Finite Group Databasebeta

← #15617408

Subgroups — #15617408

Order 2816.

2666 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623276C211yesmaximal, characteristic
2C22×#66954C211yesmaximal, characteristic
3#13081817C211yesmaximal, characteristic
4#13077183C218yesmaximal, complemented
5#13077181C218yesmaximal, complemented
6#13077180C211yesmaximal, characteristic, complemented
7#13077179C211yesmaximal, characteristic, complemented
8#13077177C214yesmaximal, complemented
9C2×#10622715C211yesmaximal, characteristic, complemented
10D11×#424C214yesmaximal, complemented
11C2×C11×#424C211yesmaximal, characteristic, complemented
12C22×#4339C2211yescharacteristic
13C22×C11×M16C2211yescharacteristic
14C23×C8×C11C2211yescharacteristic
15C2×C11×#117C2211yescharacteristic
16C2×#66979C2211yescharacteristic
17C22×#4318C2211yescharacteristic
18C22×#4318C2211yescharacteristic
19#10623276—28no—
20C2×#66960C2214yes—
21C2×M16×D11C2214yes—
22C2×#66954—28no—
23C2×#66954C2214yes—
24C2×#66954C2214yes—
25C2×#66954C2214yes—
26C22×#4313C2212yes—
27C22×C8×D11C2212yes—
28#10623054C414yes—
29#10623053C2214yes—
30#10623052C412yes—
31D11×#117C2214yes—
32#10623047C412yes—
33#10623035C414yes—
34#10623017C414yes—
35C4×#4339C2214yes—
36C11×#424C2212yes—
37C11×#424C2212yes—
38C11×#424C2214yescomplemented
39C2×C11×C4⋊C8C2214yescomplemented
40#10622732C2214yes—
41#10622731C2214yescomplemented
42#10622715C2212yes—
43#10622715C2212yes—
44#10622715C2214yescomplemented
45#10622715C2214yescomplemented
46C2×Dic11⋊C8C2214yescomplemented
47#10622612C2214yes—
48#10622612C2214yescomplemented
49#10622537C2214yescomplemented
50#10622452C22116yescomplemented
51#10622452C22116yescomplemented
52#10622450C22116yescomplemented
53D11×C4⋊C8C22116yescomplemented
54C23×C4×C11C2311yescharacteristic
55C22×C22⋊D11C2×C412yes—
56C2×#4339C2×C412yes—
57C2×#4339C2×C412yes—
58C2×#4339D418yes—
59C2×#4339Q818yes—
60C2×#4339C2312yes—
61C2×#4339C2312yes—
62C22×D44C2×C411yescharacteristic
63C22×C4×D11C2312yes—
64C22×Dic22C2×C411yescharacteristic
65C2×C11×M16—24no—
66C2×C11×M16C2312yes—
67C2×C11×M16C2312yes—
68C22×C8×C11—24no—
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2312yes—
72C22×C8×C11C2312yes—
73C22×C8×C11C2312yes—
74C11×#117C2×C412yes—
75C11×#117C2×C412yes—
76C11×#117C2312yes—
77C11×#117C2312yes—
78C2×C11×C4⋊C4C2×C412yes—
79C2×C11×C22⋊C4C2×C412yes—
80C2×C42×C11C2312yes—
81C2×C22⋊Dic11C2×C412yes—
82C4×C22⋊D11C2×C4116yes—
83#66979C2×C412yes—
84#66979C2×C412yes—
85#66979C2312yes—
86#66979C2312yes—
87C2×C4⋊Dic11C2×C412yes—
88C2×C4×Dic11C2312yes—
89C2×#4318—24no—
90C2×#4318—24no—
91C2×#4318C2312yes—
92C2×#4318C2312yes—
93C2×#4318C2312yes—
94C2×#4318C2312yes—
95C22×C11⋊C8C2312yes—
96C22×C11⋊C8C2312yes—
97#66960—216no—
98M16×D11—216no—
99#66954—216no—
100#66954—216no—
101#66954—216no—
102C2×#4313—28no—
103C2×#4313C2318yes—
104C2×#4313C2318yes—
105C2×C8×D11—28no—
106C2×C8×D11C2318yes—
107C2×C8×D11C2318yes—
108#66946C2×C418yes—
109#66945C2×C418yes—
110C4⋊C4×D11C2×C418yes—
111#66940C2×C418yes—
112(C22⋊D11)⋊C4C2×C4116yes—
113C22⋊C4×D11C2×C418yes—
114#66930C2×C418yes—
115C4×D44C2×C418yes—
116#66925C2318yes—
117C42×D11C2318yes—
118C4×Dic22C2×C418yes—
119C11×C4⋊C8C2318yes—
120C11×C4⋊C8C2318yes—
121Dic11⋊C8C23116yes—
122Dic11⋊C8C2318yes—
123Dic11⋊C8C2318yes—
124C4⋊(C11⋊C8)C23116yes—
125#60100—111nomaximal, Sylow
126C24×C11C22×C411yescharacteristic
127C23×D11C22×C412yes—
128C22×C4×C11C22×C414yes—
129C22×C4×C11C22×C411yescharacteristic
130C22×C4×C11C22×C411yescharacteristic
131C22×C4×C11C22×C411yescharacteristic
132C22×C4×C11C2×D414yes—
133C22×C4×C11C2×Q814yes—
134C22×C4×C11C2411yescharacteristic
135C22×C4×C11C2411yescharacteristic
136C22×C4×C11C2411yescharacteristic
137C2×C22⋊D11C4⋊C4116yes—
138C2×C22⋊D11C22×C414yes—
139C2×C22⋊D11C22×C414yes—
140C22×Dic11C22×C414yes—
141C22×Dic11C22×C412yes—
142#4339C4⋊C4116yes—
143#4339C4⋊C4116yes—
144#4339C2×D418yes—
145#4339C2×D418yes—
146#4339C2×Q818yes—
147#4339C2×Q818yes—
148C2×D44C4⋊C418yes—
149C2×D44C22×C412yes—
150C2×D44C22×C412yes—
151C2×C4×D11C22×C4116yes—
152C2×C4×D11C22×C414yes—
153C2×C4×D11C2×D418yes—
154C2×C4×D11C2×Q818yes—
155C2×C4×D11C2414yes—
156C2×Dic22C4⋊C418yes—
157C2×Dic22C22×C412yes—
158C2×Dic22C22×C412yes—
159C11×M16—24no—
160C11×M16—24no—
161C2×C8×C11—22no—
162C2×C8×C11—22no—
163C2×C8×C11—24no—
164C2×C8×C11—24no—
165C2×C8×C11—24no—
166C2×C8×C11C2412yes—
167C2×C8×C11C2414yes—
168C2×C8×C11C2412yes—
169C11×C4⋊C4C22×C414yes—
170C11×C4⋊C4C22×C414yes—
171C11×C22⋊C4C22×C414yes—
172C11×C22⋊C4C22×C414yes—
173C42×C11C22×C414yes—
174C42×C11C2414yes—
175C22⋊Dic11C22×C414yes—
176C22⋊Dic11C22×C414yes—
177(C2×D11)⋊C4C22×C4116yes—
178C4⋊Dic11C22×C414yes—
179C4⋊Dic11C22×C414yes—
180Dic11⋊C4C22×C4116yes—
181C4×Dic11C22×C4116yes—
182C4×Dic11C22×C414yes—
183C4×Dic11C2414yes—
184#4318—24no—
185#4318—24no—
186#4318—24no—
187#4318—24no—
188C2×C11⋊C8—24no—
189C2×C11⋊C8—24no—
190C2×C11⋊C8C2414yes—
191C2×C11⋊C8C2414yes—
192#4313—216no—
193#4313—216no—
194C8×D11—216no—
195C8×D11—216no—
196C2×#568—111no—
197C22×#131—111no—
198#3428—111no—
199#2906—118no—
200#2906—118no—
201#2905—114no—
202#2905—111no—
203#2905—111no—
204C2×#424—114no—
205C2×#424—111no—
206C2×#424D1111yescharacteristic, complemented
207C23×C11—42no—
208C23×C11C2×C4⋊C414yes—
209C23×C11C23×C411yescharacteristic
210C23×C11C23×C411yescharacteristic
211C23×C11C23×C411yescharacteristic
212C22×D11—44no—
213C22×D11C2×C4⋊C418yes—
214C22×D11C23×C414yes—
215C2×C4×C11—44no—
216C2×C4×C11C2×C4⋊C414yes—
217C2×C4×C11C2×C4⋊C414yes—
218C2×C4×C11C2×C4⋊C414yes—
219C2×C4×C11C23×C418yes—
220C2×C4×C11C23×C411yescharacteristic
221C2×C4×C11C23×C411yescharacteristic
222C2×C4×C11C23×C411yescharacteristic
223C2×C4×C11C22×D412yes—
224C2×C4×C11C22×D412yes—
225C2×C4×C11C22×D412yes—
226C2×C4×C11C22×Q812yes—
227C2×C4×C11C22×Q812yes—
228C2×C4×C11C22×Q812yes—
229C2×C4×C11C2511yescharacteristic
230C22⋊D11C2×C4⋊C4116yes—
231C22⋊D11C2×C4⋊C4116yes—
232C2×Dic11—44no—
233C2×Dic11C2×C4⋊C418yes—
234C2×Dic11C23×C418yes—
235C2×Dic11C23×C414yes—
236D44C2×C4⋊C418yes—
237D44C2×C4⋊C418yes—
238C4×D11—416no—
239C4×D11C2×C4⋊C4116yes—
240C4×D11C22×D418yes—
241C4×D11C22×Q818yes—
242Dic22C2×C4⋊C418yes—
243Dic22C2×C4⋊C418yes—
244C8×C11—22no—
245C8×C11—24no—
246C8×C11—22no—
247C11⋊C8—24no—
248C11⋊C8—24no—
249C22×#41—111no—
250#568—228no—
251C2×#131—114no—
252C2×#131—114no—
253C2×#131—114no—
254C2×#131—114no—
255C2×#131—228no—
256C22×M16—111no—
257C22×M16—111no—
258C22×M16—114no—
259C22×M16—112no—
260C22×M16C2×D1111yescharacteristic
261C23×C8—112no—
262C23×C8C2×D1111yescharacteristic
263#520—114no—
264#520—114no—
265#519—112no—
266#518—112no—
267#518—114no—
268C4×#41—114no—
269C4×#41—114no—
270C2×#117—111no—
271C2×#117—114no—
272C2×#117C2×D1111yescharacteristic
273#424—114no—
274#424—112no—
275#424—112no—
276#424—114no—
277#424—114no—
278#424—114no—
279#424—114no—
280#424—1116no—
281#424—1116no—
282#424C2×D1112yes—
283#424C2×D1112yes—
284#424C2×D1114yescomplemented
285#423—114no—
286#423—114no—
287#423—1116no—
288C2×C4⋊C8—114no—
289C2×C4⋊C8—1116no—
290C2×C4⋊C8C2×D1114yescomplemented
291C22×C11—22no—
292C22×C11—22no—
293C22×C11—22no—
294C22×C11—44no—
295C22×C11C22×C4⋊C412yes—
296C22×C11C22×C4⋊C412yes—
297C22×C11C22×C4⋊C412yes—
298C22×C11C24×C411yescharacteristic
299C2×D11—28no—
300C2×D11—48no—
301C2×D11C22×C4⋊C418yes—
302C4×C11—28no—
303C4×C11C22×C4⋊C412yes—
304C4×C11C22×C4⋊C412yes—
305C4×C11C22×C4⋊C412yes—
306C4×C11C23×D411yescharacteristic
307C4×C11C23×Q811yescharacteristic
308Dic11—28no—
309Dic11C22×C4⋊C418yes—
310C2×#41—112no—
311C2×#41—112no—
312C2×#41—118no—
313C2×#41—118no—
314C2×#41—112no—
315C2×#41—112no—
316C22×Q8—111no—
317C22×D4—112no—
318C22×D4—111no—
319C23×C4—112no—
320C23×C4C22×D1111yescharacteristic
321#131—2216no—
322#131—2216no—
323#131—2216no—
324#131—2216no—
325C2×M16—24no—
326C2×M16—112no—
327C2×M16—112no—
328C2×M16—112no—
329C2×M16—112no—
330C2×M16—118no—
331C2×M16—118no—
332C2×M16—228no—
333C2×M16—2216no—
334C2×M16—224no—
335C2×M16—224no—
336C2×M16C22×D1112yes—
337C2×M16C22×D1112yes—
338C22×C8—24no—
339C22×C8—112no—
340C22×C8—112no—
341C22×C8—118no—
342C22×C8—118no—
343C22×C8—228no—
344C22×C8C22×D1111yescharacteristic
345C22×C8C22×D1111yescharacteristic
346C22×C8C22×D1112yes—
347C22×C8C22×D1112yes—
348C22×C8C22×D1112yes—
349C4×Q8—118no—
350C4×Q8—118no—
351C4×D4—1116no—
352C4×D4—118no—
353C4×D4—1116no—
354C4×D4—118no—
355#117—112no—
356#117—112no—
357#117—112no—
358#117—112no—
359#117—118no—
360#117—118no—
361#117—118no—
362#117C4×D1112yes—
363#117C4×D1112yes—
364#117C22×D1112yes—
365#117C22×D1112yes—
366C2×C4⋊C4—112no—
367C2×C4⋊C4—118no—
368C2×C4⋊C4C4×D1112yes—
369C2×C22⋊C4—112no—
370C2×C22⋊C4—118no—
371C2×C22⋊C4C4×D1112yes—
372C2×C42—112no—
373C2×C42—118no—
374C2×C42C22×D1112yes—
375C4⋊C8—118no—
376C4⋊C8—1116no—
377C4⋊C8—118no—
378C4⋊C8—1116no—
379C4⋊C8C22×D1118yes—
380C4⋊C8C22×D1118yes—
381C2×C11—22no—
382C2×C11—22no—
383C2×C11—22no—
384C2×C11C23×C4⋊C411yescharacteristic
385C2×C11#357312yes—
386D11—28no—
387C24—112no—
388C24C2×C4×D1111yescharacteristic
389#41—1116no—
390#41—1116no—
391#41—118no—
392#41—118no—
393#41—118no—
394#41—118no—
395C2×Q8—118no—
396C2×Q8—112no—
397C2×Q8—112no—
398C2×D4—1116no—
399C2×D4—114no—
400C2×D4—114no—
401C2×D4—118no—
402C2×D4—112no—
403C2×D4—112no—
404C22×C4—112no—
405C22×C4—114no—
406C22×C4—118no—
407C22×C4—118no—
408C22×C4—114no—
409C22×C4—114no—
410C22×C4—1116no—
411C22×C4C2×C4×D1114yes—
412C22×C4C2×C4×D1111yescharacteristic
413C22×C4C2×C4×D1111yescharacteristic
414C22×C4C2×C4×D1111yescharacteristic
415C22×C4D4×D1114yes—
416C22×C4Q8×D1114yes—
417C22×C4C23×D1111yescharacteristic
418C22×C4C23×D1111yescharacteristic
419C22×C4C23×D1111yescharacteristic
420M16—24no—
421M16—24no—
422M16—2216no—
423M16—2216no—
424M16—224no—
425M16—224no—
426M16—224no—
427M16—224no—
428C2×C8—22no—
429C2×C8—22no—
430C2×C8—24no—
431C2×C8—24no—
432C2×C8—24no—
433C2×C8—114no—
434C2×C8—114no—
435C2×C8—2216no—
436C2×C8—2216no—
437C2×C8—224no—
438C2×C8—224no—
439C2×C8C23×D1112yes—
440C2×C8C23×D1114yes—
441C2×C8C23×D1112yes—
442C4⋊C4—114no—
443C4⋊C4—1116no—
444C4⋊C4—114no—
445C4⋊C4C2×C4×D1114yes—
446C4⋊C4C2×C4×D1114yes—
447C22⋊C4—114no—
448C22⋊C4—114no—
449C22⋊C4—1116no—
450C22⋊C4C2×C4×D1114yes—
451C22⋊C4C2×C4×D1114yes—
452C42—1116no—
453C42—114no—
454C42—114no—
455C42C2×C4×D1114yes—
456C42C23×D1114yes—
457C11#6010011yescharacteristic, complemented, Sylow
458C23—42no—
459C23—114no—
460C23—118no—
461C23—444no—
462C23C4⋊C4×D1114yes—
463C23C22×C4×D1111yescharacteristic
464C23C22×C4×D1111yescharacteristic
465C23C22×C4×D1111yescharacteristic
466Q8—118no—
467Q8—118no—
468D4—1116no—
469D4—1116no—
470D4—118no—
471D4—118no—
472C2×C4—44no—
473C2×C4—118no—
474C2×C4—114no—
475C2×C4—1116no—
476C2×C4—118no—
477C2×C4—118no—
478C2×C4—118no—
479C2×C4—4416no—
480C2×C4—444no—
481C2×C4C4⋊C4×D1114yes—
482C2×C4C4⋊C4×D1114yes—
483C2×C4C4⋊C4×D1114yes—
484C2×C4C22×C4×D1118yes—
485C2×C4C22×C4×D1111yescharacteristic
486C2×C4C22×C4×D1111yescharacteristic
487C2×C4C22×C4×D1111yescharacteristic
488C2×C4C2×D4×D1112yes—
489C2×C4C2×D4×D1112yes—
490C2×C4C2×D4×D1112yes—
491C2×C4C2×Q8×D1112yes—
492C2×C4C2×Q8×D1112yes—
493C2×C4C2×Q8×D1112yes—
494C2×C4C24×D1111yescharacteristic
495C8—22no—
496C8—22no—
497C8—24no—
498C8—224no—
499C8—224no—
500C22—22no—
501C22—22no—
502C22—22no—
503C22—44no—
504C22—118no—
505C22—228no—
506C22—448no—
507C22C2×C4⋊C4×D1112yes—
508C22C2×C4⋊C4×D1112yes—
509C22C2×C4⋊C4×D1112yes—
510C22C23×C4×D1111yescharacteristic
511C4—28no—
512C4—118no—
513C4—228no—
514C4C2×C4⋊C4×D1112yes—
515C4C2×C4⋊C4×D1112yes—
516C4C2×C4⋊C4×D1112yes—
517C4C22×D4×D1111yescharacteristic
518C4C22×Q8×D1111yescharacteristic
519C2—22no—
520C2—22no—
521C2—22no—
522C2—228no—
523C2C22×C4⋊C4×D1111yescharacteristic
524C2#1308332712yes—
subgroupG/H
center, FrattiniC2×C4C24×D11
commutator, socleC22×C11C24×C4
FittingC2×C11×#424C2
prime radicalC22×#4339C22
cosocleC2×C4×C11C25
hypercenterC2×#424D11
hypocenterC11#60100
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×#424

Complements

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

NH ≅ G/Ntype
4. #13077183C2semidirect
5. #13077181C2semidirect
6. #13077180C2semidirect
7. #13077179C2semidirect
8. #13077177C2semidirect
9. C2×#10622715C2semidirect
10. D11×#424C2semidirect
11. C2×C11×#424C2semidirect
38. C11×#424C22semidirect
39. C2×C11×C4⋊C8C22semidirect
41. #10622731C22semidirect
44. #10622715C22semidirect
45. #10622715C22semidirect
46. C2×Dic11⋊C8C22semidirect
48. #10622612C22semidirect
49. #10622537C22semidirect
50. #10622452C22semidirect
51. #10622452C22semidirect
52. #10622450C22semidirect
53. D11×C4⋊C8C22semidirect
206. C2×#424D11semidirect
284. #424C2×D11semidirect
290. C2×C4⋊C8C2×D11semidirect
457. C11#60100semidirect

Maximal subgroups

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

subgroupindex
C2×#106232762
C22×#669542
#130818172
#130771832
#130771812
#130771802
#130771792
#130771772
C2×#106227152
D11×#4242
C2×C11×#4242
#6010011