Finite Group Databasebeta

← #76559

Subgroups — #76559

Order 384.

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

normal subgroups only

This group has 416 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
1C2×#944C211yesmaximal, characteristic
2C2×#890C211yesmaximal, characteristic
3C3×#391C211yesmaximal, characteristic
4#5229C211yesmaximal, characteristic
5#4973C211yesmaximal, characteristic
6#4932C211yesmaximal, characteristic
7#4929C211yesmaximal, characteristic
8#4660C214yesmaximal
9#4658C214yesmaximal
10#2642—31nomaximal, Sylow
11C22×C3×Q8C2211yescharacteristic
12C22×Dic6C2211yescharacteristic
13C2×C3×C4⋊C4C2211yescharacteristic
14C2×C3×C42C2211yescharacteristic
15#944—24no—
16C2×C4⋊Dic3C2212yes—
17C2×C4⋊Dic3C2211yescharacteristic
18C2×Dic3⋊C4C2212yes—
19C2×Dic3⋊C4C2212yes—
20C2×Dic3⋊C4C2212yes—
21C2×C4×Dic3C2211yescharacteristic
22C2×C4×Dic3C2211yescharacteristic
23#890—24no—
24C3×#95C2214yes—
25C3⋊#95C2212yes—
26C3⋊#95C2214yes—
27C3⋊#95C2214yes—
28C3⋊#95C2214yes—
29C3⋊#95C2212yes—
30C2×C4⋊Q8—31no—
31C2×#125—31no—
32#400—34no—
33#400—34no—
34#391—31no—
35#391—31no—
36#391—31no—
37#391D311yescharacteristic
38#376—31no—
39C2×C3×Q8—22no—
40C2×C3×Q8—22no—
41C2×C3×Q8—22no—
42C22×C3×C4C2312yes—
43C22×C3×C4C2312yes—
44C22×C3×C4C2312yes—
45C22×C3×C4C2311yescharacteristic
46C22×Dic3C2312yes—
47C22×Dic3C2312yes—
48C22×Dic3C2312yes—
49C22×Dic3C2311yescharacteristic
50C22×Dic3C2311yescharacteristic
51C2×Dic6—22no—
52C2×Dic6—22no—
53C2×Dic6—22no—
54C3×C4⋊C4—22no—
55C3×C42—22no—
56C4⋊Dic3—22no—
57C4⋊Dic3—24no—
58Dic3⋊C4—24no—
59Dic3⋊C4—24no—
60Dic3⋊C4—24no—
61C4×Dic3—22no—
62C4×Dic3D414yes—
63C22×Q8—31no—
64C22×Q8C2×D311yescharacteristic
65C4⋊Q8—64no—
66#125—64no—
67C2×C4⋊C4—31no—
68C2×C4⋊C4—32no—
69C2×C4⋊C4—32no—
70C2×C4⋊C4—32no—
71C2×C4⋊C4—32no—
72C2×C4⋊C4C2×D311yescharacteristic
73C2×C42—31no—
74C2×C42—31no—
75C2×C42C2×D311yescharacteristic
76#95—32no—
77#95—32no—
78#95—34no—
79#95—34no—
80#95—34no—
81#95C2×D314yes—
82C23×C3C2411yescharacteristic
83C3×Q8—44no—
84C2×C3×C4—22no—
85C2×C3×C4—22no—
86C2×C3×C4—22no—
87C2×C3×C4—22no—
88C2×C3×C4—22no—
89C2×C3×C4—22no—
90C2×C3×C4—24no—
91C2×C3×C4—22no—
92C2×C3×C4C2×D412yes—
93C2×C3×C4#4112yes—
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—24no—
103C2×Dic3—22no—
104C2×Dic3—22no—
105C2×Dic3C2×D412yes—
106C2×Dic3C2×D412yes—
107Dic6—44no—
108C2×Q8—22no—
109C2×Q8—22no—
110C2×Q8—22no—
111C2×Q8—62no—
112C2×Q8—62no—
113C2×Q8—62no—
114C22×C4—31no—
115C22×C4—31no—
116C22×C4—32no—
117C22×C4—32no—
118C22×C4—32no—
119C22×C4C22×D312yes—
120C22×C4C22×D312yes—
121C22×C4C22×D312yes—
122C22×C4C22×D311yescharacteristic
123C4⋊C4—22no—
124C4⋊C4—64no—
125C4⋊C4—64no—
126C4⋊C4—64no—
127C4⋊C4—64no—
128C4⋊C4—62no—
129C42—22no—
130C42—34no—
131C42—62no—
132C22×C3C22×D411yescharacteristic
133C22×C3C2×#4111yescharacteristic
134C22×C3C2×#4111yescharacteristic
135C22×C32−1+412yes—
136C22×C32−1+412yes—
137C3×C4—42no—
138C3×C4—42no—
139C3×C4—42no—
140C3×C4#12414yes—
141Dic3—22no—
142Dic3—22no—
143Dic3—42no—
144Dic3—42no—
145Dic3—42no—
146C23C23×D311yescharacteristic
147Q8—44no—
148Q8—124no—
149C2×C4—22no—
150C2×C4—22no—
151C2×C4—22no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—24no—
156C2×C4—22no—
157C2×C4—32no—
158C2×C4—32no—
159C2×C4—62no—
160C2×C4—62no—
161C2×C4—62no—
162C2×C4—62no—
163C2×C4—62no—
164C2×C4—62no—
165C2×C4—62no—
166C2×C4—64no—
167C2×C4—62no—
168C2×C4—62no—
169C2×C4#23512yes—
170C2×C4D3×D412yes—
171C2×C4#23712yes—
172C2×C3C2×#12411yescharacteristic
173C2×C3#53611yescharacteristic
174C2×C3#53611yescharacteristic
175C2×C3#54112yes—
176C2×C3#54112yes—
177C22C2×#23511yescharacteristic
178C22C2×D3×D411yescharacteristic
179C22C2×#23711yescharacteristic
180C22#100712yes—
181C22#101012yes—
182C4—42no—
183C4—42no—
184C4—42no—
185C4—62no—
186C4—62no—
187C4—122no—
188C4—122no—
189C4—122no—
190C4#88514yes—
191C3#264211yescharacteristic, complemented, Sylow
192C2C2×#88511yescharacteristic
193C2#558312yes—
194C2#562512yes—
195C2#567511yescharacteristic
196C2#572411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, prime radical, cosocleC23×C3C24
FittingC3×#391C2
hypercenter#391D3
hypocenterC3#2642
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
191. C3#2642semidirect

Maximal subgroups

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

subgroupindex
C2×#9442
C2×#8902
C3×#3912
#52292
#49732
#49322
#49292
#46602
#46582
#26423