Finite Group Databasebeta

← #11773868

Subgroups — #11773868

Order 1152.

936 conjugacy classes of subgroups; only the 197 normal subgroups are shown.

normal subgroups only

This group has 936 conjugacy classes of subgroups — too many to draw. Only its 197 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
1C22×#3750C211yesmaximal, characteristic
2C32×#407C211yesmaximal, characteristic
3#10592906C211yesmaximal, characteristic
4#10589335C214yesmaximal, complemented
5#69971—34nomaximal
6C23×C32×C4C2211yescharacteristic
7C23×C3⋊Dic3C411yescharacteristic
8C23×C3⋊Dic3C411yescharacteristic
9C2×C32×M16—21no—
10C2×#3750—21no—
11C2×#3750—21no—
12C2×#3750—21no—
13C2×#3750—21no—
14C2×#3750C412yes—
15C2×#3750C2212yes—
16C2×#3748—21no—
17C32×C22⋊C8—21no—
18C32×C22⋊C8C2212yes—
19#63657—21no—
20#63657C2212yes—
21C22×Dic3⋊C4—34no—
22C3×#407D314yes—
23#5207—34no—
24#4469—316no—
25C24×C32C2×C411yescharacteristic
26C22×C32×C4—42no—
27C22×C32×C4C2×C411yescharacteristic
28C22×C32×C4D411yescharacteristic
29C22×C32×C4D411yescharacteristic
30C22×C32×C4D411yescharacteristic
31C22×C32×C4D411yescharacteristic
32C22×C32×C4C2311yescharacteristic
33C22×C3⋊Dic3—21no—
34C22×C3⋊Dic3—21no—
35C22×C3⋊Dic3—24no—
36C22×C3⋊Dic3—21no—
37C22×C3⋊Dic3—21no—
38C22×C3⋊Dic3—42no—
39C22×C3⋊Dic3C2×C412yes—
40C22×C3⋊Dic3C2×C412yes—
41C32×M16—42no—
42C2×C32×C8—22no—
43#3750—22no—
44#3750—22no—
45#3750—22no—
46#3750—22no—
47#3748—42no—
48C2×C3⋊(C3⋊C8)—22no—
49#1463—91noSylow
50C23×C3×C4C2×D314yes—
51C23×Dic3—34no—
52C23×Dic3—34no—
53C2×C3×M16—24no—
54C2×Dic3⋊C4—38no—
55C2×Dic3⋊C4—38no—
56C2×Dic3⋊C4—64no—
57C2×Dic3⋊C4—64no—
58C2×Dic3⋊C4—64no—
59C2×Dic3⋊C4—64no—
60C2×#208—64no—
61C3×C22⋊C8—24no—
62C3×C22⋊C8C2×D318yes—
63#830—38no—
64#830—64no—
65C23×C32—22no—
66C23×C32—22no—
67C23×C32—22no—
68C23×C32C22⋊C411yescharacteristic
69C23×C32C22⋊C411yescharacteristic
70C23×C32C22×C411yescharacteristic
71C2×C32×C4—22no—
72C2×C32×C4—22no—
73C2×C32×C4—41no—
74C2×C32×C4—41no—
75C2×C32×C4—41no—
76C2×C32×C4—41no—
77C2×C32×C4C22⋊C411yescharacteristic
78C2×C32×C4C22⋊C411yescharacteristic
79C2×C32×C4C2×D411yescharacteristic
80C2×C32×C4C2×D411yescharacteristic
81C2×C3⋊Dic3—24no—
82C2×C3⋊Dic3—24no—
83C2×C3⋊Dic3—22no—
84C2×C3⋊Dic3—22no—
85C2×C3⋊Dic3—22no—
86C2×C3⋊Dic3—42no—
87C2×C3⋊Dic3—42no—
88C2×C3⋊Dic3—42no—
89C2×C3⋊Dic3M1614yescomplemented
90C32×C8—42no—
91C3⋊(C3⋊C8)—42no—
92C22×C4⋊C4—91no—
93#407—91no—
94#407C3⋊D311yescharacteristic
95#324—94no—
96C24×C3C4×D314yes—
97C22×C3×C4—48no—
98C22×C3×C4C4×D314yes—
99C22×C3×C4D1214yes—
100C22×C3×C4D1214yes—
101C22×C3×C4#6714yes—
102C22×C3×C4#6714yes—
103C22×C3×C4C22×D314yes—
104C22×Dic3—38no—
105C22×Dic3—38no—
106C22×Dic3—616no—
107C22×Dic3—64no—
108C22×Dic3—64no—
109C22×Dic3—64no—
110C22×Dic3—64no—
111C22×Dic3—128no—
112C3×M16—48no—
113C2×C3×C8—28no—
114Dic3⋊C4—68no—
115Dic3⋊C4—68no—
116Dic3⋊C4—68no—
117Dic3⋊C4—68no—
118#208—128no—
119C2×C3⋊C8—68no—
120C22×C32—28no—
121C22×C32—21no—
122C22×C32—21no—
123C22×C32—21no—
124C22×C32—21no—
125C22×C32—21no—
126C22×C32—21no—
127C22×C32#9912yes—
128C22×C32#10112yes—
129C22×C32C2×C22⋊C411yescharacteristic
130C22×C32C2×M1612yes—
131C32×C4—21no—
132C32×C4—21no—
133C32×C4—21no—
134C32×C4—21no—
135C3⋊Dic3—24no—
136C3⋊Dic3—42no—
137C23×C4—91no—
138C23×C4—91no—
139C23×C4C2×C3⋊D311yescharacteristic
140C2×M16—21no—
141C2×M16—181no—
142C2×C4⋊C4—92no—
143C2×C4⋊C4—92no—
144C2×C4⋊C4—181no—
145C2×C4⋊C4—181no—
146C2×C4⋊C4—181no—
147C2×C4⋊C4—181no—
148C22⋊C8—21no—
149C22⋊C8—92no—
150C22⋊C8—181no—
151C22⋊C8C2×C3⋊D312yes—
152C23×C3—28no—
153C23×C3—28no—
154C23×C3—28no—
155C23×C3(C2×D3)⋊C414yes—
156C23×C3(C2×D3)⋊C414yes—
157C23×C3C2×C4×D314yes—
158C2×C3×C4—28no—
159C2×C3×C4—28no—
160C2×C3×C4—44no—
161C2×C3×C4—44no—
162C2×C3×C4—44no—
163C2×C3×C4—44no—
164C2×C3×C4(C2×D3)⋊C414yes—
165C2×C3×C4(C2×D3)⋊C414yes—
166C2×C3×C4C2×D1214yes—
167C2×C3×C4C2×#6714yes—
168C2×Dic3—316no—
169C2×Dic3—616no—
170C2×Dic3—616no—
171C2×Dic3—68no—
172C2×Dic3—68no—
173C2×Dic3—68no—
174C2×Dic3—128no—
175C2×Dic3—128no—
176C2×Dic3—128no—
177C3×C8—48no—
178C3⋊C8—128no—
179C2×C32—22no—
180C2×C32—22no—
181C2×C32—22no—
182C2×C32#40711yescharacteristic
183C2×C32C2×#9911yescharacteristic
184C2×C32C2×#10111yescharacteristic
185C24C4×C3⋊D311yescharacteristic
186C22×C4—42no—
187C22×C4—92no—
188C22×C4—92no—
189C22×C4—184no—
190C22×C4—181no—
191C22×C4—181no—
192C22×C4—181no—
193C22×C4—181no—
194C22×C4—362no—
195C22×C4C4×C3⋊D311yescharacteristic
196C22×C4C4⋊(C3⋊D3)11yescharacteristic
197C22×C4C4⋊(C3⋊D3)11yescharacteristic
198C22×C4#63811yescharacteristic
199C22×C4#63811yescharacteristic
200C22×C4C22×C3⋊D311yescharacteristic
201M16—42no—
202M16—362no—
203C2×C8—22no—
204C2×C8—182no—
205C4⋊C4—182no—
206C4⋊C4—182no—
207C4⋊C4—182no—
208C4⋊C4—182no—
209C22×C3—232no—
210C22×C3—24no—
211C22×C3—24no—
212C22×C3—24no—
213C22×C3—24no—
214C22×C3—24no—
215C22×C3—24no—
216C22×C3#80618yes—
217C22×C3#82418yes—
218C22×C3D3×M1618yes—
219C22×C3C2×(C2×D3)⋊C414yes—
220C3×C4—24no—
221C3×C4—24no—
222C3×C4—24no—
223C3×C4—24no—
224Dic3—616no—
225Dic3—128no—
226C32#146311yescharacteristic, complemented, Sylow
227C23—22no—
228C23—22no—
229C23—22no—
230C23#375211yescharacteristic
231C23#375211yescharacteristic
232C23C2×C4×C3⋊D311yescharacteristic
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—94no—
240C2×C4—184no—
241C2×C4—184no—
242C2×C4—182no—
243C2×C4—182no—
244C2×C4—182no—
245C2×C4—362no—
246C2×C4—362no—
247C2×C4—362no—
248C2×C4#375211yescharacteristic
249C2×C4#375211yescharacteristic
250C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
251C2×C4C2×#63811yescharacteristic
252C8—42no—
253C8—362no—
254C2×C3—28no—
255C2×C3—28no—
256C2×C3—28no—
257C2×C3C2×#80614yes—
258C2×C3#512614yes—
259C2×C3C2×#82414yes—
260C22—28no—
261C22—21no—
262C22—21no—
263C22—21no—
264C22—21no—
265C22—21no—
266C22—21no—
267C22#6363312yes—
268C22#6365112yes—
269C22M16×C3⋊D312yes—
270C22C2×#375211yescharacteristic
271C4—21no—
272C4—21no—
273C4—21no—
274C4—21no—
275C4—184no—
276C4—362no—
277C3#6997114yescomplemented
278C2—22no—
279C2—22no—
280C2—22no—
281C2C2×#6363311yescharacteristic
282C2#1059282511yescharacteristic
283C2C2×#6365111yescharacteristic
subgroupG/H
centerC22C2×#3752
commutatorC23×C32C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#407C2
socleC22×C32C2×C22⋊C4
prime radicalC24×C32C2×C4
cosocleC22×C32×C4C23
hypercenter#407C3⋊D3
hypocenterC32#1463
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
4. #10589335C2semidirect
89. C2×C3⋊Dic3M16semidirect
226. C32#1463semidirect
277. C3#69971semidirect

Maximal subgroups

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

subgroupindex
C22×#37502
C32×#4072
#105929062
#105893352
#699713