Finite Group Databasebeta

← #11904534

Subgroups — #11904534

Order 1152.

4608 conjugacy classes of subgroups.

The subgroup lattice has 633 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#10596305C211yesmaximal, characteristic, complemented
5#10596288C211yesmaximal, characteristic, complemented
6#10596148C213yesmaximal, complemented
7#10596145C213yesmaximal, complemented
8#10596104C213yesmaximal, complemented
9#10596098C213yesmaximal, complemented
10#10596078C213yesmaximal, complemented
11#10596070C213yesmaximal, complemented
12#10596048C211yesmaximal, characteristic, complemented
13#10596043C211yesmaximal, characteristic, complemented
14#10596024C213yesmaximal, complemented
15#10596018C213yesmaximal, complemented
16#86736—34nomaximal
17C2×C32×#41C2211yescharacteristic
18C22×C32×Q8C2211yescharacteristic, complemented
19#41×C3⋊D3—28no—
20#64364—28no—
21C2×#3832C2213yes—
22C2×#3832C2211yescharacteristic
23C2×#3832C2211yescharacteristic, complemented
24C2×Q8×C3⋊D3C2211yescharacteristic
25C2×Q8×C3⋊D3C2213yescomplemented
26C2×#3830C2213yes—
27C2×D4×C3⋊D3C2213yes—
28C2×#3828C2213yes—
29C2×#3828C2213yes—
30C2×#3828C2213yescomplemented
31C22×C4×C3⋊D3C2213yes—
32C32×#124C2213yescomplemented
33C32×C22⋊Q8C2213yescomplemented
34C32×#121C2213yescomplemented
35C32×C4×Q8C2211yescharacteristic, complemented
36C32×C4×D4C2213yescomplemented
37#64156C2213yescomplemented
38#64155C2213yescomplemented
39Q8×C3⋊Dic3C2211yescharacteristic, complemented
40#64149C2213yescomplemented
41#64149C2216yescomplemented
42#64148C2213yescomplemented
43#64147C2213yescomplemented
44#64146C2213yes—
45#64139C2213yescomplemented
46#64139C2213yescomplemented
47C4×#638C2213yescomplemented
48C4×#638C2213yescomplemented
49#64105C2213yescomplemented
50#64104C2213yescomplemented
51#64104C2213yescomplemented
52#64103C2213yes—
53#64102C2216yescomplemented
54#64101C2213yes—
55#64096C2213yescomplemented
56#64094C2216yescomplemented
57#64093C2216yescomplemented
58#64093C2216yescomplemented
59#64093C2213yescomplemented
60#64092C2211yescharacteristic
61#64091C2216yes—
62#64091C2213yes—
63#64090C2216yescomplemented
64#64087C2213yescomplemented
65#64083C2213yescomplemented
66C4×C4⋊(C3⋊D3)C2213yescomplemented
67#64081C2213yes—
68C4×#634C2213yescomplemented
69C2×D3×#41—34no—
70C2×#1007—34no—
71C3×#548D314yescomplemented
72#5834—34no—
73#5817—34no—
74#5677—312no—
75#5674—312no—
76#5633—312no—
77#5627—312no—
78#5607—312no—
79#5599—312no—
80#5577—34no—
81#5572—34no—
82#5553—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×#638C2311yescharacteristic
94C2×#638C2316yes—
95C2×#638C2313yes—
96C2×#638C2316yes—
97C2×#638C2313yes—
98C2×#638C2313yes—
99C22×C3⋊Dic3C2313yes—
100#3832—24no—
101#3832—24no—
102#3832—212no—
103Q8×C3⋊D3—212no—
104Q8×C3⋊D3D418yescomplemented
105#3830—212no—
106D4×C3⋊D3—212no—
107#3828—212no—
108#3828—212no—
109#3828—212no—
110C2×C4⋊(C3⋊D3)C2313yes—
111C2×C4⋊(C3⋊D3)C2313yes—
112C2×C4⋊(C3⋊D3)C2313yes—
113C2×C4⋊(C3⋊D3)C2313yes—
114C2×C4⋊(C3⋊D3)C2316yes—
115C2×C4×C3⋊D3—212no—
116C2×C4×C3⋊D3C2313yes—
117C2×C4×C3⋊D3C2313yes—
118C2×C4×C3⋊D3C2316yes—
119C2×C4×C3⋊D3C2311yescharacteristic
120C2×C4×C3⋊D3C2313yes—
121C2×C4×C3⋊D3C2313yes—
122C2×#634C2313yes—
123C2×#634C2313yes—
124C32×C4⋊C4C2313yes—
125C32×C4⋊C4C2313yes—
126C32×C22⋊C4C2313yes—
127C32×C22⋊C4C2316yes—
128C32×C22⋊C4C2311yescharacteristic
129C32×C42C2313yes—
130#3757C2313yes—
131#3757C2311yescharacteristic
132#3752C2311yescharacteristic
133#3752C2313yes—
134#3752C2313yes—
135#3752C2313yes—
136#3752C2313yes—
137#3752C2316yes—
138#3752C2313yes—
139C4⋊(C3⋊Dic3)C2313yes—
140C4⋊(C3⋊Dic3)C2311yescharacteristic
141#3750C2313yes—
142#3750C2313yes—
143#3750C2313yes—
144#3750C2311yescharacteristic
145C4×C3⋊Dic3C2316yes—
146C4×C3⋊Dic3C2313yes—
147#3487—91noSylow
148C2×C3×#41C2×D314yes—
149C22×C3×Q8C2×D314yescomplemented
150D3×#41—632no—
151#1007—632no—
152C2×#239—312no—
153C2×#239—34no—
154C2×#239—34no—
155C2×D3×Q8—34no—
156C2×D3×Q8—312no—
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#947—312no—
169#946—312no—
170Q8×Dic3—34no—
171#940—312no—
172#940—324no—
173#939—312no—
174#938—312no—
175#937—312no—
176#930—312no—
177#930—312no—
178C4×#67—312no—
179C4×#67—312no—
180#896—312no—
181#895—312no—
182#895—312no—
183#894—312no—
184#893—324no—
185#892—312no—
186#887—312no—
187#885—324no—
188#884—324no—
189#884—324no—
190#884—312no—
191#883—34no—
192#882—312no—
193#882—324no—
194#67⋊C4—324no—
195#878—312no—
196#874—312no—
197C4×D12—312no—
198#872—312no—
199C4×Dic6—312no—
200C23×C32C2413yes—
201C23×C32C2411yescharacteristic
202C22×C3⋊D3—26no—
203C22×C3⋊D3—43no—
204C22×C3⋊D3—43no—
205C22×C3⋊D3C2413yes—
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×C4C2413yes—
217C2×C32×C4C2411yescharacteristic
218C2×C32×C4C2413yes—
219#638—22no—
220#638—26no—
221#638—212no—
222#638—43no—
223#638—46no—
224#638—43no—
225C2×C3⋊Dic3—26no—
226C2×C3⋊Dic3C2411yescharacteristic
227C2×C3⋊Dic3C2413yes—
228C2×C3⋊Dic3C2411yescharacteristic
229C2×C3⋊Dic3C2411yescharacteristic
230C2×C3⋊Dic3C2413yes—
231C4⋊(C3⋊D3)—26no—
232C4⋊(C3⋊D3)—26no—
233C4⋊(C3⋊D3)—26no—
234C4⋊(C3⋊D3)—43no—
235C4⋊(C3⋊D3)—46no—
236C4×C3⋊D3—22no—
237C4×C3⋊D3—26no—
238C4×C3⋊D3—26no—
239C4×C3⋊D3—26no—
240C4×C3⋊D3—212no—
241C4×C3⋊D3C2×D4112yes—
242#634—26no—
243#634C2×D4112yes—
244C2×2−1+4—91no—
245C22×#41—91no—
246#550—91no—
247#550—93no—
248#550—91no—
249#550—93no—
250#548—91no—
251#548—93no—
252#548—93no—
253#548C3⋊D311yescharacteristic, complemented
254#535—93no—
255#535—93no—
256#525—93no—
257#525—93no—
258#519—91no—
259C23×D3—312no—
260C3×#41—216no—
261C2×C3×Q8—216no—
262C2×C3×Q8C22×D3112yes—
263C2×C3×Q8C22×D314yes—
264C2×C3×D4C22×D3112yes—
265C2×C3×D4C22×D3112yes—
266C22×C3×C4C22×D3112yes—
267C22×C3×C4C22×D3112yes—
268C2×#67—34no—
269C2×#67—324no—
270C2×#67—312no—
271C2×#67—324no—
272C2×#67—312no—
273C2×#67—312no—
274C22×Dic3—312no—
275#239—648no—
276#239—616no—
277#239—616no—
278D3×Q8—332no—
279D3×Q8—648no—
280#237—648no—
281D3×D4—648no—
282#235—648no—
283#235—648no—
284#235—648no—
285C2×D12—312no—
286C2×D12—312no—
287C2×D12—312no—
288C2×D12—312no—
289C2×D12—324no—
290C2×C4×D3—312no—
291C2×C4×D3—312no—
292C2×C4×D3—312no—
293C2×C4×D3—324no—
294C2×C4×D3—34no—
295C2×C4×D3—312no—
296C2×C4×D3—648no—
297C2×Dic6—312no—
298C2×Dic6—312no—
299C3×C4⋊C4C22×D3112yes—
300C3×C4⋊C4C22×D3112yes—
301C3×C22⋊C4C22×D3112yes—
302C3×C22⋊C4C22×D3124yes—
303C3×C22⋊C4C22×D314yes—
304C3×C42C22×D3112yes—
305#217—312no—
306#217—34no—
307(C2×D3)⋊C4—34no—
308(C2×D3)⋊C4—312no—
309(C2×D3)⋊C4—312no—
310(C2×D3)⋊C4—312no—
311(C2×D3)⋊C4—312no—
312(C2×D3)⋊C4—324no—
313(C2×D3)⋊C4—312no—
314C4⋊Dic3—312no—
315C4⋊Dic3—34no—
316Dic3⋊C4—312no—
317Dic3⋊C4—312no—
318Dic3⋊C4—312no—
319Dic3⋊C4—34no—
320C4×Dic3—324no—
321C4×Dic3—312no—
322C22×C32—23no—
323C22×C32—21no—
324C22×C32—21no—
325C22×C32—23no—
326C22×C32—23no—
327C22×C32—21no—
328C22×C32C2511yescharacteristic
329C2×C3⋊D3—21no—
330C2×C3⋊D3—21no—
331C2×C3⋊D3—23no—
332C2×C3⋊D3—23no—
333C2×C3⋊D3—23no—
334C2×C3⋊D3—23no—
335C2×C3⋊D3—23no—
336C2×C3⋊D3—23no—
337C2×C3⋊D3—412no—
338C2×C3⋊D3C22×D412yes—
339C32×C4—23no—
340C32×C4—21no—
341C32×C4—21no—
342C32×C4—23no—
343C32×C4C22×D416yes—
344C3⋊Dic3—21no—
345C3⋊Dic3—21no—
346C3⋊Dic3—21no—
347C3⋊Dic3—23no—
348C3⋊Dic3C22×D416yes—
3492−1+4—188no—
350C2×#41—93no—
351C2×#41—91no—
352C2×#41—91no—
353C2×#41—93no—
354C2×#41—93no—
355C2×#41—93no—
356C2×#41—93no—
357C2×#41—188no—
358C2×#41C2×C3⋊D311yescharacteristic
359C22×Q8—91no—
360C22×Q8—93no—
361C22×Q8C2×C3⋊D311yescharacteristic, complemented
362C22×D4—93no—
363C23×C4—93no—
364#127—96no—
365#127—93no—
366#127—93no—
367#124—93no—
368#124—96no—
369#124C2×C3⋊D313yescomplemented
370#123—93no—
371#123—91no—
372C22⋊Q8—93no—
373C22⋊Q8—93no—
374C22⋊Q8—93no—
375C22⋊Q8C2×C3⋊D313yescomplemented
376#121—93no—
377#121—93no—
378#121—93no—
379#121—93no—
380#121—93no—
381#121—93no—
382#121—93no—
383#121—96no—
384#121—96no—
385#121C2×C3⋊D313yescomplemented
386#120—93no—
387#120—96no—
388#120—93no—
389C4×Q8—91no—
390C4×Q8—93no—
391C4×Q8—93no—
392C4×Q8C2×C3⋊D311yescharacteristic, complemented
393C4×D4—93no—
394C4×D4—93no—
395C4×D4—96no—
396C4×D4—96no—
397C4×D4—93no—
398C4×D4C2×C3⋊D313yescomplemented
399#117—93no—
400#117—93no—
401C23×C3C23×D3112yes—
402C23×C3C23×D314yes—
403C22×D3—34no—
404C22×D3—312no—
405C22×D3—312no—
406C22×D3—624no—
407C22×D3—1212no—
408C22×D3—1212no—
409C3×Q8—224no—
410C3×Q8D3×D4116yes—
411C3×D4—224no—
412C3×D4—412no—
413C2×C3×C4—224no—
414C2×C3×C4—224no—
415C2×C3×C4C23×D3112yes—
416C2×C3×C4C23×D314yes—
417C2×C3×C4C23×D3112yes—
418C2×C3×C4C23×D314yes—
419C2×C3×C4C23×D3112yes—
420#67—624no—
421#67—648no—
422#67—68no—
423#67—1212no—
424#67—1224no—
425#67—1212no—
426C2×Dic3—312no—
427C2×Dic3—34no—
428C2×Dic3—312no—
429C2×Dic3—34no—
430C2×Dic3—34no—
431C2×Dic3—624no—
432D12—624no—
433D12—624no—
434D12—624no—
435D12—1224no—
436D12—1212no—
437C4×D3—348no—
438C4×D3—624no—
439C4×D3—648no—
440C4×D3—68no—
441C4×D3—624no—
442C4×D3—624no—
443Dic6—348no—
444Dic6—624no—
445C2×C32—43no—
446C2×C32—41no—
447C2×C32C23×D411yescharacteristic
448C2×C32#58511yescharacteristic
449C2×C32#58511yescharacteristic
450C3⋊D3—22no—
451C3⋊D3—43no—
452C3⋊D3—43no—
453C24—93no—
454#41—24no—
455#41—1812no—
456#41—1812no—
457#41—1812no—
458#41—1812no—
459#41—1812no—
460#41—184no—
461#41—184no—
462C2×Q8—24no—
463C2×Q8—98no—
464C2×Q8—93no—
465C2×Q8—93no—
466C2×Q8—1812no—
467C2×Q8C22×C3⋊D313yes—
468C2×Q8C22×C3⋊D311yescharacteristic
469C2×D4—91no—
470C2×D4—96no—
471C2×D4—93no—
472C2×D4—93no—
473C2×D4—93no—
474C2×D4—96no—
475C2×D4—93no—
476C2×D4—93no—
477C2×D4—93no—
478C2×D4—96no—
479C2×D4—93no—
480C2×D4—1812no—
481C2×D4C22×C3⋊D313yes—
482C2×D4C22×C3⋊D313yes—
483C22×C4—93no—
484C22×C4—93no—
485C22×C4—96no—
486C22×C4—93no—
487C22×C4—93no—
488C22×C4—93no—
489C22×C4—91no—
490C22×C4—1812no—
491C22×C4C22×C3⋊D313yes—
492C22×C4C22×C3⋊D313yes—
493C4⋊C4—93no—
494C4⋊C4—93no—
495C4⋊C4—93no—
496C4⋊C4—91no—
497C4⋊C4—93no—
498C4⋊C4—91no—
499C4⋊C4C22×C3⋊D313yes—
500C4⋊C4C22×C3⋊D313yes—
501C22⋊C4—91no—
502C22⋊C4—93no—
503C22⋊C4—93no—
504C22⋊C4—91no—
505C22⋊C4—93no—
506C22⋊C4—93no—
507C22⋊C4—93no—
508C22⋊C4—96no—
509C22⋊C4—93no—
510C22⋊C4C22×C3⋊D316yes—
511C22⋊C4C22×C3⋊D311yescharacteristic
512C22⋊C4C22×C3⋊D313yes—
513C42—96no—
514C42—93no—
515C42C22×C3⋊D313yes—
516C22×C3—212no—
517C22×C3—24no—
518C22×C3—212no—
519C22×C3—24no—
520C22×C3—24no—
521C22×C3—212no—
522C22×C3C24×D314yes—
523C2×D3—38no—
524C2×D3—64no—
525C2×D3—64no—
526C2×D3—612no—
527C2×D3—612no—
528C2×D3—612no—
529C2×D3—612no—
530C2×D3—612no—
531C2×D3—612no—
532C2×D3—1248no—
533C3×C4—212no—
534C3×C4—24no—
535C3×C4—212no—
536C3×C4—24no—
537C3×C4C2×D3×D4124yes—
538Dic3—324no—
539Dic3—64no—
540Dic3—64no—
541Dic3—64no—
542Dic3—612no—
543C32#348711yescharacteristic, complemented, Sylow
544C23—91no—
545C23—93no—
546C23—93no—
547C23—186no—
548C23—363no—
549C23—363no—
550C23C23×C3⋊D313yes—
551C23C23×C3⋊D311yescharacteristic
552Q8—26no—
553Q8—912no—
554Q8—186no—
555Q8D4×C3⋊D314yes—
556D4—26no—
557D4—43no—
558D4—186no—
559D4—1812no—
560D4—186no—
561D4—182no—
562D4—186no—
563D4—186no—
564D4—366no—
565D4—363no—
566D4—363no—
567D4—363no—
568D4—366no—
569C2×C4—26no—
570C2×C4—26no—
571C2×C4—93no—
572C2×C4—912no—
573C2×C4—91no—
574C2×C4—93no—
575C2×C4—91no—
576C2×C4—91no—
577C2×C4—186no—
578C2×C4—1812no—
579C2×C4—182no—
580C2×C4—186no—
581C2×C4—186no—
582C2×C4—186no—
583C2×C4C23×C3⋊D313yes—
584C2×C4C23×C3⋊D311yescharacteristic
585C2×C4C23×C3⋊D313yes—
586C2×C4C23×C3⋊D311yescharacteristic
587C2×C4C23×C3⋊D313yes—
588C2×C3—412no—
589C2×C3—44no—
590C2×C3C22×D3×D414yes—
591C2×C3#596414yes—
592C2×C3#596814yes—
593D3—68no—
594D3—1212no—
595D3—1212no—
596C22—21no—
597C22—23no—
598C22—21no—
599C22—23no—
600C22—21no—
601C22—23no—
602C22—92no—
603C22—181no—
604C22—181no—
605C22—183no—
606C22—183no—
607C22—183no—
608C22—183no—
609C22—183no—
610C22—183no—
611C22—3612no—
612C22C24×C3⋊D311yescharacteristic
613C4—21no—
614C4—23no—
615C4—23no—
616C4—21no—
617C4—96no—
618C4—181no—
619C4—181no—
620C4—181no—
621C4—183no—
622C4C2×D4×C3⋊D316yes—
623C3#8673614yescomplemented
624C2—43no—
625C2—41no—
626C2—182no—
627C2—363no—
628C2—363no—
629C2C22×D4×C3⋊D311yescharacteristic
630C2#1059675611yescharacteristic
631C2#1059676011yescharacteristic
subgroupG/H
center, FrattiniC22C24×C3⋊D3
commutator, socle, cosocleC22×C32C25
FittingC32×#548C2
hypercenter#548C3⋊D3
hypocenterC32#3487
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. #10596305C2semidirect
5. #10596288C2semidirect
6. #10596148C2semidirect
7. #10596145C2semidirect
8. #10596104C2semidirect
9. #10596098C2semidirect
10. #10596078C2semidirect
11. #10596070C2semidirect
12. #10596048C2semidirect
13. #10596043C2semidirect
14. #10596024C2semidirect
15. #10596018C2semidirect
18. C22×C32×Q8C22semidirect
23. C2×#3832C22semidirect
25. C2×Q8×C3⋊D3C22semidirect
30. C2×#3828C22semidirect
32. C32×#124C22semidirect
33. C32×C22⋊Q8C22semidirect
34. C32×#121C22semidirect
35. C32×C4×Q8C22semidirect
36. C32×C4×D4C22semidirect
37. #64156C22semidirect
38. #64155C22semidirect
39. Q8×C3⋊Dic3C22semidirect
40. #64149C22semidirect
41. #64149C22semidirect
42. #64148C22semidirect
43. #64147C22semidirect
45. #64139C22semidirect
46. #64139C22semidirect
47. C4×#638C22semidirect
48. C4×#638C22semidirect
49. #64105C22semidirect
50. #64104C22semidirect
51. #64104C22semidirect
53. #64102C22semidirect
55. #64096C22semidirect
56. #64094C22semidirect
57. #64093C22semidirect
58. #64093C22semidirect
59. #64093C22semidirect
63. #64090C22semidirect
64. #64087C22semidirect
65. #64083C22semidirect
66. C4×C4⋊(C3⋊D3)C22semidirect
68. C4×#634C22semidirect
71. C3×#548D3semidirect
104. Q8×C3⋊D3D4semidirect
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
253. #548C3⋊D3semidirect
361. C22×Q8C2×C3⋊D3semidirect
369. #124C2×C3⋊D3semidirect
375. C22⋊Q8C2×C3⋊D3semidirect
385. #121C2×C3⋊D3semidirect
392. C4×Q8C2×C3⋊D3semidirect
398. C4×D4C2×C3⋊D3semidirect
543. C32#3487semidirect
623. C3#86736semidirect

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
#105963052
#105962882
#105961482
#105961452
#105961042
#105960982
#105960782
#105960702
#105960482
#105960432
#105960242
#105960182
#867363