Finite Group Databasebeta

← #11869653

Subgroups — #11869653

Order 1152.

1260 conjugacy classes of subgroups.

The subgroup lattice has 549 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596098C211yesmaximal, characteristic
2C3⋊D3×#117C211yesmaximal, characteristic, complemented
3C32×#485C211yesmaximal, characteristic, complemented
4#10592744C211yesmaximal, characteristic, complemented
5#10592702C211yesmaximal, characteristic, complemented
6#10592581C211yesmaximal, characteristic, complemented
7#10592579C211yesmaximal, characteristic, complemented
8#10592562C211yesmaximal, characteristic, complemented
9#10592559C211yesmaximal, characteristic, complemented
10#10592510C211yesmaximal, characteristic, complemented
11#10592504C211yesmaximal, characteristic, complemented
12#10592503C211yesmaximal, characteristic, complemented
13#10592503C211yesmaximal, characteristic, complemented
14#10592436C211yesmaximal, characteristic, complemented
15C3⋊D3×C22⋊C8C211yesmaximal, characteristic, complemented
16#81515—34nomaximal
17C2×#3832C2211yescharacteristic
18C22×C4×C3⋊D3C2211yescharacteristic
19C32×C22⋊Q8C2211yescharacteristic
20C32×#117C2211yescharacteristic
21#64155C2211yescharacteristic
22#64139C2211yescharacteristic
23#64135C2211yescharacteristic
24C2×C8×C3⋊D3C2211yescharacteristic
25C2×C8×C3⋊D3C2211yescharacteristic
26#64104C2211yescharacteristic
27#64103—21no—
28#64102—21no—
29#64101C2211yescharacteristic
30#64101C2211yescharacteristic
31#64101C2211yescharacteristic
32C4⋊C4×C3⋊D3C2211yescharacteristic
33C4⋊C4×C3⋊D3C2211yescharacteristic
34#64091—21no—
35#64090—21no—
36C22⋊C4×C3⋊D3—21no—
37#64086—21no—
38#64081—21no—
39C42×C3⋊D3—21no—
40C32×#107C2211yescharacteristic, complemented
41C32×#106C2211yescharacteristic, complemented
42C32×#103C2211yescharacteristic, complemented
43C32×#103C2211yescharacteristic, complemented
44C32×C22⋊C8C2211yescharacteristic
45#63662C2211yescharacteristic, complemented
46#63662C2211yescharacteristic, complemented
47#63657C2211yescharacteristic
48#63648C2211yescharacteristic, complemented
49#63648C2211yescharacteristic, complemented
50#63647C2211yescharacteristic
51#63647C2211yescharacteristic
52#63645C2211yescharacteristic, complemented
53#63644C2211yescharacteristic, complemented
54#63636C2211yescharacteristic, complemented
55#63636C2211yescharacteristic, complemented
56#63635C2211yescharacteristic, complemented
57#63635C2211yescharacteristic, complemented
58#63634C2211yescharacteristic, complemented
59#63634C2211yescharacteristic, complemented
60#5627—34no—
61D3×#117—34no—
62C3×#485D314yescomplemented
63#5045—34no—
64#5003—34no—
65#4882—34no—
66#4880—34no—
67#4863—34no—
68#4860—34no—
69#4811—34no—
70#4805—34no—
71#4804—34no—
72#4804—34no—
73#4737—34no—
74D3×C22⋊C8—34no—
75C23×C3⋊D3D411yescharacteristic
76C2×C32×Q8C2311yescharacteristic
77C22×C32×C4C2311yescharacteristic
78C2×#638—21no—
79C22×C3⋊Dic3D411yescharacteristic
80#3832—22no—
81#3832—22no—
82C2×C4⋊(C3⋊D3)—21no—
83C2×C4⋊(C3⋊D3)—21no—
84C2×C4⋊(C3⋊D3)C2311yescharacteristic
85C2×C4×C3⋊D3—22no—
86C2×C4×C3⋊D3—22no—
87C2×C4×C3⋊D3—21no—
88C2×C4×C3⋊D3—21no—
89C2×C4×C3⋊D3—21no—
90C2×C4×C3⋊D3D411yescharacteristic
91C2×C4×C3⋊D3D411yescharacteristic
92C2×C4×C3⋊D3C2311yescharacteristic
93C2×C4×C3⋊D3C2311yescharacteristic
94C2×C32×C8C2311yescharacteristic
95C2×C32×C8C2311yescharacteristic
96C32×C4⋊C4—21no—
97C32×C4⋊C4C2311yescharacteristic
98C32×C4⋊C4C2311yescharacteristic
99C32×C4⋊C4C2311yescharacteristic
100C32×C22⋊C4—21no—
101C32×C22⋊C4—21no—
102C32×C42—21no—
103#3757—21no—
104#3752—21no—
105#3752—21no—
106#3752—21no—
107#3752—21no—
108#3752—21no—
109#3752—21no—
110C4⋊(C3⋊Dic3)C2311yescharacteristic
111C4⋊(C3⋊Dic3)C2311yescharacteristic
112C4⋊(C3⋊Dic3)C2311yescharacteristic
113#3750—21no—
114#3750—21no—
115#3750—21no—
116C4×C3⋊Dic3—21no—
117C4×C3⋊Dic3—21no—
118C4×C3⋊Dic3—21no—
119C4×C3⋊Dic3—21no—
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C8×C3⋊D3—22no—
123C8×C3⋊D3—22no—
124#3091—91noSylow
125C2×#239—34no—
126C22×C4×D3—34no—
127C3×C22⋊Q8C2×D314yes—
128C3×#117C2×D314yes—
129#946—34no—
130#930—34no—
131#926—34no—
132C2×D3×C8—34no—
133C2×D3×C8—34no—
134#895—34no—
135#894—64no—
136#893—64no—
137#892—34no—
138#892—34no—
139#892—34no—
140D3×C4⋊C4—34no—
141D3×C4⋊C4—34no—
142#882—64no—
143#67⋊C4—64no—
144D3×C22⋊C4—64no—
145#877—64no—
146#872—64no—
147C42×D3—64no—
148C3×#107C2×D314yescomplemented
149C3×#106C2×D314yescomplemented
150C3×#103C2×D314yescomplemented
151C3×#103C2×D314yescomplemented
152C3×C22⋊C8C2×D314yes—
153#835—34no—
154#835—34no—
155#830—34no—
156#821—34no—
157#821—34no—
158(C2×D3)⋊C8—34no—
159(C2×D3)⋊C8—34no—
160#818—34no—
161#817—34no—
162#809—34no—
163#809—34no—
164#808—34no—
165#808—34no—
166#807—34no—
167#807—34no—
168C23×C32C2×D411yescharacteristic
169C22×C3⋊D3—22no—
170C22×C3⋊D3—22no—
171C22×C3⋊D3—21no—
172C22×C3⋊D3—41no—
173C22×C3⋊D3C2×D411yescharacteristic
174C22×C3⋊D3C2×D411yescharacteristic
175C32×Q8—21no—
176C32×Q8—21no—
177C2×C32×C4—21no—
178C2×C32×C4—21no—
179C2×C32×C4—21no—
180C2×C32×C4—21no—
181C2×C32×C4—21no—
182C2×C32×C4—21no—
183C2×C32×C4C2×D411yescharacteristic
184C2×C32×C4C2411yescharacteristic
185#638—42no—
186C2×C3⋊Dic3—22no—
187C2×C3⋊Dic3—21no—
188C2×C3⋊Dic3—21no—
189C2×C3⋊Dic3—21no—
190C2×C3⋊Dic3C2×D411yescharacteristic
191C2×C3⋊Dic3C2×D411yescharacteristic
192C4⋊(C3⋊D3)—21no—
193C4⋊(C3⋊D3)—21no—
194C4⋊(C3⋊D3)—42no—
195C4⋊(C3⋊D3)—42no—
196C4×C3⋊D3—22no—
197C4×C3⋊D3—21no—
198C4×C3⋊D3—21no—
199C4×C3⋊D3—22no—
200C4×C3⋊D3—42no—
201C4×C3⋊D3—42no—
202C4×C3⋊D3—42no—
203C4×C3⋊D3#4112yes—
204C4×C3⋊D3#4112yes—
205C32×C8—21no—
206C32×C8—21no—
207C3⋊(C3⋊C8)—21no—
208C3⋊(C3⋊C8)—21no—
209#525—91no—
210C2×#117—91no—
211#485—91no—
212#485C3⋊D311yescharacteristic, complemented
213#484—91no—
214#483—91no—
215#482—91no—
216#482—91no—
217#481—91no—
218#480—91no—
219#427—91no—
220#427—91no—
221#416—91no—
222#416—91no—
223C2×C22⋊C8—91no—
224C23×D3—34no—
225C2×C3×Q8C22×D314yes—
226C22×C3×C4C22×D314yes—
227C2×#67—64no—
228C22×Dic3—34no—
229#239—68no—
230#239—68no—
231C2×D12—34no—
232C2×D12—64no—
233C2×D12—64no—
234C2×C4×D3—34no—
235C2×C4×D3—34no—
236C2×C4×D3—34no—
237C2×C4×D3—34no—
238C2×C4×D3—68no—
239C2×C4×D3—68no—
240C2×C4×D3—64no—
241C2×C4×D3—64no—
242C2×C4×D3—64no—
243C2×C3×C8C22×D314yes—
244C2×C3×C8C22×D314yes—
245C3×C4⋊C4—24no—
246C3×C4⋊C4C22×D314yes—
247C3×C4⋊C4C22×D314yes—
248C3×C4⋊C4C22×D314yes—
249C3×C22⋊C4—24no—
250C3×C22⋊C4—24no—
251C3×C42—24no—
252#217—64no—
253(C2×D3)⋊C4—64no—
254(C2×D3)⋊C4—64no—
255(C2×D3)⋊C4—64no—
256(C2×D3)⋊C4—64no—
257(C2×D3)⋊C4—64no—
258(C2×D3)⋊C4—64no—
259C4⋊Dic3—34no—
260C4⋊Dic3—34no—
261C4⋊Dic3—34no—
262Dic3⋊C4—64no—
263Dic3⋊C4—64no—
264Dic3⋊C4—64no—
265C4×Dic3—64no—
266C4×Dic3—64no—
267C4×Dic3—64no—
268C4×Dic3—64no—
269C2×C3⋊C8—34no—
270C2×C3⋊C8—34no—
271D3×C8—68no—
272D3×C8—68no—
273C22×C32—21no—
274C22×C32—21no—
275C22×C32—21no—
276C22×C32C22×D411yescharacteristic
277C2×C3⋊D3—21no—
278C2×C3⋊D3—21no—
279C2×C3⋊D3—21no—
280C2×C3⋊D3—21no—
281C2×C3⋊D3—44no—
282C2×C3⋊D3—41no—
283C2×C3⋊D3—41no—
284C2×C3⋊D3—41no—
285C2×C3⋊D3#12312yes—
286C2×C3⋊D3#13512yes—
287C32×C4—21no—
288C32×C4—41no—
289C32×C4—41no—
290C32×C4—41no—
291C32×C4—41no—
292C32×C4C2×#4111yescharacteristic
293C32×C4C2×#4111yescharacteristic
294C3⋊Dic3—21no—
295C3⋊Dic3—41no—
296C3⋊Dic3—41no—
297C3⋊Dic3—41no—
298C3⋊Dic3#12312yes—
299C2×#41—91no—
300C23×C4—91no—
301C22×C8—91no—
302C22×C8—91no—
303#123—181no—
304C22⋊Q8—91no—
305C22⋊Q8C2×C3⋊D311yescharacteristic
306#121—91no—
307#121—91no—
308#120—181no—
309C4×D4—181no—
310C4×D4—181no—
311#117—91no—
312#117—91no—
313#117—91no—
314#117—91no—
315#117—181no—
316#117—181no—
317#117C2×C3⋊D311yescharacteristic
318C2×C4⋊C4—91no—
319C2×C4⋊C4—91no—
320C2×C22⋊C4—181no—
321C2×C42—181no—
322#107—91no—
323#107—91no—
324#107—91no—
325#107C2×C3⋊D311yescharacteristic, complemented
326#106—91no—
327#106—91no—
328#106—91no—
329#106C2×C3⋊D311yescharacteristic, complemented
330#103—91no—
331#103—91no—
332#103C2×C3⋊D311yescharacteristic, complemented
333#103C2×C3⋊D311yescharacteristic, complemented
334#102—91no—
335#102—91no—
336#102—91no—
337#102—91no—
338C22⋊C8—91no—
339C22⋊C8—91no—
340C22⋊C8—91no—
341C22⋊C8C2×C3⋊D311yescharacteristic
342C23×C3D3×D414yes—
343C22×D3—34no—
344C22×D3—34no—
345C22×D3—68no—
346C22×D3—68no—
347C22×D3—64no—
348C22×D3—124no—
349C3×Q8—24no—
350C3×Q8—24no—
351C2×C3×C4—24no—
352C2×C3×C4—24no—
353C2×C3×C4—24no—
354C2×C3×C4—24no—
355C2×C3×C4—24no—
356C2×C3×C4—24no—
357C2×C3×C4D3×D414yes—
358C2×C3×C4C23×D314yes—
359#67—128no—
360C2×Dic3—34no—
361C2×Dic3—34no—
362C2×Dic3—68no—
363C2×Dic3—64no—
364C2×Dic3—64no—
365C2×Dic3—64no—
366D12—64no—
367D12—64no—
368D12—128no—
369D12—128no—
370C4×D3—38no—
371C4×D3—38no—
372C4×D3—68no—
373C4×D3—68no—
374C4×D3—64no—
375C4×D3—64no—
376C4×D3—128no—
377C4×D3—128no—
378C4×D3—128no—
379C3×C8—24no—
380C3×C8—24no—
381C3⋊C8—64no—
382C3⋊C8—64no—
383C2×C32—41no—
384C2×C32C2×#12311yescharacteristic
385C2×C32C2×#13511yescharacteristic
386C2×C32#57511yescharacteristic
387C3⋊D3—22no—
388C3⋊D3—22no—
389C3⋊D3—81no—
390C24—91no—
391#41—182no—
392#41—182no—
393C2×Q8C22×C3⋊D311yescharacteristic
394C2×D4—91no—
395C2×D4—181no—
396C2×D4—181no—
397C2×D4—181no—
398C22×C4—91no—
399C22×C4—91no—
400C22×C4—91no—
401C22×C4—91no—
402C22×C4—91no—
403C22×C4—182no—
404C22×C4—182no—
405C22×C4—181no—
406C22×C4—181no—
407C22×C4—181no—
408C22×C4C22×C3⋊D311yescharacteristic
409C2×C8—91no—
410C2×C8—91no—
411C2×C8—182no—
412C2×C8—182no—
413C2×C8C22×C3⋊D311yescharacteristic
414C2×C8C22×C3⋊D311yescharacteristic
415C4⋊C4—21no—
416C4⋊C4—91no—
417C4⋊C4—91no—
418C4⋊C4—91no—
419C4⋊C4—181no—
420C4⋊C4—181no—
421C4⋊C4—181no—
422C4⋊C4C22×C3⋊D311yescharacteristic
423C4⋊C4C22×C3⋊D311yescharacteristic
424C4⋊C4C22×C3⋊D311yescharacteristic
425C22⋊C4—21no—
426C22⋊C4—21no—
427C22⋊C4—181no—
428C22⋊C4—181no—
429C22⋊C4—181no—
430C22⋊C4—181no—
431C22⋊C4—181no—
432C22⋊C4—181no—
433C22⋊C4—181no—
434C42—21no—
435C42—181no—
436C42—181no—
437C42—181no—
438C42—181no—
439C22×C3—24no—
440C22×C3—24no—
441C22×C3—24no—
442C22×C3C2×D3×D414yes—
443C2×D3—38no—
444C2×D3—38no—
445C2×D3—64no—
446C2×D3—64no—
447C2×D3—64no—
448C2×D3—64no—
449C2×D3—1216no—
450C2×D3—124no—
451C2×D3—124no—
452C2×D3—124no—
453C3×C4—24no—
454C3×C4—44no—
455C3×C4—44no—
456C3×C4—44no—
457C3×C4—44no—
458C3×C4D3×#4114yes—
459C3×C4D3×#4114yes—
460Dic3—38no—
461Dic3—64no—
462Dic3—124no—
463Dic3—124no—
464Dic3—124no—
465C32#309111yescharacteristic, complemented, Sylow
466C23—91no—
467C23—91no—
468C23—182no—
469C23—182no—
470C23—181no—
471C23—361no—
472C23D4×C3⋊D311yescharacteristic
473Q8—21no—
474Q8—21no—
475D4—181no—
476D4—181no—
477D4—362no—
478D4—362no—
479D4—362no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—91no—
487C2×C4—92no—
488C2×C4—92no—
489C2×C4—91no—
490C2×C4—182no—
491C2×C4—182no—
492C2×C4—182no—
493C2×C4—181no—
494C2×C4—181no—
495C2×C4—181no—
496C2×C4—181no—
497C2×C4—181no—
498C2×C4—362no—
499C2×C4—362no—
500C2×C4—362no—
501C2×C4D4×C3⋊D311yescharacteristic
502C2×C4C23×C3⋊D311yescharacteristic
503C8—21no—
504C8—21no—
505C8—181no—
506C8—181no—
507C2×C3—44no—
508C2×C3D3×#12314yes—
509C2×C3D3×#13514yes—
510C2×C3#577714yes—
511D3—68no—
512D3—68no—
513D3—244no—
514C22—21no—
515C22—21no—
516C22—21no—
517C22—92no—
518C22—92no—
519C22—181no—
520C22—181no—
521C22—181no—
522C22—181no—
523C22—364no—
524C22—361no—
525C22—361no—
526C22—361no—
527C22C2×D4×C3⋊D311yescharacteristic
528C4—21no—
529C4—41no—
530C4—41no—
531C4—41no—
532C4—41no—
533C4—92no—
534C4—181no—
535C4—361no—
536C4—361no—
537C4—361no—
538C4#41×C3⋊D311yescharacteristic
539C4#41×C3⋊D311yescharacteristic
540C3#8151514yescomplemented
541C2—41no—
542C2—182no—
543C2—182no—
544C2—721no—
545C2C3⋊D3×#12311yescharacteristic
546C2C3⋊D3×#13511yescharacteristic
547C2#1059624811yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#485C2
socleC22×C32C22×D4
prime radical#10596098C2
hypercenter#485C3⋊D3
hypocenterC32#3091
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
2. C3⋊D3×#117C2semidirect
3. C32×#485C2semidirect
4. #10592744C2semidirect
5. #10592702C2semidirect
6. #10592581C2semidirect
7. #10592579C2semidirect
8. #10592562C2semidirect
9. #10592559C2semidirect
10. #10592510C2semidirect
11. #10592504C2semidirect
12. #10592503C2semidirect
13. #10592503C2semidirect
14. #10592436C2semidirect
15. C3⋊D3×C22⋊C8C2semidirect
40. C32×#107C22semidirect
41. C32×#106C22semidirect
42. C32×#103C22semidirect
43. C32×#103C22semidirect
45. #63662C22semidirect
46. #63662C22semidirect
48. #63648C22semidirect
49. #63648C22semidirect
52. #63645C22semidirect
53. #63644C22semidirect
54. #63636C22semidirect
55. #63636C22semidirect
56. #63635C22semidirect
57. #63635C22semidirect
58. #63634C22semidirect
59. #63634C22semidirect
62. C3×#485D3semidirect
148. C3×#107C2×D3semidirect
149. C3×#106C2×D3semidirect
150. C3×#103C2×D3semidirect
151. C3×#103C2×D3semidirect
212. #485C3⋊D3semidirect
325. #107C2×C3⋊D3semidirect
329. #106C2×C3⋊D3semidirect
332. #103C2×C3⋊D3semidirect
333. #103C2×C3⋊D3semidirect
465. C32#3091semidirect
540. C3#81515semidirect

Maximal subgroups

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

subgroupindex
#105960982
C3⋊D3×#1172
C32×#4852
#105927442
#105927022
#105925812
#105925792
#105925622
#105925592
#105925102
#105925042
#105925032
#105924362
C3⋊D3×C22⋊C82
#815153