Finite Group Databasebeta

← #11778318

Subgroups — #11778318

Order 1152.

423 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 423 conjugacy classes of subgroups — too many to draw. Only its 72 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#10589612C211yesmaximal, characteristic
2C9×#395C211yesmaximal, characteristic, complemented
3#10588908C212yesmaximal, complemented
4#10588205C211yesmaximal, characteristic, complemented
5#10588129C212yesmaximal, complemented
6#69706—31nomaximal
7C22×Q8×C9C2211yescharacteristic
8C2×#3697—21no—
9C2×C9×C4⋊C4—21no—
10C2×C9×C4⋊C4C2211yescharacteristic
11C2×#3675—22no—
12#63492—21no—
13#63492C2212yes—
14#63459—22no—
15#63457—22no—
16C9×#95—21no—
17C9×#95C2211yescharacteristic
18#63395—22no—
19#63389C2212yes—
20#5510—31no—
21C3×#395D311yescharacteristic
22#5227—32no—
23#4528—31no—
24#4451—32no—
25C2×Q8×C9—22no—
26C2×Q8×C9—42no—
27C22×C4×C9—21no—
28C22×C4×C9—21no—
29C22×C4×C9D411yescharacteristic
30C22×C4×C9D411yescharacteristic
31C22×C4×C9C2311yescharacteristic
32C2×#611—22no—
33#3697—42no—
34#3697—42no—
35C2×D36—21no—
36C2×D36—21no—
37C2×D36D412yes—
38C2×C4×D9—22no—
39C2×Dic18—21no—
40C9×C4⋊C4—22no—
41C9×C4⋊C4—42no—
42#3675—44no—
43(C2×D9)⋊C4—22no—
44(C2×D9)⋊C4—22no—
45C4⋊Dic9—21no—
46C4⋊Dic9D412yes—
47C2×C9⋊C8—22no—
48#1604—91noSylow
49C22×C3×Q8C2×D311yescharacteristic
50C2×#235—61no—
51C2×C3×C4⋊C4—21no—
52C2×C3×C4⋊C4C2×D311yescharacteristic
53C2×#215—62no—
54#930—32no—
55#930—61no—
56#897—62no—
57#895—62no—
58C3×#95—21no—
59C3×#95C2×D311yescharacteristic
60#835—62no—
61#830—32no—
62C23×C9C2×D411yescharacteristic
63C22×D9—22no—
64Q8×C9—24no—
65Q8×C9—42no—
66C2×C4×C9—21no—
67C2×C4×C9—21no—
68C2×C4×C9—22no—
69C2×C4×C9—22no—
70C2×C4×C9—21no—
71C2×C4×C9—41no—
72C2×C4×C9—41no—
73C2×C4×C9—41no—
74C2×C4×C9—41no—
75C2×C4×C9—41no—
76C2×C4×C9—41no—
77C2×C4×C9SD1612yescomplemented
78C2×C4×C9C2×D412yes—
79#611—42no—
80#611—42no—
81C2×Dic9—22no—
82D36—42no—
83D36—42no—
84D36—81no—
85C4×D9—44no—
86Dic18—42no—
87C9⋊C8—42no—
88#537—91no—
89#448—92no—
90#395D911yescharacteristic, complemented
91#327—92no—
92#324—91no—
93C2×C3×Q8—22no—
94C2×C3×Q8—42no—
95C22×C3×C4—21no—
96C22×C3×C4—21no—
97C22×C3×C4#6711yescharacteristic
98C22×C3×C4#6711yescharacteristic
99C22×C3×C4C22×D311yescharacteristic
100C2×#67—62no—
101#235—122no—
102#235—122no—
103C2×D12—32no—
104C2×D12—61no—
105C2×D12—61no—
106C2×C4×D3—62no—
107C2×Dic6—61no—
108C3×C4⋊C4—22no—
109C3×C4⋊C4—42no—
110#215—124no—
111(C2×D3)⋊C4—62no—
112(C2×D3)⋊C4—62no—
113C4⋊Dic3—32no—
114C4⋊Dic3—61no—
115C2×C3⋊C8—62no—
116C22×C9—21no—
117C22×C9—21no—
118C22×C9#12011yescharacteristic
119C22×C9C2×SD1611yescharacteristic
120C22×C9AGL(1,ℤ/8)11yescharacteristic
121C2×D9—42no—
122C2×D9—42no—
123C2×D9—42no—
124C4×C9—22no—
125C4×C9—22no—
126C4×C9—42no—
127C4×C9—41no—
128C4×C9—42no—
129Dic9—42no—
130C2×#41—181no—
131C22×Q8C2×D911yescharacteristic
132C2×SD16—182no—
133C22⋊Q8—182no—
134#121—92no—
135#121—182no—
136#121—181no—
137C2×C4⋊C4—21no—
138C2×C4⋊C4C2×D911yescharacteristic
139#103—182no—
140C22⋊C8—92no—
141#95—21no—
142#95C2×D911yescharacteristic
143C23×C3C2×#6711yescharacteristic
144C22×D3—62no—
145C3×Q8—24no—
146C3×Q8—42no—
147C2×C3×C4—21no—
148C2×C3×C4—21no—
149C2×C3×C4—22no—
150C2×C3×C4—22no—
151C2×C3×C4—21no—
152C2×C3×C4—41no—
153C2×C3×C4—41no—
154C2×C3×C4—41no—
155C2×C3×C4—41no—
156C2×C3×C4—41no—
157C2×C3×C4—41no—
158C2×C3×C4#21512yes—
159C2×C3×C4D3×D412yes—
160#67—122no—
161#67—122no—
162C2×Dic3—62no—
163D12—122no—
164D12—122no—
165D12—241no—
166C4×D3—124no—
167Dic6—122no—
168C3⋊C8—122no—
169C2×C9—21no—
170C2×C9—21no—
171C2×C9#45011yescharacteristic
172C2×C9#45611yescharacteristic
173C2×C9B(4,𝔽2)11yescharacteristic
174D9—82no—
175#41—362no—
176#41—362no—
177C2×Q8—22no—
178C2×Q8—42no—
179C2×Q8—181no—
180C2×D4—92no—
181C2×D4—181no—
182C2×D4—181no—
183C2×D4—182no—
184C22×C4—21no—
185C22×C4—21no—
186C22×C4—182no—
187C22×C4#61111yescharacteristic
188C22×C4#61111yescharacteristic
189C22×C4C22×D911yescharacteristic
190SD16—364no—
191C2×C8—182no—
192C4⋊C4—22no—
193C4⋊C4—42no—
194C4⋊C4—92no—
195C4⋊C4—181no—
196C22⋊C4—182no—
197C22⋊C4—182no—
198C22×C3—21no—
199C22×C3—21no—
200C22×C3#93711yescharacteristic
201C22×C3C2×#21511yescharacteristic
202C22×C3#94911yescharacteristic
203C2×D3—122no—
204C2×D3—122no—
205C2×D3—122no—
206C3×C4—22no—
207C3×C4—22no—
208C3×C4—42no—
209C3×C4—41no—
210C3×C4—42no—
211Dic3—122no—
212C9#160411yescharacteristic, complemented, Sylow
213C23—182no—
214C23C2×#61111yescharacteristic
215Q8—24no—
216Q8—42no—
217Q8—362no—
218D4—362no—
219D4—362no—
220D4—362no—
221D4—362no—
222D4—721no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—21no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—182no—
235C2×C4—364no—
236C2×C4#367512yescomplemented
237C2×C4D4×D912yes—
238C8—362no—
239C2×C3—21no—
240C2×C3—21no—
241C2×C3#503211yescharacteristic
242C2×C3#504611yescharacteristic
243C2×C3#509511yescharacteristic
244D3—242no—
245C22—21no—
246C22—21no—
247C22—362no—
248C22—362no—
249C22—362no—
250C22#6349911yescharacteristic
251C22C2×#367511yescharacteristic
252C22#6351211yescharacteristic
253C4—22no—
254C4—22no—
255C4—42no—
256C4—42no—
257C4—41no—
258C4—362no—
259C3#6970611yescharacteristic
260C2—21no—
261C2—21no—
262C2—722no—
263C2#1058871211yescharacteristic
264C2#1058872911yescharacteristic
265C2#1058877511yescharacteristic
subgroupG/H
centerC22#63499
commutator, cosocleC22×C4×C9C23
FrattiniC22×C3×C4C22×D3
FittingC9×#395C2
socleC22×C3#937
prime radical#10589612C2
hypercenter#395D9
hypocenterC9#1604
LCSG ▷ C22×C4×C9 ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ C22×C4 ◁ #395

Complements

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

NH ≅ G/Ntype
2. C9×#395C2semidirect
3. #10588908C2semidirect
4. #10588205C2semidirect
5. #10588129C2semidirect
77. C2×C4×C9SD16semidirect
90. #395D9semidirect
212. C9#1604semidirect
236. C2×C4#3675semidirect

Maximal subgroups

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

subgroupindex
#105896122
C9×#3952
#105889082
#105882052
#105881292
#697063