Finite Group Databasebeta

← #11870365

Subgroups — #11870365

Order 1152.

855 conjugacy classes of subgroups.

The subgroup lattice has 577 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5510C211yesmaximal, characteristic
2#10594986C211yesmaximal, characteristic, complemented
3#10592663C211yesmaximal, characteristic, complemented
4C2×C3×#808C211yesmaximal, characteristic, complemented
5#10591087C211yesmaximal, characteristic, complemented
6#10591084C211yesmaximal, characteristic, complemented
7#10591070C211yesmaximal, characteristic, complemented
8#10590449C212yesmaximal, complemented
9#10590447C212yesmaximal, complemented
10#10590441C212yesmaximal, complemented
11#10590439C212yesmaximal, complemented
12#83419—31nomaximal
13#79112—31nomaximal
14C2×C3×#235C2211yescharacteristic
15C2×C3×#235C2211yescharacteristic
16C2×C32×C4⋊C4C2211yescharacteristic
17#64135C2211yescharacteristic
18C2×#3748C2211yescharacteristic
19C3×#930—22no—
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22C3×#897—21no—
23C3×#897C2212yes—
24C3×#895—21no—
25C3×#895C2212yes—
26Dic3×#67—22no—
27#63898—21no—
28D3×C4⋊Dic3C2212yes—
29#63843—21no—
30#63841C2212yes—
31#63635C2212yes—
32#63634C2212yes—
33C3×#808C2212yes—
34C3×#808C2212yes—
35#63566C2211yescharacteristic
36#63566C2211yescharacteristic
37#63565C2212yes—
38#63563C2211yescharacteristic
39#63563C2211yescharacteristic
40#63562C2212yes—
41(C2×D3)⋊(C3⋊C8)C2212yes—
42(C2×D3)⋊(C3⋊C8)C2212yes—
43C3×#537—31no—
44#5827—31no—
45#5510D311yescharacteristic
46#5504—31no—
47C2×C3×#106—31no—
48#5234—31no—
49#5233—31no—
50#5232—31no—
51#5113—31no—
52#5110—31no—
53#5045—32no—
54#5043—32no—
55#5035—32no—
56#5034—32no—
57#4966—31no—
58#4964—31no—
59#4964—31no—
60#4964—61no—
61C2×#808D311yescharacteristic, complemented
62#4868—32no—
63#4866—32no—
64#4863—32no—
65#4862—32no—
66C22×C32×C4—21no—
67C22×C32×C4C2311yescharacteristic
68C2×C3×#67—21no—
69C2×C3×#67D412yes—
70C22×C3×Dic3—21no—
71C3×#235—22no—
72C3×#235—22no—
73C3×#235—22no—
74C3×#235—22no—
75C2×C3×D12—22no—
76C2×C3×D12D411yescharacteristic
77C2×C3×D12C2311yescharacteristic
78C2×C3×C4×D3—21no—
79C2×C3×C4×D3C2312yes—
80C2×C3×Dic6D411yescharacteristic
81C2×C3×Dic6C2311yescharacteristic
82C2×D3×Dic3—22no—
83C32×C4⋊C4—21no—
84C32×C4⋊C4C2312yes—
85#3757—21no—
86C4⋊(C3⋊Dic3)C2311yescharacteristic
87C4⋊(C3⋊Dic3)C2311yescharacteristic
88C4×C3⋊Dic3—21no—
89#3748—22no—
90C2×C3⋊(C3⋊C8)C2312yes—
91C3×(C2×D3)⋊C4—22no—
92C3×(C2×D3)⋊C4—22no—
93C3×C4⋊Dic3—21no—
94C3×C4⋊Dic3—22no—
95C3×C4⋊Dic3C2312yes—
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—31no—
104C2×C3×#41—31no—
105C2×#235C2×D311yescharacteristic
106C2×#235C2×D311yescharacteristic
107C22×C3×C8—31no—
108C3×C22⋊Q8—32no—
109C3×C22⋊Q8—61no—
110C3×#121—32no—
111C3×#121—61no—
112C3×#121—62no—
113C2×C3×C4⋊C4—21no—
114C2×C3×C4⋊C4—31no—
115C2×C3×C4⋊C4C2×D311yescharacteristic
116C2×C3×C4⋊C4C2×D311yescharacteristic
117Q8×Dic3—61no—
118D4×Dic3—61no—
119D4×Dic3—62no—
120#930—22no—
121C4×#67—62no—
122#926—31no—
123#926—31no—
124#926—32no—
125#926—61no—
126C2×C4⋊Dic3—32no—
127C2×C4⋊Dic3C2×D311yescharacteristic
128C2×#208—31no—
129C2×#208—31no—
130C2×#208—61no—
131C22×C3⋊C8C2×D311yescharacteristic
132#897—21no—
133#897C2×D312yes—
134#895—21no—
135#895C2×D312yes—
136#893—61no—
137#892—32no—
138D3×C4⋊C4—32no—
139#887—61no—
140C3×#106—32no—
141C3×#106—32no—
142#835—32no—
143#835—31no—
144#835—31no—
145#832—32no—
146#832—31no—
147#832—31no—
148#830—32no—
149#830—32no—
150#821—31no—
151#821—31no—
152(C2×D3)⋊C8—32no—
153(C2×D3)⋊C8—32no—
154#816—31no—
155#816—31no—
156#810—32no—
157#809—32no—
158#808—32no—
159#808—32no—
160#808—62no—
161#808C2×D312yes—
162#808C2×D312yes—
163#807—32no—
164#807—32no—
165#807—62no—
166C23×C32C2×D411yescharacteristic
167C22×C3×D3—21no—
168C22×C3×D3C2×D412yes—
169C2×C32×C4—22no—
170C2×C32×C4—81no—
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4#4112yes—
173C2×C32×C4#4112yes—
174C2×C32×C4C2411yescharacteristic
175C2×C3⋊Dic3—21no—
176C2×C3⋊Dic3—21no—
177C3×#67—24no—
178C3×#67—42no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—21no—
181C2×C3×Dic3—81no—
182C2×C3×Dic3C2×D412yes—
183C3×D12—22no—
184C3×D12—21no—
185C3×D12—21no—
186C3×D12—82no—
187C3×C4×D3—22no—
188C3×C4×D3—22no—
189C3×C4×D3—42no—
190C3×Dic6—22no—
191C3×Dic6—21no—
192C3×Dic6—21no—
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—31no—
205#417—91no—
206#416—91no—
207#408—91no—
208C3×#41—62no—
209C3×#41—62no—
210C3×#41—62no—
211C3×#41—62no—
212C2×C3×Q8—31no—
213C2×C3×Q8—31no—
214C2×C3×D4—32no—
215C2×C3×D4—31no—
216C2×C3×D4—31no—
217C2×C3×D4—62no—
218C2×C3×D4—61no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—32no—
223C22×C3×C4—41no—
224C22×C3×C4—61no—
225C22×C3×C4—61no—
226C22×C3×C4C22×D311yescharacteristic
227C22×C3×C4C22×D311yescharacteristic
228C2×#67—21no—
229C2×#67#6712yes—
230C22×Dic3—21no—
231C22×Dic3—62no—
232#235—22no—
233#235—22no—
234#235—22no—
235#235—22no—
236C2×D12—22no—
237C2×D12#6711yescharacteristic
238C2×D12C22×D311yescharacteristic
239C2×C4×D3—21no—
240C2×C4×D3—62no—
241C2×C4×D3C22×D312yes—
242C2×Dic6#6711yescharacteristic
243C2×Dic6C22×D311yescharacteristic
244C2×C3×C8—31no—
245C2×C3×C8—31no—
246C2×C3×C8—62no—
247C3×C4⋊C4—21no—
248C3×C4⋊C4—21no—
249C3×C4⋊C4—22no—
250C3×C4⋊C4—32no—
251C3×C4⋊C4—41no—
252C3×C4⋊C4—62no—
253C3×C4⋊C4—61no—
254C3×C4⋊C4C22×D312yes—
255C3×C4⋊C4C22×D312yes—
256C3×C22⋊C4—62no—
257C3×C22⋊C4—62no—
258#217—62no—
259#217—61no—
260#217—61no—
261#217—121no—
262(C2×D3)⋊C4—22no—
263(C2×D3)⋊C4—22no—
264(C2×D3)⋊C4—62no—
265C4⋊Dic3—21no—
266C4⋊Dic3—22no—
267C4⋊Dic3—31no—
268C4⋊Dic3—31no—
269C4⋊Dic3—31no—
270C4⋊Dic3—31no—
271C4⋊Dic3—61no—
272C4⋊Dic3—61no—
273C4⋊Dic3—62no—
274C4⋊Dic3C22×D312yes—
275Dic3⋊C4—62no—
276C4×Dic3—62no—
277C4×Dic3—61no—
278C4×Dic3—61no—
279C4×Dic3—62no—
280C4×Dic3—121no—
281#208—64no—
282#208—62no—
283#208—62no—
284C2×C3⋊C8—22no—
285C2×C3⋊C8—32no—
286C2×C3⋊C8—32no—
287C2×C3⋊C8—62no—
288C2×C3⋊C8C22×D311yescharacteristic
289C2×C3⋊C8C22×D311yescharacteristic
290C22×C32—21no—
291C22×C32—21no—
292C22×C32#12312yes—
293C22×C32C22×D411yescharacteristic
294C2×C3×D3—22no—
295C2×C3×D3—22no—
296C2×C3×D3—22no—
297C2×C3×D3—41no—
298C2×C3×D3—41no—
299C2×C3×D3—41no—
300C32×C4—42no—
301C32×C4#12312yes—
302C32×C4C2×#4111yescharacteristic
303C32×C4C2×#4111yescharacteristic
304C3⋊Dic3—41no—
305C3⋊Dic3—41no—
306C3×Dic3—22no—
307C3×Dic3—41no—
308C3×Dic3—42no—
309C2×#41—31no—
310C2×#41—31no—
311C2×M16—91no—
312C22×C8—31no—
313C22⋊Q8—32no—
314C22⋊Q8—61no—
315#121—32no—
316#121—61no—
317#121—62no—
318C4×Q8—181no—
319C4×D4—181no—
320C4×D4—182no—
321#117—92no—
322#117—91no—
323C2×C4⋊C4—31no—
324C2×C4⋊C4—92no—
325C2×C4⋊C4D3211yescharacteristic
326#107—92no—
327#106—32no—
328#106—32no—
329#106—92no—
330#103—92no—
331#103—91no—
332#103—91no—
333#102—92no—
334#102—91no—
335#102—91no—
336C22⋊C8—92no—
337C22⋊C8—92no—
338C23×C3—21no—
339C23×C3—32no—
340C23×C3—61no—
341C23×C3D3×D411yescharacteristic
342C23×C3C2×#6711yescharacteristic
343C22×D3—21no—
344C22×D3C2×#6712yes—
345C3×Q8—62no—
346C3×Q8—61no—
347C3×Q8—61no—
348C3×D4—64no—
349C3×D4—62no—
350C3×D4—61no—
351C3×D4—61no—
352C3×D4—122no—
353C3×D4—242no—
354C2×C3×C4—22no—
355C2×C3×C4—22no—
356C2×C3×C4—21no—
357C2×C3×C4—22no—
358C2×C3×C4—22no—
359C2×C3×C4—21no—
360C2×C3×C4—32no—
361C2×C3×C4—42no—
362C2×C3×C4—62no—
363C2×C3×C4—62no—
364C2×C3×C4—61no—
365C2×C3×C4—62no—
366C2×C3×C4—81no—
367C2×C3×C4—81no—
368C2×C3×C4—82no—
369C2×C3×C4—122no—
370C2×C3×C4—241no—
371C2×C3×C4#23512yes—
372C2×C3×C4D3×D411yescharacteristic
373C2×C3×C4#23712yes—
374C2×C3×C4#23712yes—
375C2×C3×C4#23912yes—
376C2×C3×C4C2×#6711yescharacteristic
377C2×C3×C4C23×D311yescharacteristic
378C2×C3×C4C23×D311yescharacteristic
379#67—24no—
380#67—42no—
381C2×Dic3—22no—
382C2×Dic3—21no—
383C2×Dic3—61no—
384C2×Dic3—61no—
385C2×Dic3—61no—
386C2×Dic3—61no—
387C2×Dic3—81no—
388C2×Dic3—121no—
389C2×Dic3—121no—
390C2×Dic3—242no—
391C2×Dic3C2×#6712yes—
392D12—22no—
393D12—21no—
394D12—21no—
395D12—82no—
396C4×D3—22no—
397C4×D3—22no—
398C4×D3—42no—
399C4×D3—242no—
400Dic6—22no—
401Dic6—21no—
402Dic6—21no—
403C3×C8—61no—
404C3×C8—61no—
405C3⋊C8—21no—
406C3⋊C8—21no—
407C3⋊C8—64no—
408C3⋊C8—62no—
409C3⋊C8—62no—
410C2×C32—22no—
411C2×C32C2×#12311yescharacteristic
412C2×C32#57711yescharacteristic
413C2×C32#57711yescharacteristic
414C3×D3—42no—
415C3×D3—81no—
416#41—62no—
417#41—62no—
418#41—62no—
419#41—62no—
420C2×Q8—31no—
421C2×Q8—31no—
422C2×D4—32no—
423C2×D4—31no—
424C2×D4—31no—
425C2×D4—62no—
426C2×D4—61no—
427C22×C4—21no—
428C22×C4—32no—
429C22×C4—61no—
430C22×C4—61no—
431C22×C4—182no—
432C22×C4C2×D3211yescharacteristic
433M16—182no—
434C2×C8—31no—
435C2×C8—31no—
436C2×C8—62no—
437C2×C8—92no—
438C4⋊C4—21no—
439C4⋊C4—32no—
440C4⋊C4—62no—
441C4⋊C4—61no—
442C4⋊C4—91no—
443C4⋊C4—91no—
444C4⋊C4—182no—
445C4⋊C4C2×D3212yes—
446C22⋊C4—62no—
447C22⋊C4—62no—
448C22⋊C4—182no—
449C22⋊C4—181no—
450C42—182no—
451C42—181no—
452C22×C3—21no—
453C22×C3—21no—
454C22×C3—21no—
455C22×C3—21no—
456C22×C3—21no—
457C22×C3—22no—
458C22×C3—41no—
459C22×C3—41no—
460C22×C3—62no—
461C22×C3—62no—
462C22×C3—62no—
463C22×C3—121no—
464C22×C3—121no—
465C22×C3—121no—
466C22×C3#89412yes—
467C22×C3#93512yes—
468C22×C3C2×D3×D411yescharacteristic
469C22×C3C22×#6711yescharacteristic
470C2×D3—22no—
471C2×D3—22no—
472C2×D3—22no—
473C2×D3—41no—
474C2×D3—41no—
475C2×D3—41no—
476C3×C4—21no—
477C3×C4—21no—
478C3×C4—22no—
479C3×C4—42no—
480C3×C4—42no—
481C3×C4—62no—
482C3×C4—82no—
483C3×C4—121no—
484C3×C4—122no—
485C3×C4#89412yes—
486C3×C4#93512yes—
487C3×C4C2×#23511yescharacteristic
488C3×C4C2×#23711yescharacteristic
489C3×C4C2×#23711yescharacteristic
490C3×C4C2×#23911yescharacteristic
491Dic3—22no—
492Dic3—42no—
493Dic3—41no—
494Dic3—121no—
495Dic3—121no—
496Dic3—121no—
497Dic3—121no—
498Dic3—241no—
499Dic3—241no—
500C32#309911yescharacteristic, complemented, Sylow
501C23—32no—
502C23—61no—
503C23D3×#6711yescharacteristic
504Q8—62no—
505Q8—61no—
506Q8—61no—
507D4—64no—
508D4—61no—
509D4—61no—
510D4—62no—
511D4—122no—
512D4—242no—
513C2×C4—22no—
514C2×C4—32no—
515C2×C4—62no—
516C2×C4—62no—
517C2×C4—62no—
518C2×C4—61no—
519C2×C4—81no—
520C2×C4—122no—
521C2×C4—181no—
522C2×C4—181no—
523C2×C4—241no—
524C2×C4—722no—
525C2×C4#379512yes—
526C2×C4#379612yes—
527C2×C4D3×#6711yescharacteristic
528C2×C4C22×D3211yescharacteristic
529C8—61no—
530C8—61no—
531C8—182no—
532C2×C3—22no—
533C2×C3—22no—
534C2×C3—21no—
535C2×C3—21no—
536C2×C3—21no—
537C2×C3—42no—
538C2×C3—122no—
539C2×C3—241no—
540C2×C3C2×#89411yescharacteristic
541C2×C3#576211yescharacteristic
542C2×C3#576211yescharacteristic
543C2×C3C2×#93511yescharacteristic
544C2×C3#583611yescharacteristic
545C2×C3#583711yescharacteristic
546D3—42no—
547D3—81no—
548C22—21no—
549C22—21no—
550C22—62no—
551C22—62no—
552C22—62no—
553C22—121no—
554C22—121no—
555C22—121no—
556C22#6388412yes—
557C22C2×D3×#6711yescharacteristic
558C4—42no—
559C4—62no—
560C4—121no—
561C4—122no—
562C4—361no—
563C4—361no—
564C4#6388412yes—
565C4C2×#379511yescharacteristic
566C4C2×#379611yescharacteristic
567C3—21no—
568C3#7911211yescharacteristic, complemented
569C3#8341911yescharacteristic, complemented
570C2—22no—
571C2—122no—
572C2—241no—
573C2C2×#6388411yescharacteristic
574C2#1059510511yescharacteristic
575C2#1059531811yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C22×D4
prime radicalC3×#5510C2
hypercenterC2×C4⋊C4D32
hypocenterC32#3099
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #10594986C2semidirect
3. #10592663C2semidirect
4. C2×C3×#808C2semidirect
5. #10591087C2semidirect
6. #10591084C2semidirect
7. #10591070C2semidirect
8. #10590449C2semidirect
9. #10590447C2semidirect
10. #10590441C2semidirect
11. #10590439C2semidirect
61. C2×#808D3semidirect
500. C32#3099semidirect
568. C3#79112semidirect
569. C3#83419semidirect

Maximal subgroups

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

subgroupindex
C3×#55102
#105949862
#105926632
C2×C3×#8082
#105910872
#105910842
#105910702
#105904492
#105904472
#105904412
#105904392
#834193
#791123