Finite Group Databasebeta

← #14910332

Subgroups — #14910332

Order 2816.

680 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622808C211yesmaximal, characteristic, complemented
2C2×#10622807C211yesmaximal, characteristic, complemented
3#13080359C211yesmaximal, characteristic, complemented
4#13070880C211yesmaximal, characteristic, complemented
5#13070717C211yesmaximal, characteristic, complemented
6#13070710C211yesmaximal, characteristic, complemented
7#13070678C211yesmaximal, characteristic, complemented
8#13070653C211yesmaximal, characteristic, complemented
9#13070556C211yesmaximal, characteristic, complemented
10#13070539C211yesmaximal, characteristic, complemented
11#13070537C211yesmaximal, characteristic, complemented
12#13070532C211yesmaximal, characteristic, complemented
13#13070485C211yesmaximal, characteristic, complemented
14#13070442C211yesmaximal, characteristic, complemented
15C11×#3287C211yesmaximal, characteristic, complemented
16C2×C11×#135C2211yescharacteristic
17C2×C11×#135C2211yescharacteristic
18C11×#550—21no—
19C22×Dic44C2211yescharacteristic
20C2×#66957C2211yescharacteristic
21#10623083—21no—
22C11×#493C2211yescharacteristic
23C11×#466C2211yescharacteristic
24C11×#466C2211yescharacteristic
25C11×#460—21no—
26C11×#449—21no—
27C11×#449—21no—
28C4×C11×Q16C2211yescharacteristic
29C8×D4×C11C2211yescharacteristic
30#10622808—24no—
31#10622807—24no—
32C2×#66893C2211yescharacteristic
33C2×#66893C2211yescharacteristic
34C2×#66892C2211yescharacteristic
35C2×#66891C2211yescharacteristic
36C2×#66891C2211yescharacteristic
37C2×#66891C2211yescharacteristic
38C2×#66891C2211yescharacteristic
39C2×#66890C2211yescharacteristic
40C2×#66890C2211yescharacteristic
41#10622729C2211yescharacteristic
42#10622728C2211yescharacteristic
43C2×#66876C2211yescharacteristic
44C22×C11⋊C16C2211yescharacteristic
45#10622458—21no—
46#10622351—21no—
47#10622346—21no—
48C4×Dic44C2211yescharacteristic
49#10622309C2211yescharacteristic
50#10622202C2211yescharacteristic
51#10622200C2211yescharacteristic
52#10622200C2211yescharacteristic
53C22⋊(C11⋊C16)C2211yescharacteristic
54C22⋊(C11⋊C16)C2211yescharacteristic
55#10622130C2211yescharacteristic
56#10622130C2211yescharacteristic
57#10622129C2211yescharacteristic
58#10622128C2211yescharacteristic
59C4⋊(C11⋊C16)C2211yescharacteristic
60#10622099C2211yescharacteristic
61C2×C11×#41—21no—
62C2×C11×#41—21no—
63C2×#4339—21no—
64C22×Dic22—21no—
65C11×#135—22no—
66C11×#135—22no—
67C11×#135—41no—
68C11×#135—41no—
69C2×C11×Q16C2311yescharacteristic
70C2×C11×SD16—21no—
71C2×C11×SD16—21no—
72C2×C11×D8—21no—
73C2×C11×D8C2311yescharacteristic
74C2×C11×D8C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C11×#127—21no—
78C11×#127—41no—
79C11×#121—21no—
80C11×#121—21no—
81C11×#121—41no—
82C11×#121—41no—
83C4×Q8×C11—21no—
84C4×D4×C11—41no—
85C4×D4×C11D411yescharacteristic
86#66992—41no—
87#66983—21no—
88#66977—21no—
89C2×Dic44—22no—
90C2×Dic44—21no—
91C2×Dic44—41no—
92C2×Dic44C2311yescharacteristic
93C2×Dic44C2311yescharacteristic
94#66957—22no—
95#66957—41no—
96C2×D88C2311yescharacteristic
97C2×#4314—21no—
98C2×#4314—21no—
99#66949—41no—
100#66938—41no—
101(C22⋊D11)⋊C4—41no—
102#66928—21no—
103C4×Dic22—21no—
104C11×#107C2311yescharacteristic
105C11×C4⋊C8D411yescharacteristic
106C11×#103—21no—
107C11×#102—21no—
108C11×#102—21no—
109C11×C22⋊C8D411yescharacteristic
110C11×C22⋊C8D411yescharacteristic
111C4×C8×C11C2311yescharacteristic
112#66893—22no—
113#66893D414yescomplemented
114#66892—22no—
115#66891—22no—
116#66891—22no—
117#66891—22no—
118#66891—41no—
119#66890—22no—
120#66890—41no—
121#66885—21no—
122#66882C2311yescharacteristic
123#66880—21no—
124#66880—21no—
125#66876—22no—
126C2×C11⋊C16—22no—
127C2×C11⋊C16C2311yescharacteristic
128C2×C11⋊C16C2311yescharacteristic
129C2×C11⋊C16C2311yescharacteristic
130C2×C11⋊C16C2311yescharacteristic
131#33837—111nomaximal, Sylow
132C11×#41—42no—
133C11×#41—42no—
134C11×#41—81no—
135C11×#41—81no—
136C2×Q8×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11—41no—
140C2×D4×C11—41no—
141C2×D4×C11—41no—
142C2×D4×C11—41no—
143C2×D4×C11—41no—
144C2×D4×C11—41no—
145C2×D4×C11D811yescharacteristic
146C22×C4×C11—41no—
147C22×C4×C11—41no—
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C2×C22⋊D11—41no—
151C2×C22⋊D11—41no—
152C22×Dic11—41no—
153#4339—42no—
154#4339—81no—
155C2×D44—21no—
156C2×C4×D11—41no—
157C2×Dic22—21no—
158C2×Dic22—21no—
159C2×Dic22—42no—
160C2×Dic22—41no—
161C2×Dic22—81no—
162C11×Q16—21no—
163C11×Q16C2×D412yes—
164C11×SD16—42no—
165C11×SD16—42no—
166C11×D8—21no—
167C11×D8—21no—
168C11×D8—21no—
169C11×D8—21no—
170C11×D8—81no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11C2×D411yescharacteristic
176C2×C8×C11C2×D411yescharacteristic
177C2×C8×C11C2×D411yescharacteristic
178C2×C8×C11C2411yescharacteristic
179C11×C4⋊C4—21no—
180C11×C4⋊C4—41no—
181C11×C4⋊C4D811yescharacteristic
182C11×C22⋊C4—41no—
183C11×C22⋊C4—41no—
184C11×C22⋊C4D811yescharacteristic
185C11×C22⋊C4D811yescharacteristic
186C42×C11—41no—
187C42×C11C2×D411yescharacteristic
188C22⋊Dic11—41no—
189(C2×D11)⋊C4—41no—
190(C2×D11)⋊C4—41no—
191(C2×D11)⋊C4—41no—
192C4⋊Dic11—21no—
193Dic11⋊C4—41no—
194Dic11⋊C4—41no—
195C4×Dic11—41no—
196Dic44—21no—
197Dic44—21no—
198Dic44—21no—
199Dic44—42no—
200Dic44C2×D412yes—
201D88—21no—
202D88—21no—
203#4314—42no—
204#4314—81no—
205C11⋊C16—21no—
206C11⋊C16—21no—
207C11⋊C16—21no—
208C11⋊C16C2×D412yes—
209C2×#510—111no—
210C2×#508—111no—
211#3287D1111yescharacteristic, complemented
212#3285—111no—
213#2250—111no—
214#2218—111no—
215#2217—111no—
216#2211—111no—
217#2207—111no—
218#2189—111no—
219#2186—111no—
220#2186—111no—
221#2185—111no—
222#2176—111no—
223#2168—111no—
224C23×C11—41no—
225C23×C11—41no—
226C23×C11C2×D811yescharacteristic
227C23×C11C2×D811yescharacteristic
228C22×D11—41no—
229Q8×C11—22no—
230Q8×C11—41no—
231D4×C11—41no—
232D4×C11—41no—
233D4×C11—41no—
234D4×C11—41no—
235D4×C11—41no—
236D4×C11—82no—
237D4×C11—82no—
238D4×C11—82no—
239D4×C11—161no—
240D4×C11—161no—
241D4×C11—161no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—82no—
249C2×C4×C11—82no—
250C2×C4×C11C2×D811yescharacteristic
251C2×C4×C11C2×D811yescharacteristic
252C2×C4×C11C2×D811yescharacteristic
253C2×C4×C11C2×D811yescharacteristic
254C2×C4×C11C22×D411yescharacteristic
255C22⋊D11—82no—
256C22⋊D11—82no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—82no—
261D44—41no—
262D44—41no—
263C4×D11—82no—
264Dic22—22no—
265Dic22—41no—
266Dic22—41no—
267Dic22—41no—
268Dic22—82no—
269C8×C11—21no—
270C8×C11—21no—
271C8×C11—21no—
272C8×C11C22×D411yescharacteristic
273C8×C11H(5,𝔽2)11yescharacteristic
274C2×#135—111no—
275C2×#135C2×D1111yescharacteristic
276C2×#135C2×D1111yescharacteristic
277C22×Q16—111no—
278#550—21no—
279#548—221no—
280#510—224no—
281#508—224no—
282C2×Q32—111no—
283C2×Q32—111no—
284C2×SD32—111no—
285C2×SD32—111no—
286C2×SD32—111no—
287C2×SD32—111no—
288C2×SD32—111no—
289C2×D16—111no—
290C2×D16—111no—
291C2×M32—111no—
292C22×C16—111no—
293#495—111no—
294#493C2×D1111yescharacteristic
295#467—111no—
296#466—111no—
297#466C2×D1111yescharacteristic
298#466C2×D1111yescharacteristic
299#464—221no—
300#460—21no—
301#452—221no—
302#449—21no—
303#449—21no—
304#448—221no—
305C4×Q16—111no—
306C4×Q16C2×D1111yescharacteristic
307C8×D4C2×D1111yescharacteristic
308#367—111no—
309C4⋊C16—111no—
310#358—111no—
311#358—111no—
312#358—111no—
313#357—111no—
314#357—111no—
315#357—111no—
316C22⋊C16—111no—
317C22⋊C16—111no—
318#346—111no—
319C22×C11—21no—
320C22×C11—21no—
321C22×C11—21no—
322C22×C11—21no—
323C22×C11—21no—
324C22×C11—21no—
325C22×C11—81no—
326C22×C11—81no—
327C22×C11—81no—
328C22×C11—81no—
329C22×C11—81no—
330C22×C11—81no—
331C22×C11C22×D811yescharacteristic
332C2×D11—81no—
333C2×D11—81no—
334C2×D11—81no—
335C4×C11—21no—
336C4×C11—21no—
337C4×C11—21no—
338C4×C11—21no—
339C4×C11—42no—
340C4×C11—81no—
341C4×C11D4211yescharacteristic
342C4×C11#57611yescharacteristic
343Dic11—42no—
344Dic11—81no—
345Dic11—81no—
346C2×#41—21no—
347C2×#41—21no—
348C2×#41—221no—
349C22×Q8—221no—
350#135—22no—
351#135—22no—
352#135—41no—
353#135—41no—
354#135—222no—
355#135—441no—
356C2×Q16—111no—
357C2×Q16—111no—
358C2×Q16—222no—
359C2×Q16—221no—
360C2×Q16—441no—
361C2×Q16C22×D1111yescharacteristic
362C2×SD16—21no—
363C2×SD16—21no—
364C2×SD16—221no—
365C2×SD16—221no—
366C2×D8—21no—
367C2×D8—111no—
368C2×D8C22×D1111yescharacteristic
369C2×D8C22×D1111yescharacteristic
370C22×C8C22×D1111yescharacteristic
371C22×C8C22×D1111yescharacteristic
372#127—21no—
373#127—41no—
374#124—221no—
375#124—441no—
376C22⋊Q8—221no—
377C22⋊Q8—441no—
378#121—21no—
379#121—21no—
380#121—41no—
381#121—41no—
382#121—221no—
383#121—441no—
384C4×Q8—21no—
385C4×Q8—221no—
386C4×D4—41no—
387C4×D4—441no—
388C4×D4C22⋊D1111yescharacteristic
389Q32—114no—
390Q32—222no—
391SD32—222no—
392SD32—222no—
393SD32—222no—
394SD32—222no—
395SD32—441no—
396D16—222no—
397D16—441no—
398M32—222no—
399C2×C16—111no—
400C2×C16—111no—
401C2×C16—111no—
402C2×C16—111no—
403C2×C16—222no—
404#107—111no—
405#107C22×D1111yescharacteristic
406C4⋊C8C22⋊D1111yescharacteristic
407#103—21no—
408#103—221no—
409#103—221no—
410#102—21no—
411#102—21no—
412#102—221no—
413C22⋊C8C22⋊D1111yescharacteristic
414C22⋊C8C22⋊D1111yescharacteristic
415C4×C8C22×D1111yescharacteristic
416C2×C11—41no—
417C2×C11—41no—
418C2×C11—161no—
419C2×C11—161no—
420C2×C11D4×D811yescharacteristic
421C2×C11#341411yescharacteristic
422C2×C11#341611yescharacteristic
423D11—161no—
424#41—42no—
425#41—42no—
426#41—81no—
427#41—81no—
428#41—442no—
429#41—881no—
430C2×Q8—21no—
431C2×Q8—221no—
432C2×Q8—221no—
433C2×Q8—442no—
434C2×Q8—441no—
435C2×Q8—881no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—41no—
439C2×D4—41no—
440C2×D4—41no—
441C2×D4—41no—
442C2×D4—41no—
443C2×D4—41no—
444C2×D4—221no—
445C2×D4—441no—
446C2×D4—441no—
447C2×D4#432311yescharacteristic
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—441no—
451C22×C4—441no—
452C22×C4C2×C22⋊D1111yescharacteristic
453C22×C4C2×C22⋊D1111yescharacteristic
454Q16—21no—
455Q16—112no—
456Q16—221no—
457Q16—221no—
458Q16—221no—
459Q16—442no—
460Q16D4×D1112yes—
461SD16—42no—
462SD16—42no—
463SD16—442no—
464SD16—881no—
465D8—21no—
466D8—21no—
467D8—21no—
468D8—21no—
469D8—81no—
470D8—221no—
471D8—221no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8C2×C22⋊D1111yescharacteristic
477C2×C8C2×C22⋊D1111yescharacteristic
478C2×C8C2×C22⋊D1111yescharacteristic
479C2×C8C23×D1111yescharacteristic
480C4⋊C4—21no—
481C4⋊C4—41no—
482C4⋊C4—221no—
483C4⋊C4—441no—
484C4⋊C4—441no—
485C4⋊C4#432311yescharacteristic
486C22⋊C4—41no—
487C22⋊C4—41no—
488C22⋊C4—441no—
489C22⋊C4—441no—
490C22⋊C4—441no—
491C22⋊C4—441no—
492C22⋊C4#432311yescharacteristic
493C22⋊C4#432311yescharacteristic
494C42—41no—
495C42—441no—
496C42C2×C22⋊D1111yescharacteristic
497C16—112no—
498C16—221no—
499C16—221no—
500C16—221no—
501C11#3383711yescharacteristic, complemented, Sylow
502C23—41no—
503C23—41no—
504C23—441no—
505C23C2×#432311yescharacteristic
506C23C2×#432311yescharacteristic
507Q8—22no—
508Q8—41no—
509Q8—222no—
510Q8—441no—
511Q8—441no—
512Q8—441no—
513Q8—882no—
514D4—41no—
515D4—41no—
516D4—41no—
517D4—41no—
518D4—41no—
519D4—82no—
520D4—82no—
521D4—82no—
522D4—161no—
523D4—161no—
524D4—161no—
525D4—441no—
526D4—441no—
527D4—882no—
528D4—882no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—82no—
536C2×C4—82no—
537C2×C4—441no—
538C2×C4—441no—
539C2×C4—441no—
540C2×C4—882no—
541C2×C4—882no—
542C2×C4C2×#432311yescharacteristic
543C2×C4C2×#432311yescharacteristic
544C2×C4C2×#432311yescharacteristic
545C2×C4C2×#432311yescharacteristic
546C2×C4C22×C22⋊D1111yescharacteristic
547C8—21no—
548C8—21no—
549C8—21no—
550C8C2×D4×D1111yescharacteristic
551C8#6703711yescharacteristic
552C22—21no—
553C22—21no—
554C22—21no—
555C22—21no—
556C22—21no—
557C22—21no—
558C22—81no—
559C22—81no—
560C22—81no—
561C22—81no—
562C22—81no—
563C22—81no—
564C22—881no—
565C22—881no—
566C22—881no—
567C22C22×#432311yescharacteristic
568C4—21no—
569C4—21no—
570C4—21no—
571C4—21no—
572C4—42no—
573C4—81no—
574C4—442no—
575C4—881no—
576C4—881no—
577C4D4×C22⋊D1111yescharacteristic
578C4#1062336611yescharacteristic
579C2—41no—
580C2—41no—
581C2—161no—
582C2—161no—
583C2—1761no—
584C2D4×#432311yescharacteristic
585C2#1308175011yescharacteristic
586C2#1308176311yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3287C2
socleC22×C11C22×D8
hypercenter#3287D11
hypocenterC11#33837
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3287

Complements

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

NH ≅ G/Ntype
1. C2×#10622808C2semidirect
2. C2×#10622807C2semidirect
3. #13080359C2semidirect
4. #13070880C2semidirect
5. #13070717C2semidirect
6. #13070710C2semidirect
7. #13070678C2semidirect
8. #13070653C2semidirect
9. #13070556C2semidirect
10. #13070539C2semidirect
11. #13070537C2semidirect
12. #13070532C2semidirect
13. #13070485C2semidirect
14. #13070442C2semidirect
15. C11×#3287C2semidirect
113. #66893D4semidirect
211. #3287D11semidirect
501. C11#33837semidirect

Maximal subgroups

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

subgroupindex
C2×#106228082
C2×#106228072
#130803592
#130708802
#130707172
#130707102
#130706782
#130706532
#130705562
#130705392
#130705372
#130705322
#130704852
#130704422
C11×#32872
#3383711