Finite Group Databasebeta

← #14730999

Subgroups — #14730999

Order 2816.

1282 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
1#13079734C211yesmaximal, characteristic, complemented
2C2×#10622683C211yesmaximal, characteristic, complemented
3#13078103C211yesmaximal, characteristic, complemented
4#13067809C214yesmaximal, complemented
5#13067795C214yesmaximal, complemented
6#13067284C211yesmaximal, characteristic, complemented
7#13067067C211yesmaximal, characteristic, complemented
8#13066998C211yesmaximal, characteristic, complemented
9C11×#3498C211yesmaximal, characteristic
10C2×C11×H(5,𝔽2)—21no—
11C11×#550—21no—
12C11×#550C2212yes—
13D42×C11—22no—
14D42×C11—22no—
15D42×C11—21no—
16D42×C11C2212yes—
17C11×#535—22no—
18C11×#535—21no—
19C11×#532—21no—
20C11×#532C2211yescharacteristic
21C2×C11×#127—21no—
22C2×C11×#127C2211yescharacteristic
23C4×C11×#41C2211yescharacteristic
24C2×#67004—21no—
25C2×#66922C2211yescharacteristic, complemented
26C2×#66896—22no—
27#10622691—21no—
28#10622683—22no—
29#10622683—21no—
30#10622683C2214yescomplemented
31#10622646—22no—
32#10622644—21no—
33#10622644C2212yescomplemented
34#10622632—21no—
35#10622632C2212yescomplemented
36#10622620C2214yescomplemented
37#10622617—21no—
38#10622538C2211yescharacteristic, complemented
39#10622537C2211yescharacteristic, complemented
40C2×C4×C11⋊C8C2211yescharacteristic, complemented
41#10622182C2214yescomplemented
42Q8⋊(C11⋊C8)C2212yescomplemented
43D4⋊(C11⋊C8)C2212yescomplemented
44D4⋊(C11⋊C8)C2214yescomplemented
45C11×H(5,𝔽2)—44no—
46C11×H(5,𝔽2)—44no—
47C2×C11×#41—22no—
48C2×C11×#41—22no—
49C2×C11×#41—21no—
50C2×C11×#41D411yescharacteristic
51C22×D4×C11—22no—
52C22×D4×C11—24no—
53C22×D4×C11—22no—
54C22×D4×C11—22no—
55C22×D4×C11—22no—
56C22×D4×C11—21no—
57C22×D4×C11—21no—
58C22×D4×C11D412yes—
59C22×Dic22—21no—
60C11×C4⋊Q8D411yescharacteristic
61C11×#127—22no—
62C11×#127—22no—
63C11×#127—22no—
64C11×#127—21no—
65C11×#127—21no—
66C11×#127D411yescharacteristic
67C11×#127D412yes—
68C11×#127C2312yes—
69C11×#124—22no—
70C11×#124—21no—
71C11×#121—22no—
72C11×#121—24no—
73C11×#121—24no—
74C11×#121—21no—
75C11×#121—22no—
76C11×#121—22no—
77C11×#121—22no—
78C11×#121D412yes—
79C11×#120—24no—
80C11×#120—24no—
81C11×#120—24no—
82C4×Q8×C11D411yescharacteristic
83C4×Q8×C11C2311yescharacteristic
84C4×D4×C11—22no—
85C4×D4×C11—21no—
86C4×D4×C11—21no—
87C4×D4×C11—22no—
88C4×D4×C11—21no—
89C4×D4×C11D411yescharacteristic
90C4×D4×C11C2311yescharacteristic
91C4×D4×C11C2312yes—
92C11×#117—21no—
93C11×#117D411yescharacteristic
94C2×C42×C11—21no—
95C2×C42×C11C2311yescharacteristic
96#67004—44no—
97C2×#4326—22no—
98C2×#4324—22no—
99C2×C4⋊Dic11—21no—
100C2×C4⋊Dic11—21no—
101C2×#4318—21no—
102C22×C11⋊C8—21no—
103#66922—21no—
104#66922—21no—
105#66922—21no—
106#66922C2312yes—
107#66896—28no—
108#66896—24no—
109C22⋊(C11⋊C8)—21no—
110#66874—22no—
111#66874—22no—
112#66871—24no—
113C4⋊(C11⋊C8)—21no—
114C4⋊(C11⋊C8)C2312yes—
115C4⋊(C11⋊C8)C2312yes—
116C4×C11⋊C8—21no—
117C4×C11⋊C8—21no—
118C4×C11⋊C8C2312yes—
119#18630—111nomaximal, Sylow
120C24×C11—24no—
121C24×C11—22no—
122C11×#41—22no—
123C11×#41—48no—
124C11×#41—44no—
125C11×#41—44no—
126C11×#41—42no—
127C11×#41—42no—
128C11×#41D814yes—
129C2×Q8×C11—21no—
130C2×Q8×C11C2×D411yescharacteristic
131C2×D4×C11—21no—
132C2×D4×C11—24no—
133C2×D4×C11—24no—
134C2×D4×C11—22no—
135C2×D4×C11—24no—
136C2×D4×C11—24no—
137C2×D4×C11—22no—
138C2×D4×C11—21no—
139C2×D4×C11—22no—
140C2×D4×C11—21no—
141C2×D4×C11—22no—
142C2×D4×C11—22no—
143C2×D4×C11—22no—
144C2×D4×C11—48no—
145C2×D4×C11—44no—
146C2×D4×C11—416no—
147C2×D4×C11—44no—
148C2×D4×C11—44no—
149C2×D4×C11—42no—
150C2×D4×C11—42no—
151C2×D4×C11—82no—
152C2×D4×C11—84no—
153C2×D4×C11—84no—
154C2×D4×C11C2×D412yes—
155C2×D4×C11C2×D411yescharacteristic
156C2×D4×C11C2×D414yes—
157C22×C4×C11—21no—
158C22×C4×C11—24no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—22no—
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2×D411yescharacteristic
165C22×Dic11—41no—
166C2×Dic22—22no—
167C2×Dic22—41no—
168C2×Dic22—42no—
169C2×Dic22—42no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4C2×D412yes—
174C11×C4⋊C4C2×D411yescharacteristic
175C11×C4⋊C4C2×D411yescharacteristic
176C11×C22⋊C4—24no—
177C11×C22⋊C4—24no—
178C11×C22⋊C4—21no—
179C11×C22⋊C4—21no—
180C11×C22⋊C4—22no—
181C11×C22⋊C4—21no—
182C11×C22⋊C4—22no—
183C42×C11—21no—
184C42×C11—21no—
185C42×C11—21no—
186C42×C11C2×D411yescharacteristic
187C42×C11C2×D411yescharacteristic
188C42×C11C2×D411yescharacteristic
189C42×C11C2411yescharacteristic
190#4326—44no—
191#4324—44no—
192C4⋊Dic11—22no—
193C4⋊Dic11—22no—
194C4⋊Dic11—41no—
195C4⋊Dic11—41no—
196#4318—42no—
197C2×C11⋊C8—22no—
198C2×C11⋊C8—22no—
199C2×C11⋊C8—22no—
200C2×C11⋊C8—42no—
201#3498D1111yescharacteristic
202#3226—111no—
203C2×#486—111no—
204#3039—111no—
205#1641—114no—
206#1639—114no—
207#1545—111no—
208#1492—111no—
209#1476—111no—
210C23×C11—21no—
211C23×C11—22no—
212C23×C11—24no—
213C23×C11—48no—
214C23×C11—44no—
215C23×C11—82no—
216C23×C11—82no—
217C23×C11—84no—
218C23×C11—84no—
219C23×C11#12011yescharacteristic
220Q8×C11—21no—
221Q8×C11—42no—
222Q8×C11C2×D812yes—
223D4×C11—24no—
224D4×C11—21no—
225D4×C11—24no—
226D4×C11—44no—
227D4×C11—48no—
228D4×C11—48no—
229D4×C11—44no—
230D4×C11—42no—
231D4×C11—42no—
232D4×C11—44no—
233D4×C11—42no—
234D4×C11—44no—
235D4×C11—44no—
236D4×C11—42no—
237D4×C11—82no—
238D4×C11—84no—
239D4×C11—84no—
240D4×C11C2×D812yes—
241C2×C4×C11—21no—
242C2×C4×C11—22no—
243C2×C4×C11—24no—
244C2×C4×C11—22no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—22no—
248C2×C4×C11—48no—
249C2×C4×C11—42no—
250C2×C4×C11—42no—
251C2×C4×C11—42no—
252C2×C4×C11—42no—
253C2×C4×C11#12011yescharacteristic
254C2×C4×C11#12011yescharacteristic
255C2×C4×C11#12011yescharacteristic
256C2×C4×C11C2×D812yes—
257C2×C4×C11AGL(1,ℤ/8)12yes—
258C2×C4×C11C22×D411yescharacteristic
259C2×C4×C11C22×D411yescharacteristic
260C2×C4×C11C22×D411yescharacteristic
261C2×Dic11—42no—
262C2×Dic11—82no—
263Dic22—42no—
264Dic22—42no—
265Dic22—82no—
266C11⋊C8—42no—
267C11⋊C8—42no—
268C11⋊C8—42no—
269C2×H(5,𝔽2)—21no—
270C2×#137—221no—
271#550—21no—
272#550C2×D1112yes—
273D42—22no—
274D42—22no—
275D42—21no—
276D42C2×D1112yes—
277#535—22no—
278#535—21no—
279#532—21no—
280#532C2×D1111yescharacteristic
281C2×C4⋊Q8—111no—
282C2×#127—21no—
283C2×#127C2×D1111yescharacteristic
284C4×#41C2×D1111yescharacteristic
285#500—221no—
286#486—114no—
287#486—222no—
288#486—221no—
289#480—222no—
290#474—114no—
291#462—112no—
292#462—221no—
293#461—112no—
294#461—221no—
295#431—111no—
296#423—111no—
297#419—221no—
298C2×#102—222no—
299C2×C4×C8—111no—
300#331—114no—
301Q8⋊C8—112no—
302D4⋊C8—112no—
303D4⋊C8—114no—
304C22×C11—21no—
305C22×C11—21no—
306C22×C11—22no—
307C22×C11—41no—
308C22×C11—41no—
309C22×C11—44no—
310C22×C11—42no—
311C22×C11—42no—
312C22×C11—44no—
313C22×C11—44no—
314C22×C11—42no—
315C22×C11—164no—
316C22×C11—168no—
317C22×C11#44712yes—
318C22×C11C2×#12011yescharacteristic
319C4×C11—22no—
320C4×C11—21no—
321C4×C11—21no—
322C4×C11—42no—
323C4×C11—41no—
324C4×C11—41no—
325C4×C11#44712yes—
326C4×C11#45512yes—
327C4×C11C22×D811yescharacteristic
328C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
329C4×C11#57712yes—
330Dic11—82no—
331H(5,𝔽2)—44no—
332H(5,𝔽2)—44no—
333C2×#41—22no—
334C2×#41—22no—
335C2×#41—21no—
336C2×#41C22⋊D1111yescharacteristic
337C22×Q8—221no—
338C22×D4—22no—
339C22×D4—24no—
340C22×D4—22no—
341C22×D4—22no—
342C22×D4—22no—
343C22×D4—21no—
344C22×D4—21no—
345C22×D4C22⋊D1112yes—
346#137—444no—
347C2×Q16—222no—
348C2×SD16—222no—
349C2×M16—221no—
350C22×C8—221no—
351C4⋊Q8—112no—
352C4⋊Q8—221no—
353C4⋊Q8—221no—
354C4⋊Q8—221no—
355C4⋊Q8C22⋊D1111yescharacteristic
356#127—22no—
357#127—22no—
358#127—22no—
359#127—21no—
360#127—21no—
361#127C22⋊D1111yescharacteristic
362#127C22⋊D1112yes—
363#127C22×D1112yes—
364#124—22no—
365#124—21no—
366#121—22no—
367#121—24no—
368#121—24no—
369#121—21no—
370#121—22no—
371#121—22no—
372#121—22no—
373#121C22⋊D1112yes—
374#120—24no—
375#120—24no—
376#120—24no—
377C4×Q8C22⋊D1111yescharacteristic
378C4×Q8C22×D1111yescharacteristic
379C4×D4—22no—
380C4×D4—21no—
381C4×D4—21no—
382C4×D4—22no—
383C4×D4—21no—
384C4×D4C22⋊D1111yescharacteristic
385C4×D4C22×D1111yescharacteristic
386C4×D4C22×D1112yes—
387#117—21no—
388#117C22⋊D1111yescharacteristic
389C2×C4⋊C4—221no—
390C2×C4⋊C4—221no—
391C2×C42—21no—
392C2×C42C22×D1111yescharacteristic
393#107—224no—
394C4⋊C8—112no—
395C4⋊C8—112no—
396C4⋊C8—221no—
397#103—222no—
398#103—222no—
399#102—228no—
400#102—224no—
401C22⋊C8—221no—
402C4×C8—112no—
403C4×C8—221no—
404C4×C8—221no—
405C2×C11—22no—
406C2×C11—42no—
407C2×C11—82no—
408C2×C11—84no—
409C2×C11C2×#44711yescharacteristic
410C2×C11#300911yescharacteristic
411C2×C11C2×#45511yescharacteristic
412C24—24no—
413C24—22no—
414#41—22no—
415#41—48no—
416#41—44no—
417#41—44no—
418#41—42no—
419#41—42no—
420#41#432314yes—
421C2×Q8—21no—
422C2×Q8—222no—
423C2×Q8—441no—
424C2×Q8—442no—
425C2×Q8—442no—
426C2×Q8C2×C22⋊D1111yescharacteristic
427C2×D4—21no—
428C2×D4—24no—
429C2×D4—24no—
430C2×D4—22no—
431C2×D4—24no—
432C2×D4—24no—
433C2×D4—22no—
434C2×D4—21no—
435C2×D4—22no—
436C2×D4—21no—
437C2×D4—22no—
438C2×D4—22no—
439C2×D4—22no—
440C2×D4—48no—
441C2×D4—44no—
442C2×D4—416no—
443C2×D4—44no—
444C2×D4—44no—
445C2×D4—42no—
446C2×D4—42no—
447C2×D4—82no—
448C2×D4—84no—
449C2×D4—84no—
450C2×D4C2×C22⋊D1112yes—
451C2×D4C2×C22⋊D1111yescharacteristic
452C2×D4C2×C22⋊D1114yes—
453C22×C4—21no—
454C22×C4—24no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—441no—
459C22×C4C2×C22⋊D1111yescharacteristic
460C22×C4C2×C22⋊D1111yescharacteristic
461C22×C4C2×C22⋊D1111yescharacteristic
462Q16—444no—
463SD16—444no—
464M16—442no—
465C2×C8—222no—
466C2×C8—222no—
467C2×C8—222no—
468C2×C8—442no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—222no—
473C4⋊C4—222no—
474C4⋊C4—441no—
475C4⋊C4—441no—
476C4⋊C4C2×C22⋊D1111yescharacteristic
477C4⋊C4C2×C22⋊D1111yescharacteristic
478C4⋊C4C2×C22⋊D1112yes—
479C22⋊C4—24no—
480C22⋊C4—24no—
481C22⋊C4—21no—
482C22⋊C4—21no—
483C22⋊C4—22no—
484C22⋊C4—21no—
485C22⋊C4—22no—
486C42—21no—
487C42—21no—
488C42—21no—
489C42C2×C22⋊D1111yescharacteristic
490C42C2×C22⋊D1111yescharacteristic
491C42C2×C22⋊D1111yescharacteristic
492C42C23×D1111yescharacteristic
493C11#1863011yescharacteristic, complemented, Sylow
494C23—21no—
495C23—22no—
496C23—24no—
497C23—48no—
498C23—44no—
499C23—82no—
500C23—82no—
501C23—84no—
502C23—84no—
503C23#6700611yescharacteristic
504Q8—21no—
505Q8—42no—
506Q8—442no—
507Q8—442no—
508Q8—882no—
509Q8C2×#432312yes—
510D4—24no—
511D4—21no—
512D4—24no—
513D4—44no—
514D4—48no—
515D4—48no—
516D4—44no—
517D4—42no—
518D4—42no—
519D4—42no—
520D4—44no—
521D4—44no—
522D4—42no—
523D4—44no—
524D4—82no—
525D4—84no—
526D4—84no—
527D4C2×#432312yes—
528C2×C4—21no—
529C2×C4—24no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—22no—
535C2×C4—48no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—442no—
541C2×C4—882no—
542C2×C4C2×#432312yes—
543C2×C4#6698512yes—
544C2×C4#6700611yescharacteristic
545C2×C4#6700611yescharacteristic
546C2×C4#6700611yescharacteristic
547C2×C4C22×C22⋊D1111yescharacteristic
548C2×C4C22×C22⋊D1111yescharacteristic
549C2×C4C22×C22⋊D1111yescharacteristic
550C8—442no—
551C8—442no—
552C8—442no—
553C22—21no—
554C22—21no—
555C22—22no—
556C22—41no—
557C22—41no—
558C22—44no—
559C22—42no—
560C22—42no—
561C22—44no—
562C22—44no—
563C22—42no—
564C22—164no—
565C22—168no—
566C22#1062283012yes—
567C22C2×#6700611yescharacteristic
568C4—22no—
569C4—21no—
570C4—21no—
571C4—42no—
572C4—41no—
573C4—41no—
574C4—882no—
575C4#1062283012yes—
576C4#1062285512yes—
577C4C22×#432311yescharacteristic
578C4C2×#6698511yescharacteristic
579C4#1062336712yes—
580C2—22no—
581C2—42no—
582C2—82no—
583C2—84no—
584C2C2×#1062283011yescharacteristic
585C2#1307789311yescharacteristic
586C2C2×#1062285511yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC11×#3498C2
socleC22×C11C2×#120
hypercenter#3498D11
hypocenterC11#18630
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3498

Complements

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

NH ≅ G/Ntype
1. #13079734C2semidirect
2. C2×#10622683C2semidirect
3. #13078103C2semidirect
4. #13067809C2semidirect
5. #13067795C2semidirect
6. #13067284C2semidirect
7. #13067067C2semidirect
8. #13066998C2semidirect
25. C2×#66922C22semidirect
30. #10622683C22semidirect
33. #10622644C22semidirect
35. #10622632C22semidirect
36. #10622620C22semidirect
38. #10622538C22semidirect
39. #10622537C22semidirect
40. C2×C4×C11⋊C8C22semidirect
41. #10622182C22semidirect
42. Q8⋊(C11⋊C8)C22semidirect
43. D4⋊(C11⋊C8)C22semidirect
44. D4⋊(C11⋊C8)C22semidirect
493. C11#18630semidirect

Maximal subgroups

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

subgroupindex
#130797342
C2×#106226832
#130781032
#130678092
#130677952
#130672842
#130670672
#130669982
C11×#34982
#1863011