Finite Group Databasebeta

← #11865766

Subgroups — #11865766

Order 1152.

1046 conjugacy classes of subgroups.

The subgroup lattice has 643 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5725C211yesmaximal, characteristic, complemented
2C2×#63947C212yesmaximal, complemented
3C4×#3795C211yesmaximal, characteristic, complemented
4#10592789C211yesmaximal, characteristic, complemented
5C3×#5083C211yesmaximal, characteristic, complemented
6#10591577C212yesmaximal, complemented
7#10591567C212yesmaximal, complemented
8#10591556C212yesmaximal, complemented
9#10590377C211yesmaximal, characteristic, complemented
10#10590347C211yesmaximal, characteristic, complemented
11D3×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
12#83296—31nomaximal
13#80427—31nomaximal
14C2×C3×#239C2212yes—
15C2×#3795C2211yescharacteristic
16C32×C4⋊Q8C2211yescharacteristic
17C2×#3756C2212yes—
18C4×#634C2211yescharacteristic
19C3×#947C2212yes—
20C2×C3×#215C2212yes—
21C3×#895—21no—
22C3×#895—21no—
23C3×#893—21no—
24C3×#893—21no—
25C3×#874C2211yescharacteristic
26C3×C4×D12C2211yescharacteristic
27C3×C42×D3C2211yescharacteristic
28#63947—28no—
29C4×#625—21no—
30Dic3×D12C2211yescharacteristic
31#63879—21no—
32#63877—21no—
33C4×D3×Dic3—21no—
34#63844C2211yescharacteristic
35#63841C2211yescharacteristic
36C2×#3716C2212yes—
37C2×#3713C2212yes—
38C2×D3×C3⋊C8C2212yes—
39#63662C2212yes—
40C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
41C3×#835C2212yes—
42C3×C4⋊(C3⋊C8)C2211yescharacteristic
43Dic3⋊(C3⋊C8)C2212yes—
44#63563C2212yes—
45#63562C2212yes—
46C3×#532—31no—
47C2×#950—32no—
48C2×#916—32no—
49#5725D311yescharacteristic, complemented
50C4×#237—31no—
51C4×#235—31no—
52C3×#461—31no—
53#5233—32no—
54#5165—32no—
55#5090—31no—
56#5090—31no—
57#5090—61no—
58#5083D311yescharacteristic, complemented
59#5075—31no—
60#5072—31no—
61#5057—32no—
62#5054—32no—
63#5015—31no—
64C2×C4⋊(C3⋊C8)—31no—
65#4848—31no—
66D3×C4⋊C8—31no—
67#4804—32no—
68#4798—32no—
69C2×C32×Q8C2312yes—
70C2×#634C2311yescharacteristic
71C3×#239—24no—
72C3×#239—24no—
73C2×C3×D12—22no—
74C2×C3×D12—21no—
75C2×C3×D12—21no—
76C2×C3×D12C2312yes—
77C2×C3×D12C2311yescharacteristic
78C2×C3×C4×D3—21no—
79C2×C3×C4×D3—22no—
80C2×C3×C4×D3D411yescharacteristic
81C2×C3×C4×D3D411yescharacteristic
82C2×C3×C4×D3C2311yescharacteristic
83C2×#625—21no—
84C2×D3×Dic3—21no—
85C2×D3×Dic3—21no—
86#3795—22no—
87#3795D414yescomplemented
88C32×C4⋊C4—21no—
89C32×C4⋊C4—21no—
90C32×C42C2311yescharacteristic
91#3756—24no—
92C4⋊(C3⋊Dic3)C2311yescharacteristic
93#3750—21no—
94C4×C3⋊Dic3—21no—
95C2×C3⋊(C3⋊C8)C2312yes—
96C3×#215—24no—
97C3×(C2×D3)⋊C4—21no—
98C3×(C2×D3)⋊C4—22no—
99C3×(C2×D3)⋊C4—22no—
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#3716—24no—
111#3713—24no—
112D3×C3⋊C8—24no—
113#3035—91noSylow
114C2×C3×#41—32no—
115C2×#239C2×D312yes—
116C2×#237—31no—
117C2×#235—31no—
118C2×C3×SD16—32no—
119C3×C4⋊Q8—21no—
120C3×C4⋊Q8C2×D311yescharacteristic
121C3×C4⋊Q8C2×D311yescharacteristic
122C3×#127—31no—
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—
131#947C2×D312yes—
132C2×#216—32no—
133C2×#216—32no—
134C2×#216—62no—
135C2×#215C2×D312yes—
136D4×Dic3—31no—
137C2×#214—32no—
138C2×#213—32no—
139C2×#213—32no—
140C4×#67—61no—
141C4×#67—61no—
142C4×#67—61no—
143#926—31no—
144C2×C4×Dic3—61no—
145C22×C3⋊C8—32no—
146#916—68no—
147C2×#204—32no—
148C2×D3×C8—32no—
149#895—21no—
150#895—21no—
151#893—21no—
152#893—21no—
153#892—31no—
154#887—31no—
155#67⋊C4—61no—
156#877—61no—
157#874C2×D311yescharacteristic
158C4×D12—31no—
159C4×D12C2×D311yescharacteristic
160#872—61no—
161C42×D3—61no—
162C42×D3C2×D311yescharacteristic
163C4×Dic6—31no—
164C4×Dic6—31no—
165C4×Dic6—31no—
166C4×Dic6—61no—
167C3×C4⋊C8—31no—
168C3×#103—32no—
169#835—32no—
170#835—32no—
171#835—62no—
172#835C2×D312yes—
173#832—32no—
174#832—32no—
175#821—32no—
176Dic3⋊C8—32no—
177#809—32no—
178C4⋊(C3⋊C8)—31no—
179C4⋊(C3⋊C8)—31no—
180C4⋊(C3⋊C8)—32no—
181C4⋊(C3⋊C8)—61no—
182C4⋊(C3⋊C8)C2×D311yescharacteristic
183C22×C3×D3—21no—
184C22×C3×D3—22no—
185C22×C3×D3C2×D411yescharacteristic
186C32×Q8—22no—
187C32×Q8—22no—
188C2×C32×C4—22no—
189C2×C32×C4C2×D411yescharacteristic
190C2×C32×C4C2×D411yescharacteristic
191C2×C32×C4C2411yescharacteristic
192C2×C3⋊Dic3—21no—
193C2×C3⋊Dic3—21no—
194#634—21no—
195#634C2×D412yes—
196C2×C3×Dic3—21no—
197C2×C3×Dic3C2×D411yescharacteristic
198C2×C3×Dic3C2×D411yescharacteristic
199C2×C3×Dic3C2×D411yescharacteristic
200C3×D12—22no—
201C3×D12—21no—
202C3×D12—22no—
203C3×D12—42no—
204C3×D12—44no—
205C3×D12—42no—
206C3×D12C2×D412yes—
207C3×C4×D3—22no—
208C3×C4×D3—41no—
209C3×C4×D3—42no—
210C3×C4×D3—44no—
211C3×C4×D3C2×D412yes—
212C3×C4×D3#4112yes—
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—31no—
225#460—91no—
226#459—91no—
227C2×C4⋊C8—91no—
228#416—92no—
229C3×#41—64no—
230C3×#41—64no—
231C2×C3×Q8—22no—
232C2×C3×Q8C22×D312yes—
233C2×C3×Q8C22×D312yes—
234C2×C3×D4—31no—
235C2×C3×D4—32no—
236C2×C3×D4—62no—
237C2×C3×D4—61no—
238C2×C3×D4—61no—
239C22×C3×C4—31no—
240C22×C3×C4—31no—
241C22×C3×C4—31no—
242C22×C3×C4—62no—
243C22×C3×C4—61no—
244C2×#67—61no—
245C2×#67—61no—
246C22×Dic3—61no—
247C22×Dic3—61no—
248#239—24no—
249#239—24no—
250#237—34no—
251#237—62no—
252#235—34no—
253#235—62no—
254C2×D12—22no—
255C2×D12—21no—
256C2×D12—21no—
257C2×D12C22×D312yes—
258C2×D12C22×D311yescharacteristic
259C2×C4×D3—21no—
260C2×C4×D3—22no—
261C2×C4×D3—61no—
262C2×C4×D3—61no—
263C2×C4×D3#6711yescharacteristic
264C2×C4×D3#6711yescharacteristic
265C2×C4×D3C22×D311yescharacteristic
266C2×Dic6—31no—
267C2×Dic6—31no—
268C2×Dic6—61no—
269C3×SD16—64no—
270C2×C3×C8—32no—
271C3×C4⋊C4—21no—
272C3×C4⋊C4—21no—
273C3×C4⋊C4—21no—
274C3×C4⋊C4—21no—
275C3×C4⋊C4—31no—
276C3×C4⋊C4—41no—
277C3×C4⋊C4—41no—
278C3×C22⋊C4—62no—
279C3×C22⋊C4—62no—
280C3×C22⋊C4—61no—
281C3×C42—21no—
282C3×C42—31no—
283C3×C42—31no—
284C3×C42—31no—
285C3×C42C22×D311yescharacteristic
286C3×C42C22×D311yescharacteristic
287#217—61no—
288#217—61no—
289#216—64no—
290#216—64no—
291#216—124no—
292#215—24no—
293#214—64no—
294#213—64no—
295#213—64no—
296(C2×D3)⋊C4—21no—
297(C2×D3)⋊C4—22no—
298(C2×D3)⋊C4—22no—
299(C2×D3)⋊C4—61no—
300(C2×D3)⋊C4—61no—
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—
325#204—64no—
326D3×C8—64no—
327C22×C32C22×D411yescharacteristic
328C2×C3×D3—21no—
329C2×C3×D3—21no—
330C2×C3×D3—22no—
331C2×C3×D3—41no—
332C2×C3×D3—41no—
333C2×C3×D3—42no—
334C2×C3×D3—42no—
335C2×C3×D3—42no—
336C2×C3×D3#12112yes—
337C32×C4—21no—
338C32×C4—42no—
339C32×C4#13512yescomplemented
340C32×C4C22×D411yescharacteristic
341C32×C4C2×#4111yescharacteristic
342C3⋊Dic3—22no—
343C3⋊Dic3—41no—
344C3×Dic3—21no—
345C3×Dic3—21no—
346C3×Dic3—41no—
347C3×Dic3#12112yes—
348C2×#41—32no—
349C2×#41—91no—
350#135—188no—
351C2×Q16—92no—
352C2×SD16—32no—
353C2×SD16—92no—
354C2×D8—92no—
355C22×C8—92no—
356C4⋊Q8D3211yescharacteristic
357#127—31no—
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—32no—
377#103—92no—
378#102—92no—
379#102—92no—
380C23×C3—31no—
381C23×C3—61no—
382C23×C3—62no—
383C22×D3—21no—
384C22×D3—22no—
385C22×D3C2×#6711yescharacteristic
386C3×Q8—22no—
387C3×Q8—22no—
388C3×Q8—22no—
389C3×Q8—22no—
390C3×Q8—42no—
391C3×Q8—42no—
392C3×D4—32no—
393C3×D4—62no—
394C3×D4—61no—
395C3×D4—62no—
396C3×D4—122no—
397C3×D4—124no—
398C3×D4—122no—
399C2×C3×C4—22no—
400C2×C3×C4—22no—
401C2×C3×C4—21no—
402C2×C3×C4—21no—
403C2×C3×C4—21no—
404C2×C3×C4—31no—
405C2×C3×C4—32no—
406C2×C3×C4—32no—
407C2×C3×C4—31no—
408C2×C3×C4—31no—
409C2×C3×C4—42no—
410C2×C3×C4—62no—
411C2×C3×C4—61no—
412C2×C3×C4—121no—
413C2×C3×C4—124no—
414C2×C3×C4—122no—
415C2×C3×C4D3×D411yescharacteristic
416C2×C3×C4D3×D411yescharacteristic
417C2×C3×C4C2×#6711yescharacteristic
418C2×C3×C4C2×#6711yescharacteristic
419C2×C3×C4C23×D311yescharacteristic
420C2×C3×C4C23×D311yescharacteristic
421#67—64no—
422#67—64no—
423C2×Dic3—21no—
424C2×Dic3—61no—
425C2×Dic3—61no—
426C2×Dic3—64no—
427C2×Dic3—61no—
428C2×Dic3—61no—
429C2×Dic3—121no—
430C2×Dic3—121no—
431C2×Dic3—122no—
432C2×Dic3C2×#6711yescharacteristic
433C2×Dic3C2×#6711yescharacteristic
434C2×Dic3C2×#6711yescharacteristic
435D12—22no—
436D12—22no—
437D12—21no—
438D12—42no—
439D12—44no—
440D12—42no—
441D12D3×D412yes—
442C4×D3—22no—
443C4×D3—41no—
444C4×D3—42no—
445C4×D3—44no—
446C4×D3—64no—
447C4×D3—122no—
448C4×D3D3×D412yes—
449C4×D3#23712yes—
450Dic6—32no—
451Dic6—32no—
452Dic6—62no—
453Dic6—61no—
454Dic6—61no—
455Dic6—121no—
456C3×C8—62no—
457C3⋊C8—22no—
458C3⋊C8—62no—
459C3⋊C8—62no—
460C3⋊C8—122no—
461C2×C32C2×#12111yescharacteristic
462C2×C32C2×#13511yescharacteristic
463C2×C32#57511yescharacteristic
464C3×D3—22no—
465C3×D3—42no—
466C3×D3—82no—
467#41—64no—
468#41—64no—
469#41—94no—
470#41—182no—
471C2×Q8—91no—
472C2×Q8C2×D3212yes—
473C2×D4—31no—
474C2×D4—32no—
475C2×D4—62no—
476C2×D4—61no—
477C2×D4—61no—
478C2×D4—181no—
479C22×C4—31no—
480C22×C4—31no—
481C22×C4—31no—
482C22×C4—62no—
483C22×C4—61no—
484C22×C4—181no—
485C22×C4—181no—
486Q16—184no—
487SD16—64no—
488SD16—184no—
489D8—184no—
490C2×C8—32no—
491C2×C8—92no—
492C2×C8—184no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—31no—
496C4⋊C4—91no—
497C4⋊C4—181no—
498C4⋊C4—181no—
499C22⋊C4—62no—
500C22⋊C4—62no—
501C22⋊C4—61no—
502C22⋊C4—181no—
503C22⋊C4—181no—
504C42—31no—
505C42—31no—
506C42—31no—
507C42—181no—
508C42—181no—
509C42—181no—
510C42C2×D3211yescharacteristic
511C22×C3—21no—
512C22×C3—32no—
513C22×C3—61no—
514C22×C3—61no—
515C22×C3—62no—
516C22×C3—121no—
517C22×C3—121no—
518C22×C3—122no—
519C22×C3—122no—
520C22×C3—122no—
521C22×C3C2×D3×D411yescharacteristic
522C22×C3C22×#6711yescharacteristic
523C2×D3—21no—
524C2×D3—21no—
525C2×D3—22no—
526C2×D3—41no—
527C2×D3—41no—
528C2×D3—42no—
529C2×D3—42no—
530C2×D3—42no—
531C2×D3#93812yes—
532C3×C4—21no—
533C3×C4—21no—
534C3×C4—21no—
535C3×C4—21no—
536C3×C4—22no—
537C3×C4—32no—
538C3×C4—41no—
539C3×C4—42no—
540C3×C4—42no—
541C3×C4—61no—
542C3×C4—61no—
543C3×C4—82no—
544C3×C4—121no—
545C3×C4#91612yescomplemented
546C3×C4#95012yescomplemented
547C3×C4C2×D3×D411yescharacteristic
548C3×C4C2×D3×D411yescharacteristic
549C3×C4C2×#23711yescharacteristic
550C3×C4D3×#4111yescharacteristic
551Dic3—21no—
552Dic3—21no—
553Dic3—41no—
554Dic3—62no—
555Dic3—62no—
556Dic3—122no—
557Dic3—121no—
558Dic3—121no—
559Dic3—241no—
560Dic3#93812yes—
561C32#303511yescharacteristic, complemented, Sylow
562C23—31no—
563C23—61no—
564C23—62no—
565Q8—22no—
566Q8—22no—
567Q8—92no—
568Q8—181no—
569D4—32no—
570D4—62no—
571D4—61no—
572D4—62no—
573D4—122no—
574D4—124no—
575D4—122no—
576D4—184no—
577C2×C4—22no—
578C2×C4—31no—
579C2×C4—32no—
580C2×C4—32no—
581C2×C4—31no—
582C2×C4—31no—
583C2×C4—62no—
584C2×C4—61no—
585C2×C4—121no—
586C2×C4—124no—
587C2×C4—122no—
588C2×C4—184no—
589C2×C4—181no—
590C2×C4—181no—
591C2×C4—362no—
592C2×C4D3×#6711yescharacteristic
593C2×C4D3×#6711yescharacteristic
594C2×C4C22×D3211yescharacteristic
595C8—62no—
596C8—182no—
597C2×C3—21no—
598C2×C3—21no—
599C2×C3—21no—
600C2×C3—62no—
601C2×C3—122no—
602C2×C3—242no—
603C2×C3D3×#12111yescharacteristic
604C2×C3C2×#91611yescharacteristic
605C2×C3#577711yescharacteristic
606C2×C3C2×#93811yescharacteristic
607C2×C3C2×#95011yescharacteristic
608C2×C3#582211yescharacteristic
609D3—22no—
610D3—42no—
611D3—82no—
612C22—32no—
613C22—61no—
614C22—61no—
615C22—62no—
616C22—121no—
617C22—121no—
618C22—122no—
619C22—122no—
620C22—122no—
621C22C2×D3×#6711yescharacteristic
622C4—21no—
623C4—32no—
624C4—42no—
625C4—61no—
626C4—61no—
627C4—121no—
628C4—182no—
629C4—361no—
630C4#6394712yescomplemented
631C4D32×D411yescharacteristic
632C4D3×#23711yescharacteristic
633C3—21no—
634C3#8042711yescharacteristic, complemented
635C3#8329611yescharacteristic, complemented
636C2—62no—
637C2—122no—
638C2—242no—
639C2D3×#93811yescharacteristic
640C2#1059531711yescharacteristic
641C2C2×#6394711yescharacteristic
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×#5725C2semidirect
2. C2×#63947C2semidirect
3. C4×#3795C2semidirect
4. #10592789C2semidirect
5. C3×#5083C2semidirect
6. #10591577C2semidirect
7. #10591567C2semidirect
8. #10591556C2semidirect
9. #10590377C2semidirect
10. #10590347C2semidirect
11. D3×C4⋊(C3⋊C8)C2semidirect
49. #5725D3semidirect
58. #5083D3semidirect
87. #3795D4semidirect
339. C32×C4#135semidirect
545. C3×C4#916semidirect
546. C3×C4#950semidirect
561. C32#3035semidirect
630. C4#63947semidirect
634. C3#80427semidirect
635. C3#83296semidirect

Maximal subgroups

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

subgroupindex
C3×#57252
C2×#639472
C4×#37952
#105927892
C3×#50832
#105915772
#105915672
#105915562
#105903772
#105903472
D3×C4⋊(C3⋊C8)2
#832963
#804273