Finite Group Databasebeta

← #11870373

Subgroups — #11870373

Order 1152.

875 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595043C211yesmaximal, characteristic
2#10594990C211yesmaximal, characteristic, complemented
3#10592828C211yesmaximal, characteristic, complemented
4C3×#5133C211yesmaximal, characteristic, complemented
5C3×#5121C211yesmaximal, characteristic, complemented
6C2×#63574C211yesmaximal, characteristic, complemented
7#10591083C211yesmaximal, characteristic, complemented
8#10590715C212yesmaximal, complemented
9#10590686C212yesmaximal, complemented
10#10590651C212yesmaximal, complemented
11#10590649C212yesmaximal, complemented
12#79222—31nomaximal
13#78875—31nomaximal
14C2×#3828C2211yescharacteristic
15C2×C3×#235C2211yescharacteristic
16C2×C32×M16C2211yescharacteristic
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18C3×#926C2211yescharacteristic
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×C4⋊Dic3C2211yescharacteristic
21#63978—22no—
22#63952—22no—
23#63916C2212yes—
24#63909—21no—
25#63900C2212yes—
26#63894—21no—
27#63871C2212yes—
28#63857—21no—
29#63849C2212yes—
30#63844—21no—
31#63647C2212yes—
32#63647C2212yes—
33C3×#821C2212yes—
34C3×#818C2212yes—
35C3×#817C2212yes—
36C3×#816C2212yes—
37#63574C2212yes—
38#63574C2212yes—
39#63565C2211yescharacteristic
40#63565C2211yescharacteristic
41#63562C2211yescharacteristic
42#63562C2211yescharacteristic
43#5833—31no—
44#5523—31no—
45#5510—31no—
46#5504—31no—
47C3×#428—31no—
48C3×#417—31no—
49#5233—31no—
50#5133D311yescharacteristic, complemented
51#5129—31no—
52#5129—31no—
53#5129—61no—
54#5121D311yescharacteristic, complemented
55#5002—31no—
56C2×#808—31no—
57C2×#808—31no—
58#4888—32no—
59#4885—32no—
60#4863—32no—
61#4862—32no—
62#4814—32no—
63#4805—32no—
64#4784—32no—
65#4777—32no—
66C22×C32×C4C2311yescharacteristic
67C2×#638D412yes—
68#3828—22no—
69#3828—22no—
70C2×C4⋊(C3⋊D3)D411yescharacteristic
71C2×C4×C3⋊D3C2312yes—
72C2×#634D411yescharacteristic
73C2×C3×#67—21no—
74C22×C3×Dic3—21no—
75C22×C3×Dic3—21no—
76C3×#235—22no—
77C3×#235—22no—
78C2×C3×D12C2311yescharacteristic
79C2×C3×C4×D3—21no—
80C2×C3×Dic6C2311yescharacteristic
81C2×#626—22no—
82C2×#624—22no—
83C32×M16—22no—
84C2×C32×C8C2312yes—
85C2×C3⋊(C3⋊C8)—22no—
86C2×C3⋊(C3⋊C8)C2311yescharacteristic
87C2×C3⋊(C3⋊C8)C2311yescharacteristic
88C3×#217—21no—
89C3×C4⋊Dic3—21no—
90C3×C4⋊Dic3—21no—
91C3×C4⋊Dic3C2312yes—
92C3×C4⋊Dic3C2312yes—
93C3×C4⋊Dic3C2311yescharacteristic
94C3×C4⋊Dic3C2311yescharacteristic
95C3×C4×Dic3—21no—
96#3724—22no—
97Dic3⋊Dic3—22no—
98#3722—22no—
99#3722—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
111C3×#117—31no—
112C2×C3×C4⋊C4—31no—
113C2×C3×C4⋊C4—31no—
114#946—32no—
115#939—62no—
116#938—32no—
117#930—61no—
118#930—62no—
119C4×#67—62no—
120#926C2×D311yescharacteristic
121C2×C4⋊Dic3C2×D311yescharacteristic
122C2×C4⋊Dic3C2×D311yescharacteristic
123#924—61no—
124C22×C3⋊C8—31no—
125C22×C3⋊C8—31no—
126C22×C3⋊C8—61no—
127#897—32no—
128#897—61no—
129#895—32no—
130#895—61no—
131#893—61no—
132#892—32no—
133#892—32no—
134D3×C4⋊C4—32no—
135D3×C4⋊C4—32no—
136#887—61no—
137#67⋊C4—62no—
138C4×D12—61no—
139C4×Dic6—61no—
140C3×#107—32no—
141C3×#106—32no—
142C3×#103—32no—
143C3×#102—32no—
144#835—31no—
145#835—31no—
146#832—31no—
147#832—31no—
148#821C2×D312yes—
149(C2×D3)⋊C8—32no—
150(C2×D3)⋊C8—32no—
151(C2×D3)⋊C8—32no—
152(C2×D3)⋊C8—32no—
153(C2×D3)⋊C8—62no—
154(C2×D3)⋊C8—62no—
155#818C2×D312yes—
156#817C2×D312yes—
157#816C2×D312yes—
158#810—31no—
159#810—31no—
160#809—31no—
161#809—31no—
162#808—32no—
163#808—32no—
164#808—32no—
165#808—32no—
166C23×C32C2×D411yescharacteristic
167C22×C3⋊D3C2×D412yes—
168C22×C3×D3—21no—
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4#4112yes—
171C2×C32×C4#4112yes—
172C2×C32×C4C2411yescharacteristic
173#638—24no—
174C2×C3⋊Dic3C2×D412yes—
175C4⋊(C3⋊D3)—22no—
176C4×C3⋊D3—22no—
177C4×C3⋊D3—22no—
178#634—22no—
179C3×#67—42no—
180C2×C3×Dic3—21no—
181C2×C3×Dic3—22no—
182C2×C3×Dic3—22no—
183C2×C3×Dic3—21no—
184C2×C3×Dic3—21no—
185C2×C3×Dic3—81no—
186C2×C3×Dic3—81no—
187C3×D12—21no—
188C3×D12—21no—
189C3×C4×D3—42no—
190C3×Dic6—21no—
191C3×Dic6—21no—
192#626—82no—
193#624—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—31no—
206#416—91no—
207#408—91no—
208C3×#41—62no—
209C3×#41—62no—
210C2×C3×Q8—31no—
211C2×C3×D4—31no—
212C2×C3×D4—61no—
213C22×C3×C4—21no—
214C22×C3×C4—61no—
215C22×C3×C4—61no—
216C22×C3×C4—61no—
217C22×C3×C4C22×D311yescharacteristic
218C22×C3×C4C22×D311yescharacteristic
219C2×#67—21no—
220C2×#67—32no—
221C2×#67—32no—
222C2×#67—62no—
223C2×#67—62no—
224C22×Dic3—21no—
225C22×Dic3—21no—
226#235—22no—
227#235—22no—
228#235—62no—
229#235—62no—
230#235—62no—
231#235—62no—
232#235—122no—
233#235—122no—
234C2×D12—31no—
235C2×D12—31no—
236C2×D12—61no—
237C2×D12—62no—
238C2×D12C22×D311yescharacteristic
239C2×C4×D3—21no—
240C2×C4×D3—32no—
241C2×C4×D3—32no—
242C2×C4×D3—62no—
243C2×C4×D3—62no—
244C2×C4×D3—62no—
245C2×Dic6—31no—
246C2×Dic6—31no—
247C2×Dic6—61no—
248C2×Dic6C22×D311yescharacteristic
249C3×M16—22no—
250C3×M16—22no—
251C3×M16—42no—
252C2×C3×C8—22no—
253C2×C3×C8C22×D312yes—
254C2×C3×C8C22×D312yes—
255C3×C4⋊C4—32no—
256C3×C4⋊C4—32no—
257C3×C4⋊C4—31no—
258C3×C4⋊C4—31no—
259C3×C4⋊C4—61no—
260C3×C4⋊C4—61no—
261C3×C22⋊C4—61no—
262C3×C42—61no—
263#217—21no—
264#217—62no—
265(C2×D3)⋊C4—62no—
266(C2×D3)⋊C4—62no—
267(C2×D3)⋊C4—62no—
268(C2×D3)⋊C4—62no—
269(C2×D3)⋊C4—62no—
270C4⋊Dic3—21no—
271C4⋊Dic3—21no—
272C4⋊Dic3—62no—
273C4⋊Dic3C22×D312yes—
274C4⋊Dic3C22×D312yes—
275C4⋊Dic3C22×D311yescharacteristic
276C4⋊Dic3C22×D311yescharacteristic
277Dic3⋊C4—62no—
278Dic3⋊C4—62no—
279Dic3⋊C4—62no—
280C4×Dic3—21no—
281C4×Dic3—62no—
282C4×Dic3—62no—
283C2×C3⋊C8—31no—
284C2×C3⋊C8—31no—
285C2×C3⋊C8—31no—
286C2×C3⋊C8—31no—
287C2×C3⋊C8—61no—
288C2×C3⋊C8—61no—
289C2×C3⋊C8—62no—
290C2×C3⋊C8—62no—
291C2×C3⋊C8—122no—
292C22×C32—21no—
293C22×C32—21no—
294C22×C32#12312yes—
295C22×C32C22×D411yescharacteristic
296C2×C3⋊D3—22no—
297C2×C3⋊D3—22no—
298C2×C3⋊D3—22no—
299C2×C3×D3—41no—
300C2×C3×D3—41no—
301C2×C3×D3—41no—
302C32×C4#12312yes—
303C32×C4C2×#4111yescharacteristic
304C32×C4C2×#4111yescharacteristic
305C3⋊Dic3—22no—
306C3×Dic3—41no—
307C3×Dic3—41no—
308C3×Dic3—42no—
309C3×Dic3—42no—
310C3×Dic3—41no—
311C2×#41—31no—
312C2×#41—91no—
313C2×M16D3211yescharacteristic
314C22×C8—91no—
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—31no—
327C2×C4⋊C4—92no—
328#107—32no—
329#106—32no—
330#106—92no—
331#106—92no—
332#103—32no—
333#103—91no—
334#103—91no—
335#102—32no—
336#102—91no—
337#102—91no—
338C22⋊C8—92no—
339C22⋊C8—92no—
340C23×C3—21no—
341C23×C3—61no—
342C23×C3D3×D411yescharacteristic
343C23×C3D3×D411yescharacteristic
344C22×D3—21no—
345C22×D3—32no—
346C22×D3—32no—
347C22×D3—62no—
348C3×Q8—61no—
349C3×Q8—61no—
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—61no—
358C2×C3×C4—62no—
359C2×C3×C4—61no—
360C2×C3×C4—61no—
361C2×C3×C4—62no—
362C2×C3×C4—122no—
363C2×C3×C4—241no—
364C2×C3×C4—241no—
365C2×C3×C4#23512yes—
366C2×C3×C4#23512yes—
367C2×C3×C4D3×D411yescharacteristic
368C2×C3×C4D3×D411yescharacteristic
369C2×C3×C4#23712yes—
370C2×C3×C4#23912yes—
371C2×C3×C4C23×D311yescharacteristic
372C2×C3×C4C23×D311yescharacteristic
373#67—42no—
374#67—64no—
375#67—64no—
376#67—124no—
377#67—242no—
378C2×Dic3—21no—
379C2×Dic3—21no—
380C2×Dic3—22no—
381C2×Dic3—22no—
382C2×Dic3—21no—
383C2×Dic3—32no—
384C2×Dic3—32no—
385C2×Dic3—62no—
386C2×Dic3—81no—
387C2×Dic3—81no—
388D12—21no—
389D12—21no—
390D12—62no—
391D12—62no—
392D12—122no—
393D12—242no—
394C4×D3—42no—
395C4×D3—62no—
396C4×D3—62no—
397C4×D3—62no—
398C4×D3—62no—
399C4×D3—122no—
400C4×D3—122no—
401C4×D3—242no—
402C4×D3—242no—
403Dic6—21no—
404Dic6—21no—
405Dic6—62no—
406Dic6—62no—
407Dic6—122no—
408C3×C8—22no—
409C3×C8—22no—
410C3×C8—42no—
411C3⋊C8—61no—
412C3⋊C8—61no—
413C3⋊C8—61no—
414C3⋊C8—61no—
415C3⋊C8—121no—
416C3⋊C8—121no—
417C2×C32—22no—
418C2×C32C2×#12311yescharacteristic
419C2×C32#57711yescharacteristic
420C2×C32#57711yescharacteristic
421C3⋊D3—42no—
422C3×D3—81no—
423#41—62no—
424#41—62no—
425#41—182no—
426#41—182no—
427C2×Q8—31no—
428C2×Q8—91no—
429C2×D4—31no—
430C2×D4—61no—
431C2×D4—92no—
432C2×D4—91no—
433C2×D4—182no—
434C22×C4—61no—
435C22×C4—61no—
436C22×C4—61no—
437C22×C4—92no—
438C22×C4—182no—
439C22×C4C2×D3211yescharacteristic
440M16—22no—
441C2×C8—91no—
442C2×C8—91no—
443C2×C8—182no—
444C2×C8C2×D3212yes—
445C4⋊C4—32no—
446C4⋊C4—31no—
447C4⋊C4—31no—
448C4⋊C4—32no—
449C4⋊C4—61no—
450C4⋊C4—61no—
451C4⋊C4—182no—
452C4⋊C4—182no—
453C22⋊C4—61no—
454C22⋊C4—182no—
455C22⋊C4—182no—
456C22⋊C4—182no—
457C42—61no—
458C42—182no—
459C22×C3—21no—
460C22×C3—21no—
461C22×C3—21no—
462C22×C3—21no—
463C22×C3—21no—
464C22×C3—22no—
465C22×C3—41no—
466C22×C3—41no—
467C22×C3—121no—
468C22×C3—121no—
469C22×C3—121no—
470C22×C3#88312yes—
471C22×C3#89412yes—
472C22×C3C2×D3×D411yescharacteristic
473C22×C3C2×D3×D411yescharacteristic
474C2×D3—41no—
475C2×D3—41no—
476C2×D3—41no—
477C2×D3—62no—
478C2×D3—62no—
479C2×D3—62no—
480C2×D3—62no—
481C2×D3—62no—
482C2×D3—62no—
483C2×D3—122no—
484C2×D3—122no—
485C2×D3—122no—
486C3×C4—21no—
487C3×C4—21no—
488C3×C4—22no—
489C3×C4—121no—
490C3×C4—121no—
491C3×C4—122no—
492C3×C4—122no—
493C3×C4—121no—
494C3×C4#88312yes—
495C3×C4#89412yes—
496C3×C4C2×#23511yescharacteristic
497C3×C4C2×#23511yescharacteristic
498C3×C4C2×#23711yescharacteristic
499C3×C4C2×#23911yescharacteristic
500Dic3—41no—
501Dic3—42no—
502Dic3—42no—
503Dic3—41no—
504Dic3—41no—
505Dic3—62no—
506Dic3—62no—
507Dic3—122no—
508C32#309911yescharacteristic, complemented, Sylow
509C23—61no—
510C23—92no—
511C23#380211yescharacteristic
512Q8—61no—
513Q8—61no—
514Q8—182no—
515D4—61no—
516D4—61no—
517D4—122no—
518D4—184no—
519D4—182no—
520D4—722no—
521C2×C4—61no—
522C2×C4—61no—
523C2×C4—62no—
524C2×C4—62no—
525C2×C4—61no—
526C2×C4—92no—
527C2×C4—122no—
528C2×C4—182no—
529C2×C4—182no—
530C2×C4—241no—
531C2×C4—241no—
532C2×C4—722no—
533C2×C4#379912yes—
534C2×C4#380211yescharacteristic
535C2×C4#380412yes—
536C2×C4C22×D3211yescharacteristic
537C8—22no—
538C8—181no—
539C8—181no—
540C2×C3—22no—
541C2×C3—22no—
542C2×C3—21no—
543C2×C3—21no—
544C2×C3—21no—
545C2×C3—42no—
546C2×C3—241no—
547C2×C3C2×#88311yescharacteristic
548C2×C3C2×#89411yescharacteristic
549C2×C3#577511yescharacteristic
550C2×C3#577511yescharacteristic
551C2×C3#577811yescharacteristic
552C2×C3#577811yescharacteristic
553D3—81no—
554D3—122no—
555D3—122no—
556D3—242no—
557C22—21no—
558C22—21no—
559C22—121no—
560C22—121no—
561C22—121no—
562C22—182no—
563C22—182no—
564C22—182no—
565C22#6385412yes—
566C22C2×#380211yescharacteristic
567C4—121no—
568C4—122no—
569C4—122no—
570C4—121no—
571C4—121no—
572C4—182no—
573C4#6385412yes—
574C4C2×#379911yescharacteristic
575C4C2×#380411yescharacteristic
576C3—21no—
577C3#7887511yescharacteristic, complemented
578C3#7922211yescharacteristic, complemented
579C2—22no—
580C2—241no—
581C2—362no—
582C2#1059471911yescharacteristic
583C2#1059471911yescharacteristic
584C2C2×#6385411yescharacteristic
subgroupG/H
centerC22C2×#3802
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. #10594990C2semidirect
3. #10592828C2semidirect
4. C3×#5133C2semidirect
5. C3×#5121C2semidirect
6. C2×#63574C2semidirect
7. #10591083C2semidirect
8. #10590715C2semidirect
9. #10590686C2semidirect
10. #10590651C2semidirect
11. #10590649C2semidirect
50. #5133D3semidirect
54. #5121D3semidirect
508. C32#3099semidirect
577. C3#78875semidirect
578. C3#79222semidirect

Maximal subgroups

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

subgroupindex
#105950432
#105949902
#105928282
C3×#51332
C3×#51212
C2×#635742
#105910832
#105907152
#105906862
#105906512
#105906492
#792223
#788753