Finite Group Databasebeta

← #11861102

Subgroups — #11861102

Order 1152.

1043 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596239C211yesmaximal, characteristic
2#10595442C212yesmaximal, complemented
3C3×#5197C211yesmaximal, characteristic, complemented
4C3×#5196C211yesmaximal, characteristic, complemented
5#10591672C212yesmaximal, complemented
6#10591663C212yesmaximal, complemented
7#10591662C212yesmaximal, complemented
8#10590918C211yesmaximal, characteristic, complemented
9#10590917C211yesmaximal, characteristic, complemented
10#10590914C211yesmaximal, characteristic, complemented
11#10590910C211yesmaximal, characteristic, complemented
12#79897—31nomaximal
13#79888—31nomaximal
14#41×C3⋊D3C2212yes—
15C32×#135C2211yescharacteristic
16#64159C2212yes—
17#64127C412yescomplemented
18#64124C412yescomplemented
19#64123C412yescomplemented
20#64120C412yescomplemented
21#64113C2211yescharacteristic
22C2×#3743C2211yescharacteristic
23C3×#948C2212yescomplemented
24C3×#948C2212yescomplemented
25#63874C2211yescharacteristic
26#63818—22no—
27#63818C2212yes—
28#63817—22no—
29#63817—22no—
30#63817C2212yescomplemented
31#63817C2212yescomplemented
32C2×#3710—22no—
33C2×#3710C2211yescharacteristic
34C3×#837C2212yescomplemented
35C3×#837C2212yescomplemented
36C3×#819C2211yescharacteristic, complemented
37C3×#819C2211yescharacteristic, complemented
38C3×#815C2211yescharacteristic, complemented
39C3×C8×Dic3C2211yescharacteristic, complemented
40#63578C2212yescomplemented
41#63570C2212yescomplemented
42#63570C2212yescomplemented
43#63554C2211yescharacteristic, complemented
44Dic3×C3⋊C8C2211yescharacteristic, complemented
45#5768—31no—
46#5768—31no—
47#5768—61no—
48D3×#131—32no—
49D3×#131—32no—
50C3×#444—31no—
51C3×#443—31no—
52#5197D311yescharacteristic, complemented
53#5196D311yescharacteristic, complemented
54#5145—32no—
55#5144—32no—
56#4895—31no—
57#4894—31no—
58#4893—31no—
59#4893—31no—
60#4824—32no—
61#4823—32no—
62#4821—32no—
63#4821—32no—
64#4717—31no—
65#4708—31no—
66#4700—31no—
67#4689—31no—
68C32×#41C2312yes—
69#3832C2×C412yes—
70Q8×C3⋊D3C2×C412yes—
71#3830—22no—
72#3830C2×C412yes—
73D4×C3⋊D3—22no—
74D4×C3⋊D3C2×C412yes—
75#3828—22no—
76#3828C2312yes—
77C2×C4×C3⋊D3—22no—
78C2×C4×C3⋊D3C2311yescharacteristic
79C32×Q16C2×C411yescharacteristic
80C32×SD16C2×C412yes—
81C32×D8C2×C411yescharacteristic
82C2×C32×C8C2311yescharacteristic
83#3756C2×C412yes—
84#3755C2×C412yes—
85#3754C2×C412yes—
86#3753C2×C412yes—
87C2×C3⋊(C3⋊C8)C2311yescharacteristic
88#3746C2×C411yescharacteristic
89#3745C2×C411yescharacteristic
90#3744C2×C412yes—
91#3743C2×C412yes—
92#3743C2×C412yes—
93C3×C4×Dic3C2311yescharacteristic
94C3×C4×Dic3C2311yescharacteristic
95C3×#208—22no—
96C3×#208—22no—
97C3×#208C2312yes—
98C3×#208C2312yes—
99C2×C3×C3⋊C8—22no—
100C2×C3×C3⋊C8—22no—
101C2×C3×C3⋊C8C2311yescharacteristic
102C2×C3×C3⋊C8C2311yescharacteristic
103#3724—21no—
104#3722—21no—
105#3712—22no—
106#3712—22no—
107#3712—22no—
108#3710—22no—
109#3710—22no—
110#3710—22no—
111#3710D412yes—
112#3710D412yes—
113#2955—91noSylow
114D3×#41—32no—
115D3×#41—32no—
116D3×#41—62no—
117C3×#135—21no—
118C3×#135C2×D311yescharacteristic
119C3×#135C2×D311yescharacteristic
120C3×#131—32no—
121C3×#131—32no—
122#950—32no—
123#950—32no—
124#950—62no—
125#948C2×D312yescomplemented
126#948C2×D312yescomplemented
127#918—32no—
128#918—32no—
129#918—62no—
130#915—32no—
131#915—32no—
132#915—62no—
133#914—32no—
134#914—32no—
135#914—62no—
136#911—32no—
137#911—32no—
138#911—62no—
139#907—32no—
140#907—32no—
141#907—62no—
142#907—62no—
143D3×M16—32no—
144D3×M16—32no—
145D3×M16—62no—
146D3×M16—62no—
147#904—31no—
148#904—31no—
149#904—61no—
150#901—32no—
151#901—32no—
152#901—62no—
153#901—62no—
154C2×ΓL(1,𝔽25)—31no—
155C2×ΓL(1,𝔽25)—31no—
156C2×ΓL(1,𝔽25)—61no—
157C2×D3×C8—31no—
158C2×D3×C8—31no—
159C2×D3×C8—62no—
160C2×D3×C8—62no—
161#872—31no—
162#872—31no—
163C3×#108—31no—
164C3×#108—31no—
165C3×#104—32no—
166C3×#104—32no—
167C3×#97—31no—
168C3×C4×C8—31no—
169#837C2×D312yescomplemented
170#837C2×D312yescomplemented
171#825—32no—
172#825—32no—
173#822—32no—
174#822—32no—
175#819C2×D311yescharacteristic, complemented
176#819C2×D311yescharacteristic, complemented
177#815—31no—
178#815C2×D311yescharacteristic, complemented
179C8×Dic3—31no—
180C8×Dic3C2×D311yescharacteristic, complemented
181#805—32no—
182#805—32no—
183#803—31no—
184C4×C3⋊C8—31no—
185C22×C3⋊D3—22no—
186C22×C3⋊D3#4111yescharacteristic
187C32×Q8C22×C412yes—
188C32×D4—22no—
189C32×D4C22×C412yes—
190C2×C32×C4—22no—
191C2×C32×C4C2411yescharacteristic
192#638—22no—
193#638—22no—
194#638—22no—
195C2×C3⋊Dic3—22no—
196C2×C3⋊Dic3#4111yescharacteristic
197C4⋊(C3⋊D3)—22no—
198C4⋊(C3⋊D3)C22×C412yes—
199C4×C3⋊D3—22no—
200C4×C3⋊D3—22no—
201C4×C3⋊D3—22no—
202C4×C3⋊D3C22×C412yes—
203C4×C3⋊D3C2×D412yes—
204#634—22no—
205#634C22×C412yes—
206C2×C3×Dic3—21no—
207C2×C3×Dic3—21no—
208C32×C8C22×C411yescharacteristic
209C32×C8C22×C411yescharacteristic
210C3⋊(C3⋊C8)C22×C412yes—
211C3×C3⋊C8—22no—
212C3×C3⋊C8—22no—
213C3×C3⋊C8C2×D411yescharacteristic
214C3×C3⋊C8C2×D412yes—
215C3×C3⋊C8C2×D411yescharacteristic
216#575—91no—
217C2×#131—92no—
218#444—31no—
219#444—91no—
220#444—92no—
221#443—31no—
222#443—91no—
223#443—92no—
224#430—91no—
225#421—92no—
226#405—91no—
227C3×#41—22no—
228C3×#41C22×D312yes—
229C3×#41C22×D312yes—
230#239—32no—
231#239—32no—
232#239—62no—
233D3×Q8—32no—
234D3×Q8—32no—
235D3×Q8—62no—
236#237—32no—
237#237—32no—
238#237—62no—
239#237—62no—
240#237—62no—
241#237—122no—
242D3×D4—32no—
243D3×D4—32no—
244D3×D4—62no—
245D3×D4—62no—
246D3×D4—62no—
247D3×D4—122no—
248#235—32no—
249#235—32no—
250#235—62no—
251#235—62no—
252#235—62no—
253#235—122no—
254C2×C4×D3—31no—
255C2×C4×D3—31no—
256C2×C4×D3—61no—
257C2×C4×D3—62no—
258C2×C4×D3—62no—
259C2×C4×D3—122no—
260C3×Q16—21no—
261C3×Q16C4×D311yescharacteristic
262C3×Q16C4×D311yescharacteristic
263C3×SD16—22no—
264C3×SD16C4×D312yes—
265C3×SD16C4×D312yes—
266C3×D8—21no—
267C3×D8C4×D311yescharacteristic
268C3×D8C4×D311yescharacteristic
269C3×M16—32no—
270C3×M16—32no—
271C3×M16—62no—
272C3×M16—62no—
273C2×C3×C8—21no—
274C2×C3×C8—31no—
275C2×C3×C8—31no—
276C2×C3×C8—62no—
277C2×C3×C8—62no—
278C2×C3×C8C22×D311yescharacteristic
279C2×C3×C8C22×D311yescharacteristic
280C3×C42—31no—
281C3×C42—31no—
282#216—32no—
283#216—32no—
284#216—62no—
285#215—32no—
286#215—32no—
287#215—62no—
288#214—32no—
289#214—32no—
290#214—62no—
291#213—32no—
292#213—32no—
293#213—62no—
294(C2×D3)⋊C4—61no—
295(C2×D3)⋊C4—61no—
296Dic3⋊C4—61no—
297Dic3⋊C4—61no—
298C4×Dic3C22×D311yescharacteristic
299C4×Dic3C22×D311yescharacteristic
300#208—22no—
301#208—22no—
302#208C22×D312yes—
303#208C22×D312yes—
304C2×C3⋊C8—22no—
305C2×C3⋊C8—22no—
306C2×C3⋊C8—31no—
307C2×C3⋊C8—31no—
308C2×C3⋊C8—61no—
309C2×C3⋊C8C22×D311yescharacteristic
310C2×C3⋊C8C22×D311yescharacteristic
311Dic12—31no—
312Dic12—31no—
313Dic12—61no—
314D24—31no—
315D24—31no—
316D24—61no—
317#204—32no—
318#204—32no—
319#204—62no—
320ΓL(1,𝔽25)—32no—
321ΓL(1,𝔽25)—32no—
322ΓL(1,𝔽25)—32no—
323ΓL(1,𝔽25)—32no—
324ΓL(1,𝔽25)—62no—
325ΓL(1,𝔽25)—62no—
326ΓL(1,𝔽25)—62no—
327ΓL(1,𝔽25)—62no—
328ΓL(1,𝔽25)—62no—
329ΓL(1,𝔽25)—62no—
330ΓL(1,𝔽25)—62no—
331ΓL(1,𝔽25)—62no—
332D3×C8—32no—
333D3×C8—32no—
334D3×C8—32no—
335D3×C8—32no—
336D3×C8—62no—
337D3×C8—62no—
338D3×C8—62no—
339D3×C8—62no—
340D3×C8—62no—
341D3×C8—62no—
342C22×C32—22no—
343C22×C32C2×#4111yescharacteristic
344C2×C3⋊D3—22no—
345C2×C3⋊D3—41no—
346C2×C3⋊D3—44no—
347C2×C3⋊D3C4×D412yes—
348C32×C4—22no—
349C32×C4C23×C411yescharacteristic
350C32×C4C22×D411yescharacteristic
351C3⋊Dic3—22no—
352C3⋊Dic3C4×D412yes—
353C3×Dic3—41no—
354C3×Dic3—41no—
355C2×#41—92no—
356#137—92no—
357#137—92no—
358AGL(1,ℤ/8)—92no—
359AGL(1,ℤ/8)—92no—
360#135—92no—
361#135—91no—
362#135D3211yescharacteristic
363#131—32no—
364#131—32no—
365#131—92no—
366#131—92no—
367#131—182no—
368#131—182no—
369C2×M16—91no—
370C2×M16—92no—
371C2×M16—182no—
372C22×C8—91no—
373C22×C8—182no—
374#117—91no—
375#108—31no—
376#108—31no—
377#108—92no—
378#104—32no—
379#104—32no—
380#104—92no—
381#104—92no—
382#97—31no—
383#97—91no—
384C4×C8—31no—
385C4×C8—91no—
386C22×D3—31no—
387C22×D3—31no—
388C22×D3—61no—
389C22×D3—62no—
390C22×D3—62no—
391C22×D3—122no—
392C3×Q8—22no—
393C3×Q8C2×C4×D312yes—
394C3×Q8C2×C4×D312yes—
395C3×D4—22no—
396C3×D4—22no—
397C3×D4—22no—
398C3×D4—42no—
399C3×D4C2×C4×D312yes—
400C3×D4C2×C4×D312yes—
401C2×C3×C4—22no—
402C2×C3×C4—22no—
403C2×C3×C4—21no—
404C2×C3×C4—42no—
405C2×C3×C4—61no—
406C2×C3×C4—61no—
407C2×C3×C4C23×D311yescharacteristic
408C2×C3×C4C23×D311yescharacteristic
409#67—62no—
410#67—62no—
411#67—62no—
412#67—62no—
413#67—62no—
414#67—62no—
415#67—122no—
416#67—122no—
417#67—122no—
418C2×Dic3—21no—
419C2×Dic3—21no—
420C2×Dic3—31no—
421C2×Dic3—31no—
422C2×Dic3—61no—
423C2×Dic3—62no—
424C2×Dic3—62no—
425C2×Dic3—122no—
426D12—32no—
427D12—32no—
428D12—62no—
429D12—62no—
430D12—62no—
431D12—122no—
432C4×D3—32no—
433C4×D3—32no—
434C4×D3—32no—
435C4×D3—32no—
436C4×D3—62no—
437C4×D3—62no—
438C4×D3—62no—
439C4×D3—62no—
440C4×D3—62no—
441C4×D3—62no—
442C4×D3—62no—
443C4×D3—62no—
444C4×D3—122no—
445C4×D3—122no—
446C4×D3—122no—
447Dic6—32no—
448Dic6—32no—
449Dic6—62no—
450Dic6—62no—
451Dic6—62no—
452Dic6—122no—
453C3×C8—21no—
454C3×C8—21no—
455C3×C8—31no—
456C3×C8—32no—
457C3×C8—31no—
458C3×C8—62no—
459C3×C8—62no—
460C3×C8C2×C4×D311yescharacteristic
461C3×C8C2×C4×D311yescharacteristic
462C3×C8C2×C4×D311yescharacteristic
463C3×C8C2×C4×D311yescharacteristic
464C3⋊C8—22no—
465C3⋊C8—22no—
466C3⋊C8—32no—
467C3⋊C8—32no—
468C3⋊C8—62no—
469C3⋊C8D3×D411yescharacteristic
470C3⋊C8D3×D412yes—
471C3⋊C8D3×D411yescharacteristic
472C2×C32—21no—
473C2×C32—42no—
474C2×C32C2×C4×D411yescharacteristic
475C3⋊D3—22no—
476C3⋊D3—42no—
477#41—92no—
478#41—92no—
479#41—92no—
480#41—182no—
481#41—182no—
482#41C2×D3212yes—
483C2×Q8—92no—
484C2×D4—92no—
485C2×D4—182no—
486C22×C4—91no—
487C22×C4—182no—
488Q16—92no—
489Q16—91no—
490Q16#62411yescharacteristic
491SD16—92no—
492SD16—92no—
493SD16—92no—
494SD16#62412yes—
495D8—92no—
496D8—91no—
497D8#62411yescharacteristic
498M16—32no—
499M16—32no—
500M16—62no—
501M16—62no—
502M16—92no—
503M16—92no—
504M16—182no—
505M16—182no—
506M16—182no—
507C2×C8—31no—
508C2×C8—31no—
509C2×C8—62no—
510C2×C8—62no—
511C2×C8—92no—
512C2×C8—92no—
513C2×C8—91no—
514C2×C8—182no—
515C2×C8—182no—
516C2×C8—182no—
517C2×C8C2×D3211yescharacteristic
518C4⋊C4—181no—
519C22⋊C4—181no—
520C42—31no—
521C42—31no—
522C22×C3—22no—
523C22×C3—22no—
524C22×C3—21no—
525C22×C3—42no—
526C22×C3D3×#4111yescharacteristic
527C22×C3D3×#4111yescharacteristic
528C2×D3—32no—
529C2×D3—32no—
530C2×D3—62no—
531C2×D3—62no—
532C2×D3—62no—
533C2×D3—122no—
534C2×D3—121no—
535C2×D3—121no—
536C2×D3—124no—
537C2×D3—124no—
538C2×D3—241no—
539C2×D3—244no—
540C3×C4—22no—
541C3×C4—22no—
542C3×C4—21no—
543C3×C4—21no—
544C3×C4—42no—
545C3×C4—121no—
546C3×C4—121no—
547C3×C4C22×C4×D311yescharacteristic
548C3×C4C22×C4×D311yescharacteristic
549C3×C4C2×D3×D411yescharacteristic
550C3×C4C2×D3×D411yescharacteristic
551Dic3—32no—
552Dic3—32no—
553Dic3—41no—
554Dic3—41no—
555Dic3—62no—
556Dic3—62no—
557Dic3—62no—
558Dic3—122no—
559C32#295511yescharacteristic, complemented, Sylow
560C23—91no—
561C23—182no—
562Q8—92no—
563Q8—182no—
564Q8C2×#62412yes—
565D4—22no—
566D4—92no—
567D4—182no—
568D4—182no—
569D4—182no—
570D4—182no—
571D4C2×#62412yes—
572C2×C4—22no—
573C2×C4—61no—
574C2×C4—61no—
575C2×C4—91no—
576C2×C4—92no—
577C2×C4—92no—
578C2×C4—182no—
579C2×C4—182no—
580C2×C4—182no—
581C2×C4—182no—
582C2×C4C22×D3211yescharacteristic
583C8—31no—
584C8—32no—
585C8—31no—
586C8—62no—
587C8—62no—
588C8—92no—
589C8C2×#62411yescharacteristic
590C8C2×#62411yescharacteristic
591C2×C3—21no—
592C2×C3—21no—
593C2×C3—21no—
594C2×C3—41no—
595C2×C3—42no—
596C2×C3—42no—
597C2×C3—82no—
598C2×C3C4×D3×D411yescharacteristic
599C2×C3C4×D3×D411yescharacteristic
600D3—62no—
601D3—62no—
602D3—122no—
603D3—122no—
604D3—122no—
605D3—242no—
606C22—22no—
607C22—92no—
608C22—182no—
609C22—361no—
610C22—364no—
611C22#6431211yescharacteristic
612C4—22no—
613C4—92no—
614C4—121no—
615C4—121no—
616C4—182no—
617C4D32×D411yescharacteristic
618C4C22×#62411yescharacteristic
619C3—21no—
620C3#7988811yescharacteristic, complemented
621C3#7989711yescharacteristic, complemented
622C2—21no—
623C2—42no—
624C2—182no—
625C2—362no—
626C2D4×#62411yescharacteristic
subgroupG/H
centerC4D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#135C22
socleC2×C32C2×C4×D4
prime radical#10596239C2
cosocleC2×C32×C4C24
hypercenter#135D32
hypocenterC32#2955
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ #135

Complements

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

NH ≅ G/Ntype
2. #10595442C2semidirect
3. C3×#5197C2semidirect
4. C3×#5196C2semidirect
5. #10591672C2semidirect
6. #10591663C2semidirect
7. #10591662C2semidirect
8. #10590918C2semidirect
9. #10590917C2semidirect
10. #10590914C2semidirect
11. #10590910C2semidirect
17. #64127C4semidirect
18. #64124C4semidirect
19. #64123C4semidirect
20. #64120C4semidirect
23. C3×#948C22semidirect
24. C3×#948C22semidirect
30. #63817C22semidirect
31. #63817C22semidirect
34. C3×#837C22semidirect
35. C3×#837C22semidirect
36. C3×#819C22semidirect
37. C3×#819C22semidirect
38. C3×#815C22semidirect
39. C3×C8×Dic3C22semidirect
40. #63578C22semidirect
41. #63570C22semidirect
42. #63570C22semidirect
43. #63554C22semidirect
44. Dic3×C3⋊C8C22semidirect
52. #5197D3semidirect
53. #5196D3semidirect
125. #948C2×D3semidirect
126. #948C2×D3semidirect
169. #837C2×D3semidirect
170. #837C2×D3semidirect
175. #819C2×D3semidirect
176. #819C2×D3semidirect
178. #815C2×D3semidirect
180. C8×Dic3C2×D3semidirect
559. C32#2955semidirect
620. C3#79888semidirect
621. C3#79897semidirect

Maximal subgroups

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

subgroupindex
#105962392
#105954422
C3×#51972
C3×#51962
#105916722
#105916632
#105916622
#105909182
#105909172
#105909142
#105909102
#798973
#798883