Finite Group Databasebeta

← #68951

Subgroups — #68951

Order 384.

420 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 137 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×#877C211yesmaximal, characteristic
2C2×#877C212yesmaximal
3C3×#342C211yesmaximal, characteristic
4#4527C212yesmaximal
5#4526C211yesmaximal, characteristic
6#1740—31nomaximal, Sylow
7C23×Dic3C2211yescharacteristic
8C2×C3×C22⋊C4C2211yescharacteristic
9C2×C3×C22⋊C4C2212yes—
10C2×#217C2211yescharacteristic
11C2×#217C2212yes—
12C2×Dic3⋊C4—22no—
13C2×Dic3⋊C4C412yescomplemented
14C2×C4×Dic3—22no—
15C2×C4×Dic3C412yescomplemented
16#877—22no—
17#877—22no—
18#877—24no—
19#877C418yescomplemented
20C2×#117—31no—
21C2×#117—32no—
22#342—31no—
23#342—32no—
24#342D311yescharacteristic
25C24×C3C2311yescharacteristic
26C22×C3×C4—22no—
27C22×C3×C4C2×C412yes—
28C22×Dic3—22no—
29C22×Dic3C2×C412yes—
30C22×Dic3C2×C414yes—
31C22×Dic3C2×C411yescharacteristic
32C22×Dic3C2×C411yescharacteristic
33C22×Dic3D412yes—
34C22×Dic3D412yes—
35C22×Dic3D412yes—
36C22×Dic3Q812yes—
37C3×C22⋊C4—22no—
38C3×C22⋊C4—22no—
39C3×C22⋊C4C2×C414yes—
40#217—22no—
41#217—22no—
42#217C2×C414yes—
43Dic3⋊C4—24no—
44Dic3⋊C4—28no—
45C4×Dic3—22no—
46C4×Dic3—22no—
47C4×Dic3—28no—
48C23×C4—31no—
49#117—38no—
50#117—62no—
51#117—62no—
52#117—64no—
53C2×C4⋊C4—32no—
54C2×C4⋊C4—62no—
55C2×C22⋊C4—32no—
56C2×C22⋊C4—31no—
57C2×C22⋊C4C2×D311yescharacteristic
58C2×C22⋊C4C2×D312yes—
59C2×C42—32no—
60C2×C42—62no—
61C23×C3—42no—
62C23×C3C22×C411yescharacteristic
63C23×C3C22×C412yes—
64C23×C3C2×D412yes—
65C23×C3C2×D411yescharacteristic
66C23×C3C2×Q811yescharacteristic
67C2×C3×C4—22no—
68C2×C3×C4—24no—
69C2×C3×C4—44no—
70C2×C3×C4—42no—
71C2×Dic3—22no—
72C2×Dic3—24no—
73C2×Dic3—44no—
74C2×Dic3—42no—
75C2×Dic3C4212yes—
76C2×Dic3C4212yes—
77C2×Dic3C22⋊C414yes—
78C2×Dic3C22⋊C411yescharacteristic
79C2×Dic3C22⋊C411yescharacteristic
80C2×Dic3C22⋊C414yes—
81C2×Dic3C22⋊C412yes—
82C2×Dic3C4⋊C414yes—
83C2×Dic3C4⋊C414yes—
84C2×Dic3C4⋊C412yes—
85C2×Dic3C4⋊C412yes—
86C24C22×D311yescharacteristic
87C22×C4—22no—
88C22×C4—31no—
89C22×C4—31no—
90C22×C4—34no—
91C22×C4—32no—
92C22×C4—32no—
93C22×C4—32no—
94C22×C4—32no—
95C22×C4—32no—
96C22×C4—62no—
97C22×C4C4×D312yes—
98C4⋊C4—64no—
99C4⋊C4—68no—
100C22⋊C4—22no—
101C22⋊C4—22no—
102C22⋊C4—34no—
103C22⋊C4—62no—
104C22⋊C4—62no—
105C22⋊C4C4×D314yes—
106C42—62no—
107C42—62no—
108C42—68no—
109C22×C3—22no—
110C22×C3—24no—
111C22×C3—42no—
112C22×C3—41no—
113C22×C3—41no—
114C22×C3C2×C4211yescharacteristic
115C22×C3C2×C22⋊C412yes—
116C22×C3C2×C22⋊C411yescharacteristic
117C22×C3C2×C4⋊C411yescharacteristic
118C22×C3C2×C4⋊C412yes—
119C3×C4—44no—
120C3×C4—42no—
121Dic3—44no—
122Dic3—42no—
123Dic3#9512yes—
124Dic3#9514yes—
125Dic3#9512yes—
126C23—42no—
127C23C2×C4×D311yescharacteristic
128C23C2×C4×D312yes—
129C23D3×D412yes—
130C23D3×D411yescharacteristic
131C23D3×Q811yescharacteristic
132C2×C4—24no—
133C2×C4—22no—
134C2×C4—32no—
135C2×C4—32no—
136C2×C4—34no—
137C2×C4—34no—
138C2×C4—31no—
139C2×C4—31no—
140C2×C4—32no—
141C2×C4—32no—
142C2×C4—32no—
143C2×C4—34no—
144C2×C4—34no—
145C2×C4—44no—
146C2×C4—42no—
147C2×C4—64no—
148C2×C4—62no—
149C2×C4—124no—
150C2×C4—122no—
151C2×C3—22no—
152C2×C3—21no—
153C2×C3—21no—
154C2×C3—22no—
155C2×C3C2×#9511yescharacteristic
156C2×C3#41012yes—
157C22—22no—
158C22—24no—
159C22—42no—
160C22—41no—
161C22—41no—
162C22C42×D311yescharacteristic
163C22D3×C22⋊C412yes—
164C22D3×C22⋊C411yescharacteristic
165C22D3×C4⋊C411yescharacteristic
166C22D3×C4⋊C412yes—
167C4—32no—
168C4—34no—
169C4—32no—
170C4—44no—
171C4—42no—
172C4—124no—
173C4—122no—
174C3#174011yescharacteristic, complemented, Sylow
175C2—22no—
176C2—21no—
177C2—21no—
178C2—22no—
179C2D3×#9511yescharacteristic
180C2#474012yes—
subgroupG/H
centerC22D3×C22⋊C4
commutatorC22×C3C2×C42
FrattiniC24C22×D3
FittingC3×#342C2
socleC22×C3C2×C22⋊C4
prime radical, cosocleC24×C3C23
hypercenter#342D3
hypocenterC3#1740
LCSG ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
13. C2×Dic3⋊C4C4semidirect
15. C2×C4×Dic3C4semidirect
19. #877C4semidirect
174. C3#1740semidirect

Maximal subgroups

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

subgroupindex
C2×#8772
C3×#3422
#45272
#45262
#17403