Finite Group Databasebeta

← #11904522

Subgroups — #11904522

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×#64367C211yesmaximal, characteristic, complemented
2C2×#41×C3⋊D3C211yesmaximal, characteristic, complemented
3C32×#550C211yesmaximal, characteristic, complemented
4#10596305C211yesmaximal, characteristic, complemented
5#10596302C211yesmaximal, characteristic, complemented
6#10596189C213yesmaximal, complemented
7#10596186C213yesmaximal, complemented
8#10596078C213yesmaximal, complemented
9#10596077C213yesmaximal, complemented
10#10596070C213yesmaximal, complemented
11#10596069C213yesmaximal, complemented
12#10596047C211yesmaximal, characteristic, complemented
13#10596043C211yesmaximal, characteristic, complemented
14#10596023C213yesmaximal, complemented
15#10596018C213yesmaximal, complemented
16#86783—34nomaximal
17C2×C32×#41C2211yescharacteristic
18C2×C32×#41C2211yescharacteristic, complemented
19#64367—28no—
20#41×C3⋊D3—28no—
21C2×#3832C2211yescharacteristic
22C2×Q8×C3⋊D3C2211yescharacteristic
23C2×Q8×C3⋊D3C2211yescharacteristic, complemented
24C2×#3830C2213yes—
25C2×#3830C2213yes—
26C2×#3830C2213yescomplemented
27C2×D4×C3⋊D3C2213yes—
28C2×#3828C2213yes—
29C2×#3828C2213yes—
30C22×C4×C3⋊D3C2213yes—
31C22×#634C2213yescomplemented
32C32×#127C2213yescomplemented
33C32×#121C2213yescomplemented
34C32×#121C2213yescomplemented
35C32×C4×Q8C2211yescharacteristic, complemented
36C32×C4×D4C2213yescomplemented
37Q8×C3⋊Dic3C2211yescharacteristic, complemented
38#64149C2213yescomplemented
39#64149C2216yescomplemented
40#64148C2216yescomplemented
41#64148C2216yescomplemented
42#64148C2213yescomplemented
43#64147C2213yescomplemented
44#64147C2213yescomplemented
45#64146C2213yes—
46#64146C2216yes—
47#64145C2213yescomplemented
48D4×C3⋊Dic3C2216yescomplemented
49#64139C2213yescomplemented
50C4×#638C2213yescomplemented
51C4×#638C2213yescomplemented
52#64133C2213yescomplemented
53#64106C2213yescomplemented
54#64105C2213yescomplemented
55#64104C2213yescomplemented
56#64103C2211yescharacteristic
57#64101C2213yes—
58#64096C2213yescomplemented
59#64094C2216yescomplemented
60#64093C2213yescomplemented
61#64092C2213yes—
62#64091C2213yes—
63#64090C2216yescomplemented
64#64087C2213yescomplemented
65#64084C2213yescomplemented
66C4×C4⋊(C3⋊D3)C2213yescomplemented
67#64081C2213yes—
68C4×#634C2213yescomplemented
69C2×#1010—34no—
70C2×D3×#41—34no—
71C3×#550D314yescomplemented
72#5834—34no—
73#5831—34no—
74#5718—312no—
75#5715—312no—
76#5607—312no—
77#5606—312no—
78#5599—312no—
79#5598—312no—
80#5576—34no—
81#5572—34no—
82#5552—312no—
83#5547—312no—
84C23×C3⋊D3C2313yes—
85C32×#41—24no—
86C32×#41—24no—
87C2×C32×Q8C2311yescharacteristic
88C2×C32×D4C2313yes—
89C2×C32×D4C2313yes—
90C2×C32×D4C2316yes—
91C2×C32×D4C2313yes—
92C22×C32×C4C2313yes—
93C22×C32×C4C2313yes—
94C2×#638C2313yes—
95C2×#638C2313yes—
96C2×#638C2316yes—
97C2×#638C2316yes—
98C2×#638C2313yes—
99C2×#638C2313yes—
100C22×C3⋊Dic3C2313yes—
101C22×C3⋊Dic3C2316yes—
102#3832—24no—
103Q8×C3⋊D3—24no—
104Q8×C3⋊D3D418yescomplemented
105#3830—212no—
106#3830—212no—
107#3830—212no—
108D4×C3⋊D3—212no—
109#3828—212no—
110#3828—212no—
111C2×C4⋊(C3⋊D3)C2313yes—
112C2×C4⋊(C3⋊D3)C2311yescharacteristic
113C2×C4⋊(C3⋊D3)C2313yes—
114C2×C4×C3⋊D3—212no—
115C2×C4×C3⋊D3C2313yes—
116C2×C4×C3⋊D3C2313yes—
117C2×C4×C3⋊D3C2313yes—
118C2×C4×C3⋊D3C2311yescharacteristic
119C2×C4×C3⋊D3C2313yes—
120C2×#634—212no—
121C2×#634C2313yes—
122C2×#634C2313yes—
123C2×#634C2313yes—
124C32×C4⋊C4C2313yes—
125C32×C4⋊C4C2311yescharacteristic
126C32×C22⋊C4C2313yes—
127C32×C22⋊C4C2313yes—
128C32×C42C2313yes—
129#3757C2313yes—
130#3757C2313yes—
131#3757C2316yes—
132#3752C2311yescharacteristic
133#3752C2313yes—
134#3752C2311yescharacteristic
135#3752C2313yes—
136#3752C2316yes—
137#3752C2313yes—
138#3752C2311yescharacteristic
139C4⋊(C3⋊Dic3)C2313yes—
140C4⋊(C3⋊Dic3)C2313yes—
141#3750C2313yes—
142#3750C2313yes—
143#3750C2311yescharacteristic
144#3750C2313yes—
145C4×C3⋊Dic3C2316yes—
146C4×C3⋊Dic3C2313yes—
147#3487—91noSylow
148C2×C3×#41C2×D314yes—
149C2×C3×#41C2×D314yescomplemented
150#1010—632no—
151D3×#41—632no—
152C2×#239—34no—
153C2×D3×Q8—34no—
154C2×D3×Q8—34no—
155C2×#237—312no—
156C2×#237—312no—
157C2×#237—312no—
158C2×D3×D4—312no—
159C2×#235—312no—
160C2×#235—312no—
161C22×C4×D3—312no—
162C22×Dic6—312no—
163C3×#127C2×D3112yescomplemented
164C3×#121C2×D3112yescomplemented
165C3×#121C2×D3112yescomplemented
166C3×C4×Q8C2×D314yescomplemented
167C3×C4×D4C2×D3112yescomplemented
168Q8×Dic3—34no—
169#940—312no—
170#940—324no—
171#939—324no—
172#939—324no—
173#939—312no—
174#938—312no—
175#938—312no—
176#937—312no—
177#937—324no—
178#936—312no—
179D4×Dic3—324no—
180#930—312no—
181C4×#67—312no—
182C4×#67—312no—
183#924—312no—
184#897—312no—
185#896—312no—
186#895—312no—
187#894—34no—
188#892—312no—
189#887—312no—
190#885—324no—
191#884—312no—
192#883—312no—
193#882—312no—
194#67⋊C4—324no—
195#878—312no—
196#875—312no—
197C4×D12—312no—
198#872—312no—
199C4×Dic6—312no—
200C23×C32C2413yes—
201C23×C32C2413yes—
202C22×C3⋊D3—26no—
203C22×C3⋊D3—43no—
204C22×C3⋊D3—43no—
205C22×C3⋊D3C2413yes—
206C22×C3⋊D3C2411yescharacteristic
207C22×C3⋊D3C2411yescharacteristic
208C32×Q8C2×D414yes—
209C32×D4—26no—
210C32×D4—26no—
211C32×D4—46no—
212C32×D4—43no—
213C2×C32×C4—26no—
214C2×C32×C4—26no—
215C2×C32×C4C2413yes—
216C2×C32×C4C2411yescharacteristic
217C2×C32×C4C2411yescharacteristic
218C2×C32×C4C2411yescharacteristic
219C2×C32×C4C2413yes—
220#638—26no—
221#638—212no—
222#638—26no—
223#638—43no—
224#638—43no—
225#638—46no—
226C2×C3⋊Dic3—212no—
227C2×C3⋊Dic3—26no—
228C2×C3⋊Dic3C2411yescharacteristic
229C2×C3⋊Dic3C2413yes—
230C2×C3⋊Dic3C2411yescharacteristic
231C2×C3⋊Dic3C2413yes—
232C2×C3⋊Dic3C2413yes—
233C4⋊(C3⋊D3)—22no—
234C4⋊(C3⋊D3)—26no—
235C4⋊(C3⋊D3)—43no—
236C4×C3⋊D3—22no—
237C4×C3⋊D3—26no—
238C4×C3⋊D3—26no—
239C4×C3⋊D3—26no—
240C4×C3⋊D3C2×D4112yes—
241#634—26no—
242#634—26no—
243#634C2×D4112yes—
244C2×2−1+4—91no—
245C22×#41—91no—
246#550—91no—
247#550—93no—
248#550—93no—
249#550C3⋊D311yescharacteristic, complemented
250#548—91no—
251#548—93no—
252#548—91no—
253#548—93no—
254#535—93no—
255#535—93no—
256#525—93no—
257#525—93no—
258#519—91no—
259C23×D3—312no—
260C3×#41—216no—
261C3×#41—216no—
262C2×C3×Q8C22×D314yes—
263C2×C3×D4C22×D3112yes—
264C2×C3×D4C22×D3112yes—
265C2×C3×D4C22×D3124yes—
266C2×C3×D4C22×D3112yes—
267C22×C3×C4C22×D3112yes—
268C22×C3×C4C22×D3112yes—
269C2×#67—312no—
270C2×#67—312no—
271C2×#67—324no—
272C2×#67—324no—
273C2×#67—312no—
274C2×#67—312no—
275C22×Dic3—312no—
276C22×Dic3—324no—
277#239—616no—
278D3×Q8—332no—
279D3×Q8—616no—
280#237—648no—
281#237—648no—
282#237—648no—
283D3×D4—648no—
284#235—648no—
285#235—648no—
286C2×D12—312no—
287C2×D12—34no—
288C2×D12—312no—
289C2×C4×D3—312no—
290C2×C4×D3—312no—
291C2×C4×D3—312no—
292C2×C4×D3—312no—
293C2×C4×D3—34no—
294C2×C4×D3—648no—
295C2×Dic6—312no—
296C2×Dic6—312no—
297C2×Dic6—312no—
298C2×Dic6—648no—
299C3×C4⋊C4C22×D3112yes—
300C3×C4⋊C4C22×D314yes—
301C3×C22⋊C4C22×D3112yes—
302C3×C22⋊C4C22×D3112yes—
303C3×C42C22×D3112yes—
304#217—312no—
305#217—312no—
306#217—324no—
307(C2×D3)⋊C4—34no—
308(C2×D3)⋊C4—312no—
309(C2×D3)⋊C4—34no—
310(C2×D3)⋊C4—312no—
311(C2×D3)⋊C4—324no—
312(C2×D3)⋊C4—312no—
313(C2×D3)⋊C4—34no—
314C4⋊Dic3—312no—
315C4⋊Dic3—312no—
316Dic3⋊C4—312no—
317Dic3⋊C4—312no—
318Dic3⋊C4—34no—
319Dic3⋊C4—312no—
320C4×Dic3—324no—
321C4×Dic3—312no—
322C22×C32—23no—
323C22×C32—23no—
324C22×C32—23no—
325C22×C32—23no—
326C22×C32—23no—
327C22×C32—23no—
328C22×C32C2511yescharacteristic
329C2×C3⋊D3—21no—
330C2×C3⋊D3—21no—
331C2×C3⋊D3—21no—
332C2×C3⋊D3—23no—
333C2×C3⋊D3—21no—
334C2×C3⋊D3—23no—
335C2×C3⋊D3—21no—
336C2×C3⋊D3—23no—
337C2×C3⋊D3—412no—
338C2×C3⋊D3C22×D412yes—
339C32×C4—21no—
340C32×C4—21no—
341C32×C4—23no—
342C32×C4—21no—
343C32×C4C22×D416yes—
344C3⋊Dic3—23no—
345C3⋊Dic3—21no—
346C3⋊Dic3—23no—
347C3⋊Dic3—21no—
348C3⋊Dic3C22×D416yes—
3492−1+4—188no—
350C2×#41—91no—
351C2×#41—93no—
352C2×#41—93no—
353C2×#41—93no—
354C2×#41—93no—
355C2×#41—93no—
356C2×#41—188no—
357C2×#41C2×C3⋊D311yescharacteristic
358C2×#41C2×C3⋊D311yescharacteristic, complemented
359C22×Q8—91no—
360C22×Q8—91no—
361C22×Q8—93no—
362C22×D4—93no—
363C23×C4—93no—
364#127—96no—
365#127—93no—
366#127C2×C3⋊D313yescomplemented
367#124—93no—
368#124—96no—
369#124—93no—
370#123—91no—
371#123—93no—
372C22⋊Q8—93no—
373C22⋊Q8—93no—
374C22⋊Q8—93no—
375C22⋊Q8—93no—
376#121—93no—
377#121—93no—
378#121—93no—
379#121—96no—
380#121—96no—
381#121—93no—
382#121—93no—
383#121—93no—
384#121C2×C3⋊D313yescomplemented
385#121C2×C3⋊D313yescomplemented
386#120—96no—
387#120—93no—
388#120—93no—
389C4×Q8—91no—
390C4×Q8—93no—
391C4×Q8—93no—
392C4×Q8C2×C3⋊D311yescharacteristic, complemented
393C4×D4—96no—
394C4×D4—93no—
395C4×D4—93no—
396C4×D4—96no—
397C4×D4—93no—
398C4×D4C2×C3⋊D313yescomplemented
399#117—93no—
400#117—93no—
401C23×C3C23×D3112yes—
402C23×C3C23×D3112yes—
403C22×D3—34no—
404C22×D3—312no—
405C22×D3—34no—
406C22×D3—624no—
407C22×D3—1212no—
408C22×D3—1212no—
409C3×Q8D3×D4116yes—
410C3×D4—224no—
411C3×D4—224no—
412C3×D4—412no—
413C3×D4—424no—
414C2×C3×C4—224no—
415C2×C3×C4—224no—
416C2×C3×C4C23×D3112yes—
417C2×C3×C4C23×D314yes—
418C2×C3×C4C23×D314yes—
419C2×C3×C4C23×D314yes—
420C2×C3×C4C23×D3112yes—
421#67—648no—
422#67—624no—
423#67—624no—
424#67—1212no—
425#67—1224no—
426#67—1212no—
427C2×Dic3—312no—
428C2×Dic3—34no—
429C2×Dic3—312no—
430C2×Dic3—34no—
431C2×Dic3—312no—
432C2×Dic3—648no—
433C2×Dic3—624no—
434D12—68no—
435D12—624no—
436D12—1212no—
437C4×D3—348no—
438C4×D3—624no—
439C4×D3—68no—
440C4×D3—624no—
441C4×D3—624no—
442Dic6—348no—
443Dic6—624no—
444Dic6—624no—
445C2×C32—43no—
446C2×C32—43no—
447C2×C32C23×D411yescharacteristic
448C2×C32#58511yescharacteristic
449C2×C32#58511yescharacteristic
450C3⋊D3—22no—
451C3⋊D3—41no—
452C3⋊D3—43no—
453C24—93no—
454#41—24no—
455#41—24no—
456#41—1812no—
457#41—1812no—
458#41—1812no—
459#41—1812no—
460#41—1812no—
461#41—184no—
462C2×Q8—98no—
463C2×Q8—93no—
464C2×Q8—93no—
465C2×Q8—93no—
466C2×Q8—1812no—
467C2×Q8—184no—
468C2×Q8C22×C3⋊D311yescharacteristic
469C2×D4—93no—
470C2×D4—96no—
471C2×D4—93no—
472C2×D4—93no—
473C2×D4—96no—
474C2×D4—93no—
475C2×D4—91no—
476C2×D4—93no—
477C2×D4—93no—
478C2×D4—1812no—
479C2×D4C22×C3⋊D313yes—
480C2×D4C22×C3⋊D313yes—
481C2×D4C22×C3⋊D316yes—
482C2×D4C22×C3⋊D313yes—
483C22×C4—93no—
484C22×C4—96no—
485C22×C4—93no—
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—93no—
497C4⋊C4—91no—
498C4⋊C4—93no—
499C4⋊C4C22×C3⋊D313yes—
500C4⋊C4C22×C3⋊D311yescharacteristic
501C22⋊C4—93no—
502C22⋊C4—96no—
503C22⋊C4—93no—
504C22⋊C4—93no—
505C22⋊C4—91no—
506C22⋊C4—91no—
507C22⋊C4—91no—
508C22⋊C4—93no—
509C22⋊C4—96no—
510C22⋊C4—93no—
511C22⋊C4C22×C3⋊D313yes—
512C22⋊C4C22×C3⋊D313yes—
513C42—96no—
514C42—93no—
515C42C22×C3⋊D313yes—
516C22×C3—212no—
517C22×C3—212no—
518C22×C3—212no—
519C22×C3—212no—
520C22×C3—212no—
521C22×C3—212no—
522C22×C3C24×D314yes—
523C2×D3—38no—
524C2×D3—64no—
525C2×D3—64no—
526C2×D3—64no—
527C2×D3—612no—
528C2×D3—64no—
529C2×D3—612no—
530C2×D3—64no—
531C2×D3—612no—
532C2×D3—1248no—
533C3×C4—24no—
534C3×C4—24no—
535C3×C4—24no—
536C3×C4—212no—
537C3×C4C2×D3×D4124yes—
538Dic3—324no—
539Dic3—612no—
540Dic3—64no—
541Dic3—612no—
542Dic3—64no—
543C32#348711yescharacteristic, complemented, Sylow
544C23—91no—
545C23—93no—
546C23—91no—
547C23—186no—
548C23—363no—
549C23—363no—
550C23C23×C3⋊D313yes—
551C23C23×C3⋊D313yes—
552Q8—912no—
553Q8—186no—
554Q8—186no—
555Q8D4×C3⋊D314yes—
556D4—26no—
557D4—26no—
558D4—43no—
559D4—46no—
560D4—182no—
561D4—1812no—
562D4—186no—
563D4—186no—
564D4—186no—
565D4—363no—
566D4—366no—
567D4—363no—
568D4—363no—
569C2×C4—26no—
570C2×C4—26no—
571C2×C4—93no—
572C2×C4—912no—
573C2×C4—93no—
574C2×C4—91no—
575C2×C4—93no—
576C2×C4—91no—
577C2×C4—186no—
578C2×C4—182no—
579C2×C4—186no—
580C2×C4—1812no—
581C2×C4—186no—
582C2×C4—186no—
583C2×C4C23×C3⋊D313yes—
584C2×C4C23×C3⋊D311yescharacteristic
585C2×C4C23×C3⋊D311yescharacteristic
586C2×C4C23×C3⋊D311yescharacteristic
587C2×C4C23×C3⋊D313yes—
588C2×C3—412no—
589C2×C3—412no—
590C2×C3C22×D3×D414yes—
591C2×C3#596414yes—
592C2×C3#596614yes—
593D3—68no—
594D3—1212no—
595D3—124no—
596C22—23no—
597C22—23no—
598C22—23no—
599C22—23no—
600C22—23no—
601C22—23no—
602C22—92no—
603C22—181no—
604C22—181no—
605C22—181no—
606C22—183no—
607C22—181no—
608C22—183no—
609C22—181no—
610C22—183no—
611C22—3612no—
612C22C24×C3⋊D311yescharacteristic
613C4—21no—
614C4—21no—
615C4—21no—
616C4—23no—
617C4—96no—
618C4—181no—
619C4—183no—
620C4—183no—
621C4—181no—
622C4C2×D4×C3⋊D316yes—
623C3#8678314yescomplemented
624C2—43no—
625C2—43no—
626C2—182no—
627C2—363no—
628C2—361no—
629C2C22×D4×C3⋊D311yescharacteristic
630C2#1059675611yescharacteristic
631C2#1059675811yescharacteristic
subgroupG/H
center, FrattiniC22C24×C3⋊D3
commutator, socle, cosocleC22×C32C25
FittingC32×#550C2
hypercenter#550C3⋊D3
hypocenterC32#3487
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #550

Complements

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

NH ≅ G/Ntype
1. C2×#64367C2semidirect
2. C2×#41×C3⋊D3C2semidirect
3. C32×#550C2semidirect
4. #10596305C2semidirect
5. #10596302C2semidirect
6. #10596189C2semidirect
7. #10596186C2semidirect
8. #10596078C2semidirect
9. #10596077C2semidirect
10. #10596070C2semidirect
11. #10596069C2semidirect
12. #10596047C2semidirect
13. #10596043C2semidirect
14. #10596023C2semidirect
15. #10596018C2semidirect
18. C2×C32×#41C22semidirect
23. C2×Q8×C3⋊D3C22semidirect
26. C2×#3830C22semidirect
31. C22×#634C22semidirect
32. C32×#127C22semidirect
33. C32×#121C22semidirect
34. C32×#121C22semidirect
35. C32×C4×Q8C22semidirect
36. C32×C4×D4C22semidirect
37. Q8×C3⋊Dic3C22semidirect
38. #64149C22semidirect
39. #64149C22semidirect
40. #64148C22semidirect
41. #64148C22semidirect
42. #64148C22semidirect
43. #64147C22semidirect
44. #64147C22semidirect
47. #64145C22semidirect
48. D4×C3⋊Dic3C22semidirect
49. #64139C22semidirect
50. C4×#638C22semidirect
51. C4×#638C22semidirect
52. #64133C22semidirect
53. #64106C22semidirect
54. #64105C22semidirect
55. #64104C22semidirect
58. #64096C22semidirect
59. #64094C22semidirect
60. #64093C22semidirect
63. #64090C22semidirect
64. #64087C22semidirect
65. #64084C22semidirect
66. C4×C4⋊(C3⋊D3)C22semidirect
68. C4×#634C22semidirect
71. C3×#550D3semidirect
104. Q8×C3⋊D3D4semidirect
149. C2×C3×#41C2×D3semidirect
163. C3×#127C2×D3semidirect
164. C3×#121C2×D3semidirect
165. C3×#121C2×D3semidirect
166. C3×C4×Q8C2×D3semidirect
167. C3×C4×D4C2×D3semidirect
249. #550C3⋊D3semidirect
358. C2×#41C2×C3⋊D3semidirect
366. #127C2×C3⋊D3semidirect
384. #121C2×C3⋊D3semidirect
385. #121C2×C3⋊D3semidirect
392. C4×Q8C2×C3⋊D3semidirect
398. C4×D4C2×C3⋊D3semidirect
543. C32#3487semidirect
623. C3#86783semidirect

Maximal subgroups

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

subgroupindex
C2×#643672
C2×#41×C3⋊D32
C32×#5502
#105963052
#105963022
#105961892
#105961862
#105960782
#105960772
#105960702
#105960692
#105960472
#105960432
#105960232
#105960182
#867833