42×D11—21no—
91C4×Dic22—21no—
92C11×#108C2×C412yescomplemented
93C11×#108C2×C412yescomplemented
94C11×#107—21no—
95C11×#106—21no—
96C11×#97—22no—
97C11×#97D411yescharacteristic
98C11×#97D411yescharacteristic
99C11×#97D411yescharacteristic
100C11×#97D411yescharacteristic
101C4×C8×C11—22no—
102#66888C2×C414yescomplemented
103#66887C2×C414yescomplemented
104#66883—21no—
105#66883—21no—
106#66883—24no—
107#66879—21no—
108#66879—21no—
109C8×Dic11—21no—
110C8×Dic11—21no—
111#66870—24no—
112#66869—24no—
113#66869—22no—
114#66869—22no—
115#66869—24no—
116#66867—21no—
117C4×C11⋊C8—21no—
118#21559—111nomaximal, Sylow
119C22×C4×C11—21no—
120C22×C4×C11C2411yescharacteristic
121C2×C22⋊D11—21no—
122C2×C22⋊D11—22no—
123#4339—22no—
124#4339—22no—
125#4339—21no—
126#4339—21no—
127#4339—22no—
128#4339—22no—
129#4339C22×C412yes—
130#4339C2×D412yes—
131C2×D44C22×C412yes—
132C2×D44#4111yescharacteristic
133C2×C4×D11—22no—
134C2×C4×D11—21no—
135C2×C4×D11—22no—
136C2×Dic22C22×C412yes—
137C2×Dic22#4111yescharacteristic
138C11×M16—22no—
139C11×M16C22×C414yes—
140C2×C8×C11—22no—
141C2×C8×C11C22×C411yescharacteristic
142C2×C8×C11C22×C411yescharacteristic
143C2×C8×C11C2×D411yescharacteristic
144C2×C8×C11C2×D411yescharacteristic
145C2×C8×C11C2×D411yescharacteristic
146C2×C8×C11C2×D411yescharacteristic
147C2×C8×C11C2×D412yes—
148C2×C8×C11#4111yescharacteristic
149C2×C8×C11#4111yescharacteristic
150C2×C8×C11#4112yes—
151C11×C4⋊C4—22no—
152C11×C22⋊C4—22no—
153C42×C11—21no—
154C42×C11—22no—
155C42×C11C2×D411yescharacteristic
156C42×C11C2×D411yescharacteristic
157C22⋊Dic11#4112yes—
158(C2×D11)⋊C4—22no—
159C4⋊Dic11—21no—
160Dic11⋊C4—22no—
161C4×Dic11—22no—
162C4×Dic11—21no—
163#4318—22no—
164#4318—22no—
165#4318—21no—
166#4318—21no—
167#4318C22×C412yes—
168#4318C2×D412yes—
169C2×C11⋊C8—21no—
170C2×C11⋊C8—21no—
171C2×C11⋊C8—22no—
172Dic44—24no—
173Dic44—21no—
174Dic44—21no—
175D88—24no—
176D88—21no—
177D88—21no—
178#4314—24no—
179#4314—24no—
180#4314—22no—
181#4314—22no—
182#4313—22no—
183#4313—22no—
184#4313—24no—
185#4313—42no—
186#4313—42no—
187C8×D11—22no—
188C8×D11—22no—
189C8×D11—24no—
190C8×D11—42no—
191C8×D11—42no—
192#3067—111no—
193#2955—112no—
194C2×#444—111no—
195#2875—111no—
196#1976—111no—
197#1953—111no—
198#1932—112no—
199#1906—112no—
200#1814—111no—
201#1773D1111yescharacteristic, complemented
202#1757—112no—
203C23×C11C2×#4111yescharacteristic
204C22×D11—21no—
205C22×D11—22no—
206C2×C4×C11—21no—
207C2×C4×C11—21no—
208C2×C4×C11—42no—
209C2×C4×C11—81no—
210C2×C4×C11C23×C411yescharacteristic
211C2×C4×C11C22×D411yescharacteristic
212C2×C4×C11C22×D411yescharacteristic
213C2×C4×C11C2×#4111yescharacteristic
214C2×C4×C11C2×#4111yescharacteristic
215C2×C4×C11C2×#4111yescharacteristic
216C22⋊D11—22no—
217C22⋊D11—22no—
218C22⋊D11—42no—
219C22⋊D11—42no—
220C2×Dic11—21no—
221C2×Dic11—22no—
222C2×Dic11—22no—
223D44—22no—
224D44—22no—
225D44—21no—
226D44C4×D412yes—
227C4×D11—22no—
228C4×D11—22no—
229C4×D11—42no—
230C4×D11—42no—
231C4×D11—82no—
232Dic22—21no—
233Dic22—22no—
234Dic22—22no—
235Dic22C4×D412yes—
236C8×C11—24no—
237C8×C11C4×D411yescharacteristic
238C8×C11C4×D411yescharacteristic
239C8×C11C4×D411yescharacteristic
240C8×C11C4×D411yescharacteristic
241C8×C11#12112yes—
242C8×C11#12112yes—
243C11⋊C8—22no—
244C11⋊C8—22no—
245C11⋊C8—42no—
246#575—112no—
247C2×#135—111no—
248C2×#131—111no—
249C2×#131—111no—
250C2×#131—112no—
251C4×#41—111no—
252#473—112no—
253#472—112no—
254#471—114no—
255#444—224no—
256#444—221no—
257#444—221no—
258#444—221no—
259#444—221no—
260#443—224no—
261#430—112no—
262C2×#108—111no—
263C2×#108C2×D1111yescharacteristic
264#427C2×D1111yescharacteristic
265#421—112no—
266#421—112no—
267C2×#104—112no—
268#413—112no—
269#410—112no—
270#405—111no—
271#405—111no—
272#405—221no—
273#405—221no—
274#405C2×D1112yes—
275C4×M16—111no—
276C4×M16—221no—
277C2×#97—221no—
278C2×#97C2×D1111yescharacteristic
279#344—112no—
280#344—112no—
281#339C2×D1112yes—
282C22×C11—41no—
283C22×C11C4×#4111yescharacteristic
284C22×C11#52511yescharacteristic
285C22×C11#53211yescharacteristic
286C2×D11—22no—
287C2×D11—42no—
288C2×D11—42no—
289C2×D11—82no—
290C4×C11—41no—
291C4×C11—41no—
292C4×C11—82no—
293C4×C11C2×C4×D411yescharacteristic
294C4×C11C2×C4×D411yescharacteristic
295C4×C11C2×#12111yescharacteristic
296C4×C11#52911yescharacteristic
297Dic11—22no—
298Dic11—42no—
299Dic11—42no—
300C2×#41—111no—
301C2×#41—112no—
302#137—114no—
303#137—222no—
304AGL(1,ℤ/8)—114no—
305AGL(1,ℤ/8)—222no—
306#135—224no—
307#135—221no—
308#135—221no—
309#135—221no—
310#135—221no—
311C2×Q16—111no—
312C2×SD16—112no—
313C2×D8—111no—
314#131—112no—
315#131—112no—
316#131—114no—
317#131—221no—
318#131—221no—
319#131—222no—
320#131—222no—
321#131—222no—
322#131—222no—
323#131—222no—
324C2×M16—111no—
325C2×M16—111no—
326C2×M16—112no—
327C2×M16—221no—
328C2×M16—221no—
329C2×M16—222no—
330C2×M16C22×D1112yes—
331C22×C8—221no—
332C22×C8—221no—
333C22×C8—222no—
334C22×C8C22×D1111yescharacteristic
335C22×C8C22×D1111yescharacteristic
336C4×Q8—221no—
337C4×D4—221no—
338C4×D4—222no—
339#117—111no—
340#117—221no—
341#117C22×D1112yes—
342C2×C42—221no—
343C2×C42C22×D1111yescharacteristic
344#108—224no—
345#108—221no—
346#108—221no—
347#108C4×D1112yescomplemented
348#108C4×D1112yescomplemented
349#107—21no—
350#106—21no—
351#104—224no—
352#104—224no—
353#104—222no—
354#104—222no—
355#101—114no—
356#100—114no—
357#99—224no—
358#97—22no—
359#97—221no—
360#97—221no—
361#97—221no—
362#97D4411yescharacteristic
363#97D4411yescharacteristic
364#97D4411yescharacteristic
365#97D4411yescharacteristic
366C4×C8—22no—
367C4×C8—221no—
368C4×C8—221no—
369C4×C8—221no—
370C2×C11—21no—
371C2×C11—21no—
372C2×C11—21no—
373C2×C11C4×#12111yescharacteristic
374D11—42no—
375D11—82no—
376#41—112no—
377#41—112no—
378#41—221no—
379#41—221no—
380#41—222no—
381#41—222no—
382#41—222no—
383#41—222no—
384C2×Q8—112no—
385C2×Q8—111no—
386C2×D4—112no—
387C2×D4—111no—
388C2×D4—221no—
389C2×D4—222no—
390C22×C4—21no—
391C22×C4—222no—
392C22×C4—221no—
393C22×C4—222no—
394C22×C4C23×D1111yescharacteristic
395Q16—224no—
396Q16—221no—
397Q16—221no—
398SD16—224no—
399SD16—224no—
400SD16—222no—
401SD16—222no—
402D8—224no—
403D8—221no—
404D8—221no—
405M16—22no—
406M16—112no—
407M16—112no—
408M16—221no—
409M16—221no—
410M16—222no—
411M16—222no—
412M16—224no—
413M16—222no—
414M16—222no—
415M16—442no—
416M16—442no—
417M16C2×C4×D1114yes—
418C2×C8—22no—
419C2×C8—221no—
420C2×C8—221no—
421C2×C8—222no—
422C2×C8—222no—
423C2×C8—224no—
424C2×C8—222no—
425C2×C8—442no—
426C2×C8—442no—
427C2×C8C2×C4×D1111yescharacteristic
428C2×C8C2×C4×D1111yescharacteristic
429C2×C8C2×D4411yescharacteristic
430C2×C8C2×D4411yescharacteristic
431C2×C8C2×D4411yescharacteristic
432C2×C8C2×D4411yescharacteristic
433C2×C8#433911yescharacteristic
434C2×C8#433911yescharacteristic
435C2×C8D4×D1112yes—
436C2×C8#434312yes—
437C4⋊C4—22no—
438C4⋊C4—222no—
439C4⋊C4—221no—
440C22⋊C4—22no—
441C22⋊C4—112no—
442C22⋊C4—222no—
443C42—21no—
444C42—22no—
445C42—222no—
446C42—221no—
447C42C2×D4411yescharacteristic
448C42C2×D4411yescharacteristic
449C11#2155911yescharacteristic, complemented, Sylow
450C23—221no—
451C23—222no—
452C23#41×D1111yescharacteristic
453Q8—112no—
454Q8—221no—
455Q8—222no—
456Q8—222no—
457D4—112no—
458D4—222no—
459D4—222no—
460D4—222no—
461D4—222no—
462D4—221no—
463D4—442no—
464D4—442no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—42no—
468C2×C4—81no—
469C2×C4—221no—
470C2×C4—222no—
471C2×C4—222no—
472C2×C4—222no—
473C2×C4—222no—
474C2×C4—442no—
475C2×C4—442no—
476C2×C4—882no—
477C2×C4C22×C4×D1111yescharacteristic
478C2×C4C22×D4411yescharacteristic
479C2×C4C2×#433911yescharacteristic
480C2×C4C2×D4×D1111yescharacteristic
481C2×C4C2×#434311yescharacteristic
482C2×C4#41×D1111yescharacteristic
483C8—24no—
484C8—222no—
485C8—222no—
486C8—442no—
487C8C4×D4411yescharacteristic
488C8C4×D4411yescharacteristic
489C8C4×D4411yescharacteristic
490C8C4×D4411yescharacteristic
491C8#6694812yes—
492C8#6694812yes—
493C22—41no—
494C22—222no—
495C22—442no—
496C22—442no—
497C22—882no—
498C22#1062305511yescharacteristic
499C22#1062307911yescharacteristic
500C22C4×#434311yescharacteristic
501C4—41no—
502C4—41no—
503C4—82no—
504C4—222no—
505C4—442no—
506C4—442no—
507C4C2×C4×D4411yescharacteristic
508C4C2×#6694811yescharacteristic
509C4C4×D4×D1111yescharacteristic
510C4#1062311111yescharacteristic
511C2—21no—
512C2—21no—
513C2—21no—
514C2—442no—
515C2—882no—
516C2C4×#6694811yescharacteristic
subgroupG/H
centerC4C2×#66948
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1773C2
socleC2×C11C4×#121
prime radical#13078337C2
cosocleC22×C4×C11C24
hypercenter#1773D11
hypocenterC11#21559
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C22×C8 ◁ #1773

Complements

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

NH ≅ G/Ntype
2. #13077520C2semidirect
3. C2×#10622330C2semidirect
4. #13077041C2semidirect
5. #13069512C2semidirect
6. #13069407C2semidirect
7. #13069286C2semidirect
8. #13069116C2semidirect
9. #13068667C2semidirect
10. #13068417C2semidirect
11. C11×#1773C2semidirect
32. #10622511C4semidirect
33. #10622510C4semidirect
34. #10622509C4semidirect
64. C2×Dic44C2×C4semidirect
70. C2×D88C2×C4semidirect
71. C2×#4314C2×C4semidirect
92. C11×#108C2×C4semidirect
93. C11×#108C2×C4semidirect
102. #66888C2×C4semidirect
103. #66887C2×C4semidirect
201. #1773D11semidirect
347. #108C4×D11semidirect
348. #108C4×D11semidirect
449. C11#21559semidirect

Maximal subgroups

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

subgroupindex
#130783372
#130775202
C2×#106223302
#130770412
#130695122
#130694072
#130692862
#130691162
#130686672
#130684172
C11×#17732
#2155911