Finite Group Databasebeta

← #11775732

Subgroups — #11775732

Order 1152.

810 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 810 conjugacy classes of subgroups — too many to draw. Only its 123 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
1#10596139C211yesmaximal, characteristic
2#10592406C212yesmaximal, complemented
3C32×#329C211yesmaximal, characteristic, complemented
4#10589406C211yesmaximal, characteristic, complemented
5#10589330C212yesmaximal, complemented
6#68342—34nomaximal
7C2×#3832C411yescharacteristic
8C2×#3830C411yescharacteristic
9C32×#124C2211yescharacteristic
10#64153C411yescharacteristic
11#64149C411yescharacteristic
12C2×#3743—22no—
13#64093—22no—
14#64090—22no—
15#64084C2211yescharacteristic
16C42×C3⋊D3C2211yescharacteristic
17C32×#97C2212yes—
18C8×C3⋊Dic3—22no—
19#63630C2212yes—
20#5668—34no—
21#4707—38no—
22C3×#329D314yescomplemented
23#4540—34no—
24#4464—38no—
25C2×C32×Q8C2×C411yescharacteristic
26C2×C32×D4C2×C411yescharacteristic
27C2×#638—21no—
28C2×#638—22no—
29C22×C3⋊Dic3—21no—
30#3832—42no—
31#3830—42no—
32C2×C4⋊(C3⋊D3)—21no—
33C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
34C2×C4×C3⋊D3—21no—
35C2×C4×C3⋊D3C2×C411yescharacteristic
36C2×C4×C3⋊D3D412yes—
37C2×#634C2×C411yescharacteristic
38C2×C32×C8—22no—
39C32×C22⋊C4—22no—
40C32×C42C2311yescharacteristic
41#3752—22no—
42#3750—22no—
43C4×C3⋊Dic3C2×C411yescharacteristic
44C4×C3⋊Dic3D412yes—
45C2×C3⋊(C3⋊C8)—22no—
46#3743—28no—
47#1525—91noSylow
48C2×#239—34no—
49C2×#237—34no—
50C3×#124C2×D314yes—
51#944—34no—
52#940—34no—
53C2×ΓL(1,𝔽25)—68no—
54#884—68no—
55#67⋊C4—68no—
56#875—34no—
57C42×D3—34no—
58C3×#97C2×D318yes—
59C8×Dic3—68no—
60#803—38no—
61C23×C32—21no—
62C22×C3⋊D3—21no—
63C22×C3⋊D3C22⋊C411yescharacteristic
64C32×Q8—41no—
65C32×D4—41no—
66C2×C32×C4—21no—
67C2×C32×C4C22×C411yescharacteristic
68C2×C32×C4C2×D412yes—
69#638—42no—
70#638—44no—
71C2×C3⋊Dic3—21no—
72C2×C3⋊Dic3—42no—
73C2×C3⋊Dic3C22⋊C411yescharacteristic
74C2×C3⋊Dic3C22⋊C412yes—
75C4⋊(C3⋊D3)—41no—
76C4⋊(C3⋊D3)—42no—
77C4×C3⋊D3—22no—
78C4×C3⋊D3—24no—
79C4×C3⋊D3—42no—
80#634—41no—
81C32×C8—24no—
82C3⋊(C3⋊C8)—24no—
83#532—91no—
84C4×M16—92no—
85#329—91no—
86#329—92no—
87#329C3⋊D311yescharacteristic, complemented
88C2×C3×Q8C4×D314yes—
89C2×C3×D4C4×D314yes—
90C2×#67—68no—
91C2×#67—64no—
92C22×Dic3—64no—
93#239—128no—
94#237—128no—
95C2×D12—34no—
96C2×D12—64no—
97C2×C4×D3—34no—
98C2×C4×D3—38no—
99C2×C4×D3—64no—
100C2×Dic6—34no—
101C2×C3×C8—28no—
102C3×C22⋊C4—28no—
103C3×C42C22×D314yes—
104(C2×D3)⋊C4—68no—
105Dic3⋊C4—68no—
106C4×Dic3—34no—
107C4×Dic3—38no—
108C2×C3⋊C8—68no—
109ΓL(1,𝔽25)—632no—
110C22×C32—41no—
111C22×C32—42no—
112C22×C32C2×C22⋊C411yescharacteristic
113C2×C3⋊D3—21no—
114C2×C3⋊D3—22no—
115C2×C3⋊D3—41no—
116C2×C3⋊D3—42no—
117C32×C4—21no—
118C32×C4—22no—
119C32×C4—41no—
120C3⋊Dic3—41no—
121C3⋊Dic3#10012yes—
122C3⋊Dic3#10414yes—
123C2×#41—91no—
124C2×#41—91no—
125C2×M16—182no—
126C4⋊Q8—91no—
127#127—91no—
128#124—91no—
129#124C2×C3⋊D311yescharacteristic
130#121—182no—
131C4×D4—182no—
132C2×C42—91no—
133#97—92no—
134#97C2×C3⋊D312yes—
135C4×C8—182no—
136C23×C3—24no—
137C22×D3—34no—
138C22×D3—64no—
139C3×Q8—44no—
140C3×D4—44no—
141C2×C3×C4—24no—
142C2×C3×C4C2×C4×D314yes—
143C2×C3×C4D3×D418yes—
144#67—1216no—
145#67—128no—
146C2×Dic3—38no—
147C2×Dic3—34no—
148C2×Dic3—64no—
149C2×Dic3—128no—
150D12—124no—
151D12—128no—
152C4×D3—616no—
153C4×D3—68no—
154C4×D3—128no—
155Dic6—124no—
156C3×C8—216no—
157C3⋊C8—616no—
158C2×C32—81no—
159C2×C32C2×#10011yescharacteristic
160C2×C32C2×#10412yes—
161C3⋊D3—41no—
162C3⋊D3—81no—
163#41—362no—
164#41—362no—
165C2×Q8—91no—
166C2×Q8C4×C3⋊D311yescharacteristic
167C2×D4—91no—
168C2×D4—181no—
169C2×D4—182no—
170C2×D4—181no—
171C2×D4C4×C3⋊D311yescharacteristic
172C22×C4—91no—
173C22×C4—92no—
174C22×C4—181no—
175C22×C4—181no—
176M16—188no—
177C2×C8—22no—
178C2×C8—182no—
179C4⋊C4—182no—
180C22⋊C4—22no—
181C22⋊C4—182no—
182C42—91no—
183C42—92no—
184C42C22×C3⋊D311yescharacteristic
185C22×C3—44no—
186C22×C3—48no—
187C22×C3D3×C22⋊C414yes—
188C2×D3—64no—
189C2×D3—68no—
190C2×D3—124no—
191C2×D3—128no—
192C3×C4—24no—
193C3×C4—28no—
194C3×C4—44no—
195Dic3—38no—
196Dic3—316no—
197Dic3—124no—
198C32#152511yescharacteristic, complemented, Sylow
199C23—21no—
200C23—91no—
201C23—181no—
202Q8—41no—
203Q8—361no—
204D4—41no—
205D4—361no—
206D4—362no—
207D4—364no—
208D4—362no—
209C2×C4—21no—
210C2×C4—92no—
211C2×C4—91no—
212C2×C4—184no—
213C2×C4—182no—
214C2×C4—181no—
215C2×C4—362no—
216C2×C4—362no—
217C2×C4C2×C4×C3⋊D311yescharacteristic
218C2×C4D4×C3⋊D312yes—
219C8—24no—
220C8—184no—
221C2×C3—84no—
222C2×C3D3×#10014yes—
223C2×C3D3×#10418yes—
224D3—124no—
225D3—244no—
226C22—42no—
227C22—41no—
228C22—182no—
229C22—181no—
230C22—362no—
231C22—361no—
232C22C22⋊C4×C3⋊D311yescharacteristic
233C4—22no—
234C4—21no—
235C4—41no—
236C4—94no—
237C4—92no—
238C4—361no—
239C3#6834214yescomplemented
240C2—81no—
241C2—361no—
242C2—721no—
243C2C3⋊D3×#10011yescharacteristic
244C2C3⋊D3×#10412yes—
subgroupG/H
centerC22C22⋊C4×C3⋊D3
commutatorC2×C32×C4C22×C4
FrattiniC42C22×C3⋊D3
FittingC32×#329C2
socleC22×C32C2×C22⋊C4
prime radical#10596139C2
cosocleC32×C42C23
hypercenter#329C3⋊D3
hypocenterC32#1525
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #10592406C2semidirect
3. C32×#329C2semidirect
4. #10589406C2semidirect
5. #10589330C2semidirect
22. C3×#329D3semidirect
87. #329C3⋊D3semidirect
198. C32#1525semidirect
239. C3#68342semidirect

Maximal subgroups

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

subgroupindex
#105961392
#105924062
C32×#3292
#105894062
#105893302
#683423