Finite Group Databasebeta

← #11772568

Subgroups — #11772568

Order 1152.

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

normal subgroups only

This group has 498 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
1C32×#410C211yesmaximal, characteristic
2#10592939C211yesmaximal, characteristic
3#10592933C211yesmaximal, characteristic
4#67696—34nomaximal
5C2×C32×#41C2211yescharacteristic
6C32×#117—21no—
7#64135—21no—
8C2×#3748C411yescharacteristic, complemented
9C22×C3⋊(C3⋊C8)C411yescharacteristic, complemented
10C32×#99—21no—
11C32×#99C412yescomplemented
12#63661—21no—
13#63661C412yescomplemented
14#63657—21no—
15#63657—21no—
16C3×#410D314yes—
17#5240—34no—
18#5234—34no—
19C32×#41—41no—
20C32×#41—41no—
21C2×C32×Q8Q811yescharacteristic
22C2×C32×D4C2×C411yescharacteristic
23C2×C32×D4C2×C411yescharacteristic
24C2×C32×D4D411yescharacteristic
25C22×C32×C4C2×C411yescharacteristic
26C22×C32×C4D411yescharacteristic
27C22×C32×C4D411yescharacteristic
28C32×C4⋊C4—41no—
29C32×C22⋊C4—22no—
30C32×C42—41no—
31#3757—22no—
32C4⋊(C3⋊Dic3)—41no—
33C4×C3⋊Dic3—41no—
34#3748—41no—
35C2×C3⋊(C3⋊C8)—21no—
36C2×C3⋊(C3⋊C8)—21no—
37C2×C3⋊(C3⋊C8)—41no—
38#1391—91noSylow
39C2×C3×#41C2×D314yes—
40C3×#117—24no—
41#926—64no—
42C2×#208—34no—
43C22×C3⋊C8—34no—
44C3×#99—24no—
45C3×#99Dic318yescomplemented
46#834—38no—
47#834—64no—
48#830—64no—
49#830—64no—
50C23×C32C4211yescharacteristic
51C23×C32C22⋊C411yescharacteristic
52C23×C32C22⋊C411yescharacteristic
53C32×Q8—41no—
54C32×D4—41no—
55C32×D4—41no—
56C32×D4—41no—
57C2×C32×C4—21no—
58C2×C32×C4—21no—
59C2×C32×C4—21no—
60C2×C32×C4—21no—
61C2×C32×C4—21no—
62C2×C32×C4—21no—
63C2×C32×C4—42no—
64C2×C32×C4C22⋊C411yescharacteristic
65C2×C32×C4C4⋊C411yescharacteristic
66C2×C32×C4C4⋊C411yescharacteristic
67C2×C32×C4C4⋊C411yescharacteristic
68C2×C3⋊Dic3—42no—
69C3⋊(C3⋊C8)—41no—
70C3⋊(C3⋊C8)—41no—
71#410—91no—
72#410C3⋊D311yescharacteristic
73#408—91no—
74C3×#41—44no—
75C3×#41—44no—
76C2×C3×Q8Dic614yes—
77C2×C3×D4C4×D314yes—
78C2×C3×D4C2×Dic314yes—
79C2×C3×D4#6714yes—
80C22×C3×C4C4×D314yes—
81C22×C3×C4D1214yes—
82C22×C3×C4#6714yes—
83C3×C4⋊C4—44no—
84C3×C22⋊C4—28no—
85C3×C42—44no—
86#217—68no—
87C4⋊Dic3—124no—
88C4×Dic3—124no—
89#208—124no—
90C2×C3⋊C8—64no—
91C2×C3⋊C8—64no—
92C2×C3⋊C8—124no—
93C22×C32—21no—
94C22×C32—21no—
95C22×C32—21no—
96C22×C32—41no—
97C22×C32—41no—
98C22×C32—41no—
99C22×C32#9511yescharacteristic
100C32×C4—21no—
101C32×C4—21no—
102C32×C4—21no—
103C32×C4—82no—
104C32×C4#9911yescharacteristic
105C32×C4#9911yescharacteristic
106C3⋊Dic3—82no—
107C2×#41C2×C3⋊D311yescharacteristic
108C2×M16—91no—
109C22×C8—91no—
110#117—21no—
111#117—181no—
112#99—21no—
113#99—92no—
114#99—181no—
115#99C3⋊Dic312yescomplemented
116C22⋊C8—181no—
117C22⋊C8—181no—
118C23×C3C4×Dic314yes—
119C23×C3(C2×D3)⋊C414yes—
120C23×C3#21714yes—
121C3×Q8—44no—
122C3×D4—44no—
123C3×D4—44no—
124C3×D4—44no—
125C2×C3×C4—24no—
126C2×C3×C4—24no—
127C2×C3×C4—24no—
128C2×C3×C4—24no—
129C2×C3×C4—24no—
130C2×C3×C4—24no—
131C2×C3×C4—48no—
132C2×C3×C4Dic3⋊C414yes—
133C2×C3×C4Dic3⋊C414yes—
134C2×C3×C4C4⋊Dic314yes—
135C2×C3×C4(C2×D3)⋊C414yes—
136C2×Dic3—128no—
137C3⋊C8—124no—
138C3⋊C8—124no—
139C2×C32—21no—
140C2×C32—41no—
141C2×C32—41no—
142C2×C32—41no—
143C2×C32#34211yescharacteristic
144#41—41no—
145#41—41no—
146C2×Q8#63411yescharacteristic
147C2×D4C4×C3⋊D311yescharacteristic
148C2×D4C2×C3⋊Dic311yescharacteristic
149C2×D4#63811yescharacteristic
150C22×C4C4×C3⋊D311yescharacteristic
151C22×C4C4⋊(C3⋊D3)11yescharacteristic
152C22×C4#63811yescharacteristic
153M16—361no—
154C2×C8—181no—
155C2×C8—181no—
156C2×C8—361no—
157C4⋊C4—41no—
158C4⋊C4—361no—
159C22⋊C4—22no—
160C22⋊C4—182no—
161C42—41no—
162C42—361no—
163C22×C3—24no—
164C22×C3—24no—
165C22×C3—24no—
166C22×C3—44no—
167C22×C3—44no—
168C22×C3—44no—
169C22×C3C3⋊#9514yes—
170C3×C4—24no—
171C3×C4—24no—
172C3×C4—24no—
173C3×C4—88no—
174C3×C4#80614yes—
175C3×C4#80614yes—
176Dic3—248no—
177C32#139111yescharacteristic, complemented, Sylow
178C23C4×C3⋊Dic311yescharacteristic
179C23#375211yescharacteristic
180C23#375711yescharacteristic
181Q8—41no—
182D4—41no—
183D4—41no—
184D4—41no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—42no—
192C2×C4—362no—
193C2×C4#375011yescharacteristic
194C2×C4#375011yescharacteristic
195C2×C4C4⋊(C3⋊Dic3)11yescharacteristic
196C2×C4#375211yescharacteristic
197C8—361no—
198C8—361no—
199C2×C3—24no—
200C2×C3—44no—
201C2×C3—44no—
202C2×C3—44no—
203C2×C3#452714yes—
204C22—21no—
205C22—21no—
206C22—21no—
207C22—41no—
208C22—41no—
209C22—41no—
210C22#6365811yescharacteristic
211C4—21no—
212C4—21no—
213C4—21no—
214C4—82no—
215C4—722no—
216C4#6363311yescharacteristic
217C4#6363311yescharacteristic
218C3#6769614yescomplemented
219C2—21no—
220C2—41no—
221C2—41no—
222C2—41no—
223C2#1058939311yescharacteristic
subgroupG/H
centerC4#63633
commutatorC23×C32C42
FrattiniC2×#41C2×C3⋊D3
FittingC32×#410C2
socleC2×C32#342
prime radical, cosocleC2×C32×#41C22
hypercenter#410C3⋊D3
hypocenterC32#1391
LCSG ▷ C23×C32 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #410

Complements

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

NH ≅ G/Ntype
8. C2×#3748C4semidirect
9. C22×C3⋊(C3⋊C8)C4semidirect
11. C32×#99C4semidirect
13. #63661C4semidirect
45. C3×#99Dic3semidirect
115. #99C3⋊Dic3semidirect
177. C32#1391semidirect
218. C3#67696semidirect

Maximal subgroups

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

subgroupindex
C32×#4102
#105929392
#105929332
#676963