Finite Group Databasebeta

← #14907110

Subgroups — #14907110

Order 2816.

696 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622527C211yesmaximal, characteristic
2#13077491C211yesmaximal, characteristic, complemented
3#13077463C211yesmaximal, characteristic, complemented
4#13070491C211yesmaximal, characteristic, complemented
5#13070490C211yesmaximal, characteristic, complemented
6#13070481C211yesmaximal, characteristic, complemented
7#13070478C211yesmaximal, characteristic, complemented
8#13070465C211yesmaximal, characteristic, complemented
9C4×D176C211yesmaximal, characteristic, complemented
10#13070460C211yesmaximal, characteristic, complemented
11#13070403C211yesmaximal, characteristic, complemented
12#13070322C211yesmaximal, characteristic, complemented
13D11×#357C211yesmaximal, characteristic, complemented
14#13070211C211yesmaximal, characteristic, complemented
15C4×C11×SD32C211yesmaximal, characteristic, complemented
16C2×#66972C2211yescharacteristic
17C2×D8×D11C2211yescharacteristic
18#10623105—21no—
19#10623076—21no—
20C2×C11×SD32C2211yescharacteristic
21C4×C11×Q16C2211yescharacteristic, complemented
22C4×C11×D8C2211yescharacteristic
23Q16×Dic11C2211yescharacteristic, complemented
24C2×#66892C2211yescharacteristic
25D8×Dic11C2211yescharacteristic
26C2×#66890C2211yescharacteristic
27#10622639—21no—
28#10622627—21no—
29#10622527C418yescomplemented
30C2×D176C2211yescharacteristic
31C2×#66862C2211yescharacteristic
32C2×C16×D11C2211yescharacteristic
33#10622493C2211yescharacteristic
34D11×#107C2211yescharacteristic
35#10622485C2211yescharacteristic
36#10622485C2211yescharacteristic, complemented
37#10622430—21no—
38#10622416—21no—
39#10622398—21no—
40#10622383—21no—
41C4×D88C2211yescharacteristic
42C4×D88C2211yescharacteristic, complemented
43#10622302C2211yescharacteristic
44C11×#367C2211yescharacteristic, complemented
45C11×#358C2211yescharacteristic, complemented
46C11×#357C2211yescharacteristic
47C4×C11×C16C2211yescharacteristic, complemented
48#10622202C2211yescharacteristic, complemented
49#10622200C2211yescharacteristic
50#10622147C2211yescharacteristic
51#10622147C2211yescharacteristic, complemented
52#10622142C2211yescharacteristic, complemented
53#10622140C2211yescharacteristic, complemented
54C16×Dic11C2211yescharacteristic, complemented
55#10622129C2211yescharacteristic
56#10622129C2211yescharacteristic, complemented
57#10622128C2211yescharacteristic, complemented
58#10622127C2211yescharacteristic, complemented
59#10622099C2211yescharacteristic, complemented
60C2×#4343—21no—
61C2×D4×D11—21no—
62C2×C11×Q16C2311yescharacteristic
63C2×C11×D8C2311yescharacteristic
64C4×Q8×C11—21no—
65C4×D4×C11—21no—
66Q8×Dic11—21no—
67C2×#4325—21no—
68D4×Dic11—21no—
69C2×#4323—21no—
70C4×C22⋊D11—41no—
71C2×(C2×D11)⋊C4—41no—
72#66972—22no—
73#66972C2×C414yescomplemented
74D8×D11—22no—
75D8×D11C2×C414yescomplemented
76C2×D88C2311yescharacteristic
77C2×D88C2311yescharacteristic
78C2×#4313D411yescharacteristic
79C2×C8×D11C2311yescharacteristic
80#66946—21no—
81#66946—21no—
82#66946—41no—
83#66945—21no—
84C4⋊C4×D11—21no—
85C4⋊C4×D11—41no—
86(C22⋊D11)⋊C4—41no—
87C22⋊C4×D11—41no—
88C4×D44—21no—
89C4×D44—21no—
90C4×D44—41no—
91#66925—41no—
92#66925D411yescharacteristic
93C11×SD32C2×C414yescomplemented
94C2×C11×C16C2311yescharacteristic
95C2×C11×C16C2311yescharacteristic
96C11×#107C2311yescharacteristic
97C11×#107C2311yescharacteristic
98C11×#103—21no—
99C11×#102—21no—
100C4×C8×C11C2311yescharacteristic
101#66899—21no—
102#66896—21no—
103#66892C2×C414yescomplemented
104#66890C2×C414yescomplemented
105#66885—21no—
106#66885—21no—
107#66882C2311yescharacteristic
108#66882C2311yescharacteristic
109#66879D411yescharacteristic
110C8×Dic11C2311yescharacteristic
111C2×C11⋊C16C2311yescharacteristic
112C2×C11⋊C16C2311yescharacteristic
113#66873—21no—
114#66873—21no—
115#66872—21no—
116#66871—21no—
117#66867D411yescharacteristic
118D176C2×C414yescomplemented
119#66862C2×C414yescomplemented
120C16×D11—22no—
121#33454—111nomaximal, Sylow
122C23×D11—41no—
123C2×Q8×C11—21no—
124C2×D4×C11—21no—
125C22×C4×C11—41no—
126C2×C22⋊D11—41no—
127C22×Dic11—41no—
128#4343—24no—
129#4343—42no—
130D4×D11—24no—
131D4×D11—42no—
132C2×D44—21no—
133C2×D44—21no—
134C2×D44—41no—
135C2×C4×D11—41no—
136C2×C4×D11—41no—
137C2×C4×D11—41no—
138C2×C4×D11—41no—
139C2×C4×D11—41no—
140C2×C4×D11—41no—
141C2×C4×D11C2×D411yescharacteristic
142C11×Q16—21no—
143C11×Q16C22×C412yes—
144C11×D8—21no—
145C11×D8C22×C412yes—
146C2×C8×C11C2×D411yescharacteristic
147C2×C8×C11C2411yescharacteristic
148C11×C4⋊C4—21no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—41no—
151C11×C22⋊C4—41no—
152C42×C11—41no—
153C42×C11C2×D411yescharacteristic
154C22⋊Dic11—41no—
155#4325—24no—
156#4323—24no—
157(C2×D11)⋊C4—41no—
158(C2×D11)⋊C4—41no—
159(C2×D11)⋊C4—41no—
160(C2×D11)⋊C4—41no—
161(C2×D11)⋊C4—41no—
162(C2×D11)⋊C4D811yescharacteristic
163(C2×D11)⋊C4D811yescharacteristic
164C4⋊Dic11—21no—
165C4⋊Dic11—21no—
166C4⋊Dic11—41no—
167Dic11⋊C4—41no—
168Dic11⋊C4D811yescharacteristic
169Dic11⋊C4D811yescharacteristic
170C4×Dic11—41no—
171C4×Dic11—41no—
172C4×Dic11C2×D411yescharacteristic
173C2×C11⋊C8C2×D411yescharacteristic
174C2×C11⋊C8C2×D411yescharacteristic
175D88—21no—
176D88—21no—
177D88C22×C412yes—
178D88C22×C412yes—
179#4313—22no—
180C8×D11C22×C412yes—
181C8×D11#4112yes—
182C11×C16—21no—
183C11×C16C22×C412yes—
184C11⋊C16—21no—
185C11⋊C16C22×C412yes—
186C2×#509—111no—
187#2951—111no—
188#2948—111no—
189#2177—111no—
190#2177—111no—
191#2175—111no—
192#2175—111no—
193C4×SD32—111no—
194C4×SD32D1111yescharacteristic, complemented
195C4×D16—111no—
196C4×D16—111no—
197#2159—111no—
198#2138—111no—
199C2×#357—111no—
200#2108—111no—
201C23×C11—41no—
202C22×D11—41no—
203C22×D11—41no—
204C22×D11—44no—
205C22×D11—161no—
206C22×D11—161no—
207C22×D11C2×D811yescharacteristic
208Q8×C11—22no—
209Q8×C11—41no—
210D4×C11—22no—
211D4×C11—41no—
212C2×C4×C11—41no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11—161no—
216C2×C4×C11C2×D811yescharacteristic
217C2×C4×C11C2×D811yescharacteristic
218C2×C4×C11C22×D411yescharacteristic
219C22⋊D11—44no—
220C2×Dic11—41no—
221C2×Dic11—41no—
222C2×Dic11—161no—
223C2×Dic11C2×D811yescharacteristic
224C2×Dic11C2×D811yescharacteristic
225C2×Dic11C2×D811yescharacteristic
226D44—22no—
227D44—22no—
228D44—44no—
229D44—41no—
230D44—41no—
231C4×D11—44no—
232C4×D11—161no—
233C4×D11—161no—
234C4×D11—161no—
235C4×D11—161no—
236C4×D11—161no—
237C4×D11C4×D412yes—
238C4×D11#13512yes—
239C8×C11—21no—
240C8×C11C23×C411yescharacteristic
241C8×C11C2×#4111yescharacteristic
242C11⋊C8—21no—
243C11⋊C8C4×D412yes—
244C2×#135—111no—
245C22×D8—111no—
246#520—221no—
247#518—221no—
248#509—118no—
249C2×SD32—111no—
250C2×SD32C2×D1111yescharacteristic
251C2×D16—111no—
252C2×D16—111no—
253C2×M32—111no—
254C22×C16—111no—
255#442—221no—
256#442—221no—
257#440—221no—
258#440—221no—
259C4×Q16—111no—
260C4×Q16C2×D1111yescharacteristic, complemented
261C4×D8—111no—
262C4×D8—111no—
263C4×D8—111no—
264C4×D8—111no—
265C4×D8—111no—
266C4×D8C2×D1111yescharacteristic
267#427—111no—
268C2×#107—111no—
269#418—221no—
270#417—221no—
271#405—111no—
272#367—111no—
273#367C2×D1111yescharacteristic, complemented
274#366—111no—
275#366—111no—
276#358—111no—
277#358C2×D1111yescharacteristic, complemented
278#357—111no—
279#357—111no—
280#357—111no—
281#357—111no—
282#357—111no—
283#357C2×D1111yescharacteristic
284#346—111no—
285#346—111no—
286C4×C16—111no—
287C4×C16C2×D1111yescharacteristic, complemented
288C22×C11—42no—
289C22×C11—81no—
290C22×C11—81no—
291C22×C11C22×D811yescharacteristic
292C2×D11—21no—
293C2×D11—21no—
294C2×D11—42no—
295C2×D11—42no—
296C2×D11—81no—
297C2×D11—81no—
298C2×D11—81no—
299C2×D11—81no—
300C2×D11—164no—
301C2×D11C4×D812yes—
302C4×C11—21no—
303C4×C11—21no—
304C4×C11—42no—
305C4×C11—81no—
306C4×C11—81no—
307C4×C11C2×C4×D411yescharacteristic
308C4×C11C2×#13511yescharacteristic
309Dic11—21no—
310Dic11—21no—
311Dic11—81no—
312Dic11—81no—
313Dic11C4×D812yes—
314C2×#41—221no—
315C22×D4—221no—
316#135—114no—
317#135—222no—
318C2×Q16C22×D1111yescharacteristic
319C2×SD16—221no—
320C2×D8—114no—
321C2×D8—111no—
322C2×D8—111no—
323C2×D8—222no—
324C2×D8—221no—
325C2×D8C22×D1111yescharacteristic
326C2×M16—111no—
327C22×C8—111no—
328C4×Q8—21no—
329C4×Q8—221no—
330C4×D4—21no—
331C4×D4—221no—
332C4×D4—221no—
333C4×D4—221no—
334C4×D4—221no—
335C4×D4—221no—
336C4×D4—441no—
337C4×D4—441no—
338C4×D4—441no—
339C4×D4—441no—
340#117—111no—
341#117—221no—
342#117—441no—
343C2×C4⋊C4—221no—
344C2×C4⋊C4—441no—
345C2×C22⋊C4—441no—
346C2×C22⋊C4—441no—
347SD32—114no—
348SD32C4×D1114yescomplemented
349D16—114no—
350D16—114no—
351M32—114no—
352C2×C16—111no—
353C2×C16—111no—
354C2×C16—222no—
355C2×C16C22×D1111yescharacteristic
356C2×C16C22×D1111yescharacteristic
357#107—111no—
358#107—111no—
359#107—221no—
360#107C22×D1111yescharacteristic
361#107C22×D1111yescharacteristic
362#106—221no—
363#103—21no—
364#103—221no—
365#102—21no—
366#102—221no—
367#102—221no—
368#102—221no—
369#102—221no—
370#102—221no—
371#97—111no—
372#97—111no—
373C4×C8—111no—
374C4×C8C22×D1111yescharacteristic
375C2×C11—82no—
376C2×C11C2×C4×D811yescharacteristic
377C2×C11#341511yescharacteristic
378C2×C11#341611yescharacteristic
379D11—22no—
380D11—82no—
381D11—82no—
382C24—441no—
383#41—224no—
384#41—442no—
385C2×Q8—21no—
386C2×D4—21no—
387C2×D4—224no—
388C2×D4—221no—
389C2×D4—221no—
390C2×D4—441no—
391C2×D4—442no—
392C2×D4—441no—
393C22×C4—41no—
394C22×C4—111no—
395C22×C4—441no—
396C22×C4—441no—
397C22×C4—441no—
398C22×C4—441no—
399C22×C4—441no—
400C22×C4—441no—
401C22×C4—441no—
402Q16—21no—
403Q16C2×C4×D1112yes—
404SD16—224no—
405D8—21no—
406D8—112no—
407D8—112no—
408D8—224no—
409D8—221no—
410D8—221no—
411D8C2×C4×D1112yes—
412M16—222no—
413C2×C8—111no—
414C2×C8—112no—
415C2×C8—112no—
416C2×C8—111no—
417C2×C8D4×D1111yescharacteristic
418C2×C8C23×D1111yescharacteristic
419C4⋊C4—21no—
420C4⋊C4—21no—
421C4⋊C4—41no—
422C4⋊C4—111no—
423C4⋊C4—111no—
424C4⋊C4—221no—
425C4⋊C4—221no—
426C4⋊C4—441no—
427C4⋊C4—441no—
428C22⋊C4—41no—
429C22⋊C4—111no—
430C22⋊C4—111no—
431C22⋊C4—441no—
432C22⋊C4—441no—
433C22⋊C4—441no—
434C22⋊C4—441no—
435C22⋊C4—441no—
436C22⋊C4—441no—
437C42—41no—
438C42—111no—
439C42—441no—
440C42—441no—
441C42D4×D1111yescharacteristic
442C16—21no—
443C16—112no—
444C16—221no—
445C16C2×C4×D1112yes—
446C11#3345411yescharacteristic, complemented, Sylow
447C23—41no—
448C23—111no—
449C23—444no—
450C23—441no—
451C23—441no—
452C23—1761no—
453C23—1761no—
454Q8—22no—
455Q8—41no—
456D4—22no—
457D4—41no—
458D4—222no—
459D4—222no—
460D4—444no—
461D4—444no—
462D4—441no—
463D4—441no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—111no—
468C2×C4—112no—
469C2×C4—112no—
470C2×C4—111no—
471C2×C4—111no—
472C2×C4—161no—
473C2×C4—444no—
474C2×C4—441no—
475C2×C4—441no—
476C2×C4—1761no—
477C2×C4—1761no—
478C2×C4—1761no—
479C2×C4—1761no—
480C2×C4—1761no—
481C2×C4—1761no—
482C2×C4D8×D1111yescharacteristic
483C2×C4D8×D1111yescharacteristic
484C2×C4C2×D4×D1111yescharacteristic
485C8—21no—
486C8—112no—
487C8—221no—
488C8C22×C4×D1111yescharacteristic
489C8#41×D1111yescharacteristic
490C22—42no—
491C22—81no—
492C22—81no—
493C22—112no—
494C22—221no—
495C22—221no—
496C22—442no—
497C22—442no—
498C22—881no—
499C22—881no—
500C22—881no—
501C22—881no—
502C22—1764no—
503C22C2×D8×D1111yescharacteristic
504C4—21no—
505C4—21no—
506C4—42no—
507C4—81no—
508C4—81no—
509C4—112no—
510C4—221no—
511C4—221no—
512C4—881no—
513C4—881no—
514C4C4×D4×D1111yescharacteristic
515C4D11×#13511yescharacteristic
516C2—82no—
517C2—222no—
518C2—882no—
519C2—882no—
520C2C4×D8×D1111yescharacteristic
521C2#1308175411yescharacteristic
522C2#1308175811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutatorC8×C11C23×C4
FrattiniC2×C8C23×D11
FittingC4×C11×SD32C2
socleC22×C11C22×D8
prime radicalC2×#10622527C2
cosocleC2×C8×C11C24
hypercenterC4×SD32D11
hypocenterC11#33454
LCSG ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ C4×SD32

Complements

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

NH ≅ G/Ntype
2. #13077491C2semidirect
3. #13077463C2semidirect
4. #13070491C2semidirect
5. #13070490C2semidirect
6. #13070481C2semidirect
7. #13070478C2semidirect
8. #13070465C2semidirect
9. C4×D176C2semidirect
10. #13070460C2semidirect
11. #13070403C2semidirect
12. #13070322C2semidirect
13. D11×#357C2semidirect
14. #13070211C2semidirect
15. C4×C11×SD32C2semidirect
21. C4×C11×Q16C22semidirect
23. Q16×Dic11C22semidirect
29. #10622527C4semidirect
36. #10622485C22semidirect
42. C4×D88C22semidirect
44. C11×#367C22semidirect
45. C11×#358C22semidirect
47. C4×C11×C16C22semidirect
48. #10622202C22semidirect
51. #10622147C22semidirect
52. #10622142C22semidirect
53. #10622140C22semidirect
54. C16×Dic11C22semidirect
56. #10622129C22semidirect
57. #10622128C22semidirect
58. #10622127C22semidirect
59. #10622099C22semidirect
73. #66972C2×C4semidirect
75. D8×D11C2×C4semidirect
93. C11×SD32C2×C4semidirect
103. #66892C2×C4semidirect
104. #66890C2×C4semidirect
118. D176C2×C4semidirect
119. #66862C2×C4semidirect
194. C4×SD32D11semidirect
260. C4×Q16C2×D11semidirect
273. #367C2×D11semidirect
277. #358C2×D11semidirect
287. C4×C16C2×D11semidirect
348. SD32C4×D11semidirect
446. C11#33454semidirect

Maximal subgroups

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

subgroupindex
C2×#106225272
#130774912
#130774632
#130704912
#130704902
#130704812
#130704782
#130704652
C4×D1762
#130704602
#130704032
#130703222
D11×#3572
#130702112
C4×C11×SD322
#3345411