Finite Group Databasebeta

← #77912

Subgroups — #77912

Order 384.

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

normal subgroups only

This group has 384 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×#398C211yesmaximal, characteristic
2#4984C212yesmaximal
3#4981C212yesmaximal
4#4979C211yesmaximal, characteristic
5#4978C212yesmaximal
6#4975C211yesmaximal, characteristic
7#4656C212yesmaximal
8#4652C212yesmaximal
9#4647C212yesmaximal
10#2792—31nomaximal, Sylow
11C22×Dic6C2211yescharacteristic
12C2×C3×C4⋊C4C2212yes—
13C2×C3×C4⋊C4C2211yescharacteristic
14C2×C3×C4⋊C4C2211yescharacteristic
15C2×C4⋊Dic3C2212yes—
16C2×C4⋊Dic3C2212yes—
17C2×C4⋊Dic3C2211yescharacteristic
18C2×Dic3⋊C4C2212yes—
19C2×Dic3⋊C4C2212yes—
20C2×Dic3⋊C4C2212yes—
21C2×Dic3⋊C4C2212yes—
22C2×C4×Dic3C2211yescharacteristic
23C2×C4×Dic3C2212yes—
24C3×#95C2211yescharacteristic
25C3×#95C2212yes—
26C3⋊#95C2212yes—
27C3⋊#95C2211yescharacteristic
28C3⋊#95C2212yes—
29C3⋊#95C2212yes—
30C3⋊#95C2212yes—
31C3⋊#95C2212yes—
32#398—32no—
33#398D311yescharacteristic
34#395—31no—
35#395—32no—
36#389—32no—
37#389—32no—
38#387—32no—
39#387—32no—
40#384—31no—
41C22×C3×C4C2312yes—
42C22×C3×C4C2311yescharacteristic
43C22×C3×C4C2311yescharacteristic
44C22×C3×C4C2312yes—
45C22×C3×C4C2311yescharacteristic
46C22×Dic3C2312yes—
47C22×Dic3C2312yes—
48C22×Dic3C2312yes—
49C22×Dic3C2312yes—
50C2×Dic6—42no—
51C2×Dic6—41no—
52C3×C4⋊C4—24no—
53C3×C4⋊C4—41no—
54C3×C4⋊C4—41no—
55C4⋊Dic3—42no—
56C4⋊Dic3—41no—
57C4⋊Dic3—42no—
58Dic3⋊C4—42no—
59Dic3⋊C4—42no—
60Dic3⋊C4—42no—
61Dic3⋊C4Q818yescomplemented
62C4×Dic3—22no—
63C4×Dic3—42no—
64C22×Q8—31no—
65C2×C4⋊C4—32no—
66C2×C4⋊C4—32no—
67C2×C4⋊C4—31no—
68C2×C4⋊C4—32no—
69C2×C4⋊C4—32no—
70C2×C4⋊C4—32no—
71C2×C4⋊C4—32no—
72C2×C4⋊C4C2×D312yes—
73C2×C4⋊C4C2×D311yescharacteristic
74C2×C4⋊C4C2×D311yescharacteristic
75C2×C42—31no—
76C2×C42—32no—
77#95—31no—
78#95—32no—
79#95—32no—
80#95—32no—
81#95—32no—
82#95—32no—
83#95C2×D312yes—
84#95C2×D311yescharacteristic
85C23×C3C2411yescharacteristic
86C2×C3×C4—22no—
87C2×C3×C4—22no—
88C2×C3×C4—21no—
89C2×C3×C4—21no—
90C2×C3×C4—22no—
91C2×C3×C4—22no—
92C2×C3×C4—22no—
93C2×C3×C4—22no—
94C2×C3×C4—21no—
95C2×C3×C4—21no—
96C2×C3×C4—22no—
97C2×C3×C4C2×Q814yes—
98C2×C3×C4#4112yes—
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—22no—
108C2×Dic3—22no—
109C2×Dic3C2×Q814yes—
110C2×Dic3C2×Q814yes—
111Dic6—44no—
112C2×Q8—121no—
113C2×Q8—122no—
114C22×C4—32no—
115C22×C4—32no—
116C22×C4—32no—
117C22×C4—32no—
118C22×C4C22×D312yes—
119C22×C4C22×D311yescharacteristic
120C22×C4C22×D311yescharacteristic
121C22×C4C22×D311yescharacteristic
122C22×C4C22×D312yes—
123C4⋊C4—24no—
124C4⋊C4—38no—
125C4⋊C4—41no—
126C4⋊C4—41no—
127C4⋊C4—122no—
128C4⋊C4—122no—
129C4⋊C4—122no—
130C4⋊C4—121no—
131C4⋊C4—122no—
132C4⋊C4—122no—
133C42—62no—
134C42—122no—
135C22×C3C22×Q812yes—
136C22×C3C2×#4111yescharacteristic
137C22×C3H(5,𝔽2)11yescharacteristic
138C22×C3H(5,𝔽2)12yes—
139C22×C32−1+411yescharacteristic
140C3×C4—22no—
141C3×C4—24no—
142C3×C4—42no—
143C3×C4—41no—
144C3×C4—41no—
145Dic3—24no—
146Dic3—24no—
147Dic3—42no—
148Dic3—42no—
149C23C23×D311yescharacteristic
150Q8—124no—
151C2×C4—22no—
152C2×C4—21no—
153C2×C4—22no—
154C2×C4—21no—
155C2×C4—22no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—21no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—34no—
163C2×C4—34no—
164C2×C4—62no—
165C2×C4—62no—
166C2×C4—62no—
167C2×C4—62no—
168C2×C4—62no—
169C2×C4—62no—
170C2×C4—62no—
171C2×C4—62no—
172C2×C4—62no—
173C2×C4—62no—
174C2×C4#23712yes—
175C2×C4D3×Q814yes—
176C2×C3#53911yescharacteristic
177C2×C3#54412yes—
178C2×C3#55412yes—
179C2×C3Q8211yescharacteristic
180C2×C3#56011yescharacteristic
181C22C2×#23711yescharacteristic
182C22#100411yescharacteristic
183C22C2×D3×Q812yes—
184C22#100912yes—
185C22#101011yescharacteristic
186C4—24no—
187C4—22no—
188C4—41no—
189C4—41no—
190C4—42no—
191C4—64no—
192C4—64no—
193C4—122no—
194C4—122no—
195C3#279211yescharacteristic, complemented, Sylow
196C2#560211yescharacteristic
197C2#563512yes—
198C2#566611yescharacteristic
199C2#568912yes—
200C2#572211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, prime radical, cosocleC23×C3C24
FittingC3×#398C2
hypercenter#398D3
hypocenterC3#2792
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
61. Dic3⋊C4Q8semidirect
195. C3#2792semidirect

Maximal subgroups

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

subgroupindex
C3×#3982
#49842
#49812
#49792
#49782
#49752
#46562
#46522
#46472
#27923