Finite Group Databasebeta

← #11860627

Subgroups — #11860627

Order 1152.

1073 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595987C211yesmaximal, characteristic, complemented
2C3×#5523C211yesmaximal, characteristic
3C2×#63831C211yesmaximal, characteristic
4C3×#4997C211yesmaximal, characteristic, complemented
5#10591130C211yesmaximal, characteristic, complemented
6C2×#63567C211yesmaximal, characteristic, complemented
7#10591084C211yesmaximal, characteristic
8#10590383C212yesmaximal, complemented
9C4×#3719C212yesmaximal, complemented
10#10590360C212yesmaximal, complemented
11C4×#3716C212yesmaximal, complemented
12#82571—31nomaximal
13#78571—31nomaximal
14C22×#634C2211yescharacteristic
15C2×C3×#235C2211yescharacteristic
16C32×#117C2211yescharacteristic
17#64135C2211yescharacteristic
18#64096—21no—
19#64096—21no—
20#64086—22no—
21C4×#634C2212yes—
22C4×#634C2212yes—
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×#208C2211yescharacteristic
25C22×C3×C3⋊C8C2211yescharacteristic
26C3×#892—21no—
27C3×D3×C4⋊C4—21no—
28C3×#67⋊C4—22no—
29C3×C4×D12C2212yes—
30C3×C4×Dic6C2212yes—
31C2×#3719C2212yes—
32#63831C418yescomplemented
33C2×#3716C2212yes—
34C3×#803C2212yes—
35C3×C4×C3⋊C8C2212yes—
36#63575C2212yes—
37#63573C2212yes—
38#63567C2212yes—
39#63567C2212yes—
40#63566C2211yescharacteristic
41#63566C2211yescharacteristic
42#63563C2211yescharacteristic
43#63563C2211yescharacteristic
44C3×#520—31no—
45C2×#951—31no—
46C2×#909—31no—
47#5523D311yescharacteristic
48#5516—31no—
49#5516—31no—
50#5516—61no—
51C3×#405—31no—
52#5233—31no—
53#5121—31no—
54#5113—31no—
55C2×#816—31no—
56#5030—32no—
57C4×#216—32no—
58#5018—32no—
59C4×#214—32no—
60#4997D311yescharacteristic, complemented
61C2×#810—31no—
62#4964—31no—
63#4716—32no—
64#4710—32no—
65C4×Dic12—32no—
66C4×#204—32no—
67C22×C32×C4C2311yescharacteristic
68C22×C3⋊Dic3—21no—
69C2×#634—21no—
70C2×#634—22no—
71C2×#634C2×C414yescomplemented
72C2×#634C2312yes—
73C2×C3×#67—21no—
74C22×C3×Dic3—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⋊C4D411yescharacteristic
82C32×C4⋊C4D411yescharacteristic
83C32×C22⋊C4D412yes—
84C32×C42C2312yes—
85#3757—21no—
86C4⋊(C3⋊Dic3)C2311yescharacteristic
87C4⋊(C3⋊Dic3)C2311yescharacteristic
88#3750—22no—
89#3750—22no—
90C4×C3⋊Dic3—22no—
91C4×C3⋊Dic3—22no—
92C4×C3⋊Dic3—21no—
93C3×(C2×D3)⋊C4—22no—
94C3×C4⋊Dic3—21no—
95C3×C4⋊Dic3C2312yes—
96C3×Dic3⋊C4—22no—
97C3×C4×Dic3—22no—
98C3×#208C2×C414yescomplemented
99C2×C3×C3⋊C8—22no—
100C2×C3×C3⋊C8C2311yescharacteristic
101C2×C3×C3⋊C8C2311yescharacteristic
102C2×C3×C3⋊C8C2312yes—
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—
112C22×C3×C8—31no—
113C3×C4×Q8—32no—
114C3×C4×D4—32no—
115C3×C4×D4—62no—
116C3×#117—21no—
117C3×#117—61no—
118C3×#117C2×D311yescharacteristic
119C3×#117C2×D311yescharacteristic
120C2×C3×C4⋊C4—31no—
121C2×C3×C4⋊C4—61no—
122#951—38no—
123C2×#216—32no—
124C2×#214—32no—
125#926—31no—
126#926—31no—
127#926—61no—
128C2×C4⋊Dic3C2×D311yescharacteristic
129C2×#208C2×D311yescharacteristic
130C22×C3⋊C8C2×D311yescharacteristic
131#909—38no—
132C2×Dic12—32no—
133C2×#204—32no—
134#892—21no—
135D3×C4⋊C4—21no—
136#887—62no—
137#887—62no—
138#887—61no—
139#887—61no—
140#887—61no—
141#887—61no—
142#67⋊C4—22no—
143#877—64no—
144#877—62no—
145#877—62no—
146C4×D12C2×D312yes—
147C4×Dic6—32no—
148C4×Dic6—32no—
149C4×Dic6—32no—
150C4×Dic6—32no—
151C4×Dic6—62no—
152C4×Dic6—62no—
153C4×Dic6C2×D312yes—
154C3×#97—32no—
155C3×C4×C8—32no—
156#835—31no—
157#835—31no—
158#832—31no—
159#832—31no—
160#821—31no—
161#821—31no—
162#818—32no—
163#817—32no—
164#816—31no—
165#816—31no—
166#816—32no—
167#816—32no—
168#810—32no—
169#810—32no—
170#808—32no—
171#807—32no—
172#803C2×D312yes—
173C4×C3⋊C8C2×D312yes—
174C23×C32C2×D411yescharacteristic
175C22×C3×D3—21no—
176C2×C32×C4C22×C412yes—
177C2×C32×C4C2×D412yes—
178C2×C32×C4C2×D412yes—
179C2×C32×C4C2×D411yescharacteristic
180C2×C32×C4#4112yes—
181C2×C32×C4C2411yescharacteristic
182C2×C3⋊Dic3—24no—
183C2×C3⋊Dic3—22no—
184C2×C3⋊Dic3—21no—
185C2×C3⋊Dic3—21no—
186#634—24no—
187#634—22no—
188#634C22×C414yes—
189C3×#67—24no—
190C2×C3×Dic3—21no—
191C2×C3×Dic3—22no—
192C2×C3×Dic3—81no—
193C3×D12—21no—
194C3×D12C22×C412yes—
195C3×C4×D3—24no—
196C3×C4×D3—82no—
197C3×Dic6—21no—
198C3×Dic6C22×C412yes—
199C3×C3⋊C8—21no—
200C3×C3⋊C8—21no—
201C3×C3⋊C8C22×C414yes—
202C2×#137—91no—
203#520—31no—
204#519—91no—
205#441—92no—
206#440—92no—
207C4×Q16—92no—
208C4×SD16—92no—
209#428—91no—
210#416—91no—
211C2×#103—91no—
212#405—31no—
213C3×#41—34no—
214C3×#41—62no—
215C2×C3×Q8—31no—
216C2×C3×D4—31no—
217C2×C3×D4—61no—
218C22×C3×C4—21no—
219C22×C3×C4—61no—
220C22×C3×C4—61no—
221C22×C3×C4—62no—
222C22×C3×C4C22×D311yescharacteristic
223C22×C3×C4C22×D311yescharacteristic
224C2×#67—21no—
225C22×Dic3—21no—
226C22×Dic3—62no—
227C22×Dic3—61no—
228C22×Dic3—61no—
229#235—22no—
230#235C4×D314yes—
231C2×D12C22×D311yescharacteristic
232C2×C4×D3—21no—
233C2×C4×D3—22no—
234C2×Dic6—34no—
235C2×Dic6—34no—
236C2×Dic6—32no—
237C2×Dic6—32no—
238C2×Dic6—62no—
239C2×Dic6—64no—
240C2×Dic6—62no—
241C2×Dic6—64no—
242C2×Dic6—61no—
243C2×Dic6—62no—
244C2×Dic6—62no—
245C2×Dic6—61no—
246C2×Dic6C22×D311yescharacteristic
247C3×M16—34no—
248C2×C3×C8—32no—
249C2×C3×C8—31no—
250C2×C3×C8—31no—
251C2×C3×C8—62no—
252C3×C4⋊C4—21no—
253C3×C4⋊C4—21no—
254C3×C4⋊C4—32no—
255C3×C4⋊C4—62no—
256C3×C4⋊C4—61no—
257C3×C4⋊C4D1211yescharacteristic
258C3×C4⋊C4D1211yescharacteristic
259C3×C4⋊C4#6711yescharacteristic
260C3×C4⋊C4#6711yescharacteristic
261C3×C22⋊C4—22no—
262C3×C22⋊C4—62no—
263C3×C22⋊C4D1212yes—
264C3×C22⋊C4#6712yes—
265C3×C42—22no—
266C3×C42—62no—
267C3×C42C22×D312yes—
268C3×C42C22×D312yes—
269#217—62no—
270#217—61no—
271#217—61no—
272#216—38no—
273#214—38no—
274(C2×D3)⋊C4—22no—
275C4⋊Dic3—21no—
276C4⋊Dic3—31no—
277C4⋊Dic3—31no—
278C4⋊Dic3—31no—
279C4⋊Dic3—31no—
280C4⋊Dic3—61no—
281C4⋊Dic3—61no—
282C4⋊Dic3C22×D312yes—
283Dic3⋊C4—22no—
284Dic3⋊C4—64no—
285Dic3⋊C4—64no—
286Dic3⋊C4—62no—
287Dic3⋊C4—62no—
288Dic3⋊C4—62no—
289Dic3⋊C4—62no—
290C4×Dic3—22no—
291C4×Dic3—64no—
292C4×Dic3—64no—
293C4×Dic3—62no—
294C4×Dic3—62no—
295C4×Dic3—62no—
296C4×Dic3—61no—
297C4×Dic3—62no—
298C4×Dic3—62no—
299C4×Dic3—61no—
300#208C4×D314yescomplemented
301C2×C3⋊C8—22no—
302C2×C3⋊C8C22×D311yescharacteristic
303C2×C3⋊C8C22×D311yescharacteristic
304C2×C3⋊C8C22×D312yes—
305Dic12—38no—
306#204—38no—
307C22×C32—21no—
308C22×C32—21no—
309C22×C32C4×D412yes—
310C22×C32C22×D411yescharacteristic
311C2×C3×D3—22no—
312C2×C3×D3—41no—
313C2×C3×D3—41no—
314C32×C4—22no—
315C32×C4—22no—
316C32×C4C4×D412yes—
317C32×C4C23×C411yescharacteristic
318C32×C4C2×#4111yescharacteristic
319C3⋊Dic3—24no—
320C3⋊Dic3—41no—
321C3⋊Dic3—41no—
322C3×Dic3—22no—
323C3×Dic3—42no—
324C2×#41—31no—
325C22×Q8—91no—
326#137—98no—
327C2×Q16—92no—
328C2×SD16—92no—
329C2×M16—31no—
330C22×C8—31no—
331C4×Q8—32no—
332C4×Q8—92no—
333C4×Q8—92no—
334C4×Q8—181no—
335C4×Q8—181no—
336C4×D4—32no—
337C4×D4—62no—
338#117—61no—
339#117—91no—
340#117—182no—
341#117D3211yescharacteristic
342C2×C4⋊C4—31no—
343C2×C4⋊C4—61no—
344#107—92no—
345#106—92no—
346#103—92no—
347#103—92no—
348#103—91no—
349#103—91no—
350#102—91no—
351#102—91no—
352#97—32no—
353C4×C8—32no—
354C23×C3—21no—
355C23×C3—61no—
356C23×C3C2×D1211yescharacteristic
357C23×C3C2×#6711yescharacteristic
358C22×D3—21no—
359C3×Q8—32no—
360C3×Q8—61no—
361C3×D4—32no—
362C3×D4—64no—
363C3×D4—61no—
364C2×C3×C4—21no—
365C2×C3×C4—22no—
366C2×C3×C4—22no—
367C2×C3×C4—21no—
368C2×C3×C4—22no—
369C2×C3×C4—22no—
370C2×C3×C4—61no—
371C2×C3×C4—64no—
372C2×C3×C4—62no—
373C2×C3×C4—242no—
374C2×C3×C4—241no—
375C2×C3×C4C2×C4×D312yes—
376C2×C3×C4C2×C4×D312yes—
377C2×C3×C4C2×D1212yes—
378C2×C3×C4C2×D1212yes—
379C2×C3×C4C2×D1211yescharacteristic
380C2×C3×C4#23512yes—
381C2×C3×C4#23512yes—
382C2×C3×C4C2×#6712yes—
383C2×C3×C4C2×#6712yes—
384C2×C3×C4C2×#6711yescharacteristic
385C2×C3×C4C23×D311yescharacteristic
386C2×C3×C4C23×D311yescharacteristic
387#67—24no—
388C2×Dic3—21no—
389C2×Dic3—22no—
390C2×Dic3—64no—
391C2×Dic3—68no—
392C2×Dic3—64no—
393C2×Dic3—64no—
394C2×Dic3—62no—
395C2×Dic3—62no—
396C2×Dic3—62no—
397C2×Dic3—62no—
398C2×Dic3—61no—
399C2×Dic3—61no—
400C2×Dic3—61no—
401C2×Dic3—61no—
402C2×Dic3—81no—
403D12—21no—
404D12C2×C4×D312yes—
405C4×D3—24no—
406C4×D3—82no—
407Dic6—21no—
408Dic6—34no—
409Dic6—34no—
410Dic6—64no—
411Dic6—64no—
412Dic6—68no—
413Dic6—64no—
414Dic6—64no—
415Dic6—62no—
416Dic6—62no—
417Dic6C2×C4×D312yes—
418C3×C8—34no—
419C3×C8—61no—
420C3×C8—61no—
421C3⋊C8—21no—
422C3⋊C8—21no—
423C3⋊C8C2×C4×D314yes—
424C2×C32—22no—
425C2×C32C2×C4×D411yescharacteristic
426C2×C32#57711yescharacteristic
427C2×C32#57811yescharacteristic
428C3×D3—42no—
429#41—34no—
430#41—62no—
431C2×Q8—31no—
432C2×Q8—92no—
433C2×Q8—94no—
434C2×Q8—182no—
435C2×Q8—181no—
436C2×D4—31no—
437C2×D4—61no—
438C22×C4—61no—
439C22×C4—61no—
440C22×C4—62no—
441C22×C4—181no—
442C22×C4C2×D3211yescharacteristic
443Q16—98no—
444SD16—98no—
445M16—34no—
446C2×C8—32no—
447C2×C8—31no—
448C2×C8—31no—
449C2×C8—62no—
450C4⋊C4—32no—
451C4⋊C4—61no—
452C4⋊C4—62no—
453C4⋊C4—91no—
454C4⋊C4—91no—
455C4⋊C4—182no—
456C4⋊C4—182no—
457C4⋊C4#62611yescharacteristic
458C4⋊C4#62611yescharacteristic
459C22⋊C4—62no—
460C22⋊C4—181no—
461C22⋊C4#62612yes—
462C42—62no—
463C42—181no—
464C42—182no—
465C42—182no—
466C42C2×D3212yes—
467C22×C3—21no—
468C22×C3—21no—
469C22×C3—21no—
470C22×C3—21no—
471C22×C3—21no—
472C22×C3—22no—
473C22×C3—41no—
474C22×C3—41no—
475C22×C3—62no—
476C22×C3—121no—
477C22×C3—121no—
478C22×C3C4×D1212yes—
479C22×C3C4×#6712yes—
480C22×C3C22×D1211yescharacteristic
481C22×C3C22×#6711yescharacteristic
482C2×D3—22no—
483C2×D3—41no—
484C2×D3—41no—
485C3×C4—22no—
486C3×C4—22no—
487C3×C4—22no—
488C3×C4—22no—
489C3×C4—21no—
490C3×C4—21no—
491C3×C4—22no—
492C3×C4—42no—
493C3×C4—42no—
494C3×C4—62no—
495C3×C4—122no—
496C3×C4C4×D1212yes—
497C3×C4C4×#6712yes—
498C3×C4C22×C4×D311yescharacteristic
499C3×C4C22×C4×D311yescharacteristic
500C3×C4C2×#23511yescharacteristic
501C3×C4C2×#23511yescharacteristic
502Dic3—22no—
503Dic3—42no—
504Dic3—68no—
505Dic3—64no—
506Dic3—64no—
507Dic3—122no—
508Dic3—122no—
509Dic3—121no—
510Dic3—121no—
511Dic3—121no—
512Dic3—121no—
513C32#294711yescharacteristic, complemented, Sylow
514C23—61no—
515C23C2×#62611yescharacteristic
516Q8—32no—
517Q8—61no—
518Q8—94no—
519Q8—182no—
520Q8—184no—
521D4—32no—
522D4—64no—
523D4—61no—
524C2×C4—61no—
525C2×C4—64no—
526C2×C4—62no—
527C2×C4—182no—
528C2×C4—184no—
529C2×C4—181no—
530C2×C4—181no—
531C2×C4—242no—
532C2×C4—241no—
533C2×C4#379812yes—
534C2×C4C4×D3212yes—
535C2×C4C2×#62612yes—
536C2×C4C2×#62612yes—
537C2×C4C2×#62611yescharacteristic
538C2×C4C22×D3211yescharacteristic
539C8—34no—
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×C4×D1211yescharacteristic
550C2×C3#575111yescharacteristic
551C2×C3#575311yescharacteristic
552C2×C3C2×C4×#6711yescharacteristic
553C2×C3#583611yescharacteristic
554C2×C3#583811yescharacteristic
555D3—42no—
556C22—21no—
557C22—21no—
558C22—62no—
559C22—121no—
560C22—121no—
561C22C4×#62612yes—
562C22C22×#62611yescharacteristic
563C4—22no—
564C4—22no—
565C4—62no—
566C4—122no—
567C4—184no—
568C4—361no—
569C4—361no—
570C4C4×#62612yes—
571C4C2×#379811yescharacteristic
572C4C2×C4×D3211yescharacteristic
573C3—21no—
574C3#7857111yescharacteristic, complemented
575C3#8257111yescharacteristic, complemented
576C2—22no—
577C2—122no—
578C2C2×C4×#62611yescharacteristic
579C2#1059544711yescharacteristic
580C2#1059545011yescharacteristic
subgroupG/H
centerC22C22×#626
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radicalC2×C3×#235C22
cosocleC2×C32×C4C24
hypercenter#117D32
hypocenterC32#2947
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #10595987C2semidirect
4. C3×#4997C2semidirect
5. #10591130C2semidirect
6. C2×#63567C2semidirect
8. #10590383C2semidirect
9. C4×#3719C2semidirect
10. #10590360C2semidirect
11. C4×#3716C2semidirect
32. #63831C4semidirect
60. #4997D3semidirect
71. C2×#634C2×C4semidirect
98. C3×#208C2×C4semidirect
103. #3719C2×C4semidirect
104. #3716C2×C4semidirect
300. #208C4×D3semidirect
513. C32#2947semidirect
574. C3#78571semidirect
575. C3#82571semidirect

Maximal subgroups

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

subgroupindex
#105959872
C3×#55232
C2×#638312
C3×#49972
#105911302
C2×#635672
#105910842
#105903832
C4×#37192
#105903602
C4×#37162
#825713
#785713