Finite Group Databasebeta

← #11887700

Subgroups — #11887700

Order 1152.

1158 conjugacy classes of subgroups.

The subgroup lattice has 537 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596165C211yesmaximal, characteristic, complemented
2#10596047C211yesmaximal, characteristic
3C32×#479C211yesmaximal, characteristic, complemented
4#10592767C211yesmaximal, characteristic, complemented
5C4×#3756C211yesmaximal, characteristic, complemented
6#10592586C211yesmaximal, characteristic, complemented
7#10592581C211yesmaximal, characteristic, complemented
8#10592567C211yesmaximal, characteristic, complemented
9#10592563C211yesmaximal, characteristic, complemented
10#10592544C211yesmaximal, characteristic, complemented
11#10592533C211yesmaximal, characteristic, complemented
12#10592508C211yesmaximal, characteristic, complemented
13#10592507C211yesmaximal, characteristic, complemented
14#10592503C211yesmaximal, characteristic, complemented
15C3⋊D3×#103C211yesmaximal, characteristic, complemented
16#81245—34nomaximal
17C2×#3832C2211yescharacteristic
18C2×Q8×C3⋊D3C2211yescharacteristic
19C32×#125C2211yescharacteristic
20C32×C4×Q8C2211yescharacteristic
21C2×#3756C2211yescharacteristic
22C2×#3746C2211yescharacteristic
23C2×#3744C2211yescharacteristic
24C2×C8×C3⋊D3C2211yescharacteristic
25C2×C8×C3⋊D3C2211yescharacteristic
26#64107—21no—
27#64106—21no—
28#64106C2211yescharacteristic
29#64106C2211yescharacteristic
30#64106C2211yescharacteristic
31#64104—21no—
32#64104C2211yescharacteristic
33#64103—21no—
34#64101—21no—
35#64101C2211yescharacteristic
36C4⋊C4×C3⋊D3C2211yescharacteristic
37#64099—21no—
38#64084—21no—
39#64084C2211yescharacteristic
40C4×C4⋊(C3⋊D3)—21no—
41C4×C4⋊(C3⋊D3)C2211yescharacteristic
42C4×#634C2211yescharacteristic
43C32×#107C2211yescharacteristic
44C32×#106C2211yescharacteristic
45C32×C4⋊C8C2211yescharacteristic
46C32×#103C2211yescharacteristic
47C32×#103C2211yescharacteristic
48#63662C2211yescharacteristic
49#63648C2211yescharacteristic
50#63647C2211yescharacteristic
51#63647C2211yescharacteristic
52#63643C2211yescharacteristic
53#63637C2211yescharacteristic
54#63637C2211yescharacteristic
55#63637C2211yescharacteristic
56#63636C2211yescharacteristic
57#63636C2211yescharacteristic
58#63634C2211yescharacteristic
59C4×C3⋊(C3⋊C8)C2211yescharacteristic
60#5694—34no—
61#5576—34no—
62C3×#479D314yescomplemented
63#5068—34no—
64C4×#216—34no—
65#4887—34no—
66#4882—34no—
67#4868—34no—
68#4864—34no—
69#4845—34no—
70#4834—34no—
71#4809—34no—
72#4808—34no—
73#4804—34no—
74D3×#103—34no—
75C2×C32×Q8C2311yescharacteristic
76#3832—22no—
77#3832—41no—
78Q8×C3⋊D3—22no—
79Q8×C3⋊D3—41no—
80C2×C4⋊(C3⋊D3)—21no—
81C2×C4⋊(C3⋊D3)—21no—
82C2×C4⋊(C3⋊D3)D411yescharacteristic
83C2×C4⋊(C3⋊D3)C2311yescharacteristic
84C2×C4×C3⋊D3—21no—
85C2×C4×C3⋊D3—21no—
86C2×C4×C3⋊D3—21no—
87C2×C4×C3⋊D3C2311yescharacteristic
88C2×C4×C3⋊D3C2311yescharacteristic
89C2×#634—21no—
90C2×#634C2311yescharacteristic
91C2×#634C2311yescharacteristic
92C2×C32×C8C2311yescharacteristic
93C2×C32×C8C2311yescharacteristic
94C32×C4⋊C4—21no—
95C32×C4⋊C4—21no—
96C32×C4⋊C4—21no—
97C32×C4⋊C4C2311yescharacteristic
98C32×C4⋊C4C2311yescharacteristic
99C32×C4⋊C4C2311yescharacteristic
100C32×C42—21no—
101C32×C42C2311yescharacteristic
102#3756—22no—
103#3752—21no—
104#3752—21no—
105#3752—21no—
106#3752—21no—
107#3752—21no—
108#3752—21no—
109#3752—21no—
110#3752D411yescharacteristic
111#3752D411yescharacteristic
112C4⋊(C3⋊Dic3)—21no—
113C4⋊(C3⋊Dic3)—21no—
114C4⋊(C3⋊Dic3)—21no—
115C4⋊(C3⋊Dic3)D411yescharacteristic
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117#3750—21no—
118#3750—21no—
119C4×C3⋊Dic3—21no—
120C4×C3⋊Dic3—21no—
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C2×C3⋊(C3⋊C8)C2311yescharacteristic
123#3746—41no—
124#3744—41no—
125C8×C3⋊D3—41no—
126C8×C3⋊D3—41no—
127#3300—91noSylow
128C2×#239—34no—
129C2×D3×Q8—34no—
130C3×#125C2×D314yes—
131C3×C4×Q8C2×D314yes—
132C2×#216—34no—
133C2×Dic12—34no—
134C2×#204—34no—
135C2×D3×C8—34no—
136C2×D3×C8—34no—
137#898—64no—
138#897—34no—
139#897—34no—
140#897—34no—
141#897—64no—
142#895—34no—
143#895—64no—
144#894—64no—
145#892—34no—
146#892—64no—
147D3×C4⋊C4—34no—
148#890—64no—
149#875—34no—
150#875—64no—
151C4×D12—34no—
152C4×D12—64no—
153C4×Dic6—34no—
154C3×#107C2×D314yes—
155C3×#106C2×D314yes—
156C3×C4⋊C8C2×D314yes—
157C3×#103C2×D314yes—
158C3×#103C2×D314yes—
159#835—34no—
160#821—34no—
161(C2×D3)⋊C8—34no—
162(C2×D3)⋊C8—34no—
163#816—34no—
164#810—34no—
165#810—34no—
166#810—34no—
167#809—34no—
168#809—34no—
169#807—34no—
170C4×C3⋊C8—34no—
171C22×C3⋊D3—21no—
172C22×C3⋊D3C2×D411yescharacteristic
173C22×C3⋊D3C2×D411yescharacteristic
174C32×Q8—21no—
175C32×Q8#4112yes—
176C2×C32×C4—21no—
177C2×C32×C4—21no—
178C2×C32×C4—21no—
179C2×C32×C4—21no—
180C2×C32×C4C2×D411yescharacteristic
181C2×C32×C4C2×D411yescharacteristic
182C2×C32×C4C2411yescharacteristic
183C2×C3⋊Dic3—21no—
184C2×C3⋊Dic3—21no—
185C2×C3⋊Dic3—21no—
186C2×C3⋊Dic3C2×D411yescharacteristic
187C2×C3⋊Dic3C2×D411yescharacteristic
188C4⋊(C3⋊D3)—22no—
189C4⋊(C3⋊D3)—21no—
190C4⋊(C3⋊D3)—21no—
191C4⋊(C3⋊D3)—42no—
192C4⋊(C3⋊D3)—42no—
193C4×C3⋊D3—21no—
194C4×C3⋊D3—21no—
195C4×C3⋊D3—21no—
196C4×C3⋊D3—21no—
197C4×C3⋊D3—42no—
198C4×C3⋊D3—42no—
199C4×C3⋊D3—42no—
200#634—21no—
201#634—21no—
202#634—21no—
203#634—21no—
204#634—42no—
205C32×C8—21no—
206C32×C8—21no—
207C3⋊(C3⋊C8)—21no—
208C3⋊(C3⋊C8)—21no—
209#552—91no—
210#548—91no—
211#488—91no—
212#485—91no—
213#480—91no—
214#479C3⋊D311yescharacteristic, complemented
215#467—91no—
216#465—91no—
217#464—91no—
218#452—91no—
219#451—91no—
220C4×Q16—91no—
221C8×D4—91no—
222#416—91no—
223C2×#103—91no—
224C2×C3×Q8C22×D314yes—
225#239—68no—
226#239—124no—
227D3×Q8—68no—
228D3×Q8—124no—
229C2×D12—34no—
230C2×D12—34no—
231C2×D12—64no—
232C2×D12—64no—
233C2×C4×D3—34no—
234C2×C4×D3—34no—
235C2×C4×D3—64no—
236C2×C4×D3—64no—
237C2×C4×D3—64no—
238C2×Dic6—34no—
239C2×Dic6—34no—
240C2×Dic6—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#216—68no—
252(C2×D3)⋊C4—34no—
253(C2×D3)⋊C4—34no—
254(C2×D3)⋊C4—64no—
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—34no—
263C4⋊Dic3—64no—
264C4⋊Dic3—64no—
265C4⋊Dic3—64no—
266Dic3⋊C4—64no—
267Dic3⋊C4—64no—
268C4×Dic3—64no—
269C4×Dic3—64no—
270C2×C3⋊C8—34no—
271C2×C3⋊C8—34no—
272Dic12—124no—
273#204—124no—
274D3×C8—124no—
275D3×C8—124no—
276C22×C32C22×D411yescharacteristic
277C2×C3⋊D3—21no—
278C2×C3⋊D3—21no—
279C2×C3⋊D3—21no—
280C2×C3⋊D3—21no—
281C2×C3⋊D3—21no—
282C2×C3⋊D3—41no—
283C2×C3⋊D3—41no—
284C2×C3⋊D3—41no—
285C2×C3⋊D3#13512yes—
286C32×C4—22no—
287C32×C4—21no—
288C32×C4—21no—
289C32×C4—41no—
290C32×C4—41no—
291C32×C4—41no—
292C32×C4C2×#4111yescharacteristic
293C32×C4H(5,𝔽2)11yescharacteristic
294C3⋊Dic3—21no—
295C3⋊Dic3—21no—
296C3⋊Dic3—41no—
297C3⋊Dic3—41no—
298C3⋊Dic3—41no—
299C2×#41—91no—
300C22×Q8—91no—
301C2×Q16—91no—
302C2×Q16—91no—
303C2×SD16—91no—
304C22×C8—91no—
305C22×C8—91no—
306#126—181no—
307#125—181no—
308#125C2×C3⋊D311yescharacteristic
309#124—91no—
310#124—181no—
311#123—181no—
312C22⋊Q8—91no—
313C22⋊Q8—91no—
314C22⋊Q8—91no—
315C22⋊Q8—181no—
316#121—91no—
317#121—181no—
318C4×Q8—91no—
319C4×Q8C2×C3⋊D311yescharacteristic
320C4×D4—91no—
321C4×D4—181no—
322#117—91no—
323#117—181no—
324C2×C4⋊C4—91no—
325#107—91no—
326#107C2×C3⋊D311yescharacteristic
327#106C2×C3⋊D311yescharacteristic
328C4⋊C8C2×C3⋊D311yescharacteristic
329#103—91no—
330#103—91no—
331#103—91no—
332#103—91no—
333#103—91no—
334#103C2×C3⋊D311yescharacteristic
335#103C2×C3⋊D311yescharacteristic
336#102—91no—
337#102—91no—
338#102—91no—
339C22⋊C8—91no—
340C22⋊C8—91no—
341C4×C8—91no—
342C22×D3—34no—
343C22×D3—34no—
344C22×D3—64no—
345C3×Q8—24no—
346C3×Q8#23918yes—
347C2×C3×C4—24no—
348C2×C3×C4—24no—
349C2×C3×C4—24no—
350C2×C3×C4—24no—
351C2×C3×C4D3×D414yes—
352C2×C3×C4D3×D414yes—
353C2×C3×C4C23×D314yes—
354C2×Dic3—34no—
355C2×Dic3—34no—
356C2×Dic3—64no—
357C2×Dic3—64no—
358C2×Dic3—64no—
359D12—68no—
360D12—64no—
361D12—64no—
362D12—128no—
363D12—128no—
364C4×D3—64no—
365C4×D3—64no—
366C4×D3—64no—
367C4×D3—64no—
368C4×D3—128no—
369C4×D3—128no—
370C4×D3—128no—
371Dic6—64no—
372Dic6—64no—
373Dic6—64no—
374Dic6—64no—
375Dic6—128no—
376C3×C8—24no—
377C3×C8—24no—
378C3⋊C8—64no—
379C3⋊C8—64no—
380C2×C32#54611yescharacteristic
381C2×C32C2×#13511yescharacteristic
382C2×C32#57811yescharacteristic
383C3⋊D3—22no—
384C3⋊D3—41no—
385C3⋊D3—81no—
386#41—182no—
387#41—361no—
388C2×Q8—91no—
389C2×Q8—91no—
390C2×Q8—181no—
391C2×Q8—182no—
392C2×Q8—361no—
393C2×Q8C22×C3⋊D311yescharacteristic
394C2×D4—91no—
395C2×D4—91no—
396C2×D4—181no—
397C2×D4—181no—
398C22×C4—91no—
399C22×C4—91no—
400C22×C4—181no—
401C22×C4—181no—
402C22×C4—181no—
403Q16—182no—
404Q16—361no—
405SD16—361no—
406C2×C8—91no—
407C2×C8—91no—
408C2×C8—361no—
409C2×C8—361no—
410C2×C8C22×C3⋊D311yescharacteristic
411C2×C8C22×C3⋊D311yescharacteristic
412C4⋊C4—21no—
413C4⋊C4—21no—
414C4⋊C4—21no—
415C4⋊C4—91no—
416C4⋊C4—91no—
417C4⋊C4—181no—
418C4⋊C4—181no—
419C4⋊C4—181no—
420C4⋊C4—181no—
421C4⋊C4—181no—
422C4⋊C4C22×C3⋊D311yescharacteristic
423C4⋊C4C22×C3⋊D311yescharacteristic
424C4⋊C4C22×C3⋊D311yescharacteristic
425C22⋊C4—91no—
426C22⋊C4—91no—
427C22⋊C4—181no—
428C22⋊C4—181no—
429C22⋊C4—181no—
430C22⋊C4—181no—
431C22⋊C4—181no—
432C22⋊C4—181no—
433C22⋊C4—181no—
434C42—21no—
435C42—181no—
436C42—181no—
437C42C22×C3⋊D311yescharacteristic
438C22×C3C2×D3×D414yes—
439C2×D3—38no—
440C2×D3—64no—
441C2×D3—64no—
442C2×D3—64no—
443C2×D3—64no—
444C2×D3—64no—
445C2×D3—124no—
446C2×D3—124no—
447C2×D3—124no—
448C3×C4—24no—
449C3×C4—24no—
450C3×C4—28no—
451C3×C4—44no—
452C3×C4—44no—
453C3×C4—44no—
454C3×C4C2×#23914yes—
455C3×C4#100914yes—
456Dic3—64no—
457Dic3—64no—
458Dic3—124no—
459Dic3—124no—
460Dic3—124no—
461C32#330011yescharacteristic, complemented, Sylow
462C23—91no—
463C23—91no—
464C23—181no—
465Q8—21no—
466Q8—181no—
467Q8—181no—
468Q8—181no—
469Q8—181no—
470Q8—362no—
471Q8#383212yes—
472D4—182no—
473D4—181no—
474D4—181no—
475D4—362no—
476D4—362no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—91no—
482C2×C4—91no—
483C2×C4—181no—
484C2×C4—181no—
485C2×C4—181no—
486C2×C4—181no—
487C2×C4—181no—
488C2×C4—181no—
489C2×C4—181no—
490C2×C4—362no—
491C2×C4—362no—
492C2×C4—362no—
493C2×C4D4×C3⋊D311yescharacteristic
494C2×C4D4×C3⋊D311yescharacteristic
495C2×C4C23×C3⋊D311yescharacteristic
496C8—21no—
497C8—21no—
498C8—181no—
499C8—181no—
500C2×C3#563014yes—
501C2×C3D3×#13514yes—
502C2×C3#577914yes—
503D3—68no—
504D3—124no—
505D3—244no—
506C22—92no—
507C22—181no—
508C22—181no—
509C22—181no—
510C22—181no—
511C22—181no—
512C22—361no—
513C22—361no—
514C22—361no—
515C22C2×D4×C3⋊D311yescharacteristic
516C4—22no—
517C4—21no—
518C4—21no—
519C4—41no—
520C4—41no—
521C4—41no—
522C4—181no—
523C4—181no—
524C4—361no—
525C4—361no—
526C4—361no—
527C4C2×#383211yescharacteristic
528C4#6436611yescharacteristic
529C3#8124514yescomplemented
530C2—182no—
531C2—361no—
532C2—721no—
533C2#1059610111yescharacteristic
534C2C3⋊D3×#13511yescharacteristic
535C2#1059625011yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#479C2
socleC22×C32C22×D4
prime radical#10596047C2
hypercenter#479C3⋊D3
hypocenterC32#3300
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. #10596165C2semidirect
3. C32×#479C2semidirect
4. #10592767C2semidirect
5. C4×#3756C2semidirect
6. #10592586C2semidirect
7. #10592581C2semidirect
8. #10592567C2semidirect
9. #10592563C2semidirect
10. #10592544C2semidirect
11. #10592533C2semidirect
12. #10592508C2semidirect
13. #10592507C2semidirect
14. #10592503C2semidirect
15. C3⋊D3×#103C2semidirect
62. C3×#479D3semidirect
214. #479C3⋊D3semidirect
461. C32#3300semidirect
529. C3#81245semidirect

Maximal subgroups

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

subgroupindex
#105961652
#105960472
C32×#4792
#105927672
C4×#37562
#105925862
#105925812
#105925672
#105925632
#105925442
#105925332
#105925082
#105925072
#105925032
C3⋊D3×#1032
#812453