Finite Group Databasebeta

← #78323

Subgroups — #78323

Order 384.

332 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 117 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×#400C211yesmaximal, characteristic
2#4986C212yesmaximal
3#4981C211yesmaximal, characteristic
4#4973C211yesmaximal, characteristic
5C3⋊#401C212yesmaximal
6#4661C212yesmaximal
7#4660C212yesmaximal
8#4656C212yesmaximal
9#4652C212yesmaximal
10#2833—31nomaximal, Sylow
11C22×Dic6C2211yescharacteristic
12C2×C3×C4⋊C4C2211yescharacteristic
13C2×C3×C4⋊C4C2211yescharacteristic
14C2×C4⋊Dic3C2212yes—
15C2×C4⋊Dic3C2212yes—
16C2×C4⋊Dic3C2211yescharacteristic
17C2×Dic3⋊C4C2212yes—
18C2×Dic3⋊C4C2212yes—
19C2×C4×Dic3C2211yescharacteristic
20C3×#95C2212yes—
21C3×#95C2211yescharacteristic
22C3×#95C2212yes—
23C3⋊#95C2212yes—
24C3⋊#95C2212yes—
25C3⋊#95C2212yes—
26C3⋊#95C2212yes—
27C3⋊#95C2212yes—
28C3⋊#95C2212yes—
29C3⋊#95C2212yes—
30C3⋊#95C2212yes—
31C3⋊#95C2211yescharacteristic
32#401—32no—
33#400—32no—
34#400—32no—
35#400D311yescharacteristic
36#398—31no—
37#398—32no—
38#395—32no—
39#391—31no—
40#387—32no—
41C22×C3×C4C2311yescharacteristic
42C22×C3×C4C2312yes—
43C22×C3×C4C2311yescharacteristic
44C22×C3×C4C2312yes—
45C22×C3×C4C2311yescharacteristic
46C22×Dic3C2312yes—
47C22×Dic3C2312yes—
48C22×Dic3C2312yes—
49C22×Dic3C2312yes—
50C2×Dic6—22no—
51C2×Dic6—41no—
52C2×Dic6—41no—
53C3×C4⋊C4—41no—
54C3×C4⋊C4—41no—
55C4⋊Dic3—42no—
56C4⋊Dic3—41no—
57C4⋊Dic3—42no—
58Dic3⋊C4—24no—
59Dic3⋊C4—42no—
60C4×Dic3—41no—
61C22×Q8—31no—
62C2×C4⋊C4—32no—
63C2×C4⋊C4—32no—
64C2×C4⋊C4—32no—
65C2×C4⋊C4—32no—
66C2×C4⋊C4—31no—
67C2×C4⋊C4C2×D311yescharacteristic
68C2×C4⋊C4C2×D311yescharacteristic
69C2×C42—31no—
70#95—32no—
71#95—32no—
72#95—32no—
73#95—32no—
74#95—32no—
75#95—32no—
76#95—32no—
77#95—32no—
78#95—31no—
79#95C2×D312yes—
80#95C2×D312yes—
81#95C2×D311yescharacteristic
82C23×C3C2411yescharacteristic
83C2×C3×C4—21no—
84C2×C3×C4—21no—
85C2×C3×C4—22no—
86C2×C3×C4—21no—
87C2×C3×C4—22no—
88C2×C3×C4—21no—
89C2×C3×C4—22no—
90C2×C3×C4—22no—
91C2×C3×C4—24no—
92C2×C3×C4—22no—
93C2×C3×C4—22no—
94C2×C3×C4#4112yes—
95C2×Dic3—22no—
96C2×Dic3—22no—
97C2×Dic3—22no—
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—
107Dic6—44no—
108C2×Q8—62no—
109C2×Q8—121no—
110C2×Q8—121no—
111C22×C4—32no—
112C22×C4—32no—
113C22×C4—32no—
114C22×C4—32no—
115C22×C4C22×D311yescharacteristic
116C22×C4C22×D312yes—
117C22×C4C22×D311yescharacteristic
118C22×C4C22×D312yes—
119C22×C4C22×D311yescharacteristic
120C4⋊C4—41no—
121C4⋊C4—41no—
122C4⋊C4—64no—
123C4⋊C4—122no—
124C4⋊C4—121no—
125C4⋊C4—122no—
126C4⋊C4—122no—
127C42—121no—
128C22×C3C2×#4111yescharacteristic
129C22×C3H(5,𝔽2)11yescharacteristic
130C22×C3H(5,𝔽2)11yescharacteristic
131C22×C32−1+412yes—
132C22×C32−1+412yes—
133C3×C4—22no—
134C3×C4—41no—
135C3×C4—41no—
136C3×C4—42no—
137C3×C4—42no—
138Dic3—42no—
139Dic3—42no—
140Dic3—42no—
141Dic3—42no—
142C23C23×D311yescharacteristic
143Q8—124no—
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—22no—
149C2×C4—22no—
150C2×C4—22no—
151C2×C4—22no—
152C2×C4—24no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—62no—
156C2×C4—62no—
157C2×C4—62no—
158C2×C4—62no—
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#23912yes—
168C2×C3#53811yescharacteristic
169C2×C3#54112yes—
170C2×C3#56311yescharacteristic
171C2×C3#56311yescharacteristic
172C2×C3#56312yes—
173C22#100411yescharacteristic
174C22C2×#23911yescharacteristic
175C22#100911yescharacteristic
176C22#101012yes—
177C22#101012yes—
178C4—22no—
179C4—41no—
180C4—41no—
181C4—42no—
182C4—42no—
183C4—122no—
184C4—122no—
185C4—122no—
186C4—122no—
187C3#283311yescharacteristic, complemented, Sylow
188C2#564411yescharacteristic
189C2#565111yescharacteristic
190C2#567211yescharacteristic
191C2#569812yes—
192C2#571212yes—
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, prime radical, cosocleC23×C3C24
FittingC3×#400C2
hypercenter#400D3
hypocenterC3#2833
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
187. C3#2833semidirect

Maximal subgroups

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

subgroupindex
C3×#4002
#49862
#49812
#49732
C3⋊#4012
#46612
#46602
#46562
#46522
#28333