Finite Group Databasebeta

← #11773747

Subgroups — #11773747

Order 1152.

792 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 792 conjugacy classes of subgroups — too many to draw. Only its 155 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×#64086C211yesmaximal, characteristic
2#10592417C212yesmaximal, complemented
3C32×#323C211yesmaximal, characteristic
4#10589391C211yesmaximal, characteristic
5#10589335C212yesmaximal, complemented
6#68100—34nomaximal
7C23×C3⋊Dic3C411yescharacteristic
8C2×C32×C22⋊C4C2211yescharacteristic
9C2×#3757C411yescharacteristic
10C2×#3750C411yescharacteristic
11C2×#3750C2211yescharacteristic
12C2×C4×C3⋊Dic3C411yescharacteristic
13C2×C4×C3⋊Dic3C2211yescharacteristic
14#64086—22no—
15#64086—22no—
16C32×C22⋊C8C2212yes—
17#63657C2212yes—
18#63641—22no—
19C8×C3⋊Dic3—22no—
20C2×#877—34no—
21#4718—38no—
22C3×#323D314yes—
23#4525—34no—
24#4469—38no—
25C24×C32C2×C411yescharacteristic
26C22×C32×C4C2×C411yescharacteristic
27C22×C32×C4C2311yescharacteristic
28C22×C3⋊Dic3—21no—
29C22×C3⋊Dic3—21no—
30C22×C3⋊Dic3—22no—
31C22×C3⋊Dic3C814yescomplemented
32C22×C3⋊Dic3C2×C411yescharacteristic
33C22×C3⋊Dic3C2×C411yescharacteristic
34C22×C3⋊Dic3C2×C411yescharacteristic
35C22×C3⋊Dic3C2×C411yescharacteristic
36C2×C32×C8—22no—
37C32×C22⋊C4—22no—
38#3757—22no—
39#3750—22no—
40#3750—22no—
41C4×C3⋊Dic3—21no—
42C4×C3⋊Dic3—21no—
43C4×C3⋊Dic3D412yes—
44C4×C3⋊Dic3D412yes—
45C2×C3⋊(C3⋊C8)—22no—
46#1458—91noSylow
47C23×Dic3—34no—
48C2×C3×C22⋊C4C2×D314yes—
49C2×#217—34no—
50C2×Dic3⋊C4—34no—
51C2×Dic3⋊C4—34no—
52C2×C4×Dic3—34no—
53C2×C4×Dic3—34no—
54#877—68no—
55#877—68no—
56C3×C22⋊C8C2×D318yes—
57#830—38no—
58Dic3⋊C8—68no—
59C8×Dic3—68no—
60C23×C32—21no—
61C23×C32—21no—
62C23×C32—41no—
63C23×C32—41no—
64C23×C32C2×C812yes—
65C23×C32C22×C411yescharacteristic
66C2×C32×C4—21no—
67C2×C32×C4—41no—
68C2×C32×C4—41no—
69C2×C32×C4C2×D412yes—
70C2×C3⋊Dic3—21no—
71C2×C3⋊Dic3—21no—
72C2×C3⋊Dic3—24no—
73C2×C3⋊Dic3—24no—
74C2×C3⋊Dic3—21no—
75C2×C3⋊Dic3—41no—
76C2×C3⋊Dic3—41no—
77C2×C3⋊Dic3C22⋊C412yes—
78C2×C3⋊Dic3C22⋊C411yescharacteristic
79C2×C3⋊Dic3C22⋊C411yescharacteristic
80C2×C3⋊Dic3C2×C812yes—
81C2×C3⋊Dic3C2×C812yes—
82C2×C3⋊Dic3M1612yes—
83C32×C8—42no—
84C3⋊(C3⋊C8)—42no—
85C2×#117—91no—
86#431—92no—
87#324—92no—
88#323—91no—
89#323C3⋊D311yescharacteristic
90C24×C3C4×D314yes—
91C22×C3×C4C4×D314yes—
92C22×C3×C4C22×D314yes—
93C22×Dic3—34no—
94C22×Dic3—316no—
95C22×Dic3—34no—
96C22×Dic3—34no—
97C22×Dic3—34no—
98C22×Dic3—64no—
99C22×Dic3—64no—
100C22×Dic3—68no—
101C2×C3×C8—28no—
102C3×C22⋊C4—28no—
103#217—68no—
104Dic3⋊C4—68no—
105Dic3⋊C4—68no—
106C4×Dic3—38no—
107C4×Dic3—38no—
108C4×Dic3—64no—
109C4×Dic3—64no—
110C2×C3⋊C8—68no—
111C22×C32—21no—
112C22×C32—21no—
113C22×C32—22no—
114C22×C32—42no—
115C22×C32—42no—
116C22×C32—41no—
117C22×C32—41no—
118C22×C32C2×C22⋊C411yescharacteristic
119C22×C32C22×C811yescharacteristic
120C22×C32C2×M1611yescharacteristic
121C32×C4—22no—
122C32×C4—41no—
123C3⋊Dic3—22no—
124C3⋊Dic3—22no—
125C3⋊Dic3—41no—
126C3⋊Dic3C22⋊C812yes—
127C3⋊Dic3C22⋊C812yes—
128C23×C4—91no—
129#117—182no—
130#117—182no—
131C2×C4⋊C4—91no—
132C2×C4⋊C4—91no—
133C2×C22⋊C4—91no—
134C2×C22⋊C4C2×C3⋊D311yescharacteristic
135C2×C42—91no—
136C2×C42—91no—
137C4⋊C8—182no—
138C22⋊C8—92no—
139C22⋊C8C2×C3⋊D312yes—
140C4×C8—182no—
141C23×C3—24no—
142C23×C3—24no—
143C23×C3—44no—
144C23×C3—44no—
145C23×C3D3×C818yes—
146C23×C3C2×C4×D314yes—
147C2×C3×C4—24no—
148C2×C3×C4—44no—
149C2×C3×C4—44no—
150C2×C3×C4D3×D418yes—
151C2×Dic3—34no—
152C2×Dic3—34no—
153C2×Dic3—38no—
154C2×Dic3—38no—
155C2×Dic3—38no—
156C2×Dic3—38no—
157C2×Dic3—616no—
158C2×Dic3—616no—
159C2×Dic3—64no—
160C2×Dic3—64no—
161C2×Dic3—64no—
162C2×Dic3—124no—
163C2×Dic3—124no—
164C3×C8—48no—
165C3⋊C8—128no—
166C2×C32—21no—
167C2×C32—21no—
168C2×C32—42no—
169C2×C32C2×C22⋊C811yescharacteristic
170C2×C32#41011yescharacteristic
171C2×C32#41311yescharacteristic
172C24C4×C3⋊D311yescharacteristic
173C22×C4—91no—
174C22×C4—94no—
175C22×C4—91no—
176C22×C4—91no—
177C22×C4—91no—
178C22×C4—181no—
179C22×C4—181no—
180C22×C4—182no—
181C22×C4C4×C3⋊D311yescharacteristic
182C22×C4C22×C3⋊D311yescharacteristic
183C2×C8—22no—
184C2×C8—182no—
185C4⋊C4—182no—
186C4⋊C4—182no—
187C22⋊C4—22no—
188C22⋊C4—182no—
189C42—92no—
190C42—92no—
191C42—181no—
192C42—181no—
193C22×C3—24no—
194C22×C3—24no—
195C22×C3—28no—
196C22×C3—48no—
197C22×C3—48no—
198C22×C3—44no—
199C22×C3—44no—
200C22×C3D3×C22⋊C414yes—
201C22×C3C2×D3×C814yes—
202C22×C3D3×M1614yes—
203C3×C4—28no—
204C3×C4—44no—
205Dic3—38no—
206Dic3—38no—
207Dic3—68no—
208Dic3—68no—
209Dic3—124no—
210C32#145811yescharacteristic, complemented, Sylow
211C23—21no—
212C23—21no—
213C23—41no—
214C23—41no—
215C23C8×C3⋊D312yes—
216C23C2×C4×C3⋊D311yescharacteristic
217C2×C4—21no—
218C2×C4—41no—
219C2×C4—41no—
220C2×C4—91no—
221C2×C4—91no—
222C2×C4—92no—
223C2×C4—92no—
224C2×C4—92no—
225C2×C4—92no—
226C2×C4—184no—
227C2×C4—184no—
228C2×C4—181no—
229C2×C4—181no—
230C2×C4—181no—
231C2×C4—361no—
232C2×C4—361no—
233C2×C4D4×C3⋊D312yes—
234C8—42no—
235C8—362no—
236C2×C3—24no—
237C2×C3—24no—
238C2×C3—48no—
239C2×C3D3×C22⋊C814yes—
240C2×C3#474014yes—
241C2×C3#474514yes—
242C22—21no—
243C22—21no—
244C22—22no—
245C22—42no—
246C22—42no—
247C22—41no—
248C22—41no—
249C22C22⋊C4×C3⋊D311yescharacteristic
250C22C2×C8×C3⋊D311yescharacteristic
251C22M16×C3⋊D311yescharacteristic
252C4—22no—
253C4—41no—
254C4—92no—
255C4—92no—
256C4—182no—
257C4—182no—
258C4—361no—
259C3#6810014yescomplemented
260C2—21no—
261C2—21no—
262C2—42no—
263C2C3⋊D3×C22⋊C811yescharacteristic
264C2#1059243911yescharacteristic
265C2#1059244411yescharacteristic
subgroupG/H
centerC22C22⋊C4×C3⋊D3
commutatorC22×C32C22×C8
FrattiniC22×C4C22×C3⋊D3
FittingC32×#323C2
socleC22×C32C2×C22⋊C4
prime radicalC24×C32C2×C4
cosocleC22×C32×C4C23
hypercenter#323C3⋊D3
hypocenterC32#1458
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #10592417C2semidirect
5. #10589335C2semidirect
31. C22×C3⋊Dic3C8semidirect
210. C32#1458semidirect
259. C3#68100semidirect

Maximal subgroups

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

subgroupindex
C2×#640862
#105924172
C32×#3232
#105893912
#105893352
#681003