Finite Group Databasebeta

← #11870547

Subgroups — #11870547

Order 1152.

1188 conjugacy classes of subgroups.

The subgroup lattice has 525 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596071C211yesmaximal, characteristic, complemented
2#10595993C211yesmaximal, characteristic, complemented
3C32×#482C211yesmaximal, characteristic, complemented
4#10592736C211yesmaximal, characteristic
5#10592695C211yesmaximal, characteristic, complemented
6#10592590C211yesmaximal, characteristic, complemented
7#10592572C211yesmaximal, characteristic, complemented
8#10592556C211yesmaximal, characteristic, complemented
9#10592551C211yesmaximal, characteristic, complemented
10#10592486C211yesmaximal, characteristic, complemented
11#10592466C211yesmaximal, characteristic, complemented
12#10592457C211yesmaximal, characteristic, complemented
13#10592455C211yesmaximal, characteristic, complemented
14#10592432C211yesmaximal, characteristic, complemented
15#10592417C211yesmaximal, characteristic, complemented
16#81348—34nomaximal
17C2×#3828C2211yescharacteristic
18C32×#121C2211yescharacteristic
19C32×#117C2211yescharacteristic
20#64145C2211yescharacteristic
21#64144—21no—
22D4×C3⋊Dic3—21no—
23D4×C3⋊Dic3C2211yescharacteristic
24C2×#3754C2211yescharacteristic
25C2×#3753C2211yescharacteristic
26#64133C2211yescharacteristic
27C2×C4×C3⋊Dic3C2211yescharacteristic
28C2×#3746C2211yescharacteristic
29C2×#3744C2211yescharacteristic
30#64102C2211yescharacteristic
31#64102C2211yescharacteristic
32#64099C2211yescharacteristic
33#64096C2211yescharacteristic
34#64096C2211yescharacteristic
35#64096C2211yescharacteristic
36#64090—21no—
37#64090—21no—
38#64088—21no—
39#64086—21no—
40#64081—21no—
41C42×C3⋊D3—21no—
42C32×#107C2211yescharacteristic
43C32×#106C2211yescharacteristic
44C32×#102C2211yescharacteristic
45C32×#102C2211yescharacteristic
46C32×C22⋊C8C2211yescharacteristic
47#63657C2211yescharacteristic
48#63648C2211yescharacteristic
49#63643C2211yescharacteristic
50#63641C2211yescharacteristic
51#63641C2211yescharacteristic
52C8×C3⋊Dic3C2211yescharacteristic
53C8×C3⋊Dic3C2211yescharacteristic
54#63637C2211yescharacteristic
55#63637C2211yescharacteristic
56#63637C2211yescharacteristic
57#63636C2211yescharacteristic
58#63635C2211yescharacteristic
59#63634C2211yescharacteristic
60#5600—34no—
61#5522—34no—
62C3×#482D314yescomplemented
63#5037—34no—
64#4996—34no—
65#4891—34no—
66#4873—34no—
67#4857—34no—
68#4852—34no—
69#4787—34no—
70#4767—34no—
71#4758—34no—
72#4756—34no—
73#4733—34no—
74#4718—34no—
75C2×C32×D4—21no—
76C2×C32×D4C2311yescharacteristic
77C22×C32×C4C2311yescharacteristic
78C2×#638—21no—
79C22×C3⋊Dic3—21no—
80C22×C3⋊Dic3D411yescharacteristic
81C22×C3⋊Dic3D411yescharacteristic
82#3828—22no—
83#3828—22no—
84C2×C4⋊(C3⋊D3)C2311yescharacteristic
85C2×C4×C3⋊D3—21no—
86C2×C4×C3⋊D3—21no—
87C2×C4×C3⋊D3—21no—
88C2×#634C2311yescharacteristic
89C2×#634C2311yescharacteristic
90C2×C32×C8C2311yescharacteristic
91C2×C32×C8C2311yescharacteristic
92C32×C4⋊C4C2311yescharacteristic
93C32×C4⋊C4C2311yescharacteristic
94C32×C4⋊C4C2311yescharacteristic
95C32×C22⋊C4—21no—
96C32×C22⋊C4—21no—
97C32×C42—21no—
98#3757—21no—
99#3757—21no—
100#3757—21no—
101#3757—21no—
102#3754—22no—
103#3753—22no—
104#3752—21no—
105#3752—21no—
106C4⋊(C3⋊Dic3)—21no—
107C4⋊(C3⋊Dic3)C2311yescharacteristic
108#3750—21no—
109#3750—21no—
110#3750—21no—
111#3750—21no—
112#3750—21no—
113C4×C3⋊Dic3—21no—
114C4×C3⋊Dic3—21no—
115C4×C3⋊Dic3—21no—
116C4×C3⋊Dic3D411yescharacteristic
117C4×C3⋊Dic3D411yescharacteristic
118C4×C3⋊Dic3C2311yescharacteristic
119C4×C3⋊Dic3C2311yescharacteristic
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122#3746—22no—
123#3744—22no—
124#3102—91noSylow
125C2×#235—34no—
126C3×#121C2×D314yes—
127C3×#117C2×D314yes—
128#936—34no—
129#935—64no—
130D4×Dic3—34no—
131D4×Dic3—64no—
132C2×#214—34no—
133C2×#213—34no—
134#924—34no—
135C2×C4×Dic3—34no—
136C2×Dic12—34no—
137C2×#204—34no—
138#893—34no—
139#893—34no—
140#890—34no—
141#887—34no—
142#887—34no—
143#887—34no—
144#67⋊C4—64no—
145#67⋊C4—64no—
146#879—64no—
147#877—64no—
148#872—64no—
149C42×D3—64no—
150C3×#107C2×D314yes—
151C3×#106C2×D314yes—
152C3×#102C2×D314yes—
153C3×#102C2×D314yes—
154C3×C22⋊C8C2×D314yes—
155#830—34no—
156#821—34no—
157#816—34no—
158Dic3⋊C8—34no—
159Dic3⋊C8—34no—
160C8×Dic3—34no—
161C8×Dic3—34no—
162#810—34no—
163#810—34no—
164#810—34no—
165#809—34no—
166#808—34no—
167#807—34no—
168C23×C32—21no—
169C23×C32C2×D411yescharacteristic
170C22×C3⋊D3—21no—
171C32×D4—21no—
172C32×D4—21no—
173C32×D4—42no—
174C2×C32×C4—21no—
175C2×C32×C4—21no—
176C2×C32×C4—21no—
177C2×C32×C4—21no—
178C2×C32×C4—21no—
179C2×C32×C4C2×D411yescharacteristic
180C2×C32×C4C2411yescharacteristic
181#638—24no—
182C2×C3⋊Dic3—21no—
183C2×C3⋊Dic3—22no—
184C2×C3⋊Dic3—21no—
185C2×C3⋊Dic3—21no—
186C2×C3⋊Dic3—41no—
187C2×C3⋊Dic3—42no—
188C2×C3⋊Dic3C2×D411yescharacteristic
189C2×C3⋊Dic3C2×D411yescharacteristic
190C2×C3⋊Dic3C2×D411yescharacteristic
191C2×C3⋊Dic3C2×D411yescharacteristic
192C4⋊(C3⋊D3)—21no—
193C4⋊(C3⋊D3)#4112yes—
194C4×C3⋊D3—24no—
195C4×C3⋊D3—42no—
196C4×C3⋊D3—42no—
197#634—21no—
198#634—21no—
199#634—21no—
200#634#4112yes—
201C32×C8—21no—
202C32×C8—21no—
203C3⋊(C3⋊C8)—21no—
204C3⋊(C3⋊C8)—21no—
205#529—91no—
206C4×#41—91no—
207#485—91no—
208#482C3⋊D311yescharacteristic, complemented
209#479—91no—
210#478—91no—
211#464—91no—
212#463—91no—
213#452—91no—
214#449—91no—
215C4×Q16—91no—
216C4×SD16—91no—
217C4×SD16—91no—
218C4×D8—91no—
219#431—91no—
220C2×C3×D4—24no—
221C2×C3×D4C22×D314yes—
222C22×C3×C4C22×D314yes—
223C2×#67—64no—
224C22×Dic3—34no—
225C22×Dic3—34no—
226C22×Dic3—64no—
227#235—68no—
228#235—68no—
229C2×D12—34no—
230C2×C4×D3—64no—
231C2×C4×D3—64no—
232C2×C4×D3—64no—
233C2×Dic6—34no—
234C2×Dic6—34no—
235C2×C3×C8C22×D314yes—
236C2×C3×C8C22×D314yes—
237C3×C4⋊C4C22×D314yes—
238C3×C4⋊C4C22×D314yes—
239C3×C4⋊C4C22×D314yes—
240C3×C22⋊C4—24no—
241C3×C22⋊C4—24no—
242C3×C42—24no—
243#217—64no—
244#217—64no—
245#217—64no—
246#217—64no—
247#214—68no—
248#213—68no—
249(C2×D3)⋊C4—64no—
250(C2×D3)⋊C4—64no—
251C4⋊Dic3—34no—
252C4⋊Dic3—64no—
253Dic3⋊C4—64no—
254Dic3⋊C4—64no—
255Dic3⋊C4—64no—
256Dic3⋊C4—64no—
257Dic3⋊C4—64no—
258C4×Dic3—34no—
259C4×Dic3—34no—
260C4×Dic3—34no—
261C4×Dic3—34no—
262C4×Dic3—64no—
263C4×Dic3—64no—
264C4×Dic3—64no—
265C2×C3⋊C8—34no—
266C2×C3⋊C8—34no—
267Dic12—68no—
268#204—68no—
269C22×C32—21no—
270C22×C32—21no—
271C22×C32—21no—
272C22×C32—41no—
273C22×C32—41no—
274C22×C32—41no—
275C22×C32C22×D411yescharacteristic
276C2×C3⋊D3—22no—
277C2×C3⋊D3—41no—
278C2×C3⋊D3—41no—
279C32×C4—21no—
280C32×C4—41no—
281C32×C4—41no—
282C32×C4—41no—
283C32×C4C2×#4111yescharacteristic
284C32×C4C2×#4111yescharacteristic
285C3⋊Dic3—22no—
286C3⋊Dic3—21no—
287C3⋊Dic3—21no—
288C3⋊Dic3—21no—
289C3⋊Dic3—41no—
290C3⋊Dic3—41no—
291C3⋊Dic3#13512yes—
292C2×#41—91no—
293C2×Q16—91no—
294C2×SD16—91no—
295C2×SD16—91no—
296C2×D8—91no—
297#126—181no—
298#125—91no—
299#124—91no—
300#123—181no—
301C22⋊Q8—91no—
302#121C2×C3⋊D311yescharacteristic
303C4×Q8—91no—
304C4×Q8—91no—
305C4×Q8—91no—
306C4×D4—91no—
307C4×D4—91no—
308C4×D4—91no—
309C4×D4—181no—
310C4×D4—181no—
311C4×D4—181no—
312#117—181no—
313#117—181no—
314#117C2×C3⋊D311yescharacteristic
315C2×C42—91no—
316C2×C42—181no—
317#107—91no—
318#107C2×C3⋊D311yescharacteristic
319#106—91no—
320#106C2×C3⋊D311yescharacteristic
321C4⋊C8—91no—
322C4⋊C8—91no—
323#103—91no—
324#103—91no—
325#103—91no—
326#103—91no—
327#102—91no—
328#102—91no—
329#102C2×C3⋊D311yescharacteristic
330#102C2×C3⋊D311yescharacteristic
331C22⋊C8—91no—
332C22⋊C8C2×C3⋊D311yescharacteristic
333C4×C8—91no—
334C4×C8—91no—
335C23×C3—24no—
336C23×C3D3×D414yes—
337C22×D3—64no—
338C3×D4—24no—
339C3×D4—24no—
340C3×D4—48no—
341C2×C3×C4—24no—
342C2×C3×C4—24no—
343C2×C3×C4—24no—
344C2×C3×C4—24no—
345C2×C3×C4—24no—
346C2×C3×C4D3×D414yes—
347C2×C3×C4C23×D314yes—
348#67—616no—
349C2×Dic3—34no—
350C2×Dic3—34no—
351C2×Dic3—34no—
352C2×Dic3—34no—
353C2×Dic3—68no—
354C2×Dic3—64no—
355C2×Dic3—64no—
356C2×Dic3—64no—
357C2×Dic3—128no—
358C2×Dic3—124no—
359D12—38no—
360D12—64no—
361C4×D3—616no—
362C4×D3—128no—
363C4×D3—128no—
364Dic6—38no—
365Dic6—64no—
366Dic6—64no—
367Dic6—64no—
368C3×C8—24no—
369C3×C8—24no—
370C3⋊C8—64no—
371C3⋊C8—64no—
372C2×C32—41no—
373C2×C32—81no—
374C2×C32#52511yescharacteristic
375C2×C32C2×#13511yescharacteristic
376C2×C32#57511yescharacteristic
377C3⋊D3—42no—
378#41—182no—
379#41—182no—
380C2×Q8—91no—
381C2×Q8—91no—
382C2×D4—21no—
383C2×D4—91no—
384C2×D4—181no—
385C2×D4C22×C3⋊D311yescharacteristic
386C22×C4—91no—
387C22×C4—91no—
388C22×C4—181no—
389C22×C4—181no—
390C22×C4—181no—
391C22×C4—181no—
392C22×C4C22×C3⋊D311yescharacteristic
393Q16—182no—
394SD16—182no—
395SD16—182no—
396D8—182no—
397C2×C8—91no—
398C2×C8—91no—
399C2×C8C22×C3⋊D311yescharacteristic
400C2×C8C22×C3⋊D311yescharacteristic
401C4⋊C4—91no—
402C4⋊C4—181no—
403C4⋊C4—181no—
404C4⋊C4—181no—
405C4⋊C4—181no—
406C4⋊C4—181no—
407C4⋊C4—181no—
408C4⋊C4C22×C3⋊D311yescharacteristic
409C4⋊C4C22×C3⋊D311yescharacteristic
410C4⋊C4C22×C3⋊D311yescharacteristic
411C22⋊C4—21no—
412C22⋊C4—21no—
413C22⋊C4—181no—
414C22⋊C4—181no—
415C22⋊C4—181no—
416C22⋊C4—181no—
417C22⋊C4—181no—
418C22⋊C4—181no—
419C42—21no—
420C42—91no—
421C42—91no—
422C42—91no—
423C42—91no—
424C42—181no—
425C42—181no—
426C42—181no—
427C22×C3—24no—
428C22×C3—24no—
429C22×C3—24no—
430C22×C3—44no—
431C22×C3—44no—
432C22×C3—44no—
433C22×C3C2×D3×D414yes—
434C2×D3—68no—
435C2×D3—124no—
436C2×D3—124no—
437C3×C4—24no—
438C3×C4—44no—
439C3×C4—44no—
440C3×C4—44no—
441C3×C4D3×#4114yes—
442C3×C4D3×#4114yes—
443Dic3—38no—
444Dic3—68no—
445Dic3—64no—
446Dic3—64no—
447Dic3—64no—
448Dic3—124no—
449Dic3—124no—
450C32#310211yescharacteristic, complemented, Sylow
451C23—21no—
452C23—181no—
453C23D4×C3⋊D311yescharacteristic
454Q8—92no—
455Q8—181no—
456Q8—181no—
457Q8—181no—
458D4—21no—
459D4—21no—
460D4—42no—
461D4—92no—
462D4—184no—
463D4—181no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—91no—
470C2×C4—91no—
471C2×C4—91no—
472C2×C4—91no—
473C2×C4—184no—
474C2×C4—182no—
475C2×C4—181no—
476C2×C4—181no—
477C2×C4—181no—
478C2×C4—362no—
479C2×C4—362no—
480C2×C4—362no—
481C2×C4—361no—
482C2×C4D4×C3⋊D311yescharacteristic
483C2×C4C23×C3⋊D311yescharacteristic
484C8—21no—
485C8—21no—
486C8—181no—
487C8—181no—
488C2×C3—44no—
489C2×C3—84no—
490C2×C3#565614yes—
491C2×C3D3×#13514yes—
492C2×C3#577314yes—
493D3—128no—
494C22—21no—
495C22—21no—
496C22—21no—
497C22—41no—
498C22—41no—
499C22—41no—
500C22—182no—
501C22—361no—
502C22—361no—
503C22C2×D4×C3⋊D311yescharacteristic
504C4—21no—
505C4—41no—
506C4—41no—
507C4—41no—
508C4—92no—
509C4—182no—
510C4—181no—
511C4—181no—
512C4—181no—
513C4—361no—
514C4—361no—
515C4#41×C3⋊D311yescharacteristic
516C4#41×C3⋊D311yescharacteristic
517C3#8134814yescomplemented
518C2—41no—
519C2—81no—
520C2—362no—
521C2#1059612711yescharacteristic
522C2C3⋊D3×#13511yescharacteristic
523C2#1059624411yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#482C2
socleC22×C32C22×D4
prime radical#10592736C2
hypercenter#482C3⋊D3
hypocenterC32#3102
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #10596071C2semidirect
2. #10595993C2semidirect
3. C32×#482C2semidirect
5. #10592695C2semidirect
6. #10592590C2semidirect
7. #10592572C2semidirect
8. #10592556C2semidirect
9. #10592551C2semidirect
10. #10592486C2semidirect
11. #10592466C2semidirect
12. #10592457C2semidirect
13. #10592455C2semidirect
14. #10592432C2semidirect
15. #10592417C2semidirect
62. C3×#482D3semidirect
208. #482C3⋊D3semidirect
450. C32#3102semidirect
517. C3#81348semidirect

Maximal subgroups

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

subgroupindex
#105960712
#105959932
C32×#4822
#105927362
#105926952
#105925902
#105925722
#105925562
#105925512
#105924862
#105924662
#105924572
#105924552
#105924322
#105924172
#813483