Finite Group Databasebeta

← #11866351

Subgroups — #11866351

Order 1152.

1147 conjugacy classes of subgroups.

The subgroup lattice has 533 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595996C211yesmaximal, characteristic
2C3×#5516C211yesmaximal, characteristic, complemented
3C2×#63833C211yesmaximal, characteristic, complemented
4C22×#3717C211yesmaximal, characteristic, complemented
5C3×#4999C211yesmaximal, characteristic, complemented
6#10591105C211yesmaximal, characteristic, complemented
7#10591096C211yesmaximal, characteristic, complemented
8#10590368C214yesmaximal, complemented
9#10590367C214yesmaximal, complemented
10#82551—31nomaximal
11#79099—31nomaximal
12C2×#3828C2211yescharacteristic
13C22×C4⋊(C3⋊D3)C2211yescharacteristic
14C22×C3×Dic6C2211yescharacteristic
15C32×#117C2211yescharacteristic
16#64104—22no—
17#64091—22no—
18#64084C2212yes—
19#64083C2212yes—
20C3×#926C2211yescharacteristic
21C2×C3×#208C2211yescharacteristic
22C22×C3×C3⋊C8C2211yescharacteristic
23C3×#887—22no—
24C3×#877—22no—
25C3×C4×Dic6C2214yescomplemented
26C2×#3719C2212yescomplemented
27#63833—24no—
28C2×#3717—24no—
29C2×#3717C2214yes—
30C2×#3717C2212yescomplemented
31C3×C4⋊(C3⋊C8)C2214yescomplemented
32#63567C2212yescomplemented
33#63564C2214yes—
34#63564C2212yescomplemented
35C3×#519—31no—
36C2×#942—31no—
37C22×#215—31no—
38C2×#909—31no—
39C22×#204—31no—
40#5525—31no—
41#5525—31no—
42#5525—61no—
43#5516D311yescharacteristic, complemented
44C3×#424—31no—
45#5131—31no—
46#5113—31no—
47#5028—34no—
48#5027—34no—
49#5002—31no—
50#5001—31no—
51#4999D311yescharacteristic, complemented
52#4848—34no—
53#4845—34no—
54C23×C3⋊D3—21no—
55C22×C32×C4C2311yescharacteristic
56C2×#638—21no—
57#3828—22no—
58#3828—22no—
59C2×C4⋊(C3⋊D3)—22no—
60C2×C4⋊(C3⋊D3)—22no—
61C2×C4⋊(C3⋊D3)—21no—
62C2×C4⋊(C3⋊D3)—24no—
63C2×C4⋊(C3⋊D3)C2312yes—
64C2×C4⋊(C3⋊D3)C2311yescharacteristic
65C2×C4×C3⋊D3—21no—
66C2×#634C2311yescharacteristic
67C22×C3×Dic3—21no—
68C2×C3×Dic6—21no—
69C2×C3×Dic6—22no—
70C2×C3×Dic6D414yescomplemented
71C2×C3×Dic6C2312yes—
72C32×C4⋊C4D412yes—
73C32×C22⋊C4D412yes—
74C32×C42C2312yes—
75#3752—24no—
76C3×#217—21no—
77C3×C4⋊Dic3C2312yes—
78C3×Dic3⋊C4—24no—
79C3×C4×Dic3—24no—
80C3×C4×Dic3—21no—
81C3×#208—22no—
82C2×C3×C3⋊C8—22no—
83C2×C3×C3⋊C8C2312yes—
84C2×C3×C3⋊C8C2312yes—
85#3719—24no—
86#3717—28no—
87#3717—24no—
88#3043—91noSylow
89C22×C3×Q8—31no—
90C2×#235—31no—
91C2×#235—31no—
92C2×#235—61no—
93C22×D12—31no—
94C22×D12—31no—
95C22×D12—61no—
96C22×Dic6C2×D311yescharacteristic
97C2×C3×M16—31no—
98C22×C3×C8—31no—
99C3×C4×Q8—34no—
100C3×C4×Q8—62no—
101C3×#117—21no—
102C3×#117—31no—
103C3×#117—62no—
104C3×#117C2×D311yescharacteristic
105C3×#117C2×D311yescharacteristic
106C2×#216—32no—
107#942—64no—
108C2×#215—34no—
109C2×#215—32no—
110C2×#215—64no—
111#926C2×D311yescharacteristic
112C2×#208C2×D311yescharacteristic
113C22×C3⋊C8C2×D311yescharacteristic
114#909—64no—
115C2×Dic12—32no—
116C2×#204—34no—
117C2×#204—32no—
118C2×#204—64no—
119#895—64no—
120#895—62no—
121#895—62no—
122#887—22no—
123#882—64no—
124#882—62no—
125#882—62no—
126#877—22no—
127#875—32no—
128#875—32no—
129#875—62no—
130#874—32no—
131#874—32no—
132#874—62no—
133C4×Dic6C2×D314yescomplemented
134C3×C4⋊C8—34no—
135#821—34no—
136#821—32no—
137#816—32no—
138#810—32no—
139#809—34no—
140#809—32no—
141C4⋊(C3⋊C8)C2×D314yescomplemented
142C23×C32C2×D411yescharacteristic
143C22×C3⋊D3—22no—
144C22×C3⋊D3—21no—
145C22×C3⋊D3—42no—
146C22×C3⋊D3—82no—
147C2×C32×C4C2×D412yes—
148C2×C32×C4C2×D414yes—
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4#4112yes—
151C2×C32×C4C2411yescharacteristic
152#638—42no—
153C2×C3⋊Dic3—21no—
154C4⋊(C3⋊D3)—22no—
155C4⋊(C3⋊D3)—21no—
156C4⋊(C3⋊D3)—22no—
157C4⋊(C3⋊D3)—21no—
158C4⋊(C3⋊D3)—42no—
159C4⋊(C3⋊D3)—84no—
160C4×C3⋊D3—42no—
161#634—21no—
162#634—21no—
163C2×C3×Dic3—24no—
164C2×C3×Dic3—22no—
165C2×C3×Dic3—22no—
166C3×Dic6—24no—
167C3×Dic6—22no—
168C3×Dic6C2×D414yes—
169C3×C3⋊C8—22no—
170C3×C3⋊C8—22no—
171C2×#137—91no—
172C22×SD16—91no—
173#535—91no—
174#519—31no—
175#464—94no—
176#460—94no—
177#424—31no—
178#418—91no—
179#416—91no—
180C23×D3—62no—
181C23×D3—61no—
182C23×D3—61no—
183C2×C3×Q8—34no—
184C2×C3×Q8—32no—
185C2×C3×Q8—61no—
186C2×C3×Q8—62no—
187C22×C3×C4—21no—
188C22×C3×C4—61no—
189C22×C3×C4C22×D311yescharacteristic
190C22×C3×C4C22×D311yescharacteristic
191C2×#67—62no—
192C2×#67—61no—
193C2×#67—61no—
194C22×Dic3—21no—
195#235—62no—
196#235—62no—
197#235—62no—
198#235—62no—
199#235—122no—
200#235—122no—
201C2×D12—31no—
202C2×D12—32no—
203C2×D12—31no—
204C2×D12—32no—
205C2×D12—61no—
206C2×D12—62no—
207C2×D12—62no—
208C2×D12—62no—
209C2×D12—62no—
210C2×D12—62no—
211C2×D12—62no—
212C2×D12—61no—
213C2×D12—61no—
214C2×D12—68no—
215C2×D12—64no—
216C2×D12—64no—
217C2×D12—122no—
218C2×D12—122no—
219C2×C4×D3—62no—
220C2×C4×D3—61no—
221C2×C4×D3—61no—
222C2×Dic6—22no—
223C2×Dic6—21no—
224C2×Dic6—31no—
225C2×Dic6—31no—
226C2×Dic6—61no—
227C2×Dic6D1214yescomplemented
228C2×Dic6C22×D312yes—
229C3×M16—62no—
230C2×C3×C8—32no—
231C2×C3×C8—32no—
232C2×C3×C8—62no—
233C3×C4⋊C4—22no—
234C3×C4⋊C4—32no—
235C3×C4⋊C4—64no—
236C3×C4⋊C4D1212yes—
237C3×C4⋊C4#6712yes—
238C3×C22⋊C4—22no—
239C3×C22⋊C4—61no—
240C3×C22⋊C4D1212yes—
241C3×C22⋊C4#6712yes—
242C3×C42—22no—
243C3×C42—61no—
244C3×C42—64no—
245C3×C42C22×D312yes—
246C3×C42C22×D312yes—
247#217—21no—
248#216—64no—
249#215—68no—
250#215—64no—
251(C2×D3)⋊C4—68no—
252(C2×D3)⋊C4—64no—
253(C2×D3)⋊C4—64no—
254C4⋊Dic3C22×D312yes—
255Dic3⋊C4—24no—
256C4×Dic3—24no—
257C4×Dic3—21no—
258#208—22no—
259C2×C3⋊C8—22no—
260C2×C3⋊C8C22×D312yes—
261C2×C3⋊C8C22×D312yes—
262Dic12—64no—
263#204—68no—
264#204—64no—
265C22×C32—22no—
266C22×C32#12112yes—
267C22×C32C22×D411yescharacteristic
268C2×C3⋊D3—41no—
269C2×C3⋊D3—42no—
270C2×C3⋊D3—42no—
271C2×C3⋊D3—44no—
272C2×C3⋊D3—84no—
273C32×C4—24no—
274C32×C4#12112yes—
275C32×C4C22×D411yescharacteristic
276C32×C4C2×#4111yescharacteristic
277C3⋊Dic3—41no—
278C3×Dic3—24no—
279C3×Dic3—42no—
280C2×#41—91no—
281C22×Q8—31no—
282C22×D4—91no—
283#137—184no—
284C2×Q16—92no—
285C2×SD16—94no—
286C2×SD16—92no—
287C2×SD16—184no—
288C2×M16—31no—
289C22×C8—31no—
290#127—92no—
291#124—92no—
292#121—182no—
293#120—182no—
294C4×Q8—34no—
295C4×Q8—62no—
296#117—31no—
297#117—62no—
298#117D3211yescharacteristic
299C4⋊C8—34no—
300#103—92no—
301#102—92no—
302#102—94no—
303C23×C3—21no—
304C23×C3C2×D1211yescharacteristic
305C23×C3C2×#6711yescharacteristic
306C22×D3—64no—
307C22×D3—62no—
308C22×D3—62no—
309C22×D3—61no—
310C22×D3—62no—
311C22×D3—61no—
312C22×D3—124no—
313C22×D3—122no—
314C22×D3—122no—
315C22×D3—242no—
316C22×D3—242no—
317C22×D3—244no—
318C3×Q8—34no—
319C3×Q8—64no—
320C3×Q8—62no—
321C2×C3×C4—21no—
322C2×C3×C4—22no—
323C2×C3×C4—22no—
324C2×C3×C4—21no—
325C2×C3×C4—24no—
326C2×C3×C4—64no—
327C2×C3×C4—62no—
328C2×C3×C4—62no—
329C2×C3×C4C2×D1212yes—
330C2×C3×C4C2×D1214yes—
331C2×C3×C4C2×D1211yescharacteristic
332C2×C3×C4#23512yes—
333C2×C3×C4D3×D412yes—
334C2×C3×C4#23912yes—
335C2×C3×C4C2×#6714yes—
336C2×C3×C4C2×#6711yescharacteristic
337C2×C3×C4C23×D311yescharacteristic
338C2×C3×C4C23×D311yescharacteristic
339#67—124no—
340#67—122no—
341#67—122no—
342C2×Dic3—24no—
343C2×Dic3—22no—
344C2×Dic3—22no—
345C2×Dic3—62no—
346C2×Dic3—61no—
347C2×Dic3—61no—
348D12—62no—
349D12—61no—
350D12—62no—
351D12—61no—
352D12—62no—
353D12—61no—
354D12—62no—
355D12—61no—
356D12—122no—
357D12—122no—
358D12—121no—
359D12—121no—
360D12—124no—
361D12—122no—
362D12—122no—
363D12—244no—
364D12—244no—
365D12—248no—
366C4×D3—124no—
367C4×D3—122no—
368C4×D3—122no—
369Dic6—24no—
370Dic6—22no—
371Dic6—61no—
372Dic6—61no—
373Dic6—61no—
374Dic6—61no—
375Dic6—121no—
376Dic6—121no—
377Dic6C2×D1214yes—
378C3×C8—62no—
379C3×C8—62no—
380C3⋊C8—22no—
381C3⋊C8—22no—
382C2×C32—22no—
383C2×C32C2×#12111yescharacteristic
384C2×C32#57712yes—
385C3⋊D3—81no—
386C3⋊D3—82no—
387C24—181no—
388#41—182no—
389#41—182no—
390C2×Q8—32no—
391C2×Q8—34no—
392C2×Q8—62no—
393C2×Q8—61no—
394C2×Q8—91no—
395C2×D4—92no—
396C2×D4—91no—
397C2×D4—181no—
398C2×D4—182no—
399C2×D4—182no—
400C2×D4—181no—
401C2×D4—184no—
402C22×C4—61no—
403C22×C4—181no—
404C22×C4C2×D3211yescharacteristic
405Q16—184no—
406SD16—188no—
407SD16—184no—
408M16—62no—
409C2×C8—32no—
410C2×C8—32no—
411C2×C8—62no—
412C4⋊C4—32no—
413C4⋊C4—64no—
414C4⋊C4#62612yes—
415C22⋊C4—61no—
416C22⋊C4—184no—
417C22⋊C4#62612yes—
418C42—61no—
419C42—64no—
420C42C2×D3212yes—
421C22×C3—22no—
422C22×C3—22no—
423C22×C3—21no—
424C22×C3—22no—
425C22×C3—42no—
426C22×C3#89512yes—
427C22×C3#93012yes—
428C22×C3C22×D1211yescharacteristic
429C22×C3C22×#6711yescharacteristic
430C2×D3—122no—
431C2×D3—124no—
432C2×D3—124no—
433C2×D3—128no—
434C2×D3—122no—
435C2×D3—124no—
436C2×D3—121no—
437C2×D3—122no—
438C2×D3—121no—
439C2×D3—122no—
440C2×D3—122no—
441C2×D3—124no—
442C2×D3—244no—
443C2×D3—244no—
444C2×D3—248no—
445C3×C4—24no—
446C3×C4—24no—
447C3×C4—21no—
448C3×C4—21no—
449C3×C4—22no—
450C3×C4—44no—
451C3×C4—64no—
452C3×C4—122no—
453C3×C4#89512yes—
454C3×C4#93012yes—
455C3×C4C22×D1211yescharacteristic
456C3×C4C2×#23511yescharacteristic
457C3×C4C2×D3×D411yescharacteristic
458C3×C4C2×#23911yescharacteristic
459Dic3—24no—
460Dic3—42no—
461Dic3—122no—
462Dic3—121no—
463Dic3—121no—
464C32#304311yescharacteristic, complemented, Sylow
465C23—182no—
466C23—181no—
467C23—362no—
468C23—722no—
469C23C2×#62611yescharacteristic
470Q8—34no—
471Q8—62no—
472Q8—64no—
473Q8—181no—
474Q8—181no—
475D4—182no—
476D4—181no—
477D4—182no—
478D4—181no—
479D4—362no—
480D4—362no—
481D4—724no—
482C2×C4—62no—
483C2×C4—64no—
484C2×C4—62no—
485C2×C4—181no—
486C2×C4—362no—
487C2×C4#379912yes—
488C2×C4D3×D1212yes—
489C2×C4C2×#62614yes—
490C2×C4C2×#62611yescharacteristic
491C2×C4C22×D3211yescharacteristic
492C8—62no—
493C8—62no—
494C2×C3—22no—
495C2×C3—22no—
496C2×C3—22no—
497C2×C3—21no—
498C2×C3—42no—
499C2×C3C2×#89511yescharacteristic
500C2×C3#575112yes—
501C2×C3C2×#93011yescharacteristic
502C2×C3#583712yes—
503D3—244no—
504D3—242no—
505D3—242no—
506D3—241no—
507D3—242no—
508D3—241no—
509C22—22no—
510C22—362no—
511C22—364no—
512C22—361no—
513C22—362no—
514C22—724no—
515C22#6390912yes—
516C22C22×#62611yescharacteristic
517C4—24no—
518C4—64no—
519C4—122no—
520C4—361no—
521C4#6390912yes—
522C4C2×#379911yescharacteristic
523C4C2×D3×D1211yescharacteristic
524C3—21no—
525C3#7909911yescharacteristic, complemented
526C3#8255111yescharacteristic, complemented
527C2—22no—
528C2—722no—
529C2—721no—
530C2C2×#6390911yescharacteristic
531C2#1059544812yes—
subgroupG/H
centerC22C22×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radical#10595996C2
hypercenter#117D32
hypocenterC32#3043
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
2. C3×#5516C2semidirect
3. C2×#63833C2semidirect
4. C22×#3717C2semidirect
5. C3×#4999C2semidirect
6. #10591105C2semidirect
7. #10591096C2semidirect
8. #10590368C2semidirect
9. #10590367C2semidirect
25. C3×C4×Dic6C22semidirect
26. C2×#3719C22semidirect
30. C2×#3717C22semidirect
31. C3×C4⋊(C3⋊C8)C22semidirect
32. #63567C22semidirect
34. #63564C22semidirect
43. #5516D3semidirect
51. #4999D3semidirect
70. C2×C3×Dic6D4semidirect
133. C4×Dic6C2×D3semidirect
141. C4⋊(C3⋊C8)C2×D3semidirect
227. C2×Dic6D12semidirect
464. C32#3043semidirect
525. C3#79099semidirect
526. C3#82551semidirect

Maximal subgroups

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

subgroupindex
#105959962
C3×#55162
C2×#638332
C22×#37172
C3×#49992
#105911052
#105910962
#105903682
#105903672
#825513
#790993