Finite Group Databasebeta

← #11771226

Subgroups — #11771226

Order 1152.

600 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 600 conjugacy classes of subgroups — too many to draw. Only its 169 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
1C32×#380C211yesmaximal, characteristic
2#10592906C211yesmaximal, characteristic
3#10592906C211yesmaximal, characteristic
4#67626—34nomaximal
5C23×C32×C4C2211yescharacteristic
6C2×C32×C4⋊C4—21no—
7C2×C32×C22⋊C4C412yes—
8C2×#3748—21no—
9C2×#3748C412yescomplemented
10C32×#95—21no—
11#63657—21no—
12#63657—21no—
13#63657—21no—
14#63657C412yescomplemented
15C3×#380D314yes—
16#5207—34no—
17#5207—34no—
18C24×C32C2×C411yescharacteristic
19C22×C32×C4—22no—
20C22×C32×C4—42no—
21C22×C32×C4C2×C411yescharacteristic
22C22×C32×C4C2×C411yescharacteristic
23C22×C32×C4D411yescharacteristic
24C22×C32×C4D411yescharacteristic
25C22×C32×C4D411yescharacteristic
26C22×C32×C4Q811yescharacteristic
27C32×C4⋊C4—42no—
28C32×C22⋊C4—42no—
29#3748—42no—
30#3748—42no—
31C2×C3⋊(C3⋊C8)—22no—
32C2×C3⋊(C3⋊C8)—22no—
33#1305—91noSylow
34C23×C3×C4C2×D314yes—
35C2×C3×C4⋊C4—24no—
36C2×C3×C22⋊C4Dic318yes—
37C2×#208—38no—
38C2×#208—64no—
39C3×#95—24no—
40#830—38no—
41#830—64no—
42#830—64no—
43#830—64no—
44C23×C32—21no—
45C23×C32—21no—
46C23×C32—41no—
47C23×C32—41no—
48C23×C32C4211yescharacteristic
49C23×C32C22⋊C411yescharacteristic
50C23×C32C4⋊C411yescharacteristic
51C2×C32×C4—22no—
52C2×C32×C4—22no—
53C2×C32×C4—22no—
54C2×C32×C4—41no—
55C2×C32×C4—41no—
56C2×C32×C4—41no—
57C2×C32×C4—42no—
58C2×C32×C4—42no—
59C2×C32×C4—42no—
60C2×C32×C4C22⋊C411yescharacteristic
61C2×C32×C4C22⋊C411yescharacteristic
62C2×C32×C4C4⋊C411yescharacteristic
63C2×C32×C4C4⋊C411yescharacteristic
64C3⋊(C3⋊C8)—42no—
65C3⋊(C3⋊C8)—42no—
66#407—91no—
67#407—91no—
68#380C3⋊D311yescharacteristic
69C24×C3C2×Dic314yes—
70C22×C3×C4—28no—
71C22×C3×C4—48no—
72C22×C3×C4Dic614yes—
73C22×C3×C4C4×D314yes—
74C22×C3×C4C4×D314yes—
75C22×C3×C4D1214yes—
76C22×C3×C4#6714yes—
77C22×C3×C4#6714yes—
78C3×C4⋊C4—48no—
79C3×C22⋊C4—48no—
80#208—128no—
81#208—128no—
82C2×C3⋊C8—68no—
83C2×C3⋊C8—68no—
84C22×C32—21no—
85C22×C32—21no—
86C22×C32—21no—
87C22×C32—21no—
88C22×C32—21no—
89C22×C32—21no—
90C22×C32—21no—
91C22×C32—21no—
92C22×C32—42no—
93C22×C32—42no—
94C22×C32#9511yescharacteristic
95C22×C32#10011yescharacteristic
96C22×C32#10111yescharacteristic
97C32×C4—21no—
98C32×C4—21no—
99C32×C4—21no—
100C32×C4—82no—
101C32×C4#9912yes—
102C23×C4C2×C3⋊D311yescharacteristic
103C2×M16—92no—
104C2×M16—181no—
105C2×C4⋊C4—21no—
106C2×C22⋊C4C3⋊Dic312yes—
107C22⋊C8—92no—
108C22⋊C8—181no—
109C22⋊C8—181no—
110C22⋊C8—181no—
111#95—21no—
112C23×C3—24no—
113C23×C3—24no—
114C23×C3—44no—
115C23×C3—44no—
116C23×C3C4×Dic314yes—
117C23×C3C4⋊Dic314yes—
118C23×C3#21714yes—
119C2×C3×C4—28no—
120C2×C3×C4—28no—
121C2×C3×C4—28no—
122C2×C3×C4—44no—
123C2×C3×C4—44no—
124C2×C3×C4—44no—
125C2×C3×C4—48no—
126C2×C3×C4—48no—
127C2×C3×C4—48no—
128C2×C3×C4Dic3⋊C414yes—
129C2×C3×C4Dic3⋊C414yes—
130C2×C3×C4(C2×D3)⋊C414yes—
131C2×C3×C4(C2×D3)⋊C414yes—
132C3⋊C8—128no—
133C3⋊C8—128no—
134C2×C32—21no—
135C2×C32—21no—
136C2×C32—41no—
137C2×C32—41no—
138C2×C32#34211yescharacteristic
139C2×C32#34311yescharacteristic
140C2×C32#34411yescharacteristic
141C24C2×C3⋊Dic311yescharacteristic
142C22×C4—22no—
143C22×C4—42no—
144C22×C4#63411yescharacteristic
145C22×C4C4×C3⋊D311yescharacteristic
146C22×C4C4×C3⋊D311yescharacteristic
147C22×C4C4⋊(C3⋊D3)11yescharacteristic
148C22×C4#63811yescharacteristic
149C22×C4#63811yescharacteristic
150M16—362no—
151M16—362no—
152C2×C8—182no—
153C2×C8—182no—
154C4⋊C4—42no—
155C22⋊C4—42no—
156C22×C3—24no—
157C22×C3—24no—
158C22×C3—24no—
159C22×C3—24no—
160C22×C3—24no—
161C22×C3—24no—
162C22×C3—24no—
163C22×C3—24no—
164C22×C3—48no—
165C22×C3—48no—
166C22×C3C3⋊#9514yes—
167C22×C3#83314yes—
168C22×C3#83614yes—
169C3×C4—24no—
170C3×C4—24no—
171C3×C4—24no—
172C3×C4—88no—
173C3×C4#80618yes—
174C32#130511yescharacteristic, complemented, Sylow
175C23—21no—
176C23—21no—
177C23—41no—
178C23—41no—
179C23C4×C3⋊Dic311yescharacteristic
180C23C4⋊(C3⋊Dic3)11yescharacteristic
181C23#375711yescharacteristic
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—42no—
189C2×C4—42no—
190C2×C4—42no—
191C2×C4#375011yescharacteristic
192C2×C4#375011yescharacteristic
193C2×C4#375211yescharacteristic
194C2×C4#375211yescharacteristic
195C8—362no—
196C8—362no—
197C2×C3—24no—
198C2×C3—24no—
199C2×C3—44no—
200C2×C3—44no—
201C2×C3#452714yes—
202C2×C3#453014yes—
203C2×C3#453314yes—
204C22—21no—
205C22—21no—
206C22—21no—
207C22—21no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22—21no—
212C22—42no—
213C22—42no—
214C22#6365811yescharacteristic
215C22#6366011yescharacteristic
216C22#6366311yescharacteristic
217C4—21no—
218C4—21no—
219C4—21no—
220C4—82no—
221C4#6363312yes—
222C3#6762614yescomplemented
223C2—21no—
224C2—21no—
225C2—41no—
226C2—41no—
227C2#1058939311yescharacteristic
228C2#1058939611yescharacteristic
229C2#1058939911yescharacteristic
subgroupG/H
centerC22#63658
commutatorC23×C32C42
FrattiniC23×C4C2×C3⋊D3
FittingC32×#380C2
socleC22×C32#95
prime radicalC24×C32C2×C4
cosocleC23×C32×C4C22
hypercenter#380C3⋊D3
hypocenterC32#1305
LCSG ▷ C23×C32 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
9. C2×#3748C4semidirect
14. #63657C4semidirect
174. C32#1305semidirect
222. C3#67626semidirect

Maximal subgroups

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

subgroupindex
C32×#3802
#105929062
#676263