Finite Group Databasebeta

← #11901177

Subgroups — #11901177

Order 1152.

4668 conjugacy classes of subgroups.

The subgroup lattice has 513 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×C3⋊D3C212yesmaximal, complemented
2C32×#537C211yesmaximal, characteristic, complemented
3#10596304C212yesmaximal, complemented
4#10596099C214yesmaximal, complemented
5#10596098C214yesmaximal, complemented
6#10596078C214yesmaximal, complemented
7#10596077C214yesmaximal, complemented
8#10596076C214yesmaximal, complemented
9#10596067C214yesmaximal, complemented
10#10595981C211yesmaximal, characteristic, complemented
11C2×#64101C211yesmaximal, characteristic, complemented
12#86363—34nomaximal
13C2×C32×#41C2212yescomplemented
14#41×C3⋊D3—216no—
15C2×#3832C2212yes—
16C2×Q8×C3⋊D3C2212yescomplemented
17C2×#3830C2212yes—
18C2×#3830C2214yescomplemented
19C2×D4×C3⋊D3C2214yes—
20C2×D4×C3⋊D3C2212yescomplemented
21C2×#3828C2214yes—
22C2×#3828C2212yescomplemented
23C22×C4×C3⋊D3C2211yescharacteristic
24C22×C4×C3⋊D3C2214yescomplemented
25C32×C22⋊Q8C2214yescomplemented
26C32×#121C2214yescomplemented
27C32×#121C2214yescomplemented
28C2×C32×C4⋊C4C2211yescharacteristic, complemented
29#64155C2214yescomplemented
30#64149C2214yescomplemented
31#64148C2218yescomplemented
32#64147C2214yescomplemented
33#64146C2218yescomplemented
34D4×C3⋊Dic3C2214yescomplemented
35#64139C2214yescomplemented
36#64139C2214yescomplemented
37C2×#3752C2212yes—
38C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
39#64133C2214yescomplemented
40C2×C4×C3⋊Dic3C2212yescomplemented
41#64106C2214yescomplemented
42#64104C2214yescomplemented
43#64103C2218yescomplemented
44#64102C2214yescomplemented
45#64101C2214yescomplemented
46#64101C2214yescomplemented
47#64097C2214yescomplemented
48#64094C2218yescomplemented
49#64092C2218yescomplemented
50#64091C2218yescomplemented
51#64090C2218yescomplemented
52C2×D3×#41—38no—
53C3×#537D314yescomplemented
54#5833—38no—
55#5628—316no—
56#5627—316no—
57#5607—316no—
58#5606—316no—
59#5605—316no—
60#5596—316no—
61#5510—34no—
62C2×#892—34no—
63C23×C3⋊D3C2314yes—
64C23×C3⋊D3C2311yescharacteristic
65C32×#41—28no—
66C2×C32×Q8C2312yes—
67C2×C32×D4C2314yes—
68C2×C32×D4C2312yes—
69C2×C32×D4C2314yes—
70C22×C32×C4C2314yes—
71C22×C32×C4C2312yes—
72C22×C32×C4C2311yescharacteristic
73C2×#638C2314yes—
74C2×#638C2314yes—
75C2×#638C2314yes—
76C2×#638C2318yes—
77C22×C3⋊Dic3C2314yes—
78C22×C3⋊Dic3C2312yes—
79C22×C3⋊Dic3C2311yescharacteristic
80#3832—28no—
81Q8×C3⋊D3—28no—
82#3830—216no—
83#3830—28no—
84D4×C3⋊D3—216no—
85D4×C3⋊D3—28no—
86#3828—28no—
87#3828—216no—
88C2×C4⋊(C3⋊D3)C2314yes—
89C2×C4⋊(C3⋊D3)C2312yes—
90C2×C4⋊(C3⋊D3)C2314yes—
91C2×C4×C3⋊D3—216no—
92C2×C4×C3⋊D3D418yescomplemented
93C2×C4×C3⋊D3C2314yes—
94C2×C4×C3⋊D3C2314yes—
95C2×C4×C3⋊D3C2314yes—
96C2×C4×C3⋊D3C2312yes—
97C2×C4×C3⋊D3C2312yes—
98C2×#634C2314yes—
99C2×#634C2312yes—
100C32×C4⋊C4C2314yes—
101C32×C4⋊C4C2314yes—
102C32×C22⋊C4C2318yes—
103#3757C2318yes—
104#3752C2318yes—
105#3752C2318yes—
106#3752C2318yes—
107C4⋊(C3⋊Dic3)C2314yes—
108C4⋊(C3⋊Dic3)C2314yes—
109#3750C2318yes—
110C4×C3⋊Dic3C2314yes—
111C4×C3⋊Dic3C2314yes—
112#3449—91noSylow
113C2×C3×#41C2×D318yescomplemented
114D3×#41—664no—
115C2×#239—38no—
116C2×D3×Q8—38no—
117C2×#237—38no—
118C2×#237—316no—
119C2×D3×D4—316no—
120C2×D3×D4—38no—
121C2×#235—316no—
122C2×#235—38no—
123C22×C4×D3—34no—
124C22×C4×D3—316no—
125C3×C22⋊Q8C2×D3116yescomplemented
126C3×#121C2×D3116yescomplemented
127C3×#121C2×D3116yescomplemented
128C2×C3×C4⋊C4C2×D314yescomplemented
129#946—316no—
130#940—316no—
131#939—332no—
132#938—316no—
133#937—332no—
134D4×Dic3—316no—
135#930—316no—
136#930—316no—
137C2×(C2×D3)⋊C4—38no—
138C2×C4⋊Dic3—34no—
139#924—316no—
140C2×C4×Dic3—38no—
141#897—316no—
142#895—316no—
143#894—332no—
144#893—316no—
145#892—316no—
146#892—316no—
147#888—316no—
148#885—332no—
149#883—332no—
150#882—332no—
151#67⋊C4—332no—
152C23×C32C2414yes—
153C23×C32C2411yescharacteristic
154C22×C3⋊D3—28no—
155C22×C3⋊D3—41no—
156C22×C3⋊D3—41no—
157C22×C3⋊D3—44no—
158C22×C3⋊D3—44no—
159C22×C3⋊D3C2×D414yes—
160C22×C3⋊D3C2414yes—
161C22×C3⋊D3C2412yes—
162C32×Q8—24no—
163C32×D4—28no—
164C32×D4—24no—
165C32×D4—44no—
166C2×C32×C4—28no—
167C2×C32×C4—42no—
168C2×C32×C4C2×D414yes—
169C2×C32×C4C2414yes—
170C2×C32×C4C2414yes—
171C2×C32×C4C2412yes—
172#638—28no—
173#638—28no—
174#638—28no—
175#638—48no—
176C2×C3⋊Dic3—28no—
177C2×C3⋊Dic3—42no—
178C2×C3⋊Dic3C2×D414yes—
179C2×C3⋊Dic3C2414yes—
180C2×C3⋊Dic3C2414yes—
181C2×C3⋊Dic3C2411yescharacteristic
182C2×C3⋊Dic3C2411yescharacteristic
183C4⋊(C3⋊D3)—28no—
184C4⋊(C3⋊D3)—24no—
185C4⋊(C3⋊D3)—44no—
186C4×C3⋊D3—28no—
187C4×C3⋊D3—28no—
188C4×C3⋊D3—28no—
189C4×C3⋊D3C2×D418yes—
190C4×C3⋊D3C2×D418yes—
191#634—24no—
192#634—28no—
193C22×#41—92no—
194#537—92no—
195#537—91no—
196#537C3⋊D311yescharacteristic, complemented
197#536—94no—
198#535—94no—
199#534—94no—
200#532—94no—
201#525—94no—
202#525—94no—
203C2×#117—91no—
204C23×D3—34no—
205C23×D3—316no—
206C3×#41—232no—
207C2×C3×Q8C22×D318yes—
208C2×C3×D4C22×D318yes—
209C2×C3×D4C22×D3116yes—
210C2×C3×D4C22×D3116yes—
211C22×C3×C4C22×D3116yes—
212C22×C3×C4C22×D318yes—
213C22×C3×C4C22×D314yes—
214C2×#67—316no—
215C2×#67—316no—
216C2×#67—316no—
217C2×#67—332no—
218C22×Dic3—34no—
219C22×Dic3—316no—
220C22×Dic3—38no—
221#239—632no—
222D3×Q8—632no—
223#237—632no—
224#237—664no—
225D3×D4—632no—
226D3×D4—664no—
227#235—664no—
228#235—632no—
229C2×D12—316no—
230C2×D12—38no—
231C2×D12—316no—
232C2×C4×D3—332no—
233C2×C4×D3—38no—
234C2×C4×D3—38no—
235C2×C4×D3—316no—
236C2×C4×D3—316no—
237C2×C4×D3—316no—
238C2×C4×D3—664no—
239C2×Dic6—316no—
240C2×Dic6—38no—
241C3×C4⋊C4C22×D3116yes—
242C3×C4⋊C4C22×D3116yes—
243C3×C22⋊C4C22×D3132yes—
244#217—332no—
245(C2×D3)⋊C4—332no—
246(C2×D3)⋊C4—332no—
247(C2×D3)⋊C4—332no—
248C4⋊Dic3—316no—
249C4⋊Dic3—316no—
250Dic3⋊C4—332no—
251C4×Dic3—316no—
252C4×Dic3—316no—
253C22×C32—21no—
254C22×C32—21no—
255C22×C32—24no—
256C22×C32—24no—
257C22×C32—24no—
258C22×C32C22×D412yes—
259C22×C32C2511yescharacteristic
260C2×C3⋊D3—22no—
261C2×C3⋊D3—22no—
262C2×C3⋊D3—24no—
263C2×C3⋊D3—24no—
264C2×C3⋊D3—24no—
265C2×C3⋊D3—44no—
266C2×C3⋊D3—416no—
267C2×C3⋊D3C22×D414yes—
268C32×C4—24no—
269C32×C4—24no—
270C32×C4C22×D414yes—
271C3⋊Dic3—24no—
272C3⋊Dic3—24no—
273C3⋊Dic3C22×D412yes—
274C3⋊Dic3C22×D412yes—
275C2×#41—92no—
276C2×#41—92no—
277C2×#41—94no—
278C2×#41—94no—
279C2×#41—92no—
280C2×#41—1816no—
281C2×#41C2×C3⋊D312yescomplemented
282C22×Q8—92no—
283C22×D4—94no—
284C22×D4—92no—
285C23×C4—91no—
286C23×C4—94no—
287C4⋊Q8—94no—
288#127—94no—
289#124—98no—
290#123—98no—
291#123—98no—
292C22⋊Q8—94no—
293C22⋊Q8—94no—
294C22⋊Q8—94no—
295C22⋊Q8C2×C3⋊D314yescomplemented
296#121—94no—
297#121—98no—
298#121—94no—
299#121—94no—
300#121—94no—
301#121C2×C3⋊D314yescomplemented
302#121C2×C3⋊D314yescomplemented
303#120—98no—
304#120—98no—
305C4×D4—94no—
306C4×D4—94no—
307C4×D4—98no—
308#117—94no—
309#117—94no—
310C2×C4⋊C4—91no—
311C2×C4⋊C4C2×C3⋊D311yescharacteristic, complemented
312C2×C22⋊C4—92no—
313C2×C42—92no—
314C23×C3C23×D3116yes—
315C23×C3C23×D314yes—
316C22×D3—38no—
317C22×D3—316no—
318C22×D3—316no—
319C22×D3—632no—
320C22×D3—124no—
321C22×D3—1216no—
322C22×D3—124no—
323C22×D3—1216no—
324C3×Q8—216no—
325C3×D4—232no—
326C3×D4—216no—
327C3×D4—416no—
328C2×C3×C4—232no—
329C2×C3×C4—48no—
330C2×C3×C4D3×D4116yes—
331C2×C3×C4C23×D3116yes—
332C2×C3×C4C23×D3116yes—
333C2×C3×C4C23×D318yes—
334#67—632no—
335#67—632no—
336#67—632no—
337#67—1232no—
338C2×Dic3—316no—
339C2×Dic3—34no—
340C2×Dic3—34no—
341C2×Dic3—316no—
342C2×Dic3—316no—
343C2×Dic3—632no—
344C2×Dic3—128no—
345D12—632no—
346D12—616no—
347D12—1216no—
348C4×D3—332no—
349C4×D3—332no—
350C4×D3—632no—
351C4×D3—632no—
352C4×D3—632no—
353Dic6—632no—
354Dic6—616no—
355C2×C32—22no—
356C2×C32—44no—
357C2×C32C23×D411yescharacteristic
358C2×C32#58511yescharacteristic
359C2×C32#58511yescharacteristic
360C3⋊D3—24no—
361C3⋊D3—44no—
362C24—91no—
363C24—94no—
364#41—28no—
365#41—1816no—
366#41—1816no—
367#41—188no—
368#41—188no—
369#41—188no—
370C2×Q8—92no—
371C2×Q8—94no—
372C2×Q8—188no—
373C2×Q8C22×C3⋊D312yes—
374C2×D4—94no—
375C2×D4—94no—
376C2×D4—94no—
377C2×D4—98no—
378C2×D4—94no—
379C2×D4—92no—
380C2×D4—94no—
381C2×D4—188no—
382C2×D4—1816no—
383C2×D4C22×C3⋊D314yes—
384C2×D4C22×C3⋊D312yes—
385C2×D4C22×C3⋊D314yes—
386C22×C4—91no—
387C22×C4—92no—
388C22×C4—92no—
389C22×C4—98no—
390C22×C4—94no—
391C22×C4—92no—
392C22×C4—94no—
393C22×C4—94no—
394C22×C4—94no—
395C22×C4—1816no—
396C22×C4C22×C3⋊D314yes—
397C22×C4C22×C3⋊D312yes—
398C22×C4C22×C3⋊D311yescharacteristic
399C4⋊C4—94no—
400C4⋊C4—98no—
401C4⋊C4—94no—
402C4⋊C4C22×C3⋊D314yes—
403C4⋊C4C22×C3⋊D314yes—
404C22⋊C4—98no—
405C22⋊C4—98no—
406C22⋊C4—98no—
407C22⋊C4—98no—
408C22⋊C4C22×C3⋊D318yes—
409C42—94no—
410C42—94no—
411C22×C3—24no—
412C22×C3—24no—
413C22×C3—216no—
414C22×C3—216no—
415C22×C3—216no—
416C22×C3C2×D3×D418yes—
417C22×C3C24×D314yes—
418C2×D3—316no—
419C2×D3—68no—
420C2×D3—68no—
421C2×D3—616no—
422C2×D3—616no—
423C2×D3—616no—
424C2×D3—1216no—
425C2×D3—1264no—
426C3×C4—216no—
427C3×C4—216no—
428C3×C4C2×D3×D4116yes—
429Dic3—38no—
430Dic3—38no—
431Dic3—616no—
432Dic3—616no—
433C32#344911yescharacteristic, complemented, Sylow
434C23—92no—
435C23—94no—
436C23—94no—
437C23—188no—
438C23—361no—
439C23—361no—
440C23—364no—
441C23—364no—
442C23C23×C3⋊D314yes—
443C23C23×C3⋊D311yescharacteristic
444Q8—24no—
445Q8—188no—
446Q8—184no—
447D4—28no—
448D4—24no—
449D4—44no—
450D4—188no—
451D4—188no—
452D4—188no—
453D4—188no—
454D4—184no—
455D4—364no—
456D4—368no—
457C2×C4—28no—
458C2×C4—42no—
459C2×C4—94no—
460C2×C4—91no—
461C2×C4—91no—
462C2×C4—98no—
463C2×C4—98no—
464C2×C4—94no—
465C2×C4—94no—
466C2×C4—188no—
467C2×C4—188no—
468C2×C4—188no—
469C2×C4—188no—
470C2×C4—362no—
471C2×C4D4×C3⋊D314yes—
472C2×C4C23×C3⋊D314yes—
473C2×C4C23×C3⋊D314yes—
474C2×C4C23×C3⋊D312yes—
475C2×C3—28no—
476C2×C3—416no—
477C2×C3C22×D3×D414yes—
478C2×C3#596614yes—
479C2×C3#596814yes—
480D3—616no—
481D3—1216no—
482C22—21no—
483C22—21no—
484C22—24no—
485C22—24no—
486C22—24no—
487C22—94no—
488C22—182no—
489C22—182no—
490C22—184no—
491C22—184no—
492C22—184no—
493C22—364no—
494C22—3616no—
495C22C2×D4×C3⋊D312yes—
496C22C24×C3⋊D311yescharacteristic
497C4—24no—
498C4—24no—
499C4—92no—
500C4—92no—
501C4—184no—
502C4—184no—
503C4C2×D4×C3⋊D314yes—
504C3#8636314yescomplemented
505C2—22no—
506C2—44no—
507C2—184no—
508C2—364no—
509C2C22×D4×C3⋊D311yescharacteristic
510C2#1059675811yescharacteristic
511C2#1059676011yescharacteristic
subgroupG/H
center, FrattiniC22C24×C3⋊D3
commutator, socle, cosocleC22×C32C25
FittingC32×#537C2
hypercenter#537C3⋊D3
hypocenterC32#3449
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #537

Complements

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

NH ≅ G/Ntype
1. C2×#41×C3⋊D3C2semidirect
2. C32×#537C2semidirect
3. #10596304C2semidirect
4. #10596099C2semidirect
5. #10596098C2semidirect
6. #10596078C2semidirect
7. #10596077C2semidirect
8. #10596076C2semidirect
9. #10596067C2semidirect
10. #10595981C2semidirect
11. C2×#64101C2semidirect
13. C2×C32×#41C22semidirect
16. C2×Q8×C3⋊D3C22semidirect
18. C2×#3830C22semidirect
20. C2×D4×C3⋊D3C22semidirect
22. C2×#3828C22semidirect
24. C22×C4×C3⋊D3C22semidirect
25. C32×C22⋊Q8C22semidirect
26. C32×#121C22semidirect
27. C32×#121C22semidirect
28. C2×C32×C4⋊C4C22semidirect
29. #64155C22semidirect
30. #64149C22semidirect
31. #64148C22semidirect
32. #64147C22semidirect
33. #64146C22semidirect
34. D4×C3⋊Dic3C22semidirect
35. #64139C22semidirect
36. #64139C22semidirect
38. C2×C4⋊(C3⋊Dic3)C22semidirect
39. #64133C22semidirect
40. C2×C4×C3⋊Dic3C22semidirect
41. #64106C22semidirect
42. #64104C22semidirect
43. #64103C22semidirect
44. #64102C22semidirect
45. #64101C22semidirect
46. #64101C22semidirect
47. #64097C22semidirect
48. #64094C22semidirect
49. #64092C22semidirect
50. #64091C22semidirect
51. #64090C22semidirect
53. C3×#537D3semidirect
92. C2×C4×C3⋊D3D4semidirect
113. C2×C3×#41C2×D3semidirect
125. C3×C22⋊Q8C2×D3semidirect
126. C3×#121C2×D3semidirect
127. C3×#121C2×D3semidirect
128. C2×C3×C4⋊C4C2×D3semidirect
196. #537C3⋊D3semidirect
281. C2×#41C2×C3⋊D3semidirect
295. C22⋊Q8C2×C3⋊D3semidirect
301. #121C2×C3⋊D3semidirect
302. #121C2×C3⋊D3semidirect
311. C2×C4⋊C4C2×C3⋊D3semidirect
433. C32#3449semidirect
504. C3#86363semidirect

Maximal subgroups

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

subgroupindex
C2×#41×C3⋊D32
C32×#5372
#105963042
#105960992
#105960982
#105960782
#105960772
#105960762
#105960672
#105959812
C2×#641012
#863633