Finite Group Databasebeta

← #14738749

Subgroups — #14738749

Order 2816.

588 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13080007C211yesmaximal, characteristic, complemented
2#13079627C211yesmaximal, characteristic
3#13077563C211yesmaximal, characteristic, complemented
4#13068181C211yesmaximal, characteristic, complemented
5#13068167C211yesmaximal, characteristic, complemented
6#13068131C211yesmaximal, characteristic, complemented
7#13068085C211yesmaximal, characteristic, complemented
8#13068057C211yesmaximal, characteristic, complemented
9#13068043C211yesmaximal, characteristic, complemented
10#13068007C211yesmaximal, characteristic, complemented
11#13067961C211yesmaximal, characteristic, complemented
12#13067383C211yesmaximal, characteristic, complemented
13#13067316C211yesmaximal, characteristic, complemented
14#13067293C211yesmaximal, characteristic
15C11×#3182C211yesmaximal, characteristic
16C11×#533C2211yescharacteristic
17C11×#532C2211yescharacteristic
18#10623001C2211yescharacteristic
19C11×#500C2211yescharacteristic
20C11×#492C2211yescharacteristic
21C11×#487C2211yescharacteristic
22C11×#486C2211yescharacteristic
23C11×#468—21no—
24C11×#468—21no—
25C11×#440—21no—
26C11×#440—21no—
27C4×C11×M16C2211yescharacteristic
28#10622852—21no—
29#10622852—21no—
30#10622735—21no—
31#10622732—21no—
32#10622707C2211yescharacteristic
33#10622707C2211yescharacteristic
34#10622703C2211yescharacteristic
35#10622703C2211yescharacteristic
36#10622703C2211yescharacteristic
37#10622703C2211yescharacteristic
38#10622688C2211yescharacteristic
39#10622688C2211yescharacteristic
40#10622673—21no—
41#10622668—21no—
42#10622665—21no—
43#10622665—21no—
44#10622644—21no—
45#10622633—21no—
46#10622539C2211yescharacteristic
47#10622537C2211yescharacteristic
48C2×C4⋊(C11⋊C8)C2211yescharacteristic
49#10622314—21no—
50#10622314—21no—
51#10622292C2211yescharacteristic
52#10622292C2211yescharacteristic
53C8×Dic22C2211yescharacteristic
54C8×Dic22C2211yescharacteristic
55#10622185C2211yescharacteristic
56#10622185C2211yescharacteristic
57#10622185C2211yescharacteristic
58#10622185C2211yescharacteristic
59#10622185C2211yescharacteristic
60#10622185C2211yescharacteristic
61#10622182C2211yescharacteristic
62#10622182C2211yescharacteristic
63#10622096C2211yescharacteristic
64#10622096C2211yescharacteristic
65#10622095C2211yescharacteristic
66#10622095C2211yescharacteristic
67C2×C11×#41—21no—
68C2×C11×SD16—21no—
69C2×C11×SD16—21no—
70C2×C11×M16D411yescharacteristic
71C2×C11×M16D411yescharacteristic
72C11×C4⋊Q8C2311yescharacteristic
73C11×C4⋊Q8C2311yescharacteristic
74C11×C4⋊Q8C2311yescharacteristic
75C11×#127C2311yescharacteristic
76C11×#125—21no—
77C11×#124—21no—
78C11×C22⋊Q8—21no—
79C11×C22⋊Q8—21no—
80C11×#121—21no—
81C11×#121—21no—
82C4×Q8×C11—21no—
83C4×Q8×C11—21no—
84C4×D4×C11—21no—
85C4×D4×C11—21no—
86C11×#117—21no—
87C2×C42×C11C2311yescharacteristic
88C2×#4326—21no—
89C2×#4326—21no—
90C2×#4326—21no—
91C2×#4326—21no—
92C2×#4324—21no—
93C2×#4324—21no—
94#66979—21no—
95#66977—21no—
96#66977D411yescharacteristic
97#66977D411yescharacteristic
98C2×#4318—21no—
99C22×C11⋊C8—21no—
100#66923—21no—
101#66922D411yescharacteristic
102#66922D411yescharacteristic
103C4×Dic22—21no—
104C4×Dic22C2311yescharacteristic
105C4×Dic22C2311yescharacteristic
106C11×#107—21no—
107C11×#107—21no—
108C11×#103—21no—
109C11×#103—21no—
110C11×#102—21no—
111C11×#102—21no—
112C11×#97D411yescharacteristic
113C11×#97D411yescharacteristic
114C4×C8×C11C2311yescharacteristic
115C4×C8×C11C2311yescharacteristic
116#66899—21no—
117#66899—21no—
118#66899—21no—
119#66899—21no—
120#66896—21no—
121#66896—21no—
122C22⋊(C11⋊C8)—21no—
123#66879—21no—
124#66879—21no—
125Dic11⋊C8—21no—
126Dic11⋊C8—21no—
127Dic11⋊C8—21no—
128Dic11⋊C8—21no—
129C8×Dic11—21no—
130C8×Dic11—21no—
131#66874—21no—
132#66874—21no—
133#66872—21no—
134#66872—21no—
135C4⋊(C11⋊C8)—21no—
136C4⋊(C11⋊C8)—21no—
137C4⋊(C11⋊C8)C2311yescharacteristic
138C4⋊(C11⋊C8)C2311yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4⋊(C11⋊C8)C2311yescharacteristic
143#66867—21no—
144#19372—111nomaximal, Sylow
145C11×#41—81no—
146C11×#41—81no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—41no—
154C22×C4×C11—41no—
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11#4111yescharacteristic
158C2×Dic22—21no—
159C2×Dic22C2×D411yescharacteristic
160C2×Dic22C2×D411yescharacteristic
161C11×SD16—42no—
162C11×SD16—42no—
163C11×M16—22no—
164C11×M16—41no—
165C2×C8×C11C2×D411yescharacteristic
166C2×C8×C11C2×D411yescharacteristic
167C2×C8×C11C2×D411yescharacteristic
168C2×C8×C11C2×D411yescharacteristic
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—41no—
176C11×C4⋊C4—41no—
177C11×C22⋊C4—41no—
178C11×C22⋊C4—41no—
179C11×C22⋊C4—41no—
180C42×C11—41no—
181C42×C11C2×D411yescharacteristic
182C42×C11C2×D411yescharacteristic
183C42×C11#4111yescharacteristic
184C42×C11C2411yescharacteristic
185C22⋊Dic11—21no—
186C22⋊Dic11—21no—
187#4326—81no—
188#4326—81no—
189#4326—81no—
190#4326—81no—
191#4324—81no—
192#4324—81no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11C2×D411yescharacteristic
197C4⋊Dic11C2×D411yescharacteristic
198Dic11⋊C4—21no—
199Dic11⋊C4—21no—
200Dic11⋊C4—21no—
201Dic11⋊C4—21no—
202C4×Dic11—21no—
203C4×Dic11—21no—
204#4318—81no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—42no—
212#3255—111no—
213#3216—111no—
214#3182D1111yescharacteristic
215#2962—111no—
216#1702—111no—
217#1700—111no—
218#1694—111no—
219#1686—111no—
220#1682—111no—
221#1680—111no—
222#1674—111no—
223#1666—111no—
224#1569—111no—
225#1552—111no—
226#1547—111no—
227C23×C11—41no—
228C23×C11#12111yescharacteristic
229Q8×C11—41no—
230Q8×C11—41no—
231Q8×C11—41no—
232Q8×C11—41no—
233Q8×C11—41no—
234Q8×C11—41no—
235D4×C11—41no—
236D4×C11—41no—
237D4×C11—41no—
238D4×C11—41no—
239D4×C11—81no—
240D4×C11—82no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—82no—
250C2×C4×C11#12111yescharacteristic
251C2×C4×C11#12111yescharacteristic
252C2×C4×C11#12111yescharacteristic
253C2×C4×C11C22×D411yescharacteristic
254C2×C4×C11C22×D411yescharacteristic
255C2×C4×C11C2×#4111yescharacteristic
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11—21no—
259C2×Dic11—21no—
260Dic22—21no—
261Dic22—21no—
262Dic22—21no—
263Dic22—21no—
264Dic22—81no—
265C8×C11—21no—
266C8×C11—21no—
267C8×C11—21no—
268C8×C11#13712yes—
269C11⋊C8—41no—
270C11⋊C8—41no—
271C11⋊C8—41no—
272C11⋊C8—41no—
273C11⋊C8—41no—
274C11⋊C8—41no—
275#533—111no—
276#533C2×D1111yescharacteristic
277#532C2×D1111yescharacteristic
278#500C2×D1111yescharacteristic
279#497—221no—
280#492C2×D1111yescharacteristic
281#489—221no—
282#487C2×D1111yescharacteristic
283#486C2×D1111yescharacteristic
284#475—111no—
285#475—111no—
286#475—221no—
287#470—221no—
288#470—221no—
289#468—21no—
290#468—21no—
291#462—111no—
292#462—111no—
293#462—111no—
294#462—111no—
295#462—221no—
296#460—111no—
297#460—111no—
298#452—221no—
299#452—221no—
300#446—111no—
301#446—111no—
302#446—221no—
303#446—221no—
304C8×Q8—111no—
305C8×Q8—111no—
306#440—21no—
307#440—21no—
308#432—111no—
309#424—221no—
310#423—111no—
311C2×C4⋊C8—111no—
312#405—221no—
313C4×M16C2×D1111yescharacteristic
314#335—111no—
315#335—111no—
316#334—111no—
317#334—111no—
318#332—111no—
319#332—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—21no—
329C22×C11—81no—
330C22×C11—81no—
331C22×C11—81no—
332C22×C11C2×#12111yescharacteristic
333C4×C11—21no—
334C4×C11—21no—
335C4×C11—21no—
336C4×C11—21no—
337C4×C11—81no—
338C4×C11—81no—
339C4×C11—81no—
340C4×C11C2×#13711yescharacteristic
341C4×C11#57511yescharacteristic
342C4×C11#57611yescharacteristic
343C4×C11#57711yescharacteristic
344Dic11—41no—
345Dic11—41no—
346Dic11—41no—
347Dic11—41no—
348C2×#41—21no—
349C2×Q16—221no—
350C2×Q16—221no—
351C2×Q16—221no—
352C2×Q16—221no—
353C2×SD16—21no—
354C2×SD16—21no—
355C2×SD16—221no—
356C2×SD16—221no—
357C2×M16—221no—
358C2×M16C22⋊D1111yescharacteristic
359C2×M16C22⋊D1111yescharacteristic
360C22×C8—221no—
361C4⋊Q8—111no—
362C4⋊Q8—111no—
363C4⋊Q8C22×D1111yescharacteristic
364C4⋊Q8C22×D1111yescharacteristic
365C4⋊Q8C22×D1111yescharacteristic
366#127C22×D1111yescharacteristic
367#125—21no—
368#125—221no—
369#124—21no—
370C22⋊Q8—21no—
371C22⋊Q8—21no—
372C22⋊Q8—111no—
373C22⋊Q8—111no—
374C22⋊Q8—221no—
375#121—21no—
376#121—21no—
377C4×Q8—21no—
378C4×Q8—21no—
379C4×Q8—111no—
380C4×Q8—111no—
381C4×Q8—221no—
382C4×D4—21no—
383C4×D4—21no—
384#117—21no—
385#117—221no—
386C2×C42C22×D1111yescharacteristic
387#107—21no—
388#107—21no—
389#106—221no—
390#106—221no—
391C4⋊C8—111no—
392C4⋊C8—111no—
393C4⋊C8—111no—
394C4⋊C8—111no—
395C4⋊C8—111no—
396C4⋊C8—111no—
397C4⋊C8—221no—
398C4⋊C8—221no—
399C4⋊C8—221no—
400C4⋊C8—221no—
401C4⋊C8—221no—
402C4⋊C8—221no—
403#103—21no—
404#103—21no—
405#103—221no—
406#103—221no—
407#103—221no—
408#103—221no—
409#103—221no—
410#103—221no—
411#102—21no—
412#102—21no—
413#102—221no—
414#102—221no—
415C22⋊C8—221no—
416#97—221no—
417#97—221no—
418#97—221no—
419#97C22⋊D1111yescharacteristic
420#97C22⋊D1111yescharacteristic
421C4×C8—221no—
422C4×C8—221no—
423C4×C8C22×D1111yescharacteristic
424C4×C8C22×D1111yescharacteristic
425C2×C11—41no—
426C2×C11—161no—
427C2×C11#303711yescharacteristic
428C2×C11#306211yescharacteristic
429C2×C11#306911yescharacteristic
430#41—81no—
431#41—81no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—111no—
436C2×Q8—111no—
437C2×Q8—221no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—41no—
442C22×C4—41no—
443C22×C4D4×D1111yescharacteristic
444C22×C4#434111yescharacteristic
445C22×C4C2×C22⋊D1111yescharacteristic
446Q16—881no—
447Q16—881no—
448Q16—881no—
449Q16—881no—
450SD16—42no—
451SD16—42no—
452SD16—881no—
453SD16—881no—
454M16—22no—
455M16—41no—
456M16—881no—
457C2×C8—221no—
458C2×C8—221no—
459C2×C8—221no—
460C2×C8—221no—
461C2×C8—221no—
462C2×C8—221no—
463C2×C8—442no—
464C2×C8C2×C22⋊D1111yescharacteristic
465C2×C8C2×C22⋊D1111yescharacteristic
466C2×C8C2×C22⋊D1111yescharacteristic
467C2×C8C2×C22⋊D1111yescharacteristic
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—41no—
475C4⋊C4—41no—
476C4⋊C4—111no—
477C4⋊C4—111no—
478C4⋊C4—221no—
479C4⋊C4—221no—
480C4⋊C4—221no—
481C4⋊C4—221no—
482C4⋊C4—221no—
483C4⋊C4—221no—
484C4⋊C4—221no—
485C22⋊C4—41no—
486C22⋊C4—41no—
487C22⋊C4—41no—
488C22⋊C4—221no—
489C22⋊C4—221no—
490C42—41no—
491C42—221no—
492C42—221no—
493C42D4×D1111yescharacteristic
494C42#434111yescharacteristic
495C42C2×C22⋊D1111yescharacteristic
496C42C23×D1111yescharacteristic
497C11#1937211yescharacteristic, complemented, Sylow
498C23—41no—
499C23#6699111yescharacteristic
500Q8—41no—
501Q8—41no—
502Q8—41no—
503Q8—41no—
504Q8—41no—
505Q8—41no—
506Q8—221no—
507Q8—221no—
508Q8—221no—
509Q8—221no—
510Q8—881no—
511D4—41no—
512D4—41no—
513D4—41no—
514D4—41no—
515D4—81no—
516D4—82no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—82no—
526C2×C4—221no—
527C2×C4—221no—
528C2×C4—221no—
529C2×C4—221no—
530C2×C4#6699111yescharacteristic
531C2×C4#6699111yescharacteristic
532C2×C4#6699111yescharacteristic
533C2×C4C2×D4×D1111yescharacteristic
534C2×C4C2×#434111yescharacteristic
535C2×C4C22×C22⋊D1111yescharacteristic
536C8—21no—
537C8—21no—
538C8—21no—
539C8—441no—
540C8—441no—
541C8—441no—
542C8—441no—
543C8—441no—
544C8—441no—
545C8#6700412yes—
546C22—21no—
547C22—21no—
548C22—21no—
549C22—81no—
550C22—81no—
551C22—81no—
552C22C2×#6699111yescharacteristic
553C4—21no—
554C4—21no—
555C4—21no—
556C4—21no—
557C4—81no—
558C4—81no—
559C4—81no—
560C4—441no—
561C4—441no—
562C4—441no—
563C4—441no—
564C4#1062330511yescharacteristic
565C4#1062330611yescharacteristic
566C4#1062335311yescharacteristic
567C4C2×#6700411yescharacteristic
568C2—41no—
569C2—161no—
570C2#1307808411yescharacteristic
571C2#1307829011yescharacteristic
572C2#1307834911yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3182C2
socleC22×C11C2×#121
prime radicalC11×#532C22
hypercenter#3182D11
hypocenterC11#19372
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3182

Complements

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

NH ≅ G/Ntype
1. #13080007C2semidirect
3. #13077563C2semidirect
4. #13068181C2semidirect
5. #13068167C2semidirect
6. #13068131C2semidirect
7. #13068085C2semidirect
8. #13068057C2semidirect
9. #13068043C2semidirect
10. #13068007C2semidirect
11. #13067961C2semidirect
12. #13067383C2semidirect
13. #13067316C2semidirect
497. C11#19372semidirect

Maximal subgroups

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

subgroupindex
#130800072
#130796272
#130775632
#130681812
#130681672
#130681312
#130680852
#130680572
#130680432
#130680072
#130679612
#130673832
#130673162
#130672932
C11×#31822
#1937211