Finite Group Databasebeta

← #11902853

Subgroups — #11902853

Order 1152.

3436 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64319C212yesmaximal, complemented
2Q8×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
3C3×#5577C211yesmaximal, characteristic, complemented
4C3×C4×#239C211yesmaximal, characteristic, complemented
5#10595414C212yesmaximal, complemented
6#10594630C216yesmaximal, complemented
7#10594626C216yesmaximal, complemented
8#10594004C213yesmaximal, complemented
9C4×D3×D12C213yesmaximal, complemented
10#10593897C213yesmaximal, complemented
11#10593895C213yesmaximal, complemented
12#86766—31nomaximal
13#41×D12—31nomaximal
14C2×Q8×C3⋊D3C2212yescomplemented
15C2×C3×#239C2211yescharacteristic
16C2×C3×#239C2212yescomplemented
17#64319—216no—
18C2×#3802C2216yescomplemented
19C2×D3×D12C2213yes—
20C2×C4×D32C2216yescomplemented
21C2×#3795C2216yescomplemented
22C2×#3795C2216yescomplemented
23C32×C4×Q8C2211yescharacteristic, complemented
24#64106C2216yescomplemented
25C4×C4⋊(C3⋊D3)C2213yes—
26#64078C2213yescomplemented
27C3×Q8×Dic3C2211yescharacteristic, complemented
28C3×#895C2216yescomplemented
29C3×#893C2213yescomplemented
30C3×#892C2213yescomplemented
31C3×#874C2213yescomplemented
32C3×C4×D12C2213yescomplemented
33C3×C4×D12C2213yescomplemented
34C3×C42×D3C2213yescomplemented
35#63922C22112yescomplemented
36D3×(C2×D3)⋊C4C2216yescomplemented
37#63916C2216yescomplemented
38#63908C2216yescomplemented
39#63908C2216yescomplemented
40C4×#626C2216yescomplemented
41#63894C2211yescharacteristic
42Dic3×D12C2216yescomplemented
43Dic3×D12C2213yescomplemented
44#63891C22112yescomplemented
45D3×C4⋊Dic3C2213yescomplemented
46#63880C2216yescomplemented
47#63860C2216yescomplemented
48#63857C2216yescomplemented
49C2×D3×#41—32no—
50C2×D3×#41—32no—
51C3×#550—31no—
52C3×C4×#41—31no—
53#5831—32no—
54#5717—33no—
55#5716—33no—
56#5612—36no—
57#5606—36no—
58#5577D311yescharacteristic, complemented
59#5576—32no—
60Q8×D12—31no—
61Q8×D12—31no—
62Q8×D12—61no—
63C4×#239D311yescharacteristic, complemented
64#5555—33no—
65#5554—36no—
66#5551—33no—
67D4×D12—33no—
68C4×D3×D4—33no—
69#5524—36no—
70#5477—33no—
71C2×C4×D12—33no—
72C22×D32C2316yes—
73C2×C32×Q8C2311yescharacteristic
74Q8×C3⋊D3—28no—
75C2×C4⋊(C3⋊D3)C2311yescharacteristic
76C2×C4×C3⋊D3C2316yes—
77C2×#634C2316yes—
78C3×#239—28no—
79C3×#239D418yescomplemented
80C2×C3×D12C2316yes—
81C2×C3×D12C2313yes—
82C2×C3×D12C2316yes—
83C2×C3×D12C2313yes—
84C2×C3×C4×D3C2316yes—
85C2×C3×C4×D3C2313yes—
86C2×C3×C4×D3C2313yes—
87C2×C3×C4×D3C2313yes—
88C2×#626C2316yes—
89C2×#625C23112yes—
90C2×#624C2312yes—
91C2×D3×Dic3C2316yes—
92C2×D3×Dic3C2316yes—
93#3802—224no—
94D3×D12—212no—
95C4×D32—224no—
96#3795—224no—
97#3795—224no—
98C32×C4⋊C4C2313yes—
99C32×C42C2313yes—
100#3752C2316yes—
101C4⋊(C3⋊Dic3)C2313yes—
102C4⋊(C3⋊Dic3)C2316yes—
103C3×(C2×D3)⋊C4C2316yes—
104C3×(C2×D3)⋊C4C2316yes—
105C3×C4⋊Dic3C2313yes—
106C3×C4⋊Dic3C2311yescharacteristic
107C3×C4×Dic3C2313yes—
108C3×C4×Dic3C2313yes—
109C3×C4×Dic3C2311yescharacteristic
110Dic3⋊Dic3C2316yes—
111#3722C2312yes—
112(C2×D3)⋊Dic3C23112yes—
113(C2×D3)⋊Dic3C2316yes—
114D4×#41—91noSylow
115C2×C3×#41—31no—
116C2×C3×#41—32no—
117D3×#41—616no—
118D3×#41—616no—
119C2×#239C2×D311yescharacteristic
120C2×#239C2×D312yescomplemented
121C2×D3×Q8—32no—
122C2×D3×Q8—32no—
123C2×D3×Q8—62no—
124C2×#237—36no—
125C2×#237—36no—
126C2×D3×D4—36no—
127C2×D3×D4—36no—
128C2×D3×D4—33no—
129C2×#235—36no—
130C2×#235—36no—
131C22×D12—33no—
132C22×C4×D3—36no—
133C22×C4×D3—36no—
134C3×#127—33no—
135C3×#121—36no—
136C3×C4×Q8—21no—
137C3×C4×Q8—31no—
138C3×C4×Q8C2×D311yescharacteristic, complemented
139C3×C4×Q8C2×D311yescharacteristic, complemented
140C3×C4×D4—33no—
141C3×C4×D4—33no—
142C3×C4×D4—33no—
143C3×#117—33no—
144C2×C3×C42—33no—
145Q8×Dic3C2×D311yescharacteristic, complemented
146#938—36no—
147#938—36no—
148#938—36no—
149#937—312no—
150#936—36no—
151D4×Dic3—33no—
152D4×Dic3—36no—
153#930—36no—
154#930—36no—
155C4×#67—36no—
156C2×(C2×D3)⋊C4—36no—
157C2×C4⋊Dic3—33no—
158#924—36no—
159#897—36no—
160#897—36no—
161#897—36no—
162#897—66no—
163#895—36no—
164#895C2×D316yescomplemented
165#893—31no—
166#893C2×D313yescomplemented
167#892C2×D313yescomplemented
168D3×C4⋊C4—33no—
169#886—312no—
170#883—312no—
171#882—312no—
172#67⋊C4—36no—
173D3×C22⋊C4—36no—
174#875—36no—
175#874C2×D313yescomplemented
176C4×D12—33no—
177C4×D12—36no—
178C4×D12—36no—
179C4×D12—33no—
180C4×D12—33no—
181C4×D12—36no—
182C4×D12—31no—
183C4×D12—63no—
184C4×D12C2×D313yescomplemented
185C4×D12C2×D313yescomplemented
186C42×D3C2×D313yescomplemented
187#869—33no—
188#869—33no—
189#869—63no—
190C22×C3⋊D3C2412yes—
191C22×C3×D3C2416yes—
192C22×C3×D3C2413yes—
193C2×D32—212no—
194C2×D32—212no—
195C2×D32—46no—
196C32×Q8C2×D414yescomplemented
197C2×C32×C4C2413yes—
198C2×C32×C4C2413yes—
199C2×C32×C4C2411yescharacteristic
200C2×C3⋊Dic3C2416yes—
201C4⋊(C3⋊D3)#4114yescomplemented
202C4×C3⋊D3—212no—
203#634—212no—
204C2×C3×Dic3C2411yescharacteristic
205C2×C3×Dic3C2413yes—
206C2×C3×Dic3C2412yes—
207C2×C3×Dic3C2411yescharacteristic
208C3×D12—212no—
209C3×D12—26no—
210C3×D12—46no—
211C3×D12C2×D4112yescomplemented
212C3×C4×D3—212no—
213C3×C4×D3—26no—
214C3×C4×D3—43no—
215C3×C4×D3C2×D4112yescomplemented
216#626—212no—
217#625—224no—
218#624—24no—
219D3×Dic3—212no—
220D3×Dic3—212no—
221C22×#41—92no—
222#550—31no—
223D4×Q8—91no—
224#548—92no—
225#547—93no—
226#546—96no—
227D42—93no—
228#532—93no—
229#525—96no—
230C4×#41—31no—
231C2×C4×D4—93no—
232C23×D3—36no—
233C23×D3—36no—
234C3×#41—38no—
235C3×#41—68no—
236C2×C3×Q8—21no—
237C2×C3×Q8C22×D311yescharacteristic
238C2×C3×Q8C22×D311yescharacteristic
239C2×C3×D4—33no—
240C2×C3×D4—33no—
241C2×C3×D4—36no—
242C2×C3×D4—36no—
243C22×C3×C4—33no—
244C22×C3×C4—36no—
245C22×C3×C4—33no—
246C22×C3×C4—33no—
247C2×#67—312no—
248C2×#67—312no—
249C2×#67—36no—
250C22×Dic3—36no—
251C22×Dic3—36no—
252#239—28no—
253#239D1218yescomplemented
254D3×Q8—68no—
255D3×Q8—68no—
256D3×Q8—128no—
257#237—624no—
258#237—624no—
259D3×D4—612no—
260D3×D4—624no—
261D3×D4—624no—
262#235—624no—
263#235—624no—
264C2×D12—31no—
265C2×D12—31no—
266C2×D12—36no—
267C2×D12—61no—
268C2×D12—612no—
269C2×D12C22×D313yes—
270C2×D12C22×D316yes—
271C2×D12C22×D316yes—
272C2×D12C22×D313yes—
273C2×C4×D3—36no—
274C2×C4×D3—36no—
275C2×C4×D3—36no—
276C2×C4×D3—36no—
277C2×C4×D3—32no—
278C2×C4×D3—32no—
279C2×C4×D3—66no—
280C2×C4×D3—624no—
281C2×C4×D3—624no—
282C2×C4×D3C22×D313yes—
283C2×C4×D3C22×D316yes—
284C2×C4×D3C22×D313yes—
285C2×C4×D3C22×D313yes—
286C2×Dic6—36no—
287C2×Dic6—36no—
288C2×Dic6—66no—
289C3×C4⋊C4—23no—
290C3×C4⋊C4—31no—
291C3×C4⋊C4—33no—
292C3×C4⋊C4C22×D313yes—
293C3×C4⋊C4C22×D313yes—
294C3×C22⋊C4—36no—
295C3×C22⋊C4—36no—
296C3×C42—23no—
297C3×C42—31no—
298C3×C42—33no—
299C3×C42—33no—
300C3×C42C22×D313yes—
301C3×C42C22×D313yes—
302#217—36no—
303#217—312no—
304(C2×D3)⋊C4—36no—
305(C2×D3)⋊C4—312no—
306(C2×D3)⋊C4—36no—
307(C2×D3)⋊C4—36no—
308(C2×D3)⋊C4—32no—
309(C2×D3)⋊C4—32no—
310(C2×D3)⋊C4—66no—
311(C2×D3)⋊C4C22×D316yes—
312(C2×D3)⋊C4C22×D316yes—
313C4⋊Dic3—33no—
314C4⋊Dic3—33no—
315C4⋊Dic3—36no—
316C4⋊Dic3—36no—
317C4⋊Dic3—36no—
318C4⋊Dic3—63no—
319C4⋊Dic3—66no—
320C4⋊Dic3C22×D311yescharacteristic
321C4⋊Dic3C22×D313yes—
322Dic3⋊C4—36no—
323C4×Dic3C22×D311yescharacteristic
324C4×Dic3C22×D313yes—
325C4×Dic3C22×D313yes—
326C22×C32C2511yescharacteristic
327C2×C3⋊D3—22no—
328C2×C3⋊D3—22no—
329C2×C3⋊D3C2×#4114yescomplemented
330C2×C3×D3—23no—
331C2×C3×D3—23no—
332C2×C3×D3—26no—
333C2×C3×D3—26no—
334C2×C3×D3—26no—
335C2×C3×D3C22×D416yes—
336D32—424no—
337C32×C4—23no—
338C32×C4C22×D416yes—
339C32×C4C2×#4112yescomplemented
340C3⋊Dic3—26no—
341C3×Dic3—22no—
342C3×Dic3—23no—
343C3×Dic3—21no—
344C3×Dic3C22×D412yes—
345C2×#41—31no—
346C2×#41—32no—
347C2×#41—96no—
348C2×#41—96no—
349C2×#41—1816no—
350C22×Q8—92no—
351C22×D4—93no—
352C22×D4—96no—
353C23×C4—96no—
354C4⋊Q8—93no—
355#127—33no—
356#124—96no—
357#123—912no—
358C22⋊Q8—96no—
359C22⋊Q8—96no—
360#121—36no—
361#121—96no—
362#121—96no—
363#121—96no—
364#120—912no—
365C4×Q8—31no—
366C4×Q8D3211yescharacteristic, complemented
367C4×D4—33no—
368C4×D4—33no—
369C4×D4—33no—
370C4×D4—96no—
371C4×D4—91no—
372C4×D4—96no—
373C4×D4—93no—
374C4×D4—96no—
375C4×D4—93no—
376#117—33no—
377C2×C4⋊C4—93no—
378C2×C22⋊C4—96no—
379C2×C42—33no—
380C23×C3—33no—
381C23×C3—36no—
382C22×D3—32no—
383C22×D3—32no—
384C22×D3—62no—
385C22×D3—612no—
386C22×D3—612no—
387C22×D3—612no—
388C22×D3—612no—
389C22×D3—126no—
390C22×D3—126no—
391C22×D3C23×D316yes—
392C22×D3C23×D313yes—
393C3×Q8—24no—
394C3×Q8C2×D1214yescomplemented
395C3×Q8D3×D414yescomplemented
396C3×D4—312no—
397C3×D4—612no—
398C3×D4—66no—
399C3×D4—126no—
400C2×C3×C4—21no—
401C2×C3×C4—23no—
402C2×C3×C4—23no—
403C2×C3×C4—31no—
404C2×C3×C4—312no—
405C2×C3×C4—32no—
406C2×C3×C4—33no—
407C2×C3×C4—31no—
408C2×C3×C4—612no—
409C2×C3×C4—66no—
410C2×C3×C4—123no—
411C2×C3×C4C23×D313yes—
412C2×C3×C4C23×D313yes—
413C2×C3×C4C23×D313yes—
414C2×C3×C4C23×D313yes—
415C2×C3×C4C23×D311yescharacteristic
416C2×C3×C4C23×D311yescharacteristic
417#67—612no—
418#67—624no—
419#67—624no—
420C2×Dic3—36no—
421C2×Dic3—36no—
422C2×Dic3—66no—
423C2×Dic3—612no—
424C2×Dic3—612no—
425C2×Dic3C23×D311yescharacteristic
426C2×Dic3C23×D313yes—
427C2×Dic3C23×D312yes—
428C2×Dic3C23×D311yescharacteristic
429D12—212no—
430D12—26no—
431D12—34no—
432D12—34no—
433D12—46no—
434D12—64no—
435D12—612no—
436D12C2×D12112yescomplemented
437C4×D3—212no—
438C4×D3—26no—
439C4×D3—43no—
440C4×D3—64no—
441C4×D3—612no—
442C4×D3—612no—
443C4×D3—612no—
444C4×D3—612no—
445C4×D3—64no—
446C4×D3—1212no—
447C4×D3C2×D12112yescomplemented
448Dic6—612no—
449Dic6—612no—
450Dic6—1212no—
451C2×C32C23×D411yescharacteristic
452C2×C32C22×#4111yescharacteristic
453C2×C32#58511yescharacteristic
454C3⋊D3—24no—
455C3×D3—26no—
456C3×D3—46no—
457C24—96no—
458#41—38no—
459#41—68no—
460#41—1824no—
461#41—1824no—
462C2×Q8—96no—
463C2×Q8—188no—
464C2×Q8C2×D3211yescharacteristic
465C2×D4—33no—
466C2×D4—33no—
467C2×D4—36no—
468C2×D4—36no—
469C2×D4—96no—
470C2×D4—912no—
471C2×D4—91no—
472C2×D4—1812no—
473C2×D4—1824no—
474C22×C4—33no—
475C22×C4—33no—
476C22×C4—36no—
477C22×C4—33no—
478C22×C4—92no—
479C22×C4—96no—
480C22×C4—96no—
481C22×C4—96no—
482C22×C4—1824no—
483C4⋊C4—31no—
484C4⋊C4—33no—
485C4⋊C4—96no—
486C4⋊C4—93no—
487C4⋊C4—96no—
488C4⋊C4C2×D3213yes—
489C22⋊C4—36no—
490C22⋊C4—36no—
491C22⋊C4—92no—
492C22⋊C4—96no—
493C22⋊C4—912no—
494C22⋊C4—96no—
495C42—31no—
496C42—33no—
497C42—33no—
498C42C2×D3213yes—
499C22×C3—21no—
500C22×C3—36no—
501C22×C3—63no—
502C22×C3—63no—
503C22×C3—66no—
504C22×C3—66no—
505C22×C3—66no—
506C22×C3C24×D311yescharacteristic
507C22×C3C24×D311yescharacteristic
508C2×D3—23no—
509C2×D3—23no—
510C2×D3—26no—
511C2×D3—26no—
512C2×D3—26no—
513C2×D3—34no—
514C2×D3—34no—
515C2×D3—64no—
516C2×D3—62no—
517C2×D3—62no—
518C2×D3—62no—
519C2×D3—62no—
520C2×D3—122no—
521C2×D3—122no—
522C2×D3—1224no—
523C2×D3—1224no—
524C2×D3C22×D1216yes—
525C3×C4—23no—
526C3×C4—23no—
527C3×C4—26no—
528C3×C4—22no—
529C3×C4—32no—
530C3×C4—43no—
531C3×C4—62no—
532C3×C4—63no—
533C3×C4—61no—
534C3×C4C22×D1216yes—
535C3×C4C2×D3×D416yes—
536C3×C4D3×#4112yescomplemented
537C3×C4D3×#4112yescomplemented
538Dic3—22no—
539Dic3—23no—
540Dic3—21no—
541Dic3—66no—
542Dic3—66no—
543Dic3—126no—
544Dic3C22×D1212yes—
545C32D4×#4111yescharacteristic, complemented, Sylow
546C23—33no—
547C23—36no—
548C23—92no—
549C23—1812no—
550C23—1812no—
551C23—366no—
552Q8—1812no—
553Q8D3×D1214yescomplemented
554D4—312no—
555D4—612no—
556D4—66no—
557D4—94no—
558D4—126no—
559D4—1812no—
560D4—1824no—
561C2×C4—31no—
562C2×C4—312no—
563C2×C4—31no—
564C2×C4—33no—
565C2×C4—32no—
566C2×C4—612no—
567C2×C4—66no—
568C2×C4—96no—
569C2×C4—123no—
570C2×C4—184no—
571C2×C4—1812no—
572C2×C4—1812no—
573C2×C4—1812no—
574C2×C4C22×D3213yes—
575C2×C4C22×D3213yes—
576C2×C4C22×D3211yescharacteristic
577C2×C3—21no—
578C2×C3—21no—
579C2×C3—21no—
580C2×C3—66no—
581C2×C3—126no—
582C2×C3C23×D1211yescharacteristic
583C2×C3C22×D3×D411yescharacteristic
584C2×C3C2×D3×#4111yescharacteristic
585C2×C3C2×D3×#4111yescharacteristic
586C2×C3#596411yescharacteristic
587C2×C3#596611yescharacteristic
588D3—26no—
589D3—46no—
590D3—64no—
591D3—64no—
592D3—124no—
593C22—36no—
594C22—63no—
595C22—63no—
596C22—66no—
597C22—66no—
598C22—66no—
599C22—94no—
600C22—182no—
601C22—182no—
602C22—3624no—
603C22C23×D3211yescharacteristic
604C4—23no—
605C4—32no—
606C4—62no—
607C4—63no—
608C4—61no—
609C4—186no—
610C4C2×D3×D1216yes—
611C4#6431912yescomplemented
612C3—21no—
613C3#41×D1211yescharacteristic, complemented
614C3#8676611yescharacteristic, complemented
615C2—66no—
616C2—126no—
617C2—184no—
618C2C22×D3×D1211yescharacteristic
619C2C2×#6431911yescharacteristic
620C2#1059669611yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×Q8C22
hypercenterC4×Q8D32
hypocenterC32D4×#41
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#64319C2semidirect
2. Q8×C4⋊(C3⋊D3)C2semidirect
3. C3×#5577C2semidirect
4. C3×C4×#239C2semidirect
5. #10595414C2semidirect
6. #10594630C2semidirect
7. #10594626C2semidirect
8. #10594004C2semidirect
9. C4×D3×D12C2semidirect
10. #10593897C2semidirect
11. #10593895C2semidirect
14. C2×Q8×C3⋊D3C22semidirect
16. C2×C3×#239C22semidirect
18. C2×#3802C22semidirect
20. C2×C4×D32C22semidirect
21. C2×#3795C22semidirect
22. C2×#3795C22semidirect
23. C32×C4×Q8C22semidirect
24. #64106C22semidirect
26. #64078C22semidirect
27. C3×Q8×Dic3C22semidirect
28. C3×#895C22semidirect
29. C3×#893C22semidirect
30. C3×#892C22semidirect
31. C3×#874C22semidirect
32. C3×C4×D12C22semidirect
33. C3×C4×D12C22semidirect
34. C3×C42×D3C22semidirect
35. #63922C22semidirect
36. D3×(C2×D3)⋊C4C22semidirect
37. #63916C22semidirect
38. #63908C22semidirect
39. #63908C22semidirect
40. C4×#626C22semidirect
42. Dic3×D12C22semidirect
43. Dic3×D12C22semidirect
44. #63891C22semidirect
45. D3×C4⋊Dic3C22semidirect
46. #63880C22semidirect
47. #63860C22semidirect
48. #63857C22semidirect
58. #5577D3semidirect
63. C4×#239D3semidirect
79. C3×#239D4semidirect
120. C2×#239C2×D3semidirect
138. C3×C4×Q8C2×D3semidirect
139. C3×C4×Q8C2×D3semidirect
145. Q8×Dic3C2×D3semidirect
164. #895C2×D3semidirect
166. #893C2×D3semidirect
167. #892C2×D3semidirect
175. #874C2×D3semidirect
184. C4×D12C2×D3semidirect
185. C4×D12C2×D3semidirect
186. C42×D3C2×D3semidirect
196. C32×Q8C2×D4semidirect
201. C4⋊(C3⋊D3)#41semidirect
211. C3×D12C2×D4semidirect
215. C3×C4×D3C2×D4semidirect
253. #239D12semidirect
329. C2×C3⋊D3C2×#41semidirect
339. C32×C4C2×#41semidirect
366. C4×Q8D32semidirect
394. C3×Q8C2×D12semidirect
395. C3×Q8D3×D4semidirect
436. D12C2×D12semidirect
447. C4×D3C2×D12semidirect
536. C3×C4D3×#41semidirect
537. C3×C4D3×#41semidirect
545. C32D4×#41semidirect
553. Q8D3×D12semidirect
611. C4#64319semidirect
613. C3#41×D12semidirect
614. C3#86766semidirect

Maximal subgroups

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

subgroupindex
C2×#643192
Q8×C4⋊(C3⋊D3)2
C3×#55772
C3×C4×#2392
#105954142
#105946302
#105946262
#105940042
C4×D3×D122
#105938972
#105938952
#867663
#41×D123