Finite Group Databasebeta

← #81283

Subgroups — #81283

Order 384.

462 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#121C211yesmaximal, characteristic
2C2×#892C211yesmaximal, characteristic, complemented
3C3×#480C211yesmaximal, characteristic, complemented
4#5034C211yesmaximal, characteristic, complemented
5#4967C211yesmaximal, characteristic, complemented
6#4885C212yesmaximal, complemented
7#4881C212yesmaximal, complemented
8#4779C212yesmaximal, complemented
9#4770C212yesmaximal, complemented
10#4735C211yesmaximal, characteristic, complemented
11#4726C211yesmaximal, characteristic, complemented
12#3094—31nomaximal, Sylow
13C2×D3×D4—21no—
14C2×D3×D4C2211yescharacteristic
15C22×C4×D3C2211yescharacteristic
16C3×#121C2211yescharacteristic
17C2×C3×C4⋊C4C2211yescharacteristic, complemented
18#939—21no—
19#938C2211yescharacteristic
20#930C2211yescharacteristic
21C2×(C2×D3)⋊C4—21no—
22C2×C4⋊Dic3C2211yescharacteristic, complemented
23C2×C4×Dic3—21no—
24C2×ΓL(1,𝔽25)C2212yes—
25#895C2211yescharacteristic
26#892—21no—
27#892—21no—
28#892C2212yes—
29#892C2212yescomplemented
30D3×C4⋊C4C2211yescharacteristic
31#884—21no—
32D3×C22⋊C4—21no—
33C3×#107C2212yescomplemented
34C3×#102C2212yescomplemented
35C3×C22⋊C8C2211yescharacteristic, complemented
36#832C2212yescomplemented
37#830C2211yescharacteristic, complemented
38#821C2212yescomplemented
39(C2×D3)⋊C8C2212yescomplemented
40#817C2212yescomplemented
41#809C2212yescomplemented
42#808C2212yescomplemented
43#807C2212yescomplemented
44C2×#121—31no—
45C2×#117—31no—
46#482—32no—
47#482—32no—
48#481—31no—
49#481—31no—
50#480—31no—
51#480D311yescharacteristic, complemented
52#428—32no—
53#418—32no—
54#407—31no—
55C23×D3—21no—
56C23×D3D411yescharacteristic
57C2×C3×D4—21no—
58C2×C3×D4C2311yescharacteristic
59C22×C3×C4—21no—
60C22×C3×C4C2311yescharacteristic
61C2×#67—21no—
62C2×#67—21no—
63C2×#67—21no—
64C22×Dic3—21no—
65C22×Dic3D411yescharacteristic
66D3×D4—24no—
67D3×D4—44no—
68C2×D12—21no—
69C2×D12C2311yescharacteristic
70C2×C4×D3—24no—
71C2×C4×D3—21no—
72C2×C4×D3D411yescharacteristic
73C2×C4×D3D411yescharacteristic
74C2×C4×D3C2311yescharacteristic
75C2×C4×D3C2311yescharacteristic
76C2×C3×C8C2312yes—
77C3×C4⋊C4—21no—
78C3×C4⋊C4C2312yes—
79C3×C4⋊C4C2311yescharacteristic
80C3×C22⋊C4—21no—
81#217—21no—
82(C2×D3)⋊C4—22no—
83(C2×D3)⋊C4—22no—
84(C2×D3)⋊C4—21no—
85(C2×D3)⋊C4—21no—
86C4⋊Dic3—21no—
87C4⋊Dic3C2311yescharacteristic
88C4⋊Dic3C2312yes—
89Dic3⋊C4—21no—
90C4×Dic3—22no—
91C4×Dic3—22no—
92C2×C3⋊C8C2312yes—
93ΓL(1,𝔽25)—24no—
94C22×D4—31no—
95C22×D4—61no—
96C23×C4—31no—
97C2×M16—32no—
98#121—31no—
99#121—31no—
100#121—31no—
101#121—61no—
102#121—61no—
103#121C2×D311yescharacteristic
104#117—32no—
105#117—32no—
106#117—61no—
107#117—61no—
108C2×C4⋊C4—31no—
109C2×C4⋊C4—31no—
110C2×C4⋊C4C2×D311yescharacteristic, complemented
111C2×C22⋊C4—61no—
112C2×C22⋊C4—61no—
113C2×C42—61no—
114#107—32no—
115#107C2×D312yescomplemented
116#106—32no—
117#106—32no—
118#102—32no—
119#102—32no—
120#102—32no—
121#102C2×D312yescomplemented
122C22⋊C8—31no—
123C22⋊C8—32no—
124C22⋊C8C2×D311yescharacteristic, complemented
125C23×C3—21no—
126C23×C3C2×D411yescharacteristic
127C22×D3—22no—
128C22×D3—22no—
129C22×D3—21no—
130C22×D3—41no—
131C22×D3—42no—
132C22×D3—42no—
133C22×D3—42no—
134C22×D3C2×D411yescharacteristic
135C22×D3C2×D411yescharacteristic
136C3×D4—22no—
137C3×D4—42no—
138C2×C3×C4—22no—
139C2×C3×C4—22no—
140C2×C3×C4—21no—
141C2×C3×C4—42no—
142C2×C3×C4C2×D411yescharacteristic
143C2×C3×C4C2411yescharacteristic
144#67—42no—
145#67—42no—
146#67—42no—
147C2×Dic3—22no—
148C2×Dic3—22no—
149C2×Dic3—21no—
150C2×Dic3—42no—
151C2×Dic3C2×D411yescharacteristic
152C2×Dic3C2×D411yescharacteristic
153D12—22no—
154D12—42no—
155C4×D3—22no—
156C4×D3—22no—
157C4×D3—22no—
158C4×D3—42no—
159C4×D3#4114yes—
160C3×C8—22no—
161C3⋊C8—22no—
162C24—31no—
163C24—61no—
164C2×D4—21no—
165C2×D4—31no—
166C2×D4—61no—
167C2×D4—64no—
168C2×D4—61no—
169C2×D4—61no—
170C2×D4—61no—
171C2×D4—124no—
172C2×D4C22×D311yescharacteristic
173C22×C4—21no—
174C22×C4—31no—
175C22×C4—31no—
176C22×C4—31no—
177C22×C4—31no—
178C22×C4—31no—
179C22×C4—64no—
180C22×C4—61no—
181C22×C4—61no—
182C22×C4C22×D311yescharacteristic
183M16—64no—
184C2×C8—32no—
185C2×C8C22×D312yes—
186C4⋊C4—21no—
187C4⋊C4—32no—
188C4⋊C4—31no—
189C4⋊C4—61no—
190C4⋊C4—61no—
191C4⋊C4C22×D312yes—
192C4⋊C4C22×D311yescharacteristic
193C22⋊C4—21no—
194C22⋊C4—61no—
195C22⋊C4—62no—
196C22⋊C4—62no—
197C22⋊C4—61no—
198C22⋊C4—61no—
199C42—62no—
200C42—62no—
201C22×C3—21no—
202C22×C3—21no—
203C22×C3—41no—
204C22×C3—41no—
205C22×C3—41no—
206C22×C3AGL(1,ℤ/8)12yes—
207C22×C3C22×D411yescharacteristic
208C2×D3—21no—
209C2×D3—21no—
210C2×D3—21no—
211C2×D3—21no—
212C2×D3—21no—
213C2×D3—44no—
214C2×D3—41no—
215C2×D3—41no—
216C2×D3—41no—
217C2×D3—84no—
218C2×D3#12312yes—
219C3×C4—21no—
220C3×C4—41no—
221C3×C4—42no—
222C3×C4C2×#4112yes—
223Dic3—21no—
224Dic3—41no—
225Dic3—42no—
226Dic3#12312yes—
227C23—21no—
228C23—31no—
229C23—31no—
230C23—62no—
231C23—62no—
232C23—61no—
233C23—121no—
234C23—122no—
235C23—122no—
236C23—122no—
237C23D3×D411yescharacteristic
238D4—22no—
239D4—42no—
240D4—62no—
241D4—122no—
242D4—122no—
243D4—122no—
244D4—122no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—21no—
248C2×C4—31no—
249C2×C4—34no—
250C2×C4—31no—
251C2×C4—42no—
252C2×C4—62no—
253C2×C4—62no—
254C2×C4—62no—
255C2×C4—62no—
256C2×C4—62no—
257C2×C4—61no—
258C2×C4—122no—
259C2×C4—122no—
260C2×C4D3×D411yescharacteristic
261C2×C4C23×D311yescharacteristic
262C8—22no—
263C8—62no—
264C2×C3—22no—
265C2×C3—81no—
266C2×C3C2×#12311yescharacteristic
267C2×C3C2×AGL(1,ℤ/8)11yescharacteristic
268C2×C3#57511yescharacteristic
269D3—22no—
270D3—41no—
271D3—81no—
272C22—21no—
273C22—21no—
274C22—32no—
275C22—41no—
276C22—41no—
277C22—41no—
278C22—61no—
279C22—61no—
280C22—61no—
281C22—61no—
282C22—61no—
283C22—124no—
284C22—121no—
285C22—121no—
286C22—121no—
287C22—244no—
288C22#91112yes—
289C22C2×D3×D411yescharacteristic
290C4—21no—
291C4—32no—
292C4—42no—
293C4—41no—
294C4—61no—
295C4—121no—
296C4—122no—
297C4D3×#4112yes—
298C3#309411yescharacteristic, complemented, Sylow
299C2—22no—
300C2—62no—
301C2—81no—
302C2—121no—
303C2—241no—
304C2D3×#12311yescharacteristic
305C2C2×#91111yescharacteristic
306C2#577711yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#480C2
socleC22×C3C22×D4
prime radicalD3×#121C2
hypercenter#480D3
hypocenterC3#3094
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
2. C2×#892C2semidirect
3. C3×#480C2semidirect
4. #5034C2semidirect
5. #4967C2semidirect
6. #4885C2semidirect
7. #4881C2semidirect
8. #4779C2semidirect
9. #4770C2semidirect
10. #4735C2semidirect
11. #4726C2semidirect
17. C2×C3×C4⋊C4C22semidirect
22. C2×C4⋊Dic3C22semidirect
29. #892C22semidirect
33. C3×#107C22semidirect
34. C3×#102C22semidirect
35. C3×C22⋊C8C22semidirect
36. #832C22semidirect
37. #830C22semidirect
38. #821C22semidirect
39. (C2×D3)⋊C8C22semidirect
40. #817C22semidirect
41. #809C22semidirect
42. #808C22semidirect
43. #807C22semidirect
51. #480D3semidirect
110. C2×C4⋊C4C2×D3semidirect
115. #107C2×D3semidirect
121. #102C2×D3semidirect
124. C22⋊C8C2×D3semidirect
298. C3#3094semidirect

Maximal subgroups

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

subgroupindex
D3×#1212
C2×#8922
C3×#4802
#50342
#49672
#48852
#48812
#47792
#47702
#47352
#47262
#30943