Finite Group Databasebeta

← #11860620

Subgroups — #11860620

Order 1152.

1021 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5504C211yesmaximal, characteristic
2#10594828C211yesmaximal, characteristic, complemented
3C2×#63831C211yesmaximal, characteristic
4C2×#63637C211yesmaximal, characteristic, complemented
5C3×#4964C211yesmaximal, characteristic, complemented
6#10591083C211yesmaximal, characteristic
7#10591057C211yesmaximal, characteristic, complemented
8#10590590C212yesmaximal, complemented
9#10590481C212yesmaximal, complemented
10#10590480C212yesmaximal, complemented
11#10590479C212yesmaximal, complemented
12#82571—31nomaximal
13#79202—31nomaximal
14C22×#634C2211yescharacteristic
15C2×C3×#235C2211yescharacteristic
16C2×C32×C4⋊C4C2211yescharacteristic
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18C3×C4×#67—22no—
19C3×#926C2211yescharacteristic
20C3×#926C2211yescharacteristic
21C2×C3×#208C2211yescharacteristic
22C3×#893C2212yes—
23C3×#892—21no—
24C3×D3×C4⋊C4—21no—
25C3×#887C2212yes—
26#63957—22no—
27#63844—21no—
28#63844—21no—
29#63844C2212yes—
30#63844C2212yes—
31C2×#3719C2212yes—
32#63831C418yescomplemented
33C2×#3716C2212yes—
34#63637C2212yes—
35#63637C2212yes—
36C3×#808C2212yes—
37C3×#807C2212yes—
38#63565C2211yescharacteristic
39#63565C2211yescharacteristic
40#63562C2211yescharacteristic
41#63562C2211yescharacteristic
42#63554C2212yes—
43Dic3×C3⋊C8C2212yes—
44C3×#520—31no—
45C2×#951—31no—
46C2×#909—31no—
47#5516—31no—
48#5516—31no—
49#5504D311yescharacteristic
50C3×#428—31no—
51#5233—31no—
52#5122—31no—
53#5030—32no—
54C4×#216—32no—
55#5018—32no—
56C4×#214—32no—
57#5002—31no—
58#4997—31no—
59C2×#810—31no—
60C2×#810—31no—
61C2×#810—61no—
62#4964D311yescharacteristic, complemented
63#4889—32no—
64#4873—32no—
65#4853—32no—
66#4852—32no—
67C22×C32×C4—21no—
68C22×C32×C4C2311yescharacteristic
69C22×C3⋊Dic3—21no—
70C2×#634—21no—
71C2×#634—22no—
72C2×#634C2×C414yescomplemented
73C2×#634C2312yes—
74C2×C3×#67—21no—
75C3×#235—22no—
76C3×#235C2×C414yes—
77C2×C3×D12C2311yescharacteristic
78C2×C3×C4×D3—21no—
79C2×C3×C4×D3—22no—
80C2×C3×Dic6C2311yescharacteristic
81C32×C4⋊C4—21no—
82C32×C4⋊C4C2312yes—
83C2×C3⋊(C3⋊C8)—22no—
84C2×C3⋊(C3⋊C8)C2311yescharacteristic
85C2×C3⋊(C3⋊C8)C2311yescharacteristic
86C3×#217—21no—
87C3×#217D412yes—
88C3×(C2×D3)⋊C4—22no—
89C3×C4⋊Dic3D411yescharacteristic
90C3×C4⋊Dic3D411yescharacteristic
91C3×C4⋊Dic3C2311yescharacteristic
92C3×C4⋊Dic3C2311yescharacteristic
93C3×Dic3⋊C4—22no—
94C3×C4×Dic3—21no—
95C3×C4×Dic3—22no—
96C3×C4×Dic3C2312yes—
97C3×#208C2×C414yescomplemented
98C2×C3×C3⋊C8C2312yes—
99#3724—22no—
100#3724—22no—
101Dic32—22no—
102Dic32—22no—
103#3719C2×C418yescomplemented
104#3716C2×C418yescomplemented
105#2947—91noSylow
106C2×C3×#41—31no—
107C2×#235C2×D311yescharacteristic
108C22×Dic6—31no—
109C22×Dic6—31no—
110C22×Dic6—61no—
111C2×C3×M16—31no—
112C3×C4×Q8—32no—
113C3×C4×D4—32no—
114C3×C4×D4—62no—
115C3×#117—31no—
116C3×#117—31no—
117C3×#117—61no—
118C2×C3×C4⋊C4—21no—
119C2×C3×C4⋊C4—61no—
120C2×C3×C4⋊C4C2×D311yescharacteristic
121C2×C3×C4⋊C4C2×D311yescharacteristic
122#951—38no—
123C2×#216—32no—
124C2×#214—32no—
125C4×#67—22no—
126#926C2×D311yescharacteristic
127#926C2×D311yescharacteristic
128C2×#208C2×D311yescharacteristic
129C22×C3⋊C8—31no—
130C22×C3⋊C8—31no—
131C22×C3⋊C8—61no—
132#909—38no—
133C2×Dic12—32no—
134C2×#204—32no—
135#893C2×D312yes—
136#892—21no—
137D3×C4⋊C4—21no—
138#887—32no—
139#887—32no—
140#887—61no—
141#887—61no—
142#887C2×D312yes—
143#877—62no—
144#877—62no—
145C4×Dic6—32no—
146C4×Dic6—32no—
147C4×Dic6—61no—
148C4×Dic6—61no—
149C3×#107—32no—
150C3×#106—32no—
151#835—31no—
152#835—31no—
153#832—31no—
154#832—31no—
155#815—32no—
156C8×Dic3—32no—
157#810—31no—
158#810—31no—
159#810—32no—
160#810—32no—
161#810—32no—
162#810—32no—
163#810—62no—
164#810—62no—
165#809—31no—
166#809—31no—
167#808C2×D312yes—
168#807C2×D312yes—
169#803—32no—
170C4×C3⋊C8—32no—
171C23×C32C2×D411yescharacteristic
172C22×C3×D3—21no—
173C2×C32×C4—22no—
174C2×C32×C4—81no—
175C2×C32×C4C22×C412yes—
176C2×C32×C4C2×D411yescharacteristic
177C2×C32×C4#4112yes—
178C2×C32×C4C2411yescharacteristic
179C2×C3⋊Dic3—24no—
180C2×C3⋊Dic3—22no—
181#634—24no—
182#634—22no—
183#634C22×C414yes—
184C3×#67—24no—
185C2×C3×Dic3—21no—
186C2×C3×Dic3—21no—
187C2×C3×Dic3—21no—
188C2×C3×Dic3C2×D412yes—
189C2×C3×Dic3C2×D412yes—
190C3×D12—21no—
191C3×D12C22×C412yes—
192C3×C4×D3—24no—
193C3×C4×D3—82no—
194C3×Dic6—21no—
195C3×Dic6C22×C412yes—
196C3⋊(C3⋊C8)—21no—
197C3⋊(C3⋊C8)—21no—
198C3×C3⋊C8C22×C414yes—
199C2×#137—91no—
200#520—31no—
201#519—91no—
202#441—92no—
203#440—92no—
204C4×Q16—92no—
205C4×SD16—92no—
206#428—31no—
207#416—91no—
208C2×#103—91no—
209#405—91no—
210C3×#41—34no—
211C3×#41—62no—
212C2×C3×Q8—31no—
213C2×C3×D4—31no—
214C2×C3×D4—61no—
215C22×C3×C4—21no—
216C22×C3×C4—21no—
217C22×C3×C4—21no—
218C22×C3×C4—41no—
219C22×C3×C4—62no—
220C22×C3×C4—61no—
221C22×C3×C4C22×D311yescharacteristic
222C22×C3×C4C22×D311yescharacteristic
223C2×#67—21no—
224C22×Dic3—61no—
225C22×Dic3—61no—
226C22×Dic3—121no—
227#235—22no—
228#235C4×D314yes—
229C2×D12C22×D311yescharacteristic
230C2×C4×D3—21no—
231C2×C4×D3—22no—
232C2×Dic6—34no—
233C2×Dic6—34no—
234C2×Dic6—32no—
235C2×Dic6—32no—
236C2×Dic6—62no—
237C2×Dic6—64no—
238C2×Dic6—62no—
239C2×Dic6—61no—
240C2×Dic6—62no—
241C2×Dic6—61no—
242C2×Dic6—122no—
243C2×Dic6—121no—
244C2×Dic6C22×D311yescharacteristic
245C3×M16—34no—
246C2×C3×C8—32no—
247C3×C4⋊C4—21no—
248C3×C4⋊C4—21no—
249C3×C4⋊C4—22no—
250C3×C4⋊C4—31no—
251C3×C4⋊C4—31no—
252C3×C4⋊C4—31no—
253C3×C4⋊C4—31no—
254C3×C4⋊C4—41no—
255C3×C4⋊C4—62no—
256C3×C4⋊C4C22×D312yes—
257C3×C4⋊C4C22×D312yes—
258C3×C22⋊C4—32no—
259C3×C22⋊C4—62no—
260C3×C22⋊C4—61no—
261C3×C42—32no—
262C3×C42—62no—
263C3×C42—61no—
264#217—21no—
265#217#6712yes—
266#216—38no—
267#214—38no—
268(C2×D3)⋊C4—22no—
269C4⋊Dic3#6711yescharacteristic
270C4⋊Dic3#6711yescharacteristic
271C4⋊Dic3C22×D311yescharacteristic
272C4⋊Dic3C22×D311yescharacteristic
273Dic3⋊C4—22no—
274Dic3⋊C4—62no—
275Dic3⋊C4—62no—
276Dic3⋊C4—62no—
277Dic3⋊C4—62no—
278C4×Dic3—21no—
279C4×Dic3—22no—
280C4×Dic3—62no—
281C4×Dic3—62no—
282C4×Dic3—62no—
283C4×Dic3—62no—
284C4×Dic3C22×D312yes—
285#208C4×D314yescomplemented
286C2×C3⋊C8—31no—
287C2×C3⋊C8—31no—
288C2×C3⋊C8—31no—
289C2×C3⋊C8—31no—
290C2×C3⋊C8—61no—
291C2×C3⋊C8—61no—
292C2×C3⋊C8—62no—
293C2×C3⋊C8—62no—
294C2×C3⋊C8—122no—
295C2×C3⋊C8C22×D312yes—
296Dic12—38no—
297#204—38no—
298C22×C32—21no—
299C22×C32—21no—
300C22×C32C4×D412yes—
301C22×C32C22×D411yescharacteristic
302C2×C3×D3—22no—
303C2×C3×D3—41no—
304C2×C3×D3—41no—
305C32×C4—42no—
306C32×C4C4×D412yes—
307C32×C4C23×C411yescharacteristic
308C32×C4C2×#4111yescharacteristic
309C3⋊Dic3—24no—
310C3×Dic3—22no—
311C3×Dic3—22no—
312C3×Dic3—22no—
313C3×Dic3—41no—
314C3×Dic3—41no—
315C2×#41—31no—
316C22×Q8—91no—
317#137—98no—
318C2×Q16—92no—
319C2×SD16—92no—
320C2×M16—31no—
321C22×C8—91no—
322C4×Q8—32no—
323C4×Q8—92no—
324C4×Q8—92no—
325C4×Q8—181no—
326C4×Q8—181no—
327C4×D4—32no—
328C4×D4—62no—
329#117—31no—
330#117—31no—
331#117—61no—
332#117—182no—
333C2×C4⋊C4—61no—
334C2×C4⋊C4D3211yescharacteristic
335#107—32no—
336#106—32no—
337#103—91no—
338#103—91no—
339#103—92no—
340#103—92no—
341#102—91no—
342#102—91no—
343#97—92no—
344C4×C8—92no—
345C23×C3—21no—
346C23×C3—61no—
347C23×C3D3×D411yescharacteristic
348C23×C3C2×#6711yescharacteristic
349C22×D3—21no—
350C3×Q8—32no—
351C3×Q8—61no—
352C3×D4—32no—
353C3×D4—64no—
354C3×D4—61no—
355C2×C3×C4—22no—
356C2×C3×C4—22no—
357C2×C3×C4—21no—
358C2×C3×C4—22no—
359C2×C3×C4—22no—
360C2×C3×C4—21no—
361C2×C3×C4—32no—
362C2×C3×C4—32no—
363C2×C3×C4—42no—
364C2×C3×C4—61no—
365C2×C3×C4—64no—
366C2×C3×C4—61no—
367C2×C3×C4—61no—
368C2×C3×C4—81no—
369C2×C3×C4—81no—
370C2×C3×C4—82no—
371C2×C3×C4—242no—
372C2×C3×C4C2×C4×D312yes—
373C2×C3×C4C2×C4×D312yes—
374C2×C3×C4#23512yes—
375C2×C3×C4D3×D411yescharacteristic
376C2×C3×C4#23912yes—
377C2×C3×C4C2×#6711yescharacteristic
378C2×C3×C4C23×D311yescharacteristic
379C2×C3×C4C23×D311yescharacteristic
380#67—24no—
381C2×Dic3—21no—
382C2×Dic3—21no—
383C2×Dic3—21no—
384C2×Dic3—64no—
385C2×Dic3—64no—
386C2×Dic3—62no—
387C2×Dic3—62no—
388C2×Dic3—122no—
389C2×Dic3—124no—
390C2×Dic3C2×#6712yes—
391C2×Dic3C2×#6712yes—
392D12—21no—
393D12C2×C4×D312yes—
394C4×D3—24no—
395C4×D3—82no—
396Dic6—21no—
397Dic6—34no—
398Dic6—34no—
399Dic6—64no—
400Dic6—64no—
401Dic6—64no—
402Dic6—62no—
403Dic6—62no—
404Dic6—122no—
405Dic6—124no—
406Dic6C2×C4×D312yes—
407C3×C8—34no—
408C3⋊C8—61no—
409C3⋊C8—61no—
410C3⋊C8—61no—
411C3⋊C8—61no—
412C3⋊C8—121no—
413C3⋊C8—121no—
414C3⋊C8C2×C4×D314yes—
415C2×C32—22no—
416C2×C32C2×C4×D411yescharacteristic
417C2×C32#57711yescharacteristic
418C2×C32#57811yescharacteristic
419C3×D3—42no—
420#41—34no—
421#41—62no—
422C2×Q8—31no—
423C2×Q8—92no—
424C2×Q8—94no—
425C2×Q8—182no—
426C2×Q8—181no—
427C2×D4—31no—
428C2×D4—61no—
429C22×C4—21no—
430C22×C4—62no—
431C22×C4—61no—
432C22×C4—181no—
433C22×C4C2×D3211yescharacteristic
434Q16—98no—
435SD16—98no—
436M16—34no—
437C2×C8—32no—
438C2×C8—91no—
439C2×C8—91no—
440C2×C8—182no—
441C4⋊C4—21no—
442C4⋊C4—31no—
443C4⋊C4—31no—
444C4⋊C4—31no—
445C4⋊C4—31no—
446C4⋊C4—62no—
447C4⋊C4—182no—
448C4⋊C4—182no—
449C4⋊C4C2×D3212yes—
450C22⋊C4—32no—
451C22⋊C4—62no—
452C22⋊C4—61no—
453C42—32no—
454C42—62no—
455C42—61no—
456C42—182no—
457C42—182no—
458C22×C3—22no—
459C22×C3—22no—
460C22×C3—21no—
461C22×C3—21no—
462C22×C3—21no—
463C22×C3—21no—
464C22×C3—21no—
465C22×C3—22no—
466C22×C3—62no—
467C22×C3—121no—
468C22×C3—121no—
469C22×C3#89312yes—
470C22×C3C4×#6712yes—
471C22×C3C2×D3×D411yescharacteristic
472C22×C3C22×#6711yescharacteristic
473C2×D3—22no—
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—62no—
483C3×C4—62no—
484C3×C4—82no—
485C3×C4—121no—
486C3×C4—121no—
487C3×C4#89312yes—
488C3×C4C4×#6712yes—
489C3×C4C22×C4×D311yescharacteristic
490C3×C4C22×C4×D311yescharacteristic
491C3×C4C2×#23511yescharacteristic
492C3×C4C2×#23911yescharacteristic
493Dic3—22no—
494Dic3—22no—
495Dic3—22no—
496Dic3—41no—
497Dic3—41no—
498Dic3—64no—
499Dic3—64no—
500Dic3—124no—
501C32#294711yescharacteristic, complemented, Sylow
502C23—61no—
503C23D3×#6711yescharacteristic
504Q8—32no—
505Q8—61no—
506Q8—94no—
507Q8—182no—
508Q8—184no—
509D4—32no—
510D4—64no—
511D4—61no—
512C2×C4—22no—
513C2×C4—32no—
514C2×C4—32no—
515C2×C4—61no—
516C2×C4—64no—
517C2×C4—61no—
518C2×C4—61no—
519C2×C4—81no—
520C2×C4—182no—
521C2×C4—184no—
522C2×C4—242no—
523C2×C4#379912yes—
524C2×C4C4×D3212yes—
525C2×C4D3×#6711yescharacteristic
526C2×C4C22×D3211yescharacteristic
527C8—34no—
528C8—181no—
529C8—181no—
530C2×C3—24no—
531C2×C3—22no—
532C2×C3—22no—
533C2×C3—21no—
534C2×C3—21no—
535C2×C3—21no—
536C2×C3—122no—
537C2×C3C2×#89311yescharacteristic
538C2×C3#577511yescharacteristic
539C2×C3#577911yescharacteristic
540C2×C3C2×C4×#6711yescharacteristic
541C2×C3#583611yescharacteristic
542C2×C3#583811yescharacteristic
543D3—42no—
544C22—21no—
545C22—21no—
546C22—62no—
547C22—121no—
548C22—121no—
549C22#6390412yes—
550C22C2×D3×#6711yescharacteristic
551C4—42no—
552C4—62no—
553C4—62no—
554C4—62no—
555C4—121no—
556C4—121no—
557C4—184no—
558C4#6390412yes—
559C4C2×#379911yescharacteristic
560C4C2×C4×D3211yescharacteristic
561C3—21no—
562C3#7920211yescharacteristic, complemented
563C3#8257111yescharacteristic, complemented
564C2—22no—
565C2—122no—
566C2C2×#6390411yescharacteristic
567C2#1059510611yescharacteristic
568C2#1059532811yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C22×D4
prime radicalC2×C3×#235C22
cosocleC2×C32×C4C24
hypercenterC2×C4⋊C4D32
hypocenterC32#2947
LCSG ▷ 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. #10594828C2semidirect
4. C2×#63637C2semidirect
5. C3×#4964C2semidirect
7. #10591057C2semidirect
8. #10590590C2semidirect
9. #10590481C2semidirect
10. #10590480C2semidirect
11. #10590479C2semidirect
32. #63831C4semidirect
62. #4964D3semidirect
72. C2×#634C2×C4semidirect
97. C3×#208C2×C4semidirect
103. #3719C2×C4semidirect
104. #3716C2×C4semidirect
285. #208C4×D3semidirect
501. C32#2947semidirect
562. C3#79202semidirect
563. C3#82571semidirect

Maximal subgroups

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

subgroupindex
C3×#55042
#105948282
C2×#638312
C2×#636372
C3×#49642
#105910832
#105910572
#105905902
#105904812
#105904802
#105904792
#825713
#792023