Finite Group Databasebeta

← #11808735

Subgroups — #11808735

Order 1152.

1260 conjugacy classes of subgroups; only the 210 normal subgroups are shown.

normal subgroups only

This group has 1260 conjugacy classes of subgroups — too many to draw. Only its 210 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×D4×Dic9C213yesmaximal, complemented
2C2×#611⋊C4C213yesmaximal, complemented
3C9×#392C211yesmaximal, characteristic, complemented
4#10588903C213yesmaximal, complemented
5#10588629C213yesmaximal, complemented
6#10588357C211yesmaximal, characteristic, complemented
7#10588328C211yesmaximal, characteristic, complemented
8#76667—31nomaximal
9C22×D4×C9C2213yes—
10C22×#611C2213yes—
11C23×Dic9C2213yes—
12C22×C4×D9C2211yescharacteristic
13C2×C9×C22⋊C4C2213yes—
14C2×#3676C2216yes—
15D4×Dic9—212no—
16C2×(C2×D9)⋊C4C2213yes—
17C2×C4⋊Dic9C2213yes—
18C2×Dic9⋊C4C2213yes—
19C2×C4×Dic9C2213yes—
20#611⋊C4—212no—
21C9×#95C2211yescharacteristic
22C9⋊#95C2213yes—
23C2×D4×Dic3—33no—
24C2×#67⋊C4—33no—
25C3×#392D311yescharacteristic
26#5223—33no—
27#4949—33no—
28#4677—31no—
29#4648—31no—
30C24×C9C2313yes—
31C23×D9C2311yescharacteristic
32C2×D4×C9—212no—
33C2×D4×C9—26no—
34C22×C4×C9C2311yescharacteristic
35C22×C4×C9C2313yes—
36C2×#611—26no—
37C2×#611—26no—
38C2×#611—26no—
39C22×Dic9—212no—
40C22×Dic9—26no—
41C22×Dic9C2313yes—
42C22×Dic9C2313yes—
43C22×Dic9C2311yescharacteristic
44C2×C4×D9—26no—
45C9×C22⋊C4—26no—
46#3676—212no—
47(C2×D9)⋊C4—26no—
48C4⋊Dic9—26no—
49Dic9⋊C4—26no—
50C4×Dic9D4112yescomplemented
51#2397—91noSylow
52C22×C3×D4C2×D313yes—
53C22×#67—33no—
54C23×Dic3—33no—
55C22×C4×D3—31no—
56C2×C3×C22⋊C4C2×D313yes—
57C2×#217—36no—
58D4×Dic3—612no—
59C2×(C2×D3)⋊C4—33no—
60C2×C4⋊Dic3—33no—
61C2×Dic3⋊C4—33no—
62C2×C4×Dic3—33no—
63#67⋊C4—612no—
64C3×#95C2×D311yescharacteristic
65C3⋊#95—33no—
66C23×C9—26no—
67C23×C9—23no—
68C23×C9—23no—
69C23×C9—26no—
70C23×C9#4116yes—
71C23×C9C2411yescharacteristic
72C22×D9—23no—
73C22×D9—23no—
74C22×D9#4112yes—
75D4×C9—224no—
76C2×C4×C9—26no—
77C2×C4×C9—23no—
78C2×C4×C9C2×D416yes—
79#611—224no—
80C2×Dic9—23no—
81C2×Dic9—23no—
82C2×Dic9—23no—
83C2×Dic9—26no—
84C2×Dic9—412no—
85C2×Dic9C2×D416yes—
86C2×Dic9C2×D416yes—
87C4×D9—44no—
88C2×C4×D4—93no—
89C2×C4×D4—93no—
90#399—93no—
91#399—91no—
92#392—93no—
93#392D911yescharacteristic, complemented
94#376—91no—
95C24×C3C22×D313yes—
96C23×D3—31no—
97C2×C3×D4—212no—
98C2×C3×D4—26no—
99C22×C3×C4C22×D311yescharacteristic
100C22×C3×C4C22×D313yes—
101C2×#67—66no—
102C2×#67—66no—
103C2×#67—66no—
104C22×Dic3—31no—
105C22×Dic3—33no—
106C22×Dic3—33no—
107C22×Dic3—66no—
108C22×Dic3—612no—
109C2×C4×D3—66no—
110C3×C22⋊C4—26no—
111#217—612no—
112(C2×D3)⋊C4—66no—
113C4⋊Dic3—66no—
114Dic3⋊C4—66no—
115C4×Dic3—312no—
116C22×C9—26no—
117C22×C9—212no—
118C22×C9—43no—
119C22×C9—46no—
120C22×C9—43no—
121C22×C9C22×D413yes—
122C22×C9C2×#4113yes—
123C22×C9C2×#4111yescharacteristic
124C2×D9—26no—
125C2×D9—43no—
126C2×D9—41no—
127C4×C9—26no—
128C4×C9—41no—
129Dic9—26no—
130Dic9—43no—
131Dic9#12714yes—
132C22×D4—93no—
133C22×D4C2×D913yes—
134C23×C4—93no—
135C23×C4—91no—
136C4×D4—1812no—
137C4×D4—1812no—
138C2×C4⋊C4—93no—
139C2×C4⋊C4—93no—
140C2×C22⋊C4—96no—
141C2×C22⋊C4—93no—
142C2×C22⋊C4C2×D913yes—
143C2×C42—93no—
144#95—93no—
145#95C2×D911yescharacteristic
146C23×C3—26no—
147C23×C3—23no—
148C23×C3—26no—
149C23×C3—23no—
150C23×C3#23716yes—
151C23×C3C23×D311yescharacteristic
152C22×D3—32no—
153C22×D3—63no—
154C22×D3—63no—
155C3×D4—224no—
156C2×C3×C4—26no—
157C2×C3×C4—23no—
158C2×C3×C4D3×D416yes—
159#67—624no—
160C2×Dic3—36no—
161C2×Dic3—36no—
162C2×Dic3—63no—
163C2×Dic3—63no—
164C2×Dic3—63no—
165C2×Dic3—66no—
166C2×Dic3—1212no—
167C4×D3—124no—
168C2×C9—46no—
169C2×C9#52513yes—
170C2×C9#52513yes—
171C2×C9C2×#12711yescharacteristic
172D9—42no—
173C24—91no—
174C24C22×D913yes—
175C2×D4—212no—
176C2×D4—26no—
177C2×D4—186no—
178C2×D4—186no—
179C2×D4—186no—
180C22×C4—91no—
181C22×C4—93no—
182C22×C4—93no—
183C22×C4—186no—
184C22×C4—186no—
185C22×C4—1812no—
186C22×C4C22×D911yescharacteristic
187C22×C4C22×D913yes—
188C4⋊C4—186no—
189C4⋊C4—186no—
190C22⋊C4—26no—
191C22⋊C4—1812no—
192C22⋊C4—186no—
193C42—912no—
194C22×C3—212no—
195C22×C3—26no—
196C22×C3—43no—
197C22×C3—43no—
198C22×C3—46no—
199C22×C3C2×D3×D413yes—
200C22×C3C2×#23713yes—
201C22×C3D3×#4111yescharacteristic
202C2×D3—66no—
203C2×D3—121no—
204C2×D3—123no—
205C3×C4—26no—
206C3×C4—41no—
207Dic3—34no—
208Dic3—66no—
209Dic3—123no—
210C9#239711yescharacteristic, complemented, Sylow
211C23—23no—
212C23—26no—
213C23—26no—
214C23—23no—
215C23—92no—
216C23—183no—
217C23—183no—
218C23#369916yes—
219C23C23×D911yescharacteristic
220D4—224no—
221D4—1824no—
222C2×C4—26no—
223C2×C4—23no—
224C2×C4—96no—
225C2×C4—96no—
226C2×C4—183no—
227C2×C4—183no—
228C2×C4—186no—
229C2×C4—183no—
230C2×C4—364no—
231C2×C4—3612no—
232C2×C4D4×D916yes—
233C2×C3—46no—
234C2×C3#558613yes—
235C2×C3#560613yes—
236C2×C3D3×#12711yescharacteristic
237D3—122no—
238C22—26no—
239C22—212no—
240C22—46no—
241C22—43no—
242C22—43no—
243C22—186no—
244C22—361no—
245C22—363no—
246C22C2×D4×D913yes—
247C22C2×#369913yes—
248C22#41×D911yescharacteristic
249C4—26no—
250C4—41no—
251C4—94no—
252C4—186no—
253C4—363no—
254C3#7666711yescharacteristic
255C2—46no—
256C2—362no—
257C2#1058968813yes—
258C2#1058970813yes—
259C2D9×#12711yescharacteristic
subgroupG/H
centerC23C23×D9
commutator, cosocleC23×C9C24
Frattini, socleC23×C3C23×D3
FittingC9×#392C2
hypercenter#392D9
hypocenterC9#2397
LCSG ▷ C23×C9 ▷ C9
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×D4×Dic9C2semidirect
2. C2×#611⋊C4C2semidirect
3. C9×#392C2semidirect
4. #10588903C2semidirect
5. #10588629C2semidirect
6. #10588357C2semidirect
7. #10588328C2semidirect
50. C4×Dic9D4semidirect
93. #392D9semidirect
210. C9#2397semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic92
C2×#611⋊C42
C9×#3922
#105889032
#105886292
#105883572
#105883282
#766673