Finite Group Databasebeta

← #74192

Subgroups — #74192

Order 384.

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

normal subgroups only

This group has 388 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×#382C211yesmaximal, characteristic
2#4986C211yesmaximal, characteristic
3#4982C212yesmaximal
4#4979C211yesmaximal, characteristic
5#4932C212yesmaximal
6#4655C212yesmaximal
7#4654C212yesmaximal
8#4647C212yesmaximal
9#4646C212yesmaximal
10#2612—31nomaximal, Sylow
11C22×Dic6C2211yescharacteristic
12C2×C3×C4⋊C4C2211yescharacteristic
13C2×C3×C4⋊C4C2211yescharacteristic
14C2×C3×C42C2211yescharacteristic
15C2×C4⋊Dic3C2212yes—
16C2×C4⋊Dic3C2211yescharacteristic
17C2×Dic3⋊C4C2212yes—
18C2×Dic3⋊C4C2212yes—
19C2×Dic3⋊C4C2212yes—
20C2×C4×Dic3C2212yes—
21C2×C4×Dic3C2212yes—
22C3×#95C2212yes—
23C3×#95C2212yes—
24C3⋊#95C2212yes—
25C3⋊#95C2212yes—
26C3⋊#95C2212yes—
27C3⋊#95C2211yescharacteristic
28C3⋊#95C2212yes—
29C3⋊#95C2211yescharacteristic
30C3⋊#95C2212yes—
31C3⋊#95C2212yes—
32#400—31no—
33#398—32no—
34#395—31no—
35#391—32no—
36#389—32no—
37#387—32no—
38#387—32no—
39#382D311yescharacteristic
40#376—32no—
41C22×C3×C4C2311yescharacteristic
42C22×C3×C4C2311yescharacteristic
43C22×C3×C4C2312yes—
44C22×C3×C4C2311yescharacteristic
45C22×C3×C4C2312yes—
46C22×Dic3C2312yes—
47C22×Dic3C2312yes—
48C22×Dic3C2312yes—
49C22×Dic3C2312yes—
50C2×Dic6—24no—
51C2×Dic6—41no—
52C3×C4⋊C4—41no—
53C3×C4⋊C4—41no—
54C3×C42Q814yescomplemented
55C4⋊Dic3—24no—
56C4⋊Dic3—41no—
57Dic3⋊C4—24no—
58Dic3⋊C4—24no—
59Dic3⋊C4—42no—
60C4×Dic3—24no—
61C4×Dic3—24no—
62C22×Q8—31no—
63C2×C4⋊C4—32no—
64C2×C4⋊C4—32no—
65C2×C4⋊C4—32no—
66C2×C4⋊C4—31no—
67C2×C4⋊C4—32no—
68C2×C4⋊C4C2×D311yescharacteristic
69C2×C4⋊C4C2×D311yescharacteristic
70C2×C42—32no—
71C2×C42—32no—
72C2×C42C2×D311yescharacteristic
73#95—32no—
74#95—32no—
75#95—32no—
76#95—32no—
77#95—31no—
78#95—31no—
79#95—32no—
80#95—32no—
81#95C2×D312yes—
82#95C2×D312yes—
83C23×C3C2411yescharacteristic
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×C4—22no—
93C2×C3×C4—21no—
94C2×C3×C4—21no—
95C2×C3×C4C2×Q814yes—
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×Dic3—22no—
107C2×Dic3#4114yes—
108C2×Dic3#4114yes—
109Dic6—44no—
110C2×Q8—64no—
111C2×Q8—121no—
112C22×C4—32no—
113C22×C4—32no—
114C22×C4—32no—
115C22×C4—32no—
116C22×C4C22×D311yescharacteristic
117C22×C4C22×D311yescharacteristic
118C22×C4C22×D312yes—
119C22×C4C22×D311yescharacteristic
120C22×C4C22×D312yes—
121C4⋊C4—41no—
122C4⋊C4—41no—
123C4⋊C4—64no—
124C4⋊C4—64no—
125C4⋊C4—64no—
126C4⋊C4—122no—
127C4⋊C4—121no—
128C42—64no—
129C42—64no—
130C42Dic614yescomplemented
131C22×C3C22×Q811yescharacteristic
132C22×C3C2×#4112yes—
133C22×C3C2×#4112yes—
134C22×C3H(5,𝔽2)11yescharacteristic
135C22×C32−1+411yescharacteristic
136C3×C4—24no—
137C3×C4—22no—
138C3×C4—41no—
139C3×C4—41no—
140C3×C4—42no—
141Dic3—24no—
142Dic3—24no—
143Dic3—42no—
144Dic3—42no—
145C23C23×D311yescharacteristic
146Q8—124no—
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—22no—
150C2×C4—22no—
151C2×C4—22no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—22no—
157C2×C4—22no—
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×C4—62no—
170C2×C4C2×Dic612yes—
171C2×C4C2×Dic614yes—
172C2×C3#53312yes—
173C2×C3#54411yescharacteristic
174C2×C3#55111yescharacteristic
175C2×C3#55212yes—
176C2×C3#55511yescharacteristic
177C22C22×Dic611yescharacteristic
178C22#100411yescharacteristic
179C22#100711yescharacteristic
180C22D3×#4112yes—
181C22D3×#4112yes—
182C4—22no—
183C4—24no—
184C4—42no—
185C4—41no—
186C4—41no—
187C4—64no—
188C4—64no—
189C4—122no—
190C4—122no—
191C3#261211yescharacteristic, complemented, Sylow
192C2#550011yescharacteristic
193C2#551712yes—
194C2#567011yescharacteristic
195C2#567911yescharacteristic
196C2#569312yes—
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, prime radical, cosocleC23×C3C24
FittingC3×#382C2
hypercenter#382D3
hypocenterC3#2612
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
54. C3×C42Q8semidirect
130. C42Dic6semidirect
191. C3#2612semidirect

Maximal subgroups

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

subgroupindex
C3×#3822
#49862
#49822
#49792
#49322
#46552
#46542
#46472
#46462
#26123