Finite Group Databasebeta

← #11861171

Subgroups — #11861171

Order 1152.

1045 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596290C211yesmaximal, characteristic, complemented
2C3×#5822C211yesmaximal, characteristic
3#10594776C211yesmaximal, characteristic, complemented
4C2×C3×#837C211yesmaximal, characteristic, complemented
5#10591676C214yesmaximal, complemented
6#10591675C214yesmaximal, complemented
7#10591141C211yesmaximal, characteristic, complemented
8C2×#63569C211yesmaximal, characteristic, complemented
9Dic3×#208C211yesmaximal, characteristic, complemented
10#84000—31nomaximal
11#78980—31nomaximal
12C2×C32×#41C2211yescharacteristic
13C2×C3×#235C2211yescharacteristic
14#64157—22no—
15#64157C2214yescomplemented
16C2×#3748—22no—
17C2×#3748C2211yescharacteristic
18C2×#3748C2211yescharacteristic
19C3×#951C412yescomplemented
20C3×#950C2214yes—
21C3×#949C412yescomplemented
22C3×#942C412yescomplemented
23C3×#932C412yescomplemented
24C2×C3×C4×Dic3C2211yescharacteristic
25C2×C3×#208C2211yescharacteristic
26C2×C3×#208C2211yescharacteristic
27#63815C2214yescomplemented
28#63814—22no—
29D3×#208—22no—
30C3×#837C2212yescomplemented
31C3×#837C2212yescomplemented
32#63577C2214yescomplemented
33#63569C2212yescomplemented
34#63569C2212yescomplemented
35#63554C2212yescomplemented
36Dic3×C3⋊C8C2212yescomplemented
37C3×#575—31no—
38#5822D311yescharacteristic
39#5819—31no—
40#5819—31no—
41#5819—31no—
42#5819—61no—
43#5745—31no—
44C2×C3×#104—31no—
45C2×#837—31no—
46C2×#837D311yescharacteristic, complemented
47#5197—34no—
48#5196—34no—
49#5125—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×C3×#67—21no—
66C22×C3×Dic3—21no—
67C3×#235—21no—
68C3×#235—21no—
69C3×#235C2×C412yes—
70C3×#235C2312yes—
71C2×C3×D12C2×C411yescharacteristic
72C2×C3×C4×D3—21no—
73C2×C3×Dic6C2×C411yescharacteristic
74#3748—21no—
75#3748—24no—
76#3748D412yes—
77#3748D412yes—
78#3748C2312yes—
79C2×C3⋊(C3⋊C8)—21no—
80C2×C3⋊(C3⋊C8)—24no—
81C2×C3⋊(C3⋊C8)C2312yes—
82C3×#216C2×C414yescomplemented
83C3×#215C2×C414yescomplemented
84C3×#214C2×C414yescomplemented
85C3×#213C2×C414yescomplemented
86C3×C4×Dic3—21no—
87C3×C4×Dic3C2311yescharacteristic
88C3×C4×Dic3C2311yescharacteristic
89C3×#208—21no—
90C3×#208C2×C412yes—
91C3×#208C2×C412yes—
92C3×#208C2312yes—
93C2×C3×C3⋊C8—21no—
94C2×C3×C3⋊C8C2312yes—
95#3711—24no—
96D3×C3⋊C8—24no—
97#2956—91noSylow
98C2×C3×#41—21no—
99C2×C3×#41—31no—
100C2×C3×#41C2×D311yescharacteristic
101C2×C3×#41C2×D311yescharacteristic
102C2×#235C2×D311yescharacteristic
103C3×#137—32no—
104C3×#137—32no—
105C3×AGL(1,ℤ/8)—32no—
106C3×AGL(1,ℤ/8)—32no—
107C3×#135—34no—
108C2×C3×M16—31no—
109C2×C3×M16—31no—
110C2×C3×C42—31no—
111#951Dic312yescomplemented
112#950C2×D314yes—
113#949Dic312yescomplemented
114#948—34no—
115#948—34no—
116#948—34no—
117#948—64no—
118#948—62no—
119#948—62no—
120#948—62no—
121#948—64no—
122#942Dic312yescomplemented
123#932Dic312yescomplemented
124C2×C4×Dic3C2×D311yescharacteristic
125C2×#208—31no—
126C2×#208—31no—
127C2×#208—31no—
128C2×#208—31no—
129C2×#208—61no—
130C2×#208—61no—
131C2×#208—62no—
132C2×#208—62no—
133C2×#208—62no—
134C2×#208—64no—
135C2×#208C2×D311yescharacteristic
136C2×#208C2×D311yescharacteristic
137#907—34no—
138D3×M16—62no—
139#901—62no—
140C3×#104—32no—
141C3×#104—32no—
142#837—32no—
143#837—32no—
144#837C2×D312yescomplemented
145#837C2×D312yescomplemented
146#822—34no—
147#819—34no—
148#815—32no—
149C8×Dic3—32no—
150#805—32no—
151#805—32no—
152#803—32no—
153C4×C3⋊C8—32no—
154C23×C32—21no—
155C23×C32#4111yescharacteristic
156C22×C3×D3—21no—
157C32×Q8—21no—
158C32×Q8C22×C412yes—
159C32×D4—22no—
160C32×D4—22no—
161C32×D4—21no—
162C32×D4C22×C412yes—
163C2×C32×C4—21no—
164C2×C32×C4—22no—
165C2×C32×C4—22no—
166C2×C32×C4C22×C411yescharacteristic
167C2×C32×C4C22×C411yescharacteristic
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4#4111yescharacteristic
171C2×C32×C4C2411yescharacteristic
172C3×#67—22no—
173C3×#67—22no—
174C2×C3×Dic3—21no—
175C2×C3×Dic3—21no—
176C2×C3×Dic3—21no—
177C2×C3×Dic3—42no—
178C3×D12—21no—
179C3×D12C22×C412yes—
180C3×C4×D3—22no—
181C3×C4×D3—22no—
182C3×Dic6—21no—
183C3×Dic6C22×C412yes—
184C3⋊(C3⋊C8)—22no—
185C3⋊(C3⋊C8)C2×D414yes—
186C3×C3⋊C8—22no—
187C3×C3⋊C8C22×C414yes—
188#575—31no—
189#568—91no—
190#568—91no—
191#444—94no—
192#443—94no—
193#430—91no—
194C2×#104—31no—
195C2×#104—91no—
196C4×M16—91no—
197C3×#41—22no—
198C3×#41—22no—
199C3×#41—21no—
200C3×#41—21no—
201C3×#41—21no—
202C3×#41—21no—
203C3×#41—22no—
204C3×#41—22no—
205C3×#41—32no—
206C3×#41—32no—
207C3×#41—61no—
208C3×#41—61no—
209C3×#41C4×D312yes—
210C3×#41C2×Dic312yes—
211C3×#41C22×D312yes—
212C3×#41C22×D312yes—
213C2×C3×Q8—21no—
214C2×C3×Q8—31no—
215C2×C3×Q8C4×D311yescharacteristic
216C2×C3×Q8C2×Dic311yescharacteristic
217C2×C3×D4—22no—
218C2×C3×D4—21no—
219C2×C3×D4—21no—
220C2×C3×D4—21no—
221C2×C3×D4—31no—
222C2×C3×D4—61no—
223C2×C3×D4C4×D311yescharacteristic
224C2×C3×D4C2×Dic311yescharacteristic
225C22×C3×C4—22no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—61no—
230C22×C3×C4—61no—
231C22×C3×C4C22×D311yescharacteristic
232C22×C3×C4C22×D311yescharacteristic
233C2×#67—21no—
234C22×Dic3—21no—
235#235—21no—
236#235—21no—
237#235C2×Dic312yes—
238#235C22×D312yes—
239C2×D12C2×Dic311yescharacteristic
240C2×C4×D3—21no—
241C2×Dic6C2×Dic311yescharacteristic
242C3×Q16—34no—
243C3×SD16—34no—
244C3×SD16—34no—
245C3×D8—34no—
246C3×M16—32no—
247C3×M16—32no—
248C3×M16—32no—
249C3×M16—61no—
250C2×C3×C8—32no—
251C2×C3×C8—61no—
252C3×C42—31no—
253C3×C42—31no—
254C3×C42—61no—
255#216C2×Dic314yescomplemented
256#215C2×Dic314yescomplemented
257#214C2×Dic314yescomplemented
258#213C2×Dic314yescomplemented
259C4×Dic3—21no—
260C4×Dic3C22×D311yescharacteristic
261C4×Dic3C22×D311yescharacteristic
262#208—21no—
263#208—32no—
264#208—32no—
265#208—32no—
266#208—32no—
267#208—32no—
268#208—32no—
269#208—62no—
270#208—62no—
271#208—62no—
272#208—64no—
273#208—64no—
274#208—64no—
275#208—62no—
276#208—68no—
277#208—61no—
278#208—61no—
279#208C2×Dic312yes—
280#208C2×Dic312yes—
281#208C22×D312yes—
282C2×C3⋊C8—21no—
283C2×C3⋊C8—32no—
284C2×C3⋊C8—32no—
285C2×C3⋊C8—62no—
286C2×C3⋊C8—64no—
287C2×C3⋊C8—64no—
288C2×C3⋊C8—64no—
289C2×C3⋊C8—68no—
290C2×C3⋊C8—62no—
291C2×C3⋊C8—61no—
292C2×C3⋊C8—61no—
293C2×C3⋊C8C22×D312yes—
294ΓL(1,𝔽25)—64no—
295D3×C8—64no—
296C22×C32—22no—
297C22×C32—41no—
298C22×C32—81no—
299C22×C32C4×D411yescharacteristic
300C22×C32C4×D411yescharacteristic
301C22×C32C2×#4111yescharacteristic
302C2×C3×D3—22no—
303C2×C3×D3—81no—
304C32×C4—22no—
305C32×C4C4×D411yescharacteristic
306C32×C4C4×D411yescharacteristic
307C32×C4C23×C411yescharacteristic
308C32×C4C22×D411yescharacteristic
309C3×Dic3—22no—
310C3×Dic3—22no—
311C3×Dic3—41no—
312C2×#41—31no—
313C2×#41D3211yescharacteristic
314#137—32no—
315#137—32no—
316AGL(1,ℤ/8)—32no—
317AGL(1,ℤ/8)—32no—
318#135—34no—
319#131—94no—
320#131—94no—
321#131—182no—
322#131—182no—
323C2×M16—31no—
324C2×M16—31no—
325C2×M16—91no—
326C2×M16—91no—
327C2×M16—182no—
328C2×M16—182no—
329C2×C42—31no—
330#108—94no—
331#104—32no—
332#104—32no—
333#104—92no—
334#104—92no—
335#97—92no—
336C4×C8—92no—
337C23×C3—22no—
338C23×C3—21no—
339C23×C3—21no—
340C23×C3—21no—
341C23×C3—61no—
342C23×C3#23711yescharacteristic
343C23×C3#23711yescharacteristic
344C22×D3—21no—
345C3×Q8—22no—
346C3×Q8—21no—
347C3×Q8—21no—
348C3×Q8—22no—
349C3×Q8—32no—
350C3×Q8—61no—
351C3×Q8C2×C4×D312yes—
352C3×Q8C22×Dic312yes—
353C3×D4—24no—
354C3×D4—24no—
355C3×D4—22no—
356C3×D4—22no—
357C3×D4—22no—
358C3×D4—22no—
359C3×D4—22no—
360C3×D4—21no—
361C3×D4—21no—
362C3×D4—22no—
363C3×D4—32no—
364C3×D4—62no—
365C3×D4—62no—
366C3×D4—61no—
367C3×D4C2×C4×D312yes—
368C3×D4C22×Dic312yes—
369C2×C3×C4—24no—
370C2×C3×C4—22no—
371C2×C3×C4—24no—
372C2×C3×C4—21no—
373C2×C3×C4—21no—
374C2×C3×C4—22no—
375C2×C3×C4—22no—
376C2×C3×C4—22no—
377C2×C3×C4—22no—
378C2×C3×C4—21no—
379C2×C3×C4—21no—
380C2×C3×C4—21no—
381C2×C3×C4—21no—
382C2×C3×C4—21no—
383C2×C3×C4—21no—
384C2×C3×C4—61no—
385C2×C3×C4—61no—
386C2×C3×C4—62no—
387C2×C3×C4—62no—
388C2×C3×C4—61no—
389C2×C3×C4—122no—
390C2×C3×C4C2×C4×D311yescharacteristic
391C2×C3×C4C2×C4×D311yescharacteristic
392C2×C3×C4D3×D411yescharacteristic
393C2×C3×C4D3×D411yescharacteristic
394C2×C3×C4D3×D411yescharacteristic
395C2×C3×C4D3×D411yescharacteristic
396C2×C3×C4#23711yescharacteristic
397C2×C3×C4#23711yescharacteristic
398C2×C3×C4C22×Dic311yescharacteristic
399C2×C3×C4C22×Dic311yescharacteristic
400C2×C3×C4C23×D311yescharacteristic
401C2×C3×C4C23×D311yescharacteristic
402#67—22no—
403#67—22no—
404C2×Dic3—21no—
405C2×Dic3—21no—
406C2×Dic3—21no—
407C2×Dic3—42no—
408D12—21no—
409D12C22×Dic312yes—
410C4×D3—22no—
411C4×D3—22no—
412Dic6—21no—
413Dic6C22×Dic312yes—
414C3×C8—34no—
415C3×C8—62no—
416C3⋊C8—22no—
417C3⋊C8—34no—
418C3⋊C8—34no—
419C3⋊C8—64no—
420C3⋊C8—64no—
421C3⋊C8—62no—
422C3⋊C8—62no—
423C3⋊C8C22×Dic314yes—
424C2×C32—21no—
425C2×C32—21no—
426C2×C32—21no—
427C2×C32—42no—
428C2×C32C2×C4×D411yescharacteristic
429C3×D3—42no—
430#41—21no—
431#41—21no—
432#41—32no—
433#41—32no—
434#41—61no—
435#41—61no—
436#41D3×Dic312yes—
437#41C2×D3212yes—
438C2×Q8—31no—
439C2×Q8D3×Dic311yescharacteristic
440C2×D4—21no—
441C2×D4—31no—
442C2×D4—61no—
443C2×D4D3×Dic311yescharacteristic
444C22×C4—21no—
445C22×C4—61no—
446C22×C4—61no—
447C22×C4C2×D3211yescharacteristic
448Q16—34no—
449SD16—34no—
450SD16—34no—
451D8—34no—
452M16—32no—
453M16—32no—
454M16—32no—
455M16—61no—
456M16—92no—
457M16—92no—
458M16—92no—
459M16—184no—
460M16—184no—
461M16—181no—
462C2×C8—32no—
463C2×C8—61no—
464C2×C8—92no—
465C2×C8—184no—
466C2×C8—184no—
467C2×C8—181no—
468C42—31no—
469C42—31no—
470C42—61no—
471C22×C3—24no—
472C22×C3—22no—
473C22×C3—22no—
474C22×C3—21no—
475C22×C3—21no—
476C22×C3—21no—
477C22×C3—41no—
478C22×C3—41no—
479C22×C3—62no—
480C22×C3—81no—
481C22×C3—81no—
482C22×C3—81no—
483C22×C3—82no—
484C22×C3—241no—
485C22×C3#67⋊C411yescharacteristic
486C22×C3#67⋊C411yescharacteristic
487C22×C3D4×Dic311yescharacteristic
488C22×C3D4×Dic311yescharacteristic
489C22×C3C2×#23711yescharacteristic
490C22×C3C2×#23711yescharacteristic
491C2×D3—22no—
492C2×D3—81no—
493C3×C4—24no—
494C3×C4—22no—
495C3×C4—22no—
496C3×C4—21no—
497C3×C4—21no—
498C3×C4—21no—
499C3×C4—21no—
500C3×C4—62no—
501C3×C4—62no—
502C3×C4—121no—
503C3×C4#67⋊C411yescharacteristic
504C3×C4#67⋊C411yescharacteristic
505C3×C4D4×Dic311yescharacteristic
506C3×C4D4×Dic311yescharacteristic
507C3×C4C22×C4×D311yescharacteristic
508C3×C4C2×D3×D411yescharacteristic
509C3×C4C2×D3×D411yescharacteristic
510C3×C4C23×Dic311yescharacteristic
511Dic3—22no—
512Dic3—22no—
513Dic3—41no—
514C32#295611yescharacteristic, complemented, Sylow
515C23—21no—
516C23—61no—
517C23#380511yescharacteristic
518Q8—21no—
519Q8—32no—
520Q8—61no—
521Q8C2×D3×Dic312yes—
522D4—22no—
523D4—22no—
524D4—21no—
525D4—32no—
526D4—62no—
527D4—62no—
528D4—61no—
529D4C2×D3×Dic312yes—
530C2×C4—21no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—61no—
534C2×C4—61no—
535C2×C4—62no—
536C2×C4—62no—
537C2×C4—61no—
538C2×C4—122no—
539C2×C4C2×D3×Dic311yescharacteristic
540C2×C4C2×D3×Dic311yescharacteristic
541C2×C4#380511yescharacteristic
542C2×C4#381111yescharacteristic
543C2×C4#381111yescharacteristic
544C2×C4C22×D3211yescharacteristic
545C8—34no—
546C8—62no—
547C8—94no—
548C8—182no—
549C2×C3—21no—
550C2×C3—21no—
551C2×C3—21no—
552C2×C3—21no—
553C2×C3—21no—
554C2×C3—21no—
555C2×C3—21no—
556C2×C3—41no—
557C2×C3—41no—
558C2×C3—41no—
559C2×C3—44no—
560C2×C3—42no—
561C2×C3—42no—
562C2×C3—122no—
563C2×C3C2×#67⋊C411yescharacteristic
564C2×C3C2×D4×Dic311yescharacteristic
565D3—42no—
566C22—22no—
567C22—41no—
568C22—62no—
569C22—81no—
570C22—241no—
571C22#67⋊Dic311yescharacteristic
572C22#67⋊Dic311yescharacteristic
573C22C2×#380511yescharacteristic
574C4—22no—
575C4—62no—
576C4—62no—
577C4—121no—
578C4#67⋊Dic311yescharacteristic
579C4#67⋊Dic311yescharacteristic
580C4C22×D3×Dic311yescharacteristic
581C4C2×#381111yescharacteristic
582C3—21no—
583C3#7898011yescharacteristic, complemented
584C3#8400011yescharacteristic, complemented
585C2—21no—
586C2—21no—
587C2—21no—
588C2—42no—
589C2—122no—
590C2C2×#67⋊Dic311yescharacteristic
subgroupG/H
centerC4C2×#3811
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC2×C32C2×C4×D4
prime radicalC3×#5822C2
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
1. #10596290C2semidirect
3. #10594776C2semidirect
4. C2×C3×#837C2semidirect
5. #10591676C2semidirect
6. #10591675C2semidirect
7. #10591141C2semidirect
8. C2×#63569C2semidirect
9. Dic3×#208C2semidirect
15. #64157C22semidirect
19. C3×#951C4semidirect
21. C3×#949C4semidirect
22. C3×#942C4semidirect
23. C3×#932C4semidirect
27. #63815C22semidirect
30. C3×#837C22semidirect
31. C3×#837C22semidirect
32. #63577C22semidirect
33. #63569C22semidirect
34. #63569C22semidirect
35. #63554C22semidirect
36. Dic3×C3⋊C8C22semidirect
46. C2×#837D3semidirect
82. C3×#216C2×C4semidirect
83. C3×#215C2×C4semidirect
84. C3×#214C2×C4semidirect
85. C3×#213C2×C4semidirect
111. #951Dic3semidirect
113. #949Dic3semidirect
122. #942Dic3semidirect
123. #932Dic3semidirect
144. #837C2×D3semidirect
145. #837C2×D3semidirect
255. #216C2×Dic3semidirect
256. #215C2×Dic3semidirect
257. #214C2×Dic3semidirect
258. #213C2×Dic3semidirect
514. C32#2956semidirect
583. C3#78980semidirect
584. C3#84000semidirect

Maximal subgroups

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

subgroupindex
#105962902
C3×#58222
#105947762
C2×C3×#8372
#105916762
#105916752
#105911412
C2×#635692
Dic3×#2082
#840003
#789803