Finite Group Databasebeta

← #80730

Subgroups — #80730

Order 384.

526 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 123 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
1C2×D3×D8C211yesmaximal, characteristic, complemented
2C2×#904C211yesmaximal, characteristic, complemented
3#5612C212yesmaximal, complemented
4C3×#466C211yesmaximal, characteristic, complemented
5#5155C211yesmaximal, characteristic, complemented
6C8×#67C211yesmaximal, characteristic, complemented
7#5037C212yesmaximal, complemented
8#4887C211yesmaximal, characteristic, complemented
9#4872C211yesmaximal, characteristic, complemented
10#4787C212yesmaximal, complemented
11#4776C212yesmaximal, complemented
12#3280—31nomaximal, Sylow
13C2×D3×D4C2212yes—
14C2×#235C2212yescomplemented
15C2×C3×D8C2211yescharacteristic
16C22×C3×C8C2211yescharacteristic, complemented
17C3×#121C2212yescomplemented
18#938—22no—
19#937—22no—
20#936C2212yescomplemented
21C2×#214C2212yescomplemented
22C2×#213C2212yes—
23C4×#67C2211yescharacteristic
24D3×D8—24no—
25C2×Dic12C2211yescharacteristic, complemented
26#904—24no—
27C2×D24C2211yescharacteristic
28C2×#204C2212yescomplemented
29C2×D3×C8C2211yescharacteristic
30#897C2212yes—
31#893C2212yescomplemented
32#883—22no—
33D3×C22⋊C4—22no—
34C3×#107C2211yescharacteristic, complemented
35C3×#102C2212yescomplemented
36#830C2211yescharacteristic, complemented
37(C2×D3)⋊C8C2211yescharacteristic
38Dic3⋊C8C2211yescharacteristic, complemented
39C8×Dic3C2211yescharacteristic, complemented
40#810C2212yescomplemented
41#809C2212yescomplemented
42C2×#135—31no—
43C22×D8—31no—
44#546—32no—
45#495—31no—
46#467—31no—
47#466D311yescharacteristic, complemented
48#463—32no—
49#450—32no—
50#449—32no—
51C4×D8—31no—
52C8×D4—31no—
53C23×D3—22no—
54C2×C3×D4—22no—
55C2×C3×D4C2312yes—
56C22×C3×C4C2311yescharacteristic
57C2×#67—22no—
58C2×#67—22no—
59C2×#67D411yescharacteristic
60D3×D4—24no—
61D3×D4—42no—
62#235—24no—
63#235—42no—
64C2×D12C2312yes—
65C2×C4×D3—22no—
66C2×C4×D3—22no—
67C2×C4×D3C2311yescharacteristic
68C2×Dic6C2312yes—
69C3×D8—22no—
70C2×C3×C8—22no—
71C2×C3×C8C2311yescharacteristic
72C2×C3×C8C2311yescharacteristic
73C3×C4⋊C4C2312yes—
74C3×C22⋊C4—22no—
75#217—22no—
76#217—22no—
77#217D411yescharacteristic
78#214—42no—
79#213—24no—
80(C2×D3)⋊C4—22no—
81(C2×D3)⋊C4—22no—
82(C2×D3)⋊C4D411yescharacteristic
83C4⋊Dic3—22no—
84Dic3⋊C4D411yescharacteristic
85C4×Dic3C2311yescharacteristic
86C2×C3⋊C8C2311yescharacteristic
87C2×C3⋊C8C2311yescharacteristic
88Dic12—22no—
89D24D414yescomplemented
90#204—24no—
91D3×C8—22no—
92C2×#41—32no—
93C22×D4—32no—
94#135—64no—
95C2×Q16—31no—
96C2×SD16—32no—
97C2×SD16—32no—
98C2×D8—32no—
99C2×D8—31no—
100C2×D8—64no—
101C2×D8C2×D311yescharacteristic
102C22×C8—31no—
103C22×C8C2×D311yescharacteristic, complemented
104#124—32no—
105#123—62no—
106C22⋊Q8—32no—
107#121—62no—
108#121C2×D312yescomplemented
109#120—62no—
110C4×D4—31no—
111C4×D4—32no—
112C2×C22⋊C4—62no—
113#107C2×D311yescharacteristic, complemented
114C4⋊C8—31no—
115#103—32no—
116#102—32no—
117#102C2×D312yescomplemented
118C22⋊C8—31no—
119C22⋊C8—31no—
120C4×C8—31no—
121C23×C3—22no—
122C23×C3C2×D411yescharacteristic
123C22×D3—22no—
124C22×D3—44no—
125C22×D3—44no—
126C22×D3—82no—
127C22×D3C2×D411yescharacteristic
128C3×D4—22no—
129C3×D4—22no—
130C3×D4—82no—
131C2×C3×C4—21no—
132C2×C3×C4—21no—
133C2×C3×C4—22no—
134C2×C3×C4C2×D411yescharacteristic
135C2×C3×C4C2411yescharacteristic
136#67—22no—
137#67—44no—
138#67—44no—
139C2×Dic3—22no—
140C2×Dic3C2×D411yescharacteristic
141C2×Dic3C2×D411yescharacteristic
142C2×Dic3C2×D411yescharacteristic
143D12—22no—
144D12C2×D414yes—
145C4×D3—21no—
146C4×D3—21no—
147C4×D3—44no—
148C4×D3—82no—
149Dic6—22no—
150Dic6—22no—
151C3×C8—21no—
152C3×C8C2×D412yes—
153C3⋊C8—21no—
154C3⋊C8—21no—
155C24—62no—
156#41—64no—
157#41—122no—
158C2×Q8—32no—
159C2×D4—22no—
160C2×D4—31no—
161C2×D4—32no—
162C2×D4—62no—
163C2×D4—64no—
164C2×D4—62no—
165C2×D4—122no—
166C2×D4C22×D312yes—
167C22×C4—31no—
168C22×C4—62no—
169C22×C4—62no—
170C22×C4C22×D311yescharacteristic
171Q16—62no—
172SD16—64no—
173SD16—122no—
174D8—22no—
175D8—34no—
176D8—64no—
177C2×C8—22no—
178C2×C8—31no—
179C2×C8—31no—
180C2×C8—62no—
181C2×C8C22×D311yescharacteristic
182C2×C8C22×D311yescharacteristic
183C4⋊C4—31no—
184C4⋊C4—62no—
185C4⋊C4C22×D312yes—
186C22⋊C4—22no—
187C22⋊C4—31no—
188C22⋊C4—31no—
189C22⋊C4—62no—
190C22⋊C4—62no—
191C22⋊C4—62no—
192C22⋊C4—62no—
193C42—31no—
194C22×C3—21no—
195C22×C3—21no—
196C22×C3—21no—
197C22×C3—42no—
198C22×C3—42no—
199C22×C3—42no—
200C22×C3C22×D411yescharacteristic
201C2×D3—21no—
202C2×D3—21no—
203C2×D3—24no—
204C2×D3—42no—
205C2×D3—42no—
206C2×D3—88no—
207C2×D3#13512yescomplemented
208C3×C4—21no—
209C3×C4—42no—
210C3×C4C22×D411yescharacteristic
211C3×C4H(5,𝔽2)11yescharacteristic
212Dic3—21no—
213Dic3—21no—
214Dic3—21no—
215Dic3—42no—
216C23—22no—
217C23—31no—
218C23—62no—
219C23—124no—
220C23—124no—
221C23—242no—
222C23D3×D411yescharacteristic
223Q8—62no—
224Q8—62no—
225D4—22no—
226D4—22no—
227D4—34no—
228D4—62no—
229D4—62no—
230D4—82no—
231D4—124no—
232D4—124no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—22no—
236C2×C4—31no—
237C2×C4—31no—
238C2×C4—31no—
239C2×C4—61no—
240C2×C4—61no—
241C2×C4—62no—
242C2×C4—124no—
243C2×C4—242no—
244C2×C4D3×D411yescharacteristic
245C2×C4C23×D311yescharacteristic
246C8—21no—
247C8—61no—
248C8—61no—
249C8D3×D412yes—
250C2×C3—41no—
251C2×C3—82no—
252C2×C3D4211yescharacteristic
253C2×C3C2×#13511yescharacteristic
254C2×C3#57611yescharacteristic
255D3—22no—
256D3—44no—
257C22—21no—
258C22—21no—
259C22—21no—
260C22—32no—
261C22—42no—
262C22—42no—
263C22—42no—
264C22—61no—
265C22—61no—
266C22—64no—
267C22—122no—
268C22—122no—
269C22—248no—
270C22C2×D3×D411yescharacteristic
271C4—21no—
272C4—42no—
273C4—61no—
274C4—61no—
275C4—61no—
276C4—122no—
277C4C2×D3×D411yescharacteristic
278C4#100911yescharacteristic
279C3#328011yescharacteristic, complemented, Sylow
280C2—41no—
281C2—62no—
282C2—82no—
283C2—124no—
284C2#560911yescharacteristic
285C2#575711yescharacteristic
286C2D3×#13511yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#466C2
socleC22×C3C22×D4
hypercenter#466D3
hypocenterC3#3280
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. C2×D3×D8C2semidirect
2. C2×#904C2semidirect
3. #5612C2semidirect
4. C3×#466C2semidirect
5. #5155C2semidirect
6. C8×#67C2semidirect
7. #5037C2semidirect
8. #4887C2semidirect
9. #4872C2semidirect
10. #4787C2semidirect
11. #4776C2semidirect
14. C2×#235C22semidirect
16. C22×C3×C8C22semidirect
17. C3×#121C22semidirect
20. #936C22semidirect
21. C2×#214C22semidirect
25. C2×Dic12C22semidirect
28. C2×#204C22semidirect
31. #893C22semidirect
34. C3×#107C22semidirect
35. C3×#102C22semidirect
36. #830C22semidirect
38. Dic3⋊C8C22semidirect
39. C8×Dic3C22semidirect
40. #810C22semidirect
41. #809C22semidirect
47. #466D3semidirect
89. D24D4semidirect
103. C22×C8C2×D3semidirect
108. #121C2×D3semidirect
113. #107C2×D3semidirect
117. #102C2×D3semidirect
207. C2×D3#135semidirect
279. C3#3280semidirect

Maximal subgroups

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

subgroupindex
C2×D3×D82
C2×#9042
#56122
C3×#4662
#51552
C8×#672
#50372
#48872
#48722
#47872
#47762
#32803