Finite Group Databasebeta

← #11866208

Subgroups — #11866208

Order 1152.

1201 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
1C2×#64158C211yesmaximal, characteristic, complemented
2C3×#5830C211yesmaximal, characteristic, complemented
3#10594996C211yesmaximal, characteristic, complemented
4C22×#3714C211yesmaximal, characteristic, complemented
5C3×#5233C211yesmaximal, characteristic, complemented
6#10591568C214yesmaximal, complemented
7#10591429C214yesmaximal, complemented
8#10591116C211yesmaximal, characteristic, complemented
9#10591085C211yesmaximal, characteristic, complemented
10#83384—31nomaximal
11#78862—31nomaximal
12C2×C32×#41C2211yescharacteristic
13C22×C4⋊(C3⋊D3)C2211yescharacteristic
14C22×C3×D12C2211yescharacteristic
15#64158—24no—
16C2×#3755C2212yescomplemented
17C2×#3753C2212yescomplemented
18C2×#3748C2211yescharacteristic
19C3×#947C2212yescomplemented
20C3×#940C2212yescomplemented
21C3×#937—22no—
22C3×#930—22no—
23C3×#926C2211yescharacteristic
24C3×#926C2211yescharacteristic
25C22×C3×C3⋊C8C2211yescharacteristic
26#63974—22no—
27#63894—22no—
28#63894C2214yescomplemented
29C2×#3714—24no—
30C2×#3714C2214yes—
31C3×#835C2212yescomplemented
32C3×#832C2212yescomplemented
33Dic3⋊(C3⋊C8)C2214yescomplemented
34#63562C2214yescomplemented
35C3×#535—31no—
36#5830D311yescharacteristic, complemented
37C2×#949—31no—
38C2×#949—31no—
39C2×#949—61no—
40C22×#213—31no—
41C22×D24—31no—
42#5521—31no—
43#5521—31no—
44C3×#416—31no—
45#5233D311yescharacteristic, complemented
46#5215—31no—
47#5102—31no—
48#5072—34no—
49#5057—34no—
50#5001—31no—
51#4999—31no—
52#4819—34no—
53#4786—34no—
54C23×C3⋊D3—21no—
55C23×C3×D3—21no—
56C32×#41—22no—
57C32×#41—22no—
58C2×C32×Q8C2311yescharacteristic
59C2×C32×D4—21no—
60C2×C32×D4C2311yescharacteristic
61C22×C32×C4—21no—
62C22×C32×C4C2311yescharacteristic
63C2×C4⋊(C3⋊D3)—21no—
64C2×C4⋊(C3⋊D3)—22no—
65C2×C4⋊(C3⋊D3)D414yescomplemented
66C2×C4⋊(C3⋊D3)C2312yes—
67C2×C3×#67—24no—
68C2×C3×D12—22no—
69C2×C3×D12—22no—
70C2×C3×D12—21no—
71C2×C3×D12C2312yes—
72C2×#624—24no—
73#3755—24no—
74#3753—24no—
75#3748—22no—
76C2×C3⋊(C3⋊C8)C2312yes—
77C3×#217—21no—
78C3×#217D412yes—
79C3×(C2×D3)⋊C4—24no—
80C3×C4⋊Dic3D412yes—
81C3×C4⋊Dic3C2312yes—
82C3×C4×Dic3—21no—
83C3×C4×Dic3C2312yes—
84C2×C3×C3⋊C8—22no—
85C2×C3×C3⋊C8C2312yes—
86#3722—24no—
87#3714—28no—
88#3041—91noSylow
89C2×C3×#41—21no—
90C2×C3×#41C2×D311yescharacteristic
91C2×C3×#41C2×D311yescharacteristic
92C22×C3×D4—31no—
93C22×D12—31no—
94C22×D12—31no—
95C22×D12—61no—
96C22×D12C2×D311yescharacteristic
97C22×C3×C8—31no—
98C3×#127—32no—
99C3×#124—32no—
100C3×#121—62no—
101C3×#120—62no—
102C3×#117—31no—
103C3×#117—31no—
104#949—64no—
105#949—64no—
106#949—68no—
107#947C2×D312yescomplemented
108C2×#215—32no—
109C2×#215—32no—
110C2×#215—62no—
111#940C2×D312yescomplemented
112#937—22no—
113C2×#213—32no—
114C2×#213—32no—
115C2×#213—34no—
116C2×#213—62no—
117C2×#213—64no—
118#930—22no—
119#926C2×D311yescharacteristic
120#926C2×D311yescharacteristic
121C2×#208—31no—
122C2×#208—31no—
123C2×#208—61no—
124C22×C3⋊C8C2×D311yescharacteristic
125C2×D24—34no—
126C2×D24—64no—
127#893—34no—
128#893—62no—
129D3×C22⋊C4—62no—
130D3×C22⋊C4—62no—
131C4×D12—34no—
132C4×D12—62no—
133C3×#103—32no—
134C3×#102—32no—
135#835C2×D312yescomplemented
136#832—34no—
137#832C2×D312yescomplemented
138Dic3⋊C8—34no—
139#809—34no—
140C4⋊(C3⋊C8)—34no—
141C23×C32—21no—
142C23×C32C2×D411yescharacteristic
143C22×C3⋊D3—22no—
144C22×C3⋊D3—24no—
145C22×C3⋊D3—82no—
146C22×C3×D3—22no—
147C22×C3×D3—42no—
148C22×C3×D3—82no—
149C32×Q8—21no—
150C32×Q8—21no—
151C32×D4—21no—
152C32×D4—21no—
153C32×D4—42no—
154C2×C32×C4—21no—
155C2×C32×C4—42no—
156C2×C32×C4C2×D412yes—
157C2×C32×C4C2×D411yescharacteristic
158C2×C32×C4#4112yes—
159C2×C32×C4C2411yescharacteristic
160C4⋊(C3⋊D3)—24no—
161C4⋊(C3⋊D3)—22no—
162C4⋊(C3⋊D3)C2×D414yes—
163C3×#67—84no—
164C2×C3×Dic3—22no—
165C2×C3×Dic3C2×D414yes—
166C3×D12—22no—
167C3×D12—22no—
168C3×D12—42no—
169#624—84no—
170C3⋊(C3⋊C8)—22no—
171C3×C3⋊C8—22no—
172C2×AGL(1,ℤ/8)—91no—
173C22×D8—91no—
174#535—31no—
175#518—91no—
176#463—94no—
177#459—94no—
178#424—91no—
179#418—91no—
180#416—31no—
181C24×C3—61no—
182C23×D3—21no—
183C23×D3—61no—
184C23×D3—61no—
185C23×D3—121no—
186C3×#41—24no—
187C3×#41—22no—
188C3×#41—22no—
189C3×#41—22no—
190C3×#41—22no—
191C3×#41—42no—
192C2×C3×Q8—21no—
193C2×C3×Q8C22×D311yescharacteristic
194C2×C3×Q8C22×D311yescharacteristic
195C2×C3×D4—21no—
196C2×C3×D4—21no—
197C2×C3×D4—21no—
198C2×C3×D4—32no—
199C2×C3×D4—41no—
200C2×C3×D4—64no—
201C2×C3×D4—62no—
202C2×C3×D4—62no—
203C2×C3×D4—61no—
204C2×C3×D4C22×D311yescharacteristic
205C2×C3×D4C22×D311yescharacteristic
206C22×C3×C4—21no—
207C22×C3×C4—21no—
208C22×C3×C4—21no—
209C22×C3×C4—41no—
210C22×C3×C4C22×D311yescharacteristic
211C22×C3×C4C22×D311yescharacteristic
212C2×#67—24no—
213C2×D12—22no—
214C2×D12—22no—
215C2×D12—21no—
216C2×D12—34no—
217C2×D12—34no—
218C2×D12—32no—
219C2×D12—32no—
220C2×D12—62no—
221C2×D12—64no—
222C2×D12—62no—
223C2×D12—61no—
224C2×D12—62no—
225C2×D12—61no—
226C2×D12—122no—
227C2×D12—121no—
228C2×D12C22×D312yes—
229C2×C4×D3—64no—
230C2×C4×D3—64no—
231C2×C3×C8—32no—
232C2×C3×C8—62no—
233C3×C4⋊C4—32no—
234C3×C4⋊C4—32no—
235C3×C22⋊C4—32no—
236C3×C22⋊C4—64no—
237C3×C22⋊C4—61no—
238C3×C42—32no—
239C3×C42—61no—
240#217—21no—
241#217#6712yes—
242#215—64no—
243#215—64no—
244#215—68no—
245#213—68no—
246#213—64no—
247#213—64no—
248#213—68no—
249(C2×D3)⋊C4—24no—
250(C2×D3)⋊C4—64no—
251(C2×D3)⋊C4—64no—
252C4⋊Dic3#6712yes—
253C4⋊Dic3C22×D312yes—
254C4×Dic3—21no—
255C4×Dic3C22×D312yes—
256#208—64no—
257#208—62no—
258#208—62no—
259C2×C3⋊C8—22no—
260C2×C3⋊C8—32no—
261C2×C3⋊C8—32no—
262C2×C3⋊C8—62no—
263C2×C3⋊C8C22×D312yes—
264D24—68no—
265C22×C32—22no—
266C22×C32—41no—
267C22×C32—42no—
268C22×C32#12112yes—
269C22×C32C22×D411yescharacteristic
270C2×C3⋊D3—24no—
271C2×C3⋊D3—44no—
272C2×C3⋊D3—84no—
273C2×C3×D3—42no—
274C2×C3×D3—44no—
275C2×C3×D3—84no—
276C32×C4—41no—
277C32×C4#12112yes—
278C32×C4C22×D411yescharacteristic
279C32×C4C2×#4111yescharacteristic
280C3×Dic3—24no—
281C3×Dic3—42no—
282C2×#41D3211yescharacteristic
283C22×D4—31no—
284C22×D4—91no—
285AGL(1,ℤ/8)—184no—
286C2×SD16—92no—
287C2×D8—94no—
288C2×D8—92no—
289C2×D8—184no—
290C2×M16—91no—
291C22×C8—31no—
292#127—32no—
293#124—32no—
294#121—62no—
295#120—62no—
296C4×D4—94no—
297C4×D4—182no—
298#117—31no—
299#117—31no—
300C2×C22⋊C4—182no—
301C4⋊C8—94no—
302#103—32no—
303#102—32no—
304#102—94no—
305C23×C3—21no—
306C23×C3—21no—
307C23×C3—21no—
308C23×C3—41no—
309C23×C3—62no—
310C23×C3—122no—
311C23×C3—242no—
312C23×C3D3×D411yescharacteristic
313C23×C3C2×#6711yescharacteristic
314C22×D3—22no—
315C22×D3—42no—
316C22×D3—62no—
317C22×D3—62no—
318C22×D3—64no—
319C22×D3—64no—
320C22×D3—82no—
321C22×D3—122no—
322C22×D3—124no—
323C22×D3—242no—
324C22×D3—242no—
325C22×D3—244no—
326C3×Q8—22no—
327C3×Q8—21no—
328C3×Q8—21no—
329C3×Q8—21no—
330C3×Q8—21no—
331C3×Q8—41no—
332C3×D4—22no—
333C3×D4—21no—
334C3×D4—21no—
335C3×D4—21no—
336C3×D4—21no—
337C3×D4—41no—
338C3×D4—44no—
339C3×D4—42no—
340C3×D4—42no—
341C3×D4—62no—
342C3×D4—62no—
343C3×D4—122no—
344C3×D4—244no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—22no—
349C2×C3×C4—21no—
350C2×C3×C4—22no—
351C2×C3×C4—34no—
352C2×C3×C4—41no—
353C2×C3×C4—44no—
354C2×C3×C4—42no—
355C2×C3×C4—42no—
356C2×C3×C4—62no—
357C2×C3×C4#23512yes—
358C2×C3×C4D3×D411yescharacteristic
359C2×C3×C4D3×D412yes—
360C2×C3×C4D3×D412yes—
361C2×C3×C4#23712yes—
362C2×C3×C4C2×#6711yescharacteristic
363C2×C3×C4C23×D311yescharacteristic
364C2×C3×C4C23×D311yescharacteristic
365#67—84no—
366C2×Dic3—22no—
367C2×Dic3C2×#6714yes—
368D12—22no—
369D12—22no—
370D12—34no—
371D12—34no—
372D12—42no—
373D12—64no—
374D12—64no—
375D12—64no—
376D12—62no—
377D12—62no—
378D12—122no—
379D12—124no—
380C4×D3—244no—
381C4×D3—244no—
382C3×C8—62no—
383C3⋊C8—22no—
384C3⋊C8—64no—
385C3⋊C8—62no—
386C3⋊C8—62no—
387C2×C32—22no—
388C2×C32—81no—
389C2×C32C2×#12111yescharacteristic
390C2×C32#57612yes—
391C3⋊D3—44no—
392C3×D3—82no—
393C24—61no—
394C24—181no—
395#41—22no—
396#41—22no—
397C2×Q8C2×D3211yescharacteristic
398C2×D4—21no—
399C2×D4—32no—
400C2×D4—64no—
401C2×D4—62no—
402C2×D4—61no—
403C2×D4—62no—
404C2×D4—92no—
405C2×D4—94no—
406C2×D4—182no—
407C2×D4—181no—
408C2×D4C2×D3211yescharacteristic
409C22×C4—21no—
410C22×C4—184no—
411C22×C4C2×D3211yescharacteristic
412SD16—184no—
413D8—188no—
414D8—184no—
415M16—182no—
416C2×C8—32no—
417C2×C8—62no—
418C2×C8—92no—
419C4⋊C4—32no—
420C4⋊C4—32no—
421C22⋊C4—32no—
422C22⋊C4—64no—
423C22⋊C4—61no—
424C22⋊C4—184no—
425C42—32no—
426C42—61no—
427C22×C3—22no—
428C22×C3—22no—
429C22×C3—21no—
430C22×C3—22no—
431C22×C3—42no—
432C22×C3—42no—
433C22×C3—41no—
434C22×C3—42no—
435C22×C3—41no—
436C22×C3—42no—
437C22×C3—82no—
438C22×C3—122no—
439C22×C3—124no—
440C22×C3—244no—
441C22×C3#88412yes—
442C22×C3#93812yes—
443C22×C3C2×D3×D411yescharacteristic
444C22×C3C22×#6711yescharacteristic
445C2×D3—42no—
446C2×D3—44no—
447C2×D3—64no—
448C2×D3—64no—
449C2×D3—84no—
450C2×D3—124no—
451C2×D3—124no—
452C2×D3—124no—
453C2×D3—244no—
454C2×D3—244no—
455C2×D3—244no—
456C2×D3—248no—
457C3×C4—21no—
458C3×C4—21no—
459C3×C4—22no—
460C3×C4—42no—
461C3×C4—41no—
462C3×C4—41no—
463C3×C4—64no—
464C3×C4—122no—
465C3×C4#88412yes—
466C3×C4#93812yes—
467C3×C4C2×#23511yescharacteristic
468C3×C4C2×D3×D411yescharacteristic
469C3×C4C2×D3×D411yescharacteristic
470C3×C4C2×#23711yescharacteristic
471Dic3—24no—
472Dic3—42no—
473C32#304111yescharacteristic, complemented, Sylow
474C23—21no—
475C23—62no—
476C23—122no—
477C23—182no—
478C23—184no—
479C23—242no—
480C23—722no—
481C23D3×#6711yescharacteristic
482Q8—21no—
483Q8—21no—
484D4—21no—
485D4—21no—
486D4—42no—
487D4—62no—
488D4—62no—
489D4—94no—
490D4—122no—
491D4—182no—
492D4—184no—
493D4—244no—
494C2×C4—21no—
495C2×C4—34no—
496C2×C4—42no—
497C2×C4—62no—
498C2×C4—724no—
499C2×C4#380412yes—
500C2×C4D3×#6711yescharacteristic
501C2×C4#381112yes—
502C2×C4C22×D3211yescharacteristic
503C8—62no—
504C8—182no—
505C2×C3—22no—
506C2×C3—22no—
507C2×C3—22no—
508C2×C3—21no—
509C2×C3—42no—
510C2×C3—82no—
511C2×C3—81no—
512C2×C3—81no—
513C2×C3—242no—
514C2×C3C2×#88411yescharacteristic
515C2×C3#576912yes—
516C2×C3C2×#93811yescharacteristic
517C2×C3#583512yes—
518D3—82no—
519D3—124no—
520D3—124no—
521D3—244no—
522C22—22no—
523C22—42no—
524C22—41no—
525C22—124no—
526C22—122no—
527C22—184no—
528C22—244no—
529C22—364no—
530C22—724no—
531C22#6395812yes—
532C22C2×D3×#6711yescharacteristic
533C4—41no—
534C4—64no—
535C4—122no—
536C4#6395812yes—
537C4C2×#380411yescharacteristic
538C4C2×#381111yescharacteristic
539C3—21no—
540C3#7886211yescharacteristic, complemented
541C3#8338411yescharacteristic, complemented
542C2—22no—
543C2—81no—
544C2—242no—
545C2—364no—
546C2#1059545612yes—
547C2C2×#6395811yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
hypercenterC2×#41D32
hypocenterC32#3041
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#64158C2semidirect
2. C3×#5830C2semidirect
3. #10594996C2semidirect
4. C22×#3714C2semidirect
5. C3×#5233C2semidirect
6. #10591568C2semidirect
7. #10591429C2semidirect
8. #10591116C2semidirect
9. #10591085C2semidirect
16. C2×#3755C22semidirect
17. C2×#3753C22semidirect
19. C3×#947C22semidirect
20. C3×#940C22semidirect
28. #63894C22semidirect
31. C3×#835C22semidirect
32. C3×#832C22semidirect
33. Dic3⋊(C3⋊C8)C22semidirect
34. #63562C22semidirect
36. #5830D3semidirect
45. #5233D3semidirect
65. C2×C4⋊(C3⋊D3)D4semidirect
107. #947C2×D3semidirect
111. #940C2×D3semidirect
135. #835C2×D3semidirect
137. #832C2×D3semidirect
473. C32#3041semidirect
540. C3#78862semidirect
541. C3#83384semidirect

Maximal subgroups

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

subgroupindex
C2×#641582
C3×#58302
#105949962
C22×#37142
C3×#52332
#105915682
#105914292
#105911162
#105910852
#833843
#788623