Finite Group Databasebeta

← #11866364

Subgroups — #11866364

Order 1152.

1113 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595987C211yesmaximal, characteristic, complemented
2#10595040C211yesmaximal, characteristic
3C2×#63831C211yesmaximal, characteristic, complemented
4C22×#3716C211yesmaximal, characteristic, complemented
5C3×#5002C211yesmaximal, characteristic, complemented
6C3×#5001C211yesmaximal, characteristic, complemented
7#10591119C211yesmaximal, characteristic, complemented
8#10590553C214yesmaximal, complemented
9#10590538C214yesmaximal, complemented
10#78945—31nomaximal
11#78864—31nomaximal
12C22×#634C2211yescharacteristic
13C2×C3×#235C2211yescharacteristic
14C22×C3×D12C2211yescharacteristic
15C32×#117C2211yescharacteristic
16#64135C2211yescharacteristic
17#64096C2214yescomplemented
18#64086—22no—
19C4×#634—22no—
20C2×C3×#208C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22#63976—22no—
23#63914C2212yes—
24#63908—22no—
25#63863C2212yes—
26C2×#3719C2212yescomplemented
27#63831—24no—
28C2×#3716—24no—
29C2×#3716C2214yes—
30C2×#3716C2212yescomplemented
31C3×#810C2212yescomplemented
32C3×#809C2214yes—
33C3×#809C2212yescomplemented
34#63572C2214yescomplemented
35#5830—31no—
36C2×#951—31no—
37#5805—31no—
38C22×#214—31no—
39C2×#909—31no—
40C22×#204—31no—
41#5516—31no—
42#5516—31no—
43#5516—61no—
44C3×#418—31no—
45C3×#416—31no—
46#5119—31no—
47#5102—31no—
48#5002D311yescharacteristic, complemented
49#5001D311yescharacteristic, complemented
50#4798—34no—
51#4767—34no—
52#4762—34no—
53#4762—34no—
54C23×C3×D3—21no—
55C22×C32×C4C2311yescharacteristic
56C22×C3⋊Dic3—21no—
57C2×#634—21no—
58C2×#634—22no—
59C2×#634D414yescomplemented
60C2×#634C2312yes—
61C2×C3×#67—21no—
62C3×#235—22no—
63C3×#235—22no—
64C2×C3×D12—22no—
65C2×C3×D12—22no—
66C2×C3×D12—21no—
67C2×C3×D12C2312yes—
68C2×C3×D12C2311yescharacteristic
69C2×C3×C4×D3—21no—
70C2×C3×Dic6C2311yescharacteristic
71C2×#625—24no—
72C32×C4⋊C4C2312yes—
73C32×C22⋊C4—21no—
74C32×C42—21no—
75#3757D412yes—
76C4⋊(C3⋊Dic3)D412yes—
77#3750—24no—
78C4×C3⋊Dic3—24no—
79C4×C3⋊Dic3C2312yes—
80C3×#208—22no—
81C2×C3×C3⋊C8—22no—
82C2×C3×C3⋊C8C2312yes—
83C2×C3×C3⋊C8C2312yes—
84(C2×D3)⋊Dic3—24no—
85#3719—24no—
86#3716—28no—
87#3716—24no—
88#3043—91noSylow
89C2×C3×#41—31no—
90C22×C3×D4—31no—
91C2×#235C2×D311yescharacteristic
92C22×D12C2×D311yescharacteristic
93C22×Dic6—31no—
94C22×Dic6—31no—
95C22×Dic6—61no—
96C2×C3×M16—31no—
97C22×C3×C8—31no—
98C3×#117—21no—
99C3×#117C2×D311yescharacteristic
100C3×#117C2×D311yescharacteristic
101#953—62no—
102#951—64no—
103#947—32no—
104C2×#216—32no—
105#940—32no—
106#940—32no—
107#938—62no—
108#937—62no—
109#936—32no—
110C2×#214—34no—
111C2×#214—32no—
112C2×#214—64no—
113#930—62no—
114#926—31no—
115#926—31no—
116#926—61no—
117C2×#208C2×D311yescharacteristic
118C22×C3⋊C8C2×D311yescharacteristic
119#909—64no—
120C2×Dic12—32no—
121C2×#204—34no—
122C2×#204—32no—
123C2×#204—64no—
124#887—34no—
125#887—34no—
126#887—64no—
127#877—62no—
128#877—62no—
129#877—64no—
130C4×Dic6—62no—
131C4×Dic6—62no—
132C4×Dic6—64no—
133C3×#103—32no—
134C3×#102—34no—
135C3×#102—32no—
136Dic3⋊C8—34no—
137Dic3⋊C8—34no—
138#810C2×D312yescomplemented
139#809C2×D314yes—
140#809C2×D312yescomplemented
141C23×C32C2×D411yescharacteristic
142C22×C3×D3—22no—
143C22×C3×D3—21no—
144C22×C3×D3—42no—
145C22×C3×D3—82no—
146C2×C32×C4—22no—
147C2×C32×C4C2×D411yescharacteristic
148C2×C32×C4C2×D412yes—
149C2×C32×C4#4112yes—
150C2×C32×C4C2411yescharacteristic
151C2×C3⋊Dic3—24no—
152C2×C3⋊Dic3—22no—
153C2×C3⋊Dic3C2×D414yes—
154#634—24no—
155#634—22no—
156#634C2×D414yes—
157C3×#67—42no—
158C2×C3×Dic3—21no—
159C3×D12—22no—
160C3×D12—21no—
161C3×D12—22no—
162C3×D12—21no—
163C3×D12—42no—
164C3×C4×D3—42no—
165C3×Dic6—21no—
166C3×Dic6—21no—
167#625—84no—
168C3×C3⋊C8—22no—
169C3×C3⋊C8—22no—
170C2×#137—91no—
171C22×SD16—91no—
172#535—91no—
173#519—91no—
174#464—94no—
175#460—94no—
176#424—91no—
177#418—31no—
178#416—31no—
179C24×C3—61no—
180C23×D3—21no—
181C3×#41—62no—
182C3×#41—62no—
183C2×C3×Q8—31no—
184C2×C3×D4—32no—
185C2×C3×D4—31no—
186C2×C3×D4—61no—
187C2×C3×D4—62no—
188C2×C3×D4—62no—
189C2×C3×D4—61no—
190C22×C3×C4—21no—
191C22×C3×C4—61no—
192C22×C3×C4C22×D311yescharacteristic
193C22×C3×C4C22×D311yescharacteristic
194C2×#67—21no—
195C2×#67—64no—
196C2×#67—64no—
197C22×Dic3—62no—
198C22×Dic3—61no—
199C22×Dic3—61no—
200#235—22no—
201#235—22no—
202C2×D12—22no—
203C2×D12—22no—
204C2×D12—21no—
205C2×D12C22×D312yes—
206C2×D12C22×D311yescharacteristic
207C2×C4×D3—21no—
208C2×Dic6—34no—
209C2×Dic6—34no—
210C2×Dic6—32no—
211C2×Dic6—32no—
212C2×Dic6—62no—
213C2×Dic6—64no—
214C2×Dic6—62no—
215C2×Dic6—64no—
216C2×Dic6—62no—
217C2×Dic6—62no—
218C2×Dic6—61no—
219C2×Dic6—61no—
220C2×Dic6C22×D311yescharacteristic
221C3×M16—62no—
222C2×C3×C8—32no—
223C2×C3×C8—32no—
224C2×C3×C8—62no—
225C3×C4⋊C4—22no—
226C3×C4⋊C4C22×D312yes—
227C3×C4⋊C4C22×D312yes—
228C3×C22⋊C4—22no—
229C3×C22⋊C4—21no—
230C3×C22⋊C4—21no—
231C3×C42—22no—
232C3×C42—21no—
233C3×C42—21no—
234#217—32no—
235#217—32no—
236#217—62no—
237#217—64no—
238#216—64no—
239#214—68no—
240#214—64no—
241(C2×D3)⋊C4—64no—
242C4⋊Dic3—32no—
243C4⋊Dic3—32no—
244C4⋊Dic3—62no—
245Dic3⋊C4—64no—
246Dic3⋊C4—64no—
247Dic3⋊C4—68no—
248C4×Dic3—32no—
249C4×Dic3—32no—
250C4×Dic3—62no—
251C4×Dic3—64no—
252C4×Dic3—64no—
253C4×Dic3—68no—
254#208—22no—
255C2×C3⋊C8—22no—
256C2×C3⋊C8C22×D312yes—
257C2×C3⋊C8C22×D312yes—
258Dic12—64no—
259#204—68no—
260#204—64no—
261C22×C32—22no—
262C22×C32#12112yes—
263C22×C32C22×D411yescharacteristic
264C2×C3×D3—41no—
265C2×C3×D3—42no—
266C2×C3×D3—42no—
267C2×C3×D3—44no—
268C2×C3×D3—84no—
269C32×C4—42no—
270C32×C4#12112yes—
271C32×C4C22×D411yescharacteristic
272C32×C4C2×#4111yescharacteristic
273C3⋊Dic3—24no—
274C3⋊Dic3—24no—
275C3×Dic3—41no—
276C2×#41—31no—
277C22×Q8—91no—
278C22×D4—31no—
279#137—184no—
280C2×Q16—92no—
281C2×SD16—94no—
282C2×SD16—92no—
283C2×SD16—184no—
284C2×M16—31no—
285C22×C8—31no—
286#127—92no—
287#124—92no—
288#121—182no—
289#120—182no—
290C4×Q8—94no—
291C4×Q8—182no—
292#117—91no—
293#117—182no—
294#117D3211yescharacteristic
295C4⋊C8—94no—
296#103—32no—
297#102—34no—
298#102—32no—
299C23×C3—21no—
300C23×C3—62no—
301C23×C3—61no—
302C23×C3—122no—
303C23×C3—242no—
304C23×C3D3×D411yescharacteristic
305C23×C3D3×D411yescharacteristic
306C22×D3—22no—
307C22×D3—21no—
308C22×D3—42no—
309C22×D3—82no—
310C3×Q8—61no—
311C3×Q8—61no—
312C3×D4—62no—
313C3×D4—61no—
314C3×D4—62no—
315C3×D4—61no—
316C3×D4—122no—
317C3×D4—122no—
318C2×C3×C4—24no—
319C2×C3×C4—22no—
320C2×C3×C4—22no—
321C2×C3×C4—21no—
322C2×C3×C4—22no—
323C2×C3×C4—22no—
324C2×C3×C4—21no—
325C2×C3×C4—61no—
326C2×C3×C4—122no—
327C2×C3×C4#23512yes—
328C2×C3×C4#23512yes—
329C2×C3×C4D3×D412yes—
330C2×C3×C4D3×D412yes—
331C2×C3×C4D3×D411yescharacteristic
332C2×C3×C4D3×D411yescharacteristic
333C2×C3×C4C23×D311yescharacteristic
334C2×C3×C4C23×D311yescharacteristic
335#67—42no—
336#67—244no—
337#67—244no—
338C2×Dic3—21no—
339C2×Dic3—34no—
340C2×Dic3—34no—
341C2×Dic3—64no—
342C2×Dic3—64no—
343C2×Dic3—68no—
344C2×Dic3—64no—
345C2×Dic3—64no—
346C2×Dic3—62no—
347C2×Dic3—62no—
348D12—22no—
349D12—21no—
350D12—22no—
351D12—21no—
352D12—42no—
353C4×D3—42no—
354Dic6—21no—
355Dic6—21no—
356Dic6—34no—
357Dic6—34no—
358Dic6—64no—
359Dic6—64no—
360Dic6—68no—
361Dic6—64no—
362Dic6—64no—
363Dic6—62no—
364Dic6—62no—
365C3×C8—62no—
366C3×C8—62no—
367C3⋊C8—22no—
368C3⋊C8—22no—
369C2×C32—22no—
370C2×C32C2×#12111yescharacteristic
371C2×C32#57712yes—
372C3×D3—81no—
373C3×D3—82no—
374C24—61no—
375#41—62no—
376#41—62no—
377C2×Q8—31no—
378C2×Q8—92no—
379C2×Q8—94no—
380C2×Q8—182no—
381C2×Q8—181no—
382C2×D4—32no—
383C2×D4—31no—
384C2×D4—61no—
385C2×D4—62no—
386C2×D4—62no—
387C2×D4—61no—
388C2×D4—184no—
389C22×C4—61no—
390C22×C4—181no—
391C22×C4C2×D3211yescharacteristic
392Q16—184no—
393SD16—188no—
394SD16—184no—
395M16—62no—
396C2×C8—32no—
397C2×C8—32no—
398C2×C8—62no—
399C4⋊C4—92no—
400C4⋊C4—184no—
401C4⋊C4C2×D3212yes—
402C22⋊C4—21no—
403C22⋊C4—92no—
404C22⋊C4—184no—
405C42—21no—
406C42—92no—
407C42—184no—
408C22×C3—22no—
409C22×C3—22no—
410C22×C3—21no—
411C22×C3—22no—
412C22×C3—42no—
413C22×C3—121no—
414C22×C3—122no—
415C22×C3—124no—
416C22×C3—122no—
417C22×C3—244no—
418C22×C3#88412yes—
419C22×C3#88412yes—
420C22×C3C2×D3×D411yescharacteristic
421C22×C3C2×D3×D411yescharacteristic
422C2×D3—41no—
423C2×D3—42no—
424C2×D3—42no—
425C2×D3—44no—
426C2×D3—84no—
427C3×C4—21no—
428C3×C4—21no—
429C3×C4—22no—
430C3×C4—44no—
431C3×C4—42no—
432C3×C4—42no—
433C3×C4—121no—
434C3×C4#88412yes—
435C3×C4#88412yes—
436C3×C4C2×#23511yescharacteristic
437C3×C4C2×#23511yescharacteristic
438C3×C4C2×D3×D411yescharacteristic
439C3×C4C2×D3×D411yescharacteristic
440Dic3—41no—
441Dic3—68no—
442Dic3—64no—
443Dic3—64no—
444Dic3—64no—
445Dic3—64no—
446Dic3—124no—
447C32#304311yescharacteristic, complemented, Sylow
448C23—62no—
449C23—61no—
450C23—122no—
451C23—242no—
452C23#381111yescharacteristic
453Q8—61no—
454Q8—61no—
455Q8—94no—
456Q8—182no—
457Q8—184no—
458D4—62no—
459D4—61no—
460D4—62no—
461D4—61no—
462D4—122no—
463D4—122no—
464D4—724no—
465C2×C4—22no—
466C2×C4—61no—
467C2×C4—94no—
468C2×C4—122no—
469C2×C4—182no—
470C2×C4—184no—
471C2×C4#379812yes—
472C2×C4#380212yes—
473C2×C4#381111yescharacteristic
474C2×C4C22×D3211yescharacteristic
475C8—62no—
476C8—62no—
477C2×C3—22no—
478C2×C3—22no—
479C2×C3—22no—
480C2×C3—21no—
481C2×C3—42no—
482C2×C3—242no—
483C2×C3—241no—
484C2×C3C2×#88411yescharacteristic
485C2×C3C2×#88411yescharacteristic
486C2×C3#577012yes—
487C2×C3#577512yes—
488D3—81no—
489D3—82no—
490C22—22no—
491C22—122no—
492C22—124no—
493C22—121no—
494C22—122no—
495C22—244no—
496C22#6391212yes—
497C22C2×#381111yescharacteristic
498C4—42no—
499C4—121no—
500C4—184no—
501C4—184no—
502C4#6391212yes—
503C4C2×#379811yescharacteristic
504C4C2×#380211yescharacteristic
505C3—21no—
506C3#7886411yescharacteristic, complemented
507C3#7894511yescharacteristic, complemented
508C2—22no—
509C2—242no—
510C2—241no—
511C2C2×#6391211yescharacteristic
512C2#1059546212yes—
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radical#10595040C2
hypercenter#117D32
hypocenterC32#3043
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. #10595987C2semidirect
3. C2×#63831C2semidirect
4. C22×#3716C2semidirect
5. C3×#5002C2semidirect
6. C3×#5001C2semidirect
7. #10591119C2semidirect
8. #10590553C2semidirect
9. #10590538C2semidirect
17. #64096C22semidirect
26. C2×#3719C22semidirect
30. C2×#3716C22semidirect
31. C3×#810C22semidirect
33. C3×#809C22semidirect
34. #63572C22semidirect
48. #5002D3semidirect
49. #5001D3semidirect
59. C2×#634D4semidirect
138. #810C2×D3semidirect
140. #809C2×D3semidirect
447. C32#3043semidirect
506. C3#78864semidirect
507. C3#78945semidirect

Maximal subgroups

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

subgroupindex
#105959872
#105950402
C2×#638312
C22×#37162
C3×#50022
C3×#50012
#105911192
#105905532
#105905382
#789453
#788643