Finite Group Databasebeta

← #14744005

Subgroups — #14744005

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#13081513C211yesmaximal, characteristic
2#13081004C211yesmaximal, characteristic, complemented
3#13080486C211yesmaximal, characteristic, complemented
4#13068294C211yesmaximal, characteristic, complemented
5#13068141C211yesmaximal, characteristic, complemented
6#13068069C211yesmaximal, characteristic, complemented
7#13068013C211yesmaximal, characteristic, complemented
8#13067998C211yesmaximal, characteristic, complemented
9#13067830C211yesmaximal, characteristic, complemented
10#13067780C211yesmaximal, characteristic, complemented
11#13067750C211yesmaximal, characteristic, complemented
12#13067748C211yesmaximal, characteristic, complemented
13#13067466C211yesmaximal, characteristic, complemented
14#13067440C211yesmaximal, characteristic
15C11×#3380C211yesmaximal, characteristic
16C11×#554C2211yescharacteristic
17C11×#554C2211yescharacteristic
18#10623074C2211yescharacteristic
19D4×Dic22C2211yescharacteristic
20C11×#500C2211yescharacteristic
21C11×#499—21no—
22C11×#478—21no—
23C11×#478—21no—
24C11×#476C2211yescharacteristic
25C11×#476C2211yescharacteristic
26C8×Q8×C11C2211yescharacteristic
27C4×C11×D8—21no—
28C4×C11×D8C2211yescharacteristic
29#10622765—21no—
30#10622706C2211yescharacteristic
31#10622705C2211yescharacteristic
32#10622704C2211yescharacteristic
33#10622704C2211yescharacteristic
34#10622694C2211yescharacteristic
35#10622691C2211yescharacteristic
36#10622664—21no—
37#10622664—21no—
38#10622663—21no—
39#10622657—21no—
40#10622644C2211yescharacteristic
41C4×#4326C2211yescharacteristic
42#10622634C2211yescharacteristic
43D4×C11⋊C8C2211yescharacteristic
44D4×C11⋊C8C2211yescharacteristic
45#10622621C2211yescharacteristic
46#10622620C2211yescharacteristic
47#10622583—21no—
48#10622583—21no—
49C2×#66874—21no—
50C2×#66871—21no—
51#10622489—21no—
52#10622376—21no—
53#10622374—21no—
54#10622293C2211yescharacteristic
55#10622292C2211yescharacteristic
56#10622184C2211yescharacteristic
57#10622184C2211yescharacteristic
58Q8⋊(C11⋊C8)C2211yescharacteristic
59D4⋊(C11⋊C8)C2211yescharacteristic
60D4⋊(C11⋊C8)C2211yescharacteristic
61#10622124C2211yescharacteristic
62#10622122C2211yescharacteristic
63#10622119C2211yescharacteristic
64#10622117C2211yescharacteristic
65#10622095C2211yescharacteristic
66#10622093C2211yescharacteristic
67C22×Dic22—21no—
68C2×C11×D8D411yescharacteristic
69C11×C4⋊Q8C2311yescharacteristic
70C11×C4⋊Q8C2311yescharacteristic
71C11×#125—21no—
72C11×#125—21no—
73C11×C22⋊Q8—21no—
74C11×C22⋊Q8—21no—
75C11×C22⋊Q8—41no—
76C11×C22⋊Q8—41no—
77C4×Q8×C11C2311yescharacteristic
78C4×D4×C11—21no—
79C4×D4×C11—21no—
80C4×D4×C11C2311yescharacteristic
81C4×D4×C11C2311yescharacteristic
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4—21no—
84C2×#4326—21no—
85C2×#4326—41no—
86C2×#4326D411yescharacteristic
87D4×Dic11—21no—
88D4×Dic11—21no—
89C2×C4⋊Dic11—21no—
90#66977—21no—
91#66977—21no—
92C22×C11⋊C8—21no—
93C22×C11⋊C8—21no—
94#66943—21no—
95#66941—21no—
96#66931—41no—
97#66931—41no—
98#66922C2311yescharacteristic
99#66922C2311yescharacteristic
100C4×Dic22C2311yescharacteristic
101C11×#107—21no—
102C11×#107—21no—
103C11×#107D411yescharacteristic
104C11×#106—21no—
105C11×#106—21no—
106C11×C4⋊C8—21no—
107C11×C4⋊C8C2311yescharacteristic
108C11×#102—21no—
109C11×#102—21no—
110C11×#102D411yescharacteristic
111C11×#102D411yescharacteristic
112C4×C8×C11—21no—
113C4×C8×C11C2311yescharacteristic
114#66899—21no—
115#66899—41no—
116#66899D411yescharacteristic
117#66896—21no—
118#66896—21no—
119C22⋊(C11⋊C8)—21no—
120C22⋊(C11⋊C8)—21no—
121#66881—21no—
122#66881—21no—
123#66879—21no—
124Dic11⋊C8—21no—
125#66874—21no—
126#66874—21no—
127#66874—21no—
128#66874—21no—
129#66874—21no—
130#66874D411yescharacteristic
131#66872—21no—
132#66871—21no—
133#66871—21no—
134#66871—21no—
135#66871—21no—
136#66871—21no—
137#66871—21no—
138#66871D411yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#19814—111nomaximal, Sylow
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11C2×D411yescharacteristic
148C2×D4×C11C2×D411yescharacteristic
149C2×D4×C11C2×D411yescharacteristic
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—41no—
153C22×C4×C11—41no—
154C22×Dic11—41no—
155C22×Dic11—41no—
156C2×Dic22—21no—
157C2×Dic22—21no—
158C2×Dic22—41no—
159C2×Dic22—42no—
160C2×Dic22—81no—
161C2×Dic22C2×D411yescharacteristic
162C11×D8Q1614yescomplemented
163C2×C8×C11—21no—
164C2×C8×C11C2×D411yescharacteristic
165C2×C8×C11C2×D411yescharacteristic
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—41no—
172C11×C4⋊C4—41no—
173C11×C4⋊C4—41no—
174C11×C4⋊C4—41no—
175C11×C4⋊C4C2×D411yescharacteristic
176C11×C4⋊C4C2×D411yescharacteristic
177C11×C4⋊C4C2×D411yescharacteristic
178C11×C22⋊C4—21no—
179C11×C22⋊C4—21no—
180C11×C22⋊C4—41no—
181C11×C22⋊C4—41no—
182C42×C11—21no—
183C42×C11C2411yescharacteristic
184C22⋊Dic11—41no—
185C22⋊Dic11—41no—
186#4326—41no—
187#4326—81no—
188#4326—82no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—41no—
194C4⋊Dic11C2×D411yescharacteristic
195Dic11⋊C4—21no—
196Dic11⋊C4—41no—
197Dic11⋊C4—41no—
198C4×Dic11—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—42no—
204C2×C11⋊C8—81no—
205C2×C11⋊C8C2×D411yescharacteristic
206C2×C11⋊C8C2×D411yescharacteristic
207#3384—111no—
208#3380D1111yescharacteristic
209#3338—111no—
210#3299—111no—
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—
223C23×C11—21no—
224Q8×C11—21no—
225Q8×C11—21no—
226Q8×C11—81no—
227Q8×C11—81no—
228D4×C11—21no—
229D4×C11—21no—
230D4×C11C2×Q1612yes—
231D4×C11C2×Q1612yes—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—161no—
243C2×C4×C11—161no—
244C2×C4×C11C22×D411yescharacteristic
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11H(5,𝔽2)11yescharacteristic
247C2×Dic11—21no—
248C2×Dic11—21no—
249C2×Dic11—41no—
250C2×Dic11—41no—
251C2×Dic11—82no—
252C2×Dic11—161no—
253Dic22—21no—
254Dic22—21no—
255Dic22—41no—
256Dic22—41no—
257Dic22—82no—
258Dic22—81no—
259C8×C11—21no—
260C8×C11—41no—
261C8×C11C2×Q1612yes—
262C11⋊C8—21no—
263C11⋊C8—21no—
264C11⋊C8—41no—
265C11⋊C8—41no—
266C11⋊C8—41no—
267C11⋊C8—41no—
268#554—111no—
269#554C2×D1111yescharacteristic
270#554C2×D1111yescharacteristic
271D4×Q8—111no—
272#501—221no—
273#500—111no—
274#500C2×D1111yescharacteristic
275#499—21no—
276#498—111no—
277#494—111no—
278#487—111no—
279#487—111no—
280#484—221no—
281#484—221no—
282#484—221no—
283#478—21no—
284#478—21no—
285#478—221no—
286#477—111no—
287#477—111no—
288#477—111no—
289#476—111no—
290#476—221no—
291#476C2×D1111yescharacteristic
292#476C2×D1111yescharacteristic
293#474—111no—
294#467—221no—
295#467—221no—
296#462—111no—
297#451—221no—
298#446—111no—
299C8×Q8C2×D1111yescharacteristic
300#442—221no—
301C4×Q16—111no—
302C4×D8—21no—
303C4×D8C2×D1111yescharacteristic
304C8×D4—111no—
305C8×D4—111no—
306C2×#107—221no—
307C2×#103—221no—
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—22no—
321C22×C11—41no—
322C22×C11—41no—
323C22×C11—41no—
324C22×C11—41no—
325C22×C11D4211yescharacteristic
326C4×C11—21no—
327C4×C11—41no—
328C4×C11—41no—
329C4×C11—41no—
330C4×C11—41no—
331C4×C11—81no—
332C4×C11—81no—
333C4×C11C22×Q1611yescharacteristic
334C4×C11#57511yescharacteristic
335C4×C11#57711yescharacteristic
336C4×C11#57811yescharacteristic
337Dic11—41no—
338Dic11—41no—
339Dic11—81no—
340Dic11—81no—
341C22×Q8—221no—
342C2×Q16—111no—
343C2×Q16—221no—
344C2×Q16—441no—
345C2×D8C22⋊D1111yescharacteristic
346C22×C8—221no—
347C22×C8—221no—
348C4⋊Q8—111no—
349C4⋊Q8—111no—
350C4⋊Q8—221no—
351C4⋊Q8C22×D1111yescharacteristic
352C4⋊Q8C22×D1111yescharacteristic
353#125—21no—
354#125—21no—
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×Q8—111no—
365C4×Q8C22×D1111yescharacteristic
366C4×D4—21no—
367C4×D4—21no—
368C4×D4—221no—
369C4×D4—221no—
370C4×D4C22×D1111yescharacteristic
371C4×D4C22×D1111yescharacteristic
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—221no—
375#107—21no—
376#107—21no—
377#107—111no—
378#107—221no—
379#107—221no—
380#107—221no—
381#107—221no—
382#107—221no—
383#107—221no—
384#107C22⋊D1111yescharacteristic
385#106—21no—
386#106—21no—
387#106—221no—
388#106—221no—
389#106—221no—
390C4⋊C8—21no—
391C4⋊C8—111no—
392C4⋊C8—111no—
393C4⋊C8—111no—
394C4⋊C8—221no—
395C4⋊C8C22×D1111yescharacteristic
396#103—111no—
397#103—111no—
398#103—221no—
399#103—221no—
400#103—221no—
401#103—221no—
402#103—221no—
403#103—221no—
404#103—441no—
405#102—21no—
406#102—21no—
407#102—221no—
408#102—221no—
409#102C22⋊D1111yescharacteristic
410#102C22⋊D1111yescharacteristic
411C22⋊C8—221no—
412C22⋊C8—221no—
413#97—221no—
414C4×C8—21no—
415C4×C8—111no—
416C4×C8—111no—
417C4×C8C22×D1111yescharacteristic
418C2×C11—42no—
419C2×C11—42no—
420C2×C11#326711yescharacteristic
421C2×C11D4×Q1611yescharacteristic
422C2×C11#328811yescharacteristic
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—111no—
426C2×Q8—221no—
427C2×Q8—221no—
428C2×Q8—441no—
429C2×Q8—442no—
430C2×Q8—881no—
431C2×Q8D4×D1111yescharacteristic
432C2×D4C2×C22⋊D1111yescharacteristic
433C2×D4C2×C22⋊D1111yescharacteristic
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—441no—
439C22×C4—441no—
440Q16—441no—
441Q16—881no—
442Q16—882no—
443D8#432614yescomplemented
444C2×C8—21no—
445C2×C8—111no—
446C2×C8—111no—
447C2×C8—221no—
448C2×C8—221no—
449C2×C8—221no—
450C2×C8—221no—
451C2×C8—442no—
452C2×C8—881no—
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—41no—
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—221no—
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—21no—
478C22⋊C4—41no—
479C22⋊C4—41no—
480C22⋊C4—441no—
481C22⋊C4—441no—
482C42—21no—
483C42—221no—
484C42C23×D1111yescharacteristic
485C11#1981411yescharacteristic, complemented, Sylow
486C23—21no—
487C23—21no—
488Q8—21no—
489Q8—21no—
490Q8—81no—
491Q8—81no—
492Q8—221no—
493Q8—221no—
494Q8—441no—
495Q8—441no—
496Q8—881no—
497Q8—882no—
498D4—21no—
499D4—21no—
500D4C2×#432612yes—
501D4C2×#432612yes—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—161no—
513C2×C4—161no—
514C2×C4—221no—
515C2×C4—221no—
516C2×C4—441no—
517C2×C4—441no—
518C2×C4—882no—
519C2×C4—1761no—
520C2×C4C2×D4×D1111yescharacteristic
521C2×C4#6703711yescharacteristic
522C2×C4C22×C22⋊D1111yescharacteristic
523C8—21no—
524C8—41no—
525C8—221no—
526C8—221no—
527C8—441no—
528C8—441no—
529C8—441no—
530C8—441no—
531C8C2×#432612yes—
532C22—22no—
533C22—22no—
534C22—41no—
535C22—41no—
536C22—41no—
537C22—41no—
538C22D4×C22⋊D1111yescharacteristic
539C4—21no—
540C4—41no—
541C4—41no—
542C4—41no—
543C4—41no—
544C4—81no—
545C4—81no—
546C4—441no—
547C4—441no—
548C4—881no—
549C4—881no—
550C4#1062329911yescharacteristic
551C4#1062330111yescharacteristic
552C4C22×#432611yescharacteristic
553C4#1062336911yescharacteristic
554C2—42no—
555C2—42no—
556C2#1308014111yescharacteristic
557C2D4×#432611yescharacteristic
558C2#1308038011yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3380C2
socleC22×C11D42
prime radicalC2×C11×D8D4
hypercenter#3380D11
hypocenterC11#19814
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #3380

Complements

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

NH ≅ G/Ntype
2. #13081004C2semidirect
3. #13080486C2semidirect
4. #13068294C2semidirect
5. #13068141C2semidirect
6. #13068069C2semidirect
7. #13068013C2semidirect
8. #13067998C2semidirect
9. #13067830C2semidirect
10. #13067780C2semidirect
11. #13067750C2semidirect
12. #13067748C2semidirect
13. #13067466C2semidirect
162. C11×D8Q16semidirect
443. D8#4326semidirect
485. C11#19814semidirect

Maximal subgroups

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

subgroupindex
#130815132
#130810042
#130804862
#130682942
#130681412
#130680692
#130680132
#130679982
#130678302
#130677802
#130677502
#130677482
#130674662
#130674402
C11×#33802
#1981411