Finite Group Databasebeta

← #11904472

Subgroups — #11904472

Order 1152.

4476 conjugacy classes of subgroups.

The subgroup lattice has 627 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64364C211yesmaximal, characteristic, complemented
2C22×Q8×C3⋊D3C211yesmaximal, characteristic, complemented
3C32×D4×Q8C211yesmaximal, characteristic, complemented
4#10596288C211yesmaximal, characteristic, complemented
5Q8×#638C211yesmaximal, characteristic, complemented
6#10596198C213yesmaximal, complemented
7#10596195C213yesmaximal, complemented
8#10596104C213yesmaximal, complemented
9#10596103C213yesmaximal, complemented
10#10596099C213yesmaximal, complemented
11#10596098C213yesmaximal, complemented
12#10596047C211yesmaximal, characteristic, complemented
13#10596043C211yesmaximal, characteristic, complemented
14#10596023C213yesmaximal, complemented
15#10596018C213yesmaximal, complemented
16#86759—34nomaximal
17C22×C32×Q8C2211yescharacteristic
18C22×C32×Q8C2211yescharacteristic, complemented
19#64364—28no—
20C2×#3832C2213yes—
21C2×#3832C2211yescharacteristic, complemented
22C2×Q8×C3⋊D3—28no—
23C2×Q8×C3⋊D3C2213yes—
24C2×Q8×C3⋊D3C2213yes—
25C2×Q8×C3⋊D3C2211yescharacteristic
26C2×Q8×C3⋊D3C2211yescharacteristic
27C2×Q8×C3⋊D3C2213yescomplemented
28C2×#3828C2213yes—
29C2×#3828C2213yescomplemented
30C22×C4×C3⋊D3C2213yes—
31C22×#634C2213yes—
32C32×C4⋊Q8C2213yescomplemented
33C32×C22⋊Q8C2213yes—
34C32×C22⋊Q8C2213yescomplemented
35C32×C4×Q8C2211yescharacteristic, complemented
36C32×C4×D4C2213yes—
37#64156C2213yescomplemented
38#64155C2213yes—
39#64155C2213yescomplemented
40Q8×C3⋊Dic3C2211yescharacteristic, complemented
41#64153C2213yescomplemented
42#64148C2213yes—
43#64146C2211yescharacteristic
44#64139C2213yes—
45C4×#638C2213yes—
46C4×#638C2213yes—
47#64133C2213yescomplemented
48#64106C2213yescomplemented
49#64105C2213yes—
50#64105C2216yescomplemented
51#64105C2216yescomplemented
52#64104C2213yes—
53#64103C2216yes—
54#64103C2213yes—
55#64102C2216yes—
56#64101C2213yes—
57#64097C2216yescomplemented
58#64096C2213yescomplemented
59#64094C2216yescomplemented
60#64093C2213yes—
61#64092C2213yes—
62#64091C2213yes—
63#64090C2216yes—
64#64087C2213yes—
65#64084C2213yescomplemented
66C4×C4⋊(C3⋊D3)C2213yes—
67#64081C2213yes—
68C4×#634C2213yescomplemented
69C2×#1007—34no—
70C22×D3×Q8—34no—
71C3×D4×Q8D314yescomplemented
72#5817—34no—
73Q8×#67—34no—
74#5727—312no—
75#5724—312no—
76#5633—312no—
77#5632—312no—
78#5628—312no—
79#5627—312no—
80#5576—34no—
81#5572—34no—
82#5552—312no—
83#5547—312no—
84C23×C3⋊D3C2311yescharacteristic
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×#638C2313yes—
94C2×#638C2311yescharacteristic
95C2×#638C2311yescharacteristic
96C2×#638C2313yes—
97C22×C3⋊Dic3C2313yes—
98#3832—24no—
99#3832—212no—
100Q8×C3⋊D3—24no—
101Q8×C3⋊D3—212no—
102Q8×C3⋊D3—212no—
103Q8×C3⋊D3—212no—
104Q8×C3⋊D3D418yescomplemented
105#3828—212no—
106#3828—212no—
107C2×C4⋊(C3⋊D3)C2313yes—
108C2×C4⋊(C3⋊D3)C2313yes—
109C2×C4⋊(C3⋊D3)C2313yes—
110C2×C4×C3⋊D3—212no—
111C2×C4×C3⋊D3C2313yes—
112C2×C4×C3⋊D3C2313yes—
113C2×C4×C3⋊D3C2316yes—
114C2×C4×C3⋊D3C2313yes—
115C2×C4×C3⋊D3C2313yes—
116C2×C4×C3⋊D3C2313yes—
117C2×#634—212no—
118C2×#634C2313yes—
119C2×#634C2313yes—
120C2×#634C2316yes—
121C2×#634C2313yes—
122C32×C4⋊C4C2313yes—
123C32×C4⋊C4C2316yes—
124C32×C4⋊C4C2313yes—
125C32×C22⋊C4C2313yes—
126C32×C22⋊C4C2313yes—
127C32×C42C2313yes—
128#3757C2311yescharacteristic
129#3757C2313yes—
130#3752C2311yescharacteristic
131#3752C2313yes—
132#3752C2311yescharacteristic
133#3752C2313yes—
134#3752C2316yes—
135#3752C2313yes—
136#3752C2313yes—
137#3752C2316yes—
138C4⋊(C3⋊Dic3)C2313yes—
139C4⋊(C3⋊Dic3)C2313yes—
140#3750C2313yes—
141#3750C2313yes—
142#3750C2313yes—
143#3750C2316yes—
144#3750C2313yes—
145C4×C3⋊Dic3C2316yes—
146C4×C3⋊Dic3C2313yes—
147#3486—91noSylow
148C22×C3×Q8C2×D314yes—
149C22×C3×Q8C2×D314yescomplemented
150#1007—632no—
151C2×#239—312no—
152C2×#239—34no—
153C2×D3×Q8—34no—
154C2×D3×Q8—312no—
155C2×D3×Q8—312no—
156C2×D3×Q8—312no—
157C2×D3×Q8—34no—
158C2×D3×Q8—632no—
159C2×#235—312no—
160C2×#235—312no—
161C22×C4×D3—312no—
162C22×Dic6—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—312no—
174#937—34no—
175#930—312no—
176C4×#67—312no—
177C4×#67—312no—
178#924—312no—
179#897—312no—
180#896—324no—
181#896—324no—
182#896—312no—
183#895—312no—
184#894—312no—
185#894—324no—
186#893—324no—
187#892—312no—
188#888—324no—
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×C32C2411yescharacteristic
201C23×C32C2411yescharacteristic
202C22×C3⋊D3—22no—
203C22×C3⋊D3—22no—
204C22×C3⋊D3—22no—
205C22×C3⋊D3C2413yes—
206C22×C3⋊D3C2411yescharacteristic
207C22×C3⋊D3C2411yescharacteristic
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×C4C2411yescharacteristic
216C2×C32×C4C2413yes—
217C2×C32×C4C2413yes—
218C2×C32×C4C2413yes—
219#638—26no—
220#638—22no—
221#638—22no—
222#638—26no—
223C2×C3⋊Dic3—26no—
224C2×C3⋊Dic3C2411yescharacteristic
225C2×C3⋊Dic3C2413yes—
226C2×C3⋊Dic3C2411yescharacteristic
227C2×C3⋊Dic3C2413yes—
228C2×C3⋊Dic3C2413yes—
229C4⋊(C3⋊D3)—26no—
230C4⋊(C3⋊D3)—26no—
231C4⋊(C3⋊D3)—26no—
232C4×C3⋊D3—26no—
233C4×C3⋊D3—26no—
234C4×C3⋊D3—26no—
235C4×C3⋊D3—26no—
236C4×C3⋊D3—212no—
237C4×C3⋊D3C2×D4112yes—
238#634—26no—
239#634—212no—
240#634—26no—
241#634C2×D4112yes—
242C2×2−1+4—91no—
243C23×Q8—91no—
244D4×Q8—91no—
245D4×Q8—93no—
246D4×Q8—93no—
247D4×Q8C3⋊D311yescharacteristic, complemented
248#548—91no—
249#548—93no—
250#548—91no—
251#548—93no—
252#536—93no—
253#536—93no—
254#525—93no—
255#525—93no—
256#519—91no—
257C23×D3—34no—
258C2×C3×Q8—216no—
259C2×C3×Q8—216no—
260C2×C3×Q8C22×D3112yes—
261C2×C3×Q8C22×D3112yes—
262C2×C3×Q8C22×D314yes—
263C2×C3×D4C22×D314yes—
264C22×C3×C4C22×D3112yes—
265C22×C3×C4C22×D3112yes—
266C2×#67—312no—
267C2×#67—34no—
268C2×#67—34no—
269C2×#67—312no—
270C22×Dic3—312no—
271#239—648no—
272#239—616no—
273D3×Q8—332no—
274D3×Q8—648no—
275D3×Q8—648no—
276D3×Q8—648no—
277D3×Q8—616no—
278#235—648no—
279#235—648no—
280C2×D12—312no—
281C2×D12—312no—
282C2×D12—312no—
283C2×C4×D3—312no—
284C2×C4×D3—312no—
285C2×C4×D3—312no—
286C2×C4×D3—324no—
287C2×C4×D3—312no—
288C2×C4×D3—312no—
289C2×C4×D3—648no—
290C2×Dic6—312no—
291C2×Dic6—312no—
292C2×Dic6—312no—
293C2×Dic6—324no—
294C2×Dic6—648no—
295C3×C4⋊C4C22×D3112yes—
296C3×C4⋊C4C22×D3124yes—
297C3×C4⋊C4C22×D3112yes—
298C3×C22⋊C4C22×D3112yes—
299C3×C22⋊C4C22×D3112yes—
300C3×C42C22×D3112yes—
301#217—34no—
302#217—312no—
303(C2×D3)⋊C4—34no—
304(C2×D3)⋊C4—312no—
305(C2×D3)⋊C4—34no—
306(C2×D3)⋊C4—312no—
307(C2×D3)⋊C4—324no—
308(C2×D3)⋊C4—312no—
309(C2×D3)⋊C4—312no—
310(C2×D3)⋊C4—324no—
311C4⋊Dic3—312no—
312C4⋊Dic3—312no—
313Dic3⋊C4—312no—
314Dic3⋊C4—312no—
315Dic3⋊C4—312no—
316Dic3⋊C4—324no—
317Dic3⋊C4—312no—
318C4×Dic3—324no—
319C4×Dic3—312no—
320C22×C32—21no—
321C22×C32—21no—
322C22×C32—21no—
323C22×C32—21no—
324C22×C32—21no—
325C22×C322−1+412yescomplemented
326C22×C32C2511yescharacteristic
327C2×C3⋊D3—28no—
328C2×C3⋊D3—21no—
329C2×C3⋊D3—21no—
330C2×C3⋊D3—21no—
331C2×C3⋊D3—21no—
332C2×C3⋊D3—23no—
333C2×C3⋊D3—23no—
334C2×C3⋊D3—23no—
335C2×C3⋊D3C22×D412yes—
336C2×C3⋊D32−1+412yescomplemented
337C32×C4—23no—
338C32×C4—23no—
339C32×C4—23no—
340C32×C4—21no—
341C32×C4C22×D416yes—
342C3⋊Dic3—23no—
343C3⋊Dic3—21no—
344C3⋊Dic3—23no—
345C3⋊Dic3—21no—
346C3⋊Dic3C22×D416yes—
3472−1+4—188no—
348C2×#41—93no—
349C2×#41—91no—
350C2×#41—93no—
351C2×#41—93no—
352C22×Q8—91no—
353C22×Q8—93no—
354C22×Q8—93no—
355C22×Q8—91no—
356C22×Q8—93no—
357C22×Q8—93no—
358C22×Q8—188no—
359C22×Q8C2×C3⋊D311yescharacteristic
360C22×Q8C2×C3⋊D311yescharacteristic, complemented
361C23×C4—93no—
362C4⋊Q8—93no—
363C4⋊Q8—96no—
364C4⋊Q8C2×C3⋊D313yescomplemented
365#124—93no—
366#124—96no—
367#124—93no—
368#123—96no—
369#123—93no—
370#123—93no—
371C22⋊Q8—93no—
372C22⋊Q8—93no—
373C22⋊Q8—93no—
374C22⋊Q8—93no—
375C22⋊Q8—96no—
376C22⋊Q8—96no—
377C22⋊Q8—93no—
378C22⋊Q8—93no—
379C22⋊Q8C2×C3⋊D313yes—
380C22⋊Q8C2×C3⋊D313yescomplemented
381#121—93no—
382#121—93no—
383#121—93no—
384#121—93no—
385#120—91no—
386#120—93no—
387C4×Q8—91no—
388C4×Q8—93no—
389C4×Q8—93no—
390C4×Q8C2×C3⋊D311yescharacteristic, complemented
391C4×D4—93no—
392C4×D4—93no—
393C4×D4—96no—
394C4×D4—96no—
395C4×D4—93no—
396C4×D4C2×C3⋊D313yes—
397#117—93no—
398#117—93no—
399C23×C3C23×D314yes—
400C23×C3C23×D314yes—
401C22×D3—34no—
402C22×D3—34no—
403C22×D3—312no—
404C22×D3—68no—
405C22×D3—68no—
406C22×D3—68no—
407C3×Q8—224no—
408C3×Q8—224no—
409C3×Q8D3×D4116yes—
410C3×D4—28no—
411C2×C3×C4—224no—
412C2×C3×C4—224no—
413C2×C3×C4C23×D3112yes—
414C2×C3×C4C23×D314yes—
415C2×C3×C4C23×D3112yes—
416C2×C3×C4C23×D3112yes—
417C2×C3×C4C23×D3112yes—
418#67—624no—
419#67—68no—
420#67—68no—
421#67—624no—
422C2×Dic3—312no—
423C2×Dic3—34no—
424C2×Dic3—312no—
425C2×Dic3—34no—
426C2×Dic3—312no—
427C2×Dic3—624no—
428D12—624no—
429D12—624no—
430D12—624no—
431C4×D3—348no—
432C4×D3—624no—
433C4×D3—648no—
434C4×D3—624no—
435C4×D3—624no—
436C4×D3—624no—
437Dic6—348no—
438Dic6—648no—
439Dic6—624no—
440Dic6—624no—
441C2×C32—22no—
442C2×C32—41no—
443C2×C32C23×D411yescharacteristic
444C2×C32C2×2−1+411yescharacteristic
445C2×C32C2×2−1+411yescharacteristic
446C3⋊D3—22no—
447C3⋊D3—22no—
448C3⋊D3—43no—
449C24—91no—
450#41—1812no—
451#41—1812no—
452#41—1812no—
453#41—184no—
454C2×Q8—24no—
455C2×Q8—24no—
456C2×Q8—98no—
457C2×Q8—93no—
458C2×Q8—96no—
459C2×Q8—93no—
460C2×Q8—93no—
461C2×Q8—1812no—
462C2×Q8—1812no—
463C2×Q8—1812no—
464C2×Q8—1812no—
465C2×Q8—184no—
466C2×Q8C22×C3⋊D313yes—
467C2×Q8C22×C3⋊D313yes—
468C2×Q8C22×C3⋊D311yescharacteristic
469C2×D4—91no—
470C2×D4—93no—
471C2×D4—91no—
472C2×D4—93no—
473C2×D4—93no—
474C2×D4—93no—
475C2×D4—93no—
476C2×D4C22×C3⋊D311yescharacteristic
477C22×C4—93no—
478C22×C4—93no—
479C22×C4—93no—
480C22×C4—93no—
481C22×C4—96no—
482C22×C4—93no—
483C22×C4—93no—
484C22×C4—1812no—
485C22×C4C22×C3⋊D313yes—
486C22×C4C22×C3⋊D313yes—
487C4⋊C4—93no—
488C4⋊C4—93no—
489C4⋊C4—93no—
490C4⋊C4—93no—
491C4⋊C4—96no—
492C4⋊C4—93no—
493C4⋊C4—93no—
494C4⋊C4C22×C3⋊D313yes—
495C4⋊C4C22×C3⋊D316yes—
496C4⋊C4C22×C3⋊D313yes—
497C22⋊C4—91no—
498C22⋊C4—93no—
499C22⋊C4—93no—
500C22⋊C4—91no—
501C22⋊C4—93no—
502C22⋊C4—91no—
503C22⋊C4—93no—
504C22⋊C4—96no—
505C22⋊C4—96no—
506C22⋊C4—93no—
507C22⋊C4C22×C3⋊D313yes—
508C22⋊C4C22×C3⋊D313yes—
509C42—96no—
510C42—93no—
511C42C22×C3⋊D313yes—
512C22×C3—24no—
513C22×C3—24no—
514C22×C3—24no—
515C22×C3—24no—
516C22×C3—24no—
517C22×C3#100718yescomplemented
518C22×C3C24×D314yes—
519C2×D3—38no—
520C2×D3—38no—
521C2×D3—632no—
522C2×D3—64no—
523C2×D3—64no—
524C2×D3—64no—
525C2×D3—64no—
526C2×D3—612no—
527C2×D3—612no—
528C2×D3—612no—
529C3×C4—212no—
530C3×C4—212no—
531C3×C4—24no—
532C3×C4—212no—
533C3×C4C2×D3×D4124yes—
534Dic3—324no—
535Dic3—612no—
536Dic3—64no—
537Dic3—612no—
538Dic3—64no—
539C32#348611yescharacteristic, complemented, Sylow
540C23—91no—
541C23—91no—
542C23—93no—
543C23—182no—
544C23—182no—
545C23—182no—
546C23C23×C3⋊D311yescharacteristic
547C23C23×C3⋊D311yescharacteristic
548Q8—26no—
549Q8—26no—
550Q8—912no—
551Q8—1812no—
552Q8—186no—
553Q8—186no—
554Q8D4×C3⋊D314yes—
555D4—22no—
556D4—186no—
557D4—186no—
558D4—186no—
559D4—182no—
560D4—182no—
561D4—186no—
562D4—186no—
563C2×C4—26no—
564C2×C4—26no—
565C2×C4—93no—
566C2×C4—912no—
567C2×C4—93no—
568C2×C4—91no—
569C2×C4—93no—
570C2×C4—91no—
571C2×C4—186no—
572C2×C4—1812no—
573C2×C4—186no—
574C2×C4—186no—
575C2×C4—186no—
576C2×C4—186no—
577C2×C4C23×C3⋊D313yes—
578C2×C4C23×C3⋊D311yescharacteristic
579C2×C4C23×C3⋊D313yes—
580C2×C4C23×C3⋊D313yes—
581C2×C4C23×C3⋊D313yes—
582C2×C3—28no—
583C2×C3—44no—
584C2×C3C22×D3×D414yes—
585C2×C3C2×#100714yes—
586C2×C3D3×2−1+414yes—
587D3—68no—
588D3—68no—
589D3—1212no—
590C22—21no—
591C22—21no—
592C22—21no—
593C22—21no—
594C22—21no—
595C22—92no—
596C22—92no—
597C22—188no—
598C22—181no—
599C22—181no—
600C22—181no—
601C22—181no—
602C22—183no—
603C22—183no—
604C22—183no—
605C22#6436412yescomplemented
606C22C24×C3⋊D311yescharacteristic
607C4—23no—
608C4—23no—
609C4—21no—
610C4—23no—
611C4—96no—
612C4—181no—
613C4—183no—
614C4—183no—
615C4—181no—
616C4C2×D4×C3⋊D316yes—
617C3#8675914yescomplemented
618C2—22no—
619C2—41no—
620C2—182no—
621C2—182no—
622C2—363no—
623C2C22×D4×C3⋊D311yescharacteristic
624C2C2×#6436411yescharacteristic
625C2C3⋊D3×2−1+411yescharacteristic
subgroupG/H
center, FrattiniC22C24×C3⋊D3
commutator, socle, cosocleC22×C32C25
FittingC32×D4×Q8C2
hypercenterD4×Q8C3⋊D3
hypocenterC32#3486
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×Q8×C3⋊D3C2semidirect
3. C32×D4×Q8C2semidirect
4. #10596288C2semidirect
5. Q8×#638C2semidirect
6. #10596198C2semidirect
7. #10596195C2semidirect
8. #10596104C2semidirect
9. #10596103C2semidirect
10. #10596099C2semidirect
11. #10596098C2semidirect
12. #10596047C2semidirect
13. #10596043C2semidirect
14. #10596023C2semidirect
15. #10596018C2semidirect
18. C22×C32×Q8C22semidirect
21. C2×#3832C22semidirect
27. C2×Q8×C3⋊D3C22semidirect
29. C2×#3828C22semidirect
32. C32×C4⋊Q8C22semidirect
34. C32×C22⋊Q8C22semidirect
35. C32×C4×Q8C22semidirect
37. #64156C22semidirect
39. #64155C22semidirect
40. Q8×C3⋊Dic3C22semidirect
41. #64153C22semidirect
47. #64133C22semidirect
48. #64106C22semidirect
50. #64105C22semidirect
51. #64105C22semidirect
57. #64097C22semidirect
58. #64096C22semidirect
59. #64094C22semidirect
65. #64084C22semidirect
68. C4×#634C22semidirect
71. C3×D4×Q8D3semidirect
104. Q8×C3⋊D3D4semidirect
149. C22×C3×Q8C2×D3semidirect
163. C3×C4⋊Q8C2×D3semidirect
165. C3×C22⋊Q8C2×D3semidirect
166. C3×C4×Q8C2×D3semidirect
247. D4×Q8C3⋊D3semidirect
325. C22×C322−1+4semidirect
336. C2×C3⋊D32−1+4semidirect
360. C22×Q8C2×C3⋊D3semidirect
364. C4⋊Q8C2×C3⋊D3semidirect
380. C22⋊Q8C2×C3⋊D3semidirect
390. C4×Q8C2×C3⋊D3semidirect
517. C22×C3#1007semidirect
539. C32#3486semidirect
605. C22#64364semidirect
617. C3#86759semidirect

Maximal subgroups

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

subgroupindex
C2×#643642
C22×Q8×C3⋊D32
C32×D4×Q82
#105962882
Q8×#6382
#105961982
#105961952
#105961042
#105961032
#105960992
#105960982
#105960472
#105960432
#105960232
#105960182
#867593