Finite Group Databasebeta

← #85840

Subgroups — #85840

Order 384.

1132 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×#41C211yesmaximal, characteristic, complemented
2#5828C212yesmaximal, complemented
3#5584C211yesmaximal, characteristic, complemented
4#5581C212yesmaximal, complemented
5#5579C211yesmaximal, characteristic, complemented
6#5563C211yesmaximal, characteristic, complemented
7#5558C212yesmaximal, complemented
8#5556C214yesmaximal, complemented
9#5551C211yesmaximal, characteristic, complemented
10#5550C212yesmaximal, complemented
11#5541C212yesmaximal, complemented
12#5528C214yesmaximal, complemented
13D3×#117C212yesmaximal, complemented
14#5479C212yesmaximal, complemented
15C4×#235C212yesmaximal, complemented
16C2×C4×D12C211yesmaximal, characteristic, complemented
17#5470C211yesmaximal, characteristic, complemented
18#3475—31nomaximal, Sylow
19C2×C3×#41C2211yescharacteristic
20C2×#235C2212yes—
21C22×D12C2211yescharacteristic
22C22×C4×D3C2212yes—
23C3×C4×Q8C2211yescharacteristic, complemented
24C3×C4×Q8C2211yescharacteristic, complemented
25C3×C4×D4C2212yes—
26C3×C4×D4C2212yes—
27C3×C4×D4C2211yescharacteristic, complemented
28C3×C4×D4C2211yescharacteristic, complemented
29C3×#117C2211yescharacteristic
30C3×#117C2212yescomplemented
31C2×C3×C42C2211yescharacteristic
32C2×C3×C42C2212yescomplemented
33#946C2212yescomplemented
34#946C2212yescomplemented
35#938C2212yescomplemented
36#938C2212yescomplemented
37#937C2214yes—
38#935C2214yes—
39#930C2212yes—
40#929C2214yescomplemented
41C4×#67C2214yescomplemented
42C4×#67C2214yescomplemented
43C4×#67C2214yescomplemented
44C2×(C2×D3)⋊C4C2212yes—
45#926C2212yes—
46#926C2212yescomplemented
47C2×C4⋊Dic3C2211yescharacteristic
48#924C2212yes—
49#924C2212yes—
50#924C2212yescomplemented
51#898C2214yescomplemented
52#896C2214yescomplemented
53#894C2214yes—
54#892C2212yescomplemented
55#892C2212yescomplemented
56D3×C4⋊C4C2212yescomplemented
57D3×C4⋊C4C2212yescomplemented
58#889C2214yescomplemented
59#885C2214yescomplemented
60#884C2214yes—
61#883C2214yescomplemented
62D3×C22⋊C4C2214yes—
63#879C2214yescomplemented
64#877C2214yes—
65#876C2214yescomplemented
66#875C2212yes—
67C4×D12C2211yescharacteristic
68C4×D12C2211yescharacteristic
69C4×D12C2212yes—
70C4×D12C2211yescharacteristic
71C4×D12C2212yes—
72C4×D12C2211yescharacteristic
73C4×D12C2212yes—
74#872C2214yescomplemented
75#872C2214yescomplemented
76C42×D3C2214yescomplemented
77#870C2212yescomplemented
78#870C2212yescomplemented
79#869C2211yescharacteristic, complemented
80#869C2211yescharacteristic, complemented
81C4×Dic6C2212yescomplemented
82C4×Dic6C2212yescomplemented
83C4×Dic6C2212yescomplemented
84#556—31no—
85#555—31no—
86#554—31no—
87#553—32no—
88#552—32no—
89#552—32no—
90#551—34no—
91#547—31no—
92#546—32no—
93#533—31no—
94#529—34no—
95#529—32no—
96#525—32no—
97C4×#41—32no—
98C4×#41D311yescharacteristic, complemented
99C2×C4×D4—31no—
100C2×#117—32no—
101C23×D3C2312yes—
102C3×#41—24no—
103C2×C3×Q8C2311yescharacteristic
104C2×C3×D4C2312yes—
105C2×C3×D4C2311yescharacteristic
106C22×C3×C4C2311yescharacteristic
107C22×C3×C4C2312yes—
108C22×C3×C4C2312yes—
109C22×C3×C4C2311yescharacteristic
110C22×C3×C4C2312yes—
111C22×C3×C4C2311yescharacteristic
112C2×#67C2314yes—
113C2×#67C2314yes—
114C22×Dic3C2312yes—
115#235—28no—
116C2×D12—24no—
117C2×D12C2311yescharacteristic
118C2×D12C2312yes—
119C2×D12C2311yescharacteristic
120C2×C4×D3—28no—
121C2×C4×D3C2312yes—
122C2×C4×D3C2314yes—
123C2×C4×D3C2312yes—
124C2×C4×D3C2312yes—
125C2×C4×D3C2312yes—
126C2×C4×D3C2314yes—
127C2×Dic6C2312yes—
128C2×Dic6C2312yes—
129C3×C4⋊C4C2312yes—
130C3×C4⋊C4C2311yescharacteristic
131C3×C4⋊C4C2311yescharacteristic
132C3×C4⋊C4C2312yes—
133C3×C22⋊C4C2312yes—
134C3×C22⋊C4C2312yes—
135C3×C22⋊C4C2312yes—
136C3×C42C2311yescharacteristic
137C3×C42C2311yescharacteristic
138C3×C42C2312yes—
139C3×C42C2311yescharacteristic
140C3×C42C2311yescharacteristic
141C3×C42C2312yes—
142C3×C42C2312yes—
143#217C2314yes—
144#217C2314yes—
145#217C2314yes—
146(C2×D3)⋊C4C2312yes—
147(C2×D3)⋊C4C2314yes—
148(C2×D3)⋊C4C2314yes—
149(C2×D3)⋊C4C2314yes—
150(C2×D3)⋊C4C2312yes—
151(C2×D3)⋊C4C2312yes—
152(C2×D3)⋊C4C2312yes—
153(C2×D3)⋊C4C2314yes—
154C4⋊Dic3C2311yescharacteristic
155C4⋊Dic3C2312yes—
156C4⋊Dic3C2312yes—
157C4⋊Dic3C2312yes—
158C4⋊Dic3C2312yes—
159C4⋊Dic3C2311yescharacteristic
160C4⋊Dic3C2312yes—
161Dic3⋊C4C2314yes—
162Dic3⋊C4C2314yes—
163Dic3⋊C4C2314yes—
164Dic3⋊C4C2314yes—
165Dic3⋊C4C2314yes—
166Dic3⋊C4C2314yes—
167C4×Dic3C2314yes—
168C4×Dic3C2314yes—
169C4×Dic3C2314yes—
170C2×#41—32no—
171C2×#41C2×D311yescharacteristic
172C22×D4—31no—
173C23×C4—32no—
174C4⋊Q8—31no—
175C4⋊Q8—31no—
176#126—34no—
177#126—34no—
178#126—34no—
179#125—34no—
180#125—32no—
181#125—32no—
182#124—34no—
183#124—32no—
184#123—34no—
185#123—34no—
186#123—34no—
187#123—34no—
188C22⋊Q8—32no—
189C22⋊Q8—32no—
190C22⋊Q8—32no—
191C22⋊Q8—32no—
192C22⋊Q8—32no—
193C22⋊Q8—34no—
194#121—32no—
195#121—32no—
196#121—32no—
197#121—34no—
198#120—34no—
199C4×Q8—32no—
200C4×Q8—32no—
201C4×Q8—32no—
202C4×Q8C2×D311yescharacteristic, complemented
203C4×Q8C2×D311yescharacteristic, complemented
204C4×D4—34no—
205C4×D4—34no—
206C4×D4—34no—
207C4×D4—31no—
208C4×D4—31no—
209C4×D4—32no—
210C4×D4—31no—
211C4×D4—32no—
212C4×D4—31no—
213C4×D4—32no—
214C4×D4C2×D312yes—
215C4×D4C2×D312yes—
216C4×D4C2×D311yescharacteristic, complemented
217C4×D4C2×D311yescharacteristic, complemented
218#117—32no—
219#117—32no—
220#117—32no—
221#117—32no—
222#117—34no—
223#117—34no—
224#117—34no—
225#117C2×D311yescharacteristic
226#117C2×D312yescomplemented
227C2×C4⋊C4—31no—
228C2×C4⋊C4—32no—
229C2×C4⋊C4—32no—
230C2×C22⋊C4—32no—
231C2×C22⋊C4—34no—
232C2×C42—34no—
233C2×C42C2×D311yescharacteristic
234C2×C42C2×D312yescomplemented
235C23×C3C2412yes—
236C23×C3C2411yescharacteristic
237C22×D3—24no—
238C22×D3—24no—
239C22×D3—42no—
240C22×D3C2412yes—
241C22×D3C2412yes—
242C3×Q8—22no—
243C3×D4—24no—
244C3×D4—22no—
245C2×C3×C4—22no—
246C2×C3×C4—24no—
247C2×C3×C4—24no—
248C2×C3×C4—41no—
249C2×C3×C4—42no—
250C2×C3×C4#4114yescomplemented
251C2×C3×C4C2412yes—
252C2×C3×C4C2412yes—
253C2×C3×C4C2411yescharacteristic
254C2×C3×C4C2411yescharacteristic
255C2×C3×C4C2412yes—
256C2×C3×C4C2411yescharacteristic
257C2×C3×C4C2411yescharacteristic
258C2×C3×C4C2411yescharacteristic
259C2×C3×C4C2411yescharacteristic
260#67—28no—
261#67—44no—
262C2×Dic3—24no—
263C2×Dic3C2412yes—
264C2×Dic3C2414yes—
265C2×Dic3C2414yes—
266C2×Dic3C2412yes—
267D12—24no—
268D12—22no—
269D12#4114yescomplemented
270C4×D3—28no—
271C4×D3—24no—
272C4×D3—24no—
273C4×D3—24no—
274C4×D3—24no—
275C4×D3—44no—
276Dic6—24no—
277Dic6—42no—
278C24—32no—
279#41—24no—
280#41—68no—
281C2×Q8—32no—
282C2×Q8—32no—
283C2×Q8C22×D311yescharacteristic
284C2×D4—34no—
285C2×D4—34no—
286C2×D4—31no—
287C2×D4—32no—
288C2×D4—31no—
289C2×D4—64no—
290C2×D4C22×D312yes—
291C2×D4C22×D311yescharacteristic
292C22×C4—32no—
293C22×C4—34no—
294C22×C4—32no—
295C22×C4—32no—
296C22×C4—32no—
297C22×C4—32no—
298C22×C4—34no—
299C22×C4—68no—
300C22×C4C22×D311yescharacteristic
301C22×C4C22×D312yes—
302C22×C4C22×D312yes—
303C22×C4C22×D311yescharacteristic
304C22×C4C22×D312yes—
305C22×C4C22×D311yescharacteristic
306C4⋊C4—31no—
307C4⋊C4—32no—
308C4⋊C4—32no—
309C4⋊C4—34no—
310C4⋊C4—34no—
311C4⋊C4—31no—
312C4⋊C4—32no—
313C4⋊C4—32no—
314C4⋊C4—34no—
315C4⋊C4—34no—
316C4⋊C4—34no—
317C4⋊C4—34no—
318C4⋊C4—32no—
319C4⋊C4C22×D311yescharacteristic
320C4⋊C4C22×D311yescharacteristic
321C4⋊C4C22×D312yes—
322C4⋊C4C22×D312yes—
323C22⋊C4—34no—
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—34no—
334C22⋊C4C22×D312yes—
335C22⋊C4C22×D312yes—
336C22⋊C4C22×D312yes—
337C42—34no—
338C42—34no—
339C42—34no—
340C42C22×D311yescharacteristic
341C42C22×D311yescharacteristic
342C42C22×D312yes—
343C42C22×D312yes—
344C42C22×D312yes—
345C42C22×D311yescharacteristic
346C42C22×D311yescharacteristic
347C22×C3—21no—
348C22×C3—21no—
349C22×C3—22no—
350C22×C3—22no—
351C22×C3—22no—
352C22×C3C2×#4112yes—
353C22×C3C2511yescharacteristic
354C2×D3—22no—
355C2×D3—22no—
356C2×D3—22no—
357C2×D3—22no—
358C2×D3—22no—
359C2×D3—48no—
360C2×D3C2×#4114yes—
361C3×C4—22no—
362C3×C4—21no—
363C3×C4—22no—
364C3×C4—21no—
365C3×C4—22no—
366C3×C4—21no—
367C3×C4C2×#4112yes—
368C3×C4C2×#4112yes—
369C3×C4C2×#4112yes—
370Dic3—24no—
371Dic3—22no—
372Dic3—22no—
373Dic3—24no—
374C23—32no—
375C23—32no—
376C23—64no—
377C23—64no—
378C23—122no—
379C23C23×D312yes—
380C23C23×D311yescharacteristic
381Q8—22no—
382Q8—64no—
383Q8—122no—
384D4—24no—
385D4—22no—
386D4—34no—
387D4—64no—
388D4—68no—
389D4—62no—
390D4—124no—
391C2×C4—24no—
392C2×C4—22no—
393C2×C4—24no—
394C2×C4—32no—
395C2×C4—34no—
396C2×C4—34no—
397C2×C4—32no—
398C2×C4—42no—
399C2×C4—41no—
400C2×C4—68no—
401C2×C4—64no—
402C2×C4—64no—
403C2×C4—64no—
404C2×C4—64no—
405C2×C4—64no—
406C2×C4—124no—
407C2×C4#23514yescomplemented
408C2×C4C23×D312yes—
409C2×C4C23×D312yes—
410C2×C4C23×D311yescharacteristic
411C2×C4C23×D311yescharacteristic
412C2×C4C23×D312yes—
413C2×C4C23×D311yescharacteristic
414C2×C4C23×D311yescharacteristic
415C2×C4C23×D311yescharacteristic
416C2×C4C23×D311yescharacteristic
417C2×C3—22no—
418C2×C3—42no—
419C2×C3C22×#4111yescharacteristic
420C2×C3C22×#4111yescharacteristic
421C2×C3#58511yescharacteristic
422D3—24no—
423D3—42no—
424C22—21no—
425C22—21no—
426C22—22no—
427C22—22no—
428C22—22no—
429C22—34no—
430C22—62no—
431C22—62no—
432C22—62no—
433C22—62no—
434C22—62no—
435C22—128no—
436C22C2×#23512yes—
437C22C24×D311yescharacteristic
438C4—22no—
439C4—22no—
440C4—21no—
441C4—21no—
442C4—22no—
443C4—21no—
444C4—62no—
445C4—62no—
446C4—64no—
447C4—64no—
448C4C2×#23512yes—
449C4C2×#23512yes—
450C4D3×#4112yes—
451C3#347511yescharacteristic, complemented, Sylow
452C2—22no—
453C2—42no—
454C2—64no—
455C2—122no—
456C2C22×#23511yescharacteristic
457C2C2×D3×#4111yescharacteristic
458C2#596411yescharacteristic
subgroupG/H
centerC2×C4C23×D3
commutator, socle, cosocleC22×C3C25
FrattiniC22C24×D3
FittingC3×C4×#41C2
hypercenterC4×#41D3
hypocenterC3#3475
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
1. C3×C4×#41C2semidirect
2. #5828C2semidirect
3. #5584C2semidirect
4. #5581C2semidirect
5. #5579C2semidirect
6. #5563C2semidirect
7. #5558C2semidirect
8. #5556C2semidirect
9. #5551C2semidirect
10. #5550C2semidirect
11. #5541C2semidirect
12. #5528C2semidirect
13. D3×#117C2semidirect
14. #5479C2semidirect
15. C4×#235C2semidirect
16. C2×C4×D12C2semidirect
17. #5470C2semidirect
23. C3×C4×Q8C22semidirect
24. C3×C4×Q8C22semidirect
27. C3×C4×D4C22semidirect
28. C3×C4×D4C22semidirect
30. C3×#117C22semidirect
32. C2×C3×C42C22semidirect
33. #946C22semidirect
34. #946C22semidirect
35. #938C22semidirect
36. #938C22semidirect
40. #929C22semidirect
41. C4×#67C22semidirect
42. C4×#67C22semidirect
43. C4×#67C22semidirect
46. #926C22semidirect
50. #924C22semidirect
51. #898C22semidirect
52. #896C22semidirect
54. #892C22semidirect
55. #892C22semidirect
56. D3×C4⋊C4C22semidirect
57. D3×C4⋊C4C22semidirect
58. #889C22semidirect
59. #885C22semidirect
61. #883C22semidirect
63. #879C22semidirect
65. #876C22semidirect
74. #872C22semidirect
75. #872C22semidirect
76. C42×D3C22semidirect
77. #870C22semidirect
78. #870C22semidirect
79. #869C22semidirect
80. #869C22semidirect
81. C4×Dic6C22semidirect
82. C4×Dic6C22semidirect
83. C4×Dic6C22semidirect
98. C4×#41D3semidirect
202. C4×Q8C2×D3semidirect
203. C4×Q8C2×D3semidirect
216. C4×D4C2×D3semidirect
217. C4×D4C2×D3semidirect
226. #117C2×D3semidirect
234. C2×C42C2×D3semidirect
250. C2×C3×C4#41semidirect
269. D12#41semidirect
407. C2×C4#235semidirect
451. C3#3475semidirect

Maximal subgroups

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

subgroupindex
C3×C4×#412
#58282
#55842
#55812
#55792
#55632
#55582
#55562
#55512
#55502
#55412
#55282
D3×#1172
#54792
C4×#2352
C2×C4×D122
#54702
#34753