Finite Group Databasebeta

← #79355

Subgroups — #79355

Order 384.

424 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 129 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#5477C211yesmaximal, characteristic
2C2×C4×Dic6C211yesmaximal, characteristic, complemented
3C3×#432C211yesmaximal, characteristic, complemented
4#4850C212yesmaximal, complemented
5#4848C212yesmaximal, complemented
6#4738C212yesmaximal, complemented
7#4736C212yesmaximal, complemented
8#4710C214yesmaximal, complemented
9#3112—31nomaximal, Sylow
10C2×#235—21no—
11C22×Dic6C2211yescharacteristic
12C2×C3×C42C2211yescharacteristic
13#930—21no—
14#930C2212yes—
15C2×C4⋊Dic3C2211yescharacteristic
16C2×Dic3⋊C4—21no—
17C2×C4×Dic3—21no—
18C2×#204C2214yes—
19#875—21no—
20#874C2211yescharacteristic
21C4×D12—21no—
22C4×D12C2212yes—
23#869C2211yescharacteristic
24C4×Dic6—21no—
25C4×Dic6—21no—
26C4×Dic6C2212yes—
27C4×Dic6C2212yes—
28C3×C4⋊C8C2212yes—
29C3×C22⋊C8C2212yes—
30C3×#97C2212yes—
31#821C2214yes—
32#818C2214yes—
33#816C2214yes—
34#532—31no—
35C2×C4×Q8—31no—
36#480—32no—
37#477—32no—
38#460—32no—
39#448—32no—
40#440—34no—
41#432D311yescharacteristic, complemented
42C22×C3×C4D411yescharacteristic
43C22×C3×C4D411yescharacteristic
44C22×C3×C4C2311yescharacteristic
45C2×#67—22no—
46C22×Dic3—21no—
47C22×Dic3—21no—
48#235—44no—
49C2×D12—21no—
50C2×D12—21no—
51C2×D12C2312yes—
52C2×C4×D3—22no—
53C2×Dic6—21no—
54C2×Dic6—24no—
55C2×Dic6—21no—
56C2×Dic6C2312yes—
57C2×C3×C8C2314yes—
58C3×C42D411yescharacteristic
59C3×C42D411yescharacteristic
60C3×C42C2311yescharacteristic
61C3×C42C2311yescharacteristic
62(C2×D3)⋊C4—22no—
63(C2×D3)⋊C4—22no—
64C4⋊Dic3—21no—
65C4⋊Dic3—21no—
66C4⋊Dic3C2312yes—
67C4⋊Dic3C2312yes—
68Dic3⋊C4—22no—
69Dic3⋊C4—22no—
70C4×Dic3—22no—
71C4×Dic3—22no—
72#204—28no—
73C2×#41—61no—
74C22×Q8—31no—
75C2×SD16—34no—
76C4⋊Q8—31no—
77#127—31no—
78#124—61no—
79#121—32no—
80#121—61no—
81C4×Q8—32no—
82C4×Q8—32no—
83C4×Q8—61no—
84C4×Q8—61no—
85C4×D4—32no—
86C4×D4—61no—
87C2×C4⋊C4—31no—
88C2×C4⋊C4—61no—
89C2×C42—61no—
90C2×C42C2×D311yescharacteristic
91#107—34no—
92C4⋊C8C2×D312yes—
93#103—34no—
94#102—34no—
95C22⋊C8C2×D312yes—
96#97C2×D312yes—
97C23×C3C2×D411yescharacteristic
98C22×D3—22no—
99C2×C3×C4—22no—
100C2×C3×C4—22no—
101C2×C3×C4—22no—
102C2×C3×C4C2×D411yescharacteristic
103C2×C3×C4C2×D411yescharacteristic
104C2×C3×C4C2×D411yescharacteristic
105C2×C3×C4C2×D411yescharacteristic
106C2×C3×C4C2×D411yescharacteristic
107C2×C3×C4C2411yescharacteristic
108#67—44no—
109C2×Dic3—24no—
110C2×Dic3—22no—
111C2×Dic3—22no—
112C2×Dic3—22no—
113C2×Dic3—42no—
114D12—24no—
115D12—42no—
116D12—42no—
117C4×D3—44no—
118Dic6—24no—
119Dic6—22no—
120Dic6—42no—
121Dic6#4114yescomplemented
122C3×C8—24no—
123#41—124no—
124C2×Q8—32no—
125C2×Q8—64no—
126C2×Q8—61no—
127C2×Q8—61no—
128C2×D4—32no—
129C2×D4—62no—
130C2×D4—61no—
131C2×D4—61no—
132C22×C4—61no—
133C22×C4—61no—
134C22×C4—62no—
135C22×C4D1211yescharacteristic
136C22×C4D1211yescharacteristic
137C22×C4C22×D311yescharacteristic
138SD16—68no—
139C2×C8C22×D314yes—
140C4⋊C4—32no—
141C4⋊C4—32no—
142C4⋊C4—61no—
143C4⋊C4—62no—
144C4⋊C4—62no—
145C4⋊C4—61no—
146C22⋊C4—62no—
147C22⋊C4—62no—
148C42—62no—
149C42—62no—
150C42D1211yescharacteristic
151C42D1211yescharacteristic
152C42C22×D311yescharacteristic
153C42C22×D311yescharacteristic
154C22×C3—21no—
155C22×C3—21no—
156C22×C3AGL(1,ℤ/8)12yes—
157C22×C3C22×D411yescharacteristic
158C2×D3—42no—
159C2×D3—42no—
160C2×D3—42no—
161C3×C4—21no—
162C3×C4—21no—
163C3×C4—21no—
164C3×C4—21no—
165C3×C4#13712yes—
166C3×C4C2×#4112yes—
167Dic3—24no—
168Dic3—42no—
169Dic3—42no—
170C23—62no—
171C23C2×D1211yescharacteristic
172Q8—34no—
173Q8—64no—
174Q8—62no—
175Q8—122no—
176D4—64no—
177D4—122no—
178D4—124no—
179D4—122no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—64no—
184C2×C4—62no—
185C2×C4—62no—
186C2×C4—62no—
187C2×C4—124no—
188C2×C4—122no—
189C2×C4C2×D1211yescharacteristic
190C2×C4C2×D1211yescharacteristic
191C2×C4C2×D1211yescharacteristic
192C2×C4C2×D1211yescharacteristic
193C2×C4C2×D1211yescharacteristic
194C2×C4C23×D311yescharacteristic
195C8—24no—
196C2×C3—22no—
197C2×C3#52511yescharacteristic
198C2×C3C2×AGL(1,ℤ/8)11yescharacteristic
199C2×C3C2×#13711yescharacteristic
200D3—82no—
201C22—21no—
202C22—21no—
203C22—122no—
204C22—122no—
205C22—122no—
206C22#90812yes—
207C22C22×D1211yescharacteristic
208C4—21no—
209C4—21no—
210C4—21no—
211C4—21no—
212C4—64no—
213C4—122no—
214C4—122no—
215C4#90912yes—
216C4D3×#4112yes—
217C3#311211yescharacteristic, complemented, Sylow
218C2—22no—
219C2—242no—
220C2#552411yescharacteristic
221C2C2×#90811yescharacteristic
222C2C2×#90911yescharacteristic
subgroupG/H
centerC22C22×D12
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#432C2
socleC22×C3C22×D4
prime radical#5477C2
hypercenter#432D3
hypocenterC3#3112
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. C2×C4×Dic6C2semidirect
3. C3×#432C2semidirect
4. #4850C2semidirect
5. #4848C2semidirect
6. #4738C2semidirect
7. #4736C2semidirect
8. #4710C2semidirect
41. #432D3semidirect
121. Dic6#41semidirect
217. C3#3112semidirect

Maximal subgroups

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

subgroupindex
#54772
C2×C4×Dic62
C3×#4322
#48502
#48482
#47382
#47362
#47102
#31123