Finite Group Databasebeta

← #76549

Subgroups — #76549

Order 384.

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

normal subgroups only

This group has 412 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×#391C211yesmaximal, characteristic
2#5230C212yesmaximal
3#4981C211yesmaximal, characteristic
4#4979C211yesmaximal, characteristic
5C4×Dic3⋊C4C212yesmaximal
6#4652C212yesmaximal
7#4652C212yesmaximal
8#4647C212yesmaximal
9#4646C212yesmaximal
10#2586—31nomaximal, Sylow
11C22×C3×Q8C2211yescharacteristic
12C22×Dic6C2211yescharacteristic
13C2×C3×C4⋊C4C2211yescharacteristic
14C2×C3×C42C2211yescharacteristic
15C2×C4⋊Dic3C2211yescharacteristic
16C2×Dic3⋊C4C2212yes—
17C2×Dic3⋊C4C2212yes—
18C2×Dic3⋊C4C2212yes—
19C2×Dic3⋊C4C2212yes—
20C2×Dic3⋊C4C2212yes—
21C2×C4×Dic3C2212yes—
22C2×C4×Dic3C2212yes—
23C3×#95C2212yes—
24C3×#95C2212yes—
25C3⋊#95C2212yes—
26C3⋊#95C2212yes—
27C3⋊#95C2212yes—
28C3⋊#95C2212yes—
29C3⋊#95C2211yescharacteristic
30C3⋊#95C2211yescharacteristic
31C3⋊#95C2212yes—
32#398—31no—
33#395—32no—
34#395—31no—
35#391—32no—
36#391D311yescharacteristic
37#389—32no—
38#387—32no—
39#387—32no—
40C4×C4⋊C4—32no—
41C2×C3×Q8—22no—
42C2×C3×Q8—41no—
43C2×C3×Q8—41no—
44C22×C3×C4C2311yescharacteristic
45C22×C3×C4C2312yes—
46C22×C3×C4C2311yescharacteristic
47C22×C3×C4C2312yes—
48C22×C3×C4C2311yescharacteristic
49C22×Dic3C2312yes—
50C22×Dic3C2312yes—
51C22×Dic3C2312yes—
52C22×Dic3C2312yes—
53C2×Dic6—24no—
54C2×Dic6—41no—
55C3×C4⋊C4—41no—
56C3×C42—41no—
57C4⋊Dic3—41no—
58Dic3⋊C4—24no—
59Dic3⋊C4—24no—
60Dic3⋊C4—42no—
61Dic3⋊C4—42no—
62Dic3⋊C4Q818yescomplemented
63C4×Dic3—24no—
64C4×Dic3—42no—
65C22×Q8—31no—
66C22×Q8C2×D311yescharacteristic
67C2×C4⋊C4—32no—
68C2×C4⋊C4—32no—
69C2×C4⋊C4—32no—
70C2×C4⋊C4—32no—
71C2×C4⋊C4—31no—
72C2×C4⋊C4—32no—
73C2×C4⋊C4C2×D311yescharacteristic
74C2×C42—32no—
75C2×C42—32no—
76C2×C42C2×D311yescharacteristic
77#95—32no—
78#95—32no—
79#95—32no—
80#95—31no—
81#95—31no—
82#95—32no—
83#95—32no—
84#95C2×D312yes—
85#95C2×D312yes—
86C23×C3C2411yescharacteristic
87C3×Q8—44no—
88C2×C3×C4—22no—
89C2×C3×C4—22no—
90C2×C3×C4—21no—
91C2×C3×C4—21no—
92C2×C3×C4—22no—
93C2×C3×C4—22no—
94C2×C3×C4—22no—
95C2×C3×C4—22no—
96C2×C3×C4—22no—
97C2×C3×C4—21no—
98C2×C3×C4—21no—
99C2×C3×C4C2×Q814yes—
100C2×C3×C4#4112yes—
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×Dic3—22no—
110C2×Dic3C2×Q814yes—
111C2×Dic3C2×Q814yes—
112C2×Dic3#4114yes—
113Dic6—44no—
114C2×Q8—22no—
115C2×Q8—41no—
116C2×Q8—41no—
117C2×Q8—64no—
118C2×Q8—121no—
119C22×C4—32no—
120C22×C4—32no—
121C22×C4—32no—
122C22×C4—32no—
123C22×C4C22×D311yescharacteristic
124C22×C4C22×D312yes—
125C22×C4C22×D311yescharacteristic
126C22×C4C22×D311yescharacteristic
127C22×C4C22×D312yes—
128C4⋊C4—38no—
129C4⋊C4—41no—
130C4⋊C4—64no—
131C4⋊C4—64no—
132C4⋊C4—122no—
133C4⋊C4—122no—
134C4⋊C4—121no—
135C42—41no—
136C42—64no—
137C42—122no—
138C22×C3C22×Q812yes—
139C22×C3C2×#4111yescharacteristic
140C22×C3C2×#4112yes—
141C22×C3H(5,𝔽2)11yescharacteristic
142C22×C3H(5,𝔽2)11yescharacteristic
143C3×C4—22no—
144C3×C4—24no—
145C3×C4—42no—
146C3×C4—41no—
147C3×C4—41no—
148Dic3—24no—
149Dic3—24no—
150Dic3—24no—
151Dic3—42no—
152C23C23×D311yescharacteristic
153Q8—44no—
154Q8—124no—
155C2×C4—22no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—34no—
167C2×C4—34no—
168C2×C4—34no—
169C2×C4—62no—
170C2×C4—62no—
171C2×C4—62no—
172C2×C4—62no—
173C2×C4—62no—
174C2×C4—62no—
175C2×C4—62no—
176C2×C4—62no—
177C2×C4—62no—
178C2×C4#23512yes—
179C2×C4D3×Q814yes—
180C2×C3#53312yes—
181C2×C3#53811yescharacteristic
182C2×C3#55111yescharacteristic
183C2×C3#55412yes—
184C2×C3Q8211yescharacteristic
185C22C2×#23511yescharacteristic
186C22#100411yescharacteristic
187C22#100411yescharacteristic
188C22C2×D3×Q812yes—
189C22D3×#4112yes—
190C4—24no—
191C4—22no—
192C4—41no—
193C4—41no—
194C4—42no—
195C4—64no—
196C4—64no—
197C4—64no—
198C4—122no—
199C3#258611yescharacteristic, complemented, Sylow
200C2#549411yescharacteristic
201C2#557812yes—
202C2#563612yes—
203C2#567911yescharacteristic
204C2#572211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, prime radical, cosocleC23×C3C24
FittingC3×#391C2
hypercenter#391D3
hypocenterC3#2586
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
62. Dic3⋊C4Q8semidirect
199. C3#2586semidirect

Maximal subgroups

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

subgroupindex
C3×#3912
#52302
#49812
#49792
C4×Dic3⋊C42
#46522
#46472
#46462
#25863