Finite Group Databasebeta

← #11773912

Subgroups — #11773912

Order 1152.

948 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 948 conjugacy classes of subgroups — too many to draw. Only its 145 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×#64090C211yesmaximal, characteristic
2#10592425C212yesmaximal, complemented
3C32×#323C211yesmaximal, characteristic, complemented
4#10589391C211yesmaximal, characteristic, complemented
5#10589335C212yesmaximal, complemented
6#68121—34nomaximal
7C22×#638C411yescharacteristic
8C23×C3⋊Dic3C411yescharacteristic
9C22×C4×C3⋊D3C2211yescharacteristic
10C2×C32×C22⋊C4C2211yescharacteristic
11C2×#3752C411yescharacteristic
12C2×#3750C2211yescharacteristic
13C2×C4×C3⋊Dic3C411yescharacteristic
14C2×#3743—22no—
15#64090—22no—
16#64090—22no—
17C32×C22⋊C8C2212yes—
18#63657C2212yes—
19#63647—22no—
20C2×#67⋊C4—34no—
21#4726—38no—
22C3×#323D314yescomplemented
23#4525—34no—
24#4469—38no—
25C24×C32C2×C411yescharacteristic
26C23×C3⋊D3C2×C411yescharacteristic
27C22×C32×C4C2×C411yescharacteristic
28C22×C32×C4C2311yescharacteristic
29C2×#638—22no—
30C2×#638—22no—
31C2×#638—22no—
32C22×C3⋊Dic3—21no—
33C22×C3⋊Dic3—21no—
34C22×C3⋊Dic3—42no—
35C22×C3⋊Dic3C2×C411yescharacteristic
36C22×C3⋊Dic3C2×C411yescharacteristic
37C22×C3⋊Dic3C2×C411yescharacteristic
38C2×C4×C3⋊D3—42no—
39C2×C4×C3⋊D3D412yes—
40C2×C4×C3⋊D3D412yes—
41C2×C32×C8—22no—
42C32×C22⋊C4—22no—
43#3752—22no—
44#3750—22no—
45C4×C3⋊Dic3—21no—
46C4×C3⋊Dic3—21no—
47C2×C3⋊(C3⋊C8)—22no—
48#3743—44no—
49#1465—91noSylow
50C22×#67—34no—
51C23×Dic3—34no—
52C22×C4×D3—34no—
53C2×C3×C22⋊C4C2×D314yes—
54C2×(C2×D3)⋊C4—34no—
55C2×Dic3⋊C4—34no—
56C2×C4×Dic3—34no—
57C2×ΓL(1,𝔽25)—68no—
58#67⋊C4—68no—
59#67⋊C4—68no—
60C3×C22⋊C8C2×D318yes—
61#830—38no—
62(C2×D3)⋊C8—68no—
63C23×C32—21no—
64C23×C32—21no—
65C23×C32—41no—
66C23×C32—41no—
67C23×C32M1612yescomplemented
68C23×C32C22×C411yescharacteristic
69C22×C3⋊D3—21no—
70C22×C3⋊D3—21no—
71C22×C3⋊D3—41no—
72C22×C3⋊D3—41no—
73C22×C3⋊D3C22⋊C412yes—
74C2×C32×C4—21no—
75C2×C32×C4—41no—
76C2×C32×C4—41no—
77C2×C32×C4C2×D412yes—
78#638—28no—
79C2×C3⋊Dic3—21no—
80C2×C3⋊Dic3—21no—
81C2×C3⋊Dic3—22no—
82C2×C3⋊Dic3—21no—
83C2×C3⋊Dic3—42no—
84C2×C3⋊Dic3—42no—
85C2×C3⋊Dic3—41no—
86C2×C3⋊Dic3C22⋊C411yescharacteristic
87C2×C3⋊Dic3C22⋊C411yescharacteristic
88C2×C3⋊Dic3M1612yescomplemented
89C4×C3⋊D3—24no—
90C4×C3⋊D3—42no—
91C32×C8—42no—
92C3⋊(C3⋊C8)—42no—
93C2×C4×D4—91no—
94#407—92no—
95#324—92no—
96#323—91no—
97#323C3⋊D311yescharacteristic, complemented
98C24×C3C4×D314yes—
99C23×D3—34no—
100C22×C3×C4C4×D314yes—
101C22×C3×C4C22×D314yes—
102C2×#67—68no—
103C2×#67—68no—
104C2×#67—68no—
105C22×Dic3—34no—
106C22×Dic3—34no—
107C22×Dic3—34no—
108C22×Dic3—64no—
109C22×Dic3—64no—
110C22×Dic3—128no—
111C2×C4×D3—38no—
112C2×C4×D3—38no—
113C2×C4×D3—128no—
114C2×C3×C8—28no—
115C3×C22⋊C4—28no—
116(C2×D3)⋊C4—68no—
117Dic3⋊C4—68no—
118C4×Dic3—64no—
119C4×Dic3—64no—
120C2×C3⋊C8—68no—
121ΓL(1,𝔽25)—1216no—
122C22×C32—21no—
123C22×C32—21no—
124C22×C32—22no—
125C22×C32—42no—
126C22×C32—42no—
127C22×C32—41no—
128C22×C32—41no—
129C22×C32C2×C22⋊C411yescharacteristic
130C22×C32C2×M1611yescharacteristic
131C22×C32C2×M1611yescharacteristic
132C2×C3⋊D3—22no—
133C2×C3⋊D3—22no—
134C2×C3⋊D3—22no—
135C2×C3⋊D3—42no—
136C2×C3⋊D3—42no—
137C32×C4—22no—
138C32×C4—41no—
139C3⋊Dic3—22no—
140C3⋊Dic3—21no—
141C3⋊Dic3—41no—
142C3⋊Dic3#9912yes—
143C22×D4—91no—
144C23×C4—91no—
145C23×C4—91no—
146C2×M16—182no—
147C4×D4—182no—
148C4×D4—182no—
149C2×C4⋊C4—91no—
150C2×C22⋊C4—91no—
151C2×C22⋊C4C2×C3⋊D311yescharacteristic
152C2×C42—91no—
153C22⋊C8—92no—
154C22⋊C8—182no—
155C22⋊C8C2×C3⋊D312yes—
156C23×C3—24no—
157C23×C3—24no—
158C23×C3—44no—
159C23×C3—44no—
160C23×C3ΓL(1,𝔽25)18yescomplemented
161C23×C3C2×C4×D314yes—
162C22×D3—38no—
163C22×D3—64no—
164C22×D3—64no—
165C22×D3—124no—
166C22×D3—124no—
167C2×C3×C4—24no—
168C2×C3×C4—44no—
169C2×C3×C4—44no—
170C2×C3×C4D3×D418yes—
171#67—632no—
172C2×Dic3—34no—
173C2×Dic3—34no—
174C2×Dic3—38no—
175C2×Dic3—68no—
176C2×Dic3—64no—
177C2×Dic3—64no—
178C2×Dic3—64no—
179C2×Dic3—128no—
180C2×Dic3—128no—
181C2×Dic3—124no—
182C4×D3—616no—
183C4×D3—128no—
184C3×C8—48no—
185C3⋊C8—128no—
186C2×C32—21no—
187C2×C32—21no—
188C2×C32—42no—
189C2×C32#40711yescharacteristic
190C2×C32C2×#9911yescharacteristic
191C2×C32#41311yescharacteristic
192C3⋊D3—42no—
193C24—91no—
194C24C4×C3⋊D311yescharacteristic
195C2×D4—182no—
196C2×D4—182no—
197C2×D4—182no—
198C22×C4—91no—
199C22×C4—91no—
200C22×C4—92no—
201C22×C4—92no—
202C22×C4—91no—
203C22×C4—181no—
204C22×C4—181no—
205C22×C4—362no—
206C22×C4—362no—
207C22×C4C4×C3⋊D311yescharacteristic
208C22×C4C22×C3⋊D311yescharacteristic
209M16—364no—
210C2×C8—22no—
211C2×C8—182no—
212C4⋊C4—182no—
213C22⋊C4—22no—
214C22⋊C4—182no—
215C42—181no—
216C42—181no—
217C22×C3—24no—
218C22×C3—24no—
219C22×C3—28no—
220C22×C3—48no—
221C22×C3—48no—
222C22×C3—44no—
223C22×C3—44no—
224C22×C3D3×C22⋊C414yes—
225C22×C3C2×ΓL(1,𝔽25)14yes—
226C22×C3D3×M1614yes—
227C2×D3—68no—
228C2×D3—68no—
229C2×D3—68no—
230C2×D3—128no—
231C2×D3—128no—
232C3×C4—28no—
233C3×C4—44no—
234Dic3—38no—
235Dic3—68no—
236Dic3—64no—
237Dic3—124no—
238C32#146511yescharacteristic, complemented, Sylow
239C23—21no—
240C23—21no—
241C23—41no—
242C23—41no—
243C23—92no—
244C23—181no—
245C23—181no—
246C23—361no—
247C23—361no—
248C23#374312yescomplemented
249C23C2×C4×C3⋊D311yescharacteristic
250D4—188no—
251C2×C4—21no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—91no—
255C2×C4—91no—
256C2×C4—92no—
257C2×C4—184no—
258C2×C4—182no—
259C2×C4—181no—
260C2×C4—181no—
261C2×C4—181no—
262C2×C4—362no—
263C2×C4—362no—
264C2×C4—362no—
265C2×C4—361no—
266C2×C4D4×C3⋊D312yes—
267C8—42no—
268C8—362no—
269C2×C3—24no—
270C2×C3—24no—
271C2×C3—48no—
272C2×C3#472614yes—
273C2×C3D3×#9914yes—
274C2×C3#474514yes—
275D3—128no—
276C22—21no—
277C22—21no—
278C22—22no—
279C22—42no—
280C22—42no—
281C22—41no—
282C22—41no—
283C22—182no—
284C22—182no—
285C22—182no—
286C22—362no—
287C22—362no—
288C22C22⋊C4×C3⋊D311yescharacteristic
289C22C2×#374311yescharacteristic
290C22M16×C3⋊D311yescharacteristic
291C4—22no—
292C4—41no—
293C4—92no—
294C4—182no—
295C4—181no—
296C4—361no—
297C3#6812114yescomplemented
298C2—21no—
299C2—21no—
300C2—42no—
301C2—362no—
302C2#1059242511yescharacteristic
303C2C3⋊D3×#9911yescharacteristic
304C2#1059244411yescharacteristic
subgroupG/H
centerC22C22⋊C4×C3⋊D3
commutatorC23×C32C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#323C2
socleC22×C32C2×C22⋊C4
prime radicalC22×#638C4
cosocleC22×C32×C4C23
hypercenter#323C3⋊D3
hypocenterC32#1465
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #10592425C2semidirect
3. C32×#323C2semidirect
4. #10589391C2semidirect
5. #10589335C2semidirect
22. C3×#323D3semidirect
67. C23×C32M16semidirect
88. C2×C3⋊Dic3M16semidirect
97. #323C3⋊D3semidirect
160. C23×C3ΓL(1,𝔽25)semidirect
238. C32#1465semidirect
248. C23#3743semidirect
297. C3#68121semidirect

Maximal subgroups

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

subgroupindex
C2×#640902
#105924252
C32×#3232
#105893912
#105893352
#681213