Finite Group Databasebeta

← #11900880

Subgroups — #11900880

Order 1152.

3636 conjugacy classes of subgroups.

The subgroup lattice has 471 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#533C211yesmaximal, characteristic, complemented
2#10596199C212yesmaximal, complemented
3#10596196C212yesmaximal, complemented
4#10596162C214yesmaximal, complemented
5#10596098C214yesmaximal, complemented
6#10596095C214yesmaximal, complemented
7#10596051C214yesmaximal, complemented
8C4×#3832C214yesmaximal, complemented
9#10595995C212yesmaximal, complemented
10#10595993C212yesmaximal, complemented
11#10595948C211yesmaximal, characteristic, complemented
12C2×C42×C3⋊D3C211yesmaximal, characteristic, complemented
13#86257—34nomaximal
14C2×#3832C2214yes—
15C2×#3828C2212yes—
16C22×C4×C3⋊D3C2212yes—
17C22×C4×C3⋊D3C2211yescharacteristic
18C32×C4⋊Q8C2212yescomplemented
19C32×#125C2212yescomplemented
20C32×C22⋊Q8C2214yes—
21C32×C4×Q8C2214yescomplemented
22C32×#117C2212yes—
23C2×C32×C42C2211yescharacteristic
24#64156C2214yescomplemented
25#64155C2214yes—
26Q8×C3⋊Dic3C2214yescomplemented
27#64139C2214yes—
28C2×C4×C3⋊Dic3C2211yescharacteristic
29C2×C4×C3⋊Dic3C2212yes—
30#64107C2218yescomplemented
31#64106C2214yes—
32#64104C2214yes—
33#64104C2214yes—
34#64103C2218yes—
35#64102C2218yes—
36#64102C2214yescomplemented
37#64102C2214yescomplemented
38#64101C2214yes—
39#64101C2218yescomplemented
40#64099C2214yescomplemented
41#64096C2214yescomplemented
42#64095C2214yes—
43#64091C2214yes—
44#64090C2218yes—
45#64084C2212yescomplemented
46#64083C2211yescharacteristic, complemented
47C4×C4⋊(C3⋊D3)C2218yes—
48C4×C4⋊(C3⋊D3)C2214yescomplemented
49#64081C2214yescomplemented
50C42×C3⋊D3C2212yes—
51C42×C3⋊D3C2212yes—
52C42×C3⋊D3C2212yes—
53C42×C3⋊D3C2212yes—
54C42×C3⋊D3C2214yescomplemented
55#64078C2211yescharacteristic, complemented
56C3×#533D314yescomplemented
57#5728—38no—
58#5725—38no—
59#5691—316no—
60#5627—316no—
61#5624—316no—
62#5580—316no—
63C4×#239—316no—
64#5524—38no—
65#5522—38no—
66#5477—34no—
67C2×C42×D3—34no—
68C23×C3⋊D3C2311yescharacteristic
69C2×C32×Q8C2314yes—
70C22×C32×C4C2312yes—
71C22×C32×C4C2311yescharacteristic
72C2×#638C2314yes—
73C22×C3⋊Dic3C2312yes—
74C22×C3⋊Dic3C2311yescharacteristic
75#3832—216no—
76#3828—28no—
77C2×C4⋊(C3⋊D3)C2318yes—
78C2×C4⋊(C3⋊D3)C2314yes—
79C2×C4⋊(C3⋊D3)C2312yes—
80C2×C4×C3⋊D3—24no—
81C2×C4×C3⋊D3—28no—
82C2×C4×C3⋊D3C2312yes—
83C2×C4×C3⋊D3C2312yes—
84C2×C4×C3⋊D3C2312yes—
85C2×C4×C3⋊D3C2312yes—
86C2×C4×C3⋊D3C2312yes—
87C2×C4×C3⋊D3C2314yes—
88C2×C4×C3⋊D3C2318yes—
89C2×C4×C3⋊D3C2312yes—
90C2×#634C2312yes—
91C32×C4⋊C4C2314yes—
92C32×C4⋊C4C2314yes—
93C32×C4⋊C4C2318yes—
94C32×C22⋊C4C2314yes—
95C32×C42C2311yescharacteristic
96C32×C42C2312yes—
97C32×C42C2311yescharacteristic
98C32×C42C2314yes—
99#3752C2318yes—
100#3752C2318yes—
101#3752C2318yes—
102#3752C2318yes—
103C4⋊(C3⋊Dic3)C2314yes—
104C4⋊(C3⋊Dic3)C2318yes—
105#3750C2318yes—
106C4×C3⋊Dic3C2311yescharacteristic
107C4×C3⋊Dic3C2311yescharacteristic
108C4×C3⋊Dic3C2312yes—
109C4×C3⋊Dic3C2312yes—
110C4×C3⋊Dic3C2312yes—
111C4×C3⋊Dic3C2312yes—
112C4×C3⋊Dic3C2312yes—
113C4×C3⋊Dic3C2318yes—
114#3444—91noSylow
115C2×#239—316no—
116C2×#235—38no—
117C22×C4×D3—34no—
118C22×C4×D3—38no—
119C3×C4⋊Q8C2×D318yescomplemented
120C3×#125C2×D318yescomplemented
121C3×C22⋊Q8C2×D3116yes—
122C3×C4×Q8C2×D3116yescomplemented
123C3×#117C2×D318yes—
124C2×C3×C42C2×D314yes—
125#947—316no—
126#946—316no—
127Q8×Dic3—316no—
128#930—316no—
129C2×C4×Dic3—34no—
130C2×C4×Dic3—38no—
131#898—332no—
132#897—316no—
133#895—316no—
134#895—316no—
135#894—332no—
136#893—316no—
137#893—332no—
138#893—316no—
139#892—332no—
140#892—316no—
141#890—316no—
142#887—316no—
143#886—316no—
144#882—316no—
145#67⋊C4—332no—
146#875—38no—
147#874—34no—
148C4×D12—332no—
149C4×D12—316no—
150#872—316no—
151C42×D3—38no—
152C42×D3—38no—
153C42×D3—38no—
154C42×D3—38no—
155C42×D3—316no—
156#869—34no—
157C23×C32C2411yescharacteristic
158C22×C3⋊D3—22no—
159C22×C3⋊D3—24no—
160C22×C3⋊D3C2414yes—
161C22×C3⋊D3C2412yes—
162C32×Q8—28no—
163C2×C32×C4—24no—
164C2×C32×C4#4114yescomplemented
165C2×C32×C4C2412yes—
166C2×C32×C4C2418yes—
167C2×C32×C4C2412yes—
168C2×C32×C4C2411yescharacteristic
169C2×C32×C4C2411yescharacteristic
170#638—28no—
171C2×C3⋊Dic3—22no—
172C2×C3⋊Dic3—24no—
173C2×C3⋊Dic3C2412yes—
174C2×C3⋊Dic3C2412yes—
175C2×C3⋊Dic3C2414yes—
176C2×C3⋊Dic3C2412yes—
177C4⋊(C3⋊D3)—216no—
178C4⋊(C3⋊D3)—24no—
179C4⋊(C3⋊D3)—28no—
180C4×C3⋊D3—24no—
181C4×C3⋊D3—24no—
182C4×C3⋊D3—24no—
183C4×C3⋊D3—24no—
184C4×C3⋊D3—28no—
185C4×C3⋊D3—24no—
186C4×C3⋊D3—216no—
187C4×C3⋊D3#4118yescomplemented
188#634—24no—
189#533—92no—
190#533C3⋊D311yescharacteristic, complemented
191#532—92no—
192#532—91no—
193#529—94no—
194#529—94no—
195#529—94no—
196#525—94no—
197#525—92no—
198C4×#41—94no—
199C4×#41—92no—
200C22×C42—91no—
201C23×D3—34no—
202C2×C3×Q8C22×D3116yes—
203C22×C3×C4C22×D318yes—
204C22×C3×C4C22×D314yes—
205C2×#67—316no—
206C22×Dic3—38no—
207C22×Dic3—34no—
208#239—664no—
209#235—632no—
210C2×D12—316no—
211C2×D12—332no—
212C2×D12—38no—
213C2×C4×D3—38no—
214C2×C4×D3—38no—
215C2×C4×D3—38no—
216C2×C4×D3—38no—
217C2×C4×D3—38no—
218C2×C4×D3—38no—
219C2×C4×D3—316no—
220C2×C4×D3—332no—
221C2×C4×D3—632no—
222C2×C4×D3—616no—
223C2×Dic6—38no—
224C3×C4⋊C4C22×D3116yes—
225C3×C4⋊C4C22×D3116yes—
226C3×C4⋊C4C22×D3132yes—
227C3×C22⋊C4C22×D3116yes—
228C3×C42C22×D314yes—
229C3×C42C22×D318yes—
230C3×C42C22×D314yes—
231C3×C42C22×D3116yes—
232(C2×D3)⋊C4—332no—
233(C2×D3)⋊C4—332no—
234(C2×D3)⋊C4—332no—
235(C2×D3)⋊C4—332no—
236C4⋊Dic3—316no—
237C4⋊Dic3—332no—
238Dic3⋊C4—332no—
239C4×Dic3—34no—
240C4×Dic3—34no—
241C4×Dic3—38no—
242C4×Dic3—38no—
243C4×Dic3—38no—
244C4×Dic3—38no—
245C4×Dic3—38no—
246C4×Dic3—332no—
247C22×C32—22no—
248C22×C32C2×#4112yes—
249C22×C32C2511yescharacteristic
250C2×C3⋊D3—28no—
251C2×C3⋊D3—22no—
252C2×C3⋊D3—22no—
253C2×C3⋊D3—28no—
254C2×C3⋊D3—24no—
255C2×C3⋊D3C2×#4114yes—
256C32×C4—22no—
257C32×C4—28no—
258C32×C4C2×#4112yes—
259C32×C4C2×#4112yes—
260C32×C4C2×#4114yes—
261C3⋊Dic3—24no—
262C3⋊Dic3—22no—
263C3⋊Dic3—22no—
264C3⋊Dic3C2×#4114yes—
265C2×#41—94no—
266C2×#41—92no—
267C23×C4—92no—
268C23×C4—91no—
269C4⋊Q8—91no—
270C4⋊Q8C2×C3⋊D312yescomplemented
271#127—91no—
272#126—98no—
273#125—94no—
274#125C2×C3⋊D312yescomplemented
275#124—94no—
276#124—92no—
277#123—98no—
278#123—94no—
279C22⋊Q8—94no—
280C22⋊Q8—94no—
281C22⋊Q8C2×C3⋊D314yes—
282#121—94no—
283#121—94no—
284#121—94no—
285#120—94no—
286C4×Q8—94no—
287C4×Q8—94no—
288C4×Q8C2×C3⋊D314yescomplemented
289C4×D4—98no—
290C4×D4—94no—
291C4×D4—94no—
292C4×D4—98no—
293C4×D4—98no—
294C4×D4—94no—
295#117—94no—
296#117—98no—
297#117—94no—
298#117C2×C3⋊D312yes—
299C2×C42—91no—
300C2×C42—92no—
301C2×C42—94no—
302C2×C42—92no—
303C2×C42—92no—
304C2×C42—92no—
305C2×C42—92no—
306C2×C42C2×C3⋊D311yescharacteristic
307C23×C3C23×D314yes—
308C22×D3—38no—
309C22×D3—316no—
310C22×D3—616no—
311C22×D3—68no—
312C3×Q8—232no—
313C2×C3×C4—216no—
314C2×C3×C4#239116yescomplemented
315C2×C3×C4C23×D318yes—
316C2×C3×C4C23×D3132yes—
317C2×C3×C4C23×D314yes—
318C2×C3×C4C23×D318yes—
319C2×C3×C4C23×D314yes—
320#67—632no—
321C2×Dic3—38no—
322C2×Dic3—38no—
323C2×Dic3—38no—
324C2×Dic3—316no—
325C2×Dic3—616no—
326C2×Dic3—68no—
327D12—664no—
328D12—616no—
329D12—632no—
330C4×D3—332no—
331C4×D3—616no—
332C4×D3—664no—
333C4×D3—616no—
334C4×D3—616no—
335C4×D3—616no—
336C4×D3—632no—
337C4×D3—616no—
338Dic6—616no—
339C2×C32—22no—
340C2×C32C22×#4111yescharacteristic
341C2×C32C22×#4112yes—
342C3⋊D3—24no—
343C3⋊D3—44no—
344C24—91no—
345#41—1816no—
346#41—188no—
347C2×Q8—92no—
348C2×Q8C22×C3⋊D314yes—
349C2×D4—94no—
350C2×D4—98no—
351C2×D4—92no—
352C2×D4—94no—
353C22×C4—92no—
354C22×C4—92no—
355C22×C4—91no—
356C22×C4—92no—
357C22×C4—92no—
358C22×C4—92no—
359C22×C4—92no—
360C22×C4—98no—
361C22×C4—92no—
362C22×C4—94no—
363C22×C4—188no—
364C22×C4—184no—
365C22×C4C22×C3⋊D312yes—
366C22×C4C22×C3⋊D311yescharacteristic
367C4⋊C4—94no—
368C4⋊C4—98no—
369C4⋊C4—98no—
370C4⋊C4C22×C3⋊D314yes—
371C4⋊C4C22×C3⋊D318yes—
372C4⋊C4C22×C3⋊D314yes—
373C22⋊C4—98no—
374C22⋊C4—98no—
375C22⋊C4—98no—
376C22⋊C4—98no—
377C22⋊C4C22×C3⋊D314yes—
378C42—92no—
379C42—92no—
380C42—92no—
381C42—92no—
382C42—92no—
383C42—98no—
384C42—91no—
385C42—91no—
386C42C22×C3⋊D311yescharacteristic
387C42C22×C3⋊D311yescharacteristic
388C42C22×C3⋊D312yes—
389C42C22×C3⋊D314yes—
390C22×C3—28no—
391C22×C3C2×#23918yes—
392C22×C3C24×D314yes—
393C2×D3—316no—
394C2×D3—632no—
395C2×D3—68no—
396C2×D3—68no—
397C2×D3—616no—
398C2×D3—632no—
399C3×C4—28no—
400C3×C4—232no—
401C3×C4C2×#23918yes—
402C3×C4C2×#23918yes—
403C3×C4D3×#41116yes—
404Dic3—316no—
405Dic3—616no—
406Dic3—68no—
407Dic3—68no—
408C32#344411yescharacteristic, complemented, Sylow
409C23—92no—
410C23—94no—
411C23—184no—
412C23—182no—
413C23C23×C3⋊D311yescharacteristic
414Q8—28no—
415Q8—184no—
416D4—1816no—
417D4—188no—
418D4—184no—
419D4—188no—
420C2×C4—24no—
421C2×C4—92no—
422C2×C4—98no—
423C2×C4—92no—
424C2×C4—92no—
425C2×C4—94no—
426C2×C4—184no—
427C2×C4—1816no—
428C2×C4—184no—
429C2×C4—184no—
430C2×C4—182no—
431C2×C4—184no—
432C2×C4—184no—
433C2×C4—188no—
434C2×C4—184no—
435C2×C4#383214yescomplemented
436C2×C4C23×C3⋊D312yes—
437C2×C4C23×C3⋊D318yes—
438C2×C4C23×C3⋊D311yescharacteristic
439C2×C4C23×C3⋊D312yes—
440C2×C4C23×C3⋊D311yescharacteristic
441C2×C3—28no—
442C2×C3C22×#23914yes—
443C2×C3C2×D3×#4118yes—
444D3—616no—
445D3—1216no—
446C22—22no—
447C22—94no—
448C22—188no—
449C22—182no—
450C22—182no—
451C22—184no—
452C22—188no—
453C22C2×#383212yes—
454C22C24×C3⋊D311yescharacteristic
455C4—22no—
456C4—28no—
457C4—94no—
458C4—182no—
459C4—184no—
460C4—182no—
461C4C2×#383212yes—
462C4C2×#383212yes—
463C4#41×C3⋊D314yes—
464C3#8625714yescomplemented
465C2—22no—
466C2—184no—
467C2—364no—
468C2C22×#383211yescharacteristic
469C2C2×#41×C3⋊D312yes—
subgroupG/H
centerC2×C4C23×C3⋊D3
commutator, socle, cosocleC22×C32C25
FrattiniC22C24×C3⋊D3
FittingC32×#533C2
hypercenter#533C3⋊D3
hypocenterC32#3444
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ #533

Complements

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

NH ≅ G/Ntype
1. C32×#533C2semidirect
2. #10596199C2semidirect
3. #10596196C2semidirect
4. #10596162C2semidirect
5. #10596098C2semidirect
6. #10596095C2semidirect
7. #10596051C2semidirect
8. C4×#3832C2semidirect
9. #10595995C2semidirect
10. #10595993C2semidirect
11. #10595948C2semidirect
12. C2×C42×C3⋊D3C2semidirect
18. C32×C4⋊Q8C22semidirect
19. C32×#125C22semidirect
21. C32×C4×Q8C22semidirect
24. #64156C22semidirect
26. Q8×C3⋊Dic3C22semidirect
30. #64107C22semidirect
36. #64102C22semidirect
37. #64102C22semidirect
39. #64101C22semidirect
40. #64099C22semidirect
41. #64096C22semidirect
45. #64084C22semidirect
46. #64083C22semidirect
48. C4×C4⋊(C3⋊D3)C22semidirect
49. #64081C22semidirect
54. C42×C3⋊D3C22semidirect
55. #64078C22semidirect
56. C3×#533D3semidirect
119. C3×C4⋊Q8C2×D3semidirect
120. C3×#125C2×D3semidirect
122. C3×C4×Q8C2×D3semidirect
164. C2×C32×C4#41semidirect
187. C4×C3⋊D3#41semidirect
190. #533C3⋊D3semidirect
270. C4⋊Q8C2×C3⋊D3semidirect
274. #125C2×C3⋊D3semidirect
288. C4×Q8C2×C3⋊D3semidirect
314. C2×C3×C4#239semidirect
408. C32#3444semidirect
435. C2×C4#3832semidirect
464. C3#86257semidirect

Maximal subgroups

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

subgroupindex
C32×#5332
#105961992
#105961962
#105961622
#105960982
#105960952
#105960512
C4×#38322
#105959952
#105959932
#105959482
C2×C42×C3⋊D32
#862573