Finite Group Databasebeta

← #11870375

Subgroups — #11870375

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
1#10595043C211yesmaximal, characteristic
2#10594992C211yesmaximal, characteristic, complemented
3#10592832C211yesmaximal, characteristic, complemented
4C3×#5129C211yesmaximal, characteristic, complemented
5C3×#5121C211yesmaximal, characteristic, complemented
6C2×#63573C211yesmaximal, characteristic, complemented
7#10591105C211yesmaximal, characteristic, complemented
8#10590708C212yesmaximal, complemented
9#10590705C212yesmaximal, complemented
10#10590677C212yesmaximal, complemented
11#10590674C212yesmaximal, complemented
12#79222—31nomaximal
13#78654—31nomaximal
14C2×#3828C2211yescharacteristic
15C2×C3×#235C2211yescharacteristic
16C2×C32×M16C2211yescharacteristic
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C3×#926C2211yescharacteristic
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21#63978—22no—
22#67⋊Dic3—22no—
23#63916—21no—
24#63909C2212yes—
25Dic3×D12—21no—
26D3×C4⋊Dic3C2212yes—
27#63871—21no—
28#63857C2212yes—
29Dic3×Dic6—21no—
30#63841C2212yes—
31#63648C2212yes—
32#63643C2212yes—
33C3×(C2×D3)⋊C8C2212yes—
34C3×(C2×D3)⋊C8C2212yes—
35C3×#818C2212yes—
36C3×#817C2212yes—
37#63573C2212yes—
38#63573C2212yes—
39#63567C2211yescharacteristic
40#63567C2211yescharacteristic
41#63564C2211yescharacteristic
42#63564C2211yescharacteristic
43#5833—31no—
44#5827—31no—
45#5523—31no—
46#5510—31no—
47C3×#428—31no—
48C3×#408—31no—
49#5133—31no—
50#5133—31no—
51#5133—61no—
52#5129D311yescharacteristic, complemented
53#5121D311yescharacteristic, complemented
54#5113—31no—
55C2×#817—31no—
56#5002—31no—
57C2×#808—31no—
58#4888—32no—
59#4885—32no—
60#4863—32no—
61#4862—32no—
62#4737—32no—
63#4735—32no—
64#4723—32no—
65#4721—32no—
66C22×C32×C4C2311yescharacteristic
67C2×#638—21no—
68C22×C3⋊Dic3—21no—
69#3828—22no—
70#3828—22no—
71C2×C4⋊(C3⋊D3)C2311yescharacteristic
72C2×C4×C3⋊D3—21no—
73C2×#634C2311yescharacteristic
74C2×C3×#67D412yes—
75C22×C3×Dic3—21no—
76C3×#235—22no—
77C3×#235—22no—
78C2×C3×D12D411yescharacteristic
79C2×C3×C4×D3C2312yes—
80C2×C3×Dic6D411yescharacteristic
81C2×#626—22no—
82C2×D3×Dic3—22no—
83C32×M16—22no—
84C2×C32×C8C2312yes—
85C4⋊(C3⋊Dic3)—21no—
86C4⋊(C3⋊Dic3)C2312yes—
87C3×#217—21no—
88C3×C4⋊Dic3—21no—
89C3×C4⋊Dic3C2312yes—
90C3×C4⋊Dic3C2311yescharacteristic
91C3×C4⋊Dic3C2311yescharacteristic
92C3×C4×Dic3—21no—
93C2×C3×C3⋊C8—22no—
94C2×C3×C3⋊C8C2311yescharacteristic
95C2×C3×C3⋊C8C2311yescharacteristic
96Dic3⋊Dic3—22no—
97Dic3⋊Dic3—22no—
98#3722—22no—
99(C2×D3)⋊Dic3—22no—
100(C2×D3)⋊Dic3—22no—
101Dic32—22no—
102#3099—91noSylow
103C2×C3×#41—31no—
104C2×#235—31no—
105C2×#235—31no—
106C2×#235—61no—
107C2×#235C2×D311yescharacteristic
108C2×C3×M16—21no—
109C2×C3×M16C2×D311yescharacteristic
110C2×C3×M16C2×D311yescharacteristic
111C22×C3×C8—31no—
112C3×#117—31no—
113C2×C3×C4⋊C4—31no—
114#946—61no—
115Q8×Dic3—61no—
116#939—62no—
117#938—61no—
118D4×Dic3—61no—
119D4×Dic3—62no—
120#930—32no—
121#930—62no—
122#926—32no—
123#926C2×D311yescharacteristic
124C2×C4⋊Dic3—31no—
125C2×C4⋊Dic3—31no—
126C2×C4⋊Dic3—32no—
127C2×C4⋊Dic3—61no—
128C2×C4⋊Dic3C2×D311yescharacteristic
129#924—32no—
130C22×C3⋊C8C2×D311yescharacteristic
131#897—32no—
132#897—61no—
133#895—32no—
134#895—61no—
135#892—32no—
136D3×C4⋊C4—32no—
137#67⋊C4—62no—
138C4×D12—61no—
139C4×Dic6—61no—
140C3×#107—32no—
141C3×#106—32no—
142C3×C22⋊C8—32no—
143C3×C22⋊C8—32no—
144#821—32no—
145#821—32no—
146#821—31no—
147#821—31no—
148#821—62no—
149(C2×D3)⋊C8C2×D312yes—
150(C2×D3)⋊C8C2×D312yes—
151#818C2×D312yes—
152#817—32no—
153#817—32no—
154#817C2×D312yes—
155#816—32no—
156#816—32no—
157#816—31no—
158#816—31no—
159#816—62no—
160#810—31no—
161#810—31no—
162#809—31no—
163#809—31no—
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
173#638—42no—
174C2×C3⋊Dic3—22no—
175C2×C3⋊Dic3—21no—
176C2×C3⋊Dic3—81no—
177C4⋊(C3⋊D3)—21no—
178C4⋊(C3⋊D3)—21no—
179C4×C3⋊D3—42no—
180#634—21no—
181#634—21no—
182C3×#67—24no—
183C2×C3×Dic3—21no—
184C2×C3×Dic3—22no—
185C2×C3×Dic3—21no—
186C2×C3×Dic3—81no—
187C2×C3×Dic3C2×D412yes—
188C3×D12—22no—
189C3×C4×D3—22no—
190C3×C4×D3—22no—
191C3×Dic6—22no—
192#626—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—31no—
204C2×#106—91no—
205#417—91no—
206#416—91no—
207#408—31no—
208C3×#41—62no—
209C3×#41—62no—
210C2×C3×Q8—31no—
211C2×C3×D4—32no—
212C2×C3×D4—31no—
213C22×C3×C4—21no—
214C22×C3×C4—32no—
215C22×C3×C4—61no—
216C22×C3×C4C22×D311yescharacteristic
217C22×C3×C4C22×D311yescharacteristic
218C2×#67—62no—
219C2×#67—61no—
220C2×#67—61no—
221C2×#67—121no—
222C2×#67D1212yes—
223C22×Dic3—21no—
224C22×Dic3—62no—
225C22×Dic3—61no—
226C22×Dic3—61no—
227C22×Dic3—121no—
228#235—22no—
229#235—22no—
230#235—64no—
231#235—62no—
232#235—62no—
233#235—62no—
234#235—62no—
235#235—122no—
236C2×D12—31no—
237C2×D12—31no—
238C2×D12—61no—
239C2×D12—62no—
240C2×D12D1211yescharacteristic
241C2×C4×D3—61no—
242C2×C4×D3—61no—
243C2×C4×D3—62no—
244C2×C4×D3—121no—
245C2×C4×D3C22×D312yes—
246C2×Dic6—31no—
247C2×Dic6—31no—
248C2×Dic6—61no—
249C2×Dic6D1211yescharacteristic
250C3×M16—22no—
251C3×M16—22no—
252C3×M16—42no—
253C2×C3×C8—22no—
254C2×C3×C8—31no—
255C2×C3×C8—31no—
256C2×C3×C8—62no—
257C2×C3×C8C22×D312yes—
258C2×C3×C8C22×D312yes—
259C3×C4⋊C4—32no—
260C3×C4⋊C4—31no—
261C3×C4⋊C4—31no—
262C3×C4⋊C4—61no—
263C3×C22⋊C4—61no—
264C3×C42—61no—
265#217—21no—
266#217—62no—
267#217—62no—
268(C2×D3)⋊C4—62no—
269(C2×D3)⋊C4—62no—
270(C2×D3)⋊C4—62no—
271(C2×D3)⋊C4—62no—
272C4⋊Dic3—21no—
273C4⋊Dic3—32no—
274C4⋊Dic3—32no—
275C4⋊Dic3—62no—
276C4⋊Dic3—62no—
277C4⋊Dic3—61no—
278C4⋊Dic3—61no—
279C4⋊Dic3—62no—
280C4⋊Dic3—121no—
281C4⋊Dic3C22×D311yescharacteristic
282C4⋊Dic3C22×D311yescharacteristic
283C4⋊Dic3C22×D312yes—
284Dic3⋊C4—62no—
285Dic3⋊C4—62no—
286C4×Dic3—21no—
287C4×Dic3—62no—
288C4×Dic3—62no—
289C2×C3⋊C8—22no—
290C2×C3⋊C8C22×D311yescharacteristic
291C2×C3⋊C8C22×D311yescharacteristic
292C22×C32—21no—
293C22×C32—21no—
294C22×C32#12312yes—
295C22×C32C22×D411yescharacteristic
296C2×C3⋊D3—41no—
297C2×C3⋊D3—41no—
298C2×C3⋊D3—41no—
299C2×C3×D3—22no—
300C2×C3×D3—22no—
301C2×C3×D3—22no—
302C32×C4#12312yes—
303C32×C4C2×#4111yescharacteristic
304C32×C4C2×#4111yescharacteristic
305C3⋊Dic3—41no—
306C3⋊Dic3—42no—
307C3×Dic3—22no—
308C3×Dic3—41no—
309C3×Dic3—42no—
310C3×Dic3—41no—
311C2×#41—31no—
312C2×#41—91no—
313C2×M16D3211yescharacteristic
314C22×C8—31no—
315C22⋊Q8—92no—
316C22⋊Q8—181no—
317#121—92no—
318#121—181no—
319#121—182no—
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—32no—
329#106—32no—
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—32no—
339C22⋊C8—32no—
340C23×C3—21no—
341C23×C3—32no—
342C23×C3C2×D1211yescharacteristic
343C23×C3D3×D411yescharacteristic
344C22×D3—61no—
345C22×D3—61no—
346C22×D3—121no—
347C22×D3C2×D1212yes—
348C3×Q8—62no—
349C3×D4—64no—
350C3×D4—62no—
351C2×C3×C4—21no—
352C2×C3×C4—22no—
353C2×C3×C4—21no—
354C2×C3×C4—22no—
355C2×C3×C4—32no—
356C2×C3×C4—62no—
357C2×C3×C4—62no—
358C2×C3×C4—61no—
359C2×C3×C4—61no—
360C2×C3×C4—62no—
361C2×C3×C4—241no—
362C2×C3×C4C2×D1211yescharacteristic
363C2×C3×C4#23512yes—
364C2×C3×C4D3×D411yescharacteristic
365C2×C3×C4#23712yes—
366C2×C3×C4#23712yes—
367C2×C3×C4#23912yes—
368C2×C3×C4C23×D311yescharacteristic
369C2×C3×C4C23×D311yescharacteristic
370#67—24no—
371#67—124no—
372#67—122no—
373#67—122no—
374#67—242no—
375C2×Dic3—21no—
376C2×Dic3—21no—
377C2×Dic3—22no—
378C2×Dic3—62no—
379C2×Dic3—61no—
380C2×Dic3—62no—
381C2×Dic3—61no—
382C2×Dic3—81no—
383C2×Dic3—121no—
384C2×Dic3—122no—
385C2×Dic3—242no—
386C2×Dic3—241no—
387C2×Dic3—241no—
388C2×Dic3—242no—
389C2×Dic3C2×D1212yes—
390D12—22no—
391D12—62no—
392D12—61no—
393D12—61no—
394D12—61no—
395D12—61no—
396D12—121no—
397D12—242no—
398C4×D3—22no—
399C4×D3—22no—
400C4×D3—124no—
401C4×D3—122no—
402C4×D3—122no—
403C4×D3—242no—
404Dic6—22no—
405Dic6—62no—
406Dic6—61no—
407Dic6—61no—
408Dic6—61no—
409Dic6—61no—
410Dic6—121no—
411C3×C8—22no—
412C3×C8—22no—
413C3×C8—42no—
414C3×C8—61no—
415C3×C8—61no—
416C3⋊C8—21no—
417C3⋊C8—21no—
418C2×C32—22no—
419C2×C32C2×#12311yescharacteristic
420C2×C32#57711yescharacteristic
421C2×C32#57711yescharacteristic
422C3⋊D3—81no—
423C3×D3—42no—
424#41—62no—
425#41—62no—
426#41—182no—
427#41—182no—
428C2×Q8—31no—
429C2×Q8—91no—
430C2×D4—32no—
431C2×D4—31no—
432C2×D4—91no—
433C2×D4—182no—
434C2×D4—181no—
435C22×C4—32no—
436C22×C4—61no—
437C22×C4—182no—
438C22×C4—181no—
439C22×C4—181no—
440C22×C4C2×D3211yescharacteristic
441M16—22no—
442C2×C8—31no—
443C2×C8—31no—
444C2×C8—62no—
445C2×C8C2×D3212yes—
446C4⋊C4—31no—
447C4⋊C4—31no—
448C4⋊C4—32no—
449C4⋊C4—61no—
450C4⋊C4—92no—
451C4⋊C4—182no—
452C4⋊C4—182no—
453C4⋊C4—181no—
454C22⋊C4—61no—
455C22⋊C4—182no—
456C22⋊C4—182no—
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—62no—
469C22×C3—62no—
470C22×C3—62no—
471C22×C3#88612yes—
472C22×C3#89412yes—
473C22×C3C22×D1211yescharacteristic
474C22×C3C2×D3×D411yescharacteristic
475C2×D3—22no—
476C2×D3—22no—
477C2×D3—22no—
478C2×D3—122no—
479C2×D3—121no—
480C2×D3—121no—
481C2×D3—121no—
482C2×D3—121no—
483C2×D3—121no—
484C2×D3—121no—
485C2×D3—241no—
486C2×D3—241no—
487C3×C4—21no—
488C3×C4—21no—
489C3×C4—22no—
490C3×C4—62no—
491C3×C4—121no—
492C3×C4—122no—
493C3×C4—121no—
494C3×C4#88612yes—
495C3×C4#89412yes—
496C3×C4C2×#23511yescharacteristic
497C3×C4C2×#23711yescharacteristic
498C3×C4C2×#23711yescharacteristic
499C3×C4C2×#23911yescharacteristic
500Dic3—22no—
501Dic3—42no—
502Dic3—41no—
503Dic3—41no—
504Dic3—122no—
505Dic3—121no—
506Dic3—122no—
507Dic3—121no—
508Dic3—122no—
509Dic3—242no—
510C32#309911yescharacteristic, complemented, Sylow
511C23—32no—
512C23—181no—
513C23D3×D1211yescharacteristic
514Q8—62no—
515Q8—181no—
516Q8—181no—
517D4—64no—
518D4—62no—
519D4—181no—
520D4—181no—
521D4—362no—
522D4—722no—
523C2×C4—32no—
524C2×C4—62no—
525C2×C4—62no—
526C2×C4—61no—
527C2×C4—61no—
528C2×C4—62no—
529C2×C4—182no—
530C2×C4—181no—
531C2×C4—241no—
532C2×C4—362no—
533C2×C4—722no—
534C2×C4—721no—
535C2×C4#379612yes—
536C2×C4D3×D1211yescharacteristic
537C2×C4#380412yes—
538C2×C4C22×D3211yescharacteristic
539C8—22no—
540C8—61no—
541C8—61no—
542C2×C3—22no—
543C2×C3—22no—
544C2×C3—21no—
545C2×C3—21no—
546C2×C3—21no—
547C2×C3—42no—
548C2×C3—122no—
549C2×C3C2×#88611yescharacteristic
550C2×C3C2×#89411yescharacteristic
551C2×C3#575111yescharacteristic
552C2×C3#575111yescharacteristic
553C2×C3#577511yescharacteristic
554C2×C3#577811yescharacteristic
555D3—42no—
556D3—242no—
557D3—241no—
558D3—241no—
559C22—21no—
560C22—21no—
561C22—62no—
562C22—62no—
563C22—62no—
564C22—361no—
565C22—361no—
566C22—361no—
567C22#6389012yes—
568C22C2×D3×D1211yescharacteristic
569C4—62no—
570C4—122no—
571C4—121no—
572C4—121no—
573C4—361no—
574C4—362no—
575C4#6389012yes—
576C4C2×#379611yescharacteristic
577C4C2×#380411yescharacteristic
578C3—21no—
579C3#7865411yescharacteristic, complemented
580C3#7922211yescharacteristic, complemented
581C2—22no—
582C2—122no—
583C2—721no—
584C2#1059471311yescharacteristic
585C2#1059471511yescharacteristic
586C2C2×#6389011yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
prime radical#10595043C2
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. #10594992C2semidirect
3. #10592832C2semidirect
4. C3×#5129C2semidirect
5. C3×#5121C2semidirect
6. C2×#63573C2semidirect
7. #10591105C2semidirect
8. #10590708C2semidirect
9. #10590705C2semidirect
10. #10590677C2semidirect
11. #10590674C2semidirect
52. #5129D3semidirect
53. #5121D3semidirect
510. C32#3099semidirect
579. C3#78654semidirect
580. C3#79222semidirect

Maximal subgroups

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

subgroupindex
#105950432
#105949922
#105928322
C3×#51292
C3×#51212
C2×#635732
#105911052
#105907082
#105907052
#105906772
#105906742
#792223
#786543