Finite Group Databasebeta

← #86469

Subgroups — #86469

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×#540C211yesmaximal, characteristic, complemented
2#5719C211yesmaximal, characteristic, complemented
3#5716C211yesmaximal, characteristic, complemented
4#5698C211yesmaximal, characteristic, complemented
5D3×#125C211yesmaximal, characteristic, complemented
6#5661C214yesmaximal, complemented
7#5650C214yesmaximal, complemented
8#5614C214yesmaximal, complemented
9#5608C212yesmaximal, complemented
10#5601C214yesmaximal, complemented
11#5600C212yesmaximal, complemented
12#5557C212yesmaximal, complemented
13#5546C212yesmaximal, complemented
14#5522C211yesmaximal, characteristic, complemented
15#5518C211yesmaximal, characteristic, complemented
16#3512—31nomaximal, Sylow
17C2×#237C2212yes—
18C2×#235C2211yescharacteristic
19C3×#127C2211yescharacteristic
20C3×#125C2211yescharacteristic
21C3×#123C2214yes—
22C3×#121C2212yes—
23C3×#121C2214yes—
24C3×C4×D4C2212yes—
25C3×#117C2211yescharacteristic
26#939C2214yes—
27#939C2214yes—
28#938C2214yes—
29#938C2212yes—
30#938C2214yes—
31#936C2212yes—
32#935C2214yes—
33#935C2214yes—
34D4×Dic3C2214yes—
35D4×Dic3C2212yes—
36D4×Dic3C2214yes—
37C4×#67C2214yes—
38C4×#67C2214yes—
39#926C2214yes—
40#924C2212yes—
41C2×Dic3⋊C4C2214yes—
42C2×C4×Dic3C2211yescharacteristic
43#898C2214yes—
44#897C2212yes—
45#893C2212yes—
46D3×C4⋊C4C2214yes—
47D3×C4⋊C4C2212yes—
48#890C2214yes—
49#890C2212yes—
50#889C2214yes—
51#889C2214yes—
52#887C2212yes—
53#887C2212yes—
54#884C2214yes—
55#883C2214yes—
56#67⋊C4C2214yes—
57#67⋊C4C2212yes—
58#67⋊C4C2212yes—
59#879C2214yes—
60#879C2214yes—
61#879C2214yes—
62#878C2214yes—
63#877C2214yes—
64#877C2214yes—
65#872C2211yescharacteristic
66#872C2211yescharacteristic
67C42×D3C2211yescharacteristic
68C42×D3C2211yescharacteristic
69#870C2211yescharacteristic
70#869C2211yescharacteristic
71C4×Dic6C2212yes—
72#553—34no—
73#553—34no—
74#553—34no—
75#552—34no—
76#541—31no—
77#541—31no—
78#540—31no—
79#540D311yescharacteristic, complemented
80#537—32no—
81#532—31no—
82#529—32no—
83#529—32no—
84C2×#125—31no—
85#520—32no—
86C4×#41—31no—
87C2×C3×D4C2312yes—
88C2×C3×D4C2314yes—
89C2×C3×D4C2314yes—
90C22×C3×C4C2311yescharacteristic
91C22×C3×C4C2314yes—
92C2×#67C2311yescharacteristic
93C2×#67C2311yescharacteristic
94C2×#67C2314yes—
95C2×#67C2314yes—
96C22×Dic3C2314yes—
97C22×Dic3C2314yes—
98C22×Dic3C2312yes—
99#237—28no—
100#235—24no—
101C2×D12C2311yescharacteristic
102C2×C4×D3C2311yescharacteristic
103C2×C4×D3C2312yes—
104C2×C4×D3C2312yes—
105C2×C4×D3C2314yes—
106C2×C4×D3C2311yescharacteristic
107C2×Dic6C2312yes—
108C2×Dic6C2311yescharacteristic
109C3×C4⋊C4C2312yes—
110C3×C4⋊C4C2312yes—
111C3×C4⋊C4C2314yes—
112C3×C22⋊C4C2314yes—
113C3×C22⋊C4C2314yes—
114C3×C22⋊C4C2312yes—
115C3×C42C2311yescharacteristic
116C3×C42C2311yescharacteristic
117#217C2314yes—
118#217C2314yes—
119#217C2314yes—
120#217C2314yes—
121#217C2314yes—
122(C2×D3)⋊C4C2312yes—
123(C2×D3)⋊C4C2312yes—
124(C2×D3)⋊C4C2314yes—
125C4⋊Dic3C2312yes—
126C4⋊Dic3C2314yes—
127C4⋊Dic3C2314yes—
128C4⋊Dic3C2314yes—
129Dic3⋊C4C2314yes—
130Dic3⋊C4C2314yes—
131Dic3⋊C4C2312yes—
132Dic3⋊C4C2312yes—
133Dic3⋊C4C2314yes—
134Dic3⋊C4C2314yes—
135Dic3⋊C4C2314yes—
136Dic3⋊C4C2314yes—
137C4×Dic3C2314yes—
138C4×Dic3C2311yescharacteristic
139C4×Dic3C2312yes—
140C4×Dic3C2312yes—
141C4×Dic3C2311yescharacteristic
142C4×Dic3C2312yes—
143C4×Dic3C2314yes—
144C2×#41—32no—
145C2×#41—31no—
146C4⋊Q8—31no—
147#127C2×D311yescharacteristic
148#126—34no—
149#126—34no—
150#126—34no—
151#126—34no—
152#125—32no—
153#125—34no—
154#125—34no—
155#125—34no—
156#125—31no—
157#125C2×D311yescharacteristic
158#124—32no—
159#123—34no—
160#123—34no—
161#123—34no—
162#123C2×D314yes—
163C22⋊Q8—32no—
164C22⋊Q8—32no—
165C22⋊Q8—34no—
166#121—32no—
167#121—34no—
168#121—34no—
169#121—34no—
170#121—34no—
171#121—34no—
172#121C2×D312yes—
173#121C2×D314yes—
174C4×Q8—32no—
175C4×Q8—32no—
176C4×Q8—32no—
177C4×D4—32no—
178C4×D4—34no—
179C4×D4—34no—
180C4×D4—34no—
181C4×D4—34no—
182C4×D4—32no—
183C4×D4—32no—
184C4×D4—32no—
185C4×D4—34no—
186C4×D4C2×D312yes—
187#117—34no—
188#117—34no—
189#117—34no—
190#117—31no—
191#117—31no—
192#117C2×D311yescharacteristic
193C2×C4⋊C4—34no—
194C2×C4⋊C4—32no—
195C2×C4⋊C4—34no—
196C2×C42—31no—
197C2×C42—31no—
198C2×C42—31no—
199C23×C3C2414yes—
200C23×C3C2411yescharacteristic
201C22×D3C2411yescharacteristic
202C22×D3C2411yescharacteristic
203C3×D4—24no—
204C3×D4—44no—
205C3×D4—44no—
206C2×C3×C4—22no—
207C2×C3×C4—44no—
208C2×C3×C4C2412yes—
209C2×C3×C4C2411yescharacteristic
210C2×C3×C4C2412yes—
211C2×C3×C4C2414yes—
212C2×C3×C4C2411yescharacteristic
213#67—22no—
214#67—28no—
215#67—22no—
216#67—44no—
217C2×Dic3—28no—
218C2×Dic3—42no—
219C2×Dic3—44no—
220C2×Dic3C2412yes—
221C2×Dic3C2412yes—
222C2×Dic3C2414yes—
223C2×Dic3C2411yescharacteristic
224C2×Dic3C2414yes—
225C2×Dic3C2411yescharacteristic
226D12—22no—
227C4×D3—22no—
228C4×D3—42no—
229C4×D3—42no—
230C4×D3—44no—
231C4×D3#4114yes—
232Dic6—24no—
233Dic6—22no—
234#41—64no—
235#41—68no—
236C2×Q8—31no—
237C2×Q8—32no—
238C2×D4—31no—
239C2×D4—34no—
240C2×D4—31no—
241C2×D4—34no—
242C2×D4—31no—
243C2×D4C22×D312yes—
244C2×D4C22×D314yes—
245C2×D4C22×D314yes—
246C22×C4—31no—
247C22×C4—34no—
248C22×C4—32no—
249C22×C4—34no—
250C22×C4—31no—
251C22×C4—32no—
252C22×C4—32no—
253C22×C4—34no—
254C22×C4C22×D311yescharacteristic
255C22×C4C22×D314yes—
256C4⋊C4—32no—
257C4⋊C4—34no—
258C4⋊C4—34no—
259C4⋊C4—34no—
260C4⋊C4—32no—
261C4⋊C4—34no—
262C4⋊C4—34no—
263C4⋊C4—34no—
264C4⋊C4—32no—
265C4⋊C4—34no—
266C4⋊C4—34no—
267C4⋊C4—34no—
268C4⋊C4C22×D312yes—
269C4⋊C4C22×D314yes—
270C4⋊C4C22×D312yes—
271C22⋊C4—34no—
272C22⋊C4—34no—
273C22⋊C4—34no—
274C22⋊C4—34no—
275C22⋊C4—34no—
276C22⋊C4—32no—
277C22⋊C4—32no—
278C22⋊C4—34no—
279C22⋊C4C22×D314yes—
280C22⋊C4C22×D314yes—
281C22⋊C4C22×D312yes—
282C42—31no—
283C42—31no—
284C42—32no—
285C42—32no—
286C42—32no—
287C42—34no—
288C42—34no—
289C42C22×D311yescharacteristic
290C42C22×D311yescharacteristic
291C22×C3—24no—
292C22×C3—21no—
293C22×C3—24no—
294C22×C3—22no—
295C22×C3—24no—
296C22×C3C2511yescharacteristic
297C2×D3—22no—
298C2×D3—21no—
299C2×D3—22no—
300C2×D3C2×#4112yes—
301C3×C4—21no—
302C3×C4—22no—
303C3×C4—24no—
304C3×C4—22no—
305C3×C4C2×#4112yes—
306Dic3—21no—
307Dic3—24no—
308Dic3—22no—
309Dic3—24no—
310Dic3—22no—
311Dic3C2×#4112yes—
312C23—31no—
313C23—31no—
314C23C23×D311yescharacteristic
315C23C23×D314yes—
316Q8—62no—
317Q8—64no—
318D4—24no—
319D4—44no—
320D4—44no—
321D4—62no—
322D4—62no—
323D4—62no—
324D4—68no—
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—34no—
334C2×C4—44no—
335C2×C4—68no—
336C2×C4—62no—
337C2×C4—122no—
338C2×C4—124no—
339C2×C4—122no—
340C2×C4—122no—
341C2×C4—124no—
342C2×C4C23×D312yes—
343C2×C4C23×D311yescharacteristic
344C2×C4C23×D312yes—
345C2×C4C23×D314yes—
346C2×C4C23×D311yescharacteristic
347C2×C3—44no—
348C2×C3—41no—
349C2×C3C22×#4111yescharacteristic
350C2×C3#58512yes—
351D3—22no—
352D3—41no—
353C22—21no—
354C22—24no—
355C22—24no—
356C22—22no—
357C22—24no—
358C22—32no—
359C22—62no—
360C22—61no—
361C22—62no—
362C22C24×D311yescharacteristic
363C4—21no—
364C4—22no—
365C4—24no—
366C4—22no—
367C4—32no—
368C4—64no—
369C4—61no—
370C4—62no—
371C4—62no—
372C4—64no—
373C4D3×#4112yes—
374C3#351211yescharacteristic, complemented, Sylow
375C2—41no—
376C2—44no—
377C2—62no—
378C2—121no—
379C2C2×D3×#4111yescharacteristic
380C2#596612yes—
subgroupG/H
center, FrattiniC22C24×D3
commutator, socle, cosocleC22×C3C25
FittingC3×#540C2
hypercenter#540D3
hypocenterC3#3512
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ #540

Complements

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

NH ≅ G/Ntype
1. C3×#540C2semidirect
2. #5719C2semidirect
3. #5716C2semidirect
4. #5698C2semidirect
5. D3×#125C2semidirect
6. #5661C2semidirect
7. #5650C2semidirect
8. #5614C2semidirect
9. #5608C2semidirect
10. #5601C2semidirect
11. #5600C2semidirect
12. #5557C2semidirect
13. #5546C2semidirect
14. #5522C2semidirect
15. #5518C2semidirect
79. #540D3semidirect
374. C3#3512semidirect

Maximal subgroups

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

subgroupindex
C3×#5402
#57192
#57162
#56982
D3×#1252
#56612
#56502
#56142
#56082
#56012
#56002
#55572
#55462
#55222
#55182
#35123