Finite Group Databasebeta

← #14730653

Subgroups — #14730653

Order 2816.

944 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079623C211yesmaximal, characteristic, complemented
2#13079335C211yesmaximal, characteristic, complemented
3#13078616C211yesmaximal, characteristic
4#13067865C212yesmaximal, complemented
5#13067830C212yesmaximal, complemented
6#13067719C212yesmaximal, complemented
7#13067688C212yesmaximal, complemented
8#13067326C211yesmaximal, characteristic, complemented
9#13067059C211yesmaximal, characteristic, complemented
10#13067037C211yesmaximal, characteristic, complemented
11C11×#3501C211yesmaximal, characteristic, complemented
12C11×#554—21no—
13C11×#554—22no—
14C11×#554—22no—
15C11×#554C2212yes—
16D4×Q8×C11—21no—
17D4×Q8×C11C2212yes—
18C11×#544—21no—
19C11×#543—22no—
20C11×#533C2211yescharacteristic
21C11×#533C2211yescharacteristic
22C2×C11×C22⋊Q8—22no—
23C11×#518—21no—
24C2×C4×D4×C11C2211yescharacteristic
25#10623008C2211yescharacteristic
26#10622830—21no—
27#10622702—21no—
28#10622701C2211yescharacteristic, complemented
29#10622699—21no—
30#10622698C2211yescharacteristic, complemented
31#10622694C2211yescharacteristic, complemented
32#10622691C2211yescharacteristic, complemented
33#10622662—22no—
34#10622660—22no—
35#10622644C2212yescomplemented
36#10622640C2212yescomplemented
37#10622639—22no—
38#10622628C2212yes—
39C4×#4323—22no—
40#10622620C2212yes—
41#10622580—21no—
42#10622539C2211yescharacteristic
43#10622538C2211yescharacteristic
44C4×#4318C2211yescharacteristic
45#10622185C2212yescomplemented
46#10622184C2212yescomplemented
47Q8⋊(C11⋊C8)C2212yescomplemented
48Q8⋊(C11⋊C8)C2212yescomplemented
49D4⋊(C11⋊C8)C2212yes—
50D4⋊(C11⋊C8)C2212yes—
51C22×Q8×C11—22no—
52C22×D4×C11D411yescharacteristic
53C23×C4×C11—21no—
54C2×#4339—21no—
55C11×C4⋊Q8—22no—
56C11×C4⋊Q8—22no—
57C11×C4⋊Q8D411yescharacteristic
58C11×C4⋊Q8D411yescharacteristic
59C11×C4⋊Q8C2311yescharacteristic
60C11×C4⋊Q8C2311yescharacteristic
61C11×#125—22no—
62C11×#125—22no—
63C11×#125—21no—
64C11×#125—21no—
65C11×C22⋊Q8—24no—
66C11×C22⋊Q8—24no—
67C11×C22⋊Q8—24no—
68C11×C22⋊Q8—24no—
69C11×C22⋊Q8—22no—
70C11×C22⋊Q8—24no—
71C11×C22⋊Q8—21no—
72C11×C22⋊Q8—21no—
73C11×C22⋊Q8—22no—
74C11×C22⋊Q8—24no—
75C11×C22⋊Q8D412yes—
76C11×C22⋊Q8D412yes—
77C4×Q8×C11—21no—
78C4×Q8×C11—21no—
79C4×Q8×C11D412yes—
80C4×Q8×C11C2312yes—
81C4×D4×C11—22no—
82C4×D4×C11—22no—
83C4×D4×C11—22no—
84C4×D4×C11—22no—
85C4×D4×C11—21no—
86C4×D4×C11—21no—
87C4×D4×C11D412yes—
88C4×D4×C11C2312yes—
89C11×#117—21no—
90C11×#117—21no—
91C2×C11×C4⋊C4—24no—
92C2×C11×C4⋊C4—22no—
93C2×C11×C4⋊C4D411yescharacteristic
94C2×C11×C22⋊C4—24no—
95C2×C11×C22⋊C4—21no—
96C2×C42×C11C2311yescharacteristic
97C2×#4326—22no—
98C2×#4325—22no—
99C2×#4325—22no—
100C2×#4323—22no—
101#66983—21no—
102#66983—21no—
103C2×#4318—21no—
104#66928—21no—
105#66927C2311yescharacteristic
106C4×D44—21no—
107C4×D44—21no—
108#66922C2311yescharacteristic
109#66899—22no—
110#66896—22no—
111C22⋊(C11⋊C8)—21no—
112C22⋊(C11⋊C8)—21no—
113#66874—22no—
114#66873—22no—
115#66873—22no—
116#66873—22no—
117#66871—22no—
118#66871—22no—
119C4⋊(C11⋊C8)C2312yes—
120C4⋊(C11⋊C8)C2312yes—
121#66867—21no—
122#66867—21no—
123C4×C11⋊C8—21no—
124C4×C11⋊C8C2311yescharacteristic
125C4×C11⋊C8C2311yescharacteristic
126#18600—111nomaximal, Sylow
127C24×C11—21no—
128C2×Q8×C11—24no—
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—82no—
132C2×Q8×C11—82no—
133C2×Q8×C11C2×D412yes—
134C2×Q8×C11C2×D412yes—
135C2×D4×C11—24no—
136C2×D4×C11—21no—
137C2×D4×C11C2×D412yes—
138C22×C4×C11—24no—
139C22×C4×C11—24no—
140C22×C4×C11—21no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—82no—
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C2×C22⋊D11—41no—
148#4339—82no—
149C2×D44—21no—
150C2×D44—21no—
151C2×D44—21no—
152C2×C4×D11—41no—
153C2×Dic22—21no—
154C11×C4⋊C4—24no—
155C11×C4⋊C4—24no—
156C11×C4⋊C4—24no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4C2×D412yes—
169C11×C4⋊C4C2×D412yes—
170C11×C4⋊C4C2×D412yes—
171C11×C22⋊C4—24no—
172C11×C22⋊C4—24no—
173C11×C22⋊C4—22no—
174C11×C22⋊C4—22no—
175C11×C22⋊C4—22no—
176C11×C22⋊C4—22no—
177C42×C11—22no—
178C42×C11—22no—
179C42×C11C2×D411yescharacteristic
180C42×C11C2×D411yescharacteristic
181C42×C11C2×D411yescharacteristic
182C42×C11C2411yescharacteristic
183#4326—82no—
184#4325—44no—
185#4325—82no—
186#4323—44no—
187(C2×D11)⋊C4—41no—
188(C2×D11)⋊C4—41no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191#4318—42no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8—22no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—22no—
196#3501D1111yescharacteristic, complemented
197#3216—111no—
198#3182—111no—
199#3100—111no—
200#1649—112no—
201#1644—112no—
202#1627—112no—
203#1622—112no—
204#1554—111no—
205#1490—111no—
206#1485—111no—
207C23×C11—24no—
208C23×C11—22no—
209C23×C11—81no—
210C23×C11—81no—
211C23×C11#12011yescharacteristic
212C22×D11—41no—
213Q8×C11—22no—
214Q8×C11—22no—
215Q8×C11—42no—
216Q8×C11—42no—
217Q8×C11—81no—
218Q8×C11—84no—
219D4×C11—24no—
220D4×C11—22no—
221D4×C11#13714yes—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—41no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11—82no—
233C2×C4×C11—81no—
234C2×C4×C11—84no—
235C2×C4×C11—84no—
236C2×C4×C11#12011yescharacteristic
237C2×C4×C11#12011yescharacteristic
238C2×C4×C11#12011yescharacteristic
239C2×C4×C11C22×D411yescharacteristic
240C2×C4×C11C22×D411yescharacteristic
241C2×C4×C11C22×D411yescharacteristic
242C22⋊D11—82no—
243C2×Dic11—41no—
244D44—42no—
245D44—42no—
246D44—42no—
247C4×D11—82no—
248Dic22—42no—
249C11⋊C8—22no—
250C11⋊C8—41no—
251C11⋊C8—42no—
252C11⋊C8—42no—
253#554—21no—
254#554—22no—
255#554—22no—
256#554C2×D1112yes—
257D4×Q8—21no—
258D4×Q8C2×D1112yes—
259#544—21no—
260#543—22no—
261#533C2×D1111yescharacteristic
262#533C2×D1111yescharacteristic
263#532—111no—
264C2×C22⋊Q8—22no—
265#518—21no—
266C2×C4×D4C2×D1111yescharacteristic
267#500—111no—
268#497—221no—
269#492—111no—
270#489—221no—
271#487—111no—
272#486—111no—
273#480—221no—
274#474—112no—
275#468—222no—
276#462—112no—
277#460—112no—
278#459—112no—
279#452—222no—
280#447—221no—
281#440—222no—
282C4×D8—222no—
283#432—111no—
284#431—111no—
285C4×M16—111no—
286#333—112no—
287#332—112no—
288Q8⋊C8—112no—
289Q8⋊C8—112no—
290D4⋊C8—112no—
291D4⋊C8—112no—
292C22×C11—21no—
293C22×C11—24no—
294C22×C11—21no—
295C22×C11—21no—
296C22×C11—42no—
297C22×C11—42no—
298C22×C11—84no—
299C22×C11C2×#12011yescharacteristic
300C2×D11—81no—
301C2×D11—81no—
302C2×D11—81no—
303C4×C11—21no—
304C4×C11—21no—
305C4×C11—21no—
306C4×C11—21no—
307C4×C11—42no—
308C4×C11—42no—
309C4×C11—42no—
310C4×C11—42no—
311C4×C11—42no—
312C4×C11C2×#13712yes—
313C4×C11#57612yes—
314Dic11—81no—
315C2×#41—221no—
316C22×Q8—22no—
317C22×D4C22⋊D1111yescharacteristic
318C23×C4—21no—
319C2×Q16—222no—
320C2×SD16—222no—
321C2×SD16—222no—
322C2×D8—222no—
323C2×M16—221no—
324C4⋊Q8—22no—
325C4⋊Q8—22no—
326C4⋊Q8—111no—
327C4⋊Q8C22⋊D1111yescharacteristic
328C4⋊Q8C22⋊D1111yescharacteristic
329C4⋊Q8C22×D1111yescharacteristic
330C4⋊Q8C22×D1111yescharacteristic
331#127—111no—
332#125—22no—
333#125—22no—
334#125—21no—
335#125—21no—
336#124—221no—
337C22⋊Q8—24no—
338C22⋊Q8—24no—
339C22⋊Q8—24no—
340C22⋊Q8—24no—
341C22⋊Q8—22no—
342C22⋊Q8—24no—
343C22⋊Q8—21no—
344C22⋊Q8—21no—
345C22⋊Q8—22no—
346C22⋊Q8—24no—
347C22⋊Q8C22⋊D1112yes—
348C22⋊Q8C22⋊D1112yes—
349#121—221no—
350#121—221no—
351C4×Q8—21no—
352C4×Q8—21no—
353C4×Q8C22⋊D1112yes—
354C4×Q8C22×D1112yes—
355C4×D4—22no—
356C4×D4—22no—
357C4×D4—22no—
358C4×D4—22no—
359C4×D4—21no—
360C4×D4—21no—
361C4×D4—221no—
362C4×D4—221no—
363C4×D4C22⋊D1112yes—
364C4×D4C22×D1112yes—
365#117—21no—
366#117—21no—
367C2×C4⋊C4—24no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4C22⋊D1111yescharacteristic
370C2×C22⋊C4—24no—
371C2×C22⋊C4—21no—
372C2×C42C22×D1111yescharacteristic
373#107—222no—
374#107—222no—
375C4⋊C8—112no—
376C4⋊C8—112no—
377#103—222no—
378#103—222no—
379#102—222no—
380#102—222no—
381#102—222no—
382#102—222no—
383C22⋊C8—221no—
384C22⋊C8—221no—
385#97—221no—
386#97—221no—
387C4×C8—111no—
388C4×C8—111no—
389C4×C8—221no—
390C2×C11—41no—
391C2×C11—44no—
392C2×C11#300411yescharacteristic
393C2×C11#300811yescharacteristic
394C2×C11#301811yescharacteristic
395D11—161no—
396C24—21no—
397#41—882no—
398C2×Q8—24no—
399C2×Q8—21no—
400C2×Q8—21no—
401C2×Q8—82no—
402C2×Q8—82no—
403C2×Q8—221no—
404C2×Q8C2×C22⋊D1112yes—
405C2×Q8C2×C22⋊D1112yes—
406C2×D4—24no—
407C2×D4—21no—
408C2×D4—221no—
409C2×D4—221no—
410C2×D4—221no—
411C2×D4—441no—
412C2×D4C2×C22⋊D1112yes—
413C22×C4—24no—
414C22×C4—24no—
415C22×C4—21no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—82no—
419C22×C4—441no—
420C22×C4C2×C22⋊D1111yescharacteristic
421C22×C4C2×C22⋊D1111yescharacteristic
422C22×C4C2×C22⋊D1111yescharacteristic
423Q16—882no—
424SD16—444no—
425SD16—882no—
426D8—444no—
427M16—442no—
428C2×C8—221no—
429C2×C8—221no—
430C2×C8—222no—
431C2×C8—222no—
432C4⋊C4—24no—
433C4⋊C4—24no—
434C4⋊C4—24no—
435C4⋊C4—22no—
436C4⋊C4—22no—
437C4⋊C4—21no—
438C4⋊C4—21no—
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4—22no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—22no—
446C4⋊C4—221no—
447C4⋊C4—221no—
448C4⋊C4C2×C22⋊D1112yes—
449C4⋊C4C2×C22⋊D1112yes—
450C4⋊C4C2×C22⋊D1112yes—
451C22⋊C4—24no—
452C22⋊C4—24no—
453C22⋊C4—22no—
454C22⋊C4—22no—
455C22⋊C4—22no—
456C22⋊C4—22no—
457C22⋊C4—441no—
458C22⋊C4—441no—
459C42—22no—
460C42—22no—
461C42C2×C22⋊D1111yescharacteristic
462C42C2×C22⋊D1111yescharacteristic
463C42C2×C22⋊D1111yescharacteristic
464C42C23×D1111yescharacteristic
465C11#1860011yescharacteristic, complemented, Sylow
466C23—24no—
467C23—22no—
468C23—81no—
469C23—81no—
470C23—441no—
471C23#6700611yescharacteristic
472Q8—22no—
473Q8—22no—
474Q8—42no—
475Q8—42no—
476Q8—81no—
477Q8—84no—
478Q8—442no—
479D4—24no—
480D4—22no—
481D4—442no—
482D4—442no—
483D4—442no—
484D4—882no—
485D4#6699514yes—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—41no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—82no—
497C2×C4—81no—
498C2×C4—84no—
499C2×C4—84no—
500C2×C4—441no—
501C2×C4—882no—
502C2×C4#6700611yescharacteristic
503C2×C4#6700611yescharacteristic
504C2×C4#6700611yescharacteristic
505C2×C4C22×C22⋊D1111yescharacteristic
506C2×C4C22×C22⋊D1111yescharacteristic
507C2×C4C22×C22⋊D1111yescharacteristic
508C8—222no—
509C8—441no—
510C8—442no—
511C8—442no—
512C22—21no—
513C22—24no—
514C22—21no—
515C22—21no—
516C22—42no—
517C22—42no—
518C22—84no—
519C22—881no—
520C22—881no—
521C22—881no—
522C22C2×#6700611yescharacteristic
523C4—21no—
524C4—21no—
525C4—21no—
526C4—21no—
527C4—42no—
528C4—42no—
529C4—42no—
530C4—42no—
531C4—42no—
532C4—881no—
533C4C2×#6699512yes—
534C4#1062336612yes—
535C2—41no—
536C2—44no—
537C2—1761no—
538C2#1307785011yescharacteristic
539C2#1307788411yescharacteristic
540C2#1307796511yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3501C2
socleC22×C11C2×#120
prime radical#13078616C2
hypercenter#3501D11
hypocenterC11#18600
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3501

Complements

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

NH ≅ G/Ntype
1. #13079623C2semidirect
2. #13079335C2semidirect
4. #13067865C2semidirect
5. #13067830C2semidirect
6. #13067719C2semidirect
7. #13067688C2semidirect
8. #13067326C2semidirect
9. #13067059C2semidirect
10. #13067037C2semidirect
11. C11×#3501C2semidirect
28. #10622701C22semidirect
30. #10622698C22semidirect
31. #10622694C22semidirect
32. #10622691C22semidirect
35. #10622644C22semidirect
36. #10622640C22semidirect
45. #10622185C22semidirect
46. #10622184C22semidirect
47. Q8⋊(C11⋊C8)C22semidirect
48. Q8⋊(C11⋊C8)C22semidirect
196. #3501D11semidirect
465. C11#18600semidirect

Maximal subgroups

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

subgroupindex
#130796232
#130793352
#130786162
#130678652
#130678302
#130677192
#130676882
#130673262
#130670592
#130670372
C11×#35012
#1860011