Finite Group Databasebeta

← #14737246

Subgroups — #14737246

Order 2816.

606 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#13079942C211yesmaximal, characteristic
2#13079176C211yesmaximal, characteristic, complemented
3#13077592C211yesmaximal, characteristic, complemented
4#13068120C211yesmaximal, characteristic, complemented
5#13068113C211yesmaximal, characteristic, complemented
6#13068090C211yesmaximal, characteristic, complemented
7#13068083C211yesmaximal, characteristic, complemented
8#13068072C211yesmaximal, characteristic, complemented
9#13068065C211yesmaximal, characteristic, complemented
10#13068062C211yesmaximal, characteristic, complemented
11#13068055C211yesmaximal, characteristic, complemented
12C2×#10622117C211yesmaximal, characteristic, complemented
13#13067316C211yesmaximal, characteristic, complemented
14#13067309C211yesmaximal, characteristic, complemented
15C11×#3248C211yesmaximal, characteristic, complemented
16C11×#533C2211yescharacteristic
17C11×#529C2211yescharacteristic
18#10623008C2211yescharacteristic
19C11×#479—21no—
20C11×#475C2211yescharacteristic
21C11×#474C2211yescharacteristic
22C11×#467—21no—
23C11×#465—21no—
24C11×#464—21no—
25C11×#462C2211yescharacteristic
26C11×#461C2211yescharacteristic
27C2×C11×C4⋊C8C2211yescharacteristic
28#10622701C2211yescharacteristic
29#10622698C2211yescharacteristic
30#10622694C2211yescharacteristic
31#10622692C2211yescharacteristic
32#10622679—21no—
33#10622670—21no—
34#10622661—21no—
35#10622661—21no—
36#10622661—21no—
37#10622651—21no—
38#10622640C2211yescharacteristic
39C4×#4325—21no—
40C4×#4325—21no—
41#10622637C2211yescharacteristic
42Q8×C11⋊C8C2211yescharacteristic
43#10622634C2211yescharacteristic
44#10622628C2211yescharacteristic
45#10622625C2211yescharacteristic
46#10622624—21no—
47D4×C11⋊C8—21no—
48D4×C11⋊C8C2211yescharacteristic
49#10622621C2211yescharacteristic
50#10622613—21no—
51#10622610—21no—
52#10622539C2211yescharacteristic
53C2×C4⋊(C11⋊C8)C2211yescharacteristic
54C2×C4×C11⋊C8C2211yescharacteristic
55#10622185C2211yescharacteristic
56#10622185C2211yescharacteristic
57#10622185C2211yescharacteristic
58#10622185C2211yescharacteristic
59#10622123C2211yescharacteristic
60#10622123C2211yescharacteristic
61#10622119C2211yescharacteristic
62#10622119C2211yescharacteristic
63#10622117C2211yescharacteristic
64#10622117C2211yescharacteristic
65#10622117C2211yescharacteristic
66#10622117C2211yescharacteristic
67C2×#4339—21no—
68C2×C11×Q16—21no—
69C2×C11×SD16—21no—
70C22×C8×C11—21no—
71C11×C4⋊Q8C2311yescharacteristic
72C11×C4⋊Q8C2311yescharacteristic
73C11×#126—21no—
74C11×#125—21no—
75C11×#125D411yescharacteristic
76C11×#124D411yescharacteristic
77C11×#123—21no—
78C11×C22⋊Q8—21no—
79C11×C22⋊Q8—21no—
80C11×C22⋊Q8D411yescharacteristic
81C11×#121D411yescharacteristic
82C4×Q8×C11—21no—
83C4×Q8×C11—21no—
84C4×Q8×C11C2311yescharacteristic
85C4×D4×C11—21no—
86C4×D4×C11C2311yescharacteristic
87C11×#117—21no—
88C11×#117—21no—
89C2×C42×C11C2311yescharacteristic
90C2×#4325—21no—
91C2×#4325—21no—
92C2×#4325—21no—
93C2×#4323—21no—
94#66983—21no—
95#66983—21no—
96C2×#4318—21no—
97C22×C11⋊C8—21no—
98C22×C11⋊C8—21no—
99C22×C11⋊C8D411yescharacteristic
100C22×C11⋊C8D411yescharacteristic
101#66928—21no—
102#66927C2311yescharacteristic
103C4×D44—21no—
104C4×D44—21no—
105#66922C2311yescharacteristic
106C11×#107—21no—
107C11×#106—21no—
108C11×C4⋊C8—21no—
109C11×C4⋊C8C2311yescharacteristic
110C11×C4⋊C8C2311yescharacteristic
111C11×#103—21no—
112C11×#103—21no—
113C11×#103—21no—
114C11×#102—21no—
115#66899—21no—
116#66899—21no—
117#66899—21no—
118#66896—21no—
119C22⋊(C11⋊C8)—21no—
120C22⋊(C11⋊C8)—21no—
121C22⋊(C11⋊C8)—21no—
122#66873—21no—
123#66873—21no—
124#66873—21no—
125#66873—21no—
126#66872—21no—
127#66872—21no—
128#66872—21no—
129#66871—21no—
130C4⋊(C11⋊C8)—21no—
131C4⋊(C11⋊C8)—21no—
132C4⋊(C11⋊C8)—21no—
133C4⋊(C11⋊C8)C2311yescharacteristic
134C4⋊(C11⋊C8)C2311yescharacteristic
135C4⋊(C11⋊C8)C2311yescharacteristic
136C4⋊(C11⋊C8)C2311yescharacteristic
137#66867—21no—
138#66867—21no—
139C4×C11⋊C8—21no—
140C4×C11⋊C8D411yescharacteristic
141C4×C11⋊C8D411yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#19229—111nomaximal, Sylow
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11C2×D411yescharacteristic
148C2×D4×C11—21no—
149C2×D4×C11C2×D411yescharacteristic
150C22×C4×C11—21no—
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11#4111yescharacteristic
154C2×C22⋊D11—41no—
155#4339—82no—
156C2×D44—21no—
157C2×D44—21no—
158C2×D44—21no—
159C2×C4×D11—41no—
160C2×Dic22—21no—
161C11×Q16—81no—
162C11×SD16—81no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—81no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—41no—
175C11×C4⋊C4—41no—
176C11×C4⋊C4C2×D411yescharacteristic
177C11×C4⋊C4C2×D411yescharacteristic
178C11×C22⋊C4—21no—
179C11×C22⋊C4—21no—
180C11×C22⋊C4—21no—
181C11×C22⋊C4—21no—
182C11×C22⋊C4—21no—
183C11×C22⋊C4—41no—
184C42×C11—21no—
185C42×C11—41no—
186C42×C11C2×D411yescharacteristic
187C42×C11C2×D411yescharacteristic
188C42×C11#4111yescharacteristic
189C42×C11C2411yescharacteristic
190#4325—42no—
191#4325—42no—
192#4325—81no—
193#4323—81no—
194(C2×D11)⋊C4—41no—
195(C2×D11)⋊C4—41no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198#4318—42no—
199C2×C11⋊C8—22no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—41no—
205C2×C11⋊C8—42no—
206C2×C11⋊C8—81no—
207C2×C11⋊C8C2×D411yescharacteristic
208C2×C11⋊C8C2×D411yescharacteristic
209C2×C11⋊C8C2×D411yescharacteristic
210C2×C11⋊C8C2×D411yescharacteristic
211#3248D1111yescharacteristic, complemented
212#3247—111no—
213#3167—111no—
214#2966—111no—
215#1692—111no—
216#1691—111no—
217#1686—111no—
218#1685—111no—
219#1684—111no—
220#1683—111no—
221#1682—111no—
222#1681—111no—
223C2×#335—111no—
224#1552—111no—
225#1551—111no—
226C23×C11—21no—
227C23×C11#12111yescharacteristic
228C22×D11—41no—
229Q8×C11—21no—
230Q8×C11—21no—
231Q8×C11—41no—
232Q8×C11—41no—
233Q8×C11—41no—
234Q8×C11—41no—
235D4×C11—21no—
236D4×C11—21no—
237D4×C11—42no—
238C2×C4×C11—22no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11#12111yescharacteristic
251C2×C4×C11#12111yescharacteristic
252C2×C4×C11#12111yescharacteristic
253C2×C4×C11C22×D411yescharacteristic
254C2×C4×C11C22×D411yescharacteristic
255C2×C4×C11C2×#4111yescharacteristic
256C22⋊D11—82no—
257C2×Dic11—41no—
258D44—41no—
259D44—41no—
260D44—41no—
261D44—41no—
262D44—81no—
263C4×D11—82no—
264Dic22—81no—
265C8×C11—41no—
266C8×C11—41no—
267C11⋊C8—21no—
268C11⋊C8—21no—
269C11⋊C8—21no—
270C11⋊C8—41no—
271C11⋊C8—41no—
272C11⋊C8—41no—
273C11⋊C8—41no—
274C11⋊C8#13512yes—
275#533C2×D1111yescharacteristic
276#532—111no—
277#529C2×D1111yescharacteristic
278#498—111no—
279#492—111no—
280#487—111no—
281#486—111no—
282#479—21no—
283#478—221no—
284#477—111no—
285#476—111no—
286#475C2×D1111yescharacteristic
287#474C2×D1111yescharacteristic
288#467—21no—
289#466—221no—
290#465—21no—
291#465—221no—
292#465—221no—
293#465—221no—
294#464—21no—
295#463—221no—
296#462C2×D1111yescharacteristic
297#461C2×D1111yescharacteristic
298#460—111no—
299#459—111no—
300#446—111no—
301C8×Q8—111no—
302C4×SD16—221no—
303C4×SD16—221no—
304#436—111no—
305#435—221no—
306C8×D4—111no—
307C8×D4—221no—
308#433—221no—
309#432—111no—
310C2×C4⋊C8—111no—
311C2×C4⋊C8C2×D1111yescharacteristic
312#405—221no—
313C2×C4×C8—111no—
314#335—111no—
315#335—111no—
316#335—111no—
317#335—111no—
318#333—111no—
319#333—111no—
320#332—111no—
321#332—111no—
322#332—111no—
323#332—111no—
324#331—111no—
325#331—111no—
326C22×C11—21no—
327C22×C11—21no—
328C22×C11—41no—
329C22×C11—41no—
330C22×C11—41no—
331C22×C11#47112yes—
332C22×C11C2×#12111yescharacteristic
333C2×D11—81no—
334C2×D11—81no—
335C2×D11—81no—
336C4×C11—21no—
337C4×C11—21no—
338C4×C11—21no—
339C4×C11—21no—
340C4×C11—41no—
341C4×C11—41no—
342C4×C11—41no—
343C4×C11—81no—
344C4×C11—81no—
345C4×C11C2×#13511yescharacteristic
346C4×C11#57511yescharacteristic
347C4×C11#57611yescharacteristic
348C4×C11#57811yescharacteristic
349Dic11—81no—
350C2×#41—221no—
351C2×Q16—21no—
352C2×SD16—21no—
353C2×SD16—221no—
354C2×SD16—221no—
355C2×SD16—221no—
356C2×D8—221no—
357C2×M16—221no—
358C22×C8—21no—
359C22×C8—111no—
360C22×C8—111no—
361C22×C8—221no—
362C22×C8—221no—
363C4⋊Q8—111no—
364C4⋊Q8C22×D1111yescharacteristic
365C4⋊Q8C22×D1111yescharacteristic
366#127—111no—
367#126—21no—
368#125—21no—
369#125C22⋊D1111yescharacteristic
370#124—221no—
371#124C22⋊D1111yescharacteristic
372#123—21no—
373C22⋊Q8—21no—
374C22⋊Q8—21no—
375C22⋊Q8C22⋊D1111yescharacteristic
376#121—221no—
377#121—221no—
378#121C22⋊D1111yescharacteristic
379C4×Q8—21no—
380C4×Q8—21no—
381C4×Q8C22×D1111yescharacteristic
382C4×D4—21no—
383C4×D4—221no—
384C4×D4—221no—
385C4×D4C22×D1111yescharacteristic
386#117—21no—
387#117—21no—
388C2×C42C22×D1111yescharacteristic
389#107—21no—
390#107—221no—
391#106—21no—
392#106—221no—
393#106—221no—
394#106—221no—
395C4⋊C8—21no—
396C4⋊C8—111no—
397C4⋊C8—111no—
398C4⋊C8—111no—
399C4⋊C8—111no—
400C4⋊C8—221no—
401C4⋊C8—221no—
402C4⋊C8—221no—
403C4⋊C8C22×D1111yescharacteristic
404C4⋊C8C22×D1111yescharacteristic
405#103—21no—
406#103—21no—
407#103—21no—
408#103—221no—
409#103—221no—
410#103—221no—
411#102—21no—
412#102—221no—
413#102—221no—
414#102—221no—
415#102—221no—
416#102—221no—
417C22⋊C8—221no—
418C22⋊C8—221no—
419C22⋊C8—221no—
420#97—221no—
421#97—221no—
422C4×C8—111no—
423C4×C8—111no—
424C4×C8—111no—
425C4×C8—111no—
426C4×C8—221no—
427C2×C11—22no—
428C2×C11—81no—
429C2×C11#303511yescharacteristic
430C2×C11#306111yescharacteristic
431C2×C11C2×#47111yescharacteristic
432D11—161no—
433#41—882no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—221no—
437C2×Q8C2×C22⋊D1111yescharacteristic
438C2×D4—21no—
439C2×D4—221no—
440C2×D4—221no—
441C2×D4—221no—
442C2×D4—441no—
443C2×D4C2×C22⋊D1111yescharacteristic
444C22×C4—21no—
445C22×C4—441no—
446C22×C4D4×D1111yescharacteristic
447C22×C4#434111yescharacteristic
448C22×C4C2×C22⋊D1111yescharacteristic
449Q16—81no—
450SD16—81no—
451SD16—442no—
452SD16—442no—
453SD16—881no—
454D8—881no—
455M16—442no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—81no—
459C2×C8—111no—
460C2×C8—111no—
461C2×C8—111no—
462C2×C8—111no—
463C2×C8—222no—
464C2×C8—221no—
465C2×C8—221no—
466C2×C8—221no—
467C2×C8—221no—
468C2×C8—441no—
469C2×C8—442no—
470C2×C8—881no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—41no—
480C4⋊C4—41no—
481C4⋊C4—221no—
482C4⋊C4—221no—
483C4⋊C4C2×C22⋊D1111yescharacteristic
484C4⋊C4C2×C22⋊D1111yescharacteristic
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—21no—
489C22⋊C4—21no—
490C22⋊C4—41no—
491C22⋊C4—441no—
492C22⋊C4—441no—
493C42—21no—
494C42—41no—
495C42D4×D1111yescharacteristic
496C42#434111yescharacteristic
497C42C2×C22⋊D1111yescharacteristic
498C42C23×D1111yescharacteristic
499C11#1922911yescharacteristic, complemented, Sylow
500C23—21no—
501C23—441no—
502C23#6699211yescharacteristic
503Q8—21no—
504Q8—21no—
505Q8—41no—
506Q8—41no—
507Q8—41no—
508Q8—41no—
509Q8—881no—
510D4—21no—
511D4—21no—
512D4—42no—
513D4—441no—
514D4—441no—
515D4—441no—
516D4—441no—
517D4—881no—
518D4—882no—
519C2×C4—22no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—441no—
532C2×C4—882no—
533C2×C4#6699211yescharacteristic
534C2×C4#6699211yescharacteristic
535C2×C4#6699211yescharacteristic
536C2×C4C2×D4×D1111yescharacteristic
537C2×C4C2×#434111yescharacteristic
538C2×C4C22×C22⋊D1111yescharacteristic
539C8—41no—
540C8—41no—
541C8—112no—
542C8—221no—
543C8—221no—
544C8—221no—
545C8—441no—
546C8—441no—
547C8—441no—
548C8—441no—
549C22—21no—
550C22—21no—
551C22—41no—
552C22—41no—
553C22—41no—
554C22—881no—
555C22—881no—
556C22—881no—
557C22#1062281612yes—
558C22C2×#6699211yescharacteristic
559C4—21no—
560C4—21no—
561C4—21no—
562C4—21no—
563C4—41no—
564C4—41no—
565C4—41no—
566C4—81no—
567C4—81no—
568C4—881no—
569C4D11×#13511yescharacteristic
570C4#1062329911yescharacteristic
571C4#1062336611yescharacteristic
572C4#1062336911yescharacteristic
573C2—22no—
574C2—81no—
575C2—1761no—
576C2#1307806711yescharacteristic
577C2#1307828311yescharacteristic
578C2C2×#1062281611yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3248C2
socleC22×C11C2×#121
prime radical#13079942C2
hypercenter#3248D11
hypocenterC11#19229
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3248

Complements

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

NH ≅ G/Ntype
2. #13079176C2semidirect
3. #13077592C2semidirect
4. #13068120C2semidirect
5. #13068113C2semidirect
6. #13068090C2semidirect
7. #13068083C2semidirect
8. #13068072C2semidirect
9. #13068065C2semidirect
10. #13068062C2semidirect
11. #13068055C2semidirect
12. C2×#10622117C2semidirect
13. #13067316C2semidirect
14. #13067309C2semidirect
15. C11×#3248C2semidirect
211. #3248D11semidirect
499. C11#19229semidirect

Maximal subgroups

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

subgroupindex
#130799422
#130791762
#130775922
#130681202
#130681132
#130680902
#130680832
#130680722
#130680652
#130680622
#130680552
C2×#106221172
#130673162
#130673092
C11×#32482
#1922911