Finite Group Databasebeta

← #11865769

Subgroups — #11865769

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
1C2×#63806C212yesmaximal, complemented
2#10593970C211yesmaximal, characteristic, complemented
3C4×#3795C211yesmaximal, characteristic, complemented
4#10592547C211yesmaximal, characteristic, complemented
5C3×#4841C211yesmaximal, characteristic, complemented
6C3×D3×C4⋊C8C211yesmaximal, characteristic, complemented
7#10590813C212yesmaximal, complemented
8#10590754C212yesmaximal, complemented
9#10590690C212yesmaximal, complemented
10#10590388C211yesmaximal, characteristic, complemented
11#10590349C211yesmaximal, characteristic, complemented
12#80427—31nomaximal
13#79021—31nomaximal
14C2×#3799C2212yes—
15C2×#3795C2211yescharacteristic
16C2×#3744C2212yes—
17#64083C2211yescharacteristic
18C4×#634C2211yescharacteristic
19C2×C3×#204C2212yes—
20C2×C3×D3×C8C2212yes—
21C3×C4×D12C2211yescharacteristic
22C3×C42×D3C2211yescharacteristic
23C3×#869C2211yescharacteristic
24#63909—21no—
25#63909—21no—
26C4×#625—21no—
27#63894—21no—
28#63894—21no—
29Dic3×D12C2211yescharacteristic
30#63879—21no—
31#63877—21no—
32C4×D3×Dic3—21no—
33#63864C2212yes—
34#63844C2211yescharacteristic
35#63841C2211yescharacteristic
36C2×#3719C2212yes—
37C2×#3714C2212yes—
38#63806—28no—
39C32×C4⋊C8C2211yescharacteristic
40#63648C2212yes—
41C3×#816C2212yes—
42C3×Dic3⋊C8C2212yes—
43C3×C4⋊(C3⋊C8)C2211yescharacteristic
44#63566C2212yes—
45#63564C2212yes—
46C2×#916—32no—
47C2×#904—32no—
48#5725—31no—
49C4×#237—31no—
50#5477—31no—
51C4×#235—31no—
52C3×#461—31no—
53C2×C3×C4⋊C8—31no—
54#5165—32no—
55#5113—32no—
56#5090—31no—
57#5015—31no—
58#4849—31no—
59#4848—31no—
60#4848—31no—
61#4848—61no—
62#4845—32no—
63#4844—32no—
64#4843—31no—
65#4841D311yescharacteristic, complemented
66D3×C4⋊C8D311yescharacteristic, complemented
67#4804—32no—
68#4798—32no—
69C2×C4⋊(C3⋊D3)—21no—
70C2×C4⋊(C3⋊D3)—21no—
71C2×C4⋊(C3⋊D3)C2312yes—
72C2×#634C2311yescharacteristic
73C2×C3×D12C2311yescharacteristic
74C2×C3×C4×D3—21no—
75C2×C3×C4×D3D411yescharacteristic
76C2×C3×C4×D3D411yescharacteristic
77C2×C3×C4×D3C2311yescharacteristic
78C2×C3×Dic6C2312yes—
79C2×#626—22no—
80C2×#625—21no—
81C2×#624—22no—
82C2×D3×Dic3—21no—
83C2×D3×Dic3—21no—
84#3799—24no—
85#3799—24no—
86#3795—22no—
87#3795D414yescomplemented
88C2×C32×C8C2312yes—
89C32×C42C2311yescharacteristic
90C4⋊(C3⋊Dic3)C2311yescharacteristic
91#3750—21no—
92C4×C3⋊Dic3—21no—
93#3744—24no—
94C3×(C2×D3)⋊C4—21no—
95C3×C4⋊Dic3—21no—
96C3×C4⋊Dic3—21no—
97C3×C4⋊Dic3C2311yescharacteristic
98C3×C4×Dic3D411yescharacteristic
99C3×C4×Dic3D411yescharacteristic
100C3×C4×Dic3C2311yescharacteristic
101C2×C3×C3⋊C8C2312yes—
102C3×#204—24no—
103C3×D3×C8—24no—
104#3724—21no—
105#3722—22no—
106#3722—22no—
107(C2×D3)⋊Dic3—21no—
108(C2×D3)⋊Dic3—21no—
109Dic32—21no—
110Dic32—21no—
111#3719—24no—
112#3714—24no—
113#3035—91noSylow
114C2×#239—32no—
115C2×#237—31no—
116C2×#235—31no—
117C2×#235—32no—
118C2×C3×SD16—32no—
119C22×C3×C8—32no—
120C3×C4⋊Q8—31no—
121C3×C4×D4—31no—
122C2×C3×C42—31no—
123#947—32no—
124C2×#216—32no—
125D4×Dic3—31no—
126C2×#213—32no—
127#930—61no—
128#930—61no—
129C4×#67—61no—
130C4×#67—61no—
131C4×#67—61no—
132#926—31no—
133C2×C4×Dic3—61no—
134#916—68no—
135C2×Dic12—32no—
136#904—68no—
137C2×D24—32no—
138C2×#204—32no—
139C2×#204—32no—
140C2×#204—62no—
141C2×#204C2×D312yes—
142C2×D3×C8C2×D312yes—
143#895—61no—
144#895—61no—
145#893—61no—
146#893—61no—
147#892—31no—
148#887—31no—
149#67⋊C4—61no—
150#877—61no—
151#875—32no—
152#874—31no—
153#874—31no—
154#874—61no—
155C4×D12—31no—
156C4×D12—61no—
157C4×D12—61no—
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—21no—
168C3×C4⋊C8—32no—
169C3×C4⋊C8—31no—
170C3×C4⋊C8C2×D311yescharacteristic
171C3×C4⋊C8C2×D311yescharacteristic
172C3×#103—32no—
173#835—32no—
174#821—32no—
175#821—32no—
176#821—32no—
177#821—62no—
178#816—32no—
179#816C2×D312yes—
180Dic3⋊C8C2×D312yes—
181#809—32no—
182C4⋊(C3⋊C8)C2×D311yescharacteristic
183C22×C3⋊D3—22no—
184C22×C3×D3—21no—
185C22×C3×D3C2×D411yescharacteristic
186C2×C32×C4C2×D411yescharacteristic
187C2×C32×C4C2×D411yescharacteristic
188C2×C32×C4C2411yescharacteristic
189C2×C3⋊Dic3—21no—
190C2×C3⋊Dic3—21no—
191C4⋊(C3⋊D3)—22no—
192C4⋊(C3⋊D3)—22no—
193C4⋊(C3⋊D3)—42no—
194C4⋊(C3⋊D3)—42no—
195#634—21no—
196#634C2×D412yes—
197C2×C3×Dic3—21no—
198C2×C3×Dic3—22no—
199C2×C3×Dic3C2×D411yescharacteristic
200C2×C3×Dic3C2×D411yescharacteristic
201C2×C3×Dic3C2×D411yescharacteristic
202C3×D12—21no—
203C3×D12C2×D412yes—
204C3×C4×D3—22no—
205C3×C4×D3—41no—
206C3×C4×D3—42no—
207C3×C4×D3C2×D412yes—
208C3×C4×D3#4112yes—
209C3×Dic6—22no—
210C3×Dic6—22no—
211#626—44no—
212#625—24no—
213#624—44no—
214D3×Dic3—24no—
215D3×Dic3—42no—
216C32×C8—22no—
217C3×C3⋊C8—22no—
218C2×#135—92no—
219#532—91no—
220C4×#41—91no—
221#464—92no—
222#463—92no—
223#462—91no—
224#461—31no—
225#460—91no—
226#459—91no—
227C2×C4⋊C8—31no—
228#416—92no—
229C2×C3×Q8—32no—
230C2×C3×D4—31no—
231C22×C3×C4—31no—
232C22×C3×C4—31no—
233C22×C3×C4—31no—
234C22×C3×C4—61no—
235C2×#67—62no—
236C2×#67—61no—
237C2×#67—61no—
238C22×Dic3—61no—
239C22×Dic3—61no—
240#239—64no—
241#239—64no—
242#237—34no—
243#237—62no—
244#235—34no—
245#235—64no—
246#235—64no—
247#235—62no—
248C2×D12—32no—
249C2×D12—32no—
250C2×D12—62no—
251C2×D12—62no—
252C2×D12—61no—
253C2×D12—61no—
254C2×D12—61no—
255C2×D12—61no—
256C2×D12—121no—
257C2×D12—121no—
258C2×D12C22×D311yescharacteristic
259C2×C4×D3—21no—
260C2×C4×D3—61no—
261C2×C4×D3—62no—
262C2×C4×D3—61no—
263C2×C4×D3—62no—
264C2×C4×D3D1211yescharacteristic
265C2×C4×D3D1211yescharacteristic
266C2×C4×D3C22×D311yescharacteristic
267C2×Dic6—31no—
268C2×Dic6—31no—
269C2×Dic6—61no—
270C2×Dic6C22×D312yes—
271C3×SD16—64no—
272C2×C3×C8—22no—
273C2×C3×C8—32no—
274C2×C3×C8—64no—
275C2×C3×C8C22×D312yes—
276C2×C3×C8C22×D312yes—
277C3×C4⋊C4—31no—
278C3×C4⋊C4—61no—
279C3×C4⋊C4—61no—
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#213—64no—
291(C2×D3)⋊C4—21no—
292(C2×D3)⋊C4—62no—
293(C2×D3)⋊C4—62no—
294(C2×D3)⋊C4—61no—
295(C2×D3)⋊C4—61no—
296(C2×D3)⋊C4—62no—
297(C2×D3)⋊C4—62no—
298C4⋊Dic3—21no—
299C4⋊Dic3—21no—
300C4⋊Dic3—31no—
301C4⋊Dic3—31no—
302C4⋊Dic3—61no—
303C4⋊Dic3C22×D311yescharacteristic
304Dic3⋊C4—61no—
305Dic3⋊C4—61no—
306Dic3⋊C4—61no—
307Dic3⋊C4—61no—
308Dic3⋊C4—121no—
309C4×Dic3—61no—
310C4×Dic3—61no—
311C4×Dic3—61no—
312C4×Dic3—61no—
313C4×Dic3—61no—
314C4×Dic3—61no—
315C4×Dic3—121no—
316C4×Dic3D1211yescharacteristic
317C4×Dic3D1211yescharacteristic
318C4×Dic3C22×D311yescharacteristic
319C2×C3⋊C8C22×D312yes—
320Dic12—64no—
321D24—64no—
322#204—24no—
323#204—64no—
324#204—64no—
325#204—124no—
326D3×C8—24no—
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—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—91no—
349C2×#41—92no—
350#135—188no—
351C2×Q16—92no—
352C2×SD16—32no—
353C2×SD16—92no—
354C2×D8—92no—
355C22×C8—32no—
356C4⋊Q8—31no—
357#127—91no—
358#124—92no—
359#121—181no—
360#121—181no—
361C4×Q8—91no—
362C4×Q8—91no—
363C4×D4—31no—
364C4×D4—91no—
365C4×D4—181no—
366C4×D4—181no—
367C4×D4—181no—
368C4×D4—181no—
369#117—91no—
370#117—181no—
371C2×C42—31no—
372C2×C42—181no—
373C4⋊C8—32no—
374C4⋊C8—31no—
375C4⋊C8D3211yescharacteristic
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×D1211yescharacteristic
387C3×Q8—62no—
388C3×Q8—62no—
389C3×D4—32no—
390C3×D4—61no—
391C2×C3×C4—21no—
392C2×C3×C4—21no—
393C2×C3×C4—21no—
394C2×C3×C4—31no—
395C2×C3×C4—32no—
396C2×C3×C4—32no—
397C2×C3×C4—31no—
398C2×C3×C4—31no—
399C2×C3×C4—62no—
400C2×C3×C4—61no—
401C2×C3×C4—62no—
402C2×C3×C4—121no—
403C2×C3×C4—122no—
404C2×C3×C4C2×D1211yescharacteristic
405C2×C3×C4C2×D1211yescharacteristic
406C2×C3×C4D3×D411yescharacteristic
407C2×C3×C4D3×D411yescharacteristic
408C2×C3×C4C23×D311yescharacteristic
409C2×C3×C4C23×D311yescharacteristic
410#67—64no—
411#67—64no—
412#67—124no—
413C2×Dic3—21no—
414C2×Dic3—22no—
415C2×Dic3—61no—
416C2×Dic3—61no—
417C2×Dic3—64no—
418C2×Dic3—61no—
419C2×Dic3—61no—
420C2×Dic3—121no—
421C2×Dic3—121no—
422C2×Dic3—122no—
423C2×Dic3C2×D1211yescharacteristic
424C2×Dic3C2×D1211yescharacteristic
425C2×Dic3C2×D1211yescharacteristic
426D12—21no—
427D12—62no—
428D12—62no—
429D12—62no—
430D12—62no—
431D12—122no—
432D12—122no—
433D12—122no—
434D12—122no—
435D12—124no—
436D12—122no—
437D12—122no—
438D12—242no—
439D12—242no—
440D12D3×D412yes—
441C4×D3—22no—
442C4×D3—41no—
443C4×D3—42no—
444C4×D3—64no—
445C4×D3—124no—
446C4×D3—122no—
447C4×D3—124no—
448C4×D3D3×D412yes—
449C4×D3#23912yes—
450Dic6—22no—
451Dic6—22no—
452Dic6—32no—
453Dic6—32no—
454Dic6—62no—
455Dic6—61no—
456Dic6—61no—
457Dic6—121no—
458C3×C8—22no—
459C3×C8—22no—
460C3×C8—42no—
461C3×C8—62no—
462C3⋊C8—22no—
463C2×C32C2×#12111yescharacteristic
464C2×C32C2×#13511yescharacteristic
465C2×C32#57511yescharacteristic
466C3⋊D3—82no—
467C3×D3—22no—
468C3×D3—42no—
469#41—94no—
470#41—182no—
471#41—184no—
472#41—184no—
473C2×Q8—32no—
474C2×Q8—91no—
475C2×D4—31no—
476C2×D4—92no—
477C2×D4—182no—
478C2×D4—181no—
479C2×D4—181no—
480C2×D4—181no—
481C22×C4—31no—
482C22×C4—31no—
483C22×C4—31no—
484C22×C4—61no—
485C22×C4—182no—
486C22×C4—181no—
487C22×C4—181no—
488Q16—184no—
489SD16—64no—
490SD16—184no—
491D8—184no—
492C2×C8—32no—
493C2×C8—64no—
494C2×C8C2×D3212yes—
495C4⋊C4—31no—
496C4⋊C4—61no—
497C4⋊C4—61no—
498C4⋊C4—91no—
499C4⋊C4—181no—
500C4⋊C4—181no—
501C22⋊C4—61no—
502C22⋊C4—182no—
503C22⋊C4—182no—
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—61no—
516C22×C3—61no—
517C22×C3—62no—
518C22×C3—121no—
519C22×C3—121no—
520C22×C3C22×D1211yescharacteristic
521C22×C3C2×D3×D411yescharacteristic
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#89512yes—
537C3×C4—21no—
538C3×C4—21no—
539C3×C4—21no—
540C3×C4—22no—
541C3×C4—21no—
542C3×C4—32no—
543C3×C4—41no—
544C3×C4—61no—
545C3×C4—61no—
546C3×C4—121no—
547C3×C4—122no—
548C3×C4#90412yescomplemented
549C3×C4#91612yescomplemented
550C3×C4C2×D3×D411yescharacteristic
551C3×C4C2×D3×D411yescharacteristic
552C3×C4C2×#23911yescharacteristic
553C3×C4D3×#4111yescharacteristic
554Dic3—21no—
555Dic3—21no—
556Dic3—41no—
557Dic3—42no—
558Dic3—62no—
559Dic3—62no—
560Dic3—122no—
561Dic3—121no—
562Dic3—121no—
563Dic3—241no—
564Dic3#89512yes—
565C32#303511yescharacteristic, complemented, Sylow
566C23—31no—
567C23—61no—
568C23—182no—
569Q8—62no—
570Q8—62no—
571Q8—92no—
572Q8—181no—
573D4—32no—
574D4—61no—
575D4—184no—
576D4—182no—
577D4—182no—
578D4—362no—
579D4—364no—
580D4—362no—
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—122no—
591C2×C4—184no—
592C2×C4—181no—
593C2×C4—181no—
594C2×C4—364no—
595C2×C4—362no—
596C2×C4D3×D1211yescharacteristic
597C2×C4D3×D1211yescharacteristic
598C2×C4C22×D3211yescharacteristic
599C8—22no—
600C8—62no—
601C2×C3—21no—
602C2×C3—21no—
603C2×C3—21no—
604C2×C3—62no—
605C2×C3—122no—
606C2×C3C2×#89511yescharacteristic
607C2×C3D3×#12111yescharacteristic
608C2×C3C2×#90411yescharacteristic
609C2×C3#574811yescharacteristic
610C2×C3C2×#91611yescharacteristic
611C2×C3#577711yescharacteristic
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×D1211yescharacteristic
627C4—21no—
628C4—32no—
629C4—61no—
630C4—61no—
631C4—122no—
632C4—121no—
633C4—182no—
634C4—361no—
635C4#6380612yescomplemented
636C4D32×D411yescharacteristic
637C4D3×#23911yescharacteristic
638C3—21no—
639C3#7902111yescharacteristic, complemented
640C3#8042711yescharacteristic, complemented
641C2—62no—
642C2—122no—
643C2—722no—
644C2D3×#89511yescharacteristic
645C2C2×#6380611yescharacteristic
646C2#1059471111yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
hypercenterC4⋊C8D32
hypocenterC32#3035
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×#63806C2semidirect
2. #10593970C2semidirect
3. C4×#3795C2semidirect
4. #10592547C2semidirect
5. C3×#4841C2semidirect
6. C3×D3×C4⋊C8C2semidirect
7. #10590813C2semidirect
8. #10590754C2semidirect
9. #10590690C2semidirect
10. #10590388C2semidirect
11. #10590349C2semidirect
65. #4841D3semidirect
66. D3×C4⋊C8D3semidirect
87. #3795D4semidirect
338. C32×C4#135semidirect
548. C3×C4#904semidirect
549. C3×C4#916semidirect
565. C32#3035semidirect
635. C4#63806semidirect
639. C3#79021semidirect
640. C3#80427semidirect

Maximal subgroups

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

subgroupindex
C2×#638062
#105939702
C4×#37952
#105925472
C3×#48412
C3×D3×C4⋊C82
#105908132
#105907542
#105906902
#105903882
#105903492
#804273
#790213