Finite Group Databasebeta

← #11870356

Subgroups — #11870356

Order 1152.

875 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5833C211yesmaximal, characteristic
2#10594986C211yesmaximal, characteristic, complemented
3#10592932C211yesmaximal, characteristic, complemented
4C3×#5232C211yesmaximal, characteristic, complemented
5#10591558C212yesmaximal, complemented
6#10591549C212yesmaximal, complemented
7#10591423C212yesmaximal, complemented
8#10591415C212yesmaximal, complemented
9#10591130C211yesmaximal, characteristic, complemented
10C2×#63574C211yesmaximal, characteristic, complemented
11#10591071C211yesmaximal, characteristic, complemented
12#83419—31nomaximal
13#78875—31nomaximal
14C2×C32×#41C2211yescharacteristic
15C2×C3×#235C2211yescharacteristic
16#64135C2211yescharacteristic
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18C3×#946C2212yes—
19C3×#939—22no—
20C3×#938C2212yes—
21C3×#930—21no—
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C3×#924—21no—
25C2×C3×#208C2211yescharacteristic
26Dic3×#67—22no—
27#63898—21no—
28D3×C4⋊Dic3C2212yes—
29#63843—21no—
30#63841C2212yes—
31#63662C2211yescharacteristic
32#63662C2211yescharacteristic
33#63659C2211yescharacteristic
34#63659C2211yescharacteristic
35C3×#835C2212yes—
36C3×#832C2212yes—
37#63575C2212yes—
38#63574C2212yes—
39#63574C2212yes—
40#63573C2212yes—
41(C2×D3)⋊(C3⋊C8)C2212yes—
42(C2×D3)⋊(C3⋊C8)C2212yes—
43C3×#537—31no—
44#5833D311yescharacteristic
45#5827—31no—
46#5504—31no—
47C3×#417—31no—
48#5234—31no—
49#5233—31no—
50#5233—31no—
51#5233—61no—
52#5232D311yescharacteristic, complemented
53#5129—31no—
54#5121—31no—
55#5045—32no—
56#5043—32no—
57#5035—32no—
58#5034—32no—
59#4964—31no—
60C2×#808—31no—
61C2×#808—31no—
62#4814—32no—
63#4805—32no—
64#4784—32no—
65#4777—32no—
66C32×#41—22no—
67C32×#41—22no—
68C2×C32×Q8C2311yescharacteristic
69C2×C32×D4—21no—
70C2×C32×D4C2311yescharacteristic
71C22×C32×C4—21no—
72C22×C32×C4C2311yescharacteristic
73C2×C3×#67—22no—
74C2×C3×#67D412yes—
75C22×C3×Dic3—21no—
76C22×C3×Dic3—21no—
77C3×#235—22no—
78C3×#235—22no—
79C2×C3×D12D411yescharacteristic
80C2×C3×C4×D3C2312yes—
81C2×C3×Dic6D411yescharacteristic
82C2×D3×Dic3—22no—
83#3757—21no—
84C4⋊(C3⋊Dic3)C2311yescharacteristic
85C4⋊(C3⋊Dic3)C2311yescharacteristic
86C4×C3⋊Dic3—21no—
87C2×C3⋊(C3⋊C8)—22no—
88C2×C3⋊(C3⋊C8)C2311yescharacteristic
89C2×C3⋊(C3⋊C8)C2311yescharacteristic
90C3×#217—22no—
91C3×(C2×D3)⋊C4—22no—
92C3×C4⋊Dic3—21no—
93C3×C4⋊Dic3—21no—
94C3×C4⋊Dic3C2312yes—
95C3×C4⋊Dic3C2312yes—
96C3×Dic3⋊C4—22no—
97C3×#208—22no—
98C2×C3×C3⋊C8C2312yes—
99Dic3⋊Dic3—22no—
100(C2×D3)⋊Dic3—22no—
101Dic32—22no—
102#3099—91noSylow
103C2×C3×#41—21no—
104C2×C3×#41—31no—
105C2×C3×#41C2×D311yescharacteristic
106C2×C3×#41C2×D311yescharacteristic
107C2×#235C2×D311yescharacteristic
108C2×C3×M16—31no—
109C3×C22⋊Q8—32no—
110C3×C22⋊Q8—61no—
111C3×#121—32no—
112C3×#121—61no—
113C3×#121—62no—
114C2×C3×C4⋊C4—31no—
115C2×C3×C4⋊C4—31no—
116#946C2×D312yes—
117Q8×Dic3—61no—
118#939—22no—
119#938C2×D312yes—
120D4×Dic3—61no—
121D4×Dic3—62no—
122#930—21no—
123C4×#67—62no—
124#926—31no—
125#926—31no—
126#926—32no—
127#926—61no—
128C2×C4⋊Dic3—32no—
129C2×C4⋊Dic3C2×D311yescharacteristic
130C2×C4⋊Dic3C2×D311yescharacteristic
131#924—21no—
132C2×#208C2×D311yescharacteristic
133C22×C3⋊C8—31no—
134C22×C3⋊C8—31no—
135C22×C3⋊C8—61no—
136#893—61no—
137#892—32no—
138D3×C4⋊C4—32no—
139#887—61no—
140C3×#103—32no—
141C3×#102—32no—
142#835—31no—
143#835—31no—
144#835—31no—
145#835—31no—
146#835—61no—
147#835—61no—
148#835C2×D312yes—
149#832—31no—
150#832—31no—
151#832—31no—
152#832—31no—
153#832—61no—
154#832—61no—
155#832C2×D312yes—
156#830—32no—
157#830—32no—
158(C2×D3)⋊C8—32no—
159(C2×D3)⋊C8—32no—
160#818—32no—
161#817—32no—
162#808—32no—
163#808—32no—
164#808—32no—
165#808—32no—
166#808—32no—
167#807—32no—
168C23×C32—21no—
169C23×C32C2×D411yescharacteristic
170C22×C3×D3C2×D412yes—
171C32×Q8—21no—
172C32×Q8—21no—
173C32×D4—21no—
174C32×D4—21no—
175C32×D4—42no—
176C2×C32×C4—21no—
177C2×C32×C4—42no—
178C2×C32×C4C2×D411yescharacteristic
179C2×C32×C4#4112yes—
180C2×C32×C4#4112yes—
181C2×C32×C4C2411yescharacteristic
182C2×C3⋊Dic3—21no—
183C2×C3⋊Dic3—21no—
184C3×#67—24no—
185C3×#67—82no—
186C2×C3×Dic3—22no—
187C2×C3×Dic3—22no—
188C2×C3×Dic3—81no—
189C2×C3×Dic3—81no—
190C2×C3×Dic3C2×D412yes—
191C3×D12—22no—
192C3×C4×D3—22no—
193C3×C4×D3—22no—
194C3×Dic6—22no—
195D3×Dic3—82no—
196C3⋊(C3⋊C8)—21no—
197C3⋊(C3⋊C8)—21no—
198C3×C3⋊C8—22no—
199#537—31no—
200#520—91no—
201#485—92no—
202#483—92no—
203#482—92no—
204#481—92no—
205#428—91no—
206C2×#106—91no—
207#417—31no—
208#416—91no—
209#408—91no—
210C3×#41—24no—
211C3×#41—22no—
212C3×#41—22no—
213C3×#41—22no—
214C3×#41—22no—
215C3×#41—42no—
216C3×#41—62no—
217C3×#41—62no—
218C2×C3×Q8—21no—
219C2×C3×Q8—31no—
220C2×C3×Q8C22×D311yescharacteristic
221C2×C3×Q8C22×D311yescharacteristic
222C2×C3×D4—21no—
223C2×C3×D4—21no—
224C2×C3×D4—21no—
225C2×C3×D4—32no—
226C2×C3×D4—31no—
227C2×C3×D4—41no—
228C2×C3×D4—62no—
229C2×C3×D4C22×D311yescharacteristic
230C2×C3×D4C22×D311yescharacteristic
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—32no—
235C22×C3×C4—41no—
236C22×C3×C4—61no—
237C22×C3×C4—61no—
238C22×C3×C4C22×D311yescharacteristic
239C22×C3×C4C22×D311yescharacteristic
240C2×#67—22no—
241C2×#67#6712yes—
242C22×Dic3—21no—
243C22×Dic3—21no—
244C22×Dic3—62no—
245#235—22no—
246#235—22no—
247C2×D12#6711yescharacteristic
248C2×C4×D3—62no—
249C2×C4×D3C22×D312yes—
250C2×Dic6#6711yescharacteristic
251C3×M16—62no—
252C2×C3×C8—32no—
253C3×C4⋊C4—32no—
254C3×C4⋊C4—32no—
255C3×C4⋊C4—62no—
256C3×C4⋊C4—61no—
257C3×C4⋊C4—61no—
258C3×C22⋊C4—62no—
259C3×C22⋊C4—62no—
260#217—22no—
261#217—62no—
262#217—61no—
263#217—61no—
264#217—121no—
265(C2×D3)⋊C4—22no—
266(C2×D3)⋊C4—62no—
267C4⋊Dic3—21no—
268C4⋊Dic3—21no—
269C4⋊Dic3—31no—
270C4⋊Dic3—31no—
271C4⋊Dic3—31no—
272C4⋊Dic3—31no—
273C4⋊Dic3—61no—
274C4⋊Dic3—61no—
275C4⋊Dic3—62no—
276C4⋊Dic3C22×D312yes—
277C4⋊Dic3C22×D312yes—
278Dic3⋊C4—22no—
279Dic3⋊C4—62no—
280C4×Dic3—62no—
281C4×Dic3—61no—
282C4×Dic3—61no—
283C4×Dic3—62no—
284C4×Dic3—121no—
285#208—22no—
286C2×C3⋊C8—31no—
287C2×C3⋊C8—31no—
288C2×C3⋊C8—31no—
289C2×C3⋊C8—31no—
290C2×C3⋊C8—61no—
291C2×C3⋊C8—61no—
292C2×C3⋊C8—62no—
293C2×C3⋊C8—62no—
294C2×C3⋊C8—122no—
295C2×C3⋊C8C22×D312yes—
296C22×C32—21no—
297C22×C32—21no—
298C22×C32—41no—
299C22×C32—41no—
300C22×C32—41no—
301C22×C32#12312yes—
302C22×C32C22×D411yescharacteristic
303C2×C3×D3—22no—
304C2×C3×D3—22no—
305C2×C3×D3—22no—
306C32×C4—41no—
307C32×C4#12312yes—
308C32×C4C2×#4111yescharacteristic
309C32×C4C2×#4111yescharacteristic
310C3⋊Dic3—41no—
311C3⋊Dic3—41no—
312C3×Dic3—22no—
313C3×Dic3—42no—
314C3×Dic3—42no—
315C2×#41—31no—
316C2×#41D3211yescharacteristic
317C2×M16—31no—
318C22×C8—91no—
319C22⋊Q8—32no—
320C22⋊Q8—61no—
321#121—32no—
322#121—61no—
323#121—62no—
324C4×Q8—181no—
325C4×D4—181no—
326C4×D4—182no—
327#117—92no—
328#117—91no—
329C2×C4⋊C4—31no—
330C2×C4⋊C4—31no—
331C2×C4⋊C4—92no—
332#107—92no—
333#106—92no—
334#106—92no—
335#106—92no—
336#103—32no—
337#103—91no—
338#103—91no—
339#102—32no—
340#102—91no—
341#102—91no—
342C22⋊C8—92no—
343C22⋊C8—92no—
344C23×C3—21no—
345C23×C3—21no—
346C23×C3—21no—
347C23×C3—32no—
348C23×C3—41no—
349C23×C3D3×D411yescharacteristic
350C23×C3C2×#6711yescharacteristic
351C22×D3C2×#6712yes—
352C3×Q8—22no—
353C3×Q8—21no—
354C3×Q8—21no—
355C3×Q8—21no—
356C3×Q8—21no—
357C3×Q8—41no—
358C3×Q8—62no—
359C3×D4—22no—
360C3×D4—21no—
361C3×D4—21no—
362C3×D4—21no—
363C3×D4—21no—
364C3×D4—41no—
365C3×D4—44no—
366C3×D4—42no—
367C3×D4—42no—
368C3×D4—64no—
369C3×D4—62no—
370C3×D4—242no—
371C2×C3×C4—21no—
372C2×C3×C4—21no—
373C2×C3×C4—21no—
374C2×C3×C4—22no—
375C2×C3×C4—22no—
376C2×C3×C4—21no—
377C2×C3×C4—32no—
378C2×C3×C4—41no—
379C2×C3×C4—44no—
380C2×C3×C4—42no—
381C2×C3×C4—42no—
382C2×C3×C4—62no—
383C2×C3×C4—62no—
384C2×C3×C4—62no—
385C2×C3×C4—62no—
386C2×C3×C4—241no—
387C2×C3×C4—241no—
388C2×C3×C4#23512yes—
389C2×C3×C4D3×D411yescharacteristic
390C2×C3×C4#23712yes—
391C2×C3×C4#23712yes—
392C2×C3×C4#23712yes—
393C2×C3×C4C2×#6711yescharacteristic
394C2×C3×C4C23×D311yescharacteristic
395C2×C3×C4C23×D311yescharacteristic
396#67—24no—
397#67—82no—
398C2×Dic3—22no—
399C2×Dic3—22no—
400C2×Dic3—61no—
401C2×Dic3—61no—
402C2×Dic3—61no—
403C2×Dic3—61no—
404C2×Dic3—81no—
405C2×Dic3—81no—
406C2×Dic3—121no—
407C2×Dic3—121no—
408C2×Dic3—242no—
409C2×Dic3C2×#6712yes—
410D12—22no—
411C4×D3—22no—
412C4×D3—22no—
413C4×D3—242no—
414Dic6—22no—
415C3×C8—62no—
416C3⋊C8—22no—
417C3⋊C8—61no—
418C3⋊C8—61no—
419C3⋊C8—61no—
420C3⋊C8—61no—
421C3⋊C8—121no—
422C3⋊C8—121no—
423C2×C32—22no—
424C2×C32—81no—
425C2×C32C2×#12311yescharacteristic
426C2×C32#57711yescharacteristic
427C2×C32#57711yescharacteristic
428C3×D3—42no—
429#41—22no—
430#41—22no—
431#41—62no—
432#41—62no—
433C2×Q8—31no—
434C2×Q8C2×D3211yescharacteristic
435C2×D4—21no—
436C2×D4—32no—
437C2×D4—31no—
438C2×D4—62no—
439C2×D4C2×D3211yescharacteristic
440C22×C4—21no—
441C22×C4—32no—
442C22×C4—61no—
443C22×C4—61no—
444C22×C4—182no—
445C22×C4C2×D3211yescharacteristic
446M16—62no—
447C2×C8—32no—
448C2×C8—91no—
449C2×C8—91no—
450C2×C8—182no—
451C4⋊C4—32no—
452C4⋊C4—32no—
453C4⋊C4—62no—
454C4⋊C4—61no—
455C4⋊C4—61no—
456C4⋊C4—91no—
457C4⋊C4—91no—
458C4⋊C4—182no—
459C22⋊C4—62no—
460C22⋊C4—62no—
461C22⋊C4—182no—
462C22⋊C4—181no—
463C42—182no—
464C42—181no—
465C22×C3—21no—
466C22×C3—21no—
467C22×C3—21no—
468C22×C3—21no—
469C22×C3—21no—
470C22×C3—22no—
471C22×C3—41no—
472C22×C3—41no—
473C22×C3—42no—
474C22×C3—41no—
475C22×C3—41no—
476C22×C3—41no—
477C22×C3—41no—
478C22×C3—41no—
479C22×C3—41no—
480C22×C3—62no—
481C22×C3—62no—
482C22×C3—62no—
483C22×C3—81no—
484C22×C3—81no—
485C22×C3#88312yes—
486C22×C3#93512yes—
487C22×C3C2×D3×D411yescharacteristic
488C22×C3C22×#6711yescharacteristic
489C2×D3—22no—
490C2×D3—22no—
491C2×D3—22no—
492C3×C4—21no—
493C3×C4—21no—
494C3×C4—22no—
495C3×C4—42no—
496C3×C4—41no—
497C3×C4—41no—
498C3×C4—62no—
499C3×C4—122no—
500C3×C4—122no—
501C3×C4#88312yes—
502C3×C4#93512yes—
503C3×C4C2×#23511yescharacteristic
504C3×C4C2×#23711yescharacteristic
505C3×C4C2×#23711yescharacteristic
506C3×C4C2×#23711yescharacteristic
507Dic3—22no—
508Dic3—42no—
509Dic3—42no—
510Dic3—121no—
511Dic3—121no—
512Dic3—121no—
513Dic3—121no—
514Dic3—241no—
515Dic3—241no—
516C32#309911yescharacteristic, complemented, Sylow
517C23—21no—
518C23—32no—
519C23D3×#6711yescharacteristic
520Q8—21no—
521Q8—21no—
522Q8—62no—
523D4—21no—
524D4—21no—
525D4—42no—
526D4—64no—
527D4—62no—
528D4—242no—
529C2×C4—21no—
530C2×C4—32no—
531C2×C4—42no—
532C2×C4—62no—
533C2×C4—62no—
534C2×C4—62no—
535C2×C4—62no—
536C2×C4—181no—
537C2×C4—181no—
538C2×C4—241no—
539C2×C4—241no—
540C2×C4—722no—
541C2×C4#380412yes—
542C2×C4#380512yes—
543C2×C4D3×#6711yescharacteristic
544C2×C4C22×D3211yescharacteristic
545C8—62no—
546C8—181no—
547C8—181no—
548C2×C3—22no—
549C2×C3—22no—
550C2×C3—21no—
551C2×C3—21no—
552C2×C3—21no—
553C2×C3—42no—
554C2×C3—82no—
555C2×C3—81no—
556C2×C3—81no—
557C2×C3—122no—
558C2×C3C2×#88311yescharacteristic
559C2×C3#577511yescharacteristic
560C2×C3#577811yescharacteristic
561C2×C3C2×#93511yescharacteristic
562C2×C3#583611yescharacteristic
563C2×C3#583711yescharacteristic
564D3—42no—
565C22—21no—
566C22—21no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—62no—
571C22—62no—
572C22—62no—
573C22#6396912yes—
574C22C2×D3×#6711yescharacteristic
575C4—41no—
576C4—62no—
577C4—122no—
578C4—122no—
579C4—361no—
580C4—361no—
581C4#6396912yes—
582C4C2×#380411yescharacteristic
583C4C2×#380511yescharacteristic
584C3—21no—
585C3#7887511yescharacteristic, complemented
586C3#8341911yescharacteristic, complemented
587C2—22no—
588C2—81no—
589C2—122no—
590C2#1059545511yescharacteristic
591C2#1059546411yescharacteristic
592C2C2×#6396911yescharacteristic
subgroupG/H
centerC22C2×D3×#67
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 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. #10594986C2semidirect
3. #10592932C2semidirect
4. C3×#5232C2semidirect
5. #10591558C2semidirect
6. #10591549C2semidirect
7. #10591423C2semidirect
8. #10591415C2semidirect
9. #10591130C2semidirect
10. C2×#63574C2semidirect
11. #10591071C2semidirect
52. #5232D3semidirect
516. C32#3099semidirect
585. C3#78875semidirect
586. C3#83419semidirect

Maximal subgroups

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

subgroupindex
C3×#58332
#105949862
#105929322
C3×#52322
#105915582
#105915492
#105914232
#105914152
#105911302
C2×#635742
#105910712
#834193
#788753