Finite Group Databasebeta

← #11864174

Subgroups — #11864174

Order 1152.

2262 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×C3⋊D3C211yesmaximal, characteristic
2C2×C32×#137C211yesmaximal, characteristic, complemented
3C2×#64155C211yesmaximal, characteristic, complemented
4C2×#64151C211yesmaximal, characteristic, complemented
5#10592931C211yesmaximal, characteristic, complemented
6#10592886C212yesmaximal, complemented
7#10592885C212yesmaximal, complemented
8#10592872C212yesmaximal, complemented
9#10592868C212yesmaximal, complemented
10#10592832C211yesmaximal, characteristic, complemented
11#10592825C211yesmaximal, characteristic, complemented
12#83981—34nomaximal
13C2×C32×#41C2211yescharacteristic
14C22×C32×Q8C2211yescharacteristic, complemented
15#41×C3⋊D3—24no—
16#41×C3⋊D3—24no—
17C2×#3832C2211yescharacteristic
18C2×Q8×C3⋊D3C2211yescharacteristic
19C2×#3830—21no—
20C2×#3830C2211yescharacteristic
21C2×D4×C3⋊D3—21no—
22C2×D4×C3⋊D3C2211yescharacteristic
23C2×#3828—21no—
24C2×#3828C2211yescharacteristic
25C22×C4×C3⋊D3—21no—
26C22×C4×C3⋊D3C2211yescharacteristic
27C32×#137—24no—
28C2×C32×Q16C2212yescomplemented
29C2×C32×SD16C2212yescomplemented
30C2×C32×M16C2211yescharacteristic, complemented
31#64155—21no—
32#64155—21no—
33#64155C2212yes—
34#64155C2212yescomplemented
35C2×#3756C2212yescomplemented
36#64151—24no—
37C2×#3755C2212yescomplemented
38C2×#3752—21no—
39C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
40C2×#3750—21no—
41C2×#3748C2211yescharacteristic, complemented
42#63662C2212yescomplemented
43#63659C2212yescomplemented
44#63648C2212yescomplemented
45#63647C2212yes—
46#63647C2212yescomplemented
47#63643C2212yescomplemented
48C2×D3×#41—34no—
49C2×C3×#137D314yescomplemented
50C2×#946—34no—
51C2×#942—34no—
52#5232—34no—
53#5187—38no—
54#5186—38no—
55#5173—38no—
56#5169—38no—
57#5133—34no—
58#5126—34no—
59C23×C3⋊D3—21no—
60C23×C3⋊D3D411yescharacteristic
61C32×#41—22no—
62C32×#41D414yes—
63C2×C32×Q8—21no—
64C2×C32×Q8—22no—
65C2×C32×Q8—22no—
66C2×C32×Q8C2312yes—
67C2×C32×Q8C2311yescharacteristic
68C2×C32×D4—21no—
69C2×C32×D4C2311yescharacteristic
70C22×C32×C4—21no—
71C22×C32×C4—21no—
72C22×C32×C4C2311yescharacteristic
73C2×#638—21no—
74C2×#638—21no—
75C2×#638—21no—
76C22×C3⋊Dic3—21no—
77C22×C3⋊Dic3—21no—
78C22×C3⋊Dic3D411yescharacteristic
79#3832—22no—
80#3832—22no—
81Q8×C3⋊D3—22no—
82Q8×C3⋊D3—22no—
83#3830—28no—
84#3830—22no—
85#3830—22no—
86D4×C3⋊D3—28no—
87D4×C3⋊D3—22no—
88D4×C3⋊D3—22no—
89#3828—28no—
90#3828—22no—
91#3828D414yes—
92C2×C4⋊(C3⋊D3)—21no—
93C2×C4⋊(C3⋊D3)C2311yescharacteristic
94C2×C4×C3⋊D3—28no—
95C2×C4×C3⋊D3—21no—
96C2×C4×C3⋊D3—21no—
97C2×C4×C3⋊D3—22no—
98C2×C4×C3⋊D3—22no—
99C2×C4×C3⋊D3—21no—
100C2×C4×C3⋊D3D411yescharacteristic
101C2×C4×C3⋊D3D411yescharacteristic
102C2×C4×C3⋊D3C2311yescharacteristic
103C2×C4×C3⋊D3C2311yescharacteristic
104C2×#634—21no—
105C2×#634C2311yescharacteristic
106C32×Q16—24no—
107C32×SD16—24no—
108C32×M16—22no—
109C2×C32×C8C2312yes—
110#3756—24no—
111#3755—24no—
112#3752—22no—
113#3752—22no—
114C4⋊(C3⋊Dic3)—21no—
115C4⋊(C3⋊Dic3)C2312yes—
116#3750—22no—
117#3750—22no—
118#3748—22no—
119C2×C3⋊(C3⋊C8)C2312yes—
120#3007—91noSylow
121C2×C3×#41C2×D314yes—
122C22×C3×Q8C2×D314yescomplemented
123D3×#41—616no—
124D3×#41—616no—
125C2×#239—34no—
126C2×D3×Q8—34no—
127C2×#237—34no—
128C2×#237—64no—
129C2×D3×D4—34no—
130C2×D3×D4—64no—
131C2×#235—34no—
132C2×#235—64no—
133C22×C4×D3—34no—
134C22×C4×D3—64no—
135C3×#137—216no—
136C2×C3×Q16C2×D318yescomplemented
137C2×C3×SD16C2×D318yescomplemented
138C2×C3×M16C2×D314yescomplemented
139#946—38no—
140#946—38no—
141#946—64no—
142#946—64no—
143C2×#216—38no—
144#942—616no—
145C2×#215—38no—
146C2×(C2×D3)⋊C4—64no—
147C2×C4⋊Dic3—34no—
148C2×Dic3⋊C4—64no—
149C2×#208—34no—
150#835—38no—
151#832—38no—
152#821—38no—
153(C2×D3)⋊C8—38no—
154(C2×D3)⋊C8—38no—
155#816—38no—
156C23×C32—21no—
157C23×C32C2×D411yescharacteristic
158C22×C3⋊D3—24no—
159C22×C3⋊D3—22no—
160C22×C3⋊D3—21no—
161C22×C3⋊D3—22no—
162C22×C3⋊D3—41no—
163C22×C3⋊D3—42no—
164C22×C3⋊D3—42no—
165C22×C3⋊D3C2×D411yescharacteristic
166C22×C3⋊D3C2×D411yescharacteristic
167C32×Q8—21no—
168C32×Q8—22no—
169C32×Q8—22no—
170C32×Q8—42no—
171C32×Q8C2×D412yes—
172C32×D4—24no—
173C32×D4—21no—
174C32×D4C2×D412yes—
175C2×C32×C4—21no—
176C2×C32×C4—24no—
177C2×C32×C4—22no—
178C2×C32×C4—42no—
179C2×C32×C4C2×D411yescharacteristic
180C2×C32×C4C2×D412yes—
181C2×C32×C4C2×D412yes—
182C2×C32×C4C2411yescharacteristic
183#638—24no—
184#638—24no—
185#638—24no—
186C2×C3⋊Dic3—24no—
187C2×C3⋊Dic3—22no—
188C2×C3⋊Dic3—21no—
189C2×C3⋊Dic3—22no—
190C2×C3⋊Dic3—42no—
191C2×C3⋊Dic3C2×D411yescharacteristic
192C2×C3⋊Dic3C2×D411yescharacteristic
193C4⋊(C3⋊D3)—24no—
194C4⋊(C3⋊D3)—21no—
195C4⋊(C3⋊D3)C2×D412yes—
196C4×C3⋊D3—24no—
197C4×C3⋊D3—24no—
198C4×C3⋊D3—22no—
199C4×C3⋊D3—24no—
200C4×C3⋊D3—22no—
201C4×C3⋊D3—21no—
202C4×C3⋊D3—21no—
203C4×C3⋊D3—21no—
204C4×C3⋊D3—21no—
205#634—24no—
206#634—21no—
207#634C2×D412yes—
208C32×C8—22no—
209C3⋊(C3⋊C8)—22no—
210C22×#41—91no—
211C2×#137—91no—
212C2×#137C3⋊D311yescharacteristic, complemented
213C2×C22⋊Q8—91no—
214#452—92no—
215#452—92no—
216#451—92no—
217#450—92no—
218#417—91no—
219#417—91no—
220#407—91no—
221C23×D3—34no—
222C23×D3—64no—
223C3×#41—28no—
224C3×#41#67116yes—
225C2×C3×Q8—24no—
226C2×C3×Q8—28no—
227C2×C3×Q8—28no—
228C2×C3×Q8C22×D318yes—
229C2×C3×Q8C22×D314yes—
230C2×C3×D4—24no—
231C2×C3×D4C22×D314yes—
232C22×C3×C4—24no—
233C22×C3×C4—24no—
234C22×C3×C4C22×D314yes—
235C2×#67—64no—
236C2×#67—64no—
237C2×#67—64no—
238C22×Dic3—34no—
239C22×Dic3—64no—
240C22×Dic3—64no—
241#239—68no—
242#239—68no—
243D3×Q8—68no—
244D3×Q8—68no—
245#237—68no—
246#237—632no—
247#237—68no—
248D3×D4—68no—
249D3×D4—632no—
250D3×D4—68no—
251#235—316no—
252#235—632no—
253#235—68no—
254C2×D12—34no—
255C2×D12—64no—
256C2×C4×D3—34no—
257C2×C4×D3—34no—
258C2×C4×D3—34no—
259C2×C4×D3—34no—
260C2×C4×D3—64no—
261C2×C4×D3—64no—
262C2×C4×D3—632no—
263C2×C4×D3—68no—
264C2×C4×D3—64no—
265C2×C4×D3—68no—
266C2×Dic6—34no—
267C2×Dic6—64no—
268C3×Q16—216no—
269C3×SD16—216no—
270C3×M16—28no—
271C2×C3×C8C22×D318yes—
272#216—616no—
273#215—616no—
274(C2×D3)⋊C4—68no—
275(C2×D3)⋊C4—68no—
276C4⋊Dic3—38no—
277C4⋊Dic3—64no—
278Dic3⋊C4—68no—
279Dic3⋊C4—68no—
280#208—68no—
281C2×C3⋊C8—38no—
282C22×C32—21no—
283C22×C32—21no—
284C22×C32—22no—
285C22×C32—41no—
286C22×C32—41no—
287C22×C32#12012yes—
288C22×C32C22×D411yescharacteristic
289C2×C3⋊D3—21no—
290C2×C3⋊D3—21no—
291C2×C3⋊D3—21no—
292C2×C3⋊D3—22no—
293C2×C3⋊D3—21no—
294C2×C3⋊D3—21no—
295C2×C3⋊D3—44no—
296C2×C3⋊D3—48no—
297C2×C3⋊D3—41no—
298C2×C3⋊D3—41no—
299C2×C3⋊D3#13712yescomplemented
300C32×C4—22no—
301C32×C4—42no—
302C32×C4#12012yes—
303C32×C4C22×D411yescharacteristic
304C32×C4C22×D411yescharacteristic
305C3⋊Dic3—21no—
306C3⋊Dic3—22no—
307C3⋊Dic3—21no—
308C3⋊Dic3—42no—
309C2×#41—91no—
310C2×#41—91no—
311C2×#41—91no—
312C2×#41—181no—
313C2×#41—181no—
314C2×#41—184no—
315C2×#41—184no—
316C2×#41C2×C3⋊D311yescharacteristic
317C22×Q8—91no—
318C22×Q8C2×C3⋊D311yescharacteristic, complemented
319C22×D4—91no—
320C22×D4—181no—
321C23×C4—91no—
322C23×C4—181no—
323#137—24no—
324#137—184no—
325C2×Q16—92no—
326C2×Q16C2×C3⋊D312yescomplemented
327C2×SD16—92no—
328C2×SD16C2×C3⋊D312yescomplemented
329C2×M16—91no—
330C2×M16C2×C3⋊D311yescharacteristic, complemented
331C22⋊Q8—92no—
332C22⋊Q8—92no—
333C22⋊Q8—181no—
334C22⋊Q8—181no—
335C2×C4⋊C4—91no—
336C2×C4⋊C4—181no—
337C2×C22⋊C4—181no—
338#103—92no—
339#103—92no—
340#102—92no—
341#102—92no—
342C22⋊C8—92no—
343C22⋊C8—92no—
344C23×C3—24no—
345C23×C3D3×D414yes—
346C22×D3—34no—
347C22×D3—34no—
348C22×D3—68no—
349C22×D3—616no—
350C22×D3—68no—
351C22×D3—64no—
352C22×D3—128no—
353C22×D3—124no—
354C22×D3—128no—
355C3×Q8—24no—
356C3×Q8—28no—
357C3×Q8—28no—
358C3×Q8—48no—
359C3×Q8C2×#6718yes—
360C3×D4—216no—
361C3×D4—24no—
362C3×D4C2×#6718yes—
363C2×C3×C4—24no—
364C2×C3×C4—216no—
365C2×C3×C4—28no—
366C2×C3×C4—48no—
367C2×C3×C4D3×D414yes—
368C2×C3×C4D3×D418yes—
369C2×C3×C4C2×#6718yes—
370C2×C3×C4C23×D314yes—
371#67—616no—
372#67—616no—
373#67—616no—
374C2×Dic3—34no—
375C2×Dic3—34no—
376C2×Dic3—616no—
377C2×Dic3—68no—
378C2×Dic3—64no—
379C2×Dic3—68no—
380C2×Dic3—128no—
381D12—38no—
382D12—616no—
383D12—64no—
384C4×D3—616no—
385C4×D3—616no—
386C4×D3—68no—
387C4×D3—68no—
388C4×D3—616no—
389C4×D3—64no—
390C4×D3—64no—
391C4×D3—64no—
392C4×D3—64no—
393Dic6—38no—
394Dic6—616no—
395Dic6—64no—
396C3×C8—28no—
397C3⋊C8—68no—
398C2×C32—22no—
399C2×C32—42no—
400C2×C32C2×#12011yescharacteristic
401C2×C32C2×#13711yescharacteristic
402C2×C32#57511yescharacteristic
403C3⋊D3—22no—
404C3⋊D3—41no—
405C3⋊D3—42no—
406C24—91no—
407C24—181no—
408#41—22no—
409#41—94no—
410#41—188no—
411#41—182no—
412#41—188no—
413#41—182no—
414#41—182no—
415#41—182no—
416#41—182no—
417#41#63814yes—
418C2×Q8—21no—
419C2×Q8—22no—
420C2×Q8—22no—
421C2×Q8—91no—
422C2×Q8—181no—
423C2×Q8—182no—
424C2×Q8—182no—
425C2×Q8C22×C3⋊D312yes—
426C2×Q8C22×C3⋊D311yescharacteristic
427C2×D4—21no—
428C2×D4—91no—
429C2×D4—181no—
430C2×D4—181no—
431C2×D4—182no—
432C2×D4—188no—
433C2×D4—181no—
434C2×D4—181no—
435C2×D4—182no—
436C2×D4C22×C3⋊D311yescharacteristic
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—91no—
440C22×C4—91no—
441C22×C4—91no—
442C22×C4—91no—
443C22×C4—91no—
444C22×C4—181no—
445C22×C4—181no—
446C22×C4—188no—
447C22×C4—181no—
448C22×C4—182no—
449C22×C4—181no—
450C22×C4—182no—
451C22×C4—181no—
452C22×C4C22×C3⋊D311yescharacteristic
453Q16—24no—
454Q16—184no—
455SD16—24no—
456SD16—184no—
457M16—22no—
458M16—182no—
459C2×C8—92no—
460C2×C8C22×C3⋊D312yes—
461C4⋊C4—92no—
462C4⋊C4—182no—
463C4⋊C4—182no—
464C4⋊C4—181no—
465C22⋊C4—182no—
466C22⋊C4—182no—
467C22×C3—24no—
468C22×C3—24no—
469C22×C3—28no—
470C22×C3—44no—
471C22×C3—44no—
472C22×C3#93718yes—
473C22×C3C2×D3×D414yes—
474C2×D3—38no—
475C2×D3—64no—
476C2×D3—64no—
477C2×D3—64no—
478C2×D3—64no—
479C2×D3—68no—
480C2×D3—64no—
481C2×D3—1216no—
482C2×D3—1232no—
483C2×D3—124no—
484C2×D3—124no—
485C3×C4—28no—
486C3×C4—48no—
487C3×C4#93718yes—
488C3×C4C2×D3×D414yes—
489C3×C4C22×#6714yes—
490Dic3—68no—
491Dic3—64no—
492Dic3—64no—
493Dic3—128no—
494C32#300711yescharacteristic, complemented, Sylow
495C23—21no—
496C23—91no—
497C23—91no—
498C23—182no—
499C23—184no—
500C23—181no—
501C23—182no—
502C23—361no—
503C23—362no—
504C23—362no—
505C23D4×C3⋊D311yescharacteristic
506Q8—21no—
507Q8—22no—
508Q8—22no—
509Q8—42no—
510Q8—92no—
511Q8—184no—
512Q8—181no—
513Q8C2×#63812yes—
514D4—24no—
515D4—21no—
516D4—92no—
517D4—184no—
518D4—184no—
519D4—184no—
520D4—184no—
521D4—181no—
522D4C2×#63812yes—
523C2×C4—21no—
524C2×C4—24no—
525C2×C4—22no—
526C2×C4—42no—
527C2×C4—91no—
528C2×C4—91no—
529C2×C4—184no—
530C2×C4—184no—
531C2×C4—184no—
532C2×C4—181no—
533C2×C4—182no—
534C2×C4—181no—
535C2×C4—181no—
536C2×C4—181no—
537C2×C4—181no—
538C2×C4—182no—
539C2×C4—182no—
540C2×C4—184no—
541C2×C4—182no—
542C2×C4—362no—
543C2×C4D4×C3⋊D312yes—
544C2×C4D4×C3⋊D311yescharacteristic
545C2×C4C2×#63812yes—
546C2×C4C23×C3⋊D311yescharacteristic
547C8—22no—
548C8—182no—
549C2×C3—28no—
550C2×C3—48no—
551C2×C3D3×#13714yes—
552C2×C3#577714yes—
553C2×C3C2×#93714yes—
554D3—68no—
555D3—124no—
556D3—128no—
557C22—21no—
558C22—21no—
559C22—22no—
560C22—41no—
561C22—41no—
562C22—92no—
563C22—181no—
564C22—181no—
565C22—181no—
566C22—181no—
567C22—182no—
568C22—181no—
569C22—364no—
570C22—368no—
571C22—361no—
572C22—361no—
573C22#6414612yes—
574C22C2×D4×C3⋊D311yescharacteristic
575C4—22no—
576C4—42no—
577C4—181no—
578C4—181no—
579C4—182no—
580C4—362no—
581C4#6414612yes—
582C4C2×D4×C3⋊D311yescharacteristic
583C4C22×#63811yescharacteristic
584C3#8398114yescomplemented
585C2—22no—
586C2—42no—
587C2—182no—
588C2—361no—
589C2—362no—
590C2C3⋊D3×#13711yescharacteristic
591C2#1059624811yescharacteristic
592C2C2×#6414611yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC2×C32×#137C2
socleC22×C32C22×D4
prime radicalC2×#41×C3⋊D3C2
hypercenterC2×#137C3⋊D3
hypocenterC32#3007
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
2. C2×C32×#137C2semidirect
3. C2×#64155C2semidirect
4. C2×#64151C2semidirect
5. #10592931C2semidirect
6. #10592886C2semidirect
7. #10592885C2semidirect
8. #10592872C2semidirect
9. #10592868C2semidirect
10. #10592832C2semidirect
11. #10592825C2semidirect
14. C22×C32×Q8C22semidirect
28. C2×C32×Q16C22semidirect
29. C2×C32×SD16C22semidirect
30. C2×C32×M16C22semidirect
34. #64155C22semidirect
35. C2×#3756C22semidirect
37. C2×#3755C22semidirect
39. C2×C4⋊(C3⋊Dic3)C22semidirect
41. C2×#3748C22semidirect
42. #63662C22semidirect
43. #63659C22semidirect
44. #63648C22semidirect
46. #63647C22semidirect
47. #63643C22semidirect
49. C2×C3×#137D3semidirect
122. C22×C3×Q8C2×D3semidirect
136. C2×C3×Q16C2×D3semidirect
137. C2×C3×SD16C2×D3semidirect
138. C2×C3×M16C2×D3semidirect
212. C2×#137C3⋊D3semidirect
299. C2×C3⋊D3#137semidirect
318. C22×Q8C2×C3⋊D3semidirect
326. C2×Q16C2×C3⋊D3semidirect
328. C2×SD16C2×C3⋊D3semidirect
330. C2×M16C2×C3⋊D3semidirect
494. C32#3007semidirect
584. C3#83981semidirect

Maximal subgroups

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

subgroupindex
C2×#41×C3⋊D32
C2×C32×#1372
C2×#641552
C2×#641512
#105929312
#105928862
#105928852
#105928722
#105928682
#105928322
#105928252
#839813