Finite Group Databasebeta

← #11861239

Subgroups — #11861239

Order 1152.

956 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594706C212yesmaximal, complemented
2D3×#904C211yesmaximal, characteristic
3#10592593C211yesmaximal, characteristic, complemented
4C3×#4894C211yesmaximal, characteristic, complemented
5C3×D3×#108C211yesmaximal, characteristic, complemented
6#10591005C212yesmaximal, complemented
7#10590995C212yesmaximal, complemented
8#10590977C212yesmaximal, complemented
9#10590920C211yesmaximal, characteristic, complemented
10#10590918C211yesmaximal, characteristic, complemented
11#10590693C211yesmaximal, characteristic, complemented
12#79899—31nomaximal
13#79249—31nomaximal
14D3×#235C2212yes—
15#64116C2212yescomplemented
16#64113C2211yescharacteristic
17C3×#907C2212yescomplemented
18C3×D3×M16C2212yes—
19C3×#904C2211yescharacteristic
20C2×C3×D3×C8C2211yescharacteristic
21#63855C2211yescharacteristic
22#63829C2212yes—
23C2×#3711C2211yescharacteristic
24#63817C2212yescomplemented
25#63815C2212yescomplemented
26#63808C411yescharacteristic, complemented
27#63807C411yescharacteristic, complemented
28#63806C412yescomplemented
29#63804—22no—
30#63803—22no—
31D3×Dic12C411yescharacteristic, complemented
32D3×D24C411yescharacteristic, complemented
33D3×#204C412yescomplemented
34#63791—22no—
35D3×ΓL(1,𝔽25)—22no—
36C32×#108C2211yescharacteristic, complemented
37#63652C2212yescomplemented
38#63642C2211yescharacteristic, complemented
39C3×#825C2212yescomplemented
40C3×#822C2212yescomplemented
41C3×#819C2211yescharacteristic, complemented
42C3×#815C2211yescharacteristic, complemented
43#63570C2212yescomplemented
44#63568C2212yescomplemented
45#63553C2211yescharacteristic, complemented
46Dic3×C3⋊C8C2211yescharacteristic, complemented
47D3×#135—31no—
48#5750—32no—
49#5745—32no—
50C2×#904—31no—
51C3×#444—31no—
52C2×C3×#108—31no—
53#5197—31no—
54#5144—32no—
55#5139—32no—
56#5101—31no—
57#4895—32no—
58#4895—32no—
59#4894—31no—
60#4894—31no—
61#4894—31no—
62#4894—31no—
63#4894—61no—
64#4894D311yescharacteristic, complemented
65D3×#108D311yescharacteristic, complemented
66#4824—32no—
67#4821—32no—
68#4717—31no—
69#4708—31no—
70#3828C2312yes—
71C3×#235C2312yes—
72C2×C3×C4×D3C2311yescharacteristic
73D3×#67—22no—
74#3804—22no—
75D3×D12C2×C412yes—
76C4×D32—22no—
77#3799C2×C412yes—
78#3798—22no—
79#3795C2×C412yes—
80D3×Dic6C2×C412yes—
81C32×M16C2312yes—
82C2×C32×C8C2311yescharacteristic
83C4×C3⋊Dic3C2311yescharacteristic
84C2×C3⋊(C3⋊C8)C2311yescharacteristic
85#3746C2×C411yescharacteristic
86#3745C2×C411yescharacteristic
87#3744C2×C412yes—
88#3743—22no—
89C8×C3⋊D3—22no—
90C3×C4×Dic3C2311yescharacteristic
91C3×#208C2312yes—
92C2×C3×C3⋊C8C2311yescharacteristic
93C2×C3×C3⋊C8C2311yescharacteristic
94C3×Dic12C2×C411yescharacteristic
95C3×D24C2×C411yescharacteristic
96C3×#204C2×C412yes—
97C3×ΓL(1,𝔽25)—22no—
98C3×ΓL(1,𝔽25)—22no—
99C3×D3×C8—22no—
100C3×D3×C8—22no—
101C3×D3×C8C2×C411yescharacteristic
102C3×D3×C8C2×C411yescharacteristic
103C3×D3×C8C2×C411yescharacteristic
104C3×D3×C8C2×C411yescharacteristic
105Dic3⋊Dic3—21no—
106(C2×D3)⋊Dic3—21no—
107#3719C2×C412yes—
108#3717C2×C412yes—
109#3716C2×C412yes—
110#3714C2×C412yes—
111#3712—22no—
112#3711—22no—
113#3711D412yes—
114#3711D412yes—
115#3710—22no—
116D3×C3⋊C8—22no—
117#2957—91noSylow
118D3×#41—32no—
119C2×#235—32no—
120C3×#135—31no—
121C3×#131—32no—
122C2×C3×M16—32no—
123C22×C3×C8—31no—
124#950—32no—
125#948—32no—
126#926—31no—
127C2×#208—31no—
128#919—31no—
129D3×Q16—31no—
130#916—32no—
131D3×SD16—32no—
132#912—31no—
133D3×D8—31no—
134#907—32no—
135#907—32no—
136#907—32no—
137#907—32no—
138#907—62no—
139#907—62no—
140#907C2×D312yescomplemented
141D3×M16—62no—
142D3×M16—62no—
143D3×M16—62no—
144D3×M16C2×D312yes—
145C2×Dic12—31no—
146#904—32no—
147#904—31no—
148#904—31no—
149#904—31no—
150#904—31no—
151#904—32no—
152#904—61no—
153#904C2×D311yescharacteristic
154C2×D24—31no—
155C2×#204—32no—
156#901—32no—
157#901—62no—
158#901—62no—
159#901—62no—
160C2×ΓL(1,𝔽25)—31no—
161C2×ΓL(1,𝔽25)—62no—
162C2×D3×C8C2×D311yescharacteristic
163#872—31no—
164C3×#108—21no—
165C3×#108—32no—
166C3×#108—31no—
167C3×#108C2×D311yescharacteristic, complemented
168C3×#108C2×D311yescharacteristic, complemented
169C3×#104—32no—
170C3×#97—31no—
171#837—32no—
172#825—32no—
173#825—32no—
174#825—32no—
175#825—32no—
176#825—62no—
177#825C2×D312yescomplemented
178#822C2×D312yescomplemented
179#819C2×D311yescharacteristic, complemented
180#815—31no—
181#815—31no—
182#815—61no—
183#815C2×D311yescharacteristic, complemented
184C8×Dic3—31no—
185C8×Dic3—31no—
186C8×Dic3—31no—
187#805—32no—
188C4×C3⋊C8—31no—
189C22×C3×D3#4111yescharacteristic
190C2×D32—22no—
191C2×C32×C4C2411yescharacteristic
192#638—22no—
193C2×C3⋊Dic3—21no—
194C4⋊(C3⋊D3)C22×C412yes—
195C4×C3⋊D3—22no—
196#634C22×C412yes—
197C3×#67—22no—
198C2×C3×Dic3—21no—
199C2×C3×Dic3#4111yescharacteristic
200C3×D12C22×C412yes—
201C3×C4×D3—22no—
202C3×C4×D3C22×C411yescharacteristic
203C3×C4×D3C22×C411yescharacteristic
204C3×C4×D3C2×D411yescharacteristic
205C3×C4×D3C2×D411yescharacteristic
206C3×Dic6C22×C412yes—
207#627—22no—
208#626—22no—
209#626—22no—
210#625—22no—
211#624—22no—
212D3×Dic3—22no—
213D3×Dic3—22no—
214C32×C8—22no—
215C32×C8C22×C411yescharacteristic
216C32×C8C22×C411yescharacteristic
217C3⋊(C3⋊C8)C2×D412yes—
218C3×C3⋊C8—22no—
219C3×C3⋊C8C22×C411yescharacteristic
220C3×C3⋊C8C22×C411yescharacteristic
221C3×C3⋊C8C2×D412yes—
222C2×#135—91no—
223#568—92no—
224#444—31no—
225#444—91no—
226#444—91no—
227#444—91no—
228#443—92no—
229#443—92no—
230C2×#108—31no—
231#421—92no—
232#405—91no—
233C3×#41—32no—
234C22×C3×C4—31no—
235C2×#67—62no—
236#239—32no—
237D3×Q8—32no—
238#237—32no—
239#237—62no—
240D3×D4—32no—
241D3×D4—62no—
242#235—32no—
243#235—32no—
244#235—32no—
245#235—32no—
246#235—62no—
247#235—62no—
248#235—62no—
249#235—62no—
250#235C22×D312yes—
251C2×D12—32no—
252C2×C4×D3—62no—
253C2×C4×D3—62no—
254C2×C4×D3C22×D311yescharacteristic
255C2×Dic6—32no—
256C3×Q16—31no—
257C3×SD16—32no—
258C3×D8—31no—
259C3×M16—22no—
260C3×M16—32no—
261C3×M16—62no—
262C3×M16—62no—
263C3×M16C22×D312yes—
264C3×M16C22×D312yes—
265C2×C3×C8—21no—
266C2×C3×C8—31no—
267C2×C3×C8—31no—
268C2×C3×C8—31no—
269C2×C3×C8—31no—
270C2×C3×C8—31no—
271C2×C3×C8—31no—
272C2×C3×C8—62no—
273C2×C3×C8—62no—
274C2×C3×C8C22×D311yescharacteristic
275C2×C3×C8C22×D311yescharacteristic
276C3×C42—31no—
277#217—61no—
278#216—32no—
279#215—32no—
280#214—32no—
281#213—32no—
282(C2×D3)⋊C4—61no—
283C4⋊Dic3—61no—
284Dic3⋊C4—61no—
285C4×Dic3—31no—
286C4×Dic3—31no—
287C4×Dic3—61no—
288C4×Dic3C22×D311yescharacteristic
289#208—32no—
290#208—32no—
291#208—62no—
292#208C22×D312yes—
293C2×C3⋊C8—31no—
294C2×C3⋊C8—31no—
295C2×C3⋊C8—61no—
296C2×C3⋊C8—62no—
297C2×C3⋊C8C22×D311yescharacteristic
298C2×C3⋊C8C22×D311yescharacteristic
299Dic12—32no—
300Dic12—31no—
301Dic12—31no—
302Dic12—61no—
303Dic12C4×D311yescharacteristic
304D24—32no—
305D24—31no—
306D24—31no—
307D24—61no—
308D24C4×D311yescharacteristic
309#204—32no—
310#204—32no—
311#204—32no—
312#204—32no—
313#204—62no—
314#204C4×D312yes—
315ΓL(1,𝔽25)—22no—
316ΓL(1,𝔽25)—22no—
317ΓL(1,𝔽25)—32no—
318ΓL(1,𝔽25)—32no—
319ΓL(1,𝔽25)—62no—
320ΓL(1,𝔽25)—62no—
321ΓL(1,𝔽25)—62no—
322ΓL(1,𝔽25)—62no—
323ΓL(1,𝔽25)—62no—
324ΓL(1,𝔽25)—122no—
325D3×C8—22no—
326D3×C8—22no—
327D3×C8—62no—
328D3×C8—62no—
329D3×C8—62no—
330D3×C8—62no—
331D3×C8—62no—
332D3×C8—122no—
333D3×C8C4×D311yescharacteristic
334D3×C8C4×D311yescharacteristic
335D3×C8C4×D311yescharacteristic
336D3×C8C4×D311yescharacteristic
337C22×C32C2×#4111yescharacteristic
338C2×C3⋊D3—22no—
339C2×C3×D3—22no—
340C2×C3×D3—41no—
341C2×C3×D3C4×D411yescharacteristic
342C2×C3×D3C4×D411yescharacteristic
343D32—82no—
344C32×C4C23×C411yescharacteristic
345C32×C4C22×D411yescharacteristic
346C3⋊Dic3—22no—
347C3⋊Dic3—41no—
348C3×Dic3—22no—
349C3×Dic3—41no—
350C3×Dic3C4×D411yescharacteristic
351C3×Dic3C4×D411yescharacteristic
352C2×#41—92no—
353#135—31no—
354#135—91no—
355#135—92no—
356#135—91no—
357#135—92no—
358#135—91no—
359C2×Q16—91no—
360C2×SD16—92no—
361C2×D8—91no—
362#131—32no—
363#131—92no—
364#131—92no—
365#131—92no—
366#131—182no—
367#131—182no—
368C2×M16—32no—
369C2×M16—91no—
370C2×M16—182no—
371C2×M16—182no—
372C22×C8—31no—
373#117—91no—
374#108—32no—
375#108—31no—
376#108D3211yescharacteristic, complemented
377#104—32no—
378#104—92no—
379#104—92no—
380#104—92no—
381#97—31no—
382#97—91no—
383C4×C8—91no—
384C4×C8—91no—
385C23×C3—31no—
386C22×D3—62no—
387C22×D3—62no—
388C22×D3#23911yescharacteristic
389C3×Q8—32no—
390C3×D4—32no—
391C3×D4—62no—
392C2×C3×C4—21no—
393C2×C3×C4—31no—
394C2×C3×C4—31no—
395C2×C3×C4—31no—
396C2×C3×C4—31no—
397C2×C3×C4—31no—
398C2×C3×C4—62no—
399C2×C3×C4—61no—
400C2×C3×C4C23×D311yescharacteristic
401C2×C3×C4C23×D311yescharacteristic
402#67—22no—
403#67—62no—
404#67—62no—
405#67—62no—
406#67—62no—
407#67—62no—
408#67—62no—
409#67—122no—
410C2×Dic3—21no—
411C2×Dic3—62no—
412C2×Dic3—62no—
413C2×Dic3—61no—
414C2×Dic3—61no—
415C2×Dic3—121no—
416C2×Dic3#23911yescharacteristic
417D12—32no—
418D12—32no—
419D12—62no—
420D12—62no—
421D12—62no—
422D12C2×C4×D312yes—
423C4×D3—22no—
424C4×D3—62no—
425C4×D3—62no—
426C4×D3—62no—
427C4×D3—62no—
428C4×D3—62no—
429C4×D3—62no—
430C4×D3—122no—
431C4×D3C2×C4×D311yescharacteristic
432C4×D3C2×C4×D311yescharacteristic
433C4×D3D3×D411yescharacteristic
434C4×D3D3×D411yescharacteristic
435Dic6—32no—
436Dic6—32no—
437Dic6—62no—
438Dic6—62no—
439Dic6—62no—
440Dic6C2×C4×D312yes—
441C3×C8—22no—
442C3×C8—22no—
443C3×C8—21no—
444C3×C8—21no—
445C3×C8—31no—
446C3×C8—31no—
447C3×C8—32no—
448C3×C8—42no—
449C3×C8—62no—
450C3×C8C2×C4×D311yescharacteristic
451C3×C8C2×C4×D311yescharacteristic
452C3×C8C2×C4×D311yescharacteristic
453C3×C8C2×C4×D311yescharacteristic
454C3⋊C8—22no—
455C3⋊C8—32no—
456C3⋊C8—32no—
457C3⋊C8—62no—
458C3⋊C8C2×C4×D311yescharacteristic
459C3⋊C8C2×C4×D311yescharacteristic
460C3⋊C8D3×D412yes—
461C2×C32—21no—
462C2×C32C2×C4×D411yescharacteristic
463C3⋊D3—42no—
464C3×D3—21no—
465C3×D3—21no—
466C3×D3—42no—
467#41—32no—
468#41—92no—
469#41—92no—
470#41—92no—
471#41—182no—
472#41—182no—
473C2×Q8—92no—
474C2×D4—92no—
475C2×D4—182no—
476C22×C4—31no—
477C22×C4—182no—
478Q16—31no—
479Q16—92no—
480Q16—91no—
481SD16—32no—
482SD16—92no—
483SD16—92no—
484SD16—92no—
485D8—31no—
486D8—92no—
487D8—91no—
488M16—32no—
489M16—62no—
490M16—62no—
491M16—92no—
492M16—92no—
493M16—182no—
494M16—182no—
495M16—182no—
496M16C2×D3212yes—
497C2×C8—31no—
498C2×C8—31no—
499C2×C8—31no—
500C2×C8—31no—
501C2×C8—31no—
502C2×C8—31no—
503C2×C8—62no—
504C2×C8—62no—
505C2×C8—91no—
506C2×C8—182no—
507C2×C8—182no—
508C2×C8—182no—
509C2×C8C2×D3211yescharacteristic
510C4⋊C4—181no—
511C22⋊C4—181no—
512C42—31no—
513C42—91no—
514C22×C3—21no—
515C22×C3—31no—
516C22×C3—31no—
517C22×C3—62no—
518C22×C3—121no—
519C22×C3C2×#23911yescharacteristic
520C22×C3D3×#4111yescharacteristic
521C2×D3—22no—
522C2×D3—41no—
523C2×D3—62no—
524C2×D3—62no—
525C2×D3—122no—
526C2×D3—242no—
527C2×D3—242no—
528C2×D3#89311yescharacteristic
529C2×D3#89311yescharacteristic
530C3×C4—21no—
531C3×C4—21no—
532C3×C4—31no—
533C3×C4—31no—
534C3×C4—62no—
535C3×C4—121no—
536C3×C4C22×C4×D311yescharacteristic
537C3×C4C22×C4×D311yescharacteristic
538C3×C4C2×D3×D411yescharacteristic
539C3×C4C2×D3×D411yescharacteristic
540Dic3—22no—
541Dic3—41no—
542Dic3—62no—
543Dic3—62no—
544Dic3—122no—
545Dic3—121no—
546Dic3—121no—
547Dic3—241no—
548Dic3#89311yescharacteristic
549Dic3#89311yescharacteristic
550C32#295711yescharacteristic, complemented, Sylow
551C23—31no—
552C23—182no—
553Q8—32no—
554Q8—92no—
555Q8—182no—
556D4—32no—
557D4—62no—
558D4—92no—
559D4—182no—
560D4—182no—
561D4—182no—
562D4—182no—
563C2×C4—31no—
564C2×C4—31no—
565C2×C4—31no—
566C2×C4—31no—
567C2×C4—31no—
568C2×C4—62no—
569C2×C4—61no—
570C2×C4—182no—
571C2×C4—182no—
572C2×C4—182no—
573C2×C4—182no—
574C2×C4—181no—
575C2×C4C22×D3211yescharacteristic
576C8—22no—
577C8—31no—
578C8—31no—
579C8—32no—
580C8—62no—
581C8—92no—
582C8C4×D3211yescharacteristic
583C8C4×D3211yescharacteristic
584C2×C3—21no—
585C2×C3—21no—
586C2×C3—21no—
587C2×C3—41no—
588C2×C3—61no—
589C2×C3—61no—
590C2×C3—122no—
591C2×C3C2×#89311yescharacteristic
592C2×C3C4×D3×D411yescharacteristic
593D3—21no—
594D3—21no—
595D3—42no—
596D3—122no—
597D3—122no—
598D3—242no—
599C22—31no—
600C22—31no—
601C22—62no—
602C22—121no—
603C22—182no—
604C22—722no—
605C22D3×#23911yescharacteristic
606C4—31no—
607C4—31no—
608C4—62no—
609C4—121no—
610C4—182no—
611C4—361no—
612C4C2×C4×D3211yescharacteristic
613C4D32×D411yescharacteristic
614C3—21no—
615C3#7924911yescharacteristic, complemented
616C3#7989911yescharacteristic, complemented
617C2—21no—
618C2—61no—
619C2—61no—
620C2—122no—
621C2—362no—
622C2D3×#89311yescharacteristic
subgroupG/H
centerC4D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#108C22
socleC2×C32C2×C4×D4
prime radicalD3×#904C2
cosocleC2×C32×C4C24
hypercenter#108D32
hypocenterC32#2957
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ #108

Complements

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

NH ≅ G/Ntype
1. #10594706C2semidirect
3. #10592593C2semidirect
4. C3×#4894C2semidirect
5. C3×D3×#108C2semidirect
6. #10591005C2semidirect
7. #10590995C2semidirect
8. #10590977C2semidirect
9. #10590920C2semidirect
10. #10590918C2semidirect
11. #10590693C2semidirect
15. #64116C22semidirect
17. C3×#907C22semidirect
24. #63817C22semidirect
25. #63815C22semidirect
26. #63808C4semidirect
27. #63807C4semidirect
28. #63806C4semidirect
31. D3×Dic12C4semidirect
32. D3×D24C4semidirect
33. D3×#204C4semidirect
36. C32×#108C22semidirect
37. #63652C22semidirect
38. #63642C22semidirect
39. C3×#825C22semidirect
40. C3×#822C22semidirect
41. C3×#819C22semidirect
42. C3×#815C22semidirect
43. #63570C22semidirect
44. #63568C22semidirect
45. #63553C22semidirect
46. Dic3×C3⋊C8C22semidirect
64. #4894D3semidirect
65. D3×#108D3semidirect
140. #907C2×D3semidirect
167. C3×#108C2×D3semidirect
168. C3×#108C2×D3semidirect
177. #825C2×D3semidirect
178. #822C2×D3semidirect
179. #819C2×D3semidirect
183. #815C2×D3semidirect
376. #108D32semidirect
550. C32#2957semidirect
615. C3#79249semidirect
616. C3#79899semidirect

Maximal subgroups

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

subgroupindex
#105947062
D3×#9042
#105925932
C3×#48942
C3×D3×#1082
#105910052
#105909952
#105909772
#105909202
#105909182
#105906932
#798993
#792493