Finite Group Databasebeta

← #11904725

Subgroups — #11904725

Order 1152.

4566 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64364C211yesmaximal, characteristic, complemented
2C22×#3832C211yesmaximal, characteristic, complemented
3C32×D4×Q8C211yesmaximal, characteristic, complemented
4#10596288C211yesmaximal, characteristic, complemented
5Q8×#638C211yesmaximal, characteristic, complemented
6#10596197C213yesmaximal, complemented
7#10596195C213yesmaximal, complemented
8#10596102C213yesmaximal, complemented
9#10596101C213yesmaximal, complemented
10#10596100C213yesmaximal, complemented
11C3⋊D3×C22⋊Q8C213yesmaximal, complemented
12#10596047C211yesmaximal, characteristic, complemented
13#10596045C211yesmaximal, characteristic, complemented
14#10596021C213yesmaximal, complemented
15#10596018C213yesmaximal, complemented
16#86745—34nomaximal
17C22×C32×Q8C2211yescharacteristic
18C22×C32×Q8C2211yescharacteristic, complemented
19#64364—28no—
20C2×#3832—28no—
21C2×#3832C2213yes—
22C2×#3832C2213yes—
23C2×#3832C2211yescharacteristic
24C2×#3832C2211yescharacteristic
25C2×#3832C2213yescomplemented
26C2×Q8×C3⋊D3C2213yescomplemented
27C2×Q8×C3⋊D3C2211yescharacteristic, complemented
28C2×#3828C2213yescomplemented
29C2×#3828C2213yescomplemented
30C22×C4⋊(C3⋊D3)C2213yes—
31C22×C4×C3⋊D3C2213yes—
32C32×C4⋊Q8C2213yescomplemented
33C32×C22⋊Q8C2213yes—
34C32×C22⋊Q8C2213yescomplemented
35C32×C4×Q8C2211yescharacteristic, complemented
36C32×C4×D4C2213yes—
37#64156C2213yescomplemented
38#64155C2213yescomplemented
39#64155C2213yescomplemented
40Q8×C3⋊Dic3C2211yescharacteristic, complemented
41#64153C2213yescomplemented
42#64148C2211yescharacteristic
43#64146C2213yes—
44#64139C2213yescomplemented
45C4×#638C2213yes—
46C4×#638C2213yescomplemented
47#64133C2213yes—
48#64106C2213yescomplemented
49#64105C2216yescomplemented
50#64105C2213yescomplemented
51#64104C2216yescomplemented
52#64104C2213yescomplemented
53#64103C2216yescomplemented
54#64103C2216yescomplemented
55#64103C2213yescomplemented
56#64102C2213yescomplemented
57C4⋊C4×C3⋊D3C2213yescomplemented
58C4⋊C4×C3⋊D3C2216yescomplemented
59#64093C2213yescomplemented
60#64093C2216yescomplemented
61#64092C2213yescomplemented
62#64091C2213yes—
63C22⋊C4×C3⋊D3C2216yes—
64#64087C2213yes—
65#64084C2213yescomplemented
66C4×C4⋊(C3⋊D3)C2213yescomplemented
67C4×C4⋊(C3⋊D3)C2213yescomplemented
68#64081C2213yescomplemented
69C2×#1007—34no—
70C22×#239—34no—
71C3×D4×Q8D314yescomplemented
72#5817—34no—
73Q8×#67—34no—
74#5726—312no—
75#5724—312no—
76#5631—312no—
77#5630—312no—
78#5629—312no—
79D3×C22⋊Q8—312no—
80#5576—34no—
81#5574—34no—
82#5550—312no—
83#5547—312no—
84C23×C3⋊D3C2313yes—
85C2×C32×Q8—24no—
86C2×C32×Q8—24no—
87C2×C32×Q8C2313yes—
88C2×C32×Q8C2313yes—
89C2×C32×Q8C2311yescharacteristic
90C2×C32×D4C2311yescharacteristic
91C22×C32×C4C2313yes—
92C22×C32×C4C2313yes—
93C2×#638C2311yescharacteristic
94C2×#638C2313yes—
95C2×#638C2311yescharacteristic
96C2×#638C2313yes—
97C22×C3⋊Dic3C2311yescharacteristic
98#3832—24no—
99#3832—212no—
100#3832—212no—
101#3832—212no—
102#3832D418yescomplemented
103Q8×C3⋊D3—24no—
104Q8×C3⋊D3—212no—
105#3828—212no—
106#3828—212no—
107C2×C4⋊(C3⋊D3)—212no—
108C2×C4⋊(C3⋊D3)C2313yes—
109C2×C4⋊(C3⋊D3)C2313yes—
110C2×C4⋊(C3⋊D3)C2316yes—
111C2×C4⋊(C3⋊D3)C2313yes—
112C2×C4⋊(C3⋊D3)C2313yes—
113C2×C4×C3⋊D3—212no—
114C2×C4×C3⋊D3C2313yes—
115C2×C4×C3⋊D3C2313yes—
116C2×C4×C3⋊D3C2316yes—
117C2×C4×C3⋊D3C2313yes—
118C2×C4×C3⋊D3C2313yes—
119C2×C4×C3⋊D3C2316yes—
120C2×C4×C3⋊D3C2313yes—
121C2×#634C2313yes—
122C2×#634C2313yes—
123C32×C4⋊C4C2313yes—
124C32×C4⋊C4C2316yes—
125C32×C4⋊C4C2313yes—
126C32×C22⋊C4C2313yes—
127C32×C22⋊C4C2313yes—
128C32×C42C2313yes—
129#3757C2313yes—
130#3757C2311yescharacteristic
131#3752C2313yes—
132#3752C2313yes—
133#3752C2311yescharacteristic
134#3752C2313yes—
135#3752C2316yes—
136#3752C2316yes—
137#3752C2313yes—
138#3752C2313yes—
139C4⋊(C3⋊Dic3)C2313yes—
140C4⋊(C3⋊Dic3)C2313yes—
141#3750C2311yescharacteristic
142#3750C2313yes—
143#3750C2313yes—
144#3750C2313yes—
145#3750C2316yes—
146C4×C3⋊Dic3C2313yes—
147#3489—91noSylow
148C22×C3×Q8C2×D314yes—
149C22×C3×Q8C2×D314yescomplemented
150#1007—632no—
151C2×#239—34no—
152C2×#239—312no—
153C2×#239—312no—
154C2×#239—34no—
155C2×#239—312no—
156C2×#239—632no—
157C2×D3×Q8—312no—
158C2×D3×Q8—34no—
159C2×#235—312no—
160C2×#235—312no—
161C22×D12—312no—
162C22×C4×D3—312no—
163C3×C4⋊Q8C2×D3112yescomplemented
164C3×C22⋊Q8C2×D3112yes—
165C3×C22⋊Q8C2×D3112yescomplemented
166C3×C4×Q8C2×D314yescomplemented
167C3×C4×D4C2×D3112yes—
168#947—312no—
169#946—312no—
170#946—312no—
171Q8×Dic3—34no—
172#944—312no—
173#939—34no—
174#937—312no—
175#930—312no—
176C4×#67—312no—
177C4×#67—312no—
178#924—312no—
179#897—312no—
180#896—312no—
181#896—324no—
182#895—324no—
183#895—312no—
184#894—324no—
185#894—324no—
186#894—312no—
187#893—312no—
188D3×C4⋊C4—324no—
189D3×C4⋊C4—312no—
190#884—312no—
191#884—324no—
192#883—312no—
193#882—312no—
194D3×C22⋊C4—324no—
195#878—312no—
196#875—312no—
197C4×D12—312no—
198C4×D12—312no—
199#872—312no—
200C23×C32C2411yescharacteristic
201C23×C32C2411yescharacteristic
202C22×C3⋊D3—26no—
203C22×C3⋊D3—26no—
204C22×C3⋊D3—43no—
205C22×C3⋊D3C2413yes—
206C22×C3⋊D3C2411yescharacteristic
207C22×C3⋊D3C2413yes—
208C32×Q8—26no—
209C32×Q8—26no—
210C32×Q8C2×D414yes—
211C32×D4—22no—
212C2×C32×C4—26no—
213C2×C32×C4—26no—
214C2×C32×C4C2413yes—
215C2×C32×C4C2413yes—
216C2×C32×C4C2411yescharacteristic
217C2×C32×C4C2413yes—
218C2×C32×C4C2413yes—
219#638—22no—
220#638—26no—
221#638—22no—
222#638—43no—
223C2×C3⋊Dic3—22no—
224C2×C3⋊Dic3C2411yescharacteristic
225C2×C3⋊Dic3C2413yes—
226C2×C3⋊Dic3C2411yescharacteristic
227C2×C3⋊Dic3C2413yes—
228C2×C3⋊Dic3C2411yescharacteristic
229C4⋊(C3⋊D3)—212no—
230C4⋊(C3⋊D3)—26no—
231C4⋊(C3⋊D3)—26no—
232C4⋊(C3⋊D3)—43no—
233C4⋊(C3⋊D3)C2×D4112yes—
234C4×C3⋊D3—26no—
235C4×C3⋊D3—212no—
236C4×C3⋊D3—26no—
237C4×C3⋊D3—26no—
238C4×C3⋊D3—26no—
239C4×C3⋊D3—46no—
240C4×C3⋊D3C2×D4112yes—
241#634—26no—
242#634—26no—
243C2×2−1+4—91no—
244C22×#41—91no—
245D4×Q8—91no—
246D4×Q8C3⋊D311yescharacteristic, complemented
247#548—91no—
248#548—91no—
249#547—93no—
250#547—93no—
251#546—93no—
252#546—93no—
253#537—93no—
254#536—93no—
255#525—93no—
256C2×C22⋊Q8—93no—
257#520—91no—
258C23×D3—312no—
259C2×C3×Q8—216no—
260C2×C3×Q8—216no—
261C2×C3×Q8C22×D3112yes—
262C2×C3×Q8C22×D3112yes—
263C2×C3×Q8C22×D314yes—
264C2×C3×D4C22×D314yes—
265C22×C3×C4C22×D3112yes—
266C22×C3×C4C22×D3112yes—
267C2×#67—34no—
268C2×#67—312no—
269C2×#67—34no—
270C2×#67—312no—
271C22×Dic3—34no—
272#239—332no—
273#239—648no—
274#239—648no—
275#239—648no—
276#239—616no—
277D3×Q8—648no—
278D3×Q8—616no—
279#235—648no—
280#235—648no—
281C2×D12—312no—
282C2×D12—312no—
283C2×D12—312no—
284C2×D12—324no—
285C2×D12—312no—
286C2×D12—648no—
287C2×C4×D3—312no—
288C2×C4×D3—312no—
289C2×C4×D3—312no—
290C2×C4×D3—324no—
291C2×C4×D3—312no—
292C2×C4×D3—312no—
293C2×C4×D3—324no—
294C2×C4×D3—648no—
295C2×Dic6—312no—
296C2×Dic6—312no—
297C3×C4⋊C4C22×D3112yes—
298C3×C4⋊C4C22×D3124yes—
299C3×C4⋊C4C22×D3112yes—
300C3×C22⋊C4C22×D3112yes—
301C3×C22⋊C4C22×D3112yes—
302C3×C42C22×D3112yes—
303#217—312no—
304#217—34no—
305(C2×D3)⋊C4—312no—
306(C2×D3)⋊C4—312no—
307(C2×D3)⋊C4—34no—
308(C2×D3)⋊C4—312no—
309(C2×D3)⋊C4—324no—
310(C2×D3)⋊C4—324no—
311(C2×D3)⋊C4—312no—
312(C2×D3)⋊C4—312no—
313C4⋊Dic3—312no—
314C4⋊Dic3—312no—
315Dic3⋊C4—34no—
316Dic3⋊C4—312no—
317Dic3⋊C4—312no—
318Dic3⋊C4—312no—
319Dic3⋊C4—324no—
320C4×Dic3—312no—
321C22×C32—21no—
322C22×C32—21no—
323C22×C32—21no—
324C22×C32—21no—
325C22×C32—21no—
326C22×C322−1+412yescomplemented
327C22×C32C2511yescharacteristic
328C2×C3⋊D3—23no—
329C2×C3⋊D3—23no—
330C2×C3⋊D3—21no—
331C2×C3⋊D3—23no—
332C2×C3⋊D3—21no—
333C2×C3⋊D3—23no—
334C2×C3⋊D3—21no—
335C2×C3⋊D3—23no—
336C2×C3⋊D3—412no—
337C2×C3⋊D3C22×D416yes—
338C32×C4—23no—
339C32×C4—23no—
340C32×C4—21no—
341C32×C4—23no—
342C32×C4C22×D416yes—
343C3⋊Dic3—23no—
344C3⋊Dic3—21no—
345C3⋊Dic3—21no—
346C3⋊Dic3—23no—
347C3⋊Dic3C22×D412yes—
3482−1+4—188no—
349C2×#41—91no—
350C2×#41—93no—
351C2×#41—93no—
352C2×#41—93no—
353C2×#41—91no—
354C2×#41—93no—
355C2×#41—93no—
356C2×#41—188no—
357C22×Q8—93no—
358C22×Q8—91no—
359C22×Q8C2×C3⋊D311yescharacteristic
360C22×Q8C2×C3⋊D311yescharacteristic, complemented
361C22×D4—93no—
362C23×C4—93no—
363C4⋊Q8—93no—
364C4⋊Q8C2×C3⋊D313yescomplemented
365#124—93no—
366#124—93no—
367#123—93no—
368#123—96no—
369#123—96no—
370#123—93no—
371C22⋊Q8—93no—
372C22⋊Q8—93no—
373C22⋊Q8—93no—
374C22⋊Q8—96no—
375C22⋊Q8—93no—
376C22⋊Q8—93no—
377C22⋊Q8—93no—
378C22⋊Q8C2×C3⋊D313yes—
379C22⋊Q8C2×C3⋊D313yescomplemented
380#121—91no—
381#121—93no—
382#121—96no—
383#121—93no—
384#121—93no—
385#121—96no—
386#120—93no—
387#120—93no—
388C4×Q8—91no—
389C4×Q8C2×C3⋊D311yescharacteristic, complemented
390C4×D4—93no—
391C4×D4—93no—
392C4×D4—93no—
393C4×D4—93no—
394C4×D4—93no—
395C4×D4C2×C3⋊D313yes—
396#117—93no—
397C2×C4⋊C4—93no—
398C2×C4⋊C4—96no—
399C2×C22⋊C4—96no—
400C23×C3C23×D314yes—
401C23×C3C23×D314yes—
402C22×D3—312no—
403C22×D3—312no—
404C22×D3—34no—
405C22×D3—624no—
406C22×D3—624no—
407C22×D3—1212no—
408C3×Q8—224no—
409C3×Q8—224no—
410C3×Q8D3×D4116yes—
411C3×D4—28no—
412C2×C3×C4—224no—
413C2×C3×C4—224no—
414C2×C3×C4C23×D3112yes—
415C2×C3×C4C23×D3112yes—
416C2×C3×C4C23×D314yes—
417C2×C3×C4C23×D3112yes—
418C2×C3×C4C23×D3112yes—
419#67—68no—
420#67—624no—
421#67—68no—
422#67—1212no—
423C2×Dic3—34no—
424C2×Dic3—34no—
425C2×Dic3—312no—
426C2×Dic3—34no—
427C2×Dic3—312no—
428C2×Dic3—68no—
429D12—348no—
430D12—648no—
431D12—624no—
432D12—624no—
433D12—1212no—
434C4×D3—348no—
435C4×D3—624no—
436C4×D3—624no—
437C4×D3—648no—
438C4×D3—624no—
439C4×D3—624no—
440C4×D3—1224no—
441Dic6—624no—
442Dic6—624no—
443C2×C32—22no—
444C2×C32—41no—
445C2×C32C23×D411yescharacteristic
446C2×C32C2×2−1+411yescharacteristic
447C2×C32#58511yescharacteristic
448C3⋊D3—26no—
449C3⋊D3—41no—
450C3⋊D3—43no—
451C24—93no—
452#41—98no—
453#41—1812no—
454#41—1812no—
455#41—1812no—
456#41—1812no—
457#41—1812no—
458#41—184no—
459C2×Q8—24no—
460C2×Q8—24no—
461C2×Q8—93no—
462C2×Q8—93no—
463C2×Q8—1812no—
464C2×Q8—184no—
465C2×Q8C22×C3⋊D313yes—
466C2×Q8C22×C3⋊D313yes—
467C2×Q8C22×C3⋊D311yescharacteristic
468C2×D4—91no—
469C2×D4—93no—
470C2×D4—91no—
471C2×D4—93no—
472C2×D4—93no—
473C2×D4—93no—
474C2×D4—96no—
475C2×D4—93no—
476C2×D4—93no—
477C2×D4—1812no—
478C2×D4C22×C3⋊D311yescharacteristic
479C22×C4—93no—
480C22×C4—91no—
481C22×C4—96no—
482C22×C4—93no—
483C22×C4—93no—
484C22×C4—93no—
485C22×C4—93no—
486C22×C4—96no—
487C22×C4—1812no—
488C22×C4C22×C3⋊D313yes—
489C22×C4C22×C3⋊D313yes—
490C4⋊C4—93no—
491C4⋊C4—93no—
492C4⋊C4—93no—
493C4⋊C4—93no—
494C4⋊C4—96no—
495C4⋊C4—91no—
496C4⋊C4—93no—
497C4⋊C4C22×C3⋊D313yes—
498C4⋊C4C22×C3⋊D316yes—
499C4⋊C4C22×C3⋊D313yes—
500C22⋊C4—93no—
501C22⋊C4—91no—
502C22⋊C4—96no—
503C22⋊C4—96no—
504C22⋊C4—93no—
505C22⋊C4—93no—
506C22⋊C4—91no—
507C22⋊C4—93no—
508C22⋊C4—93no—
509C22⋊C4—93no—
510C22⋊C4C22×C3⋊D313yes—
511C22⋊C4C22×C3⋊D313yes—
512C42—93no—
513C42C22×C3⋊D313yes—
514C22×C3—24no—
515C22×C3—24no—
516C22×C3—24no—
517C22×C3—24no—
518C22×C3—24no—
519C22×C3#100718yescomplemented
520C22×C3C24×D314yes—
521C2×D3—324no—
522C2×D3—612no—
523C2×D3—612no—
524C2×D3—64no—
525C2×D3—612no—
526C2×D3—64no—
527C2×D3—612no—
528C2×D3—64no—
529C2×D3—612no—
530C2×D3—1248no—
531C3×C4—212no—
532C3×C4—212no—
533C3×C4—24no—
534C3×C4—212no—
535C3×C4C2×D3×D4124yes—
536Dic3—38no—
537Dic3—612no—
538Dic3—64no—
539Dic3—64no—
540Dic3—612no—
541C32#348911yescharacteristic, complemented, Sylow
542C23—93no—
543C23—93no—
544C23—91no—
545C23—186no—
546C23—186no—
547C23—363no—
548C23C23×C3⋊D311yescharacteristic
549C23C23×C3⋊D311yescharacteristic
550Q8—26no—
551Q8—26no—
552Q8—186no—
553Q8—186no—
554Q8D4×C3⋊D314yes—
555D4—22no—
556D4—912no—
557D4—1812no—
558D4—186no—
559D4—182no—
560D4—186no—
561D4—182no—
562D4—186no—
563D4—363no—
564D4—363no—
565C2×C4—26no—
566C2×C4—26no—
567C2×C4—91no—
568C2×C4—912no—
569C2×C4—91no—
570C2×C4—93no—
571C2×C4—93no—
572C2×C4—91no—
573C2×C4—186no—
574C2×C4—186no—
575C2×C4—1812no—
576C2×C4—182no—
577C2×C4—186no—
578C2×C4—186no—
579C2×C4—366no—
580C2×C4C23×C3⋊D311yescharacteristic
581C2×C4C23×C3⋊D313yes—
582C2×C4C23×C3⋊D313yes—
583C2×C4C23×C3⋊D313yes—
584C2×C4C23×C3⋊D313yes—
585C2×C3—28no—
586C2×C3—44no—
587C2×C3C22×D3×D414yes—
588C2×C3C2×#100714yes—
589C2×C3#596814yes—
590D3—624no—
591D3—1212no—
592D3—124no—
593C22—21no—
594C22—21no—
595C22—21no—
596C22—21no—
597C22—21no—
598C22—96no—
599C22—183no—
600C22—183no—
601C22—181no—
602C22—183no—
603C22—181no—
604C22—183no—
605C22—181no—
606C22—183no—
607C22—3612no—
608C22#6436412yescomplemented
609C22C24×C3⋊D311yescharacteristic
610C4—23no—
611C4—23no—
612C4—21no—
613C4—23no—
614C4—92no—
615C4—181no—
616C4—183no—
617C4—181no—
618C4—183no—
619C4C2×D4×C3⋊D316yes—
620C3#8674514yescomplemented
621C2—22no—
622C2—41no—
623C2—186no—
624C2—363no—
625C2—361no—
626C2C22×D4×C3⋊D311yescharacteristic
627C2C2×#6436411yescharacteristic
628C2#1059676011yescharacteristic
subgroupG/H
center, FrattiniC22C24×C3⋊D3
commutator, socle, cosocleC22×C32C25
FittingC32×D4×Q8C2
hypercenterD4×Q8C3⋊D3
hypocenterC32#3489
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ D4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#64364C2semidirect
2. C22×#3832C2semidirect
3. C32×D4×Q8C2semidirect
4. #10596288C2semidirect
5. Q8×#638C2semidirect
6. #10596197C2semidirect
7. #10596195C2semidirect
8. #10596102C2semidirect
9. #10596101C2semidirect
10. #10596100C2semidirect
11. C3⋊D3×C22⋊Q8C2semidirect
12. #10596047C2semidirect
13. #10596045C2semidirect
14. #10596021C2semidirect
15. #10596018C2semidirect
18. C22×C32×Q8C22semidirect
25. C2×#3832C22semidirect
26. C2×Q8×C3⋊D3C22semidirect
27. C2×Q8×C3⋊D3C22semidirect
28. C2×#3828C22semidirect
29. C2×#3828C22semidirect
32. C32×C4⋊Q8C22semidirect
34. C32×C22⋊Q8C22semidirect
35. C32×C4×Q8C22semidirect
37. #64156C22semidirect
38. #64155C22semidirect
39. #64155C22semidirect
40. Q8×C3⋊Dic3C22semidirect
41. #64153C22semidirect
44. #64139C22semidirect
46. C4×#638C22semidirect
48. #64106C22semidirect
49. #64105C22semidirect
50. #64105C22semidirect
51. #64104C22semidirect
52. #64104C22semidirect
53. #64103C22semidirect
54. #64103C22semidirect
55. #64103C22semidirect
56. #64102C22semidirect
57. C4⋊C4×C3⋊D3C22semidirect
58. C4⋊C4×C3⋊D3C22semidirect
59. #64093C22semidirect
60. #64093C22semidirect
61. #64092C22semidirect
65. #64084C22semidirect
66. C4×C4⋊(C3⋊D3)C22semidirect
67. C4×C4⋊(C3⋊D3)C22semidirect
68. #64081C22semidirect
71. C3×D4×Q8D3semidirect
102. #3832D4semidirect
149. C22×C3×Q8C2×D3semidirect
163. C3×C4⋊Q8C2×D3semidirect
165. C3×C22⋊Q8C2×D3semidirect
166. C3×C4×Q8C2×D3semidirect
246. D4×Q8C3⋊D3semidirect
326. C22×C322−1+4semidirect
360. C22×Q8C2×C3⋊D3semidirect
364. C4⋊Q8C2×C3⋊D3semidirect
379. C22⋊Q8C2×C3⋊D3semidirect
389. C4×Q8C2×C3⋊D3semidirect
519. C22×C3#1007semidirect
541. C32#3489semidirect
608. C22#64364semidirect
620. C3#86745semidirect

Maximal subgroups

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

subgroupindex
C2×#643642
C22×#38322
C32×D4×Q82
#105962882
Q8×#6382
#105961972
#105961952
#105961022
#105961012
#105961002
C3⋊D3×C22⋊Q82
#105960472
#105960452
#105960212
#105960182
#867453