Finite Group Databasebeta

← #11870719

Subgroups — #11870719

Order 1152.

1011 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
1#10596067C211yesmaximal, characteristic
2C2×#63843C211yesmaximal, characteristic, complemented
3C3×#5040C211yesmaximal, characteristic, complemented
4C3×#5034C211yesmaximal, characteristic, complemented
5#10591445C212yesmaximal, complemented
6#10591444C212yesmaximal, complemented
7#10591174C211yesmaximal, characteristic, complemented
8#10591125C211yesmaximal, characteristic, complemented
9#10591061C211yesmaximal, characteristic, complemented
10#10590497C212yesmaximal, complemented
11#10590483C212yesmaximal, complemented
12#81308—31nomaximal
13#80028—31nomaximal
14C2×#3830—21no—
15C22×C3×Dic6C2211yescharacteristic
16C32×#121C2211yescharacteristic
17#64149C2211yescharacteristic
18#64148—21no—
19D4×C3⋊Dic3C2211yescharacteristic
20#64139C2211yescharacteristic
21C2×C4×C3⋊Dic3C2211yescharacteristic
22#64102C2211yescharacteristic
23#64097C2211yescharacteristic
24#64094—21no—
25#64090—21no—
26C2×C3×#214C2212yes—
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C2×Dic3⋊Dic3—21no—
29C2×Dic32—21no—
30#63843—21no—
31#63843—21no—
32#63843C2212yes—
33#63843C2212yes—
34C2×#3717C2212yes—
35C3×#832C2212yes—
36C3×#830C2211yescharacteristic
37C3×#830C2211yescharacteristic
38C3×#810C2212yes—
39C3×#808C2212yes—
40#63573C2212yes—
41#63572C2212yes—
42#63566C2212yes—
43#63564C2212yes—
44#63553C2212yes—
45C2×Q8×Dic3—31no—
46#5596—31no—
47#5596—31no—
48#5596—61no—
49C2×#887—31no—
50C3×#481—31no—
51C3×#448—31no—
52#5227—31no—
53#5163—32no—
54Dic3×SD16—32no—
55#5040D311yescharacteristic, complemented
56#5034D311yescharacteristic, complemented
57#4968—31no—
58#4854—32no—
59#4852—32no—
60#4791—32no—
61#4788—32no—
62#4762—32no—
63#4758—32no—
64#4738—31no—
65#4735—31no—
66#4718—31no—
67#4718—31no—
68C2×C32×D4—21no—
69C2×C32×D4C2311yescharacteristic
70C22×C32×C4C2311yescharacteristic
71C2×#638—21no—
72C2×#638—21no—
73C2×#638—21no—
74C22×C3⋊Dic3—21no—
75C22×C3⋊Dic3D411yescharacteristic
76C22×C3⋊Dic3D411yescharacteristic
77#3830—44no—
78C2×C4⋊(C3⋊D3)C2311yescharacteristic
79C2×C4×C3⋊D3—21no—
80C2×#634—21no—
81C22×C3×Dic3—21no—
82C22×C3×Dic3—21no—
83C2×C3×Dic6—21no—
84C2×C3×Dic6—24no—
85C2×C3×Dic6C2312yes—
86C32×C4⋊C4C2311yescharacteristic
87C32×C22⋊C4—21no—
88#3757—21no—
89#3752—21no—
90#3752—21no—
91C4⋊(C3⋊Dic3)C2311yescharacteristic
92#3750—21no—
93C4×C3⋊Dic3D411yescharacteristic
94C4×C3⋊Dic3D411yescharacteristic
95C4×C3⋊Dic3C2311yescharacteristic
96C4×C3⋊Dic3C2311yescharacteristic
97C3×#214—24no—
98C3×C4⋊Dic3—21no—
99C3×C4⋊Dic3C2312yes—
100C2×C3×C3⋊C8C2312yes—
101C2×C3×C3⋊C8C2312yes—
102Dic3⋊Dic3—22no—
103Dic3⋊Dic3—22no—
104Dic32—22no—
105Dic32—22no—
106#3717—24no—
107#3103—91noSylow
108C22×C3×Q8—31no—
109C2×#237—61no—
110C2×#237—61no—
111C2×#237—62no—
112C22×Dic6C2×D311yescharacteristic
113C2×C3×SD16—32no—
114C3×#121—21no—
115C3×#121C2×D311yescharacteristic
116C3×#121C2×D311yescharacteristic
117C2×C3×C4⋊C4—31no—
118Q8×Dic3—32no—
119Q8×Dic3—32no—
120Q8×Dic3—61no—
121Q8×Dic3—61no—
122C2×#215—32no—
123#940—31no—
124#940—31no—
125#940—61no—
126#939—61no—
127#939—61no—
128#939—62no—
129D4×Dic3—31no—
130D4×Dic3—31no—
131D4×Dic3—61no—
132C2×#214C2×D312yes—
133#930—31no—
134#930—31no—
135#930—61no—
136C2×C4⋊Dic3—61no—
137C2×C4⋊Dic3C2×D311yescharacteristic
138C2×Dic3⋊C4—61no—
139C2×C4×Dic3—31no—
140C2×C4×Dic3—31no—
141C2×C4×Dic3—61no—
142C2×C4×Dic3—61no—
143C2×C4×Dic3—61no—
144C2×#204—32no—
145#893—31no—
146#893—31no—
147#893—61no—
148#888—31no—
149#888—31no—
150#888—61no—
151#887—32no—
152#887—32no—
153#887—61no—
154#887—61no—
155#885—61no—
156#885—61no—
157#885—62no—
158#67⋊C4—61no—
159#67⋊C4—61no—
160#67⋊C4—62no—
161C3×#106—32no—
162C3×#103—32no—
163C3×#102—32no—
164C3×C22⋊C8—31no—
165C3×C22⋊C8—31no—
166#835—32no—
167#832C2×D312yes—
168#830C2×D311yescharacteristic
169#830C2×D311yescharacteristic
170#821—32no—
171#817—32no—
172#816—32no—
173Dic3⋊C8—32no—
174Dic3⋊C8—32no—
175C8×Dic3—32no—
176C8×Dic3—32no—
177#810C2×D312yes—
178#809—32no—
179#808—32no—
180#808C2×D312yes—
181C23×C32—21no—
182C23×C32C2×D411yescharacteristic
183C22×C3⋊D3—21no—
184C32×D4—22no—
185C32×D4—42no—
186C2×C32×C4—21no—
187C2×C32×C4—22no—
188C2×C32×C4C2×D411yescharacteristic
189C2×C32×C4C2411yescharacteristic
190#638—42no—
191#638—42no—
192#638—42no—
193C2×C3⋊Dic3—21no—
194C2×C3⋊Dic3—41no—
195C2×C3⋊Dic3—42no—
196C2×C3⋊Dic3SD1614yescomplemented
197C2×C3⋊Dic3C2×D411yescharacteristic
198C2×C3⋊Dic3C2×D411yescharacteristic
199C2×C3⋊Dic3C2×D411yescharacteristic
200C2×C3⋊Dic3C2×D411yescharacteristic
201C4⋊(C3⋊D3)—22no—
202C4×C3⋊D3—42no—
203#634—42no—
204C2×C3×Dic3—24no—
205C2×C3×Dic3—22no—
206C2×C3×Dic3—22no—
207C2×C3×Dic3—42no—
208C3×Dic6—24no—
209C3×Dic6—22no—
210C3×Dic6#4114yescomplemented
211C3×C3⋊C8—22no—
212C3×C3⋊C8—22no—
213#532—91no—
214C2×C4×Q8—91no—
215#481—31no—
216#481—91no—
217#475—92no—
218#460—92no—
219#448—31no—
220#448—91no—
221C4×SD16—92no—
222C4×SD16—92no—
223#431—91no—
224C2×C3×Q8—32no—
225C2×C3×Q8—64no—
226C2×C3×Q8—61no—
227C2×C3×D4—22no—
228C2×C3×D4—21no—
229C2×C3×D4—21no—
230C2×C3×D4—21no—
231C2×C3×D4C22×D311yescharacteristic
232C2×C3×D4C22×D311yescharacteristic
233C22×C3×C4—21no—
234C22×C3×C4—61no—
235C22×C3×C4—61no—
236C22×C3×C4C22×D311yescharacteristic
237C22×C3×C4C22×D311yescharacteristic
238C2×#67—61no—
239C2×#67—61no—
240C2×#67—61no—
241C2×#67—61no—
242C2×#67—62no—
243C2×#67—62no—
244C2×#67—62no—
245C2×#67—61no—
246C2×#67—61no—
247C22×Dic3—21no—
248C22×Dic3—21no—
249C22×Dic3—31no—
250C22×Dic3—31no—
251C22×Dic3—31no—
252C22×Dic3—31no—
253C22×Dic3—61no—
254C22×Dic3—61no—
255C22×Dic3—61no—
256C22×Dic3—61no—
257C22×Dic3—62no—
258#237—124no—
259#237—124no—
260#237—128no—
261C2×D12—31no—
262C2×D12—31no—
263C2×D12—61no—
264C2×C4×D3—61no—
265C2×C4×D3—61no—
266C2×C4×D3—62no—
267C2×Dic6—21no—
268C2×Dic6—24no—
269C2×Dic6—61no—
270C2×Dic6—61no—
271C2×Dic6—62no—
272C2×Dic6C22×D312yes—
273C3×SD16—64no—
274C2×C3×C8—32no—
275C2×C3×C8—32no—
276C3×C4⋊C4—21no—
277C3×C4⋊C4—32no—
278C3×C4⋊C4—61no—
279C3×C4⋊C4C22×D311yescharacteristic
280C3×C4⋊C4C22×D311yescharacteristic
281C3×C22⋊C4—22no—
282C3×C22⋊C4—21no—
283C3×C22⋊C4—21no—
284#217—61no—
285#217—61no—
286#217—62no—
287#215—64no—
288#214—24no—
289(C2×D3)⋊C4—61no—
290(C2×D3)⋊C4—61no—
291(C2×D3)⋊C4—62no—
292(C2×D3)⋊C4—62no—
293(C2×D3)⋊C4—61no—
294(C2×D3)⋊C4—61no—
295C4⋊Dic3—21no—
296C4⋊Dic3—31no—
297C4⋊Dic3—31no—
298C4⋊Dic3—61no—
299C4⋊Dic3—62no—
300C4⋊Dic3—62no—
301C4⋊Dic3C22×D312yes—
302Dic3⋊C4—62no—
303Dic3⋊C4—62no—
304Dic3⋊C4—61no—
305Dic3⋊C4—61no—
306Dic3⋊C4—62no—
307C4×Dic3—31no—
308C4×Dic3—31no—
309C4×Dic3—31no—
310C4×Dic3—31no—
311C4×Dic3—31no—
312C4×Dic3—31no—
313C4×Dic3—31no—
314C4×Dic3—31no—
315C4×Dic3—61no—
316C4×Dic3—61no—
317C4×Dic3—61no—
318C4×Dic3—61no—
319C4×Dic3—62no—
320C4×Dic3—62no—
321C4×Dic3—62no—
322C4×Dic3—62no—
323C2×C3⋊C8C22×D312yes—
324C2×C3⋊C8C22×D312yes—
325#204—64no—
326C22×C32—21no—
327C22×C32—21no—
328C22×C32—41no—
329C22×C32—41no—
330C22×C32—41no—
331C22×C32C2×SD1612yes—
332C22×C32C22×D411yescharacteristic
333C2×C3⋊D3—41no—
334C2×C3⋊D3—41no—
335C2×C3⋊D3—41no—
336C32×C4—21no—
337C32×C4—41no—
338C32×C4C2×#4112yes—
339C3⋊Dic3—21no—
340C3⋊Dic3—21no—
341C3⋊Dic3—41no—
342C3⋊Dic3C2×SD1612yes—
343C3⋊Dic3C2×SD1612yes—
344C3×Dic3—24no—
345C3×Dic3—42no—
346C2×#41—181no—
347C22×Q8—31no—
348C2×SD16—32no—
349C2×SD16—92no—
350C4⋊Q8—91no—
351#127—91no—
352#124—181no—
353#121—91no—
354#121—181no—
355#121D3211yescharacteristic
356C4×Q8—92no—
357C4×Q8—92no—
358C4×Q8—181no—
359C4×Q8—181no—
360C4×D4—91no—
361C4×D4—91no—
362C4×D4—181no—
363C2×C4⋊C4—31no—
364C2×C4⋊C4—181no—
365C2×C42—91no—
366C2×C42—181no—
367#106—32no—
368#106—92no—
369C4⋊C8—92no—
370#103—32no—
371#103—92no—
372#102—32no—
373#102—92no—
374C22⋊C8—31no—
375C22⋊C8—31no—
376C4×C8—92no—
377C23×C3—22no—
378C23×C3—21no—
379C23×C3—21no—
380C23×C3—21no—
381C23×C3D3×D411yescharacteristic
382C23×C3D3×D411yescharacteristic
383C22×D3—62no—
384C22×D3—61no—
385C22×D3—61no—
386C3×Q8—34no—
387C3×Q8—64no—
388C3×Q8—62no—
389C3×D4—22no—
390C3×D4—22no—
391C3×D4—42no—
392C3×D4—44no—
393C3×D4—42no—
394C3×D4—42no—
395C2×C3×C4—22no—
396C2×C3×C4—22no—
397C2×C3×C4—22no—
398C2×C3×C4—21no—
399C2×C3×C4—21no—
400C2×C3×C4—21no—
401C2×C3×C4—21no—
402C2×C3×C4—42no—
403C2×C3×C4—64no—
404C2×C3×C4—62no—
405C2×C3×C4—62no—
406C2×C3×C4—122no—
407C2×C3×C4D3×D411yescharacteristic
408C2×C3×C4D3×D411yescharacteristic
409C2×C3×C4C23×D311yescharacteristic
410C2×C3×C4C23×D311yescharacteristic
411#67—122no—
412#67—122no—
413#67—124no—
414#67—124no—
415#67—122no—
416#67—122no—
417#67—124no—
418#67—122no—
419#67—122no—
420C2×Dic3—24no—
421C2×Dic3—22no—
422C2×Dic3—22no—
423C2×Dic3—34no—
424C2×Dic3—34no—
425C2×Dic3—31no—
426C2×Dic3—31no—
427C2×Dic3—31no—
428C2×Dic3—31no—
429C2×Dic3—31no—
430C2×Dic3—31no—
431C2×Dic3—31no—
432C2×Dic3—31no—
433C2×Dic3—42no—
434C2×Dic3—64no—
435C2×Dic3—61no—
436C2×Dic3—61no—
437C2×Dic3—61no—
438C2×Dic3—61no—
439C2×Dic3—62no—
440C2×Dic3—61no—
441C2×Dic3—61no—
442C2×Dic3—122no—
443C2×Dic3—122no—
444C2×Dic3—121no—
445C2×Dic3—121no—
446C2×Dic3—124no—
447C2×Dic3—122no—
448D12—62no—
449D12—62no—
450D12—122no—
451C4×D3—122no—
452C4×D3—122no—
453C4×D3—124no—
454Dic6—24no—
455Dic6—22no—
456Dic6—122no—
457Dic6—122no—
458Dic6—124no—
459Dic6#23714yescomplemented
460C3×C8—62no—
461C3×C8—62no—
462C3⋊C8—22no—
463C3⋊C8—22no—
464C2×C32—22no—
465C2×C32—81no—
466C2×C32#52511yescharacteristic
467C2×C32C22×SD1611yescharacteristic
468C2×C32#57511yescharacteristic
469C3⋊D3—81no—
470#41—364no—
471C2×Q8—32no—
472C2×Q8—64no—
473C2×Q8—61no—
474C2×Q8—181no—
475C2×D4—21no—
476C2×D4—91no—
477C2×D4—181no—
478C2×D4—181no—
479C2×D4—181no—
480C2×D4C2×D3211yescharacteristic
481C22×C4—61no—
482C22×C4—61no—
483C22×C4—91no—
484C22×C4—91no—
485C22×C4—181no—
486C22×C4—181no—
487C22×C4C2×D3211yescharacteristic
488SD16—64no—
489SD16—184no—
490C2×C8—32no—
491C2×C8—32no—
492C4⋊C4—32no—
493C4⋊C4—61no—
494C4⋊C4—91no—
495C4⋊C4—181no—
496C4⋊C4—182no—
497C4⋊C4—182no—
498C4⋊C4C2×D3211yescharacteristic
499C22⋊C4—21no—
500C22⋊C4—181no—
501C22⋊C4—181no—
502C22⋊C4—181no—
503C42—91no—
504C42—91no—
505C42—91no—
506C42—91no—
507C42—182no—
508C42—182no—
509C22×C3—21no—
510C22×C3—21no—
511C22×C3—21no—
512C22×C3—21no—
513C22×C3—21no—
514C22×C3—22no—
515C22×C3—41no—
516C22×C3—41no—
517C22×C3—42no—
518C22×C3—42no—
519C22×C3—42no—
520C22×C3—41no—
521C22×C3—41no—
522C22×C3—41no—
523C22×C3—41no—
524C22×C3—41no—
525C22×C3—41no—
526C22×C3D3×SD1612yes—
527C22×C3D3×SD1612yes—
528C22×C3C2×D3×D411yescharacteristic
529C22×C3C2×D3×D411yescharacteristic
530C2×D3—122no—
531C2×D3—122no—
532C2×D3—122no—
533C2×D3—121no—
534C2×D3—121no—
535C2×D3—121no—
536C2×D3—121no—
537C2×D3—121no—
538C2×D3—121no—
539C3×C4—21no—
540C3×C4—21no—
541C3×C4—22no—
542C3×C4—41no—
543C3×C4—42no—
544C3×C4—41no—
545C3×C4—41no—
546C3×C4—64no—
547C3×C4—122no—
548C3×C4C2×#23712yes—
549C3×C4D3×#4112yes—
550Dic3—24no—
551Dic3—32no—
552Dic3—32no—
553Dic3—32no—
554Dic3—32no—
555Dic3—42no—
556Dic3—62no—
557Dic3—62no—
558Dic3—62no—
559Dic3—61no—
560Dic3—61no—
561Dic3—61no—
562Dic3—61no—
563Dic3—121no—
564Dic3—122no—
565Dic3—121no—
566Dic3—121no—
567C32#310311yescharacteristic, complemented, Sylow
568C23—21no—
569C23—181no—
570C23#381111yescharacteristic
571Q8—34no—
572Q8—64no—
573Q8—62no—
574Q8—362no—
575D4—22no—
576D4—42no—
577D4—182no—
578D4—362no—
579D4—362no—
580D4—362no—
581C2×C4—22no—
582C2×C4—21no—
583C2×C4—64no—
584C2×C4—62no—
585C2×C4—62no—
586C2×C4—91no—
587C2×C4—91no—
588C2×C4—94no—
589C2×C4—91no—
590C2×C4—91no—
591C2×C4—122no—
592C2×C4—181no—
593C2×C4—362no—
594C2×C4—362no—
595C2×C4—361no—
596C2×C4#381111yescharacteristic
597C2×C4C22×D3211yescharacteristic
598C8—62no—
599C8—62no—
600C2×C3—22no—
601C2×C3—22no—
602C2×C3—21no—
603C2×C3—21no—
604C2×C3—21no—
605C2×C3—42no—
606C2×C3—82no—
607C2×C3—81no—
608C2×C3—81no—
609C2×C3#558611yescharacteristic
610C2×C3#565611yescharacteristic
611C2×C3C2×D3×SD1611yescharacteristic
612C2×C3C2×D3×SD1611yescharacteristic
613C2×C3#577311yescharacteristic
614C2×C3#577711yescharacteristic
615D3—242no—
616D3—241no—
617D3—241no—
618C22—21no—
619C22—21no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22—361no—
624C22—361no—
625C22—361no—
626C22#6393012yes—
627C22C2×#381111yescharacteristic
628C4—21no—
629C4—41no—
630C4—64no—
631C4—92no—
632C4—92no—
633C4—122no—
634C4—181no—
635C4—181no—
636C4—361no—
637C4D3×#23712yes—
638C3—21no—
639C3#8002811yescharacteristic, complemented
640C3#8130811yescharacteristic, complemented
641C2—22no—
642C2—81no—
643C2—721no—
644C2C2×#6393011yescharacteristic
645C2#1059516011yescharacteristic
646C2#1059547111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#121C22
socleC22×C32C22×D4
prime radical#10596067C2
hypercenter#121D32
hypocenterC32#3103
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
2. C2×#63843C2semidirect
3. C3×#5040C2semidirect
4. C3×#5034C2semidirect
5. #10591445C2semidirect
6. #10591444C2semidirect
7. #10591174C2semidirect
8. #10591125C2semidirect
9. #10591061C2semidirect
10. #10590497C2semidirect
11. #10590483C2semidirect
55. #5040D3semidirect
56. #5034D3semidirect
196. C2×C3⋊Dic3SD16semidirect
210. C3×Dic6#41semidirect
459. Dic6#237semidirect
567. C32#3103semidirect
639. C3#80028semidirect
640. C3#81308semidirect

Maximal subgroups

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

subgroupindex
#105960672
C2×#638432
C3×#50402
C3×#50342
#105914452
#105914442
#105911742
#105911252
#105910612
#105904972
#105904832
#813083
#800283