Finite Group Databasebeta

← #14739187

Subgroups — #14739187

Order 2816.

758 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079536C211yesmaximal, characteristic, complemented
2#13078096C211yesmaximal, characteristic, complemented
3#13078071C211yesmaximal, characteristic, complemented
4#13068060C212yesmaximal, complemented
5#13068053C212yesmaximal, complemented
6#13067976C212yesmaximal, complemented
7#13067971C212yesmaximal, complemented
8#13067391C211yesmaximal, characteristic, complemented
9#13067291C211yesmaximal, characteristic, complemented
10C2×#10622123C211yesmaximal, characteristic, complemented
11C11×#2988C211yesmaximal, characteristic, complemented
12C4×C11×#41C2211yescharacteristic
13C2×#67003—21no—
14C2×#67002—21no—
15#10623008C2211yescharacteristic
16C2×#66927C2211yescharacteristic
17C8×Q8×C11C2212yescomplemented
18C8×D4×C11—22no—
19C8×D4×C11C2212yescomplemented
20C11×#431—21no—
21C11×#431C2211yescharacteristic
22C2×C11×C4⋊C8—21no—
23C2×C11×C4⋊C8C2211yescharacteristic
24#10622644C2211yescharacteristic, complemented
25#10622641—21no—
26#10622640—21no—
27#10622640C2212yes—
28#10622640C2211yescharacteristic, complemented
29#10622632C2211yescharacteristic, complemented
30#10622629—21no—
31#10622628—21no—
32#10622628C2212yes—
33#10622628C2211yescharacteristic, complemented
34#10622615—21no—
35#10622614—21no—
36#10622537C2211yescharacteristic
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38#10622456—21no—
39#10622456—21no—
40#10622345—22no—
41#10622308C2212yes—
42#10622307C2212yes—
43#10622124C2212yescomplemented
44#10622123C2212yes—
45#10622123C2212yes—
46#10622123C2212yescomplemented
47#10622096C2212yescomplemented
48#10622096C2212yescomplemented
49C2×C11×#41D411yescharacteristic
50C2×#4339—21no—
51C22×D44—21no—
52C22×D44—21no—
53C22×D44—21no—
54C22×C8×C11—21no—
55C22×C8×C11—22no—
56C4×Q8×C11D411yescharacteristic
57C4×Q8×C11C2311yescharacteristic
58C4×D4×C11—21no—
59C4×D4×C11—21no—
60C4×D4×C11D411yescharacteristic
61C4×D4×C11C2311yescharacteristic
62C11×#117—21no—
63C11×#117D411yescharacteristic
64C2×C42×C11—21no—
65C2×C42×C11C2311yescharacteristic
66#67003—44no—
67#67002—44no—
68C2×#4326—21no—
69C2×#4325—22no—
70C2×#4325—21no—
71C2×#4324—21no—
72C2×#4323—22no—
73C2×#4323—21no—
74#66983—21no—
75#66983—21no—
76C2×#4318—21no—
77C22×C11⋊C8—21no—
78C2×D88—22no—
79C2×D88—22no—
80#66928—21no—
81#66927—21no—
82#66927—21no—
83#66927—21no—
84#66927C2312yes—
85#66927C2311yescharacteristic
86C4×D44—21no—
87C4×D44—21no—
88#66922C2311yescharacteristic
89C11×C4⋊C8—22no—
90C11×C4⋊C8—21no—
91C11×C4⋊C8D411yescharacteristic
92C11×C4⋊C8D411yescharacteristic
93C11×C4⋊C8C2312yes—
94C11×C22⋊C8—22no—
95C11×C22⋊C8D412yes—
96C4×C8×C11—22no—
97C4×C8×C11C2312yes—
98#66885—22no—
99#66885—22no—
100#66874—21no—
101#66874—21no—
102#66873—22no—
103#66873—22no—
104#66873—21no—
105#66873—21no—
106C4⋊(C11⋊C8)—21no—
107C4⋊(C11⋊C8)—21no—
108C4⋊(C11⋊C8)C2311yescharacteristic
109C4⋊(C11⋊C8)C2311yescharacteristic
110C4⋊(C11⋊C8)C2312yes—
111#19410—111nomaximal, Sylow
112C23×D11—41no—
113C11×#41—22no—
114C11×#41D814yescomplemented
115C2×Q8×C11C2×D411yescharacteristic
116C2×D4×C11—21no—
117C2×D4×C11C2×D411yescharacteristic
118C22×C4×C11—21no—
119C22×C4×C11—21no—
120C22×C4×C11—21no—
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11#4111yescharacteristic
124C2×C22⋊D11—41no—
125#4339—42no—
126#4339—42no—
127C2×D44—22no—
128C2×D44—21no—
129C2×D44—22no—
130C2×D44—21no—
131C2×D44—21no—
132C2×D44—22no—
133C2×D44—41no—
134C2×D44—41no—
135C2×D44—41no—
136C2×D44—42no—
137C2×D44—42no—
138C2×D44—81no—
139C2×D44—81no—
140C2×D44—82no—
141C2×C4×D11—41no—
142C2×Dic22—21no—
143C2×C8×C11—22no—
144C2×C8×C11—81no—
145C2×C8×C11—82no—
146C2×C8×C11C2×D412yes—
147C2×C8×C11C2×D412yes—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4C2×D411yescharacteristic
151C11×C4⋊C4C2×D411yescharacteristic
152C11×C22⋊C4—21no—
153C11×C22⋊C4—21no—
154C11×C22⋊C4—21no—
155C42×C11—21no—
156C42×C11—21no—
157C42×C11—21no—
158C42×C11C2×D411yescharacteristic
159C42×C11C2×D411yescharacteristic
160C42×C11#4111yescharacteristic
161C42×C11C2411yescharacteristic
162#4326—42no—
163#4325—44no—
164#4325—42no—
165#4324—42no—
166#4323—44no—
167#4323—42no—
168(C2×D11)⋊C4—41no—
169(C2×D11)⋊C4—41no—
170C4⋊Dic11—21no—
171C4⋊Dic11—21no—
172#4318—42no—
173C2×C11⋊C8—22no—
174C2×C11⋊C8—21no—
175C2×C11⋊C8—21no—
176C2×C11⋊C8—42no—
177D88—82no—
178D88—82no—
179#3205—111no—
180#3038—111no—
181#3035—111no—
182#2988D1111yescharacteristic, complemented
183#1682—112no—
184#1681—112no—
185#1668—112no—
186#1667—112no—
187#1571—111no—
188#1547—111no—
189C2×#331—111no—
190C23×C11—21no—
191C23×C11#12111yescharacteristic
192C22×D11—41no—
193C22×D11—42no—
194C22×D11—82no—
195C22×D11—82no—
196C22×D11—82no—
197Q8×C11—21no—
198Q8×C11C2×D812yes—
199D4×C11—24no—
200D4×C11—21no—
201D4×C11C2×D812yes—
202C2×C4×C11—21no—
203C2×C4×C11—21no—
204C2×C4×C11—21no—
205C2×C4×C11—24no—
206C2×C4×C11—21no—
207C2×C4×C11—21no—
208C2×C4×C11—41no—
209C2×C4×C11—41no—
210C2×C4×C11—41no—
211C2×C4×C11—81no—
212C2×C4×C11#12111yescharacteristic
213C2×C4×C11#12111yescharacteristic
214C2×C4×C11#12111yescharacteristic
215C2×C4×C11C2×D812yes—
216C2×C4×C11#13512yes—
217C2×C4×C11C22×D411yescharacteristic
218C2×C4×C11C22×D411yescharacteristic
219C2×C4×C11C2×#4111yescharacteristic
220C22⋊D11—82no—
221C2×Dic11—41no—
222D44—42no—
223D44—41no—
224D44—42no—
225D44—41no—
226D44—41no—
227D44—42no—
228D44—41no—
229D44—42no—
230D44—81no—
231D44—82no—
232D44—82no—
233D44—82no—
234D44—82no—
235C4×D11—82no—
236Dic22—41no—
237Dic22—41no—
238C8×C11—22no—
239C8×C11—22no—
240C8×C11—42no—
241C11⋊C8—41no—
242C11⋊C8—41no—
243C11⋊C8—42no—
244C2×AGL(1,ℤ/8)—221no—
245C2×#135—221no—
246#532—111no—
247C2×#127—111no—
248C4×#41C2×D1111yescharacteristic
249#493—112no—
250#486—112no—
251#464—221no—
252#463—221no—
253#462—111no—
254#461—111no—
255#460—111no—
256#460—112no—
257#460—221no—
258#459—111no—
259#459—112no—
260#459—221no—
261#459—221no—
262#459—221no—
263#447—222no—
264C8×Q8C2×D1112yescomplemented
265C8×D4—22no—
266C8×D4C2×D1112yescomplemented
267#431—21no—
268#431C2×D1111yescharacteristic
269#423—111no—
270C2×C4⋊C8—21no—
271C2×C4⋊C8—111no—
272C2×C4⋊C8C2×D1111yescharacteristic
273#418—221no—
274#416—221no—
275#335—112no—
276#335—112no—
277#332—112no—
278#331—112no—
279#331—112no—
280#331—112no—
281C22×C11—21no—
282C22×C11—21no—
283C22×C11—22no—
284C22×C11—41no—
285C22×C11—41no—
286C22×C11#46612yes—
287C22×C11C2×#12111yescharacteristic
288C2×D11—82no—
289C2×D11—81no—
290C2×D11—82no—
291C2×D11—81no—
292C2×D11—82no—
293C2×D11—81no—
294C2×D11—164no—
295C4×C11—21no—
296C4×C11—22no—
297C4×C11—21no—
298C4×C11—21no—
299C4×C11—41no—
300C4×C11—41no—
301C4×C11#46612yes—
302C4×C11C22×D811yescharacteristic
303C4×C11C2×#13511yescharacteristic
304C4×C11#57611yescharacteristic
305C4×C11#57711yescharacteristic
306Dic11—81no—
307C2×#41—221no—
308C2×#41D4411yescharacteristic
309C22×D4—221no—
310C22×D4—221no—
311C22×D4—221no—
312AGL(1,ℤ/8)—444no—
313#135—444no—
314C2×Q16—221no—
315C2×SD16—221no—
316C2×SD16—222no—
317C2×SD16—221no—
318C2×D8—221no—
319C2×D8—222no—
320C2×D8—222no—
321C2×D8—222no—
322C2×M16—221no—
323C22×C8—21no—
324C22×C8—22no—
325C22×C8—221no—
326C4⋊Q8—111no—
327#127—112no—
328#127—111no—
329#127—221no—
330#127—221no—
331#127—221no—
332#124—221no—
333#121—221no—
334#121—221no—
335C4×Q8D4411yescharacteristic
336C4×Q8C22×D1111yescharacteristic
337C4×D4—21no—
338C4×D4—21no—
339C4×D4—221no—
340C4×D4—221no—
341C4×D4D4411yescharacteristic
342C4×D4C22×D1111yescharacteristic
343#117—21no—
344#117D4411yescharacteristic
345C2×C42—21no—
346C2×C42C22×D1111yescharacteristic
347C4⋊C8—22no—
348C4⋊C8—21no—
349C4⋊C8—111no—
350C4⋊C8—111no—
351C4⋊C8—112no—
352C4⋊C8—221no—
353C4⋊C8—221no—
354C4⋊C8C22⋊D1111yescharacteristic
355C4⋊C8C22⋊D1111yescharacteristic
356C4⋊C8C22×D1112yes—
357#103—221no—
358#103—221no—
359#102—222no—
360#102—222no—
361#102—221no—
362#102—221no—
363#102—222no—
364#102—222no—
365C22⋊C8—22no—
366C22⋊C8C22⋊D1112yes—
367C4×C8—22no—
368C4×C8C22×D1112yes—
369C2×C11—22no—
370C2×C11—42no—
371C2×C11#304511yescharacteristic
372C2×C11C2×#46611yescharacteristic
373C2×C11#306811yescharacteristic
374D11—161no—
375D11—162no—
376C24—441no—
377#41—22no—
378#41—442no—
379#41—442no—
380#41D8814yescomplemented
381C2×Q8—221no—
382C2×Q8C2×D4411yescharacteristic
383C2×D4—21no—
384C2×D4—221no—
385C2×D4—222no—
386C2×D4—221no—
387C2×D4—222no—
388C2×D4—222no—
389C2×D4—221no—
390C2×D4—441no—
391C2×D4—442no—
392C2×D4—442no—
393C2×D4—441no—
394C2×D4—441no—
395C2×D4—441no—
396C2×D4—881no—
397C2×D4—881no—
398C2×D4—882no—
399C2×D4C2×D4411yescharacteristic
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—441no—
404C22×C4C2×D4411yescharacteristic
405C22×C4#433911yescharacteristic
406C22×C4C2×C22⋊D1111yescharacteristic
407Q16—442no—
408SD16—442no—
409SD16—444no—
410SD16—442no—
411D8—442no—
412D8—444no—
413D8—882no—
414D8—882no—
415M16—442no—
416C2×C8—22no—
417C2×C8—82no—
418C2×C8—81no—
419C2×C8—222no—
420C2×C8—221no—
421C2×C8—221no—
422C2×C8—442no—
423C2×C8C2×C22⋊D1112yes—
424C2×C8C2×C22⋊D1112yes—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—221no—
428C4⋊C4—221no—
429C4⋊C4C2×D4411yescharacteristic
430C4⋊C4C2×D4411yescharacteristic
431C22⋊C4—21no—
432C22⋊C4—21no—
433C22⋊C4—21no—
434C22⋊C4—441no—
435C22⋊C4—441no—
436C42—21no—
437C42—21no—
438C42—21no—
439C42C2×D4411yescharacteristic
440C42#433911yescharacteristic
441C42C2×C22⋊D1111yescharacteristic
442C42C23×D1111yescharacteristic
443C11#1941011yescharacteristic, complemented, Sylow
444C23—21no—
445C23—441no—
446C23—442no—
447C23—882no—
448C23—882no—
449C23—882no—
450C23#6698311yescharacteristic
451Q8—21no—
452Q8—441no—
453Q8—441no—
454Q8C2×D8812yes—
455D4—24no—
456D4—21no—
457D4—442no—
458D4—441no—
459D4—442no—
460D4—441no—
461D4—441no—
462D4—442no—
463D4—441no—
464D4—442no—
465D4—882no—
466D4—881no—
467D4—882no—
468D4—882no—
469D4—882no—
470D4—882no—
471D4C2×D8812yes—
472C2×C4—21no—
473C2×C4—24no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—81no—
482C2×C4—441no—
483C2×C4—882no—
484C2×C4C2×D8812yes—
485C2×C4#6695712yes—
486C2×C4#6698311yescharacteristic
487C2×C4#6698311yescharacteristic
488C2×C4#6698311yescharacteristic
489C2×C4C22×D4411yescharacteristic
490C2×C4C2×#433911yescharacteristic
491C2×C4C22×C22⋊D1111yescharacteristic
492C8—22no—
493C8—22no—
494C8—42no—
495C8—441no—
496C8—441no—
497C8—442no—
498C22—21no—
499C22—21no—
500C22—22no—
501C22—41no—
502C22—41no—
503C22—882no—
504C22—881no—
505C22—882no—
506C22—881no—
507C22—881no—
508C22—882no—
509C22—1764no—
510C22#1062272812yes—
511C22C2×#6698311yescharacteristic
512C4—21no—
513C4—21no—
514C4—21no—
515C4—22no—
516C4—41no—
517C4—41no—
518C4—881no—
519C4#1062272812yes—
520C4C22×D8811yescharacteristic
521C4C2×#6695711yescharacteristic
522C4#1062336611yescharacteristic
523C4#1062336811yescharacteristic
524C2—22no—
525C2—42no—
526C2—1762no—
527C2—1761no—
528C2#1307815511yescharacteristic
529C2C2×#1062272811yescharacteristic
530C2#1307834411yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2988C2
socleC22×C11C2×#121
hypercenter#2988D11
hypocenterC11#19410
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2988

Complements

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

NH ≅ G/Ntype
1. #13079536C2semidirect
2. #13078096C2semidirect
3. #13078071C2semidirect
4. #13068060C2semidirect
5. #13068053C2semidirect
6. #13067976C2semidirect
7. #13067971C2semidirect
8. #13067391C2semidirect
9. #13067291C2semidirect
10. C2×#10622123C2semidirect
11. C11×#2988C2semidirect
17. C8×Q8×C11C22semidirect
19. C8×D4×C11C22semidirect
24. #10622644C22semidirect
28. #10622640C22semidirect
29. #10622632C22semidirect
33. #10622628C22semidirect
43. #10622124C22semidirect
46. #10622123C22semidirect
47. #10622096C22semidirect
48. #10622096C22semidirect
114. C11×#41D8semidirect
182. #2988D11semidirect
264. C8×Q8C2×D11semidirect
266. C8×D4C2×D11semidirect
380. #41D88semidirect
443. C11#19410semidirect

Maximal subgroups

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

subgroupindex
#130795362
#130780962
#130780712
#130680602
#130680532
#130679762
#130679712
#130673912
#130672912
C2×#106221232
C11×#29882
#1941011