Finite Group Databasebeta

← #79676

Subgroups — #79676

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#5579C211yesmaximal, characteristic, complemented
2D4×D12C211yesmaximal, characteristic
3C3×C4×SD16C211yesmaximal, characteristic, complemented
4#5169C212yesmaximal, complemented
5#5027C211yesmaximal, characteristic, complemented
6#5008C211yesmaximal, characteristic, complemented
7#4863C212yesmaximal, complemented
8#4807C212yesmaximal, complemented
9D3×#102C212yesmaximal, complemented
10#4694C211yesmaximal, characteristic, complemented
11C8×D12C211yesmaximal, characteristic, complemented
12#3295—31nomaximal, Sylow
13C2×D3×D4C2212yes—
14C22×D12—21no—
15C2×C3×SD16C2211yescharacteristic
16C3×C4×Q8C2211yescharacteristic, complemented
17C3×C4×D4C2211yescharacteristic
18#946C2212yescomplemented
19C2×#215C2212yescomplemented
20#930—21no—
21C2×D3×C8C2212yescomplemented
22#896—22no—
23#895C2212yes—
24D3×C4⋊C4C2212yescomplemented
25#882—22no—
26#874C2211yescharacteristic
27C4×D12—21no—
28C4×D12C2211yescharacteristic
29#870—21no—
30#869C2211yescharacteristic, complemented
31C3×#106C2211yescharacteristic, complemented
32C3×#103C2211yescharacteristic, complemented
33C3×#102C2211yescharacteristic
34C3×C4×C8C2211yescharacteristic, complemented
35#832C2212yes—
36#821C2212yescomplemented
37#821C2212yescomplemented
38(C2×D3)⋊C8C2212yescomplemented
39#809C2212yescomplemented
40#808C2212yescomplemented
41C4⋊(C3⋊C8)C2211yescharacteristic, complemented
42#554—31no—
43D42—31no—
44#486—31no—
45#481—32no—
46#476—31no—
47#465—32no—
48#460—31no—
49#450—32no—
50C4×SD16D311yescharacteristic, complemented
51C8×D4—31no—
52C2×#102—32no—
53C23×D3—22no—
54C2×C3×Q8C2311yescharacteristic
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×Dic6—21no—
69C3×SD16—22no—
70C2×C3×C8C2311yescharacteristic
71C2×C3×C8C2311yescharacteristic
72C3×C4⋊C4—21no—
73C3×C4⋊C4C2311yescharacteristic
74C3×C4⋊C4C2311yescharacteristic
75C3×C22⋊C4—21no—
76C3×C42—21no—
77C3×C42C2311yescharacteristic
78#215—42no—
79(C2×D3)⋊C4—22no—
80(C2×D3)⋊C4—22no—
81(C2×D3)⋊C4D412yes—
82C4⋊Dic3—21no—
83C4⋊Dic3D411yescharacteristic
84C4⋊Dic3C2312yes—
85Dic3⋊C4—22no—
86Dic3⋊C4—22no—
87C2×C3⋊C8C2312yes—
88D3×C8—42no—
89C22×D4—32no—
90C22×D4—61no—
91C2×SD16—32no—
92C2×SD16C2×D311yescharacteristic
93C22×C8—32no—
94C4⋊Q8—31no—
95#127—31no—
96#125—61no—
97C22⋊Q8—32no—
98C22⋊Q8—62no—
99#121—32no—
100#121—61no—
101#120—62no—
102C4×Q8C2×D311yescharacteristic, complemented
103C4×D4—31no—
104C4×D4—61no—
105C4×D4C2×D311yescharacteristic
106C2×C4⋊C4—32no—
107#106—32no—
108#106C2×D311yescharacteristic, complemented
109C4⋊C8—31no—
110#103C2×D311yescharacteristic, complemented
111#102—32no—
112#102—32no—
113#102—32no—
114#102—32no—
115#102C2×D311yescharacteristic
116C22⋊C8—32no—
117C4×C8C2×D311yescharacteristic, complemented
118C23×C3—21no—
119C22×D3—22no—
120C22×D3—44no—
121C22×D3—44no—
122C22×D3—82no—
123C22×D3C2×D412yes—
124C3×Q8—21no—
125C3×Q8—21no—
126C3×D4—21no—
127C3×D4#4112yes—
128C2×C3×C4—21no—
129C2×C3×C4—21no—
130C2×C3×C4—21no—
131C2×C3×C4—42no—
132C2×C3×C4C2×D411yescharacteristic
133C2×C3×C4C2×D411yescharacteristic
134C2×C3×C4C2411yescharacteristic
135#67—44no—
136C2×Dic3—22no—
137C2×Dic3C2×D412yes—
138D12—22no—
139D12—22no—
140D12—44no—
141D12—42no—
142D12—81no—
143D12SD1614yescomplemented
144C4×D3—22no—
145C4×D3—22no—
146C4×D3—82no—
147Dic6—81no—
148C3×C8—21no—
149C3×C8—21no—
150C3⋊C8—22no—
151C24—62no—
152C2×Q8—61no—
153C2×Q8C22×D311yescharacteristic
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—22no—
168SD16—122no—
169C2×C8—32no—
170C2×C8—122no—
171C2×C8C22×D311yescharacteristic
172C2×C8C22×D311yescharacteristic
173C4⋊C4—21no—
174C4⋊C4—31no—
175C4⋊C4—32no—
176C4⋊C4—62no—
177C4⋊C4—62no—
178C4⋊C4—61no—
179C4⋊C4C22×D311yescharacteristic
180C4⋊C4C22×D311yescharacteristic
181C22⋊C4—21no—
182C22⋊C4—32no—
183C22⋊C4—62no—
184C22⋊C4—62no—
185C42—21no—
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—41no—
201C3×C4—41no—
202C3×C4C2×SD1612yes—
203C3×C4C2×#4111yescharacteristic
204C3×C4H(5,𝔽2)11yescharacteristic
205Dic3—22no—
206Dic3—42no—
207C23—21no—
208C23—32no—
209C23—62no—
210C23—124no—
211C23—124no—
212C23—242no—
213Q8—21no—
214Q8—21no—
215Q8—241no—
216D4—21no—
217D4—34no—
218D4—62no—
219D4—62no—
220D4—124no—
221D4—124no—
222D4—122no—
223D4—241no—
224D4#23512yes—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—32no—
229C2×C4—42no—
230C2×C4—62no—
231C2×C4—62no—
232C2×C4—62no—
233C2×C4—242no—
234C2×C4D3×D411yescharacteristic
235C2×C4D3×D411yescharacteristic
236C2×C4C23×D311yescharacteristic
237C8—21no—
238C8—21no—
239C8—62no—
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—41no—
260C4—41no—
261C4—62no—
262C4—122no—
263C4D3×SD1612yes—
264C4C2×#23511yescharacteristic
265C4#100911yescharacteristic
266C3#329511yescharacteristic, complemented, Sylow
267C2—42no—
268C2—64no—
269C2—242no—
270C2#555011yescharacteristic
271C2C2×D3×SD1611yescharacteristic
272C2#576911yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×C4×SD16C2
socleC22×C3C22×D4
prime radicalD4×D12C2
hypercenterC4×SD16D3
hypocenterC3#3295
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #5579C2semidirect
3. C3×C4×SD16C2semidirect
4. #5169C2semidirect
5. #5027C2semidirect
6. #5008C2semidirect
7. #4863C2semidirect
8. #4807C2semidirect
9. D3×#102C2semidirect
10. #4694C2semidirect
11. C8×D12C2semidirect
16. C3×C4×Q8C22semidirect
18. #946C22semidirect
19. C2×#215C22semidirect
21. C2×D3×C8C22semidirect
24. D3×C4⋊C4C22semidirect
30. #869C22semidirect
31. C3×#106C22semidirect
32. C3×#103C22semidirect
34. C3×C4×C8C22semidirect
36. #821C22semidirect
37. #821C22semidirect
38. (C2×D3)⋊C8C22semidirect
39. #809C22semidirect
40. #808C22semidirect
41. C4⋊(C3⋊C8)C22semidirect
50. C4×SD16D3semidirect
102. C4×Q8C2×D3semidirect
108. #106C2×D3semidirect
110. #103C2×D3semidirect
117. C4×C8C2×D3semidirect
143. D12SD16semidirect
266. C3#3295semidirect

Maximal subgroups

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

subgroupindex
#55792
D4×D122
C3×C4×SD162
#51692
#50272
#50082
#48632
#48072
D3×#1022
#46942
C8×D122
#32953