Finite Group Databasebeta

← #11872276

Subgroups — #11872276

Order 1152.

1188 conjugacy classes of subgroups.

The subgroup lattice has 543 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596168C211yesmaximal, characteristic, complemented
2#10596045C211yesmaximal, characteristic, complemented
3C32×#479C211yesmaximal, characteristic, complemented
4#10592765C211yesmaximal, characteristic, complemented
5#10592726C211yesmaximal, characteristic, complemented
6#10592581C211yesmaximal, characteristic, complemented
7#10592571C211yesmaximal, characteristic, complemented
8#10592568C211yesmaximal, characteristic, complemented
9#10592562C211yesmaximal, characteristic, complemented
10#10592542C211yesmaximal, characteristic, complemented
11#10592539C211yesmaximal, characteristic, complemented
12#10592516C211yesmaximal, characteristic, complemented
13#10592509C211yesmaximal, characteristic, complemented
14#10592509C211yesmaximal, characteristic, complemented
15#10592487C211yesmaximal, characteristic, complemented
16#81208—34nomaximal
17C2×#3832C2211yescharacteristic
18C32×#125C2211yescharacteristic
19C32×C4×Q8C2211yescharacteristic
20Q8×C3⋊Dic3C2211yescharacteristic
21C2×#3755C2211yescharacteristic
22C2×#3755C2211yescharacteristic
23C2×#3745C2211yescharacteristic
24C2×#3745C2211yescharacteristic
25#64104—21no—
26#64104—21no—
27#64104C2211yescharacteristic
28#64104C2211yescharacteristic
29#64103—21no—
30#64103—21no—
31#64102—21no—
32#64102C2211yescharacteristic
33#64102C2211yescharacteristic
34#64102C2211yescharacteristic
35C4⋊C4×C3⋊D3—21no—
36C4⋊C4×C3⋊D3C2211yescharacteristic
37#64083C2211yescharacteristic
38C4×C4⋊(C3⋊D3)—21no—
39C4×C4⋊(C3⋊D3)C2211yescharacteristic
40#64081—21no—
41#64081C2211yescharacteristic
42C32×#107C2211yescharacteristic
43C32×#106C2211yescharacteristic
44C32×C4⋊C8C2211yescharacteristic
45C32×#103C2211yescharacteristic
46C32×#103C2211yescharacteristic
47#63648C2211yescharacteristic
48#63648C2211yescharacteristic
49#63647C2211yescharacteristic
50#63647C2211yescharacteristic
51#63642C2211yescharacteristic
52C8×C3⋊Dic3C2211yescharacteristic
53#63636C2211yescharacteristic
54#63636C2211yescharacteristic
55#63636C2211yescharacteristic
56#63636C2211yescharacteristic
57#63635C2211yescharacteristic
58#63634C2211yescharacteristic
59C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
60#5697—34no—
61#5574—34no—
62C3×#479D314yescomplemented
63#5066—34no—
64#5027—34no—
65#4882—34no—
66#4872—34no—
67#4869—34no—
68#4863—34no—
69#4843—34no—
70#4840—34no—
71#4817—34no—
72#4810—34no—
73#4810—34no—
74#4788—34no—
75C2×C32×Q8C2311yescharacteristic
76#3832—22no—
77#3832—22no—
78C2×C4⋊(C3⋊D3)—21no—
79C2×C4⋊(C3⋊D3)—21no—
80C2×C4⋊(C3⋊D3)—21no—
81C2×C4⋊(C3⋊D3)—21no—
82C2×C4⋊(C3⋊D3)—21no—
83C2×C4⋊(C3⋊D3)C2311yescharacteristic
84C2×C4⋊(C3⋊D3)C2311yescharacteristic
85C2×C4⋊(C3⋊D3)C2311yescharacteristic
86C2×C4×C3⋊D3—21no—
87C2×C4×C3⋊D3—21no—
88C2×C4×C3⋊D3—21no—
89C2×C4×C3⋊D3—21no—
90C2×C4×C3⋊D3—21no—
91C2×C4×C3⋊D3—21no—
92C2×C4×C3⋊D3C2311yescharacteristic
93C2×C32×C8C2311yescharacteristic
94C2×C32×C8C2311yescharacteristic
95C32×C4⋊C4—21no—
96C32×C4⋊C4—21no—
97C32×C4⋊C4—21no—
98C32×C4⋊C4C2311yescharacteristic
99C32×C4⋊C4C2311yescharacteristic
100C32×C4⋊C4C2311yescharacteristic
101C32×C42—21no—
102C32×C42C2311yescharacteristic
103#3755—22no—
104#3755—22no—
105#3752—21no—
106#3752—21no—
107#3752—21no—
108#3752—21no—
109#3752—21no—
110#3752—21no—
111#3752D411yescharacteristic
112#3752D411yescharacteristic
113C4⋊(C3⋊Dic3)—21no—
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115#3750—21no—
116#3750D411yescharacteristic
117#3750D411yescharacteristic
118C4×C3⋊Dic3—21no—
119C4×C3⋊Dic3C2311yescharacteristic
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122#3745—22no—
123#3745—22no—
124#3119—91noSylow
125C2×#239—34no—
126C3×#125C2×D314yes—
127C3×C4×Q8C2×D314yes—
128Q8×Dic3—34no—
129C2×#215—34no—
130C2×#215—34no—
131C2×D24—34no—
132C2×D24—34no—
133#895—34no—
134#895—34no—
135#895—64no—
136#895—64no—
137#894—64no—
138#894—64no—
139#893—34no—
140#893—34no—
141#893—34no—
142#893—64no—
143D3×C4⋊C4—34no—
144D3×C4⋊C4—64no—
145#874—34no—
146C4×D12—34no—
147C4×D12—64no—
148#872—34no—
149#872—64no—
150C3×#107C2×D314yes—
151C3×#106C2×D314yes—
152C3×C4⋊C8C2×D314yes—
153C3×#103C2×D314yes—
154C3×#103C2×D314yes—
155#821—34no—
156#821—34no—
157(C2×D3)⋊C8—34no—
158(C2×D3)⋊C8—34no—
159#815—34no—
160C8×Dic3—34no—
161#809—34no—
162#809—34no—
163#809—34no—
164#809—34no—
165#808—34no—
166#807—34no—
167C4⋊(C3⋊C8)—34no—
168C22×C3⋊D3—21no—
169C22×C3⋊D3—21no—
170C22×C3⋊D3—21no—
171C22×C3⋊D3C2×D411yescharacteristic
172C32×Q8—21no—
173C32×Q8#4112yes—
174C2×C32×C4—21no—
175C2×C32×C4—21no—
176C2×C32×C4—21no—
177C2×C32×C4—21no—
178C2×C32×C4C2×D411yescharacteristic
179C2×C32×C4C2×D411yescharacteristic
180C2×C32×C4C2411yescharacteristic
181C2×C3⋊Dic3—21no—
182C2×C3⋊Dic3C2×D411yescharacteristic
183C2×C3⋊Dic3C2×D411yescharacteristic
184C2×C3⋊Dic3C2×D411yescharacteristic
185C4⋊(C3⋊D3)—24no—
186C4⋊(C3⋊D3)—21no—
187C4⋊(C3⋊D3)—21no—
188C4⋊(C3⋊D3)—21no—
189C4⋊(C3⋊D3)—21no—
190C4⋊(C3⋊D3)—21no—
191C4⋊(C3⋊D3)—81no—
192C4⋊(C3⋊D3)—81no—
193C4⋊(C3⋊D3)—81no—
194C4⋊(C3⋊D3)—81no—
195C4⋊(C3⋊D3)#4112yes—
196C4×C3⋊D3—24no—
197C4×C3⋊D3—21no—
198C4×C3⋊D3—21no—
199C4×C3⋊D3—81no—
200C4×C3⋊D3—81no—
201C4×C3⋊D3—81no—
202C4×C3⋊D3—81no—
203C4×C3⋊D3—81no—
204C32×C8—21no—
205C32×C8—21no—
206C3⋊(C3⋊C8)—21no—
207C3⋊(C3⋊C8)—21no—
208#540—91no—
209#520—91no—
210#481—91no—
211#480—91no—
212#479C3⋊D311yescharacteristic, complemented
213#478—91no—
214#460—91no—
215#459—91no—
216#449—91no—
217#449—91no—
218#442—91no—
219#440—91no—
220C4×SD16—91no—
221C4×D8—91no—
222#433—91no—
223C2×C3×Q8C22×D314yes—
224#239—68no—
225#239—68no—
226C2×D12—34no—
227C2×D12—34no—
228C2×D12—34no—
229C2×D12—64no—
230C2×D12—64no—
231C2×D12—64no—
232C2×D12—64no—
233C2×D12—64no—
234C2×C4×D3—34no—
235C2×C4×D3—64no—
236C2×C4×D3—64no—
237C2×C4×D3—64no—
238C2×C4×D3—64no—
239C2×C4×D3—64no—
240C2×C4×D3—64no—
241C2×C3×C8C22×D314yes—
242C2×C3×C8C22×D314yes—
243C3×C4⋊C4—24no—
244C3×C4⋊C4—24no—
245C3×C4⋊C4—24no—
246C3×C4⋊C4C22×D314yes—
247C3×C4⋊C4C22×D314yes—
248C3×C4⋊C4C22×D314yes—
249C3×C42—24no—
250C3×C42C22×D314yes—
251#215—68no—
252#215—68no—
253(C2×D3)⋊C4—34no—
254(C2×D3)⋊C4—34no—
255(C2×D3)⋊C4—64no—
256(C2×D3)⋊C4—64no—
257(C2×D3)⋊C4—64no—
258(C2×D3)⋊C4—64no—
259(C2×D3)⋊C4—64no—
260(C2×D3)⋊C4—64no—
261C4⋊Dic3—34no—
262C4⋊Dic3—64no—
263Dic3⋊C4—34no—
264Dic3⋊C4—34no—
265Dic3⋊C4—64no—
266C4×Dic3—34no—
267C4×Dic3—64no—
268C2×C3⋊C8—34no—
269C2×C3⋊C8—34no—
270D24—68no—
271D24—68no—
272C22×C32C22×D411yescharacteristic
273C2×C3⋊D3—21no—
274C2×C3⋊D3—22no—
275C2×C3⋊D3—21no—
276C2×C3⋊D3—21no—
277C2×C3⋊D3—41no—
278C2×C3⋊D3—41no—
279C2×C3⋊D3—41no—
280C2×C3⋊D3—41no—
281C2×C3⋊D3—41no—
282C2×C3⋊D3—41no—
283C2×C3⋊D3—41no—
284C2×C3⋊D3—41no—
285C32×C4—22no—
286C32×C4—21no—
287C32×C4—21no—
288C32×C4—41no—
289C32×C4—41no—
290C32×C4—41no—
291C32×C4C2×#4111yescharacteristic
292C32×C4C2×#4111yescharacteristic
293C3⋊Dic3—21no—
294C3⋊Dic3—21no—
295C3⋊Dic3—21no—
296C3⋊Dic3—41no—
297C2×#41—91no—
298C2×SD16—91no—
299C2×SD16—91no—
300C2×D8—91no—
301C2×D8—91no—
302#127—91no—
303#125C2×C3⋊D311yescharacteristic
304#123—181no—
305#123—181no—
306#121—91no—
307#121—91no—
308#121—181no—
309#121—181no—
310C4×Q8—91no—
311C4×Q8C2×C3⋊D311yescharacteristic
312C4×D4—91no—
313C4×D4—91no—
314C4×D4—91no—
315C4×D4—91no—
316C4×D4—181no—
317C4×D4—181no—
318#117—91no—
319#117—181no—
320C2×C4⋊C4—91no—
321C2×C4⋊C4—181no—
322#107—91no—
323#107C2×C3⋊D311yescharacteristic
324#106—91no—
325#106C2×C3⋊D311yescharacteristic
326C4⋊C8—91no—
327C4⋊C8C2×C3⋊D311yescharacteristic
328#103C2×C3⋊D311yescharacteristic
329#103C2×C3⋊D311yescharacteristic
330#102—91no—
331#102—91no—
332#102—91no—
333#102—91no—
334#102—91no—
335#102—91no—
336C22⋊C8—91no—
337C22⋊C8—91no—
338#97—91no—
339C4×C8—91no—
340C22×D3—34no—
341C22×D3—64no—
342C22×D3—64no—
343C22×D3—64no—
344C3×Q8—24no—
345C3×Q8#23918yes—
346C2×C3×C4—24no—
347C2×C3×C4—24no—
348C2×C3×C4—24no—
349C2×C3×C4—24no—
350C2×C3×C4D3×D414yes—
351C2×C3×C4D3×D414yes—
352C2×C3×C4C23×D314yes—
353C2×Dic3—34no—
354C2×Dic3—34no—
355C2×Dic3—34no—
356C2×Dic3—64no—
357D12—38no—
358D12—616no—
359D12—64no—
360D12—64no—
361D12—64no—
362D12—64no—
363D12—64no—
364D12—244no—
365D12—244no—
366D12—244no—
367D12—244no—
368C4×D3—616no—
369C4×D3—64no—
370C4×D3—64no—
371C4×D3—244no—
372C4×D3—244no—
373C4×D3—244no—
374C4×D3—244no—
375C4×D3—244no—
376C3×C8—24no—
377C3×C8—24no—
378C3⋊C8—64no—
379C3⋊C8—64no—
380C2×C32#52511yescharacteristic
381C2×C32#57611yescharacteristic
382C2×C32#57711yescharacteristic
383C3⋊D3—41no—
384C3⋊D3—42no—
385C3⋊D3—81no—
386C3⋊D3—81no—
387#41—182no—
388#41—182no—
389C2×Q8C22×C3⋊D311yescharacteristic
390C2×D4—91no—
391C2×D4—91no—
392C2×D4—91no—
393C2×D4—181no—
394C2×D4—181no—
395C2×D4—181no—
396C2×D4—181no—
397C2×D4—181no—
398C22×C4—91no—
399C22×C4—181no—
400C22×C4—181no—
401C22×C4—181no—
402C22×C4—181no—
403C22×C4—181no—
404C22×C4—181no—
405SD16—182no—
406SD16—182no—
407D8—182no—
408D8—182no—
409C2×C8—91no—
410C2×C8—91no—
411C2×C8C22×C3⋊D311yescharacteristic
412C2×C8C22×C3⋊D311yescharacteristic
413C4⋊C4—21no—
414C4⋊C4—21no—
415C4⋊C4—21no—
416C4⋊C4—91no—
417C4⋊C4—91no—
418C4⋊C4—91no—
419C4⋊C4—181no—
420C4⋊C4—181no—
421C4⋊C4C22×C3⋊D311yescharacteristic
422C4⋊C4C22×C3⋊D311yescharacteristic
423C4⋊C4C22×C3⋊D311yescharacteristic
424C22⋊C4—91no—
425C22⋊C4—91no—
426C22⋊C4—181no—
427C22⋊C4—181no—
428C22⋊C4—181no—
429C22⋊C4—181no—
430C22⋊C4—181no—
431C22⋊C4—181no—
432C42—21no—
433C42—91no—
434C42—181no—
435C42C22×C3⋊D311yescharacteristic
436C22×C3C2×D3×D414yes—
437C2×D3—64no—
438C2×D3—64no—
439C2×D3—68no—
440C2×D3—64no—
441C2×D3—124no—
442C2×D3—124no—
443C2×D3—124no—
444C2×D3—124no—
445C2×D3—124no—
446C2×D3—124no—
447C2×D3—124no—
448C2×D3—124no—
449C3×C4—24no—
450C3×C4—24no—
451C3×C4—28no—
452C3×C4—44no—
453C3×C4—44no—
454C3×C4—44no—
455C3×C4C2×#23914yes—
456C3×C4D3×#4114yes—
457Dic3—64no—
458Dic3—64no—
459Dic3—64no—
460Dic3—124no—
461C32#311911yescharacteristic, complemented, Sylow
462C23—91no—
463C23—181no—
464C23—181no—
465C23—181no—
466Q8—21no—
467Q8#383212yes—
468D4—92no—
469D4—184no—
470D4—181no—
471D4—181no—
472D4—181no—
473D4—181no—
474D4—181no—
475D4—721no—
476D4—721no—
477D4—721no—
478D4—721no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—91no—
484C2×C4—91no—
485C2×C4—91no—
486C2×C4—184no—
487C2×C4—181no—
488C2×C4—181no—
489C2×C4—181no—
490C2×C4—721no—
491C2×C4—721no—
492C2×C4—721no—
493C2×C4—721no—
494C2×C4—721no—
495C2×C4D4×C3⋊D311yescharacteristic
496C2×C4D4×C3⋊D311yescharacteristic
497C2×C4C23×C3⋊D311yescharacteristic
498C8—21no—
499C8—21no—
500C8—181no—
501C8—181no—
502C2×C3#562714yes—
503C2×C3#576914yes—
504C2×C3#577814yes—
505D3—124no—
506D3—128no—
507D3—244no—
508D3—244no—
509C22—182no—
510C22—181no—
511C22—181no—
512C22—181no—
513C22—361no—
514C22—361no—
515C22—361no—
516C22—361no—
517C22—361no—
518C22—361no—
519C22—361no—
520C22—361no—
521C22C2×D4×C3⋊D311yescharacteristic
522C4—22no—
523C4—21no—
524C4—21no—
525C4—41no—
526C4—41no—
527C4—41no—
528C4—181no—
529C4—181no—
530C4—181no—
531C4—361no—
532C4C2×#383211yescharacteristic
533C4#41×C3⋊D311yescharacteristic
534C3#8120814yescomplemented
535C2—361no—
536C2—362no—
537C2—721no—
538C2—721no—
539C2#1059609811yescharacteristic
540C2#1059624011yescharacteristic
541C2#1059624911yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#479C2
socleC22×C32C22×D4
hypercenter#479C3⋊D3
hypocenterC32#3119
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
1. #10596168C2semidirect
2. #10596045C2semidirect
3. C32×#479C2semidirect
4. #10592765C2semidirect
5. #10592726C2semidirect
6. #10592581C2semidirect
7. #10592571C2semidirect
8. #10592568C2semidirect
9. #10592562C2semidirect
10. #10592542C2semidirect
11. #10592539C2semidirect
12. #10592516C2semidirect
13. #10592509C2semidirect
14. #10592509C2semidirect
15. #10592487C2semidirect
62. C3×#479D3semidirect
212. #479C3⋊D3semidirect
461. C32#3119semidirect
534. C3#81208semidirect

Maximal subgroups

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

subgroupindex
#105961682
#105960452
C32×#4792
#105927652
#105927262
#105925812
#105925712
#105925682
#105925622
#105925422
#105925392
#105925162
#105925092
#105924872
#812083