Finite Group Databasebeta

← #14731008

Subgroups — #14731008

Order 2816.

1262 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079538C211yesmaximal, characteristic, complemented
2C2×#10622683C211yesmaximal, characteristic, complemented
3#13078431C211yesmaximal, characteristic, complemented
4#13067816C214yesmaximal, 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×#66922C2211yescharacteristic, complemented
25#10622845—21no—
26C2×#66896—22no—
27#10622706—21no—
28#10622689—21no—
29#10622683—22no—
30#10622683C2214yescomplemented
31#10622653—22no—
32#10622634—21no—
33#10622633C2212yescomplemented
34#10622632C2214yescomplemented
35#10622621—21no—
36#10622620C2212yescomplemented
37#10622608—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
96C2×#4324—24no—
97C2×C4⋊Dic11—21no—
98C2×C4⋊Dic11—21no—
99C2×#4318—21no—
100C22×C11⋊C8—21no—
101#66922—21no—
102#66922—21no—
103#66922—21no—
104#66922C2312yes—
105#66899—22no—
106#66896—28no—
107#66896—22no—
108C22⋊(C11⋊C8)—21no—
109#66874—24no—
110#66872—22no—
111#66871—22no—
112C4⋊(C11⋊C8)—21no—
113C4⋊(C11⋊C8)C2312yes—
114C4⋊(C11⋊C8)C2312yes—
115C4×C11⋊C8—21no—
116C4×C11⋊C8—21no—
117C4×C11⋊C8C2312yes—
118#18631—111nomaximal, Sylow
119C24×C11—24no—
120C24×C11—22no—
121C11×#41—22no—
122C11×#41—48no—
123C11×#41—44no—
124C11×#41—44no—
125C11×#41—42no—
126C11×#41—42no—
127C11×#41SD1614yescomplemented
128C2×Q8×C11—21no—
129C2×Q8×C11C2×D411yescharacteristic
130C2×D4×C11—21no—
131C2×D4×C11—24no—
132C2×D4×C11—24no—
133C2×D4×C11—22no—
134C2×D4×C11—24no—
135C2×D4×C11—24no—
136C2×D4×C11—22no—
137C2×D4×C11—21no—
138C2×D4×C11—22no—
139C2×D4×C11—21no—
140C2×D4×C11—22no—
141C2×D4×C11—22no—
142C2×D4×C11—22no—
143C2×D4×C11—48no—
144C2×D4×C11—44no—
145C2×D4×C11—416no—
146C2×D4×C11—44no—
147C2×D4×C11—44no—
148C2×D4×C11—42no—
149C2×D4×C11—42no—
150C2×D4×C11—82no—
151C2×D4×C11—84no—
152C2×D4×C11—84no—
153C2×D4×C11C2×D412yes—
154C2×D4×C11C2×D411yescharacteristic
155C2×D4×C11C2×D414yes—
156C22×C4×C11—21no—
157C22×C4×C11—24no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—22no—
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D411yescharacteristic
164C22×Dic11—41no—
165C2×Dic22—22no—
166C2×Dic22—41no—
167C2×Dic22—82no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4C2×D411yescharacteristic
172C11×C4⋊C4C2×D411yescharacteristic
173C11×C4⋊C4C2×D412yes—
174C11×C22⋊C4—24no—
175C11×C22⋊C4—24no—
176C11×C22⋊C4—21no—
177C11×C22⋊C4—21no—
178C11×C22⋊C4—22no—
179C11×C22⋊C4—21no—
180C11×C22⋊C4—22no—
181C42×C11—21no—
182C42×C11—21no—
183C42×C11—21no—
184C42×C11C2×D411yescharacteristic
185C42×C11C2×D411yescharacteristic
186C42×C11C2×D411yescharacteristic
187C42×C11C2411yescharacteristic
188#4324—84no—
189C4⋊Dic11—22no—
190C4⋊Dic11—22no—
191C4⋊Dic11—41no—
192C4⋊Dic11—41no—
193#4318—42no—
194C2×C11⋊C8—22no—
195C2×C11⋊C8—22no—
196C2×C11⋊C8—22no—
197C2×C11⋊C8—42no—
198#3498D1111yescharacteristic
199#3206—111no—
200C2×#486—111no—
201#3079—111no—
202#1642—114no—
203#1639—114no—
204#1545—111no—
205#1492—111no—
206#1476—111no—
207C23×C11—21no—
208C23×C11—22no—
209C23×C11—24no—
210C23×C11—48no—
211C23×C11—44no—
212C23×C11—82no—
213C23×C11—82no—
214C23×C11—84no—
215C23×C11—84no—
216C23×C11#12011yescharacteristic
217Q8×C11—21no—
218Q8×C11—42no—
219Q8×C11C2×SD1612yes—
220D4×C11—24no—
221D4×C11—21no—
222D4×C11—24no—
223D4×C11—44no—
224D4×C11—48no—
225D4×C11—48no—
226D4×C11—44no—
227D4×C11—42no—
228D4×C11—42no—
229D4×C11—44no—
230D4×C11—42no—
231D4×C11—44no—
232D4×C11—44no—
233D4×C11—42no—
234D4×C11—82no—
235D4×C11—84no—
236D4×C11—84no—
237D4×C11C2×SD1612yes—
238C2×C4×C11—21no—
239C2×C4×C11—22no—
240C2×C4×C11—24no—
241C2×C4×C11—22no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—22no—
245C2×C4×C11—48no—
246C2×C4×C11—42no—
247C2×C4×C11—42no—
248C2×C4×C11—42no—
249C2×C4×C11—42no—
250C2×C4×C11#12011yescharacteristic
251C2×C4×C11#12011yescharacteristic
252C2×C4×C11#12011yescharacteristic
253C2×C4×C11C2×SD1612yes—
254C2×C4×C11AGL(1,ℤ/8)12yes—
255C2×C4×C11C22×D411yescharacteristic
256C2×C4×C11C22×D411yescharacteristic
257C2×C4×C11C22×D411yescharacteristic
258C2×Dic11—42no—
259C2×Dic11—82no—
260Dic22—44no—
261Dic22—82no—
262C11⋊C8—42no—
263C11⋊C8—42no—
264C11⋊C8—42no—
265C2×H(5,𝔽2)—21no—
266#550—21no—
267#550C2×D1112yes—
268D42—22no—
269D42—22no—
270D42—21no—
271D42C2×D1112yes—
272#535—22no—
273#535—21no—
274#532—21no—
275#532C2×D1111yescharacteristic
276C2×C4⋊Q8—111no—
277C2×#127—21no—
278C2×#127C2×D1111yescharacteristic
279C4×#41C2×D1111yescharacteristic
280#492—221no—
281#487—221no—
282#486—114no—
283#486—222no—
284#477—221no—
285#476—221no—
286#475—112no—
287#474—112no—
288#461—114no—
289#448—222no—
290#431—111no—
291#428—221no—
292#423—111no—
293#417—221no—
294C2×#102—222no—
295C2×C4×C8—111no—
296#331—114no—
297Q8⋊C8—112no—
298D4⋊C8—112no—
299D4⋊C8—114no—
300C22×C11—21no—
301C22×C11—21no—
302C22×C11—22no—
303C22×C11—41no—
304C22×C11—41no—
305C22×C11—44no—
306C22×C11—42no—
307C22×C11—42no—
308C22×C11—44no—
309C22×C11—44no—
310C22×C11—42no—
311C22×C11—164no—
312C22×C11—168no—
313C22×C11#45012yes—
314C22×C11C2×#12011yescharacteristic
315C4×C11—22no—
316C4×C11—21no—
317C4×C11—21no—
318C4×C11—42no—
319C4×C11—41no—
320C4×C11—41no—
321C4×C11#45012yes—
322C4×C11#45512yes—
323C4×C11C22×SD1611yescharacteristic
324C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
325C4×C11#57612yes—
326Dic11—82no—
327H(5,𝔽2)—44no—
328H(5,𝔽2)—44no—
329C2×#41—22no—
330C2×#41—22no—
331C2×#41—21no—
332C2×#41C22⋊D1111yescharacteristic
333C22×Q8—221no—
334C22×D4—22no—
335C22×D4—24no—
336C22×D4—22no—
337C22×D4—22no—
338C22×D4—22no—
339C22×D4—21no—
340C22×D4—21no—
341C22×D4C22⋊D1112yes—
342C2×SD16—224no—
343C2×M16—221no—
344C22×C8—221no—
345C4⋊Q8—112no—
346C4⋊Q8—221no—
347C4⋊Q8—221no—
348C4⋊Q8—221no—
349C4⋊Q8C22⋊D1111yescharacteristic
350#127—22no—
351#127—22no—
352#127—22no—
353#127—21no—
354#127—21no—
355#127C22⋊D1111yescharacteristic
356#127C22⋊D1112yes—
357#127C22×D1112yes—
358#124—22no—
359#124—21no—
360#121—22no—
361#121—24no—
362#121—24no—
363#121—21no—
364#121—22no—
365#121—22no—
366#121—22no—
367#121C22⋊D1112yes—
368#120—24no—
369#120—24no—
370#120—24no—
371C4×Q8C22⋊D1111yescharacteristic
372C4×Q8C22×D1111yescharacteristic
373C4×D4—22no—
374C4×D4—21no—
375C4×D4—21no—
376C4×D4—22no—
377C4×D4—21no—
378C4×D4C22⋊D1111yescharacteristic
379C4×D4C22×D1111yescharacteristic
380C4×D4C22×D1112yes—
381#117—21no—
382#117C22⋊D1111yescharacteristic
383C2×C4⋊C4—221no—
384C2×C4⋊C4—221no—
385C2×C42—21no—
386C2×C42C22×D1111yescharacteristic
387#107—222no—
388#106—222no—
389C4⋊C8—112no—
390C4⋊C8—112no—
391C4⋊C8—221no—
392#103—222no—
393#103—224no—
394#102—228no—
395#102—222no—
396C22⋊C8—221no—
397C4×C8—112no—
398C4×C8—221no—
399C4×C8—221no—
400C2×C11—22no—
401C2×C11—42no—
402C2×C11—82no—
403C2×C11—84no—
404C2×C11C2×#45011yescharacteristic
405C2×C11#300811yescharacteristic
406C2×C11C2×#45511yescharacteristic
407C24—24no—
408C24—22no—
409#41—22no—
410#41—48no—
411#41—44no—
412#41—44no—
413#41—42no—
414#41—42no—
415#41#432414yescomplemented
416C2×Q8—21no—
417C2×Q8—222no—
418C2×Q8—441no—
419C2×Q8—882no—
420C2×Q8C2×C22⋊D1111yescharacteristic
421C2×D4—21no—
422C2×D4—24no—
423C2×D4—24no—
424C2×D4—22no—
425C2×D4—24no—
426C2×D4—24no—
427C2×D4—22no—
428C2×D4—21no—
429C2×D4—22no—
430C2×D4—21no—
431C2×D4—22no—
432C2×D4—22no—
433C2×D4—22no—
434C2×D4—48no—
435C2×D4—44no—
436C2×D4—416no—
437C2×D4—44no—
438C2×D4—44no—
439C2×D4—42no—
440C2×D4—42no—
441C2×D4—82no—
442C2×D4—84no—
443C2×D4—84no—
444C2×D4C2×C22⋊D1112yes—
445C2×D4C2×C22⋊D1111yescharacteristic
446C2×D4C2×C22⋊D1114yes—
447C22×C4—21no—
448C22×C4—24no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—22no—
452C22×C4—441no—
453C22×C4C2×C22⋊D1111yescharacteristic
454C22×C4C2×C22⋊D1111yescharacteristic
455C22×C4C2×C22⋊D1111yescharacteristic
456SD16—884no—
457M16—442no—
458C2×C8—222no—
459C2×C8—222no—
460C2×C8—222no—
461C2×C8—442no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—222no—
466C4⋊C4—222no—
467C4⋊C4—441no—
468C4⋊C4—441no—
469C4⋊C4C2×C22⋊D1112yes—
470C4⋊C4C2×C22⋊D1111yescharacteristic
471C4⋊C4C2×C22⋊D1111yescharacteristic
472C22⋊C4—24no—
473C22⋊C4—24no—
474C22⋊C4—21no—
475C22⋊C4—21no—
476C22⋊C4—22no—
477C22⋊C4—21no—
478C22⋊C4—22no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42C2×C22⋊D1111yescharacteristic
483C42C2×C22⋊D1111yescharacteristic
484C42C2×C22⋊D1111yescharacteristic
485C42C23×D1111yescharacteristic
486C11#1863111yescharacteristic, complemented, Sylow
487C23—21no—
488C23—22no—
489C23—24no—
490C23—48no—
491C23—44no—
492C23—82no—
493C23—82no—
494C23—84no—
495C23—84no—
496C23#6700611yescharacteristic
497Q8—21no—
498Q8—42no—
499Q8—444no—
500Q8—882no—
501Q8C2×#432412yes—
502D4—24no—
503D4—21no—
504D4—24no—
505D4—44no—
506D4—48no—
507D4—48no—
508D4—44no—
509D4—42no—
510D4—42no—
511D4—42no—
512D4—44no—
513D4—44no—
514D4—44no—
515D4—42no—
516D4—82no—
517D4—84no—
518D4—84no—
519D4C2×#432412yes—
520C2×C4—21no—
521C2×C4—24no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—22no—
527C2×C4—48no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—442no—
533C2×C4—882no—
534C2×C4#6698512yes—
535C2×C4C2×#432412yes—
536C2×C4#6700611yescharacteristic
537C2×C4#6700611yescharacteristic
538C2×C4#6700611yescharacteristic
539C2×C4C22×C22⋊D1111yescharacteristic
540C2×C4C22×C22⋊D1111yescharacteristic
541C2×C4C22×C22⋊D1111yescharacteristic
542C8—442no—
543C8—442no—
544C8—442no—
545C22—21no—
546C22—21no—
547C22—22no—
548C22—41no—
549C22—41no—
550C22—44no—
551C22—42no—
552C22—42no—
553C22—44no—
554C22—44no—
555C22—42no—
556C22—164no—
557C22—168no—
558C22#1062283112yes—
559C22C2×#6700611yescharacteristic
560C4—22no—
561C4—21no—
562C4—21no—
563C4—42no—
564C4—41no—
565C4—41no—
566C4—882no—
567C4#1062283112yes—
568C4#1062285512yes—
569C4C2×#6698511yescharacteristic
570C4C22×#432411yescharacteristic
571C4#1062336612yes—
572C2—22no—
573C2—42no—
574C2—82no—
575C2—84no—
576C2C2×#1062283111yescharacteristic
577C2#1307788411yescharacteristic
578C2C2×#1062285511yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC11×#3498C2
socleC22×C11C2×#120
hypercenter#3498D11
hypocenterC11#18631
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. #13079538C2semidirect
2. C2×#10622683C2semidirect
3. #13078431C2semidirect
4. #13067816C2semidirect
5. #13067795C2semidirect
6. #13067284C2semidirect
7. #13067067C2semidirect
8. #13066998C2semidirect
24. C2×#66922C22semidirect
30. #10622683C22semidirect
33. #10622633C22semidirect
34. #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
127. C11×#41SD16semidirect
415. #41#4324semidirect
486. C11#18631semidirect

Maximal subgroups

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

subgroupindex
#130795382
C2×#106226832
#130784312
#130678162
#130677952
#130672842
#130670672
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