Finite Group Databasebeta

← #25249932

Subgroups — #25249932

Order 11008.

696 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583333C211yesmaximal, characteristic
2#19143465C211yesmaximal, characteristic, complemented
3#19143442C211yesmaximal, characteristic, complemented
4#19136471C211yesmaximal, characteristic, complemented
5#19136469C211yesmaximal, characteristic, complemented
6#19136459C211yesmaximal, characteristic, complemented
7#19136458C211yesmaximal, characteristic, complemented
8#19136450C211yesmaximal, characteristic, complemented
9C4×#13063270C211yesmaximal, characteristic, complemented
10#19136439C211yesmaximal, characteristic, complemented
11#19136380C211yesmaximal, characteristic, complemented
12#19136299C211yesmaximal, characteristic, complemented
13#357×D43C211yesmaximal, characteristic, complemented
14#19136190C211yesmaximal, characteristic, complemented
15C4×D16×C43C211yesmaximal, characteristic, complemented
16C2×#13063344C2211yescharacteristic
17C2×D8×D43C2211yescharacteristic
18#14583378—21no—
19#14583371—21no—
20#14583333C418yescomplemented
21C2×#13063270C2211yescharacteristic
22C2×#13063269C2211yescharacteristic
23C2×#13063266C2211yescharacteristic
24C2×#13063264C2211yescharacteristic
25C2×C16×D43C2211yescharacteristic
26#14583009—21no—
27#14583008—21no—
28#14582999—21no—
29#14582996—21no—
30C4×Dic172C2211yescharacteristic, complemented
31#14582993C2211yescharacteristic, complemented
32C4×D344C2211yescharacteristic
33D8×Dic43C2211yescharacteristic
34D8×Dic43C2211yescharacteristic, complemented
35#14582981C2211yescharacteristic
36#14582936C2211yescharacteristic
37#107×D43C2211yescharacteristic
38#14582902—21no—
39#14582897—21no—
40#14582853C2211yescharacteristic
41#14582727C2211yescharacteristic, complemented
42#14582726C2211yescharacteristic, complemented
43#14582724C2211yescharacteristic, complemented
44#14582704C2211yescharacteristic, complemented
45#14582702C2211yescharacteristic, complemented
46#14582701C2211yescharacteristic
47#14582700C2211yescharacteristic
48#14582700C2211yescharacteristic, complemented
49#14582699C2211yescharacteristic
50#14582675C2211yescharacteristic, complemented
51#14582674C2211yescharacteristic, complemented
52C16×Dic43C2211yescharacteristic, complemented
53C2×D16×C43C2211yescharacteristic
54C4×D8×C43C2211yescharacteristic
55C4×D8×C43C2211yescharacteristic, complemented
56C43×#366C2211yescharacteristic, complemented
57C43×#357C2211yescharacteristic
58C43×#357C2211yescharacteristic, complemented
59C4×C16×C43C2211yescharacteristic, complemented
60C2×#10621900—21no—
61C2×D4×D43—21no—
62#13063344—22no—
63#13063344C2×C414yescomplemented
64C2×Dic172C2311yescharacteristic
65C2×#10621883—21no—
66C2×D344C2311yescharacteristic
67C2×#10621882—21no—
68D8×D43—22no—
69D8×D43C2×C414yescomplemented
70C2×#10621872D411yescharacteristic
71C2×C8×D43C2311yescharacteristic
72C4×Dic86—21no—
73#13063290—21no—
74C4×D172—21no—
75D4×Dic43—21no—
76D4×Dic43—21no—
77#13063287—21no—
78C4×C22⋊D43—41no—
79C4×C22⋊D43—41no—
80(C22⋊D43)⋊C4—41no—
81(C22⋊D43)⋊C4—41no—
82#13063283—21no—
83#13063282D411yescharacteristic
84#13063281—41no—
85C2×Dic43⋊C4—41no—
86C4⋊C4×D43—21no—
87C2×(C2×D43)⋊C4—41no—
88C22⋊C4×D43—41no—
89#13063270C2×C414yescomplemented
90#13063269C2×C414yescomplemented
91#13063266C2×C414yescomplemented
92#13063264C2×C414yescomplemented
93C2×C43⋊C16C2311yescharacteristic
94C2×C43⋊C16C2311yescharacteristic
95C16×D43—22no—
96#13063259C2311yescharacteristic
97#13063259C2311yescharacteristic
98#13063258—21no—
99#13063256—21no—
100#13063250—21no—
101#13063248—21no—
102#13063247—21no—
103#13063246—21no—
104#13063246—21no—
105#13063245—21no—
106#13063236D411yescharacteristic
107#13063235D411yescharacteristic
108C8×Dic43C2311yescharacteristic
109C2×D8×C43C2311yescharacteristic
110C2×D8×C43C2311yescharacteristic
111C4×D4×C43—21no—
112C4×D4×C43—21no—
113D16×C43C2×C414yescomplemented
114C2×C16×C43C2311yescharacteristic
115C2×C16×C43C2311yescharacteristic
116#107×C43C2311yescharacteristic
117#107×C43C2311yescharacteristic
118#102×C43—21no—
119#102×C43—21no—
120C4×C8×C43C2311yescharacteristic
121C23×D43—41no—
122C2×D4×C43—21no—
123C2×D4×C43—21no—
124C22×C4×C43—41no—
125C22×C4×C43—41no—
126C2×C22⋊D43—41no—
127C2×C22⋊D43—41no—
128C22×Dic43—41no—
129C22×Dic43—41no—
130C22×Dic43—41no—
131#10621900—24no—
132#10621900—42no—
133D4×D43—24no—
134D4×D43—42no—
135C2×D172—21no—
136C2×C4×D43—41no—
137C2×C4×D43—41no—
138C2×C4×D43—41no—
139C2×C4×D43C2×D411yescharacteristic
140C2×Dic86—21no—
141D8×C43—21no—
142D8×C43—21no—
143D8×C43C22×C412yes—
144D8×C43C22×C412yes—
145C2×C8×C43C2×D411yescharacteristic
146C2×C8×C43C2411yescharacteristic
147C4⋊C4×C43—21no—
148C4⋊C4×C43—21no—
149C22⋊C4×C43—41no—
150C22⋊C4×C43—41no—
151C42×C43C2×D411yescharacteristic
152C22⋊Dic43—41no—
153C22⋊Dic43—41no—
154#10621883—24no—
155#10621882—24no—
156(C2×D43)⋊C4—41no—
157(C2×D43)⋊C4—41no—
158(C2×D43)⋊C4—41no—
159(C2×D43)⋊C4D811yescharacteristic
160(C2×D43)⋊C4D811yescharacteristic
161C4⋊Dic43—21no—
162C4⋊Dic43—21no—
163Dic43⋊C4—41no—
164Dic43⋊C4—41no—
165Dic43⋊C4—41no—
166Dic43⋊C4D811yescharacteristic
167Dic43⋊C4D811yescharacteristic
168C4×Dic43—41no—
169C4×Dic43—41no—
170C4×Dic43—41no—
171C4×Dic43C2×D411yescharacteristic
172C2×C43⋊C8C2×D411yescharacteristic
173C2×C43⋊C8C2×D411yescharacteristic
174Dic172—21no—
175Dic172C22×C412yes—
176D344—21no—
177D344C22×C412yes—
178#10621872—22no—
179C8×D43C22×C412yes—
180C8×D43#4112yes—
181C16×C43—21no—
182C16×C43C22×C412yes—
183C43⋊C16—21no—
184C43⋊C16C22×C412yes—
185C23×C43—41no—
186C23×C43—41no—
187C22×D43—41no—
188C22×D43—44no—
189C22×D43—161no—
190C22×D43—161no—
191C22×D43C2×D811yescharacteristic
192D4×C43—22no—
193D4×C43—22no—
194D4×C43—41no—
195D4×C43—41no—
196C2×C4×C43—41no—
197C2×C4×C43—41no—
198C2×C4×C43—161no—
199C2×C4×C43—161no—
200C2×C4×C43C2×D811yescharacteristic
201C2×C4×C43C2×D811yescharacteristic
202C2×C4×C43C22×D411yescharacteristic
203C22⋊D43—44no—
204C22⋊D43—44no—
205C2×Dic43—41no—
206C2×Dic43—44no—
207C2×Dic43—41no—
208C2×Dic43—41no—
209C2×Dic43—161no—
210C2×Dic43—161no—
211C2×Dic43C2×D811yescharacteristic
212C2×Dic43C2×D811yescharacteristic
213C2×Dic43C2×D811yescharacteristic
214D172—22no—
215D172—41no—
216C4×D43—161no—
217C4×D43—161no—
218C4×D43—161no—
219C4×D43C4×D412yes—
220C4×D43#13512yes—
221Dic86—22no—
222Dic86—41no—
223C8×C43—21no—
224C8×C43C23×C411yescharacteristic
225C8×C43C2×#4111yescharacteristic
226C43⋊C8—21no—
227C43⋊C8C4×D412yes—
228#33454—431nomaximal, Sylow
229C22×C43—42no—
230C22×C43—42no—
231C22×C43—81no—
232C22×C43—81no—
233C22×C43—81no—
234C22×C43—81no—
235C22×C43C22×D811yescharacteristic
236C2×D43—21no—
237C2×D43—21no—
238C2×D43—42no—
239C2×D43—81no—
240C2×D43—81no—
241C2×D43—164no—
242C2×D43C4×D812yes—
243C4×C43—21no—
244C4×C43—21no—
245C4×C43—81no—
246C4×C43—81no—
247C4×C43C2×C4×D411yescharacteristic
248C4×C43C2×#13511yescharacteristic
249Dic43—21no—
250Dic43—21no—
251Dic43—42no—
252Dic43—81no—
253Dic43—81no—
254Dic43C4×D812yes—
255C2×#509—431no—
256#2951—431no—
257#2948—431no—
258#2177—431no—
259#2177—431no—
260#2175—431no—
261#2175—431no—
262C4×SD32—431no—
263C4×SD32—431no—
264C4×D16—431no—
265C4×D16D4311yescharacteristic, complemented
266#2159—431no—
267#2138—431no—
268C2×#357—431no—
269#2108—431no—
270C2×C43—82no—
271C2×C43—82no—
272C2×C43C2×C4×D811yescharacteristic
273C2×C43#341511yescharacteristic
274C2×C43#341611yescharacteristic
275D43—22no—
276D43—82no—
277C2×#135—431no—
278C22×D8—431no—
279#520—861no—
280#518—861no—
281#509—438no—
282C2×SD32—431no—
283C2×SD32—431no—
284C2×D16—431no—
285C2×D16C2×D4311yescharacteristic
286C2×M32—431no—
287C22×C16—431no—
288#442—861no—
289#442—861no—
290#440—861no—
291#440—861no—
292C4×Q16—431no—
293C4×Q16—431no—
294C4×D8—431no—
295C4×D8—431no—
296C4×D8—431no—
297C4×D8—431no—
298C4×D8C2×D4311yescharacteristic
299C4×D8C2×D4311yescharacteristic, complemented
300#427—431no—
301C2×#107—431no—
302#418—861no—
303#417—861no—
304#405—431no—
305#367—431no—
306#367—431no—
307#366—431no—
308#366C2×D4311yescharacteristic, complemented
309#358—431no—
310#358—431no—
311#357—431no—
312#357—431no—
313#357—431no—
314#357—431no—
315#357C2×D4311yescharacteristic
316#357C2×D4311yescharacteristic, complemented
317#346—431no—
318#346—431no—
319C4×C16—431no—
320C4×C16C2×D4311yescharacteristic, complemented
321C43#3345411yescharacteristic, complemented, Sylow
322C2×#41—861no—
323C22×D4—861no—
324#135—434no—
325#135—862no—
326C2×Q16—431no—
327C2×SD16—861no—
328C2×D8—434no—
329C2×D8—431no—
330C2×D8—862no—
331C2×D8—861no—
332C2×D8C22×D4311yescharacteristic
333C2×D8C22×D4311yescharacteristic
334C2×M16—431no—
335C22×C8—431no—
336C4×Q8—861no—
337C4×Q8—861no—
338C4×D4—21no—
339C4×D4—21no—
340C4×D4—861no—
341C4×D4—861no—
342C4×D4—861no—
343C4×D4—861no—
344C4×D4—1721no—
345C4×D4—1721no—
346C4×D4—1721no—
347C4×D4—1721no—
348#117—431no—
349#117—861no—
350#117—1721no—
351C2×C4⋊C4—861no—
352C2×C4⋊C4—1721no—
353C2×C22⋊C4—1721no—
354C2×C22⋊C4—1721no—
355SD32—434no—
356SD32—434no—
357D16—434no—
358D16C4×D4314yescomplemented
359M32—434no—
360C2×C16—431no—
361C2×C16—431no—
362C2×C16—862no—
363C2×C16C22×D4311yescharacteristic
364C2×C16C22×D4311yescharacteristic
365#107—431no—
366#107—431no—
367#107—861no—
368#107C22×D4311yescharacteristic
369#107C22×D4311yescharacteristic
370#106—861no—
371#103—861no—
372#103—861no—
373#102—21no—
374#102—21no—
375#102—861no—
376#102—861no—
377#102—861no—
378#102—861no—
379#97—431no—
380#97—431no—
381C4×C8—431no—
382C4×C8C22×D4311yescharacteristic
383C24—1721no—
384#41—864no—
385#41—1722no—
386C2×Q8—861no—
387C2×D4—21no—
388C2×D4—21no—
389C2×D4—864no—
390C2×D4—861no—
391C2×D4—1722no—
392C2×D4—1721no—
393C2×D4—1721no—
394C22×C4—41no—
395C22×C4—41no—
396C22×C4—431no—
397C22×C4—1721no—
398C22×C4—1721no—
399C22×C4—1721no—
400C22×C4—1721no—
401C22×C4—1721no—
402C22×C4—1721no—
403Q16—432no—
404Q16—861no—
405SD16—864no—
406D8—21no—
407D8—21no—
408D8—432no—
409D8—864no—
410D8—861no—
411D8C2×C4×D4312yes—
412D8C2×C4×D4312yes—
413M16—862no—
414C2×C8—431no—
415C2×C8—432no—
416C2×C8—432no—
417C2×C8—431no—
418C2×C8D4×D4311yescharacteristic
419C2×C8C23×D4311yescharacteristic
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—431no—
423C4⋊C4—431no—
424C4⋊C4—861no—
425C4⋊C4—861no—
426C4⋊C4—1721no—
427C4⋊C4—1721no—
428C4⋊C4—1721no—
429C22⋊C4—41no—
430C22⋊C4—41no—
431C22⋊C4—431no—
432C22⋊C4—431no—
433C22⋊C4—1721no—
434C22⋊C4—1721no—
435C22⋊C4—1721no—
436C22⋊C4—1721no—
437C22⋊C4—1721no—
438C42—431no—
439C42—1721no—
440C42—1721no—
441C42—1721no—
442C42D4×D4311yescharacteristic
443C16—21no—
444C16—432no—
445C16—861no—
446C16C2×C4×D4312yes—
447C23—41no—
448C23—41no—
449C23—431no—
450C23—1724no—
451C23—1721no—
452C23—6881no—
453C23—6881no—
454Q8—862no—
455Q8—1721no—
456D4—22no—
457D4—22no—
458D4—41no—
459D4—41no—
460D4—862no—
461D4—1724no—
462D4—1724no—
463D4—1721no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—161no—
467C2×C4—161no—
468C2×C4—431no—
469C2×C4—432no—
470C2×C4—432no—
471C2×C4—431no—
472C2×C4—431no—
473C2×C4—1724no—
474C2×C4—1721no—
475C2×C4—1721no—
476C2×C4—1721no—
477C2×C4—6881no—
478C2×C4—6881no—
479C2×C4—6881no—
480C2×C4—6881no—
481C2×C4—6881no—
482C2×C4D8×D4311yescharacteristic
483C2×C4D8×D4311yescharacteristic
484C2×C4C2×D4×D4311yescharacteristic
485C8—21no—
486C8—432no—
487C8—861no—
488C8C22×C4×D4311yescharacteristic
489C8#41×D4311yescharacteristic
490C22—42no—
491C22—42no—
492C22—81no—
493C22—81no—
494C22—81no—
495C22—81no—
496C22—432no—
497C22—861no—
498C22—861no—
499C22—3441no—
500C22—3441no—
501C22—1722no—
502C22—6884no—
503C22C2×D8×D4311yescharacteristic
504C4—21no—
505C4—21no—
506C4—81no—
507C4—81no—
508C4—432no—
509C4—861no—
510C4—861no—
511C4—3441no—
512C4—3441no—
513C4—1722no—
514C4C4×D4×D4311yescharacteristic
515C4#135×D4311yescharacteristic
516C2—82no—
517C2—82no—
518C2—862no—
519C2—3442no—
520C2C4×D8×D4311yescharacteristic
521C2#1914773211yescharacteristic
522C2#1914773811yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutatorC8×C43C23×C4
FrattiniC2×C8C23×D43
FittingC4×D16×C43C2
socleC22×C43C22×D8
prime radicalC2×#14583333C2
cosocleC2×C8×C43C24
hypercenterC4×D16D43
hypocenterC43#33454
LCSG ▷ C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ C4×D16

Complements

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

NH ≅ G/Ntype
2. #19143465C2semidirect
3. #19143442C2semidirect
4. #19136471C2semidirect
5. #19136469C2semidirect
6. #19136459C2semidirect
7. #19136458C2semidirect
8. #19136450C2semidirect
9. C4×#13063270C2semidirect
10. #19136439C2semidirect
11. #19136380C2semidirect
12. #19136299C2semidirect
13. #357×D43C2semidirect
14. #19136190C2semidirect
15. C4×D16×C43C2semidirect
20. #14583333C4semidirect
30. C4×Dic172C22semidirect
31. #14582993C22semidirect
34. D8×Dic43C22semidirect
41. #14582727C22semidirect
42. #14582726C22semidirect
43. #14582724C22semidirect
44. #14582704C22semidirect
45. #14582702C22semidirect
48. #14582700C22semidirect
50. #14582675C22semidirect
51. #14582674C22semidirect
52. C16×Dic43C22semidirect
55. C4×D8×C43C22semidirect
56. C43×#366C22semidirect
58. C43×#357C22semidirect
59. C4×C16×C43C22semidirect
63. #13063344C2×C4semidirect
69. D8×D43C2×C4semidirect
89. #13063270C2×C4semidirect
90. #13063269C2×C4semidirect
91. #13063266C2×C4semidirect
92. #13063264C2×C4semidirect
113. D16×C43C2×C4semidirect
265. C4×D16D43semidirect
299. C4×D8C2×D43semidirect
308. #366C2×D43semidirect
316. #357C2×D43semidirect
320. C4×C16C2×D43semidirect
321. C43#33454semidirect
358. D16C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145833332
#191434652
#191434422
#191364712
#191364692
#191364592
#191364582
#191364502
C4×#130632702
#191364392
#191363802
#191362992
#357×D432
#191361902
C4×D16×C432
#3345443