Finite Group Databasebeta

← #81941

Subgroups — #81941

Order 384.

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

normal subgroups only

This group has 404 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#5725C211yesmaximal, characteristic
2D3×C4⋊Q8C211yesmaximal, characteristic, complemented
3C3×#500C211yesmaximal, characteristic, complemented
4#5088C211yesmaximal, characteristic, complemented
5#5078C211yesmaximal, characteristic, complemented
6#4890C214yesmaximal, complemented
7#4882C214yesmaximal, complemented
8#4694C211yesmaximal, characteristic, complemented
9#4685C211yesmaximal, characteristic, complemented
10#3226—31nomaximal, Sylow
11C2×#239—21no—
12C2×D3×Q8—21no—
13C3×C4⋊Q8C2211yescharacteristic
14C3×C4⋊Q8C2211yescharacteristic
15#947—21no—
16#944—21no—
17#895—21no—
18#895C2212yes—
19#893—21no—
20#893C2212yes—
21D3×C4⋊C4—21no—
22D3×C4⋊C4C2212yes—
23#888—21no—
24#888C2212yes—
25#874C2211yescharacteristic
26C42×D3C2211yescharacteristic
27#869C2211yescharacteristic
28C3×#107C2214yes—
29C3×C4×C8C2211yescharacteristic
30#821C2214yes—
31(C2×D3)⋊C8C2212yes—
32Dic3⋊C8C2212yes—
33#809C2214yes—
34#807C2214yes—
35C4×C3⋊C8C2211yescharacteristic
36#532—31no—
37C2×C4⋊Q8—31no—
38#500—31no—
39#500D311yescharacteristic, complemented
40#486—31no—
41#486—31no—
42#480—34no—
43#474—34no—
44#431—31no—
45C2×C3×Q8—21no—
46C2×C3×Q8—21no—
47#239—44no—
48D3×Q8—44no—
49C2×D12—22no—
50C2×D12—21no—
51C2×D12—21no—
52C2×D12C2312yes—
53C2×C4×D3—22no—
54C2×C4×D3—22no—
55C2×C4×D3D411yescharacteristic
56C2×C4×D3D411yescharacteristic
57C2×C4×D3C2311yescharacteristic
58C2×Dic6—21no—
59C2×Dic6—22no—
60C2×C3×C8C2312yes—
61C3×C4⋊C4—21no—
62C3×C4⋊C4—21no—
63C3×C4⋊C4C2312yes—
64C3×C4⋊C4C2312yes—
65C3×C42C2311yescharacteristic
66(C2×D3)⋊C4—22no—
67(C2×D3)⋊C4—22no—
68C4⋊Dic3—21no—
69C4⋊Dic3C2312yes—
70Dic3⋊C4—22no—
71Dic3⋊C4—22no—
72C4×Dic3D411yescharacteristic
73C4×Dic3D411yescharacteristic
74C4×Dic3C2311yescharacteristic
75C2×C3⋊C8C2312yes—
76C2×#41—61no—
77C22×Q8—61no—
78C4⋊Q8—32no—
79C4⋊Q8—31no—
80C4⋊Q8—61no—
81C4⋊Q8—61no—
82C4⋊Q8C2×D311yescharacteristic
83C4⋊Q8C2×D311yescharacteristic
84#127—31no—
85#124—61no—
86#121—32no—
87#121—61no—
88C4×D4—32no—
89C4×D4—61no—
90C2×C4⋊C4—32no—
91C2×C4⋊C4—61no—
92C2×C42—31no—
93#107—34no—
94#107C2×D314yes—
95C4⋊C8—32no—
96#102—34no—
97#102—34no—
98C22⋊C8—32no—
99C4×C8—31no—
100C4×C8C2×D311yescharacteristic
101C22×D3—22no—
102C22×D3C2×D411yescharacteristic
103C3×Q8—42no—
104C3×Q8—42no—
105C2×C3×C4—22no—
106C2×C3×C4—22no—
107C2×C3×C4C2×D411yescharacteristic
108C2×C3×C4C2×D411yescharacteristic
109C2×C3×C4C2411yescharacteristic
110C2×Dic3—22no—
111C2×Dic3C2×D411yescharacteristic
112C2×Dic3C2×D411yescharacteristic
113C2×Dic3C2×D411yescharacteristic
114D12—24no—
115D12—44no—
116D12—42no—
117D12—42no—
118C4×D3—22no—
119C4×D3—22no—
120C4×D3—44no—
121C4×D3—44no—
122C4×D3D814yes—
123Dic6—42no—
124Dic6—44no—
125C3×C8—22no—
126C3⋊C8—22no—
127#41—124no—
128C2×Q8—21no—
129C2×Q8—21no—
130C2×Q8—62no—
131C2×Q8—61no—
132C2×Q8—124no—
133C2×D4—32no—
134C2×D4—62no—
135C2×D4—61no—
136C2×D4—61no—
137C22×C4—31no—
138C22×C4—31no—
139C22×C4—31no—
140C22×C4—62no—
141C22×C4—62no—
142C2×C8—32no—
143C2×C8C22×D312yes—
144C4⋊C4—21no—
145C4⋊C4—21no—
146C4⋊C4—32no—
147C4⋊C4—62no—
148C4⋊C4—62no—
149C4⋊C4—61no—
150C4⋊C4C22×D312yes—
151C4⋊C4C22×D312yes—
152C22⋊C4—62no—
153C22⋊C4—62no—
154C42—31no—
155C42—31no—
156C42—31no—
157C42C22×D311yescharacteristic
158C22×C3C22×D411yescharacteristic
159C2×D3—21no—
160C2×D3—21no—
161C2×D3—42no—
162C2×D3—42no—
163C2×D3—42no—
164C2×D3C2×D812yes—
165C3×C4—42no—
166C3×C4—42no—
167C3×C4C2×D812yes—
168C3×C4#13712yes—
169C3×C42−1+412yes—
170Dic3—21no—
171Dic3—21no—
172Dic3—42no—
173Dic3C2×D812yes—
174C23—31no—
175C23—62no—
176Q8—42no—
177Q8—42no—
178Q8—124no—
179Q8—122no—
180D4—64no—
181D4—124no—
182D4—122no—
183D4—122no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—31no—
187C2×C4—34no—
188C2×C4—31no—
189C2×C4—31no—
190C2×C4—62no—
191C2×C4—62no—
192C2×C4—62no—
193C2×C4—124no—
194C2×C4—124no—
195C2×C4D3×D411yescharacteristic
196C2×C4D3×D411yescharacteristic
197C2×C4C23×D311yescharacteristic
198C8—22no—
199C8—62no—
200C2×C3#53611yescharacteristic
201C2×C3C22×D811yescharacteristic
202C2×C3C2×#13711yescharacteristic
203D3—22no—
204D3—82no—
205C22—32no—
206C22—61no—
207C22—61no—
208C22—122no—
209C22—122no—
210C22—122no—
211C22C2×D3×D411yescharacteristic
212C4—32no—
213C4—42no—
214C4—42no—
215C4—61no—
216C4—61no—
217C4—122no—
218C4D3×D812yes—
219C4#91812yes—
220C4#100712yes—
221C3#322611yescharacteristic, complemented, Sylow
222C2—62no—
223C2—242no—
224C2#572411yescharacteristic
225C2C2×D3×D811yescharacteristic
226C2C2×#91811yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#500C2
socleC22×C3C22×D4
prime radical#5725C2
hypercenter#500D3
hypocenterC3#3226
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C42 ◁ #500

Complements

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

NH ≅ G/Ntype
2. D3×C4⋊Q8C2semidirect
3. C3×#500C2semidirect
4. #5088C2semidirect
5. #5078C2semidirect
6. #4890C2semidirect
7. #4882C2semidirect
8. #4694C2semidirect
9. #4685C2semidirect
39. #500D3semidirect
221. C3#3226semidirect

Maximal subgroups

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

subgroupindex
#57252
D3×C4⋊Q82
C3×#5002
#50882
#50782
#48902
#48822
#46942
#46852
#32263