Finite Group Databasebeta

← #86246

Subgroups — #86246

Order 384.

1142 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#532C211yesmaximal, characteristic, complemented
2#5831C212yesmaximal, complemented
3#5829C212yesmaximal, complemented
4#5732C211yesmaximal, characteristic, complemented
5#5727C211yesmaximal, characteristic, complemented
6#5717C211yesmaximal, characteristic, complemented
7#5713C211yesmaximal, characteristic, complemented
8#5680C212yesmaximal, complemented
9D3×#124C212yesmaximal, complemented
10#5616C212yesmaximal, complemented
11#5613C214yesmaximal, complemented
12#5612C212yesmaximal, complemented
13#5561C212yesmaximal, complemented
14#5556C214yesmaximal, complemented
15#5545C212yesmaximal, complemented
16#5479C211yesmaximal, characteristic, complemented
17C4×#235C211yesmaximal, characteristic, complemented
18#3514—31nomaximal, Sylow
19C2×C3×#41C2212yescomplemented
20C2×D3×Q8C2212yescomplemented
21C2×D3×D4C2212yes—
22C2×D3×D4C2212yes—
23C2×#235C2211yescharacteristic
24C3×C4⋊Q8C2211yescharacteristic, complemented
25C3×#127C2211yescharacteristic
26C3×#124C2212yescomplemented
27C3×#121C2212yescomplemented
28C3×#121C2212yescomplemented
29C3×C4×D4C2212yescomplemented
30C3×C4×D4C2212yescomplemented
31C2×C3×C42C2211yescharacteristic, complemented
32#947C2212yes—
33#946C2212yescomplemented
34Q8×Dic3C2212yescomplemented
35#939C2214yescomplemented
36#938C2212yes—
37#938C2212yes—
38#938C2214yescomplemented
39#937C2214yes—
40#937C2214yescomplemented
41#936C2212yescomplemented
42#936C2212yescomplemented
43#936C2214yescomplemented
44#935C2214yescomplemented
45D4×Dic3C2212yescomplemented
46D4×Dic3C2212yescomplemented
47#930C2211yescharacteristic
48#929C2212yescomplemented
49#929C2214yescomplemented
50C4×#67C2212yescomplemented
51C4×#67C2212yescomplemented
52C4×#67C2212yescomplemented
53C4×#67C2214yescomplemented
54C2×(C2×D3)⋊C4C2214yescomplemented
55#926C2211yescharacteristic, complemented
56#924C2211yescharacteristic, complemented
57#924C2214yescomplemented
58#898C2214yescomplemented
59#897C2212yescomplemented
60#896C2214yescomplemented
61#893C2212yes—
62#892C2212yescomplemented
63#888C2212yescomplemented
64#885C2214yescomplemented
65#885C2214yescomplemented
66#883C2214yescomplemented
67#67⋊C4C2214yescomplemented
68D3×C22⋊C4C2214yescomplemented
69D3×C22⋊C4C2214yescomplemented
70#879C2214yescomplemented
71#877C2214yescomplemented
72#876C2212yescomplemented
73#875C2211yescharacteristic
74C4×D12C2211yescharacteristic
75C4×D12C2211yescharacteristic
76C4×D12C2211yescharacteristic
77#872C2212yescomplemented
78#872C2212yescomplemented
79C42×D3C2212yescomplemented
80#870C2211yescharacteristic, complemented
81C4×Dic6C2211yescharacteristic, complemented
82C4×Dic6C2211yescharacteristic, complemented
83C4×Dic6C2211yescharacteristic, complemented
84#559—31no—
85#556—31no—
86#555—32no—
87#551—34no—
88D4×Q8—31no—
89#548—32no—
90#546—32no—
91#546—32no—
92D42—31no—
93#542—32no—
94#538—34no—
95#532D311yescharacteristic, complemented
96#529—32no—
97#529—31no—
98C2×#124—32no—
99#518—32no—
100C4×#41—31no—
101C23×D3C2314yes—
102C3×#41—44no—
103C2×C3×Q8C2312yes—
104C2×C3×D4C2312yes—
105C2×C3×D4C2312yes—
106C2×C3×D4C2312yes—
107C2×C3×D4C2314yes—
108C22×C3×C4C2311yescharacteristic
109C22×C3×C4C2311yescharacteristic
110C22×C3×C4C2314yes—
111C22×C3×C4C2311yescharacteristic
112C2×#67C2314yes—
113C2×#67C2312yes—
114C2×#67C2314yes—
115C2×#67C2312yes—
116C22×Dic3C2314yes—
117D3×Q8—44no—
118D3×D4—28no—
119D3×D4—44no—
120#235—24no—
121C2×D12C2311yescharacteristic
122C2×D12C2311yescharacteristic
123C2×C4×D3C2312yes—
124C2×C4×D3C2312yes—
125C2×C4×D3C2312yes—
126C2×C4×D3C2312yes—
127C2×C4×D3C2314yes—
128C2×Dic6C2311yescharacteristic
129C2×Dic6C2311yescharacteristic
130C2×Dic6C2314yes—
131C3×C4⋊C4C2312yes—
132C3×C4⋊C4C2312yes—
133C3×C22⋊C4C2314yes—
134C3×C22⋊C4C2314yes—
135C3×C42C2311yescharacteristic
136C3×C42C2311yescharacteristic
137C3×C42C2311yescharacteristic
138C3×C42C2311yescharacteristic
139#217C2314yes—
140#217C2314yes—
141#217C2314yes—
142#217C2314yes—
143#217C2312yes—
144#217C2312yes—
145(C2×D3)⋊C4C2312yes—
146(C2×D3)⋊C4C2312yes—
147(C2×D3)⋊C4C2312yes—
148(C2×D3)⋊C4C2312yes—
149(C2×D3)⋊C4C2312yes—
150(C2×D3)⋊C4C2312yes—
151(C2×D3)⋊C4C2314yes—
152(C2×D3)⋊C4C2314yes—
153(C2×D3)⋊C4C2314yes—
154C4⋊Dic3C2311yescharacteristic
155C4⋊Dic3C2311yescharacteristic
156C4⋊Dic3C2311yescharacteristic
157C4⋊Dic3C2311yescharacteristic
158C4⋊Dic3C2314yes—
159Dic3⋊C4C2312yes—
160Dic3⋊C4C2312yes—
161Dic3⋊C4C2312yes—
162Dic3⋊C4C2312yes—
163Dic3⋊C4C2312yes—
164Dic3⋊C4C2312yes—
165Dic3⋊C4C2314yes—
166C4×Dic3C2312yes—
167C4×Dic3C2312yes—
168C4×Dic3C2312yes—
169C4×Dic3C2312yes—
170C4×Dic3C2314yes—
171C2×#41—31no—
172C2×#41C2×D312yescomplemented
173C22×Q8—32no—
174C22×D4—32no—
175C22×D4—32no—
176C4⋊Q8—32no—
177C4⋊Q8C2×D311yescharacteristic, complemented
178#127C2×D311yescharacteristic
179#126—34no—
180#126—34no—
181#126—32no—
182#125—31no—
183#124—32no—
184#124—32no—
185#124—34no—
186#124—32no—
187#124—34no—
188#124—34no—
189#124—31no—
190#124C2×D312yescomplemented
191#123—34no—
192#123—32no—
193#123—34no—
194#123—34no—
195C22⋊Q8—32no—
196C22⋊Q8—31no—
197C22⋊Q8—34no—
198C22⋊Q8—34no—
199C22⋊Q8—32no—
200#121—32no—
201#121—34no—
202#121—34no—
203#121—32no—
204#121—31no—
205#121C2×D312yescomplemented
206#121C2×D312yescomplemented
207#120—34no—
208#120—34no—
209C4×Q8—32no—
210C4×Q8—31no—
211C4×Q8—31no—
212C4×Q8—31no—
213C4×D4—32no—
214C4×D4—32no—
215C4×D4—32no—
216C4×D4—32no—
217C4×D4—34no—
218C4×D4—32no—
219C4×D4—32no—
220C4×D4—34no—
221C4×D4—31no—
222C4×D4—31no—
223C4×D4—31no—
224C4×D4C2×D312yescomplemented
225C4×D4C2×D312yescomplemented
226#117—31no—
227#117—32no—
228#117—34no—
229#117—32no—
230#117—32no—
231C2×C22⋊C4—34no—
232C2×C22⋊C4—34no—
233C2×C22⋊C4—34no—
234C2×C42—32no—
235C2×C42C2×D311yescharacteristic, complemented
236C23×C3C2414yes—
237C23×C3C2411yescharacteristic
238C22×D3—28no—
239C22×D3—44no—
240C22×D3—44no—
241C22×D3C2412yes—
242C22×D3C2412yes—
243C3×Q8—24no—
244C3×D4—24no—
245C3×D4—24no—
246C3×D4—42no—
247C3×D4—44no—
248C2×C3×C4—22no—
249C2×C3×C4—22no—
250C2×C3×C4—41no—
251C2×C3×C4—44no—
252C2×C3×C4C2411yescharacteristic
253C2×C3×C4C2411yescharacteristic
254C2×C3×C4C2414yes—
255C2×C3×C4C2411yescharacteristic
256C2×C3×C4C2411yescharacteristic
257C2×C3×C4C2411yescharacteristic
258C2×C3×C4C2411yescharacteristic
259#67—24no—
260#67—28no—
261#67—44no—
262#67—42no—
263C2×Dic3—44no—
264C2×Dic3C2412yes—
265C2×Dic3C2412yes—
266C2×Dic3C2412yes—
267C2×Dic3C2412yes—
268C2×Dic3C2412yes—
269C2×Dic3C2412yes—
270D12—22no—
271D12#4114yescomplemented
272C4×D3—24no—
273C4×D3—24no—
274C4×D3—24no—
275C4×D3—42no—
276C4×D3—44no—
277Dic6—22no—
278Dic6—22no—
279Dic6—44no—
280C24—34no—
281#41—44no—
282#41—64no—
283C2×Q8—31no—
284C2×Q8—31no—
285C2×Q8—34no—
286C2×Q8—124no—
287C2×Q8C22×D312yes—
288C2×D4—32no—
289C2×D4—34no—
290C2×D4—32no—
291C2×D4—34no—
292C2×D4—31no—
293C2×D4—31no—
294C2×D4—68no—
295C2×D4—124no—
296C2×D4C22×D312yes—
297C2×D4C22×D312yes—
298C2×D4C22×D312yes—
299C2×D4C22×D314yes—
300C22×C4—34no—
301C22×C4—32no—
302C22×C4—32no—
303C22×C4—32no—
304C22×C4—32no—
305C22×C4—34no—
306C22×C4C22×D311yescharacteristic
307C22×C4C22×D311yescharacteristic
308C22×C4C22×D311yescharacteristic
309C22×C4C22×D314yes—
310C4⋊C4—31no—
311C4⋊C4—32no—
312C4⋊C4—32no—
313C4⋊C4—32no—
314C4⋊C4—31no—
315C4⋊C4—32no—
316C4⋊C4—32no—
317C4⋊C4—34no—
318C4⋊C4—31no—
319C4⋊C4—31no—
320C4⋊C4—34no—
321C4⋊C4—32no—
322C4⋊C4C22×D312yes—
323C4⋊C4C22×D312yes—
324C22⋊C4—34no—
325C22⋊C4—34no—
326C22⋊C4—32no—
327C22⋊C4—34no—
328C22⋊C4—34no—
329C22⋊C4—32no—
330C22⋊C4—32no—
331C22⋊C4—32no—
332C22⋊C4—34no—
333C22⋊C4—32no—
334C22⋊C4—32no—
335C22⋊C4—34no—
336C22⋊C4—34no—
337C22⋊C4—32no—
338C22⋊C4—32no—
339C22⋊C4C22×D314yes—
340C22⋊C4C22×D314yes—
341C42—32no—
342C42—32no—
343C42—32no—
344C42—34no—
345C42—32no—
346C42C22×D311yescharacteristic
347C42C22×D311yescharacteristic
348C42C22×D311yescharacteristic
349C42C22×D311yescharacteristic
350C22×C3—21no—
351C22×C3—24no—
352C22×C3—24no—
353C22×C3—21no—
354C22×C3—24no—
355C22×C3—21no—
356C22×C3C2511yescharacteristic
357C2×D3—22no—
358C2×D3—22no—
359C2×D3—22no—
360C2×D3—22no—
361C2×D3—22no—
362C2×D3—88no—
363C2×D3C2×#4114yes—
364C3×C4—21no—
365C3×C4—24no—
366C3×C4—21no—
367C3×C4—21no—
368C3×C4—21no—
369C3×C4C2×#4112yes—
370C3×C4H(5,𝔽2)12yes—
371Dic3—22no—
372Dic3—22no—
373Dic3—22no—
374Dic3—22no—
375Dic3—22no—
376Dic3—22no—
377C23—32no—
378C23—32no—
379C23—68no—
380C23—124no—
381C23—124no—
382C23C23×D314yes—
383C23C23×D311yescharacteristic
384Q8—24no—
385Q8—62no—
386Q8—62no—
387Q8—124no—
388D4—24no—
389D4—24no—
390D4—34no—
391D4—44no—
392D4—42no—
393D4—68no—
394D4—64no—
395D4—62no—
396D4—124no—
397D4—122no—
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—32no—
401C2×C4—32no—
402C2×C4—32no—
403C2×C4—32no—
404C2×C4—32no—
405C2×C4—32no—
406C2×C4—44no—
407C2×C4—41no—
408C2×C4—64no—
409C2×C4—64no—
410C2×C4—64no—
411C2×C4—124no—
412C2×C4—122no—
413C2×C4—124no—
414C2×C4C23×D311yescharacteristic
415C2×C4C23×D311yescharacteristic
416C2×C4C23×D314yes—
417C2×C4C23×D311yescharacteristic
418C2×C4C23×D311yescharacteristic
419C2×C4C23×D311yescharacteristic
420C2×C4C23×D311yescharacteristic
421C2×C3—44no—
422C2×C3—41no—
423C2×C3C22×#4111yescharacteristic
424C2×C3C2×H(5,𝔽2)11yescharacteristic
425C2×C3#58511yescharacteristic
426D3—24no—
427D3—42no—
428C22—21no—
429C22—24no—
430C22—21no—
431C22—24no—
432C22—21no—
433C22—24no—
434C22—34no—
435C22—62no—
436C22—62no—
437C22—62no—
438C22—62no—
439C22—62no—
440C22—248no—
441C22C24×D311yescharacteristic
442C4—21no—
443C4—24no—
444C4—21no—
445C4—21no—
446C4—21no—
447C4—62no—
448C4—62no—
449C4—62no—
450C4—62no—
451C4—62no—
452C4—62no—
453C4#100412yes—
454C4D3×#4112yes—
455C3#351411yescharacteristic, complemented, Sylow
456C2—44no—
457C2—41no—
458C2—64no—
459C2—122no—
460C2C2×#100411yescharacteristic
461C2C2×D3×#4111yescharacteristic
462C2#596411yescharacteristic
subgroupG/H
center, FrattiniC22C24×D3
commutator, socle, cosocleC22×C3C25
FittingC3×#532C2
hypercenter#532D3
hypocenterC3#3514
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ #532

Complements

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

NH ≅ G/Ntype
1. C3×#532C2semidirect
2. #5831C2semidirect
3. #5829C2semidirect
4. #5732C2semidirect
5. #5727C2semidirect
6. #5717C2semidirect
7. #5713C2semidirect
8. #5680C2semidirect
9. D3×#124C2semidirect
10. #5616C2semidirect
11. #5613C2semidirect
12. #5612C2semidirect
13. #5561C2semidirect
14. #5556C2semidirect
15. #5545C2semidirect
16. #5479C2semidirect
17. C4×#235C2semidirect
19. C2×C3×#41C22semidirect
20. C2×D3×Q8C22semidirect
24. C3×C4⋊Q8C22semidirect
26. C3×#124C22semidirect
27. C3×#121C22semidirect
28. C3×#121C22semidirect
29. C3×C4×D4C22semidirect
30. C3×C4×D4C22semidirect
31. C2×C3×C42C22semidirect
33. #946C22semidirect
34. Q8×Dic3C22semidirect
35. #939C22semidirect
38. #938C22semidirect
40. #937C22semidirect
41. #936C22semidirect
42. #936C22semidirect
43. #936C22semidirect
44. #935C22semidirect
45. D4×Dic3C22semidirect
46. D4×Dic3C22semidirect
48. #929C22semidirect
49. #929C22semidirect
50. C4×#67C22semidirect
51. C4×#67C22semidirect
52. C4×#67C22semidirect
53. C4×#67C22semidirect
54. C2×(C2×D3)⋊C4C22semidirect
55. #926C22semidirect
56. #924C22semidirect
57. #924C22semidirect
58. #898C22semidirect
59. #897C22semidirect
60. #896C22semidirect
62. #892C22semidirect
63. #888C22semidirect
64. #885C22semidirect
65. #885C22semidirect
66. #883C22semidirect
67. #67⋊C4C22semidirect
68. D3×C22⋊C4C22semidirect
69. D3×C22⋊C4C22semidirect
70. #879C22semidirect
71. #877C22semidirect
72. #876C22semidirect
77. #872C22semidirect
78. #872C22semidirect
79. C42×D3C22semidirect
80. #870C22semidirect
81. C4×Dic6C22semidirect
82. C4×Dic6C22semidirect
83. C4×Dic6C22semidirect
95. #532D3semidirect
172. C2×#41C2×D3semidirect
177. C4⋊Q8C2×D3semidirect
190. #124C2×D3semidirect
205. #121C2×D3semidirect
206. #121C2×D3semidirect
224. C4×D4C2×D3semidirect
225. C4×D4C2×D3semidirect
235. C2×C42C2×D3semidirect
271. D12#41semidirect
455. C3#3514semidirect

Maximal subgroups

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

subgroupindex
C3×#5322
#58312
#58292
#57322
#57272
#57172
#57132
#56802
D3×#1242
#56162
#56132
#56122
#55612
#55562
#55452
#54792
C4×#2352
#35143