Finite Group Databasebeta

← #11899729

Subgroups — #11899729

Order 1152.

765 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5757C211yesmaximal, characteristic, complemented
2#10594692C211yesmaximal, characteristic, complemented
3C2×#63654C211yesmaximal, characteristic, complemented
4C3×#5147C211yesmaximal, characteristic, complemented
5#10591032C212yesmaximal, complemented
6#10591031C212yesmaximal, complemented
7#10591028C212yesmaximal, complemented
8D3×#827C212yesmaximal, complemented
9#10590638C211yesmaximal, characteristic, complemented
10#10590629C211yesmaximal, characteristic, complemented
11#10590622C211yesmaximal, characteristic, complemented
12#84008—31nomaximal
13#82037—31nomaximal
14C3×#1004—21no—
15#64298—21no—
16C2×C32×D8C2211yescharacteristic
17C2×#3746C2211yescharacteristic, complemented
18C3×#932—21no—
19C3×#912C2212yes—
20C3×#911—22no—
21C3×D3×D8C2212yes—
22C3×#904C2211yescharacteristic
23C3×#904C2211yescharacteristic, complemented
24C3×#901C2211yescharacteristic
25#63831—21no—
26#63807C2212yescomplemented
27#63800—22no—
28D3×Dic12C2212yescomplemented
29#63654C2212yescomplemented
30#63654C2212yescomplemented
31C2×C3⋊(C3⋊C16)C2211yescharacteristic, complemented
32C3×#827C2212yescomplemented
33C3×#826C2212yescomplemented
34C3×#812C2211yescharacteristic, complemented
35#63551C2212yescomplemented
36#63550C2211yescharacteristic, complemented
37#63548C2212yescomplemented
38#63547C2211yescharacteristic, complemented
39#63547C2211yescharacteristic, complemented
40#63545C2211yescharacteristic, complemented
41#63543C2212yescomplemented
42D3×C3⋊C16C2212yescomplemented
43C3×#576—31no—
44#5771—31no—
45#5757D311yescharacteristic, complemented
46#5753—31no—
47C3×#509—31no—
48#5195—32no—
49#5195—31no—
50#5194—31no—
51#5194—31no—
52#5194—32no—
53C2×#827—31no—
54C2×#827—31no—
55C2×#827—32no—
56C2×#827—61no—
57#5147—32no—
58#5147D311yescharacteristic, complemented
59#5140—31no—
60#4915—32no—
61D3×SD32—32no—
62#4912—32no—
63#4911—32no—
64#4909—31no—
65#4907—31no—
66C2×C32×D4—21no—
67C2×#634—21no—
68C2×C3×#67—42no—
69C3×#237—22no—
70C3×#237—41no—
71C3×D3×D4—22no—
72C3×D3×D4—41no—
73C3×#235—21no—
74C3×#235—21no—
75C3×#235D411yescharacteristic
76#3805—42no—
77#3795—22no—
78#3795—41no—
79D3×Dic6—22no—
80D3×Dic6—41no—
81C32×D8—21no—
82C32×D8C2312yes—
83C2×C32×C8C2311yescharacteristic
84#3746—21no—
85#3746C2312yes—
86C3×#214—22no—
87C3×#213—22no—
88C3×#208D411yescharacteristic
89C3×Dic12C2311yescharacteristic
90C3×Dic12C2311yescharacteristic
91C3×D24C2311yescharacteristic
92C3×D24C2311yescharacteristic
93C3×#204—21no—
94C3×#204—21no—
95C3×ΓL(1,𝔽25)D412yes—
96C3×D3×C8C2312yes—
97#3719—22no—
98#3716—22no—
99C3⋊(C3⋊C16)C2311yescharacteristic
100C3⋊(C3⋊C16)C2311yescharacteristic
101C3×C3⋊C16C2312yes—
102#3416—91noSylow
103C3×H(5,𝔽2)—61no—
104#1010—61no—
105#1010—61no—
106#1004—21no—
107C3×AGL(1,ℤ/8)—62no—
108C3×AGL(1,ℤ/8)—61no—
109C3×#135—32no—
110C3×#135—31no—
111C3×#135—31no—
112C2×C3×D8—21no—
113C2×C3×D8—32no—
114C2×C3×D8C2×D311yescharacteristic
115C2×C3×D8C2×D311yescharacteristic
116C3×#131—31no—
117#951—61no—
118#932—21no—
119D3×Q16—32no—
120#915—62no—
121#912—32no—
122#912C2×D312yes—
123#911—22no—
124D3×D8C2×D312yes—
125#909—62no—
126#909—61no—
127C2×Dic12—31no—
128C2×Dic12—31no—
129C2×Dic12—32no—
130C2×Dic12—61no—
131#904—32no—
132#904C2×D311yescharacteristic
133#904C2×D311yescharacteristic, complemented
134#901C2×D311yescharacteristic
135C3×SD32—32no—
136C3×D16—32no—
137C3×M32—31no—
138#829—31no—
139#829—31no—
140#829—32no—
141#828—31no—
142#828—31no—
143#827—32no—
144#827—32no—
145#827—32no—
146#827—32no—
147#827—31no—
148#827—31no—
149#827—32no—
150#827—62no—
151#827—62no—
152#827C2×D312yescomplemented
153#826—31no—
154#826—31no—
155#826C2×D312yescomplemented
156#812—32no—
157#812C2×D311yescharacteristic, complemented
158C2×C3⋊C16—31no—
159C2×C3⋊C16—31no—
160C2×C3⋊C16—32no—
161C2×C3⋊C16—61no—
162Dic24—32no—
163#800—32no—
164#798—32no—
165D3×C16—32no—
166C23×C32—41no—
167C22×C3×D3—42no—
168C32×D4—22no—
169C32×D4—41no—
170C2×C32×C4C2×D411yescharacteristic
171C2×C3⋊Dic3—41no—
172#634—22no—
173#634—41no—
174C3×#67—41no—
175C3×#67—41no—
176C3×#67—42no—
177C3×#67—42no—
178C3×#67D812yes—
179C2×C3×Dic3—42no—
180C3×D12—21no—
181C3×D12—21no—
182C3×D12D811yescharacteristic
183C3×C4×D3—41no—
184C3×C4×D3—41no—
185C3×C4×D3C2×D412yes—
186C3×Dic6—21no—
187C3×Dic6—21no—
188C3×Dic6D811yescharacteristic
189#627—42no—
190#625—42no—
191D3×Dic3—42no—
192D3×Dic3—42no—
193C32×C8C2×D411yescharacteristic
194C32×C8C2411yescharacteristic
195C3×C3⋊C8C2×D412yes—
196#578—91no—
197#576—31no—
198#510—91no—
199#510—92no—
200#509—31no—
201#509—92no—
202#508—92no—
203#508—91no—
204C2×SD32—92no—
205C2×SD32—91no—
206#504—91no—
207C3×#41—31no—
208C3×#41—62no—
209C3×#41—61no—
210C3×#41—61no—
211C3×#41—121no—
212C2×C3×D4—21no—
213C2×C3×D4—21no—
214C2×C3×D4—41no—
215C2×C3×D4—62no—
216C2×C3×D4—121no—
217C2×C3×D4—122no—
218C2×#67—42no—
219D3×Q8—62no—
220D3×Q8—121no—
221#237—22no—
222#237—41no—
223#237—62no—
224#237—121no—
225#237—122no—
226#237—122no—
227D3×D4—22no—
228D3×D4—41no—
229#235—21no—
230#235—21no—
231#235—62no—
232#235—121no—
233#235#6711yescharacteristic
234C2×Dic6—62no—
235C2×Dic6—61no—
236C2×Dic6—61no—
237C2×Dic6—121no—
238C2×Dic6—121no—
239C3×Q16—31no—
240C3×Q16—31no—
241C3×SD16—62no—
242C3×SD16—61no—
243C3×SD16—61no—
244C3×D8—21no—
245C3×D8—21no—
246C3×D8—22no—
247C3×D8—31no—
248C3×D8—31no—
249C3×D8—41no—
250C3×D8—62no—
251C3×D8C22×D312yes—
252C3×D8C22×D312yes—
253C3×M16—31no—
254C3×M16—32no—
255C2×C3×C8—21no—
256C2×C3×C8—32no—
257C2×C3×C8C22×D311yescharacteristic
258C2×C3×C8C22×D311yescharacteristic
259#216—62no—
260#214—22no—
261#214—62no—
262#213—22no—
263#208#6711yescharacteristic
264Dic12—32no—
265Dic12—32no—
266Dic12—62no—
267Dic12—62no—
268Dic12—61no—
269Dic12—61no—
270Dic12—121no—
271Dic12C22×D311yescharacteristic
272Dic12C22×D311yescharacteristic
273D24C22×D311yescharacteristic
274D24C22×D311yescharacteristic
275#204—21no—
276#204—21no—
277#204—62no—
278ΓL(1,𝔽25)#6712yes—
279D3×C8C22×D312yes—
280C3×C16—32no—
281C3⋊C16—31no—
282C3⋊C16—31no—
283C3⋊C16—31no—
284C3⋊C16—31no—
285C3⋊C16—61no—
286C3⋊C16—61no—
287C3⋊C16C22×D312yes—
288C22×C32—42no—
289C22×C32—161no—
290C22×C32C2×D811yescharacteristic
291C2×C3×D3—41no—
292C2×C3×D3—41no—
293C2×C3×D3—162no—
294C2×C3×D3C2×D812yes—
295C32×C4C2×D811yescharacteristic
296C32×C4C22×D411yescharacteristic
297C3⋊Dic3—42no—
298C3×Dic3—41no—
299C3×Dic3—41no—
300C3×Dic3C2×D812yes—
3012−1+4—181no—
302H(5,𝔽2)—61no—
303#137—182no—
304#137—181no—
305AGL(1,ℤ/8)—62no—
306AGL(1,ℤ/8)—61no—
307#135—32no—
308#135—31no—
309#135—31no—
310#135—92no—
311C2×Q16—92no—
312C2×Q16—91no—
313C2×D8—32no—
314C2×D8D3211yescharacteristic
315#131—31no—
316Q32—92no—
317Q32—91no—
318SD32—32no—
319SD32—92no—
320SD32—91no—
321SD32—91no—
322SD32—92no—
323SD32—92no—
324D16—32no—
325D16—91no—
326M32—31no—
327M32—92no—
328C2×C16—92no—
329C2×C16—91no—
330C23×C3—41no—
331C23×C3—41no—
332C23×C3—81no—
333C23×C3—122no—
334C22×D3—42no—
335C3×Q8—31no—
336C3×Q8—61no—
337C3×Q8—61no—
338C3×D4—22no—
339C3×D4—22no—
340C3×D4—32no—
341C3×D4—31no—
342C3×D4—42no—
343C3×D4—41no—
344C3×D4—41no—
345C3×D4—61no—
346C3×D4—61no—
347C3×D4—81no—
348C3×D4—122no—
349C3×D4—122no—
350C3×D4—121no—
351C3×D4—121no—
352C2×C3×C4—21no—
353C2×C3×C4—32no—
354C2×C3×C4—122no—
355C2×C3×C4—121no—
356C2×C3×C4—121no—
357C2×C3×C4D3×D411yescharacteristic
358C2×C3×C4C2×#6711yescharacteristic
359#67—41no—
360#67—41no—
361#67—42no—
362#67—42no—
363#67—122no—
364#67—122no—
365#67#21312yes—
366C2×Dic3—42no—
367C2×Dic3—122no—
368C2×Dic3—121no—
369C2×Dic3—121no—
370C2×Dic3—122no—
371C2×Dic3—241no—
372D12—21no—
373D12—21no—
374D12#21311yescharacteristic
375C4×D3—41no—
376C4×D3—41no—
377C4×D3—122no—
378C4×D3—122no—
379C4×D3C2×#6712yes—
380Dic6—21no—
381Dic6—21no—
382Dic6—62no—
383Dic6—62no—
384Dic6—122no—
385Dic6—122no—
386Dic6—121no—
387Dic6—121no—
388Dic6—122no—
389Dic6—241no—
390Dic6#21311yescharacteristic
391C3×C8—21no—
392C3×C8—21no—
393C3×C8—32no—
394C3×C8D3×D411yescharacteristic
395C3×C8C2×#6711yescharacteristic
396C3×C8C23×D311yescharacteristic
397C3×C8C23×D311yescharacteristic
398C3⋊C8C2×#6712yes—
399C2×C32—21no—
400C2×C32—82no—
401C2×C32C22×D811yescharacteristic
402C3×D3—22no—
403C3×D3—81no—
404C3×D3—81no—
405#41—31no—
406#41—62no—
407#41—61no—
408#41—61no—
409#41—121no—
410#41—182no—
411#41—361no—
412#41—362no—
413C2×Q8—182no—
414C2×Q8—181no—
415C2×Q8—361no—
416C2×D4—21no—
417C2×D4—62no—
418C2×D4—121no—
419C2×D4—122no—
420Q16—31no—
421Q16—31no—
422Q16—92no—
423Q16—182no—
424Q16—181no—
425SD16—62no—
426SD16—61no—
427SD16—61no—
428SD16—182no—
429D8—21no—
430D8—31no—
431D8—31no—
432D8—62no—
433D8C2×D3212yes—
434M16—31no—
435M16—32no—
436C2×C8—32no—
437C2×C8C2×D3211yescharacteristic
438C16—32no—
439C16—91no—
440C16—91no—
441C22×C3—21no—
442C22×C3—32no—
443C22×C3—42no—
444C22×C3—42no—
445C22×C3—82no—
446C22×C3—121no—
447C22×C3—121no—
448C22×C3—161no—
449C22×C3—161no—
450C22×C3—162no—
451C22×C3—482no—
452C22×C3D3×D811yescharacteristic
453C22×C3C2×#21311yescharacteristic
454C2×D3—41no—
455C2×D3—41no—
456C2×D3—162no—
457C2×D3C2×#21312yes—
458C3×C4—21no—
459C3×C4—21no—
460C3×C4—32no—
461C3×C4—121no—
462C3×C4—121no—
463C3×C4D3×D811yescharacteristic
464C3×C4C2×#21311yescharacteristic
465C3×C4C2×D3×D411yescharacteristic
466C3×C4C22×#6711yescharacteristic
467Dic3—41no—
468Dic3—41no—
469Dic3—122no—
470Dic3—122no—
471Dic3—242no—
472Dic3C2×#21312yes—
473C32#341611yescharacteristic, complemented, Sylow
474C23—41no—
475C23—122no—
476Q8—31no—
477Q8—61no—
478Q8—61no—
479Q8—182no—
480Q8—362no—
481Q8—361no—
482D4—22no—
483D4—32no—
484D4—31no—
485D4—41no—
486D4—61no—
487D4—61no—
488D4—122no—
489D4—122no—
490D4—121no—
491D4—121no—
492D4—362no—
493C2×C4—32no—
494C2×C4—122no—
495C2×C4—121no—
496C2×C4—121no—
497C2×C4—362no—
498C2×C4—362no—
499C2×C4—361no—
500C2×C4D3×#6711yescharacteristic
501C8—32no—
502C8D3×#6711yescharacteristic
503C8C22×D3211yescharacteristic
504C2×C3—22no—
505C2×C3—21no—
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—62no—
509C2×C3—82no—
510C2×C3—82no—
511C2×C3—162no—
512C2×C3—241no—
513C2×C3—241no—
514C2×C3C2×D3×D811yescharacteristic
515C2×C3C22×#21311yescharacteristic
516D3—22no—
517D3—81no—
518D3—81no—
519C22—32no—
520C22—42no—
521C22—121no—
522C22—121no—
523C22—161no—
524C22—482no—
525C22D3×#21311yescharacteristic
526C4—32no—
527C4—121no—
528C4—121no—
529C4—362no—
530C4D3×#21311yescharacteristic
531C4C2×D3×#6711yescharacteristic
532C3—21no—
533C3#8203711yescharacteristic, complemented
534C3#8400811yescharacteristic, complemented
535C2—21no—
536C2—62no—
537C2—82no—
538C2—241no—
539C2—241no—
540C2C2×D3×#21311yescharacteristic
subgroupG/H
centerC2C2×D3×#213
commutator, cosocleC32×C8C24
FrattiniC8C22×D32
FittingC2×C32×D8C22
socleC2×C32C22×D8
hypercenterC2×D8D32
hypocenterC32#3416
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. C3×#5757C2semidirect
2. #10594692C2semidirect
3. C2×#63654C2semidirect
4. C3×#5147C2semidirect
5. #10591032C2semidirect
6. #10591031C2semidirect
7. #10591028C2semidirect
8. D3×#827C2semidirect
9. #10590638C2semidirect
10. #10590629C2semidirect
11. #10590622C2semidirect
17. C2×#3746C22semidirect
23. C3×#904C22semidirect
26. #63807C22semidirect
28. D3×Dic12C22semidirect
29. #63654C22semidirect
30. #63654C22semidirect
31. C2×C3⋊(C3⋊C16)C22semidirect
32. C3×#827C22semidirect
33. C3×#826C22semidirect
34. C3×#812C22semidirect
35. #63551C22semidirect
36. #63550C22semidirect
37. #63548C22semidirect
38. #63547C22semidirect
39. #63547C22semidirect
40. #63545C22semidirect
41. #63543C22semidirect
42. D3×C3⋊C16C22semidirect
45. #5757D3semidirect
58. #5147D3semidirect
133. #904C2×D3semidirect
152. #827C2×D3semidirect
155. #826C2×D3semidirect
157. #812C2×D3semidirect
473. C32#3416semidirect
533. C3#82037semidirect
534. C3#84008semidirect

Maximal subgroups

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

subgroupindex
C3×#57572
#105946922
C2×#636542
C3×#51472
#105910322
#105910312
#105910282
D3×#8272
#105906382
#105906292
#105906222
#840083
#820373