Finite Group Databasebeta

← #73405

Subgroups — #73405

Order 384.

380 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 145 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×#376C211yesmaximal, characteristic
2#4937C211yesmaximal, characteristic
3C4×C4⋊Dic3C211yesmaximal, characteristic
4#4933C212yesmaximal
5#4928C212yesmaximal
6#4661C212yesmaximal
7#4657C212yesmaximal
8#4654C212yesmaximal
9#4647C212yesmaximal
10#2606—31nomaximal, Sylow
11C2×C3×C42C2212yes—
12C2×C3×C42C2211yescharacteristic
13C2×C4⋊Dic3C2212yes—
14C2×C4⋊Dic3C2212yes—
15C2×C4⋊Dic3C2212yes—
16C2×Dic3⋊C4C2212yes—
17C2×Dic3⋊C4C2212yes—
18C2×Dic3⋊C4C2212yes—
19C2×Dic3⋊C4C2212yes—
20C2×C4×Dic3C2211yescharacteristic
21C2×C4×Dic3C2211yescharacteristic
22C3×#95C2212yes—
23C3×#95C2211yescharacteristic
24C3×#95C2211yescharacteristic
25C3⋊#95C2212yes—
26C3⋊#95C2212yes—
27C3⋊#95C2212yes—
28C3⋊#95C2212yes—
29C3⋊#95C2211yescharacteristic
30C3⋊#95C2212yes—
31C3⋊#95C2211yescharacteristic
32#398—32no—
33#398—32no—
34#389—32no—
35#389—32no—
36#387—32no—
37#387—32no—
38#383—31no—
39C4×C4⋊C4—31no—
40#376D311yescharacteristic
41C22×C3×C4C2312yes—
42C22×C3×C4C2311yescharacteristic
43C22×C3×C4C2311yescharacteristic
44C22×C3×C4C2311yescharacteristic
45C22×C3×C4C2312yes—
46C22×Dic3C2312yes—
47C22×Dic3C2312yes—
48C22×Dic3C2312yes—
49C22×Dic3C2312yes—
50C3×C42—24no—
51C3×C42Q814yes—
52C4⋊Dic3—24no—
53C4⋊Dic3—24no—
54C4⋊Dic3—24no—
55Dic3⋊C4—24no—
56Dic3⋊C4—24no—
57Dic3⋊C4—42no—
58Dic3⋊C4—42no—
59C4×Dic3—41no—
60C4×Dic3—41no—
61C2×C4⋊C4—32no—
62C2×C4⋊C4—32no—
63C2×C4⋊C4—32no—
64C2×C4⋊C4—32no—
65C2×C4⋊C4—32no—
66C2×C4⋊C4—32no—
67C2×C4⋊C4—32no—
68C2×C42—31no—
69C2×C42—31no—
70C2×C42C2×D312yes—
71C2×C42C2×D311yescharacteristic
72#95—32no—
73#95—31no—
74#95—32no—
75#95—31no—
76#95—32no—
77#95—32no—
78#95—32no—
79#95C2×D312yes—
80#95C2×D311yescharacteristic
81#95C2×D311yescharacteristic
82C23×C3C2411yescharacteristic
83C2×C3×C4—22no—
84C2×C3×C4—22no—
85C2×C3×C4—22no—
86C2×C3×C4—21no—
87C2×C3×C4—21no—
88C2×C3×C4—22no—
89C2×C3×C4—22no—
90C2×C3×C4—22no—
91C2×C3×C4—22no—
92C2×C3×C4C2×Q812yes—
93C2×C3×C4C2×Q812yes—
94C2×C3×C4C2×Q812yes—
95C2×C3×C4#4114yes—
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—
107C2×Dic3#4114yes—
108C22×C4—32no—
109C22×C4—32no—
110C22×C4—32no—
111C22×C4—32no—
112C22×C4C22×D312yes—
113C22×C4C22×D311yescharacteristic
114C22×C4C22×D311yescharacteristic
115C22×C4C22×D311yescharacteristic
116C22×C4C22×D312yes—
117C4⋊C4—64no—
118C4⋊C4—64no—
119C4⋊C4—64no—
120C4⋊C4—64no—
121C4⋊C4—64no—
122C4⋊C4—122no—
123C4⋊C4—122no—
124C42—24no—
125C42—121no—
126C42—121no—
127C42Dic614yes—
128C22×C3C22×Q811yescharacteristic
129C22×C3C2×#4112yes—
130C22×C3C2×#4112yes—
131C22×C3H(5,𝔽2)11yescharacteristic
132C22×C32−1+411yescharacteristic
133C3×C4—22no—
134C3×C4—22no—
135C3×C4—22no—
136C3×C4—24no—
137C3×C4—42no—
138Dic3—24no—
139Dic3—42no—
140Dic3—42no—
141Dic3—42no—
142C23C23×D311yescharacteristic
143C2×C4—22no—
144C2×C4—22no—
145C2×C4—22no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—22no—
149C2×C4—22no—
150C2×C4—22no—
151C2×C4—22no—
152C2×C4—34no—
153C2×C4—62no—
154C2×C4—62no—
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×C4C2×Dic612yes—
165C2×C4C2×Dic612yes—
166C2×C4C2×Dic612yes—
167C2×C4#23514yes—
168C2×C3#53311yescharacteristic
169C2×C3#53311yescharacteristic
170C2×C3#54411yescharacteristic
171C2×C3#55212yes—
172C2×C3#55312yes—
173C22C22×Dic611yescharacteristic
174C22C2×#23512yes—
175C22D3×#4112yes—
176C22#100911yescharacteristic
177C22#101011yescharacteristic
178C4—22no—
179C4—22no—
180C4—22no—
181C4—24no—
182C4—42no—
183C4—64no—
184C4—122no—
185C4—122no—
186C4—122no—
187C3#260611yescharacteristic, complemented, Sylow
188C2#547011yescharacteristic
189C2#551711yescharacteristic
190C2#551911yescharacteristic
191C2#553012yes—
192C2#553112yes—
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, prime radical, cosocleC23×C3C24
FittingC3×#376C2
hypercenter#376D3
hypocenterC3#2606
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #376

Complements

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

NH ≅ G/Ntype
187. C3#2606semidirect

Maximal subgroups

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

subgroupindex
C3×#3762
#49372
C4×C4⋊Dic32
#49332
#49282
#46612
#46572
#46542
#46472
#26063