Finite Group Databasebeta

← #14909104

Subgroups — #14909104

Order 2816.

602 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
1#13079153C211yesmaximal, characteristic, complemented
2#13079098C211yesmaximal, characteristic
3#13070859C211yesmaximal, characteristic, complemented
4#13070856C211yesmaximal, characteristic, complemented
5#13070854C211yesmaximal, characteristic, complemented
6#13070852C211yesmaximal, characteristic, complemented
7#13070849C211yesmaximal, characteristic, complemented
8#13070840C211yesmaximal, characteristic, complemented
9#13070838C211yesmaximal, characteristic, complemented
10#13070330C211yesmaximal, characteristic, complemented
11#13070327C211yesmaximal, characteristic, complemented
12#13070322C211yesmaximal, characteristic, complemented
13D11×#357C211yesmaximal, characteristic, complemented
14#13070211C211yesmaximal, characteristic, complemented
15C11×#2242C211yesmaximal, characteristic, complemented
16C2×#66972C2211yescharacteristic
17C2×#66967—21no—
18C2×D8×D11C2211yescharacteristic
19#10623220—21no—
20#10623205—21no—
21C11×#499C2211yescharacteristic, complemented
22C11×#495C2211yescharacteristic
23#10622804C2211yescharacteristic
24#10622789—21no—
25#10622764C2211yescharacteristic
26#10622678—21no—
27#10622671—21no—
28C2×#66862C2211yescharacteristic
29C2×C16×D11C2211yescharacteristic
30#10622493C2211yescharacteristic
31D11×#107C2211yescharacteristic
32#10622491C2211yescharacteristic, complemented
33#10622487C2211yescharacteristic, complemented
34#10622474—21no—
35#10622469—21no—
36#10622308C2211yescharacteristic
37#10622302C2211yescharacteristic
38#10622295C2211yescharacteristic, complemented
39C11×#358C2211yescharacteristic, complemented
40C11×#358C2211yescharacteristic, complemented
41C11×#357C2211yescharacteristic
42C11×#357C2211yescharacteristic
43C4×C11×C16C2211yescharacteristic, complemented
44#10622202C2211yescharacteristic, complemented
45#10622202C2211yescharacteristic, complemented
46#10622200C2211yescharacteristic
47#10622200C2211yescharacteristic
48#10622147C2211yescharacteristic
49#10622147C2211yescharacteristic
50#10622147C2211yescharacteristic, complemented
51#10622147C2211yescharacteristic, complemented
52#10622140C2211yescharacteristic, complemented
53C16×Dic11C2211yescharacteristic, complemented
54#10622129C2211yescharacteristic
55#10622129C2211yescharacteristic
56#10622129C2211yescharacteristic, complemented
57#10622129C2211yescharacteristic, complemented
58#10622099C2211yescharacteristic, complemented
59C2×#4343—21no—
60C2×D4×D11—21no—
61C2×C11×Q16C2311yescharacteristic
62C2×C11×SD16—21no—
63C2×C11×D8C2311yescharacteristic
64C11×#125—21no—
65C11×#124—21no—
66#67000—21no—
67C2×#4325—21no—
68C2×#4325—21no—
69#66993—21no—
70C2×#4323—21no—
71C2×#4323—21no—
72#66972—22no—
73#66972—22no—
74#66967—44no—
75D8×D11—22no—
76D8×D11—22no—
77C2×D88—21no—
78C2×D88C2311yescharacteristic
79C2×D88C2311yescharacteristic
80C2×#4313D411yescharacteristic
81C2×C8×D11C2311yescharacteristic
82#66950—41no—
83#66949—41no—
84#66945—21no—
85C4⋊C4×D11—21no—
86#66943—21no—
87#66942—41no—
88#66941—21no—
89#66941—41no—
90#66937—41no—
91#66937—41no—
92#66935—41no—
93#66935—41no—
94#66927—21no—
95#66925D411yescharacteristic
96#66922—21no—
97C2×C11×C16C2311yescharacteristic
98C2×C11×C16C2311yescharacteristic
99C11×#107C2311yescharacteristic
100C11×#107C2311yescharacteristic
101C11×#106—21no—
102C4×C8×C11C2311yescharacteristic
103#66882—21no—
104#66882C2311yescharacteristic
105#66882C2311yescharacteristic
106#66879D411yescharacteristic
107C8×Dic11C2311yescharacteristic
108C2×C11⋊C16C2311yescharacteristic
109C2×C11⋊C16C2311yescharacteristic
110#66872—21no—
111#66872—21no—
112#66871—21no—
113#66871—21no—
114#66867D411yescharacteristic
115#66862—22no—
116C16×D11—22no—
117#33702—111nomaximal, Sylow
118C23×D11—41no—
119C2×Q8×C11—21no—
120C2×D4×C11—21no—
121C2×C22⋊D11—41no—
122C2×C22⋊D11—41no—
123C2×C22⋊D11—41no—
124#4343—42no—
125#4343—42no—
126D4×D11—42no—
127D4×D11—42no—
128C2×D44—21no—
129C2×D44—21no—
130C2×D44—41no—
131C2×D44—41no—
132C2×D44—41no—
133C2×C4×D11—41no—
134C2×C4×D11—41no—
135C2×C4×D11C2×D411yescharacteristic
136C2×Dic22—41no—
137C2×Dic22—41no—
138C11×Q16—21no—
139C11×Q16—21no—
140C11×SD16—42no—
141C11×D8—21no—
142C11×D8—21no—
143C2×C8×C11C2×D411yescharacteristic
144C2×C8×C11C2411yescharacteristic
145C11×C4⋊C4—21no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—41no—
148C11×C4⋊C4—41no—
149C11×C22⋊C4—41no—
150C11×C22⋊C4—41no—
151C42×C11C2×D411yescharacteristic
152#4325—42no—
153#4325—42no—
154#4323—42no—
155#4323—42no—
156(C2×D11)⋊C4—41no—
157(C2×D11)⋊C4—41no—
158(C2×D11)⋊C4—41no—
159(C2×D11)⋊C4D811yescharacteristic
160(C2×D11)⋊C4D811yescharacteristic
161C4⋊Dic11—21no—
162C4⋊Dic11—21no—
163C4⋊Dic11—41no—
164C4⋊Dic11—41no—
165Dic11⋊C4—41no—
166Dic11⋊C4—41no—
167Dic11⋊C4—41no—
168Dic11⋊C4D811yescharacteristic
169Dic11⋊C4D811yescharacteristic
170C4×Dic11—41no—
171C4×Dic11C2×D411yescharacteristic
172C2×C11⋊C8C2×D411yescharacteristic
173C2×C11⋊C8C2×D411yescharacteristic
174D88—21no—
175D88—21no—
176D88—21no—
177D88—21no—
178D88—42no—
179#4313SD1614yes—
180C8×D11#4112yes—
181C8×D11#4112yes—
182C11×C16—21no—
183C11×C16—21no—
184C11⋊C16—21no—
185C11⋊C16—21no—
186#3164—111no—
187#3155—111no—
188#2244—111no—
189#2244—111no—
190#2243—111no—
191#2243—111no—
192#2242—111no—
193#2242D1111yescharacteristic, complemented
194#2240—111no—
195#2240—111no—
196#2140—111no—
197#2139—111no—
198#2138—111no—
199C2×#357—111no—
200#2108—111no—
201C23×C11—41no—
202C22×D11—41no—
203C22×D11—41no—
204C22×D11—82no—
205C22×D11—161no—
206C22×D11—161no—
207C22×D11C2×D811yescharacteristic
208Q8×C11—41no—
209Q8×C11—41no—
210D4×C11—41no—
211D4×C11—41no—
212C2×C4×C11—41no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11C2×D811yescharacteristic
216C2×C4×C11C2×D811yescharacteristic
217C2×C4×C11C22×D411yescharacteristic
218C22⋊D11—82no—
219C22⋊D11—161no—
220C22⋊D11—161no—
221C2×Dic11—41no—
222C2×Dic11—41no—
223C2×Dic11C2×D811yescharacteristic
224C2×Dic11C2×D811yescharacteristic
225C2×Dic11C2×D811yescharacteristic
226D44—41no—
227D44—41no—
228D44—41no—
229D44—41no—
230D44—82no—
231D44—161no—
232D44—161no—
233C4×D11—82no—
234C4×D11—161no—
235C4×D11#12412yes—
236C4×D11C2×SD1612yes—
237Dic22—161no—
238Dic22—161no—
239C8×C11C2×SD1612yes—
240C8×C11C2×#4111yescharacteristic
241C8×C11C2×#4111yescharacteristic
242C11⋊C8#12412yes—
243C11⋊C8C2×SD1612yes—
244C2×AGL(1,ℤ/8)—221no—
245C2×#135—111no—
246C22×D8—111no—
247#544—221no—
248#535—221no—
249C2×M32—111no—
250C22×C16—111no—
251#501—221no—
252#501—221no—
253#500—111no—
254#500—111no—
255#499—111no—
256#499C2×D1111yescharacteristic, complemented
257#496—221no—
258#496—221no—
259#495—111no—
260#495C2×D1111yescharacteristic
261#493—111no—
262#493—111no—
263#428—221no—
264#427—111no—
265C2×#107—111no—
266#405—111no—
267#358—111no—
268#358—111no—
269#358C2×D1111yescharacteristic, complemented
270#358C2×D1111yescharacteristic, complemented
271#357—111no—
272#357—111no—
273#357—111no—
274#357—111no—
275#357—111no—
276#357—111no—
277#357—111no—
278#357—111no—
279#357—111no—
280#357—111no—
281#357C2×D1111yescharacteristic
282#357C2×D1111yescharacteristic
283#346—111no—
284#346—111no—
285C4×C16—111no—
286C4×C16C2×D1111yescharacteristic, complemented
287C22×C11—81no—
288C22×C11—81no—
289C22×C11—81no—
290C22×C11C22×D811yescharacteristic
291C2×D11—21no—
292C2×D11—21no—
293C2×D11—81no—
294C2×D11—81no—
295C2×D11—81no—
296C2×D11—81no—
297C2×D11—81no—
298C2×D11—81no—
299C2×D11—164no—
300C2×D11#48612yes—
301C4×C11—21no—
302C4×C11—21no—
303C4×C11—81no—
304C4×C11—81no—
305C4×C11—81no—
306C4×C11C2×#12411yescharacteristic
307C4×C11C22×SD1611yescharacteristic
308Dic11—21no—
309Dic11—21no—
310Dic11—81no—
311Dic11—81no—
312Dic11#48612yes—
313C2×#41—221no—
314C22×D4—221no—
315AGL(1,ℤ/8)—444no—
316#135—222no—
317#135—222no—
318C2×Q16C22×D1111yescharacteristic
319C2×SD16—21no—
320C2×SD16—221no—
321C2×SD16—221no—
322C2×D8—111no—
323C2×D8—111no—
324C2×D8—222no—
325C2×D8—222no—
326C2×D8—221no—
327C2×D8—221no—
328C2×D8—221no—
329C2×D8C22×D1111yescharacteristic
330C2×M16—111no—
331C22×C8—111no—
332C4⋊Q8—221no—
333C4⋊Q8—221no—
334C4⋊Q8—441no—
335#127—221no—
336#127—221no—
337#125—21no—
338#125—221no—
339#125—441no—
340#124—21no—
341#124—221no—
342C22⋊Q8—441no—
343C22⋊Q8—441no—
344#121—441no—
345#121—441no—
346#120—441no—
347#120—441no—
348#117—111no—
349#117—221no—
350C2×C4⋊C4—221no—
351M32—222no—
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#107—221no—
361#107—221no—
362#107C22×D1111yescharacteristic
363#107C22×D1111yescharacteristic
364#106—21no—
365#106—221no—
366#106—221no—
367#97—111no—
368#97—111no—
369C4×C8—111no—
370C4×C8C22×D1111yescharacteristic
371C2×C11—161no—
372C2×C11C2×#48611yescharacteristic
373C2×C11#341511yescharacteristic
374C2×C11#341611yescharacteristic
375D11—22no—
376D11—161no—
377D11—161no—
378C24—441no—
379#41—442no—
380#41—442no—
381C2×Q8—21no—
382C2×Q8—441no—
383C2×Q8—441no—
384C2×D4—21no—
385C2×D4—221no—
386C2×D4—221no—
387C2×D4—441no—
388C2×D4—442no—
389C2×D4—442no—
390C2×D4—441no—
391C2×D4—441no—
392C2×D4—441no—
393C2×D4—441no—
394C2×D4—441no—
395C22×C4—111no—
396C22×C4—441no—
397C22×C4—441no—
398Q16—21no—
399Q16—21no—
400SD16—42no—
401SD16—442no—
402SD16—442no—
403D8—21no—
404D8—21no—
405D8—221no—
406D8—221no—
407D8—221no—
408D8—221no—
409D8—442no—
410D8—442no—
411D8—442no—
412M16—114no—
413C2×C8—111no—
414C2×C8—111no—
415C2×C8—112no—
416C2×C8—112no—
417C2×C8D4×D1111yescharacteristic
418C2×C8C23×D1111yescharacteristic
419C4⋊C4—21no—
420C4⋊C4—21no—
421C4⋊C4—41no—
422C4⋊C4—41no—
423C4⋊C4—111no—
424C4⋊C4—111no—
425C4⋊C4—221no—
426C4⋊C4—221no—
427C4⋊C4—441no—
428C4⋊C4—441no—
429C4⋊C4—441no—
430C4⋊C4—441no—
431C4⋊C4—441no—
432C22⋊C4—41no—
433C22⋊C4—41no—
434C22⋊C4—111no—
435C22⋊C4—111no—
436C22⋊C4—441no—
437C22⋊C4—441no—
438C22⋊C4—441no—
439C42—111no—
440C42—441no—
441C42D4×D1111yescharacteristic
442C16—21no—
443C16—21no—
444C16—221no—
445C16—221no—
446C11#3370211yescharacteristic, complemented, Sylow
447C23—41no—
448C23—111no—
449C23—441no—
450C23—441no—
451C23—882no—
452C23—1761no—
453C23—1761no—
454Q8—41no—
455Q8—41no—
456Q8—1761no—
457Q8—1761no—
458D4—41no—
459D4—41no—
460D4—441no—
461D4—441no—
462D4—441no—
463D4—441no—
464D4—882no—
465D4—882no—
466D4—1761no—
467D4—1761no—
468D4—1761no—
469D4—1761no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—111no—
474C2×C4—112no—
475C2×C4—112no—
476C2×C4—111no—
477C2×C4—111no—
478C2×C4—441no—
479C2×C4—441no—
480C2×C4—882no—
481C2×C4—1761no—
482C2×C4D8×D1111yescharacteristic
483C2×C4D8×D1111yescharacteristic
484C2×C4C2×D4×D1111yescharacteristic
485C8—112no—
486C8—112no—
487C8SD16×D1112yes—
488C8#41×D1111yescharacteristic
489C8#41×D1111yescharacteristic
490C22—81no—
491C22—81no—
492C22—81no—
493C22—112no—
494C22—221no—
495C22—221no—
496C22—881no—
497C22—881no—
498C22—881no—
499C22—881no—
500C22—881no—
501C22—881no—
502C22—1764no—
503C22C2×D8×D1111yescharacteristic
504C4—21no—
505C4—21no—
506C4—81no—
507C4—81no—
508C4—81no—
509C4—112no—
510C4—221no—
511C4—221no—
512C4—881no—
513C4—881no—
514C4D11×#12411yescharacteristic
515C4C2×SD16×D1111yescharacteristic
516C2—161no—
517C2—222no—
518C2—1761no—
519C2—1761no—
520C2D11×#48611yescharacteristic
521C2#1308175411yescharacteristic
522C2#1308175911yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2242C2
socleC22×C11C22×D8
prime radical#13079098C2
hypercenter#2242D11
hypocenterC11#33702
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2242

Complements

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

NH ≅ G/Ntype
1. #13079153C2semidirect
3. #13070859C2semidirect
4. #13070856C2semidirect
5. #13070854C2semidirect
6. #13070852C2semidirect
7. #13070849C2semidirect
8. #13070840C2semidirect
9. #13070838C2semidirect
10. #13070330C2semidirect
11. #13070327C2semidirect
12. #13070322C2semidirect
13. D11×#357C2semidirect
14. #13070211C2semidirect
15. C11×#2242C2semidirect
21. C11×#499C22semidirect
32. #10622491C22semidirect
33. #10622487C22semidirect
38. #10622295C22semidirect
39. C11×#358C22semidirect
40. C11×#358C22semidirect
43. C4×C11×C16C22semidirect
44. #10622202C22semidirect
45. #10622202C22semidirect
50. #10622147C22semidirect
51. #10622147C22semidirect
52. #10622140C22semidirect
53. C16×Dic11C22semidirect
56. #10622129C22semidirect
57. #10622129C22semidirect
58. #10622099C22semidirect
193. #2242D11semidirect
256. #499C2×D11semidirect
269. #358C2×D11semidirect
270. #358C2×D11semidirect
286. C4×C16C2×D11semidirect
446. C11#33702semidirect

Maximal subgroups

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

subgroupindex
#130791532
#130790982
#130708592
#130708562
#130708542
#130708522
#130708492
#130708402
#130708382
#130703302
#130703272
#130703222
D11×#3572
#130702112
C11×#22422
#3370211