Finite Group Databasebeta

← #79892

Subgroups — #79892

Order 384.

454 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 125 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#5771C211yesmaximal, characteristic, complemented
2#5769C211yesmaximal, characteristic, complemented
3#5751C212yesmaximal, complemented
4C3×#443C211yesmaximal, characteristic, complemented
5#5141C212yesmaximal, complemented
6#4897C211yesmaximal, characteristic, complemented
7#4896C211yesmaximal, characteristic, complemented
8#4827C212yesmaximal, complemented
9#4825C212yesmaximal, complemented
10#4700C211yesmaximal, characteristic, complemented
11#4696C211yesmaximal, characteristic, complemented
12#3290—31nomaximal, Sylow
13#1010C2212yescomplemented
14#1009C2212yes—
15C3×#135C2211yescharacteristic
16C3×#131C2212yescomplemented
17#951C2212yescomplemented
18#949C2212yes—
19#919—21no—
20D3×Q16—21no—
21#915—22no—
22#914—22no—
23#912—21no—
24D3×D8—21no—
25#909—22no—
26#909C2212yes—
27#908—22no—
28#908C2212yescomplemented
29C2×Dic12C2211yescharacteristic, complemented
30#904—22no—
31#904C2211yescharacteristic
32C2×D24C2211yescharacteristic
33C2×#204—22no—
34C2×#204C2212yescomplemented
35#901C2211yescharacteristic
36#901C2211yescharacteristic, complemented
37#875C2212yescomplemented
38C3×#108C2211yescharacteristic, complemented
39C3×#104C2212yescomplemented
40C3×C4×C8C2211yescharacteristic, complemented
41#824C2212yescomplemented
42#823C2212yescomplemented
43#819C2211yescharacteristic, complemented
44#805C2211yescharacteristic
45#805C2211yescharacteristic, complemented
46#578—31no—
47#577—32no—
48#576—31no—
49#495—31no—
50#473—31no—
51#472—31no—
52#471—32no—
53#455—32no—
54#454—32no—
55#443—31no—
56#443D311yescharacteristic, complemented
57C3×#41C2312yes—
58#239—22no—
59D3×Q8—22no—
60#237—22no—
61#237—42no—
62D3×D4—22no—
63D3×D4—42no—
64#235—22no—
65#235—22no—
66#235C2311yescharacteristic
67#235C2311yescharacteristic
68C2×D12—22no—
69C2×D12C2312yes—
70C2×Dic6—22no—
71C2×Dic6C2312yes—
72C3×Q16D411yescharacteristic
73C3×SD16D412yes—
74C3×D8D411yescharacteristic
75C3×M16—22no—
76C3×M16C2312yes—
77C2×C3×C8—22no—
78C2×C3×C8C2311yescharacteristic
79C2×C3×C8C2311yescharacteristic
80C3×C42C2311yescharacteristic
81#216—22no—
82#215—22no—
83#214—22no—
84#213—22no—
85(C2×D3)⋊C4—42no—
86#208C2311yescharacteristic
87#208C2311yescharacteristic
88Dic12—22no—
89Dic12—21no—
90Dic12—21no—
91Dic12D411yescharacteristic
92D24—22no—
93D24—21no—
94D24—21no—
95D24D411yescharacteristic
96#204—22no—
97#204—22no—
98#204—22no—
99#204—22no—
100#204D411yescharacteristic
101#204D411yescharacteristic
102ΓL(1,𝔽25)—21no—
103ΓL(1,𝔽25)—21no—
104D3×C8—21no—
105D3×C8—21no—
1062−1+4—32no—
107H(5,𝔽2)—32no—
108#137—32no—
109#137—32no—
110#137—62no—
111#137—62no—
112AGL(1,ℤ/8)—32no—
113AGL(1,ℤ/8)—32no—
114AGL(1,ℤ/8)—62no—
115AGL(1,ℤ/8)—62no—
116#135—31no—
117#135—62no—
118#135—61no—
119#135—61no—
120#135C2×D311yescharacteristic
121C2×Q16—31no—
122C2×Q16—61no—
123C2×SD16—32no—
124C2×SD16—62no—
125C2×D8—31no—
126C2×D8—61no—
127#131—31no—
128#131—31no—
129#131C2×D312yescomplemented
130#124—32no—
131#108—31no—
132#108C2×D311yescharacteristic, complemented
133#104—31no—
134#104—31no—
135#104C2×D312yescomplemented
136#101—32no—
137#100—32no—
138C4×C8C2×D311yescharacteristic, complemented
139C22×D3—22no—
140C22×D3—42no—
141C3×Q8C2×D412yes—
142C3×D4—22no—
143C3×D4C2×D412yes—
144C2×C3×C4—22no—
145C2×C3×C4—21no—
146C2×C3×C4C2411yescharacteristic
147#67—21no—
148#67—21no—
149#67—42no—
150#67—42no—
151C2×Dic3—22no—
152C2×Dic3—42no—
153D12—22no—
154D12—22no—
155D12—42no—
156D12C2×D411yescharacteristic
157D12C2×D411yescharacteristic
158C4×D3—21no—
159C4×D3—21no—
160C4×D3—42no—
161C4×D3—42no—
162Dic6—22no—
163Dic6—22no—
164Dic6—42no—
165Dic6C2×D411yescharacteristic
166Dic6C2×D411yescharacteristic
167C3×C8—22no—
168C3×C8C2×D411yescharacteristic
169C3×C8C2×D411yescharacteristic
170C3×C8C2×D411yescharacteristic
171C3×C8C2×D411yescharacteristic
172C3⋊C8—21no—
173C3⋊C8—21no—
174#41—31no—
175#41—31no—
176#41—62no—
177#41—62no—
178#41—62no—
179#41—62no—
180#41—122no—
181#41C22×D312yes—
182C2×Q8—32no—
183C2×Q8—62no—
184C2×Q8—62no—
185C2×D4—32no—
186C2×D4—62no—
187C2×D4—62no—
188C2×D4—122no—
189Q16—31no—
190Q16—62no—
191Q16—62no—
192Q16—61no—
193Q16—61no—
194Q16D1211yescharacteristic
195SD16—31no—
196SD16—31no—
197SD16—62no—
198SD16—62no—
199SD16—62no—
200SD16—62no—
201SD16—62no—
202SD16—62no—
203SD16D1212yes—
204D8—31no—
205D8—62no—
206D8—62no—
207D8—61no—
208D8—61no—
209D8D1211yescharacteristic
210M16—22no—
211M16—31no—
212M16—31no—
213M16—61no—
214M16—61no—
215M16C22×D312yes—
216C2×C8—22no—
217C2×C8—61no—
218C2×C8—61no—
219C2×C8C22×D311yescharacteristic
220C2×C8C22×D311yescharacteristic
221C22⋊C4—122no—
222C42C22×D311yescharacteristic
223C22×C3—22no—
224C22×C3H(5,𝔽2)11yescharacteristic
225C2×D3—21no—
226C2×D3—21no—
227C2×D3—42no—
228C2×D3—82no—
229C2×D3—162no—
230C3×C4—22no—
231C3×C4—41no—
232C3×C4C22×D411yescharacteristic
233C3×C4C22×D411yescharacteristic
234Dic3—21no—
235Dic3—21no—
236Dic3—42no—
237C23—62no—
238C23—122no—
239Q8—31no—
240Q8—31no—
241Q8—62no—
242Q8—62no—
243Q8—122no—
244Q8C2×D1212yes—
245D4—22no—
246D4—31no—
247D4—31no—
248D4—61no—
249D4—61no—
250D4—62no—
251D4—62no—
252D4—122no—
253D4—122no—
254D4—122no—
255D4C2×D1212yes—
256C2×C4—22no—
257C2×C4—21no—
258C2×C4—61no—
259C2×C4—61no—
260C2×C4—62no—
261C2×C4—122no—
262C2×C4—122no—
263C2×C4—122no—
264C2×C4C23×D311yescharacteristic
265C8—22no—
266C8—61no—
267C8—61no—
268C8C2×D1211yescharacteristic
269C8C2×D1211yescharacteristic
270C8D3×D411yescharacteristic
271C8D3×D411yescharacteristic
272C2×C3—21no—
273C2×C3—42no—
274C2×C3D4211yescharacteristic
275D3—41no—
276D3—41no—
277D3—82no—
278C22—22no—
279C22—61no—
280C22—61no—
281C22—122no—
282C22—242no—
283C22—482no—
284C22#100911yescharacteristic
285C4—22no—
286C4—41no—
287C4—61no—
288C4—61no—
289C4—122no—
290C4C22×D1211yescharacteristic
291C4C2×D3×D411yescharacteristic
292C3#329011yescharacteristic, complemented, Sylow
293C2—21no—
294C2—42no—
295C2—121no—
296C2—121no—
297C2—242no—
298C2D4×D1211yescharacteristic
subgroupG/H
centerC2D4×D12
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#443C2
socleC2×C3D42
hypercenter#443D3
hypocenterC3#3290
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2 ◁ C2×C4 ◁ #443

Complements

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

NH ≅ G/Ntype
1. #5771C2semidirect
2. #5769C2semidirect
3. #5751C2semidirect
4. C3×#443C2semidirect
5. #5141C2semidirect
6. #4897C2semidirect
7. #4896C2semidirect
8. #4827C2semidirect
9. #4825C2semidirect
10. #4700C2semidirect
11. #4696C2semidirect
13. #1010C22semidirect
16. C3×#131C22semidirect
17. #951C22semidirect
28. #908C22semidirect
29. C2×Dic12C22semidirect
34. C2×#204C22semidirect
36. #901C22semidirect
37. #875C22semidirect
38. C3×#108C22semidirect
39. C3×#104C22semidirect
40. C3×C4×C8C22semidirect
41. #824C22semidirect
42. #823C22semidirect
43. #819C22semidirect
45. #805C22semidirect
56. #443D3semidirect
129. #131C2×D3semidirect
132. #108C2×D3semidirect
135. #104C2×D3semidirect
138. C4×C8C2×D3semidirect
292. C3#3290semidirect

Maximal subgroups

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

subgroupindex
#57712
#57692
#57512
C3×#4432
#51412
#48972
#48962
#48272
#48252
#47002
#46962
#32903