Finite Group Databasebeta

← #78183

Subgroups — #78183

Order 384.

380 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 141 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#4986C211yesmaximal, characteristic
3#4976C212yesmaximal
4#4975C211yesmaximal, characteristic
5#4660C212yesmaximal
6#4650C212yesmaximal
7#4650C212yesmaximal
8#4649C212yesmaximal
9#4647C212yesmaximal
10#2571—31nomaximal, Sylow
11C2×C3×C4⋊C4C2211yescharacteristic
12C2×C3×C4⋊C4C2211yescharacteristic
13C2×C4⋊Dic3C2211yescharacteristic
14C2×C4⋊Dic3C2211yescharacteristic
15C2×Dic3⋊C4C2212yes—
16C2×Dic3⋊C4C2212yes—
17C2×Dic3⋊C4C2212yes—
18C2×Dic3⋊C4C2212yes—
19C2×Dic3⋊C4C2212yes—
20C2×C4×Dic3C2212yes—
21C2×C4×Dic3C2212yes—
22C2×C4×Dic3C2211yescharacteristic
23C3×#95C2212yes—
24C3×#95C2212yes—
25C3×#95C2211yescharacteristic
26C3⋊#95C2212yes—
27C3⋊#95C2212yes—
28C3⋊#95C2212yes—
29C3⋊#95C2211yescharacteristic
30C3⋊#95C2212yes—
31C3⋊#95C2212yes—
32#400—31no—
33#400—32no—
34#400D311yescharacteristic
35#389—32no—
36#389—32no—
37#384—31no—
38#382—32no—
39#382—32no—
40C4×C4⋊C4—32no—
41C22×C3×C4C2312yes—
42C22×C3×C4C2311yescharacteristic
43C22×C3×C4C2312yes—
44C22×C3×C4C2311yescharacteristic
45C22×C3×C4C2311yescharacteristic
46C22×Dic3C2312yes—
47C22×Dic3C2312yes—
48C22×Dic3C2312yes—
49C22×Dic3C2312yes—
50C3×C4⋊C4—41no—
51C3×C4⋊C4—41no—
52C4⋊Dic3—41no—
53C4⋊Dic3—41no—
54Dic3⋊C4—24no—
55Dic3⋊C4—24no—
56Dic3⋊C4—24no—
57Dic3⋊C4—24no—
58Dic3⋊C4—42no—
59C4×Dic3—24no—
60C4×Dic3—24no—
61C4×Dic3Q814yes—
62C2×C4⋊C4—32no—
63C2×C4⋊C4—32no—
64C2×C4⋊C4—32no—
65C2×C4⋊C4—32no—
66C2×C4⋊C4—31no—
67C2×C4⋊C4—32no—
68C2×C4⋊C4—31no—
69C2×C4⋊C4C2×D311yescharacteristic
70C2×C4⋊C4C2×D311yescharacteristic
71C2×C42—31no—
72C2×C42—32no—
73C2×C42—32no—
74#95—32no—
75#95—31no—
76#95—32no—
77#95—32no—
78#95—32no—
79#95—32no—
80#95C2×D312yes—
81#95C2×D311yescharacteristic
82#95C2×D312yes—
83C23×C3C2411yescharacteristic
84C2×C3×C4—21no—
85C2×C3×C4—21no—
86C2×C3×C4—22no—
87C2×C3×C4—22no—
88C2×C3×C4—22no—
89C2×C3×C4—22no—
90C2×C3×C4—22no—
91C2×C3×C4—22no—
92C2×C3×C4—22no—
93C2×C3×C4—21no—
94C2×C3×C4—21no—
95C2×C3×C4—22no—
96C2×C3×C4C2×Q812yes—
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×Dic3C2×Q814yes—
107C2×Dic3#4114yes—
108C2×Dic3#4114yes—
109C22×C4—32no—
110C22×C4—32no—
111C22×C4—32no—
112C22×C4—32no—
113C22×C4C22×D312yes—
114C22×C4C22×D311yescharacteristic
115C22×C4C22×D312yes—
116C22×C4C22×D311yescharacteristic
117C22×C4C22×D311yescharacteristic
118C4⋊C4—41no—
119C4⋊C4—41no—
120C4⋊C4—64no—
121C4⋊C4—64no—
122C4⋊C4—64no—
123C4⋊C4—64no—
124C4⋊C4—122no—
125C4⋊C4—121no—
126C4⋊C4—121no—
127C42—34no—
128C42—64no—
129C42—64no—
130C22×C3C22×Q811yescharacteristic
131C22×C3C2×#4112yes—
132C22×C3C2×#4112yes—
133C22×C3H(5,𝔽2)11yescharacteristic
134C22×C32−1+411yescharacteristic
135C3×C4—22no—
136C3×C4—42no—
137C3×C4—42no—
138C3×C4—41no—
139C3×C4—41no—
140Dic3—42no—
141Dic3—42no—
142Dic3—42no—
143Dic3#12518yes—
144C23C23×D311yescharacteristic
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—22no—
150C2×C4—22no—
151C2×C4—22no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—22no—
157C2×C4—34no—
158C2×C4—34no—
159C2×C4—34no—
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×C4D3×Q812yes—
170C2×C3C2×#12512yes—
171C2×C3#54411yescharacteristic
172C2×C3#55511yescharacteristic
173C2×C3#55612yes—
174C2×C3#55911yescharacteristic
175C22#100411yescharacteristic
176C22C2×D3×Q811yescharacteristic
177C22D3×#4112yes—
178C22D3×#4112yes—
179C22#101011yescharacteristic
180C4—22no—
181C4—38no—
182C4—41no—
183C4—41no—
184C4—42no—
185C4—42no—
186C4—122no—
187C4—122no—
188C4—122no—
189C3#257111yescharacteristic, complemented, Sylow
190C2#562311yescharacteristic
191C2#566411yescharacteristic
192C2#567011yescharacteristic
193C2D3×#12512yes—
194C2#570212yes—
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, prime radical, cosocleC23×C3C24
FittingC3×#400C2
hypercenter#400D3
hypocenterC3#2571
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
189. C3#2571semidirect

Maximal subgroups

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

subgroupindex
C3×#4002
#49862
#49762
#49752
#46602
#46502
#46492
#46472
#25713