Finite Group Databasebeta

← #14744001

Subgroups — #14744001

Order 2816.

590 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081511C211yesmaximal, characteristic
2#13081479C211yesmaximal, characteristic
3#13081010C211yesmaximal, characteristic, complemented
4#13068296C211yesmaximal, characteristic, complemented
5#13068142C211yesmaximal, characteristic, complemented
6#13068064C211yesmaximal, characteristic, complemented
7#13068015C211yesmaximal, characteristic, complemented
8#13067996C211yesmaximal, characteristic, complemented
9#13067828C211yesmaximal, characteristic, complemented
10#13067781C211yesmaximal, characteristic, complemented
11#13067750C211yesmaximal, characteristic, complemented
12#13067749C211yesmaximal, characteristic, complemented
13#13067467C211yesmaximal, characteristic, complemented
14#13067438C211yesmaximal, characteristic
15C11×#3299C211yesmaximal, characteristic, complemented
16C11×#554C2211yescharacteristic
17D4×Q8×C11C2211yescharacteristic
18#10623110C2211yescharacteristic
19#10623110C2211yescharacteristic
20C11×#487C2211yescharacteristic
21C11×#484—21no—
22C11×#477C2211yescharacteristic
23C11×#467—21no—
24C11×#462C2211yescharacteristic
25C11×#451—21no—
26C4×C11×Q16C2211yescharacteristic
27C8×D4×C11C2211yescharacteristic
28C2×C11×#103—21no—
29#10622801—21no—
30#10622706C2211yescharacteristic
31#10622705C2211yescharacteristic
32#10622700C2211yescharacteristic
33#10622697—21no—
34#10622697C2211yescharacteristic
35#10622693—21no—
36#10622692C2211yescharacteristic
37#10622691C2211yescharacteristic
38#10622679—21no—
39#10622677—21no—
40#10622637C2211yescharacteristic
41Q8×C11⋊C8C2211yescharacteristic
42#10622634C2211yescharacteristic
43#10622634C2211yescharacteristic
44#10622627—21no—
45C4×#4323—21no—
46C4×#4323C2211yescharacteristic
47#10622622—21no—
48#10622622—21no—
49#10622621C2211yescharacteristic
50#10622621C2211yescharacteristic
51D11×#107—21no—
52#10622422—21no—
53#10622422—21no—
54C8×D44C2211yescharacteristic
55#10622295C2211yescharacteristic
56#10622185C2211yescharacteristic
57#10622184C2211yescharacteristic
58Q8⋊(C11⋊C8)C2211yescharacteristic
59Q8⋊(C11⋊C8)C2211yescharacteristic
60D4⋊(C11⋊C8)C2211yescharacteristic
61#10622121C2211yescharacteristic
62#10622119C2211yescharacteristic
63#10622119C2211yescharacteristic
64#10622118C2211yescharacteristic
65#10622096C2211yescharacteristic
66#10622092C2211yescharacteristic
67C22×Q8×C11—21no—
68C2×C11×Q16—21no—
69C2×C11×Q16D411yescharacteristic
70C22×C8×C11—21no—
71C11×C4⋊Q8—21no—
72C11×C4⋊Q8C2311yescharacteristic
73C11×C4⋊Q8C2311yescharacteristic
74C11×#125—21no—
75C11×C22⋊Q8—21no—
76C11×C22⋊Q8—21no—
77C11×C22⋊Q8—41no—
78C11×C22⋊Q8—41no—
79C4×Q8×C11C2311yescharacteristic
80C4×Q8×C11C2311yescharacteristic
81C4×D4×C11—21no—
82C4×D4×C11—21no—
83C4×D4×C11C2311yescharacteristic
84C2×C11×C4⋊C4—21no—
85#66999—21no—
86#66999—21no—
87C2×#4326—41no—
88C2×#4323D411yescharacteristic
89C2×C8×D11—21no—
90#66949—41no—
91#66949—41no—
92C4⋊C4×D11—21no—
93C4⋊C4×D11—21no—
94C4×D44—21no—
95C4×D44—21no—
96C4×D44C2311yescharacteristic
97#66923—21no—
98#66923—21no—
99#66922C2311yescharacteristic
100#66922C2311yescharacteristic
101C11×#107—21no—
102C11×#107D411yescharacteristic
103C11×C4⋊C8C2311yescharacteristic
104C11×#103—21no—
105C11×#103—21no—
106C11×#103—21no—
107C11×#103—21no—
108C11×#103D411yescharacteristic
109C11×#103D411yescharacteristic
110C11×C22⋊C8—21no—
111C4×C8×C11C2311yescharacteristic
112#66899—21no—
113#66899—21no—
114#66896—21no—
115#66896—21no—
116#66896D411yescharacteristic
117(C2×D11)⋊C8—21no—
118#66882—21no—
119#66882—21no—
120#66874—41no—
121#66873—21no—
122#66873—21no—
123#66873D411yescharacteristic
124#66872—21no—
125#66872—21no—
126#66872—21no—
127#66872—21no—
128#66872—21no—
129#66871—21no—
130#66871—21no—
131#66871—21no—
132#66871—21no—
133#66871—21no—
134#66871D411yescharacteristic
135C4⋊(C11⋊C8)—21no—
136C4⋊(C11⋊C8)—21no—
137C4⋊(C11⋊C8)C2311yescharacteristic
138C4⋊(C11⋊C8)C2311yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
140#66867—21no—
141C4×C11⋊C8—21no—
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#19814—111nomaximal, Sylow
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—41no—
148C2×Q8×C11—42no—
149C2×Q8×C11—81no—
150C2×Q8×C11C2×D411yescharacteristic
151C2×Q8×C11C2×D411yescharacteristic
152C2×D4×C11C2×D411yescharacteristic
153C22×C4×C11—21no—
154C22×C4×C11—41no—
155C22×C4×C11—41no—
156C2×D44C2×D411yescharacteristic
157C2×C4×D11—21no—
158C2×C4×D11—41no—
159C2×C4×D11—41no—
160C2×Dic22—21no—
161C2×Dic22—21no—
162C11×Q16—41no—
163C11×Q16—81no—
164C2×C8×C11—21no—
165C2×C8×C11—81no—
166C2×C8×C11C2×D411yescharacteristic
167C2×C8×C11C2×D411yescharacteristic
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—41no—
175C11×C4⋊C4—41no—
176C11×C4⋊C4—41no—
177C11×C4⋊C4C2×D411yescharacteristic
178C11×C4⋊C4C2×D411yescharacteristic
179C11×C4⋊C4C2×D411yescharacteristic
180C11×C22⋊C4—21no—
181C11×C22⋊C4—41no—
182C11×C22⋊C4—41no—
183C42×C11—21no—
184C42×C11—21no—
185C42×C11C2411yescharacteristic
186#4326—82no—
187#4323Q1614yescomplemented
188(C2×D11)⋊C4—21no—
189(C2×D11)⋊C4—41no—
190(C2×D11)⋊C4—41no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11C2×D411yescharacteristic
196Dic11⋊C4—41no—
197Dic11⋊C4—41no—
198Dic11⋊C4—41no—
199Dic11⋊C4—41no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8C2×D411yescharacteristic
205C2×C11⋊C8C2×D411yescharacteristic
206C8×D11—42no—
207#3384—111no—
208#3380—111no—
209#3338—111no—
210#3299D1111yescharacteristic, complemented
211#1723—111no—
212#1696—111no—
213#1683—111no—
214#1675—111no—
215#1672—111no—
216#1644—111no—
217#1637—111no—
218#1632—111no—
219#1632—111no—
220#1584—111no—
221#1580—111no—
222C23×C11—21no—
223C22×D11—21no—
224Q8×C11—21no—
225Q8×C11—21no—
226Q8×C11—21no—
227Q8×C11—21no—
228Q8×C11—41no—
229Q8×C11—41no—
230Q8×C11—81no—
231Q8×C11—82no—
232D4×C11—21no—
233D4×C11C2×Q1612yes—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—82no—
244C2×C4×C11—161no—
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C22×D411yescharacteristic
247C2×C4×C11H(5,𝔽2)11yescharacteristic
248C2×Dic11—21no—
249C2×Dic11—41no—
250C2×Dic11—41no—
251D44—21no—
252D44C2×Q1612yes—
253C4×D11—41no—
254C4×D11—41no—
255C4×D11—161no—
256C4×D11—161no—
257Dic22—81no—
258Dic22—81no—
259C8×C11—21no—
260C8×C11—21no—
261C8×C11—41no—
262C11⋊C8—21no—
263C11⋊C8—41no—
264C11⋊C8—41no—
265C11⋊C8—41no—
266C11⋊C8—41no—
267C11⋊C8C2×Q1612yes—
268#554—111no—
269#554—111no—
270#554C2×D1111yescharacteristic
271D4×Q8C2×D1111yescharacteristic
272#501—221no—
273#500—111no—
274#500—111no—
275#499—221no—
276#498—111no—
277#494—111no—
278#487—111no—
279#487C2×D1111yescharacteristic
280#484—21no—
281#484—221no—
282#484—221no—
283#478—221no—
284#478—221no—
285#478—221no—
286#477—111no—
287#477—111no—
288#477C2×D1111yescharacteristic
289#476—111no—
290#476—111no—
291#476—111no—
292#476—221no—
293#474—111no—
294#467—21no—
295#467—221no—
296#462C2×D1111yescharacteristic
297#451—21no—
298#446—111no—
299C8×Q8—111no—
300#442—221no—
301C4×Q16C2×D1111yescharacteristic
302C4×D8—111no—
303C4×D8—221no—
304C8×D4—111no—
305C8×D4C2×D1111yescharacteristic
306C2×#107—221no—
307C2×#103—21no—
308#335—111no—
309#334—111no—
310#333—111no—
311#333—111no—
312#333—111no—
313#332—111no—
314Q8⋊C8—111no—
315Q8⋊C8—111no—
316D4⋊C8—111no—
317D4⋊C8—111no—
318#322—111no—
319C22×C11—22no—
320C22×C11—41no—
321C22×C11—41no—
322C22×C11D4211yescharacteristic
323C2×D11—22no—
324C2×D11—41no—
325C2×D11—41no—
326C4×C11—21no—
327C4×C11—41no—
328C4×C11—41no—
329C4×C11—41no—
330C4×C11—41no—
331C4×C11—41no—
332C4×C11—81no—
333C4×C11—81no—
334C4×C11C22×Q1611yescharacteristic
335C4×C11#57511yescharacteristic
336C4×C11#57711yescharacteristic
337C4×C11#57811yescharacteristic
338Dic11—41no—
339Dic11—81no—
340Dic11—81no—
341C22×Q8—21no—
342C2×Q16—21no—
343C2×Q16—441no—
344C2×Q16C22⋊D1111yescharacteristic
345C2×D8—111no—
346C22×C8—21no—
347C22×C8—221no—
348C4⋊Q8—21no—
349C4⋊Q8—111no—
350C4⋊Q8—111no—
351C4⋊Q8C22×D1111yescharacteristic
352C4⋊Q8C22×D1111yescharacteristic
353#125—21no—
354#125—221no—
355#125—221no—
356C22⋊Q8—21no—
357C22⋊Q8—21no—
358C22⋊Q8—41no—
359C22⋊Q8—41no—
360C22⋊Q8—221no—
361C22⋊Q8—221no—
362C22⋊Q8—441no—
363C22⋊Q8—441no—
364C4×Q8C22×D1111yescharacteristic
365C4×Q8C22×D1111yescharacteristic
366C4×D4—21no—
367C4×D4—21no—
368C4×D4—111no—
369C4×D4—221no—
370C4×D4—221no—
371C4×D4C22×D1111yescharacteristic
372C2×C4⋊C4—21no—
373C2×C4⋊C4—221no—
374C2×C4⋊C4—221no—
375#107—21no—
376#107—111no—
377#107—221no—
378#107—221no—
379#107—221no—
380#107—221no—
381#107—221no—
382#107—221no—
383#107—221no—
384#107C22⋊D1111yescharacteristic
385#106—221no—
386#106—221no—
387#106—221no—
388#106—221no—
389#106—221no—
390C4⋊C8—111no—
391C4⋊C8—111no—
392C4⋊C8—111no—
393C4⋊C8—221no—
394C4⋊C8—221no—
395C4⋊C8C22×D1111yescharacteristic
396#103—21no—
397#103—21no—
398#103—21no—
399#103—21no—
400#103—221no—
401#103—221no—
402#103—441no—
403#103C22⋊D1111yescharacteristic
404#103C22⋊D1111yescharacteristic
405#102—111no—
406#102—111no—
407#102—221no—
408#102—221no—
409#102—221no—
410#102—221no—
411C22⋊C8—21no—
412C22⋊C8—221no—
413#97—221no—
414C4×C8—111no—
415C4×C8—111no—
416C4×C8—221no—
417C4×C8C22×D1111yescharacteristic
418C2×C11—42no—
419C2×C11#326711yescharacteristic
420C2×C11D4×Q1611yescharacteristic
421C2×C11#328811yescharacteristic
422D11—42no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—41no—
426C2×Q8—42no—
427C2×Q8—81no—
428C2×Q8—221no—
429C2×Q8—221no—
430C2×Q8C2×C22⋊D1111yescharacteristic
431C2×Q8C2×C22⋊D1111yescharacteristic
432C2×D4—111no—
433C2×D4D4×D1111yescharacteristic
434C22×C4—21no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—221no—
438C22×C4—441no—
439C22×C4—441no—
440Q16—41no—
441Q16—81no—
442Q16—882no—
443D8—114no—
444C2×C8—21no—
445C2×C8—81no—
446C2×C8—111no—
447C2×C8—111no—
448C2×C8—221no—
449C2×C8—221no—
450C2×C8—221no—
451C2×C8—221no—
452C2×C8—442no—
453C2×C8C2×C22⋊D1111yescharacteristic
454C2×C8C2×C22⋊D1111yescharacteristic
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—41no—
462C4⋊C4—41no—
463C4⋊C4—41no—
464C4⋊C4—111no—
465C4⋊C4—221no—
466C4⋊C4—221no—
467C4⋊C4—221no—
468C4⋊C4—221no—
469C4⋊C4—441no—
470C4⋊C4—441no—
471C4⋊C4—441no—
472C4⋊C4—441no—
473C4⋊C4D4×D1111yescharacteristic
474C4⋊C4C2×C22⋊D1111yescharacteristic
475C4⋊C4C2×C22⋊D1111yescharacteristic
476C22⋊C4—21no—
477C22⋊C4—41no—
478C22⋊C4—41no—
479C22⋊C4—221no—
480C22⋊C4—441no—
481C22⋊C4—441no—
482C42—21no—
483C42—21no—
484C42C23×D1111yescharacteristic
485C11#1981411yescharacteristic, complemented, Sylow
486C23—21no—
487C23—221no—
488Q8—21no—
489Q8—21no—
490Q8—21no—
491Q8—21no—
492Q8—41no—
493Q8—41no—
494Q8—81no—
495Q8—82no—
496Q8—881no—
497Q8—881no—
498D4—21no—
499D4—112no—
500D4—221no—
501D4Q16×D1112yes—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—82no—
512C2×C4—161no—
513C2×C4—221no—
514C2×C4—441no—
515C2×C4—441no—
516C2×C4—441no—
517C2×C4—441no—
518C2×C4—1761no—
519C2×C4—1761no—
520C2×C4C2×D4×D1111yescharacteristic
521C2×C4#6703711yescharacteristic
522C2×C4C22×C22⋊D1111yescharacteristic
523C8—21no—
524C8—21no—
525C8—41no—
526C8—112no—
527C8—221no—
528C8—441no—
529C8—441no—
530C8—441no—
531C8—441no—
532C22—22no—
533C22—41no—
534C22—41no—
535C22—222no—
536C22—441no—
537C22—441no—
538C22D4×C22⋊D1111yescharacteristic
539C4—21no—
540C4—41no—
541C4—41no—
542C4—41no—
543C4—41no—
544C4—41no—
545C4—81no—
546C4—81no—
547C4—441no—
548C4—881no—
549C4—881no—
550C4C2×Q16×D1111yescharacteristic
551C4#1062329711yescharacteristic
552C4#1062335311yescharacteristic
553C4#1062336711yescharacteristic
554C2—42no—
555C2—442no—
556C2#1308013711yescharacteristic
557C2Q16×C22⋊D1111yescharacteristic
558C2#1308037811yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3299C2
socleC22×C11D42
prime radicalC2×#4323D4
hypercenter#3299D11
hypocenterC11#19814
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #3299

Complements

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

NH ≅ G/Ntype
3. #13081010C2semidirect
4. #13068296C2semidirect
5. #13068142C2semidirect
6. #13068064C2semidirect
7. #13068015C2semidirect
8. #13067996C2semidirect
9. #13067828C2semidirect
10. #13067781C2semidirect
11. #13067750C2semidirect
12. #13067749C2semidirect
13. #13067467C2semidirect
15. C11×#3299C2semidirect
187. #4323Q16semidirect
210. #3299D11semidirect
485. C11#19814semidirect

Maximal subgroups

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

subgroupindex
#130815112
#130814792
#130810102
#130682962
#130681422
#130680642
#130680152
#130679962
#130678282
#130677812
#130677502
#130677492
#130674672
#130674382
C11×#32992
#1981411