Finite Group Databasebeta

← #86495

Subgroups — #86495

Order 384.

1040 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#541C211yesmaximal, characteristic, complemented
2#5731C211yesmaximal, characteristic, complemented
3#5725C211yesmaximal, characteristic, complemented
4#5706C214yesmaximal, complemented
5#5704C214yesmaximal, complemented
6#5697C211yesmaximal, characteristic, complemented
7#5692C214yesmaximal, complemented
8#5691C214yesmaximal, complemented
9#5688C211yesmaximal, characteristic, complemented
10#5643C212yesmaximal, complemented
11#5627C212yesmaximal, complemented
12#5582C212yesmaximal, complemented
13C4×#239C212yesmaximal, complemented
14#5535C211yesmaximal, characteristic, complemented
15D3×#117C211yesmaximal, characteristic, complemented
16#3455—31nomaximal, Sylow
17C2×#239C2212yes—
18C22×C4×D3C2211yescharacteristic
19C3×C4⋊Q8C2211yescharacteristic, complemented
20C3×#126C2214yes—
21C3×#125C2211yescharacteristic, complemented
22C3×#125C2214yescomplemented
23C3×C22⋊Q8C2212yes—
24C3×C4×Q8C2212yescomplemented
25C3×#117C2211yescharacteristic
26#947C2212yescomplemented
27#946C2212yes—
28Q8×Dic3C2212yescomplemented
29#930C2212yes—
30#926C2211yescharacteristic
31#898C2214yes—
32#898C2214yescomplemented
33#897C2214yescomplemented
34#896C2214yes—
35#896C2214yescomplemented
36#895C2214yes—
37#895C2214yes—
38#895C2212yes—
39#894C2214yes—
40#894C2214yes—
41#894C2214yescomplemented
42#894C2214yescomplemented
43#893C2214yes—
44#893C2214yes—
45#893C2212yescomplemented
46#893C2214yescomplemented
47#892C2212yes—
48#892C2212yes—
49#892C2214yescomplemented
50D3×C4⋊C4C2212yes—
51#889C2214yescomplemented
52#888C2212yescomplemented
53#887C2214yescomplemented
54#885C2214yes—
55#884C2214yes—
56#883C2214yes—
57#882C2214yes—
58#67⋊C4C2214yes—
59D3×C22⋊C4C2212yes—
60#877C2212yes—
61#876C2214yescomplemented
62#875C2214yes—
63#874C2211yescharacteristic, complemented
64C4×D12C2214yes—
65C4×D12C2212yescomplemented
66#872C2211yescharacteristic
67#872C2211yescharacteristic
68C42×D3C2211yescharacteristic
69C42×D3C2211yescharacteristic
70C42×D3C2214yescomplemented
71#870C2211yescharacteristic, complemented
72#542—32no—
73#542—32no—
74#541—31no—
75#541D311yescharacteristic, complemented
76#540—31no—
77#540—31no—
78#539—34no—
79#538—34no—
80#533—31no—
81#532—31no—
82#529—34no—
83#529—34no—
84#525—32no—
85C4×#41—32no—
86C2×#117—31no—
87C23×D3C2311yescharacteristic
88C2×C3×Q8C2312yes—
89C22×C3×C4C2311yescharacteristic
90C2×#67C2314yes—
91C22×Dic3C2311yescharacteristic
92#239—28no—
93C2×D12C2314yes—
94C2×D12C2312yes—
95C2×D12C2314yes—
96C2×D12C2314yes—
97C2×C4×D3—24no—
98C2×C4×D3C2314yes—
99C2×C4×D3C2311yescharacteristic
100C2×C4×D3C2311yescharacteristic
101C2×C4×D3C2311yescharacteristic
102C2×C4×D3C2312yes—
103C2×C4×D3C2312yes—
104C2×C4×D3C2314yes—
105C2×C4×D3C2314yes—
106C2×C4×D3C2311yescharacteristic
107C2×Dic6C2314yes—
108C3×C4⋊C4C2314yes—
109C3×C4⋊C4C2312yes—
110C3×C4⋊C4C2314yes—
111C3×C4⋊C4C2312yes—
112C3×C4⋊C4C2314yes—
113C3×C4⋊C4C2314yes—
114C3×C22⋊C4C2312yes—
115C3×C22⋊C4C2314yes—
116C3×C42C2311yescharacteristic
117C3×C42C2311yescharacteristic
118C3×C42C2314yes—
119#217C2312yes—
120(C2×D3)⋊C4C2312yes—
121(C2×D3)⋊C4C2312yes—
122(C2×D3)⋊C4C2314yes—
123(C2×D3)⋊C4C2314yes—
124(C2×D3)⋊C4C2314yes—
125(C2×D3)⋊C4C2314yes—
126(C2×D3)⋊C4C2314yes—
127(C2×D3)⋊C4C2314yes—
128(C2×D3)⋊C4C2314yes—
129(C2×D3)⋊C4C2314yes—
130C4⋊Dic3C2312yes—
131C4⋊Dic3C2314yes—
132C4⋊Dic3C2312yes—
133Dic3⋊C4C2314yes—
134Dic3⋊C4C2312yes—
135Dic3⋊C4C2312yes—
136Dic3⋊C4C2314yes—
137Dic3⋊C4C2314yes—
138C4×Dic3C2312yes—
139C4×Dic3C2311yescharacteristic
140C4×Dic3C2311yescharacteristic
141C4×Dic3C2312yes—
142C4×Dic3C2314yes—
143C4×Dic3C2314yes—
144C2×#41—32no—
145C23×C4—31no—
146C4⋊Q8—32no—
147C4⋊Q8C2×D311yescharacteristic, complemented
148#127—31no—
149#126—34no—
150#126—34no—
151#126—34no—
152#126C2×D314yes—
153#125—34no—
154#125—31no—
155#125C2×D314yescomplemented
156#125C2×D311yescharacteristic, complemented
157#124—32no—
158#124—34no—
159#124—34no—
160#123—34no—
161#123—34no—
162#123—34no—
163#123—34no—
164#123—34no—
165C22⋊Q8—32no—
166C22⋊Q8—34no—
167C22⋊Q8—34no—
168C22⋊Q8—34no—
169C22⋊Q8C2×D312yes—
170#121—32no—
171#121—32no—
172#121—34no—
173#121—34no—
174#121—34no—
175#120—34no—
176C4×Q8—32no—
177C4×Q8—34no—
178C4×Q8C2×D312yescomplemented
179C4×D4—34no—
180C4×D4—32no—
181C4×D4—34no—
182C4×D4—34no—
183C4×D4—34no—
184C4×D4—34no—
185C4×D4—32no—
186#117—31no—
187#117—32no—
188#117—32no—
189#117—34no—
190#117—32no—
191#117—31no—
192#117—31no—
193#117C2×D311yescharacteristic
194C2×C4⋊C4—32no—
195C2×C22⋊C4—32no—
196C2×C42—31no—
197C2×C42—31no—
198C2×C42—34no—
199C23×C3C2411yescharacteristic
200C22×D3—22no—
201C22×D3—42no—
202C22×D3C2411yescharacteristic
203C22×D3C2414yes—
204C22×D3C2411yescharacteristic
205C3×Q8—24no—
206C2×C3×C4—22no—
207C2×C3×C4C2412yes—
208C2×C3×C4C2414yes—
209C2×C3×C4C2412yes—
210C2×C3×C4C2414yes—
211C2×C3×C4C2411yescharacteristic
212C2×C3×C4C2411yescharacteristic
213#67—44no—
214C2×Dic3—22no—
215C2×Dic3C2412yes—
216C2×Dic3C2414yes—
217C2×Dic3C2412yes—
218C2×Dic3C2411yescharacteristic
219C2×Dic3C2411yescharacteristic
220D12—28no—
221D12—24no—
222D12—44no—
223D12—44no—
224C4×D3—22no—
225C4×D3—22no—
226C4×D3—22no—
227C4×D3—28no—
228C4×D3—42no—
229C4×D3—44no—
230C4×D3—44no—
231C4×D3—42no—
232C4×D3#4114yes—
233Dic6—44no—
234C24—31no—
235#41—68no—
236C2×Q8—34no—
237C2×Q8C22×D312yes—
238C2×D4—34no—
239C2×D4—34no—
240C2×D4—32no—
241C2×D4—34no—
242C2×D4—34no—
243C22×C4—31no—
244C22×C4—31no—
245C22×C4—34no—
246C22×C4—31no—
247C22×C4—31no—
248C22×C4—31no—
249C22×C4—32no—
250C22×C4—32no—
251C22×C4—34no—
252C22×C4—34no—
253C22×C4—64no—
254C22×C4C22×D311yescharacteristic
255C4⋊C4—32no—
256C4⋊C4—32no—
257C4⋊C4—32no—
258C4⋊C4—32no—
259C4⋊C4—34no—
260C4⋊C4—34no—
261C4⋊C4—34no—
262C4⋊C4—34no—
263C4⋊C4C22×D312yes—
264C4⋊C4C22×D312yes—
265C4⋊C4C22×D314yes—
266C4⋊C4C22×D314yes—
267C4⋊C4C22×D314yes—
268C4⋊C4C22×D314yes—
269C22⋊C4—32no—
270C22⋊C4—32no—
271C22⋊C4—32no—
272C22⋊C4—34no—
273C22⋊C4—34no—
274C22⋊C4—34no—
275C22⋊C4—34no—
276C22⋊C4—34no—
277C22⋊C4—34no—
278C22⋊C4—34no—
279C22⋊C4—34no—
280C22⋊C4C22×D312yes—
281C22⋊C4C22×D314yes—
282C42—32no—
283C42—32no—
284C42—34no—
285C42—31no—
286C42—31no—
287C42—34no—
288C42C22×D311yescharacteristic
289C42C22×D311yescharacteristic
290C42C22×D314yes—
291C22×C3—21no—
292C22×C3—22no—
293C22×C3C2511yescharacteristic
294C2×D3—22no—
295C2×D3—21no—
296C2×D3—24no—
297C2×D3—24no—
298C2×D3—24no—
299C2×D3—22no—
300C2×D3—44no—
301C2×D3C2×#4112yes—
302C3×C4—21no—
303C3×C4—24no—
304C3×C4—24no—
305C3×C4—22no—
306C3×C4—22no—
307C3×C4C2×#4112yes—
308Dic3—21no—
309Dic3—22no—
310Dic3—24no—
311Dic3—22no—
312Dic3C2×#4112yes—
313C23—31no—
314C23—31no—
315C23—34no—
316C23—62no—
317C23—122no—
318C23C23×D311yescharacteristic
319Q8—24no—
320Q8—124no—
321D4—68no—
322D4—64no—
323D4—124no—
324D4—124no—
325D4—124no—
326C2×C4—22no—
327C2×C4—31no—
328C2×C4—34no—
329C2×C4—32no—
330C2×C4—32no—
331C2×C4—34no—
332C2×C4—31no—
333C2×C4—62no—
334C2×C4—68no—
335C2×C4—62no—
336C2×C4—62no—
337C2×C4—62no—
338C2×C4—122no—
339C2×C4—124no—
340C2×C4—122no—
341C2×C4—124no—
342C2×C4C23×D312yes—
343C2×C4C23×D314yes—
344C2×C4C23×D314yes—
345C2×C4C23×D312yes—
346C2×C4C23×D311yescharacteristic
347C2×C4C23×D311yescharacteristic
348C2×C3—41no—
349C2×C3C22×#4111yescharacteristic
350C2×C3#58512yes—
351D3—22no—
352D3—44no—
353D3—41no—
354C22—21no—
355C22—22no—
356C22—32no—
357C22—62no—
358C22—61no—
359C22—64no—
360C22—64no—
361C22—64no—
362C22—62no—
363C22—124no—
364C22C24×D311yescharacteristic
365C4—21no—
366C4—24no—
367C4—22no—
368C4—22no—
369C4—24no—
370C4—32no—
371C4—61no—
372C4—62no—
373C4—64no—
374C4—62no—
375C4D3×#4112yes—
376C3#345511yescharacteristic, complemented, Sylow
377C2—41no—
378C2—62no—
379C2—121no—
380C2—124no—
381C2C2×D3×#4111yescharacteristic
382C2#596812yes—
subgroupG/H
center, FrattiniC22C24×D3
commutator, socle, cosocleC22×C3C25
FittingC3×#541C2
hypercenter#541D3
hypocenterC3#3455
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ #541

Complements

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

NH ≅ G/Ntype
1. C3×#541C2semidirect
2. #5731C2semidirect
3. #5725C2semidirect
4. #5706C2semidirect
5. #5704C2semidirect
6. #5697C2semidirect
7. #5692C2semidirect
8. #5691C2semidirect
9. #5688C2semidirect
10. #5643C2semidirect
11. #5627C2semidirect
12. #5582C2semidirect
13. C4×#239C2semidirect
14. #5535C2semidirect
15. D3×#117C2semidirect
19. C3×C4⋊Q8C22semidirect
21. C3×#125C22semidirect
22. C3×#125C22semidirect
24. C3×C4×Q8C22semidirect
26. #947C22semidirect
28. Q8×Dic3C22semidirect
32. #898C22semidirect
33. #897C22semidirect
35. #896C22semidirect
41. #894C22semidirect
42. #894C22semidirect
45. #893C22semidirect
46. #893C22semidirect
49. #892C22semidirect
51. #889C22semidirect
52. #888C22semidirect
53. #887C22semidirect
61. #876C22semidirect
63. #874C22semidirect
65. C4×D12C22semidirect
70. C42×D3C22semidirect
71. #870C22semidirect
75. #541D3semidirect
147. C4⋊Q8C2×D3semidirect
155. #125C2×D3semidirect
156. #125C2×D3semidirect
178. C4×Q8C2×D3semidirect
376. C3#3455semidirect

Maximal subgroups

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

subgroupindex
C3×#5412
#57312
#57252
#57062
#57042
#56972
#56922
#56912
#56882
#56432
#56272
#55822
C4×#2392
#55352
D3×#1172
#34553