Finite Group Databasebeta

← #81692

Subgroups — #81692

Order 384.

328 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 109 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#5728C211yesmaximal, characteristic, complemented
2#5680C211yesmaximal, characteristic
3C3×#489C211yesmaximal, characteristic, complemented
4#5081C211yesmaximal, characteristic, complemented
5#5055C211yesmaximal, characteristic, complemented
6#4815C212yesmaximal, complemented
7#4796C212yesmaximal, complemented
8#4784C212yesmaximal
9#4763C212yesmaximal, complemented
10#4705C211yesmaximal, characteristic, complemented
11#4702C211yesmaximal, characteristic, complemented
12#3240—31nomaximal, Sylow
13C3×C4⋊Q8C2211yescharacteristic
14C3×#124C2211yescharacteristic
15#946—21no—
16#946C2211yescharacteristic
17Q8×Dic3—21no—
18Q8×Dic3C2211yescharacteristic
19#938C2211yescharacteristic
20D4×Dic3C2211yescharacteristic
21#897—21no—
22#892C2212yes—
23#890C2212yes—
24#887—21no—
25#883—21no—
26#67⋊C4—21no—
27#879—21no—
28#877—21no—
29C42×D3C2211yescharacteristic
30#870C2211yescharacteristic
31#869C2211yescharacteristic
32C3×#103C2212yes—
33C3×#102C2212yes—
34C3×#97C2211yescharacteristic
35#835C2212yes—
36#832C2212yes—
37(C2×D3)⋊C8C2212yes—
38#818C2212yes—
39#817C2212yes—
40Dic3⋊C8C2212yes—
41#808C2212yes—
42#807C2212yes—
43#803C2211yescharacteristic
44#533—31no—
45#529—31no—
46#501—31no—
47#501—31no—
48#489—31no—
49#489D311yescharacteristic, complemented
50#485—32no—
51#482—32no—
52#479—32no—
53#478—32no—
54#432—31no—
55C2×C3×Q8—21no—
56C2×C3×Q8C2311yescharacteristic
57C2×C3×D4C2311yescharacteristic
58C2×#67—21no—
59C22×Dic3—21no—
60C2×C4×D3D411yescharacteristic
61C2×C4×D3D411yescharacteristic
62C2×C4×D3C2311yescharacteristic
63C2×Dic6—21no—
64C2×C3×C8C2312yes—
65C3×C4⋊C4—21no—
66C3×C4⋊C4C2312yes—
67C3×C22⋊C4—21no—
68C3×C22⋊C4—21no—
69C3×C42C2311yescharacteristic
70#217—21no—
71#217—21no—
72(C2×D3)⋊C4—21no—
73(C2×D3)⋊C4—22no—
74C4⋊Dic3—21no—
75C4⋊Dic3—21no—
76C4⋊Dic3—22no—
77C4⋊Dic3C2311yescharacteristic
78C4⋊Dic3C2311yescharacteristic
79C4⋊Dic3C2312yes—
80Dic3⋊C4—21no—
81Dic3⋊C4—21no—
82Dic3⋊C4—21no—
83Dic3⋊C4—22no—
84C4×Dic3—21no—
85C4×Dic3—22no—
86C4×Dic3D411yescharacteristic
87C4×Dic3D411yescharacteristic
88C4×Dic3C2311yescharacteristic
89C2×C3⋊C8C2312yes—
90C4⋊Q8—31no—
91C4⋊Q8C2×D311yescharacteristic
92#126—61no—
93#125—32no—
94#125—31no—
95#124C2×D311yescharacteristic
96#123—61no—
97C22⋊Q8—31no—
98C22⋊Q8—61no—
99C22⋊Q8—61no—
100#121—31no—
101C4×Q8—31no—
102C4×Q8—61no—
103C4×Q8—61no—
104C4×D4—31no—
105C4×D4—61no—
106#117—32no—
107#117—61no—
108C2×C42—31no—
109#107—32no—
110#107—32no—
111#106—32no—
112#106—32no—
113C4⋊C8—32no—
114#103—32no—
115#103C2×D312yes—
116#102—32no—
117#102C2×D312yes—
118C22⋊C8—32no—
119#97—31no—
120#97C2×D311yescharacteristic
121C23×C3—21no—
122C22×D3C2×D411yescharacteristic
123C3×Q8—22no—
124C3×Q8—42no—
125C3×D4—22no—
126C2×C3×C4—21no—
127C2×C3×C4—22no—
128C2×C3×C4C2×D411yescharacteristic
129C2×C3×C4C2×D411yescharacteristic
130C2×C3×C4C2411yescharacteristic
131#67—42no—
132C2×Dic3—21no—
133C2×Dic3—22no—
134C2×Dic3—21no—
135C2×Dic3—42no—
136C2×Dic3C2×D411yescharacteristic
137C2×Dic3C2×D411yescharacteristic
138C2×Dic3C2×D411yescharacteristic
139C4×D3—22no—
140C4×D3—41no—
141C4×D3—41no—
142Dic6—42no—
143C3×C8—22no—
144C3⋊C8—22no—
145C2×Q8—21no—
146C2×Q8—61no—
147C2×Q8C22×D311yescharacteristic
148C2×D4—61no—
149C2×D4C22×D311yescharacteristic
150C22×C4—31no—
151C22×C4—31no—
152C22×C4—31no—
153C22×C4—61no—
154C2×C8—32no—
155C2×C8C22×D312yes—
156C4⋊C4—21no—
157C4⋊C4—32no—
158C4⋊C4—31no—
159C4⋊C4—31no—
160C4⋊C4—61no—
161C4⋊C4—61no—
162C4⋊C4—62no—
163C4⋊C4—62no—
164C4⋊C4—61no—
165C4⋊C4—61no—
166C4⋊C4—61no—
167C4⋊C4C22×D312yes—
168C22⋊C4—21no—
169C22⋊C4—21no—
170C22⋊C4—62no—
171C22⋊C4—61no—
172C22⋊C4—61no—
173C22⋊C4—61no—
174C42—31no—
175C42—31no—
176C42—31no—
177C42—62no—
178C42—61no—
179C42C22×D311yescharacteristic
180C22×C3—41no—
181C22×C3—41no—
182C22×C3—41no—
183C22×C3C22×D411yescharacteristic
184C2×D3—21no—
185C2×D3—21no—
186C2×D3—21no—
187C3×C4—21no—
188C3×C4—21no—
189C3×C4—41no—
190C3×C4—42no—
191C3×C42−1+412yes—
192Dic3—21no—
193Dic3—21no—
194Dic3—21no—
195Dic3—42no—
196Dic3—41no—
197Dic3—41no—
198C23—21no—
199C23—31no—
200Q8—22no—
201Q8—42no—
202Q8—122no—
203D4—22no—
204D4—122no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—31no—
208C2×C4—31no—
209C2×C4—31no—
210C2×C4—62no—
211C2×C4—61no—
212C2×C4—62no—
213C2×C4—61no—
214C2×C4—121no—
215C2×C4—121no—
216C2×C4—122no—
217C2×C4D3×D411yescharacteristic
218C2×C4D3×D411yescharacteristic
219C2×C4C23×D311yescharacteristic
220C8—22no—
221C8—62no—
222C2×C3—81no—
223C2×C3#53611yescharacteristic
224C2×C3#57511yescharacteristic
225C2×C3#57511yescharacteristic
226D3—41no—
227C22—41no—
228C22—41no—
229C22—41no—
230C22—61no—
231C22—61no—
232C22—61no—
233C22C2×D3×D411yescharacteristic
234C4—21no—
235C4—21no—
236C4—41no—
237C4—42no—
238C4—61no—
239C4—61no—
240C4—61no—
241C4—121no—
242C4—121no—
243C4—122no—
244C4#101012yes—
245C3#324011yescharacteristic, complemented, Sylow
246C2—81no—
247C2—121no—
248C2#567511yescharacteristic
249C2#577311yescharacteristic
250C2#577711yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#489C2
socleC22×C3C22×D4
prime radical#938C22
hypercenter#489D3
hypocenterC3#3240
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #5728C2semidirect
3. C3×#489C2semidirect
4. #5081C2semidirect
5. #5055C2semidirect
6. #4815C2semidirect
7. #4796C2semidirect
9. #4763C2semidirect
10. #4705C2semidirect
11. #4702C2semidirect
49. #489D3semidirect
245. C3#3240semidirect

Maximal subgroups

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

subgroupindex
#57282
#56802
C3×#4892
#50812
#50552
#48152
#47962
#47842
#47632
#47052
#47022
#32403