Finite Group Databasebeta

← #11882218

Subgroups — #11882218

Order 1152.

1176 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596093C211yesmaximal, characteristic, complemented
2#10596067C211yesmaximal, characteristic
3C32×#465C211yesmaximal, characteristic, complemented
4#10592862C211yesmaximal, characteristic, complemented
5#10592861C211yesmaximal, characteristic, complemented
6#10592813C211yesmaximal, characteristic, complemented
7C2×#63641C211yesmaximal, characteristic, complemented
8#10592747C211yesmaximal, characteristic, complemented
9#10592740C211yesmaximal, characteristic, complemented
10#10592569C211yesmaximal, characteristic, complemented
11#10592553C211yesmaximal, characteristic, complemented
12#10592517C211yesmaximal, characteristic, complemented
13#10592490C211yesmaximal, characteristic, complemented
14#10592461C211yesmaximal, characteristic, complemented
15#10592460C211yesmaximal, characteristic, complemented
16#80640—34nomaximal
17C2×#3830—21no—
18C2×C32×SD16C2211yescharacteristic
19C22×C32×C8C2211yescharacteristic
20C32×C22⋊Q8C2211yescharacteristic
21C32×#121C2211yescharacteristic
22Q8×C3⋊Dic3C2211yescharacteristic
23#64153C2211yescharacteristic
24C2×#3755C2211yescharacteristic
25#64149C2211yescharacteristic
26#64148—21no—
27D4×C3⋊Dic3C2211yescharacteristic
28C2×#3754C2211yescharacteristic
29#64139C2211yescharacteristic
30#64133C2211yescharacteristic
31C2×C4×C3⋊Dic3C2211yescharacteristic
32C22×C3⋊(C3⋊C8)C2211yescharacteristic
33C2×#3744C2211yescharacteristic
34#64102C2211yescharacteristic
35#64098—21no—
36#64097C2211yescharacteristic
37#64097C2211yescharacteristic
38#64096—21no—
39#64096C2211yescharacteristic
40#64094—21no—
41#64090—21no—
42#64087—21no—
43#64086—21no—
44C32×#106C2211yescharacteristic
45C32×#103C2211yescharacteristic
46C32×#102C2211yescharacteristic
47#63662C2211yescharacteristic
48#63659C2211yescharacteristic
49#63648C2211yescharacteristic
50#63644C2211yescharacteristic
51#63643C2211yescharacteristic
52#63641C2211yescharacteristic
53#63641C2211yescharacteristic
54#63641C2211yescharacteristic
55#63641C2211yescharacteristic
56#63637C2211yescharacteristic
57#63636C2211yescharacteristic
58#63635C2211yescharacteristic
59#63635C2211yescharacteristic
60#5622—34no—
61#5596—34no—
62C3×#465D314yescomplemented
63#5163—34no—
64#5162—34no—
65#5114—34no—
66C2×Dic3⋊C8—34no—
67#5048—34no—
68#5041—34no—
69#4870—34no—
70#4854—34no—
71#4818—34no—
72#4791—34no—
73#4762—34no—
74#4761—34no—
75C2×C32×Q8C2311yescharacteristic
76C2×C32×D4—21no—
77C2×C32×D4C2311yescharacteristic
78C22×C32×C4C2311yescharacteristic
79C2×#638—21no—
80C2×#638—21no—
81C2×#638—21no—
82C22×C3⋊Dic3—21no—
83C22×C3⋊Dic3D411yescharacteristic
84C22×C3⋊Dic3D411yescharacteristic
85#3830—44no—
86C2×C4⋊(C3⋊D3)C2311yescharacteristic
87C2×C4×C3⋊D3—21no—
88C2×#634—21no—
89C2×#634—21no—
90C2×#634C2311yescharacteristic
91C32×SD16—41no—
92C2×C32×C8—41no—
93C2×C32×C8C2311yescharacteristic
94C2×C32×C8C2311yescharacteristic
95C32×C4⋊C4—21no—
96C32×C4⋊C4C2311yescharacteristic
97C32×C4⋊C4C2311yescharacteristic
98C32×C22⋊C4—21no—
99C32×C22⋊C4—21no—
100#3757—21no—
101#3757—21no—
102#3755—41no—
103#3754—41no—
104#3752—21no—
105#3752—21no—
106C4⋊(C3⋊Dic3)—21no—
107C4⋊(C3⋊Dic3)C2311yescharacteristic
108C4⋊(C3⋊Dic3)C2311yescharacteristic
109#3750—21no—
110#3750—21no—
111#3750—21no—
112#3750—21no—
113#3750—21no—
114#3750—21no—
115C4×C3⋊Dic3—21no—
116C4×C3⋊Dic3—21no—
117C4×C3⋊Dic3D411yescharacteristic
118C4×C3⋊Dic3D411yescharacteristic
119C4×C3⋊Dic3C2311yescharacteristic
120C4×C3⋊Dic3C2311yescharacteristic
121C2×C3⋊(C3⋊C8)—41no—
122C2×C3⋊(C3⋊C8)C2311yescharacteristic
123C2×C3⋊(C3⋊C8)C2311yescharacteristic
124#3744—41no—
125#3246—91noSylow
126C2×#237—64no—
127C2×C3×SD16C2×D314yes—
128C22×C3×C8C2×D314yes—
129C3×C22⋊Q8C2×D314yes—
130C3×#121C2×D314yes—
131Q8×Dic3—34no—
132#944—34no—
133C2×#215—34no—
134#940—34no—
135#939—64no—
136D4×Dic3—34no—
137C2×#214—34no—
138#930—34no—
139#924—34no—
140C2×C4×Dic3—34no—
141C22×C3⋊C8—34no—
142C2×#204—34no—
143#893—34no—
144#889—64no—
145#888—34no—
146#888—34no—
147#887—34no—
148#887—64no—
149#885—64no—
150#67⋊C4—64no—
151#878—64no—
152#877—64no—
153C3×#106C2×D314yes—
154C3×#103C2×D314yes—
155C3×#102C2×D314yes—
156#835—34no—
157#832—34no—
158#821—34no—
159#817—34no—
160#816—34no—
161Dic3⋊C8—34no—
162Dic3⋊C8—34no—
163Dic3⋊C8—34no—
164Dic3⋊C8—34no—
165#810—34no—
166#809—34no—
167#808—34no—
168#808—34no—
169C23×C32—21no—
170C23×C32C2×D411yescharacteristic
171C22×C3⋊D3—21no—
172C32×Q8—21no—
173C32×Q8—21no—
174C32×D4—21no—
175C32×D4—21no—
176C32×D4—42no—
177C2×C32×C4—21no—
178C2×C32×C4—21no—
179C2×C32×C4—21no—
180C2×C32×C4—21no—
181C2×C32×C4—21no—
182C2×C32×C4C2×D411yescharacteristic
183C2×C32×C4C2411yescharacteristic
184#638—42no—
185#638—42no—
186#638—42no—
187C2×C3⋊Dic3—21no—
188C2×C3⋊Dic3—21no—
189C2×C3⋊Dic3—21no—
190C2×C3⋊Dic3—41no—
191C2×C3⋊Dic3—42no—
192C2×C3⋊Dic3SD1614yescomplemented
193C2×C3⋊Dic3C2×D411yescharacteristic
194C2×C3⋊Dic3C2×D411yescharacteristic
195C2×C3⋊Dic3C2×D411yescharacteristic
196C2×C3⋊Dic3C2×D411yescharacteristic
197C4⋊(C3⋊D3)—21no—
198C4⋊(C3⋊D3)—21no—
199C4×C3⋊D3—42no—
200#634—21no—
201#634—21no—
202#634—42no—
203#634—42no—
204C32×C8—21no—
205C32×C8—21no—
206C3⋊(C3⋊C8)—21no—
207C3⋊(C3⋊C8)—21no—
208#533—91no—
209#532—91no—
210#476—91no—
211#476—91no—
212#475—91no—
213#475—91no—
214#465—91no—
215#465—91no—
216#465—91no—
217#465C3⋊D311yescharacteristic, complemented
218#461—91no—
219#461—91no—
220#460—91no—
221#460—91no—
222C2×C4⋊C8—91no—
223C2×C3×Q8C22×D314yes—
224C2×C3×D4—24no—
225C2×C3×D4C22×D314yes—
226C22×C3×C4C22×D314yes—
227C2×#67—64no—
228C2×#67—64no—
229C2×#67—64no—
230C22×Dic3—34no—
231C22×Dic3—34no—
232C22×Dic3—64no—
233#237—1216no—
234C2×D12—34no—
235C2×C4×D3—64no—
236C2×Dic6—34no—
237C2×Dic6—64no—
238C2×Dic6—64no—
239C3×SD16—44no—
240C2×C3×C8—44no—
241C2×C3×C8C22×D314yes—
242C2×C3×C8C22×D314yes—
243C3×C4⋊C4—24no—
244C3×C4⋊C4C22×D314yes—
245C3×C4⋊C4C22×D314yes—
246C3×C22⋊C4—24no—
247C3×C22⋊C4—24no—
248#217—64no—
249#217—64no—
250#215—124no—
251#214—124no—
252(C2×D3)⋊C4—64no—
253(C2×D3)⋊C4—64no—
254C4⋊Dic3—34no—
255C4⋊Dic3—34no—
256C4⋊Dic3—64no—
257Dic3⋊C4—64no—
258Dic3⋊C4—64no—
259Dic3⋊C4—64no—
260Dic3⋊C4—64no—
261Dic3⋊C4—64no—
262Dic3⋊C4—64no—
263C4×Dic3—34no—
264C4×Dic3—34no—
265C4×Dic3—34no—
266C4×Dic3—34no—
267C4×Dic3—64no—
268C4×Dic3—64no—
269C2×C3⋊C8—34no—
270C2×C3⋊C8—34no—
271C2×C3⋊C8—124no—
272#204—124no—
273C22×C32—21no—
274C22×C32—21no—
275C22×C32—41no—
276C22×C32—41no—
277C22×C32—41no—
278C22×C32C2×SD1612yes—
279C22×C32C22×D411yescharacteristic
280C2×C3⋊D3—41no—
281C2×C3⋊D3—41no—
282C2×C3⋊D3—41no—
283C32×C4—21no—
284C32×C4—41no—
285C32×C4—41no—
286C32×C4—41no—
287C32×C4H(5,𝔽2)11yescharacteristic
288C32×C42−1+411yescharacteristic
289C3⋊Dic3—21no—
290C3⋊Dic3—21no—
291C3⋊Dic3—41no—
292C3⋊Dic3—41no—
293C3⋊Dic3—41no—
294C3⋊Dic3C2×SD1612yes—
295C3⋊Dic3C2×SD1612yes—
296C2×#41—181no—
297C2×SD16—91no—
298C2×SD16—91no—
299C2×SD16—91no—
300C2×SD16C2×C3⋊D311yescharacteristic
301C22×C8—91no—
302C22×C8C2×C3⋊D311yescharacteristic
303C4⋊Q8—91no—
304C4⋊Q8—91no—
305C4⋊Q8—91no—
306#127—91no—
307#125—181no—
308#124—181no—
309C22⋊Q8—91no—
310C22⋊Q8—181no—
311C22⋊Q8C2×C3⋊D311yescharacteristic
312#121—91no—
313#121—181no—
314#121C2×C3⋊D311yescharacteristic
315C4×Q8—91no—
316C4×Q8—91no—
317C4×Q8—181no—
318C4×D4—91no—
319C4×D4—91no—
320C4×D4—181no—
321#117—181no—
322C2×C42—91no—
323#106—91no—
324#106—91no—
325#106—91no—
326#106C2×C3⋊D311yescharacteristic
327C4⋊C8—91no—
328C4⋊C8—91no—
329C4⋊C8—91no—
330C4⋊C8—91no—
331#103—91no—
332#103—91no—
333#103—91no—
334#103C2×C3⋊D311yescharacteristic
335#102—91no—
336#102—91no—
337#102—91no—
338#102C2×C3⋊D311yescharacteristic
339C23×C3—24no—
340C23×C3D3×D414yes—
341C22×D3—64no—
342C3×Q8—24no—
343C3×Q8—24no—
344C3×D4—24no—
345C3×D4—24no—
346C3×D4—48no—
347C2×C3×C4—24no—
348C2×C3×C4—24no—
349C2×C3×C4—24no—
350C2×C3×C4—24no—
351C2×C3×C4—24no—
352C2×C3×C4D3×D414yes—
353C2×C3×C4C23×D314yes—
354#67—128no—
355#67—128no—
356#67—128no—
357C2×Dic3—316no—
358C2×Dic3—34no—
359C2×Dic3—34no—
360C2×Dic3—34no—
361C2×Dic3—34no—
362C2×Dic3—64no—
363C2×Dic3—64no—
364C2×Dic3—64no—
365C2×Dic3—128no—
366C2×Dic3—124no—
367D12—64no—
368D12—64no—
369C4×D3—128no—
370Dic6—64no—
371Dic6—64no—
372Dic6—128no—
373Dic6—128no—
374C3×C8—24no—
375C3×C8—24no—
376C3⋊C8—64no—
377C3⋊C8—64no—
378C2×C32—22no—
379C2×C32—81no—
380C2×C32#53711yescharacteristic
381C2×C32C22×SD1611yescharacteristic
382C2×C32#57511yescharacteristic
383C3⋊D3—81no—
384#41—364no—
385C2×Q8—91no—
386C2×Q8—181no—
387C2×Q8—181no—
388C2×Q8C22×C3⋊D311yescharacteristic
389C2×D4—21no—
390C2×D4—91no—
391C2×D4—181no—
392C2×D4—181no—
393C2×D4—181no—
394C2×D4C22×C3⋊D311yescharacteristic
395C22×C4—91no—
396C22×C4—91no—
397C22×C4—181no—
398C22×C4—181no—
399C22×C4C22×C3⋊D311yescharacteristic
400SD16—41no—
401SD16—361no—
402SD16—361no—
403SD16—361no—
404C2×C8—41no—
405C2×C8—91no—
406C2×C8—91no—
407C2×C8—361no—
408C2×C8C22×C3⋊D311yescharacteristic
409C2×C8C22×C3⋊D311yescharacteristic
410C4⋊C4—21no—
411C4⋊C4—91no—
412C4⋊C4—91no—
413C4⋊C4—181no—
414C4⋊C4—181no—
415C4⋊C4—181no—
416C4⋊C4—181no—
417C4⋊C4—181no—
418C4⋊C4—181no—
419C4⋊C4—181no—
420C4⋊C4C22×C3⋊D311yescharacteristic
421C4⋊C4C22×C3⋊D311yescharacteristic
422C22⋊C4—21no—
423C22⋊C4—21no—
424C22⋊C4—181no—
425C22⋊C4—181no—
426C22⋊C4—181no—
427C22⋊C4—181no—
428C42—91no—
429C42—91no—
430C42—91no—
431C42—91no—
432C42—181no—
433C42—181no—
434C22×C3—24no—
435C22×C3—24no—
436C22×C3—44no—
437C22×C3—44no—
438C22×C3—44no—
439C22×C3D3×SD1618yes—
440C22×C3C2×D3×D414yes—
441C2×D3—124no—
442C2×D3—124no—
443C2×D3—124no—
444C3×C4—24no—
445C3×C4—44no—
446C3×C4—44no—
447C3×C4—44no—
448C3×C4#100414yes—
449C3×C4#101014yes—
450Dic3—38no—
451Dic3—38no—
452Dic3—64no—
453Dic3—64no—
454Dic3—124no—
455Dic3—124no—
456Dic3—124no—
457C32#324611yescharacteristic, complemented, Sylow
458C23—21no—
459C23—181no—
460C23D4×C3⋊D311yescharacteristic
461Q8—21no—
462Q8—21no—
463Q8—181no—
464Q8—181no—
465Q8—362no—
466Q8—362no—
467D4—21no—
468D4—21no—
469D4—42no—
470D4—181no—
471D4—181no—
472D4—362no—
473D4—362no—
474D4—362no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—91no—
481C2×C4—91no—
482C2×C4—94no—
483C2×C4—91no—
484C2×C4—91no—
485C2×C4—181no—
486C2×C4—181no—
487C2×C4—181no—
488C2×C4—362no—
489C2×C4—362no—
490C2×C4—361no—
491C2×C4D4×C3⋊D311yescharacteristic
492C2×C4C23×C3⋊D311yescharacteristic
493C8—21no—
494C8—21no—
495C8—181no—
496C8—181no—
497C2×C3—28no—
498C2×C3—84no—
499C2×C3#559714yes—
500C2×C3C2×D3×SD1614yes—
501C2×C3#576814yes—
502D3—244no—
503C22—21no—
504C22—21no—
505C22—41no—
506C22—41no—
507C22—41no—
508C22—361no—
509C22—361no—
510C22—361no—
511C22SD16×C3⋊D312yes—
512C22C2×D4×C3⋊D311yescharacteristic
513C4—21no—
514C4—41no—
515C4—41no—
516C4—41no—
517C4—92no—
518C4—92no—
519C4—181no—
520C4—181no—
521C4—361no—
522C4—361no—
523C4—361no—
524C4#6436111yescharacteristic
525C4#6436711yescharacteristic
526C3#8064014yescomplemented
527C2—22no—
528C2—81no—
529C2—721no—
530C2#1059606811yescharacteristic
531C2C2×SD16×C3⋊D311yescharacteristic
532C2#1059623911yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#465C2
socleC22×C32C22×D4
prime radical#10596067C2
hypercenter#465C3⋊D3
hypocenterC32#3246
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #10596093C2semidirect
3. C32×#465C2semidirect
4. #10592862C2semidirect
5. #10592861C2semidirect
6. #10592813C2semidirect
7. C2×#63641C2semidirect
8. #10592747C2semidirect
9. #10592740C2semidirect
10. #10592569C2semidirect
11. #10592553C2semidirect
12. #10592517C2semidirect
13. #10592490C2semidirect
14. #10592461C2semidirect
15. #10592460C2semidirect
62. C3×#465D3semidirect
192. C2×C3⋊Dic3SD16semidirect
217. #465C3⋊D3semidirect
457. C32#3246semidirect
526. C3#80640semidirect

Maximal subgroups

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

subgroupindex
#105960932
#105960672
C32×#4652
#105928622
#105928612
#105928132
C2×#636412
#105927472
#105927402
#105925692
#105925532
#105925172
#105924902
#105924612
#105924602
#806403