Finite Group Databasebeta

← #11870722

Subgroups — #11870722

Order 1152.

915 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594929C211yesmaximal, characteristic
2C2×#63843C211yesmaximal, characteristic, complemented
3#10592417C211yesmaximal, characteristic, complemented
4C3×#4738C211yesmaximal, characteristic, complemented
5C3×#4735C211yesmaximal, characteristic, complemented
6#10591171C211yesmaximal, characteristic, complemented
7#10591091C211yesmaximal, characteristic, complemented
8#10590876C212yesmaximal, complemented
9#10590816C212yesmaximal, complemented
10#10590775C212yesmaximal, complemented
11#10590742C212yesmaximal, complemented
12#81308—31nomaximal
13#80028—31nomaximal
14C22×C3×Dic6C2211yescharacteristic
15C2×#3805—21no—
16C2×C4×C3⋊Dic3C2211yescharacteristic
17C3×#930C2211yescharacteristic
18C3×#930C2211yescharacteristic
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×#204C2212yes—
21#63980—21no—
22C2×Dic3⋊Dic3—21no—
23C2×Dic32—21no—
24#63919C2211yescharacteristic
25#63915—21no—
26#63914C2211yescharacteristic
27#63902—21no—
28#63898C2211yescharacteristic
29#63898C2211yescharacteristic
30#63843—21no—
31#63843—21no—
32#63843C2212yes—
33#63843C2212yes—
34C2×#3715C2212yes—
35C32×C22⋊C8C2211yescharacteristic
36#63657C2211yescharacteristic
37#63641C2212yes—
38C8×C3⋊Dic3C2212yes—
39C3×#821C2212yes—
40C3×#817C2212yes—
41C3×#816C2212yes—
42#63574C2212yes—
43#63565C2212yes—
44#63562C2212yes—
45C2×Q8×Dic3—31no—
46#5596—31no—
47#5596—31no—
48C2×#887—31no—
49C3×#481—31no—
50C3×#448—31no—
51#5227—31no—
52#5163—32no—
53Dic3×SD16—32no—
54#5040—31no—
55#5034—31no—
56#4968—31no—
57#4854—32no—
58#4852—32no—
59#4791—32no—
60#4788—32no—
61#4762—32no—
62#4758—32no—
63#4738D311yescharacteristic, complemented
64#4735D311yescharacteristic, complemented
65#4718—31no—
66#4718—31no—
67#4718—61no—
68C22×C32×C4C2311yescharacteristic
69C22×C3⋊Dic3D411yescharacteristic
70C22×C3⋊Dic3D411yescharacteristic
71C2×C3×#67—21no—
72C2×C3×#67—21no—
73C22×C3×Dic3—21no—
74C22×C3×Dic3—21no—
75C2×C3×D12C2311yescharacteristic
76C2×C3×D12C2311yescharacteristic
77C2×C3×Dic6—21no—
78C2×C3×Dic6—24no—
79C2×C3×Dic6C2312yes—
80C2×#627—21no—
81C2×#625—21no—
82C2×#625—21no—
83#3805—44no—
84C2×D3×Dic3—21no—
85C2×D3×Dic3—21no—
86C2×C32×C8C2312yes—
87C4×C3⋊Dic3D411yescharacteristic
88C4×C3⋊Dic3D411yescharacteristic
89C4×C3⋊Dic3C2311yescharacteristic
90C4×C3⋊Dic3C2311yescharacteristic
91C2×C3⋊(C3⋊C8)C2312yes—
92C3×(C2×D3)⋊C4—21no—
93C3×(C2×D3)⋊C4—21no—
94C3×C4⋊Dic3—21no—
95C3×C4⋊Dic3C2312yes—
96C3×C4⋊Dic3C2311yescharacteristic
97C3×C4⋊Dic3C2311yescharacteristic
98C3×#204—24no—
99#3724—21no—
100Dic3⋊Dic3—22no—
101Dic3⋊Dic3—22no—
102(C2×D3)⋊Dic3—21no—
103(C2×D3)⋊Dic3—21no—
104Dic32—22no—
105Dic32—22no—
106#3715—24no—
107#3103—91noSylow
108C22×C3×Q8—31no—
109C2×#237—61no—
110C2×#237—61no—
111C22×Dic6C2×D311yescharacteristic
112C2×C3×SD16—32no—
113C3×#121—31no—
114C3×#121—31no—
115C2×C3×C4⋊C4—31no—
116Q8×Dic3—32no—
117Q8×Dic3—32no—
118Q8×Dic3—61no—
119Q8×Dic3—61no—
120C2×#215—32no—
121#940—31no—
122#940—31no—
123#939—61no—
124#939—61no—
125D4×Dic3—31no—
126D4×Dic3—31no—
127C2×#214—32no—
128#930C2×D311yescharacteristic
129#930C2×D311yescharacteristic
130C2×C4⋊Dic3—61no—
131C2×C4⋊Dic3C2×D311yescharacteristic
132C2×Dic3⋊C4—61no—
133C2×C4×Dic3—31no—
134C2×C4×Dic3—31no—
135C2×C4×Dic3—61no—
136C2×C4×Dic3—61no—
137C2×C4×Dic3—61no—
138C2×#204C2×D312yes—
139#893—31no—
140#893—31no—
141#888—31no—
142#888—31no—
143#887—32no—
144#887—32no—
145#887—61no—
146#887—61no—
147#885—61no—
148#885—61no—
149#67⋊C4—61no—
150#67⋊C4—61no—
151C3×#106—32no—
152C3×#103—32no—
153C3×#102—32no—
154C3×C22⋊C8—21no—
155C3×C22⋊C8C2×D311yescharacteristic
156C3×C22⋊C8C2×D311yescharacteristic
157#835—32no—
158#832—32no—
159#830—31no—
160#830—31no—
161#830—61no—
162#821C2×D312yes—
163#817C2×D312yes—
164#816C2×D312yes—
165Dic3⋊C8—32no—
166Dic3⋊C8—32no—
167Dic3⋊C8—62no—
168C8×Dic3—32no—
169C8×Dic3—32no—
170C8×Dic3—62no—
171#810—32no—
172#809—32no—
173#808—32no—
174#808—32no—
175C23×C32C2×D411yescharacteristic
176C22×C3×D3—21no—
177C22×C3×D3—21no—
178C2×C32×C4—22no—
179C2×C32×C4C2×D411yescharacteristic
180C2×C32×C4C2411yescharacteristic
181C2×C3⋊Dic3—41no—
182C2×C3⋊Dic3SD1614yescomplemented
183C2×C3⋊Dic3C2×D411yescharacteristic
184C2×C3⋊Dic3C2×D411yescharacteristic
185C2×C3⋊Dic3C2×D411yescharacteristic
186C2×C3⋊Dic3C2×D411yescharacteristic
187C3×#67—42no—
188C3×#67—42no—
189C2×C3×Dic3—24no—
190C2×C3×Dic3—22no—
191C2×C3×Dic3—22no—
192C2×C3×Dic3—21no—
193C2×C3×Dic3—21no—
194C2×C3×Dic3—42no—
195C3×D12—22no—
196C3×D12—22no—
197C3×Dic6—24no—
198C3×Dic6—22no—
199C3×Dic6#4114yescomplemented
200#627—42no—
201#625—42no—
202#625—42no—
203D3×Dic3—42no—
204D3×Dic3—42no—
205C32×C8—22no—
206C3⋊(C3⋊C8)—22no—
207#532—91no—
208C2×C4×Q8—91no—
209#481—31no—
210#481—91no—
211#475—92no—
212#460—92no—
213#448—31no—
214#448—91no—
215C4×SD16—92no—
216C4×SD16—92no—
217#431—91no—
218C2×C3×Q8—32no—
219C2×C3×Q8—64no—
220C2×C3×Q8—61no—
221C2×C3×D4—31no—
222C2×C3×D4—31no—
223C2×C3×D4—61no—
224C2×C3×D4—61no—
225C22×C3×C4—21no—
226C22×C3×C4—61no—
227C22×C3×C4—61no—
228C22×C3×C4C22×D311yescharacteristic
229C22×C3×C4C22×D311yescharacteristic
230C2×#67—21no—
231C2×#67—21no—
232C2×#67—61no—
233C2×#67—61no—
234C2×#67—61no—
235C2×#67—61no—
236C22×Dic3—21no—
237C22×Dic3—21no—
238C22×Dic3—31no—
239C22×Dic3—31no—
240C22×Dic3—31no—
241C22×Dic3—31no—
242C22×Dic3—61no—
243C22×Dic3—61no—
244C22×Dic3—61no—
245C22×Dic3—61no—
246#237—124no—
247#237—124no—
248C2×D12C22×D311yescharacteristic
249C2×D12C22×D311yescharacteristic
250C2×C4×D3—61no—
251C2×C4×D3—61no—
252C2×Dic6—21no—
253C2×Dic6—24no—
254C2×Dic6—61no—
255C2×Dic6—61no—
256C2×Dic6C22×D312yes—
257C3×SD16—64no—
258C2×C3×C8—22no—
259C2×C3×C8C22×D312yes—
260C2×C3×C8C22×D312yes—
261C3×C4⋊C4—31no—
262C3×C4⋊C4—32no—
263C3×C4⋊C4—31no—
264C3×C4⋊C4—61no—
265C3×C22⋊C4—61no—
266C3×C22⋊C4—61no—
267#217—61no—
268#217—61no—
269#215—64no—
270#214—64no—
271(C2×D3)⋊C4—21no—
272(C2×D3)⋊C4—21no—
273(C2×D3)⋊C4—61no—
274(C2×D3)⋊C4—61no—
275C4⋊Dic3—21no—
276C4⋊Dic3—62no—
277C4⋊Dic3—62no—
278C4⋊Dic3C22×D311yescharacteristic
279C4⋊Dic3C22×D312yes—
280C4⋊Dic3C22×D311yescharacteristic
281Dic3⋊C4—61no—
282Dic3⋊C4—61no—
283Dic3⋊C4—62no—
284Dic3⋊C4—62no—
285C4×Dic3—31no—
286C4×Dic3—31no—
287C4×Dic3—31no—
288C4×Dic3—31no—
289C4×Dic3—31no—
290C4×Dic3—31no—
291C4×Dic3—31no—
292C4×Dic3—31no—
293C4×Dic3—61no—
294C4×Dic3—61no—
295C4×Dic3—61no—
296C4×Dic3—61no—
297C4×Dic3—62no—
298C4×Dic3—62no—
299C4×Dic3—62no—
300C4×Dic3—62no—
301C2×C3⋊C8—32no—
302C2×C3⋊C8—32no—
303C2×C3⋊C8—62no—
304#204—24no—
305C22×C32—21no—
306C22×C32—21no—
307C22×C32C2×SD1612yes—
308C22×C32C22×D411yescharacteristic
309C2×C3×D3—41no—
310C2×C3×D3—41no—
311C2×C3×D3—41no—
312C2×C3×D3—41no—
313C2×C3×D3—41no—
314C2×C3×D3—41no—
315C32×C4—21no—
316C32×C4C2×#4112yes—
317C3⋊Dic3—21no—
318C3⋊Dic3—21no—
319C3⋊Dic3C2×SD1612yes—
320C3⋊Dic3C2×SD1612yes—
321C3×Dic3—24no—
322C3×Dic3—41no—
323C3×Dic3—41no—
324C3×Dic3—42no—
325C2×#41—181no—
326C22×Q8—31no—
327C2×SD16—32no—
328C2×SD16—92no—
329C4⋊Q8—91no—
330#127—91no—
331#124—181no—
332#121—31no—
333#121—31no—
334#121—181no—
335C4×Q8—92no—
336C4×Q8—92no—
337C4×Q8—181no—
338C4×Q8—181no—
339C4×D4—91no—
340C4×D4—91no—
341C4×D4—181no—
342C2×C4⋊C4—31no—
343C2×C4⋊C4—181no—
344C2×C42—91no—
345C2×C42—181no—
346#106—32no—
347#106—92no—
348C4⋊C8—92no—
349#103—32no—
350#103—92no—
351#102—32no—
352#102—92no—
353C22⋊C8—91no—
354C22⋊C8D3211yescharacteristic
355C4×C8—92no—
356C23×C3—21no—
357C23×C3—61no—
358C23×C3—61no—
359C23×C3D3×D411yescharacteristic
360C23×C3D3×D411yescharacteristic
361C22×D3—21no—
362C22×D3—21no—
363C3×Q8—34no—
364C3×Q8—64no—
365C3×Q8—62no—
366C3×D4—62no—
367C3×D4—62no—
368C3×D4—122no—
369C3×D4—122no—
370C2×C3×C4—22no—
371C2×C3×C4—22no—
372C2×C3×C4—21no—
373C2×C3×C4—21no—
374C2×C3×C4—42no—
375C2×C3×C4—64no—
376C2×C3×C4—62no—
377C2×C3×C4—62no—
378C2×C3×C4—61no—
379C2×C3×C4—61no—
380C2×C3×C4—122no—
381C2×C3×C4D3×D411yescharacteristic
382C2×C3×C4D3×D411yescharacteristic
383C2×C3×C4C23×D311yescharacteristic
384C2×C3×C4C23×D311yescharacteristic
385#67—42no—
386#67—42no—
387#67—122no—
388#67—122no—
389#67—122no—
390#67—122no—
391C2×Dic3—24no—
392C2×Dic3—22no—
393C2×Dic3—22no—
394C2×Dic3—21no—
395C2×Dic3—21no—
396C2×Dic3—34no—
397C2×Dic3—34no—
398C2×Dic3—31no—
399C2×Dic3—31no—
400C2×Dic3—31no—
401C2×Dic3—31no—
402C2×Dic3—31no—
403C2×Dic3—31no—
404C2×Dic3—31no—
405C2×Dic3—31no—
406C2×Dic3—42no—
407C2×Dic3—64no—
408C2×Dic3—61no—
409C2×Dic3—61no—
410C2×Dic3—61no—
411C2×Dic3—61no—
412C2×Dic3—122no—
413C2×Dic3—122no—
414C2×Dic3—121no—
415C2×Dic3—121no—
416C2×Dic3—122no—
417D12—22no—
418D12—22no—
419C4×D3—122no—
420C4×D3—122no—
421Dic6—24no—
422Dic6—22no—
423Dic6—122no—
424Dic6—122no—
425Dic6#23714yescomplemented
426C3×C8—22no—
427C3×C8—22no—
428C3×C8—42no—
429C3⋊C8—62no—
430C3⋊C8—62no—
431C3⋊C8—122no—
432C2×C32—22no—
433C2×C32#52511yescharacteristic
434C2×C32C22×SD1611yescharacteristic
435C2×C32#57511yescharacteristic
436C3×D3—81no—
437C3×D3—81no—
438#41—364no—
439C2×Q8—32no—
440C2×Q8—64no—
441C2×Q8—61no—
442C2×Q8—181no—
443C2×D4—31no—
444C2×D4—31no—
445C2×D4—61no—
446C2×D4—61no—
447C2×D4—181no—
448C2×D4—181no—
449C22×C4—61no—
450C22×C4—61no—
451C22×C4—91no—
452C22×C4—91no—
453C22×C4—181no—
454C22×C4—181no—
455C22×C4C2×D3211yescharacteristic
456SD16—64no—
457SD16—184no—
458C2×C8—92no—
459C2×C8C2×D3212yes—
460C4⋊C4—32no—
461C4⋊C4—31no—
462C4⋊C4—31no—
463C4⋊C4—61no—
464C4⋊C4—182no—
465C4⋊C4—182no—
466C4⋊C4—181no—
467C22⋊C4—61no—
468C22⋊C4—61no—
469C22⋊C4—181no—
470C22⋊C4—181no—
471C42—91no—
472C42—91no—
473C42—91no—
474C42—91no—
475C42—182no—
476C42—182no—
477C22×C3—21no—
478C22×C3—21no—
479C22×C3—21no—
480C22×C3—21no—
481C22×C3—21no—
482C22×C3—22no—
483C22×C3—41no—
484C22×C3—41no—
485C22×C3—121no—
486C22×C3—121no—
487C22×C3—121no—
488C22×C3—121no—
489C22×C3—121no—
490C22×C3—121no—
491C22×C3D3×SD1612yes—
492C22×C3D3×SD1612yes—
493C22×C3C2×D3×D411yescharacteristic
494C22×C3C2×D3×D411yescharacteristic
495C2×D3—41no—
496C2×D3—41no—
497C2×D3—41no—
498C2×D3—41no—
499C2×D3—41no—
500C2×D3—41no—
501C3×C4—21no—
502C3×C4—21no—
503C3×C4—22no—
504C3×C4—41no—
505C3×C4—64no—
506C3×C4—121no—
507C3×C4—121no—
508C3×C4—122no—
509C3×C4C2×#23712yes—
510C3×C4D3×#4112yes—
511Dic3—24no—
512Dic3—32no—
513Dic3—32no—
514Dic3—32no—
515Dic3—32no—
516Dic3—41no—
517Dic3—41no—
518Dic3—42no—
519Dic3—62no—
520Dic3—62no—
521Dic3—62no—
522Dic3—61no—
523Dic3—61no—
524Dic3—61no—
525Dic3—61no—
526Dic3—121no—
527C32#310311yescharacteristic, complemented, Sylow
528C23—61no—
529C23—61no—
530C23#380211yescharacteristic
531Q8—34no—
532Q8—64no—
533Q8—62no—
534Q8—362no—
535D4—62no—
536D4—62no—
537D4—122no—
538D4—122no—
539D4—362no—
540D4—362no—
541C2×C4—22no—
542C2×C4—64no—
543C2×C4—62no—
544C2×C4—62no—
545C2×C4—61no—
546C2×C4—61no—
547C2×C4—91no—
548C2×C4—91no—
549C2×C4—94no—
550C2×C4—91no—
551C2×C4—91no—
552C2×C4—122no—
553C2×C4—362no—
554C2×C4—362no—
555C2×C4—361no—
556C2×C4#380211yescharacteristic
557C2×C4C22×D3211yescharacteristic
558C8—22no—
559C8—182no—
560C2×C3—22no—
561C2×C3—22no—
562C2×C3—21no—
563C2×C3—21no—
564C2×C3—21no—
565C2×C3—42no—
566C2×C3—241no—
567C2×C3—241no—
568C2×C3#558611yescharacteristic
569C2×C3#565611yescharacteristic
570C2×C3C2×D3×SD1611yescharacteristic
571C2×C3C2×D3×SD1611yescharacteristic
572C2×C3#577311yescharacteristic
573C2×C3#577711yescharacteristic
574D3—81no—
575D3—81no—
576C22—21no—
577C22—21no—
578C22—121no—
579C22—121no—
580C22—121no—
581C22—121no—
582C22—121no—
583C22—121no—
584C22#6379612yes—
585C22C2×#380211yescharacteristic
586C4—21no—
587C4—64no—
588C4—92no—
589C4—92no—
590C4—121no—
591C4—121no—
592C4—122no—
593C4—181no—
594C4—181no—
595C4D3×#23712yes—
596C3—21no—
597C3#8002811yescharacteristic, complemented
598C3#8130811yescharacteristic, complemented
599C2—22no—
600C2—241no—
601C2—241no—
602C2#1059408211yescharacteristic
603C2C2×#6379611yescharacteristic
604C2#1059471811yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
prime radical#10594929C2
hypercenterC22⋊C8D32
hypocenterC32#3103
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#63843C2semidirect
3. #10592417C2semidirect
4. C3×#4738C2semidirect
5. C3×#4735C2semidirect
6. #10591171C2semidirect
7. #10591091C2semidirect
8. #10590876C2semidirect
9. #10590816C2semidirect
10. #10590775C2semidirect
11. #10590742C2semidirect
63. #4738D3semidirect
64. #4735D3semidirect
182. C2×C3⋊Dic3SD16semidirect
199. C3×Dic6#41semidirect
425. Dic6#237semidirect
527. C32#3103semidirect
597. C3#80028semidirect
598. C3#81308semidirect

Maximal subgroups

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

subgroupindex
#105949292
C2×#638432
#105924172
C3×#47382
C3×#47352
#105911712
#105910912
#105908762
#105908162
#105907752
#105907422
#813083
#800283