Finite Group Databasebeta

← #86497

Subgroups — #86497

Order 384.

1032 conjugacy classes of subgroups.

The subgroup lattice has 382 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#5709C214yesmaximal, complemented
5#5709C214yesmaximal, complemented
6#5697C211yesmaximal, characteristic, complemented
7#5695C214yesmaximal, complemented
8#5693C214yesmaximal, complemented
9D3×#125C211yesmaximal, characteristic, complemented
10#5629C212yesmaximal, complemented
11#5624C212yesmaximal, complemented
12#5580C212yesmaximal, complemented
13#5574C212yesmaximal, complemented
14#5535C211yesmaximal, characteristic, complemented
15#5522C211yesmaximal, characteristic, complemented
16#3512—31nomaximal, Sylow
17C2×#239C2212yes—
18C2×#235C2211yescharacteristic
19C3×C4⋊Q8C2211yescharacteristic
20C3×#126C2214yes—
21C3×#125C2211yescharacteristic
22C3×#125C2214yes—
23C3×C22⋊Q8C2212yes—
24C3×C4×Q8C2212yes—
25C3×#117C2211yescharacteristic
26#947C2212yes—
27#946C2212yes—
28Q8×Dic3C2212yes—
29#930C2212yes—
30C2×C4×Dic3C2211yescharacteristic
31#898C2214yes—
32#898C2214yes—
33#898C2214yes—
34#896C2214yes—
35#895C2214yes—
36#895C2214yes—
37#895C2214yes—
38#895C2212yes—
39#894C2214yes—
40#894C2214yes—
41#894C2214yes—
42#893C2214yes—
43#893C2212yes—
44#893C2214yes—
45#893C2212yes—
46#892C2214yes—
47D3×C4⋊C4C2214yes—
48D3×C4⋊C4C2212yes—
49D3×C4⋊C4C2214yes—
50#890C2212yes—
51#889C2214yes—
52#889C2214yes—
53#887C2212yes—
54#886C2214yes—
55#884C2214yes—
56#884C2214yes—
57#884C2214yes—
58#67⋊C4C2212yes—
59#67⋊C4C2212yes—
60#67⋊C4C2214yes—
61#874C2211yescharacteristic
62C4×D12C2214yes—
63C4×D12C2214yes—
64C4×D12C2212yes—
65#872C2214yes—
66#872C2214yes—
67#872C2211yescharacteristic
68#872C2211yescharacteristic
69C42×D3C2211yescharacteristic
70C42×D3C2211yescharacteristic
71#870C2211yescharacteristic
72#553—34no—
73#553—34no—
74#553—34no—
75#552—34no—
76#541—31no—
77#541D311yescharacteristic, complemented
78#540—31no—
79#540—31no—
80#537—32no—
81#532—31no—
82#529—32no—
83#529—32no—
84C2×#125—31no—
85#520—32no—
86C4×#41—31no—
87C2×C3×Q8C2312yes—
88C22×C3×C4C2311yescharacteristic
89C2×#67C2311yescharacteristic
90C2×#67C2311yescharacteristic
91C2×#67C2314yes—
92C22×Dic3C2312yes—
93#239—28no—
94#235—24no—
95C2×D12C2312yes—
96C2×D12C2314yes—
97C2×D12C2311yescharacteristic
98C2×D12C2314yes—
99C2×D12C2314yes—
100C2×C4×D3C2311yescharacteristic
101C2×C4×D3C2314yes—
102C2×C4×D3C2312yes—
103C2×C4×D3C2312yes—
104C2×C4×D3C2314yes—
105C2×C4×D3C2314yes—
106C2×C4×D3C2314yes—
107C2×C4×D3C2311yescharacteristic
108C2×Dic6C2311yescharacteristic
109C3×C4⋊C4C2312yes—
110C3×C4⋊C4C2314yes—
111C3×C4⋊C4C2314yes—
112C3×C4⋊C4C2312yes—
113C3×C4⋊C4C2314yes—
114C3×C4⋊C4C2314yes—
115C3×C22⋊C4C2312yes—
116C3×C22⋊C4C2314yes—
117C3×C42C2311yescharacteristic
118C3×C42C2311yescharacteristic
119C3×C42C2314yes—
120(C2×D3)⋊C4C2312yes—
121(C2×D3)⋊C4C2314yes—
122(C2×D3)⋊C4C2312yes—
123(C2×D3)⋊C4C2314yes—
124(C2×D3)⋊C4C2314yes—
125(C2×D3)⋊C4C2314yes—
126(C2×D3)⋊C4C2314yes—
127(C2×D3)⋊C4C2314yes—
128(C2×D3)⋊C4C2314yes—
129C4⋊Dic3C2312yes—
130C4⋊Dic3C2314yes—
131C4⋊Dic3C2314yes—
132Dic3⋊C4C2314yes—
133Dic3⋊C4C2312yes—
134Dic3⋊C4C2312yes—
135Dic3⋊C4C2314yes—
136Dic3⋊C4C2314yes—
137Dic3⋊C4C2314yes—
138C4×Dic3C2311yescharacteristic
139C4×Dic3C2312yes—
140C4×Dic3C2312yes—
141C4×Dic3C2311yescharacteristic
142C4×Dic3C2314yes—
143C4×Dic3C2312yes—
144C2×#41—32no—
145C2×#41—31no—
146C4⋊Q8C2×D311yescharacteristic
147#127—31no—
148#126—34no—
149#126—34no—
150#126—34no—
151#126C2×D314yes—
152#125—32no—
153#125—34no—
154#125—34no—
155#125—31no—
156#125C2×D311yescharacteristic
157#125C2×D314yes—
158#124—32no—
159#123—34no—
160#123—34no—
161#123—34no—
162#123—34no—
163C22⋊Q8—32no—
164C22⋊Q8—34no—
165C22⋊Q8C2×D312yes—
166#121—32no—
167#121—32no—
168#121—34no—
169#121—34no—
170#121—34no—
171#121—34no—
172#121—34no—
173#121—34no—
174C4×Q8—32no—
175C4×Q8—32no—
176C4×Q8C2×D312yes—
177C4×D4—32no—
178C4×D4—32no—
179C4×D4—34no—
180C4×D4—34no—
181C4×D4—32no—
182C4×D4—32no—
183C4×D4—34no—
184C4×D4—32no—
185C4×D4—34no—
186C4×D4—34no—
187#117—34no—
188#117—31no—
189#117—31no—
190#117—34no—
191#117—34no—
192#117C2×D311yescharacteristic
193C2×C4⋊C4—32no—
194C2×C4⋊C4—34no—
195C2×C4⋊C4—34no—
196C2×C42—31no—
197C2×C42—31no—
198C2×C42—31no—
199C23×C3C2411yescharacteristic
200C22×D3C2414yes—
201C22×D3C2411yescharacteristic
202C22×D3C2411yescharacteristic
203C3×Q8—24no—
204C2×C3×C4—22no—
205C2×C3×C4C2411yescharacteristic
206C2×C3×C4C2412yes—
207C2×C3×C4C2414yes—
208C2×C3×C4C2412yes—
209C2×C3×C4C2414yes—
210C2×C3×C4C2411yescharacteristic
211#67—22no—
212#67—22no—
213#67—44no—
214C2×Dic3—42no—
215C2×Dic3C2412yes—
216C2×Dic3C2412yes—
217C2×Dic3C2411yescharacteristic
218C2×Dic3C2414yes—
219C2×Dic3C2411yescharacteristic
220D12—22no—
221D12—28no—
222D12—24no—
223D12—44no—
224D12—44no—
225C4×D3—22no—
226C4×D3—28no—
227C4×D3—42no—
228C4×D3—44no—
229C4×D3—42no—
230C4×D3—44no—
231C4×D3—44no—
232C4×D3#4114yes—
233Dic6—22no—
234#41—64no—
235#41—68no—
236C2×Q8—31no—
237C2×Q8C22×D312yes—
238C2×D4—31no—
239C2×D4—31no—
240C2×D4—34no—
241C2×D4—31no—
242C2×D4—34no—
243C2×D4—32no—
244C2×D4—34no—
245C2×D4—34no—
246C22×C4—31no—
247C22×C4—32no—
248C22×C4—31no—
249C22×C4—34no—
250C22×C4—32no—
251C22×C4—32no—
252C22×C4—34no—
253C22×C4—34no—
254C22×C4—34no—
255C22×C4C22×D311yescharacteristic
256C4⋊C4—32no—
257C4⋊C4—34no—
258C4⋊C4—34no—
259C4⋊C4—34no—
260C4⋊C4—32no—
261C4⋊C4—34no—
262C4⋊C4—34no—
263C4⋊C4—32no—
264C4⋊C4—34no—
265C4⋊C4C22×D312yes—
266C4⋊C4C22×D314yes—
267C4⋊C4C22×D314yes—
268C4⋊C4C22×D314yes—
269C4⋊C4C22×D312yes—
270C4⋊C4C22×D314yes—
271C22⋊C4—34no—
272C22⋊C4—32no—
273C22⋊C4—32no—
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—31no—
283C42—31no—
284C42—32no—
285C42—32no—
286C42—32no—
287C42—34no—
288C42C22×D311yescharacteristic
289C42C22×D311yescharacteristic
290C42C22×D314yes—
291C22×C3—21no—
292C22×C3—22no—
293C22×C3C2511yescharacteristic
294C2×D3—22no—
295C2×D3—24no—
296C2×D3—21no—
297C2×D3—24no—
298C2×D3—22no—
299C2×D3—24no—
300C2×D3C2×#4112yes—
301C3×C4—21no—
302C3×C4—24no—
303C3×C4—22no—
304C3×C4—24no—
305C3×C4—22no—
306C3×C4C2×#4112yes—
307Dic3—21no—
308Dic3—22no—
309Dic3—22no—
310Dic3—24no—
311Dic3C2×#4112yes—
312C23—31no—
313C23—34no—
314C23—31no—
315C23C23×D311yescharacteristic
316Q8—24no—
317Q8—62no—
318D4—62no—
319D4—68no—
320D4—62no—
321D4—62no—
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—31no—
332C2×C4—34no—
333C2×C4—68no—
334C2×C4—62no—
335C2×C4—122no—
336C2×C4—124no—
337C2×C4—124no—
338C2×C4—124no—
339C2×C4—122no—
340C2×C4—122no—
341C2×C4C23×D311yescharacteristic
342C2×C4C23×D312yes—
343C2×C4C23×D314yes—
344C2×C4C23×D312yes—
345C2×C4C23×D314yes—
346C2×C4C23×D311yescharacteristic
347C2×C3—41no—
348C2×C3C22×#4111yescharacteristic
349C2×C3#58512yes—
350D3—22no—
351D3—44no—
352D3—41no—
353C22—21no—
354C22—22no—
355C22—32no—
356C22—62no—
357C22—64no—
358C22—61no—
359C22—64no—
360C22—62no—
361C22—64no—
362C22C24×D311yescharacteristic
363C4—21no—
364C4—24no—
365C4—22no—
366C4—24no—
367C4—22no—
368C4—32no—
369C4—61no—
370C4—62no—
371C4—62no—
372C4—64no—
373C4D3×#4112yes—
374C3#351211yescharacteristic, complemented, Sylow
375C2—41no—
376C2—62no—
377C2—124no—
378C2—121no—
379C2C2×D3×#4111yescharacteristic
380C2#596812yes—
subgroupG/H
center, FrattiniC22C24×D3
commutator, socle, cosocleC22×C3C25
FittingC3×#541C2
hypercenter#541D3
hypocenterC3#3512
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. #5709C2semidirect
5. #5709C2semidirect
6. #5697C2semidirect
7. #5695C2semidirect
8. #5693C2semidirect
9. D3×#125C2semidirect
10. #5629C2semidirect
11. #5624C2semidirect
12. #5580C2semidirect
13. #5574C2semidirect
14. #5535C2semidirect
15. #5522C2semidirect
77. #541D3semidirect
374. C3#3512semidirect

Maximal subgroups

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

subgroupindex
C3×#5412
#57312
#57252
#57092
#56972
#56952
#56932
D3×#1252
#56292
#56242
#55802
#55742
#55352
#55222
#35123