Finite Group Databasebeta

← #14742953

Subgroups — #14742953

Order 2816.

704 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079752C211yesmaximal, characteristic, complemented
2#13079737C211yesmaximal, characteristic, complemented
3#13079568C211yesmaximal, characteristic, complemented
4#13079551C211yesmaximal, characteristic
5#13079541C211yesmaximal, characteristic, complemented
6#13068292C211yesmaximal, characteristic, complemented
7#13068286C211yesmaximal, characteristic, complemented
8#13068271C211yesmaximal, characteristic, complemented
9#13068270C211yesmaximal, characteristic, complemented
10#13068258C211yesmaximal, characteristic, complemented
11#13068239C211yesmaximal, characteristic, complemented
12#13068224C211yesmaximal, characteristic, complemented
13#13068209C211yesmaximal, characteristic, complemented
14#13066916C211yesmaximal, characteristic, complemented
15C11×#3230C211yesmaximal, characteristic, complemented
16C11×#533C2211yescharacteristic
17C2×C11×C4⋊Q8C2211yescharacteristic
18#10623008C2211yescharacteristic
19#10623008C2211yescharacteristic
20C11×#500C2211yescharacteristic
21C11×#500C2211yescharacteristic
22C11×#487C2211yescharacteristic
23C11×#487C2211yescharacteristic
24C11×#484—22no—
25C11×#477—22no—
26C11×#431C2211yescharacteristic
27#10622840—22no—
28#10622706C2211yescharacteristic
29#10622705C2211yescharacteristic
30#10622701C2211yescharacteristic
31#10622701C2211yescharacteristic
32#10622701C2211yescharacteristic
33#10622701C2211yescharacteristic
34#10622701C2211yescharacteristic
35#10622700—22no—
36#10622698C2211yescharacteristic
37#10622698C2211yescharacteristic
38#10622698C2211yescharacteristic
39#10622696—22no—
40#10622694C2211yescharacteristic
41#10622694C2211yescharacteristic
42#10622692C2211yescharacteristic
43#10622691C2211yescharacteristic
44#10622691C2211yescharacteristic
45#10622691C2211yescharacteristic
46#10622679—22no—
47#10622660—22no—
48#10622641—22no—
49#10622616—22no—
50#10622580—22no—
51#10622538C2211yescharacteristic
52#10622538C2211yescharacteristic
53#10622457—22no—
54#10622347—22no—
55#10622308C2211yescharacteristic
56#10622307C2211yescharacteristic
57#10622306C2211yescharacteristic
58#10622294C2211yescharacteristic
59#10622093C2211yescharacteristic
60#10622092C2211yescharacteristic
61#10622092C2211yescharacteristic
62C8×C11⋊C8C2211yescharacteristic
63C22×Q8×C11—21no—
64C2×#4339—21no—
65C2×#4339—21no—
66C11×C4⋊Q8—21no—
67C11×C4⋊Q8—21no—
68C11×C4⋊Q8—21no—
69C11×C4⋊Q8C2311yescharacteristic
70C11×C4⋊Q8C2311yescharacteristic
71C11×C4⋊Q8C2311yescharacteristic
72C11×C4⋊Q8C2311yescharacteristic
73C11×#125—21no—
74C11×C22⋊Q8—21no—
75C11×C22⋊Q8—21no—
76C4×Q8×C11—21no—
77C4×Q8×C11—21no—
78C11×#117—21no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—21no—
81C2×C42×C11C2311yescharacteristic
82C2×#4326—22no—
83C2×#4325—22no—
84C2×#4325—22no—
85C2×#4325—22no—
86#66983—21no—
87#66983—21no—
88#66983—21no—
89#66983—21no—
90C2×D88—22no—
91C2×#4314—22no—
92#66928—21no—
93#66928—21no—
94#66927C2311yescharacteristic
95#66927C2311yescharacteristic
96C4×D44—21no—
97C4×D44—21no—
98C4×D44—21no—
99C4×D44—21no—
100#66922C2311yescharacteristic
101#66922C2311yescharacteristic
102C11×#107—22no—
103C11×#107—22no—
104C11×C4⋊C8D412yes—
105C11×#103—22no—
106C11×#103—22no—
107C11×C22⋊C8D412yes—
108C4×C8×C11C2311yescharacteristic
109C4×C8×C11C2311yescharacteristic
110#66899—22no—
111#66899—22no—
112C22⋊(C11⋊C8)D412yes—
113C22⋊(C11⋊C8)D412yes—
114#66885—22no—
115#66880—22no—
116#66874—22no—
117#66873—22no—
118#66873—22no—
119#66873—22no—
120#66873—22no—
121#66873—22no—
122#66872—22no—
123#66871—22no—
124#66871—22no—
125#66871—22no—
126C4⋊(C11⋊C8)D412yes—
127C4⋊(C11⋊C8)D412yes—
128C4×C11⋊C8C2311yescharacteristic
129C4×C11⋊C8C2311yescharacteristic
130C4×C11⋊C8C2311yescharacteristic
131C4×C11⋊C8C2311yescharacteristic
132#19740—111nomaximal, Sylow
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—41no—
138C2×Q8×C11—82no—
139C22×C4×C11—41no—
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C2×C22⋊D11—41no—
144C2×C22⋊D11—41no—
145#4339—82no—
146#4339—82no—
147C2×D44—21no—
148C2×D44—21no—
149C2×D44—21no—
150C2×D44—21no—
151C2×D44—21no—
152C2×D44—21no—
153C2×C4×D11—41no—
154C2×C4×D11—41no—
155C2×Dic22—21no—
156C2×Dic22—21no—
157C2×C8×C11C2×D412yes—
158C2×C8×C11C2×D412yes—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—41no—
168C11×C4⋊C4—41no—
169C11×C4⋊C4—41no—
170C11×C4⋊C4—41no—
171C11×C22⋊C4—41no—
172C42×C11—41no—
173C42×C11C2×D411yescharacteristic
174C42×C11C2×D411yescharacteristic
175C42×C11C2×D411yescharacteristic
176C42×C11C2411yescharacteristic
177#4326—82no—
178#4325—82no—
179#4325—82no—
180#4325—82no—
181(C2×D11)⋊C4—41no—
182(C2×D11)⋊C4—41no—
183(C2×D11)⋊C4—41no—
184(C2×D11)⋊C4—41no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C2×C11⋊C8C2×D412yes—
190C2×C11⋊C8C2×D412yes—
191C2×C11⋊C8C2×D412yes—
192C2×C11⋊C8C2×D412yes—
193D88—82no—
194#4314—82no—
195#3230D1111yescharacteristic, complemented
196#3228—111no—
197#3226—111no—
198#3210—111no—
199#3207—111no—
200#3206—111no—
201#1723—111no—
202#1722—111no—
203#1719—111no—
204#1719—111no—
205#1717—111no—
206#1714—111no—
207#1710—111no—
208#1706—111no—
209#1454—111no—
210C23×C11#12711yescharacteristic
211C22×D11—41no—
212C22×D11—41no—
213Q8×C11—42no—
214Q8×C11—42no—
215Q8×C11—42no—
216Q8×C11—42no—
217Q8×C11—82no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—41no—
222C2×C4×C11—41no—
223C2×C4×C11—41no—
224C2×C4×C11—41no—
225C2×C4×C11—82no—
226C2×C4×C11#12711yescharacteristic
227C2×C4×C11#12711yescharacteristic
228C2×C4×C11#12711yescharacteristic
229C2×C4×C11C22×D411yescharacteristic
230C2×C4×C11C22×D411yescharacteristic
231C2×C4×C11C22×D411yescharacteristic
232C22⋊D11—82no—
233C22⋊D11—82no—
234C2×Dic11—41no—
235C2×Dic11—41no—
236D44—42no—
237D44—42no—
238D44—42no—
239D44—42no—
240D44—42no—
241D44—42no—
242C4×D11—82no—
243C4×D11—82no—
244Dic22—42no—
245Dic22—42no—
246C8×C11—22no—
247C8×C11—22no—
248C11⋊C8—22no—
249C11⋊C8—22no—
250C11⋊C8—22no—
251C11⋊C8—22no—
252#533C2×D1111yescharacteristic
253#532—111no—
254#532—111no—
255C2×C4⋊Q8C2×D1111yescharacteristic
256#500—111no—
257#500—111no—
258#500—111no—
259#500C2×D1111yescharacteristic
260#500C2×D1111yescharacteristic
261#498—111no—
262#494—111no—
263#493—111no—
264#492—111no—
265#492—111no—
266#492—111no—
267#492—111no—
268#487—111no—
269#487—111no—
270#487—111no—
271#487—111no—
272#487C2×D1111yescharacteristic
273#487C2×D1111yescharacteristic
274#486—111no—
275#486—111no—
276#486—111no—
277#486—111no—
278#486—111no—
279#486—111no—
280#484—22no—
281#482—222no—
282#480—222no—
283#478—222no—
284#477—22no—
285#474—222no—
286#464—222no—
287#463—222no—
288#461—222no—
289#452—222no—
290#449—222no—
291#448—222no—
292#431—111no—
293#431—111no—
294#431C2×D1111yescharacteristic
295#322—111no—
296#322—111no—
297#322—111no—
298C82—111no—
299C22×C11—21no—
300C22×C11—21no—
301C22×C11—21no—
302C22×C11C2×#12711yescharacteristic
303C2×D11—81no—
304C2×D11—81no—
305C2×D11—81no—
306C2×D11—81no—
307C2×D11—81no—
308C2×D11—81no—
309C4×C11—21no—
310C4×C11—21no—
311C4×C11—21no—
312C4×C11—81no—
313C4×C11—81no—
314C4×C11—81no—
315C4×C11—81no—
316C4×C11#57612yes—
317C4×C11#57712yes—
318C4×C11#57812yes—
319Dic11—81no—
320Dic11—81no—
321C2×#41—221no—
322C2×#41—221no—
323C22×Q8—21no—
324C2×Q16—222no—
325C2×SD16—222no—
326C2×SD16—222no—
327C2×SD16—222no—
328C2×SD16—222no—
329C2×D8—222no—
330C4⋊Q8—21no—
331C4⋊Q8—21no—
332C4⋊Q8—21no—
333C4⋊Q8—111no—
334C4⋊Q8—111no—
335C4⋊Q8C22×D1111yescharacteristic
336C4⋊Q8C22×D1111yescharacteristic
337C4⋊Q8C22×D1111yescharacteristic
338C4⋊Q8C22×D1111yescharacteristic
339#127—111no—
340#127—111no—
341#125—21no—
342#124—221no—
343#124—221no—
344C22⋊Q8—21no—
345C22⋊Q8—21no—
346#121—221no—
347#121—221no—
348#121—221no—
349#121—221no—
350C4×Q8—21no—
351C4×Q8—21no—
352C4×D4—221no—
353C4×D4—221no—
354C4×D4—221no—
355C4×D4—221no—
356#117—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C42C22×D1111yescharacteristic
360#107—22no—
361#107—22no—
362#107—222no—
363#107—222no—
364#107—222no—
365#106—222no—
366C4⋊C8—112no—
367C4⋊C8—112no—
368C4⋊C8C22⋊D1112yes—
369#103—22no—
370#103—22no—
371#103—222no—
372#103—222no—
373#103—222no—
374#103—222no—
375#102—222no—
376#102—222no—
377#102—222no—
378#102—222no—
379#102—222no—
380#102—222no—
381C22⋊C8—112no—
382C22⋊C8—112no—
383C22⋊C8C22⋊D1112yes—
384C4×C8—111no—
385C4×C8—111no—
386C4×C8—111no—
387C4×C8—111no—
388C4×C8C22×D1111yescharacteristic
389C4×C8C22×D1111yescharacteristic
390C2×C11—41no—
391C2×C11#315411yescharacteristic
392C2×C11#315511yescharacteristic
393C2×C11#315611yescharacteristic
394D11—161no—
395D11—161no—
396#41—882no—
397#41—882no—
398C2×Q8—21no—
399C2×Q8—21no—
400C2×Q8—21no—
401C2×Q8—21no—
402C2×Q8—41no—
403C2×Q8—82no—
404C2×Q8—221no—
405C2×Q8—221no—
406C2×D4—221no—
407C2×D4—221no—
408C2×D4—221no—
409C2×D4—221no—
410C2×D4—221no—
411C2×D4—221no—
412C2×D4—441no—
413C2×D4—441no—
414C22×C4—41no—
415C22×C4—441no—
416C22×C4—441no—
417C22×C4D4×D1111yescharacteristic
418C22×C4D4×D1111yescharacteristic
419C22×C4C2×C22⋊D1111yescharacteristic
420Q16—882no—
421SD16—882no—
422SD16—882no—
423SD16—882no—
424SD16—882no—
425D8—882no—
426C2×C8—112no—
427C2×C8—112no—
428C2×C8—112no—
429C2×C8—112no—
430C2×C8C2×C22⋊D1112yes—
431C2×C8C2×C22⋊D1112yes—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—21no—
436C4⋊C4—21no—
437C4⋊C4—21no—
438C4⋊C4—21no—
439C4⋊C4—21no—
440C4⋊C4—41no—
441C4⋊C4—41no—
442C4⋊C4—41no—
443C4⋊C4—41no—
444C4⋊C4—221no—
445C4⋊C4—221no—
446C4⋊C4—221no—
447C4⋊C4—221no—
448C22⋊C4—41no—
449C22⋊C4—441no—
450C22⋊C4—441no—
451C22⋊C4—441no—
452C22⋊C4—441no—
453C42—41no—
454C42D4×D1111yescharacteristic
455C42D4×D1111yescharacteristic
456C42C2×C22⋊D1111yescharacteristic
457C42C23×D1111yescharacteristic
458C11#1974011yescharacteristic, complemented, Sylow
459C23—441no—
460C23—441no—
461C23#6699311yescharacteristic
462Q8—42no—
463Q8—42no—
464Q8—42no—
465Q8—42no—
466Q8—82no—
467Q8—442no—
468Q8—442no—
469D4—442no—
470D4—442no—
471D4—442no—
472D4—442no—
473D4—442no—
474D4—442no—
475D4—882no—
476D4—882no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—82no—
485C2×C4—441no—
486C2×C4—441no—
487C2×C4—882no—
488C2×C4—882no—
489C2×C4#6699311yescharacteristic
490C2×C4#6699311yescharacteristic
491C2×C4#6699311yescharacteristic
492C2×C4C2×D4×D1111yescharacteristic
493C2×C4C2×D4×D1111yescharacteristic
494C2×C4C22×C22⋊D1111yescharacteristic
495C8—22no—
496C8—22no—
497C8—222no—
498C8—222no—
499C8—222no—
500C8—222no—
501C22—21no—
502C22—21no—
503C22—21no—
504C22—881no—
505C22—881no—
506C22—881no—
507C22—881no—
508C22—881no—
509C22—881no—
510C22C2×#6699311yescharacteristic
511C4—21no—
512C4—21no—
513C4—21no—
514C4—81no—
515C4—81no—
516C4—81no—
517C4—81no—
518C4—881no—
519C4—881no—
520C4#1062329712yes—
521C4#1062330512yes—
522C4#1062336812yes—
523C2—41no—
524C2—1761no—
525C2—1761no—
526C2#1307909411yescharacteristic
527C2#1307910111yescharacteristic
528C2#1307910511yescharacteristic
subgroupG/H
centerC22C2×#66993
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3230C2
socleC22×C11C2×#127
prime radical#13079551C2
hypercenter#3230D11
hypocenterC11#19740
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3230

Complements

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

NH ≅ G/Ntype
1. #13079752C2semidirect
2. #13079737C2semidirect
3. #13079568C2semidirect
5. #13079541C2semidirect
6. #13068292C2semidirect
7. #13068286C2semidirect
8. #13068271C2semidirect
9. #13068270C2semidirect
10. #13068258C2semidirect
11. #13068239C2semidirect
12. #13068224C2semidirect
13. #13068209C2semidirect
14. #13066916C2semidirect
15. C11×#3230C2semidirect
195. #3230D11semidirect
458. C11#19740semidirect

Maximal subgroups

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

subgroupindex
#130797522
#130797372
#130795682
#130795512
#130795412
#130682922
#130682862
#130682712
#130682702
#130682582
#130682392
#130682242
#130682092
#130669162
C11×#32302
#1974011