Finite Group Databasebeta

← #74352

Subgroups — #74352

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×#384C211yesmaximal, characteristic
2#4986C211yesmaximal, characteristic
3#4985C212yesmaximal
4#4985C212yesmaximal
5#4981C211yesmaximal, characteristic
6#4980C212yesmaximal
7#4980C212yesmaximal
8#4978C212yesmaximal
9#4933C212yesmaximal
10#2794—31nomaximal, Sylow
11C2×C3×C4⋊C4C2212yes—
12C2×C3×C4⋊C4C2212yes—
13C2×C3×C4⋊C4C2211yescharacteristic
14C2×C3×C4⋊C4C2211yescharacteristic
15C2×C3×C42C2211yescharacteristic
16C2×C4⋊Dic3C2211yescharacteristic
17C2×C4⋊Dic3C2211yescharacteristic
18C2×Dic3⋊C4C2212yes—
19C2×Dic3⋊C4C2212yes—
20C2×C4×Dic3C2212yes—
21C3⋊#95C2212yes—
22C3⋊#95C2212yes—
23C3⋊#95C2212yes—
24C3⋊#95C2212yes—
25C3⋊#95C2212yes—
26C3⋊#95C2212yes—
27C3⋊#95C2212yes—
28C3⋊#95C2212yes—
29C3⋊#95C2212yes—
30C3⋊#95C2211yescharacteristic
31C3⋊#95C2211yescharacteristic
32#400—32no—
33#400—32no—
34#400—31no—
35#398—31no—
36#387—32no—
37#387—32no—
38#387—32no—
39#387—32no—
40#384D311yescharacteristic
41C22×C3×C4C2312yes—
42C22×C3×C4C2311yescharacteristic
43C22×C3×C4C2311yescharacteristic
44C22×C3×C4C2312yes—
45C22×C3×C4C2311yescharacteristic
46C22×Dic3C2312yes—
47C22×Dic3C2312yes—
48C22×Dic3C2312yes—
49C22×Dic3C2312yes—
50C3×C4⋊C4—24no—
51C3×C4⋊C4—24no—
52C3×C4⋊C4—41no—
53C3×C4⋊C4—41no—
54C3×C42—22no—
55C4⋊Dic3—41no—
56C4⋊Dic3—41no—
57Dic3⋊C4—24no—
58Dic3⋊C4—24no—
59C4×Dic3—42no—
60C2×C4⋊C4—32no—
61C2×C4⋊C4—32no—
62C2×C4⋊C4—31no—
63C2×C4⋊C4—31no—
64C2×C4⋊C4C2×D312yes—
65C2×C4⋊C4C2×D312yes—
66C2×C4⋊C4C2×D311yescharacteristic
67C2×C4⋊C4C2×D311yescharacteristic
68C2×C42—32no—
69C2×C42C2×D311yescharacteristic
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—32no—
79#95—31no—
80#95—31no—
81C23×C3C2411yescharacteristic
82C2×C3×C4—22no—
83C2×C3×C4—21no—
84C2×C3×C4—21no—
85C2×C3×C4—22no—
86C2×C3×C4—22no—
87C2×C3×C4—22no—
88C2×C3×C4—22no—
89C2×C3×C4—22no—
90C2×C3×C4—22no—
91C2×C3×C4—21no—
92C2×C3×C4—21no—
93C2×C3×C4#4112yes—
94C2×C3×C4#4114yes—
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—24no—
106C22×C4—32no—
107C22×C4—32no—
108C22×C4—32no—
109C22×C4—32no—
110C22×C4C22×D312yes—
111C22×C4C22×D311yescharacteristic
112C22×C4C22×D311yescharacteristic
113C22×C4C22×D311yescharacteristic
114C22×C4C22×D312yes—
115C4⋊C4—24no—
116C4⋊C4—24no—
117C4⋊C4—41no—
118C4⋊C4—41no—
119C4⋊C4—64no—
120C4⋊C4—64no—
121C4⋊C4—121no—
122C4⋊C4—121no—
123C42—22no—
124C42—122no—
125C22×C3C2×#4111yescharacteristic
126C22×C3C2×#4112yes—
127C22×C3H(5,𝔽2)11yescharacteristic
128C22×C32−1+411yescharacteristic
129C22×C32−1+412yes—
130C3×C4—22no—
131C3×C4—24no—
132C3×C4—42no—
133C3×C4—41no—
134C3×C4—41no—
135Dic3—42no—
136Dic3—42no—
137Dic3—42no—
138Dic3—42no—
139C23C23×D311yescharacteristic
140C2×C4—22no—
141C2×C4—21no—
142C2×C4—22no—
143C2×C4—21no—
144C2×C4—22no—
145C2×C4—22no—
146C2×C4—22no—
147C2×C4—22no—
148C2×C4—22no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—62no—
152C2×C4—62no—
153C2×C4—62no—
154C2×C4—62no—
155C2×C4—62no—
156C2×C4—62no—
157C2×C4—62no—
158C2×C4—62no—
159C2×C4—64no—
160C2×C4—62no—
161C2×C4—62no—
162C2×C4#23512yes—
163C2×C4#23714yes—
164C2×C3#53911yescharacteristic
165C2×C3#54112yes—
166C2×C3#55212yes—
167C2×C3#55911yescharacteristic
168C2×C3#56311yescharacteristic
169C22C2×#23511yescharacteristic
170C22C2×#23712yes—
171C22#100411yescharacteristic
172C22#100711yescharacteristic
173C22#100712yes—
174C4—24no—
175C4—22no—
176C4—42no—
177C4—41no—
178C4—41no—
179C4—122no—
180C4—122no—
181C4—122no—
182C4—122no—
183C3#279411yescharacteristic, complemented, Sylow
184C2#551312yes—
185C2#551511yescharacteristic
186C2#571311yescharacteristic
187C2#573112yes—
188C2#573511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, prime radical, cosocleC23×C3C24
FittingC3×#384C2
hypercenter#384D3
hypocenterC3#2794
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #384

Complements

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

NH ≅ G/Ntype
183. C3#2794semidirect

Maximal subgroups

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

subgroupindex
C3×#3842
#49862
#49852
#49812
#49802
#49782
#49332
#27943