Finite Group Databasebeta

← #11808741

Subgroups — #11808741

Order 1152.

1260 conjugacy classes of subgroups; only the 202 normal subgroups are shown.

normal subgroups only

This group has 1260 conjugacy classes of subgroups — too many to draw. Only its 202 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×#63455C213yesmaximal, complemented
2C2×#611⋊C4C213yesmaximal, complemented
3C9×#399C211yesmaximal, characteristic, complemented
4#10588673C213yesmaximal, complemented
5#10588640C213yesmaximal, complemented
6#10588351C211yesmaximal, characteristic, complemented
7#10588328C211yesmaximal, characteristic, complemented
8#78019—31nomaximal
9C22×#611C2213yes—
10C23×Dic9C2211yescharacteristic
11C22×D36C2213yes—
12C22×C4×D9C2213yes—
13C2×C9×C4⋊C4C2213yes—
14C2×C9×C22⋊C4C2213yes—
15C2×(C2×D9)⋊C4C2213yes—
16C2×(C2×D9)⋊C4C2216yes—
17C2×Dic9⋊C4C2213yes—
18C2×C4×Dic9C2213yes—
19#63455—212no—
20#611⋊C4—212no—
21C9×#95C2211yescharacteristic
22C9⋊#95C2213yes—
23C2×#893—33no—
24C2×#67⋊C4—33no—
25C3×#399D311yescharacteristic
26#4993—33no—
27#4960—33no—
28#4671—31no—
29#4648—31no—
30C24×C9C2311yescharacteristic
31C23×D9C2313yes—
32C22×C4×C9C2313yes—
33C22×C4×C9C2313yes—
34C2×#611—26no—
35C2×#611—26no—
36C2×#611—26no—
37C22×Dic9—26no—
38C22×Dic9C2311yescharacteristic
39C22×Dic9C2313yes—
40C22×Dic9C2311yescharacteristic
41C2×D36—212no—
42C2×D36—26no—
43C2×C4×D9—26no—
44C2×C4×D9—212no—
45C9×C4⋊C4—26no—
46C9×C22⋊C4—26no—
47(C2×D9)⋊C4—26no—
48(C2×D9)⋊C4—212no—
49Dic9⋊C4—26no—
50C4×Dic9D4112yescomplemented
51#2397—91noSylow
52C22×#67—33no—
53C23×Dic3—31no—
54C22×D12—33no—
55C22×C4×D3—33no—
56C2×C3×C4⋊C4C2×D313yes—
57C2×C3×C22⋊C4C2×D313yes—
58C2×(C2×D3)⋊C4—33no—
59C2×(C2×D3)⋊C4—36no—
60C2×Dic3⋊C4—33no—
61C2×C4×Dic3—33no—
62#893—612no—
63#67⋊C4—612no—
64C3×#95C2×D311yescharacteristic
65C3⋊#95—33no—
66C23×C9—23no—
67C23×C9—23no—
68C23×C9#4112yes—
69C23×C9C2411yescharacteristic
70C22×D9—26no—
71C22×D9—23no—
72C22×D9—26no—
73C22×D9—23no—
74C22×D9#4116yes—
75C2×C4×C9—26no—
76C2×C4×C9—23no—
77C2×C4×C9—26no—
78C2×C4×C9C2×D416yes—
79#611—224no—
80C2×Dic9—23no—
81C2×Dic9—23no—
82C2×Dic9—23no—
83C2×Dic9—44no—
84C2×Dic9C2×D416yes—
85C2×Dic9C2×D416yes—
86D36—224no—
87C4×D9—412no—
88C2×C4×D4—93no—
89C2×C4×D4—93no—
90#399—93no—
91#399D911yescharacteristic, complemented
92#392—93no—
93#392—91no—
94#376—91no—
95C24×C3C22×D311yescharacteristic
96C23×D3—33no—
97C22×C3×C4C22×D313yes—
98C22×C3×C4C22×D313yes—
99C2×#67—66no—
100C2×#67—66no—
101C2×#67—66no—
102C22×Dic3—31no—
103C22×Dic3—33no—
104C22×Dic3—31no—
105C22×Dic3—66no—
106C2×D12—612no—
107C2×D12—66no—
108C2×C4×D3—66no—
109C2×C4×D3—612no—
110C3×C4⋊C4—26no—
111C3×C22⋊C4—26no—
112(C2×D3)⋊C4—612no—
113(C2×D3)⋊C4—66no—
114Dic3⋊C4—66no—
115C4×Dic3—312no—
116C22×C9—26no—
117C22×C9—43no—
118C22×C9—41no—
119C22×C9C22×D413yes—
120C22×C9C2×#4111yescharacteristic
121C22×C9C2×#4113yes—
122C2×D9—212no—
123C2×D9—26no—
124C2×D9—43no—
125C2×D9—46no—
126C2×D9—43no—
127C4×C9—26no—
128C4×C9—43no—
129Dic9—26no—
130Dic9—41no—
131Dic9#12714yes—
132C22×D4—93no—
133C22×D4—93no—
134C23×C4—91no—
135C23×C4—93no—
136C4×D4—1812no—
137C4×D4—1812no—
138C2×C4⋊C4—93no—
139C2×C4⋊C4C2×D913yes—
140C2×C22⋊C4—96no—
141C2×C22⋊C4—93no—
142C2×C22⋊C4C2×D913yes—
143C2×C42—93no—
144#95—93no—
145#95C2×D911yescharacteristic
146C23×C3—23no—
147C23×C3—23no—
148C23×C3#23912yes—
149C23×C3C23×D311yescharacteristic
150C22×D3—36no—
151C22×D3—66no—
152C22×D3—63no—
153C22×D3—63no—
154C22×D3—66no—
155C2×C3×C4—26no—
156C2×C3×C4—23no—
157C2×C3×C4—26no—
158C2×C3×C4D3×D416yes—
159#67—624no—
160C2×Dic3—36no—
161C2×Dic3—36no—
162C2×Dic3—63no—
163C2×Dic3—63no—
164C2×Dic3—63no—
165C2×Dic3—124no—
166D12—624no—
167C4×D3—1212no—
168C2×C9—42no—
169C2×C9#52513yes—
170C2×C9#52513yes—
171C2×C9C2×#12711yescharacteristic
172D9—46no—
173C24—93no—
174C24C22×D911yescharacteristic
175C2×D4—1812no—
176C2×D4—186no—
177C2×D4—186no—
178C2×D4—186no—
179C2×D4—186no—
180C22×C4—91no—
181C22×C4—93no—
182C22×C4—91no—
183C22×C4—186no—
184C22×C4—1812no—
185C22×C4—186no—
186C22×C4C22×D913yes—
187C22×C4C22×D913yes—
188C4⋊C4—26no—
189C4⋊C4—186no—
190C22⋊C4—26no—
191C22⋊C4—1812no—
192C22⋊C4—186no—
193C42—912no—
194C22×C3—26no—
195C22×C3—43no—
196C22×C3—41no—
197C22×C3C2×D3×D413yes—
198C22×C3C2×#23911yescharacteristic
199C22×C3D3×#4113yes—
200C2×D3—612no—
201C2×D3—66no—
202C2×D3—123no—
203C2×D3—123no—
204C2×D3—126no—
205C3×C4—26no—
206C3×C4—43no—
207Dic3—34no—
208Dic3—66no—
209Dic3—121no—
210C9#239711yescharacteristic, complemented, Sylow
211C23—23no—
212C23—23no—
213C23—96no—
214C23—183no—
215C23—186no—
216C23—183no—
217C23—186no—
218C23#370112yes—
219C23C23×D911yescharacteristic
220D4—1824no—
221D4—1824no—
222C2×C4—26no—
223C2×C4—23no—
224C2×C4—26no—
225C2×C4—96no—
226C2×C4—96no—
227C2×C4—183no—
228C2×C4—183no—
229C2×C4—183no—
230C2×C4—3612no—
231C2×C4—364no—
232C2×C4D4×D916yes—
233C2×C3—42no—
234C2×C3#562713yes—
235C2×C3#565613yes—
236C2×C3D3×#12711yescharacteristic
237D3—126no—
238C22—26no—
239C22—43no—
240C22—41no—
241C22—186no—
242C22—1812no—
243C22—366no—
244C22—363no—
245C22—363no—
246C22C2×D4×D913yes—
247C22C2×#370111yescharacteristic
248C22#41×D913yes—
249C4—26no—
250C4—43no—
251C4—94no—
252C4—186no—
253C4—361no—
254C3#7801911yescharacteristic
255C2—42no—
256C2—366no—
257C2#1058972913yes—
258C2#1058975813yes—
259C2D9×#12711yescharacteristic
subgroupG/H
centerC23C23×D9
commutator, cosocleC23×C9C24
Frattini, socleC23×C3C23×D3
FittingC9×#399C2
hypercenter#399D9
hypocenterC9#2397
LCSG ▷ C23×C9 ▷ C9
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. C2×#63455C2semidirect
2. C2×#611⋊C4C2semidirect
3. C9×#399C2semidirect
4. #10588673C2semidirect
5. #10588640C2semidirect
6. #10588351C2semidirect
7. #10588328C2semidirect
50. C4×Dic9D4semidirect
91. #399D9semidirect
210. C9#2397semidirect

Maximal subgroups

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

subgroupindex
C2×#634552
C2×#611⋊C42
C9×#3992
#105886732
#105886402
#105883512
#105883282
#780193