Finite Group Databasebeta

← #25251519

Subgroups — #25251519

Order 11008.

654 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145171C211yesmaximal, characteristic, complemented
2C4×D8×D43C211yesmaximal, characteristic, complemented
3#19136777C211yesmaximal, characteristic, complemented
4#19136774C211yesmaximal, characteristic, complemented
5#19136731C211yesmaximal, characteristic, complemented
6#19136730C211yesmaximal, characteristic, complemented
7#19136629C211yesmaximal, characteristic, complemented
8#19136628C211yesmaximal, characteristic, complemented
9#19136508C211yesmaximal, characteristic, complemented
10#19136505C211yesmaximal, characteristic, complemented
11C4×D688C211yesmaximal, characteristic, complemented
12C4×#13063266C211yesmaximal, characteristic, complemented
13C4×#13063266C211yesmaximal, characteristic, complemented
14#19136392C211yesmaximal, characteristic, complemented
15C4×D16×C43C211yesmaximal, characteristic, complemented
16C2×D8×D43C2211yescharacteristic
17#14583446—21no—
18C4×D4×D43—21no—
19C2×D688C2211yescharacteristic
20C2×#13063266C2211yescharacteristic
21C2×#13063266C2211yescharacteristic
22#14583303C2211yescharacteristic, complemented
23#14583274C2211yescharacteristic, complemented
24#14583244—21no—
25#14583136C2211yescharacteristic
26#14583134—21no—
27#14583132C2211yescharacteristic
28C4×D344C2211yescharacteristic
29C4×D344C2211yescharacteristic, complemented
30D8×Dic43C2211yescharacteristic
31#14582981C2211yescharacteristic
32C4×#10621882—21no—
33C4×#10621882—21no—
34#14582979—21no—
35#107×D43C2211yescharacteristic
36#102×D43—21no—
37C4×C8×D43C2211yescharacteristic
38#14582725C2211yescharacteristic, complemented
39#14582724C2211yescharacteristic, complemented
40#14582724C2211yescharacteristic, complemented
41Dic43⋊C16C2211yescharacteristic, complemented
42Dic43⋊C16C2211yescharacteristic, complemented
43#14582701C2211yescharacteristic
44#14582701C2211yescharacteristic, complemented
45#14582700C2211yescharacteristic
46#14582700C2211yescharacteristic, complemented
47#14582699C2211yescharacteristic
48#14582699C2211yescharacteristic, complemented
49(C2×D43)⋊C16C2211yescharacteristic
50(C2×D43)⋊C16C2211yescharacteristic
51C4×C43⋊C16C2211yescharacteristic, complemented
52C2×D16×C43C2211yescharacteristic
53C4×D8×C43C2211yescharacteristic
54C4×D8×C43C2211yescharacteristic, complemented
55C43×#366C2211yescharacteristic, complemented
56C43×#357C2211yescharacteristic
57C43×#357C2211yescharacteristic, complemented
58C4×C16×C43C2211yescharacteristic, complemented
59C2×#10621898—41no—
60C2×D4×D43—21no—
61C22×C4×D43—41no—
62C2×D344C2311yescharacteristic
63C2×D344C2311yescharacteristic
64C2×#10621882—21no—
65C2×#10621882—21no—
66D8×D43—22no—
67D8×D43—22no—
68C2×C8×D43D411yescharacteristic
69C2×C8×D43C2311yescharacteristic
70#13063324—21no—
71#13063321—21no—
72#13063311—41no—
73#13063300—21no—
74#13063298—41no—
75#13063296—21no—
76C4×D172—21no—
77C4×D172—21no—
78D4×Dic43—21no—
79#13063287—21no—
80C4×C22⋊D43—41no—
81C4×C22⋊D43—41no—
82(C22⋊D43)⋊C4—41no—
83C4⋊C4×D43—21no—
84C22⋊C4×D43—41no—
85C42×D43D411yescharacteristic
86D688—22no—
87#13063266—22no—
88#13063266—22no—
89C2×C43⋊C16C2311yescharacteristic
90C2×C43⋊C16C2311yescharacteristic
91#13063259C2311yescharacteristic
92#13063259C2311yescharacteristic
93#13063258—21no—
94#13063258—21no—
95#13063247—21no—
96#13063247—21no—
97#13063246—21no—
98#13063246—21no—
99#13063245—21no—
100#13063245—21no—
101C4×C43⋊C8D411yescharacteristic
102C8×Dic43D411yescharacteristic
103C8×Dic43C2311yescharacteristic
104C2×D8×C43C2311yescharacteristic
105C2×D8×C43C2311yescharacteristic
106C4×D4×C43—21no—
107C4×D4×C43—21no—
108D16×C43—22no—
109C2×C16×C43C2311yescharacteristic
110C2×C16×C43C2311yescharacteristic
111#107×C43C2311yescharacteristic
112#107×C43C2311yescharacteristic
113#102×C43—21no—
114#102×C43—21no—
115C4×C8×C43C2311yescharacteristic
116C23×D43—41no—
117C2×D4×C43—21no—
118C2×D4×C43—21no—
119C22×C4×C43—41no—
120C22×C4×C43—41no—
121C2×C22⋊D43—41no—
122C2×C22⋊D43—41no—
123C2×C22⋊D43—41no—
124C2×C22⋊D43—41no—
125C22×Dic43—41no—
126D4×D43—24no—
127D4×D43—42no—
128#10621898—84no—
129C2×D172—21no—
130C2×D172—21no—
131C2×D172—41no—
132C2×C4×D43—41no—
133C2×C4×D43—41no—
134C2×C4×D43—41no—
135C2×C4×D43—41no—
136C2×C4×D43—84no—
137C2×C4×D43D811yescharacteristic
138C2×C4×D43D811yescharacteristic
139C2×C4×D43C2×D411yescharacteristic
140C2×Dic86—41no—
141D8×C43—21no—
142D8×C43—21no—
143D8×C43—21no—
144D8×C43#4112yescomplemented
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#10621882—24no—
155#10621882—42no—
156(C2×D43)⋊C4—41no—
157(C2×D43)⋊C4—41no—
158(C2×D43)⋊C4—41no—
159(C2×D43)⋊C4—41no—
160C4⋊Dic43—21no—
161C4⋊Dic43—21no—
162Dic43⋊C4—41no—
163Dic43⋊C4—41no—
164C4×Dic43D811yescharacteristic
165C4×Dic43D811yescharacteristic
166C4×Dic43C2×D411yescharacteristic
167C2×C43⋊C8C2×D411yescharacteristic
168C2×C43⋊C8C2×D411yescharacteristic
169D344—21no—
170D344—21no—
171D344—21no—
172D344#4112yescomplemented
173C8×D43—21no—
174C8×D43—21no—
175C8×D43—41no—
176C16×C43—21no—
177C16×C43—21no—
178C43⋊C16—21no—
179C43⋊C16—21no—
180C23×C43—41no—
181C23×C43—41no—
182C22×D43—44no—
183C22×D43—41no—
184C22×D43—41no—
185C22×D43—82no—
186C22×D43—82no—
187C22×D43C2×D811yescharacteristic
188D4×C43—22no—
189D4×C43—41no—
190D4×C43—41no—
191D4×C43—41no—
192C2×C4×C43—41no—
193C2×C4×C43—41no—
194C2×C4×C43—82no—
195C2×C4×C43—82no—
196C2×C4×C43C2×D811yescharacteristic
197C2×C4×C43C2×D811yescharacteristic
198C2×C4×C43C22×D411yescharacteristic
199C22⋊D43—44no—
200C22⋊D43—82no—
201C22⋊D43—82no—
202C22⋊D43—82no—
203C2×Dic43—41no—
204C2×Dic43—41no—
205C2×Dic43—82no—
206C2×Dic43C2×D811yescharacteristic
207C2×Dic43C2×D811yescharacteristic
208C2×Dic43C2×D811yescharacteristic
209D172—22no—
210D172—41no—
211D172—41no—
212D172—41no—
213D172—82no—
214C4×D43—21no—
215C4×D43—21no—
216C4×D43—41no—
217C4×D43—82no—
218C4×D43—82no—
219C4×D43—82no—
220C4×D43—82no—
221C4×D43D1614yescomplemented
222Dic86—82no—
223C8×C43—21no—
224C8×C43C2×#4111yescharacteristic
225C8×C43C2×#4111yescharacteristic
226C43⋊C8—21no—
227C43⋊C8—21no—
228#33660—431nomaximal, Sylow
229C22×C43—42no—
230C22×C43—81no—
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—88no—
240C2×D43—81no—
241C2×D43—81no—
242C2×D43—81no—
243C2×D43—81no—
244C2×D43—81no—
245C2×D43C2×D1612yes—
246C4×C43—21no—
247C4×C43—81no—
248C4×C43—81no—
249C4×C43C2×D1612yes—
250C4×C43#52511yescharacteristic
251C4×C43#57511yescharacteristic
252Dic43—21no—
253Dic43—21no—
254Dic43—81no—
255Dic43—81no—
256Dic43C2×D1612yes—
257#3169—431no—
258C2×C4×D8—431no—
259#2232—431no—
260#2232—431no—
261#2224—431no—
262#2224—431no—
263#2206—431no—
264#2206—431no—
265#2184—431no—
266#2184—431no—
267C4×D16—431no—
268C4×D16—431no—
269C4×D16—431no—
270C4×D16D4311yescharacteristic, complemented
271#2162—431no—
272C2×C43—82no—
273C2×C43—161no—
274C2×C43#310011yescharacteristic
275C2×C43C22×D1611yescharacteristic
276C2×C43#341411yescharacteristic
277D43—22no—
278D43—82no—
279D43—161no—
280C22×D8—431no—
281#532—861no—
282C2×C4×D4—861no—
283C2×D16—431no—
284C2×D16—431no—
285C2×D16—431no—
286C2×D16C2×D4311yescharacteristic
287#500—431no—
288#493—431no—
289#486—861no—
290#466—431no—
291#466—431no—
292#466—861no—
293C4×D8—431no—
294C4×D8—431no—
295C4×D8—431no—
296C4×D8—431no—
297C4×D8—861no—
298C4×D8—861no—
299C4×D8—861no—
300C4×D8C2×D4311yescharacteristic
301C4×D8C2×D4311yescharacteristic, complemented
302C2×#107—431no—
303C2×#102—861no—
304C2×C4×C8—431no—
305#366—431no—
306#366—431no—
307#366—431no—
308#366C2×D4311yescharacteristic, complemented
309C4⋊C16—431no—
310C4⋊C16—431no—
311#357—431no—
312#357—431no—
313#357—431no—
314#357—431no—
315#357—431no—
316#357—431no—
317#357C2×D4311yescharacteristic
318#357C2×D4311yescharacteristic, complemented
319C22⋊C16—431no—
320C22⋊C16—431no—
321C4×C16—431no—
322C4×C16C2×D4311yescharacteristic, complemented
323C43#3366011yescharacteristic, complemented, Sylow
324C2×#41—1721no—
325C22×D4—861no—
326C23×C4—1721no—
327C2×D8—431no—
328C2×D8—431no—
329C2×D8—861no—
330C2×D8—861no—
331C2×D8—862no—
332C2×D8—862no—
333C2×D8C22×D4311yescharacteristic
334C2×D8C22×D4311yescharacteristic
335C22×C8—431no—
336C22×C8—431no—
337C4⋊Q8—861no—
338#127—861no—
339#124—1721no—
340#121—861no—
341#121—861no—
342#121—1721no—
343C4×D4—21no—
344C4×D4—21no—
345C4×D4—861no—
346C4×D4—861no—
347C4×D4—861no—
348C4×D4—861no—
349C4×D4—1721no—
350C4×D4—1721no—
351C4×D4—1721no—
352C2×C4⋊C4—861no—
353C2×C22⋊C4—1721no—
354C2×C42—431no—
355D16—22no—
356D16—862no—
357D16—862no—
358D16—862no—
359C2×C16—431no—
360C2×C16—431no—
361C2×C16C22×D4311yescharacteristic
362C2×C16C22×D4311yescharacteristic
363#107—431no—
364#107—431no—
365#107—861no—
366#107—861no—
367#107C22×D4311yescharacteristic
368#107C22×D4311yescharacteristic
369#102—21no—
370#102—21no—
371#102—861no—
372#102—861no—
373#102—861no—
374#102—861no—
375#102—861no—
376#102—861no—
377C4×C8—431no—
378C4×C8—431no—
379C4×C8—431no—
380C4×C8C22×D4311yescharacteristic
381C24—1721no—
382#41—3444no—
383C2×Q8—1721no—
384C2×D4—21no—
385C2×D4—21no—
386C2×D4—864no—
387C2×D4—861no—
388C2×D4—861no—
389C2×D4—1721no—
390C2×D4—1721no—
391C2×D4—1721no—
392C2×D4—1721no—
393C2×D4—1722no—
394C2×D4—1721no—
395C22×C4—41no—
396C22×C4—41no—
397C22×C4—431no—
398C22×C4—431no—
399C22×C4—431no—
400C22×C4—3444no—
401C22×C4—1721no—
402C22×C4—1721no—
403C22×C4—1721no—
404C22×C4—1721no—
405C22×C4—1721no—
406D8—21no—
407D8—21no—
408D8—21no—
409D8—432no—
410D8—864no—
411D8—861no—
412D8—861no—
413D8—861no—
414D8—1722no—
415D8#1062189812yescomplemented
416C2×C8—431no—
417C2×C8—431no—
418C2×C8—861no—
419C2×C8—861no—
420C2×C8—1721no—
421C2×C8D4×D4311yescharacteristic
422C2×C8C23×D4311yescharacteristic
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—861no—
426C4⋊C4—861no—
427C4⋊C4—1721no—
428C4⋊C4—1721no—
429C22⋊C4—41no—
430C22⋊C4—41no—
431C22⋊C4—1721no—
432C22⋊C4—1721no—
433C22⋊C4—1721no—
434C22⋊C4—1721no—
435C22⋊C4—1721no—
436C22⋊C4—1721no—
437C42—431no—
438C42—431no—
439C42—431no—
440C42D4×D4311yescharacteristic
441C16—21no—
442C16—21no—
443C16—861no—
444C16—861no—
445C23—41no—
446C23—41no—
447C23—431no—
448C23—3442no—
449C23—3442no—
450C23—1724no—
451C23—1721no—
452C23—1721no—
453Q8—3442no—
454D4—22no—
455D4—41no—
456D4—41no—
457D4—41no—
458D4—862no—
459D4—3442no—
460D4—3442no—
461D4—3442no—
462D4—3442no—
463D4—1724no—
464D4—1721no—
465D4—1721no—
466D4—1721no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—82no—
470C2×C4—82no—
471C2×C4—431no—
472C2×C4—434no—
473C2×C4—431no—
474C2×C4—431no—
475C2×C4—861no—
476C2×C4—861no—
477C2×C4—3442no—
478C2×C4—3442no—
479C2×C4—3442no—
480C2×C4—3442no—
481C2×C4—3442no—
482C2×C4—1721no—
483C2×C4—1721no—
484C2×C4—1721no—
485C2×C4D8×D4311yescharacteristic
486C2×C4D8×D4311yescharacteristic
487C2×C4C2×D4×D4311yescharacteristic
488C8—21no—
489C8—861no—
490C8—861no—
491C8#41×D4311yescharacteristic
492C8C2×#1062189811yescharacteristic
493C22—42no—
494C22—81no—
495C22—81no—
496C22—81no—
497C22—81no—
498C22—81no—
499C22—432no—
500C22—861no—
501C22—861no—
502C22—3448no—
503C22—3441no—
504C22—3441no—
505C22—3441no—
506C22—3441no—
507C22—3441no—
508C22—1722no—
509C22C2×D8×D4311yescharacteristic
510C4—21no—
511C4—81no—
512C4—81no—
513C4—432no—
514C4—861no—
515C4—861no—
516C4—3441no—
517C4—3441no—
518C4D16×D4312yes—
519C4#1458340811yescharacteristic
520C4#1458369611yescharacteristic
521C2—82no—
522C2—161no—
523C2—862no—
524C2—3442no—
525C2—6881no—
526C2#1914459311yescharacteristic
527C2C2×D16×D4311yescharacteristic
528C2#1914772811yescharacteristic
subgroupG/H
centerC2×C4D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC4×D16×C43C2
socleC22×C43C22×D8
hypercenterC4×D16D43
hypocenterC43#33660
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8 ◁ C4×D16

Complements

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

NH ≅ G/Ntype
1. #19145171C2semidirect
2. C4×D8×D43C2semidirect
3. #19136777C2semidirect
4. #19136774C2semidirect
5. #19136731C2semidirect
6. #19136730C2semidirect
7. #19136629C2semidirect
8. #19136628C2semidirect
9. #19136508C2semidirect
10. #19136505C2semidirect
11. C4×D688C2semidirect
12. C4×#13063266C2semidirect
13. C4×#13063266C2semidirect
14. #19136392C2semidirect
15. C4×D16×C43C2semidirect
22. #14583303C22semidirect
23. #14583274C22semidirect
29. C4×D344C22semidirect
38. #14582725C22semidirect
39. #14582724C22semidirect
40. #14582724C22semidirect
41. Dic43⋊C16C22semidirect
42. Dic43⋊C16C22semidirect
44. #14582701C22semidirect
46. #14582700C22semidirect
48. #14582699C22semidirect
51. C4×C43⋊C16C22semidirect
54. C4×D8×C43C22semidirect
55. C43×#366C22semidirect
57. C43×#357C22semidirect
58. C4×C16×C43C22semidirect
144. D8×C43#41semidirect
172. D344#41semidirect
221. C4×D43D16semidirect
270. C4×D16D43semidirect
301. C4×D8C2×D43semidirect
308. #366C2×D43semidirect
318. #357C2×D43semidirect
322. C4×C16C2×D43semidirect
323. C43#33660semidirect
415. D8#10621898semidirect

Maximal subgroups

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

subgroupindex
#191451712
C4×D8×D432
#191367772
#191367742
#191367312
#191367302
#191366292
#191366282
#191365082
#191365052
C4×D6882
C4×#130632662
#191363922
C4×D16×C432
#3366043