Finite Group Databasebeta

← #11870360

Subgroups — #11870360

Order 1152.

875 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5833C211yesmaximal, characteristic
2C3×#5827C211yesmaximal, characteristic, complemented
3#10592933C211yesmaximal, characteristic, complemented
4#10591139C211yesmaximal, characteristic, complemented
5C2×#63574C211yesmaximal, characteristic, complemented
6#10591102C212yesmaximal, complemented
7#10591101C212yesmaximal, complemented
8#10591091C212yesmaximal, complemented
9#10591090C212yesmaximal, complemented
10#10591087C211yesmaximal, characteristic, complemented
11#10591083C211yesmaximal, characteristic, complemented
12#83419—31nomaximal
13#82574—31nomaximal
14C2×C32×#41C2211yescharacteristic
15C2×C3×#235C2211yescharacteristic
16C2×#3748C2211yescharacteristic
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18C3×#946—21no—
19C3×Q8×Dic3—21no—
20C3×#939—22no—
21C3×#938—21no—
22C3×D4×Dic3—21no—
23C3×D4×Dic3—22no—
24C3×#930C2212yes—
25C3×#926C2211yescharacteristic
26C3×#926C2212yes—
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C2×C3×C4⋊Dic3C2212yes—
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C3×#924C2212yes—
31#63657C2212yes—
32#63657C2212yes—
33#63576C2212yes—
34#63574C2212yes—
35#63574C2212yes—
36#63574C2212yes—
37#63565C2211yescharacteristic
38#63565C2211yescharacteristic
39#63565C2212yes—
40#63562C2211yescharacteristic
41#63562C2211yescharacteristic
42#63562C2212yes—
43C3×#537—31no—
44C3×#520—31no—
45#5833D311yescharacteristic
46#5827D311yescharacteristic, complemented
47#5234—31no—
48#5234—31no—
49#5234—61no—
50#5233—31no—
51#5232—31no—
52#5045—32no—
53#5043—32no—
54#5035—32no—
55#5034—32no—
56#5003—32no—
57#5002—31no—
58#4996—32no—
59#4995—31no—
60#4971—32no—
61#4968—32no—
62#4966—31no—
63#4964—31no—
64C2×#808—31no—
65C2×#808—31no—
66C32×#41—22no—
67C32×#41—22no—
68C2×C32×Q8D411yescharacteristic
69C2×C32×D4D411yescharacteristic
70C2×C32×D4D412yes—
71C22×C32×C4C2312yes—
72C22×C32×C4C2311yescharacteristic
73C2×C3×#67—21no—
74C2×C3×#67—22no—
75C22×C3×Dic3—22no—
76C22×C3×Dic3—21no—
77C22×C3×Dic3—21no—
78C3×#235—22no—
79C3×#235—22no—
80C2×C3×D12C2311yescharacteristic
81C2×C3×C4×D3—21no—
82C2×C3×Dic6C2311yescharacteristic
83#3748—22no—
84C2×C3⋊(C3⋊C8)—22no—
85C2×C3⋊(C3⋊C8)C2311yescharacteristic
86C2×C3⋊(C3⋊C8)C2311yescharacteristic
87C2×C3⋊(C3⋊C8)C2312yes—
88C3×#217—22no—
89C3×#217—22no—
90C3×#217—21no—
91C3×(C2×D3)⋊C4—22no—
92C3×C4⋊Dic3—22no—
93C3×C4⋊Dic3—21no—
94C3×C4⋊Dic3—21no—
95C3×C4⋊Dic3C2312yes—
96C3×C4⋊Dic3C2312yes—
97C3×C4⋊Dic3C2311yescharacteristic
98C3×C4⋊Dic3C2311yescharacteristic
99C3×Dic3⋊C4—22no—
100C3×C4×Dic3—22no—
101C3×C4×Dic3—21no—
102#3099—91noSylow
103C2×C3×#41—21no—
104C2×C3×#41—31no—
105C2×C3×#41C2×D311yescharacteristic
106C2×C3×#41C2×D311yescharacteristic
107C2×#235C2×D311yescharacteristic
108C3×C22⋊Q8—32no—
109C3×C22⋊Q8—61no—
110C3×#121—32no—
111C3×#121—61no—
112C3×#121—62no—
113C3×C4×Q8—61no—
114C3×C4×D4—61no—
115C3×C4×D4—62no—
116C3×#117—31no—
117C3×#117—32no—
118C2×C3×C4⋊C4—31no—
119C2×C3×C4⋊C4—31no—
120C2×C3×C4⋊C4—32no—
121#946—21no—
122Q8×Dic3—21no—
123#939—22no—
124#938—21no—
125D4×Dic3—22no—
126D4×Dic3—21no—
127#930C2×D312yes—
128#926C2×D311yescharacteristic
129#926C2×D312yes—
130C2×C4⋊Dic3C2×D311yescharacteristic
131C2×C4⋊Dic3C2×D311yescharacteristic
132C2×C4⋊Dic3C2×D312yes—
133#924C2×D312yes—
134C2×#208—31no—
135C2×#208—31no—
136C2×#208—61no—
137C22×C3⋊C8—31no—
138C22×C3⋊C8—31no—
139C22×C3⋊C8—61no—
140#835—32no—
141#835—31no—
142#835—31no—
143#832—32no—
144#832—31no—
145#832—31no—
146#830—32no—
147#830—32no—
148#830—32no—
149#830—32no—
150#830—62no—
151#830—62no—
152#810—32no—
153#810—31no—
154#810—31no—
155#809—32no—
156#809—31no—
157#809—31no—
158#808—32no—
159#808—32no—
160#808—32no—
161#808—32no—
162#808—32no—
163#808—32no—
164#807—32no—
165#807—32no—
166C23×C32C2×D412yes—
167C23×C32C2×D411yescharacteristic
168C22×C3×D3—21no—
169C32×Q8—22no—
170C32×D4—24no—
171C32×D4—22no—
172C2×C32×C4—22no—
173C2×C32×C4—22no—
174C2×C32×C4C2×D412yes—
175C2×C32×C4C2×D411yescharacteristic
176C2×C32×C4#4112yes—
177C2×C32×C4#4112yes—
178C2×C32×C4C2411yescharacteristic
179C3×#67—42no—
180C3×#67—82no—
181C2×C3×Dic3—21no—
182C2×C3×Dic3—22no—
183C2×C3×Dic3—21no—
184C2×C3×Dic3—21no—
185C2×C3×Dic3—22no—
186C2×C3×Dic3—81no—
187C2×C3×Dic3—82no—
188C2×C3×Dic3—81no—
189C3×D12—21no—
190C3×D12—21no—
191C3×C4×D3—42no—
192C3×Dic6—21no—
193C3×Dic6—21no—
194C3⋊(C3⋊C8)—21no—
195C3⋊(C3⋊C8)—21no—
196C3⋊(C3⋊C8)—22no—
197#537—31no—
198#520—31no—
199#485—92no—
200#483—92no—
201#482—92no—
202#481—92no—
203#428—91no—
204C2×#106—91no—
205#417—91no—
206#416—91no—
207#408—91no—
208C3×#41—22no—
209C3×#41—22no—
210C3×#41—22no—
211C3×#41—22no—
212C3×#41—42no—
213C3×#41—42no—
214C3×#41—62no—
215C3×#41—62no—
216C2×C3×Q8—21no—
217C2×C3×Q8—31no—
218C2×C3×Q8#6711yescharacteristic
219C2×C3×Q8#6711yescharacteristic
220C2×C3×D4—21no—
221C2×C3×D4—22no—
222C2×C3×D4—31no—
223C2×C3×D4—61no—
224C2×C3×D4—62no—
225C2×C3×D4#6712yes—
226C2×C3×D4#6711yescharacteristic
227C2×C3×D4#6711yescharacteristic
228C2×C3×D4#6712yes—
229C22×C3×C4—21no—
230C22×C3×C4—22no—
231C22×C3×C4—62no—
232C22×C3×C4—61no—
233C22×C3×C4—61no—
234C22×C3×C4—61no—
235C22×C3×C4C22×D312yes—
236C22×C3×C4C22×D312yes—
237C22×C3×C4C22×D311yescharacteristic
238C22×C3×C4C22×D311yescharacteristic
239C2×#67—21no—
240C2×#67—22no—
241C22×Dic3—22no—
242C22×Dic3—21no—
243C22×Dic3—21no—
244#235—22no—
245#235—22no—
246C2×D12C22×D311yescharacteristic
247C2×C4×D3—21no—
248C2×Dic6C22×D311yescharacteristic
249C3×C4⋊C4—31no—
250C3×C4⋊C4—32no—
251C3×C4⋊C4—32no—
252C3×C4⋊C4—31no—
253C3×C4⋊C4—62no—
254C3×C4⋊C4—62no—
255C3×C4⋊C4—61no—
256C3×C4⋊C4—61no—
257C3×C22⋊C4—62no—
258C3×C22⋊C4—61no—
259C3×C22⋊C4—62no—
260C3×C22⋊C4—62no—
261C3×C42—62no—
262C3×C42—61no—
263#217—22no—
264#217—22no—
265#217—21no—
266(C2×D3)⋊C4—22no—
267C4⋊Dic3—22no—
268C4⋊Dic3—21no—
269C4⋊Dic3—21no—
270C4⋊Dic3C22×D311yescharacteristic
271C4⋊Dic3C22×D312yes—
272C4⋊Dic3C22×D312yes—
273C4⋊Dic3C22×D311yescharacteristic
274Dic3⋊C4—22no—
275C4×Dic3—22no—
276C4×Dic3—21no—
277#208—62no—
278#208—62no—
279#208—122no—
280C2×C3⋊C8—32no—
281C2×C3⋊C8—32no—
282C2×C3⋊C8—31no—
283C2×C3⋊C8—31no—
284C2×C3⋊C8—31no—
285C2×C3⋊C8—31no—
286C2×C3⋊C8—61no—
287C2×C3⋊C8—61no—
288C2×C3⋊C8—62no—
289C2×C3⋊C8—62no—
290C2×C3⋊C8—62no—
291C2×C3⋊C8—122no—
292C22×C32—21no—
293C22×C32—21no—
294C22×C32—22no—
295C22×C32—22no—
296C22×C32—22no—
297C22×C32#12312yes—
298C22×C32C22×D411yescharacteristic
299C2×C3×D3—41no—
300C2×C3×D3—41no—
301C2×C3×D3—41no—
302C32×C4—22no—
303C32×C4#12312yes—
304C32×C4C2×#4111yescharacteristic
305C32×C4C2×#4111yescharacteristic
306C3×Dic3—41no—
307C3×Dic3—41no—
308C3×Dic3—42no—
309C3×Dic3—41no—
310C3×Dic3—42no—
311C2×#41—31no—
312C2×#41D3211yescharacteristic
313C2×M16—91no—
314C22×C8—91no—
315C22⋊Q8—32no—
316C22⋊Q8—61no—
317#121—32no—
318#121—61no—
319#121—62no—
320C4×Q8—61no—
321C4×D4—62no—
322C4×D4—61no—
323#117—31no—
324#117—32no—
325C2×C4⋊C4—31no—
326C2×C4⋊C4—32no—
327C2×C4⋊C4—31no—
328#107—92no—
329#106—92no—
330#106—92no—
331#106—92no—
332#103—91no—
333#103—91no—
334#103—92no—
335#102—91no—
336#102—91no—
337#102—92no—
338C22⋊C8—92no—
339C22⋊C8—92no—
340C23×C3—21no—
341C23×C3—22no—
342C23×C3—61no—
343C23×C3C2×#6712yes—
344C23×C3C2×#6712yes—
345C23×C3C2×#6711yescharacteristic
346C23×C3C2×#6711yescharacteristic
347C22×D3—21no—
348C3×Q8—22no—
349C3×Q8—22no—
350C3×Q8—42no—
351C3×Q8—61no—
352C3×Q8—61no—
353C3×D4—24no—
354C3×D4—24no—
355C3×D4—22no—
356C3×D4—22no—
357C3×D4—42no—
358C3×D4—44no—
359C3×D4—61no—
360C3×D4—61no—
361C3×D4—122no—
362C3×D4—242no—
363C2×C3×C4—22no—
364C2×C3×C4—22no—
365C2×C3×C4—22no—
366C2×C3×C4—22no—
367C2×C3×C4—21no—
368C2×C3×C4—22no—
369C2×C3×C4—22no—
370C2×C3×C4—21no—
371C2×C3×C4—22no—
372C2×C3×C4—42no—
373C2×C3×C4—42no—
374C2×C3×C4—61no—
375C2×C3×C4—62no—
376C2×C3×C4—61no—
377C2×C3×C4—62no—
378C2×C3×C4—61no—
379C2×C3×C4—122no—
380C2×C3×C4—241no—
381C2×C3×C4—242no—
382C2×C3×C4—241no—
383C2×C3×C4#23512yes—
384C2×C3×C4#23512yes—
385C2×C3×C4#23712yes—
386C2×C3×C4#23712yes—
387C2×C3×C4C2×#6712yes—
388C2×C3×C4C2×#6712yes—
389C2×C3×C4C2×#6711yescharacteristic
390C2×C3×C4C2×#6711yescharacteristic
391C2×C3×C4C23×D311yescharacteristic
392C2×C3×C4C23×D311yescharacteristic
393#67—42no—
394#67—82no—
395C2×Dic3—21no—
396C2×Dic3—22no—
397C2×Dic3—21no—
398C2×Dic3—21no—
399C2×Dic3—22no—
400C2×Dic3—81no—
401C2×Dic3—82no—
402C2×Dic3—81no—
403D12—21no—
404D12—21no—
405C4×D3—42no—
406Dic6—21no—
407Dic6—21no—
408C3⋊C8—61no—
409C3⋊C8—61no—
410C3⋊C8—62no—
411C3⋊C8—61no—
412C3⋊C8—61no—
413C3⋊C8—62no—
414C3⋊C8—121no—
415C3⋊C8—121no—
416C3⋊C8—122no—
417C2×C32—22no—
418C2×C32—42no—
419C2×C32C2×#12311yescharacteristic
420C2×C32#57711yescharacteristic
421C2×C32#57711yescharacteristic
422C3×D3—81no—
423#41—22no—
424#41—22no—
425#41—62no—
426#41—62no—
427C2×Q8—31no—
428C2×Q8#62511yescharacteristic
429C2×D4—31no—
430C2×D4—61no—
431C2×D4—62no—
432C2×D4#62512yes—
433C2×D4#62511yescharacteristic
434C22×C4—62no—
435C22×C4—61no—
436C22×C4—61no—
437C22×C4—61no—
438C22×C4C2×D3212yes—
439C22×C4C2×D3211yescharacteristic
440M16—182no—
441C2×C8—91no—
442C2×C8—91no—
443C2×C8—92no—
444C2×C8—182no—
445C4⋊C4—31no—
446C4⋊C4—32no—
447C4⋊C4—31no—
448C4⋊C4—32no—
449C4⋊C4—62no—
450C4⋊C4—61no—
451C4⋊C4—61no—
452C4⋊C4—62no—
453C22⋊C4—62no—
454C22⋊C4—61no—
455C22⋊C4—62no—
456C22⋊C4—62no—
457C42—62no—
458C42—61no—
459C22×C3—21no—
460C22×C3—21no—
461C22×C3—21no—
462C22×C3—21no—
463C22×C3—22no—
464C22×C3—22no—
465C22×C3—22no—
466C22×C3—22no—
467C22×C3—22no—
468C22×C3—22no—
469C22×C3—21no—
470C22×C3—22no—
471C22×C3—41no—
472C22×C3—41no—
473C22×C3—42no—
474C22×C3—42no—
475C22×C3—42no—
476C22×C3—121no—
477C22×C3—121no—
478C22×C3—121no—
479C22×C3#92912yes—
480C22×C3#93512yes—
481C22×C3C22×#6711yescharacteristic
482C22×C3C22×#6711yescharacteristic
483C2×D3—41no—
484C2×D3—41no—
485C2×D3—41no—
486C3×C4—22no—
487C3×C4—22no—
488C3×C4—21no—
489C3×C4—21no—
490C3×C4—22no—
491C3×C4—42no—
492C3×C4—121no—
493C3×C4—121no—
494C3×C4—122no—
495C3×C4—121no—
496C3×C4—122no—
497C3×C4#92912yes—
498C3×C4#93512yes—
499C3×C4C2×#23511yescharacteristic
500C3×C4C2×#23511yescharacteristic
501C3×C4C2×#23711yescharacteristic
502C3×C4C2×#23711yescharacteristic
503Dic3—41no—
504Dic3—42no—
505Dic3—41no—
506Dic3—42no—
507Dic3—41no—
508C32#309911yescharacteristic, complemented, Sylow
509C23—61no—
510C23C2×#62512yes—
511C23C2×#62511yescharacteristic
512Q8—22no—
513Q8—61no—
514Q8—61no—
515D4—24no—
516D4—22no—
517D4—61no—
518D4—61no—
519D4—122no—
520D4—242no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—61no—
524C2×C4—62no—
525C2×C4—61no—
526C2×C4—62no—
527C2×C4—61no—
528C2×C4—122no—
529C2×C4—241no—
530C2×C4—242no—
531C2×C4—241no—
532C2×C4#380412yes—
533C2×C4#380412yes—
534C2×C4C2×#62512yes—
535C2×C4C2×#62511yescharacteristic
536C2×C4C22×D3211yescharacteristic
537C8—181no—
538C8—181no—
539C8—182no—
540C2×C3—22no—
541C2×C3—22no—
542C2×C3—21no—
543C2×C3—21no—
544C2×C3—21no—
545C2×C3—42no—
546C2×C3—42no—
547C2×C3—42no—
548C2×C3—82no—
549C2×C3—241no—
550C2×C3C2×#92911yescharacteristic
551C2×C3C2×#93511yescharacteristic
552C2×C3#583611yescharacteristic
553C2×C3#583611yescharacteristic
554C2×C3#583711yescharacteristic
555C2×C3#583711yescharacteristic
556D3—81no—
557C22—21no—
558C22—21no—
559C22—22no—
560C22—22no—
561C22—22no—
562C22—121no—
563C22—121no—
564C22—121no—
565C22#6396112yes—
566C22C22×#62511yescharacteristic
567C4—22no—
568C4—122no—
569C4—121no—
570C4—122no—
571C4—121no—
572C4—121no—
573C4#6396112yes—
574C4C2×#380411yescharacteristic
575C4C2×#380411yescharacteristic
576C3—21no—
577C3#8257411yescharacteristic, complemented
578C3#8341911yescharacteristic, complemented
579C2—22no—
580C2—42no—
581C2—241no—
582C2#1059544611yescharacteristic
583C2#1059544611yescharacteristic
584C2C2×#6396111yescharacteristic
subgroupG/H
centerC22C22×#625
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
prime radicalC3×#5833C2
hypercenterC2×#41D32
hypocenterC32#3099
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C3×#5827C2semidirect
3. #10592933C2semidirect
4. #10591139C2semidirect
5. C2×#63574C2semidirect
6. #10591102C2semidirect
7. #10591101C2semidirect
8. #10591091C2semidirect
9. #10591090C2semidirect
10. #10591087C2semidirect
11. #10591083C2semidirect
46. #5827D3semidirect
508. C32#3099semidirect
577. C3#82574semidirect
578. C3#83419semidirect

Maximal subgroups

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

subgroupindex
C3×#58332
C3×#58272
#105929332
#105911392
C2×#635742
#105911022
#105911012
#105910912
#105910902
#105910872
#105910832
#834193
#825743