Finite Group Databasebeta

← #14736498

Subgroups — #14736498

Order 2816.

620 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078681C211yesmaximal, characteristic, complemented
2#13078670C211yesmaximal, characteristic
3#13077582C211yesmaximal, characteristic, complemented
4#13068195C211yesmaximal, characteristic, complemented
5#13068188C211yesmaximal, characteristic, complemented
6#13068181C211yesmaximal, characteristic, complemented
7#13068174C211yesmaximal, characteristic, complemented
8#13068119C211yesmaximal, characteristic, complemented
9#13068112C211yesmaximal, characteristic, complemented
10#13068085C211yesmaximal, characteristic, complemented
11#13068078C211yesmaximal, characteristic, complemented
12#13067364C211yesmaximal, characteristic, complemented
13#13067281C211yesmaximal, characteristic, complemented
14#13067278C211yesmaximal, characteristic, complemented
15C11×#3167C211yesmaximal, characteristic, complemented
16C11×#533C2211yescharacteristic
17C11×#532C2211yescharacteristic
18C4×#4339C2211yescharacteristic
19C11×#498C2211yescharacteristic
20C11×#492C2211yescharacteristic
21C11×#487C2211yescharacteristic
22C11×#486C2211yescharacteristic
23C11×#465—21no—
24C11×#465—21no—
25C4×C11×SD16—21no—
26C4×C11×SD16—21no—
27C2×C4×C8×C11C2211yescharacteristic
28#10622724—21no—
29#10622724—21no—
30#10622707C2211yescharacteristic
31#10622704C2211yescharacteristic
32#10622703C2211yescharacteristic
33#10622700C2211yescharacteristic
34#10622697C2211yescharacteristic
35#10622696C2211yescharacteristic
36#10622688C2211yescharacteristic
37#10622685C2211yescharacteristic
38#10622660—21no—
39#10622658—21no—
40#10622650—21no—
41#10622648—21no—
42C4×#4326—21no—
43C4×#4325—21no—
44C4×#4324—21no—
45C4×#4323—21no—
46#10622538C2211yescharacteristic
47#10622538C2211yescharacteristic
48#10622538C2211yescharacteristic
49#10622301C2211yescharacteristic
50#10622301C2211yescharacteristic
51C4×#4313—21no—
52#10622298—21no—
53#10622292C2211yescharacteristic
54#10622292C2211yescharacteristic
55#10622185C2211yescharacteristic
56#10622185C2211yescharacteristic
57#10622185C2211yescharacteristic
58#10622185C2211yescharacteristic
59#10622184C2211yescharacteristic
60#10622184C2211yescharacteristic
61#10622182C2211yescharacteristic
62#10622182C2211yescharacteristic
63#10622096C2211yescharacteristic
64#10622096C2211yescharacteristic
65#10622095C2211yescharacteristic
66#10622095C2211yescharacteristic
67C2×C11×#41—21no—
68C2×#4339D411yescharacteristic
69C2×C11×SD16—21no—
70C2×C11×SD16—21no—
71C22×C8×C11D411yescharacteristic
72C22×C8×C11D411yescharacteristic
73C11×C4⋊Q8C2311yescharacteristic
74C11×C4⋊Q8C2311yescharacteristic
75C11×C4⋊Q8C2311yescharacteristic
76C11×#127C2311yescharacteristic
77C11×#125—21no—
78C11×#124—21no—
79C11×C22⋊Q8—21no—
80C11×C22⋊Q8—21no—
81C11×#121—21no—
82C11×#121—21no—
83C4×Q8×C11—21no—
84C4×Q8×C11—21no—
85C4×D4×C11—21no—
86C4×D4×C11—21no—
87C11×#117—21no—
88C2×C42×C11C2311yescharacteristic
89C2×#4326—21no—
90C2×#4325—21no—
91C2×#4324—21no—
92C2×#4323—21no—
93C4×C22⋊D11—21no—
94C4×C22⋊D11—21no—
95#66979D411yescharacteristic
96C2×#4313—21no—
97C2×#4313—21no—
98C4×D44D411yescharacteristic
99C4×D44C2311yescharacteristic
100#66925—21no—
101C42×D11—21no—
102C4×Dic22D411yescharacteristic
103C4×Dic22C2311yescharacteristic
104C11×#106—21no—
105C11×#106—21no—
106C11×#103—21no—
107C11×#103—21no—
108C11×#102—21no—
109C11×#102—21no—
110C4×C8×C11D411yescharacteristic
111C4×C8×C11D411yescharacteristic
112C4×C8×C11C2311yescharacteristic
113C4×C8×C11C2311yescharacteristic
114#66899—21no—
115#66899—21no—
116#66896—21no—
117#66896—21no—
118C22⋊(C11⋊C8)—21no—
119C22⋊(C11⋊C8)—21no—
120C22⋊(C11⋊C8)—21no—
121(C2×D11)⋊C8—21no—
122(C2×D11)⋊C8—21no—
123#66879—21no—
124#66879—21no—
125Dic11⋊C8—21no—
126Dic11⋊C8—21no—
127#66874—21no—
128#66874—21no—
129#66873—21no—
130#66873—21no—
131#66872—21no—
132#66872—21no—
133#66871—21no—
134#66871—21no—
135C4⋊(C11⋊C8)C2311yescharacteristic
136C4⋊(C11⋊C8)C2311yescharacteristic
137C4⋊(C11⋊C8)C2311yescharacteristic
138C4⋊(C11⋊C8)C2311yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4×C11⋊C8—21no—
142C4×C11⋊C8—21no—
143C4×C11⋊C8—21no—
144#19159—111nomaximal, Sylow
145C11×#41—82no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×D4×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—41no—
153C22×C4×C11—41no—
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11#4111yescharacteristic
157C2×C22⋊D11—21no—
158#4339—41no—
159#4339—41no—
160C2×D44C2×D411yescharacteristic
161C2×C4×D11—21no—
162C2×C4×D11—21no—
163C2×C4×D11—21no—
164C2×Dic22C2×D411yescharacteristic
165C11×SD16—42no—
166C11×SD16—42no—
167C2×C8×C11—22no—
168C2×C8×C11—41no—
169C2×C8×C11C2×D411yescharacteristic
170C2×C8×C11C2×D411yescharacteristic
171C2×C8×C11C2×D411yescharacteristic
172C2×C8×C11C2×D411yescharacteristic
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—41no—
180C11×C4⋊C4—41no—
181C11×C22⋊C4—41no—
182C11×C22⋊C4—41no—
183C11×C22⋊C4—41no—
184C42×C11—41no—
185C42×C11C2×D411yescharacteristic
186C42×C11C2×D411yescharacteristic
187C42×C11#4111yescharacteristic
188C42×C11C2411yescharacteristic
189C22⋊Dic11—21no—
190#4326—42no—
191#4325—42no—
192#4324—42no—
193#4323—42no—
194(C2×D11)⋊C4—21no—
195(C2×D11)⋊C4—21no—
196C4⋊Dic11C2×D411yescharacteristic
197C4⋊Dic11C2×D411yescharacteristic
198Dic11⋊C4—21no—
199Dic11⋊C4—21no—
200C4×Dic11—21no—
201C4×Dic11—21no—
202C4×Dic11—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209#4313—42no—
210#4313—42no—
211#3167D1111yescharacteristic, complemented
212#3107—111no—
213#3106—111no—
214#2965—111no—
215#1704—111no—
216#1703—111no—
217#1702—111no—
218#1701—111no—
219#1692—111no—
220#1691—111no—
221#1686—111no—
222#1685—111no—
223#1564—111no—
224#1544—111no—
225#1543—111no—
226C23×C11—41no—
227C23×C11#12111yescharacteristic
228C22×D11—21no—
229Q8×C11—41no—
230Q8×C11—41no—
231Q8×C11—41no—
232Q8×C11—41no—
233Q8×C11—81no—
234D4×C11—41no—
235D4×C11—41no—
236D4×C11—41no—
237D4×C11—41no—
238D4×C11—81no—
239D4×C11—82no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—22no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—82no—
249C2×C4×C11#12111yescharacteristic
250C2×C4×C11#12111yescharacteristic
251C2×C4×C11#12111yescharacteristic
252C2×C4×C11C22×D411yescharacteristic
253C2×C4×C11C22×D411yescharacteristic
254C2×C4×C11C2×#4111yescharacteristic
255C22⋊D11—42no—
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11—21no—
259D44—21no—
260D44—21no—
261C4×D11—42no—
262C4×D11—41no—
263C4×D11—41no—
264C4×D11—42no—
265Dic22—21no—
266Dic22—21no—
267C8×C11—21no—
268C8×C11—21no—
269C8×C11—21no—
270C8×C11#13512yes—
271C11⋊C8—41no—
272C11⋊C8—41no—
273C11⋊C8—41no—
274C11⋊C8—41no—
275C11⋊C8—41no—
276C11⋊C8—41no—
277#533C2×D1111yescharacteristic
278#532C2×D1111yescharacteristic
279C4×#41—111no—
280#498C2×D1111yescharacteristic
281#492C2×D1111yescharacteristic
282#487C2×D1111yescharacteristic
283#486C2×D1111yescharacteristic
284#485—221no—
285#482—221no—
286#477—111no—
287#476—111no—
288#475—111no—
289#474—111no—
290#465—21no—
291#465—21no—
292#462—111no—
293#461—111no—
294#460—111no—
295#459—111no—
296#452—221no—
297#449—221no—
298#446—111no—
299#446—111no—
300C4×Q16—221no—
301C4×SD16—21no—
302C4×SD16—21no—
303C4×SD16—221no—
304C4×SD16—221no—
305C4×D8—221no—
306#436—111no—
307#436—111no—
308#435—221no—
309#435—221no—
310#431—111no—
311#431—111no—
312#431—111no—
313#431—221no—
314C4×M16—221no—
315C2×C4×C8C2×D1111yescharacteristic
316#335—111no—
317#335—111no—
318#334—111no—
319#334—111no—
320#333—111no—
321#333—111no—
322#332—111no—
323#332—111no—
324#332—111no—
325#332—111no—
326#331—111no—
327#331—111no—
328C22×C11—21no—
329C22×C11—21no—
330C22×C11—21no—
331C22×C11—81no—
332C22×C11—81no—
333C22×C11—81no—
334C22×C11C2×#12111yescharacteristic
335C2×D11—41no—
336C2×D11—41no—
337C2×D11—41no—
338C4×C11—21no—
339C4×C11—21no—
340C4×C11—21no—
341C4×C11—81no—
342C4×C11—81no—
343C4×C11—81no—
344C4×C11#47112yes—
345C4×C11C2×#13511yescharacteristic
346C4×C11#57511yescharacteristic
347C4×C11#57511yescharacteristic
348C4×C11#57511yescharacteristic
349Dic11—41no—
350Dic11—41no—
351Dic11—41no—
352C2×#41—21no—
353C2×#41—111no—
354C2×Q16—221no—
355C2×SD16—21no—
356C2×SD16—21no—
357C2×SD16—221no—
358C2×SD16—221no—
359C2×D8—221no—
360C2×M16—221no—
361C2×M16—221no—
362C22×C8C22⋊D1111yescharacteristic
363C22×C8C22⋊D1111yescharacteristic
364C4⋊Q8C22×D1111yescharacteristic
365C4⋊Q8C22×D1111yescharacteristic
366C4⋊Q8C22×D1111yescharacteristic
367#127C22×D1111yescharacteristic
368#125—21no—
369#124—21no—
370C22⋊Q8—21no—
371C22⋊Q8—21no—
372#121—21no—
373#121—21no—
374C4×Q8—21no—
375C4×Q8—21no—
376C4×Q8—111no—
377C4×Q8—111no—
378C4×D4—21no—
379C4×D4—21no—
380C4×D4—111no—
381C4×D4—111no—
382C4×D4—221no—
383C4×D4—221no—
384#117—21no—
385#117—111no—
386#117—221no—
387C2×C42—221no—
388C2×C42C22×D1111yescharacteristic
389#107—221no—
390#107—221no—
391#106—21no—
392#106—21no—
393#106—221no—
394#106—221no—
395C4⋊C8—111no—
396C4⋊C8—111no—
397C4⋊C8—111no—
398C4⋊C8—111no—
399C4⋊C8—111no—
400C4⋊C8—111no—
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#102—21no—
410#102—21no—
411#102—221no—
412#102—221no—
413#102—221no—
414#102—221no—
415C22⋊C8—221no—
416C22⋊C8—221no—
417C22⋊C8—221no—
418C22⋊C8—221no—
419C22⋊C8—221no—
420#97—221no—
421#97—221no—
422C4×C8—221no—
423C4×C8—221no—
424C4×C8—221no—
425C4×C8C22⋊D1111yescharacteristic
426C4×C8C22⋊D1111yescharacteristic
427C4×C8C22×D1111yescharacteristic
428C4×C8C22×D1111yescharacteristic
429C2×C11—41no—
430C2×C11—161no—
431C2×C11#303511yescharacteristic
432C2×C11#305411yescharacteristic
433C2×C11C2×#47111yescharacteristic
434D11—81no—
435#41—82no—
436#41—441no—
437#41—441no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—111no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—41no—
446C2×D4—111no—
447C2×D4—221no—
448C22×C4—41no—
449C22×C4—221no—
450C22×C4—221no—
451C22×C4—221no—
452C22×C4D4×D1111yescharacteristic
453C22×C4#434111yescharacteristic
454C22×C4C2×C22⋊D1111yescharacteristic
455Q16—442no—
456SD16—42no—
457SD16—42no—
458SD16—442no—
459SD16—442no—
460D8—442no—
461M16—442no—
462M16—442no—
463C2×C8—22no—
464C2×C8—41no—
465C2×C8—221no—
466C2×C8—221no—
467C2×C8—221no—
468C2×C8—221no—
469C2×C8—221no—
470C2×C8—221no—
471C2×C8C2×C22⋊D1111yescharacteristic
472C2×C8C2×C22⋊D1111yescharacteristic
473C2×C8C2×C22⋊D1111yescharacteristic
474C2×C8C2×C22⋊D1111yescharacteristic
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—41no—
482C4⋊C4—41no—
483C4⋊C4—111no—
484C4⋊C4—111no—
485C4⋊C4—221no—
486C4⋊C4—221no—
487C22⋊C4—41no—
488C22⋊C4—41no—
489C22⋊C4—41no—
490C22⋊C4—221no—
491C22⋊C4—221no—
492C22⋊C4—221no—
493C42—41no—
494C42—221no—
495C42—221no—
496C42—221no—
497C42D4×D1111yescharacteristic
498C42#434111yescharacteristic
499C42C2×C22⋊D1111yescharacteristic
500C42C23×D1111yescharacteristic
501C11#1915911yescharacteristic, complemented, Sylow
502C23—41no—
503C23—221no—
504C23#6699111yescharacteristic
505Q8—41no—
506Q8—41no—
507Q8—41no—
508Q8—41no—
509Q8—81no—
510Q8—221no—
511Q8—221no—
512D4—41no—
513D4—41no—
514D4—41no—
515D4—41no—
516D4—81no—
517D4—82no—
518D4—221no—
519D4—221no—
520D4—442no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—22no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—82no—
530C2×C4—221no—
531C2×C4—221no—
532C2×C4—221no—
533C2×C4—442no—
534C2×C4—442no—
535C2×C4—441no—
536C2×C4—441no—
537C2×C4#6699111yescharacteristic
538C2×C4#6699111yescharacteristic
539C2×C4#6699111yescharacteristic
540C2×C4C2×D4×D1111yescharacteristic
541C2×C4C2×#434111yescharacteristic
542C2×C4C22×C22⋊D1111yescharacteristic
543C8—21no—
544C8—21no—
545C8—21no—
546C8—441no—
547C8—441no—
548C8—441no—
549C8—441no—
550C8—441no—
551C8—441no—
552C8#6700312yes—
553C22—21no—
554C22—21no—
555C22—21no—
556C22—81no—
557C22—81no—
558C22—81no—
559C22—441no—
560C22—441no—
561C22—441no—
562C22C2×#6699111yescharacteristic
563C4—21no—
564C4—21no—
565C4—21no—
566C4—81no—
567C4—81no—
568C4—81no—
569C4—441no—
570C4—441no—
571C4—441no—
572C4#1062279012yes—
573C4#1062329911yescharacteristic
574C4#1062329911yescharacteristic
575C4C2×#6700311yescharacteristic
576C4#1062335311yescharacteristic
577C2—41no—
578C2—161no—
579C2—881no—
580C2#1307806511yescharacteristic
581C2#1307822111yescharacteristic
582C2C2×#1062279011yescharacteristic
subgroupG/H
centerC2×C4#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3167C2
socleC22×C11C2×#121
prime radical#13078670C2
hypercenter#3167D11
hypocenterC11#19159
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3167

Complements

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

NH ≅ G/Ntype
1. #13078681C2semidirect
3. #13077582C2semidirect
4. #13068195C2semidirect
5. #13068188C2semidirect
6. #13068181C2semidirect
7. #13068174C2semidirect
8. #13068119C2semidirect
9. #13068112C2semidirect
10. #13068085C2semidirect
11. #13068078C2semidirect
12. #13067364C2semidirect
13. #13067281C2semidirect
14. #13067278C2semidirect
15. C11×#3167C2semidirect
211. #3167D11semidirect
501. C11#19159semidirect

Maximal subgroups

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

subgroupindex
#130786812
#130786702
#130775822
#130681952
#130681882
#130681812
#130681742
#130681192
#130681122
#130680852
#130680782
#130673642
#130672812
#130672782
C11×#31672
#1915911