Finite Group Databasebeta

← #77796

Subgroups — #77796

Order 384.

484 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 161 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×#887C212yesmaximal
2C3×#398C211yesmaximal, characteristic
3#4982C212yesmaximal
4#4981C211yesmaximal, characteristic
5#4976C212yesmaximal
6#4975C211yesmaximal, characteristic
7#4647C212yesmaximal
8#4646C212yesmaximal
9#4646C212yesmaximal
10#2582—31nomaximal, Sylow
11C22×Dic6C2212yes—
12C2×C3×C4⋊C4C2212yes—
13C2×C3×C4⋊C4C2211yescharacteristic
14C2×C3×C4⋊C4C2211yescharacteristic
15C2×C4⋊Dic3C2211yescharacteristic
16C2×C4⋊Dic3C2211yescharacteristic
17C2×Dic3⋊C4C2212yes—
18C2×Dic3⋊C4C2212yes—
19C2×Dic3⋊C4C2212yes—
20C2×Dic3⋊C4C2212yes—
21C2×Dic3⋊C4C2212yes—
22C2×C4×Dic3C2212yes—
23C2×C4×Dic3C2212yes—
24C2×C4×Dic3C2211yescharacteristic
25#887—28no—
26C3×#95C2211yescharacteristic
27C3×#95C2212yes—
28C3⋊#95C2211yescharacteristic
29C3⋊#95C2212yes—
30C3⋊#95C2212yes—
31C3⋊#95C2212yes—
32C3⋊#95C2212yes—
33C2×C4×Q8—32no—
34#398—31no—
35#398—32no—
36#398D311yescharacteristic
37#391—32no—
38#391—32no—
39#389—32no—
40#389—32no—
41#384—31no—
42C22×C3×C4C2311yescharacteristic
43C22×C3×C4C2311yescharacteristic
44C22×C3×C4C2312yes—
45C22×C3×C4C2311yescharacteristic
46C22×C3×C4C2312yes—
47C22×Dic3C2312yes—
48C22×Dic3C2312yes—
49C22×Dic3C2312yes—
50C22×Dic3C2312yes—
51C2×Dic6—24no—
52C2×Dic6—24no—
53C2×Dic6Q818yescomplemented
54C3×C4⋊C4—24no—
55C3×C4⋊C4—41no—
56C3×C4⋊C4—41no—
57C4⋊Dic3—41no—
58C4⋊Dic3—41no—
59Dic3⋊C4—24no—
60Dic3⋊C4—24no—
61Dic3⋊C4—24no—
62Dic3⋊C4—24no—
63Dic3⋊C4—42no—
64C4×Dic3—24no—
65C4×Dic3—24no—
66C4×Dic3D414yes—
67C22×Q8—32no—
68C4×Q8—68no—
69C2×C4⋊C4—32no—
70C2×C4⋊C4—32no—
71C2×C4⋊C4—32no—
72C2×C4⋊C4—32no—
73C2×C4⋊C4—31no—
74C2×C4⋊C4—32no—
75C2×C4⋊C4—31no—
76C2×C4⋊C4C2×D312yes—
77C2×C4⋊C4C2×D311yescharacteristic
78C2×C4⋊C4C2×D311yescharacteristic
79C2×C42—31no—
80C2×C42—32no—
81C2×C42—32no—
82#95—32no—
83#95—32no—
84#95—32no—
85#95—31no—
86#95—32no—
87#95C2×D312yes—
88#95C2×D311yescharacteristic
89C23×C3C2411yescharacteristic
90C2×C3×C4—22no—
91C2×C3×C4—22no—
92C2×C3×C4—21no—
93C2×C3×C4—21no—
94C2×C3×C4—22no—
95C2×C3×C4—22no—
96C2×C3×C4—22no—
97C2×C3×C4—22no—
98C2×C3×C4—21no—
99C2×C3×C4—21no—
100C2×C3×C4—22no—
101C2×C3×C4C2×D412yes—
102C2×C3×C4C2×Q814yes—
103C2×Dic3—22no—
104C2×Dic3—22no—
105C2×Dic3—22no—
106C2×Dic3—22no—
107C2×Dic3—22no—
108C2×Dic3—22no—
109C2×Dic3—22no—
110C2×Dic3—22no—
111C2×Dic3C2×D414yes—
112C2×Dic3C2×Q814yes—
113C2×Dic3C2×Q814yes—
114C2×Dic3#4114yes—
115Dic6—216no—
116C2×Q8—38no—
117C2×Q8—64no—
118C2×Q8—64no—
119C22×C4—32no—
120C22×C4—32no—
121C22×C4—32no—
122C22×C4—32no—
123C22×C4C22×D311yescharacteristic
124C22×C4C22×D311yescharacteristic
125C22×C4C22×D312yes—
126C22×C4C22×D311yescharacteristic
127C22×C4C22×D312yes—
128C4⋊C4—24no—
129C4⋊C4—41no—
130C4⋊C4—41no—
131C4⋊C4—64no—
132C4⋊C4—64no—
133C4⋊C4—64no—
134C4⋊C4—64no—
135C4⋊C4—122no—
136C4⋊C4—121no—
137C4⋊C4—121no—
138C42—34no—
139C42—64no—
140C42—64no—
141C22×C3C22×D411yescharacteristic
142C22×C3C22×Q812yes—
143C22×C3C2×#4112yes—
144C22×C3H(5,𝔽2)11yescharacteristic
145C22×C32−1+411yescharacteristic
146C3×C4—24no—
147C3×C4—22no—
148C3×C4—42no—
149C3×C4—41no—
150C3×C4—41no—
151Dic3—24no—
152Dic3—42no—
153Dic3—42no—
154Dic3C22⋊Q818yes—
155C23C23×D311yescharacteristic
156Q8—616no—
157C2×C4—22no—
158C2×C4—21no—
159C2×C4—22no—
160C2×C4—21no—
161C2×C4—22no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—34no—
169C2×C4—34no—
170C2×C4—34no—
171C2×C4—34no—
172C2×C4—62no—
173C2×C4—62no—
174C2×C4—62no—
175C2×C4—62no—
176C2×C4—62no—
177C2×C4—62no—
178C2×C4—62no—
179C2×C4—62no—
180C2×C4D3×D412yes—
181C2×C4D3×Q814yes—
182C2×C3C2×C22⋊Q812yes—
183C2×C3#53711yescharacteristic
184C2×C3#55712yes—
185C2×C3Q8211yescharacteristic
186C2×C3#55911yescharacteristic
187C22C2×D3×D411yescharacteristic
188C22#100411yescharacteristic
189C22C2×D3×Q812yes—
190C22D3×#4112yes—
191C22#101011yescharacteristic
192C4—22no—
193C4—24no—
194C4—38no—
195C4—41no—
196C4—41no—
197C4—42no—
198C4—64no—
199C4—122no—
200C4—122no—
201C3#258211yescharacteristic, complemented, Sylow
202C2#559711yescharacteristic
203C2D3×C22⋊Q812yes—
204C2#566411yescharacteristic
205C2#568512yes—
206C2#572211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, prime radical, cosocleC23×C3C24
FittingC3×#398C2
hypercenter#398D3
hypocenterC3#2582
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
53. C2×Dic6Q8semidirect
201. C3#2582semidirect

Maximal subgroups

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

subgroupindex
C2×#8872
C3×#3982
#49822
#49812
#49762
#49752
#46472
#46462
#25823