Finite Group Databasebeta

← #81075

Subgroups — #81075

Order 384.

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

normal subgroups only

This group has 462 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#5730C211yesmaximal, characteristic, complemented
2D4×D12C211yesmaximal, characteristic
3C3×#476C211yesmaximal, characteristic, complemented
4#5088C211yesmaximal, characteristic, complemented
5C4×#214C211yesmaximal, characteristic, complemented
6#4864C212yesmaximal, complemented
7#4863C212yesmaximal, complemented
8#4848C211yesmaximal, characteristic, complemented
9#4834C211yesmaximal, characteristic, complemented
10#4776C212yesmaximal, complemented
11D3×#102C212yesmaximal, complemented
12#3295—31nomaximal, Sylow
13C2×D3×D4C2212yes—
14C22×D12—21no—
15C3×C4⋊Q8C2211yescharacteristic, complemented
16C3×C4×D4C2211yescharacteristic
17#946—22no—
18C2×#214C2211yescharacteristic
19#930—21no—
20C2×#204C2212yescomplemented
21C2×D3×C8C2212yescomplemented
22#897C2212yescomplemented
23#895C2212yes—
24#893—21no—
25D3×C4⋊C4C2212yescomplemented
26#890—21no—
27#882—22no—
28#874C2211yescharacteristic
29C4×D12C2211yescharacteristic
30C4×Dic6C2211yescharacteristic, complemented
31C3×#106C2212yescomplemented
32C3×C4⋊C8C2211yescharacteristic, complemented
33C3×#102C2212yes—
34#832C2211yescharacteristic
35#821C2212yescomplemented
36(C2×D3)⋊C8C2212yescomplemented
37#810C2211yescharacteristic, complemented
38#809C2212yescomplemented
39#809C2212yescomplemented
40#808C2211yescharacteristic, complemented
41C4×C3⋊C8C2211yescharacteristic, complemented
42#554—31no—
43D42—31no—
44#486—31no—
45#481—32no—
46#476D311yescharacteristic, complemented
47#465—32no—
48#460—31no—
49#450—32no—
50C4×SD16—31no—
51C8×D4—31no—
52C2×#102—32no—
53C23×D3—22no—
54C2×C3×Q8—21no—
55C2×C3×D4C2311yescharacteristic
56C22×C3×C4—21no—
57C2×#67—22no—
58D3×D4—24no—
59D3×D4—42no—
60C2×D12—22no—
61C2×D12—21no—
62C2×D12—21no—
63C2×D12—44no—
64C2×D12D411yescharacteristic
65C2×D12C2312yes—
66C2×C4×D3—22no—
67C2×C4×D3C2312yes—
68C2×Dic6C2311yescharacteristic
69C2×C3×C8C2312yes—
70C3×C4⋊C4—21no—
71C3×C4⋊C4C2311yescharacteristic
72C3×C4⋊C4C2312yes—
73C3×C22⋊C4—21no—
74C3×C42C2311yescharacteristic
75#214—22no—
76(C2×D3)⋊C4—22no—
77(C2×D3)⋊C4—22no—
78(C2×D3)⋊C4D412yes—
79C4⋊Dic3—22no—
80C4⋊Dic3D411yescharacteristic
81C4⋊Dic3C2311yescharacteristic
82Dic3⋊C4—21no—
83Dic3⋊C4—22no—
84C4×Dic3—21no—
85C2×C3⋊C8C2311yescharacteristic
86C2×C3⋊C8C2311yescharacteristic
87#204—42no—
88D3×C8—42no—
89C22×D4—32no—
90C22×D4—61no—
91C2×SD16—31no—
92C2×SD16—32no—
93C22×C8—32no—
94C4⋊Q8C2×D311yescharacteristic, complemented
95#127—31no—
96#125—61no—
97C22⋊Q8—32no—
98C22⋊Q8—62no—
99#121—32no—
100#121—61no—
101#120—62no—
102C4×Q8—31no—
103C4×D4—31no—
104C4×D4—61no—
105C4×D4C2×D311yescharacteristic
106C2×C4⋊C4—32no—
107#106—31no—
108#106C2×D312yescomplemented
109C4⋊C8C2×D311yescharacteristic, complemented
110#103—31no—
111#102—31no—
112#102—32no—
113#102—32no—
114#102—32no—
115#102C2×D312yes—
116C22⋊C8—32no—
117C4×C8—31no—
118C23×C3—21no—
119C22×D3—22no—
120C22×D3—44no—
121C22×D3—44no—
122C22×D3—82no—
123C22×D3C2×D412yes—
124C3×Q8—81no—
125C3×D4—21no—
126C3×D4#4112yes—
127C2×C3×C4—22no—
128C2×C3×C4—21no—
129C2×C3×C4—42no—
130C2×C3×C4C2×D411yescharacteristic
131C2×C3×C4C2×D411yescharacteristic
132C2×C3×C4C2411yescharacteristic
133#67—44no—
134C2×Dic3—21no—
135C2×Dic3—21no—
136C2×Dic3C2×D412yes—
137D12—22no—
138D12—22no—
139D12—44no—
140D12—42no—
141D12—81no—
142D12SD1614yescomplemented
143C4×D3—22no—
144C4×D3—22no—
145C4×D3—82no—
146Dic6—21no—
147Dic6—21no—
148C3×C8—22no—
149C3⋊C8—21no—
150C3⋊C8—21no—
151C24—62no—
152C2×Q8—21no—
153C2×Q8—31no—
154C2×D4—31no—
155C2×D4—32no—
156C2×D4—62no—
157C2×D4—62no—
158C2×D4—64no—
159C2×D4—61no—
160C2×D4—61no—
161C2×D4—124no—
162C2×D4—122no—
163C2×D4C22×D311yescharacteristic
164C22×C4—21no—
165C22×C4—32no—
166C22×C4—62no—
167SD16—62no—
168SD16—122no—
169C2×C8—31no—
170C2×C8—31no—
171C2×C8—122no—
172C2×C8C22×D312yes—
173C4⋊C4—21no—
174C4⋊C4—31no—
175C4⋊C4—31no—
176C4⋊C4—62no—
177C4⋊C4—62no—
178C4⋊C4—61no—
179C4⋊C4C22×D312yes—
180C4⋊C4C22×D311yescharacteristic
181C22⋊C4—21no—
182C22⋊C4—32no—
183C22⋊C4—62no—
184C22⋊C4—62no—
185C42—61no—
186C42C22×D311yescharacteristic
187C22×C3—22no—
188C22×C3—41no—
189C22×C3—41no—
190C22×C3C22×D411yescharacteristic
191C2×D3—22no—
192C2×D3—22no—
193C2×D3—42no—
194C2×D3—42no—
195C2×D3—42no—
196C2×D3—88no—
197C2×D3C2×SD1614yes—
198C3×C4—21no—
199C3×C4—41no—
200C3×C4—42no—
201C3×C4C2×SD1612yes—
202C3×C4C2×#4111yescharacteristic
203C3×C4H(5,𝔽2)11yescharacteristic
204Dic3—22no—
205Dic3—41no—
206Dic3—41no—
207C23—21no—
208C23—32no—
209C23—62no—
210C23—124no—
211C23—124no—
212C23—242no—
213Q8—61no—
214Q8—61no—
215Q8—81no—
216D4—21no—
217D4—34no—
218D4—62no—
219D4—62no—
220D4—124no—
221D4—124no—
222D4—122no—
223D4—241no—
224D4#23912yes—
225C2×C4—21no—
226C2×C4—22no—
227C2×C4—32no—
228C2×C4—42no—
229C2×C4—62no—
230C2×C4—62no—
231C2×C4—61no—
232C2×C4—61no—
233C2×C4—242no—
234C2×C4D3×D411yescharacteristic
235C2×C4D3×D411yescharacteristic
236C2×C4C23×D311yescharacteristic
237C8—22no—
238C8—61no—
239C8—61no—
240C2×C3—42no—
241C2×C3#54611yescharacteristic
242C2×C3C22×SD1611yescharacteristic
243C2×C3#57611yescharacteristic
244D3—24no—
245D3—82no—
246C22—22no—
247C22—34no—
248C22—41no—
249C22—41no—
250C22—62no—
251C22—62no—
252C22—122no—
253C22—122no—
254C22—122no—
255C22—248no—
256C22C2×D3×D411yescharacteristic
257C4—21no—
258C4—41no—
259C4—42no—
260C4—62no—
261C4—121no—
262C4—121no—
263C4D3×SD1612yes—
264C4C2×#23911yescharacteristic
265C4#100911yescharacteristic
266C3#329511yescharacteristic, complemented, Sylow
267C2—42no—
268C2—64no—
269C2—242no—
270C2#563011yescharacteristic
271C2C2×D3×SD1611yescharacteristic
272C2#577411yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#476C2
socleC22×C3C22×D4
prime radicalD4×D12C2
hypercenter#476D3
hypocenterC3#3295
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #5730C2semidirect
3. C3×#476C2semidirect
4. #5088C2semidirect
5. C4×#214C2semidirect
6. #4864C2semidirect
7. #4863C2semidirect
8. #4848C2semidirect
9. #4834C2semidirect
10. #4776C2semidirect
11. D3×#102C2semidirect
15. C3×C4⋊Q8C22semidirect
20. C2×#204C22semidirect
21. C2×D3×C8C22semidirect
22. #897C22semidirect
25. D3×C4⋊C4C22semidirect
30. C4×Dic6C22semidirect
31. C3×#106C22semidirect
32. C3×C4⋊C8C22semidirect
35. #821C22semidirect
36. (C2×D3)⋊C8C22semidirect
37. #810C22semidirect
38. #809C22semidirect
39. #809C22semidirect
40. #808C22semidirect
41. C4×C3⋊C8C22semidirect
46. #476D3semidirect
94. C4⋊Q8C2×D3semidirect
108. #106C2×D3semidirect
109. C4⋊C8C2×D3semidirect
142. D12SD16semidirect
266. C3#3295semidirect

Maximal subgroups

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

subgroupindex
#57302
D4×D122
C3×#4762
#50882
C4×#2142
#48642
#48632
#48482
#48342
#47762
D3×#1022
#32953