Finite Group Databasebeta

← #14730450

Subgroups — #14730450

Order 2816.

916 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079999C211yesmaximal, characteristic, complemented
2#13079012C211yesmaximal, characteristic, complemented
3#13078676C211yesmaximal, characteristic
4#13067781C212yesmaximal, complemented
5#13067774C212yesmaximal, complemented
6#13067719C212yesmaximal, complemented
7#13067712C212yesmaximal, complemented
8#13067288C211yesmaximal, characteristic, complemented
9#13067055C211yesmaximal, characteristic, complemented
10#13067037C211yesmaximal, characteristic, complemented
11C11×#3503C211yesmaximal, characteristic, complemented
12Q82×C11—21no—
13C11×#557C2212yes—
14C11×#554—21no—
15C11×#554—22no—
16D4×Q8×C11—22no—
17D4×Q8×C11C2212yes—
18C11×#544—22no—
19C11×#544—21no—
20C11×#533—21no—
21C11×#533C2211yescharacteristic
22C2×C11×C4⋊Q8—21no—
23C2×C11×C4⋊Q8C2211yescharacteristic
24C11×#520—21no—
25C4×C11×#41C2211yescharacteristic
26#10623008C2211yescharacteristic
27#10622851—21no—
28#10622706C2212yes—
29#10622702—22no—
30#10622701C2212yes—
31#10622700—21no—
32#10622696—21no—
33#10622662—22no—
34#10622640C2211yescharacteristic
35#10622640C2212yes—
36C4×#4325—21no—
37#10622634C2212yes—
38#10622634C2211yescharacteristic
39#10622628C2211yescharacteristic
40C4×#4323—21no—
41#10622621C2211yescharacteristic
42#10622616—21no—
43#10622579—22no—
44#10622538C2211yescharacteristic
45#10622537C2211yescharacteristic
46C4×#4318C2211yescharacteristic
47#10622185C2212yes—
48#10622185C2212yes—
49Q8⋊(C11⋊C8)C2212yes—
50Q8⋊(C11⋊C8)C2212yes—
51Q8⋊(C11⋊C8)C2212yes—
52D4⋊(C11⋊C8)C2212yes—
53C2×C11×#41D411yescharacteristic
54C22×Q8×C11—22no—
55C22×Q8×C11—21no—
56C2×#4339—21no—
57C11×C4⋊Q8—22no—
58C11×C4⋊Q8—22no—
59C11×C4⋊Q8—24no—
60C11×C4⋊Q8—22no—
61C11×C4⋊Q8—22no—
62C11×C4⋊Q8—21no—
63C11×C4⋊Q8—21no—
64C11×C4⋊Q8D411yescharacteristic
65C11×C4⋊Q8D412yes—
66C11×C4⋊Q8D411yescharacteristic
67C11×C4⋊Q8C2312yes—
68C11×#125—22no—
69C11×#125—24no—
70C11×#125—22no—
71C11×#125—21no—
72C11×C22⋊Q8—22no—
73C11×C22⋊Q8—24no—
74C11×C22⋊Q8—24no—
75C11×C22⋊Q8—21no—
76C11×C22⋊Q8—22no—
77C11×C22⋊Q8—24no—
78C11×C22⋊Q8D412yes—
79C4×Q8×C11—22no—
80C4×Q8×C11—22no—
81C4×Q8×C11—22no—
82C4×Q8×C11—21no—
83C4×Q8×C11D411yescharacteristic
84C4×Q8×C11C2311yescharacteristic
85C4×Q8×C11C2312yes—
86C4×D4×C11—24no—
87C4×D4×C11—22no—
88C4×D4×C11—21no—
89C4×D4×C11—21no—
90C4×D4×C11D411yescharacteristic
91C4×D4×C11C2311yescharacteristic
92C11×#117—22no—
93C11×#117—21no—
94C11×#117—21no—
95C11×#117D411yescharacteristic
96C2×C11×C4⋊C4—22no—
97C2×C11×C4⋊C4—22no—
98C2×C11×C4⋊C4—21no—
99C2×C11×C4⋊C4D412yes—
100C2×C42×C11—21no—
101C2×C42×C11C2311yescharacteristic
102C2×#4325—21no—
103C2×#4325—22no—
104C2×#4323—21no—
105#66983—21no—
106#66983—21no—
107C2×#4318—21no—
108C2×#4318—21no—
109#66928—21no—
110#66927C2311yescharacteristic
111C4×D44—21no—
112C4×D44—21no—
113#66922C2311yescharacteristic
114#66899—21no—
115#66899—22no—
116#66896—21no—
117C22⋊(C11⋊C8)—21no—
118#66874—24no—
119#66873—24no—
120#66873—21no—
121#66873—21no—
122#66873—22no—
123#66872—21no—
124#66871—21no—
125#66871—22no—
126C4⋊(C11⋊C8)—21no—
127C4⋊(C11⋊C8)C2312yes—
128C4⋊(C11⋊C8)C2311yescharacteristic
129C4⋊(C11⋊C8)C2311yescharacteristic
130#66867—21no—
131C4×C11⋊C8—21no—
132C4×C11⋊C8C2312yes—
133#18583—111nomaximal, Sylow
134C11×#41—22no—
135C11×#41—22no—
136C2×Q8×C11—24no—
137C2×Q8×C11—21no—
138C2×Q8×C11—22no—
139C2×Q8×C11—22no—
140C2×Q8×C11—81no—
141C2×Q8×C11—81no—
142C2×Q8×C11—82no—
143C2×Q8×C11—82no—
144C2×Q8×C11C2×D412yes—
145C2×Q8×C11C2×D411yescharacteristic
146C2×D4×C11—21no—
147C2×D4×C11C2×D411yescharacteristic
148C22×C4×C11—21no—
149C22×C4×C11—24no—
150C22×C4×C11—22no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C2×C22⋊D11—41no—
157#4339—44no—
158C2×D44—21no—
159C2×D44—21no—
160C2×D44—21no—
161C2×C4×D11—41no—
162C2×Dic22—21no—
163C11×C4⋊C4—24no—
164C11×C4⋊C4—24no—
165C11×C4⋊C4—24no—
166C11×C4⋊C4—24no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—22no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—22no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4C2×D411yescharacteristic
178C11×C4⋊C4C2×D412yes—
179C11×C4⋊C4C2×D411yescharacteristic
180C11×C4⋊C4C2×D414yes—
181C11×C22⋊C4—24no—
182C11×C22⋊C4—22no—
183C11×C22⋊C4—21no—
184C11×C22⋊C4—21no—
185C11×C22⋊C4—21no—
186C42×C11—24no—
187C42×C11—21no—
188C42×C11—21no—
189C42×C11—21no—
190C42×C11—22no—
191C42×C11C2×D411yescharacteristic
192C42×C11C2×D411yescharacteristic
193C42×C11C2×D411yescharacteristic
194C42×C11C2411yescharacteristic
195#4325—42no—
196#4325—82no—
197#4323—42no—
198(C2×D11)⋊C4—41no—
199(C2×D11)⋊C4—41no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202#4318—42no—
203#4318—81no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—22no—
207C2×C11⋊C8—22no—
208#3503D1111yescharacteristic, complemented
209#3254—111no—
210#3141—111no—
211#3106—111no—
212#1637—112no—
213#1636—112no—
214#1627—112no—
215#1626—112no—
216#1546—111no—
217#1489—111no—
218#1485—111no—
219C23×C11—21no—
220C23×C11#12011yescharacteristic
221C22×D11—41no—
222Q8×C11—21no—
223Q8×C11—22no—
224Q8×C11—22no—
225Q8×C11—42no—
226Q8×C11—42no—
227Q8×C11—42no—
228Q8×C11—82no—
229Q8×C11—84no—
230Q8×C11#13712yes—
231D4×C11—24no—
232D4×C11—21no—
233D4×C11#13712yes—
234C2×C4×C11—24no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—22no—
245C2×C4×C11—24no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—42no—
249C2×C4×C11—82no—
250C2×C4×C11—84no—
251C2×C4×C11#12011yescharacteristic
252C2×C4×C11#12011yescharacteristic
253C2×C4×C11#12011yescharacteristic
254C2×C4×C11C22×D411yescharacteristic
255C2×C4×C11C22×D411yescharacteristic
256C2×C4×C11C22×D411yescharacteristic
257C22⋊D11—82no—
258C2×Dic11—41no—
259D44—42no—
260D44—41no—
261D44—41no—
262D44—41no—
263D44—41no—
264C4×D11—82no—
265Dic22—42no—
266C11⋊C8—42no—
267C11⋊C8—41no—
268C11⋊C8—41no—
269C11⋊C8—42no—
270Q82—21no—
271#557C2×D1112yes—
272#554—21no—
273#554—22no—
274D4×Q8—22no—
275D4×Q8C2×D1112yes—
276#544—22no—
277#544—21no—
278#533—21no—
279#533C2×D1111yescharacteristic
280#532—111no—
281C2×C4⋊Q8—21no—
282C2×C4⋊Q8C2×D1111yescharacteristic
283#520—21no—
284C4×#41C2×D1111yescharacteristic
285#489—222no—
286#487—112no—
287#486—112no—
288#482—221no—
289#477—111no—
290#477—112no—
291#476—111no—
292#474—221no—
293#468—222no—
294#461—221no—
295#460—111no—
296#460—112no—
297#459—111no—
298#449—221no—
299C4×SD16—221no—
300C4×D8—221no—
301#431—111no—
302#423—111no—
303#417—222no—
304C4×M16—111no—
305#332—112no—
306#332—112no—
307Q8⋊C8—112no—
308Q8⋊C8—112no—
309Q8⋊C8—112no—
310D4⋊C8—112no—
311C22×C11—21no—
312C22×C11—22no—
313C22×C11—21no—
314C22×C11—21no—
315C22×C11—41no—
316C22×C11—41no—
317C22×C11C2×#12011yescharacteristic
318C2×D11—81no—
319C2×D11—81no—
320C2×D11—81no—
321C4×C11—21no—
322C4×C11—22no—
323C4×C11—21no—
324C4×C11—21no—
325C4×C11—41no—
326C4×C11—42no—
327C4×C11—44no—
328C4×C11—41no—
329C4×C11—42no—
330C4×C11#45412yes—
331C4×C11C2×#13711yescharacteristic
332C4×C11C2×#13711yescharacteristic
333C4×C11#57611yescharacteristic
334C4×C11#57711yescharacteristic
335Dic11—81no—
336C2×#41—221no—
337C2×#41C22⋊D1111yescharacteristic
338C22×Q8—22no—
339C22×Q8—21no—
340C2×SD16—221no—
341C2×SD16—222no—
342C2×D8—221no—
343C2×M16—221no—
344C2×M16—221no—
345C4⋊Q8—22no—
346C4⋊Q8—22no—
347C4⋊Q8—24no—
348C4⋊Q8—22no—
349C4⋊Q8—22no—
350C4⋊Q8—21no—
351C4⋊Q8—21no—
352C4⋊Q8—111no—
353C4⋊Q8C22⋊D1111yescharacteristic
354C4⋊Q8C22⋊D1112yes—
355C4⋊Q8C22⋊D1111yescharacteristic
356C4⋊Q8C22×D1112yes—
357#127—111no—
358#125—22no—
359#125—24no—
360#125—22no—
361#125—21no—
362#124—221no—
363C22⋊Q8—22no—
364C22⋊Q8—24no—
365C22⋊Q8—24no—
366C22⋊Q8—21no—
367C22⋊Q8—22no—
368C22⋊Q8—24no—
369C22⋊Q8C22⋊D1112yes—
370#121—221no—
371#121—221no—
372C4×Q8—22no—
373C4×Q8—22no—
374C4×Q8—22no—
375C4×Q8—21no—
376C4×Q8C22⋊D1111yescharacteristic
377C4×Q8C22×D1111yescharacteristic
378C4×Q8C22×D1112yes—
379C4×D4—24no—
380C4×D4—22no—
381C4×D4—21no—
382C4×D4—21no—
383C4×D4—221no—
384C4×D4—221no—
385C4×D4C22⋊D1111yescharacteristic
386C4×D4C22×D1111yescharacteristic
387#117—22no—
388#117—21no—
389#117—21no—
390#117C22⋊D1111yescharacteristic
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4C22⋊D1112yes—
395C2×C42—21no—
396C2×C42C22×D1111yescharacteristic
397#107—221no—
398#107—222no—
399#106—221no—
400C4⋊C8—112no—
401C4⋊C8—111no—
402C4⋊C8—111no—
403C4⋊C8—221no—
404#103—221no—
405#103—222no—
406#103—224no—
407#102—221no—
408#102—224no—
409#102—221no—
410#102—221no—
411#102—222no—
412C22⋊C8—221no—
413#97—221no—
414C4×C8—112no—
415C4×C8—221no—
416C2×C11—41no—
417C2×C11—42no—
418C2×C11#300411yescharacteristic
419C2×C11#301211yescharacteristic
420C2×C11C2×#45411yescharacteristic
421D11—161no—
422#41—22no—
423#41—22no—
424#41—444no—
425C2×Q8—24no—
426C2×Q8—21no—
427C2×Q8—22no—
428C2×Q8—22no—
429C2×Q8—81no—
430C2×Q8—81no—
431C2×Q8—82no—
432C2×Q8—82no—
433C2×Q8—221no—
434C2×Q8C2×C22⋊D1112yes—
435C2×Q8C2×C22⋊D1111yescharacteristic
436C2×D4—21no—
437C2×D4—221no—
438C2×D4—221no—
439C2×D4—221no—
440C2×D4—441no—
441C2×D4C2×C22⋊D1111yescharacteristic
442C22×C4—21no—
443C22×C4—24no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—441no—
448C22×C4C2×C22⋊D1111yescharacteristic
449C22×C4C2×C22⋊D1111yescharacteristic
450C22×C4C2×C22⋊D1111yescharacteristic
451SD16—442no—
452SD16—882no—
453D8—442no—
454M16—442no—
455M16—881no—
456C2×C8—222no—
457C2×C8—221no—
458C2×C8—221no—
459C2×C8—222no—
460C4⋊C4—24no—
461C4⋊C4—24no—
462C4⋊C4—24no—
463C4⋊C4—24no—
464C4⋊C4—21no—
465C4⋊C4—22no—
466C4⋊C4—21no—
467C4⋊C4—22no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—22no—
471C4⋊C4—22no—
472C4⋊C4—21no—
473C4⋊C4—22no—
474C4⋊C4—221no—
475C4⋊C4—221no—
476C4⋊C4C2×C22⋊D1114yes—
477C4⋊C4C2×C22⋊D1111yescharacteristic
478C4⋊C4C2×C22⋊D1111yescharacteristic
479C4⋊C4C2×C22⋊D1112yes—
480C22⋊C4—24no—
481C22⋊C4—22no—
482C22⋊C4—21no—
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—441no—
486C22⋊C4—441no—
487C42—24no—
488C42—21no—
489C42—21no—
490C42—21no—
491C42—22no—
492C42C2×C22⋊D1111yescharacteristic
493C42C2×C22⋊D1111yescharacteristic
494C42C2×C22⋊D1111yescharacteristic
495C42C23×D1111yescharacteristic
496C11#1858311yescharacteristic, complemented, Sylow
497C23—21no—
498C23—441no—
499C23#6700611yescharacteristic
500Q8—21no—
501Q8—22no—
502Q8—22no—
503Q8—42no—
504Q8—42no—
505Q8—42no—
506Q8—82no—
507Q8—84no—
508Q8—442no—
509Q8#6699512yes—
510D4—24no—
511D4—21no—
512D4—442no—
513D4—441no—
514D4—441no—
515D4—441no—
516D4—441no—
517D4—882no—
518D4#6699512yes—
519C2×C4—24no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—22no—
530C2×C4—24no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—42no—
534C2×C4—82no—
535C2×C4—84no—
536C2×C4—441no—
537C2×C4—882no—
538C2×C4#6700611yescharacteristic
539C2×C4#6700611yescharacteristic
540C2×C4#6700611yescharacteristic
541C2×C4C22×C22⋊D1111yescharacteristic
542C2×C4C22×C22⋊D1111yescharacteristic
543C2×C4C22×C22⋊D1111yescharacteristic
544C8—442no—
545C8—441no—
546C8—441no—
547C8—442no—
548C22—21no—
549C22—22no—
550C22—21no—
551C22—21no—
552C22—41no—
553C22—41no—
554C22—881no—
555C22—881no—
556C22—881no—
557C22C2×#6700611yescharacteristic
558C4—21no—
559C4—22no—
560C4—21no—
561C4—21no—
562C4—41no—
563C4—42no—
564C4—44no—
565C4—41no—
566C4—42no—
567C4—881no—
568C4#1062285812yes—
569C4C2×#6699511yescharacteristic
570C4C2×#6699511yescharacteristic
571C4#1062336611yescharacteristic
572C4#1062336711yescharacteristic
573C2—41no—
574C2—42no—
575C2—1761no—
576C2#1307785011yescharacteristic
577C2#1307792011yescharacteristic
578C2C2×#1062285811yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3503C2
socleC22×C11C2×#120
prime radical#13078676C2
hypercenter#3503D11
hypocenterC11#18583
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3503

Complements

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

NH ≅ G/Ntype
1. #13079999C2semidirect
2. #13079012C2semidirect
4. #13067781C2semidirect
5. #13067774C2semidirect
6. #13067719C2semidirect
7. #13067712C2semidirect
8. #13067288C2semidirect
9. #13067055C2semidirect
10. #13067037C2semidirect
11. C11×#3503C2semidirect
208. #3503D11semidirect
496. C11#18583semidirect

Maximal subgroups

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

subgroupindex
#130799992
#130790122
#130786762
#130677812
#130677742
#130677192
#130677122
#130672882
#130670552
#130670372
C11×#35032
#1858311