Finite Group Databasebeta

← #11860638

Subgroups — #11860638

Order 1152.

1069 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64118C211yesmaximal, characteristic
2#10594990C211yesmaximal, characteristic
3#10594828C211yesmaximal, characteristic, complemented
4C3×#5122C211yesmaximal, characteristic, complemented
5C3×#5121C211yesmaximal, characteristic, complemented
6#10591105C211yesmaximal, characteristic
7C2×#63567C211yesmaximal, characteristic, complemented
8#10590810C212yesmaximal, complemented
9#10590807C212yesmaximal, complemented
10#10590773C212yesmaximal, complemented
11#10590758C212yesmaximal, complemented
12#79202—31nomaximal
13#78571—31nomaximal
14C2×#3828C2211yescharacteristic
15C22×#634C2211yescharacteristic
16C2×C32×M16C2211yescharacteristic
17#64118C418yescomplemented
18C2×#3746C2212yes—
19C2×#3744C2212yes—
20C3×#926C2211yescharacteristic
21C3×#926C2211yescharacteristic
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C22×C3×C3⋊C8C2211yescharacteristic
24#63957—22no—
25#63952—22no—
26#63900—21no—
27#63894C2212yes—
28#63849—21no—
29#63844—21no—
30#63844—21no—
31#63844C2212yes—
32#63844C2212yes—
33#63844C2212yes—
34C3×#818C2212yes—
35C3×#817C2212yes—
36C3×#815C2212yes—
37C3×C8×Dic3C2212yes—
38#63567C2212yes—
39#63567C2212yes—
40#63567C2211yescharacteristic
41#63567C2211yescharacteristic
42#63564C2211yescharacteristic
43#63564C2211yescharacteristic
44C2×#909—31no—
45C2×#909—31no—
46C2×#909—61no—
47#5523—31no—
48#5516—31no—
49#5516—31no—
50#5504—31no—
51C3×#428—31no—
52C3×#405—31no—
53#5122D311yescharacteristic, complemented
54#5121D311yescharacteristic, complemented
55#5113—31no—
56C2×#816—31no—
57#5002—31no—
58C2×#810—31no—
59#4889—32no—
60#4873—32no—
61#4853—32no—
62#4852—32no—
63#4716—32no—
64#4710—32no—
65C4×Dic12—32no—
66C4×#204—32no—
67C22×C32×C4C2311yescharacteristic
68C2×#638—21no—
69C22×C3⋊Dic3—21no—
70#3828—22no—
71#3828C2×C414yes—
72C2×C4⋊(C3⋊D3)C2311yescharacteristic
73C2×C4×C3⋊D3—21no—
74C2×#634—21no—
75C2×#634—22no—
76C2×#634C2×C414yescomplemented
77C2×#634C2312yes—
78C2×#634C2311yescharacteristic
79C22×C3×Dic3—21no—
80C2×#624—22no—
81C32×M16C2×C414yescomplemented
82C2×C32×C8C2312yes—
83#3746C2×C418yescomplemented
84#3744C2×C418yescomplemented
85C3×#217—21no—
86C3×#217D412yes—
87C3×C4⋊Dic3—21no—
88C3×C4⋊Dic3D411yescharacteristic
89C3×C4⋊Dic3D411yescharacteristic
90C3×C4⋊Dic3C2312yes—
91C3×C4⋊Dic3C2311yescharacteristic
92C3×C4⋊Dic3C2311yescharacteristic
93C3×C4×Dic3—21no—
94C3×C4×Dic3C2312yes—
95C2×C3×C3⋊C8—22no—
96C2×C3×C3⋊C8C2311yescharacteristic
97C2×C3×C3⋊C8C2311yescharacteristic
98#3724—22no—
99#3724—22no—
100#3724—22no—
101#3722—22no—
102Dic32—22no—
103Dic32—22no—
104Dic32—22no—
105#2947—91noSylow
106C2×#235—31no—
107C2×#235—31no—
108C2×#235—61no—
109C22×Dic6—31no—
110C22×Dic6—31no—
111C22×Dic6—61no—
112C2×C3×M16—21no—
113C2×C3×M16C2×D311yescharacteristic
114C2×C3×M16C2×D311yescharacteristic
115C22×C3×C8—31no—
116C3×#117—31no—
117C3×#117—31no—
118C2×C3×C4⋊C4—31no—
119C4×#67—62no—
120#926C2×D311yescharacteristic
121#926C2×D311yescharacteristic
122C2×C4⋊Dic3C2×D311yescharacteristic
123C22×C3⋊C8C2×D311yescharacteristic
124#909—38no—
125#909—38no—
126#909—68no—
127C2×Dic12—32no—
128C2×Dic12—32no—
129C2×Dic12—62no—
130C2×#204—32no—
131C2×#204—32no—
132C2×#204—62no—
133#893—32no—
134#892—61no—
135#892—61no—
136D3×C4⋊C4—61no—
137D3×C4⋊C4—61no—
138#887—32no—
139#887—32no—
140#887—32no—
141#887—61no—
142#887—61no—
143#67⋊C4—62no—
144#877—62no—
145#877—62no—
146C4×D12—32no—
147C4×Dic6—32no—
148C4×Dic6—32no—
149C4×Dic6—32no—
150C4×Dic6—61no—
151C4×Dic6—61no—
152C3×#107—32no—
153C3×#106—32no—
154C3×#97—32no—
155C3×C4×C8—32no—
156#821—31no—
157#821—31no—
158#818C2×D312yes—
159#817C2×D312yes—
160#816—32no—
161#816—31no—
162#816—32no—
163#816—31no—
164#815C2×D312yes—
165C8×Dic3C2×D312yes—
166#810—31no—
167#810—32no—
168#810—32no—
169#810—31no—
170#809—31no—
171#809—31no—
172C23×C32C2×D411yescharacteristic
173C22×C3⋊D3—21no—
174C2×C32×C4C22×C412yes—
175C2×C32×C4C2×D411yescharacteristic
176C2×C32×C4#4112yes—
177C2×C32×C4C2411yescharacteristic
178#638—24no—
179C2×C3⋊Dic3—24no—
180C2×C3⋊Dic3—22no—
181C2×C3⋊Dic3—21no—
182C4⋊(C3⋊D3)—21no—
183C4⋊(C3⋊D3)C22×C412yes—
184C4×C3⋊D3—24no—
185#634—24no—
186#634—22no—
187#634—21no—
188#634C22×C414yes—
189#634C22×C412yes—
190C2×C3×Dic3—21no—
191C2×C3×Dic3—21no—
192C2×C3×Dic3—22no—
193C2×C3×Dic3—81no—
194C2×C3×Dic3C2×D412yes—
195C2×C3×Dic3C2×D412yes—
196#624—82no—
197C32×C8C22×C414yes—
198C3×C3⋊C8—21no—
199C3×C3⋊C8—21no—
200C2×#137—91no—
201#520—91no—
202#519—91no—
203#441—92no—
204#440—92no—
205C4×Q16—92no—
206C4×SD16—92no—
207#428—31no—
208#416—91no—
209C2×#103—91no—
210#405—31no—
211C22×C3×C4—21no—
212C22×C3×C4—61no—
213C22×C3×C4C22×D311yescharacteristic
214C22×C3×C4C22×D311yescharacteristic
215C2×#67—61no—
216C2×#67—61no—
217C2×#67—121no—
218C22×Dic3—21no—
219C22×Dic3—61no—
220C22×Dic3—61no—
221C22×Dic3—121no—
222#235—34no—
223#235—34no—
224#235—64no—
225#235—62no—
226#235—62no—
227#235—122no—
228C2×D12—31no—
229C2×D12—31no—
230C2×D12—61no—
231C2×C4×D3—61no—
232C2×C4×D3—61no—
233C2×C4×D3—62no—
234C2×C4×D3—62no—
235C2×C4×D3—121no—
236C2×Dic6—34no—
237C2×Dic6—34no—
238C2×Dic6—32no—
239C2×Dic6—31no—
240C2×Dic6—32no—
241C2×Dic6—31no—
242C2×Dic6—62no—
243C2×Dic6—61no—
244C2×Dic6—64no—
245C2×Dic6—61no—
246C2×Dic6—62no—
247C2×Dic6—61no—
248C2×Dic6—62no—
249C2×Dic6—122no—
250C2×Dic6—121no—
251C3×M16—24no—
252C3×M16C4×D314yescomplemented
253C3×M16C4×D314yescomplemented
254C2×C3×C8—22no—
255C2×C3×C8—31no—
256C2×C3×C8—31no—
257C2×C3×C8—62no—
258C2×C3×C8C22×D312yes—
259C2×C3×C8C22×D312yes—
260C3×C4⋊C4—31no—
261C3×C4⋊C4—31no—
262C3×C4⋊C4—31no—
263C3×C4⋊C4—31no—
264C3×C4⋊C4—32no—
265C3×C4⋊C4—61no—
266C3×C22⋊C4—32no—
267C3×C22⋊C4—61no—
268C3×C42—32no—
269C3×C42—61no—
270#217—21no—
271#217D1212yes—
272(C2×D3)⋊C4—62no—
273(C2×D3)⋊C4—62no—
274C4⋊Dic3—21no—
275C4⋊Dic3D1211yescharacteristic
276C4⋊Dic3D1211yescharacteristic
277C4⋊Dic3C22×D312yes—
278C4⋊Dic3C22×D311yescharacteristic
279C4⋊Dic3C22×D311yescharacteristic
280Dic3⋊C4—62no—
281Dic3⋊C4—62no—
282Dic3⋊C4—62no—
283Dic3⋊C4—62no—
284Dic3⋊C4—62no—
285Dic3⋊C4—62no—
286C4×Dic3—21no—
287C4×Dic3—62no—
288C4×Dic3—62no—
289C4×Dic3—62no—
290C4×Dic3—62no—
291C4×Dic3—62no—
292C4×Dic3—62no—
293C4×Dic3C22×D312yes—
294C2×C3⋊C8—22no—
295C2×C3⋊C8C22×D311yescharacteristic
296C2×C3⋊C8C22×D311yescharacteristic
297Dic12—38no—
298Dic12—38no—
299Dic12—68no—
300#204—38no—
301#204—38no—
302#204—68no—
303C22×C32—21no—
304C22×C32—21no—
305C22×C32C4×D412yes—
306C22×C32C22×D411yescharacteristic
307C2×C3⋊D3—22no—
308C2×C3⋊D3—41no—
309C2×C3⋊D3—41no—
310C32×C4C4×D412yes—
311C32×C4C23×C411yescharacteristic
312C32×C4C2×#4111yescharacteristic
313C3⋊Dic3—24no—
314C3⋊Dic3—22no—
315C3×Dic3—22no—
316C3×Dic3—22no—
317C3×Dic3—42no—
318C3×Dic3—41no—
319C3×Dic3—41no—
320C2×#41—91no—
321C22×Q8—91no—
322#137—98no—
323C2×Q16—92no—
324C2×SD16—92no—
325C2×M16D3211yescharacteristic
326C22×C8—31no—
327C4×Q8—92no—
328C4×Q8—92no—
329C4×Q8—92no—
330C4×Q8—181no—
331C4×Q8—181no—
332C4×D4—92no—
333C4×D4—182no—
334#117—31no—
335#117—31no—
336#117—182no—
337#117—181no—
338C2×C4⋊C4—31no—
339C2×C4⋊C4—181no—
340#107—32no—
341#106—32no—
342#103—92no—
343#103—92no—
344#103—91no—
345#103—91no—
346#102—91no—
347#102—91no—
348#97—32no—
349C4×C8—32no—
350C23×C3—21no—
351C23×C3C2×D1211yescharacteristic
352C23×C3D3×D411yescharacteristic
353C22×D3—61no—
354C22×D3—61no—
355C22×D3—121no—
356C2×C3×C4—21no—
357C2×C3×C4—22no—
358C2×C3×C4—21no—
359C2×C3×C4—22no—
360C2×C3×C4—32no—
361C2×C3×C4—32no—
362C2×C3×C4—61no—
363C2×C3×C4—61no—
364C2×C3×C4—62no—
365C2×C3×C4—241no—
366C2×C3×C4C2×C4×D312yes—
367C2×C3×C4C2×C4×D312yes—
368C2×C3×C4C2×D1211yescharacteristic
369C2×C3×C4#23512yes—
370C2×C3×C4D3×D411yescharacteristic
371C2×C3×C4#23912yes—
372C2×C3×C4C23×D311yescharacteristic
373C2×C3×C4C23×D311yescharacteristic
374#67—64no—
375#67—64no—
376#67—124no—
377C2×Dic3—21no—
378C2×Dic3—21no—
379C2×Dic3—22no—
380C2×Dic3—64no—
381C2×Dic3—64no—
382C2×Dic3—62no—
383C2×Dic3—61no—
384C2×Dic3—62no—
385C2×Dic3—61no—
386C2×Dic3—81no—
387C2×Dic3—122no—
388C2×Dic3—124no—
389C2×Dic3—121no—
390C2×Dic3C2×D1212yes—
391C2×Dic3C2×D1212yes—
392D12—32no—
393D12—32no—
394D12—62no—
395D12—61no—
396D12—61no—
397D12—121no—
398C4×D3—64no—
399C4×D3—64no—
400C4×D3—124no—
401C4×D3—242no—
402C4×D3—242no—
403Dic6—34no—
404Dic6—34no—
405Dic6—32no—
406Dic6—32no—
407Dic6—64no—
408Dic6—62no—
409Dic6—64no—
410Dic6—64no—
411Dic6—62no—
412Dic6—61no—
413Dic6—62no—
414Dic6—61no—
415Dic6—122no—
416Dic6—124no—
417Dic6—121no—
418C3×C8—24no—
419C3×C8—61no—
420C3×C8—61no—
421C3×C8C2×C4×D314yes—
422C3×C8C2×C4×D314yes—
423C3⋊C8—21no—
424C3⋊C8—21no—
425C2×C32—22no—
426C2×C32C2×C4×D411yescharacteristic
427C2×C32#57711yescharacteristic
428C2×C32#57811yescharacteristic
429C3⋊D3—42no—
430#41—94no—
431#41—182no—
432C2×Q8—92no—
433C2×Q8—91no—
434C2×Q8—94no—
435C2×Q8—182no—
436C2×Q8—181no—
437C2×D4—91no—
438C2×D4—181no—
439C22×C4—61no—
440C22×C4—182no—
441C22×C4—181no—
442C22×C4—181no—
443C22×C4C2×D3211yescharacteristic
444Q16—98no—
445SD16—98no—
446M16#62414yescomplemented
447C2×C8—31no—
448C2×C8—31no—
449C2×C8—62no—
450C2×C8C2×D3212yes—
451C4⋊C4—31no—
452C4⋊C4—31no—
453C4⋊C4—31no—
454C4⋊C4—31no—
455C4⋊C4—32no—
456C4⋊C4—61no—
457C4⋊C4—182no—
458C4⋊C4—182no—
459C4⋊C4—182no—
460C22⋊C4—32no—
461C22⋊C4—61no—
462C22⋊C4—182no—
463C42—32no—
464C42—61no—
465C42—182no—
466C42—182no—
467C42—182no—
468C22×C3—21no—
469C22×C3—21no—
470C22×C3—21no—
471C22×C3—21no—
472C22×C3—21no—
473C22×C3—22no—
474C22×C3—41no—
475C22×C3—41no—
476C22×C3C4×D1212yes—
477C22×C3#89312yes—
478C22×C3C22×D1211yescharacteristic
479C22×C3C2×D3×D411yescharacteristic
480C2×D3—62no—
481C2×D3—62no—
482C2×D3—122no—
483C2×D3—121no—
484C2×D3—121no—
485C2×D3—121no—
486C2×D3—121no—
487C2×D3—241no—
488C2×D3—241no—
489C3×C4—21no—
490C3×C4—21no—
491C3×C4—22no—
492C3×C4—62no—
493C3×C4—62no—
494C3×C4—122no—
495C3×C4—121no—
496C3×C4—121no—
497C3×C4C4×D1212yes—
498C3×C4#89312yes—
499C3×C4C22×C4×D311yescharacteristic
500C3×C4C22×C4×D311yescharacteristic
501C3×C4C2×#23511yescharacteristic
502C3×C4C2×#23911yescharacteristic
503Dic3—22no—
504Dic3—22no—
505Dic3—42no—
506Dic3—41no—
507Dic3—41no—
508Dic3—64no—
509Dic3—62no—
510Dic3—64no—
511Dic3—62no—
512Dic3—124no—
513Dic3—122no—
514C32#294711yescharacteristic, complemented, Sylow
515C23—181no—
516C23D3×D1211yescharacteristic
517Q8—94no—
518Q8—92no—
519Q8—182no—
520Q8—181no—
521Q8—184no—
522D4—92no—
523D4—184no—
524D4—181no—
525C2×C4—32no—
526C2×C4—32no—
527C2×C4—61no—
528C2×C4—61no—
529C2×C4—62no—
530C2×C4—181no—
531C2×C4—182no—
532C2×C4—184no—
533C2×C4—184no—
534C2×C4—241no—
535C2×C4—722no—
536C2×C4#379912yes—
537C2×C4D3×D1211yescharacteristic
538C2×C4C2×#62412yes—
539C2×C4C22×D3211yescharacteristic
540C8—61no—
541C8—61no—
542C8C2×#62414yes—
543C2×C3—22no—
544C2×C3—22no—
545C2×C3—21no—
546C2×C3—21no—
547C2×C3—21no—
548C2×C3—42no—
549C2×C3C2×C4×D1211yescharacteristic
550C2×C3C2×#89311yescharacteristic
551C2×C3#575111yescharacteristic
552C2×C3#575311yescharacteristic
553C2×C3#577511yescharacteristic
554C2×C3#577911yescharacteristic
555D3—122no—
556D3—122no—
557D3—242no—
558C22—21no—
559C22—21no—
560C22—182no—
561C22—361no—
562C22—361no—
563C22#6389412yes—
564C22C2×D3×D1211yescharacteristic
565C4—62no—
566C4—62no—
567C4—122no—
568C4—121no—
569C4—121no—
570C4—182no—
571C4—184no—
572C4#6389412yes—
573C4C2×#379911yescharacteristic
574C4C22×#62411yescharacteristic
575C3—21no—
576C3#7857111yescharacteristic, complemented
577C3#7920211yescharacteristic, complemented
578C2—22no—
579C2—362no—
580C2#1059471311yescharacteristic
581C2#1059472111yescharacteristic
582C2C2×#6389411yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
prime radicalC2×#3828C22
cosocleC2×C32×C4C24
hypercenterC2×M16D32
hypocenterC32#2947
LCSG ▷ 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
3. #10594828C2semidirect
4. C3×#5122C2semidirect
5. C3×#5121C2semidirect
7. C2×#63567C2semidirect
8. #10590810C2semidirect
9. #10590807C2semidirect
10. #10590773C2semidirect
11. #10590758C2semidirect
17. #64118C4semidirect
53. #5122D3semidirect
54. #5121D3semidirect
76. C2×#634C2×C4semidirect
81. C32×M16C2×C4semidirect
83. #3746C2×C4semidirect
84. #3744C2×C4semidirect
252. C3×M16C4×D3semidirect
253. C3×M16C4×D3semidirect
446. M16#624semidirect
514. C32#2947semidirect
576. C3#78571semidirect
577. C3#79202semidirect

Maximal subgroups

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

subgroupindex
C2×#641182
#105949902
#105948282
C3×#51222
C3×#51212
#105911052
C2×#635672
#105908102
#105908072
#105907732
#105907582
#792023
#785713