Finite Group Databasebeta

← #77927

Subgroups — #77927

Order 384.

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

normal subgroups only

This group has 380 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
1C2×#889C212yesmaximal
2C3×#398C211yesmaximal, characteristic
3#4982C212yesmaximal
4#4982C212yesmaximal
5#4981C211yesmaximal, characteristic
6#4977C211yesmaximal, characteristic
7#4660C212yesmaximal
8#4658C212yesmaximal
9#4657C212yesmaximal
10#2822—31nomaximal, Sylow
11C2×C3×C4⋊C4C2212yes—
12C2×C3×C4⋊C4C2211yescharacteristic
13C2×C3×C4⋊C4C2211yescharacteristic
14C2×C4⋊Dic3C2212yes—
15C2×C4⋊Dic3C2211yescharacteristic
16C2×C4⋊Dic3C2211yescharacteristic
17C2×Dic3⋊C4C2212yes—
18C2×Dic3⋊C4C2212yes—
19C2×Dic3⋊C4C2212yes—
20C2×Dic3⋊C4C2212yes—
21C2×Dic3⋊C4C2212yes—
22C2×C4×Dic3C2211yescharacteristic
23#889—28no—
24C3×#95C2212yes—
25C3×#95C2211yescharacteristic
26C3⋊#95C2212yes—
27C3⋊#95C2212yes—
28C3⋊#95C2212yes—
29C3⋊#95C2212yes—
30C3⋊#95C2212yes—
31C3⋊#95C2211yescharacteristic
32C3⋊#95C2212yes—
33C2×#125—32no—
34#400—32no—
35#400—32no—
36#398—31no—
37#398—32no—
38#398—32no—
39#398—32no—
40#398D311yescharacteristic
41#382—31no—
42C22×C3×C4C2311yescharacteristic
43C22×C3×C4C2311yescharacteristic
44C22×C3×C4C2312yes—
45C22×C3×C4C2312yes—
46C22×C3×C4C2311yescharacteristic
47C22×Dic3C2312yes—
48C22×Dic3C2312yes—
49C22×Dic3C2312yes—
50C22×Dic3C2312yes—
51C3×C4⋊C4—24no—
52C3×C4⋊C4—41no—
53C3×C4⋊C4—41no—
54C4⋊Dic3—24no—
55C4⋊Dic3—41no—
56C4⋊Dic3—41no—
57Dic3⋊C4—24no—
58Dic3⋊C4—24no—
59Dic3⋊C4—24no—
60Dic3⋊C4—24no—
61Dic3⋊C4—42no—
62C4×Dic3D414yes—
63#125—68no—
64C2×C4⋊C4—32no—
65C2×C4⋊C4—32no—
66C2×C4⋊C4—32no—
67C2×C4⋊C4—32no—
68C2×C4⋊C4—32no—
69C2×C4⋊C4—31no—
70C2×C4⋊C4—32no—
71C2×C4⋊C4—31no—
72C2×C4⋊C4C2×D312yes—
73C2×C4⋊C4C2×D311yescharacteristic
74C2×C4⋊C4C2×D311yescharacteristic
75C2×C42—31no—
76#95—32no—
77#95—32no—
78#95—32no—
79#95—32no—
80#95—32no—
81#95—32no—
82#95—31no—
83#95C2×D312yes—
84#95C2×D311yescharacteristic
85C23×C3C2411yescharacteristic
86C2×C3×C4—21no—
87C2×C3×C4—21no—
88C2×C3×C4—22no—
89C2×C3×C4—22no—
90C2×C3×C4—22no—
91C2×C3×C4—21no—
92C2×C3×C4—21no—
93C2×C3×C4—22no—
94C2×C3×C4—22no—
95C2×C3×C4—22no—
96C2×C3×C4—22no—
97C2×C3×C4—22no—
98C2×C3×C4C2×D412yes—
99C2×Dic3—22no—
100C2×Dic3—22no—
101C2×Dic3—22no—
102C2×Dic3—22no—
103C2×Dic3—22no—
104C2×Dic3—22no—
105C2×Dic3—22no—
106C2×Dic3—24no—
107C2×Dic3—22no—
108C2×Dic3—22no—
109C2×Dic3C2×D414yes—
110C22×C4—32no—
111C22×C4—32no—
112C22×C4—32no—
113C22×C4—32no—
114C22×C4C22×D311yescharacteristic
115C22×C4C22×D311yescharacteristic
116C22×C4C22×D312yes—
117C22×C4C22×D312yes—
118C22×C4C22×D311yescharacteristic
119C4⋊C4—24no—
120C4⋊C4—41no—
121C4⋊C4—41no—
122C4⋊C4—64no—
123C4⋊C4—64no—
124C4⋊C4—64no—
125C4⋊C4—64no—
126C4⋊C4—64no—
127C4⋊C4—122no—
128C4⋊C4—121no—
129C4⋊C4—121no—
130C42—34no—
131C22×C3C22×D411yescharacteristic
132C22×C3H(5,𝔽2)11yescharacteristic
133C22×C32−1+412yes—
134C22×C32−1+412yes—
135C22×C32−1+411yescharacteristic
136C3×C4—22no—
137C3×C4—42no—
138C3×C4—42no—
139C3×C4—41no—
140C3×C4—41no—
141Dic3—24no—
142Dic3—42no—
143Dic3—42no—
144Dic3—42no—
145C23C23×D311yescharacteristic
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—22no—
149C2×C4—22no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—34no—
159C2×C4—62no—
160C2×C4—62no—
161C2×C4—62no—
162C2×C4—62no—
163C2×C4—62no—
164C2×C4—62no—
165C2×C4—64no—
166C2×C4—62no—
167C2×C4—62no—
168C2×C4—62no—
169C2×C4D3×D412yes—
170C2×C3#53612yes—
171C2×C3#53711yescharacteristic
172C2×C3#56311yescharacteristic
173C2×C3#56311yescharacteristic
174C2×C3#56412yes—
175C22C2×D3×D411yescharacteristic
176C22#100411yescharacteristic
177C22#100712yes—
178C22#101012yes—
179C22#101011yescharacteristic
180C4—22no—
181C4—41no—
182C4—41no—
183C4—42no—
184C4—42no—
185C4—64no—
186C4—122no—
187C4—122no—
188C4—122no—
189C3#282211yescharacteristic, complemented, Sylow
190C2#559711yescharacteristic
191C2#562812yes—
192C2#565111yescharacteristic
193C2C3⋊#56412yes—
194C2#573511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, prime radical, cosocleC23×C3C24
FittingC3×#398C2
hypercenter#398D3
hypocenterC3#2822
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
189. C3#2822semidirect

Maximal subgroups

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

subgroupindex
C2×#8892
C3×#3982
#49822
#49812
#49772
#46602
#46582
#46572
#28223