Finite Group Databasebeta

← #11861159

Subgroups — #11861159

Order 1152.

1001 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595460C211yesmaximal, characteristic
2#10595443C211yesmaximal, characteristic, complemented
3#10594708C211yesmaximal, characteristic, complemented
4C3⋊D3×#104C211yesmaximal, characteristic, complemented
5C3×#4823C212yesmaximal, complemented
6#10591673C212yesmaximal, complemented
7#10590995C212yesmaximal, complemented
8#10590974C211yesmaximal, characteristic, complemented
9#10590393C211yesmaximal, characteristic, complemented
10#10590342C212yesmaximal, complemented
11#10590247C211yesmaximal, characteristic, complemented
12#79898—32nomaximal
13#41×C3⋊D3C2211yescharacteristic
14#64306C2211yescharacteristic
15M16×C3⋊D3C2211yescharacteristic
16C42×C3⋊D3C2211yescharacteristic
17C3×#950C2212yes—
18C3×#948C2212yescomplemented
19C3×#907C2212yescomplemented
20#63951C412yescomplemented
21#63945C411yescharacteristic, complemented
22#63941C411yescharacteristic, complemented
23#63937C412yescomplemented
24#63931C411yescharacteristic, complemented
25#63927C411yescharacteristic, complemented
26#63829C2212yes—
27C2×#3712—21no—
28C2×#3712C2211yescharacteristic
29C2×#3712C2211yescharacteristic
30#63818—21no—
31#63818C2211yescharacteristic
32#63817—22no—
33#63817C2212yescomplemented
34#63814C2212yescomplemented
35#63805—21no—
36#63803—21no—
37D3×ΓL(1,𝔽25)—22no—
38C32×#104C2211yescharacteristic, complemented
39#63664C2211yescharacteristic, complemented
40#63652C2211yescharacteristic, complemented
41#63632C2211yescharacteristic, complemented
42C3×#822C2212yescomplemented
43C3×#805C2212yescomplemented
44C3×#803C2212yescomplemented
45#63577C2212yescomplemented
46#63568C2212yescomplemented
47#63553C2212yescomplemented
48#5768—32no—
49#5750—32no—
50#5750—32no—
51C3×#444—32no—
52#5196—32no—
53#5144—32no—
54#5144—32no—
55#4895—32no—
56#4893—32no—
57#4823—32no—
58#4823D312yescomplemented
59D3×#104—32no—
60D3×#104—32no—
61D3×#104—61no—
62#4717—32no—
63#4707—32no—
64C32×#41C2311yescharacteristic
65#3832C2×C411yescharacteristic
66Q8×C3⋊D3C2×C411yescharacteristic
67#3830—21no—
68#3830C2×C411yescharacteristic
69D4×C3⋊D3—21no—
70D4×C3⋊D3C2×C411yescharacteristic
71#3828—21no—
72#3828C2311yescharacteristic
73C2×C4×C3⋊D3—21no—
74C2×C4×C3⋊D3—21no—
75C2×C4×C3⋊D3C2311yescharacteristic
76C3×#235C2312yes—
77#3811—21no—
78#3805—21no—
79#3802C2×C411yescharacteristic
80C4×D32—21no—
81#3798—21no—
82#3797C2×C411yescharacteristic
83#3796C2×C412yes—
84C32×M16C2311yescharacteristic
85C32×C42C2311yescharacteristic
86C4×C3⋊Dic3—21no—
87C4×C3⋊Dic3C2311yescharacteristic
88#3748C2311yescharacteristic
89#3743—21no—
90C8×C3⋊D3—21no—
91C3×#216C2×C412yescomplemented
92C3×#215C2×C412yescomplemented
93C3×#214C2×C412yescomplemented
94C3×#213C2×C412yescomplemented
95C3×#208—22no—
96C3×#208C2312yes—
97C2×C3×C3⋊C8—22no—
98C2×C3×C3⋊C8C2312yes—
99C2×C3×C3⋊C8C2312yes—
100C3×ΓL(1,𝔽25)—22no—
101C3×D3×C8—22no—
102#3719C2×C412yescomplemented
103#3717C2×C412yescomplemented
104#3716C2×C412yescomplemented
105#3714C2×C412yescomplemented
106#3712—21no—
107#3712—22no—
108#3712C2×C411yescharacteristic
109#3712C2×C411yescharacteristic
110#3712C2×C412yes—
111#3712D412yes—
112#3712D411yescharacteristic
113#3712D411yescharacteristic
114#3711—22no—
115#3710—21no—
116#3710—22no—
117D3×C3⋊C8—22no—
118#2956—91noSylow
119D3×#41—32no—
120D3×#41—32no—
121D3×#41—61no—
122C3×#135—32no—
123C3×#131—32no—
124C3×#131—32no—
125#950—32no—
126#950C2×D312yes—
127#948—32no—
128#948C2×D312yescomplemented
129#918—32no—
130#918—32no—
131#915—32no—
132#915—32no—
133#914—32no—
134#914—32no—
135#911—32no—
136#911—32no—
137#907—32no—
138#907—62no—
139#907—62no—
140#907C2×D312yescomplemented
141D3×M16—32no—
142D3×M16—32no—
143D3×M16—61no—
144D3×M16—62no—
145D3×M16—62no—
146#904—32no—
147#901—32no—
148#901—32no—
149#901—62no—
150#901—62no—
151C2×ΓL(1,𝔽25)—32no—
152C2×ΓL(1,𝔽25)—32no—
153C2×ΓL(1,𝔽25)—62no—
154C2×ΓL(1,𝔽25)—62no—
155C42×D3—32no—
156C42×D3—61no—
157C3×#108—32no—
158C3×#104—21no—
159C3×#104—32no—
160C3×#104C2×D312yescomplemented
161C3×#97—32no—
162#837—32no—
163#837—32no—
164#837—61no—
165#825—32no—
166#825—32no—
167#825—61no—
168#822—32no—
169#822C2×D312yescomplemented
170#819—32no—
171C8×Dic3—32no—
172C8×Dic3—32no—
173#805—32no—
174#805—61no—
175#805C2×D312yescomplemented
176#803C2×D312yescomplemented
177C22×C3⋊D3—21no—
178C22×C3⋊D3#4111yescharacteristic
179C2×D32—21no—
180C32×Q8C22×C411yescharacteristic
181C32×D4—21no—
182C32×D4C22×C411yescharacteristic
183C2×C32×C4—21no—
184C2×C32×C4—21no—
185C2×C32×C4C2411yescharacteristic
186#638—21no—
187#638—21no—
188#638—21no—
189C2×C3⋊Dic3—21no—
190C2×C3⋊Dic3—21no—
191C2×C3⋊Dic3#4111yescharacteristic
192C4⋊(C3⋊D3)—21no—
193C4⋊(C3⋊D3)C22×C411yescharacteristic
194C4×C3⋊D3—21no—
195C4×C3⋊D3—21no—
196C4×C3⋊D3—21no—
197C4×C3⋊D3—42no—
198C4×C3⋊D3C22×C411yescharacteristic
199C4×C3⋊D3C22×C411yescharacteristic
200C4×C3⋊D3C2×D411yescharacteristic
201C4×C3⋊D3C2×D411yescharacteristic
202#634—21no—
203#634C22×C411yescharacteristic
204C3×#67—22no—
205C3×D12C22×C412yes—
206C3×C4×D3—22no—
207C3×Dic6C22×C412yes—
208#627—21no—
209#626—22no—
210#625—21no—
211#624—21no—
212D3×Dic3—22no—
213C32×C8—21no—
214C3⋊(C3⋊C8)—21no—
215C3×C3⋊C8—22no—
216C3×C3⋊C8C22×C412yes—
217C3×C3⋊C8C22×C412yes—
218C3×C3⋊C8C2×D412yes—
219C3×C3⋊C8C2×D412yes—
220#575—91no—
221#568—91no—
222#568—91no—
223#444—32no—
224#444—92no—
225#443—92no—
226#443—92no—
227#430—91no—
228C2×#104—91no—
229C2×#104—91no—
230C4×M16—91no—
231C3×#41—21no—
232C3×#41—32no—
233C3×#41C22×D312yes—
234#239—32no—
235#239—32no—
236#239—61no—
237D3×Q8—32no—
238D3×Q8—32no—
239D3×Q8—61no—
240#237—32no—
241#237—32no—
242#237—61no—
243#237—62no—
244#237—62no—
245#237—121no—
246D3×D4—32no—
247D3×D4—32no—
248D3×D4—61no—
249D3×D4—62no—
250D3×D4—62no—
251D3×D4—121no—
252#235—32no—
253#235—61no—
254#235—62no—
255#235—62no—
256#235—121no—
257#235C22×D312yes—
258C2×C4×D3—32no—
259C2×C4×D3—61no—
260C2×C4×D3—62no—
261C2×C4×D3—62no—
262C2×C4×D3—62no—
263C2×C4×D3—121no—
264C2×C4×D3—121no—
265C3×Q16—32no—
266C3×SD16—32no—
267C3×SD16—32no—
268C3×D8—32no—
269C3×M16—21no—
270C3×M16—32no—
271C3×M16—62no—
272C3×M16—62no—
273C3×M16C22×D312yes—
274C2×C3×C8—32no—
275C2×C3×C8—32no—
276C2×C3×C8—62no—
277C2×C3×C8—62no—
278C3×C42—21no—
279C3×C42C22×D312yes—
280#216—32no—
281#216C4×D312yescomplemented
282#215—32no—
283#215C4×D312yescomplemented
284#214—32no—
285#214C4×D312yescomplemented
286#213—32no—
287#213C4×D312yescomplemented
288C4×Dic3—32no—
289C4×Dic3—61no—
290C4×Dic3—62no—
291C4×Dic3—121no—
292#208—22no—
293#208—32no—
294#208—61no—
295#208—62no—
296#208C22×D312yes—
297C2×C3⋊C8—22no—
298C2×C3⋊C8—62no—
299C2×C3⋊C8C22×D312yes—
300C2×C3⋊C8C22×D312yes—
301Dic12—32no—
302D24—32no—
303#204—32no—
304#204—32no—
305ΓL(1,𝔽25)—22no—
306ΓL(1,𝔽25)—32no—
307ΓL(1,𝔽25)—32no—
308ΓL(1,𝔽25)—32no—
309ΓL(1,𝔽25)—32no—
310ΓL(1,𝔽25)—32no—
311ΓL(1,𝔽25)—32no—
312ΓL(1,𝔽25)—32no—
313ΓL(1,𝔽25)—32no—
314ΓL(1,𝔽25)—62no—
315ΓL(1,𝔽25)—62no—
316ΓL(1,𝔽25)—62no—
317ΓL(1,𝔽25)—62no—
318ΓL(1,𝔽25)—62no—
319ΓL(1,𝔽25)—121no—
320D3×C8—22no—
321D3×C8—62no—
322D3×C8—62no—
323D3×C8—62no—
324D3×C8—62no—
325D3×C8—62no—
326D3×C8—121no—
327C22×C32—21no—
328C22×C32C2×#4111yescharacteristic
329C2×C3⋊D3—21no—
330C2×C3⋊D3—41no—
331C2×C3⋊D3—81no—
332C2×C3⋊D3C4×D411yescharacteristic
333C2×C3⋊D3C4×D411yescharacteristic
334C2×C3×D3—22no—
335D32—81no—
336C32×C4—21no—
337C32×C4—41no—
338C32×C4C23×C411yescharacteristic
339C32×C4C22×D411yescharacteristic
340C3⋊Dic3—22no—
341C3⋊Dic3—21no—
342C3⋊Dic3C4×D411yescharacteristic
343C3⋊Dic3C4×D411yescharacteristic
344C3×Dic3—22no—
345C2×#41—91no—
346C2×#41—91no—
347#137—91no—
348#137—92no—
349#137—91no—
350AGL(1,ℤ/8)—91no—
351AGL(1,ℤ/8)—92no—
352AGL(1,ℤ/8)—91no—
353#135—32no—
354#135—92no—
355#131—32no—
356#131—32no—
357#131—92no—
358#131—92no—
359#131—181no—
360#131—182no—
361#131—181no—
362C2×M16—91no—
363C2×M16—91no—
364C2×M16—91no—
365C2×M16—91no—
366C2×M16—181no—
367C2×M16—182no—
368C2×M16—181no—
369C2×C42—91no—
370#108—32no—
371#108—92no—
372#104—32no—
373#104—92no—
374#104—91no—
375#104—91no—
376#104—91no—
377#104D3211yescharacteristic, complemented
378#97—32no—
379C4×C8—92no—
380C22×D3—32no—
381C22×D3—61no—
382C22×D3—62no—
383C22×D3—62no—
384C22×D3—121no—
385C3×Q8—21no—
386C3×Q8—32no—
387C3×Q8C2×C4×D312yes—
388C3×D4—22no—
389C3×D4—21no—
390C3×D4—32no—
391C3×D4—41no—
392C3×D4—62no—
393C3×D4C2×C4×D312yes—
394C2×C3×C4—22no—
395C2×C3×C4—22no—
396C2×C3×C4—21no—
397C2×C3×C4—41no—
398C2×C3×C4—41no—
399C2×C3×C4—62no—
400C2×C3×C4C23×D312yes—
401#67—22no—
402#67—62no—
403#67—62no—
404#67—62no—
405#67—62no—
406#67—62no—
407#67—121no—
408#67—121no—
409#67—121no—
410C2×Dic3—32no—
411C2×Dic3—61no—
412C2×Dic3—62no—
413C2×Dic3—62no—
414C2×Dic3—62no—
415C2×Dic3—121no—
416C2×Dic3—121no—
417D12—32no—
418D12—61no—
419D12—62no—
420D12—62no—
421D12—121no—
422D12C2×C4×D312yes—
423C4×D3—22no—
424C4×D3—32no—
425C4×D3—32no—
426C4×D3—32no—
427C4×D3—32no—
428C4×D3—61no—
429C4×D3—61no—
430C4×D3—61no—
431C4×D3—61no—
432C4×D3—62no—
433C4×D3—62no—
434C4×D3—62no—
435C4×D3—62no—
436C4×D3—62no—
437C4×D3—121no—
438C4×D3—121no—
439C4×D3—121no—
440C4×D3—124no—
441C4×D3—124no—
442Dic6—32no—
443Dic6—61no—
444Dic6—62no—
445Dic6—62no—
446Dic6—121no—
447Dic6C2×C4×D312yes—
448C3×C8—22no—
449C3×C8—32no—
450C3×C8—32no—
451C3×C8—32no—
452C3×C8—32no—
453C3×C8—41no—
454C3×C8—62no—
455C3⋊C8—22no—
456C3⋊C8—62no—
457C3⋊C8—121no—
458C3⋊C8C2×C4×D312yes—
459C3⋊C8C2×C4×D312yes—
460C3⋊C8D3×D412yes—
461C3⋊C8D3×D412yes—
462C2×C32—21no—
463C2×C32—41no—
464C2×C32C2×C4×D411yescharacteristic
465C3⋊D3—21no—
466C3⋊D3—21no—
467C3⋊D3—41no—
468C3×D3—42no—
469#41—32no—
470#41—92no—
471#41—91no—
472#41—91no—
473#41—91no—
474#41—181no—
475#41—181no—
476#41—181no—
477#41—181no—
478#41C2×D3211yescharacteristic
479C2×Q8—91no—
480C2×Q8—91no—
481C2×D4—91no—
482C2×D4—91no—
483C2×D4—181no—
484C2×D4—181no—
485C22×C4—91no—
486C22×C4—181no—
487C22×C4—181no—
488C22×C4—181no—
489Q16—32no—
490Q16—92no—
491SD16—32no—
492SD16—32no—
493SD16—92no—
494SD16—92no—
495D8—32no—
496D8—92no—
497M16—32no—
498M16—62no—
499M16—62no—
500M16—91no—
501M16—92no—
502M16—91no—
503M16—91no—
504M16—92no—
505M16—91no—
506M16—91no—
507M16—181no—
508M16—182no—
509M16—182no—
510M16—181no—
511M16C2×D3211yescharacteristic
512C2×C8—32no—
513C2×C8—32no—
514C2×C8—62no—
515C2×C8—62no—
516C2×C8—181no—
517C2×C8—182no—
518C2×C8—182no—
519C2×C8—181no—
520C42—91no—
521C42—181no—
522C42C2×D3211yescharacteristic
523C22×C3—22no—
524C22×C3—21no—
525C22×C3—41no—
526C22×C3—62no—
527C22×C3D3×#4112yes—
528C2×D3—22no—
529C2×D3—32no—
530C2×D3—32no—
531C2×D3—61no—
532C2×D3—61no—
533C2×D3—62no—
534C2×D3—121no—
535C2×D3—122no—
536C2×D3—122no—
537C2×D3—242no—
538C2×D3—242no—
539C2×D3—242no—
540C3×C4—22no—
541C3×C4—21no—
542C3×C4—21no—
543C3×C4—41no—
544C3×C4—42no—
545C3×C4—42no—
546C3×C4—62no—
547C3×C4C22×C4×D312yes—
548C3×C4C2×D3×D412yes—
549Dic3—22no—
550Dic3—32no—
551Dic3—32no—
552Dic3—61no—
553Dic3—61no—
554Dic3—64no—
555Dic3—62no—
556Dic3—121no—
557Dic3—122no—
558C32#295611yescharacteristic, complemented, Sylow
559C23—91no—
560C23—181no—
561C23—181no—
562Q8—32no—
563Q8—91no—
564Q8—181no—
565Q8—181no—
566Q8C4×D3211yescharacteristic
567D4—21no—
568D4—32no—
569D4—62no—
570D4—91no—
571D4—181no—
572D4—182no—
573D4—181no—
574D4—181no—
575D4—181no—
576D4—181no—
577D4C4×D3211yescharacteristic
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—62no—
581C2×C4—91no—
582C2×C4—91no—
583C2×C4—91no—
584C2×C4—91no—
585C2×C4—91no—
586C2×C4—181no—
587C2×C4—181no—
588C2×C4—181no—
589C2×C4—182no—
590C2×C4—181no—
591C2×C4—181no—
592C2×C4—181no—
593C2×C4—362no—
594C2×C4C22×D3211yescharacteristic
595C8—21no—
596C8—32no—
597C8—32no—
598C8—32no—
599C8—32no—
600C8—62no—
601C8—181no—
602C2×C3—22no—
603C2×C3—21no—
604C2×C3—41no—
605C2×C3—42no—
606C2×C3—81no—
607C2×C3—122no—
608C2×C3C4×D3×D412yes—
609D3—42no—
610D3—62no—
611D3—62no—
612D3—62no—
613D3—121no—
614D3—122no—
615D3—241no—
616C22—21no—
617C22—62no—
618C22—91no—
619C22—91no—
620C22—181no—
621C22—361no—
622C22—721no—
623C22—721no—
624C22#6431211yescharacteristic
625C4—21no—
626C4—41no—
627C4—62no—
628C4—91no—
629C4—91no—
630C4—182no—
631C4—181no—
632C4C2×C4×D3211yescharacteristic
633C4D32×D411yescharacteristic
634C3—21no—
635C3#7989812yescomplemented
636C2—21no—
637C2—41no—
638C2—122no—
639C2—181no—
640C2—181no—
641C2—361no—
642C2#1059425511yescharacteristic
subgroupG/H
centerC4D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#104C22
socleC2×C32C2×C4×D4
prime radical#10595460C2
cosocleC2×C32×C4C24
hypercenter#104D32
hypocenterC32#2956
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ #104

Complements

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

NH ≅ G/Ntype
2. #10595443C2semidirect
3. #10594708C2semidirect
4. C3⋊D3×#104C2semidirect
5. C3×#4823C2semidirect
6. #10591673C2semidirect
7. #10590995C2semidirect
8. #10590974C2semidirect
9. #10590393C2semidirect
10. #10590342C2semidirect
11. #10590247C2semidirect
18. C3×#948C22semidirect
19. C3×#907C22semidirect
20. #63951C4semidirect
21. #63945C4semidirect
22. #63941C4semidirect
23. #63937C4semidirect
24. #63931C4semidirect
25. #63927C4semidirect
33. #63817C22semidirect
34. #63814C22semidirect
38. C32×#104C22semidirect
39. #63664C22semidirect
40. #63652C22semidirect
41. #63632C22semidirect
42. C3×#822C22semidirect
43. C3×#805C22semidirect
44. C3×#803C22semidirect
45. #63577C22semidirect
46. #63568C22semidirect
47. #63553C22semidirect
58. #4823D3semidirect
91. C3×#216C2×C4semidirect
92. C3×#215C2×C4semidirect
93. C3×#214C2×C4semidirect
94. C3×#213C2×C4semidirect
102. #3719C2×C4semidirect
103. #3717C2×C4semidirect
104. #3716C2×C4semidirect
105. #3714C2×C4semidirect
128. #948C2×D3semidirect
140. #907C2×D3semidirect
160. C3×#104C2×D3semidirect
169. #822C2×D3semidirect
175. #805C2×D3semidirect
176. #803C2×D3semidirect
281. #216C4×D3semidirect
283. #215C4×D3semidirect
285. #214C4×D3semidirect
287. #213C4×D3semidirect
377. #104D32semidirect
558. C32#2956semidirect
635. C3#79898semidirect

Maximal subgroups

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

subgroupindex
#105954602
#105954432
#105947082
C3⋊D3×#1042
C3×#48232
#105916732
#105909952
#105909742
#105903932
#105903422
#105902472
#798983