Finite Group Databasebeta

← #11798304

Subgroups — #11798304

Order 1152.

324 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 66 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#10589850C211yesmaximal, characteristic
2#10588807C211yesmaximal, characteristic, complemented
3#10588589C212yesmaximal, complemented
4C9×#349C211yesmaximal, characteristic, complemented
5#10588194C212yesmaximal, complemented
6#69121—31nomaximal
7C2×#3697—21no—
8C2×C9×M16C2211yescharacteristic
9#63486—21no—
10#63471—22no—
11#63470—22no—
12#63467—21no—
13#63467C2212yes—
14C2×Dic36C2211yescharacteristic, complemented
15C9×M32C2212yescomplemented
16#63377C2211yescharacteristic, complemented
17#63376—21no—
18Dic72—22no—
19#63359—22no—
20#5748—31no—
21#5137—31no—
22#4909—32no—
23C3×#349D311yescharacteristic
24#4518—32no—
25C22×C4×C9D411yescharacteristic
26C2×#611—41no—
27#3697—22no—
28#3697—22no—
29#3697—41no—
30#3697—41no—
31C2×D36—21no—
32C2×C4×D9—41no—
33C2×Dic18—21no—
34C2×Dic18—21no—
35C9×M16—22no—
36C2×C8×C9D411yescharacteristic
37C2×C8×C9C2311yescharacteristic
38#3676—41no—
39C4⋊Dic9—21no—
40Dic9⋊C4—41no—
41D72—21no—
42D72D412yes—
43#3664—22no—
44#3664—22no—
45Dic36—21no—
46Dic36—22no—
47Dic36D412yes—
48C9×C16—22no—
49#2191—91noSylow
50C2×#235—61no—
51C2×C3×M16C2×D311yescharacteristic
52#924—61no—
53#909—62no—
54#908—62no—
55C2×Dic12—31no—
56#904—32no—
57#904—61no—
58C3×M32C2×D312yes—
59#817—31no—
60#816—61no—
61Dic24—62no—
62#800—62no—
63C23×C9D811yescharacteristic
64C22×D9—41no—
65C2×C4×C9—21no—
66C2×C4×C9—21no—
67C2×C4×C9D811yescharacteristic
68C2×C4×C9C2×D411yescharacteristic
69#611—42no—
70#611—42no—
71C2×Dic9—41no—
72C2×Dic9—41no—
73C2×Dic9—41no—
74D36—22no—
75D36—41no—
76C4×D9—42no—
77C4×D9—42no—
78Dic18—22no—
79Dic18—41no—
80Dic18—41no—
81Dic18—41no—
82C8×C9—21no—
83C8×C9C2×D412yes—
84#575—91no—
85#510—92no—
86#470—91no—
87#360—92no—
88#349D911yescharacteristic, complemented
89C22×C3×C4D1211yescharacteristic
90C2×#67—121no—
91#235—62no—
92#235—62no—
93#235—121no—
94#235—121no—
95C2×D12—61no—
96C2×C4×D3—121no—
97C2×Dic6—61no—
98C2×Dic6—61no—
99C3×M16—22no—
100C2×C3×C8D1211yescharacteristic
101C2×C3×C8C22×D311yescharacteristic
102#217—121no—
103C4⋊Dic3—61no—
104Dic3⋊C4—121no—
105Dic12—32no—
106Dic12—61no—
107Dic12—62no—
108D24—32no—
109D24—61no—
110#204—62no—
111#204—62no—
112C3×C16—22no—
113C22×C9—21no—
114C22×C9—41no—
115C22×C9C2×D811yescharacteristic
116C2×D9—42no—
117C2×D9—82no—
118C4×C9—21no—
119C4×C9#12011yescharacteristic
120C4×C9AGL(1,ℤ/8)11yescharacteristic
121Dic9—42no—
122Dic9—81no—
123Dic9—81no—
124C2×#41—181no—
125#137—182no—
126AGL(1,ℤ/8)—182no—
127#135—92no—
128#135—181no—
129C2×Q16—91no—
130C2×M16C2×D911yescharacteristic
131C22⋊Q8—181no—
132Q32—182no—
133SD32—182no—
134M32C2×D912yescomplemented
135#106—91no—
136#103—181no—
137C23×C3D2411yescharacteristic
138C22×D3—121no—
139C2×C3×C4—21no—
140C2×C3×C4—21no—
141C2×C3×C4D2411yescharacteristic
142C2×C3×C4C2×D1211yescharacteristic
143#67—122no—
144#67—122no—
145C2×Dic3—121no—
146C2×Dic3—121no—
147C2×Dic3—121no—
148D12—62no—
149D12—121no—
150C4×D3—122no—
151C4×D3—122no—
152Dic6—62no—
153Dic6—121no—
154Dic6—121no—
155Dic6—121no—
156C3×C8—21no—
157C3×C8D3×D412yes—
158C2×C9—21no—
159C2×C9—41no—
160C2×C9#44711yescharacteristic
161D9—82no—
162#41—182no—
163#41—182no—
164#41—361no—
165#41—361no—
166C2×Q8—181no—
167C2×Q8—181no—
168C2×D4—181no—
169C2×D4—361no—
170C22×C4—361no—
171C22×C4D3611yescharacteristic
172Q16—92no—
173Q16—181no—
174Q16—182no—
175SD16—182no—
176SD16—182no—
177D8—92no—
178D8—181no—
179M16—22no—
180C2×C8D3611yescharacteristic
181C2×C8C22×D911yescharacteristic
182C4⋊C4—181no—
183C4⋊C4—361no—
184C22⋊C4—361no—
185C16—22no—
186C22×C3—21no—
187C22×C3—41no—
188C22×C3C2×D2411yescharacteristic
189C2×D3—122no—
190C2×D3—242no—
191C3×C4—21no—
192C3×C4#88211yescharacteristic
193C3×C4#90811yescharacteristic
194Dic3—122no—
195Dic3—241no—
196Dic3—241no—
197C9#219111yescharacteristic, complemented, Sylow
198C23—361no—
199C23D7211yescharacteristic
200Q8—182no—
201Q8—361no—
202Q8—361no—
203Q8—361no—
204D4—182no—
205D4—361no—
206D4—362no—
207D4—362no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—362no—
211C2×C4—361no—
212C2×C4—362no—
213C2×C4—361no—
214C2×C4—361no—
215C2×C4D7211yescharacteristic
216C2×C4C2×D3611yescharacteristic
217C8—21no—
218C8D4×D912yes—
219C2×C3—21no—
220C2×C3—41no—
221C2×C3#473211yescharacteristic
222D3—242no—
223C22—21no—
224C22—41no—
225C22—362no—
226C22—722no—
227C22C2×D7211yescharacteristic
228C4—21no—
229C4—362no—
230C4—721no—
231C4—721no—
232C4#6344411yescharacteristic
233C4#6347011yescharacteristic
234C3#6912111yescharacteristic
235C2—21no—
236C2—41no—
237C2—722no—
238C2#1058841411yescharacteristic
subgroupG/H
centerC2#10588414
commutator, cosocleC2×C8×C9C23
FrattiniC2×C3×C8C22×D3
FittingC9×#349C2
socleC2×C3#4732
prime radical#10589850C2
hypercenter#349D9
hypocenterC9#2191
LCSG ▷ C2×C8×C9 ▷ C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #349

Complements

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

NH ≅ G/Ntype
2. #10588807C2semidirect
3. #10588589C2semidirect
4. C9×#349C2semidirect
5. #10588194C2semidirect
14. C2×Dic36C22semidirect
15. C9×M32C22semidirect
16. #63377C22semidirect
88. #349D9semidirect
134. M32C2×D9semidirect
197. C9#2191semidirect

Maximal subgroups

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

subgroupindex
#105898502
#105888072
#105885892
C9×#3492
#105881942
#691213