Finite Group Databasebeta

← #11865809

Subgroups — #11865809

Order 1152.

1056 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×#239C211yesmaximal, characteristic, complemented
2C2×#63949C212yesmaximal, complemented
3#10593970C211yesmaximal, characteristic, complemented
4#10592726C211yesmaximal, characteristic, complemented
5C3×#5031C211yesmaximal, characteristic, complemented
6#10591607C212yesmaximal, complemented
7#10590610C212yesmaximal, complemented
8#10590534C212yesmaximal, complemented
9#10590363C211yesmaximal, characteristic, complemented
10#10590349C211yesmaximal, characteristic, complemented
11D3×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
12#82525—31nomaximal
13#80475—31nomaximal
14C2×C3×#239C2211yescharacteristic
15C2×#3799C2212yes—
16C32×C4×Q8C2211yescharacteristic
17C2×#3755C2212yes—
18#64083C2211yescharacteristic
19C3×Q8×Dic3C2211yescharacteristic
20C2×C3×#216C2212yes—
21C3×#893—21no—
22C3×#893C2211yescharacteristic
23C3×#892—21no—
24C3×#892C2211yescharacteristic
25C3×C4×D12—21no—
26C3×C4×D12C2211yescharacteristic
27C3×C42×D3—21no—
28C3×C42×D3C2211yescharacteristic
29C3×#869C2211yescharacteristic
30#63949—28no—
31#63909—21no—
32#63909—21no—
33#63894—21no—
34#63894—21no—
35#63864C2212yes—
36C2×#3715C2212yes—
37C2×#3714C2212yes—
38C2×D3×C3⋊C8C2212yes—
39#63636C2212yes—
40C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
41C3×#810C2212yes—
42C3×C4⋊(C3⋊C8)C2211yescharacteristic
43Dic3⋊(C3⋊C8)C2212yes—
44#63565C2212yes—
45#63564C2212yes—
46C3×C4×#41—31no—
47C2×#950—32no—
48C2×#919—32no—
49#5725—31no—
50C4×#239D311yescharacteristic, complemented
51#5477—31no—
52C3×#462—31no—
53#5185—32no—
54#5083—31no—
55#5031D311yescharacteristic, complemented
56#5028—32no—
57#5027—31no—
58#5027—31no—
59#5027—61no—
60#5019—31no—
61#5016—32no—
62#5015—31no—
63#5002—32no—
64C2×C4⋊(C3⋊C8)—31no—
65#4843—31no—
66D3×C4⋊C8—31no—
67#4819—32no—
68#4804—32no—
69C2×C32×Q8C2311yescharacteristic
70C2×C4⋊(C3⋊D3)—21no—
71C2×C4⋊(C3⋊D3)—21no—
72C2×C4⋊(C3⋊D3)C2312yes—
73C3×#239—22no—
74C3×#239D414yescomplemented
75C2×C3×D12—21no—
76C2×C3×D12C2311yescharacteristic
77C2×C3×C4×D3—21no—
78C2×C3×C4×D3—21no—
79C2×C3×C4×D3—21no—
80C2×C3×C4×D3D411yescharacteristic
81C2×C3×C4×D3D411yescharacteristic
82C2×C3×C4×D3C2311yescharacteristic
83C2×C3×Dic6C2312yes—
84C2×#626—22no—
85C2×#624—22no—
86#3799—24no—
87#3799—24no—
88C32×C4⋊C4—21no—
89C32×C4⋊C4C2311yescharacteristic
90C32×C42—21no—
91C32×C42C2311yescharacteristic
92#3755—24no—
93C2×C3⋊(C3⋊C8)C2312yes—
94C3×#216—24no—
95C3×(C2×D3)⋊C4—21no—
96C3×(C2×D3)⋊C4—21no—
97C3×(C2×D3)⋊C4—21no—
98C3×C4⋊Dic3—21no—
99C3×C4⋊Dic3—21no—
100C3×C4⋊Dic3—21no—
101C3×C4⋊Dic3C2311yescharacteristic
102C3×C4×Dic3—21no—
103C3×C4×Dic3—21no—
104C3×C4×Dic3D411yescharacteristic
105C3×C4×Dic3D411yescharacteristic
106C3×C4×Dic3C2311yescharacteristic
107C2×C3×C3⋊C8C2312yes—
108#3722—22no—
109#3722—22no—
110#3715—24no—
111#3714—24no—
112D3×C3⋊C8—24no—
113#3035—91noSylow
114C2×C3×#41—31no—
115C2×#239—32no—
116C2×#239C2×D311yescharacteristic
117C2×#235—32no—
118C2×C3×Q16—32no—
119C3×C4⋊Q8—31no—
120C3×C4×Q8—21no—
121C3×C4×Q8—31no—
122C3×C4×Q8C2×D311yescharacteristic
123C3×C4×Q8C2×D311yescharacteristic
124C3×C4×D4—31no—
125C3×C4×D4—31no—
126C3×C4×D4—61no—
127C3×C4×D4—61no—
128C3×#117—31no—
129C3×#117—61no—
130C2×C3×C42—31no—
131C2×C3×C42—61no—
132#950—68no—
133#947—32no—
134Q8×Dic3C2×D311yescharacteristic
135C2×#216C2×D312yes—
136C2×#215—32no—
137C2×#215—32no—
138C2×#215—32no—
139C2×#215—62no—
140C2×#214—32no—
141C2×#213—32no—
142#930—61no—
143#930—61no—
144C22×C3⋊C8—32no—
145#919—68no—
146C2×D24—32no—
147C2×D3×C8—32no—
148#895—61no—
149#895—61no—
150#893—21no—
151#893—61no—
152#893—61no—
153#893C2×D311yescharacteristic
154#892—21no—
155#892C2×D311yescharacteristic
156#875—32no—
157#874—31no—
158#874—31no—
159#874—61no—
160C4×D12—21no—
161C4×D12—61no—
162C4×D12—61no—
163C4×D12C2×D311yescharacteristic
164C42×D3—21no—
165C42×D3C2×D311yescharacteristic
166#869C2×D311yescharacteristic
167C3×C4⋊C8—31no—
168C3×#103—32no—
169#835—32no—
170#821—32no—
171Dic3⋊C8—32no—
172#810—32no—
173#810C2×D312yes—
174#809—32no—
175#809—32no—
176#809—32no—
177#809—62no—
178C4⋊(C3⋊C8)—31no—
179C4⋊(C3⋊C8)—31no—
180C4⋊(C3⋊C8)—32no—
181C4⋊(C3⋊C8)—61no—
182C4⋊(C3⋊C8)C2×D311yescharacteristic
183C22×C3⋊D3—22no—
184C22×C3×D3—21no—
185C22×C3×D3C2×D411yescharacteristic
186C32×Q8—21no—
187C32×Q8C2×D412yes—
188C2×C32×C4—21no—
189C2×C32×C4—21no—
190C2×C32×C4C2×D411yescharacteristic
191C2×C32×C4C2×D411yescharacteristic
192C2×C32×C4C2411yescharacteristic
193C4⋊(C3⋊D3)—22no—
194C4⋊(C3⋊D3)—22no—
195C4⋊(C3⋊D3)—42no—
196C4⋊(C3⋊D3)—42no—
197C2×C3×Dic3—22no—
198C2×C3×Dic3—21no—
199C2×C3×Dic3C2×D411yescharacteristic
200C2×C3×Dic3C2×D411yescharacteristic
201C2×C3×Dic3C2×D411yescharacteristic
202C3×D12—24no—
203C3×D12—21no—
204C3×D12C2×D412yes—
205C3×C4×D3—22no—
206C3×C4×D3—24no—
207C3×C4×D3—41no—
208C3×C4×D3—42no—
209C3×C4×D3—42no—
210C3×C4×D3C2×D412yes—
211C3×C4×D3#4112yes—
212C3×Dic6—22no—
213C3×Dic6—22no—
214#626—44no—
215#624—44no—
216C3⋊(C3⋊C8)—22no—
217C3×C3⋊C8—22no—
218C2×#135—92no—
219#532—91no—
220C4×#41—31no—
221#464—92no—
222#463—92no—
223#462—31no—
224#461—91no—
225#460—91no—
226#459—91no—
227C2×C4⋊C8—91no—
228#416—92no—
229C3×#41—34no—
230C3×#41—62no—
231C2×C3×Q8—21no—
232C2×C3×Q8—32no—
233C2×C3×Q8C22×D311yescharacteristic
234C2×C3×Q8C22×D311yescharacteristic
235C2×C3×D4—31no—
236C2×C3×D4—61no—
237C22×C3×C4—31no—
238C22×C3×C4—31no—
239C22×C3×C4—31no—
240C22×C3×C4—61no—
241C22×C3×C4—61no—
242C22×C3×C4—61no—
243C2×#67—62no—
244#239—22no—
245#239—64no—
246#239—64no—
247#239D1214yescomplemented
248#235—64no—
249#235—64no—
250C2×D12—21no—
251C2×D12—32no—
252C2×D12—32no—
253C2×D12—62no—
254C2×D12—62no—
255C2×D12—61no—
256C2×D12—61no—
257C2×D12—61no—
258C2×D12—61no—
259C2×D12—121no—
260C2×D12—121no—
261C2×D12C22×D311yescharacteristic
262C2×C4×D3—21no—
263C2×C4×D3—21no—
264C2×C4×D3—21no—
265C2×C4×D3—62no—
266C2×C4×D3—62no—
267C2×C4×D3#6711yescharacteristic
268C2×C4×D3#6711yescharacteristic
269C2×C4×D3C22×D311yescharacteristic
270C2×Dic6C22×D312yes—
271C3×Q16—64no—
272C2×C3×C8—32no—
273C3×C4⋊C4—21no—
274C3×C4⋊C4—21no—
275C3×C4⋊C4—21no—
276C3×C4⋊C4—31no—
277C3×C4⋊C4—41no—
278C3×C4⋊C4—61no—
279C3×C4⋊C4—61no—
280C3×C4⋊C4—61no—
281C3×C4⋊C4C22×D311yescharacteristic
282C3×C4⋊C4C22×D311yescharacteristic
283C3×C22⋊C4—61no—
284C3×C22⋊C4—61no—
285C3×C22⋊C4—61no—
286C3×C42—21no—
287C3×C42—21no—
288C3×C42—21no—
289C3×C42—31no—
290C3×C42—31no—
291C3×C42—31no—
292C3×C42—41no—
293C3×C42—61no—
294C3×C42—61no—
295C3×C42C22×D311yescharacteristic
296C3×C42C22×D311yescharacteristic
297#216—24no—
298#215—64no—
299#215—64no—
300#215—64no—
301#215—124no—
302#214—64no—
303#213—64no—
304(C2×D3)⋊C4—21no—
305(C2×D3)⋊C4—21no—
306(C2×D3)⋊C4—21no—
307(C2×D3)⋊C4—62no—
308(C2×D3)⋊C4—62no—
309(C2×D3)⋊C4—62no—
310(C2×D3)⋊C4—62no—
311C4⋊Dic3—21no—
312C4⋊Dic3—21no—
313C4⋊Dic3—21no—
314C4⋊Dic3C22×D311yescharacteristic
315C4×Dic3—21no—
316C4×Dic3—21no—
317C4×Dic3#6711yescharacteristic
318C4×Dic3#6711yescharacteristic
319C4×Dic3C22×D311yescharacteristic
320C2×C3⋊C8—32no—
321C2×C3⋊C8—32no—
322C2×C3⋊C8—62no—
323C2×C3⋊C8—64no—
324C2×C3⋊C8C22×D312yes—
325D24—64no—
326D3×C8—64no—
327C22×C32C22×D411yescharacteristic
328C2×C3⋊D3—42no—
329C2×C3⋊D3—42no—
330C2×C3⋊D3—42no—
331C2×C3×D3—21no—
332C2×C3×D3—21no—
333C2×C3×D3—22no—
334C2×C3×D3—41no—
335C2×C3×D3—41no—
336C2×C3×D3#12112yes—
337C32×C4—22no—
338C32×C4—21no—
339C32×C4—41no—
340C32×C4#13512yescomplemented
341C32×C4C22×D411yescharacteristic
342C32×C4C2×#4111yescharacteristic
343C3×Dic3—21no—
344C3×Dic3—21no—
345C3×Dic3—42no—
346C3×Dic3—41no—
347C3×Dic3#12112yes—
348C2×#41—31no—
349C2×#41—92no—
350#135—188no—
351C2×Q16—32no—
352C2×SD16—92no—
353C2×SD16—92no—
354C2×D8—92no—
355C22×C8—92no—
356C4⋊Q8—31no—
357#127—91no—
358#124—92no—
359#121—181no—
360#121—181no—
361C4×Q8—31no—
362C4×Q8D3211yescharacteristic
363C4×D4—31no—
364C4×D4—31no—
365C4×D4—61no—
366C4×D4—61no—
367C4×D4—181no—
368C4×D4—181no—
369#117—31no—
370#117—61no—
371C2×C42—31no—
372C2×C42—61no—
373C4⋊C8—31no—
374C4⋊C8—92no—
375C4⋊C8—91no—
376#103—32no—
377#103—92no—
378#102—92no—
379#102—92no—
380C23×C3—31no—
381C23×C3—61no—
382C22×D3—21no—
383C22×D3—62no—
384C22×D3—62no—
385C22×D3—122no—
386C22×D3C2×#6711yescharacteristic
387C3×Q8—21no—
388C3×Q8—21no—
389C3×Q8—22no—
390C3×Q8—41no—
391C3×Q8—62no—
392C3×Q8—62no—
393C3×Q8C2×D1212yes—
394C3×Q8D3×D412yes—
395C3×D4—32no—
396C3×D4—64no—
397C3×D4—61no—
398C2×C3×C4—21no—
399C2×C3×C4—21no—
400C2×C3×C4—21no—
401C2×C3×C4—21no—
402C2×C3×C4—21no—
403C2×C3×C4—21no—
404C2×C3×C4—21no—
405C2×C3×C4—31no—
406C2×C3×C4—32no—
407C2×C3×C4—32no—
408C2×C3×C4—31no—
409C2×C3×C4—31no—
410C2×C3×C4—41no—
411C2×C3×C4—41no—
412C2×C3×C4—64no—
413C2×C3×C4—62no—
414C2×C3×C4—61no—
415C2×C3×C4—62no—
416C2×C3×C4—121no—
417C2×C3×C4—122no—
418C2×C3×C4—122no—
419C2×C3×C4D3×D411yescharacteristic
420C2×C3×C4D3×D411yescharacteristic
421C2×C3×C4C2×#6711yescharacteristic
422C2×C3×C4C2×#6711yescharacteristic
423C2×C3×C4C23×D311yescharacteristic
424C2×C3×C4C23×D311yescharacteristic
425#67—124no—
426C2×Dic3—22no—
427C2×Dic3—21no—
428C2×Dic3C2×#6711yescharacteristic
429C2×Dic3C2×#6711yescharacteristic
430C2×Dic3C2×#6711yescharacteristic
431D12—24no—
432D12—21no—
433D12—62no—
434D12—62no—
435D12—62no—
436D12—62no—
437D12—122no—
438D12—122no—
439D12—122no—
440D12—122no—
441D12—124no—
442D12—122no—
443D12—122no—
444D12—242no—
445D12—242no—
446D12C2×D1212yes—
447C4×D3—22no—
448C4×D3—24no—
449C4×D3—41no—
450C4×D3—42no—
451C4×D3—42no—
452C4×D3—124no—
453C4×D3—124no—
454C4×D3C2×D1212yes—
455C4×D3#23512yes—
456Dic6—22no—
457Dic6—22no—
458C3×C8—62no—
459C3⋊C8—22no—
460C3⋊C8—62no—
461C3⋊C8—62no—
462C3⋊C8—122no—
463C2×C32C2×#12111yescharacteristic
464C2×C32C2×#13511yescharacteristic
465C2×C32#57511yescharacteristic
466C3⋊D3—82no—
467C3×D3—22no—
468C3×D3—42no—
469#41—34no—
470#41—62no—
471#41—184no—
472#41—184no—
473C2×Q8—32no—
474C2×Q8C2×D3211yescharacteristic
475C2×D4—31no—
476C2×D4—61no—
477C2×D4—92no—
478C2×D4—182no—
479C2×D4—181no—
480C2×D4—181no—
481C22×C4—31no—
482C22×C4—31no—
483C22×C4—31no—
484C22×C4—61no—
485C22×C4—61no—
486C22×C4—61no—
487C22×C4—182no—
488Q16—64no—
489SD16—184no—
490SD16—184no—
491D8—184no—
492C2×C8—32no—
493C2×C8—92no—
494C2×C8—184no—
495C4⋊C4—21no—
496C4⋊C4—31no—
497C4⋊C4—61no—
498C4⋊C4—61no—
499C4⋊C4—61no—
500C4⋊C4C2×D3211yescharacteristic
501C22⋊C4—61no—
502C22⋊C4—61no—
503C22⋊C4—61no—
504C22⋊C4—182no—
505C22⋊C4—182no—
506C42—21no—
507C42—31no—
508C42—31no—
509C42—31no—
510C42—61no—
511C42—61no—
512C42C2×D3211yescharacteristic
513C22×C3—21no—
514C22×C3—32no—
515C22×C3—61no—
516C22×C3—61no—
517C22×C3—62no—
518C22×C3—121no—
519C22×C3—121no—
520C22×C3C2×D3×D411yescharacteristic
521C22×C3C22×#6711yescharacteristic
522C2×D3—21no—
523C2×D3—21no—
524C2×D3—22no—
525C2×D3—41no—
526C2×D3—41no—
527C2×D3—122no—
528C2×D3—122no—
529C2×D3—122no—
530C2×D3—122no—
531C2×D3—122no—
532C2×D3—122no—
533C2×D3—242no—
534C2×D3—242no—
535C2×D3—242no—
536C2×D3#93012yes—
537C3×C4—21no—
538C3×C4—22no—
539C3×C4—21no—
540C3×C4—22no—
541C3×C4—21no—
542C3×C4—21no—
543C3×C4—22no—
544C3×C4—32no—
545C3×C4—41no—
546C3×C4—42no—
547C3×C4—41no—
548C3×C4—41no—
549C3×C4—61no—
550C3×C4—61no—
551C3×C4—81no—
552C3×C4—121no—
553C3×C4—122no—
554C3×C4#91912yescomplemented
555C3×C4#95012yescomplemented
556C3×C4C22×D1211yescharacteristic
557C3×C4C2×#23511yescharacteristic
558C3×C4C2×D3×D411yescharacteristic
559C3×C4D3×#4111yescharacteristic
560Dic3—21no—
561Dic3—21no—
562Dic3—41no—
563Dic3—42no—
564Dic3#93012yes—
565C32#303511yescharacteristic, complemented, Sylow
566C23—31no—
567C23—61no—
568C23—182no—
569Q8—21no—
570Q8—62no—
571Q8—62no—
572Q8D3×D1212yes—
573D4—32no—
574D4—64no—
575D4—61no—
576D4—182no—
577D4—182no—
578D4—362no—
579D4—364no—
580D4—362no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—31no—
584C2×C4—32no—
585C2×C4—32no—
586C2×C4—31no—
587C2×C4—31no—
588C2×C4—64no—
589C2×C4—62no—
590C2×C4—61no—
591C2×C4—62no—
592C2×C4—121no—
593C2×C4—122no—
594C2×C4—122no—
595C2×C4—364no—
596C2×C4D3×#6711yescharacteristic
597C2×C4D3×#6711yescharacteristic
598C2×C4C22×D3211yescharacteristic
599C8—62no—
600C8—182no—
601C2×C3—21no—
602C2×C3—21no—
603C2×C3—21no—
604C2×C3—62no—
605C2×C3—122no—
606C2×C3D3×#12111yescharacteristic
607C2×C3C2×#91911yescharacteristic
608C2×C3#577711yescharacteristic
609C2×C3C2×#93011yescharacteristic
610C2×C3C2×#95011yescharacteristic
611C2×C3#582211yescharacteristic
612D3—22no—
613D3—42no—
614D3—242no—
615D3—242no—
616D3—482no—
617C22—32no—
618C22—61no—
619C22—61no—
620C22—62no—
621C22—121no—
622C22—121no—
623C22—362no—
624C22—362no—
625C22—362no—
626C22C2×D3×#6711yescharacteristic
627C4—21no—
628C4—22no—
629C4—32no—
630C4—41no—
631C4—61no—
632C4—61no—
633C4—121no—
634C4—122no—
635C4#6394912yescomplemented
636C4C2×D3×D1211yescharacteristic
637C4D3×#23511yescharacteristic
638C3—21no—
639C3#8047511yescharacteristic, complemented
640C3#8252511yescharacteristic, complemented
641C2—62no—
642C2—122no—
643C2—722no—
644C2D3×#93011yescharacteristic
645C2C2×#6394911yescharacteristic
646C2#1059547011yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
hypercenterC4×Q8D32
hypocenterC32#3035
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C3×C4×#239C2semidirect
2. C2×#63949C2semidirect
3. #10593970C2semidirect
4. #10592726C2semidirect
5. C3×#5031C2semidirect
6. #10591607C2semidirect
7. #10590610C2semidirect
8. #10590534C2semidirect
9. #10590363C2semidirect
10. #10590349C2semidirect
11. D3×C4⋊(C3⋊C8)C2semidirect
50. C4×#239D3semidirect
55. #5031D3semidirect
74. C3×#239D4semidirect
247. #239D12semidirect
340. C32×C4#135semidirect
554. C3×C4#919semidirect
555. C3×C4#950semidirect
565. C32#3035semidirect
635. C4#63949semidirect
639. C3#80475semidirect
640. C3#82525semidirect

Maximal subgroups

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

subgroupindex
C3×C4×#2392
C2×#639492
#105939702
#105927262
C3×#50312
#105916072
#105906102
#105905342
#105903632
#105903492
D3×C4⋊(C3⋊C8)2
#825253
#804753