Finite Group Databasebeta

← #11866203

Subgroups — #11866203

Order 1152.

1109 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5525C211yesmaximal, characteristic, complemented
2C3×#5521C211yesmaximal, characteristic, complemented
3C2×#63823C211yesmaximal, characteristic, complemented
4C22×#3713C211yesmaximal, characteristic, complemented
5#10592698C211yesmaximal, characteristic, complemented
6#10591085C211yesmaximal, characteristic, complemented
7#10591083C211yesmaximal, characteristic, complemented
8#10590348C214yesmaximal, complemented
9#10590347C214yesmaximal, complemented
10#83384—31nomaximal
11#82540—31nomaximal
12C2×C3×#235C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C22×C3×D12C2211yescharacteristic
15C32×#117C2211yescharacteristic
16C2×#3748C2211yescharacteristic
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18C3×#926C2211yescharacteristic
19C3×#895—22no—
20C3×#893—22no—
21C3×#882—22no—
22C3×D3×C22⋊C4—22no—
23C3×#875C2212yescomplemented
24C3×#874C2212yescomplemented
25C3×C4×D12C2214yescomplemented
26C2×#3715C2212yescomplemented
27#63823—24no—
28C2×#3713—24no—
29C2×#3713C2214yes—
30C2×#3713C2212yescomplemented
31C4⋊(C3⋊(C3⋊C8))C2214yescomplemented
32#63565C2212yescomplemented
33#63562C2212yescomplemented
34#63562C2214yescomplemented
35C3×#535—31no—
36C3×#518—31no—
37C2×#949—31no—
38C2×#932—31no—
39C22×#213—31no—
40C22×#213—31no—
41#5525D311yescharacteristic, complemented
42#5521D311yescharacteristic, complemented
43#5233—31no—
44#5215—31no—
45#5072—34no—
46#5057—34no—
47#5016—34no—
48#5015—34no—
49#5002—31no—
50#5001—31no—
51#4999—31no—
52#4999—31no—
53#4999—61no—
54C23×C3×D3—21no—
55C23×C3×D3—21no—
56C22×C32×C4C2311yescharacteristic
57C2×C3×#67—21no—
58C3×#235—22no—
59C3×#235—22no—
60C2×C3×D12—21no—
61C2×C3×D12—22no—
62C2×C3×D12—22no—
63C2×C3×D12—22no—
64C2×C3×D12—21no—
65C2×C3×D12—24no—
66C2×C3×D12D414yescomplemented
67C2×C3×D12C2312yes—
68C2×C3×D12C2311yescharacteristic
69C2×C3×D12C2312yes—
70C2×C3×C4×D3—21no—
71C2×C3×C4×D3—24no—
72C2×C3×Dic6C2311yescharacteristic
73C32×C4⋊C4D412yes—
74C32×C22⋊C4D412yes—
75C32×C42C2312yes—
76#3748—22no—
77C2×C3⋊(C3⋊C8)—22no—
78C2×C3⋊(C3⋊C8)C2312yes—
79C2×C3⋊(C3⋊C8)C2312yes—
80C3×#217—21no—
81C3×(C2×D3)⋊C4—24no—
82C3×(C2×D3)⋊C4—24no—
83C3×C4⋊Dic3C2312yes—
84C3×C4×Dic3—21no—
85#3715—24no—
86#3713—28no—
87#3713—24no—
88#3041—91noSylow
89C2×C3×#41—31no—
90C22×C3×D4—31no—
91C22×C3×D4—31no—
92C2×#235C2×D311yescharacteristic
93C22×D12C2×D311yescharacteristic
94C22×D12C2×D311yescharacteristic
95C3×#127—32no—
96C3×#124—32no—
97C3×#121—62no—
98C3×#120—62no—
99C3×C4×D4—34no—
100C3×C4×D4—62no—
101C3×#117—21no—
102C3×#117—31no—
103C3×#117C2×D311yescharacteristic
104C3×#117C2×D311yescharacteristic
105C2×C3×C22⋊C4—62no—
106#949—64no—
107C2×#215—32no—
108C2×#214—32no—
109#932—64no—
110C2×#213—34no—
111C2×#213—34no—
112C2×#213—32no—
113C2×#213—32no—
114C2×#213—64no—
115C2×#213—64no—
116#926C2×D311yescharacteristic
117C2×#208—31no—
118C2×#208—31no—
119C2×#208—61no—
120C22×C3⋊C8—31no—
121C22×C3⋊C8—31no—
122C22×C3⋊C8—61no—
123#895—22no—
124#893—22no—
125#882—22no—
126D3×C22⋊C4—22no—
127#875C2×D312yescomplemented
128#874C2×D312yescomplemented
129C4×D12C2×D314yescomplemented
130#835—32no—
131#832—34no—
132#832—32no—
133#810—32no—
134#809—34no—
135#809—32no—
136C4⋊(C3⋊C8)—34no—
137C4⋊(C3⋊C8)—34no—
138C4⋊(C3⋊C8)—64no—
139C23×C32C2×D411yescharacteristic
140C22×C3×D3—22no—
141C22×C3×D3—24no—
142C22×C3×D3—22no—
143C22×C3×D3—21no—
144C22×C3×D3—42no—
145C22×C3×D3—82no—
146C22×C3×D3—82no—
147C2×C32×C4C2×D412yes—
148C2×C32×C4C2×D414yes—
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4#4112yes—
151C2×C32×C4C2411yescharacteristic
152C3×#67—42no—
153C2×C3×Dic3—22no—
154C2×C3×Dic3—21no—
155C3×D12—24no—
156C3×D12—22no—
157C3×D12—21no—
158C3×D12—22no—
159C3×D12—22no—
160C3×D12—21no—
161C3×D12—42no—
162C3×D12—84no—
163C3×D12C2×D414yes—
164C3×C4×D3—42no—
165C3×C4×D3—84no—
166C3×Dic6—21no—
167C3×Dic6—21no—
168C3⋊(C3⋊C8)—22no—
169C3⋊(C3⋊C8)—22no—
170C2×AGL(1,ℤ/8)—91no—
171C22×D8—91no—
172#535—31no—
173#518—31no—
174#463—94no—
175#459—94no—
176#424—91no—
177#418—91no—
178#416—91no—
179C24×C3—61no—
180C24×C3—61no—
181C23×D3—21no—
182C23×D3—21no—
183C3×#41—62no—
184C3×#41—62no—
185C2×C3×Q8—31no—
186C2×C3×D4—34no—
187C2×C3×D4—32no—
188C2×C3×D4—32no—
189C2×C3×D4—31no—
190C2×C3×D4—61no—
191C2×C3×D4—62no—
192C2×C3×D4—62no—
193C2×C3×D4—62no—
194C2×C3×D4—61no—
195C2×C3×D4—61no—
196C2×C3×D4—64no—
197C22×C3×C4—21no—
198C22×C3×C4—61no—
199C22×C3×C4—64no—
200C22×C3×C4C22×D311yescharacteristic
201C22×C3×C4C22×D311yescharacteristic
202C2×#67—21no—
203#235—22no—
204#235—22no—
205C2×D12—22no—
206C2×D12—21no—
207C2×D12—22no—
208C2×D12—22no—
209C2×D12—21no—
210C2×D12—24no—
211C2×D12D1214yescomplemented
212C2×D12C22×D311yescharacteristic
213C2×D12C22×D312yes—
214C2×D12C22×D312yes—
215C2×C4×D3—21no—
216C2×C4×D3—24no—
217C2×Dic6C22×D311yescharacteristic
218C3×C4⋊C4—22no—
219C3×C4⋊C4—32no—
220C3×C4⋊C4#6712yes—
221C3×C4⋊C4#6712yes—
222C3×C22⋊C4—22no—
223C3×C22⋊C4—61no—
224C3×C22⋊C4—64no—
225C3×C22⋊C4—64no—
226C3×C22⋊C4#6712yes—
227C3×C22⋊C4#6712yes—
228C3×C42—22no—
229C3×C42—61no—
230C3×C42C22×D312yes—
231C3×C42C22×D312yes—
232#217—21no—
233#215—64no—
234#214—64no—
235#213—68no—
236#213—64no—
237#213—68no—
238#213—64no—
239(C2×D3)⋊C4—24no—
240(C2×D3)⋊C4—24no—
241C4⋊Dic3C22×D312yes—
242C4×Dic3—21no—
243#208—62no—
244#208—62no—
245#208—122no—
246C2×C3⋊C8—32no—
247C2×C3⋊C8—32no—
248C2×C3⋊C8—32no—
249C2×C3⋊C8—32no—
250C2×C3⋊C8—62no—
251C2×C3⋊C8—62no—
252C2×C3⋊C8—62no—
253C2×C3⋊C8—62no—
254C2×C3⋊C8—122no—
255C22×C32—22no—
256C22×C32#12112yes—
257C22×C32C22×D411yescharacteristic
258C2×C3×D3—24no—
259C2×C3×D3—44no—
260C2×C3×D3—41no—
261C2×C3×D3—42no—
262C2×C3×D3—42no—
263C2×C3×D3—44no—
264C2×C3×D3—84no—
265C2×C3×D3—84no—
266C32×C4—24no—
267C32×C4#12112yes—
268C32×C4C22×D411yescharacteristic
269C32×C4C2×#4111yescharacteristic
270C3×Dic3—41no—
271C3×Dic3—42no—
272C2×#41—31no—
273C22×D4—31no—
274C22×D4—31no—
275AGL(1,ℤ/8)—184no—
276C2×SD16—92no—
277C2×D8—94no—
278C2×D8—92no—
279C2×D8—184no—
280C2×M16—91no—
281C22×C8—91no—
282#127—32no—
283#124—32no—
284#121—62no—
285#120—62no—
286C4×D4—34no—
287C4×D4—62no—
288#117—31no—
289#117D3211yescharacteristic
290C2×C22⋊C4—62no—
291C4⋊C8—94no—
292#103—92no—
293#102—92no—
294#102—94no—
295C23×C3—21no—
296C23×C3—62no—
297C23×C3—64no—
298C23×C3—62no—
299C23×C3—61no—
300C23×C3—122no—
301C23×C3—242no—
302C23×C3—242no—
303C23×C3C2×#6711yescharacteristic
304C23×C3C2×#6711yescharacteristic
305C22×D3—22no—
306C22×D3—24no—
307C22×D3—22no—
308C22×D3—21no—
309C22×D3—42no—
310C22×D3—82no—
311C22×D3—82no—
312C3×Q8—61no—
313C3×Q8—61no—
314C3×D4—34no—
315C3×D4—64no—
316C3×D4—62no—
317C3×D4—61no—
318C3×D4—62no—
319C3×D4—61no—
320C3×D4—62no—
321C3×D4—122no—
322C3×D4—122no—
323C3×D4—244no—
324C2×C3×C4—21no—
325C2×C3×C4—22no—
326C2×C3×C4—22no—
327C2×C3×C4—21no—
328C2×C3×C4—24no—
329C2×C3×C4—62no—
330C2×C3×C4—61no—
331C2×C3×C4—122no—
332C2×C3×C4—244no—
333C2×C3×C4C2×D1212yes—
334C2×C3×C4#23512yes—
335C2×C3×C4D3×D412yes—
336C2×C3×C4#23712yes—
337C2×C3×C4C2×#6714yes—
338C2×C3×C4C2×#6714yes—
339C2×C3×C4C2×#6711yescharacteristic
340C2×C3×C4C2×#6711yescharacteristic
341C2×C3×C4C23×D311yescharacteristic
342C2×C3×C4C23×D311yescharacteristic
343#67—42no—
344C2×Dic3—22no—
345C2×Dic3—21no—
346D12—24no—
347D12—22no—
348D12—22no—
349D12—21no—
350D12—22no—
351D12—21no—
352D12—42no—
353D12—84no—
354D12C2×D1214yes—
355C4×D3—42no—
356C4×D3—84no—
357Dic6—21no—
358Dic6—21no—
359C3⋊C8—62no—
360C3⋊C8—62no—
361C3⋊C8—62no—
362C3⋊C8—62no—
363C3⋊C8—122no—
364C3⋊C8—122no—
365C2×C32—22no—
366C2×C32C2×#12111yescharacteristic
367C2×C32#57612yes—
368C3×D3—44no—
369C3×D3—81no—
370C3×D3—82no—
371C24—61no—
372C24—61no—
373#41—62no—
374#41—62no—
375C2×Q8—31no—
376C2×D4—32no—
377C2×D4—32no—
378C2×D4—31no—
379C2×D4—34no—
380C2×D4—61no—
381C2×D4—62no—
382C2×D4—62no—
383C2×D4—62no—
384C2×D4—61no—
385C2×D4—61no—
386C2×D4—64no—
387C22×C4—61no—
388C22×C4—64no—
389C22×C4C2×D3211yescharacteristic
390SD16—184no—
391D8—188no—
392D8—184no—
393M16—182no—
394C2×C8—92no—
395C2×C8—92no—
396C2×C8—182no—
397C4⋊C4—32no—
398C4⋊C4#62512yes—
399C22⋊C4—61no—
400C22⋊C4—64no—
401C22⋊C4—64no—
402C22⋊C4#62512yes—
403C42—61no—
404C42C2×D3212yes—
405C22×C3—22no—
406C22×C3—22no—
407C22×C3—21no—
408C22×C3—22no—
409C22×C3—42no—
410C22×C3—64no—
411C22×C3—124no—
412C22×C3—121no—
413C22×C3—122no—
414C22×C3—122no—
415C22×C3—124no—
416C22×C3—244no—
417C22×C3—244no—
418C22×C3#93012yes—
419C22×C3#93812yes—
420C22×C3C22×#6711yescharacteristic
421C22×C3C22×#6711yescharacteristic
422C2×D3—24no—
423C2×D3—44no—
424C2×D3—41no—
425C2×D3—42no—
426C2×D3—42no—
427C2×D3—44no—
428C2×D3—84no—
429C2×D3—84no—
430C3×C4—24no—
431C3×C4—24no—
432C3×C4—21no—
433C3×C4—21no—
434C3×C4—22no—
435C3×C4—44no—
436C3×C4—121no—
437C3×C4—122no—
438C3×C4#93012yes—
439C3×C4#93812yes—
440C3×C4C22×D1211yescharacteristic
441C3×C4C2×#23511yescharacteristic
442C3×C4C2×D3×D411yescharacteristic
443C3×C4C2×#23711yescharacteristic
444Dic3—41no—
445Dic3—42no—
446C32#304111yescharacteristic, complemented, Sylow
447C23—62no—
448C23—64no—
449C23—62no—
450C23—61no—
451C23—122no—
452C23—242no—
453C23—242no—
454C23C2×#62511yescharacteristic
455Q8—61no—
456Q8—61no—
457D4—34no—
458D4—62no—
459D4—62no—
460D4—61no—
461D4—62no—
462D4—61no—
463D4—64no—
464D4—122no—
465D4—122no—
466D4—244no—
467C2×C4—62no—
468C2×C4—61no—
469C2×C4—122no—
470C2×C4—244no—
471C2×C4#379512yes—
472C2×C4D3×D1212yes—
473C2×C4C2×#62514yes—
474C2×C4C2×#62511yescharacteristic
475C2×C4C22×D3211yescharacteristic
476C8—182no—
477C8—182no—
478C2×C3—22no—
479C2×C3—22no—
480C2×C3—22no—
481C2×C3—21no—
482C2×C3—42no—
483C2×C3—124no—
484C2×C3—242no—
485C2×C3—241no—
486C2×C3C2×#93011yescharacteristic
487C2×C3C2×#93811yescharacteristic
488C2×C3#583512yes—
489C2×C3#583512yes—
490D3—44no—
491D3—82no—
492D3—81no—
493C22—22no—
494C22—64no—
495C22—124no—
496C22—122no—
497C22—124no—
498C22—121no—
499C22—122no—
500C22—244no—
501C22—244no—
502C22#6390812yes—
503C22C22×#62511yescharacteristic
504C4—24no—
505C4—122no—
506C4—121no—
507C4#6390812yes—
508C4C2×#379511yescharacteristic
509C4C2×D3×D1211yescharacteristic
510C3—21no—
511C3#8254011yescharacteristic, complemented
512C3#8338411yescharacteristic, complemented
513C2—22no—
514C2—124no—
515C2—242no—
516C2—241no—
517C2C2×#6390811yescharacteristic
518C2#1059544412yes—
subgroupG/H
centerC22C22×#625
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 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C3×#5525C2semidirect
2. C3×#5521C2semidirect
3. C2×#63823C2semidirect
4. C22×#3713C2semidirect
5. #10592698C2semidirect
6. #10591085C2semidirect
7. #10591083C2semidirect
8. #10590348C2semidirect
9. #10590347C2semidirect
23. C3×#875C22semidirect
24. C3×#874C22semidirect
25. C3×C4×D12C22semidirect
26. C2×#3715C22semidirect
30. C2×#3713C22semidirect
31. C4⋊(C3⋊(C3⋊C8))C22semidirect
32. #63565C22semidirect
33. #63562C22semidirect
34. #63562C22semidirect
41. #5525D3semidirect
42. #5521D3semidirect
66. C2×C3×D12D4semidirect
127. #875C2×D3semidirect
128. #874C2×D3semidirect
129. C4×D12C2×D3semidirect
211. C2×D12D12semidirect
446. C32#3041semidirect
511. C3#82540semidirect
512. C3#83384semidirect

Maximal subgroups

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

subgroupindex
C3×#55252
C3×#55212
C2×#638232
C22×#37132
#105926982
#105910852
#105910832
#105903482
#105903472
#833843
#825403