Finite Group Databasebeta

← #11904731

Subgroups — #11904731

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×#41×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×#64364C211yesmaximal, characteristic, complemented
3C32×#548C211yesmaximal, characteristic, complemented
4#10596302C211yesmaximal, characteristic, complemented
5Q8×#638C211yesmaximal, characteristic, complemented
6#10596147C213yesmaximal, complemented
7#10596146C213yesmaximal, complemented
8#10596102C213yesmaximal, complemented
9C3⋊D3×C22⋊Q8C213yesmaximal, complemented
10#10596083C213yesmaximal, complemented
11#10596079C213yesmaximal, complemented
12Q8×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
13#10596045C211yesmaximal, characteristic, complemented
14#10596022C213yesmaximal, complemented
15#10596018C213yesmaximal, complemented
16#86714—34nomaximal
17C2×C32×#41C2211yescharacteristic
18C22×C32×Q8C2211yescharacteristic, complemented
19#41×C3⋊D3—28no—
20#64364—28no—
21C2×#3832C2211yescharacteristic
22C2×#3832C2213yescomplemented
23C2×Q8×C3⋊D3C2211yescharacteristic
24C2×Q8×C3⋊D3C2213yescomplemented
25C2×Q8×C3⋊D3C2211yescharacteristic, complemented
26C2×#3830C2213yes—
27C2×D4×C3⋊D3C2213yes—
28C2×#3828C2213yes—
29C2×#3828C2213yescomplemented
30C2×#3828C2213yescomplemented
31C22×C4×C3⋊D3C2213yes—
32C32×#124C2213yescomplemented
33C32×C22⋊Q8C2213yescomplemented
34C32×#121C2213yescomplemented
35C32×C4×Q8C2211yescharacteristic, complemented
36C32×C4×D4C2213yescomplemented
37#64155C2213yes—
38Q8×C3⋊Dic3C2211yescharacteristic, complemented
39#64153C2213yescomplemented
40#64148C2213yescomplemented
41#64147C2213yescomplemented
42#64147C2216yescomplemented
43#64146C2213yes—
44#64145C2213yescomplemented
45C4×#638C2213yes—
46C4×#638C2213yescomplemented
47#64133C2213yescomplemented
48#64133C2213yescomplemented
49#64106C2213yes—
50#64106C2213yescomplemented
51#64105C2213yes—
52#64103C2213yescomplemented
53#64102C2213yescomplemented
54C4⋊C4×C3⋊D3C2216yescomplemented
55C4⋊C4×C3⋊D3C2213yescomplemented
56#64093C2211yescharacteristic
57#64093C2216yescomplemented
58#64092C2216yescomplemented
59#64092C2216yescomplemented
60#64092C2213yescomplemented
61#64091C2213yes—
62C22⋊C4×C3⋊D3C2216yes—
63#64087C2216yescomplemented
64#64087C2213yescomplemented
65C4×C4⋊(C3⋊D3)C2213yes—
66C4×C4⋊(C3⋊D3)C2213yescomplemented
67#64081C2213yescomplemented
68#64078C2213yescomplemented
69C2×D3×#41—34no—
70C2×#1007—34no—
71C3×#548D314yescomplemented
72#5831—34no—
73Q8×#67—34no—
74#5676—312no—
75#5675—312no—
76#5631—312no—
77D3×C22⋊Q8—312no—
78#5612—312no—
79#5608—312no—
80Q8×D12—34no—
81#5574—34no—
82#5551—312no—
83#5547—312no—
84C23×C3⋊D3C2313yes—
85C32×#41—24no—
86C2×C32×Q8—24no—
87C2×C32×Q8C2313yes—
88C2×C32×Q8C2311yescharacteristic
89C2×C32×D4C2313yes—
90C2×C32×D4C2313yes—
91C22×C32×C4C2313yes—
92C22×C32×C4C2313yes—
93C2×#638C2316yes—
94C2×#638C2313yes—
95C2×#638C2311yescharacteristic
96C2×#638C2311yescharacteristic
97C2×#638C2313yes—
98C22×C3⋊Dic3C2313yes—
99#3832—212no—
100#3832D418yescomplemented
101Q8×C3⋊D3—24no—
102Q8×C3⋊D3—24no—
103Q8×C3⋊D3—212no—
104#3830—212no—
105D4×C3⋊D3—212no—
106#3828—212no—
107#3828—212no—
108#3828—212no—
109C2×C4⋊(C3⋊D3)C2311yescharacteristic
110C2×C4⋊(C3⋊D3)C2313yes—
111C2×C4⋊(C3⋊D3)C2313yes—
112C2×C4×C3⋊D3—212no—
113C2×C4×C3⋊D3C2313yes—
114C2×C4×C3⋊D3C2313yes—
115C2×C4×C3⋊D3C2316yes—
116C2×C4×C3⋊D3C2313yes—
117C2×C4×C3⋊D3C2311yescharacteristic
118C2×C4×C3⋊D3C2316yes—
119C2×C4×C3⋊D3C2313yes—
120C2×#634C2313yes—
121C2×#634C2313yes—
122C2×#634C2313yes—
123C32×C4⋊C4C2313yes—
124C32×C4⋊C4C2313yes—
125C32×C22⋊C4C2316yes—
126C32×C22⋊C4C2313yes—
127C32×C22⋊C4C2311yescharacteristic
128C32×C42C2313yes—
129#3757C2316yes—
130#3757C2313yes—
131#3757C2313yes—
132#3752C2313yes—
133#3752C2313yes—
134#3752C2313yes—
135#3752C2313yes—
136#3752C2313yes—
137#3752C2311yescharacteristic
138C4⋊(C3⋊Dic3)C2313yes—
139C4⋊(C3⋊Dic3)C2316yes—
140C4⋊(C3⋊Dic3)C2313yes—
141#3750C2311yescharacteristic
142#3750C2313yes—
143#3750C2313yes—
144#3750C2316yes—
145#3750C2313yes—
146C4×C3⋊Dic3C2313yes—
147#3489—91noSylow
148C2×C3×#41C2×D314yes—
149C22×C3×Q8C2×D314yescomplemented
150D3×#41—632no—
151#1007—632no—
152C2×#239—34no—
153C2×#239—312no—
154C2×D3×Q8—312no—
155C2×D3×Q8—34no—
156C2×D3×Q8—34no—
157C2×#237—312no—
158C2×D3×D4—312no—
159C2×#235—312no—
160C2×#235—312no—
161C2×#235—312no—
162C22×C4×D3—312no—
163C3×#124C2×D3112yescomplemented
164C3×C22⋊Q8C2×D3112yescomplemented
165C3×#121C2×D3112yescomplemented
166C3×C4×Q8C2×D314yescomplemented
167C3×C4×D4C2×D3112yescomplemented
168#946—312no—
169Q8×Dic3—34no—
170#944—312no—
171#939—312no—
172#938—312no—
173#938—324no—
174#937—312no—
175#936—312no—
176C4×#67—312no—
177C4×#67—312no—
178#924—312no—
179#924—312no—
180#897—312no—
181#897—312no—
182#896—312no—
183#894—312no—
184#893—312no—
185D3×C4⋊C4—324no—
186D3×C4⋊C4—312no—
187#884—324no—
188#884—34no—
189#883—324no—
190#883—324no—
191#883—312no—
192#882—312no—
193D3×C22⋊C4—324no—
194#878—312no—
195#878—324no—
196C4×D12—312no—
197C4×D12—312no—
198#872—312no—
199#869—312no—
200C23×C32C2413yes—
201C23×C32C2411yescharacteristic
202C22×C3⋊D3—26no—
203C22×C3⋊D3—26no—
204C22×C3⋊D3—43no—
205C22×C3⋊D3C2411yescharacteristic
206C22×C3⋊D3C2413yes—
207C22×C3⋊D3C2411yescharacteristic
208C32×Q8—26no—
209C32×Q8C2×D414yes—
210C32×D4—26no—
211C32×D4—43no—
212C2×C32×C4—26no—
213C2×C32×C4—26no—
214C2×C32×C4C2413yes—
215C2×C32×C4C2411yescharacteristic
216C2×C32×C4C2411yescharacteristic
217C2×C32×C4C2413yes—
218C2×C32×C4C2413yes—
219#638—26no—
220#638—212no—
221#638—22no—
222#638—22no—
223#638—43no—
224C2×C3⋊Dic3—26no—
225C2×C3⋊Dic3C2411yescharacteristic
226C2×C3⋊Dic3C2413yes—
227C2×C3⋊Dic3C2413yes—
228C2×C3⋊Dic3C2413yes—
229C2×C3⋊Dic3C2411yescharacteristic
230C4⋊(C3⋊D3)—26no—
231C4⋊(C3⋊D3)—22no—
232C4⋊(C3⋊D3)C2×D4112yes—
233C4×C3⋊D3—26no—
234C4×C3⋊D3—212no—
235C4×C3⋊D3—26no—
236C4×C3⋊D3—26no—
237C4×C3⋊D3—22no—
238C4×C3⋊D3—46no—
239C4×C3⋊D3C2×D4112yes—
240#634—26no—
241#634—26no—
242#634—26no—
243C2×2−1+4—91no—
244C22×#41—91no—
245D4×Q8—91no—
246D4×Q8—91no—
247#548—91no—
248#548C3⋊D311yescharacteristic, complemented
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—
259C3×#41—216no—
260C2×C3×Q8—216no—
261C2×C3×Q8C22×D3112yes—
262C2×C3×Q8C22×D314yes—
263C2×C3×D4C22×D3112yes—
264C2×C3×D4C22×D3112yes—
265C22×C3×C4C22×D3112yes—
266C22×C3×C4C22×D3112yes—
267C2×#67—324no—
268C2×#67—312no—
269C2×#67—34no—
270C2×#67—34no—
271C2×#67—312no—
272C22×Dic3—312no—
273#239—332no—
274#239—648no—
275D3×Q8—648no—
276D3×Q8—616no—
277D3×Q8—616no—
278#237—648no—
279D3×D4—648no—
280#235—648no—
281#235—648no—
282#235—648no—
283C2×D12—312no—
284C2×D12—34no—
285C2×D12—312no—
286C2×C4×D3—312no—
287C2×C4×D3—312no—
288C2×C4×D3—312no—
289C2×C4×D3—324no—
290C2×C4×D3—312no—
291C2×C4×D3—34no—
292C2×C4×D3—324no—
293C2×C4×D3—648no—
294C2×Dic6—312no—
295C2×Dic6—312no—
296C2×Dic6—312no—
297C3×C4⋊C4C22×D3112yes—
298C3×C4⋊C4C22×D3112yes—
299C3×C22⋊C4C22×D3124yes—
300C3×C22⋊C4C22×D3112yes—
301C3×C22⋊C4C22×D314yes—
302C3×C42C22×D3112yes—
303#217—324no—
304#217—312no—
305#217—312no—
306(C2×D3)⋊C4—312no—
307(C2×D3)⋊C4—312no—
308(C2×D3)⋊C4—312no—
309(C2×D3)⋊C4—312no—
310(C2×D3)⋊C4—312no—
311(C2×D3)⋊C4—34no—
312C4⋊Dic3—312no—
313C4⋊Dic3—324no—
314C4⋊Dic3—312no—
315Dic3⋊C4—34no—
316Dic3⋊C4—312no—
317Dic3⋊C4—312no—
318Dic3⋊C4—324no—
319Dic3⋊C4—312no—
320C4×Dic3—312no—
321C22×C32—23no—
322C22×C32—21no—
323C22×C32—21no—
324C22×C32—23no—
325C22×C32—23no—
326C22×C32—21no—
327C22×C32C2511yescharacteristic
328C2×C3⋊D3—21no—
329C2×C3⋊D3—23no—
330C2×C3⋊D3—23no—
331C2×C3⋊D3—21no—
332C2×C3⋊D3—21no—
333C2×C3⋊D3—21no—
334C2×C3⋊D3—21no—
335C2×C3⋊D3—412no—
336C2×C3⋊D3C22×D416yes—
337C2×C3⋊D32−1+412yescomplemented
338C32×C4—23no—
339C32×C4—21no—
340C32×C4—21no—
341C32×C4—23no—
342C32×C4C22×D416yes—
343C3⋊Dic3—23no—
344C3⋊Dic3—23no—
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—93no—
354C2×#41—93no—
355C2×#41—188no—
356C2×#41C2×C3⋊D311yescharacteristic
357C22×Q8—93no—
358C22×Q8—91no—
359C22×Q8—91no—
360C22×Q8C2×C3⋊D311yescharacteristic, complemented
361C22×D4—93no—
362C23×C4—93no—
363C4⋊Q8—93no—
364C4⋊Q8—93no—
365#124—93no—
366#124C2×C3⋊D313yescomplemented
367#123—93no—
368#123—93no—
369#123—96no—
370#123—96no—
371C22⋊Q8—93no—
372C22⋊Q8—93no—
373C22⋊Q8—93no—
374C22⋊Q8—93no—
375C22⋊Q8—93no—
376C22⋊Q8—93no—
377C22⋊Q8—96no—
378C22⋊Q8—93no—
379C22⋊Q8C2×C3⋊D313yescomplemented
380#121—93no—
381#121—96no—
382#121—93no—
383#121—91no—
384#121—96no—
385#121C2×C3⋊D313yescomplemented
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⋊D313yescomplemented
396#117—93no—
397C2×C4⋊C4—93no—
398C2×C4⋊C4—96no—
399C2×C22⋊C4—96no—
400C23×C3C23×D3112yes—
401C23×C3C23×D314yes—
402C22×D3—34no—
403C22×D3—312no—
404C22×D3—34no—
405C22×D3—624no—
406C22×D3—624no—
407C22×D3—1212no—
408C3×Q8—224no—
409C3×Q8D3×D4116yes—
410C3×D4—224no—
411C3×D4—412no—
412C2×C3×C4—224no—
413C2×C3×C4—224no—
414C2×C3×C4C23×D3112yes—
415C2×C3×C4C23×D314yes—
416C2×C3×C4C23×D314yes—
417C2×C3×C4C23×D3112yes—
418C2×C3×C4C23×D3112yes—
419#67—68no—
420#67—624no—
421#67—648no—
422#67—68no—
423#67—1212no—
424C2×Dic3—34no—
425C2×Dic3—34no—
426C2×Dic3—312no—
427C2×Dic3—312no—
428C2×Dic3—312no—
429C2×Dic3—624no—
430D12—348no—
431D12—68no—
432D12—624no—
433C4×D3—348no—
434C4×D3—68no—
435C4×D3—624no—
436C4×D3—648no—
437C4×D3—624no—
438C4×D3—624no—
439C4×D3—1224no—
440Dic6—624no—
441Dic6—624no—
442Dic6—624no—
443C2×C32—43no—
444C2×C32—41no—
445C2×C32C23×D411yescharacteristic
446C2×C32C2×2−1+411yescharacteristic
447C2×C32#58511yescharacteristic
448C3⋊D3—22no—
449C3⋊D3—26no—
450C3⋊D3—41no—
451C24—93no—
452#41—24no—
453#41—98no—
454#41—1812no—
455#41—1812no—
456#41—1812no—
457#41—1812no—
458#41—1812no—
459C2×Q8—24no—
460C2×Q8—93no—
461C2×Q8—93no—
462C2×Q8—93no—
463C2×Q8—1812no—
464C2×Q8—184no—
465C2×Q8—184no—
466C2×Q8C22×C3⋊D313yes—
467C2×Q8C22×C3⋊D311yescharacteristic
468C2×D4—91no—
469C2×D4—93no—
470C2×D4—91no—
471C2×D4—96no—
472C2×D4—93no—
473C2×D4—93no—
474C2×D4—91no—
475C2×D4—93no—
476C2×D4—1812no—
477C2×D4C22×C3⋊D313yes—
478C2×D4C22×C3⋊D313yes—
479C22×C4—93no—
480C22×C4—93no—
481C22×C4—96no—
482C22×C4—93no—
483C22×C4—93no—
484C22×C4—93no—
485C22×C4—91no—
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—96no—
494C4⋊C4—96no—
495C4⋊C4—91no—
496C4⋊C4—93no—
497C4⋊C4—93no—
498C4⋊C4C22×C3⋊D313yes—
499C4⋊C4C22×C3⋊D313yes—
500C22⋊C4—96no—
501C22⋊C4—93no—
502C22⋊C4—93no—
503C22⋊C4—93no—
504C22⋊C4—93no—
505C22⋊C4—93no—
506C22⋊C4—93no—
507C22⋊C4—91no—
508C22⋊C4—93no—
509C22⋊C4C22×C3⋊D316yes—
510C22⋊C4C22×C3⋊D311yescharacteristic
511C22⋊C4C22×C3⋊D313yes—
512C42—93no—
513C42C22×C3⋊D313yes—
514C22×C3—212no—
515C22×C3—24no—
516C22×C3—212no—
517C22×C3—24no—
518C22×C3—24no—
519C22×C3—212no—
520C22×C3C24×D314yes—
521C2×D3—324no—
522C2×D3—38no—
523C2×D3—64no—
524C2×D3—612no—
525C2×D3—64no—
526C2×D3—612no—
527C2×D3—64no—
528C2×D3—64no—
529C2×D3—64no—
530C2×D3—1248no—
531C3×C4—212no—
532C3×C4—24no—
533C3×C4—212no—
534C3×C4—24no—
535C3×C4C2×D3×D4124yes—
536Dic3—38no—
537Dic3—612no—
538Dic3—612no—
539Dic3—612no—
540Dic3—64no—
541C32#348911yescharacteristic, complemented, Sylow
542C23—91no—
543C23—93no—
544C23—91no—
545C23—186no—
546C23—186no—
547C23—363no—
548C23C23×C3⋊D313yes—
549C23C23×C3⋊D311yescharacteristic
550Q8—26no—
551Q8—186no—
552Q8—186no—
553Q8—186no—
554Q8D4×C3⋊D314yes—
555D4—26no—
556D4—43no—
557D4—912no—
558D4—186no—
559D4—182no—
560D4—182no—
561D4—1812no—
562D4—186no—
563D4—182no—
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—93no—
573C2×C4—182no—
574C2×C4—186no—
575C2×C4—1812no—
576C2×C4—186no—
577C2×C4—186no—
578C2×C4—186no—
579C2×C4—366no—
580C2×C4C23×C3⋊D311yescharacteristic
581C2×C4C23×C3⋊D313yes—
582C2×C4C23×C3⋊D313yes—
583C2×C4C23×C3⋊D311yescharacteristic
584C2×C4C23×C3⋊D313yes—
585C2×C3—412no—
586C2×C3—44no—
587C2×C3C22×D3×D414yes—
588C2×C3#596414yes—
589C2×C3D3×2−1+414yes—
590D3—68no—
591D3—624no—
592D3—124no—
593C22—21no—
594C22—23no—
595C22—21no—
596C22—23no—
597C22—21no—
598C22—23no—
599C22—96no—
600C22—92no—
601C22—181no—
602C22—183no—
603C22—181no—
604C22—183no—
605C22—181no—
606C22—181no—
607C22—181no—
608C22—3612no—
609C22C24×C3⋊D311yescharacteristic
610C4—21no—
611C4—23no—
612C4—23no—
613C4—21no—
614C4—92no—
615C4—183no—
616C4—183no—
617C4—183no—
618C4—181no—
619C4C2×D4×C3⋊D316yes—
620C3#8671414yescomplemented
621C2—43no—
622C2—41no—
623C2—182no—
624C2—186no—
625C2—361no—
626C2C22×D4×C3⋊D311yescharacteristic
627C2#1059675611yescharacteristic
628C2C3⋊D3×2−1+411yescharacteristic
subgroupG/H
center, FrattiniC22C24×C3⋊D3
commutator, socle, cosocleC22×C32C25
FittingC32×#548C2
hypercenter#548C3⋊D3
hypocenterC32#3489
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C2×#41×C3⋊D3C2semidirect
2. C2×#64364C2semidirect
3. C32×#548C2semidirect
4. #10596302C2semidirect
5. Q8×#638C2semidirect
6. #10596147C2semidirect
7. #10596146C2semidirect
8. #10596102C2semidirect
9. C3⋊D3×C22⋊Q8C2semidirect
10. #10596083C2semidirect
11. #10596079C2semidirect
12. Q8×C4⋊(C3⋊D3)C2semidirect
13. #10596045C2semidirect
14. #10596022C2semidirect
15. #10596018C2semidirect
18. C22×C32×Q8C22semidirect
22. C2×#3832C22semidirect
24. C2×Q8×C3⋊D3C22semidirect
25. C2×Q8×C3⋊D3C22semidirect
29. C2×#3828C22semidirect
30. C2×#3828C22semidirect
32. C32×#124C22semidirect
33. C32×C22⋊Q8C22semidirect
34. C32×#121C22semidirect
35. C32×C4×Q8C22semidirect
36. C32×C4×D4C22semidirect
38. Q8×C3⋊Dic3C22semidirect
39. #64153C22semidirect
40. #64148C22semidirect
41. #64147C22semidirect
42. #64147C22semidirect
44. #64145C22semidirect
46. C4×#638C22semidirect
47. #64133C22semidirect
48. #64133C22semidirect
50. #64106C22semidirect
52. #64103C22semidirect
53. #64102C22semidirect
54. C4⋊C4×C3⋊D3C22semidirect
55. C4⋊C4×C3⋊D3C22semidirect
57. #64093C22semidirect
58. #64092C22semidirect
59. #64092C22semidirect
60. #64092C22semidirect
63. #64087C22semidirect
64. #64087C22semidirect
66. C4×C4⋊(C3⋊D3)C22semidirect
67. #64081C22semidirect
68. #64078C22semidirect
71. C3×#548D3semidirect
100. #3832D4semidirect
149. C22×C3×Q8C2×D3semidirect
163. C3×#124C2×D3semidirect
164. C3×C22⋊Q8C2×D3semidirect
165. C3×#121C2×D3semidirect
166. C3×C4×Q8C2×D3semidirect
167. C3×C4×D4C2×D3semidirect
248. #548C3⋊D3semidirect
337. C2×C3⋊D32−1+4semidirect
360. C22×Q8C2×C3⋊D3semidirect
366. #124C2×C3⋊D3semidirect
379. C22⋊Q8C2×C3⋊D3semidirect
385. #121C2×C3⋊D3semidirect
389. C4×Q8C2×C3⋊D3semidirect
395. C4×D4C2×C3⋊D3semidirect
541. C32#3489semidirect
620. C3#86714semidirect

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×#643642
C32×#5482
#105963022
Q8×#6382
#105961472
#105961462
#105961022
C3⋊D3×C22⋊Q82
#105960832
#105960792
Q8×C4⋊(C3⋊D3)2
#105960452
#105960222
#105960182
#867143