Finite Group Databasebeta

← #11866209

Subgroups — #11866209

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×#5830C211yesmaximal, characteristic, complemented
2C2×C3×#949C211yesmaximal, characteristic, complemented
3#10594982C211yesmaximal, characteristic, complemented
4C22×#3713C211yesmaximal, characteristic, complemented
5#10592932C211yesmaximal, characteristic, complemented
6#10591567C214yesmaximal, complemented
7#10591428C214yesmaximal, complemented
8#10591117C211yesmaximal, characteristic, complemented
9#10591086C211yesmaximal, characteristic, complemented
10#83934—31nomaximal
11#83384—31nomaximal
12C2×C32×#41C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C22×C3×D12C2211yescharacteristic
15#64135C2211yescharacteristic
16C22×C3⋊(C3⋊C8)C2211yescharacteristic
17C3×#949—24no—
18C3×#947C2212yescomplemented
19C2×C3×#215C2212yescomplemented
20C3×#940C2212yescomplemented
21C3×#937—22no—
22C2×C3×#213C2212yescomplemented
23C3×#930—22no—
24C3×#926C2211yescharacteristic
25C2×C3×#208C2211yescharacteristic
26D3×#217—22no—
27#63898—22no—
28Dic3×D12C2214yescomplemented
29C2×#3713—24no—
30C2×#3713C2214yes—
31#63662C2212yescomplemented
32#63659C2212yescomplemented
33Dic3⋊(C3⋊C8)C2214yescomplemented
34#63563C2214yescomplemented
35C2×C3×AGL(1,ℤ/8)—31no—
36C3×#535—31no—
37#5830D311yescharacteristic, complemented
38C2×#949D311yescharacteristic, complemented
39#5798—31no—
40C22×#213—31no—
41C22×#213—31no—
42#5521—31no—
43#5233—31no—
44#5233—31no—
45#5233—61no—
46#5215—31no—
47#5165—34no—
48#5150—34no—
49#5131—31no—
50#5119—31no—
51#5072—34no—
52#5057—34no—
53#4999—31no—
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×C3×#67—24no—
64C2×C3×D12—21no—
65C2×C3×D12—22no—
66C2×C3×D12—22no—
67C2×C3×D12—22no—
68C2×C3×D12—21no—
69C2×C3×D12D414yescomplemented
70C2×C3×D12C2312yes—
71C2×C3×D12C2312yes—
72C2×D3×Dic3—24no—
73#3757—21no—
74C4⋊(C3⋊Dic3)C2312yes—
75C4×C3⋊Dic3—21no—
76C2×C3⋊(C3⋊C8)—22no—
77C2×C3⋊(C3⋊C8)C2312yes—
78C3×#217D412yes—
79C3×#215—24no—
80C3×#213—24no—
81C3×(C2×D3)⋊C4—24no—
82C3×C4⋊Dic3D412yes—
83C3×C4×Dic3C2312yes—
84C3×#208—22no—
85C2×C3×C3⋊C8C2312yes—
86(C2×D3)⋊Dic3—24no—
87#3713—28no—
88#3041—91noSylow
89C2×C3×#41—21no—
90C2×C3×#41C2×D311yescharacteristic
91C2×C3×#41C2×D311yescharacteristic
92C22×C3×D4—31no—
93C22×C3×D4—31no—
94C22×D12C2×D311yescharacteristic
95C22×D12C2×D311yescharacteristic
96C3×AGL(1,ℤ/8)—64no—
97C2×C3×SD16—32no—
98C2×C3×D8—32no—
99C2×C3×M16—31no—
100C3×#127—32no—
101C3×#124—32no—
102C3×#121—62no—
103C3×#120—62no—
104C3×#117—31no—
105C2×#217—62no—
106#949—24no—
107#947C2×D312yescomplemented
108C2×#215C2×D312yescomplemented
109#940C2×D312yescomplemented
110#937—22no—
111D4×Dic3—34no—
112D4×Dic3—62no—
113C2×#213—34no—
114C2×#213—34no—
115C2×#213—64no—
116C2×#213—64no—
117C2×#213C2×D312yescomplemented
118#930—22no—
119#926—31no—
120#926—31no—
121#926—61no—
122#926C2×D311yescharacteristic
123C2×#208C2×D311yescharacteristic
124C22×C3⋊C8—31no—
125C22×C3⋊C8—31no—
126C22×C3⋊C8—61no—
127#893—62no—
128D3×C22⋊C4—62no—
129C4×D12—34no—
130#835—32no—
131#835—32no—
132#835—62no—
133#832—32no—
134#832—32no—
135#832—34no—
136#832—62no—
137#821—34no—
138Dic3⋊C8—34no—
139C4⋊(C3⋊C8)—34no—
140C23×C32—21no—
141C23×C32C2×D411yescharacteristic
142C22×C3×D3—22no—
143C22×C3×D3—24no—
144C22×C3×D3—22no—
145C22×C3×D3—42no—
146C22×C3×D3—82no—
147C22×C3×D3—82no—
148C32×Q8—21no—
149C32×Q8—21no—
150C32×D4—21no—
151C32×D4—21no—
152C32×D4—42no—
153C2×C32×C4—21no—
154C2×C32×C4—42no—
155C2×C32×C4C2×D411yescharacteristic
156C2×C32×C4C2×D412yes—
157C2×C32×C4#4112yes—
158C2×C32×C4C2411yescharacteristic
159C2×C3⋊Dic3—22no—
160C3×#67—84no—
161C2×C3×Dic3C2×D414yes—
162C3×D12—24no—
163C3×D12—22no—
164C3×D12—22no—
165C3×D12—22no—
166C3×D12—42no—
167C3×D12C2×D414yes—
168D3×Dic3—84no—
169C3⋊(C3⋊C8)—22no—
170C3×C3⋊C8—22no—
171C2×AGL(1,ℤ/8)—31no—
172C22×D8—91no—
173#535—31no—
174#518—91no—
175#463—94no—
176#459—94no—
177#424—91no—
178#418—91no—
179#416—91no—
180C24×C3—61no—
181C24×C3—61no—
182C23×D3—21no—
183C23×D3—21no—
184C3×#41—24no—
185C3×#41—22no—
186C3×#41—22no—
187C3×#41—22no—
188C3×#41—22no—
189C3×#41—42no—
190C2×C3×Q8—21no—
191C2×C3×Q8C22×D311yescharacteristic
192C2×C3×Q8C22×D311yescharacteristic
193C2×C3×D4—21no—
194C2×C3×D4—21no—
195C2×C3×D4—21no—
196C2×C3×D4—34no—
197C2×C3×D4—32no—
198C2×C3×D4—32no—
199C2×C3×D4—41no—
200C2×C3×D4—64no—
201C2×C3×D4—61no—
202C2×C3×D4—62no—
203C2×C3×D4—62no—
204C2×C3×D4—61no—
205C2×C3×D4—62no—
206C2×C3×D4C22×D311yescharacteristic
207C2×C3×D4C22×D311yescharacteristic
208C22×C3×C4—21no—
209C22×C3×C4—21no—
210C22×C3×C4—21no—
211C22×C3×C4—41no—
212C22×C3×C4C22×D311yescharacteristic
213C22×C3×C4C22×D311yescharacteristic
214C2×#67—24no—
215C22×Dic3—64no—
216C2×D12—21no—
217C2×D12—22no—
218C2×D12—22no—
219C2×D12—22no—
220C2×D12—21no—
221C2×D12#6714yescomplemented
222C2×D12C22×D312yes—
223C2×D12C22×D312yes—
224C2×C4×D3—64no—
225C3×SD16—64no—
226C3×D8—64no—
227C3×M16—62no—
228C2×C3×C8—32no—
229C3×C4⋊C4—32no—
230C3×C22⋊C4—32no—
231C3×C22⋊C4—64no—
232C3×C42—32no—
233#217—61no—
234#217—61no—
235#217—64no—
236#217—121no—
237#217#6712yes—
238#215—24no—
239#213—24no—
240#213—68no—
241#213—68no—
242(C2×D3)⋊C4—24no—
243(C2×D3)⋊C4—64no—
244C4⋊Dic3—32no—
245C4⋊Dic3—32no—
246C4⋊Dic3—62no—
247C4⋊Dic3#6712yes—
248C4×Dic3—61no—
249C4×Dic3—61no—
250C4×Dic3—121no—
251C4×Dic3C22×D312yes—
252#208—22no—
253C2×C3⋊C8—32no—
254C2×C3⋊C8—32no—
255C2×C3⋊C8—62no—
256C2×C3⋊C8—62no—
257C2×C3⋊C8—62no—
258C2×C3⋊C8—122no—
259C2×C3⋊C8C22×D312yes—
260C22×C32—22no—
261C22×C32—41no—
262C22×C32—42no—
263C22×C32#12112yes—
264C22×C32C22×D411yescharacteristic
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—41no—
272C32×C4#12112yes—
273C32×C4C22×D411yescharacteristic
274C32×C4C2×#4111yescharacteristic
275C3⋊Dic3—42no—
276C3×Dic3—24no—
277C2×#41D3211yescharacteristic
278C22×D4—31no—
279C22×D4—31no—
280AGL(1,ℤ/8)—64no—
281C2×SD16—32no—
282C2×D8—32no—
283C2×D8—94no—
284C2×D8—184no—
285C2×M16—31no—
286C22×C8—91no—
287#127—32no—
288#124—32no—
289#121—62no—
290#120—62no—
291C4×D4—94no—
292C4×D4—182no—
293#117—31no—
294#117—91no—
295C2×C22⋊C4—182no—
296C4⋊C8—94no—
297#103—92no—
298#102—94no—
299#102—92no—
300C23×C3—21no—
301C23×C3—21no—
302C23×C3—21no—
303C23×C3—41no—
304C23×C3—62no—
305C23×C3—64no—
306C23×C3—62no—
307C23×C3—122no—
308C23×C3—242no—
309C23×C3—242no—
310C23×C3D3×D411yescharacteristic
311C23×C3C2×#6711yescharacteristic
312C22×D3—22no—
313C22×D3—24no—
314C22×D3—22no—
315C22×D3—42no—
316C22×D3—82no—
317C22×D3—82no—
318C3×Q8—22no—
319C3×Q8—21no—
320C3×Q8—21no—
321C3×Q8—21no—
322C3×Q8—21no—
323C3×Q8—41no—
324C3×D4—22no—
325C3×D4—21no—
326C3×D4—21no—
327C3×D4—21no—
328C3×D4—21no—
329C3×D4—34no—
330C3×D4—41no—
331C3×D4—44no—
332C3×D4—42no—
333C3×D4—42no—
334C3×D4—64no—
335C3×D4—62no—
336C3×D4—62no—
337C3×D4—62no—
338C3×D4—122no—
339C3×D4—244no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—22no—
344C2×C3×C4—22no—
345C2×C3×C4—21no—
346C2×C3×C4—34no—
347C2×C3×C4—41no—
348C2×C3×C4—44no—
349C2×C3×C4—42no—
350C2×C3×C4—42no—
351C2×C3×C4D3×D412yes—
352C2×C3×C4D3×D411yescharacteristic
353C2×C3×C4#23712yes—
354C2×C3×C4#23712yes—
355C2×C3×C4C2×#6711yescharacteristic
356C2×C3×C4C2×#6712yes—
357C2×C3×C4C23×D311yescharacteristic
358C2×C3×C4C23×D311yescharacteristic
359#67—84no—
360C2×Dic3—62no—
361C2×Dic3—62no—
362C2×Dic3—122no—
363C2×Dic3—244no—
364C2×Dic3C2×#6714yes—
365D12—24no—
366D12—22no—
367D12—22no—
368D12—22no—
369D12—42no—
370D12C2×#6714yes—
371C4×D3—244no—
372C3×C8—62no—
373C3⋊C8—22no—
374C3⋊C8—62no—
375C3⋊C8—62no—
376C3⋊C8—122no—
377C2×C32—22no—
378C2×C32—81no—
379C2×C32C2×#12111yescharacteristic
380C2×C32#57612yes—
381C3×D3—44no—
382C3×D3—82no—
383C24—61no—
384C24—61no—
385#41—22no—
386#41—22no—
387C2×Q8C2×D3211yescharacteristic
388C2×D4—21no—
389C2×D4—32no—
390C2×D4—32no—
391C2×D4—34no—
392C2×D4—64no—
393C2×D4—62no—
394C2×D4—62no—
395C2×D4—61no—
396C2×D4—62no—
397C2×D4—61no—
398C2×D4C2×D3211yescharacteristic
399C22×C4—21no—
400C22×C4—184no—
401C22×C4C2×D3211yescharacteristic
402SD16—64no—
403D8—64no—
404D8—188no—
405M16—62no—
406C2×C8—32no—
407C2×C8—92no—
408C2×C8—182no—
409C4⋊C4—32no—
410C4⋊C4—92no—
411C22⋊C4—32no—
412C22⋊C4—64no—
413C22⋊C4—184no—
414C22⋊C4—181no—
415C42—32no—
416C42—181no—
417C22×C3—22no—
418C22×C3—22no—
419C22×C3—21no—
420C22×C3—22no—
421C22×C3—42no—
422C22×C3—42no—
423C22×C3—42no—
424C22×C3—41no—
425C22×C3—41no—
426C22×C3—42no—
427C22×C3—64no—
428C22×C3—82no—
429C22×C3—124no—
430C22×C3—124no—
431C22×C3—122no—
432C22×C3—244no—
433C22×C3—244no—
434C22×C3#93812yes—
435C22×C3#93912yes—
436C22×C3C2×D3×D411yescharacteristic
437C22×C3C22×#6711yescharacteristic
438C2×D3—24no—
439C2×D3—44no—
440C2×D3—42no—
441C2×D3—44no—
442C2×D3—84no—
443C2×D3—84no—
444C3×C4—21no—
445C3×C4—21no—
446C3×C4—22no—
447C3×C4—42no—
448C3×C4—41no—
449C3×C4—41no—
450C3×C4—64no—
451C3×C4#93812yes—
452C3×C4#93912yes—
453C3×C4C2×D3×D411yescharacteristic
454C3×C4C2×#23711yescharacteristic
455C3×C4C2×#23711yescharacteristic
456C3×C4C22×#6711yescharacteristic
457Dic3—24no—
458Dic3—122no—
459Dic3—122no—
460Dic3—242no—
461C32#304111yescharacteristic, complemented, Sylow
462C23—21no—
463C23—62no—
464C23—64no—
465C23—62no—
466C23—122no—
467C23—242no—
468C23—242no—
469C23D3×#6711yescharacteristic
470Q8—21no—
471Q8—21no—
472D4—21no—
473D4—21no—
474D4—34no—
475D4—42no—
476D4—62no—
477D4—62no—
478D4—62no—
479D4—64no—
480D4—122no—
481D4—244no—
482C2×C4—21no—
483C2×C4—34no—
484C2×C4—42no—
485C2×C4—182no—
486C2×C4—724no—
487C2×C4#380512yes—
488C2×C4D3×#6712yes—
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—82no—
499C2×C3—81no—
500C2×C3—81no—
501C2×C3—124no—
502C2×C3—242no—
503C2×C3#577412yes—
504C2×C3C2×#93811yescharacteristic
505C2×C3C2×#93911yescharacteristic
506C2×C3#583512yes—
507D3—44no—
508D3—82no—
509C22—22no—
510C22—42no—
511C22—41no—
512C22—64no—
513C22—124no—
514C22—124no—
515C22—122no—
516C22—244no—
517C22—244no—
518C22#6397012yes—
519C22C2×D3×#6711yescharacteristic
520C4—41no—
521C4—64no—
522C4—362no—
523C4#6397012yes—
524C4C2×#380511yescharacteristic
525C4C2×D3×#6711yescharacteristic
526C3—21no—
527C3#8338411yescharacteristic, complemented
528C3#8393411yescharacteristic, complemented
529C2—22no—
530C2—81no—
531C2—124no—
532C2—242no—
533C2#1059545412yes—
534C2C2×#6397011yescharacteristic
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. C3×#5830C2semidirect
2. C2×C3×#949C2semidirect
3. #10594982C2semidirect
4. C22×#3713C2semidirect
5. #10592932C2semidirect
6. #10591567C2semidirect
7. #10591428C2semidirect
8. #10591117C2semidirect
9. #10591086C2semidirect
18. C3×#947C22semidirect
19. C2×C3×#215C22semidirect
20. C3×#940C22semidirect
22. C2×C3×#213C22semidirect
28. Dic3×D12C22semidirect
31. #63662C22semidirect
32. #63659C22semidirect
33. Dic3⋊(C3⋊C8)C22semidirect
34. #63563C22semidirect
37. #5830D3semidirect
38. C2×#949D3semidirect
69. C2×C3×D12D4semidirect
107. #947C2×D3semidirect
108. C2×#215C2×D3semidirect
109. #940C2×D3semidirect
117. C2×#213C2×D3semidirect
221. C2×D12#67semidirect
461. C32#3041semidirect
527. C3#83384semidirect
528. C3#83934semidirect

Maximal subgroups

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

subgroupindex
C3×#58302
C2×C3×#9492
#105949822
C22×#37132
#105929322
#105915672
#105914282
#105911172
#105910862
#839343
#833843