Finite Group Databasebeta

← C22×#63797 #11918541

Subgroups — C22×#63797 #11918541

Order 1152.

4121 conjugacy classes of subgroups; only the 692 normal subgroups are shown.

normal subgroups only

This group has 4121 conjugacy classes of subgroups — too many to draw. Only its 692 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
1C22×#3802C212yesmaximal, complemented
2C22×C8×C3⋊D3C211yesmaximal, characteristic, complemented
3C22×C3×D24C212yesmaximal, complemented
4C22×#3713C212yesmaximal, complemented
5C2×#63797C2124yesmaximal, direct product factor
6C22×D3×D8—32nomaximal
7C23×D32—22no—
8C22×C4×C3⋊D3C2211yescharacteristic
9C22×C3×D12C2214yescomplemented
10C22×#625—22no—
11C2×#3802—212no—
12C2×#3802C22124yescomplemented
13C22×C32×C8C2211yescharacteristic, complemented
14C22×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
15C2×C8×C3⋊D3C22112yescomplemented
16C2×C3×D24C22124yescomplemented
17C2×#3713C22124yescomplemented
18#63797C22164yesdirect product factor
19C22×D3×D4—34no—
20C22×C3×D8—32no—
21C22×#213—34no—
22C2×D3×D8—348no—
23C22×D24D312yescomplemented
24C22×D3×C8—32no—
25C22×D3×C8—61no—
26C23×C3⋊D3D411yescharacteristic
27C23×C3×D3—24no—
28C22×D32—224no—
29C22×D32—416no—
30C22×C32×C4C2311yescharacteristic
31C22×C3⋊Dic3D411yescharacteristic
32C2×C4×C3⋊D3D416yes—
33C2×C4×C3⋊D3C2316yes—
34C2×C3×D12—212no—
35C2×C3×D12C23124yescomplemented
36C2×#625—224no—
37#3802—248no—
38#3802C23132yescomplemented
39C2×C32×C8C2316yescomplemented
40C2×C3⋊(C3⋊C8)C2316yescomplemented
41C8×C3⋊D3C23116yescomplemented
42C3×D24C23132yescomplemented
43#3713C23132yescomplemented
44C23×D8—91noSylow
45C24×D3—64no—
46C22×C3×D4—34no—
47C22×#67—64no—
48C2×D3×D4—348no—
49C2×D3×D4—624no—
50C22×D12C2×D314yescomplemented
51C22×C4×D3—32no—
52C22×C4×D3—61no—
53C2×C3×D8—324no—
54C22×C3×C8—21no—
55C22×C3×C8C2×D312yescomplemented
56C2×#213—348no—
57C22×C3⋊C8—32no—
58C22×C3⋊C8—61no—
59D3×D8—3128no—
60C2×D24C2×D3124yescomplemented
61C2×D3×C8—324no—
62C2×D3×C8—612no—
63C23×C32C2×D411yescharacteristic
64C22×C3⋊D3D818yescomplemented
65C22×C3⋊D3C2×D416yes—
66C22×C3×D3—224no—
67C22×C3×D3—416no—
68C2×D32—232no—
69C2×D32—496no—
70C2×C32×C4C2×D413yes—
71C2×C32×C4C2413yes—
72C2×C3⋊Dic3C2×D416yes—
73C4×C3⋊D3C2×D4112yes—
74C4×C3⋊D3C2414yes—
75C3×D12—224no—
76C3×D12C24116yescomplemented
77#625—232no—
78C32×C8C2414yescomplemented
79C3⋊(C3⋊C8)C2414yescomplemented
80C23×D4—92no—
81C22×D8—32no—
82C22×D8—924no—
83C22×D8—92no—
84C23×C8—91no—
85C24×C3—64no—
86C23×D3—24no—
87C23×D3—32no—
88C23×D3—61no—
89C23×D3—648no—
90C23×D3—1232no—
91C2×C3×D4—324no—
92C2×C3×D4—612no—
93C22×C3×C4—21no—
94C22×C3×C4C22×D312yes—
95C2×#67—648no—
96C22×Dic3—32no—
97C22×Dic3—61no—
98D3×D4—364no—
99D3×D4—696no—
100C2×D12—212no—
101C2×D12C22×D3124yescomplemented
102C2×C4×D3—312no—
103C2×C4×D3—312no—
104C2×C4×D3—66no—
105C2×C4×D3—66no—
106C3×D8—332no—
107C2×C3×C8—26no—
108C2×C3×C8C22×D3112yescomplemented
109#213—364no—
110C2×C3⋊C8—312no—
111C2×C3⋊C8—66no—
112D24C22×D3132yescomplemented
113D3×C8—332no—
114D3×C8—616no—
115C22×C32C2×D814yescomplemented
116C22×C32C22×D413yes—
117C2×C3⋊D3C2×D8124yescomplemented
118C2×C3⋊D3C22×D414yes—
119C2×C3×D3—216no—
120C2×C3×D3—448no—
121D32—464no—
122C32×C4C22×D413yes—
123C32×C4C2511yescharacteristic
124C3⋊Dic3C22×D414yes—
125C25—182no—
126C22×D4—34no—
127C22×D4—924no—
128C22×D4—1812no—
129C22×D4—182no—
130C23×C4—91no—
131C2×D8—324no—
132C2×D8—964no—
133C2×D8—924no—
134C22×C8—91no—
135C22×C8—912no—
136C22×C8D3211yescharacteristic, complemented
137C23×C3—21no—
138C23×C3—624no—
139C23×C3—1216no—
140C23×C3D3×D412yes—
141C22×D3—224no—
142C22×D3—316no—
143C22×D3—312no—
144C22×D3—416no—
145C22×D3—68no—
146C22×D3—66no—
147C22×D3—664no—
148C22×D3—12192no—
149C3×D4—316no—
150C3×D4—624no—
151C2×C3×C4—23no—
152C2×C3×C4—23no—
153C2×C3×C4D3×D416yes—
154C2×C3×C4C23×D316yes—
155#67—664no—
156C2×Dic3—312no—
157C2×Dic3—66no—
158D12—224no—
159D12C23×D3116yescomplemented
160C4×D3—324no—
161C4×D3—38no—
162C4×D3—612no—
163C4×D3—64no—
164C3×C8—24no—
165C3×C8C23×D318yescomplemented
166C3⋊C8—38no—
167C3⋊C8—64no—
168C2×C32C22×D816yescomplemented
169C2×C32C23×D411yescharacteristic
170C3⋊D3C22×D818yescomplemented
171C3×D3—416no—
172C24—64no—
173C24—91no—
174C24—1824no—
175C24—3616no—
176C2×D4—324no—
177C2×D4—612no—
178C2×D4—932no—
179C2×D4—1848no—
180C2×D4—1824no—
181C22×C4—91no—
182C22×C4—96no—
183C22×C4—96no—
184C22×C4C2×D3211yescharacteristic
185D8—332no—
186D8—932no—
187C2×C8—96no—
188C2×C8—916no—
189C2×C8C2×D3216yescomplemented
190C22×C3—23no—
191C22×C3—24no—
192C22×C3—616no—
193C22×C3—1248no—
194C22×C3D3×D818yescomplemented
195C22×C3C2×D3×D416yes—
196C2×D3—216no—
197C2×D3—38no—
198C2×D3—348no—
199C2×D3—448no—
200C2×D3—64no—
201C2×D3—624no—
202C2×D3—12128no—
203C3×C4—23no—
204C3×C4—21no—
205C3×C4C2×D3×D416yes—
206C3×C4C24×D312yes—
207Dic3—38no—
208Dic3—64no—
209C32C23×D811yescharacteristic, complemented, Sylow
210C23—624no—
211C23—96no—
212C23—98no—
213C23—1216no—
214C23—1832no—
215C23—3696no—
216C23#380211yescharacteristic
217D4—316no—
218D4—624no—
219D4—1832no—
220C2×C4—96no—
221C2×C4—912no—
222C2×C4—94no—
223C2×C4#380213yes—
224C2×C4C22×D3213yes—
225C8—94no—
226C8C22×D3214yescomplemented
227C2×C3—21no—
228C2×C3—26no—
229C2×C3—1216no—
230C2×C3C2×D3×D8112yescomplemented
231C2×C3C22×D3×D412yes—
232D3—316no—
233D3—416no—
234D3—68no—
235C22—616no—
236C22—94no—
237C22—924no—
238C22—1248no—
239C22—3664no—
240C22#6379714yesdirect product factor
241C22C2×#380213yes—
242C4—94no—
243C4C2×#380213yes—
244C4C23×D3211yescharacteristic
245C3—21no—
246C3C22×D3×D812yescomplemented
247C2—98no—
248C2—1216no—
249C2C2×#6379716yesdirect product factor
250C2C22×#380211yescharacteristic
subgroupG/H
centerC23#3802
commutator, cosocleC32×C4C25
FrattiniC4C23×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
hypercenterC22×C8D32
hypocenterC32C23×D8
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C22×#3802C2semidirect
2. C22×C8×C3⋊D3C2semidirect
3. C22×C3×D24C2semidirect
4. C22×#3713C2semidirect
5. C2×#63797C2direct (N × H)
9. C22×C3×D12C22semidirect
12. C2×#3802C22semidirect
13. C22×C32×C8C22semidirect
14. C22×C3⋊(C3⋊C8)C22semidirect
15. C2×C8×C3⋊D3C22semidirect
16. C2×C3×D24C22semidirect
17. C2×#3713C22semidirect
18. #63797C22direct (N × H)
23. C22×D24D3semidirect
35. C2×C3×D12C23semidirect
38. #3802C23semidirect
39. C2×C32×C8C23semidirect
40. C2×C3⋊(C3⋊C8)C23semidirect
41. C8×C3⋊D3C23semidirect
42. C3×D24C23semidirect
43. #3713C23semidirect
50. C22×D12C2×D3semidirect
55. C22×C3×C8C2×D3semidirect
60. C2×D24C2×D3semidirect
64. C22×C3⋊D3D8semidirect
76. C3×D12C24semidirect
78. C32×C8C24semidirect
79. C3⋊(C3⋊C8)C24semidirect
101. C2×D12C22×D3semidirect
108. C2×C3×C8C22×D3semidirect
112. D24C22×D3semidirect
115. C22×C32C2×D8semidirect
117. C2×C3⋊D3C2×D8semidirect
136. C22×C8D32semidirect
159. D12C23×D3semidirect
165. C3×C8C23×D3semidirect
168. C2×C32C22×D8semidirect
170. C3⋊D3C22×D8semidirect
189. C2×C8C2×D32semidirect
194. C22×C3D3×D8semidirect
209. C32C23×D8semidirect
226. C8C22×D32semidirect
230. C2×C3C2×D3×D8semidirect
240. C22#63797direct (N × H)
246. C3C22×D3×D8semidirect
249. C2C2×#63797direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38022
C22×C8×C3⋊D32
C22×C3×D242
C22×#37132
C2×#637972
C22×D3×D83