Finite Group Databasebeta

← #86933

Subgroups — #86933

Order 384.

1252 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#554C211yesmaximal, characteristic, complemented
2#5734C211yesmaximal, characteristic, complemented
3#5725C211yesmaximal, characteristic, complemented
4#5697C212yesmaximal, complemented
5#5695C212yesmaximal, complemented
6#5644C214yesmaximal, complemented
7#5630C214yesmaximal, complemented
8#5630C212yesmaximal, complemented
9#5627C212yesmaximal, complemented
10#5580C211yesmaximal, characteristic, complemented
11#5577C211yesmaximal, characteristic, complemented
12D4×D12C212yesmaximal, complemented
13D4×D12C211yesmaximal, characteristic, complemented
14#5545C212yesmaximal, complemented
15C4×D3×D4C211yesmaximal, characteristic, complemented
16#5514C212yesmaximal, complemented
17C2×#895C212yesmaximal, complemented
18#3519—31nomaximal, Sylow
19C2×#239C2212yescomplemented
20C2×#239C2212yescomplemented
21C2×D3×D4C2211yescharacteristic
22C2×D3×D4C2212yes—
23C22×D12C2212yescomplemented
24C22×D12C2214yescomplemented
25C22×C4×D3C2212yescomplemented
26C3×C4⋊Q8C2211yescharacteristic, complemented
27C3×#125C2212yescomplemented
28C3×C22⋊Q8C2214yescomplemented
29C3×C22⋊Q8C2212yescomplemented
30C3×C4×Q8C2211yescharacteristic, complemented
31C3×C4×D4C2211yescharacteristic
32C3×C4×D4C2212yes—
33C2×C3×C4⋊C4C2212yescomplemented
34#947C2212yescomplemented
35#947C2214yescomplemented
36#947C2211yescharacteristic, complemented
37#946C2211yescharacteristic, complemented
38D4×Dic3C2211yescharacteristic
39#930C2214yescomplemented
40#930C2212yescomplemented
41C4×#67C2212yescomplemented
42C4×#67C2214yescomplemented
43C2×(C2×D3)⋊C4C2214yescomplemented
44#898C2212yescomplemented
45#898C2214yescomplemented
46#895C2211yescharacteristic
47#895C2214yescomplemented
48#895C2214yescomplemented
49#895C2212yescomplemented
50#895C2212yescomplemented
51#895C2214yescomplemented
52#895C2212yescomplemented
53#895C2214yescomplemented
54#895C2212yescomplemented
55#895C2212yescomplemented
56#895C2212yescomplemented
57#894C2214yescomplemented
58#894C2214yescomplemented
59#894C2214yescomplemented
60#894C2212yescomplemented
61#893C2214yescomplemented
62#893C2211yescharacteristic, complemented
63#893C2212yescomplemented
64#893C2212yescomplemented
65#892C2212yescomplemented
66#892C2212yescomplemented
67D3×C4⋊C4C2211yescharacteristic, complemented
68#890C2211yescharacteristic, complemented
69#882C2214yescomplemented
70#882C2214yescomplemented
71#882C2214yescomplemented
72#67⋊C4C2212yescomplemented
73#67⋊C4C2214yescomplemented
74D3×C22⋊C4C2212yescomplemented
75D3×C22⋊C4C2214yescomplemented
76#874C2212yescomplemented
77#874C2211yescharacteristic, complemented
78C4×D12C2212yescomplemented
79C4×D12C2212yescomplemented
80C4×D12C2211yescharacteristic, complemented
81C4×D12C2211yescharacteristic, complemented
82#872C2212yescomplemented
83C42×D3C2211yescharacteristic, complemented
84#555—31no—
85#554D311yescharacteristic, complemented
86#553—32no—
87#553—32no—
88#550—31no—
89#546—34no—
90#546—32no—
91D42—32no—
92D42—31no—
93#540—32no—
94#538—34no—
95#532—31no—
96#529—31no—
97#525—32no—
98C2×#121—32no—
99#518—32no—
100C2×C4×D4—31no—
101C23×D3C2312yes—
102C23×D3C2314yes—
103C2×C3×Q8C2311yescharacteristic
104C2×C3×Q8C2312yes—
105C2×C3×D4C2311yescharacteristic
106C22×C3×C4C2312yes—
107C22×C3×C4C2314yes—
108C2×#67C2312yes—
109C2×#67C2314yes—
110C22×Dic3C2312yes—
111#239—44no—
112#239—44no—
113D3×D4—24no—
114D3×D4—28no—
115C2×D12—44no—
116C2×D12—48no—
117C2×D12C2312yes—
118C2×D12C2311yescharacteristic
119C2×D12C2312yes—
120C2×D12C2311yescharacteristic
121C2×D12C2312yes—
122C2×D12C2314yes—
123C2×D12C2314yes—
124C2×D12C2312yes—
125C2×D12C2314yes—
126C2×D12C2314yes—
127C2×D12C2314yes—
128C2×C4×D3—44no—
129C2×C4×D3C2311yescharacteristic
130C2×C4×D3C2311yescharacteristic
131C2×C4×D3C2311yescharacteristic
132C2×C4×D3C2312yes—
133C2×C4×D3C2312yes—
134C2×C4×D3C2314yes—
135C2×C4×D3C2312yes—
136C2×C4×D3C2314yes—
137C2×C4×D3C2312yes—
138C3×C4⋊C4C2311yescharacteristic
139C3×C4⋊C4C2311yescharacteristic
140C3×C4⋊C4C2312yes—
141C3×C4⋊C4C2312yes—
142C3×C4⋊C4C2314yes—
143C3×C4⋊C4C2314yes—
144C3×C4⋊C4C2312yes—
145C3×C22⋊C4C2312yes—
146C3×C22⋊C4C2314yes—
147C3×C42C2311yescharacteristic
148C3×C42C2312yes—
149#217C2312yes—
150(C2×D3)⋊C4C2312yes—
151(C2×D3)⋊C4C2312yes—
152(C2×D3)⋊C4C2312yes—
153(C2×D3)⋊C4C2312yes—
154(C2×D3)⋊C4C2312yes—
155(C2×D3)⋊C4C2312yes—
156(C2×D3)⋊C4C2314yes—
157(C2×D3)⋊C4C2314yes—
158(C2×D3)⋊C4C2312yes—
159(C2×D3)⋊C4C2314yes—
160(C2×D3)⋊C4C2314yes—
161(C2×D3)⋊C4C2314yes—
162(C2×D3)⋊C4C2314yes—
163C4⋊Dic3C2311yescharacteristic
164C4⋊Dic3C2311yescharacteristic
165C4⋊Dic3C2312yes—
166Dic3⋊C4C2312yes—
167Dic3⋊C4C2312yes—
168Dic3⋊C4C2312yes—
169C4×Dic3C2311yescharacteristic
170C4×Dic3C2311yescharacteristic
171C4×Dic3C2311yescharacteristic
172C4×Dic3C2314yes—
173C2×#41—32no—
174C2×#41—32no—
175C22×D4—31no—
176C22×D4—32no—
177C22×D4—32no—
178C22×D4—34no—
179C23×C4—32no—
180C4⋊Q8C2×D311yescharacteristic, complemented
181#127—31no—
182#127—32no—
183#126—32no—
184#126—34no—
185#125—31no—
186#125C2×D312yescomplemented
187#124—31no—
188#124—32no—
189#124—34no—
190#123—34no—
191#123—32no—
192#123—34no—
193#123—34no—
194C22⋊Q8—31no—
195C22⋊Q8C2×D312yescomplemented
196C22⋊Q8C2×D314yescomplemented
197#121—32no—
198#121—34no—
199#121—31no—
200#121—32no—
201#121—34no—
202#121—34no—
203#121—32no—
204#121—32no—
205#121—32no—
206#121—34no—
207#121—32no—
208#121—32no—
209#121—34no—
210#120—34no—
211#120—34no—
212#120—34no—
213C4×Q8C2×D311yescharacteristic, complemented
214C4×D4—31no—
215C4×D4—32no—
216C4×D4—34no—
217C4×D4—31no—
218C4×D4—32no—
219C4×D4—34no—
220C4×D4—32no—
221C4×D4—32no—
222C4×D4—34no—
223C4×D4—31no—
224C4×D4—32no—
225C4×D4—32no—
226C4×D4—31no—
227C4×D4C2×D311yescharacteristic
228C4×D4C2×D312yes—
229#117—32no—
230#117—32no—
231#117—32no—
232C2×C4⋊C4—31no—
233C2×C4⋊C4C2×D312yescomplemented
234C2×C22⋊C4—34no—
235C2×C22⋊C4—32no—
236C2×C22⋊C4—34no—
237C2×C42—31no—
238C23×C3C2412yes—
239C22×D3—24no—
240C22×D3—28no—
241C22×D3—24no—
242C22×D3—42no—
243C22×D3—44no—
244C22×D3—44no—
245C22×D3C2412yes—
246C22×D3C2412yes—
247C22×D3C2414yes—
248C22×D3C2411yescharacteristic
249C3×Q8—22no—
250C3×Q8—42no—
251C3×D4#4114yescomplemented
252C2×C3×C4—24no—
253C2×C3×C4—44no—
254C2×C3×C4C2411yescharacteristic
255C2×C3×C4C2414yes—
256C2×C3×C4C2412yes—
257C2×C3×C4C2412yes—
258C2×C3×C4C2412yes—
259C2×C3×C4C2411yescharacteristic
260C2×C3×C4C2411yescharacteristic
261#67—24no—
262#67—28no—
263C2×Dic3—42no—
264C2×Dic3C2411yescharacteristic
265C2×Dic3C2412yes—
266C2×Dic3C2411yescharacteristic
267C2×Dic3C2411yescharacteristic
268C2×Dic3C2412yes—
269D12—24no—
270D12—28no—
271D12—22no—
272D12—24no—
273D12—22no—
274D12—24no—
275D12—44no—
276D12—44no—
277D12—44no—
278D12—42no—
279D12—44no—
280C4×D3—22no—
281C4×D3—22no—
282C4×D3—24no—
283C4×D3—22no—
284C4×D3—24no—
285C4×D3—42no—
286C4×D3—42no—
287C4×D3—44no—
288C4×D3—44no—
289C24—32no—
290C24—34no—
291#41—124no—
292#41—124no—
293C2×Q8C22×D311yescharacteristic
294C2×Q8C22×D312yes—
295C2×D4—32no—
296C2×D4—34no—
297C2×D4—31no—
298C2×D4—32no—
299C2×D4—34no—
300C2×D4—32no—
301C2×D4—31no—
302C2×D4—32no—
303C2×D4—34no—
304C2×D4—32no—
305C2×D4—34no—
306C2×D4—34no—
307C2×D4—34no—
308C2×D4—64no—
309C2×D4—68no—
310C2×D4—124no—
311C2×D4—128no—
312C2×D4C22×D311yescharacteristic
313C22×C4—32no—
314C22×C4—31no—
315C22×C4—31no—
316C22×C4—31no—
317C22×C4—32no—
318C22×C4—32no—
319C22×C4—32no—
320C22×C4—34no—
321C22×C4—34no—
322C22×C4—32no—
323C22×C4—124no—
324C22×C4C22×D312yes—
325C22×C4C22×D314yes—
326C4⋊C4—31no—
327C4⋊C4—32no—
328C4⋊C4—31no—
329C4⋊C4—32no—
330C4⋊C4—32no—
331C4⋊C4—32no—
332C4⋊C4C22×D311yescharacteristic
333C4⋊C4C22×D311yescharacteristic
334C4⋊C4C22×D312yes—
335C4⋊C4C22×D314yes—
336C4⋊C4C22×D312yes—
337C4⋊C4C22×D314yes—
338C4⋊C4C22×D312yes—
339C22⋊C4—32no—
340C22⋊C4—32no—
341C22⋊C4—34no—
342C22⋊C4—32no—
343C22⋊C4—34no—
344C22⋊C4—32no—
345C22⋊C4—34no—
346C22⋊C4—32no—
347C22⋊C4—34no—
348C22⋊C4—32no—
349C22⋊C4—32no—
350C22⋊C4—32no—
351C22⋊C4—34no—
352C22⋊C4—34no—
353C22⋊C4C22×D312yes—
354C22⋊C4C22×D314yes—
355C42—31no—
356C42—31no—
357C42—31no—
358C42—34no—
359C42C22×D311yescharacteristic
360C42C22×D312yes—
361C22×C3—22no—
362C22×C3—22no—
363C22×C3C2×#4114yes—
364C22×C3C2511yescharacteristic
365C2×D3—21no—
366C2×D3—21no—
367C2×D3—22no—
368C2×D3—22no—
369C2×D3—24no—
370C2×D3—22no—
371C2×D3—24no—
372C2×D3—24no—
373C2×D3—22no—
374C2×D3—22no—
375C2×D3—22no—
376C2×D3—48no—
377C2×D3—88no—
378C2×D3H(5,𝔽2)12yes—
379C3×C4—21no—
380C3×C4—22no—
381C3×C4—22no—
382C3×C4—24no—
383C3×C4—22no—
384C3×C4C2×#4112yes—
385C3×C4H(5,𝔽2)12yes—
386Dic3—21no—
387Dic3—22no—
388Dic3—21no—
389Dic3—22no—
390Dic3—21no—
391C23—31no—
392C23—32no—
393C23—32no—
394C23—34no—
395C23—64no—
396C23—64no—
397C23—68no—
398C23—122no—
399C23—124no—
400C23—124no—
401C23C23×D312yes—
402Q8—22no—
403Q8—42no—
404D4—64no—
405D4—68no—
406D4—64no—
407D4—68no—
408D4—62no—
409D4—64no—
410D4—62no—
411D4—64no—
412D4—124no—
413D4—124no—
414D4—124no—
415D4—124no—
416D4—122no—
417D4#23914yescomplemented
418C2×C4—24no—
419C2×C4—31no—
420C2×C4—32no—
421C2×C4—31no—
422C2×C4—32no—
423C2×C4—31no—
424C2×C4—44no—
425C2×C4—62no—
426C2×C4—62no—
427C2×C4—64no—
428C2×C4—62no—
429C2×C4—64no—
430C2×C4—122no—
431C2×C4—122no—
432C2×C4—124no—
433C2×C4—124no—
434C2×C4—122no—
435C2×C4C23×D311yescharacteristic
436C2×C4C23×D314yes—
437C2×C4C23×D312yes—
438C2×C4C23×D312yes—
439C2×C4C23×D312yes—
440C2×C4C23×D311yescharacteristic
441C2×C4C23×D311yescharacteristic
442C2×C3—24no—
443C2×C3C22×#4111yescharacteristic
444C2×C3C2×H(5,𝔽2)11yescharacteristic
445C2×C3C2×H(5,𝔽2)11yescharacteristic
446D3—22no—
447D3—42no—
448D3—44no—
449D3—42no—
450C22—22no—
451C22—22no—
452C22—32no—
453C22—61no—
454C22—61no—
455C22—62no—
456C22—62no—
457C22—64no—
458C22—62no—
459C22—64no—
460C22—62no—
461C22—64no—
462C22—62no—
463C22—62no—
464C22—128no—
465C22—248no—
466C22C2×#23914yes—
467C22C24×D311yescharacteristic
468C4—22no—
469C4—22no—
470C4—22no—
471C4—24no—
472C4—21no—
473C4—61no—
474C4—62no—
475C4—61no—
476C4—62no—
477C4—61no—
478C4C2×#23912yes—
479C4#100912yes—
480C3#351911yescharacteristic, complemented, Sylow
481C2—24no—
482C2—62no—
483C2—122no—
484C2—122no—
485C2—124no—
486C2C22×#23911yescharacteristic
487C2C2×#100911yescharacteristic
488C2D3×H(5,𝔽2)11yescharacteristic
subgroupG/H
center, FrattiniC22C24×D3
commutator, socle, cosocleC22×C3C25
FittingC3×#554C2
hypercenter#554D3
hypocenterC3#3519
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ #554

Complements

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

NH ≅ G/Ntype
1. C3×#554C2semidirect
2. #5734C2semidirect
3. #5725C2semidirect
4. #5697C2semidirect
5. #5695C2semidirect
6. #5644C2semidirect
7. #5630C2semidirect
8. #5630C2semidirect
9. #5627C2semidirect
10. #5580C2semidirect
11. #5577C2semidirect
12. D4×D12C2semidirect
13. D4×D12C2semidirect
14. #5545C2semidirect
15. C4×D3×D4C2semidirect
16. #5514C2semidirect
17. C2×#895C2semidirect
19. C2×#239C22semidirect
20. C2×#239C22semidirect
23. C22×D12C22semidirect
24. C22×D12C22semidirect
25. C22×C4×D3C22semidirect
26. C3×C4⋊Q8C22semidirect
27. C3×#125C22semidirect
28. C3×C22⋊Q8C22semidirect
29. C3×C22⋊Q8C22semidirect
30. C3×C4×Q8C22semidirect
33. C2×C3×C4⋊C4C22semidirect
34. #947C22semidirect
35. #947C22semidirect
36. #947C22semidirect
37. #946C22semidirect
39. #930C22semidirect
40. #930C22semidirect
41. C4×#67C22semidirect
42. C4×#67C22semidirect
43. C2×(C2×D3)⋊C4C22semidirect
44. #898C22semidirect
45. #898C22semidirect
47. #895C22semidirect
48. #895C22semidirect
49. #895C22semidirect
50. #895C22semidirect
51. #895C22semidirect
52. #895C22semidirect
53. #895C22semidirect
54. #895C22semidirect
55. #895C22semidirect
56. #895C22semidirect
57. #894C22semidirect
58. #894C22semidirect
59. #894C22semidirect
60. #894C22semidirect
61. #893C22semidirect
62. #893C22semidirect
63. #893C22semidirect
64. #893C22semidirect
65. #892C22semidirect
66. #892C22semidirect
67. D3×C4⋊C4C22semidirect
68. #890C22semidirect
69. #882C22semidirect
70. #882C22semidirect
71. #882C22semidirect
72. #67⋊C4C22semidirect
73. #67⋊C4C22semidirect
74. D3×C22⋊C4C22semidirect
75. D3×C22⋊C4C22semidirect
76. #874C22semidirect
77. #874C22semidirect
78. C4×D12C22semidirect
79. C4×D12C22semidirect
80. C4×D12C22semidirect
81. C4×D12C22semidirect
82. #872C22semidirect
83. C42×D3C22semidirect
85. #554D3semidirect
180. C4⋊Q8C2×D3semidirect
186. #125C2×D3semidirect
195. C22⋊Q8C2×D3semidirect
196. C22⋊Q8C2×D3semidirect
213. C4×Q8C2×D3semidirect
233. C2×C4⋊C4C2×D3semidirect
251. C3×D4#41semidirect
417. D4#239semidirect
480. C3#3519semidirect

Maximal subgroups

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

subgroupindex
C3×#5542
#57342
#57252
#56972
#56952
#56442
#56302
#56272
#55802
#55772
D4×D122
#55452
C4×D3×D42
#55142
C2×#8952
#35193