Finite Group Databasebeta

← #11773824

Subgroups — #11773824

Order 1152.

744 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 744 conjugacy classes of subgroups — too many to draw. Only its 157 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×#64096C211yesmaximal, characteristic
2#10592417C212yesmaximal
3C32×#324C211yesmaximal, characteristic
4#10589394C211yesmaximal, characteristic
5#10589335C212yesmaximal
6#68125—34nomaximal
7C22×#634C411yescharacteristic
8C2×C32×C4⋊C4C2211yescharacteristic
9C2×#3750C411yescharacteristic
10C2×#3750C2211yescharacteristic
11C2×C4×C3⋊Dic3C411yescharacteristic
12C2×C4×C3⋊Dic3C411yescharacteristic
13C2×C4×C3⋊Dic3C2211yescharacteristic
14#64096—22no—
15#64096—22no—
16C32×C22⋊C8C2212yes—
17#63657C2212yes—
18#63641—22no—
19C8×C3⋊Dic3—22no—
20C2×#887—34no—
21#4718—38no—
22C3×#324D314yes—
23#4528—34no—
24#4469—38no—
25C22×C32×C4C2×C411yescharacteristic
26C22×C32×C4C2×C411yescharacteristic
27C22×C32×C4C2311yescharacteristic
28C22×C3⋊Dic3C2×C411yescharacteristic
29C22×C3⋊Dic3C2×C411yescharacteristic
30C22×C3⋊Dic3C2×C411yescharacteristic
31C22×C3⋊Dic3C2×C411yescharacteristic
32C2×#634—22no—
33C2×#634—22no—
34C2×#634C814yescomplemented
35C2×C32×C8—22no—
36C32×C4⋊C4—22no—
37#3750—22no—
38#3750—22no—
39C4×C3⋊Dic3—21no—
40C4×C3⋊Dic3—21no—
41C4×C3⋊Dic3—21no—
42C4×C3⋊Dic3—21no—
43C4×C3⋊Dic3D412yes—
44C4×C3⋊Dic3D412yes—
45C2×C3⋊(C3⋊C8)—22no—
46#1461—91noSylow
47C22×Dic6—34no—
48C2×C3×C4⋊C4C2×D314yes—
49C2×Dic3⋊C4—34no—
50C2×Dic3⋊C4—34no—
51C2×C4×Dic3—34no—
52C2×C4×Dic3—34no—
53C2×C4×Dic3—34no—
54#887—68no—
55#887—68no—
56C3×C22⋊C8C2×D318yes—
57#830—38no—
58Dic3⋊C8—68no—
59C8×Dic3—68no—
60C23×C32C22×C411yescharacteristic
61C2×C32×C4—21no—
62C2×C32×C4—21no—
63C2×C32×C4—21no—
64C2×C32×C4—41no—
65C2×C32×C4—41no—
66C2×C32×C4C2×C812yes—
67C2×C32×C4C2×D412yes—
68C2×C3⋊Dic3—21no—
69C2×C3⋊Dic3—21no—
70C2×C3⋊Dic3—22no—
71C2×C3⋊Dic3—21no—
72C2×C3⋊Dic3—41no—
73C2×C3⋊Dic3C22⋊C411yescharacteristic
74C2×C3⋊Dic3C22⋊C412yes—
75C2×C3⋊Dic3C22⋊C411yescharacteristic
76C2×C3⋊Dic3C2×C812yes—
77C2×C3⋊Dic3C2×C812yes—
78C2×C3⋊Dic3M1612yes—
79#634—28no—
80C32×C8—42no—
81C3⋊(C3⋊C8)—42no—
82C2×C4×Q8—91no—
83#431—92no—
84#324—91no—
85#324—92no—
86#324C3⋊D311yescharacteristic
87C22×C3×C4C4×D314yes—
88C22×C3×C4C4×D314yes—
89C22×C3×C4C22×D314yes—
90C22×Dic3—34no—
91C22×Dic3—34no—
92C22×Dic3—34no—
93C22×Dic3—34no—
94C2×Dic6—316no—
95C2×Dic6—68no—
96C2×Dic6—68no—
97C2×C3×C8—28no—
98C3×C4⋊C4—28no—
99Dic3⋊C4—68no—
100Dic3⋊C4—68no—
101C4×Dic3—38no—
102C4×Dic3—38no—
103C4×Dic3—64no—
104C4×Dic3—64no—
105C4×Dic3—64no—
106C4×Dic3—64no—
107C2×C3⋊C8—68no—
108C22×C32—21no—
109C22×C32—21no—
110C22×C32C2×C22⋊C411yescharacteristic
111C22×C32C22×C811yescharacteristic
112C22×C32C2×M1611yescharacteristic
113C32×C4—22no—
114C32×C4—22no—
115C32×C4—41no—
116C3⋊Dic3—22no—
117C3⋊Dic3—21no—
118C3⋊Dic3—41no—
119C3⋊Dic3C22⋊C814yes—
120C3⋊Dic3#10112yes—
121C22×Q8—91no—
122C4×Q8—182no—
123C4×Q8—182no—
124C2×C4⋊C4—91no—
125C2×C4⋊C4—91no—
126C2×C4⋊C4C2×C3⋊D311yescharacteristic
127C2×C42—91no—
128C2×C42—91no—
129C2×C42—91no—
130C4⋊C8—182no—
131C22⋊C8—92no—
132C22⋊C8C2×C3⋊D312yes—
133C4×C8—182no—
134C23×C3C2×C4×D314yes—
135C2×C3×C4—24no—
136C2×C3×C4—24no—
137C2×C3×C4—24no—
138C2×C3×C4—44no—
139C2×C3×C4—44no—
140C2×C3×C4D3×C818yes—
141C2×C3×C4D3×D418yes—
142C2×Dic3—34no—
143C2×Dic3—38no—
144C2×Dic3—38no—
145C2×Dic3—38no—
146C2×Dic3—34no—
147C2×Dic3—38no—
148C2×Dic3—68no—
149C2×Dic3—64no—
150C2×Dic3—64no—
151C2×Dic3—64no—
152C2×Dic3—124no—
153Dic6—632no—
154C3×C8—48no—
155C3⋊C8—128no—
156C2×C32—21no—
157C2×C32—21no—
158C2×C32C2×C22⋊C811yescharacteristic
159C2×C32#41011yescharacteristic
160C2×C32C2×#10111yescharacteristic
161C2×Q8—94no—
162C2×Q8—182no—
163C2×Q8—182no—
164C22×C4—91no—
165C22×C4—91no—
166C22×C4—91no—
167C22×C4—91no—
168C22×C4C4×C3⋊D311yescharacteristic
169C22×C4C4×C3⋊D311yescharacteristic
170C22×C4C22×C3⋊D311yescharacteristic
171C2×C8—22no—
172C2×C8—182no—
173C4⋊C4—22no—
174C4⋊C4—182no—
175C4⋊C4—182no—
176C42—92no—
177C42—92no—
178C42—181no—
179C42—181no—
180C42—181no—
181C42—181no—
182C22×C3—24no—
183C22×C3—24no—
184C22×C3D3×C22⋊C414yes—
185C22×C3C2×D3×C814yes—
186C22×C3D3×M1614yes—
187C3×C4—28no—
188C3×C4—28no—
189C3×C4—44no—
190Dic3—316no—
191Dic3—38no—
192Dic3—68no—
193Dic3—64no—
194Dic3—124no—
195C32#146111yescharacteristic, complemented, Sylow
196C23C2×C4×C3⋊D311yescharacteristic
197Q8—188no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—91no—
204C2×C4—92no—
205C2×C4—92no—
206C2×C4—92no—
207C2×C4—91no—
208C2×C4—92no—
209C2×C4—182no—
210C2×C4—181no—
211C2×C4—181no—
212C2×C4—181no—
213C2×C4—361no—
214C2×C4C8×C3⋊D312yes—
215C2×C4D4×C3⋊D312yes—
216C8—42no—
217C8—362no—
218C2×C3—24no—
219C2×C3—24no—
220C2×C3D3×C22⋊C814yes—
221C2×C3#474014yes—
222C2×C3D3×#10114yes—
223C22—21no—
224C22—21no—
225C22C22⋊C4×C3⋊D311yescharacteristic
226C22C2×C8×C3⋊D311yescharacteristic
227C22M16×C3⋊D311yescharacteristic
228C4—22no—
229C4—22no—
230C4—41no—
231C4—94no—
232C4—92no—
233C4—182no—
234C4—181no—
235C4—361no—
236C3#6812514yescomplemented
237C2—21no—
238C2—21no—
239C2C3⋊D3×C22⋊C811yescharacteristic
240C2#1059243911yescharacteristic
241C2C3⋊D3×#10111yescharacteristic
subgroupG/H
centerC22C22⋊C4×C3⋊D3
commutatorC22×C32C22×C8
FrattiniC22×C4C22×C3⋊D3
FittingC32×#324C2
socleC22×C32C2×C22⋊C4
prime radicalC23×C32C22×C4
cosocleC22×C32×C4C23
hypercenter#324C3⋊D3
hypocenterC32#1461
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
34. C2×#634C8semidirect
195. C32#1461semidirect
236. C3#68125semidirect

Maximal subgroups

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

subgroupindex
C2×#640962
#105924172
C32×#3242
#105893942
#105893352
#681253