Finite Group Databasebeta

← #11887703

Subgroups — #11887703

Order 1152.

1158 conjugacy classes of subgroups.

The subgroup lattice has 537 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596069C211yesmaximal, characteristic
2#10595984C211yesmaximal, characteristic, complemented
3C32×#480C211yesmaximal, characteristic, complemented
4#10592740C211yesmaximal, characteristic, complemented
5C2×#63637C211yesmaximal, characteristic, complemented
6#10592587C211yesmaximal, characteristic, complemented
7#10592586C211yesmaximal, characteristic, complemented
8#10592576C211yesmaximal, characteristic, complemented
9#10592572C211yesmaximal, characteristic, complemented
10#10592482C211yesmaximal, characteristic, complemented
11#10592471C211yesmaximal, characteristic, complemented
12#10592467C211yesmaximal, characteristic, complemented
13#10592466C211yesmaximal, characteristic, complemented
14#10592438C211yesmaximal, characteristic, complemented
15#10592424C211yesmaximal, characteristic, complemented
16#81305—34nomaximal
17C2×#3830C2211yescharacteristic
18C22×#634C2211yescharacteristic
19C32×#121C2211yescharacteristic
20C2×C32×C4⋊C4C2211yescharacteristic
21#64148—21no—
22#64145C2211yescharacteristic
23D4×C3⋊Dic3—21no—
24C2×#3754C2211yescharacteristic
25#64138—21no—
26C4×#638C2211yescharacteristic
27#64135—21no—
28#64133C2211yescharacteristic
29C22×C3⋊(C3⋊C8)C2211yescharacteristic
30C2×#3746C2211yescharacteristic
31C2×#3746C2211yescharacteristic
32C2×C8×C3⋊D3C2211yescharacteristic
33#64107—21no—
34#64106C2211yescharacteristic
35#64106C2211yescharacteristic
36#64101C2211yescharacteristic
37#64099C2211yescharacteristic
38#64098—21no—
39#64096C2211yescharacteristic
40#64096C2211yescharacteristic
41#64094—21no—
42#64087—21no—
43C32×#107C2211yescharacteristic
44C32×#107C2211yescharacteristic
45C32×#102C2211yescharacteristic
46C32×#102C2211yescharacteristic
47C32×C22⋊C8C2211yescharacteristic
48#63659C2211yescharacteristic
49#63647C2211yescharacteristic
50#63643C2211yescharacteristic
51#63643C2211yescharacteristic
52#63641C2211yescharacteristic
53C8×C3⋊Dic3C2211yescharacteristic
54#63637C2211yescharacteristic
55#63637C2211yescharacteristic
56#63637C2211yescharacteristic
57#63637C2211yescharacteristic
58#63637C2211yescharacteristic
59#63635C2211yescharacteristic
60#5598—34no—
61#5513—34no—
62C3×#480D314yescomplemented
63#5041—34no—
64C2×#810—34no—
65#4888—34no—
66#4887—34no—
67#4877—34no—
68#4873—34no—
69#4783—34no—
70#4772—34no—
71#4768—34no—
72#4767—34no—
73#4739—34no—
74#67⋊C8—34no—
75C2×C32×D4—21no—
76C2×C32×D4C2311yescharacteristic
77C22×C32×C4—21no—
78C22×C32×C4C2311yescharacteristic
79C2×#638—21no—
80C2×#638D411yescharacteristic
81C22×C3⋊Dic3—21no—
82C22×C3⋊Dic3—21no—
83#3830—22no—
84#3830—41no—
85C2×C4×C3⋊D3C2311yescharacteristic
86C2×#634—22no—
87C2×#634—21no—
88C2×#634—41no—
89C2×#634C2311yescharacteristic
90C2×#634C2311yescharacteristic
91C2×#634C2311yescharacteristic
92C2×C32×C8C2311yescharacteristic
93C2×C32×C8C2311yescharacteristic
94C32×C4⋊C4—21no—
95C32×C4⋊C4C2311yescharacteristic
96C32×C4⋊C4C2311yescharacteristic
97C32×C4⋊C4C2311yescharacteristic
98C32×C22⋊C4—21no—
99#3757—21no—
100#3757—21no—
101#3757—21no—
102#3757D411yescharacteristic
103#3754—41no—
104#3752—21no—
105#3752—21no—
106#3752—21no—
107#3752D411yescharacteristic
108C4⋊(C3⋊Dic3)—21no—
109C4⋊(C3⋊Dic3)—21no—
110C4⋊(C3⋊Dic3)—21no—
111C4⋊(C3⋊Dic3)C2311yescharacteristic
112#3750—21no—
113#3750—21no—
114#3750—21no—
115#3750—21no—
116#3750D411yescharacteristic
117C4×C3⋊Dic3—21no—
118C4×C3⋊Dic3—21no—
119C4×C3⋊Dic3—21no—
120C4×C3⋊Dic3C2311yescharacteristic
121C2×C3⋊(C3⋊C8)—41no—
122C2×C3⋊(C3⋊C8)C2311yescharacteristic
123C2×C3⋊(C3⋊C8)C2311yescharacteristic
124#3746—22no—
125#3746—41no—
126C8×C3⋊D3—41no—
127#3300—91noSylow
128C2×#237—34no—
129C22×Dic6—34no—
130C3×#121C2×D314yes—
131C2×C3×C4⋊C4C2×D314yes—
132#939—64no—
133#936—34no—
134D4×Dic3—64no—
135C2×#214—34no—
136#929—64no—
137C4×#67—34no—
138#926—64no—
139#924—34no—
140C22×C3⋊C8—34no—
141C2×Dic12—34no—
142C2×Dic12—34no—
143C2×D3×C8—34no—
144#898—64no—
145#897—34no—
146#897—34no—
147#892—34no—
148#890—34no—
149#889—64no—
150#887—34no—
151#887—34no—
152#885—64no—
153#878—64no—
154C3×#107C2×D314yes—
155C3×#107C2×D314yes—
156C3×#102C2×D314yes—
157C3×#102C2×D314yes—
158C3×C22⋊C8C2×D314yes—
159#832—34no—
160(C2×D3)⋊C8—34no—
161#816—34no—
162#816—34no—
163Dic3⋊C8—34no—
164C8×Dic3—34no—
165#810—34no—
166#810—34no—
167#810—34no—
168#810—34no—
169#810—34no—
170#808—34no—
171C23×C32—21no—
172C23×C32C2×D411yescharacteristic
173C22×C3⋊D3C2×D411yescharacteristic
174C32×D4—21no—
175C32×D4—21no—
176C32×D4—42no—
177C2×C32×C4—21no—
178C2×C32×C4—21no—
179C2×C32×C4—21no—
180C2×C32×C4—21no—
181C2×C32×C4—21no—
182C2×C32×C4—42no—
183C2×C32×C4C2×D411yescharacteristic
184C2×C32×C4C2411yescharacteristic
185#638—22no—
186#638—42no—
187C2×C3⋊Dic3—21no—
188C2×C3⋊Dic3—21no—
189C2×C3⋊Dic3—21no—
190C2×C3⋊Dic3—21no—
191C2×C3⋊Dic3—42no—
192C2×C3⋊Dic3—42no—
193C2×C3⋊Dic3C2×D411yescharacteristic
194C2×C3⋊Dic3C2×D411yescharacteristic
195C2×C3⋊Dic3C2×D411yescharacteristic
196C4×C3⋊D3—21no—
197C4×C3⋊D3—21no—
198#634—21no—
199#634—21no—
200#634—21no—
201#634—21no—
202#634—21no—
203#634—42no—
204#634#4112yes—
205C32×C8—21no—
206C32×C8—21no—
207C3⋊(C3⋊C8)—21no—
208C3⋊(C3⋊C8)—21no—
209#552—91no—
210#548—91no—
211#488—91no—
212#485—91no—
213#480C3⋊D311yescharacteristic, complemented
214#479—91no—
215#467—91no—
216#465—91no—
217#464—91no—
218#452—91no—
219#451—91no—
220C4×Q16—91no—
221C8×D4—91no—
222#416—91no—
223C2×#103—91no—
224C2×C3×D4—24no—
225C2×C3×D4C22×D314yes—
226C22×C3×C4—24no—
227C22×C3×C4C22×D314yes—
228C2×#67—34no—
229C2×#67—64no—
230C22×Dic3—64no—
231C22×Dic3—64no—
232#237—68no—
233#237—124no—
234C2×C4×D3—34no—
235C2×Dic6—34no—
236C2×Dic6—34no—
237C2×Dic6—34no—
238C2×Dic6—68no—
239C2×Dic6—64no—
240C2×Dic6—124no—
241C2×C3×C8C22×D314yes—
242C2×C3×C8C22×D314yes—
243C3×C4⋊C4—24no—
244C3×C4⋊C4C22×D314yes—
245C3×C4⋊C4C22×D314yes—
246C3×C4⋊C4C22×D314yes—
247C3×C22⋊C4—24no—
248#217—34no—
249#217—64no—
250#217—64no—
251#217—64no—
252#214—124no—
253(C2×D3)⋊C4—34no—
254(C2×D3)⋊C4—64no—
255(C2×D3)⋊C4—64no—
256(C2×D3)⋊C4—64no—
257C4⋊Dic3—34no—
258C4⋊Dic3—64no—
259C4⋊Dic3—64no—
260C4⋊Dic3—64no—
261Dic3⋊C4—34no—
262Dic3⋊C4—64no—
263Dic3⋊C4—64no—
264Dic3⋊C4—64no—
265Dic3⋊C4—64no—
266C4×Dic3—34no—
267C4×Dic3—64no—
268C4×Dic3—64no—
269C4×Dic3—64no—
270C2×C3⋊C8—34no—
271C2×C3⋊C8—34no—
272C2×C3⋊C8—124no—
273Dic12—68no—
274Dic12—124no—
275D3×C8—124no—
276C22×C32—21no—
277C22×C32—21no—
278C22×C32—41no—
279C22×C32—41no—
280C22×C32—41no—
281C22×C32#13512yes—
282C22×C32C22×D411yescharacteristic
283C2×C3⋊D3—21no—
284C2×C3⋊D3—21no—
285C2×C3⋊D3—21no—
286C32×C4—21no—
287C32×C4—41no—
288C32×C4—41no—
289C32×C4—41no—
290C32×C4C2×#4111yescharacteristic
291C32×C4H(5,𝔽2)11yescharacteristic
292C3⋊Dic3—22no—
293C3⋊Dic3—21no—
294C3⋊Dic3—21no—
295C3⋊Dic3—21no—
296C3⋊Dic3—41no—
297C3⋊Dic3—41no—
298C3⋊Dic3—41no—
299C2×#41—91no—
300C22×Q8—91no—
301C2×Q16—91no—
302C2×Q16—91no—
303C2×SD16—91no—
304C22×C8—91no—
305C22×C8—91no—
306#126—181no—
307#125—91no—
308#125—181no—
309#124—91no—
310#124—181no—
311#123—181no—
312C22⋊Q8—91no—
313C22⋊Q8—91no—
314C22⋊Q8—91no—
315C22⋊Q8—181no—
316#121—181no—
317#121C2×C3⋊D311yescharacteristic
318C4×Q8—91no—
319C4×Q8—91no—
320C4×D4—91no—
321C4×D4—181no—
322#117—91no—
323#117—181no—
324C2×C4⋊C4C2×C3⋊D311yescharacteristic
325#107C2×C3⋊D311yescharacteristic
326#107C2×C3⋊D311yescharacteristic
327#106—91no—
328C4⋊C8—91no—
329#103—91no—
330#103—91no—
331#103—91no—
332#103—91no—
333#103—91no—
334#103—91no—
335#103—91no—
336#102—91no—
337#102C2×C3⋊D311yescharacteristic
338#102C2×C3⋊D311yescharacteristic
339C22⋊C8—91no—
340C22⋊C8C2×C3⋊D311yescharacteristic
341C4×C8—91no—
342C23×C3—24no—
343C23×C3D3×D414yes—
344C22×D3—34no—
345C3×D4—24no—
346C3×D4—24no—
347C3×D4—48no—
348C2×C3×C4—24no—
349C2×C3×C4—24no—
350C2×C3×C4—24no—
351C2×C3×C4—24no—
352C2×C3×C4—24no—
353C2×C3×C4—48no—
354C2×C3×C4D3×D414yes—
355C2×C3×C4C23×D314yes—
356#67—68no—
357#67—128no—
358C2×Dic3—34no—
359C2×Dic3—34no—
360C2×Dic3—34no—
361C2×Dic3—64no—
362C2×Dic3—64no—
363C2×Dic3—64no—
364C2×Dic3—64no—
365C2×Dic3—128no—
366C2×Dic3—128no—
367C4×D3—64no—
368C4×D3—64no—
369Dic6—38no—
370Dic6—64no—
371Dic6—64no—
372Dic6—64no—
373Dic6—64no—
374Dic6—64no—
375Dic6—128no—
376C3×C8—24no—
377C3×C8—24no—
378C3⋊C8—64no—
379C3⋊C8—64no—
380C2×C32—22no—
381C2×C32—81no—
382C2×C32#54611yescharacteristic
383C2×C32C2×#13511yescharacteristic
384C2×C32#57811yescharacteristic
385C3⋊D3—41no—
386#41—182no—
387#41—361no—
388C2×Q8—91no—
389C2×Q8—91no—
390C2×Q8—91no—
391C2×Q8—182no—
392C2×Q8—181no—
393C2×Q8—361no—
394C2×D4—21no—
395C2×D4—91no—
396C2×D4—181no—
397C2×D4C22×C3⋊D311yescharacteristic
398C22×C4—21no—
399C22×C4—91no—
400C22×C4—181no—
401C22×C4—181no—
402C22×C4C22×C3⋊D311yescharacteristic
403Q16—182no—
404Q16—361no—
405SD16—361no—
406C2×C8—91no—
407C2×C8—91no—
408C2×C8—361no—
409C2×C8—361no—
410C2×C8C22×C3⋊D311yescharacteristic
411C2×C8C22×C3⋊D311yescharacteristic
412C4⋊C4—21no—
413C4⋊C4—91no—
414C4⋊C4—91no—
415C4⋊C4—181no—
416C4⋊C4—181no—
417C4⋊C4—181no—
418C4⋊C4—181no—
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—91no—
427C22⋊C4—91no—
428C22⋊C4—181no—
429C22⋊C4—181no—
430C22⋊C4—181no—
431C22⋊C4—181no—
432C22⋊C4—181no—
433C22⋊C4—181no—
434C42—91no—
435C42—181no—
436C42—181no—
437C42—181no—
438C22×C3—24no—
439C22×C3—24no—
440C22×C3—44no—
441C22×C3—44no—
442C22×C3—44no—
443C22×C3#91218yes—
444C22×C3C2×D3×D414yes—
445C2×D3—64no—
446C2×D3—64no—
447C2×D3—64no—
448C3×C4—24no—
449C3×C4—44no—
450C3×C4—44no—
451C3×C4—44no—
452C3×C4D3×#4114yes—
453C3×C4#100914yes—
454Dic3—68no—
455Dic3—64no—
456Dic3—64no—
457Dic3—64no—
458Dic3—124no—
459Dic3—124no—
460Dic3—124no—
461C32#330011yescharacteristic, complemented, Sylow
462C23—21no—
463C23—91no—
464C23D4×C3⋊D311yescharacteristic
465Q8—92no—
466Q8—181no—
467Q8—181no—
468Q8—181no—
469Q8—181no—
470Q8—181no—
471Q8—362no—
472D4—21no—
473D4—21no—
474D4—42no—
475D4—182no—
476D4—362no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—42no—
483C2×C4—91no—
484C2×C4—91no—
485C2×C4—91no—
486C2×C4—181no—
487C2×C4—181no—
488C2×C4—181no—
489C2×C4—181no—
490C2×C4—181no—
491C2×C4—181no—
492C2×C4—362no—
493C2×C4—362no—
494C2×C4D4×C3⋊D311yescharacteristic
495C2×C4C23×C3⋊D311yescharacteristic
496C8—21no—
497C8—21no—
498C8—181no—
499C8—181no—
500C2×C3—28no—
501C2×C3—84no—
502C2×C3#565414yes—
503C2×C3C2×#91214yes—
504C2×C3#577914yes—
505D3—124no—
506C22—21no—
507C22—21no—
508C22—41no—
509C22—41no—
510C22—41no—
511C22—181no—
512C22—181no—
513C22—181no—
514C22#6412112yes—
515C22C2×D4×C3⋊D311yescharacteristic
516C4—21no—
517C4—41no—
518C4—41no—
519C4—41no—
520C4—181no—
521C4—182no—
522C4—181no—
523C4—181no—
524C4—361no—
525C4—361no—
526C4—361no—
527C4#41×C3⋊D311yescharacteristic
528C4#6436611yescharacteristic
529C3#8130514yescomplemented
530C2—22no—
531C2—81no—
532C2—361no—
533C2#1059612511yescharacteristic
534C2C2×#6412111yescharacteristic
535C2#1059625011yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#480C2
socleC22×C32C22×D4
prime radical#10596069C2
hypercenter#480C3⋊D3
hypocenterC32#3300
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
2. #10595984C2semidirect
3. C32×#480C2semidirect
4. #10592740C2semidirect
5. C2×#63637C2semidirect
6. #10592587C2semidirect
7. #10592586C2semidirect
8. #10592576C2semidirect
9. #10592572C2semidirect
10. #10592482C2semidirect
11. #10592471C2semidirect
12. #10592467C2semidirect
13. #10592466C2semidirect
14. #10592438C2semidirect
15. #10592424C2semidirect
62. C3×#480D3semidirect
213. #480C3⋊D3semidirect
461. C32#3300semidirect
529. C3#81305semidirect

Maximal subgroups

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

subgroupindex
#105960692
#105959842
C32×#4802
#105927402
C2×#636372
#105925872
#105925862
#105925762
#105925722
#105924822
#105924712
#105924672
#105924662
#105924382
#105924242
#813053