Finite Group Databasebeta

← #11864449

Subgroups — #11864449

Order 1152.

1539 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64298C211yesmaximal, characteristic, complemented
2C3×#5525C211yesmaximal, characteristic, complemented
3C22×#3716C211yesmaximal, characteristic, complemented
4C2×#63823C211yesmaximal, characteristic, complemented
5#10592703C211yesmaximal, characteristic, complemented
6C3×#5002C211yesmaximal, characteristic, complemented
7#10591070C211yesmaximal, characteristic, complemented
8#10590613C214yesmaximal, complemented
9#10590603C214yesmaximal, complemented
10#83390—31nomaximal
11#78836—31nomaximal
12C22×#634C2211yescharacteristic
13C2×C3×#235C2211yescharacteristic
14C2×C3×#235C2211yescharacteristic
15C22×C3×D12C2211yescharacteristic
16C2×#3805—22no—
17#64298—24no—
18#64298—24no—
19C2×#3795—21no—
20C2×#3795C2212yescomplemented
21C2×D3×Dic6—21no—
22C2×D3×Dic6C2212yescomplemented
23C32×#117C2211yescharacteristic
24C2×#3748C2211yescharacteristic
25C22×C3×C3⋊C8C2211yescharacteristic
26C3×#895C2214yes—
27C3×#882—22no—
28C3×#875—21no—
29C3×#874—21no—
30C2×#3716—24no—
31C2×#3716C2214yes—
32C2×#3715C2212yes—
33#63823—24no—
34C2×#3713C2212yes—
35#63637C2214yescomplemented
36C3×#810C2212yescomplemented
37C3×#809C2212yescomplemented
38(C2×D3)⋊(C3⋊C8)C2214yescomplemented
39C2×#1010—31no—
40C2×#1010—31no—
41C3×#535—31no—
42C2×#949—31no—
43C22×#214—31no—
44C2×#932—31no—
45C22×#204—31no—
46#5525D311yescharacteristic, complemented
47C3×#416—31no—
48#5234—31no—
49#5110—31no—
50#5040—34no—
51#5037—34no—
52#5004—31no—
53#5004—31no—
54#5004—61no—
55#5002D311yescharacteristic, complemented
56#4806—34no—
57#4781—34no—
58C23×C3×D3—21no—
59C22×C32×C4C2311yescharacteristic
60C22×C3⋊Dic3—21no—
61C2×#634—21no—
62C2×#634—22no—
63C2×#634D414yescomplemented
64C2×#634C2312yes—
65C2×C3×#67—21no—
66C2×C3×#67D412yes—
67C3×#235—22no—
68C3×#235—22no—
69C3×#235—22no—
70C3×#235D414yescomplemented
71C2×C3×D12—22no—
72C2×C3×D12—22no—
73C2×C3×D12—21no—
74C2×C3×D12—24no—
75C2×C3×D12D411yescharacteristic
76C2×C3×D12C2312yes—
77C2×C3×D12C2311yescharacteristic
78C2×C3×C4×D3—21no—
79C2×C3×C4×D3C2312yes—
80C2×C3×Dic6D411yescharacteristic
81C2×C3×Dic6C2311yescharacteristic
82C2×#627—22no—
83C2×#625—22no—
84#3805—216no—
85C2×D3×Dic3—22no—
86C2×D3×Dic3—22no—
87#3795—28no—
88#3795—24no—
89#3795—24no—
90D3×Dic6—28no—
91D3×Dic6—24no—
92D3×Dic6—24no—
93C32×C4⋊C4C2312yes—
94C32×C22⋊C4—21no—
95C32×C42—21no—
96#3748—22no—
97C2×C3⋊(C3⋊C8)C2312yes—
98C3×(C2×D3)⋊C4—24no—
99C2×C3×C3⋊C8—22no—
100C2×C3×C3⋊C8C2312yes—
101#3716—28no—
102#3715—24no—
103#3713—24no—
104#3010—91noSylow
105C2×C3×#41—31no—
106C2×C3×#41—31no—
107C22×C3×D4—31no—
108#1010—64no—
109#1010—64no—
110#1010—64no—
111#1010—64no—
112C2×D3×Q8—32no—
113C2×D3×Q8—61no—
114C2×#237—32no—
115C2×#237—61no—
116C2×#237—62no—
117C2×#237—62no—
118C2×#235—32no—
119C2×#235—61no—
120C2×#235C2×D311yescharacteristic
121C2×#235C2×D311yescharacteristic
122C22×D12C2×D311yescharacteristic
123C22×Dic6—31no—
124C22×Dic6—31no—
125C22×Dic6—32no—
126C22×Dic6—61no—
127C22×Dic6—61no—
128C22×C3×C8—31no—
129C3×#127—61no—
130C3×#124—61no—
131C3×#121—34no—
132C3×#120—62no—
133C3×#117—21no—
134C3×#117C2×D311yescharacteristic
135C3×#117C2×D311yescharacteristic
136#949—64no—
137C2×#215—32no—
138C2×#214—32no—
139C2×#214—34no—
140C2×#214—64no—
141#932—64no—
142C2×#213—32no—
143C2×#213—32no—
144C2×#208—31no—
145C2×#208—31no—
146C2×#208—61no—
147C22×C3⋊C8C2×D311yescharacteristic
148C2×#204—34no—
149C2×#204—64no—
150#895C2×D314yes—
151#882—22no—
152#875—21no—
153#874—21no—
154C3×#103—32no—
155C3×#102—32no—
156#830—34no—
157(C2×D3)⋊C8—34no—
158#810—34no—
159#810—34no—
160#810—64no—
161#810C2×D312yescomplemented
162#809C2×D312yescomplemented
163C23×C32C2×D411yescharacteristic
164C22×C3×D3—21no—
165C22×C3×D3—22no—
166C22×C3×D3—42no—
167C22×C3×D3—82no—
168C22×C3×D3C2×D412yes—
169C2×C32×C4—22no—
170C2×C32×C4C2×D412yes—
171C2×C32×C4C2×D412yes—
172C2×C32×C4C2×D411yescharacteristic
173C2×C32×C4C2411yescharacteristic
174C2×C3⋊Dic3—24no—
175C2×C3⋊Dic3—22no—
176#634—24no—
177#634—22no—
178#634C2×D414yes—
179C3×#67—24no—
180C3×#67—24no—
181C2×C3×Dic3—21no—
182C2×C3×Dic3C2×D412yes—
183C3×D12—22no—
184C3×D12—21no—
185C3×D12—22no—
186C3×D12—22no—
187C3×D12—42no—
188C3×D12—84no—
189C3×D12C2×D412yes—
190C3×C4×D3—24no—
191C3×C4×D3—22no—
192C3×C4×D3—22no—
193C3×Dic6—22no—
194C3×Dic6—21no—
195C3×Dic6C2×D412yes—
196#627—28no—
197#625—28no—
198D3×Dic3—28no—
199D3×Dic3—28no—
200C3⋊(C3⋊C8)—22no—
201C3×C3⋊C8—22no—
202C2×2−1+4—91no—
203C2×AGL(1,ℤ/8)—91no—
204C22×SD16—91no—
205#535—31no—
206#449—94no—
207#448—94no—
208#419—91no—
209#416—31no—
210#408—91no—
211C24×C3—61no—
212C23×D3—21no—
213C3×#41—34no—
214C3×#41—62no—
215C3×#41—62no—
216C3×#41—62no—
217C2×C3×Q8—31no—
218C2×C3×Q8—31no—
219C2×C3×D4—32no—
220C2×C3×D4—31no—
221C2×C3×D4—31no—
222C2×C3×D4—32no—
223C2×C3×D4—64no—
224C2×C3×D4—61no—
225C2×C3×D4—62no—
226C2×C3×D4—62no—
227C2×C3×D4—61no—
228C22×C3×C4—21no—
229C22×C3×C4—32no—
230C22×C3×C4—61no—
231C22×C3×C4C22×D311yescharacteristic
232C22×C3×C4C22×D311yescharacteristic
233C2×#67—21no—
234C2×#67—62no—
235C2×#67—62no—
236C2×#67#6712yes—
237C22×Dic3—62no—
238C22×Dic3—61no—
239C22×Dic3—61no—
240C22×Dic3—62no—
241C22×Dic3—121no—
242D3×Q8—64no—
243D3×Q8—64no—
244D3×Q8—68no—
245#237—64no—
246#237—64no—
247#237—68no—
248#237—616no—
249#237—616no—
250#235—22no—
251#235—22no—
252#235—22no—
253#235—64no—
254#235—68no—
255#235—64no—
256#235D1214yescomplemented
257C2×D12—22no—
258C2×D12—22no—
259C2×D12—21no—
260C2×D12—24no—
261C2×D12#6711yescharacteristic
262C2×D12C22×D312yes—
263C2×D12C22×D311yescharacteristic
264C2×C4×D3—21no—
265C2×C4×D3—62no—
266C2×C4×D3—62no—
267C2×C4×D3C22×D312yes—
268C2×Dic6—34no—
269C2×Dic6—34no—
270C2×Dic6—32no—
271C2×Dic6—32no—
272C2×Dic6—62no—
273C2×Dic6—64no—
274C2×Dic6—64no—
275C2×Dic6—68no—
276C2×Dic6—62no—
277C2×Dic6—62no—
278C2×Dic6—61no—
279C2×Dic6—62no—
280C2×Dic6—61no—
281C2×Dic6—62no—
282C2×Dic6—64no—
283C2×Dic6—122no—
284C2×Dic6—121no—
285C2×Dic6#6711yescharacteristic
286C2×Dic6C22×D311yescharacteristic
287C2×C3×C8—32no—
288C2×C3×C8—62no—
289C3×C4⋊C4—22no—
290C3×C4⋊C4C22×D312yes—
291C3×C4⋊C4C22×D312yes—
292C3×C22⋊C4—21no—
293C3×C22⋊C4—21no—
294C3×C22⋊C4—41no—
295C3×C22⋊C4—64no—
296C3×C42—21no—
297C3×C42—21no—
298C3×C42—41no—
299#215—64no—
300#214—68no—
301#214—64no—
302#213—64no—
303#213—64no—
304(C2×D3)⋊C4—24no—
305#208—62no—
306#208—62no—
307#208—122no—
308C2×C3⋊C8—22no—
309C2×C3⋊C8—32no—
310C2×C3⋊C8—32no—
311C2×C3⋊C8—62no—
312C2×C3⋊C8C22×D312yes—
313#204—68no—
314C22×C32—22no—
315C22×C32#12012yes—
316C22×C32C22×D411yescharacteristic
317C2×C3×D3—22no—
318C2×C3×D3—22no—
319C2×C3×D3—24no—
320C2×C3×D3—42no—
321C2×C3×D3—42no—
322C2×C3×D3—44no—
323C2×C3×D3—84no—
324C32×C4—42no—
325C32×C4#12012yes—
326C32×C4C22×D411yescharacteristic
327C32×C4C22×D411yescharacteristic
328C3⋊Dic3—24no—
329C3×Dic3—22no—
330C3×Dic3—22no—
3312−1+4—184no—
3322−1+4—184no—
333C2×#41—31no—
334C2×#41—31no—
335C2×#41—92no—
336C2×#41—181no—
337C2×#41—182no—
338C22×Q8—92no—
339C22×Q8—91no—
340C22×Q8—181no—
341C22×D4—31no—
342AGL(1,ℤ/8)—184no—
343C2×SD16—94no—
344C2×SD16—92no—
345C2×SD16—184no—
346C2×D8—92no—
347C2×M16—91no—
348C22×C8—31no—
349#127—61no—
350#124—61no—
351#121—34no—
352#120—62no—
353#117D3211yescharacteristic
354#103—32no—
355#103—94no—
356#102—32no—
357C22⋊C8—94no—
358C23×C3—21no—
359C23×C3—32no—
360C23×C3—61no—
361C23×C3—62no—
362C23×C3—122no—
363C23×C3—242no—
364C23×C3D3×D411yescharacteristic
365C23×C3C2×#6711yescharacteristic
366C22×D3—21no—
367C22×D3—22no—
368C22×D3—42no—
369C22×D3—82no—
370C22×D3C2×#6712yes—
371C3×Q8—32no—
372C3×Q8—62no—
373C3×Q8—61no—
374C3×D4—32no—
375C3×D4—64no—
376C3×D4—64no—
377C3×D4—62no—
378C3×D4—62no—
379C3×D4—61no—
380C3×D4—62no—
381C3×D4—122no—
382C3×D4—244no—
383C2×C3×C4—22no—
384C2×C3×C4—22no—
385C2×C3×C4—21no—
386C2×C3×C4—22no—
387C2×C3×C4—22no—
388C2×C3×C4—21no—
389C2×C3×C4—32no—
390C2×C3×C4—42no—
391C2×C3×C4—61no—
392C2×C3×C4—64no—
393C2×C3×C4—62no—
394C2×C3×C4—62no—
395C2×C3×C4C2×D1212yes—
396C2×C3×C4D3×D412yes—
397C2×C3×C4D3×D412yes—
398C2×C3×C4D3×D412yes—
399C2×C3×C4D3×D411yescharacteristic
400C2×C3×C4C2×#6711yescharacteristic
401C2×C3×C4C23×D311yescharacteristic
402C2×C3×C4C23×D311yescharacteristic
403#67—24no—
404#67—24no—
405#67—68no—
406#67—68no—
407C2×Dic3—21no—
408C2×Dic3—68no—
409C2×Dic3—68no—
410C2×Dic3—64no—
411C2×Dic3—64no—
412C2×Dic3—62no—
413C2×Dic3—62no—
414C2×Dic3—122no—
415C2×Dic3—124no—
416C2×Dic3C2×#6712yes—
417D12—22no—
418D12—21no—
419D12—22no—
420D12—22no—
421D12—42no—
422D12—84no—
423D12C2×D1212yes—
424C4×D3—24no—
425C4×D3—22no—
426C4×D3—22no—
427C4×D3—68no—
428C4×D3—68no—
429Dic6—22no—
430Dic6—21no—
431Dic6—34no—
432Dic6—34no—
433Dic6—64no—
434Dic6—68no—
435Dic6—68no—
436Dic6—64no—
437Dic6—64no—
438Dic6—62no—
439Dic6—62no—
440Dic6—122no—
441Dic6—124no—
442Dic6C2×D1212yes—
443C3×C8—62no—
444C3⋊C8—22no—
445C3⋊C8—62no—
446C3⋊C8—62no—
447C3⋊C8—122no—
448C2×C32—22no—
449C2×C32C2×#12011yescharacteristic
450C2×C32#57712yes—
451C3×D3—42no—
452C3×D3—42no—
453C3×D3—82no—
454C24—61no—
455#41—34no—
456#41—62no—
457#41—62no—
458#41—62no—
459#41—184no—
460#41—184no—
461#41—188no—
462#41—1816no—
463C2×Q8—31no—
464C2×Q8—31no—
465C2×Q8—92no—
466C2×Q8—94no—
467C2×Q8—182no—
468C2×Q8—184no—
469C2×Q8—184no—
470C2×Q8—188no—
471C2×Q8—182no—
472C2×Q8—181no—
473C2×D4—32no—
474C2×D4—31no—
475C2×D4—32no—
476C2×D4—31no—
477C2×D4—64no—
478C2×D4—61no—
479C2×D4—62no—
480C2×D4—62no—
481C2×D4—61no—
482C2×D4—182no—
483C22×C4—32no—
484C22×C4—61no—
485C22×C4—182no—
486C22×C4—182no—
487C22×C4—181no—
488C22×C4C2×D3211yescharacteristic
489SD16—188no—
490SD16—184no—
491D8—184no—
492M16—182no—
493C2×C8—32no—
494C2×C8—62no—
495C2×C8—92no—
496C4⋊C4C2×D3212yes—
497C22⋊C4—21no—
498C22⋊C4—64no—
499C42—21no—
500C22×C3—22no—
501C22×C3—22no—
502C22×C3—21no—
503C22×C3—22no—
504C22×C3—42no—
505C22×C3—62no—
506C22×C3—64no—
507C22×C3—62no—
508C22×C3—122no—
509C22×C3—122no—
510C22×C3—124no—
511C22×C3—244no—
512C22×C3#88212yes—
513C22×C3#93712yes—
514C22×C3C2×D3×D411yescharacteristic
515C22×C3C22×#6711yescharacteristic
516C2×D3—22no—
517C2×D3—22no—
518C2×D3—24no—
519C2×D3—42no—
520C2×D3—42no—
521C2×D3—44no—
522C2×D3—84no—
523C3×C4—21no—
524C3×C4—21no—
525C3×C4—22no—
526C3×C4—42no—
527C3×C4—42no—
528C3×C4—62no—
529C3×C4—62no—
530C3×C4—82no—
531C3×C4#88212yes—
532C3×C4#93712yes—
533C3×C4C22×D1211yescharacteristic
534C3×C4C2×D3×D411yescharacteristic
535C3×C4C2×D3×D411yescharacteristic
536C3×C4C2×D3×D411yescharacteristic
537Dic3—22no—
538Dic3—22no—
539Dic3—64no—
540Dic3—64no—
541Dic3—124no—
542C32#301011yescharacteristic, complemented, Sylow
543C23—32no—
544C23—61no—
545C23—62no—
546C23—122no—
547C23—242no—
548C23D3×#6711yescharacteristic
549Q8—32no—
550Q8—61no—
551Q8—62no—
552Q8—94no—
553Q8—188no—
554Q8—182no—
555Q8—184no—
556D4—32no—
557D4—64no—
558D4—64no—
559D4—62no—
560D4—61no—
561D4—62no—
562D4—62no—
563D4—122no—
564D4—188no—
565D4—244no—
566C2×C4—22no—
567C2×C4—32no—
568C2×C4—61no—
569C2×C4—62no—
570C2×C4—62no—
571C2×C4—64no—
572C2×C4—188no—
573C2×C4—188no—
574C2×C4—182no—
575C2×C4—184no—
576C2×C4D3×D1212yes—
577C2×C4#380212yes—
578C2×C4D3×#6711yescharacteristic
579C2×C4C22×D3211yescharacteristic
580C8—62no—
581C8—182no—
582C2×C3—22no—
583C2×C3—22no—
584C2×C3—22no—
585C2×C3—21no—
586C2×C3—42no—
587C2×C3—122no—
588C2×C3—122no—
589C2×C3—242no—
590C2×C3C2×#88211yescharacteristic
591C2×C3#577012yes—
592C2×C3C2×#93711yescharacteristic
593C2×C3#583612yes—
594D3—42no—
595D3—42no—
596D3—82no—
597C22—22no—
598C22—64no—
599C22—62no—
600C22—62no—
601C22—122no—
602C22—124no—
603C22—122no—
604C22—244no—
605C22#6392212yes—
606C22C2×D3×#6711yescharacteristic
607C4—42no—
608C4—62no—
609C4—62no—
610C4—184no—
611C4#6392212yes—
612C4C2×D3×D1211yescharacteristic
613C4C2×#380211yescharacteristic
614C3—21no—
615C3#7883611yescharacteristic, complemented
616C3#8339011yescharacteristic, complemented
617C2—22no—
618C2—122no—
619C2—122no—
620C2—242no—
621C2C2×#6392211yescharacteristic
622C2#1059546612yes—
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
hypercenter#117D32
hypocenterC32#3010
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. C2×#64298C2semidirect
2. C3×#5525C2semidirect
3. C22×#3716C2semidirect
4. C2×#63823C2semidirect
5. #10592703C2semidirect
6. C3×#5002C2semidirect
7. #10591070C2semidirect
8. #10590613C2semidirect
9. #10590603C2semidirect
20. C2×#3795C22semidirect
22. C2×D3×Dic6C22semidirect
35. #63637C22semidirect
36. C3×#810C22semidirect
37. C3×#809C22semidirect
38. (C2×D3)⋊(C3⋊C8)C22semidirect
46. #5525D3semidirect
55. #5002D3semidirect
63. C2×#634D4semidirect
70. C3×#235D4semidirect
161. #810C2×D3semidirect
162. #809C2×D3semidirect
256. #235D12semidirect
542. C32#3010semidirect
615. C3#78836semidirect
616. C3#83390semidirect

Maximal subgroups

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

subgroupindex
C2×#642982
C3×#55252
C22×#37162
C2×#638232
#105927032
C3×#50022
#105910702
#105906132
#105906032
#833903
#788363