Finite Group Databasebeta

← #11886869

Subgroups — #11886869

Order 1152.

973 conjugacy classes of subgroups.

The subgroup lattice has 527 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5770C212yesmaximal, complemented
2#10595446C212yesmaximal, complemented
3#10592895C211yesmaximal, characteristic, complemented
4#10591687C212yesmaximal, complemented
5#10591681C212yesmaximal, complemented
6#10591665C212yesmaximal, complemented
7#10590925C212yesmaximal, complemented
8#10590921C211yesmaximal, characteristic, complemented
9#10590884C211yesmaximal, characteristic, complemented
10#84014—32nomaximal
11C3×#1010C2212yes—
12C3×#1009C2212yescomplemented
13C32×#135C2211yescharacteristic
14#64157C2212yescomplemented
15C3×#951C2212yescomplemented
16C3×#949C2212yes—
17C3×#918—22no—
18C3×#916—22no—
19C3×D3×SD16—22no—
20C3×#911—22no—
21C2×C3×#204C2212yescomplemented
22C3×#901C2212yescomplemented
23#63914C2211yescharacteristic
24#63873C2211yescharacteristic, complemented
25#63827—22no—
26#63827C2212yescomplemented
27C2×#3715—22no—
28C2×#3715C2212yescomplemented
29#63823—22no—
30#63823C2212yes—
31#63822—22no—
32#63822C2211yescharacteristic
33#63664C2212yescomplemented
34#63646C2211yescharacteristic, complemented
35C8×C3⋊Dic3C2211yescharacteristic, complemented
36#63578C2211yescharacteristic, complemented
37#63568C2212yescomplemented
38#63560C2212yescomplemented
39#63558C2212yescomplemented
40C3×#577—32no—
41#5837—32no—
42#5836—32no—
43#5770D312yescomplemented
44#5246—32no—
45#5241—32no—
46#5205—32no—
47#5203—32no—
48#5200—32no—
49#5198—32no—
50#5196—32no—
51#5196—61no—
52#5177—32no—
53#5175—32no—
54#5144—32no—
55#5141—32no—
56C32×#41C2312yes—
57C3×#239—22no—
58C3×D3×Q8—22no—
59C3×#237—22no—
60C3×#237—42no—
61C3×D3×D4—22no—
62C3×D3×D4—42no—
63C3×#235—22no—
64C3×#235—22no—
65C3×#235C2312yes—
66C2×C3×D12—22no—
67C2×C3×D12C2312yes—
68C2×C3×Dic6—22no—
69C2×C3×Dic6C2312yes—
70C2×#625—41no—
71C32×Q16D411yescharacteristic, complemented
72C32×SD16D412yescomplemented
73C32×D8D411yescharacteristic, complemented
74C2×C32×C8C2311yescharacteristic
75C4×C3⋊Dic3C2311yescharacteristic
76#3748—22no—
77#3748C2312yes—
78C2×C3⋊(C3⋊C8)—22no—
79C2×C3⋊(C3⋊C8)C2311yescharacteristic
80C3×#216—22no—
81C3×#215—22no—
82C3×#214—22no—
83C3×#213—22no—
84C3×#208C2312yes—
85C3×#204—22no—
86C3×#204—22no—
87C3×ΓL(1,𝔽25)—22no—
88C3×D3×C8—22no—
89#3724—41no—
90#3718—22no—
91#3718D411yescharacteristic, complemented
92#3715—22no—
93#3715—22no—
94#3715—22no—
95#3715—22no—
96#3715D412yescomplemented
97#3713—22no—
98#3713D411yescharacteristic, complemented
99#3291—91noSylow
100C3×2−1+4—32no—
101C3×H(5,𝔽2)—32no—
102#1010C2×D312yes—
103#1009C2×D312yescomplemented
104C3×#137—32no—
105C3×#137—62no—
106C3×AGL(1,ℤ/8)—32no—
107C3×AGL(1,ℤ/8)—62no—
108C3×#135—21no—
109C3×#135—62no—
110C3×#135C2×D312yes—
111C2×C3×SD16—32no—
112C2×C3×SD16—62no—
113C3×#131—32no—
114#951—32no—
115#951—62no—
116#951C2×D312yescomplemented
117#950—32no—
118#950—62no—
119#950—62no—
120#949—32no—
121#949—62no—
122#949C2×D312yes—
123#948—32no—
124#948—32no—
125#948—62no—
126#944—32no—
127#942—32no—
128#942—62no—
129C2×#215—32no—
130C2×#215—62no—
131#940—32no—
132C2×#214—32no—
133C2×#214—62no—
134#932—32no—
135#932—62no—
136#918—22no—
137#916—22no—
138D3×SD16—22no—
139#911—22no—
140C2×#204C2×D312yescomplemented
141#901C2×D312yescomplemented
142#837—32no—
143#837—32no—
144#837—32no—
145#837—62no—
146#836—32no—
147#833—32no—
148#825—32no—
149#824—32no—
150#823—32no—
151#822—32no—
152#819—32no—
153#819—61no—
154C8×Dic3—32no—
155C8×Dic3—61no—
156C22×C3×D3—22no—
157C22×C3×D3—42no—
158C32×Q8C2×D412yes—
159C32×D4—22no—
160C32×D4C2×D412yes—
161C2×C32×C4—22no—
162C2×C32×C4C2411yescharacteristic
163C2×C3⋊Dic3—21no—
164C3×#67—22no—
165C3×#67—42no—
166C3×#67—42no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3—42no—
169C3×D12—22no—
170C3×D12—22no—
171C3×D12—42no—
172C3×D12C2×D412yes—
173C3×C4×D3—22no—
174C3×C4×D3—42no—
175C3×C4×D3—42no—
176C3×Dic6—22no—
177C3×Dic6—22no—
178C3×Dic6—42no—
179C3×Dic6C2×D412yes—
180#625—82no—
181C32×C8C2×D411yescharacteristic
182C32×C8C2×D411yescharacteristic
183C3⋊(C3⋊C8)—22no—
184C3⋊(C3⋊C8)C2×D411yescharacteristic
185C3⋊(C3⋊C8)C2×D411yescharacteristic
186C3×C3⋊C8—22no—
187#577—32no—
188#577—92no—
189#492—91no—
190#471—92no—
191#471—92no—
192#456—92no—
193#453—92no—
194#443—91no—
195#443—91no—
196C3×#41—22no—
197C3×#41—32no—
198C3×#41—62no—
199C3×#41—62no—
200C3×#41—62no—
201C3×#41—62no—
202C3×#41—122no—
203C3×#41C22×D312yes—
204C3×#41C22×D312yes—
205C2×C3×Q8—32no—
206C2×C3×Q8—62no—
207C2×C3×Q8—62no—
208C2×C3×D4—32no—
209C2×C3×D4—62no—
210C2×C3×D4—62no—
211C2×C3×D4—122no—
212C2×#67—122no—
213#239—22no—
214D3×Q8—22no—
215#237—22no—
216#237—42no—
217D3×D4—22no—
218D3×D4—42no—
219#235—22no—
220#235—22no—
221#235C22×D312yes—
222C2×D12—22no—
223C2×D12C22×D312yes—
224C2×Dic6—22no—
225C2×Dic6C22×D312yes—
226C3×Q16—21no—
227C3×Q16—62no—
228C3×Q16#6712yescomplemented
229C3×SD16—22no—
230C3×SD16—62no—
231C3×SD16—62no—
232C3×SD16—62no—
233C3×SD16—62no—
234C3×SD16#6712yescomplemented
235C3×SD16#6712yescomplemented
236C3×D8—21no—
237C3×D8—62no—
238C3×D8#6712yescomplemented
239C3×M16—32no—
240C3×M16—62no—
241C2×C3×C8—21no—
242C2×C3×C8—62no—
243C2×C3×C8C22×D312yes—
244#216—22no—
245#216—32no—
246#216—62no—
247#216—62no—
248#215—22no—
249#215—32no—
250#215—62no—
251#215—62no—
252#215—62no—
253#215—62no—
254#214—22no—
255#214—32no—
256#214—62no—
257#214—62no—
258#214—62no—
259#214—62no—
260#213—22no—
261#213—32no—
262#213—62no—
263#213—62no—
264Dic3⋊C4—122no—
265C4×Dic3—32no—
266C4×Dic3—61no—
267#208—32no—
268#208—32no—
269#208—62no—
270#208—62no—
271#208—62no—
272#208—122no—
273#208C22×D312yes—
274C2×C3⋊C8—32no—
275C2×C3⋊C8—61no—
276C2×C3⋊C8—62no—
277C2×C3⋊C8—62no—
278C2×C3⋊C8—122no—
279#204—22no—
280#204—22no—
281ΓL(1,𝔽25)—22no—
282D3×C8—22no—
283C22×C32—22no—
284C22×C32H(5,𝔽2)11yescharacteristic
285C2×C3×D3—22no—
286C2×C3×D3—42no—
287C2×C3×D3—82no—
288C2×C3×D3—162no—
289C32×C4—22no—
290C32×C4C22×D411yescharacteristic
291C32×C4C22×D411yescharacteristic
292C3⋊Dic3—22no—
293C3×Dic3—22no—
294C3×Dic3—42no—
2952−1+4—32no—
296H(5,𝔽2)—32no—
297#137—32no—
298#137—62no—
299#137—92no—
300#137—182no—
301AGL(1,ℤ/8)—32no—
302AGL(1,ℤ/8)—62no—
303AGL(1,ℤ/8)—92no—
304AGL(1,ℤ/8)—182no—
305#135—62no—
306#135—91no—
307#135—182no—
308#135D3211yescharacteristic
309C2×SD16—32no—
310C2×SD16—62no—
311C2×SD16—92no—
312C2×SD16—182no—
313#131—32no—
314#131—92no—
315C4⋊Q8—91no—
316#127—91no—
317#108—91no—
318#108—91no—
319#104—92no—
320#104—92no—
321#101—92no—
322#100—92no—
323C4×C8—91no—
324C23×C3—62no—
325C23×C3—122no—
326C22×D3—22no—
327C22×D3—42no—
328C3×Q8—22no—
329C3×Q8—32no—
330C3×Q8—62no—
331C3×Q8—62no—
332C3×Q8—122no—
333C3×Q8C2×#6712yes—
334C3×Q8C2×#6712yes—
335C3×D4—22no—
336C3×D4—22no—
337C3×D4—22no—
338C3×D4—32no—
339C3×D4—42no—
340C3×D4—62no—
341C3×D4—62no—
342C3×D4—62no—
343C3×D4—122no—
344C3×D4—122no—
345C3×D4—122no—
346C3×D4C2×#6712yes—
347C3×D4C2×#6712yes—
348C2×C3×C4—22no—
349C2×C3×C4—22no—
350C2×C3×C4—21no—
351C2×C3×C4—42no—
352C2×C3×C4—62no—
353C2×C3×C4—62no—
354C2×C3×C4—122no—
355C2×C3×C4—122no—
356C2×C3×C4—122no—
357C2×C3×C4C23×D312yes—
358#67—22no—
359#67—42no—
360#67—42no—
361#67—244no—
362C2×Dic3—22no—
363C2×Dic3—42no—
364C2×Dic3—62no—
365C2×Dic3—121no—
366D12—22no—
367D12—22no—
368D12—42no—
369D12D3×D412yes—
370C4×D3—22no—
371C4×D3—42no—
372C4×D3—42no—
373Dic6—22no—
374Dic6—22no—
375Dic6—42no—
376Dic6D3×D412yes—
377C3×C8—21no—
378C3×C8—21no—
379C3×C8—62no—
380C3×C8C2×#6712yes—
381C3×C8C2×#6712yes—
382C3⋊C8—22no—
383C3⋊C8—32no—
384C3⋊C8—32no—
385C3⋊C8—61no—
386C3⋊C8—61no—
387C3⋊C8—62no—
388C3⋊C8—62no—
389C3⋊C8—122no—
390C2×C32—21no—
391C2×C32—42no—
392C2×C32D4211yescharacteristic
393C3×D3—42no—
394C3×D3—82no—
395#41—32no—
396#41—62no—
397#41—62no—
398#41—62no—
399#41—62no—
400#41—122no—
401#41C2×D3212yes—
402C2×Q8—32no—
403C2×Q8—62no—
404C2×Q8—62no—
405C2×D4—32no—
406C2×D4—62no—
407C2×D4—62no—
408C2×D4—122no—
409C2×D4—361no—
410Q16—62no—
411Q16—91no—
412Q16—182no—
413Q16#62511yescharacteristic, complemented
414SD16—62no—
415SD16—62no—
416SD16—62no—
417SD16—62no—
418SD16—92no—
419SD16—182no—
420SD16—182no—
421SD16—182no—
422SD16—182no—
423SD16#62512yescomplemented
424D8—62no—
425D8—91no—
426D8—182no—
427D8#62511yescharacteristic, complemented
428M16—32no—
429M16—62no—
430M16—92no—
431M16—182no—
432C2×C8—62no—
433C2×C8—91no—
434C2×C8—182no—
435C2×C8C2×D3211yescharacteristic
436C4⋊C4—361no—
437C42—91no—
438C22×C3—22no—
439C22×C3—22no—
440C22×C3—21no—
441C22×C3—42no—
442C22×C3—62no—
443C22×C3—122no—
444C22×C3—242no—
445C22×C3—482no—
446C22×C3#100412yes—
447C2×D3—22no—
448C2×D3—42no—
449C2×D3—82no—
450C2×D3—162no—
451C3×C4—22no—
452C3×C4—22no—
453C3×C4—21no—
454C3×C4—21no—
455C3×C4—42no—
456C3×C4—62no—
457C3×C4—122no—
458C3×C4C2×D3×D412yes—
459C3×C4C22×#6712yes—
460Dic3—22no—
461Dic3—42no—
462Dic3—64no—
463Dic3—122no—
464C32#329111yescharacteristic, complemented, Sylow
465C23—62no—
466C23—122no—
467Q8—32no—
468Q8—62no—
469Q8—62no—
470Q8—122no—
471Q8C2×#62512yes—
472D4—22no—
473D4—32no—
474D4—62no—
475D4—62no—
476D4—62no—
477D4—122no—
478D4—122no—
479D4—122no—
480D4—722no—
481D4C2×#62512yes—
482C2×C4—22no—
483C2×C4—62no—
484C2×C4—62no—
485C2×C4—122no—
486C2×C4—122no—
487C2×C4—122no—
488C2×C4—181no—
489C2×C4C22×D3211yescharacteristic
490C8—62no—
491C8—91no—
492C8—91no—
493C8—182no—
494C8C2×#62511yescharacteristic
495C8C2×#62511yescharacteristic
496C2×C3—22no—
497C2×C3—21no—
498C2×C3—41no—
499C2×C3—42no—
500C2×C3—42no—
501C2×C3—82no—
502C2×C3—122no—
503C2×C3—242no—
504C2×C3D4×#6712yes—
505D3—42no—
506D3—82no—
507C22—22no—
508C22—62no—
509C22—122no—
510C22—242no—
511C22—482no—
512C22#6431311yescharacteristic
513C4—22no—
514C4—62no—
515C4—122no—
516C4—182no—
517C4D32×D411yescharacteristic
518C4C22×#62511yescharacteristic
519C3—21no—
520C3#8401412yescomplemented
521C2—21no—
522C2—42no—
523C2—122no—
524C2—242no—
525C2D4×#62511yescharacteristic
subgroupG/H
centerC2D4×#625
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#135C22
socleC2×C32D42
hypercenter#135D32
hypocenterC32#3291
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ #135

Complements

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

NH ≅ G/Ntype
1. C3×#5770C2semidirect
2. #10595446C2semidirect
3. #10592895C2semidirect
4. #10591687C2semidirect
5. #10591681C2semidirect
6. #10591665C2semidirect
7. #10590925C2semidirect
8. #10590921C2semidirect
9. #10590884C2semidirect
12. C3×#1009C22semidirect
14. #64157C22semidirect
15. C3×#951C22semidirect
21. C2×C3×#204C22semidirect
22. C3×#901C22semidirect
24. #63873C22semidirect
26. #63827C22semidirect
28. C2×#3715C22semidirect
33. #63664C22semidirect
34. #63646C22semidirect
35. C8×C3⋊Dic3C22semidirect
36. #63578C22semidirect
37. #63568C22semidirect
38. #63560C22semidirect
39. #63558C22semidirect
43. #5770D3semidirect
71. C32×Q16D4semidirect
72. C32×SD16D4semidirect
73. C32×D8D4semidirect
91. #3718D4semidirect
96. #3715D4semidirect
98. #3713D4semidirect
103. #1009C2×D3semidirect
116. #951C2×D3semidirect
140. C2×#204C2×D3semidirect
141. #901C2×D3semidirect
228. C3×Q16#67semidirect
234. C3×SD16#67semidirect
235. C3×SD16#67semidirect
238. C3×D8#67semidirect
413. Q16#625semidirect
423. SD16#625semidirect
427. D8#625semidirect
464. C32#3291semidirect
520. C3#84014semidirect

Maximal subgroups

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

subgroupindex
C3×#57702
#105954462
#105928952
#105916872
#105916812
#105916652
#105909252
#105909212
#105908842
#840143