Finite Group Databasebeta

← #14737242

Subgroups — #14737242

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#13079953C211yesmaximal, characteristic, complemented
2#13079942C211yesmaximal, characteristic
3#13079175C211yesmaximal, characteristic, complemented
4#13068122C211yesmaximal, characteristic, complemented
5#13068115C211yesmaximal, characteristic, complemented
6#13068088C211yesmaximal, characteristic, complemented
7#13068081C211yesmaximal, characteristic, complemented
8#13068074C211yesmaximal, characteristic, complemented
9#13068067C211yesmaximal, characteristic, complemented
10#13068060C211yesmaximal, characteristic, complemented
11#13068053C211yesmaximal, characteristic, complemented
12C2×#10622096C211yesmaximal, characteristic, complemented
13#13067317C211yesmaximal, characteristic, complemented
14#13067312C211yesmaximal, characteristic, complemented
15C11×#2966C211yesmaximal, characteristic, complemented
16C11×#529C2211yescharacteristic
17#10623008C2211yescharacteristic
18#10623001C2211yescharacteristic
19C11×#446C2211yescharacteristic
20C8×Q8×C11C2211yescharacteristic
21C11×#436C2211yescharacteristic
22C11×#435—21no—
23C8×D4×C11—21no—
24C8×D4×C11C2211yescharacteristic
25C11×#433—21no—
26C11×#432C2211yescharacteristic
27C11×#405—21no—
28C2×C4×C8×C11C2211yescharacteristic
29#10622727—21no—
30#10622727—21no—
31#10622679—21no—
32#10622676—21no—
33#10622670—21no—
34#10622667—21no—
35#10622664—21no—
36#10622661—21no—
37#10622654—21no—
38#10622651—21no—
39#10622644C2211yescharacteristic
40#10622640C2211yescharacteristic
41#10622634C2211yescharacteristic
42#10622633C2211yescharacteristic
43#10622632C2211yescharacteristic
44#10622628C2211yescharacteristic
45#10622621C2211yescharacteristic
46#10622620C2211yescharacteristic
47C2×C4⋊(C11⋊C8)C2211yescharacteristic
48C2×C4⋊(C11⋊C8)C2211yescharacteristic
49#10622307C2211yescharacteristic
50#10622306C2211yescharacteristic
51C4×#4314—21no—
52C4×#4314—21no—
53#10622294C2211yescharacteristic
54#10622293C2211yescharacteristic
55#10622124C2211yescharacteristic
56#10622124C2211yescharacteristic
57#10622123C2211yescharacteristic
58#10622123C2211yescharacteristic
59#10622120C2211yescharacteristic
60#10622120C2211yescharacteristic
61#10622119C2211yescharacteristic
62#10622119C2211yescharacteristic
63#10622096C2211yescharacteristic
64#10622096C2211yescharacteristic
65#10622096C2211yescharacteristic
66#10622096C2211yescharacteristic
67C2×#4339—21no—
68C2×C11×M16—21no—
69C22×C8×C11—21no—
70C22×C8×C11D411yescharacteristic
71C22×C8×C11D411yescharacteristic
72C11×#126—21no—
73C11×#125D411yescharacteristic
74C11×#124D411yescharacteristic
75C11×#123—21no—
76C11×C22⋊Q8D411yescharacteristic
77C11×#121D411yescharacteristic
78C4×Q8×C11C2311yescharacteristic
79C4×D4×C11—21no—
80C4×D4×C11C2311yescharacteristic
81C11×#117—21no—
82C2×C42×C11C2311yescharacteristic
83C2×#4326—21no—
84C2×#4325—21no—
85C2×#4324—21no—
86C2×#4323—21no—
87#66983—21no—
88#66983—21no—
89#66979—21no—
90#66977—21no—
91#66977—21no—
92C22×C11⋊C8—21no—
93C22×C11⋊C8—21no—
94C2×#4314—21no—
95C2×#4314—21no—
96#66928—21no—
97#66927C2311yescharacteristic
98C4×D44—21no—
99C4×D44—21no—
100#66923—21no—
101#66922C2311yescharacteristic
102#66922C2311yescharacteristic
103#66922C2311yescharacteristic
104C4×Dic22—21no—
105C4×Dic22—21no—
106C11×C4⋊C8—21no—
107C11×C4⋊C8—21no—
108C11×C4⋊C8C2311yescharacteristic
109C11×C4⋊C8C2311yescharacteristic
110C11×C22⋊C8—21no—
111C11×C22⋊C8—21no—
112C11×C22⋊C8—21no—
113C11×#97—21no—
114C11×#97—21no—
115C4×C8×C11—21no—
116C4×C8×C11D411yescharacteristic
117C4×C8×C11D411yescharacteristic
118C4×C8×C11C2311yescharacteristic
119C4×C8×C11C2311yescharacteristic
120#66899—21no—
121#66899—21no—
122#66896—21no—
123#66896—21no—
124#66885—21no—
125#66885—21no—
126#66881—21no—
127#66881—21no—
128#66880—21no—
129#66880—21no—
130#66874—21no—
131#66874—21no—
132#66873—21no—
133#66873—21no—
134#66872—21no—
135#66872—21no—
136#66871—21no—
137#66871—21no—
138C4⋊(C11⋊C8)—21no—
139C4⋊(C11⋊C8)—21no—
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4⋊(C11⋊C8)C2311yescharacteristic
143C4⋊(C11⋊C8)C2311yescharacteristic
144#19229—111nomaximal, Sylow
145C2×Q8×C11C2×D411yescharacteristic
146C2×D4×C11—21no—
147C2×D4×C11C2×D411yescharacteristic
148C22×C4×C11—21no—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11#4111yescharacteristic
152C2×C22⋊D11—41no—
153#4339—82no—
154C2×D44—21no—
155C2×D44—21no—
156C2×D44—21no—
157C2×C4×D11—41no—
158C2×Dic22—21no—
159C2×Dic22—21no—
160C2×Dic22—21no—
161C11×M16—42no—
162C2×C8×C11—22no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—41no—
166C2×C8×C11—42no—
167C2×C8×C11C2×D411yescharacteristic
168C2×C8×C11C2×D411yescharacteristic
169C2×C8×C11C2×D411yescharacteristic
170C2×C8×C11C2×D411yescharacteristic
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4C2×D411yescharacteristic
176C11×C4⋊C4C2×D411yescharacteristic
177C11×C22⋊C4—21no—
178C11×C22⋊C4—21no—
179C11×C22⋊C4—21no—
180C11×C22⋊C4—21no—
181C11×C22⋊C4—21no—
182C42×C11—21no—
183C42×C11C2×D411yescharacteristic
184C42×C11C2×D411yescharacteristic
185C42×C11#4111yescharacteristic
186C42×C11C2411yescharacteristic
187C22⋊Dic11—41no—
188#4326—81no—
189#4325—81no—
190#4324—81no—
191#4323—81no—
192(C2×D11)⋊C4—41no—
193(C2×D11)⋊C4—41no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200Dic11⋊C4—41no—
201Dic11⋊C4—41no—
202C4×Dic11—41no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—81no—
208C2×C11⋊C8—81no—
209#4314—42no—
210#4314—42no—
211#3248—111no—
212#3247—111no—
213#3167—111no—
214#2966D1111yescharacteristic, complemented
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—
231D4×C11—21no—
232D4×C11—21no—
233D4×C11—42no—
234C2×C4×C11—22no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11#12111yescharacteristic
245C2×C4×C11#12111yescharacteristic
246C2×C4×C11#12111yescharacteristic
247C2×C4×C11C22×D411yescharacteristic
248C2×C4×C11C22×D411yescharacteristic
249C2×C4×C11C2×#4111yescharacteristic
250C22⋊D11—82no—
251C2×Dic11—41no—
252C2×Dic11—41no—
253C2×Dic11—41no—
254D44—41no—
255D44—41no—
256D44—41no—
257D44—41no—
258D44—81no—
259C4×D11—82no—
260Dic22—41no—
261Dic22—41no—
262Dic22—41no—
263Dic22—41no—
264Dic22—81no—
265C8×C11—21no—
266C8×C11—21no—
267C8×C11—21no—
268C8×C11—41no—
269C8×C11—41no—
270C8×C11#13512yes—
271C11⋊C8—41no—
272C11⋊C8—41no—
273C11⋊C8—41no—
274C11⋊C8—41no—
275#533—111no—
276#532—111no—
277#529C2×D1111yescharacteristic
278#498—111no—
279#492—111no—
280#487—111no—
281#486—111no—
282#479—221no—
283#478—221no—
284#477—111no—
285#476—111no—
286#475—111no—
287#474—111no—
288#467—221no—
289#466—221no—
290#465—221no—
291#465—221no—
292#465—221no—
293#465—221no—
294#464—221no—
295#463—221no—
296#462—111no—
297#461—111no—
298#460—111no—
299#459—111no—
300#446C2×D1111yescharacteristic
301C8×Q8C2×D1111yescharacteristic
302C4×SD16—221no—
303C4×SD16—221no—
304#436C2×D1111yescharacteristic
305#435—21no—
306C8×D4—21no—
307C8×D4C2×D1111yescharacteristic
308#433—21no—
309#432C2×D1111yescharacteristic
310C2×C4⋊C8—111no—
311C2×C4⋊C8—111no—
312#405—21no—
313C2×C4×C8C2×D1111yescharacteristic
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×C11C2×#13511yescharacteristic
344C4×C11#57511yescharacteristic
345C4×C11#57611yescharacteristic
346C4×C11#57811yescharacteristic
347Dic11—81no—
348Dic11—81no—
349Dic11—81no—
350C2×#41—221no—
351C2×Q16—221no—
352C2×SD16—221no—
353C2×SD16—221no—
354C2×SD16—221no—
355C2×SD16—221no—
356C2×D8—221no—
357C2×M16—21no—
358C22×C8—21no—
359C22×C8—221no—
360C22×C8—221no—
361C22×C8C22⋊D1111yescharacteristic
362C22×C8C22⋊D1111yescharacteristic
363C4⋊Q8—111no—
364C4⋊Q8—111no—
365C4⋊Q8—111no—
366#127—111no—
367#126—21no—
368#125—221no—
369#125D4411yescharacteristic
370#124—221no—
371#124D4411yescharacteristic
372#123—21no—
373C22⋊Q8—221no—
374C22⋊Q8—221no—
375C22⋊Q8D4411yescharacteristic
376#121—221no—
377#121—221no—
378#121D4411yescharacteristic
379C4×Q8—221no—
380C4×Q8—221no—
381C4×Q8C22×D1111yescharacteristic
382C4×D4—21no—
383C4×D4—221no—
384C4×D4—221no—
385C4×D4C22×D1111yescharacteristic
386#117—21no—
387#117—221no—
388C2×C42C22×D1111yescharacteristic
389#107—221no—
390#107—221no—
391#106—221no—
392#106—221no—
393#106—221no—
394#106—221no—
395C4⋊C8—21no—
396C4⋊C8—21no—
397C4⋊C8—111no—
398C4⋊C8—111no—
399C4⋊C8—111no—
400C4⋊C8—111no—
401C4⋊C8—221no—
402C4⋊C8—221no—
403C4⋊C8C22×D1111yescharacteristic
404C4⋊C8C22×D1111yescharacteristic
405#103—221no—
406#103—221no—
407#103—221no—
408#103—221no—
409#103—221no—
410#103—221no—
411#102—221no—
412#102—221no—
413#102—221no—
414#102—221no—
415#102—221no—
416#102—221no—
417C22⋊C8—21no—
418C22⋊C8—21no—
419C22⋊C8—21no—
420#97—21no—
421#97—21no—
422C4×C8—21no—
423C4×C8C22⋊D1111yescharacteristic
424C4×C8C22⋊D1111yescharacteristic
425C4×C8C22×D1111yescharacteristic
426C4×C8C22×D1111yescharacteristic
427C2×C11—22no—
428C2×C11—81no—
429C2×C11#303511yescharacteristic
430C2×C11#306111yescharacteristic
431C2×C11C2×#47111yescharacteristic
432D11—161no—
433#41—882no—
434C2×Q8—221no—
435C2×Q8—221no—
436C2×Q8—221no—
437C2×Q8C2×D4411yescharacteristic
438C2×D4—21no—
439C2×D4—221no—
440C2×D4—221no—
441C2×D4—221no—
442C2×D4—441no—
443C2×D4C2×D4411yescharacteristic
444C22×C4—21no—
445C22×C4—441no—
446C22×C4C2×D4411yescharacteristic
447C22×C4#433911yescharacteristic
448C22×C4C2×C22⋊D1111yescharacteristic
449Q16—881no—
450SD16—442no—
451SD16—442no—
452SD16—881no—
453SD16—881no—
454D8—881no—
455M16—42no—
456C2×C8—22no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—41no—
460C2×C8—42no—
461C2×C8—221no—
462C2×C8—221no—
463C2×C8—221no—
464C2×C8—221no—
465C2×C8—881no—
466C2×C8—881no—
467C2×C8C2×C22⋊D1111yescharacteristic
468C2×C8C2×C22⋊D1111yescharacteristic
469C2×C8C2×C22⋊D1111yescharacteristic
470C2×C8C2×C22⋊D1111yescharacteristic
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—221no—
476C4⋊C4—221no—
477C4⋊C4—221no—
478C4⋊C4—221no—
479C4⋊C4—221no—
480C4⋊C4—221no—
481C4⋊C4—441no—
482C4⋊C4—441no—
483C4⋊C4C2×D4411yescharacteristic
484C4⋊C4C2×D4411yescharacteristic
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—21no—
489C22⋊C4—21no—
490C22⋊C4—441no—
491C22⋊C4—441no—
492C22⋊C4—441no—
493C42—21no—
494C42—441no—
495C42C2×D4411yescharacteristic
496C42#433911yescharacteristic
497C42C2×C22⋊D1111yescharacteristic
498C42C23×D1111yescharacteristic
499C11#1922911yescharacteristic, complemented, Sylow
500C23—21no—
501C23—441no—
502C23#6698311yescharacteristic
503Q8—21no—
504Q8—21no—
505Q8—441no—
506Q8—441no—
507Q8—441no—
508Q8—441no—
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—441no—
530C2×C4—441no—
531C2×C4—441no—
532C2×C4—882no—
533C2×C4#6698311yescharacteristic
534C2×C4#6698311yescharacteristic
535C2×C4#6698311yescharacteristic
536C2×C4C22×D4411yescharacteristic
537C2×C4C2×#433911yescharacteristic
538C2×C4C22×C22⋊D1111yescharacteristic
539C8—21no—
540C8—21no—
541C8—21no—
542C8—41no—
543C8—41no—
544C8—441no—
545C8—441no—
546C8—441no—
547C8—441no—
548C8#6700312yes—
549C22—21no—
550C22—21no—
551C22—41no—
552C22—41no—
553C22—41no—
554C22—881no—
555C22—881no—
556C22—881no—
557C22#1062275412yes—
558C22C2×#6698311yescharacteristic
559C4—21no—
560C4—21no—
561C4—21no—
562C4—21no—
563C4—41no—
564C4—41no—
565C4—41no—
566C4—881no—
567C4—881no—
568C4—881no—
569C4#1062328311yescharacteristic
570C4#1062328411yescharacteristic
571C4C2×#6700311yescharacteristic
572C4#1062335311yescharacteristic
573C2—22no—
574C2—81no—
575C2—1761no—
576C2#1307807111yescharacteristic
577C2#1307828611yescharacteristic
578C2C2×#1062275411yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2966C2
socleC22×C11C2×#121
prime radical#13079942C2
hypercenter#2966D11
hypocenterC11#19229
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2966

Complements

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

NH ≅ G/Ntype
1. #13079953C2semidirect
3. #13079175C2semidirect
4. #13068122C2semidirect
5. #13068115C2semidirect
6. #13068088C2semidirect
7. #13068081C2semidirect
8. #13068074C2semidirect
9. #13068067C2semidirect
10. #13068060C2semidirect
11. #13068053C2semidirect
12. C2×#10622096C2semidirect
13. #13067317C2semidirect
14. #13067312C2semidirect
15. C11×#2966C2semidirect
214. #2966D11semidirect
499. C11#19229semidirect

Maximal subgroups

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

subgroupindex
#130799532
#130799422
#130791752
#130681222
#130681152
#130680882
#130680812
#130680742
#130680672
#130680602
#130680532
C2×#106220962
#130673172
#130673122
C11×#29662
#1922911