Finite Group Databasebeta

← #11864113

Subgroups — #11864113

Order 1152.

2418 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
1C22×#3832C211yesmaximal, characteristic, complemented
2C2×#64123C212yesmaximal, complemented
3C3⋊D3×#121C211yesmaximal, characteristic, complemented
4C32×#448C211yesmaximal, characteristic, complemented
5#10592926C211yesmaximal, characteristic, complemented
6#10592871C212yesmaximal, complemented
7#10592735C211yesmaximal, characteristic, complemented
8#10592509C212yesmaximal, complemented
9#10592502C212yesmaximal, complemented
10#10592431C211yesmaximal, characteristic, complemented
11#10592425C211yesmaximal, characteristic, complemented
12#80040—34nomaximal
13C22×C32×Q8C2211yescharacteristic, complemented
14C2×#3832—28no—
15C2×#3832—21no—
16C2×#3832—21no—
17C2×#3832C2212yes—
18C2×#3832C2212yescomplemented
19C2×D4×C3⋊D3—21no—
20C2×D4×C3⋊D3C2211yescharacteristic, complemented
21C22×C4⋊(C3⋊D3)—21no—
22C22×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
23C22×C4×C3⋊D3—21no—
24C22×C4×C3⋊D3C2211yescharacteristic
25C2×C32×SD16C2212yescomplemented
26C32×#121C2211yescharacteristic
27C2×#3755C2212yescomplemented
28#64148—21no—
29#64147C2211yescharacteristic, complemented
30C2×#3753C2212yescomplemented
31#64139C2211yescharacteristic
32#64123—28no—
33C2×#3745C2212yescomplemented
34C2×#3743C2212yescomplemented
35#64104C2211yescharacteristic, complemented
36C4⋊C4×C3⋊D3C2211yescharacteristic, complemented
37#64093—21no—
38C22⋊C4×C3⋊D3—21no—
39C32×#103C2212yescomplemented
40C32×C22⋊C8C2211yescharacteristic, complemented
41#63662C2212yescomplemented
42#63657C2211yescharacteristic, complemented
43#63648C2212yescomplemented
44#63647C2212yescomplemented
45#63636C2212yescomplemented
46C22×#239—34no—
47C2×#914—38no—
48D3×#121—34no—
49C3×#448D314yescomplemented
50#5227—34no—
51#5172—38no—
52#5036—34no—
53#4810—38no—
54#4803—38no—
55#4732—34no—
56#4726—34no—
57C23×C3⋊D3—21no—
58C23×C3⋊D3—21no—
59C23×C3⋊D3D411yescharacteristic
60C2×C32×Q8—24no—
61C2×C32×Q8—21no—
62C2×C32×Q8C2312yes—
63C2×C32×D4—21no—
64C2×C32×D4C2311yescharacteristic
65C22×C32×C4—21no—
66C22×C32×C4C2311yescharacteristic
67C2×#638—21no—
68C2×#638—21no—
69C2×#638—21no—
70C22×C3⋊Dic3D411yescharacteristic
71#3832—28no—
72#3832—28no—
73#3832—24no—
74#3832—24no—
75#3832—24no—
76#3832D418yescomplemented
77D4×C3⋊D3—24no—
78D4×C3⋊D3—44no—
79C2×C4⋊(C3⋊D3)—28no—
80C2×C4⋊(C3⋊D3)—22no—
81C2×C4⋊(C3⋊D3)—22no—
82C2×C4⋊(C3⋊D3)—21no—
83C2×C4⋊(C3⋊D3)—24no—
84C2×C4⋊(C3⋊D3)—21no—
85C2×C4⋊(C3⋊D3)C2311yescharacteristic
86C2×C4⋊(C3⋊D3)C2312yes—
87C2×C4×C3⋊D3—28no—
88C2×C4×C3⋊D3—22no—
89C2×C4×C3⋊D3—22no—
90C2×C4×C3⋊D3—24no—
91C2×C4×C3⋊D3—21no—
92C2×C4×C3⋊D3D411yescharacteristic
93C2×C4×C3⋊D3D411yescharacteristic
94C2×C4×C3⋊D3C2311yescharacteristic
95C2×C4×C3⋊D3C2311yescharacteristic
96C32×SD16—24no—
97C2×C32×C8C2312yes—
98C32×C4⋊C4C2311yescharacteristic
99C32×C22⋊C4—21no—
100#3757—21no—
101#3755—24no—
102#3753—24no—
103#3752—21no—
104#3752—21no—
105C4⋊(C3⋊Dic3)C2311yescharacteristic
106#3750—21no—
107C2×C3⋊(C3⋊C8)C2312yes—
108#3745—24no—
109#3743—24no—
110#3006—91noSylow
111C22×C3×Q8C2×D314yescomplemented
112C2×#239—38no—
113C2×#239—38no—
114C2×#239—64no—
115C2×#239—64no—
116C2×#239—632no—
117C2×D3×D4—34no—
118C2×D3×D4—64no—
119C22×D12—34no—
120C22×D12—64no—
121C22×C4×D3—34no—
122C22×C4×D3—64no—
123C2×C3×SD16C2×D318yescomplemented
124C3×#121C2×D314yes—
125C2×#215—38no—
126#939—64no—
127#938—34no—
128C2×#213—38no—
129#930—34no—
130#914—632no—
131C2×D24—38no—
132C2×ΓL(1,𝔽25)—38no—
133#895—34no—
134D3×C4⋊C4—34no—
135#884—64no—
136D3×C22⋊C4—64no—
137C3×#103C2×D318yescomplemented
138C3×C22⋊C8C2×D314yescomplemented
139#835—38no—
140#830—34no—
141#821—38no—
142(C2×D3)⋊C8—38no—
143#809—38no—
144C23×C32—21no—
145C23×C32C2×D411yescharacteristic
146C22×C3⋊D3—24no—
147C22×C3⋊D3—22no—
148C22×C3⋊D3—22no—
149C22×C3⋊D3—22no—
150C22×C3⋊D3—21no—
151C22×C3⋊D3—41no—
152C22×C3⋊D3—42no—
153C22×C3⋊D3—42no—
154C22×C3⋊D3—42no—
155C22×C3⋊D3—42no—
156C22×C3⋊D3—42no—
157C22×C3⋊D3C2×D411yescharacteristic
158C22×C3⋊D3C2×D411yescharacteristic
159C32×Q8—24no—
160C32×Q8—22no—
161C32×Q8C2×D414yescomplemented
162C32×D4—22no—
163C32×D4—42no—
164C2×C32×C4—24no—
165C2×C32×C4—22no—
166C2×C32×C4—22no—
167C2×C32×C4—21no—
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4C2411yescharacteristic
170#638—42no—
171#638—42no—
172#638—42no—
173C2×C3⋊Dic3—22no—
174C2×C3⋊Dic3—21no—
175C2×C3⋊Dic3C2×D411yescharacteristic
176C2×C3⋊Dic3C2×D411yescharacteristic
177C4⋊(C3⋊D3)—28no—
178C4⋊(C3⋊D3)—24no—
179C4⋊(C3⋊D3)—28no—
180C4⋊(C3⋊D3)—22no—
181C4⋊(C3⋊D3)—22no—
182C4⋊(C3⋊D3)—42no—
183C4⋊(C3⋊D3)C2×D414yescomplemented
184C4×C3⋊D3—28no—
185C4×C3⋊D3—22no—
186C4×C3⋊D3—22no—
187C4×C3⋊D3—28no—
188C4×C3⋊D3—22no—
189C4×C3⋊D3—42no—
190C4×C3⋊D3C2×D414yes—
191C32×C8—22no—
192C3⋊(C3⋊C8)—22no—
193C22×#41—91no—
194C2×AGL(1,ℤ/8)—92no—
195C2×#121—91no—
196#449—92no—
197#449—92no—
198#448—91no—
199#448C3⋊D311yescharacteristic, complemented
200#447—91no—
201#447—91no—
202#417—92no—
203#407—91no—
204C23×D3—34no—
205C23×D3—64no—
206C23×D3—64no—
207C2×C3×Q8—216no—
208C2×C3×Q8—24no—
209C2×C3×Q8C22×D318yes—
210C2×C3×D4—24no—
211C2×C3×D4C22×D314yes—
212C22×C3×C4—24no—
213C22×C3×C4C22×D314yes—
214C2×#67—64no—
215C2×#67—64no—
216C2×#67—64no—
217C22×Dic3—34no—
218#239—332no—
219#239—616no—
220#239—616no—
221#239—632no—
222#239—632no—
223#239—616no—
224D3×D4—616no—
225D3×D4—1216no—
226C2×D12—38no—
227C2×D12—34no—
228C2×D12—616no—
229C2×D12—68no—
230C2×D12—68no—
231C2×D12—632no—
232C2×D12—64no—
233C2×D12—64no—
234C2×C4×D3—34no—
235C2×C4×D3—34no—
236C2×C4×D3—34no—
237C2×C4×D3—34no—
238C2×C4×D3—616no—
239C2×C4×D3—68no—
240C2×C4×D3—68no—
241C2×C4×D3—632no—
242C2×C4×D3—64no—
243C3×SD16—216no—
244C2×C3×C8C22×D318yes—
245C3×C4⋊C4C22×D314yes—
246C3×C22⋊C4—24no—
247#217—64no—
248#215—616no—
249#213—616no—
250(C2×D3)⋊C4—64no—
251(C2×D3)⋊C4—64no—
252C4⋊Dic3—34no—
253Dic3⋊C4—64no—
254C2×C3⋊C8—38no—
255D24—616no—
256ΓL(1,𝔽25)—616no—
257C22×C32—21no—
258C22×C32—21no—
259C22×C32—41no—
260C22×C32—41no—
261C22×C32—41no—
262C22×C32AGL(1,ℤ/8)12yescomplemented
263C22×C32C22×D411yescharacteristic
264C2×C3⋊D3—21no—
265C2×C3⋊D3—21no—
266C2×C3⋊D3—21no—
267C2×C3⋊D3—24no—
268C2×C3⋊D3—21no—
269C2×C3⋊D3—21no—
270C2×C3⋊D3—44no—
271C2×C3⋊D3—48no—
272C2×C3⋊D3—42no—
273C2×C3⋊D3—42no—
274C2×C3⋊D3—41no—
275C2×C3⋊D3—41no—
276C2×C3⋊D3—41no—
277C2×C3⋊D3—84no—
278C2×C3⋊D3#12012yes—
279C32×C4—24no—
280C32×C4—21no—
281C32×C4—41no—
282C32×C4C22×D412yes—
283C3⋊Dic3—21no—
284C3⋊Dic3—41no—
285C3⋊Dic3#12012yes—
286C2×#41—92no—
287C2×#41—92no—
288C2×#41—181no—
289C2×#41—181no—
290C2×#41—188no—
291C22×Q8C2×C3⋊D311yescharacteristic, complemented
292C22×D4—91no—
293C22×D4—91no—
294C22×D4—181no—
295C22×D4—181no—
296C23×C4—91no—
297C23×C4—181no—
298AGL(1,ℤ/8)—188no—
299C2×SD16—92no—
300C2×SD16C2×C3⋊D312yescomplemented
301C2×D8—92no—
302C2×D8—92no—
303C2×M16—92no—
304#121—91no—
305#121—91no—
306#121—91no—
307#121—181no—
308#121—181no—
309#121C2×C3⋊D311yescharacteristic
310C2×C4⋊C4—91no—
311C2×C22⋊C4—181no—
312#103—92no—
313#103C2×C3⋊D312yescomplemented
314#102—92no—
315#102—92no—
316C22⋊C8—91no—
317C22⋊C8—92no—
318C22⋊C8C2×C3⋊D311yescharacteristic, complemented
319C23×C3—24no—
320C23×C3D3×D414yes—
321C22×D3—34no—
322C22×D3—34no—
323C22×D3—68no—
324C22×D3—616no—
325C22×D3—68no—
326C22×D3—68no—
327C22×D3—64no—
328C22×D3—128no—
329C22×D3—124no—
330C22×D3—128no—
331C22×D3—128no—
332C22×D3—128no—
333C22×D3—128no—
334C3×Q8—216no—
335C3×Q8—28no—
336C3×Q8D3×D4116yescomplemented
337C3×D4—28no—
338C3×D4—48no—
339C2×C3×C4—216no—
340C2×C3×C4—28no—
341C2×C3×C4—28no—
342C2×C3×C4—24no—
343C2×C3×C4D3×D414yes—
344C2×C3×C4C23×D314yes—
345#67—128no—
346#67—128no—
347#67—128no—
348C2×Dic3—34no—
349C2×Dic3—34no—
350C2×Dic3—68no—
351C2×Dic3—64no—
352D12—316no—
353D12—632no—
354D12—632no—
355D12—616no—
356D12—68no—
357D12—68no—
358D12—128no—
359C4×D3—316no—
360C4×D3—68no—
361C4×D3—632no—
362C4×D3—68no—
363C4×D3—632no—
364C4×D3—68no—
365C4×D3—128no—
366C3×C8—28no—
367C3⋊C8—68no—
368C2×C32—22no—
369C2×C32—81no—
370C2×C32C2×#12011yescharacteristic
371C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
372C2×C32#57511yescharacteristic
373C3⋊D3—22no—
374C3⋊D3—41no—
375C3⋊D3—44no—
376C3⋊D3—81no—
377C24—91no—
378C24—181no—
379C24—181no—
380#41—98no—
381#41—184no—
382#41—184no—
383#41—188no—
384#41—188no—
385#41—184no—
386C2×Q8—24no—
387C2×Q8—21no—
388C2×Q8C22×C3⋊D312yes—
389C2×D4—21no—
390C2×D4—92no—
391C2×D4—91no—
392C2×D4—184no—
393C2×D4—182no—
394C2×D4—182no—
395C2×D4—188no—
396C2×D4—181no—
397C2×D4—184no—
398C2×D4—181no—
399C2×D4—181no—
400C2×D4—181no—
401C2×D4—181no—
402C2×D4—364no—
403C2×D4C22×C3⋊D311yescharacteristic
404C22×C4—21no—
405C22×C4—91no—
406C22×C4—91no—
407C22×C4—91no—
408C22×C4—91no—
409C22×C4—91no—
410C22×C4—184no—
411C22×C4—182no—
412C22×C4—182no—
413C22×C4—188no—
414C22×C4—181no—
415C22×C4C22×C3⋊D311yescharacteristic
416SD16—24no—
417SD16—184no—
418D8—184no—
419D8—184no—
420M16—184no—
421C2×C8—92no—
422C2×C8C22×C3⋊D312yes—
423C4⋊C4—91no—
424C4⋊C4—181no—
425C4⋊C4C22×C3⋊D311yescharacteristic
426C22⋊C4—21no—
427C22⋊C4—181no—
428C22⋊C4—181no—
429C22⋊C4—181no—
430C22×C3—24no—
431C22×C3—24no—
432C22×C3—44no—
433C22×C3—44no—
434C22×C3—44no—
435C22×C3#91418yescomplemented
436C22×C3C2×D3×D414yes—
437C2×D3—38no—
438C2×D3—64no—
439C2×D3—64no—
440C2×D3—64no—
441C2×D3—64no—
442C2×D3—616no—
443C2×D3—64no—
444C2×D3—1216no—
445C2×D3—1232no—
446C2×D3—128no—
447C2×D3—128no—
448C2×D3—124no—
449C2×D3—124no—
450C2×D3—124no—
451C2×D3—2416no—
452C3×C4—216no—
453C3×C4—24no—
454C3×C4—44no—
455C3×C4C2×D3×D418yes—
456Dic3—38no—
457Dic3—64no—
458Dic3—124no—
459C32#300611yescharacteristic, complemented, Sylow
460C23—21no—
461C23—91no—
462C23—91no—
463C23—182no—
464C23—184no—
465C23—182no—
466C23—182no—
467C23—181no—
468C23—361no—
469C23—362no—
470C23—362no—
471C23—362no—
472C23—362no—
473C23—362no—
474C23D4×C3⋊D311yescharacteristic
475Q8—24no—
476Q8—22no—
477Q8D4×C3⋊D314yescomplemented
478D4—22no—
479D4—42no—
480D4—94no—
481D4—188no—
482D4—188no—
483D4—184no—
484D4—182no—
485D4—182no—
486D4—362no—
487D4—362no—
488D4—362no—
489D4—362no—
490C2×C4—24no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—21no—
494C2×C4—91no—
495C2×C4—94no—
496C2×C4—91no—
497C2×C4—182no—
498C2×C4—188no—
499C2×C4—182no—
500C2×C4—188no—
501C2×C4—182no—
502C2×C4—182no—
503C2×C4—181no—
504C2×C4—362no—
505C2×C4D4×C3⋊D311yescharacteristic
506C2×C4C23×C3⋊D311yescharacteristic
507C8—22no—
508C8—182no—
509C2×C3—28no—
510C2×C3—84no—
511C2×C3D3×#12014yes—
512C2×C3C2×#91414yes—
513C2×C3#577714yes—
514D3—68no—
515D3—124no—
516D3—1216no—
517D3—244no—
518C22—21no—
519C22—21no—
520C22—41no—
521C22—41no—
522C22—41no—
523C22—92no—
524C22—181no—
525C22—181no—
526C22—181no—
527C22—181no—
528C22—184no—
529C22—181no—
530C22—364no—
531C22—368no—
532C22—362no—
533C22—362no—
534C22—361no—
535C22—361no—
536C22—361no—
537C22—724no—
538C22#6412312yescomplemented
539C22C2×D4×C3⋊D311yescharacteristic
540C4—24no—
541C4—21no—
542C4—41no—
543C4—92no—
544C4—181no—
545C4—361no—
546C4C2×D4×C3⋊D312yes—
547C3#8004014yescomplemented
548C2—22no—
549C2—81no—
550C2—182no—
551C2—361no—
552C2—364no—
553C2—721no—
554C2C3⋊D3×#12011yescharacteristic
555C2C2×#6412311yescharacteristic
556C2#1059624811yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#448C2
socleC22×C32C22×D4
hypercenter#448C3⋊D3
hypocenterC32#3006
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
1. C22×#3832C2semidirect
2. C2×#64123C2semidirect
3. C3⋊D3×#121C2semidirect
4. C32×#448C2semidirect
5. #10592926C2semidirect
6. #10592871C2semidirect
7. #10592735C2semidirect
8. #10592509C2semidirect
9. #10592502C2semidirect
10. #10592431C2semidirect
11. #10592425C2semidirect
13. C22×C32×Q8C22semidirect
18. C2×#3832C22semidirect
20. C2×D4×C3⋊D3C22semidirect
22. C22×C4⋊(C3⋊D3)C22semidirect
25. C2×C32×SD16C22semidirect
27. C2×#3755C22semidirect
29. #64147C22semidirect
30. C2×#3753C22semidirect
33. C2×#3745C22semidirect
34. C2×#3743C22semidirect
35. #64104C22semidirect
36. C4⋊C4×C3⋊D3C22semidirect
39. C32×#103C22semidirect
40. C32×C22⋊C8C22semidirect
41. #63662C22semidirect
42. #63657C22semidirect
43. #63648C22semidirect
44. #63647C22semidirect
45. #63636C22semidirect
49. C3×#448D3semidirect
76. #3832D4semidirect
111. C22×C3×Q8C2×D3semidirect
123. C2×C3×SD16C2×D3semidirect
137. C3×#103C2×D3semidirect
138. C3×C22⋊C8C2×D3semidirect
161. C32×Q8C2×D4semidirect
183. C4⋊(C3⋊D3)C2×D4semidirect
199. #448C3⋊D3semidirect
262. C22×C32AGL(1,ℤ/8)semidirect
291. C22×Q8C2×C3⋊D3semidirect
300. C2×SD16C2×C3⋊D3semidirect
313. #103C2×C3⋊D3semidirect
318. C22⋊C8C2×C3⋊D3semidirect
336. C3×Q8D3×D4semidirect
435. C22×C3#914semidirect
459. C32#3006semidirect
477. Q8D4×C3⋊D3semidirect
538. C22#64123semidirect
547. C3#80040semidirect

Maximal subgroups

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

subgroupindex
C22×#38322
C2×#641232
C3⋊D3×#1212
C32×#4482
#105929262
#105928712
#105927352
#105925092
#105925022
#105924312
#105924252
#800403