Finite Group Databasebeta

← #14736807

Subgroups — #14736807

Order 2816.

668 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079354C211yesmaximal, characteristic, complemented
2#13078676C211yesmaximal, characteristic, complemented
3#13078071C211yesmaximal, characteristic, complemented
4#13068177C211yesmaximal, characteristic, complemented
5#13068149C211yesmaximal, characteristic, complemented
6#13068115C211yesmaximal, characteristic, complemented
7#13068095C211yesmaximal, characteristic, complemented
8#13068060C211yesmaximal, characteristic, complemented
9#13068032C211yesmaximal, characteristic, complemented
10#13067998C211yesmaximal, characteristic, complemented
11#13067976C211yesmaximal, characteristic, complemented
12#13067368C211yesmaximal, characteristic, complemented
13#13067322C211yesmaximal, characteristic, complemented
14#13067312C211yesmaximal, characteristic, complemented
15C11×#2971C211yesmaximal, characteristic, complemented
16C4×C11×#41C2211yescharacteristic
17C2×#67003—21no—
18#10623008C2211yescharacteristic
19#10623008C2211yescharacteristic
20C8×Q8×C11C2211yescharacteristic
21C8×Q8×C11C2211yescharacteristic
22C11×#436—21no—
23C11×#436—21no—
24C11×#436C2211yescharacteristic
25C11×#436C2211yescharacteristic
26C11×#432—21no—
27C11×#432C2211yescharacteristic
28C4×C11×M16—21no—
29C4×C11×M16C2211yescharacteristic
30#10622851—21no—
31#10622748—21no—
32#10622748—21no—
33#10622644C2211yescharacteristic
34#10622641—21no—
35#10622640C2211yescharacteristic
36#10622640C2211yescharacteristic
37C4×#4325—21no—
38#10622634C2211yescharacteristic
39#10622632C2211yescharacteristic
40#10622629—21no—
41#10622628C2211yescharacteristic
42#10622628C2211yescharacteristic
43C4×#4323—21no—
44#10622621C2211yescharacteristic
45#10622616—21no—
46#10622615—21no—
47#10622538C2211yescharacteristic
48C2×C4⋊(C11⋊C8)C2211yescharacteristic
49#10622324—21no—
50#10622324—21no—
51#10622308C2211yescharacteristic
52#10622307C2211yescharacteristic
53#10622307C2211yescharacteristic
54#10622293C2211yescharacteristic
55#10622124C2211yescharacteristic
56#10622124C2211yescharacteristic
57#10622123C2211yescharacteristic
58#10622123C2211yescharacteristic
59#10622123C2211yescharacteristic
60#10622123C2211yescharacteristic
61#10622119C2211yescharacteristic
62#10622119C2211yescharacteristic
63#10622096C2211yescharacteristic
64#10622096C2211yescharacteristic
65#10622095C2211yescharacteristic
66#10622095C2211yescharacteristic
67C2×C11×#41D411yescharacteristic
68C2×#4339—21no—
69C2×#4339—21no—
70C2×C11×M16—21no—
71C2×C11×M16—21no—
72C2×C11×M16D411yescharacteristic
73C2×C11×M16D411yescharacteristic
74C4×Q8×C11D411yescharacteristic
75C4×Q8×C11C2311yescharacteristic
76C4×D4×C11—21no—
77C4×D4×C11—21no—
78C4×D4×C11D411yescharacteristic
79C4×D4×C11C2311yescharacteristic
80C11×#117—21no—
81C11×#117D411yescharacteristic
82C2×C42×C11—21no—
83C2×C42×C11C2311yescharacteristic
84#67003—44no—
85C2×#4326—21no—
86C2×#4325—21no—
87C2×#4325—21no—
88C2×#4324—21no—
89C2×#4323—21no—
90C2×#4323—21no—
91#66983—21no—
92#66983—21no—
93#66983—21no—
94#66983—21no—
95C22×C11⋊C8—21no—
96C2×D88—21no—
97C2×D88—21no—
98#66928—21no—
99#66928—21no—
100#66927C2311yescharacteristic
101#66927C2311yescharacteristic
102C4×D44—21no—
103C4×D44—21no—
104C4×D44—21no—
105C4×D44—21no—
106#66922C2311yescharacteristic
107#66922C2311yescharacteristic
108C11×C4⋊C8—21no—
109C11×C4⋊C8—21no—
110C11×C4⋊C8C2311yescharacteristic
111C11×C4⋊C8C2311yescharacteristic
112C11×C22⋊C8—21no—
113C11×C22⋊C8—21no—
114C11×C22⋊C8—21no—
115C11×#97—21no—
116C11×#97D411yescharacteristic
117C11×#97D411yescharacteristic
118C4×C8×C11—21no—
119C4×C8×C11—21no—
120C4×C8×C11C2311yescharacteristic
121C4×C8×C11C2311yescharacteristic
122#66899—21no—
123#66896—21no—
124C22⋊(C11⋊C8)—21no—
125#66885—21no—
126#66885—21no—
127#66885—21no—
128#66885—21no—
129#66881—21no—
130#66881—21no—
131#66874—21no—
132#66874—21no—
133#66873—21no—
134#66873—21no—
135#66873—21no—
136#66873—21no—
137#66872—21no—
138#66871—21no—
139C4⋊(C11⋊C8)—21no—
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4⋊(C11⋊C8)C2311yescharacteristic
143C4⋊(C11⋊C8)C2311yescharacteristic
144C4×C11⋊C8—21no—
145#19184—111nomaximal, Sylow
146C11×#41—22no—
147C11×#41—41no—
148C2×Q8×C11C2×D411yescharacteristic
149C2×D4×C11—21no—
150C2×D4×C11C2×D411yescharacteristic
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11#4111yescharacteristic
157C2×C22⋊D11—41no—
158C2×C22⋊D11—41no—
159#4339—42no—
160#4339—42no—
161#4339—82no—
162C2×D44—21no—
163C2×D44—21no—
164C2×D44—21no—
165C2×D44—21no—
166C2×D44—21no—
167C2×D44—21no—
168C2×C4×D11—41no—
169C2×C4×D11—41no—
170C2×Dic22—21no—
171C2×Dic22—21no—
172C11×M16—22no—
173C11×M16—41no—
174C11×M16—42no—
175C11×M16—42no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11C2×D411yescharacteristic
179C2×C8×C11C2×D411yescharacteristic
180C2×C8×C11C2×D411yescharacteristic
181C2×C8×C11C2×D411yescharacteristic
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4C2×D411yescharacteristic
185C11×C4⋊C4C2×D411yescharacteristic
186C11×C22⋊C4—21no—
187C11×C22⋊C4—21no—
188C11×C22⋊C4—21no—
189C42×C11—21no—
190C42×C11—21no—
191C42×C11—21no—
192C42×C11C2×D411yescharacteristic
193C42×C11C2×D411yescharacteristic
194C42×C11#4111yescharacteristic
195C42×C11C2411yescharacteristic
196#4326—42no—
197#4325—42no—
198#4325—42no—
199#4324—42no—
200#4323—42no—
201#4323—42no—
202(C2×D11)⋊C4—41no—
203(C2×D11)⋊C4—41no—
204(C2×D11)⋊C4—41no—
205(C2×D11)⋊C4—41no—
206C4⋊Dic11—21no—
207C4⋊Dic11—21no—
208C4⋊Dic11—21no—
209C4⋊Dic11—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—42no—
215D88—42no—
216D88—42no—
217#3184—111no—
218#3106—111no—
219#3035—111no—
220#2971D1111yescharacteristic, complemented
221#1701—111no—
222#1697—111no—
223#1691—111no—
224#1687—111no—
225#1682—111no—
226#1678—111no—
227#1672—111no—
228#1668—111no—
229#1565—111no—
230#1553—111no—
231#1551—111no—
232C23×C11—21no—
233C23×C11#12111yescharacteristic
234C22×D11—41no—
235C22×D11—41no—
236Q8×C11—21no—
237Q8×C11AGL(1,ℤ/8)12yes—
238D4×C11—21no—
239D4×C11—21no—
240D4×C11—42no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—41no—
249C2×C4×C11—42no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—81no—
253C2×C4×C11#12111yescharacteristic
254C2×C4×C11#12111yescharacteristic
255C2×C4×C11#12111yescharacteristic
256C2×C4×C11C22×D411yescharacteristic
257C2×C4×C11C22×D411yescharacteristic
258C2×C4×C11C2×#4111yescharacteristic
259C22⋊D11—82no—
260C22⋊D11—82no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263D44—41no—
264D44—41no—
265D44—41no—
266D44—41no—
267D44—41no—
268D44—41no—
269D44—41no—
270D44—41no—
271D44—81no—
272D44—81no—
273C4×D11—82no—
274C4×D11—82no—
275Dic22—41no—
276Dic22—41no—
277Dic22—81no—
278C8×C11—21no—
279C8×C11—21no—
280C8×C11—21no—
281C8×C11—41no—
282C8×C11—41no—
283C8×C11#13512yescomplemented
284C11⋊C8—41no—
285C11⋊C8—41no—
286C11⋊C8—41no—
287C11⋊C8—41no—
288C2×#135—221no—
289#532—111no—
290#532—111no—
291C4×#41C2×D1111yescharacteristic
292#498—111no—
293#493—111no—
294#486—111no—
295#486—111no—
296#482—221no—
297#477—111no—
298#476—111no—
299#469—221no—
300#469—221no—
301#464—221no—
302#463—221no—
303#462—111no—
304#461—111no—
305#460—111no—
306#460—111no—
307#459—111no—
308#459—111no—
309#449—221no—
310C8×Q8C2×D1111yescharacteristic
311C8×Q8C2×D1111yescharacteristic
312#442—221no—
313#442—221no—
314C4×SD16—221no—
315C4×D8—221no—
316#436—21no—
317#436—21no—
318#436C2×D1111yescharacteristic
319#436C2×D1111yescharacteristic
320#432—21no—
321#432C2×D1111yescharacteristic
322#431—111no—
323C2×C4⋊C8—111no—
324#416—221no—
325C4×M16—21no—
326C4×M16C2×D1111yescharacteristic
327#335—111no—
328#335—111no—
329#334—111no—
330#334—111no—
331#333—111no—
332#333—111no—
333#332—111no—
334#332—111no—
335#331—111no—
336#331—111no—
337#331—111no—
338#331—111no—
339C22×C11—21no—
340C22×C11—21no—
341C22×C11—21no—
342C22×C11—41no—
343C22×C11—41no—
344C22×C11—41no—
345C22×C11C2×#12111yescharacteristic
346C2×D11—81no—
347C2×D11—81no—
348C2×D11—81no—
349C2×D11—81no—
350C2×D11—81no—
351C2×D11—81no—
352C4×C11—21no—
353C4×C11—21no—
354C4×C11—22no—
355C4×C11—21no—
356C4×C11—21no—
357C4×C11—41no—
358C4×C11—41no—
359C4×C11C2×#13511yescharacteristic
360C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
361C4×C11#57511yescharacteristic
362C4×C11#57511yescharacteristic
363Dic11—81no—
364Dic11—81no—
365C2×#41—221no—
366C2×#41—221no—
367C2×#41D4411yescharacteristic
368#135—444no—
369C2×Q16—221no—
370C2×SD16—221no—
371C2×SD16—221no—
372C2×SD16—221no—
373C2×D8—221no—
374C2×D8—221no—
375C2×D8—221no—
376C2×D8—221no—
377C2×M16—21no—
378C2×M16—21no—
379C2×M16C22⋊D1111yescharacteristic
380C2×M16C22⋊D1111yescharacteristic
381C22×C8—221no—
382C4⋊Q8—111no—
383C4⋊Q8—111no—
384#127—111no—
385#127—111no—
386#124—221no—
387#124—221no—
388#121—221no—
389#121—221no—
390#121—221no—
391#121—221no—
392C4×Q8D4411yescharacteristic
393C4×Q8C22×D1111yescharacteristic
394C4×D4—21no—
395C4×D4—21no—
396C4×D4—221no—
397C4×D4—221no—
398C4×D4—221no—
399C4×D4—221no—
400C4×D4D4411yescharacteristic
401C4×D4C22×D1111yescharacteristic
402#117—21no—
403#117D4411yescharacteristic
404C2×C42—21no—
405C2×C42C22×D1111yescharacteristic
406#107—221no—
407#106—221no—
408#106—221no—
409#106—221no—
410C4⋊C8—21no—
411C4⋊C8—21no—
412C4⋊C8—111no—
413C4⋊C8—111no—
414C4⋊C8—111no—
415C4⋊C8—111no—
416C4⋊C8—221no—
417C4⋊C8C22×D1111yescharacteristic
418C4⋊C8C22×D1111yescharacteristic
419#103—221no—
420#103—221no—
421#103—221no—
422#102—221no—
423#102—221no—
424#102—221no—
425#102—221no—
426#102—221no—
427#102—221no—
428#102—221no—
429#102—221no—
430#102—221no—
431C22⋊C8—21no—
432C22⋊C8—21no—
433C22⋊C8—21no—
434C22⋊C8—221no—
435#97—21no—
436#97C22⋊D1111yescharacteristic
437#97C22⋊D1111yescharacteristic
438C4×C8—21no—
439C4×C8—21no—
440C4×C8—221no—
441C4×C8C22×D1111yescharacteristic
442C4×C8C22×D1111yescharacteristic
443C2×C11—41no—
444C2×C11—81no—
445C2×C11#303511yescharacteristic
446C2×C11#305511yescharacteristic
447C2×C11#306811yescharacteristic
448D11—161no—
449D11—161no—
450#41—22no—
451#41—41no—
452#41—442no—
453#41—442no—
454#41—882no—
455C2×Q8—221no—
456C2×Q8—221no—
457C2×Q8C2×D4411yescharacteristic
458C2×D4—21no—
459C2×D4—221no—
460C2×D4—221no—
461C2×D4—221no—
462C2×D4—221no—
463C2×D4—221no—
464C2×D4—221no—
465C2×D4—441no—
466C2×D4—441no—
467C2×D4C2×D4411yescharacteristic
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—441no—
472C22×C4—441no—
473C22×C4C2×D4411yescharacteristic
474C22×C4#433911yescharacteristic
475C22×C4C2×C22⋊D1111yescharacteristic
476Q16—442no—
477SD16—442no—
478SD16—442no—
479SD16—442no—
480D8—442no—
481D8—442no—
482D8—442no—
483D8—442no—
484M16—22no—
485M16—41no—
486M16—42no—
487M16—42no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—221no—
491C2×C8—221no—
492C2×C8—221no—
493C2×C8—221no—
494C2×C8—442no—
495C2×C8C2×C22⋊D1111yescharacteristic
496C2×C8C2×C22⋊D1111yescharacteristic
497C2×C8C2×C22⋊D1111yescharacteristic
498C2×C8C2×C22⋊D1111yescharacteristic
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—221no—
502C4⋊C4—221no—
503C4⋊C4—221no—
504C4⋊C4—221no—
505C4⋊C4C2×D4411yescharacteristic
506C4⋊C4C2×D4411yescharacteristic
507C22⋊C4—21no—
508C22⋊C4—21no—
509C22⋊C4—21no—
510C22⋊C4—441no—
511C22⋊C4—441no—
512C22⋊C4—441no—
513C22⋊C4—441no—
514C42—21no—
515C42—21no—
516C42—21no—
517C42C2×D4411yescharacteristic
518C42#433911yescharacteristic
519C42C2×C22⋊D1111yescharacteristic
520C42C23×D1111yescharacteristic
521C11#1918411yescharacteristic, complemented, Sylow
522C23—21no—
523C23—441no—
524C23—441no—
525C23#6698311yescharacteristic
526Q8—21no—
527Q8—441no—
528Q8—441no—
529Q8—881no—
530Q8#6696112yes—
531D4—21no—
532D4—21no—
533D4—42no—
534D4—441no—
535D4—441no—
536D4—441no—
537D4—441no—
538D4—441no—
539D4—441no—
540D4—441no—
541D4—441no—
542D4—881no—
543D4—881no—
544D4—882no—
545D4—882no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—41no—
554C2×C4—42no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—81no—
558C2×C4—441no—
559C2×C4—441no—
560C2×C4—882no—
561C2×C4—882no—
562C2×C4#6698311yescharacteristic
563C2×C4#6698311yescharacteristic
564C2×C4#6698311yescharacteristic
565C2×C4C22×D4411yescharacteristic
566C2×C4C2×#433911yescharacteristic
567C2×C4C22×C22⋊D1111yescharacteristic
568C8—21no—
569C8—21no—
570C8—21no—
571C8—41no—
572C8—41no—
573C8—441no—
574C8—441no—
575C8—441no—
576C8—441no—
577C8#6700312yescomplemented
578C22—21no—
579C22—21no—
580C22—21no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—881no—
585C22—881no—
586C22—881no—
587C22—881no—
588C22—881no—
589C22—881no—
590C22C2×#6698311yescharacteristic
591C4—21no—
592C4—21no—
593C4—21no—
594C4—21no—
595C4—22no—
596C4—41no—
597C4—41no—
598C4—881no—
599C4—881no—
600C4C2×#6696111yescharacteristic
601C4#1062327911yescharacteristic
602C4C2×#6700311yescharacteristic
603C4#1062335311yescharacteristic
604C2—41no—
605C2—81no—
606C2—1761no—
607C2—1761no—
608C2#1307807111yescharacteristic
609C2#1307823511yescharacteristic
610C2#1307834411yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2971C2
socleC22×C11C2×#121
hypercenter#2971D11
hypocenterC11#19184
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2971

Complements

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

NH ≅ G/Ntype
1. #13079354C2semidirect
2. #13078676C2semidirect
3. #13078071C2semidirect
4. #13068177C2semidirect
5. #13068149C2semidirect
6. #13068115C2semidirect
7. #13068095C2semidirect
8. #13068060C2semidirect
9. #13068032C2semidirect
10. #13067998C2semidirect
11. #13067976C2semidirect
12. #13067368C2semidirect
13. #13067322C2semidirect
14. #13067312C2semidirect
15. C11×#2971C2semidirect
220. #2971D11semidirect
283. C8×C11#135semidirect
521. C11#19184semidirect
577. C8#67003semidirect

Maximal subgroups

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

subgroupindex
#130793542
#130786762
#130780712
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C11×#29712
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