Finite Group Databasebeta

← #76187

Subgroups — #76187

Order 384.

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

normal subgroups only

This group has 344 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
1C3×#389C211yesmaximal, characteristic
2#4986C212yesmaximal
3#4985C212yesmaximal
4#4980C212yesmaximal
5#4978C212yesmaximal
6#4928C211yesmaximal, characteristic
7#4928C211yesmaximal, characteristic
8#4659C212yesmaximal
9#4655C212yesmaximal
10#2810—31nomaximal, Sylow
11C2×C3×C4⋊C4C2212yes—
12C2×C3×C4⋊C4C2211yescharacteristic
13C2×C3×C4⋊C4C2211yescharacteristic
14C2×C3×C42C2211yescharacteristic
15C2×C4⋊Dic3C2211yescharacteristic
16C2×C4⋊Dic3C2211yescharacteristic
17C2×C4⋊Dic3C2211yescharacteristic
18C2×C4⋊Dic3C2211yescharacteristic
19C2×Dic3⋊C4C2212yes—
20C2×Dic3⋊C4C2212yes—
21C2×C4×Dic3C2212yes—
22C3×#95C2212yes—
23C3⋊#95C2212yes—
24C3⋊#95C2212yes—
25C3⋊#95C2212yes—
26C3⋊#95C2212yes—
27C3⋊#95C2212yes—
28C3⋊#95C2212yes—
29C3⋊#95C2212yes—
30C3⋊#95C2212yes—
31C3⋊#95C2212yes—
32#400—32no—
33#400—32no—
34#400—32no—
35#389—31no—
36#389—31no—
37#389D311yescharacteristic
38#387—32no—
39#387—32no—
40#387—32no—
41C22×C3×C4C2312yes—
42C22×C3×C4C2312yes—
43C22×C3×C4C2311yescharacteristic
44C22×C3×C4C2311yescharacteristic
45C22×C3×C4C2311yescharacteristic
46C22×Dic3C2312yes—
47C22×Dic3C2312yes—
48C22×Dic3C2312yes—
49C22×Dic3C2312yes—
50C3×C4⋊C4—22no—
51C3×C4⋊C4—24no—
52C3×C4⋊C4—41no—
53C3×C42—41no—
54C4⋊Dic3—22no—
55C4⋊Dic3—22no—
56C4⋊Dic3—41no—
57C4⋊Dic3—41no—
58Dic3⋊C4—24no—
59Dic3⋊C4—24no—
60C4×Dic3—42no—
61C2×C4⋊C4—32no—
62C2×C4⋊C4—32no—
63C2×C4⋊C4—31no—
64C2×C4⋊C4—31no—
65C2×C4⋊C4—31no—
66C2×C4⋊C4—31no—
67C2×C4⋊C4C2×D312yes—
68C2×C4⋊C4C2×D311yescharacteristic
69C2×C4⋊C4C2×D311yescharacteristic
70C2×C42—32no—
71C2×C42C2×D311yescharacteristic
72#95—32no—
73#95—32no—
74#95—32no—
75#95—32no—
76#95—32no—
77#95—32no—
78#95—32no—
79#95—32no—
80#95—32no—
81#95C2×D312yes—
82C23×C3C2411yescharacteristic
83C2×C3×C4—21no—
84C2×C3×C4—21no—
85C2×C3×C4—21no—
86C2×C3×C4—21no—
87C2×C3×C4—21no—
88C2×C3×C4—21no—
89C2×C3×C4—22no—
90C2×C3×C4—22no—
91C2×C3×C4—22no—
92C2×C3×C4—22no—
93C2×C3×C4—22no—
94C2×C3×C4—22no—
95C2×C3×C4#4112yes—
96C2×C3×C4#4112yes—
97C2×C3×C4#4112yes—
98C2×Dic3—22no—
99C2×Dic3—22no—
100C2×Dic3—22no—
101C2×Dic3—22no—
102C2×Dic3—22no—
103C2×Dic3—22no—
104C2×Dic3—22no—
105C2×Dic3—22no—
106C2×Dic3—22no—
107C2×Dic3—22no—
108C2×Dic3—22no—
109C2×Dic3—22no—
110C22×C4—32no—
111C22×C4—32no—
112C22×C4—32no—
113C22×C4—32no—
114C22×C4C22×D312yes—
115C22×C4C22×D312yes—
116C22×C4C22×D311yescharacteristic
117C22×C4C22×D311yescharacteristic
118C22×C4C22×D311yescharacteristic
119C4⋊C4—22no—
120C4⋊C4—24no—
121C4⋊C4—41no—
122C4⋊C4—64no—
123C4⋊C4—62no—
124C4⋊C4—64no—
125C4⋊C4—62no—
126C4⋊C4—121no—
127C4⋊C4—121no—
128C42—41no—
129C42—122no—
130C22×C3C2×#4111yescharacteristic
131C22×C3C2×#4111yescharacteristic
132C22×C3C2×#4111yescharacteristic
133C22×C3H(5,𝔽2)11yescharacteristic
134C22×C32−1+411yescharacteristic
135C22×C32−1+411yescharacteristic
136C22×C32−1+411yescharacteristic
137C3×C4—22no—
138C3×C4—22no—
139C3×C4—22no—
140C3×C4—42no—
141C3×C4—42no—
142Dic3—42no—
143Dic3—42no—
144Dic3—42no—
145Dic3—42no—
146C23C23×D311yescharacteristic
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—62no—
160C2×C4—62no—
161C2×C4—62no—
162C2×C4—62no—
163C2×C4—62no—
164C2×C4—62no—
165C2×C4—62no—
166C2×C4—62no—
167C2×C4—62no—
168C2×C4—62no—
169C2×C4—62no—
170C2×C4—62no—
171C2×C4#23512yes—
172C2×C4#23712yes—
173C2×C4#23912yes—
174C2×C3#53911yescharacteristic
175C2×C3#53911yescharacteristic
176C2×C3#53911yescharacteristic
177C2×C3#55611yescharacteristic
178C2×C3#55611yescharacteristic
179C2×C3#55611yescharacteristic
180C2×C3#56411yescharacteristic
181C22C2×#23511yescharacteristic
182C22C2×#23711yescharacteristic
183C22#100411yescharacteristic
184C22C2×#23911yescharacteristic
185C22#100711yescharacteristic
186C22#101011yescharacteristic
187C22#101011yescharacteristic
188C4—22no—
189C4—22no—
190C4—22no—
191C4—42no—
192C4—42no—
193C4—122no—
194C4—122no—
195C4—122no—
196C4—122no—
197C3#281011yescharacteristic, complemented, Sylow
198C2#551511yescharacteristic
199C2#554211yescharacteristic
200C2#558411yescharacteristic
201C2#560211yescharacteristic
202C2#564511yescharacteristic
203C2C3⋊#56411yescharacteristic
204C2#573211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, prime radical, cosocleC23×C3C24
FittingC3×#389C2
hypercenter#389D3
hypocenterC3#2810
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
197. C3#2810semidirect

Maximal subgroups

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

subgroupindex
C3×#3892
#49862
#49852
#49802
#49782
#49282
#46592
#46552
#28103