Finite Group Databasebeta

← #11866215

Subgroups — #11866215

Order 1152.

1131 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5521C211yesmaximal, characteristic, complemented
2#10595042C211yesmaximal, characteristic, complemented
3C2×#63830C211yesmaximal, characteristic, complemented
4C22×#3713C211yesmaximal, characteristic, complemented
5#10592701C211yesmaximal, characteristic, complemented
6C3×#5001C211yesmaximal, characteristic, complemented
7#10591117C211yesmaximal, characteristic, complemented
8#10590547C214yesmaximal, complemented
9#10590530C214yesmaximal, complemented
10#82540—31nomaximal
11#78944—31nomaximal
12C2×#3828C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C22×C3×D12C2211yescharacteristic
15C32×#117C2211yescharacteristic
16C22×C3⋊(C3⋊C8)C2211yescharacteristic
17C3×#926C2211yescharacteristic
18C2×C3×#208C2211yescharacteristic
19C3×#893C2214yescomplemented
20C3×D3×C22⋊C4—22no—
21C3×C4×D12—22no—
22#63977—22no—
23#63916—22no—
24#63911C2212yescomplemented
25#63860C2212yescomplemented
26#63830—24no—
27C2×#3716C2212yescomplemented
28C2×#3714C2212yescomplemented
29C2×#3713—24no—
30C2×#3713C2214yes—
31#63637C2212yescomplemented
32#63636C2212yescomplemented
33C3×#809C2214yescomplemented
34Dic3⋊(C3⋊C8)C2214yescomplemented
35C3×#518—31no—
36#5805—31no—
37C2×#932—31no—
38C22×#213—31no—
39C22×#213—31no—
40C2×#908—31no—
41#5525—31no—
42#5521D311yescharacteristic, complemented
43C3×#418—31no—
44#5119—31no—
45#5016—34no—
46#5015—34no—
47#5002—31no—
48#5002—31no—
49#5002—61no—
50#5001D311yescharacteristic, complemented
51#4999—31no—
52#4787—34no—
53#4786—34no—
54C23×C3×D3—21no—
55C23×C3×D3—21no—
56C22×C32×C4C2311yescharacteristic
57C2×#638—21no—
58#3828—22no—
59#3828—22no—
60C2×C4⋊(C3⋊D3)C2311yescharacteristic
61C2×C4×C3⋊D3—21no—
62C2×#634C2311yescharacteristic
63C2×C3×D12—21no—
64C2×C3×D12—22no—
65C2×C3×D12—22no—
66C2×C3×D12—22no—
67C2×C3×D12—21no—
68C2×C3×D12D414yescomplemented
69C2×C3×D12C2312yes—
70C2×C3×D12C2312yes—
71C2×C3×C4×D3—24no—
72C2×#626—24no—
73C32×C4⋊C4C2312yes—
74C32×C22⋊C4—21no—
75C32×C42—21no—
76C2×C3⋊(C3⋊C8)—22no—
77C2×C3⋊(C3⋊C8)C2312yes—
78C3×#217D412yes—
79C3×(C2×D3)⋊C4—24no—
80C3×C4⋊Dic3D412yes—
81C3×C4×Dic3C2312yes—
82C3×#208—22no—
83C2×C3×C3⋊C8C2312yes—
84(C2×D3)⋊Dic3—24no—
85#3716—24no—
86#3714—24no—
87#3713—28no—
88#3041—91noSylow
89C22×C3×D4—31no—
90C22×C3×D4—31no—
91C2×#235—31no—
92C2×#235—31no—
93C2×#235—61no—
94C22×D12C2×D311yescharacteristic
95C22×D12C2×D311yescharacteristic
96C2×C3×M16—31no—
97C3×C4×D4—34no—
98C3×C4×D4—62no—
99C3×#117—21no—
100C3×#117—31no—
101C3×#117C2×D311yescharacteristic
102C3×#117C2×D311yescharacteristic
103C2×C3×C22⋊C4—62no—
104#953—62no—
105#940—32no—
106#938—62no—
107#936—32no—
108C2×#214—32no—
109#932—64no—
110C2×#213—34no—
111C2×#213—34no—
112C2×#213—32no—
113C2×#213—64no—
114C2×#213—64no—
115#926C2×D311yescharacteristic
116C2×#208C2×D311yescharacteristic
117C22×C3⋊C8—31no—
118C22×C3⋊C8—31no—
119C22×C3⋊C8—61no—
120#908—64no—
121C2×D24—32no—
122C2×#204—32no—
123#895—62no—
124#893C2×D314yescomplemented
125#882—62no—
126D3×C22⋊C4—22no—
127#875—32no—
128#874—32no—
129C4×D12—22no—
130C3×#102—34no—
131Dic3⋊C8—34no—
132#810—32no—
133#810—32no—
134#810—62no—
135#809—32no—
136#809—32no—
137#809—62no—
138#809C2×D314yescomplemented
139C4⋊(C3⋊C8)—34no—
140C23×C32C2×D411yescharacteristic
141C22×C3⋊D3—21no—
142C22×C3×D3—22no—
143C22×C3×D3—24no—
144C22×C3×D3—22no—
145C22×C3×D3—42no—
146C22×C3×D3—82no—
147C22×C3×D3—82no—
148C2×C32×C4—22no—
149C2×C32×C4C2×D412yes—
150C2×C32×C4C2×D411yescharacteristic
151C2×C32×C4#4112yes—
152C2×C32×C4C2411yescharacteristic
153#638—42no—
154C2×C3⋊Dic3—21no—
155C4⋊(C3⋊D3)—21no—
156C4⋊(C3⋊D3)—21no—
157C4×C3⋊D3—42no—
158#634—21no—
159#634—21no—
160C2×C3×Dic3C2×D414yes—
161C3×D12—24no—
162C3×D12—22no—
163C3×D12—22no—
164C3×D12—22no—
165C3×D12—42no—
166C3×D12C2×D414yes—
167C3×C4×D3—84no—
168#626—84no—
169C3⋊(C3⋊C8)—22no—
170C3×C3⋊C8—22no—
171C2×AGL(1,ℤ/8)—91no—
172C22×D8—91no—
173#535—91no—
174#518—31no—
175#463—94no—
176#459—94no—
177#424—91no—
178#418—31no—
179#416—91no—
180C24×C3—61no—
181C24×C3—61no—
182C23×D3—21no—
183C23×D3—21no—
184C2×C3×D4—34no—
185C2×C3×D4—32no—
186C2×C3×D4—32no—
187C2×C3×D4—62no—
188C2×C3×D4—62no—
189C2×C3×D4—62no—
190C2×C3×D4—61no—
191C2×C3×D4—61no—
192C22×C3×C4—21no—
193C22×C3×C4—64no—
194C22×C3×C4C22×D311yescharacteristic
195C22×C3×C4C22×D311yescharacteristic
196C2×#67—61no—
197C2×#67—61no—
198C2×#67—64no—
199C2×#67—121no—
200#235—64no—
201#235—62no—
202#235—62no—
203#235—62no—
204#235—62no—
205#235—122no—
206C2×D12—22no—
207C2×D12—21no—
208C2×D12—22no—
209C2×D12—22no—
210C2×D12—21no—
211C2×D12—31no—
212C2×D12—31no—
213C2×D12—61no—
214C2×D12—64no—
215C2×D12D1214yescomplemented
216C2×D12C22×D312yes—
217C2×D12C22×D312yes—
218C2×C4×D3—24no—
219C2×C4×D3—61no—
220C2×C4×D3—61no—
221C2×C4×D3—121no—
222C2×Dic6—31no—
223C2×Dic6—31no—
224C2×Dic6—61no—
225C3×M16—62no—
226C2×C3×C8—32no—
227C3×C4⋊C4—22no—
228C3×C4⋊C4—32no—
229C3×C4⋊C4C22×D312yes—
230C3×C4⋊C4C22×D312yes—
231C3×C22⋊C4—21no—
232C3×C22⋊C4—21no—
233C3×C22⋊C4—32no—
234C3×C22⋊C4—41no—
235C3×C22⋊C4—64no—
236C3×C42—21no—
237C3×C42—21no—
238C3×C42—32no—
239C3×C42—41no—
240#217—64no—
241#217#6712yes—
242#214—64no—
243#213—64no—
244#213—68no—
245#213—68no—
246(C2×D3)⋊C4—24no—
247(C2×D3)⋊C4—64no—
248C4⋊Dic3#6712yes—
249C4×Dic3C22×D312yes—
250#208—22no—
251C2×C3⋊C8—32no—
252C2×C3⋊C8—32no—
253C2×C3⋊C8—62no—
254C2×C3⋊C8—62no—
255C2×C3⋊C8—62no—
256C2×C3⋊C8—122no—
257C2×C3⋊C8C22×D312yes—
258D24—64no—
259#204—64no—
260C22×C32—22no—
261C22×C32#12112yes—
262C22×C32C22×D411yescharacteristic
263C2×C3⋊D3—41no—
264C2×C3⋊D3—42no—
265C2×C3×D3—24no—
266C2×C3×D3—44no—
267C2×C3×D3—42no—
268C2×C3×D3—44no—
269C2×C3×D3—84no—
270C2×C3×D3—84no—
271C32×C4—42no—
272C32×C4#12112yes—
273C32×C4C22×D411yescharacteristic
274C32×C4C2×#4111yescharacteristic
275C3⋊Dic3—41no—
276C3×Dic3—24no—
277C2×#41—91no—
278C22×D4—31no—
279C22×D4—31no—
280AGL(1,ℤ/8)—184no—
281C2×SD16—92no—
282C2×D8—92no—
283C2×D8—94no—
284C2×D8—184no—
285C2×M16—31no—
286C22×C8—91no—
287#127—92no—
288#124—92no—
289#121—182no—
290#120—182no—
291C4×D4—34no—
292C4×D4—62no—
293#117—31no—
294#117D3211yescharacteristic
295C2×C22⋊C4—62no—
296C4⋊C8—94no—
297#103—92no—
298#102—34no—
299#102—92no—
300C23×C3—21no—
301C23×C3—62no—
302C23×C3—64no—
303C23×C3—62no—
304C23×C3—122no—
305C23×C3—242no—
306C23×C3—242no—
307C23×C3D3×D411yescharacteristic
308C23×C3C2×#6711yescharacteristic
309C22×D3—22no—
310C22×D3—24no—
311C22×D3—22no—
312C22×D3—42no—
313C22×D3—61no—
314C22×D3—61no—
315C22×D3—82no—
316C22×D3—82no—
317C22×D3—121no—
318C3×D4—34no—
319C3×D4—64no—
320C3×D4—62no—
321C3×D4—62no—
322C3×D4—62no—
323C3×D4—122no—
324C2×C3×C4—22no—
325C2×C3×C4—22no—
326C2×C3×C4—21no—
327C2×C3×C4—22no—
328C2×C3×C4—22no—
329C2×C3×C4—21no—
330C2×C3×C4—34no—
331C2×C3×C4—42no—
332C2×C3×C4—244no—
333C2×C3×C4C2×D1212yes—
334C2×C3×C4#23512yes—
335C2×C3×C4#23512yes—
336C2×C3×C4D3×D412yes—
337C2×C3×C4D3×D411yescharacteristic
338C2×C3×C4C2×#6711yescharacteristic
339C2×C3×C4C23×D311yescharacteristic
340C2×C3×C4C23×D311yescharacteristic
341#67—124no—
342#67—122no—
343#67—122no—
344#67—244no—
345C2×Dic3—61no—
346C2×Dic3—61no—
347C2×Dic3—121no—
348C2×Dic3C2×#6714yes—
349D12—24no—
350D12—22no—
351D12—22no—
352D12—22no—
353D12—42no—
354D12—62no—
355D12—61no—
356D12—61no—
357D12—61no—
358D12—61no—
359D12—121no—
360D12—244no—
361D12C2×D1214yes—
362C4×D3—84no—
363C4×D3—124no—
364C4×D3—122no—
365C4×D3—122no—
366Dic6—62no—
367Dic6—61no—
368Dic6—61no—
369Dic6—61no—
370Dic6—61no—
371Dic6—121no—
372C3×C8—62no—
373C3⋊C8—22no—
374C3⋊C8—62no—
375C3⋊C8—62no—
376C3⋊C8—122no—
377C2×C32—22no—
378C2×C32C2×#12111yescharacteristic
379C2×C32#57612yes—
380C3⋊D3—81no—
381C3×D3—44no—
382C3×D3—82no—
383C24—61no—
384C24—61no—
385#41—182no—
386#41—182no—
387C2×Q8—91no—
388C2×D4—32no—
389C2×D4—32no—
390C2×D4—34no—
391C2×D4—62no—
392C2×D4—62no—
393C2×D4—62no—
394C2×D4—61no—
395C2×D4—61no—
396C2×D4—91no—
397C2×D4—184no—
398C2×D4—181no—
399C22×C4—64no—
400C22×C4—181no—
401C22×C4C2×D3211yescharacteristic
402SD16—184no—
403D8—184no—
404D8—188no—
405M16—62no—
406C2×C8—32no—
407C2×C8—92no—
408C2×C8—182no—
409C4⋊C4—32no—
410C4⋊C4C2×D3212yes—
411C22⋊C4—21no—
412C22⋊C4—32no—
413C22⋊C4—64no—
414C22⋊C4—184no—
415C42—21no—
416C42—32no—
417C22×C3—22no—
418C22×C3—22no—
419C22×C3—21no—
420C22×C3—22no—
421C22×C3—42no—
422C22×C3—64no—
423C22×C3—124no—
424C22×C3—122no—
425C22×C3—124no—
426C22×C3—244no—
427C22×C3—244no—
428C22×C3#88412yes—
429C22×C3#93012yes—
430C22×C3C2×D3×D411yescharacteristic
431C22×C3C22×#6711yescharacteristic
432C2×D3—24no—
433C2×D3—44no—
434C2×D3—42no—
435C2×D3—44no—
436C2×D3—84no—
437C2×D3—84no—
438C2×D3—122no—
439C2×D3—121no—
440C2×D3—122no—
441C2×D3—121no—
442C2×D3—122no—
443C2×D3—242no—
444C3×C4—21no—
445C3×C4—21no—
446C3×C4—22no—
447C3×C4—42no—
448C3×C4—42no—
449C3×C4—64no—
450C3×C4—82no—
451C3×C4#88412yes—
452C3×C4#93012yes—
453C3×C4C22×D1211yescharacteristic
454C3×C4C2×#23511yescharacteristic
455C3×C4C2×#23511yescharacteristic
456C3×C4C2×D3×D411yescharacteristic
457Dic3—24no—
458Dic3—122no—
459Dic3—121no—
460Dic3—121no—
461C32#304111yescharacteristic, complemented, Sylow
462C23—62no—
463C23—64no—
464C23—62no—
465C23—122no—
466C23—181no—
467C23—242no—
468C23—242no—
469C23D3×#6711yescharacteristic
470Q8—181no—
471Q8—181no—
472D4—34no—
473D4—62no—
474D4—62no—
475D4—62no—
476D4—64no—
477D4—122no—
478D4—181no—
479D4—181no—
480D4—362no—
481D4—724no—
482C2×C4—22no—
483C2×C4—34no—
484C2×C4—181no—
485C2×C4—244no—
486C2×C4—362no—
487C2×C4#379812yes—
488C2×C4D3×D1212yes—
489C2×C4D3×#6711yescharacteristic
490C2×C4C22×D3211yescharacteristic
491C8—62no—
492C8—182no—
493C2×C3—22no—
494C2×C3—22no—
495C2×C3—22no—
496C2×C3—21no—
497C2×C3—42no—
498C2×C3—124no—
499C2×C3—242no—
500C2×C3C2×#88411yescharacteristic
501C2×C3#577412yes—
502C2×C3C2×#93011yescharacteristic
503C2×C3#583512yes—
504D3—44no—
505D3—82no—
506D3—242no—
507D3—241no—
508D3—241no—
509C22—22no—
510C22—64no—
511C22—124no—
512C22—124no—
513C22—122no—
514C22—244no—
515C22—244no—
516C22—362no—
517C22—361no—
518C22#6390612yes—
519C22C2×D3×#6711yescharacteristic
520C4—42no—
521C4—64no—
522C4—361no—
523C4#6390612yes—
524C4C2×#379811yescharacteristic
525C4C2×D3×D1211yescharacteristic
526C3—21no—
527C3#7894411yescharacteristic, complemented
528C3#8254011yescharacteristic, complemented
529C2—22no—
530C2—124no—
531C2—242no—
532C2—721no—
533C2C2×#6390611yescharacteristic
534C2#1059545412yes—
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
hypercenter#117D32
hypocenterC32#3041
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C3×#5521C2semidirect
2. #10595042C2semidirect
3. C2×#63830C2semidirect
4. C22×#3713C2semidirect
5. #10592701C2semidirect
6. C3×#5001C2semidirect
7. #10591117C2semidirect
8. #10590547C2semidirect
9. #10590530C2semidirect
19. C3×#893C22semidirect
24. #63911C22semidirect
25. #63860C22semidirect
27. C2×#3716C22semidirect
28. C2×#3714C22semidirect
31. #63637C22semidirect
32. #63636C22semidirect
33. C3×#809C22semidirect
34. Dic3⋊(C3⋊C8)C22semidirect
42. #5521D3semidirect
50. #5001D3semidirect
68. C2×C3×D12D4semidirect
124. #893C2×D3semidirect
138. #809C2×D3semidirect
215. C2×D12D12semidirect
461. C32#3041semidirect
527. C3#78944semidirect
528. C3#82540semidirect

Maximal subgroups

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

subgroupindex
C3×#55212
#105950422
C2×#638302
C22×#37132
#105927012
C3×#50012
#105911172
#105905472
#105905302
#825403
#789443