Finite Group Databasebeta

← #11861222

Subgroups — #11861222

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
1D3×#904C211yesmaximal, characteristic
2#10594668C212yesmaximal, complemented
3#10592416C211yesmaximal, characteristic, complemented
4C3×#4717C211yesmaximal, characteristic, complemented
5C3×#4708C211yesmaximal, characteristic, complemented
6#10590923C212yesmaximal, complemented
7#10590918C211yesmaximal, characteristic, complemented
8#10590916C211yesmaximal, characteristic, complemented
9D3×#819C211yesmaximal, characteristic, complemented
10#10590392C212yesmaximal, complemented
11#10590341C212yesmaximal, complemented
12#79899—31nomaximal
13#78580—31nomaximal
14D3×#235C2212yes—
15#64113C2211yescharacteristic
16#64110C2212yescomplemented
17C3×#904C2211yescharacteristic
18C3×#901C2212yescomplemented
19C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
20C2×C3×D3×C8C2211yescharacteristic
21C3×#872C2211yescharacteristic
22#63829C2212yes—
23#63817C2212yescomplemented
24#63814C2212yescomplemented
25D3×#208C2212yes—
26#63808C411yescharacteristic, complemented
27#63807C411yescharacteristic, complemented
28#63806C412yescomplemented
29#63805—22no—
30#63804—22no—
31D3×Dic12C411yescharacteristic, complemented
32D3×D24C411yescharacteristic, complemented
33D3×#204C412yescomplemented
34#63791—22no—
35D3×ΓL(1,𝔽25)—22no—
36C32×#97C2211yescharacteristic, complemented
37#63646C2211yescharacteristic, complemented
38#63632C2212yescomplemented
39C3×#819C2211yescharacteristic, complemented
40C3×#815C2211yescharacteristic, complemented
41C3×C8×Dic3C2211yescharacteristic, complemented
42C3×#805C2212yescomplemented
43C3×C4×C3⋊C8C2211yescharacteristic, complemented
44#63577C2212yescomplemented
45#63570C2212yescomplemented
46#63569C2212yescomplemented
47D3×#135—31no—
48#5750—32no—
49#5745—32no—
50C2×#904—31no—
51C3×#444—31no—
52C3×#405—31no—
53#5197—31no—
54#5144—32no—
55C2×#819—31no—
56#5005—32no—
57#4894—31no—
58D3×#108—31no—
59#4824—32no—
60#4821—32no—
61#4717—31no—
62#4717—31no—
63#4717—31no—
64#4717—31no—
65#4717—61no—
66#4717D311yescharacteristic, complemented
67#4708D311yescharacteristic, complemented
68#4700—32no—
69#4700—32no—
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—
81C2×C32×C8C2311yescharacteristic
82C2×C32×C8C2311yescharacteristic
83C32×C42C2311yescharacteristic
84#3748C2312yes—
85#3746C2×C411yescharacteristic
86#3745C2×C411yescharacteristic
87#3744C2×C412yes—
88#3743—22no—
89C8×C3⋊D3—22no—
90C3×(C2×D3)⋊C4—21no—
91C3×Dic3⋊C4—21no—
92C3×C4×Dic3C2311yescharacteristic
93C3×#208C2312yes—
94C2×C3×C3⋊C8C2311yescharacteristic
95C2×C3×C3⋊C8C2311yescharacteristic
96C3×Dic12C2×C411yescharacteristic
97C3×D24C2×C411yescharacteristic
98C3×#204C2×C412yes—
99C3×ΓL(1,𝔽25)—22no—
100C3×ΓL(1,𝔽25)D412yes—
101C3×ΓL(1,𝔽25)D412yes—
102C3×D3×C8—22no—
103C3×D3×C8C2×C411yescharacteristic
104C3×D3×C8C2×C411yescharacteristic
105C3×D3×C8C2×C411yescharacteristic
106C3×D3×C8C2×C411yescharacteristic
107#3719C2×C412yes—
108#3717C2×C412yes—
109#3716C2×C412yes—
110#3714C2×C412yes—
111#3712—22no—
112#3711—22no—
113#3711—22no—
114#3710—22no—
115D3×C3⋊C8—22no—
116D3×C3⋊C8—22no—
117#2957—91noSylow
118D3×#41—32no—
119C2×#235—32no—
120C3×#135—31no—
121C3×#131—32no—
122C2×C3×M16—31no—
123C22×C3×C8—31no—
124C3×#117—31no—
125#950—32no—
126#948—32no—
127C2×#208—32no—
128#919—31no—
129D3×Q16—31no—
130#916—32no—
131D3×SD16—32no—
132#912—31no—
133D3×D8—31no—
134#907—32no—
135#907—62no—
136#907—62no—
137#907—62no—
138D3×M16—32no—
139D3×M16—62no—
140D3×M16—62no—
141D3×M16—62no—
142C2×Dic12—31no—
143#904—32no—
144#904—31no—
145#904—31no—
146#904—31no—
147#904—31no—
148#904—32no—
149#904—61no—
150#904C2×D311yescharacteristic
151C2×D24—31no—
152C2×#204—32no—
153#901—32no—
154#901—32no—
155#901—32no—
156#901—32no—
157#901—62no—
158#901—62no—
159#901C2×D312yescomplemented
160C2×ΓL(1,𝔽25)—62no—
161C2×ΓL(1,𝔽25)C2×D311yescharacteristic
162C2×D3×C8C2×D311yescharacteristic
163#872C2×D311yescharacteristic
164C3×#108—31no—
165C3×#104—32no—
166C3×#97—21no—
167C3×#97—31no—
168C3×#97C2×D311yescharacteristic, complemented
169C3×#97C2×D311yescharacteristic, complemented
170C3×C4×C8—31no—
171C3×C4×C8—31no—
172#837—32no—
173#825—32no—
174#822—32no—
175#819—31no—
176#819—31no—
177#819—32no—
178#819—61no—
179#819C2×D311yescharacteristic, complemented
180#815C2×D311yescharacteristic, complemented
181C8×Dic3C2×D311yescharacteristic, complemented
182#805—32no—
183#805—32no—
184#805—32no—
185#805—32no—
186#805—62no—
187#805C2×D312yescomplemented
188C4×C3⋊C8C2×D311yescharacteristic, complemented
189C22×C3×D3#4111yescharacteristic
190C2×D32—22no—
191C2×C32×C4—21no—
192C2×C32×C4C2411yescharacteristic
193#638—22no—
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×C8C22×C411yescharacteristic
215C32×C8C22×C411yescharacteristic
216C32×C8C2×D412yes—
217C3⋊(C3⋊C8)—22no—
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—91no—
231#421—92no—
232#405—31no—
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—32no—
260C3×M16—32no—
261C3×M16—32no—
262C3×M16—62no—
263C2×C3×C8—21no—
264C2×C3×C8—21no—
265C2×C3×C8—31no—
266C2×C3×C8—31no—
267C2×C3×C8—31no—
268C2×C3×C8—31no—
269C2×C3×C8—31no—
270C2×C3×C8—31no—
271C2×C3×C8—62no—
272C2×C3×C8C22×D311yescharacteristic
273C2×C3×C8C22×D311yescharacteristic
274C2×C3×C8C22×D311yescharacteristic
275C2×C3×C8C22×D311yescharacteristic
276C3×C4⋊C4—61no—
277C3×C22⋊C4—61no—
278C3×C42—21no—
279C3×C42—31no—
280C3×C42C22×D311yescharacteristic
281C3×C42C22×D311yescharacteristic
282#216—32no—
283#215—32no—
284#214—32no—
285#213—32no—
286(C2×D3)⋊C4—21no—
287Dic3⋊C4—21no—
288C4×Dic3C22×D311yescharacteristic
289#208—32no—
290#208—32no—
291#208—62no—
292#208—62no—
293#208—62no—
294#208C22×D312yes—
295C2×C3⋊C8—62no—
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)—62no—
317ΓL(1,𝔽25)—62no—
318ΓL(1,𝔽25)—62no—
319ΓL(1,𝔽25)—62no—
320ΓL(1,𝔽25)—62no—
321ΓL(1,𝔽25)—62no—
322ΓL(1,𝔽25)—122no—
323ΓL(1,𝔽25)D1212yes—
324ΓL(1,𝔽25)D1212yes—
325D3×C8—22no—
326D3×C8—62no—
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×C4—41no—
345C32×C4C23×C411yescharacteristic
346C32×C4C22×D411yescharacteristic
347C3⋊Dic3—22no—
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—31no—
369C2×M16—92no—
370C2×M16—182no—
371C2×M16—182no—
372C22×C8—31no—
373#117—31no—
374#108—31no—
375#108—92no—
376#108—91no—
377#104—32no—
378#104—92no—
379#104—92no—
380#104—92no—
381#97—31no—
382#97D3211yescharacteristic, complemented
383C4×C8—31no—
384C4×C8—31no—
385C23×C3—31no—
386C22×D3—62no—
387C22×D3—62no—
388C22×D3#23511yescharacteristic
389C3×Q8—32no—
390C3×D4—32no—
391C3×D4—62no—
392C2×C3×C4—21no—
393C2×C3×C4—21no—
394C2×C3×C4—21no—
395C2×C3×C4—31no—
396C2×C3×C4—31no—
397C2×C3×C4—31no—
398C2×C3×C4—31no—
399C2×C3×C4—31no—
400C2×C3×C4—41no—
401C2×C3×C4—62no—
402C2×C3×C4—61no—
403C2×C3×C4C23×D311yescharacteristic
404C2×C3×C4C23×D311yescharacteristic
405#67—22no—
406#67—62no—
407#67—62no—
408#67—62no—
409#67—62no—
410#67—62no—
411#67—62no—
412#67—122no—
413C2×Dic3—21no—
414C2×Dic3—62no—
415C2×Dic3—62no—
416C2×Dic3#23511yescharacteristic
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×D3C2×D1211yescharacteristic
434C4×D3C2×D1211yescharacteristic
435Dic6—32no—
436Dic6—32no—
437Dic6—62no—
438Dic6—62no—
439Dic6—62no—
440Dic6C2×C4×D312yes—
441C3×C8—21no—
442C3×C8—21no—
443C3×C8—22no—
444C3×C8—31no—
445C3×C8—31no—
446C3×C8—32no—
447C3×C8—62no—
448C3×C8C2×C4×D311yescharacteristic
449C3×C8C2×C4×D311yescharacteristic
450C3×C8C2×C4×D311yescharacteristic
451C3×C8C2×C4×D311yescharacteristic
452C3×C8C2×D1212yes—
453C3×C8D3×D412yes—
454C3⋊C8—22no—
455C3⋊C8—62no—
456C3⋊C8—62no—
457C3⋊C8—122no—
458C3⋊C8C2×C4×D311yescharacteristic
459C3⋊C8C2×C4×D311yescharacteristic
460C3⋊C8C2×D1212yes—
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—32no—
490M16—32no—
491M16—62no—
492M16—92no—
493M16—182no—
494M16—182no—
495M16—182no—
496M16—182no—
497C2×C8—31no—
498C2×C8—31no—
499C2×C8—31no—
500C2×C8—31no—
501C2×C8—31no—
502C2×C8—31no—
503C2×C8—62no—
504C2×C8—182no—
505C2×C8—182no—
506C2×C8—182no—
507C2×C8—182no—
508C2×C8C2×D3211yescharacteristic
509C2×C8C2×D3211yescharacteristic
510C4⋊C4—61no—
511C22⋊C4—61no—
512C42—31no—
513C42C2×D3211yescharacteristic
514C22×C3—21no—
515C22×C3—31no—
516C22×C3—31no—
517C22×C3—62no—
518C22×C3—121no—
519C22×C3C2×#23511yescharacteristic
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×D3C4×D1211yescharacteristic
529C2×D3C4×D1211yescharacteristic
530C3×C4—21no—
531C3×C4—21no—
532C3×C4—31no—
533C3×C4—31no—
534C3×C4—41no—
535C3×C4—41no—
536C3×C4—62no—
537C3×C4—81no—
538C3×C4—121no—
539C3×C4C22×C4×D311yescharacteristic
540C3×C4C22×C4×D311yescharacteristic
541C3×C4C22×D1211yescharacteristic
542C3×C4C2×D3×D411yescharacteristic
543Dic3—22no—
544Dic3—41no—
545Dic3—62no—
546Dic3—62no—
547Dic3—122no—
548Dic3C4×D1211yescharacteristic
549Dic3C4×D1211yescharacteristic
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—21no—
564C2×C4—31no—
565C2×C4—31no—
566C2×C4—31no—
567C2×C4—31no—
568C2×C4—31no—
569C2×C4—62no—
570C2×C4—61no—
571C2×C4—182no—
572C2×C4—182no—
573C2×C4—182no—
574C2×C4—182no—
575C2×C4C22×D3211yescharacteristic
576C8—31no—
577C8—31no—
578C8—32no—
579C8—62no—
580C8—182no—
581C8C4×D3211yescharacteristic
582C8C4×D3211yescharacteristic
583C8D3×D1212yes—
584C2×C3—21no—
585C2×C3—21no—
586C2×C3—21no—
587C2×C3—41no—
588C2×C3—61no—
589C2×C3—61no—
590C2×C3—122no—
591C2×C3C2×C4×D1211yescharacteristic
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×#23511yescharacteristic
606C4—31no—
607C4—31no—
608C4—41no—
609C4—62no—
610C4—121no—
611C4—182no—
612C4C2×C4×D3211yescharacteristic
613C4C2×D3×D1211yescharacteristic
614C3—21no—
615C3#7858011yescharacteristic, complemented
616C3#7989911yescharacteristic, complemented
617C2—21no—
618C2—61no—
619C2—61no—
620C2—122no—
621C2—362no—
622C2C4×D3×D1211yescharacteristic
subgroupG/H
centerC4C2×D3×D12
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#97C22
socleC2×C32C2×C4×D4
prime radicalD3×#904C2
cosocleC2×C32×C4C24
hypercenter#97D32
hypocenterC32#2957
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C8 ◁ #97

Complements

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

NH ≅ G/Ntype
2. #10594668C2semidirect
3. #10592416C2semidirect
4. C3×#4717C2semidirect
5. C3×#4708C2semidirect
6. #10590923C2semidirect
7. #10590918C2semidirect
8. #10590916C2semidirect
9. D3×#819C2semidirect
10. #10590392C2semidirect
11. #10590341C2semidirect
16. #64110C22semidirect
18. C3×#901C22semidirect
23. #63817C22semidirect
24. #63814C22semidirect
26. #63808C4semidirect
27. #63807C4semidirect
28. #63806C4semidirect
31. D3×Dic12C4semidirect
32. D3×D24C4semidirect
33. D3×#204C4semidirect
36. C32×#97C22semidirect
37. #63646C22semidirect
38. #63632C22semidirect
39. C3×#819C22semidirect
40. C3×#815C22semidirect
41. C3×C8×Dic3C22semidirect
42. C3×#805C22semidirect
43. C3×C4×C3⋊C8C22semidirect
44. #63577C22semidirect
45. #63570C22semidirect
46. #63569C22semidirect
66. #4717D3semidirect
67. #4708D3semidirect
159. #901C2×D3semidirect
168. C3×#97C2×D3semidirect
169. C3×#97C2×D3semidirect
179. #819C2×D3semidirect
180. #815C2×D3semidirect
181. C8×Dic3C2×D3semidirect
187. #805C2×D3semidirect
188. C4×C3⋊C8C2×D3semidirect
382. #97D32semidirect
550. C32#2957semidirect
615. C3#78580semidirect
616. C3#79899semidirect

Maximal subgroups

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

subgroupindex
D3×#9042
#105946682
#105924162
C3×#47172
C3×#47082
#105909232
#105909182
#105909162
D3×#8192
#105903922
#105903412
#798993
#785803