Finite Group Databasebeta

← #11899735

Subgroups — #11899735

Order 1152.

765 conjugacy classes of subgroups.

The subgroup lattice has 545 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5771C211yesmaximal, characteristic, complemented
2#10594680C211yesmaximal, characteristic, complemented
3#10592892C211yesmaximal, characteristic, complemented
4C3×#5194C211yesmaximal, characteristic, complemented
5#10591047C212yesmaximal, complemented
6D3×#828C212yesmaximal, complemented
7#10591034C212yesmaximal, complemented
8#10591024C212yesmaximal, complemented
9C2×#63549C211yesmaximal, characteristic, complemented
10#10590636C211yesmaximal, characteristic, complemented
11#10590621C211yesmaximal, characteristic, complemented
12#84016—31nomaximal
13#82032—31nomaximal
14C3×#1010—21no—
15#64308—21no—
16C32×#135C2211yescharacteristic, complemented
17C2×#3745C2211yescharacteristic
18C3×#951—21no—
19C3×D3×Q16C2212yescomplemented
20C3×#915—22no—
21C3×#912C2212yescomplemented
22C2×C3×Dic12C2211yescharacteristic, complemented
23C3×#904C2211yescharacteristic
24C3×#901C2211yescharacteristic
25#63825—21no—
26#63808C2212yes—
27#63794—22no—
28D3×D24C2212yes—
29#63655C2212yescomplemented
30#63653C2212yescomplemented
31#63639C2211yescharacteristic, complemented
32C3×#829C2211yescharacteristic, complemented
33C3×#828C2211yescharacteristic, complemented
34C3×#827C2211yescharacteristic, complemented
35C3×#826C2211yescharacteristic, complemented
36C2×C3×C3⋊C16C2211yescharacteristic, complemented
37#63550C2212yescomplemented
38#63549C2212yescomplemented
39#63549C2212yescomplemented
40#63547C2212yescomplemented
41#63543C2212yescomplemented
42D3×C3⋊C16C2212yescomplemented
43C3×#578—31no—
44#5771D311yescharacteristic, complemented
45#5769—31no—
46#5752—31no—
47C3×#508—31no—
48#5195—31no—
49#5194—32no—
50#5194D311yescharacteristic, complemented
51#5193—31no—
52#5193—31no—
53#5193—32no—
54#5193—61no—
55#5179—31no—
56#5179—32no—
57C2×#828—32no—
58C2×#828—31no—
59#5140—31no—
60#4918—32no—
61#4916—32no—
62D3×SD32—32no—
63#4911—32no—
64C2×#800—31no—
65#4901—31no—
66C32×#41—21no—
67C2×C4⋊(C3⋊D3)—21no—
68C3×D3×Q8—22no—
69C3×#237—22no—
70C3×#237—42no—
71C3×#235—21no—
72C3×#235—41no—
73C3×#235D411yescharacteristic
74C2×C3×Dic6—21no—
75C2×C3×Dic6—41no—
76#3811—42no—
77D3×D12—22no—
78D3×D12—41no—
79#3799—22no—
80#3799—41no—
81C32×Q16C2311yescharacteristic
82C32×SD16—21no—
83C32×D8C2311yescharacteristic
84C2×C32×C8C2311yescharacteristic
85#3745—21no—
86#3745C2312yes—
87C3×#216—22no—
88C3×#214—22no—
89C3×#208D411yescharacteristic
90C3×Dic12—21no—
91C3×Dic12C2311yescharacteristic
92C3×Dic12C2312yes—
93C3×D24C2311yescharacteristic
94C3×#204—21no—
95C3×ΓL(1,𝔽25)D412yes—
96C3×D3×C8C2312yes—
97#3717—22no—
98#3714—22no—
99C3⋊(C3⋊C16)C2312yes—
100C3×C3⋊C16C2311yescharacteristic
101C3×C3⋊C16C2311yescharacteristic
102#3416—91noSylow
103C3×2−1+4—61no—
104#1010—21no—
105#1009—61no—
106#1009—61no—
107C3×#137—62no—
108C3×#137—61no—
109C3×#135—21no—
110C3×#135—32no—
111C3×#135—31no—
112C3×#135C2×D311yescharacteristic, complemented
113C3×#135C2×D311yescharacteristic, complemented
114C2×C3×Q16—32no—
115C2×C3×Q16—31no—
116C3×#131—31no—
117#951—21no—
118#949—61no—
119#919—32no—
120D3×Q16C2×D312yescomplemented
121#915—22no—
122#914—62no—
123#912C2×D312yescomplemented
124D3×D8—32no—
125#908—62no—
126#908—61no—
127C2×Dic12C2×D311yescharacteristic, complemented
128#904—32no—
129#904C2×D311yescharacteristic
130C2×D24—31no—
131C2×D24—31no—
132C2×D24—32no—
133C2×D24—61no—
134#901C2×D311yescharacteristic
135C3×Q32—31no—
136C3×SD32—31no—
137C3×SD32—31no—
138C3×D16—31no—
139C2×C3×C16—31no—
140#829—32no—
141#829—32no—
142#829C2×D311yescharacteristic, complemented
143#828—32no—
144#828—32no—
145#828—32no—
146#828—32no—
147#828—32no—
148#828—62no—
149#828C2×D311yescharacteristic, complemented
150#827—32no—
151#827C2×D311yescharacteristic, complemented
152#826—32no—
153#826—32no—
154#826—62no—
155#826C2×D311yescharacteristic, complemented
156#812—31no—
157#812—31no—
158#812—32no—
159#812—61no—
160C2×C3⋊C16—32no—
161C2×C3⋊C16C2×D311yescharacteristic, complemented
162#800—32no—
163#800—32no—
164#798—32no—
165D3×C16—32no—
166C22×C3⋊D3—41no—
167C2×D32—42no—
168C32×Q8—21no—
169C32×D4—21no—
170C32×D4—41no—
171C2×C32×C4—41no—
172C2×C32×C4C2×D411yescharacteristic
173C4⋊(C3⋊D3)—22no—
174C4⋊(C3⋊D3)—41no—
175C3×#67—41no—
176C3×#67—42no—
177C3×#67D812yes—
178C2×C3×Dic3—41no—
179C2×C3×Dic3—42no—
180C3×D12—21no—
181C3×D12D811yescharacteristic
182C3×C4×D3—42no—
183C3×C4×D3—41no—
184C3×C4×D3C2×D412yes—
185C3×Dic6—21no—
186C3×Dic6—22no—
187C3×Dic6—41no—
188C3×Dic6—42no—
189C3×Dic6D811yescharacteristic
190#626—42no—
191#626—42no—
192#624—42no—
193C32×C8C2×D411yescharacteristic
194C32×C8C2411yescharacteristic
195C3×C3⋊C8C2×D412yes—
196#578—31no—
197#576—91no—
198#510—92no—
199#510—91no—
200#509—92no—
201#509—91no—
202#508—31no—
203#508—92no—
204C2×SD32—91no—
205C2×SD32—92no—
206#504—91no—
207C3×#41—21no—
208C3×#41—21no—
209C3×#41—31no—
210C3×#41—41no—
211C3×#41—62no—
212C3×#41—61no—
213C3×#41—121no—
214C3×#41—122no—
215C2×C3×Q8—62no—
216C2×C3×Q8—61no—
217C2×C3×Q8—121no—
218#239—62no—
219#239—121no—
220D3×Q8—22no—
221#237—22no—
222#237—42no—
223D3×D4—62no—
224D3×D4—121no—
225D3×D4—122no—
226D3×D4—122no—
227#235—21no—
228#235—41no—
229#235—62no—
230#235—121no—
231#235#6711yescharacteristic
232C2×D12—62no—
233C2×D12—61no—
234C2×D12—61no—
235C2×D12—121no—
236C2×D12—121no—
237C2×Dic6—21no—
238C2×Dic6—41no—
239C3×Q16—21no—
240C3×Q16—32no—
241C3×Q16—31no—
242C3×Q16—62no—
243C3×Q16—61no—
244C3×Q16C22×D311yescharacteristic
245C3×Q16C22×D311yescharacteristic
246C3×SD16—21no—
247C3×SD16—21no—
248C3×SD16—41no—
249C3×SD16—62no—
250C3×SD16—61no—
251C3×D8—21no—
252C3×D8—31no—
253C3×D8C22×D311yescharacteristic
254C3×D8C22×D311yescharacteristic
255C3×M16—31no—
256C3×M16—32no—
257C2×C3×C8—21no—
258C2×C3×C8—32no—
259C2×C3×C8C22×D311yescharacteristic
260C2×C3×C8C22×D311yescharacteristic
261#216—22no—
262#215—62no—
263#214—22no—
264#213—62no—
265#208#6711yescharacteristic
266Dic12—21no—
267Dic12C22×D312yes—
268Dic12C22×D311yescharacteristic
269D24—32no—
270D24—32no—
271D24—62no—
272D24—62no—
273D24—61no—
274D24—61no—
275D24—121no—
276D24C22×D311yescharacteristic
277#204—21no—
278#204—62no—
279ΓL(1,𝔽25)#6712yes—
280D3×C8C22×D312yes—
281C3×C16—31no—
282C3×C16—31no—
283C3⋊C16—32no—
284C3⋊C16—32no—
285C3⋊C16—62no—
286C3⋊C16C22×D311yescharacteristic
287C3⋊C16C22×D311yescharacteristic
288C22×C32—41no—
289C22×C32C2×D811yescharacteristic
290C2×C3⋊D3—42no—
291C2×C3⋊D3—161no—
292C2×C3×D3—41no—
293C2×C3×D3C2×D812yes—
294D32—162no—
295C32×C4—41no—
296C32×C4C2×D811yescharacteristic
297C32×C4C22×D411yescharacteristic
298C3×Dic3—41no—
299C3×Dic3—42no—
300C3×Dic3C2×D812yes—
3012−1+4—61no—
302H(5,𝔽2)—181no—
303#137—62no—
304#137—61no—
305AGL(1,ℤ/8)—182no—
306AGL(1,ℤ/8)—181no—
307#135—32no—
308#135—31no—
309#135—92no—
310#135D3211yescharacteristic, complemented
311C2×Q16—32no—
312C2×Q16—31no—
313C2×D8—92no—
314C2×D8—91no—
315#131—31no—
316Q32—31no—
317Q32—92no—
318SD32—31no—
319SD32—31no—
320SD32—92no—
321SD32—92no—
322SD32—92no—
323SD32—92no—
324D16—31no—
325D16—92no—
326M32—92no—
327M32—91no—
328C2×C16—31no—
329C2×C16—92no—
330C22×D3—122no—
331C22×D3—121no—
332C22×D3—121no—
333C22×D3—122no—
334C22×D3—241no—
335C3×Q8—21no—
336C3×Q8—21no—
337C3×Q8—31no—
338C3×Q8—41no—
339C3×Q8—62no—
340C3×Q8—61no—
341C3×Q8—122no—
342C3×Q8—121no—
343C3×D4—21no—
344C3×D4—21no—
345C3×D4—32no—
346C3×D4—31no—
347C3×D4—41no—
348C3×D4—41no—
349C3×D4—41no—
350C3×D4—61no—
351C3×D4—81no—
352C3×D4—122no—
353C3×D4—121no—
354C2×C3×C4—21no—
355C2×C3×C4—32no—
356C2×C3×C4—41no—
357C2×C3×C4—41no—
358C2×C3×C4—81no—
359C2×C3×C4—122no—
360C2×C3×C4—122no—
361C2×C3×C4—121no—
362C2×C3×C4—121no—
363C2×C3×C4D3×D411yescharacteristic
364C2×C3×C4C2×#6711yescharacteristic
365#67—41no—
366#67—42no—
367#67—122no—
368#67—122no—
369#67#21312yes—
370C2×Dic3—41no—
371C2×Dic3—42no—
372D12—21no—
373D12—62no—
374D12—62no—
375D12—122no—
376D12—122no—
377D12—122no—
378D12—121no—
379D12—121no—
380D12—241no—
381D12#21311yescharacteristic
382C4×D3—42no—
383C4×D3—41no—
384C4×D3—122no—
385C4×D3—122no—
386C4×D3C2×#6712yes—
387Dic6—21no—
388Dic6—22no—
389Dic6—41no—
390Dic6—42no—
391Dic6#21311yescharacteristic
392C3×C8—21no—
393C3×C8—21no—
394C3×C8—32no—
395C3×C8D3×D411yescharacteristic
396C3×C8C2×#6711yescharacteristic
397C3×C8C23×D311yescharacteristic
398C3×C8C23×D311yescharacteristic
399C3⋊C8C2×#6712yes—
400C2×C32—21no—
401C2×C32—81no—
402C2×C32C22×D811yescharacteristic
403C3⋊D3—82no—
404C3×D3—22no—
405C3×D3—81no—
406#41—21no—
407#41—31no—
408#41—62no—
409#41—61no—
410#41—121no—
411#41—122no—
412#41—182no—
413#41—361no—
414C2×Q8—62no—
415C2×Q8—61no—
416C2×Q8—121no—
417C2×D4—182no—
418C2×D4—181no—
419C2×D4—361no—
420C2×D4—362no—
421Q16—31no—
422Q16—32no—
423Q16—62no—
424Q16—61no—
425Q16C2×D3211yescharacteristic
426SD16—21no—
427SD16—62no—
428SD16—61no—
429SD16—182no—
430D8—31no—
431D8—92no—
432D8—182no—
433D8—181no—
434D8C2×D3211yescharacteristic
435M16—31no—
436M16—32no—
437C2×C8—32no—
438C2×C8C2×D3211yescharacteristic
439C16—31no—
440C16—31no—
441C16—92no—
442C22×C3—21no—
443C22×C3—32no—
444C22×C3—41no—
445C22×C3—41no—
446C22×C3—81no—
447C22×C3—121no—
448C22×C3D3×D811yescharacteristic
449C22×C3C2×#21311yescharacteristic
450C2×D3—41no—
451C2×D3—122no—
452C2×D3—122no—
453C2×D3—242no—
454C2×D3—482no—
455C2×D3—482no—
456C2×D3—481no—
457C2×D3—481no—
458C2×D3—482no—
459C2×D3C2×#21312yes—
460C3×C4—21no—
461C3×C4—21no—
462C3×C4—32no—
463C3×C4—41no—
464C3×C4—41no—
465C3×C4—81no—
466C3×C4—122no—
467C3×C4—121no—
468C3×C4D3×D811yescharacteristic
469C3×C4C2×#21311yescharacteristic
470C3×C4C2×D3×D411yescharacteristic
471C3×C4C22×#6711yescharacteristic
472Dic3—41no—
473Dic3—42no—
474Dic3C2×#21312yes—
475C32#341611yescharacteristic, complemented, Sylow
476C23—362no—
477C23—361no—
478Q8—21no—
479Q8—31no—
480Q8—61no—
481Q8—62no—
482Q8—122no—
483Q8—121no—
484D4—21no—
485D4—32no—
486D4—31no—
487D4—41no—
488D4—61no—
489D4—122no—
490D4—121no—
491D4—182no—
492D4—362no—
493D4—362no—
494D4—361no—
495C2×C4—32no—
496C2×C4—41no—
497C2×C4—122no—
498C2×C4—122no—
499C2×C4—121no—
500C2×C4—121no—
501C2×C4—362no—
502C2×C4D3×#6711yescharacteristic
503C8—32no—
504C8D3×#6711yescharacteristic
505C8C22×D3211yescharacteristic
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—21no—
509C2×C3—41no—
510C2×C3—62no—
511C2×C3—81no—
512C2×C3—81no—
513C2×C3—161no—
514C2×C3—241no—
515C2×C3C2×D3×D811yescharacteristic
516C2×C3C22×#21311yescharacteristic
517D3—22no—
518D3—81no—
519D3—242no—
520D3—242no—
521D3—482no—
522C22—32no—
523C22—41no—
524C22—121no—
525C22—362no—
526C22—1441no—
527C22—1442no—
528C22D3×#21311yescharacteristic
529C4—32no—
530C4—41no—
531C4—122no—
532C4—121no—
533C4D3×#21311yescharacteristic
534C4C2×D3×#6711yescharacteristic
535C3—21no—
536C3#8203211yescharacteristic, complemented
537C3#8401611yescharacteristic, complemented
538C2—21no—
539C2—62no—
540C2—81no—
541C2—241no—
542C2—722no—
543C2C2×D3×#21311yescharacteristic
subgroupG/H
centerC2C2×D3×#213
commutator, cosocleC32×C8C24
FrattiniC8C22×D32
FittingC32×#135C22
socleC2×C32C22×D8
hypercenter#135D32
hypocenterC32#3416
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #135

Complements

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

NH ≅ G/Ntype
1. C3×#5771C2semidirect
2. #10594680C2semidirect
3. #10592892C2semidirect
4. C3×#5194C2semidirect
5. #10591047C2semidirect
6. D3×#828C2semidirect
7. #10591034C2semidirect
8. #10591024C2semidirect
9. C2×#63549C2semidirect
10. #10590636C2semidirect
11. #10590621C2semidirect
16. C32×#135C22semidirect
19. C3×D3×Q16C22semidirect
21. C3×#912C22semidirect
22. C2×C3×Dic12C22semidirect
29. #63655C22semidirect
30. #63653C22semidirect
31. #63639C22semidirect
32. C3×#829C22semidirect
33. C3×#828C22semidirect
34. C3×#827C22semidirect
35. C3×#826C22semidirect
36. C2×C3×C3⋊C16C22semidirect
37. #63550C22semidirect
38. #63549C22semidirect
39. #63549C22semidirect
40. #63547C22semidirect
41. #63543C22semidirect
42. D3×C3⋊C16C22semidirect
44. #5771D3semidirect
50. #5194D3semidirect
112. C3×#135C2×D3semidirect
113. C3×#135C2×D3semidirect
120. D3×Q16C2×D3semidirect
123. #912C2×D3semidirect
127. C2×Dic12C2×D3semidirect
142. #829C2×D3semidirect
149. #828C2×D3semidirect
151. #827C2×D3semidirect
155. #826C2×D3semidirect
161. C2×C3⋊C16C2×D3semidirect
310. #135D32semidirect
475. C32#3416semidirect
536. C3#82032semidirect
537. C3#84016semidirect

Maximal subgroups

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

subgroupindex
C3×#57712
#105946802
#105928922
C3×#51942
#105910472
D3×#8282
#105910342
#105910242
C2×#635492
#105906362
#105906212
#840163
#820323