Finite Group Databasebeta

← #81985

Subgroups — #81985

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#5691C211yesmaximal, characteristic
3C3×#501C211yesmaximal, characteristic, complemented
4#5089C211yesmaximal, characteristic, complemented
5#5064C211yesmaximal, characteristic, complemented
6#4885C212yesmaximal
7#4877C212yesmaximal, complemented
8#4871C212yesmaximal, complemented
9#4868C212yesmaximal, complemented
10#4714C211yesmaximal, characteristic, complemented
11#4705C211yesmaximal, characteristic, complemented
12#3240—31nomaximal, Sylow
13C3×C4⋊Q8C2211yescharacteristic
14C3×#125C2211yescharacteristic
15#946—21no—
16Q8×Dic3—21no—
17#898—21no—
18#897—21no—
19#897C2211yescharacteristic
20#895C2211yescharacteristic
21#894—21no—
22#893—21no—
23#893C2211yescharacteristic
24#892—21no—
25#892C2212yes—
26#890C2212yes—
27#887—21no—
28#887C2211yescharacteristic
29#875C2211yescharacteristic
30C42×D3C2211yescharacteristic
31#869C2211yescharacteristic
32C3×#107C2212yes—
33C3×#106C2212yes—
34C3×#97C2211yescharacteristic
35#821C2212yes—
36(C2×D3)⋊C8C2212yes—
37#816C2212yes—
38Dic3⋊C8C2212yes—
39#810C2212yes—
40#809C2212yes—
41#808C2212yes—
42#807C2212yes—
43#803C2211yescharacteristic
44#533—31no—
45#529—31no—
46#501—31no—
47#501D311yescharacteristic, complemented
48#489—31no—
49#489—31no—
50#485—32no—
51#482—32no—
52#479—32no—
53#478—32no—
54#432—31no—
55C2×C3×Q8—21no—
56C2×D12—21no—
57C2×D12C2311yescharacteristic
58C2×C4×D3—21no—
59C2×C4×D3D411yescharacteristic
60C2×C4×D3D411yescharacteristic
61C2×C4×D3C2311yescharacteristic
62C2×Dic6—21no—
63C2×Dic6C2311yescharacteristic
64C2×C3×C8C2312yes—
65C3×C4⋊C4—21no—
66C3×C4⋊C4—21no—
67C3×C4⋊C4—21no—
68C3×C4⋊C4C2311yescharacteristic
69C3×C4⋊C4C2311yescharacteristic
70C3×C4⋊C4C2312yes—
71C3×C42C2311yescharacteristic
72(C2×D3)⋊C4—22no—
73(C2×D3)⋊C4—21no—
74(C2×D3)⋊C4—21no—
75(C2×D3)⋊C4—21no—
76(C2×D3)⋊C4—21no—
77(C2×D3)⋊C4—21no—
78C4⋊Dic3—21no—
79C4⋊Dic3—22no—
80C4⋊Dic3—21no—
81C4⋊Dic3C2312yes—
82Dic3⋊C4—22no—
83Dic3⋊C4—21no—
84C4×Dic3—22no—
85C4×Dic3—21no—
86C4×Dic3D411yescharacteristic
87C4×Dic3D411yescharacteristic
88C4×Dic3C2311yescharacteristic
89C2×C3⋊C8C2312yes—
90C4⋊Q8—31no—
91C4⋊Q8C2×D311yescharacteristic
92#126—61no—
93#125—32no—
94#125C2×D311yescharacteristic
95#124—31no—
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#107C2×D312yes—
111#106—32no—
112#106C2×D312yes—
113C4⋊C8—32no—
114#103—32no—
115#103—32no—
116#102—32no—
117#102—32no—
118C22⋊C8—32no—
119#97—31no—
120#97C2×D311yescharacteristic
121C22×D3—21no—
122C22×D3C2×D411yescharacteristic
123C3×Q8—42no—
124C2×C3×C4—22no—
125C2×C3×C4—21no—
126C2×C3×C4—21no—
127C2×C3×C4C2×D411yescharacteristic
128C2×C3×C4C2×D411yescharacteristic
129C2×C3×C4C2411yescharacteristic
130C2×Dic3—22no—
131C2×Dic3—21no—
132C2×Dic3C2×D411yescharacteristic
133C2×Dic3C2×D411yescharacteristic
134C2×Dic3C2×D411yescharacteristic
135D12—22no—
136D12—42no—
137C4×D3—22no—
138C4×D3—41no—
139C4×D3—41no—
140C4×D3—42no—
141Dic6—22no—
142Dic6—42no—
143C3×C8—22no—
144C3⋊C8—22no—
145C2×Q8—21no—
146C2×Q8—31no—
147C2×Q8—61no—
148C2×D4—31no—
149C2×D4—61no—
150C22×C4—31no—
151C22×C4—31no—
152C22×C4—31no—
153C22×C4—61no—
154C2×C8—32no—
155C2×C8C22×D312yes—
156C4⋊C4—21no—
157C4⋊C4—21no—
158C4⋊C4—21no—
159C4⋊C4—32no—
160C4⋊C4—61no—
161C4⋊C4—61no—
162C4⋊C4—62no—
163C4⋊C4—62no—
164C4⋊C4—61no—
165C4⋊C4C22×D312yes—
166C4⋊C4C22×D311yescharacteristic
167C4⋊C4C22×D311yescharacteristic
168C22⋊C4—61no—
169C22⋊C4—61no—
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×C3C22×D411yescharacteristic
181C2×D3—21no—
182C2×D3—21no—
183C2×D3—21no—
184C2×D3—41no—
185C2×D3—41no—
186C2×D3—41no—
187C3×C4—21no—
188C3×C4—21no—
189C3×C4—41no—
190C3×C4—41no—
191C3×C4—42no—
192C3×C42−1+412yes—
193Dic3—21no—
194Dic3—21no—
195Dic3—21no—
196Dic3—41no—
197Dic3—42no—
198C23—31no—
199C23—61no—
200Q8—42no—
201Q8—62no—
202Q8—122no—
203D4—62no—
204D4—122no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—21no—
208C2×C4—31no—
209C2×C4—31no—
210C2×C4—31no—
211C2×C4—62no—
212C2×C4—61no—
213C2×C4—62no—
214C2×C4—121no—
215C2×C4—121no—
216C2×C4—122no—
217C2×C4D3×D411yescharacteristic
218C2×C4D3×D411yescharacteristic
219C2×C4C23×D311yescharacteristic
220C8—22no—
221C8—62no—
222C2×C3#53611yescharacteristic
223C2×C3#57511yescharacteristic
224C2×C3#57511yescharacteristic
225D3—41no—
226D3—81no—
227C22—61no—
228C22—61no—
229C22—61no—
230C22—121no—
231C22—121no—
232C22—121no—
233C22C2×D3×D411yescharacteristic
234C4—21no—
235C4—21no—
236C4—41no—
237C4—42no—
238C4—41no—
239C4—61no—
240C4—61no—
241C4—61no—
242C4—121no—
243C4—122no—
244C4#100712yes—
245C3#324011yescharacteristic, complemented, Sylow
246C2—121no—
247C2—241no—
248C2#572411yescharacteristic
249C2#577311yescharacteristic
250C2#577711yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#501C2
socleC22×C3C22×D4
prime radical#895C22
hypercenter#501D3
hypocenterC3#3240
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
1. #5728C2semidirect
3. C3×#501C2semidirect
4. #5089C2semidirect
5. #5064C2semidirect
7. #4877C2semidirect
8. #4871C2semidirect
9. #4868C2semidirect
10. #4714C2semidirect
11. #4705C2semidirect
47. #501D3semidirect
245. C3#3240semidirect

Maximal subgroups

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

subgroupindex
#57282
#56912
C3×#5012
#50892
#50642
#48852
#48772
#48712
#48682
#47142
#47052
#32403