Finite Group Databasebeta

← #11899726

Subgroups — #11899726

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×#5766C211yesmaximal, characteristic, complemented
2#10594680C211yesmaximal, characteristic, complemented
3C2×#63655C211yesmaximal, characteristic, complemented
4C3×#5179C211yesmaximal, characteristic, complemented
5#10591048C212yesmaximal, complemented
6#10591047C212yesmaximal, complemented
7#10591038C212yesmaximal, complemented
8D3×#828C212yesmaximal, complemented
9#10590634C211yesmaximal, characteristic, complemented
10#10590629C211yesmaximal, characteristic, complemented
11#10590622C211yesmaximal, characteristic, complemented
12#84016—31nomaximal
13#82040—31nomaximal
14C3×#1007—21no—
15#64308—21no—
16C2×C32×Q16C2211yescharacteristic, complemented
17C2×#3745C2211yescharacteristic
18C3×#942—21no—
19C3×#919C2212yescomplemented
20C3×#918—22no—
21C3×D3×Q16C2212yescomplemented
22C3×#904C2211yescharacteristic
23C3×#904C2211yescharacteristic, complemented
24C3×#901C2211yescharacteristic
25#63825—21no—
26#63808C2212yes—
27#63794—22no—
28D3×D24C2212yes—
29#63655C2212yescomplemented
30#63655C2212yescomplemented
31C2×C3⋊(C3⋊C16)C2211yescharacteristic, complemented
32C3×#829C2212yescomplemented
33C3×#828C2212yescomplemented
34C3×#812C2211yescharacteristic, complemented
35#63550C2211yescharacteristic, complemented
36#63549C2212yescomplemented
37#63547C2211yescharacteristic, complemented
38#63547C2211yescharacteristic, complemented
39#63546C2212yescomplemented
40#63545C2211yescharacteristic, complemented
41#63543C2212yescomplemented
42D3×C3⋊C16C2212yescomplemented
43C3×#578—31no—
44#5769—31no—
45#5766D311yescharacteristic, complemented
46#5752—31no—
47C3×#510—31no—
48#5194—31no—
49#5194—31no—
50#5194—32no—
51#5193—32no—
52#5193—31no—
53#5179—32no—
54#5179D311yescharacteristic, complemented
55C2×#828—31no—
56C2×#828—31no—
57C2×#828—32no—
58C2×#828—61no—
59#5140—31no—
60#4919—32no—
61#4918—32no—
62#4914—32no—
63D3×SD32—32no—
64#4908—31no—
65#4907—31no—
66C2×C32×Q8—21no—
67C2×C4⋊(C3⋊D3)—21no—
68C3×#239—22no—
69C3×#239—41no—
70C3×D3×Q8—22no—
71C3×D3×Q8—41no—
72C3×#235—21no—
73C3×#235—21no—
74C3×#235—42no—
75C3×#235D411yescharacteristic
76#3811—42no—
77D3×D12—22no—
78D3×D12—41no—
79#3799—22no—
80#3799—41no—
81C32×Q16—21no—
82C32×Q16C2312yes—
83C2×C32×C8C2311yescharacteristic
84#3745—21no—
85#3745C2312yes—
86C3×#216—22no—
87C3×#215—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#3717—22no—
98#3714—22no—
99C3⋊(C3⋊C16)C2311yescharacteristic
100C3⋊(C3⋊C16)C2311yescharacteristic
101C3×C3⋊C16C2312yes—
102#3416—91noSylow
103C3×2−1+4—61no—
104#1009—61no—
105#1009—61no—
106#1007—21no—
107C3×#137—62no—
108C3×#137—61no—
109C3×#135—32no—
110C3×#135—31no—
111C3×#135—31no—
112C2×C3×Q16—21no—
113C2×C3×Q16—32no—
114C2×C3×Q16C2×D311yescharacteristic, complemented
115C2×C3×Q16C2×D311yescharacteristic, complemented
116C3×#131—31no—
117#949—61no—
118#942—21no—
119#919—32no—
120#919C2×D312yescomplemented
121#918—22no—
122D3×Q16C2×D312yescomplemented
123#914—62no—
124D3×D8—32no—
125#908—62no—
126#908—61no—
127#904—32no—
128#904C2×D311yescharacteristic
129#904C2×D311yescharacteristic, complemented
130C2×D24—31no—
131C2×D24—31no—
132C2×D24—32no—
133C2×D24—61no—
134#901C2×D311yescharacteristic
135C3×Q32—32no—
136C3×SD32—32no—
137C3×M32—31no—
138#829—31no—
139#829—31no—
140#829C2×D312yescomplemented
141#828—32no—
142#828—32no—
143#828—32no—
144#828—32no—
145#828—31no—
146#828—31no—
147#828—32no—
148#828—62no—
149#828—62no—
150#828C2×D312yescomplemented
151#827—31no—
152#827—31no—
153#826—31no—
154#826—31no—
155#826—32no—
156#812—32no—
157#812C2×D311yescharacteristic, complemented
158C2×C3⋊C16—31no—
159C2×C3⋊C16—31no—
160C2×C3⋊C16—32no—
161C2×C3⋊C16—61no—
162#800—32no—
163D48—32no—
164#798—32no—
165D3×C16—32no—
166C22×C3⋊D3—41no—
167C2×D32—42no—
168C32×Q8—22no—
169C32×Q8—41no—
170C2×C32×C4—41no—
171C2×C32×C4C2×D411yescharacteristic
172C4⋊(C3⋊D3)—22no—
173C4⋊(C3⋊D3)—41no—
174C3×#67—41no—
175C3×#67—41no—
176C3×#67D812yes—
177C3×D12—21no—
178C3×D12—21no—
179C3×D12—42no—
180C3×D12D811yescharacteristic
181C3×C4×D3—42no—
182C3×C4×D3—41no—
183C3×C4×D3—41no—
184C3×C4×D3—42no—
185C3×C4×D3C2×D412yes—
186C3×Dic6—21no—
187C3×Dic6—21no—
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—31no—
199#510—92no—
200#509—91no—
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—122no—
212C3×#41—121no—
213C2×C3×Q8—21no—
214C2×C3×Q8—21no—
215C2×C3×Q8—41no—
216C2×C3×Q8—62no—
217C2×C3×Q8—121no—
218#239—22no—
219#239—41no—
220#239—62no—
221#239—121no—
222D3×Q8—22no—
223D3×Q8—41no—
224D3×D4—62no—
225D3×D4—121no—
226D3×D4—122no—
227D3×D4—122no—
228#235—21no—
229#235—21no—
230#235—42no—
231#235—62no—
232#235—121no—
233#235#6711yescharacteristic
234C2×D12—62no—
235C2×D12—61no—
236C2×D12—61no—
237C2×D12—121no—
238C2×D12—121no—
239C3×Q16—21no—
240C3×Q16—21no—
241C3×Q16—22no—
242C3×Q16—31no—
243C3×Q16—31no—
244C3×Q16—41no—
245C3×Q16—62no—
246C3×Q16C22×D312yes—
247C3×Q16C22×D312yes—
248C3×SD16—62no—
249C3×SD16—61no—
250C3×SD16—61no—
251C3×D8—31no—
252C3×D8—31no—
253C3×M16—31no—
254C3×M16—32no—
255C2×C3×C8—21no—
256C2×C3×C8—32no—
257C2×C3×C8C22×D311yescharacteristic
258C2×C3×C8C22×D311yescharacteristic
259#216—22no—
260#215—22no—
261#215—62no—
262#213—62no—
263#208#6711yescharacteristic
264Dic12C22×D311yescharacteristic
265Dic12C22×D311yescharacteristic
266D24—32no—
267D24—32no—
268D24—62no—
269D24—62no—
270D24—61no—
271D24—61no—
272D24—121no—
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×C32C2×D811yescharacteristic
289C2×C3⋊D3—42no—
290C2×C3⋊D3—161no—
291C2×C3×D3—41no—
292C2×C3×D3—41no—
293C2×C3×D3C2×D812yes—
294D32—162no—
295C32×C4—42no—
296C32×C4C2×D811yescharacteristic
297C32×C4C22×D411yescharacteristic
298C3×Dic3—41no—
299C3×Dic3—41no—
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—31no—
310#135—92no—
311C2×Q16—32no—
312C2×Q16D3211yescharacteristic, complemented
313C2×D8—92no—
314C2×D8—91no—
315#131—31no—
316Q32—32no—
317Q32—91no—
318SD32—32no—
319SD32—92no—
320SD32—91no—
321SD32—91no—
322SD32—92no—
323SD32—92no—
324D16—92no—
325D16—91no—
326M32—31no—
327M32—92no—
328C2×C16—92no—
329C2×C16—91no—
330C22×D3—122no—
331C22×D3—121no—
332C22×D3—121no—
333C22×D3—122no—
334C22×D3—241no—
335C3×Q8—22no—
336C3×Q8—22no—
337C3×Q8—31no—
338C3×Q8—42no—
339C3×Q8—41no—
340C3×Q8—41no—
341C3×Q8—61no—
342C3×Q8—61no—
343C3×Q8—81no—
344C3×Q8—122no—
345C3×D4—32no—
346C3×D4—31no—
347C3×D4—61no—
348C3×D4—61no—
349C3×D4—122no—
350C3×D4—121no—
351C3×D4—121no—
352C2×C3×C4—21no—
353C2×C3×C4—32no—
354C2×C3×C4—41no—
355C2×C3×C4—41no—
356C2×C3×C4—81no—
357C2×C3×C4—122no—
358C2×C3×C4—122no—
359C2×C3×C4—121no—
360C2×C3×C4—121no—
361C2×C3×C4D3×D411yescharacteristic
362C2×C3×C4C2×#6711yescharacteristic
363#67—41no—
364#67—41no—
365#67—122no—
366#67—122no—
367#67#21312yes—
368D12—21no—
369D12—21no—
370D12—42no—
371D12—62no—
372D12—62no—
373D12—122no—
374D12—122no—
375D12—122no—
376D12—121no—
377D12—121no—
378D12—241no—
379D12#21311yescharacteristic
380C4×D3—42no—
381C4×D3—41no—
382C4×D3—41no—
383C4×D3—42no—
384C4×D3—122no—
385C4×D3—122no—
386C4×D3C2×#6712yes—
387Dic6—21no—
388Dic6—21no—
389Dic6—42no—
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×C32C22×D811yescharacteristic
401C3⋊D3—82no—
402C3×D3—22no—
403C3×D3—81no—
404C3×D3—81no—
405#41—31no—
406#41—62no—
407#41—61no—
408#41—61no—
409#41—122no—
410#41—121no—
411#41—182no—
412#41—361no—
413C2×Q8—21no—
414C2×Q8—62no—
415C2×Q8—121no—
416C2×D4—182no—
417C2×D4—181no—
418C2×D4—361no—
419C2×D4—362no—
420Q16—21no—
421Q16—31no—
422Q16—31no—
423Q16—62no—
424Q16C2×D3212yes—
425SD16—62no—
426SD16—61no—
427SD16—61no—
428SD16—182no—
429D8—31no—
430D8—31no—
431D8—92no—
432D8—182no—
433D8—181no—
434M16—31no—
435M16—32no—
436C2×C8—32no—
437C2×C8C2×D3211yescharacteristic
438C16—32no—
439C16—91no—
440C16—91no—
441C22×C3—21no—
442C22×C3—32no—
443C22×C3—121no—
444C22×C3—121no—
445C22×C3D3×D811yescharacteristic
446C22×C3C2×#21311yescharacteristic
447C2×D3—41no—
448C2×D3—41no—
449C2×D3—122no—
450C2×D3—122no—
451C2×D3—242no—
452C2×D3—482no—
453C2×D3—482no—
454C2×D3—481no—
455C2×D3—481no—
456C2×D3—482no—
457C2×D3C2×#21312yes—
458C3×C4—21no—
459C3×C4—21no—
460C3×C4—32no—
461C3×C4—42no—
462C3×C4—42no—
463C3×C4—82no—
464C3×C4—121no—
465C3×C4—121no—
466C3×C4D3×D811yescharacteristic
467C3×C4C2×#21311yescharacteristic
468C3×C4C2×D3×D411yescharacteristic
469C3×C4C22×#6711yescharacteristic
470Dic3—41no—
471Dic3—41no—
472Dic3C2×#21312yes—
473C32#341611yescharacteristic, complemented, Sylow
474C23—362no—
475C23—361no—
476Q8—22no—
477Q8—31no—
478Q8—41no—
479Q8—61no—
480Q8—61no—
481Q8—122no—
482D4—32no—
483D4—31no—
484D4—61no—
485D4—61no—
486D4—122no—
487D4—121no—
488D4—121no—
489D4—182no—
490D4—362no—
491D4—362no—
492D4—361no—
493C2×C4—32no—
494C2×C4—41no—
495C2×C4—122no—
496C2×C4—122no—
497C2×C4—121no—
498C2×C4—121no—
499C2×C4—362no—
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—241no—
510C2×C3—241no—
511C2×C3C2×D3×D811yescharacteristic
512C2×C3C22×#21311yescharacteristic
513D3—22no—
514D3—81no—
515D3—81no—
516D3—242no—
517D3—242no—
518D3—482no—
519C22—32no—
520C22—121no—
521C22—121no—
522C22—362no—
523C22—1441no—
524C22—1442no—
525C22D3×#21311yescharacteristic
526C4—32no—
527C4—42no—
528C4—121no—
529C4—121no—
530C4D3×#21311yescharacteristic
531C4C2×D3×#6711yescharacteristic
532C3—21no—
533C3#8204011yescharacteristic, complemented
534C3#8401611yescharacteristic, complemented
535C2—21no—
536C2—62no—
537C2—241no—
538C2—241no—
539C2—722no—
540C2C2×D3×#21311yescharacteristic
subgroupG/H
centerC2C2×D3×#213
commutator, cosocleC32×C8C24
FrattiniC8C22×D32
FittingC2×C32×Q16C22
socleC2×C32C22×D8
hypercenterC2×Q16D32
hypocenterC32#3416
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
1. C3×#5766C2semidirect
2. #10594680C2semidirect
3. C2×#63655C2semidirect
4. C3×#5179C2semidirect
5. #10591048C2semidirect
6. #10591047C2semidirect
7. #10591038C2semidirect
8. D3×#828C2semidirect
9. #10590634C2semidirect
10. #10590629C2semidirect
11. #10590622C2semidirect
16. C2×C32×Q16C22semidirect
19. C3×#919C22semidirect
21. C3×D3×Q16C22semidirect
23. C3×#904C22semidirect
29. #63655C22semidirect
30. #63655C22semidirect
31. C2×C3⋊(C3⋊C16)C22semidirect
32. C3×#829C22semidirect
33. C3×#828C22semidirect
34. C3×#812C22semidirect
35. #63550C22semidirect
36. #63549C22semidirect
37. #63547C22semidirect
38. #63547C22semidirect
39. #63546C22semidirect
40. #63545C22semidirect
41. #63543C22semidirect
42. D3×C3⋊C16C22semidirect
45. #5766D3semidirect
54. #5179D3semidirect
114. C2×C3×Q16C2×D3semidirect
115. C2×C3×Q16C2×D3semidirect
120. #919C2×D3semidirect
122. D3×Q16C2×D3semidirect
129. #904C2×D3semidirect
140. #829C2×D3semidirect
150. #828C2×D3semidirect
157. #812C2×D3semidirect
312. C2×Q16D32semidirect
473. C32#3416semidirect
533. C3#82040semidirect
534. C3#84016semidirect

Maximal subgroups

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

subgroupindex
C3×#57662
#105946802
C2×#636552
C3×#51792
#105910482
#105910472
#105910382
D3×#8282
#105906342
#105906292
#105906222
#840163
#820403