Finite Group Databasebeta

← #11870374

Subgroups — #11870374

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
1#10595044C211yesmaximal, characteristic
2#10594986C211yesmaximal, characteristic, complemented
3#10592820C211yesmaximal, characteristic, complemented
4C3×#5133C211yesmaximal, characteristic, complemented
5C3×#5129C211yesmaximal, characteristic, complemented
6C2×#63573C211yesmaximal, characteristic, complemented
7#10591084C211yesmaximal, characteristic, complemented
8#10590834C212yesmaximal, complemented
9#10590710C212yesmaximal, complemented
10#10590676C212yesmaximal, complemented
11#10590675C212yesmaximal, complemented
12#78875—31nomaximal
13#78654—31nomaximal
14C2×C3×#235C2211yescharacteristic
15C2×C3×#235C2211yescharacteristic
16C2×C32×M16C2211yescharacteristic
17#64135C2211yescharacteristic
18C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21#63980—22no—
22Dic3×#67—22no—
23#63908—21no—
24#63908C2212yes—
25#63898—21no—
26D3×C4⋊Dic3C2212yes—
27#63856—21no—
28#63856C2212yes—
29#63843—21no—
30#63841C2212yes—
31#63645C2212yes—
32#63644C2212yes—
33C3×#821C2212yes—
34C3×(C2×D3)⋊C8C2212yes—
35C3×(C2×D3)⋊C8C2212yes—
36C3×#816C2212yes—
37#63573C2212yes—
38#63573C2212yes—
39#63566C2211yescharacteristic
40#63566C2211yescharacteristic
41#63563C2211yescharacteristic
42#63563C2211yescharacteristic
43#5833—31no—
44#5833—31no—
45#5827—31no—
46#5504—31no—
47C3×#417—31no—
48C3×#408—31no—
49#5233—31no—
50#5133D311yescharacteristic, complemented
51#5129D311yescharacteristic, complemented
52#5121—31no—
53#5121—31no—
54#5121—61no—
55#5113—31no—
56C2×#817—31no—
57C2×#808—31no—
58#4814—32no—
59#4805—32no—
60#4784—32no—
61#4777—32no—
62#4737—32no—
63#4735—32no—
64#4723—32no—
65#4721—32no—
66C22×C32×C4C2311yescharacteristic
67C22×C3⋊Dic3—21no—
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×D12D411yescharacteristic
76C2×C3×D12C2311yescharacteristic
77C2×C3×C4×D3—21no—
78C2×C3×C4×D3C2312yes—
79C2×C3×Dic6D411yescharacteristic
80C2×C3×Dic6C2311yescharacteristic
81C2×#625—22no—
82C2×D3×Dic3—22no—
83C32×M16—22no—
84C2×C32×C8C2312yes—
85#3757—21no—
86C4⋊(C3⋊Dic3)—21no—
87C4⋊(C3⋊Dic3)C2311yescharacteristic
88C4⋊(C3⋊Dic3)C2311yescharacteristic
89C4⋊(C3⋊Dic3)C2312yes—
90C4×C3⋊Dic3—21no—
91C3×C4⋊Dic3—21no—
92C3×C4⋊Dic3C2312yes—
93C2×C3×C3⋊C8—22no—
94C2×C3×C3⋊C8C2311yescharacteristic
95C2×C3×C3⋊C8C2311yescharacteristic
96#3724—22no—
97Dic3⋊Dic3—22no—
98(C2×D3)⋊Dic3—22no—
99(C2×D3)⋊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
107C2×C3×M16—21no—
108C2×C3×M16C2×D311yescharacteristic
109C2×C3×M16C2×D311yescharacteristic
110C22×C3×C8—31no—
111C2×C3×C4⋊C4—31no—
112#946—32no—
113#946—61no—
114Q8×Dic3—61no—
115#939—62no—
116#939—62no—
117#938—32no—
118#938—61no—
119D4×Dic3—61no—
120D4×Dic3—62no—
121#930—32no—
122#930—61no—
123C4×#67—62no—
124#926—31no—
125#926—31no—
126#926—32no—
127#926—61no—
128C2×C4⋊Dic3—31no—
129C2×C4⋊Dic3—31no—
130C2×C4⋊Dic3—32no—
131C2×C4⋊Dic3—61no—
132C2×C4⋊Dic3C2×D311yescharacteristic
133#924—32no—
134#924—61no—
135C22×C3⋊C8C2×D311yescharacteristic
136#893—61no—
137#892—32no—
138D3×C4⋊C4—32no—
139#887—61no—
140C3×#103—32no—
141C3×#102—32no—
142C3×C22⋊C8—32no—
143C3×C22⋊C8—32no—
144#835—31no—
145#835—31no—
146#832—31no—
147#832—31no—
148#821—31no—
149#821—31no—
150#821C2×D312yes—
151(C2×D3)⋊C8C2×D312yes—
152(C2×D3)⋊C8C2×D312yes—
153#818—32no—
154#818—32no—
155#818—62no—
156#817—32no—
157#817—32no—
158#817—32no—
159#817—32no—
160#817—62no—
161#816—31no—
162#816—31no—
163#816C2×D312yes—
164#808—32no—
165#808—32no—
166C23×C32C2×D411yescharacteristic
167C22×C3×D3—21no—
168C22×C3×D3C2×D412yes—
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4#4112yes—
171C2×C32×C4#4112yes—
172C2×C32×C4C2411yescharacteristic
173C2×C3⋊Dic3—21no—
174C2×C3⋊Dic3—22no—
175C2×C3⋊Dic3—21no—
176C2×C3⋊Dic3—81no—
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×C4×D3—22no—
187C3×C4×D3—22no—
188C3×C4×D3—42no—
189C3×Dic6—22no—
190C3×Dic6—21no—
191C3×Dic6—21no—
192#625—82no—
193D3×Dic3—82no—
194C32×C8—22no—
195C3×C3⋊C8—21no—
196C3×C3⋊C8—21no—
197#537—91no—
198#520—91no—
199#485—92no—
200#483—92no—
201#482—92no—
202#481—92no—
203#428—91no—
204C2×#106—91no—
205#417—31no—
206#416—91no—
207#408—31no—
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—61no—
218C22×C3×C4—21no—
219C22×C3×C4—32no—
220C22×C3×C4—61no—
221C22×C3×C4—61no—
222C22×C3×C4C22×D311yescharacteristic
223C22×C3×C4C22×D311yescharacteristic
224C2×#67—21no—
225C2×#67—62no—
226C2×#67—62no—
227C2×#67D1212yes—
228C22×Dic3—21no—
229C22×Dic3—62no—
230C22×Dic3—61no—
231C22×Dic3—61no—
232C22×Dic3—121no—
233#235—22no—
234#235—22no—
235#235—22no—
236#235—22no—
237C2×D12D1211yescharacteristic
238C2×D12C22×D311yescharacteristic
239C2×C4×D3—21no—
240C2×C4×D3—62no—
241C2×C4×D3C22×D312yes—
242C2×Dic6D1211yescharacteristic
243C2×Dic6C22×D311yescharacteristic
244C3×M16—24no—
245C3×M16—22no—
246C3×M16—22no—
247C2×C3×C8—22no—
248C2×C3×C8—31no—
249C2×C3×C8—31no—
250C2×C3×C8—62no—
251C2×C3×C8C22×D312yes—
252C2×C3×C8C22×D312yes—
253C3×C4⋊C4—32no—
254C3×C4⋊C4—61no—
255#217—62no—
256#217—62no—
257#217—61no—
258#217—61no—
259#217—62no—
260#217—121no—
261(C2×D3)⋊C4—62no—
262(C2×D3)⋊C4—62no—
263(C2×D3)⋊C4—62no—
264C4⋊Dic3—21no—
265C4⋊Dic3—32no—
266C4⋊Dic3—31no—
267C4⋊Dic3—31no—
268C4⋊Dic3—32no—
269C4⋊Dic3—31no—
270C4⋊Dic3—31no—
271C4⋊Dic3—61no—
272C4⋊Dic3—62no—
273C4⋊Dic3—61no—
274C4⋊Dic3—62no—
275C4⋊Dic3—61no—
276C4⋊Dic3—61no—
277C4⋊Dic3—121no—
278C4⋊Dic3C22×D312yes—
279Dic3⋊C4—62no—
280Dic3⋊C4—62no—
281Dic3⋊C4—62no—
282C4×Dic3—62no—
283C4×Dic3—61no—
284C4×Dic3—61no—
285C4×Dic3—62no—
286C4×Dic3—121no—
287C2×C3⋊C8—22no—
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#12312yes—
301C32×C4C2×#4111yescharacteristic
302C32×C4C2×#4111yescharacteristic
303C3⋊Dic3—41no—
304C3⋊Dic3—42no—
305C3⋊Dic3—41no—
306C3×Dic3—22no—
307C3×Dic3—41no—
308C3×Dic3—42no—
309C2×#41—31no—
310C2×#41—31no—
311C2×M16D3211yescharacteristic
312C22×C8—31no—
313C22⋊Q8—92no—
314C22⋊Q8—181no—
315#121—92no—
316#121—181no—
317#121—182no—
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⋊C4—91no—
326#107—92no—
327#106—92no—
328#106—92no—
329#106—92no—
330#103—32no—
331#103—91no—
332#103—91no—
333#102—32no—
334#102—91no—
335#102—91no—
336C22⋊C8—32no—
337C22⋊C8—32no—
338C23×C3—21no—
339C23×C3—32no—
340C23×C3—61no—
341C23×C3C2×D1211yescharacteristic
342C23×C3D3×D411yescharacteristic
343C22×D3—21no—
344C22×D3C2×D1212yes—
345C3×Q8—62no—
346C3×Q8—61no—
347C3×Q8—61no—
348C3×D4—64no—
349C3×D4—62no—
350C3×D4—61no—
351C3×D4—61no—
352C3×D4—122no—
353C2×C3×C4—21no—
354C2×C3×C4—22no—
355C2×C3×C4—21no—
356C2×C3×C4—22no—
357C2×C3×C4—32no—
358C2×C3×C4—62no—
359C2×C3×C4—62no—
360C2×C3×C4—62no—
361C2×C3×C4—61no—
362C2×C3×C4—122no—
363C2×C3×C4—241no—
364C2×C3×C4C2×D1211yescharacteristic
365C2×C3×C4#23512yes—
366C2×C3×C4D3×D411yescharacteristic
367C2×C3×C4#23712yes—
368C2×C3×C4#23712yes—
369C2×C3×C4#23712yes—
370C2×C3×C4C23×D311yescharacteristic
371C2×C3×C4C23×D311yescharacteristic
372#67—24no—
373#67—42no—
374#67—242no—
375#67—242no—
376C2×Dic3—22no—
377C2×Dic3—21no—
378C2×Dic3—61no—
379C2×Dic3—61no—
380C2×Dic3—62no—
381C2×Dic3—61no—
382C2×Dic3—61no—
383C2×Dic3—62no—
384C2×Dic3—81no—
385C2×Dic3—121no—
386C2×Dic3—121no—
387C2×Dic3—122no—
388C2×Dic3—242no—
389C2×Dic3—241no—
390C2×Dic3—241no—
391C2×Dic3—242no—
392C2×Dic3C2×D1212yes—
393D12—22no—
394D12—21no—
395D12—21no—
396C4×D3—22no—
397C4×D3—22no—
398C4×D3—42no—
399C4×D3—242no—
400Dic6—22no—
401Dic6—21no—
402Dic6—21no—
403C3×C8—24no—
404C3×C8—22no—
405C3×C8—22no—
406C3×C8—61no—
407C3×C8—61no—
408C3⋊C8—21no—
409C3⋊C8—21no—
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—61no—
426C2×D4—182no—
427C22×C4—32no—
428C22×C4—61no—
429C22×C4—61no—
430C22×C4—182no—
431C22×C4—181no—
432C22×C4C2×D3211yescharacteristic
433M16—22no—
434C2×C8—31no—
435C2×C8—31no—
436C2×C8—62no—
437C2×C8C2×D3212yes—
438C4⋊C4—32no—
439C4⋊C4—61no—
440C4⋊C4—91no—
441C4⋊C4—91no—
442C4⋊C4—92no—
443C4⋊C4—182no—
444C4⋊C4—182no—
445C4⋊C4—181no—
446C22⋊C4—182no—
447C22⋊C4—182no—
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#88312yes—
467C22×C3#88612yes—
468C22×C3C22×D1211yescharacteristic
469C22×C3C2×D3×D411yescharacteristic
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—62no—
480C3×C4—121no—
481C3×C4—122no—
482C3×C4#88312yes—
483C3×C4#88612yes—
484C3×C4C2×#23511yescharacteristic
485C3×C4C2×#23711yescharacteristic
486C3×C4C2×#23711yescharacteristic
487C3×C4C2×#23711yescharacteristic
488Dic3—22no—
489Dic3—41no—
490Dic3—42no—
491Dic3—121no—
492Dic3—122no—
493Dic3—121no—
494Dic3—121no—
495Dic3—122no—
496Dic3—121no—
497Dic3—242no—
498Dic3—241no—
499Dic3—241no—
500C32#309911yescharacteristic, complemented, Sylow
501C23—32no—
502C23—61no—
503C23D3×D1211yescharacteristic
504Q8—62no—
505Q8—61no—
506Q8—61no—
507D4—64no—
508D4—61no—
509D4—61no—
510D4—62no—
511D4—122no—
512D4—722no—
513C2×C4—32no—
514C2×C4—62no—
515C2×C4—62no—
516C2×C4—62no—
517C2×C4—61no—
518C2×C4—122no—
519C2×C4—181no—
520C2×C4—181no—
521C2×C4—182no—
522C2×C4—241no—
523C2×C4—722no—
524C2×C4—721no—
525C2×C4#379512yes—
526C2×C4D3×D1211yescharacteristic
527C2×C4#380512yes—
528C2×C4C22×D3211yescharacteristic
529C8—22no—
530C8—61no—
531C8—61no—
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×#88311yescharacteristic
541C2×C3C2×#88611yescharacteristic
542C2×C3#575111yescharacteristic
543C2×C3#575111yescharacteristic
544C2×C3#577511yescharacteristic
545C2×C3#577811yescharacteristic
546D3—42no—
547D3—81no—
548C22—21no—
549C22—21no—
550C22—62no—
551C22—62no—
552C22—62no—
553C22—121no—
554C22—121no—
555C22—121no—
556C22#6389112yes—
557C22C2×D3×D1211yescharacteristic
558C4—62no—
559C4—121no—
560C4—122no—
561C4—361no—
562C4—362no—
563C4—361no—
564C4#6389112yes—
565C4C2×#379511yescharacteristic
566C4C2×#380511yescharacteristic
567C3—21no—
568C3#7865411yescharacteristic, complemented
569C3#7887511yescharacteristic, complemented
570C2—22no—
571C2—122no—
572C2—241no—
573C2#1059471311yescharacteristic
574C2#1059471511yescharacteristic
575C2C2×#6389111yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
prime radical#10595044C2
hypercenterC2×M16D32
hypocenterC32#3099
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. #10594986C2semidirect
3. #10592820C2semidirect
4. C3×#5133C2semidirect
5. C3×#5129C2semidirect
6. C2×#63573C2semidirect
7. #10591084C2semidirect
8. #10590834C2semidirect
9. #10590710C2semidirect
10. #10590676C2semidirect
11. #10590675C2semidirect
50. #5133D3semidirect
51. #5129D3semidirect
500. C32#3099semidirect
568. C3#78654semidirect
569. C3#78875semidirect

Maximal subgroups

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

subgroupindex
#105950442
#105949862
#105928202
C3×#51332
C3×#51292
C2×#635732
#105910842
#105908342
#105907102
#105906762
#105906752
#788753
#786543