Finite Group Databasebeta

← #11858594

Subgroups — #11858594

Order 1152.

1011 conjugacy classes of subgroups.

The subgroup lattice has 545 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#907C211yesmaximal, characteristic
2#10594992C211yesmaximal, characteristic
3#10594986C211yesmaximal, characteristic
4#10592820C211yesmaximal, characteristic, complemented
5C3×#5121C211yesmaximal, characteristic, complemented
6C2×#63575C211yesmaximal, characteristic, complemented
7#10591122C211yesmaximal, characteristic, complemented
8#10590706C212yesmaximal, complemented
9#10590683C212yesmaximal, complemented
10#10590681C212yesmaximal, complemented
11D3×#818C212yesmaximal, complemented
12#83785—31nomaximal
13#79210—31nomaximal
14C2×C3×#235C2211yescharacteristic
15C2×C32×M16C2211yescharacteristic
16#64135C2211yescharacteristic
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C3×#926C2211yescharacteristic
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C3×#907C418yescomplemented
22C2×C3×ΓL(1,𝔽25)C2212yes—
23C2×C3×D3×C8C2212yes—
24#67⋊Dic3—22no—
25Dic3×#67—22no—
26#63898—21no—
27Dic3×D12—21no—
28D3×C4⋊Dic3C2212yes—
29D3×C4⋊Dic3C2212yes—
30#63843—21no—
31Dic3×Dic6—21no—
32#63841C2212yes—
33#63841C2212yes—
34#63645C2212yes—
35#63644C2212yes—
36C3×#818C2212yes—
37C3×#817C2212yes—
38#63575C2211yescharacteristic
39#63575C2211yescharacteristic
40#63575C2212yes—
41#63575C2212yes—
42#63573C2211yescharacteristic
43#63573C2211yescharacteristic
44C2×C3×#131—31no—
45#5827—31no—
46#5827—31no—
47C2×#907D311yescharacteristic
48#5523—31no—
49#5504—31no—
50C3×#428—31no—
51#5121—31no—
52#5121—31no—
53#5121—32no—
54#5121—32no—
55#5121—61no—
56#5121D311yescharacteristic, complemented
57#5106—31no—
58#5106—32no—
59C2×#818—31no—
60C2×#818—32no—
61#4998—31no—
62C2×#807—31no—
63#4881—32no—
64D3×#107—32no—
65#4861—32no—
66#4860—32no—
67C22×C32×C4C2311yescharacteristic
68C22×C3⋊Dic3—21no—
69C2×C3×#67D412yes—
70C22×C3×Dic3—21no—
71C3×#235C2×C414yes—
72C3×#235Q814yes—
73C2×C3×D12D411yescharacteristic
74C2×C3×C4×D3C2312yes—
75C2×C3×Dic6D411yescharacteristic
76C2×D3×Dic3—22no—
77C2×D3×Dic3—22no—
78C32×M16C2×C414yescomplemented
79C2×C32×C8C2312yes—
80#3757—21no—
81C4⋊(C3⋊Dic3)—21no—
82C4⋊(C3⋊Dic3)C2311yescharacteristic
83C4⋊(C3⋊Dic3)C2311yescharacteristic
84C4⋊(C3⋊Dic3)C2312yes—
85C4×C3⋊Dic3—21no—
86C3×#217—21no—
87C3×C4⋊Dic3—21no—
88C3×C4⋊Dic3C2312yes—
89C3×C4⋊Dic3C2311yescharacteristic
90C3×C4⋊Dic3C2311yescharacteristic
91C3×C4×Dic3—21no—
92C2×C3×C3⋊C8C2×C414yescomplemented
93C2×C3×C3⋊C8C2311yescharacteristic
94C2×C3×C3⋊C8C2311yescharacteristic
95C3×ΓL(1,𝔽25)C2×C418yescomplemented
96C3×D3×C8C2×C418yescomplemented
97Dic3⋊Dic3—22no—
98Dic3⋊Dic3—22no—
99(C2×D3)⋊Dic3—22no—
100(C2×D3)⋊Dic3—22no—
101Dic32—22no—
102Dic32—22no—
103#2913—91noSylow
104C2×C3×#41—31no—
105C2×#235C2×D311yescharacteristic
106C3×#131—38no—
107C2×C3×M16—21no—
108C2×C3×M16—32no—
109C2×C3×M16C2×D311yescharacteristic
110C2×C3×M16C2×D311yescharacteristic
111C22×C3×C8—31no—
112C22×C3×C8—32no—
113C3×#117—31no—
114C2×C3×C4⋊C4—31no—
115Q8×Dic3—61no—
116Q8×Dic3—61no—
117D4×Dic3—61no—
118D4×Dic3—61no—
119D4×Dic3—62no—
120D4×Dic3—62no—
121C4×#67—62no—
122#926—31no—
123#926—31no—
124#926—32no—
125#926—32no—
126#926—61no—
127#926C2×D311yescharacteristic
128C2×C4⋊Dic3—31no—
129C2×C4⋊Dic3—31no—
130C2×C4⋊Dic3—32no—
131C2×C4⋊Dic3—32no—
132C2×C4⋊Dic3—61no—
133C2×C4⋊Dic3C2×D311yescharacteristic
134C22×C3⋊C8C2×D311yescharacteristic
135#907Dic318yescomplemented
136C2×ΓL(1,𝔽25)C2×D312yes—
137C2×D3×C8C2×D312yes—
138#893—61no—
139#892—32no—
140#892—32no—
141D3×C4⋊C4—32no—
142D3×C4⋊C4—32no—
143#887—61no—
144#67⋊C4—62no—
145C4×D12—61no—
146C4×Dic6—61no—
147C3×#107—32no—
148C3×#106—32no—
149#818—32no—
150#818—32no—
151#818—32no—
152#818—31no—
153#818—32no—
154#818—31no—
155#818—62no—
156#818C2×D312yes—
157#817—32no—
158#817—32no—
159#817—31no—
160#817—31no—
161#817—62no—
162#817C2×D312yes—
163#808—31no—
164#808—31no—
165#807—31no—
166#807—32no—
167#807—32no—
168#807—31no—
169C23×C32C2×D411yescharacteristic
170C22×C3×D3C2×D412yes—
171C2×C32×C4C22×C412yes—
172C2×C32×C4C2×D411yescharacteristic
173C2×C32×C4C2×Q812yes—
174C2×C32×C4C2411yescharacteristic
175C2×C3⋊Dic3—21no—
176C2×C3⋊Dic3—22no—
177C2×C3⋊Dic3—21no—
178C2×C3⋊Dic3—81no—
179C3×#67C4⋊C418yes—
180C2×C3×Dic3—21no—
181C2×C3×Dic3—22no—
182C2×C3×Dic3—21no—
183C2×C3×Dic3—81no—
184C2×C3×Dic3C2×D412yes—
185C3×D12C4⋊C414yes—
186C3×C4×D3C22×C414yes—
187C3×C4×D3C2×Q814yes—
188C3×Dic6C4⋊C414yes—
189D3×Dic3—82no—
190D3×Dic3—82no—
191C32×C8C22×C414yes—
192C3×C3⋊C8C22×C412yes—
193C3×C3⋊C8C22×C412yes—
194C2×#131—31no—
195#520—91no—
196#520—91no—
197#428—31no—
198#428—92no—
199#428—92no—
200#428—91no—
201#427—92no—
202#427—91no—
203C2×#107—92no—
204C2×#107—91no—
205C3×#41—34no—
206C3×#41—34no—
207C2×C3×Q8—31no—
208C2×C3×D4—32no—
209C2×C3×D4—31no—
210C22×C3×C4—21no—
211C22×C3×C4—32no—
212C22×C3×C4—61no—
213C22×C3×C4C22×D311yescharacteristic
214C22×C3×C4C22×D311yescharacteristic
215C2×#67D1212yes—
216C22×Dic3—21no—
217C22×Dic3—62no—
218C22×Dic3—62no—
219C22×Dic3—61no—
220C22×Dic3—61no—
221C22×Dic3—121no—
222#235Dic614yes—
223#235C2×Dic314yes—
224C2×D12D1211yescharacteristic
225C2×C4×D3—62no—
226C2×C4×D3—62no—
227C2×C4×D3C22×D312yes—
228C2×Dic6D1211yescharacteristic
229C3×M16—24no—
230C3×M16—38no—
231C3×M16C4×D314yescomplemented
232C3×M16C2×Dic314yescomplemented
233C2×C3×C8—22no—
234C2×C3×C8—34no—
235C2×C3×C8—31no—
236C2×C3×C8—31no—
237C2×C3×C8—38no—
238C2×C3×C8C22×D312yes—
239C2×C3×C8C22×D312yes—
240C3×C4⋊C4—32no—
241C3×C4⋊C4—31no—
242C3×C4⋊C4—31no—
243C3×C4⋊C4—61no—
244C3×C22⋊C4—61no—
245C3×C42—61no—
246#217—21no—
247#217—62no—
248#217—62no—
249#217—61no—
250#217—61no—
251#217—121no—
252(C2×D3)⋊C4—62no—
253(C2×D3)⋊C4—62no—
254C4⋊Dic3—21no—
255C4⋊Dic3—32no—
256C4⋊Dic3—31no—
257C4⋊Dic3—31no—
258C4⋊Dic3—31no—
259C4⋊Dic3—32no—
260C4⋊Dic3—31no—
261C4⋊Dic3—61no—
262C4⋊Dic3—62no—
263C4⋊Dic3—61no—
264C4⋊Dic3—62no—
265C4⋊Dic3—62no—
266C4⋊Dic3—61no—
267C4⋊Dic3—61no—
268C4⋊Dic3—121no—
269C4⋊Dic3C22×D311yescharacteristic
270C4⋊Dic3C22×D311yescharacteristic
271C4⋊Dic3C22×D312yes—
272Dic3⋊C4—62no—
273Dic3⋊C4—62no—
274C4×Dic3—21no—
275C4×Dic3—62no—
276C4×Dic3—62no—
277C4×Dic3—61no—
278C4×Dic3—61no—
279C4×Dic3—62no—
280C4×Dic3—62no—
281C4×Dic3—121no—
282C2×C3⋊C8C2×Dic314yescomplemented
283C2×C3⋊C8C22×D311yescharacteristic
284C2×C3⋊C8C22×D311yescharacteristic
285ΓL(1,𝔽25)C2×Dic318yescomplemented
286D3×C8C2×Dic318yescomplemented
287C22×C32—21no—
288C22×C32—21no—
289C22×C32C2×C4⋊C412yes—
290C22×C32C22×D411yescharacteristic
291C2×C3×D3—22no—
292C2×C3×D3—22no—
293C2×C3×D3C2×C4⋊C414yes—
294C32×C4C2×C4⋊C412yes—
295C32×C4C23×C411yescharacteristic
296C32×C4C22×Q811yescharacteristic
297C3⋊Dic3—41no—
298C3⋊Dic3—42no—
299C3⋊Dic3—41no—
300C3×Dic3—41no—
301C3×Dic3—42no—
302C3×Dic3—41no—
303C3×Dic3C2×C4⋊C414yes—
304C2×#41—31no—
305#131—38no—
306C2×M16—32no—
307C2×M16D3211yescharacteristic
308C22×C8—31no—
309C22×C8—32no—
310C4×Q8—181no—
311C4×Q8—181no—
312C4×D4—181no—
313C4×D4—182no—
314C4×D4—181no—
315C4×D4—182no—
316#117—31no—
317#117—92no—
318#117—92no—
319#117—91no—
320C2×C4⋊C4—31no—
321C2×C4⋊C4—92no—
322C2×C4⋊C4—92no—
323C2×C4⋊C4—91no—
324#107—32no—
325#107—92no—
326#107—91no—
327#107—92no—
328#107—91no—
329#107—92no—
330#106—32no—
331#106—91no—
332#106—91no—
333#106—92no—
334C23×C3—21no—
335C23×C3—32no—
336C23×C3C2×D1211yescharacteristic
337C23×C3D3×D411yescharacteristic
338C22×D3C2×D1212yes—
339C3×Q8—34no—
340C3×D4—38no—
341C3×D4—34no—
342C2×C3×C4—21no—
343C2×C3×C4—22no—
344C2×C3×C4—21no—
345C2×C3×C4—22no—
346C2×C3×C4—32no—
347C2×C3×C4—34no—
348C2×C3×C4—34no—
349C2×C3×C4—61no—
350C2×C3×C4—62no—
351C2×C3×C4—61no—
352C2×C3×C4—241no—
353C2×C3×C4C2×Dic612yes—
354C2×C3×C4C2×C4×D312yes—
355C2×C3×C4C2×D1211yescharacteristic
356C2×C3×C4D3×D411yescharacteristic
357C2×C3×C4D3×Q812yes—
358C2×C3×C4C22×Dic312yes—
359C2×C3×C4C23×D311yescharacteristic
360C2×C3×C4C23×D311yescharacteristic
361#67C4⋊Dic318yes—
362C2×Dic3—21no—
363C2×Dic3—21no—
364C2×Dic3—22no—
365C2×Dic3—61no—
366C2×Dic3—61no—
367C2×Dic3—62no—
368C2×Dic3—61no—
369C2×Dic3—62no—
370C2×Dic3—61no—
371C2×Dic3—81no—
372C2×Dic3—121no—
373C2×Dic3—121no—
374C2×Dic3—122no—
375C2×Dic3—242no—
376C2×Dic3—242no—
377C2×Dic3—241no—
378C2×Dic3—241no—
379C2×Dic3—242no—
380C2×Dic3C2×D1212yes—
381D12C4⋊Dic314yes—
382C4×D3—242no—
383C4×D3—242no—
384C4×D3C2×Dic614yes—
385C4×D3C22×Dic314yes—
386Dic6C4⋊Dic314yes—
387C3×C8—24no—
388C3×C8—32no—
389C3×C8—32no—
390C3×C8C2×C4×D314yes—
391C3×C8C22×Dic314yes—
392C3⋊C8C22×Dic312yes—
393C3⋊C8C22×Dic312yes—
394C2×C32—22no—
395C2×C32C22×C4⋊C411yescharacteristic
396C2×C32#57611yescharacteristic
397C2×C32#57811yescharacteristic
398C3×D3—24no—
399#41—34no—
400#41—34no—
401C2×Q8—31no—
402C2×D4—32no—
403C2×D4—31no—
404C22×C4—32no—
405C22×C4—61no—
406C22×C4—182no—
407C22×C4—182no—
408C22×C4—181no—
409C22×C4C2×D3211yescharacteristic
410M16—38no—
411M16D3×Dic314yescomplemented
412C2×C8—31no—
413C2×C8—31no—
414C2×C8—34no—
415C2×C8—38no—
416C2×C8C2×D3212yes—
417C4⋊C4—31no—
418C4⋊C4—32no—
419C4⋊C4—31no—
420C4⋊C4—61no—
421C4⋊C4—91no—
422C4⋊C4—91no—
423C4⋊C4—92no—
424C4⋊C4—182no—
425C4⋊C4—182no—
426C4⋊C4—181no—
427C22⋊C4—61no—
428C22⋊C4—182no—
429C22⋊C4—182no—
430C22⋊C4—181no—
431C42—61no—
432C42—182no—
433C42—182no—
434C42—181no—
435C22×C3—21no—
436C22×C3—21no—
437C22×C3—21no—
438C22×C3—21no—
439C22×C3—21no—
440C22×C3—22no—
441C22×C3—34no—
442C22×C3—41no—
443C22×C3—41no—
444C22×C3—62no—
445C22×C3—62no—
446C22×C3D3×C4⋊C412yes—
447C22×C3C2×C4⋊Dic312yes—
448C22×C3C22×D1211yescharacteristic
449C22×C3C2×D3×D411yescharacteristic
450C2×D3—22no—
451C2×D3—22no—
452C2×D3C2×C4⋊Dic314yes—
453C3×C4—21no—
454C3×C4—21no—
455C3×C4—22no—
456C3×C4—34no—
457C3×C4—121no—
458C3×C4—122no—
459C3×C4—121no—
460C3×C4D3×C4⋊C412yes—
461C3×C4C2×C4⋊Dic312yes—
462C3×C4C22×Dic611yescharacteristic
463C3×C4C22×C4×D311yescharacteristic
464C3×C4C2×D3×Q811yescharacteristic
465C3×C4C23×Dic311yescharacteristic
466Dic3—42no—
467Dic3—41no—
468Dic3—41no—
469Dic3—121no—
470Dic3—122no—
471Dic3—121no—
472Dic3—121no—
473Dic3—122no—
474Dic3—121no—
475Dic3—242no—
476Dic3—241no—
477Dic3—241no—
478Dic3C2×C4⋊Dic314yes—
479C32#291311yescharacteristic, complemented, Sylow
480C23—32no—
481C23D3×D1211yescharacteristic
482Q8—34no—
483D4—38no—
484D4—34no—
485C2×C4—32no—
486C2×C4—34no—
487C2×C4—34no—
488C2×C4—61no—
489C2×C4—61no—
490C2×C4—62no—
491C2×C4—181no—
492C2×C4—182no—
493C2×C4—181no—
494C2×C4—241no—
495C2×C4—722no—
496C2×C4—722no—
497C2×C4—721no—
498C2×C4D3×Dic612yes—
499C2×C4D3×D1211yescharacteristic
500C2×C4C2×D3×Dic312yes—
501C2×C4C22×D3211yescharacteristic
502C8—32no—
503C8—32no—
504C8C2×D3×Dic314yes—
505C2×C3—22no—
506C2×C3—22no—
507C2×C3—21no—
508C2×C3—21no—
509C2×C3—21no—
510C2×C3—42no—
511C2×C3—64no—
512C2×C3C2×D3×C4⋊C411yescharacteristic
513C2×C3#575211yescharacteristic
514C2×C3#575311yescharacteristic
515C2×C3#577411yescharacteristic
516C2×C3#577911yescharacteristic
517C2×C3C22×C4⋊Dic311yescharacteristic
518D3—24no—
519C22—21no—
520C22—21no—
521C22—34no—
522C22—62no—
523C22—62no—
524C22D3×C4⋊Dic312yes—
525C22C2×D3×D1211yescharacteristic
526C4—34no—
527C4—122no—
528C4—121no—
529C4—121no—
530C4—361no—
531C4—362no—
532C4—361no—
533C4D3×C4⋊Dic312yes—
534C4C2×D3×Dic611yescharacteristic
535C4C22×D3×Dic311yescharacteristic
536C3—21no—
537C3#7921011yescharacteristic, complemented
538C3#8378511yescharacteristic, complemented
539C2—22no—
540C2—64no—
541C2#1059471411yescharacteristic
542C2#1059472111yescharacteristic
543C2C2×D3×C4⋊Dic311yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
prime radicalC2×C3×#235C22
cosocleC2×C32×C4C24
hypercenterC2×M16D32
hypocenterC32#2913
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
4. #10592820C2semidirect
5. C3×#5121C2semidirect
6. C2×#63575C2semidirect
7. #10591122C2semidirect
8. #10590706C2semidirect
9. #10590683C2semidirect
10. #10590681C2semidirect
11. D3×#818C2semidirect
21. C3×#907C4semidirect
56. #5121D3semidirect
78. C32×M16C2×C4semidirect
92. C2×C3×C3⋊C8C2×C4semidirect
95. C3×ΓL(1,𝔽25)C2×C4semidirect
96. C3×D3×C8C2×C4semidirect
135. #907Dic3semidirect
231. C3×M16C4×D3semidirect
232. C3×M16C2×Dic3semidirect
282. C2×C3⋊C8C2×Dic3semidirect
285. ΓL(1,𝔽25)C2×Dic3semidirect
286. D3×C8C2×Dic3semidirect
411. M16D3×Dic3semidirect
479. C32#2913semidirect
537. C3#79210semidirect
538. C3#83785semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9072
#105949922
#105949862
#105928202
C3×#51212
C2×#635752
#105911222
#105907062
#105906832
#105906812
D3×#8182
#837853
#792103