Finite Group Databasebeta

← #81309

Subgroups — #81309

Order 384.

454 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 119 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
1#5600C211yesmaximal, characteristic, complemented
2C2×#893C211yesmaximal, characteristic, complemented
3C3×#481C211yesmaximal, characteristic, complemented
4#5036C211yesmaximal, characteristic
5#4970C211yesmaximal, characteristic, complemented
6#4871C212yesmaximal, complemented
7#4852C212yesmaximal, complemented
8#4787C212yesmaximal, complemented
9#4756C212yesmaximal, complemented
10#4731C211yesmaximal, characteristic, complemented
11#4718C211yesmaximal, characteristic, complemented
12#3105—31nomaximal, Sylow
13C22×D12C2211yescharacteristic
14C22×C4×D3—21no—
15C3×#121C2211yescharacteristic
16C2×C3×C4⋊C4C2211yescharacteristic
17#936C2211yescharacteristic, complemented
18#935—21no—
19D4×Dic3—21no—
20D4×Dic3C2211yescharacteristic, complemented
21C2×#213C2212yes—
22C2×(C2×D3)⋊C4—21no—
23#924C2211yescharacteristic
24C2×C4×Dic3C2211yescharacteristic
25C2×#204C2212yes—
26#893—21no—
27#893—21no—
28#893C2212yes—
29#893C2212yes—
30#890C2211yescharacteristic, complemented
31#887C2211yescharacteristic, complemented
32#879—21no—
33#877—21no—
34C3×#106C2212yescomplemented
35C3×#102C2212yescomplemented
36C3×C22⋊C8C2211yescharacteristic
37#830C2211yescharacteristic
38#821C2212yes—
39Dic3⋊C8C2212yescomplemented
40C8×Dic3C2212yescomplemented
41#810C2212yescomplemented
42#809C2212yes—
43#807C2212yescomplemented
44#529—31no—
45C2×C4×D4—31no—
46#484—31no—
47#481D311yescharacteristic, complemented
48#478—32no—
49#463—32no—
50#450—31no—
51#447—31no—
52C4×SD16—32no—
53C4×D8—32no—
54#431—31no—
55C23×D3—21no—
56C2×C3×D4—21no—
57C2×C3×D4C2311yescharacteristic
58C22×C3×C4—21no—
59C22×C3×C4C2311yescharacteristic
60C22×Dic3—21no—
61C22×Dic3D411yescharacteristic
62C22×Dic3D411yescharacteristic
63C2×D12—21no—
64C2×D12—24no—
65C2×D12C2312yes—
66C2×C4×D3—22no—
67C2×C4×D3—22no—
68C2×C4×D3—44no—
69C2×Dic6C2311yescharacteristic
70C2×C3×C8C2312yes—
71C3×C4⋊C4—21no—
72C3×C4⋊C4C2312yes—
73C3×C4⋊C4C2311yescharacteristic
74C3×C22⋊C4—21no—
75#217—21no—
76#217—21no—
77#217—21no—
78#217—21no—
79#213—24no—
80(C2×D3)⋊C4—22no—
81(C2×D3)⋊C4—22no—
82C4⋊Dic3—21no—
83C4⋊Dic3C2311yescharacteristic
84Dic3⋊C4—21no—
85Dic3⋊C4—21no—
86Dic3⋊C4—21no—
87C4×Dic3—21no—
88C4×Dic3D411yescharacteristic
89C4×Dic3D411yescharacteristic
90C4×Dic3C2311yescharacteristic
91C4×Dic3C2311yescharacteristic
92C2×C3⋊C8C2312yes—
93#204—24no—
94C22×D4—31no—
95C23×C4—61no—
96C2×SD16—32no—
97C2×D8—32no—
98#126—61no—
99#125—31no—
100#124—31no—
101#123—61no—
102C22⋊Q8—31no—
103#121C2×D311yescharacteristic
104C4×Q8—31no—
105C4×D4—31no—
106C4×D4—32no—
107C4×D4—32no—
108C4×D4—61no—
109C4×D4—61no—
110C4×D4—61no—
111#117—61no—
112C2×C4⋊C4C2×D311yescharacteristic
113C2×C22⋊C4—61no—
114C2×C42—31no—
115#107—32no—
116#106C2×D312yescomplemented
117C4⋊C8—32no—
118#103—32no—
119#102—32no—
120#102—32no—
121#102C2×D312yescomplemented
122C22⋊C8—31no—
123C22⋊C8C2×D311yescharacteristic
124C4×C8—32no—
125C23×C3—21no—
126C23×C3C2×D411yescharacteristic
127C22×D3—24no—
128C22×D3—22no—
129C22×D3—42no—
130C22×D3—42no—
131C3×D4—22no—
132C3×D4—42no—
133C2×C3×C4—22no—
134C2×C3×C4—21no—
135C2×C3×C4—22no—
136C2×C3×C4—42no—
137C2×C3×C4C2×D411yescharacteristic
138C2×C3×C4C2411yescharacteristic
139C2×Dic3—22no—
140C2×Dic3—22no—
141C2×Dic3—21no—
142C2×Dic3—21no—
143C2×Dic3—42no—
144C2×Dic3C2×D411yescharacteristic
145C2×Dic3C2×D411yescharacteristic
146C2×Dic3C2×D411yescharacteristic
147C2×Dic3C2×D411yescharacteristic
148D12—24no—
149D12—22no—
150D12#4114yes—
151C4×D3—44no—
152C4×D3—44no—
153Dic6—22no—
154C3×C8—22no—
155C3⋊C8—22no—
156C24—61no—
157C2×Q8—31no—
158C2×D4—21no—
159C2×D4—32no—
160C2×D4—64no—
161C2×D4—61no—
162C2×D4C22×D311yescharacteristic
163C22×C4—21no—
164C22×C4—31no—
165C22×C4—31no—
166C22×C4—62no—
167C22×C4—62no—
168C22×C4—61no—
169C22×C4—124no—
170C22×C4C22×D311yescharacteristic
171SD16—64no—
172D8—64no—
173C2×C8—32no—
174C2×C8C22×D312yes—
175C4⋊C4—21no—
176C4⋊C4—31no—
177C4⋊C4—61no—
178C4⋊C4—61no—
179C4⋊C4—61no—
180C4⋊C4—61no—
181C4⋊C4C22×D311yescharacteristic
182C4⋊C4C22×D312yes—
183C22⋊C4—21no—
184C22⋊C4—62no—
185C22⋊C4—62no—
186C22⋊C4—61no—
187C22⋊C4—61no—
188C22⋊C4—61no—
189C22⋊C4—61no—
190C42—31no—
191C42—31no—
192C42—31no—
193C42—31no—
194C42—61no—
195C22×C3—21no—
196C22×C3—21no—
197C22×C3—41no—
198C22×C3—41no—
199C22×C3—41no—
200C22×C3#13512yes—
201C22×C3C22×D411yescharacteristic
202C2×D3—24no—
203C2×D3—48no—
204C2×D3—42no—
205C2×D3—42no—
206C3×C4—21no—
207C3×C4—41no—
208C3×C4—42no—
209C3×C4C2×#4112yes—
210Dic3—21no—
211Dic3—21no—
212Dic3—21no—
213Dic3—41no—
214Dic3—41no—
215Dic3AGL(1,ℤ/8)12yes—
216C23—21no—
217C23—64no—
218C23—62no—
219C23—122no—
220C23—122no—
221C23D3×D411yescharacteristic
222Q8—62no—
223D4—22no—
224D4—34no—
225D4—42no—
226D4—64no—
227D4—62no—
228C2×C4—22no—
229C2×C4—21no—
230C2×C4—22no—
231C2×C4—31no—
232C2×C4—31no—
233C2×C4—31no—
234C2×C4—31no—
235C2×C4—42no—
236C2×C4—62no—
237C2×C4—62no—
238C2×C4—61no—
239C2×C4—61no—
240C2×C4—124no—
241C2×C4—122no—
242C2×C4—124no—
243C2×C4D3×D411yescharacteristic
244C2×C4C23×D311yescharacteristic
245C8—22no—
246C8—62no—
247C2×C3—22no—
248C2×C3—81no—
249C2×C3#52511yescharacteristic
250C2×C3C2×#13511yescharacteristic
251C2×C3C2×AGL(1,ℤ/8)11yescharacteristic
252D3—44no—
253C22—21no—
254C22—21no—
255C22—41no—
256C22—41no—
257C22—41no—
258C22—64no—
259C22—128no—
260C22—122no—
261C22—122no—
262C22#91612yes—
263C22C2×D3×D411yescharacteristic
264C4—21no—
265C4—32no—
266C4—41no—
267C4—42no—
268C4—61no—
269C4—61no—
270C4—61no—
271C4—121no—
272C4—121no—
273C4D3×#4112yes—
274C3#310511yescharacteristic, complemented, Sylow
275C2—22no—
276C2—81no—
277C2—124no—
278C2#565611yescharacteristic
279C2C2×#91611yescharacteristic
280C2D3×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#481C2
socleC22×C3C22×D4
prime radical#5036C2
hypercenter#481D3
hypocenterC3#3105
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
1. #5600C2semidirect
2. C2×#893C2semidirect
3. C3×#481C2semidirect
5. #4970C2semidirect
6. #4871C2semidirect
7. #4852C2semidirect
8. #4787C2semidirect
9. #4756C2semidirect
10. #4731C2semidirect
11. #4718C2semidirect
17. #936C22semidirect
20. D4×Dic3C22semidirect
30. #890C22semidirect
31. #887C22semidirect
34. C3×#106C22semidirect
35. C3×#102C22semidirect
39. Dic3⋊C8C22semidirect
40. C8×Dic3C22semidirect
41. #810C22semidirect
43. #807C22semidirect
47. #481D3semidirect
116. #106C2×D3semidirect
121. #102C2×D3semidirect
274. C3#3105semidirect

Maximal subgroups

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

subgroupindex
#56002
C2×#8932
C3×#4812
#50362
#49702
#48712
#48522
#47872
#47562
#47312
#47182
#31053