Finite Group Databasebeta

← #11887192

Subgroups — #11887192

Order 1152.

1224 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596101C211yesmaximal, characteristic
2#10595984C211yesmaximal, characteristic, complemented
3C32×#483C211yesmaximal, characteristic, complemented
4#10592750C211yesmaximal, characteristic, complemented
5C2×#63636C211yesmaximal, characteristic, complemented
6#10592570C211yesmaximal, characteristic, complemented
7#10592565C211yesmaximal, characteristic, complemented
8#10592563C211yesmaximal, characteristic, complemented
9#10592551C211yesmaximal, characteristic, complemented
10#10592507C211yesmaximal, characteristic, complemented
11#10592503C211yesmaximal, characteristic, complemented
12#10592499C211yesmaximal, characteristic, complemented
13#10592497C211yesmaximal, characteristic, complemented
14#10592430C211yesmaximal, characteristic, complemented
15#10592424C211yesmaximal, characteristic, complemented
16#81445—34nomaximal
17C2×#3832C2211yescharacteristic
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C32×C22⋊Q8C2211yescharacteristic
20C2×C32×C4⋊C4C2211yescharacteristic
21#64156C2211yescharacteristic
22C2×#3756C2211yescharacteristic, complemented
23#64138—21no—
24C4×#638C2211yescharacteristic
25#64135—21no—
26#64133C2211yescharacteristic
27C22×C3⋊(C3⋊C8)C2211yescharacteristic
28C2×#3744C2211yescharacteristic
29C2×#3744C2211yescharacteristic
30C2×C8×C3⋊D3C2211yescharacteristic, complemented
31#64107—21no—
32#64106C2211yescharacteristic, complemented
33#64104—21no—
34#64104C2211yescharacteristic
35#64103—21no—
36#64102C2211yescharacteristic
37#64101C2211yescharacteristic, complemented
38#64099C2211yescharacteristic, complemented
39#64098—21no—
40#64096C2211yescharacteristic, complemented
41#64091—21no—
42C22⋊C4×C3⋊D3—21no—
43C32×#106C2211yescharacteristic, complemented
44C32×#106C2211yescharacteristic, complemented
45C32×#103C2211yescharacteristic, complemented
46C32×#103C2211yescharacteristic, complemented
47C32×C22⋊C8C2211yescharacteristic
48#63662C2211yescharacteristic, complemented
49#63648C2211yescharacteristic
50#63648C2211yescharacteristic
51#63647C2211yescharacteristic, complemented
52#63641C2211yescharacteristic, complemented
53C8×C3⋊Dic3C2211yescharacteristic, complemented
54#63637C2211yescharacteristic, complemented
55#63636C2211yescharacteristic
56#63636C2211yescharacteristic
57#63636C2211yescharacteristic
58#63636C2211yescharacteristic
59#63634C2211yescharacteristic, complemented
60#5630—34no—
61#5513—34no—
62C3×#483D314yescomplemented
63#5051—34no—
64C2×#809—34no—
65#4871—34no—
66#4866—34no—
67#4864—34no—
68#4852—34no—
69#4808—34no—
70#4804—34no—
71#4800—34no—
72#4798—34no—
73#4731—34no—
74#67⋊C8—34no—
75C23×C3⋊D3—21no—
76C2×C32×Q8C2311yescharacteristic
77C22×C32×C4—21no—
78C22×C32×C4C2311yescharacteristic
79C2×#638D411yescharacteristic
80#3832—22no—
81#3832—41no—
82C2×C4⋊(C3⋊D3)—22no—
83C2×C4⋊(C3⋊D3)—21no—
84C2×C4⋊(C3⋊D3)—21no—
85C2×C4⋊(C3⋊D3)—21no—
86C2×C4⋊(C3⋊D3)—41no—
87C2×C4⋊(C3⋊D3)C2311yescharacteristic
88C2×C4⋊(C3⋊D3)C2311yescharacteristic
89C2×C4×C3⋊D3—21no—
90C2×C4×C3⋊D3—21no—
91C2×C4×C3⋊D3C2311yescharacteristic
92C2×#634C2311yescharacteristic
93C2×C32×C8C2311yescharacteristic
94C2×C32×C8C2311yescharacteristic
95C32×C4⋊C4—21no—
96C32×C4⋊C4—21no—
97C32×C4⋊C4C2311yescharacteristic
98C32×C4⋊C4C2311yescharacteristic
99C32×C4⋊C4C2311yescharacteristic
100C32×C22⋊C4—21no—
101#3757—21no—
102#3757D411yescharacteristic
103#3756—41no—
104#3752—21no—
105#3752—21no—
106#3752—21no—
107#3752—21no—
108#3752—21no—
109#3752—21no—
110#3752D411yescharacteristic
111C4⋊(C3⋊Dic3)—21no—
112C4⋊(C3⋊Dic3)—21no—
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114#3750—21no—
115#3750—21no—
116#3750—21no—
117#3750D411yescharacteristic
118C4×C3⋊Dic3—21no—
119C4×C3⋊Dic3—21no—
120C4×C3⋊Dic3C2311yescharacteristic
121C2×C3⋊(C3⋊C8)—41no—
122C2×C3⋊(C3⋊C8)C2311yescharacteristic
123C2×C3⋊(C3⋊C8)C2311yescharacteristic
124#3744—22no—
125#3744—41no—
126C8×C3⋊D3—41no—
127#3296—91noSylow
128C2×#239—34no—
129C22×D12—34no—
130C3×C22⋊Q8C2×D314yes—
131C2×C3×C4⋊C4C2×D314yes—
132#947—34no—
133C2×#216—34no—
134#929—64no—
135C4×#67—34no—
136#926—64no—
137#924—34no—
138C22×C3⋊C8—34no—
139C2×#204—34no—
140C2×#204—34no—
141C2×D3×C8—34no—
142#898—64no—
143#897—34no—
144#895—34no—
145#895—64no—
146#894—64no—
147#893—34no—
148#892—34no—
149#890—34no—
150#889—64no—
151#887—34no—
152#882—64no—
153D3×C22⋊C4—64no—
154C3×#106C2×D314yescomplemented
155C3×#106C2×D314yescomplemented
156C3×#103C2×D314yescomplemented
157C3×#103C2×D314yescomplemented
158C3×C22⋊C8C2×D314yes—
159#835—34no—
160#821—34no—
161#821—34no—
162(C2×D3)⋊C8—34no—
163Dic3⋊C8—34no—
164C8×Dic3—34no—
165#810—34no—
166#809—34no—
167#809—34no—
168#809—34no—
169#809—34no—
170#807—34no—
171C23×C32C2×D411yescharacteristic
172C22×C3⋊D3—21no—
173C22×C3⋊D3—21no—
174C22×C3⋊D3—42no—
175C22×C3⋊D3—42no—
176C22×C3⋊D3—81no—
177C22×C3⋊D3C2×D411yescharacteristic
178C32×Q8—21no—
179C32×Q8—21no—
180C2×C32×C4—21no—
181C2×C32×C4—21no—
182C2×C32×C4—21no—
183C2×C32×C4—21no—
184C2×C32×C4—21no—
185C2×C32×C4—21no—
186C2×C32×C4—42no—
187C2×C32×C4C2×D411yescharacteristic
188C2×C32×C4C2411yescharacteristic
189#638—22no—
190C2×C3⋊Dic3—21no—
191C2×C3⋊Dic3—21no—
192C2×C3⋊Dic3C2×D411yescharacteristic
193C2×C3⋊Dic3C2×D411yescharacteristic
194C2×C3⋊Dic3C2×D411yescharacteristic
195C4⋊(C3⋊D3)—21no—
196C4⋊(C3⋊D3)—21no—
197C4⋊(C3⋊D3)—21no—
198C4⋊(C3⋊D3)—42no—
199C4⋊(C3⋊D3)—42no—
200C4⋊(C3⋊D3)—81no—
201C4⋊(C3⋊D3)#4112yes—
202C4×C3⋊D3—21no—
203C4×C3⋊D3—21no—
204C4×C3⋊D3—42no—
205C4×C3⋊D3—81no—
206#634—21no—
207#634—21no—
208C32×C8—21no—
209C32×C8—21no—
210C3⋊(C3⋊C8)—21no—
211C3⋊(C3⋊C8)—21no—
212#552—91no—
213#546—91no—
214#488—91no—
215#483C3⋊D311yescharacteristic, complemented
216#482—91no—
217#478—91no—
218#467—91no—
219#465—91no—
220#464—91no—
221#452—91no—
222#450—91no—
223C4×SD16—91no—
224C8×D4—91no—
225#416—91no—
226C2×#102—91no—
227C23×D3—64no—
228C2×C3×Q8C22×D314yes—
229C22×C3×C4—24no—
230C22×C3×C4C22×D314yes—
231C2×#67—34no—
232#239—68no—
233#239—124no—
234C2×D12—34no—
235C2×D12—34no—
236C2×D12—68no—
237C2×D12—64no—
238C2×D12—64no—
239C2×D12—64no—
240C2×D12—124no—
241C2×C4×D3—34no—
242C2×C4×D3—64no—
243C2×C4×D3—64no—
244C2×Dic6—34no—
245C2×C3×C8C22×D314yes—
246C2×C3×C8C22×D314yes—
247C3×C4⋊C4—24no—
248C3×C4⋊C4—24no—
249C3×C4⋊C4C22×D314yes—
250C3×C4⋊C4C22×D314yes—
251C3×C4⋊C4C22×D314yes—
252C3×C22⋊C4—24no—
253#217—34no—
254#217—64no—
255#216—124no—
256(C2×D3)⋊C4—34no—
257(C2×D3)⋊C4—64no—
258(C2×D3)⋊C4—64no—
259(C2×D3)⋊C4—64no—
260(C2×D3)⋊C4—64no—
261(C2×D3)⋊C4—64no—
262(C2×D3)⋊C4—64no—
263C4⋊Dic3—34no—
264C4⋊Dic3—64no—
265C4⋊Dic3—64no—
266Dic3⋊C4—34no—
267Dic3⋊C4—64no—
268Dic3⋊C4—64no—
269Dic3⋊C4—64no—
270C4×Dic3—34no—
271C4×Dic3—64no—
272C4×Dic3—64no—
273C2×C3⋊C8—34no—
274C2×C3⋊C8—34no—
275C2×C3⋊C8—124no—
276#204—68no—
277#204—124no—
278D3×C8—124no—
279C22×C32—21no—
280C22×C32—21no—
281C22×C32#13512yes—
282C22×C32C22×D411yescharacteristic
283C2×C3⋊D3—21no—
284C2×C3⋊D3—22no—
285C2×C3⋊D3—21no—
286C2×C3⋊D3—21no—
287C2×C3⋊D3—41no—
288C2×C3⋊D3—41no—
289C2×C3⋊D3—41no—
290C2×C3⋊D3—41no—
291C2×C3⋊D3—41no—
292C2×C3⋊D3—84no—
293C32×C4—21no—
294C32×C4—41no—
295C32×C4—41no—
296C32×C4—41no—
297C32×C4—41no—
298C32×C4C2×#4111yescharacteristic
299C32×C4H(5,𝔽2)11yescharacteristic
300C3⋊Dic3—21no—
301C3⋊Dic3—21no—
302C3⋊Dic3—21no—
303C3⋊Dic3—41no—
304C3⋊Dic3—41no—
305C2×#41—91no—
306C22×D4—91no—
307C2×Q16—91no—
308C2×SD16—91no—
309C2×SD16—91no—
310C22×C8—91no—
311C22×C8—91no—
312#126—181no—
313#125—91no—
314#125—181no—
315#124—91no—
316#123—181no—
317#123—181no—
318C22⋊Q8—91no—
319C22⋊Q8—91no—
320C22⋊Q8C2×C3⋊D311yescharacteristic
321#121—91no—
322#121—181no—
323#120—181no—
324C4×Q8—91no—
325C4×D4—91no—
326C4×D4—91no—
327#117—91no—
328#117—181no—
329C2×C4⋊C4C2×C3⋊D311yescharacteristic
330C2×C22⋊C4—181no—
331#107—91no—
332#106C2×C3⋊D311yescharacteristic, complemented
333#106C2×C3⋊D311yescharacteristic, complemented
334C4⋊C8—91no—
335#103—91no—
336#103—91no—
337#103C2×C3⋊D311yescharacteristic, complemented
338#103C2×C3⋊D311yescharacteristic, complemented
339#102—91no—
340#102—91no—
341#102—91no—
342#102—91no—
343#102—91no—
344#102—91no—
345C22⋊C8—91no—
346C22⋊C8C2×C3⋊D311yescharacteristic
347C4×C8—91no—
348C23×C3D3×D414yes—
349C22×D3—34no—
350C22×D3—64no—
351C22×D3—64no—
352C22×D3—128no—
353C22×D3—128no—
354C22×D3—244no—
355C3×Q8—24no—
356C3×Q8—24no—
357C2×C3×C4—24no—
358C2×C3×C4—24no—
359C2×C3×C4—24no—
360C2×C3×C4—24no—
361C2×C3×C4—24no—
362C2×C3×C4—24no—
363C2×C3×C4—48no—
364C2×C3×C4D3×D414yes—
365C2×C3×C4C23×D314yes—
366#67—68no—
367C2×Dic3—34no—
368C2×Dic3—34no—
369C2×Dic3—34no—
370C2×Dic3—64no—
371C2×Dic3—64no—
372D12—38no—
373D12—64no—
374D12—64no—
375D12—64no—
376D12—128no—
377D12—128no—
378D12—244no—
379C4×D3—64no—
380C4×D3—64no—
381C4×D3—128no—
382C4×D3—244no—
383Dic6—64no—
384Dic6—64no—
385C3×C8—24no—
386C3×C8—24no—
387C3⋊C8—64no—
388C3⋊C8—64no—
389C2×C32—22no—
390C2×C32#54611yescharacteristic
391C2×C32C2×#13511yescharacteristic
392C2×C32#57711yescharacteristic
393C3⋊D3—41no—
394C3⋊D3—42no—
395C3⋊D3—81no—
396C24—181no—
397#41—182no—
398#41—361no—
399C2×Q8—91no—
400C2×Q8C22×C3⋊D311yescharacteristic
401C2×D4—91no—
402C2×D4—91no—
403C2×D4—91no—
404C2×D4—182no—
405C2×D4—181no—
406C2×D4—181no—
407C2×D4—181no—
408C2×D4—361no—
409C22×C4—21no—
410C22×C4—91no—
411C22×C4—181no—
412C22×C4—181no—
413C22×C4C22×C3⋊D311yescharacteristic
414Q16—361no—
415SD16—182no—
416SD16—361no—
417C2×C8—91no—
418C2×C8—91no—
419C2×C8—361no—
420C2×C8—361no—
421C2×C8C22×C3⋊D311yescharacteristic
422C2×C8C22×C3⋊D311yescharacteristic
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—91no—
426C4⋊C4—91no—
427C4⋊C4—181no—
428C4⋊C4—181no—
429C4⋊C4—181no—
430C4⋊C4—181no—
431C4⋊C4—181no—
432C4⋊C4C22×C3⋊D311yescharacteristic
433C4⋊C4C22×C3⋊D311yescharacteristic
434C4⋊C4C22×C3⋊D311yescharacteristic
435C22⋊C4—21no—
436C22⋊C4—91no—
437C22⋊C4—91no—
438C22⋊C4—181no—
439C22⋊C4—181no—
440C22⋊C4—181no—
441C22⋊C4—181no—
442C22⋊C4—181no—
443C22⋊C4—181no—
444C22⋊C4—181no—
445C42—91no—
446C42—181no—
447C42—181no—
448C22×C3—24no—
449C22×C3—24no—
450C22×C3#91618yes—
451C22×C3C2×D3×D414yes—
452C2×D3—64no—
453C2×D3—68no—
454C2×D3—64no—
455C2×D3—64no—
456C2×D3—124no—
457C2×D3—124no—
458C2×D3—124no—
459C2×D3—124no—
460C2×D3—124no—
461C2×D3—2416no—
462C3×C4—24no—
463C3×C4—44no—
464C3×C4—44no—
465C3×C4—44no—
466C3×C4—44no—
467C3×C4D3×#4114yes—
468C3×C4#100914yes—
469Dic3—64no—
470Dic3—64no—
471Dic3—64no—
472Dic3—124no—
473Dic3—124no—
474C32#329611yescharacteristic, complemented, Sylow
475C23—91no—
476C23—181no—
477C23—181no—
478C23—362no—
479C23—362no—
480C23—721no—
481C23D4×C3⋊D311yescharacteristic
482Q8—21no—
483Q8—21no—
484Q8—181no—
485Q8—181no—
486D4—92no—
487D4—182no—
488D4—181no—
489D4—181no—
490D4—181no—
491D4—362no—
492D4—362no—
493D4—721no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—42no—
501C2×C4—91no—
502C2×C4—91no—
503C2×C4—91no—
504C2×C4—181no—
505C2×C4—181no—
506C2×C4—181no—
507C2×C4—181no—
508C2×C4—362no—
509C2×C4—721no—
510C2×C4D4×C3⋊D311yescharacteristic
511C2×C4C23×C3⋊D311yescharacteristic
512C8—21no—
513C8—21no—
514C8—181no—
515C8—181no—
516C2×C3—28no—
517C2×C3#565414yes—
518C2×C3C2×#91614yes—
519C2×C3#577814yes—
520D3—124no—
521D3—128no—
522D3—244no—
523C22—21no—
524C22—21no—
525C22—181no—
526C22—182no—
527C22—181no—
528C22—181no—
529C22—361no—
530C22—361no—
531C22—361no—
532C22—361no—
533C22—361no—
534C22—724no—
535C22#6412512yes—
536C22C2×D4×C3⋊D311yescharacteristic
537C4—21no—
538C4—41no—
539C4—41no—
540C4—41no—
541C4—41no—
542C4—181no—
543C4—181no—
544C4—181no—
545C4—361no—
546C4—361no—
547C4#41×C3⋊D311yescharacteristic
548C4#6436611yescharacteristic
549C3#8144514yescomplemented
550C2—22no—
551C2—361no—
552C2—362no—
553C2—721no—
554C2#1059612511yescharacteristic
555C2C2×#6412511yescharacteristic
556C2#1059624911yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#483C2
socleC22×C32C22×D4
prime radical#10596101C2
hypercenter#483C3⋊D3
hypocenterC32#3296
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
2. #10595984C2semidirect
3. C32×#483C2semidirect
4. #10592750C2semidirect
5. C2×#63636C2semidirect
6. #10592570C2semidirect
7. #10592565C2semidirect
8. #10592563C2semidirect
9. #10592551C2semidirect
10. #10592507C2semidirect
11. #10592503C2semidirect
12. #10592499C2semidirect
13. #10592497C2semidirect
14. #10592430C2semidirect
15. #10592424C2semidirect
22. C2×#3756C22semidirect
30. C2×C8×C3⋊D3C22semidirect
32. #64106C22semidirect
37. #64101C22semidirect
38. #64099C22semidirect
40. #64096C22semidirect
43. C32×#106C22semidirect
44. C32×#106C22semidirect
45. C32×#103C22semidirect
46. C32×#103C22semidirect
48. #63662C22semidirect
51. #63647C22semidirect
52. #63641C22semidirect
53. C8×C3⋊Dic3C22semidirect
54. #63637C22semidirect
59. #63634C22semidirect
62. C3×#483D3semidirect
154. C3×#106C2×D3semidirect
155. C3×#106C2×D3semidirect
156. C3×#103C2×D3semidirect
157. C3×#103C2×D3semidirect
215. #483C3⋊D3semidirect
332. #106C2×C3⋊D3semidirect
333. #106C2×C3⋊D3semidirect
337. #103C2×C3⋊D3semidirect
338. #103C2×C3⋊D3semidirect
474. C32#3296semidirect
549. C3#81445semidirect

Maximal subgroups

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

subgroupindex
#105961012
#105959842
C32×#4832
#105927502
C2×#636362
#105925702
#105925652
#105925632
#105925512
#105925072
#105925032
#105924992
#105924972
#105924302
#105924242
#814453