Finite Group Databasebeta

← #11865760

Subgroups — #11865760

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×#5716C211yesmaximal, characteristic, complemented
2C2×#63933C212yesmaximal, complemented
3C4×#3795C211yesmaximal, characteristic, complemented
4#10592774C211yesmaximal, characteristic, complemented
5C3×#5072C211yesmaximal, characteristic, complemented
6#10591441C212yesmaximal, complemented
7#10591431C212yesmaximal, complemented
8#10591420C212yesmaximal, complemented
9#10590388C211yesmaximal, characteristic, complemented
10#10590363C211yesmaximal, characteristic, complemented
11D3×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
12#83296—31nomaximal
13#80331—31nomaximal
14C2×C3×#237C2212yes—
15C2×#3795C2211yescharacteristic
16C32×#127C2211yescharacteristic
17C2×#3754C2212yes—
18C4×#634C2211yescharacteristic
19C3×#938—21no—
20C3×#938—21no—
21C3×#936C2212yes—
22C3×D4×Dic3—21no—
23C3×D4×Dic3—21no—
24C2×C3×#213C2212yes—
25C3×C4×D12C2211yescharacteristic
26C3×C42×D3C2211yescharacteristic
27C3×#869C2211yescharacteristic
28#63933—28no—
29C4×#625—21no—
30Dic3×D12C2211yescharacteristic
31#63879—21no—
32#63877—21no—
33C4×D3×Dic3—21no—
34#63844C2211yescharacteristic
35#63841C2211yescharacteristic
36C2×#3719C2212yes—
37C2×#3715C2212yes—
38C2×D3×C3⋊C8C2212yes—
39#63659C2212yes—
40C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
41C3×#832C2212yes—
42C3×C4⋊(C3⋊C8)C2211yescharacteristic
43Dic3⋊(C3⋊C8)C2212yes—
44#63566C2212yes—
45#63565C2212yes—
46C3×#532—31no—
47C2×#950—32no—
48C2×#912—32no—
49#5716D311yescharacteristic, complemented
50C4×#237—31no—
51C4×#235—31no—
52C3×#459—31no—
53#5233—32no—
54#5153—32no—
55#5090—31no—
56#5083—31no—
57#5075—31no—
58#5075—31no—
59#5075—61no—
60#5072D311yescharacteristic, complemented
61#5057—32no—
62#5054—32no—
63#5019—31no—
64C2×C4⋊(C3⋊C8)—31no—
65#4849—31no—
66D3×C4⋊C8—31no—
67#4772—32no—
68#4767—32no—
69C2×C32×D4—21no—
70C2×C32×D4—21no—
71C2×C32×D4C2312yes—
72C2×#634C2311yescharacteristic
73C2×C3×#67—22no—
74C22×C3×Dic3—22no—
75C3×#237—24no—
76C3×#237—24no—
77C2×C3×D12C2311yescharacteristic
78C2×C3×C4×D3—21no—
79C2×C3×C4×D3D411yescharacteristic
80C2×C3×C4×D3D411yescharacteristic
81C2×C3×C4×D3C2311yescharacteristic
82C2×C3×Dic6C2312yes—
83C2×#625—21no—
84C2×D3×Dic3—21no—
85C2×D3×Dic3—21no—
86#3795—22no—
87#3795D414yescomplemented
88C32×C42C2311yescharacteristic
89#3754—24no—
90C4⋊(C3⋊Dic3)C2311yescharacteristic
91#3750—21no—
92C4×C3⋊Dic3—21no—
93C2×C3⋊(C3⋊C8)C2312yes—
94C3×#217—22no—
95C3×#217—22no—
96C3×#213—24no—
97C3×(C2×D3)⋊C4—21no—
98C3×C4⋊Dic3—21no—
99C3×C4⋊Dic3—21no—
100C3×C4⋊Dic3C2311yescharacteristic
101C3×C4×Dic3D411yescharacteristic
102C3×C4×Dic3D411yescharacteristic
103C3×C4×Dic3C2311yescharacteristic
104C2×C3×C3⋊C8C2312yes—
105#3724—21no—
106(C2×D3)⋊Dic3—21no—
107(C2×D3)⋊Dic3—21no—
108Dic32—21no—
109Dic32—21no—
110#3719—24no—
111#3715—24no—
112D3×C3⋊C8—24no—
113#3035—91noSylow
114C2×C3×#41—32no—
115C2×#237—31no—
116C2×#237C2×D312yes—
117C2×#235—31no—
118C2×C3×D8—32no—
119C3×C4⋊Q8—31no—
120C3×#127—21no—
121C3×#127C2×D311yescharacteristic
122C3×#127C2×D311yescharacteristic
123C3×#124—32no—
124C3×#121—61no—
125C3×#121—61no—
126C3×C4×D4—31no—
127C3×C4×D4—61no—
128C3×C4×D4—61no—
129C2×C3×C42—31no—
130#950—68no—
131C2×#216—32no—
132C2×#215—32no—
133#938—21no—
134#938—21no—
135#936C2×D312yes—
136D4×Dic3—21no—
137D4×Dic3—21no—
138D4×Dic3—31no—
139C2×#214—32no—
140C2×#214—32no—
141C2×#214—32no—
142C2×#214—62no—
143C2×#213C2×D312yes—
144C4×#67—61no—
145C4×#67—61no—
146C4×#67—61no—
147#926—31no—
148C2×C4×Dic3—61no—
149C22×C3⋊C8—32no—
150#912—68no—
151C2×Dic12—32no—
152C2×D3×C8—32no—
153#892—31no—
154#887—31no—
155#67⋊C4—61no—
156#877—61no—
157C4×D12—31no—
158C4×D12C2×D311yescharacteristic
159#872—61no—
160C42×D3—61no—
161C42×D3C2×D311yescharacteristic
162#869C2×D311yescharacteristic
163C4×Dic6—31no—
164C4×Dic6—31no—
165C4×Dic6—31no—
166C4×Dic6—61no—
167C3×C4⋊C8—31no—
168C3×#102—32no—
169#835—32no—
170#835—32no—
171#832—32no—
172#832—32no—
173#832—62no—
174#832C2×D312yes—
175#816—32no—
176Dic3⋊C8—32no—
177#810—32no—
178C4⋊(C3⋊C8)—31no—
179C4⋊(C3⋊C8)—31no—
180C4⋊(C3⋊C8)—32no—
181C4⋊(C3⋊C8)—61no—
182C4⋊(C3⋊C8)C2×D311yescharacteristic
183C23×C32—22no—
184C22×C3×D3—21no—
185C22×C3×D3C2×D411yescharacteristic
186C32×D4—22no—
187C32×D4—22no—
188C32×D4—42no—
189C32×D4—42no—
190C2×C32×C4C2×D411yescharacteristic
191C2×C32×C4C2×D411yescharacteristic
192C2×C32×C4C2411yescharacteristic
193C2×C3⋊Dic3—21no—
194C2×C3⋊Dic3—21no—
195#634—21no—
196#634C2×D412yes—
197C3×#67—44no—
198C2×C3×Dic3—21no—
199C2×C3×Dic3—22no—
200C2×C3×Dic3—44no—
201C2×C3×Dic3C2×D411yescharacteristic
202C2×C3×Dic3C2×D411yescharacteristic
203C2×C3×Dic3C2×D411yescharacteristic
204C3×D12—21no—
205C3×D12C2×D412yes—
206C3×C4×D3—22no—
207C3×C4×D3—41no—
208C3×C4×D3—42no—
209C3×C4×D3C2×D412yes—
210C3×C4×D3#4112yes—
211C3×Dic6—22no—
212C3×Dic6—22no—
213#625—24no—
214D3×Dic3—24no—
215D3×Dic3—42no—
216C3⋊(C3⋊C8)—22no—
217C3×C3⋊C8—22no—
218C2×#135—92no—
219#532—31no—
220C4×#41—91no—
221#464—92no—
222#463—92no—
223#462—91no—
224#461—91no—
225#460—91no—
226#459—31no—
227C2×C4⋊C8—91no—
228#416—92no—
229C3×#41—64no—
230C3×#41—64no—
231C2×C3×Q8—32no—
232C2×C3×D4—21no—
233C2×C3×D4—21no—
234C2×C3×D4—21no—
235C2×C3×D4—21no—
236C2×C3×D4—22no—
237C2×C3×D4—31no—
238C2×C3×D4—41no—
239C2×C3×D4—41no—
240C2×C3×D4—62no—
241C2×C3×D4C22×D312yes—
242C2×C3×D4C22×D312yes—
243C22×C3×C4—31no—
244C22×C3×C4—31no—
245C22×C3×C4—31no—
246C22×C3×C4—62no—
247C22×C3×C4—61no—
248C2×#67—22no—
249C2×#67—61no—
250C2×#67—61no—
251C22×Dic3—22no—
252C22×Dic3—61no—
253C22×Dic3—61no—
254#237—24no—
255#237—24no—
256#237—34no—
257#237—62no—
258#235—34no—
259#235—62no—
260C2×D12C22×D311yescharacteristic
261C2×C4×D3—21no—
262C2×C4×D3—61no—
263C2×C4×D3—61no—
264C2×C4×D3#6711yescharacteristic
265C2×C4×D3#6711yescharacteristic
266C2×C4×D3C22×D311yescharacteristic
267C2×Dic6—31no—
268C2×Dic6—31no—
269C2×Dic6—61no—
270C2×Dic6C22×D312yes—
271C3×D8—64no—
272C2×C3×C8—32no—
273C3×C4⋊C4—31no—
274C3×C4⋊C4—61no—
275C3×C4⋊C4—61no—
276C3×C22⋊C4—62no—
277C3×C22⋊C4—62no—
278C3×C22⋊C4—61no—
279C3×C42—21no—
280C3×C42—31no—
281C3×C42—31no—
282C3×C42—31no—
283C3×C42C22×D311yescharacteristic
284C3×C42C22×D311yescharacteristic
285#217—22no—
286#217—22no—
287#217—61no—
288#217—61no—
289#216—64no—
290#215—64no—
291#214—64no—
292#214—64no—
293#214—64no—
294#214—124no—
295#213—24no—
296(C2×D3)⋊C4—21no—
297(C2×D3)⋊C4—61no—
298(C2×D3)⋊C4—61no—
299C4⋊Dic3—21no—
300C4⋊Dic3—21no—
301C4⋊Dic3—31no—
302C4⋊Dic3—31no—
303C4⋊Dic3—61no—
304C4⋊Dic3C22×D311yescharacteristic
305Dic3⋊C4—61no—
306Dic3⋊C4—61no—
307Dic3⋊C4—61no—
308Dic3⋊C4—61no—
309Dic3⋊C4—121no—
310C4×Dic3—61no—
311C4×Dic3—61no—
312C4×Dic3—61no—
313C4×Dic3—61no—
314C4×Dic3—61no—
315C4×Dic3—61no—
316C4×Dic3—121no—
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—
325Dic12—64no—
326D3×C8—64no—
327C22×C32—42no—
328C22×C32—42no—
329C22×C32—42no—
330C22×C32C22×D411yescharacteristic
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—21no—
338C32×C4#13512yescomplemented
339C32×C4C22×D411yescharacteristic
340C32×C4C2×#4111yescharacteristic
341C3⋊Dic3—22no—
342C3⋊Dic3—41no—
343C3×Dic3—21no—
344C3×Dic3—21no—
345C3×Dic3—42no—
346C3×Dic3—41no—
347C3×Dic3#12112yes—
348C2×#41—32no—
349C2×#41—91no—
350#135—188no—
351C2×Q16—92no—
352C2×SD16—92no—
353C2×SD16—92no—
354C2×D8—32no—
355C22×C8—92no—
356C4⋊Q8—31no—
357#127D3211yescharacteristic
358#124—32no—
359#121—61no—
360#121—61no—
361C4×Q8—91no—
362C4×Q8—91no—
363C4×D4—31no—
364C4×D4—61no—
365C4×D4—61no—
366C4×D4—91no—
367C4×D4—181no—
368C4×D4—181no—
369#117—91no—
370#117—181no—
371C2×C42—31no—
372C2×C42—181no—
373C4⋊C8—31no—
374C4⋊C8—92no—
375C4⋊C8—91no—
376#103—92no—
377#103—92no—
378#102—32no—
379#102—92no—
380C23×C3—22no—
381C23×C3—22no—
382C23×C3—31no—
383C23×C3—42no—
384C23×C3—61no—
385C22×D3—21no—
386C22×D3C2×#6711yescharacteristic
387C3×Q8—62no—
388C3×Q8—62no—
389C3×D4—22no—
390C3×D4—22no—
391C3×D4—22no—
392C3×D4—22no—
393C3×D4—32no—
394C3×D4—42no—
395C3×D4—42no—
396C3×D4—42no—
397C3×D4—42no—
398C3×D4—42no—
399C3×D4—42no—
400C3×D4—61no—
401C3×D4—82no—
402C3×D4—82no—
403C3×D4—124no—
404C2×C3×C4—21no—
405C2×C3×C4—21no—
406C2×C3×C4—21no—
407C2×C3×C4—31no—
408C2×C3×C4—32no—
409C2×C3×C4—32no—
410C2×C3×C4—31no—
411C2×C3×C4—31no—
412C2×C3×C4—62no—
413C2×C3×C4—62no—
414C2×C3×C4—61no—
415C2×C3×C4—121no—
416C2×C3×C4—124no—
417C2×C3×C4—122no—
418C2×C3×C4D3×D411yescharacteristic
419C2×C3×C4D3×D411yescharacteristic
420C2×C3×C4C2×#6711yescharacteristic
421C2×C3×C4C2×#6711yescharacteristic
422C2×C3×C4C23×D311yescharacteristic
423C2×C3×C4C23×D311yescharacteristic
424#67—44no—
425#67—64no—
426#67—64no—
427C2×Dic3—21no—
428C2×Dic3—22no—
429C2×Dic3—44no—
430C2×Dic3—61no—
431C2×Dic3—61no—
432C2×Dic3—64no—
433C2×Dic3—61no—
434C2×Dic3—61no—
435C2×Dic3—121no—
436C2×Dic3—121no—
437C2×Dic3—122no—
438C2×Dic3C2×#6711yescharacteristic
439C2×Dic3C2×#6711yescharacteristic
440C2×Dic3C2×#6711yescharacteristic
441D12—21no—
442D12D3×D412yes—
443C4×D3—22no—
444C4×D3—41no—
445C4×D3—42no—
446C4×D3—64no—
447C4×D3—122no—
448C4×D3D3×D412yes—
449C4×D3#23712yes—
450Dic6—22no—
451Dic6—22no—
452Dic6—32no—
453Dic6—32no—
454Dic6—62no—
455Dic6—61no—
456Dic6—61no—
457Dic6—121no—
458C3×C8—62no—
459C3⋊C8—22no—
460C3⋊C8—62no—
461C3⋊C8—62no—
462C3⋊C8—122no—
463C2×C32—82no—
464C2×C32C2×#12111yescharacteristic
465C2×C32C2×#13511yescharacteristic
466C2×C32#57511yescharacteristic
467C3×D3—22no—
468C3×D3—42no—
469#41—64no—
470#41—64no—
471#41—94no—
472#41—182no—
473C2×Q8—32no—
474C2×Q8—91no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—31no—
478C2×D4—62no—
479C2×D4—181no—
480C2×D4C2×D3212yes—
481C22×C4—31no—
482C22×C4—31no—
483C22×C4—31no—
484C22×C4—62no—
485C22×C4—61no—
486C22×C4—181no—
487C22×C4—181no—
488Q16—184no—
489SD16—184no—
490SD16—184no—
491D8—64no—
492C2×C8—32no—
493C2×C8—92no—
494C2×C8—184no—
495C4⋊C4—31no—
496C4⋊C4—61no—
497C4⋊C4—61no—
498C4⋊C4—91no—
499C4⋊C4—181no—
500C4⋊C4—181no—
501C22⋊C4—62no—
502C22⋊C4—62no—
503C22⋊C4—61no—
504C22⋊C4—181no—
505C22⋊C4—181no—
506C42—31no—
507C42—31no—
508C42—31no—
509C42—181no—
510C42—181no—
511C42—181no—
512C42C2×D3211yescharacteristic
513C22×C3—21no—
514C22×C3—32no—
515C22×C3—42no—
516C22×C3—42no—
517C22×C3—42no—
518C22×C3—42no—
519C22×C3—42no—
520C22×C3—42no—
521C22×C3—61no—
522C22×C3—61no—
523C22×C3—62no—
524C22×C3—82no—
525C22×C3—82no—
526C22×C3—82no—
527C22×C3—121no—
528C22×C3—121no—
529C22×C3C2×D3×D411yescharacteristic
530C22×C3C22×#6711yescharacteristic
531C2×D3—21no—
532C2×D3—21no—
533C2×D3—22no—
534C2×D3—41no—
535C2×D3—41no—
536C2×D3#93812yes—
537C3×C4—21no—
538C3×C4—21no—
539C3×C4—21no—
540C3×C4—21no—
541C3×C4—22no—
542C3×C4—32no—
543C3×C4—41no—
544C3×C4—61no—
545C3×C4—61no—
546C3×C4—121no—
547C3×C4—122no—
548C3×C4#91212yescomplemented
549C3×C4#95012yescomplemented
550C3×C4C2×D3×D411yescharacteristic
551C3×C4C2×D3×D411yescharacteristic
552C3×C4C2×#23711yescharacteristic
553C3×C4D3×#4111yescharacteristic
554Dic3—21no—
555Dic3—21no—
556Dic3—41no—
557Dic3—42no—
558Dic3—62no—
559Dic3—62no—
560Dic3—122no—
561Dic3—121no—
562Dic3—121no—
563Dic3—241no—
564Dic3#93812yes—
565C32#303511yescharacteristic, complemented, Sylow
566C23—22no—
567C23—31no—
568C23—61no—
569Q8—62no—
570Q8—62no—
571Q8—92no—
572Q8—181no—
573D4—22no—
574D4—22no—
575D4—32no—
576D4—42no—
577D4—42no—
578D4—61no—
579D4—124no—
580D4—184no—
581C2×C4—31no—
582C2×C4—32no—
583C2×C4—32no—
584C2×C4—31no—
585C2×C4—31no—
586C2×C4—62no—
587C2×C4—61no—
588C2×C4—62no—
589C2×C4—121no—
590C2×C4—124no—
591C2×C4—122no—
592C2×C4—184no—
593C2×C4—181no—
594C2×C4—181no—
595C2×C4—362no—
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—82no—
606C2×C3—82no—
607C2×C3—122no—
608C2×C3—162no—
609C2×C3D3×#12111yescharacteristic
610C2×C3C2×#91211yescharacteristic
611C2×C3#577311yescharacteristic
612C2×C3C2×#93811yescharacteristic
613C2×C3C2×#95011yescharacteristic
614C2×C3#582211yescharacteristic
615D3—22no—
616D3—42no—
617C22—32no—
618C22—42no—
619C22—42no—
620C22—42no—
621C22—61no—
622C22—61no—
623C22—62no—
624C22—121no—
625C22—121no—
626C22C2×D3×#6711yescharacteristic
627C4—21no—
628C4—32no—
629C4—61no—
630C4—61no—
631C4—121no—
632C4—122no—
633C4—182no—
634C4—361no—
635C4#6393312yescomplemented
636C4D32×D411yescharacteristic
637C4D3×#23711yescharacteristic
638C3—21no—
639C3#8033111yescharacteristic, complemented
640C3#8329611yescharacteristic, complemented
641C2—62no—
642C2—82no—
643C2—122no—
644C2#1059509511yescharacteristic
645C2C2×#6393311yescharacteristic
646C2D3×#93811yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#127C22
socleC22×C32C22×D4
hypercenter#127D32
hypocenterC32#3035
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
1. C3×#5716C2semidirect
2. C2×#63933C2semidirect
3. C4×#3795C2semidirect
4. #10592774C2semidirect
5. C3×#5072C2semidirect
6. #10591441C2semidirect
7. #10591431C2semidirect
8. #10591420C2semidirect
9. #10590388C2semidirect
10. #10590363C2semidirect
11. D3×C4⋊(C3⋊C8)C2semidirect
49. #5716D3semidirect
60. #5072D3semidirect
87. #3795D4semidirect
338. C32×C4#135semidirect
548. C3×C4#912semidirect
549. C3×C4#950semidirect
565. C32#3035semidirect
635. C4#63933semidirect
639. C3#80331semidirect
640. C3#83296semidirect

Maximal subgroups

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

subgroupindex
C3×#57162
C2×#639332
C4×#37952
#105927742
C3×#50722
#105914412
#105914312
#105914202
#105903882
#105903632
D3×C4⋊(C3⋊C8)2
#832963
#803313