Finite Group Databasebeta

← #11870357

Subgroups — #11870357

Order 1152.

877 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5833C211yesmaximal, characteristic
2#10594992C211yesmaximal, characteristic, complemented
3#10592931C211yesmaximal, characteristic, complemented
4C3×#5233C211yesmaximal, characteristic, complemented
5#10591559C212yesmaximal, complemented
6#10591549C212yesmaximal, complemented
7#10591422C212yesmaximal, complemented
8#10591415C212yesmaximal, complemented
9#10591139C211yesmaximal, characteristic, complemented
10C2×#63573C211yesmaximal, characteristic, complemented
11#10591070C211yesmaximal, characteristic, complemented
12#83419—31nomaximal
13#78844—31nomaximal
14C2×C32×#41C2211yescharacteristic
15C2×C3×#235C2211yescharacteristic
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C2×#3748C2211yescharacteristic
18C3×#946C2212yes—
19C3×#939—22no—
20C3×#938C2212yes—
21C3×#930—21no—
22C3×#926C2211yescharacteristic
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C3×#924—21no—
25C22×C3×C3⋊C8C2211yescharacteristic
26#67⋊Dic3—22no—
27Dic3×D12—21no—
28D3×C4⋊Dic3C2212yes—
29Dic3×Dic6—21no—
30#63841C2212yes—
31#63662C2212yes—
32#63659C2212yes—
33C3×#835C2211yescharacteristic
34C3×#835C2211yescharacteristic
35C3×#832C2211yescharacteristic
36C3×#832C2211yescharacteristic
37#63576C2212yes—
38#63574C2212yes—
39#63573C2212yes—
40#63573C2212yes—
41(C2×D3)⋊(C3⋊C8)C2212yes—
42(C2×D3)⋊(C3⋊C8)C2212yes—
43C3×#537—31no—
44#5833D311yescharacteristic
45#5827—31no—
46#5523—31no—
47C3×#416—31no—
48#5234—31no—
49#5233D311yescharacteristic, complemented
50#5232—31no—
51#5232—31no—
52#5232—61no—
53#5110—31no—
54C2×#817—31no—
55#5045—32no—
56#5043—32no—
57#5035—32no—
58#5034—32no—
59#4995—31no—
60#4964—31no—
61C2×#808—31no—
62#4815—32no—
63#4805—32no—
64#4779—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
73C22×C3⋊Dic3—21no—
74C2×C3×#67—22no—
75C2×C3×#67D412yes—
76C22×C3×Dic3—21no—
77C3×#235—22no—
78C3×#235—22no—
79C2×C3×D12D411yescharacteristic
80C2×C3×C4×D3C2312yes—
81C2×C3×Dic6D411yescharacteristic
82C2×D3×Dic3—22no—
83C4⋊(C3⋊Dic3)—21no—
84C4⋊(C3⋊Dic3)C2312yes—
85#3748—22no—
86C2×C3⋊(C3⋊C8)C2312yes—
87C3×#217—21no—
88C3×#217—22no—
89C3×(C2×D3)⋊C4—22no—
90C3×C4⋊Dic3—21no—
91C3×C4⋊Dic3C2312yes—
92C3×C4⋊Dic3C2311yescharacteristic
93C3×C4⋊Dic3C2311yescharacteristic
94C3×Dic3⋊C4—22no—
95C3×C4×Dic3—21no—
96C2×C3×C3⋊C8—22no—
97C2×C3×C3⋊C8C2311yescharacteristic
98C2×C3×C3⋊C8C2311yescharacteristic
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
108C22×C3×C8—31no—
109C3×C22⋊Q8—32no—
110C3×C22⋊Q8—61no—
111C3×#121—32no—
112C3×#121—61no—
113C3×#121—62no—
114C3×#117—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—
123#926—32no—
124#926C2×D311yescharacteristic
125C2×C4⋊Dic3—31no—
126C2×C4⋊Dic3—31no—
127C2×C4⋊Dic3—32no—
128C2×C4⋊Dic3—61no—
129C2×C4⋊Dic3C2×D311yescharacteristic
130#924—21no—
131C2×#208—31no—
132C2×#208—31no—
133C2×#208—61no—
134C22×C3⋊C8C2×D311yescharacteristic
135#892—32no—
136D3×C4⋊C4—32no—
137#67⋊C4—62no—
138C4×D12—61no—
139C4×Dic6—61no—
140C3×#103—31no—
141C3×#103—31no—
142C3×#102—31no—
143C3×#102—31no—
144#835—32no—
145#835—32no—
146#835—62no—
147#835C2×D311yescharacteristic
148#835C2×D311yescharacteristic
149#832—32no—
150#832—32no—
151#832—62no—
152#832C2×D311yescharacteristic
153#832C2×D311yescharacteristic
154#830—32no—
155#830—32no—
156(C2×D3)⋊C8—32no—
157(C2×D3)⋊C8—32no—
158#817—32no—
159#817—32no—
160#808—32no—
161#808—32no—
162#808—32no—
163#808—32no—
164#807—32no—
165#807—32no—
166C23×C32—21no—
167C23×C32C2×D411yescharacteristic
168C22×C3×D3C2×D412yes—
169C32×Q8—21no—
170C32×Q8—21no—
171C32×D4—21no—
172C32×D4—21no—
173C32×D4—42no—
174C2×C32×C4—21no—
175C2×C32×C4—42no—
176C2×C32×C4C2×D411yescharacteristic
177C2×C32×C4#4112yes—
178C2×C32×C4#4112yes—
179C2×C32×C4C2411yescharacteristic
180C2×C3⋊Dic3—22no—
181C2×C3⋊Dic3—81no—
182C3×#67—24no—
183C3×#67—82no—
184C2×C3×Dic3—21no—
185C2×C3×Dic3—21no—
186C2×C3×Dic3—22no—
187C2×C3×Dic3—81no—
188C2×C3×Dic3C2×D412yes—
189C3×D12—22no—
190C3×C4×D3—22no—
191C3×C4×D3—22no—
192C3×Dic6—22no—
193D3×Dic3—82no—
194C3⋊(C3⋊C8)—22no—
195C3×C3⋊C8—21no—
196C3×C3⋊C8—21no—
197#537—31no—
198#520—91no—
199#485—92no—
200#483—92no—
201#482—92no—
202#481—92no—
203#428—91no—
204C2×#106—91no—
205#417—91no—
206#416—31no—
207#408—91no—
208C3×#41—24no—
209C3×#41—22no—
210C3×#41—22no—
211C3×#41—22no—
212C3×#41—22no—
213C3×#41—42no—
214C3×#41—62no—
215C3×#41—62no—
216C2×C3×Q8—21no—
217C2×C3×Q8—31no—
218C2×C3×Q8C22×D311yescharacteristic
219C2×C3×Q8C22×D311yescharacteristic
220C2×C3×D4—21no—
221C2×C3×D4—21no—
222C2×C3×D4—21no—
223C2×C3×D4—32no—
224C2×C3×D4—31no—
225C2×C3×D4—41no—
226C2×C3×D4—62no—
227C2×C3×D4C22×D311yescharacteristic
228C2×C3×D4C22×D311yescharacteristic
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—32no—
233C22×C3×C4—41no—
234C22×C3×C4—61no—
235C22×C3×C4C22×D311yescharacteristic
236C22×C3×C4C22×D311yescharacteristic
237C2×#67—22no—
238C2×#67#6712yes—
239C22×Dic3—21no—
240C22×Dic3—62no—
241C22×Dic3—61no—
242C22×Dic3—61no—
243C22×Dic3—121no—
244#235—22no—
245#235—22no—
246C2×D12#6711yescharacteristic
247C2×C4×D3—62no—
248C2×C4×D3C22×D312yes—
249C2×Dic6#6711yescharacteristic
250C2×C3×C8—31no—
251C2×C3×C8—31no—
252C2×C3×C8—62no—
253C3×C4⋊C4—31no—
254C3×C4⋊C4—32no—
255C3×C4⋊C4—31no—
256C3×C4⋊C4—62no—
257C3×C4⋊C4—61no—
258C3×C22⋊C4—62no—
259C3×C22⋊C4—62no—
260C3×C22⋊C4—61no—
261C3×C42—61no—
262#217—21no—
263#217—22no—
264#217—62no—
265(C2×D3)⋊C4—22no—
266(C2×D3)⋊C4—62no—
267C4⋊Dic3—21no—
268C4⋊Dic3—32no—
269C4⋊Dic3—32no—
270C4⋊Dic3—62no—
271C4⋊Dic3—62no—
272C4⋊Dic3—61no—
273C4⋊Dic3—61no—
274C4⋊Dic3—121no—
275C4⋊Dic3C22×D311yescharacteristic
276C4⋊Dic3C22×D312yes—
277C4⋊Dic3C22×D311yescharacteristic
278Dic3⋊C4—22no—
279Dic3⋊C4—62no—
280C4×Dic3—21no—
281C4×Dic3—62no—
282C4×Dic3—62no—
283#208—62no—
284#208—62no—
285#208—122no—
286C2×C3⋊C8—22no—
287C2×C3⋊C8—32no—
288C2×C3⋊C8—32no—
289C2×C3⋊C8—62no—
290C2×C3⋊C8C22×D311yescharacteristic
291C2×C3⋊C8C22×D311yescharacteristic
292C22×C32—21no—
293C22×C32—21no—
294C22×C32—41no—
295C22×C32—41no—
296C22×C32—41no—
297C22×C32#12312yes—
298C22×C32C22×D411yescharacteristic
299C2×C3×D3—22no—
300C2×C3×D3—22no—
301C2×C3×D3—22no—
302C32×C4—41no—
303C32×C4#12312yes—
304C32×C4C2×#4111yescharacteristic
305C32×C4C2×#4111yescharacteristic
306C3⋊Dic3—42no—
307C3×Dic3—22no—
308C3×Dic3—41no—
309C3×Dic3—41no—
310C3×Dic3—42no—
311C2×#41—31no—
312C2×#41D3211yescharacteristic
313C2×M16—91no—
314C22×C8—31no—
315C22⋊Q8—32no—
316C22⋊Q8—61no—
317#121—32no—
318#121—61no—
319#121—62no—
320C4×Q8—181no—
321C4×D4—181no—
322C4×D4—182no—
323#117—31no—
324#117—92no—
325C2×C4⋊C4—31no—
326C2×C4⋊C4—92no—
327C2×C4⋊C4—91no—
328#107—92no—
329#106—92no—
330#106—92no—
331#106—92no—
332#103—31no—
333#103—31no—
334#103—92no—
335#102—31no—
336#102—31no—
337#102—92no—
338C22⋊C8—92no—
339C22⋊C8—92no—
340C23×C3—21no—
341C23×C3—21no—
342C23×C3—21no—
343C23×C3—32no—
344C23×C3—41no—
345C23×C3D3×D411yescharacteristic
346C23×C3C2×#6711yescharacteristic
347C22×D3C2×#6712yes—
348C3×Q8—22no—
349C3×Q8—21no—
350C3×Q8—21no—
351C3×Q8—21no—
352C3×Q8—21no—
353C3×Q8—41no—
354C3×Q8—62no—
355C3×D4—22no—
356C3×D4—21no—
357C3×D4—21no—
358C3×D4—21no—
359C3×D4—21no—
360C3×D4—41no—
361C3×D4—44no—
362C3×D4—42no—
363C3×D4—42no—
364C3×D4—64no—
365C3×D4—62no—
366C3×D4—242no—
367C2×C3×C4—21no—
368C2×C3×C4—21no—
369C2×C3×C4—21no—
370C2×C3×C4—22no—
371C2×C3×C4—22no—
372C2×C3×C4—21no—
373C2×C3×C4—32no—
374C2×C3×C4—41no—
375C2×C3×C4—44no—
376C2×C3×C4—42no—
377C2×C3×C4—42no—
378C2×C3×C4—62no—
379C2×C3×C4—62no—
380C2×C3×C4—62no—
381C2×C3×C4—61no—
382C2×C3×C4—61no—
383C2×C3×C4—241no—
384C2×C3×C4#23512yes—
385C2×C3×C4D3×D411yescharacteristic
386C2×C3×C4#23712yes—
387C2×C3×C4#23712yes—
388C2×C3×C4#23712yes—
389C2×C3×C4C2×#6711yescharacteristic
390C2×C3×C4C23×D311yescharacteristic
391C2×C3×C4C23×D311yescharacteristic
392#67—24no—
393#67—82no—
394C2×Dic3—21no—
395C2×Dic3—21no—
396C2×Dic3—22no—
397C2×Dic3—62no—
398C2×Dic3—62no—
399C2×Dic3—81no—
400C2×Dic3—122no—
401C2×Dic3—242no—
402C2×Dic3—241no—
403C2×Dic3—241no—
404C2×Dic3—242no—
405C2×Dic3C2×#6712yes—
406D12—22no—
407C4×D3—22no—
408C4×D3—22no—
409C4×D3—242no—
410Dic6—22no—
411C3×C8—61no—
412C3×C8—61no—
413C3⋊C8—21no—
414C3⋊C8—21no—
415C3⋊C8—62no—
416C3⋊C8—62no—
417C3⋊C8—122no—
418C2×C32—22no—
419C2×C32—81no—
420C2×C32C2×#12311yescharacteristic
421C2×C32#57711yescharacteristic
422C2×C32#57711yescharacteristic
423C3×D3—42no—
424#41—22no—
425#41—22no—
426#41—62no—
427#41—62no—
428C2×Q8—31no—
429C2×Q8C2×D3211yescharacteristic
430C2×D4—21no—
431C2×D4—32no—
432C2×D4—31no—
433C2×D4—62no—
434C2×D4C2×D3211yescharacteristic
435C22×C4—21no—
436C22×C4—32no—
437C22×C4—61no—
438C22×C4—182no—
439C22×C4—181no—
440C22×C4C2×D3211yescharacteristic
441M16—182no—
442C2×C8—31no—
443C2×C8—31no—
444C2×C8—62no—
445C2×C8—92no—
446C4⋊C4—31no—
447C4⋊C4—31no—
448C4⋊C4—32no—
449C4⋊C4—62no—
450C4⋊C4—61no—
451C4⋊C4—92no—
452C4⋊C4—182no—
453C4⋊C4—181no—
454C22⋊C4—62no—
455C22⋊C4—62no—
456C22⋊C4—61no—
457C22⋊C4—182no—
458C42—61no—
459C42—182no—
460C22×C3—21no—
461C22×C3—21no—
462C22×C3—21no—
463C22×C3—21no—
464C22×C3—21no—
465C22×C3—22no—
466C22×C3—41no—
467C22×C3—41no—
468C22×C3—42no—
469C22×C3—41no—
470C22×C3—41no—
471C22×C3—41no—
472C22×C3—41no—
473C22×C3—41no—
474C22×C3—41no—
475C22×C3—62no—
476C22×C3—62no—
477C22×C3—62no—
478C22×C3—81no—
479C22×C3—81no—
480C22×C3#88312yes—
481C22×C3#93512yes—
482C22×C3C2×D3×D411yescharacteristic
483C22×C3C22×#6711yescharacteristic
484C2×D3—22no—
485C2×D3—22no—
486C2×D3—22no—
487C3×C4—21no—
488C3×C4—21no—
489C3×C4—22no—
490C3×C4—42no—
491C3×C4—41no—
492C3×C4—41no—
493C3×C4—62no—
494C3×C4—122no—
495C3×C4—121no—
496C3×C4—121no—
497C3×C4#88312yes—
498C3×C4#93512yes—
499C3×C4C2×#23511yescharacteristic
500C3×C4C2×#23711yescharacteristic
501C3×C4C2×#23711yescharacteristic
502C3×C4C2×#23711yescharacteristic
503Dic3—22no—
504Dic3—41no—
505Dic3—41no—
506Dic3—42no—
507Dic3—122no—
508Dic3—122no—
509Dic3—242no—
510C32#309911yescharacteristic, complemented, Sylow
511C23—21no—
512C23—32no—
513C23D3×#6711yescharacteristic
514Q8—21no—
515Q8—21no—
516Q8—62no—
517D4—21no—
518D4—21no—
519D4—42no—
520D4—64no—
521D4—62no—
522D4—242no—
523C2×C4—21no—
524C2×C4—32no—
525C2×C4—42no—
526C2×C4—62no—
527C2×C4—62no—
528C2×C4—61no—
529C2×C4—61no—
530C2×C4—62no—
531C2×C4—182no—
532C2×C4—241no—
533C2×C4—722no—
534C2×C4—721no—
535C2×C4#380412yes—
536C2×C4#380512yes—
537C2×C4D3×#6711yescharacteristic
538C2×C4C22×D3211yescharacteristic
539C8—61no—
540C8—61no—
541C8—182no—
542C2×C3—22no—
543C2×C3—22no—
544C2×C3—21no—
545C2×C3—21no—
546C2×C3—21no—
547C2×C3—42no—
548C2×C3—82no—
549C2×C3—81no—
550C2×C3—81no—
551C2×C3—122no—
552C2×C3C2×#88311yescharacteristic
553C2×C3#577011yescharacteristic
554C2×C3#577011yescharacteristic
555C2×C3C2×#93511yescharacteristic
556C2×C3#583611yescharacteristic
557C2×C3#583711yescharacteristic
558D3—42no—
559C22—21no—
560C22—21no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—62no—
565C22—62no—
566C22—62no—
567C22#6396912yes—
568C22C2×D3×#6711yescharacteristic
569C4—41no—
570C4—62no—
571C4—121no—
572C4—122no—
573C4—121no—
574C4—362no—
575C4#6396912yes—
576C4C2×#380411yescharacteristic
577C4C2×#380511yescharacteristic
578C3—21no—
579C3#7884411yescharacteristic, complemented
580C3#8341911yescharacteristic, complemented
581C2—22no—
582C2—81no—
583C2—122no—
584C2#1059545711yescharacteristic
585C2#1059546611yescharacteristic
586C2C2×#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. #10594992C2semidirect
3. #10592931C2semidirect
4. C3×#5233C2semidirect
5. #10591559C2semidirect
6. #10591549C2semidirect
7. #10591422C2semidirect
8. #10591415C2semidirect
9. #10591139C2semidirect
10. C2×#63573C2semidirect
11. #10591070C2semidirect
49. #5233D3semidirect
510. C32#3099semidirect
579. C3#78844semidirect
580. C3#83419semidirect

Maximal subgroups

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

subgroupindex
C3×#58332
#105949922
#105929312
C3×#52332
#105915592
#105915492
#105914222
#105914152
#105911392
C2×#635732
#105910702
#834193
#788443