Finite Group Databasebeta

← #86922

Subgroups — #86922

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×#554C211yesmaximal, characteristic, complemented
2#5734C211yesmaximal, characteristic, complemented
3#5728C211yesmaximal, characteristic, complemented
4#5694C212yesmaximal, complemented
5#5691C212yesmaximal, complemented
6#5642C212yesmaximal, complemented
7#5637C214yesmaximal, complemented
8#5627C212yesmaximal, complemented
9#5624C214yesmaximal, complemented
10#5584C211yesmaximal, characteristic, complemented
11C4×#239C211yesmaximal, characteristic, complemented
12#5555C211yesmaximal, characteristic, complemented
13#5554C212yesmaximal, complemented
14C4×D3×D4C211yesmaximal, characteristic, complemented
15C4×#237C212yesmaximal, complemented
16#5514C212yesmaximal, complemented
17C2×#892C212yesmaximal, complemented
18#3475—31nomaximal, Sylow
19C2×#239C2211yescharacteristic
20C2×#237C2212yes—
21C2×D3×D4C2211yescharacteristic
22C22×C4×D3C2212yes—
23C3×C4⋊Q8C2211yescharacteristic, complemented
24C3×#125C2212yescomplemented
25C3×C22⋊Q8C2214yescomplemented
26C3×C22⋊Q8C2212yescomplemented
27C3×C4×Q8C2211yescharacteristic, complemented
28C3×C4×D4C2212yes—
29C3×C4×D4C2211yescharacteristic
30C2×C3×C4⋊C4C2212yescomplemented
31#947C2214yescomplemented
32#946C2212yes—
33#946C2212yescomplemented
34Q8×Dic3C2211yescharacteristic, complemented
35Q8×Dic3C2212yescomplemented
36D4×Dic3C2211yescharacteristic
37#930C2214yes—
38#930C2212yescomplemented
39C4×#67C2212yes—
40C4×#67C2214yescomplemented
41C2×(C2×D3)⋊C4C2214yes—
42C2×C4⋊Dic3C2212yescomplemented
43C2×C4×Dic3C2214yescomplemented
44#898C2214yescomplemented
45#898C2214yescomplemented
46#898C2214yescomplemented
47#897C2212yes—
48#897C2212yescomplemented
49#895C2212yes—
50#895C2212yescomplemented
51#894C2214yes—
52#894C2214yescomplemented
53#893C2212yes—
54#893C2211yescharacteristic
55#893C2214yescomplemented
56#893C2211yescharacteristic, complemented
57#892C2214yes—
58#892C2212yes—
59#892C2211yescharacteristic
60#892C2212yescomplemented
61#892C2214yescomplemented
62#892C2212yescomplemented
63#892C2212yescomplemented
64#892C2212yescomplemented
65D3×C4⋊C4C2211yescharacteristic
66#890C2214yescomplemented
67#890C2212yescomplemented
68#887C2212yescomplemented
69#886C2214yes—
70#886C2214yescomplemented
71#882C2214yes—
72#67⋊C4C2212yes—
73#67⋊C4C2214yescomplemented
74D3×C22⋊C4C2212yes—
75#877C2214yescomplemented
76#875C2212yes—
77C4×D12C2212yes—
78C4×D12C2211yescharacteristic
79C4×D12C2211yescharacteristic, complemented
80C42×D3C2211yescharacteristic
81C42×D3C2212yescomplemented
82#869C2211yescharacteristic, complemented
83C4×Dic6C2212yescomplemented
84#556—31no—
85#555—31no—
86#554D311yescharacteristic, complemented
87#553—32no—
88#552—32no—
89#552—32no—
90#551—34no—
91#547—31no—
92#546—32no—
93#533—31no—
94#529—32no—
95#529—34no—
96#525—32no—
97C4×#41—31no—
98C4×#41—32no—
99C2×C4×D4—31no—
100C2×#117—32no—
101C23×D3C2312yes—
102C2×C3×Q8C2311yescharacteristic
103C2×C3×Q8C2312yes—
104C2×C3×D4C2311yescharacteristic
105C22×C3×C4C2312yes—
106C22×C3×C4C2314yes—
107C2×#67C2312yes—
108C2×#67C2314yes—
109C22×Dic3C2314yes—
110C22×Dic3C2312yes—
111#239—24no—
112#237—28no—
113D3×D4—24no—
114C2×D12C2311yescharacteristic
115C2×D12C2312yes—
116C2×D12C2311yescharacteristic
117C2×D12C2314yes—
118C2×C4×D3—28no—
119C2×C4×D3C2311yescharacteristic
120C2×C4×D3C2312yes—
121C2×C4×D3C2312yes—
122C2×C4×D3C2312yes—
123C2×C4×D3C2312yes—
124C2×C4×D3C2312yes—
125C2×C4×D3C2311yescharacteristic
126C2×C4×D3C2312yes—
127C2×C4×D3C2311yescharacteristic
128C2×Dic6C2312yes—
129C3×C4⋊C4C2312yes—
130C3×C4⋊C4C2312yes—
131C3×C4⋊C4C2314yes—
132C3×C4⋊C4C2311yescharacteristic
133C3×C4⋊C4C2311yescharacteristic
134C3×C4⋊C4C2314yes—
135C3×C4⋊C4C2312yes—
136C3×C22⋊C4C2314yes—
137C3×C22⋊C4C2312yes—
138C3×C42C2312yes—
139C3×C42C2311yescharacteristic
140#217C2312yes—
141(C2×D3)⋊C4C2312yes—
142(C2×D3)⋊C4C2312yes—
143(C2×D3)⋊C4C2312yes—
144(C2×D3)⋊C4C2312yes—
145(C2×D3)⋊C4C2314yes—
146(C2×D3)⋊C4C2314yes—
147(C2×D3)⋊C4C2312yes—
148(C2×D3)⋊C4C2314yes—
149(C2×D3)⋊C4C2314yes—
150(C2×D3)⋊C4C2314yes—
151(C2×D3)⋊C4C2314yes—
152C4⋊Dic3C2311yescharacteristic
153C4⋊Dic3C2312yes—
154C4⋊Dic3C2312yes—
155C4⋊Dic3C2312yes—
156C4⋊Dic3C2311yescharacteristic
157C4⋊Dic3C2314yes—
158C4⋊Dic3C2314yes—
159Dic3⋊C4C2314yes—
160Dic3⋊C4C2314yes—
161Dic3⋊C4C2312yes—
162C4×Dic3C2314yes—
163C4×Dic3C2311yescharacteristic
164C4×Dic3C2311yescharacteristic
165C4×Dic3C2311yescharacteristic
166C4×Dic3C2312yes—
167C4×Dic3C2312yes—
168C4×Dic3C2314yes—
169C4×Dic3C2314yes—
170C2×#41—31no—
171C2×#41—32no—
172C22×D4—31no—
173C23×C4—32no—
174C4⋊Q8—31no—
175C4⋊Q8C2×D311yescharacteristic, complemented
176#126—34no—
177#126—34no—
178#126—34no—
179#125—34no—
180#125—32no—
181#125C2×D312yescomplemented
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⋊Q8C2×D312yescomplemented
193C22⋊Q8C2×D314yescomplemented
194#121—32no—
195#121—34no—
196#121—32no—
197#121—32no—
198#120—34no—
199C4×Q8—31no—
200C4×Q8—32no—
201C4×Q8—32no—
202C4×Q8—32no—
203C4×Q8C2×D311yescharacteristic, complemented
204C4×D4—31no—
205C4×D4—32no—
206C4×D4—34no—
207C4×D4—31no—
208C4×D4—32no—
209C4×D4—31no—
210C4×D4—34no—
211C4×D4—32no—
212C4×D4—34no—
213C4×D4—31no—
214C4×D4—32no—
215C4×D4—31no—
216C4×D4C2×D311yescharacteristic
217C4×D4C2×D312yes—
218#117—31no—
219#117—32no—
220#117—34no—
221#117—34no—
222#117—32no—
223#117—32no—
224#117—32no—
225#117—32no—
226#117—34no—
227C2×C4⋊C4—32no—
228C2×C4⋊C4—31no—
229C2×C4⋊C4C2×D312yescomplemented
230C2×C22⋊C4—34no—
231C2×C22⋊C4—32no—
232C2×C42—34no—
233C2×C42—31no—
234C2×C42—32no—
235C23×C3C2412yes—
236C22×D3—24no—
237C22×D3—24no—
238C22×D3—42no—
239C22×D3C2412yes—
240C22×D3C2412yes—
241C22×D3C2411yescharacteristic
242C3×Q8—22no—
243C3×Q8—42no—
244C3×D4#4114yescomplemented
245C2×C3×C4—24no—
246C2×C3×C4—44no—
247C2×C3×C4C2412yes—
248C2×C3×C4C2414yes—
249C2×C3×C4C2412yes—
250C2×C3×C4C2411yescharacteristic
251C2×C3×C4C2412yes—
252C2×C3×C4C2411yescharacteristic
253C2×C3×C4C2411yescharacteristic
254#67—24no—
255#67—28no—
256C2×Dic3—28no—
257C2×Dic3—24no—
258C2×Dic3C2411yescharacteristic
259C2×Dic3C2412yes—
260C2×Dic3C2412yes—
261C2×Dic3C2411yescharacteristic
262C2×Dic3C2414yes—
263C2×Dic3C2411yescharacteristic
264D12—24no—
265D12—22no—
266D12—22no—
267D12—44no—
268C4×D3—24no—
269C4×D3—24no—
270C4×D3—22no—
271C4×D3—24no—
272C4×D3—24no—
273C4×D3—24no—
274C4×D3—42no—
275C4×D3—41no—
276C4×D3#4114yescomplemented
277Dic6—24no—
278C24—32no—
279#41—64no—
280#41—68no—
281C2×Q8—32no—
282C2×Q8C22×D311yescharacteristic
283C2×Q8C22×D312yes—
284C2×D4—34no—
285C2×D4—32no—
286C2×D4—32no—
287C2×D4—31no—
288C2×D4—31no—
289C2×D4—34no—
290C2×D4—64no—
291C2×D4C22×D311yescharacteristic
292C22×C4—31no—
293C22×C4—32no—
294C22×C4—34no—
295C22×C4—31no—
296C22×C4—32no—
297C22×C4—32no—
298C22×C4—32no—
299C22×C4—32no—
300C22×C4—32no—
301C22×C4—31no—
302C22×C4—32no—
303C22×C4—68no—
304C22×C4C22×D312yes—
305C22×C4C22×D314yes—
306C4⋊C4—31no—
307C4⋊C4—31no—
308C4⋊C4—32no—
309C4⋊C4—34no—
310C4⋊C4—32no—
311C4⋊C4—34no—
312C4⋊C4—34no—
313C4⋊C4—32no—
314C4⋊C4—34no—
315C4⋊C4—32no—
316C4⋊C4C22×D311yescharacteristic
317C4⋊C4C22×D311yescharacteristic
318C4⋊C4C22×D312yes—
319C4⋊C4C22×D314yes—
320C4⋊C4C22×D312yes—
321C4⋊C4C22×D312yes—
322C4⋊C4C22×D314yes—
323C22⋊C4—32no—
324C22⋊C4—32no—
325C22⋊C4—34no—
326C22⋊C4—34no—
327C22⋊C4—34no—
328C22⋊C4—32no—
329C22⋊C4—32no—
330C22⋊C4—32no—
331C22⋊C4—34no—
332C22⋊C4—32no—
333C22⋊C4—34no—
334C22⋊C4—34no—
335C22⋊C4C22×D312yes—
336C22⋊C4C22×D314yes—
337C42—32no—
338C42—31no—
339C42—34no—
340C42—34no—
341C42—31no—
342C42—32no—
343C42—34no—
344C42—31no—
345C42C22×D311yescharacteristic
346C42C22×D312yes—
347C22×C3—22no—
348C22×C3—22no—
349C22×C3C2×#4114yes—
350C22×C3C2511yescharacteristic
351C2×D3—21no—
352C2×D3—21no—
353C2×D3—22no—
354C2×D3—22no—
355C2×D3—22no—
356C2×D3—22no—
357C2×D3—22no—
358C2×D3—22no—
359C2×D3—48no—
360C2×D3C2×#4112yes—
361C3×C4—22no—
362C3×C4—22no—
363C3×C4—22no—
364C3×C4—21no—
365C3×C4—24no—
366C3×C4C2×#4112yes—
367C3×C4C2×#4112yes—
368Dic3—24no—
369Dic3—22no—
370Dic3—22no—
371Dic3—21no—
372Dic3—21no—
373Dic3C2×#4112yes—
374C23—31no—
375C23—32no—
376C23—32no—
377C23—64no—
378C23—64no—
379C23—122no—
380C23C23×D312yes—
381Q8—22no—
382Q8—42no—
383Q8—64no—
384D4—64no—
385D4—64no—
386D4—68no—
387D4—62no—
388D4—62no—
389D4—124no—
390D4#23914yescomplemented
391C2×C4—24no—
392C2×C4—31no—
393C2×C4—34no—
394C2×C4—32no—
395C2×C4—32no—
396C2×C4—31no—
397C2×C4—34no—
398C2×C4—31no—
399C2×C4—44no—
400C2×C4—64no—
401C2×C4—64no—
402C2×C4—64no—
403C2×C4—64no—
404C2×C4—68no—
405C2×C4—62no—
406C2×C4—64no—
407C2×C4—64no—
408C2×C4—122no—
409C2×C4—121no—
410C2×C4C23×D312yes—
411C2×C4C23×D314yes—
412C2×C4C23×D311yescharacteristic
413C2×C4C23×D312yes—
414C2×C4C23×D312yes—
415C2×C4C23×D311yescharacteristic
416C2×C4C23×D311yescharacteristic
417C2×C3—24no—
418C2×C3C22×#4111yescharacteristic
419C2×C3C22×#4111yescharacteristic
420C2×C3#58511yescharacteristic
421D3—22no—
422D3—42no—
423D3—42no—
424C22—22no—
425C22—22no—
426C22—32no—
427C22—61no—
428C22—61no—
429C22—62no—
430C22—62no—
431C22—62no—
432C22—62no—
433C22—62no—
434C22—62no—
435C22—128no—
436C22C2×#23914yes—
437C22C24×D311yescharacteristic
438C4—22no—
439C4—22no—
440C4—22no—
441C4—24no—
442C4—21no—
443C4—32no—
444C4—62no—
445C4—61no—
446C4—64no—
447C4—62no—
448C4—61no—
449C4C2×#23912yes—
450C4D3×#4112yes—
451C3#347511yescharacteristic, complemented, Sylow
452C2—24no—
453C2—62no—
454C2—122no—
455C2—122no—
456C2C22×#23911yescharacteristic
457C2C2×D3×#4111yescharacteristic
458C2#596611yescharacteristic
subgroupG/H
center, FrattiniC22C24×D3
commutator, socle, cosocleC22×C3C25
FittingC3×#554C2
hypercenter#554D3
hypocenterC3#3475
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. #5728C2semidirect
4. #5694C2semidirect
5. #5691C2semidirect
6. #5642C2semidirect
7. #5637C2semidirect
8. #5627C2semidirect
9. #5624C2semidirect
10. #5584C2semidirect
11. C4×#239C2semidirect
12. #5555C2semidirect
13. #5554C2semidirect
14. C4×D3×D4C2semidirect
15. C4×#237C2semidirect
16. #5514C2semidirect
17. C2×#892C2semidirect
23. C3×C4⋊Q8C22semidirect
24. C3×#125C22semidirect
25. C3×C22⋊Q8C22semidirect
26. C3×C22⋊Q8C22semidirect
27. C3×C4×Q8C22semidirect
30. C2×C3×C4⋊C4C22semidirect
31. #947C22semidirect
33. #946C22semidirect
34. Q8×Dic3C22semidirect
35. Q8×Dic3C22semidirect
38. #930C22semidirect
40. C4×#67C22semidirect
42. C2×C4⋊Dic3C22semidirect
43. C2×C4×Dic3C22semidirect
44. #898C22semidirect
45. #898C22semidirect
46. #898C22semidirect
48. #897C22semidirect
50. #895C22semidirect
52. #894C22semidirect
55. #893C22semidirect
56. #893C22semidirect
60. #892C22semidirect
61. #892C22semidirect
62. #892C22semidirect
63. #892C22semidirect
64. #892C22semidirect
66. #890C22semidirect
67. #890C22semidirect
68. #887C22semidirect
70. #886C22semidirect
73. #67⋊C4C22semidirect
75. #877C22semidirect
79. C4×D12C22semidirect
81. C42×D3C22semidirect
82. #869C22semidirect
83. C4×Dic6C22semidirect
86. #554D3semidirect
175. C4⋊Q8C2×D3semidirect
181. #125C2×D3semidirect
192. C22⋊Q8C2×D3semidirect
193. C22⋊Q8C2×D3semidirect
203. C4×Q8C2×D3semidirect
229. C2×C4⋊C4C2×D3semidirect
244. C3×D4#41semidirect
276. C4×D3#41semidirect
390. D4#239semidirect
451. C3#3475semidirect

Maximal subgroups

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

subgroupindex
C3×#5542
#57342
#57282
#56942
#56912
#56422
#56372
#56272
#56242
#55842
C4×#2392
#55552
#55542
C4×D3×D42
C4×#2372
#55142
C2×#8922
#34753