Finite Group Databasebeta

← #11861172

Subgroups — #11861172

Order 1152.

1047 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596293C211yesmaximal, characteristic
2C3×#5819C211yesmaximal, characteristic, complemented
3#10594780C211yesmaximal, characteristic, complemented
4C2×C3×#837C211yesmaximal, characteristic, complemented
5#10591663C214yesmaximal, complemented
6#10591662C214yesmaximal, complemented
7#10591143C211yesmaximal, characteristic, complemented
8C2×#63570C211yesmaximal, characteristic, complemented
9Dic3×#208C211yesmaximal, characteristic, complemented
10#83811—31nomaximal
11#78980—31nomaximal
12C2×C32×#41C2211yescharacteristic
13C2×#3828C2211yescharacteristic
14#64160C412yescomplemented
15#64159C2214yes—
16#64158C412yescomplemented
17#64151C412yescomplemented
18#64141C412yescomplemented
19C2×#3748C2211yescharacteristic
20C3×#948—22no—
21C3×#948C2214yescomplemented
22C2×C3×C4×Dic3C2211yescharacteristic
23C2×C3×#208—22no—
24C2×C3×#208C2211yescharacteristic
25C2×C3×#208C2211yescharacteristic
26C2×C3×#208C2211yescharacteristic
27#63818—22no—
28#63817—22no—
29#63817C2214yescomplemented
30C3×#837C2212yescomplemented
31C3×#837C2212yescomplemented
32#63578C2214yescomplemented
33#63570C2212yescomplemented
34#63570C2212yescomplemented
35#63554C2212yescomplemented
36Dic3×C3⋊C8C2212yescomplemented
37C3×#568—31no—
38#5822—31no—
39#5822—31no—
40#5822—61no—
41#5819D311yescharacteristic, complemented
42#5745—31no—
43#5745—31no—
44C2×C3×#104—31no—
45C2×#837D311yescharacteristic, complemented
46#5145—34no—
47#5144—34no—
48C2×#825—31no—
49#5124—31no—
50#5124—31no—
51Dic3×M16—31no—
52C2×#805—31no—
53C4×#208—31no—
54#4824—34no—
55#4823—34no—
56C32×#41—21no—
57C32×#41—21no—
58C32×#41C2×C412yes—
59C32×#41C2312yes—
60C2×C32×Q8C2×C411yescharacteristic
61C2×C32×D4—21no—
62C2×C32×D4C2×C411yescharacteristic
63C22×C32×C4—21no—
64C22×C32×C4C2311yescharacteristic
65C2×#638—21no—
66#3828—21no—
67#3828—21no—
68#3828C2×C412yes—
69#3828C2312yes—
70C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
71C2×C4×C3⋊D3—21no—
72C2×#634C2×C411yescharacteristic
73C22×C3×Dic3—21no—
74#3756C2×C414yescomplemented
75#3755C2×C414yescomplemented
76#3754C2×C414yescomplemented
77#3753C2×C414yescomplemented
78#3748C2×C412yes—
79#3748C2×C412yes—
80C2×C3⋊(C3⋊C8)C2312yes—
81C3×C4×Dic3—21no—
82C3×C4×Dic3C2311yescharacteristic
83C3×C4×Dic3C2311yescharacteristic
84C3×#208—21no—
85C3×#208—21no—
86C3×#208—24no—
87C3×#208D412yes—
88C3×#208D412yes—
89C3×#208C2312yes—
90C3×#208C2312yes—
91C2×C3×C3⋊C8—21no—
92C2×C3×C3⋊C8—21no—
93C2×C3×C3⋊C8—24no—
94C2×C3×C3⋊C8C2312yes—
95#3712—24no—
96#3710—24no—
97#2956—91noSylow
98C2×C3×#41—21no—
99C2×C3×#41C2×D311yescharacteristic
100C2×C3×#41C2×D311yescharacteristic
101C2×#235—31no—
102C2×#235—31no—
103C2×#235—61no—
104C3×#131—34no—
105C3×#131—62no—
106C2×C3×M16—31no—
107C2×C3×M16—31no—
108C2×C3×M16—31no—
109C2×C3×M16—62no—
110C2×C3×C42—31no—
111#951—32no—
112#951—32no—
113#951—62no—
114#950—34no—
115#950—34no—
116#950—64no—
117#949—32no—
118#949—32no—
119#949—62no—
120#948—22no—
121#948C2×D314yescomplemented
122#942—32no—
123#942—32no—
124#942—62no—
125#932—32no—
126#932—32no—
127#932—62no—
128C2×C4×Dic3C2×D311yescharacteristic
129C2×#208—22no—
130C2×#208—31no—
131C2×#208—31no—
132C2×#208—61no—
133C2×#208C2×D311yescharacteristic
134C2×#208C2×D311yescharacteristic
135C2×#208C2×D311yescharacteristic
136#907—34no—
137#907—62no—
138D3×M16—62no—
139D3×M16—62no—
140#901—34no—
141#901—62no—
142C3×#104—32no—
143C3×#104—32no—
144#837C2×D312yescomplemented
145#837C2×D312yescomplemented
146#825—32no—
147#825—32no—
148#822—34no—
149#822—34no—
150#815—32no—
151C8×Dic3—32no—
152#805—32no—
153#805—32no—
154#803—32no—
155C4×C3⋊C8—32no—
156C23×C32—21no—
157C23×C32#4111yescharacteristic
158C22×C3⋊D3—21no—
159C32×Q8—21no—
160C32×Q8C22×C412yes—
161C32×D4—22no—
162C32×D4—22no—
163C32×D4—21no—
164C32×D4C22×C412yes—
165C2×C32×C4—21no—
166C2×C32×C4—22no—
167C2×C32×C4—22no—
168C2×C32×C4C22×C411yescharacteristic
169C2×C32×C4C22×C411yescharacteristic
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4#4111yescharacteristic
173C2×C32×C4C2411yescharacteristic
174#638—22no—
175#638—22no—
176C2×C3⋊Dic3—21no—
177C4⋊(C3⋊D3)—21no—
178C4⋊(C3⋊D3)C22×C412yes—
179C4×C3⋊D3—22no—
180C4×C3⋊D3—22no—
181#634—21no—
182#634C22×C412yes—
183C2×C3×Dic3—21no—
184C2×C3×Dic3—21no—
185C2×C3×Dic3—42no—
186C3⋊(C3⋊C8)C22×C414yes—
187C3×C3⋊C8—22no—
188C3×C3⋊C8—22no—
189C3×C3⋊C8C2×D414yes—
190#575—91no—
191#568—31no—
192#568—91no—
193#444—94no—
194#443—94no—
195#430—91no—
196C2×#104—31no—
197C2×#104—91no—
198C4×M16—91no—
199C3×#41—21no—
200C3×#41—21no—
201C3×#41—21no—
202C3×#41—21no—
203C3×#41—22no—
204C3×#41—22no—
205C3×#41—41no—
206C3×#41—41no—
207C3×#41C4×D312yes—
208C3×#41C4×D312yes—
209C3×#41C22×D312yes—
210C3×#41C22×D312yes—
211C2×C3×Q8—21no—
212C2×C3×Q8C4×D311yescharacteristic
213C2×C3×Q8C4×D311yescharacteristic
214C2×C3×D4—21no—
215C2×C3×D4—21no—
216C2×C3×D4—21no—
217C2×C3×D4—41no—
218C2×C3×D4C4×D311yescharacteristic
219C2×C3×D4C4×D311yescharacteristic
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—41no—
224C22×C3×C4—61no—
225C22×C3×C4C22×D311yescharacteristic
226C22×C3×C4C22×D311yescharacteristic
227C2×#67—61no—
228C2×#67—61no—
229C2×#67—121no—
230C22×Dic3—21no—
231#235—32no—
232#235—32no—
233#235—32no—
234#235—32no—
235#235—62no—
236#235—62no—
237#235—61no—
238#235—61no—
239#235—61no—
240#235—61no—
241#235—121no—
242#235—121no—
243C2×D12—31no—
244C2×D12—31no—
245C2×D12—61no—
246C2×C4×D3—61no—
247C2×C4×D3—61no—
248C2×C4×D3—121no—
249C2×Dic6—31no—
250C2×Dic6—31no—
251C2×Dic6—61no—
252C3×M16—32no—
253C3×M16—32no—
254C3×M16—32no—
255C3×M16—32no—
256C3×M16—64no—
257C3×M16—61no—
258C3×M16—61no—
259C2×C3×C8—32no—
260C2×C3×C8—64no—
261C2×C3×C8—61no—
262C2×C3×C8—61no—
263C3×C42—31no—
264C3×C42—31no—
265C3×C42—61no—
266#216—34no—
267#216—34no—
268#216—64no—
269#215—34no—
270#215—34no—
271#215—64no—
272#214—34no—
273#214—34no—
274#214—64no—
275#213—34no—
276#213—34no—
277#213—64no—
278C4×Dic3—21no—
279C4×Dic3C22×D311yescharacteristic
280C4×Dic3C22×D311yescharacteristic
281#208—21no—
282#208—21no—
283#208—24no—
284#208—32no—
285#208—32no—
286#208—32no—
287#208—32no—
288#208—62no—
289#208—62no—
290#208#6712yes—
291#208#6712yes—
292#208C22×D312yes—
293#208C22×D312yes—
294C2×C3⋊C8—21no—
295C2×C3⋊C8—21no—
296C2×C3⋊C8—24no—
297C2×C3⋊C8—32no—
298C2×C3⋊C8—32no—
299C2×C3⋊C8—62no—
300C2×C3⋊C8C22×D312yes—
301ΓL(1,𝔽25)—64no—
302ΓL(1,𝔽25)—64no—
303D3×C8—64no—
304D3×C8—64no—
305C22×C32—22no—
306C22×C32—41no—
307C22×C32—81no—
308C22×C32C4×D411yescharacteristic
309C22×C32C4×D411yescharacteristic
310C22×C32C2×#4111yescharacteristic
311C2×C3⋊D3—22no—
312C2×C3⋊D3—81no—
313C32×C4—22no—
314C32×C4C4×D411yescharacteristic
315C32×C4C4×D411yescharacteristic
316C32×C4C23×C411yescharacteristic
317C32×C4C22×D411yescharacteristic
318C3⋊Dic3—22no—
319C3×Dic3—22no—
320C3×Dic3—41no—
321C2×#41—91no—
322C2×#41D3211yescharacteristic
323#137—92no—
324#137—92no—
325AGL(1,ℤ/8)—92no—
326AGL(1,ℤ/8)—92no—
327#135—94no—
328#131—34no—
329#131—62no—
330#131—94no—
331#131—182no—
332C2×M16—31no—
333C2×M16—31no—
334C2×M16—31no—
335C2×M16—62no—
336C2×M16—91no—
337C2×M16—182no—
338C2×C42—31no—
339#108—94no—
340#104—32no—
341#104—32no—
342#104—92no—
343#104—92no—
344#97—92no—
345C4×C8—92no—
346C23×C3—21no—
347C23×C3—21no—
348C23×C3—21no—
349C23×C3—41no—
350C23×C3#23511yescharacteristic
351C23×C3#23711yescharacteristic
352C22×D3—61no—
353C22×D3—61no—
354C22×D3—121no—
355C3×Q8—21no—
356C3×Q8—21no—
357C3×Q8—22no—
358C3×Q8—41no—
359C3×Q8C2×C4×D312yes—
360C3×Q8C2×C4×D312yes—
361C3×D4—22no—
362C3×D4—22no—
363C3×D4—22no—
364C3×D4—22no—
365C3×D4—21no—
366C3×D4—21no—
367C3×D4—22no—
368C3×D4—41no—
369C3×D4—42no—
370C3×D4—42no—
371C3×D4C2×C4×D312yes—
372C3×D4C2×C4×D312yes—
373C2×C3×C4—21no—
374C2×C3×C4—21no—
375C2×C3×C4—22no—
376C2×C3×C4—22no—
377C2×C3×C4—22no—
378C2×C3×C4—22no—
379C2×C3×C4—21no—
380C2×C3×C4—21no—
381C2×C3×C4—21no—
382C2×C3×C4—21no—
383C2×C3×C4—21no—
384C2×C3×C4—21no—
385C2×C3×C4—42no—
386C2×C3×C4—42no—
387C2×C3×C4—41no—
388C2×C3×C4—61no—
389C2×C3×C4—61no—
390C2×C3×C4—122no—
391C2×C3×C4C2×C4×D311yescharacteristic
392C2×C3×C4C2×C4×D311yescharacteristic
393C2×C3×C4C2×C4×D311yescharacteristic
394C2×C3×C4C2×C4×D311yescharacteristic
395C2×C3×C4#23511yescharacteristic
396C2×C3×C4D3×D411yescharacteristic
397C2×C3×C4D3×D411yescharacteristic
398C2×C3×C4#23711yescharacteristic
399C2×C3×C4C2×#6711yescharacteristic
400C2×C3×C4C2×#6711yescharacteristic
401C2×C3×C4C23×D311yescharacteristic
402C2×C3×C4C23×D311yescharacteristic
403#67—62no—
404#67—62no—
405#67—62no—
406#67—62no—
407#67—122no—
408#67—122no—
409C2×Dic3—21no—
410C2×Dic3—21no—
411C2×Dic3—42no—
412C2×Dic3—61no—
413C2×Dic3—61no—
414C2×Dic3—121no—
415D12—32no—
416D12—32no—
417D12—62no—
418D12—61no—
419D12—61no—
420D12—121no—
421C4×D3—62no—
422C4×D3—62no—
423C4×D3—62no—
424C4×D3—62no—
425C4×D3—122no—
426C4×D3—122no—
427Dic6—32no—
428Dic6—32no—
429Dic6—62no—
430Dic6—61no—
431Dic6—61no—
432Dic6—121no—
433C3×C8—34no—
434C3×C8—62no—
435C3×C8—62no—
436C3⋊C8—22no—
437C3⋊C8—22no—
438C3⋊C8—34no—
439C3⋊C8—34no—
440C3⋊C8—64no—
441C3⋊C8C2×#6714yes—
442C2×C32—21no—
443C2×C32—21no—
444C2×C32—21no—
445C2×C32—42no—
446C2×C32C2×C4×D411yescharacteristic
447C3⋊D3—42no—
448#41—21no—
449#41—21no—
450#41—92no—
451#41—92no—
452#41—181no—
453#41—181no—
454#41#62412yes—
455#41C2×D3212yes—
456C2×Q8—91no—
457C2×Q8#62411yescharacteristic
458C2×D4—21no—
459C2×D4—91no—
460C2×D4—181no—
461C2×D4#62411yescharacteristic
462C22×C4—21no—
463C22×C4—61no—
464C22×C4—181no—
465C22×C4C2×D3211yescharacteristic
466Q16—94no—
467SD16—94no—
468SD16—94no—
469D8—94no—
470M16—32no—
471M16—32no—
472M16—32no—
473M16—32no—
474M16—64no—
475M16—61no—
476M16—61no—
477M16—92no—
478M16—92no—
479M16—184no—
480C2×C8—32no—
481C2×C8—64no—
482C2×C8—61no—
483C2×C8—61no—
484C2×C8—92no—
485C2×C8—184no—
486C42—31no—
487C42—31no—
488C42—61no—
489C22×C3—22no—
490C22×C3—22no—
491C22×C3—21no—
492C22×C3—21no—
493C22×C3—21no—
494C22×C3—42no—
495C22×C3—41no—
496C22×C3—41no—
497C22×C3—81no—
498C22×C3—81no—
499C22×C3—81no—
500C22×C3—82no—
501C22×C3#67⋊C411yescharacteristic
502C22×C3#67⋊C411yescharacteristic
503C22×C3C4×#6711yescharacteristic
504C22×C3C4×#6711yescharacteristic
505C22×C3C2×#23511yescharacteristic
506C22×C3C2×#23711yescharacteristic
507C2×D3—62no—
508C2×D3—62no—
509C2×D3—122no—
510C2×D3—241no—
511C2×D3—241no—
512C2×D3—242no—
513C3×C4—22no—
514C3×C4—22no—
515C3×C4—21no—
516C3×C4—21no—
517C3×C4—21no—
518C3×C4—21no—
519C3×C4—42no—
520C3×C4—62no—
521C3×C4—121no—
522C3×C4#67⋊C411yescharacteristic
523C3×C4#67⋊C411yescharacteristic
524C3×C4C4×#6711yescharacteristic
525C3×C4C4×#6711yescharacteristic
526C3×C4C22×C4×D311yescharacteristic
527C3×C4C22×C4×D311yescharacteristic
528C3×C4C2×D3×D411yescharacteristic
529C3×C4C22×#6711yescharacteristic
530Dic3—22no—
531Dic3—41no—
532Dic3—62no—
533Dic3—62no—
534Dic3—122no—
535C32#295611yescharacteristic, complemented, Sylow
536C23—21no—
537C23—181no—
538C23#380411yescharacteristic
539Q8—21no—
540Q8—92no—
541Q8—181no—
542Q8C2×#62412yes—
543D4—22no—
544D4—22no—
545D4—21no—
546D4—92no—
547D4—182no—
548D4—182no—
549D4—181no—
550D4C2×#62412yes—
551C2×C4—21no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—61no—
555C2×C4—61no—
556C2×C4—122no—
557C2×C4—181no—
558C2×C4—182no—
559C2×C4—182no—
560C2×C4#380411yescharacteristic
561C2×C4C2×#62411yescharacteristic
562C2×C4C2×#62411yescharacteristic
563C2×C4D3×#6711yescharacteristic
564C2×C4D3×#6711yescharacteristic
565C2×C4C22×D3211yescharacteristic
566C8—34no—
567C8—62no—
568C8—62no—
569C8—94no—
570C2×C3—21no—
571C2×C3—21no—
572C2×C3—21no—
573C2×C3—21no—
574C2×C3—21no—
575C2×C3—21no—
576C2×C3—21no—
577C2×C3—41no—
578C2×C3—41no—
579C2×C3—41no—
580C2×C3—42no—
581C2×C3—42no—
582C2×C3—82no—
583C2×C3C2×#67⋊C411yescharacteristic
584C2×C3C2×C4×#6711yescharacteristic
585D3—122no—
586D3—122no—
587D3—242no—
588C22—22no—
589C22—41no—
590C22—81no—
591C22—182no—
592C22—721no—
593C22#6395211yescharacteristic
594C22#6395211yescharacteristic
595C22C2×#380411yescharacteristic
596C4—22no—
597C4—62no—
598C4—121no—
599C4—182no—
600C4#6395211yescharacteristic
601C4#6395211yescharacteristic
602C4C22×#62411yescharacteristic
603C4C2×D3×#6711yescharacteristic
604C3—21no—
605C3#7898011yescharacteristic, complemented
606C3#8381111yescharacteristic, complemented
607C2—21no—
608C2—21no—
609C2—21no—
610C2—42no—
611C2—362no—
612C2C2×#6395211yescharacteristic
subgroupG/H
centerC4C2×D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC2×C32C2×C4×D4
prime radical#10596293C2
cosocleC2×C32×C4C24
hypercenterC2×#41D32
hypocenterC32#2956
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C3×#5819C2semidirect
3. #10594780C2semidirect
4. C2×C3×#837C2semidirect
5. #10591663C2semidirect
6. #10591662C2semidirect
7. #10591143C2semidirect
8. C2×#63570C2semidirect
9. Dic3×#208C2semidirect
14. #64160C4semidirect
16. #64158C4semidirect
17. #64151C4semidirect
18. #64141C4semidirect
21. C3×#948C22semidirect
29. #63817C22semidirect
30. C3×#837C22semidirect
31. C3×#837C22semidirect
32. #63578C22semidirect
33. #63570C22semidirect
34. #63570C22semidirect
35. #63554C22semidirect
36. Dic3×C3⋊C8C22semidirect
41. #5819D3semidirect
45. C2×#837D3semidirect
74. #3756C2×C4semidirect
75. #3755C2×C4semidirect
76. #3754C2×C4semidirect
77. #3753C2×C4semidirect
121. #948C2×D3semidirect
144. #837C2×D3semidirect
145. #837C2×D3semidirect
535. C32#2956semidirect
605. C3#78980semidirect
606. C3#83811semidirect

Maximal subgroups

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

subgroupindex
#105962932
C3×#58192
#105947802
C2×C3×#8372
#105916632
#105916622
#105911432
C2×#635702
Dic3×#2082
#838113
#789803