Finite Group Databasebeta

← #11864360

Subgroups — #11864360

Order 1152.

1653 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64308C211yesmaximal, characteristic
2C22×#3755C211yesmaximal, characteristic, complemented
3C3×#5816C211yesmaximal, characteristic, complemented
4C2×C3×#942C211yesmaximal, characteristic, complemented
5#10591657C214yesmaximal, complemented
6#10591651C214yesmaximal, complemented
7#10591096C211yesmaximal, characteristic, complemented
8#10591083C211yesmaximal, characteristic, complemented
9#10591071C211yesmaximal, characteristic, complemented
10#83982—31nomaximal
11#83404—31nomaximal
12C22×C32×Q8C2211yescharacteristic, complemented
13C22×C4⋊(C3⋊D3)C2211yescharacteristic
14C2×C3×#235C2211yescharacteristic
15C2×C3×#235C2211yescharacteristic
16C2×#3811—22no—
17#64308—24no—
18#64308—24no—
19C2×D3×D12—21no—
20C2×D3×D12C2212yes—
21C2×#3799—21no—
22C2×#3799C2212yes—
23C2×#3755—24no—
24C2×#3755C2214yescomplemented
25C22×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
26C3×#947—21no—
27C3×#946C2214yescomplemented
28C3×#944—21no—
29C2×C3×#216C2212yescomplemented
30C3×#942—24no—
31C2×C3×#215C2212yescomplemented
32C3×#929—22no—
33C3×#926C2211yescharacteristic, complemented
34C2×C3×#208C2211yescharacteristic, complemented
35#63565C2212yescomplemented
36#63564C2214yescomplemented
37#63562C2212yescomplemented
38(C2×D3)⋊(C3⋊C8)C2214yescomplemented
39C2×#1009—31no—
40C2×#1009—31no—
41C2×C3×#137—31no—
42C3×#536—31no—
43#5816D311yescharacteristic, complemented
44C2×#942D311yescharacteristic, complemented
45C22×#215—31no—
46C22×#215—31no—
47C22×#215—61no—
48#5234—31no—
49#5233—31no—
50#5187—34no—
51#5169—34no—
52#5131—31no—
53#5129—31no—
54#5047—34no—
55#5046—34no—
56#5002—31no—
57#5001—31no—
58C23×C3⋊D3—21no—
59C22×D32—22no—
60C2×C32×Q8—21no—
61C2×C32×Q8—22no—
62C2×C32×Q8—22no—
63C2×C32×Q8C2312yes—
64C22×C32×C4—21no—
65C22×C32×C4C2311yescharacteristic
66C2×C4⋊(C3⋊D3)—21no—
67C2×C4⋊(C3⋊D3)—22no—
68C2×C4⋊(C3⋊D3)D414yes—
69C2×C4⋊(C3⋊D3)C2312yes—
70C2×C3×#67—21no—
71C2×C3×#67D412yes—
72C3×#235—22no—
73C3×#235—22no—
74C3×#235—22no—
75C3×#235D414yes—
76C2×C3×D12D411yescharacteristic
77C2×C3×D12C2311yescharacteristic
78C2×C3×C4×D3—21no—
79C2×C3×C4×D3C2312yes—
80C2×C3×Dic6D411yescharacteristic
81C2×C3×Dic6C2311yescharacteristic
82#3811—216no—
83C2×#626—22no—
84C2×#626—22no—
85C2×#624—22no—
86D3×D12—28no—
87D3×D12—24no—
88D3×D12—24no—
89#3799—28no—
90#3799—24no—
91#3799—24no—
92#3755—28no—
93C2×C3⋊(C3⋊C8)—22no—
94C2×C3⋊(C3⋊C8)C2312yes—
95C3×#217—21no—
96C3×#216—24no—
97C3×#215—24no—
98C3×(C2×D3)⋊C4—24no—
99C3×C4⋊Dic3C2312yes—
100C3×Dic3⋊C4—24no—
101C3×C4×Dic3—21no—
102C3×#208—22no—
103C2×C3×C3⋊C8C2312yes—
104#3009—91noSylow
105C2×C3×#41—31no—
106C2×C3×#41—31no—
107C22×C3×Q8—21no—
108C22×C3×Q8C2×D311yescharacteristic, complemented
109C22×C3×Q8C2×D311yescharacteristic, complemented
110#1009—64no—
111#1009—64no—
112#1009—64no—
113#1009—64no—
114C2×#239—32no—
115C2×#239—61no—
116C2×D3×D4—32no—
117C2×D3×D4—61no—
118C2×D3×D4—62no—
119C2×D3×D4—62no—
120C2×#235—32no—
121C2×#235—61no—
122C2×#235C2×D311yescharacteristic
123C2×#235C2×D311yescharacteristic
124C22×D12—31no—
125C22×D12—31no—
126C22×D12—32no—
127C22×D12—61no—
128C22×D12—61no—
129C3×#137—64no—
130C2×C3×Q16—32no—
131C2×C3×SD16—32no—
132C2×C3×M16—31no—
133C3×C4⋊Q8—61no—
134C3×#124—61no—
135C3×#123—62no—
136C3×C22⋊Q8—34no—
137C3×#117—31no—
138#947—21no—
139#946C2×D314yescomplemented
140#944—21no—
141C2×#216C2×D312yescomplemented
142#942—24no—
143C2×#215—34no—
144C2×#215—34no—
145C2×#215—64no—
146C2×#215—64no—
147C2×#215—64no—
148C2×#215—68no—
149C2×#215C2×D312yescomplemented
150#929—22no—
151#926C2×D311yescharacteristic, complemented
152C2×#208C2×D311yescharacteristic, complemented
153C22×C3⋊C8—31no—
154C22×C3⋊C8—31no—
155C22×C3⋊C8—61no—
156#835—32no—
157#832—32no—
158#830—34no—
159#821—34no—
160(C2×D3)⋊C8—34no—
161#810—32no—
162#809—32no—
163#809—34no—
164C23×C32C2×D411yescharacteristic
165C22×C3⋊D3—22no—
166C22×C3⋊D3—24no—
167C22×C3⋊D3—82no—
168C22×C3×D3—21no—
169C22×C3×D3C2×D412yes—
170C2×D32—28no—
171C2×D32—84no—
172C32×Q8—22no—
173C32×Q8—22no—
174C32×Q8—42no—
175C2×C32×C4—22no—
176C2×C32×C4—42no—
177C2×C32×C4C2×D412yes—
178C2×C32×C4C2×D411yescharacteristic
179C2×C32×C4C2×D412yes—
180C2×C32×C4C2411yescharacteristic
181C4⋊(C3⋊D3)—24no—
182C4⋊(C3⋊D3)—22no—
183C4⋊(C3⋊D3)C2×D414yes—
184C3×#67—24no—
185C3×#67—24no—
186C2×C3×Dic3—21no—
187C2×C3×Dic3—22no—
188C2×C3×Dic3C2×D412yes—
189C3×D12—22no—
190C3×D12—21no—
191C3×D12C2×D412yes—
192C3×C4×D3—24no—
193C3×C4×D3—22no—
194C3×C4×D3—22no—
195C3×Dic6—22no—
196C3×Dic6—21no—
197C3×Dic6C2×D412yes—
198#626—28no—
199#626—28no—
200#624—28no—
201C3⋊(C3⋊C8)—22no—
202C3×C3⋊C8—22no—
203C2×H(5,𝔽2)—91no—
204C2×#137—31no—
205C22×SD16—91no—
206#536—31no—
207#452—94no—
208#450—94no—
209#418—91no—
210#416—91no—
211#408—91no—
212C23×D3—62no—
213C23×D3—61no—
214C23×D3—61no—
215C23×D3—62no—
216C23×D3—121no—
217C3×#41—34no—
218C3×#41—62no—
219C3×#41—62no—
220C3×#41—62no—
221C2×C3×Q8—21no—
222C2×C3×Q8—21no—
223C2×C3×Q8—24no—
224C2×C3×Q8—22no—
225C2×C3×Q8—22no—
226C2×C3×Q8—22no—
227C2×C3×Q8—22no—
228C2×C3×Q8—22no—
229C2×C3×Q8—31no—
230C2×C3×Q8—31no—
231C2×C3×Q8—41no—
232C2×C3×Q8—42no—
233C2×C3×Q8C22×D312yes—
234C2×C3×Q8C22×D312yes—
235C2×C3×D4—32no—
236C2×C3×D4—31no—
237C2×C3×D4—31no—
238C2×C3×D4—61no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—32no—
243C22×C3×C4—41no—
244C22×C3×C4—61no—
245C22×C3×C4C22×D311yescharacteristic
246C22×C3×C4C22×D311yescharacteristic
247C2×#67—21no—
248C2×#67—62no—
249C2×#67—62no—
250C2×#67#6712yes—
251#239—64no—
252#239—64no—
253#239—68no—
254D3×D4—64no—
255D3×D4—64no—
256D3×D4—68no—
257D3×D4—616no—
258D3×D4—616no—
259#235—22no—
260#235—22no—
261#235—22no—
262#235—64no—
263#235—68no—
264#235—64no—
265#235#6714yes—
266C2×D12—34no—
267C2×D12—34no—
268C2×D12—32no—
269C2×D12—32no—
270C2×D12—64no—
271C2×D12—62no—
272C2×D12—64no—
273C2×D12—68no—
274C2×D12—62no—
275C2×D12—62no—
276C2×D12—61no—
277C2×D12—62no—
278C2×D12—61no—
279C2×D12—62no—
280C2×D12—64no—
281C2×D12—121no—
282C2×D12—122no—
283C2×D12#6711yescharacteristic
284C2×D12C22×D311yescharacteristic
285C2×C4×D3—21no—
286C2×C4×D3—62no—
287C2×C4×D3—62no—
288C2×C4×D3C22×D312yes—
289C2×Dic6#6711yescharacteristic
290C2×Dic6C22×D311yescharacteristic
291C3×Q16—64no—
292C3×SD16—64no—
293C3×M16—62no—
294C2×C3×C8—32no—
295C3×C4⋊C4—32no—
296C3×C4⋊C4—64no—
297C3×C22⋊C4—64no—
298C3×C22⋊C4—61no—
299C3×C42—61no—
300#217—21no—
301#216—24no—
302#215—24no—
303#215—68no—
304#215—68no—
305#215—616no—
306(C2×D3)⋊C4—24no—
307C4⋊Dic3C22×D312yes—
308Dic3⋊C4—24no—
309C4×Dic3—21no—
310#208—22no—
311C2×C3⋊C8—32no—
312C2×C3⋊C8—32no—
313C2×C3⋊C8—62no—
314C2×C3⋊C8—64no—
315C2×C3⋊C8—62no—
316C2×C3⋊C8—62no—
317C2×C3⋊C8C22×D312yes—
318C22×C32—22no—
319C22×C32#12012yes—
320C22×C32C22×D411yescharacteristic
321C2×C3⋊D3—24no—
322C2×C3⋊D3—44no—
323C2×C3⋊D3—84no—
324C2×C3×D3—22no—
325C2×C3×D3—22no—
326C2×C3×D3—24no—
327C2×C3×D3—42no—
328D32—88no—
329C32×C4—42no—
330C32×C4#12012yes—
331C32×C4C22×D411yescharacteristic
332C32×C4C22×D411yescharacteristic
333C3×Dic3—22no—
334C3×Dic3—22no—
335C3×Dic3—42no—
336H(5,𝔽2)—184no—
337H(5,𝔽2)—184no—
338C2×#41—31no—
339C2×#41—31no—
340C2×#41—92no—
341C2×#41—181no—
342C22×Q8D3211yescharacteristic, complemented
343C22×D4—92no—
344C22×D4—91no—
345C22×D4—181no—
346C22×D4—182no—
347#137—64no—
348C2×Q16—32no—
349C2×SD16—32no—
350C2×SD16—94no—
351C2×SD16—184no—
352C2×M16—31no—
353C22×C8—91no—
354C4⋊Q8—61no—
355#124—61no—
356#123—62no—
357C22⋊Q8—34no—
358#117—31no—
359#103—92no—
360#102—94no—
361#102—92no—
362C22⋊C8—94no—
363C23×C3—21no—
364C23×C3—32no—
365C23×C3—61no—
366C23×C3D3×D411yescharacteristic
367C23×C3C2×#6711yescharacteristic
368C22×D3—21no—
369C22×D3—68no—
370C22×D3—68no—
371C22×D3—62no—
372C22×D3—62no—
373C22×D3—64no—
374C22×D3—64no—
375C22×D3—122no—
376C22×D3—124no—
377C22×D3—244no—
378C22×D3—244no—
379C22×D3—242no—
380C22×D3—242no—
381C22×D3—244no—
382C22×D3C2×#6712yes—
383C3×Q8—24no—
384C3×Q8—22no—
385C3×Q8—22no—
386C3×Q8—22no—
387C3×Q8—22no—
388C3×Q8—32no—
389C3×Q8—42no—
390C3×Q8—44no—
391C3×Q8—42no—
392C3×Q8—42no—
393C3×Q8—62no—
394C3×Q8—61no—
395C3×D4—32no—
396C3×D4—64no—
397C3×D4—64no—
398C3×D4—62no—
399C3×D4—61no—
400C2×C3×C4—22no—
401C2×C3×C4—22no—
402C2×C3×C4—21no—
403C2×C3×C4—22no—
404C2×C3×C4—21no—
405C2×C3×C4—22no—
406C2×C3×C4—32no—
407C2×C3×C4—42no—
408C2×C3×C4—44no—
409C2×C3×C4—42no—
410C2×C3×C4—42no—
411C2×C3×C4—61no—
412C2×C3×C4—64no—
413C2×C3×C4—62no—
414C2×C3×C4—62no—
415C2×C3×C4—62no—
416C2×C3×C4D3×D411yescharacteristic
417C2×C3×C4D3×D412yes—
418C2×C3×C4D3×D412yes—
419C2×C3×C4D3×D412yes—
420C2×C3×C4C2×#6711yescharacteristic
421C2×C3×C4C2×#6712yes—
422C2×C3×C4C23×D311yescharacteristic
423C2×C3×C4C23×D311yescharacteristic
424#67—24no—
425#67—24no—
426#67—68no—
427#67—68no—
428C2×Dic3—21no—
429C2×Dic3—22no—
430C2×Dic3C2×#6712yes—
431D12—22no—
432D12—21no—
433D12—34no—
434D12—34no—
435D12—64no—
436D12—68no—
437D12—68no—
438D12—64no—
439D12—64no—
440D12—62no—
441D12—62no—
442D12—122no—
443D12—124no—
444D12C2×#6712yes—
445C4×D3—24no—
446C4×D3—22no—
447C4×D3—22no—
448C4×D3—68no—
449C4×D3—68no—
450Dic6—22no—
451Dic6—21no—
452Dic6C2×#6712yes—
453C3×C8—62no—
454C3⋊C8—22no—
455C3⋊C8—64no—
456C3⋊C8—62no—
457C3⋊C8—62no—
458C2×C32—22no—
459C2×C32C2×#12011yescharacteristic
460C2×C32#57712yes—
461C3⋊D3—44no—
462C3×D3—42no—
463C3×D3—42no—
464C24—182no—
465C24—181no—
466#41—34no—
467#41—62no—
468#41—62no—
469#41—62no—
470#41—184no—
471#41—184no—
472#41—188no—
473C2×Q8—21no—
474C2×Q8—22no—
475C2×Q8—22no—
476C2×Q8—31no—
477C2×Q8—31no—
478C2×Q8C2×D3212yes—
479C2×D4—32no—
480C2×D4—31no—
481C2×D4—31no—
482C2×D4—61no—
483C2×D4—92no—
484C2×D4—94no—
485C2×D4—182no—
486C2×D4—184no—
487C2×D4—184no—
488C2×D4—188no—
489C2×D4—182no—
490C2×D4—1816no—
491C2×D4—181no—
492C2×D4—182no—
493C22×C4—21no—
494C22×C4—32no—
495C22×C4—61no—
496C22×C4—182no—
497C22×C4C2×D3211yescharacteristic
498Q16—64no—
499SD16—64no—
500SD16—188no—
501M16—62no—
502C2×C8—32no—
503C2×C8—92no—
504C2×C8—182no—
505C4⋊C4—32no—
506C4⋊C4—64no—
507C22⋊C4—64no—
508C22⋊C4—61no—
509C42—61no—
510C22×C3—24no—
511C22×C3—22no—
512C22×C3—22no—
513C22×C3—21no—
514C22×C3—22no—
515C22×C3—64no—
516C22×C3—62no—
517C22×C3—62no—
518C22×C3—122no—
519C22×C3#93712yes—
520C22×C3#93712yes—
521C22×C3C2×D3×D411yescharacteristic
522C22×C3C22×#6711yescharacteristic
523C2×D3—22no—
524C2×D3—22no—
525C2×D3—24no—
526C2×D3—42no—
527C2×D3—64no—
528C2×D3—64no—
529C2×D3—124no—
530C2×D3—124no—
531C2×D3—124no—
532C2×D3—244no—
533C2×D3—248no—
534C2×D3—248no—
535C2×D3—244no—
536C2×D3—244no—
537C2×D3—248no—
538C3×C4—21no—
539C3×C4—21no—
540C3×C4—22no—
541C3×C4—44no—
542C3×C4—42no—
543C3×C4—42no—
544C3×C4—62no—
545C3×C4—62no—
546C3×C4—122no—
547C3×C4#93712yes—
548C3×C4#93712yes—
549C3×C4C2×D3×D411yescharacteristic
550C3×C4C2×D3×D411yescharacteristic
551C3×C4C2×D3×D411yescharacteristic
552C3×C4C22×#6711yescharacteristic
553Dic3—22no—
554Dic3—22no—
555Dic3—42no—
556C32#300911yescharacteristic, complemented, Sylow
557C23—32no—
558C23—61no—
559C23—188no—
560C23—182no—
561C23—184no—
562C23—722no—
563C23—724no—
564C23D3×#6711yescharacteristic
565Q8—22no—
566Q8—22no—
567Q8—32no—
568Q8—42no—
569Q8—61no—
570Q8—62no—
571D4—32no—
572D4—64no—
573D4—64no—
574D4—61no—
575D4—62no—
576D4—94no—
577D4—188no—
578D4—188no—
579D4—182no—
580D4—184no—
581C2×C4—22no—
582C2×C4—32no—
583C2×C4—42no—
584C2×C4—61no—
585C2×C4—62no—
586C2×C4—62no—
587C2×C4—64no—
588C2×C4—62no—
589C2×C4—188no—
590C2×C4D3×#6712yes—
591C2×C4D3×#6711yescharacteristic
592C2×C4#381112yes—
593C2×C4C22×D3211yescharacteristic
594C8—62no—
595C8—182no—
596C2×C3—24no—
597C2×C3—22no—
598C2×C3—22no—
599C2×C3—21no—
600C2×C3—22no—
601C2×C3—122no—
602C2×C3—122no—
603C2×C3#577812yes—
604C2×C3C2×#93711yescharacteristic
605C2×C3C2×#93711yescharacteristic
606C2×C3#583712yes—
607D3—42no—
608D3—42no—
609D3—124no—
610D3—124no—
611D3—244no—
612C22—22no—
613C22—62no—
614C22—62no—
615C22—64no—
616C22—122no—
617C22—184no—
618C22—364no—
619C22—724no—
620C22—728no—
621C22#6398312yes—
622C22C2×D3×#6711yescharacteristic
623C4—42no—
624C4—62no—
625C4—62no—
626C4—122no—
627C4#6398312yes—
628C4C2×D3×#6711yescharacteristic
629C4C2×#381111yescharacteristic
630C3—21no—
631C3#8340411yescharacteristic, complemented
632C3#8398211yescharacteristic, complemented
633C2—22no—
634C2—122no—
635C2—122no—
636C2—364no—
637C2#1059531912yes—
638C2C2×#6398311yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC22×C32C22×D4
prime radicalC2×#64308C2
hypercenterC22×Q8D32
hypocenterC32#3009
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. C22×#3755C2semidirect
3. C3×#5816C2semidirect
4. C2×C3×#942C2semidirect
5. #10591657C2semidirect
6. #10591651C2semidirect
7. #10591096C2semidirect
8. #10591083C2semidirect
9. #10591071C2semidirect
12. C22×C32×Q8C22semidirect
24. C2×#3755C22semidirect
25. C22×C3⋊(C3⋊C8)C22semidirect
27. C3×#946C22semidirect
29. C2×C3×#216C22semidirect
31. C2×C3×#215C22semidirect
33. C3×#926C22semidirect
34. C2×C3×#208C22semidirect
35. #63565C22semidirect
36. #63564C22semidirect
37. #63562C22semidirect
38. (C2×D3)⋊(C3⋊C8)C22semidirect
43. #5816D3semidirect
44. C2×#942D3semidirect
108. C22×C3×Q8C2×D3semidirect
109. C22×C3×Q8C2×D3semidirect
139. #946C2×D3semidirect
141. C2×#216C2×D3semidirect
149. C2×#215C2×D3semidirect
151. #926C2×D3semidirect
152. C2×#208C2×D3semidirect
342. C22×Q8D32semidirect
556. C32#3009semidirect
631. C3#83404semidirect
632. C3#83982semidirect

Maximal subgroups

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

subgroupindex
C2×#643082
C22×#37552
C3×#58162
C2×C3×#9422
#105916572
#105916512
#105910962
#105910832
#105910712
#839823
#834043