Finite Group Databasebeta

← #14725519

Subgroups — #14725519

Order 2816.

652 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077742C211yesmaximal, characteristic, complemented
2#13077741C211yesmaximal, characteristic, complemented
3C4×#67003C211yesmaximal, characteristic
4#13067522C212yesmaximal, complemented
5#13067455C212yesmaximal, complemented
6#13067449C212yesmaximal, complemented
7#13067437C212yesmaximal, complemented
8#13067371C211yesmaximal, characteristic, complemented
9#13067056C211yesmaximal, characteristic, complemented
10#13066903C211yesmaximal, characteristic, complemented
11C11×#1489C211yesmaximal, characteristic, complemented
12C4×C11×#41C2211yescharacteristic
13C2×#67003C411yescharacteristic
14C4×#4339C2211yescharacteristic
15C11×#423C2211yescharacteristic
16C4×C11×M16C2211yescharacteristic
17#10622846C411yescharacteristic
18#10622740—22no—
19C4×#4326C411yescharacteristic
20C4×#4326C2211yescharacteristic
21C4×#4325C411yescharacteristic
22C4×#4325C2211yescharacteristic
23#10622637C2212yes—
24C4×#4324C411yescharacteristic
25C4×#4324C2211yescharacteristic
26C4×#4323C411yescharacteristic
27C4×#4323C2211yescharacteristic
28#10622624—22no—
29D4×C11⋊C8C2212yes—
30#10622615C411yescharacteristic
31#10622611C411yescharacteristic
32#10622539—21no—
33#10622538C2211yescharacteristic
34#10622537C2211yescharacteristic
35C2×C4⋊(C11⋊C8)—21no—
36C2×C4×C11⋊C8C2211yescharacteristic
37#10622448—21no—
38#10622447C2212yes—
39D11×C4⋊C8—21no—
40#10622444C2212yes—
41C11×Q8⋊C8C2212yes—
42C11×D4⋊C8C2212yes—
43#10622118C2212yes—
44#10622118C2212yes—
45#10622097C2212yes—
46#10622094C2212yes—
47#10622092C2212yes—
48#10622092C2212yes—
49C2×C11×#41C2×C411yescharacteristic
50C2×#4339C2×C411yescharacteristic
51C2×C11×M16—21no—
52C2×C11×M16—21no—
53C4×Q8×C11C2×C411yescharacteristic
54C4×Q8×C11C2311yescharacteristic
55C4×D4×C11—21no—
56C4×D4×C11—21no—
57C4×D4×C11C2×C411yescharacteristic
58C4×D4×C11C2311yescharacteristic
59C11×#117—21no—
60C11×#117C2×C411yescharacteristic
61C2×C42×C11—21no—
62C2×C42×C11C2311yescharacteristic
63#67003—24no—
64C2×#4326C2×C411yescharacteristic
65C2×#4325C2×C411yescharacteristic
66C2×#4324C2×C411yescharacteristic
67C2×#4323C2×C411yescharacteristic
68C4×C22⋊D11—21no—
69C4×C22⋊D11—21no—
70#66979C2×C411yescharacteristic
71C2×#4318—21no—
72C22×C11⋊C8—22no—
73C22×C11⋊C8C2×C411yescharacteristic
74C22×C11⋊C8C2×C411yescharacteristic
75C2×C8×D11—22no—
76C4×D44C2×C411yescharacteristic
77C4×D44C2311yescharacteristic
78#66925—21no—
79C42×D11—21no—
80C4×Dic22C2×C411yescharacteristic
81C4×Dic22C2311yescharacteristic
82C11×C4⋊C8—21no—
83C11×C4⋊C8C2312yes—
84C11×#97—21no—
85C4×C8×C11C2312yes—
86#66899C2×C411yescharacteristic
87#66899C2×C411yescharacteristic
88#66896C2×C411yescharacteristic
89#66896C2×C411yescharacteristic
90C22⋊(C11⋊C8)—22no—
91C22⋊(C11⋊C8)D412yes—
92(C2×D11)⋊C8—22no—
93#66879—22no—
94Dic11⋊C8—22no—
95#66874C2×C411yescharacteristic
96#66874C2×C411yescharacteristic
97#66873C2×C411yescharacteristic
98#66873C2×C411yescharacteristic
99#66872C2×C411yescharacteristic
100#66872C2×C411yescharacteristic
101#66871C2×C411yescharacteristic
102#66871C2×C411yescharacteristic
103C4⋊(C11⋊C8)—21no—
104C4⋊(C11⋊C8)—22no—
105C4⋊(C11⋊C8)D411yescharacteristic
106C4⋊(C11⋊C8)D411yescharacteristic
107C4⋊(C11⋊C8)C2312yes—
108#66867—22no—
109C4×C11⋊C8C2×C411yescharacteristic
110C4×C11⋊C8C2×C411yescharacteristic
111C4×C11⋊C8C2311yescharacteristic
112C4×C11⋊C8C2311yescharacteristic
113C4×C11⋊C8C2312yes—
114#18065—111nomaximal, Sylow
115C11×#41—22no—
116C11×#41—41no—
117C2×Q8×C11C22×C411yescharacteristic
118C2×D4×C11—21no—
119C2×D4×C11C22×C411yescharacteristic
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11C22×C411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11#4111yescharacteristic
126C2×C22⋊D11—21no—
127#4339—22no—
128#4339—41no—
129C2×D44C22×C411yescharacteristic
130C2×C4×D11—21no—
131C2×C4×D11—21no—
132C2×C4×D11—21no—
133C2×Dic22C22×C411yescharacteristic
134C11×M16—42no—
135C11×M16—81no—
136C2×C8×C11—22no—
137C2×C8×C11—22no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4C22×C411yescharacteristic
141C11×C4⋊C4C22×C411yescharacteristic
142C11×C22⋊C4—21no—
143C11×C22⋊C4—21no—
144C11×C22⋊C4—21no—
145C42×C11—21no—
146C42×C11—21no—
147C42×C11—21no—
148C42×C11C22×C411yescharacteristic
149C42×C11C2×D411yescharacteristic
150C42×C11#4111yescharacteristic
151C42×C11C2411yescharacteristic
152C22⋊Dic11—21no—
153#4326—22no—
154#4325—22no—
155#4324—22no—
156#4323M1614yescomplemented
157(C2×D11)⋊C4—21no—
158(C2×D11)⋊C4—21no—
159C4⋊Dic11C22×C411yescharacteristic
160C4⋊Dic11C22×C411yescharacteristic
161Dic11⋊C4—21no—
162Dic11⋊C4—21no—
163C4×Dic11—21no—
164C4×Dic11—21no—
165C4×Dic11—21no—
166#4318—81no—
167C2×C11⋊C8—22no—
168C2×C11⋊C8—22no—
169C2×C11⋊C8—41no—
170C2×C11⋊C8—82no—
171C2×C11⋊C8C22×C411yescharacteristic
172C2×C11⋊C8C22×C411yescharacteristic
173C2×C11⋊C8C22×C411yescharacteristic
174C2×C11⋊C8C22×C411yescharacteristic
175C2×C11⋊C8C2×D412yes—
176C2×C11⋊C8C2×D412yes—
177C8×D11—82no—
178#2990—111no—
179#2990—111no—
180C4×#135—111no—
181#1593—112no—
182#1582—112no—
183#1582—112no—
184#1580—112no—
185#1566—111no—
186#1489—111no—
187#1489D1111yescharacteristic, complemented
188#1451—111no—
189C23×C11—21no—
190C23×C11C4×D411yescharacteristic
191C22×D11—21no—
192Q8×C11—21no—
193Q8×C11—21no—
194D4×C11—21no—
195D4×C11—42no—
196D4×C11C2×M1612yes—
197C2×C4×C11—21no—
198C2×C4×C11—21no—
199C2×C4×C11—21no—
200C2×C4×C11—21no—
201C2×C4×C11—22no—
202C2×C4×C11—21no—
203C2×C4×C11—21no—
204C2×C4×C11—21no—
205C2×C4×C11—42no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—42no—
209C2×C4×C11C4×D411yescharacteristic
210C2×C4×C11C4×D411yescharacteristic
211C2×C4×C11C4×D411yescharacteristic
212C2×C4×C11C23×C411yescharacteristic
213C2×C4×C11C22×D411yescharacteristic
214C2×C4×C11C2×#4111yescharacteristic
215C22⋊D11—42no—
216C2×Dic11—21no—
217C2×Dic11—21no—
218C2×Dic11—21no—
219D44—21no—
220D44C2×M1612yes—
221C4×D11—42no—
222C4×D11—41no—
223C4×D11—41no—
224C4×D11—42no—
225Dic22—21no—
226Dic22—21no—
227C8×C11—42no—
228C8×C11—42no—
229C11⋊C8—21no—
230C11⋊C8—21no—
231C11⋊C8—21no—
232C11⋊C8—22no—
233C11⋊C8—22no—
234C11⋊C8—42no—
235C11⋊C8C2×M1612yes—
236C2×#135—111no—
237C4×#41—111no—
238C4×#41C2×D1111yescharacteristic
239#446—112no—
240#446—112no—
241C4×Q16—111no—
242C4×Q16—111no—
243C4×SD16—111no—
244C4×SD16—111no—
245C4×SD16—111no—
246C4×SD16—111no—
247C4×D8—111no—
248C4×D8—111no—
249#435—222no—
250#435—222no—
251C8×D4—112no—
252C8×D4—112no—
253#432—221no—
254#432—221no—
255#431—111no—
256#427—111no—
257#423—111no—
258#423C2×D1111yescharacteristic
259C2×C4⋊C8—221no—
260C2×C4⋊C8—221no—
261#416—111no—
262#416—111no—
263C4×M16C2×D1111yescharacteristic
264C2×C4×C8—111no—
265#334—112no—
266#334—112no—
267Q8⋊C8—112no—
268Q8⋊C8C2×D1112yes—
269D4⋊C8—112no—
270D4⋊C8C2×D1112yes—
271#322—112no—
272#322—112no—
273C22×C11—21no—
274C22×C11—22no—
275C22×C11—21no—
276C22×C11—21no—
277C22×C11—41no—
278C22×C11—41no—
279C22×C11C2×C4×D411yescharacteristic
280C2×D11—22no—
281C2×D11—41no—
282C2×D11—41no—
283C4×C11—21no—
284C4×C11—21no—
285C4×C11—21no—
286C4×C11—41no—
287C4×C11—41no—
288C4×C11—41no—
289C4×C11#44412yes—
290C4×C11C22×M1611yescharacteristic
291C4×C11#56811yescharacteristic
292C4×C11#57711yescharacteristic
293C4×C11#57711yescharacteristic
294Dic11—41no—
295Dic11—41no—
296Dic11—41no—
297C2×#41—111no—
298C2×#41C4×D1111yescharacteristic
299#135—224no—
300C2×Q16—111no—
301C2×SD16—111no—
302C2×SD16—111no—
303C2×D8—111no—
304C2×M16—21no—
305C2×M16—21no—
306C2×M16—221no—
307C22×C8—111no—
308C22×C8—111no—
309C22×C8—222no—
310C22×C8—222no—
311C4×Q8—111no—
312C4×Q8—111no—
313C4×Q8C4×D1111yescharacteristic
314C4×Q8C22×D1111yescharacteristic
315C4×D4—21no—
316C4×D4—21no—
317C4×D4—111no—
318C4×D4—111no—
319C4×D4—221no—
320C4×D4—221no—
321C4×D4C4×D1111yescharacteristic
322C4×D4C22×D1111yescharacteristic
323#117—21no—
324#117—111no—
325#117—221no—
326#117C4×D1111yescharacteristic
327C2×C42—21no—
328C2×C42—221no—
329C2×C42C22×D1111yescharacteristic
330#107—111no—
331#107—111no—
332#106—111no—
333#106—111no—
334C4⋊C8—21no—
335C4⋊C8—111no—
336C4⋊C8—111no—
337C4⋊C8—112no—
338C4⋊C8—222no—
339C4⋊C8—222no—
340C4⋊C8—221no—
341C4⋊C8C22×D1112yes—
342#103—111no—
343#103—111no—
344#103—111no—
345#103—111no—
346#102—111no—
347#102—111no—
348#102—111no—
349#102—111no—
350C22⋊C8—112no—
351C22⋊C8—222no—
352C22⋊C8—222no—
353#97—21no—
354#97—222no—
355#97—222no—
356C4×C8—111no—
357C4×C8—111no—
358C4×C8—111no—
359C4×C8—111no—
360C4×C8—112no—
361C4×C8C22×D1112yes—
362C2×C11—41no—
363C2×C11—42no—
364C2×C11D4×M1611yescharacteristic
365C2×C11#295211yescharacteristic
366C2×C11C2×#44411yescharacteristic
367D11—42no—
368#41—22no—
369#41—41no—
370#41—222no—
371#41—441no—
372C2×Q8—111no—
373C2×Q8C2×C4×D1111yescharacteristic
374C2×D4—21no—
375C2×D4—111no—
376C2×D4—221no—
377C2×D4C2×C4×D1111yescharacteristic
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—221no—
382C22×C4—221no—
383C22×C4—221no—
384C22×C4C2×C4×D1111yescharacteristic
385C22×C4D4×D1111yescharacteristic
386C22×C4#434111yescharacteristic
387Q16—222no—
388SD16—222no—
389SD16—222no—
390D8—114no—
391M16—42no—
392M16—81no—
393M16—881no—
394C2×C8—22no—
395C2×C8—22no—
396C2×C8—111no—
397C2×C8—111no—
398C2×C8—111no—
399C2×C8—111no—
400C2×C8—112no—
401C2×C8—112no—
402C2×C8—222no—
403C2×C8—222no—
404C2×C8—441no—
405C2×C8—882no—
406C2×C8—882no—
407C4⋊C4—21no—
408C4⋊C4—21no—
409C4⋊C4—111no—
410C4⋊C4—111no—
411C4⋊C4—221no—
412C4⋊C4—221no—
413C4⋊C4C2×C4×D1111yescharacteristic
414C4⋊C4C2×C4×D1111yescharacteristic
415C22⋊C4—21no—
416C22⋊C4—21no—
417C22⋊C4—21no—
418C22⋊C4—221no—
419C22⋊C4—221no—
420C22⋊C4—221no—
421C42—21no—
422C42—21no—
423C42—21no—
424C42—221no—
425C42—221no—
426C42—221no—
427C42C2×C4×D1111yescharacteristic
428C42D4×D1111yescharacteristic
429C42#434111yescharacteristic
430C42C23×D1111yescharacteristic
431C11#1806511yescharacteristic, complemented, Sylow
432C23—21no—
433C23—221no—
434C23(C22⋊D11)⋊C411yescharacteristic
435Q8—21no—
436Q8—21no—
437Q8—221no—
438Q8—221no—
439D4—21no—
440D4—42no—
441D4—112no—
442D4—221no—
443D4—442no—
444D4M16×D1112yes—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—22no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—42no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—42no—
457C2×C4—221no—
458C2×C4—221no—
459C2×C4—221no—
460C2×C4—442no—
461C2×C4—441no—
462C2×C4—441no—
463C2×C4—442no—
464C2×C4(C22⋊D11)⋊C411yescharacteristic
465C2×C4(C22⋊D11)⋊C411yescharacteristic
466C2×C4(C22⋊D11)⋊C411yescharacteristic
467C2×C4C22×C4×D1111yescharacteristic
468C2×C4C2×D4×D1111yescharacteristic
469C2×C4C2×#434111yescharacteristic
470C8—42no—
471C8—42no—
472C8—112no—
473C8—221no—
474C8—221no—
475C8—221no—
476C8—222no—
477C8—222no—
478C8—442no—
479C22—21no—
480C22—21no—
481C22—22no—
482C22—21no—
483C22—41no—
484C22—41no—
485C22—222no—
486C22—441no—
487C22—441no—
488C22C2×(C22⋊D11)⋊C411yescharacteristic
489C4—21no—
490C4—21no—
491C4—21no—
492C4—41no—
493C4—41no—
494C4—41no—
495C4—441no—
496C4—441no—
497C4—441no—
498C4#1062243612yes—
499C4C2×M16×D1111yescharacteristic
500C4#1062327611yescharacteristic
501C4#1062330611yescharacteristic
502C4#1062330911yescharacteristic
503C2—41no—
504C2—42no—
505C2—442no—
506C2#1307734811yescharacteristic
507C2#1307749511yescharacteristic
508C2C2×#1062243611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1489C2
socleC22×C11C2×C4×D4
prime radicalC2×#67003C4
cosocleC42×C11C24
hypercenter#1489D11
hypocenterC11#18065
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1489

Complements

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

NH ≅ G/Ntype
1. #13077742C2semidirect
2. #13077741C2semidirect
4. #13067522C2semidirect
5. #13067455C2semidirect
6. #13067449C2semidirect
7. #13067437C2semidirect
8. #13067371C2semidirect
9. #13067056C2semidirect
10. #13066903C2semidirect
11. C11×#1489C2semidirect
156. #4323M16semidirect
187. #1489D11semidirect
431. C11#18065semidirect

Maximal subgroups

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

subgroupindex
#130777422
#130777412
C4×#670032
#130675222
#130674552
#130674492
#130674372
#130673712
#130670562
#130669032
C11×#14892
#1806511