Finite Group Databasebeta

← #74209

Subgroups — #74209

Order 384.

344 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 121 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×#382C211yesmaximal, characteristic
2#4986C211yesmaximal, characteristic
3#4981C211yesmaximal, characteristic
4#4976C212yesmaximal
5#4933C212yesmaximal
6#4660C212yesmaximal
7#4657C212yesmaximal
8#4652C212yesmaximal
9#4651C212yesmaximal
10#2769—31nomaximal, Sylow
11C2×C3×C4⋊C4C2211yescharacteristic
12C2×C3×C4⋊C4C2211yescharacteristic
13C2×C3×C42C2211yescharacteristic
14C2×C4⋊Dic3C2211yescharacteristic
15C2×C4⋊Dic3C2211yescharacteristic
16C2×Dic3⋊C4C2212yes—
17C2×Dic3⋊C4C2212yes—
18C2×Dic3⋊C4C2212yes—
19C2×Dic3⋊C4C2212yes—
20C2×C4×Dic3C2212yes—
21C3×#95C2212yes—
22C3×#95C2212yes—
23C3⋊#95C2211yescharacteristic
24C3⋊#95C2212yes—
25C3⋊#95C2212yes—
26C3⋊#95C2212yes—
27C3⋊#95C2212yes—
28C3⋊#95C2211yescharacteristic
29C3⋊#95C2212yes—
30C3⋊#95C2212yes—
31C3⋊#95C2212yes—
32#400—31no—
33#400—32no—
34#398—31no—
35#398—32no—
36#389—32no—
37#387—32no—
38#387—32no—
39#383—32no—
40#382D311yescharacteristic
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—41no—
51C3×C4⋊C4—41no—
52C3×C42—22no—
53C4⋊Dic3—41no—
54C4⋊Dic3—41no—
55Dic3⋊C4—24no—
56Dic3⋊C4—24no—
57Dic3⋊C4—24no—
58Dic3⋊C4—42no—
59C4×Dic3—24no—
60C2×C4⋊C4—32no—
61C2×C4⋊C4—32no—
62C2×C4⋊C4—32no—
63C2×C4⋊C4—32no—
64C2×C4⋊C4—31no—
65C2×C4⋊C4—31no—
66C2×C4⋊C4C2×D311yescharacteristic
67C2×C4⋊C4C2×D311yescharacteristic
68C2×C42—32no—
69C2×C42C2×D311yescharacteristic
70#95—31no—
71#95—32no—
72#95—32no—
73#95—32no—
74#95—32no—
75#95—31no—
76#95—32no—
77#95—32no—
78#95—32no—
79#95C2×D312yes—
80#95C2×D312yes—
81C23×C3C2411yescharacteristic
82C2×C3×C4—21no—
83C2×C3×C4—21no—
84C2×C3×C4—22no—
85C2×C3×C4—22no—
86C2×C3×C4—22no—
87C2×C3×C4—22no—
88C2×C3×C4—22no—
89C2×C3×C4—21no—
90C2×C3×C4—21no—
91C2×C3×C4—22no—
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#4114yes—
107C22×C4—32no—
108C22×C4—32no—
109C22×C4—32no—
110C22×C4—32no—
111C22×C4C22×D312yes—
112C22×C4C22×D311yescharacteristic
113C22×C4C22×D311yescharacteristic
114C22×C4C22×D312yes—
115C22×C4C22×D311yescharacteristic
116C4⋊C4—41no—
117C4⋊C4—41no—
118C4⋊C4—64no—
119C4⋊C4—64no—
120C4⋊C4—64no—
121C4⋊C4—122no—
122C4⋊C4—121no—
123C4⋊C4—121no—
124C42—22no—
125C42—64no—
126C22×C3C2×#4111yescharacteristic
127C22×C3C2×#4112yes—
128C22×C3H(5,𝔽2)11yescharacteristic
129C22×C32−1+411yescharacteristic
130C22×C32−1+412yes—
131C3×C4—22no—
132C3×C4—42no—
133C3×C4—42no—
134C3×C4—41no—
135C3×C4—41no—
136Dic3—24no—
137Dic3—42no—
138Dic3—42no—
139Dic3—42no—
140C23C23×D311yescharacteristic
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—22no—
144C2×C4—22no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—22no—
148C2×C4—22no—
149C2×C4—22no—
150C2×C4—22no—
151C2×C4—22no—
152C2×C4—22no—
153C2×C4—34no—
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×C4—62no—
165C2×C4#23512yes—
166C2×C3#53911yescharacteristic
167C2×C3#54112yes—
168C2×C3#55212yes—
169C2×C3#55511yescharacteristic
170C2×C3#56311yescharacteristic
171C22C2×#23511yescharacteristic
172C22#100411yescharacteristic
173C22#100711yescharacteristic
174C22D3×#4112yes—
175C22#101012yes—
176C4—22no—
177C4—42no—
178C4—41no—
179C4—41no—
180C4—42no—
181C4—64no—
182C4—122no—
183C4—122no—
184C4—122no—
185C3#276911yescharacteristic, complemented, Sylow
186C2#551511yescharacteristic
187C2#552912yes—
188C2#567011yescharacteristic
189C2#567211yescharacteristic
190C2#569612yes—
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, prime radical, cosocleC23×C3C24
FittingC3×#382C2
hypercenter#382D3
hypocenterC3#2769
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
185. C3#2769semidirect

Maximal subgroups

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

subgroupindex
C3×#3822
#49862
#49812
#49762
#49332
#46602
#46572
#46522
#46512
#27693