Finite Group Databasebeta

← #11788191

Subgroups — #11788191

Order 1152.

537 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 537 conjugacy classes of subgroups — too many to draw. Only its 122 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
1#10589893C211yesmaximal, characteristic
2C2×#63488C211yesmaximal, characteristic, complemented
3C9×#407C211yesmaximal, characteristic, complemented
4C2×#63384C212yesmaximal, complemented
5#10588235C212yesmaximal, complemented
6#69966—31nomaximal
7C23×C4×C9C2211yescharacteristic
8C2×#3697C2211yescharacteristic
9C2×C9×M16C2212yes—
10#63515—21no—
11C2×#3676—21no—
12#63492C412yescomplemented
13#63491—21no—
14C4×#611—22no—
15#63488—24no—
16#63488C2211yescharacteristic
17C2×C4⋊Dic9—21no—
18#63486C412yescomplemented
19C2×C4×Dic9C2212yes—
20C9×C22⋊C8—22no—
21#63384—24no—
22#5791—31no—
23C2×#926—31no—
24C3×#407D311yescharacteristic
25C2×#825—32no—
26#4555—32no—
27C24×C9D411yescharacteristic
28C22×C4×C9—22no—
29C22×C4×C9—22no—
30C22×C4×C9C2×C412yes—
31C22×C4×C9D411yescharacteristic
32C22×C4×C9D412yes—
33C22×C4×C9C2311yescharacteristic
34C2×#611—22no—
35C2×#611—21no—
36C22×Dic9—22no—
37#3697—22no—
38#3697—22no—
39C2×D36C2×C411yescharacteristic
40C2×C4×D9—21no—
41C2×Dic18C2×C411yescharacteristic
42C9×M16—22no—
43C9×M16—22no—
44C2×C8×C9—22no—
45#3676—24no—
46#3676—22no—
47#3676—21no—
48(C2×D9)⋊C4—22no—
49C4⋊Dic9—24no—
50C4⋊Dic9C2×C412yes—
51Dic9⋊C4—22no—
52C4×Dic9—22no—
53C4×Dic9—21no—
54C4×Dic9D414yescomplemented
55#1897—91noSylow
56C23×C3×C4C2×D311yescharacteristic
57C2×#235—31no—
58C2×C3×M16C2×D312yes—
59#953—61no—
60C2×#217—61no—
61#930—32no—
62#929—61no—
63C4×#67—62no—
64#926—31no—
65#926—64no—
66C2×C4⋊Dic3—61no—
67#924—32no—
68C2×C4×Dic3—32no—
69C3×C22⋊C8—22no—
70#825—64no—
71C23×C9—21no—
72C23×C9—21no—
73C23×C9—42no—
74C23×C9C22⋊C412yes—
75C23×C9C2×D411yescharacteristic
76C22×D9—21no—
77C2×C4×C9—21no—
78C2×C4×C9—21no—
79C2×C4×C9—24no—
80C2×C4×C9—24no—
81C2×C4×C9C22⋊C412yes—
82C2×C4×C9C22×C411yescharacteristic
83C2×C4×C9C2×D412yes—
84C2×C4×C9C2×D411yescharacteristic
85C2×C4×C9#4112yes—
86#611—44no—
87#611—41no—
88#611—41no—
89C2×Dic9—22no—
90C2×Dic9—21no—
91C2×Dic9—24no—
92C2×Dic9—44no—
93D36—22no—
94C4×D9—42no—
95Dic18—22no—
96C8×C9—42no—
97#525—91no—
98C2×#117—91no—
99C2×#104—92no—
100#407D911yescharacteristic, complemented
101#339—92no—
102C24×C3D1211yescharacteristic
103C22×C3×C4—22no—
104C22×C3×C4—22no—
105C22×C3×C4C4×D312yes—
106C22×C3×C4D1211yescharacteristic
107C22×C3×C4#6712yes—
108C22×C3×C4C22×D311yescharacteristic
109C2×#67—62no—
110C2×#67—61no—
111C22×Dic3—62no—
112#235—62no—
113#235—62no—
114C2×D12—31no—
115C2×C4×D3—61no—
116C2×Dic6—31no—
117C3×M16—22no—
118C3×M16—22no—
119C2×C3×C8—22no—
120#217—64no—
121#217—62no—
122#217—61no—
123(C2×D3)⋊C4—62no—
124C4⋊Dic3—32no—
125C4⋊Dic3—64no—
126Dic3⋊C4—62no—
127C4×Dic3—34no—
128C4×Dic3—62no—
129C4×Dic3—61no—
130C22×C9—22no—
131C22×C9—22no—
132C22×C9—22no—
133C22×C9—22no—
134C22×C9—42no—
135C22×C9—42no—
136C22×C9C2×C22⋊C411yescharacteristic
137C22×C9#12011yescharacteristic
138C22×C9#12311yescharacteristic
139C2×D9—41no—
140C2×D9—42no—
141C4×C9—22no—
142C4×C9C4×D412yes—
143C4×C9#12112yes—
144Dic9—44no—
145Dic9—41no—
146Dic9—42no—
147C2×#41—91no—
148C23×C4C2×D911yescharacteristic
149C2×M16C2×D912yes—
150#123—181no—
151C22⋊Q8—92no—
152#121—92no—
153#120—181no—
154C4×D4—182no—
155#117—91no—
156#117—184no—
157C2×C4⋊C4—181no—
158C2×C22⋊C4—181no—
159C2×C42—92no—
160#104—184no—
161C22⋊C8—22no—
162C23×C3—21no—
163C23×C3—21no—
164C23×C3—42no—
165C23×C3(C2×D3)⋊C412yes—
166C23×C3C2×D1211yescharacteristic
167C22×D3—61no—
168C2×C3×C4—21no—
169C2×C3×C4—21no—
170C2×C3×C4—24no—
171C2×C3×C4—24no—
172C2×C3×C4(C2×D3)⋊C412yes—
173C2×C3×C4C2×C4×D311yescharacteristic
174C2×C3×C4D3×D412yes—
175C2×C3×C4#23712yes—
176C2×C3×C4C2×#6711yescharacteristic
177#67—124no—
178#67—121no—
179#67—121no—
180C2×Dic3—64no—
181C2×Dic3—62no—
182C2×Dic3—61no—
183C2×Dic3—124no—
184D12—62no—
185C4×D3—122no—
186Dic6—62no—
187C3×C8—42no—
188C2×C9—21no—
189C2×C9—21no—
190C2×C9—42no—
191C2×C9#38611yescharacteristic
192C2×C9#42112yes—
193D9—81no—
194C24D3611yescharacteristic
195#41—182no—
196#41—182no—
197C2×Q8—91no—
198C2×D4—91no—
199C2×D4—182no—
200C2×D4—181no—
201C22×C4—22no—
202C22×C4—22no—
203C22×C4—182no—
204C22×C4—181no—
205C22×C4C4×D912yes—
206C22×C4D3611yescharacteristic
207C22×C4#61112yes—
208C22×C4C22×D911yescharacteristic
209M16—22no—
210M16—22no—
211C2×C8—22no—
212C4⋊C4—92no—
213C4⋊C4—184no—
214C4⋊C4—182no—
215C22⋊C4—184no—
216C22⋊C4—182no—
217C22⋊C4—181no—
218C22⋊C4—182no—
219C42—94no—
220C42—182no—
221C42—181no—
222C22×C3—22no—
223C22×C3—22no—
224C22×C3—22no—
225C22×C3—22no—
226C22×C3—42no—
227C22×C3—42no—
228C22×C3#88211yescharacteristic
229C22×C3#88611yescharacteristic
230C22×C3C2×(C2×D3)⋊C411yescharacteristic
231C2×D3—122no—
232C2×D3—121no—
233C3×C4—22no—
234C3×C4#67⋊C412yes—
235C3×C4#93912yes—
236Dic3—124no—
237Dic3—122no—
238Dic3—121no—
239C9#189711yescharacteristic, complemented, Sylow
240C23—21no—
241C23—21no—
242C23—42no—
243C23—181no—
244C23(C2×D9)⋊C412yes—
245C23C2×D3611yescharacteristic
246Q8—182no—
247D4—182no—
248D4—364no—
249D4—361no—
250D4—361no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—24no—
254C2×C4—24no—
255C2×C4—182no—
256C2×C4—181no—
257C2×C4—184no—
258C2×C4—364no—
259C2×C4—362no—
260C2×C4(C2×D9)⋊C412yes—
261C2×C4C2×C4×D911yescharacteristic
262C2×C4D4×D912yes—
263C2×C4#369912yes—
264C2×C4C2×#61111yescharacteristic
265C8—42no—
266C2×C3—21no—
267C2×C3—21no—
268C2×C3—42no—
269C2×C3#495811yescharacteristic
270C2×C3#513912yes—
271D3—241no—
272C22—22no—
273C22—22no—
274C22—22no—
275C22—22no—
276C22—42no—
277C22—42no—
278C22—362no—
279C22—361no—
280C22#6344411yescharacteristic
281C22#6344811yescharacteristic
282C22C2×(C2×D9)⋊C411yescharacteristic
283C4—22no—
284C4—364no—
285C4—362no—
286C4—361no—
287C4#611⋊C412yes—
288C4#6350112yes—
289C3#6996611yescharacteristic
290C2—21no—
291C2—21no—
292C2—42no—
293C2—721no—
294C2#1058863811yescharacteristic
295C2#1058881912yes—
subgroupG/H
centerC2×C4C2×#611
commutatorC2×C4×C9C22×C4
FrattiniC22×C3×C4C22×D3
FittingC9×#407C2
socleC22×C3C2×(C2×D3)⋊C4
prime radical#10589893C2
cosocleC22×C4×C9C23
hypercenter#407D9
hypocenterC9#1897
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. C2×#63488C2semidirect
3. C9×#407C2semidirect
4. C2×#63384C2semidirect
5. #10588235C2semidirect
12. #63492C4semidirect
18. #63486C4semidirect
54. C4×Dic9D4semidirect
100. #407D9semidirect
239. C9#1897semidirect

Maximal subgroups

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

subgroupindex
#105898932
C2×#634882
C9×#4072
C2×#633842
#105882352
#699663