Finite Group Databasebeta

← #11770878

Subgroups — #11770878

Order 1152.

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

normal subgroups only

This group has 678 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×#407C211yesmaximal, characteristic
2#10592910C211yesmaximal, characteristic
3C4×#3757C211yesmaximal, characteristic
4#67682—34nomaximal
5C23×C32×C4C2211yescharacteristic
6C2×C32×M16—21no—
7C2×#3757—21no—
8C2×#3757—21no—
9C2×C4×C3⋊Dic3C412yescomplemented
10C32×C22⋊C8—21no—
11C32×C22⋊C8C412yescomplemented
12#63658—21no—
13#63658—21no—
14#63658C412yescomplemented
15C3×#407D314yes—
16#5211—34no—
17C4×#217—34no—
18C24×C32D411yescharacteristic
19C22×C32×C4—42no—
20C22×C32×C4C2×C411yescharacteristic
21C22×C32×C4C2×C411yescharacteristic
22C22×C32×C4C2×C411yescharacteristic
23C22×C32×C4D411yescharacteristic
24C22×C32×C4D411yescharacteristic
25C22×C32×C4Q811yescharacteristic
26C22×C3⋊Dic3—22no—
27C22×C3⋊Dic3—22no—
28C32×M16—42no—
29C2×C32×C8—22no—
30#3757—24no—
31#3757—42no—
32C4×C3⋊Dic3—42no—
33#1284—91noSylow
34C23×C3×C4C2×D314yes—
35C2×C3×M16—24no—
36C2×#217—64no—
37C2×#217—64no—
38C2×C4×Dic3—38no—
39C3×C22⋊C8—24no—
40C3×C22⋊C8Dic318yescomplemented
41C3⋊#95—38no—
42C3⋊#95—64no—
43C3⋊#95—64no—
44C23×C32—22no—
45C23×C32—22no—
46C23×C32—41no—
47C23×C32C22⋊C411yescharacteristic
48C23×C32C22⋊C411yescharacteristic
49C23×C32C4⋊C411yescharacteristic
50C2×C32×C4—22no—
51C2×C32×C4—22no—
52C2×C32×C4—41no—
53C2×C32×C4—41no—
54C2×C32×C4—41no—
55C2×C32×C4—41no—
56C2×C32×C4C4211yescharacteristic
57C2×C32×C4C22⋊C411yescharacteristic
58C2×C32×C4C4⋊C411yescharacteristic
59C2×C32×C4C4⋊C411yescharacteristic
60C2×C3⋊Dic3—24no—
61C2×C3⋊Dic3—42no—
62C2×C3⋊Dic3—42no—
63C2×C3⋊Dic3—42no—
64C2×C3⋊Dic3—42no—
65C2×C3⋊Dic3—42no—
66C32×C8—42no—
67#407C3⋊D311yescharacteristic
68#381—91no—
69C4×C22⋊C4—91no—
70C24×C3D1214yes—
71C22×C3×C4—48no—
72C22×C3×C4Dic614yes—
73C22×C3×C4C4×D314yes—
74C22×C3×C4C4×D314yes—
75C22×C3×C4C2×Dic314yes—
76C22×C3×C4#6714yes—
77C22×C3×C4#6714yes—
78C22×Dic3—68no—
79C22×Dic3—68no—
80C3×M16—48no—
81C2×C3×C8—28no—
82#217—616no—
83#217—128no—
84C4×Dic3—128no—
85C22×C32—21no—
86C22×C32—21no—
87C22×C32—21no—
88C22×C32—21no—
89C22×C32—21no—
90C22×C32—21no—
91C22×C32—21no—
92C22×C32—44no—
93C22×C32#9511yescharacteristic
94C22×C32#9912yes—
95C22×C32#10412yes—
96C32×C4—21no—
97C32×C4—21no—
98C32×C4—21no—
99C32×C4—21no—
100C3⋊Dic3—44no—
101C3⋊Dic3—82no—
102C23×C4C2×C3⋊D311yescharacteristic
103C2×M16—21no—
104C2×C22⋊C4—181no—
105C2×C22⋊C4—181no—
106C2×C42—92no—
107C22⋊C8—21no—
108C22⋊C8C3⋊Dic312yescomplemented
109#95—92no—
110#95—181no—
111#95—181no—
112C23×C3—28no—
113C23×C3—28no—
114C23×C3—44no—
115C23×C3C4⋊Dic314yes—
116C23×C3(C2×D3)⋊C414yes—
117C23×C3(C2×D3)⋊C414yes—
118C2×C3×C4—28no—
119C2×C3×C4—28no—
120C2×C3×C4—44no—
121C2×C3×C4—44no—
122C2×C3×C4—44no—
123C2×C3×C4—44no—
124C2×C3×C4C4×Dic314yes—
125C2×C3×C4Dic3⋊C414yes—
126C2×C3×C4Dic3⋊C414yes—
127C2×C3×C4#21714yes—
128C2×Dic3—616no—
129C2×Dic3—128no—
130C2×Dic3—128no—
131C2×Dic3—128no—
132C2×Dic3—128no—
133C2×Dic3—128no—
134C3×C8—48no—
135C2×C32—22no—
136C2×C32—22no—
137C2×C32—41no—
138C2×C32H(3,ℤ/4)11yescharacteristic
139C2×C32#33911yescharacteristic
140C2×C32#34211yescharacteristic
141C24C4⋊(C3⋊D3)11yescharacteristic
142C22×C4—42no—
143C22×C4—182no—
144C22×C4—182no—
145C22×C4#63411yescharacteristic
146C22×C4C4×C3⋊D311yescharacteristic
147C22×C4C4×C3⋊D311yescharacteristic
148C22×C4C2×C3⋊Dic311yescharacteristic
149C22×C4#63811yescharacteristic
150C22×C4#63811yescharacteristic
151M16—42no—
152C2×C8—22no—
153C22⋊C4—184no—
154C22⋊C4—362no—
155C42—362no—
156C22×C3—24no—
157C22×C3—24no—
158C22×C3—24no—
159C22×C3—24no—
160C22×C3—24no—
161C22×C3—24no—
162C22×C3—24no—
163C22×C3—416no—
164C22×C3#80618yes—
165C22×C3#82518yes—
166C22×C3C3⋊#9514yes—
167C3×C4—24no—
168C3×C4—24no—
169C3×C4—24no—
170C3×C4—24no—
171Dic3—1216no—
172Dic3—248no—
173C32#128411yescharacteristic, complemented, Sylow
174C23—22no—
175C23—22no—
176C23—41no—
177C23C4⋊(C3⋊Dic3)11yescharacteristic
178C23#375211yescharacteristic
179C23#375211yescharacteristic
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—184no—
187C2×C4—362no—
188C2×C4—362no—
189C2×C4—362no—
190C2×C4—362no—
191C2×C4—362no—
192C2×C4C4×C3⋊Dic311yescharacteristic
193C2×C4#375011yescharacteristic
194C2×C4#375011yescharacteristic
195C2×C4#375711yescharacteristic
196C8—42no—
197C2×C3—28no—
198C2×C3—28no—
199C2×C3—44no—
200C2×C3#452714yes—
201C2×C3#455514yes—
202C2×C3#455714yes—
203C22—21no—
204C22—21no—
205C22—21no—
206C22—21no—
207C22—21no—
208C22—21no—
209C22—21no—
210C22—44no—
211C22#6363312yes—
212C22#6365212yes—
213C22#6365811yescharacteristic
214C4—21no—
215C4—21no—
216C4—21no—
217C4—21no—
218C4—364no—
219C4—722no—
220C3#6768214yescomplemented
221C2—22no—
222C2—22no—
223C2—41no—
224C2#1058939311yescharacteristic
225C2#1058942111yescharacteristic
226C2#1058942311yescharacteristic
subgroupG/H
centerC22#63658
commutatorC2×C32×C4C42
FrattiniC23×C4C2×C3⋊D3
FittingC32×#407C2
socleC22×C32#95
prime radicalC24×C32D4
cosocleC23×C32×C4C22
hypercenter#407C3⋊D3
hypocenterC32#1284
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
9. C2×C4×C3⋊Dic3C4semidirect
11. C32×C22⋊C8C4semidirect
14. #63658C4semidirect
40. C3×C22⋊C8Dic3semidirect
108. C22⋊C8C3⋊Dic3semidirect
173. C32#1284semidirect
220. C3#67682semidirect

Maximal subgroups

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

subgroupindex
C32×#4072
#105929102
C4×#37572
#676823