Finite Group Databasebeta

← #14731357

Subgroups — #14731357

Order 2816.

980 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079928C211yesmaximal, characteristic, complemented
2#13079176C211yesmaximal, characteristic, complemented
3#13078080C211yesmaximal, characteristic
4#13067879C212yesmaximal, complemented
5#13067823C212yesmaximal, complemented
6#13067719C212yesmaximal, complemented
7#13067688C212yesmaximal, complemented
8#13067306C211yesmaximal, characteristic, complemented
9#13067071C211yesmaximal, characteristic, complemented
10C2×D4⋊(C11⋊C8)C211yesmaximal, 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
25C2×#66985—21no—
26#10623008C2211yescharacteristic
27#10622701C2211yescharacteristic, complemented
28#10622698C2211yescharacteristic, complemented
29#10622697—21no—
30#10622696—21no—
31#10622694C2211yescharacteristic, complemented
32#10622692C2211yescharacteristic, complemented
33#10622661—22no—
34#10622661—22no—
35#10622640C2212yescomplemented
36C4×#4325—22no—
37#10622633C2212yescomplemented
38#10622632C2212yes—
39#10622629—22no—
40#10622628C2212yes—
41#10622579—21no—
42#10622537C2211yescharacteristic
43C2×C4⋊(C11⋊C8)C2211yescharacteristic
44C2×C4×C11⋊C8C2211yescharacteristic
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×#4325—22no—
98C2×#4325—22no—
99C2×#4324—22no—
100#66985—44no—
101C2×#4323—22no—
102#66983—21no—
103#66983—21no—
104C2×#4318—21no—
105C22×C11⋊C8—21no—
106C22×C11⋊C8—21no—
107#66928—21no—
108#66927C2311yescharacteristic
109C4×D44—21no—
110C4×D44—21no—
111#66922C2311yescharacteristic
112#66899—22no—
113#66899—22no—
114#66874—22no—
115#66873—22no—
116#66873—22no—
117#66873—22no—
118#66872—22no—
119#66872—22no—
120C4⋊(C11⋊C8)—21no—
121C4⋊(C11⋊C8)—21no—
122C4⋊(C11⋊C8)C2312yes—
123C4⋊(C11⋊C8)C2312yes—
124C4×C11⋊C8—21no—
125C4×C11⋊C8C2311yescharacteristic
126C4×C11⋊C8C2311yescharacteristic
127#18664—111nomaximal, Sylow
128C24×C11—21no—
129C2×Q8×C11—24no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11—82no—
133C2×Q8×C11—82no—
134C2×Q8×C11C2×D412yes—
135C2×Q8×C11C2×D412yes—
136C2×D4×C11—21no—
137C2×D4×C11—22no—
138C2×D4×C11SD1614yescomplemented
139C2×D4×C11C2×D412yes—
140C22×C4×C11—24no—
141C22×C4×C11—24no—
142C22×C4×C11—21no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—81no—
146C22×C4×C11—81no—
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C2×C22⋊D11—41no—
151#4339—42no—
152#4339—42no—
153C2×D44—21no—
154C2×D44—21no—
155C2×D44—21no—
156C2×C4×D11—41no—
157C2×Dic22—21no—
158C11×C4⋊C4—24no—
159C11×C4⋊C4—24no—
160C11×C4⋊C4—24no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—22no—
172C11×C4⋊C4C2×D412yes—
173C11×C4⋊C4C2×D412yes—
174C11×C4⋊C4C2×D412yes—
175C11×C22⋊C4—24no—
176C11×C22⋊C4—24no—
177C11×C22⋊C4—22no—
178C11×C22⋊C4—22no—
179C11×C22⋊C4—22no—
180C11×C22⋊C4—22no—
181C42×C11—22no—
182C42×C11—22no—
183C42×C11C2×D411yescharacteristic
184C42×C11C2×D411yescharacteristic
185C42×C11C2×D411yescharacteristic
186C42×C11C2411yescharacteristic
187#4325—44no—
188#4325—82no—
189#4324—44no—
190#4323—44no—
191(C2×D11)⋊C4—41no—
192(C2×D11)⋊C4—41no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195#4318—42no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—22no—
199C2×C11⋊C8—22no—
200C2×C11⋊C8—42no—
201C2×C11⋊C8—81no—
202#3501D1111yescharacteristic, complemented
203#3246—111no—
204#3167—111no—
205#3036—111no—
206#1651—112no—
207#1643—112no—
208#1627—112no—
209#1622—112no—
210#1550—111no—
211#1493—111no—
212C2×D4⋊C8—111no—
213C23×C11—22no—
214C23×C11—24no—
215C23×C11—81no—
216C23×C11—81no—
217C23×C11#12011yescharacteristic
218C22×D11—41no—
219Q8×C11—22no—
220Q8×C11—22no—
221Q8×C11—42no—
222Q8×C11—41no—
223Q8×C11—41no—
224Q8×C11—81no—
225Q8×C11—84no—
226D4×C11—22no—
227D4×C11—24no—
228D4×C11C2×SD1614yes—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—41no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—82no—
240C2×C4×C11—81no—
241C2×C4×C11—84no—
242C2×C4×C11—84no—
243C2×C4×C11#12011yescharacteristic
244C2×C4×C11#12011yescharacteristic
245C2×C4×C11#12011yescharacteristic
246C2×C4×C11C2×SD1612yes—
247C2×C4×C11#13712yes—
248C2×C4×C11C22×D411yescharacteristic
249C2×C4×C11C22×D411yescharacteristic
250C2×C4×C11C22×D411yescharacteristic
251C22⋊D11—82no—
252C2×Dic11—41no—
253D44—42no—
254D44—41no—
255D44—41no—
256D44—41no—
257D44—41no—
258C4×D11—82no—
259Dic22—41no—
260Dic22—41no—
261C11⋊C8—22no—
262C11⋊C8—41no—
263C11⋊C8—42no—
264C11⋊C8—42no—
265C2×AGL(1,ℤ/8)—221no—
266#554—21no—
267#554—22no—
268#554—22no—
269#554C2×D1112yes—
270D4×Q8—21no—
271D4×Q8C2×D1112yes—
272#544—21no—
273#543—22no—
274#533C2×D1111yescharacteristic
275#533C2×D1111yescharacteristic
276#532—111no—
277C2×C22⋊Q8—22no—
278#518—21no—
279C2×C4×D4C2×D1111yescharacteristic
280#498—111no—
281#492—111no—
282#487—111no—
283#486—111no—
284#476—221no—
285#475—112no—
286#465—222no—
287#465—222no—
288#463—222no—
289#461—112no—
290#461—221no—
291#460—112no—
292#459—112no—
293C4×SD16—222no—
294#423—111no—
295C2×C4⋊C8—111no—
296#417—221no—
297C2×C4×C8—111no—
298#333—112no—
299#332—112no—
300Q8⋊C8—112no—
301Q8⋊C8—112no—
302D4⋊C8—112no—
303D4⋊C8—112no—
304C22×C11—21no—
305C22×C11—21no—
306C22×C11—24no—
307C22×C11—42no—
308C22×C11—42no—
309C22×C11—84no—
310C22×C11#44812yes—
311C22×C11C2×#12011yescharacteristic
312C2×D11—81no—
313C2×D11—81no—
314C2×D11—81no—
315C4×C11—21no—
316C4×C11—21no—
317C4×C11—21no—
318C4×C11—42no—
319C4×C11—42no—
320C4×C11—42no—
321C4×C11—42no—
322C4×C11—42no—
323C4×C11#44812yes—
324C4×C11C22×SD1611yescharacteristic
325C4×C11C2×#13711yescharacteristic
326C4×C11#57611yescharacteristic
327C4×C11#57711yescharacteristic
328Dic11—81no—
329C2×#41—221no—
330C22×Q8—22no—
331C22×D4C22⋊D1111yescharacteristic
332C23×C4—21no—
333AGL(1,ℤ/8)—444no—
334C2×SD16—222no—
335C2×SD16—222no—
336C2×SD16—222no—
337C2×D8—222no—
338C2×M16—221no—
339C22×C8—221no—
340C22×C8—221no—
341C4⋊Q8—22no—
342C4⋊Q8—22no—
343C4⋊Q8—111no—
344C4⋊Q8C22⋊D1111yescharacteristic
345C4⋊Q8C22⋊D1111yescharacteristic
346C4⋊Q8C22×D1111yescharacteristic
347C4⋊Q8C22×D1111yescharacteristic
348#127—111no—
349#125—22no—
350#125—22no—
351#125—21no—
352#125—21no—
353#124—221no—
354C22⋊Q8—24no—
355C22⋊Q8—24no—
356C22⋊Q8—24no—
357C22⋊Q8—24no—
358C22⋊Q8—22no—
359C22⋊Q8—24no—
360C22⋊Q8—21no—
361C22⋊Q8—21no—
362C22⋊Q8—22no—
363C22⋊Q8—24no—
364C22⋊Q8C22⋊D1112yes—
365C22⋊Q8C22⋊D1112yes—
366#121—221no—
367#121—221no—
368C4×Q8—21no—
369C4×Q8—21no—
370C4×Q8C22⋊D1112yes—
371C4×Q8C22×D1112yes—
372C4×D4—22no—
373C4×D4—22no—
374C4×D4—22no—
375C4×D4—22no—
376C4×D4—21no—
377C4×D4—21no—
378C4×D4—221no—
379C4×D4—221no—
380C4×D4C22⋊D1112yes—
381C4×D4C22×D1112yes—
382#117—21no—
383#117—21no—
384C2×C4⋊C4—24no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4C22⋊D1111yescharacteristic
387C2×C22⋊C4—24no—
388C2×C22⋊C4—21no—
389C2×C42C22×D1111yescharacteristic
390#106—222no—
391#106—222no—
392C4⋊C8—112no—
393C4⋊C8—112no—
394C4⋊C8—221no—
395C4⋊C8—221no—
396#103—222no—
397#103—222no—
398#103—222no—
399#102—222no—
400#102—222no—
401#102—222no—
402C4×C8—111no—
403C4×C8—111no—
404C4×C8—221no—
405C2×C11—22no—
406C2×C11—44no—
407C2×C11C2×#44811yescharacteristic
408C2×C11#301211yescharacteristic
409C2×C11#301811yescharacteristic
410D11—161no—
411C24—21no—
412#41—442no—
413#41—442no—
414C2×Q8—24no—
415C2×Q8—21no—
416C2×Q8—21no—
417C2×Q8—82no—
418C2×Q8—82no—
419C2×Q8—221no—
420C2×Q8C2×C22⋊D1112yes—
421C2×Q8C2×C22⋊D1112yes—
422C2×D4—22no—
423C2×D4—21no—
424C2×D4—221no—
425C2×D4—221no—
426C2×D4—221no—
427C2×D4—441no—
428C2×D4#432514yescomplemented
429C2×D4C2×C22⋊D1112yes—
430C22×C4—24no—
431C22×C4—24no—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—81no—
436C22×C4—81no—
437C22×C4—441no—
438C22×C4C2×C22⋊D1111yescharacteristic
439C22×C4C2×C22⋊D1111yescharacteristic
440C22×C4C2×C22⋊D1111yescharacteristic
441SD16—444no—
442SD16—444no—
443SD16—882no—
444D8—444no—
445M16—442no—
446C2×C8—221no—
447C2×C8—221no—
448C2×C8—222no—
449C2×C8—222no—
450C2×C8—442no—
451C2×C8—881no—
452C4⋊C4—24no—
453C4⋊C4—24no—
454C4⋊C4—24no—
455C4⋊C4—22no—
456C4⋊C4—22no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—22no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—22no—
466C4⋊C4—221no—
467C4⋊C4—221no—
468C4⋊C4C2×C22⋊D1112yes—
469C4⋊C4C2×C22⋊D1112yes—
470C4⋊C4C2×C22⋊D1112yes—
471C22⋊C4—24no—
472C22⋊C4—24no—
473C22⋊C4—22no—
474C22⋊C4—22no—
475C22⋊C4—22no—
476C22⋊C4—22no—
477C22⋊C4—441no—
478C22⋊C4—441no—
479C42—22no—
480C42—22no—
481C42C2×C22⋊D1111yescharacteristic
482C42C2×C22⋊D1111yescharacteristic
483C42C2×C22⋊D1111yescharacteristic
484C42C23×D1111yescharacteristic
485C11#1866411yescharacteristic, complemented, Sylow
486C23—22no—
487C23—24no—
488C23—81no—
489C23—81no—
490C23—441no—
491C23#6700611yescharacteristic
492Q8—22no—
493Q8—22no—
494Q8—42no—
495Q8—41no—
496Q8—41no—
497Q8—81no—
498Q8—84no—
499Q8—441no—
500Q8—441no—
501D4—22no—
502D4—24no—
503D4—442no—
504D4—441no—
505D4—441no—
506D4—441no—
507D4—441no—
508D4—882no—
509D4C2×#432514yes—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—41no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—82no—
521C2×C4—81no—
522C2×C4—84no—
523C2×C4—84no—
524C2×C4—441no—
525C2×C4—882no—
526C2×C4C2×#432512yes—
527C2×C4#6699512yes—
528C2×C4#6700611yescharacteristic
529C2×C4#6700611yescharacteristic
530C2×C4#6700611yescharacteristic
531C2×C4C22×C22⋊D1111yescharacteristic
532C2×C4C22×C22⋊D1111yescharacteristic
533C2×C4C22×C22⋊D1111yescharacteristic
534C8—222no—
535C8—441no—
536C8—442no—
537C8—442no—
538C22—21no—
539C22—21no—
540C22—24no—
541C22—42no—
542C22—42no—
543C22—84no—
544C22—881no—
545C22—881no—
546C22—881no—
547C22#1062284012yes—
548C22C2×#6700611yescharacteristic
549C4—21no—
550C4—21no—
551C4—21no—
552C4—42no—
553C4—42no—
554C4—42no—
555C4—42no—
556C4—42no—
557C4—881no—
558C4#1062284012yes—
559C4C22×#432511yescharacteristic
560C4C2×#6699511yescharacteristic
561C4#1062336611yescharacteristic
562C4#1062336711yescharacteristic
563C2—22no—
564C2—44no—
565C2—1761no—
566C2C2×#1062284011yescharacteristic
567C2#1307792011yescharacteristic
568C2#1307796511yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3501C2
socleC22×C11C2×#120
prime radical#13078080C2
hypercenter#3501D11
hypocenterC11#18664
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. #13079928C2semidirect
2. #13079176C2semidirect
4. #13067879C2semidirect
5. #13067823C2semidirect
6. #13067719C2semidirect
7. #13067688C2semidirect
8. #13067306C2semidirect
9. #13067071C2semidirect
10. C2×D4⋊(C11⋊C8)C2semidirect
11. C11×#3501C2semidirect
27. #10622701C22semidirect
28. #10622698C22semidirect
31. #10622694C22semidirect
32. #10622692C22semidirect
35. #10622640C22semidirect
37. #10622633C22semidirect
45. #10622185C22semidirect
46. #10622184C22semidirect
47. Q8⋊(C11⋊C8)C22semidirect
48. Q8⋊(C11⋊C8)C22semidirect
138. C2×D4×C11SD16semidirect
202. #3501D11semidirect
428. C2×D4#4325semidirect
485. C11#18664semidirect

Maximal subgroups

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

subgroupindex
#130799282
#130791762
#130780802
#130678792
#130678232
#130677192
#130676882
#130673062
#130670712
C2×D4⋊(C11⋊C8)2
C11×#35012
#1866411