Finite Group Databasebeta

← #11773891

Subgroups — #11773891

Order 1152.

756 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 756 conjugacy classes of subgroups — too many to draw. Only its 143 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×#64101C211yesmaximal, characteristic
2#10592418C212yesmaximal, complemented
3C32×#324C211yesmaximal, characteristic, complemented
4#10589394C211yesmaximal, characteristic, complemented
5#10589334C212yesmaximal
6#68126—34nomaximal
7C22×C4×C3⋊D3C411yescharacteristic
8C2×C32×C4⋊C4C2211yescharacteristic
9C2×#3752C411yescharacteristic
10C2×#3752C2211yescharacteristic
11C2×C4⋊(C3⋊Dic3)C411yescharacteristic
12C2×C4×C3⋊Dic3C411yescharacteristic
13C2×C4×C3⋊Dic3C2211yescharacteristic
14#64101—22no—
15#64101—22no—
16C32×C22⋊C8C2212yes—
17#63657C2212yes—
18#63642—22no—
19#63641—22no—
20C2×#892—34no—
21#4719—38no—
22C3×#324D314yescomplemented
23#4528—34no—
24#4468—38no—
25C23×C3⋊D3C2×C411yescharacteristic
26C22×C32×C4C2×C411yescharacteristic
27C22×C32×C4C2×C411yescharacteristic
28C22×C32×C4C2311yescharacteristic
29C22×C3⋊Dic3C2×C411yescharacteristic
30C22×C3⋊Dic3C2×C411yescharacteristic
31C22×C3⋊Dic3C2×C411yescharacteristic
32C2×C4×C3⋊D3—22no—
33C2×C4×C3⋊D3—22no—
34C2×C4×C3⋊D3—21no—
35C2×C4×C3⋊D3—21no—
36C2×C32×C8—22no—
37C32×C4⋊C4—22no—
38#3752—22no—
39#3752—22no—
40C4⋊(C3⋊Dic3)—22no—
41C4×C3⋊Dic3—21no—
42C4×C3⋊Dic3—21no—
43C4×C3⋊Dic3D412yes—
44C4×C3⋊Dic3D412yes—
45C2×C3⋊(C3⋊C8)—22no—
46#1464—91noSylow
47C22×C4×D3—34no—
48C2×C3×C4⋊C4C2×D314yes—
49C2×(C2×D3)⋊C4—34no—
50C2×(C2×D3)⋊C4—34no—
51C2×C4⋊Dic3—34no—
52C2×C4×Dic3—34no—
53C2×C4×Dic3—34no—
54#892—68no—
55#892—68no—
56C3×C22⋊C8C2×D318yes—
57#830—38no—
58#815—68no—
59Dic3⋊C8—68no—
60C23×C32C22×C411yescharacteristic
61C22×C3⋊D3—21no—
62C22×C3⋊D3—21no—
63C22×C3⋊D3—41no—
64C22×C3⋊D3—41no—
65C22×C3⋊D3M1612yes—
66C2×C32×C4—21no—
67C2×C32×C4—21no—
68C2×C32×C4—21no—
69C2×C32×C4—41no—
70C2×C32×C4—41no—
71C2×C32×C4M1612yes—
72C2×C32×C4C2×D412yes—
73C2×C3⋊Dic3—21no—
74C2×C3⋊Dic3—21no—
75C2×C3⋊Dic3—21no—
76C2×C3⋊Dic3—41no—
77C2×C3⋊Dic3—41no—
78C2×C3⋊Dic3C22⋊C411yescharacteristic
79C2×C3⋊Dic3C22⋊C411yescharacteristic
80C2×C3⋊Dic3C22⋊C412yes—
81C4×C3⋊D3—24no—
82C4×C3⋊D3—24no—
83C32×C8—42no—
84C3⋊(C3⋊C8)—42no—
85C2×#117—91no—
86#432—92no—
87#324—91no—
88#324C3⋊D311yescharacteristic, complemented
89#323—92no—
90C23×D3—34no—
91C22×C3×C4C4×D314yes—
92C22×C3×C4C4×D314yes—
93C22×C3×C4C22×D314yes—
94C22×Dic3—34no—
95C22×Dic3—34no—
96C22×Dic3—34no—
97C2×C4×D3—64no—
98C2×C4×D3—64no—
99C2×C4×D3—68no—
100C2×C4×D3—68no—
101C2×C3×C8—28no—
102C3×C4⋊C4—28no—
103(C2×D3)⋊C4—68no—
104(C2×D3)⋊C4—68no—
105C4⋊Dic3—68no—
106C4×Dic3—38no—
107C4×Dic3—38no—
108C4×Dic3—64no—
109C4×Dic3—64no—
110C2×C3⋊C8—68no—
111C22×C32—21no—
112C22×C32—21no—
113C22×C32C2×C22⋊C411yescharacteristic
114C22×C32C2×M1611yescharacteristic
115C22×C32C2×M1611yescharacteristic
116C2×C3⋊D3—22no—
117C2×C3⋊D3—42no—
118C2×C3⋊D3—41no—
119C2×C3⋊D3—41no—
120C2×C3⋊D3—42no—
121C32×C4—22no—
122C32×C4—22no—
123C32×C4—41no—
124C3⋊Dic3—21no—
125C3⋊Dic3—21no—
126C3⋊Dic3—22no—
127C3⋊Dic3—41no—
128C23×C4—91no—
129#117—182no—
130#117—182no—
131C2×C4⋊C4—91no—
132C2×C4⋊C4C2×C3⋊D311yescharacteristic
133C2×C22⋊C4—91no—
134C2×C22⋊C4—91no—
135C2×C42—91no—
136C2×C42—91no—
137C4⋊C8—182no—
138C22⋊C8—92no—
139C22⋊C8C2×C3⋊D312yes—
140#97—182no—
141C23×C3C2×C4×D314yes—
142C22×D3—38no—
143C22×D3—64no—
144C22×D3—64no—
145C22×D3—124no—
146C22×D3—124no—
147C2×C3×C4—24no—
148C2×C3×C4—24no—
149C2×C3×C4—24no—
150C2×C3×C4—44no—
151C2×C3×C4—44no—
152C2×C3×C4ΓL(1,𝔽25)18yes—
153C2×C3×C4D3×D418yes—
154C2×Dic3—34no—
155C2×Dic3—34no—
156C2×Dic3—38no—
157C2×Dic3—64no—
158C2×Dic3—64no—
159C2×Dic3—64no—
160C2×Dic3—124no—
161C2×Dic3—124no—
162C4×D3—616no—
163C4×D3—616no—
164C3×C8—48no—
165C3⋊C8—128no—
166C2×C32—21no—
167C2×C32—21no—
168C2×C32#40711yescharacteristic
169C2×C32#41011yescharacteristic
170C2×C32#41311yescharacteristic
171C3⋊D3—42no—
172C24—91no—
173C22×C4—91no—
174C22×C4—91no—
175C22×C4—91no—
176C22×C4—181no—
177C22×C4—181no—
178C22×C4—182no—
179C22×C4—182no—
180C22×C4C4×C3⋊D311yescharacteristic
181C22×C4C4×C3⋊D311yescharacteristic
182C22×C4C22×C3⋊D311yescharacteristic
183C2×C8—22no—
184C2×C8—182no—
185C4⋊C4—22no—
186C4⋊C4—182no—
187C22⋊C4—182no—
188C22⋊C4—182no—
189C42—92no—
190C42—92no—
191C42—181no—
192C42—181no—
193C22×C3—24no—
194C22×C3—24no—
195C22×C3D3×C22⋊C414yes—
196C22×C3C2×ΓL(1,𝔽25)14yes—
197C22×C3D3×M1614yes—
198C2×D3—68no—
199C2×D3—128no—
200C2×D3—124no—
201C2×D3—124no—
202C2×D3—128no—
203C3×C4—28no—
204C3×C4—28no—
205C3×C4—44no—
206Dic3—64no—
207Dic3—64no—
208Dic3—68no—
209Dic3—124no—
210C32#146411yescharacteristic, complemented, Sylow
211C23—92no—
212C23—181no—
213C23—181no—
214C23—361no—
215C23—361no—
216C23C2×C4×C3⋊D311yescharacteristic
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—41no—
221C2×C4—41no—
222C2×C4—91no—
223C2×C4—91no—
224C2×C4—92no—
225C2×C4—184no—
226C2×C4—184no—
227C2×C4—181no—
228C2×C4—181no—
229C2×C4—181no—
230C2×C4—361no—
231C2×C4—361no—
232C2×C4#374312yes—
233C2×C4D4×C3⋊D312yes—
234C8—42no—
235C8—362no—
236C2×C3—24no—
237C2×C3—24no—
238C2×C3#472614yes—
239C2×C3#474014yes—
240C2×C3#475114yes—
241D3—128no—
242C22—21no—
243C22—21no—
244C22—182no—
245C22—362no—
246C22—362no—
247C22—361no—
248C22—361no—
249C22C22⋊C4×C3⋊D311yescharacteristic
250C22C2×#374311yescharacteristic
251C22M16×C3⋊D311yescharacteristic
252C4—22no—
253C4—22no—
254C4—41no—
255C4—181no—
256C4—181no—
257C4—182no—
258C4—361no—
259C3#6812614yescomplemented
260C2—21no—
261C2—21no—
262C2—362no—
263C2#1059242511yescharacteristic
264C2#1059243911yescharacteristic
265C2#1059245011yescharacteristic
subgroupG/H
centerC22C22⋊C4×C3⋊D3
commutatorC23×C32C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#324C2
socleC22×C32C2×C22⋊C4
prime radicalC23×C3⋊D3C2×C4
cosocleC22×C32×C4C23
hypercenter#324C3⋊D3
hypocenterC32#1464
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #10592418C2semidirect
3. C32×#324C2semidirect
4. #10589394C2semidirect
22. C3×#324D3semidirect
88. #324C3⋊D3semidirect
210. C32#1464semidirect
259. C3#68126semidirect

Maximal subgroups

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

subgroupindex
C2×#641012
#105924182
C32×#3242
#105893942
#105893342
#681263