Finite Group Databasebeta

← C22×SD16×D269 #46825602

Subgroups — C22×SD16×D269 #46825602

Order 34432.

1720 conjugacy classes of subgroups; only the 565 normal subgroups are shown.

normal subgroups only

This group has 1720 conjugacy classes of subgroups — too many to draw. Only its 565 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×Q8×D269C211yesmaximal, characteristic, complemented
2C22×D4×D269C211yesmaximal, characteristic
3C22×#16864391C211yesmaximal, characteristic, complemented
4C22×#16864390C211yesmaximal, characteristic, complemented
5C22×#16864389C211yesmaximal, characteristic, complemented
6C2×SD16×D269C2124yesmaximal, direct product factor
7C22×C8×D269C211yesmaximal, characteristic, complemented
8C22×SD16×C269C211yesmaximal, characteristic, complemented
9C24×D269—21no—
10C22×Dic538—21no—
11C22×Dic538C2211yescharacteristic, complemented
12C2×Q8×D269—26no—
13C2×Q8×D269C22112yescomplemented
14C22×D1076C2211yescharacteristic
15C22×C22⋊D269—21no—
16C2×D4×D269—26no—
17C2×D4×D269C22112yes—
18C22×C4×D269—21no—
19C22×C4×D269C2211yescharacteristic
20C2×#16864391C22112yescomplemented
21C2×#16864390C22112yescomplemented
22C2×#16864389C22112yescomplemented
23SD16×D269C22164yesdirect product factor
24C22×#14524130C2211yescharacteristic, complemented
25C2×C8×D269C22112yescomplemented
26C22×Q8×C269C2211yescharacteristic, complemented
27C22×D4×C269C2211yescharacteristic
28C2×SD16×C269C22112yescomplemented
29C22×C8×C269C2211yescharacteristic, complemented
30C23×D269—212no—
31C23×D269—21no—
32C23×D269—48no—
33C23×D269D411yescharacteristic
34C2×Dic538—212no—
35C2×Dic538—23no—
36C2×Dic538C2316yescomplemented
37Q8×D269—224no—
38Q8×D269C23116yescomplemented
39C2×D1076—23no—
40C2×D1076C2316yes—
41C2×C22⋊D269—212no—
42D4×D269—224no—
43D4×D269C23116yes—
44C22×Dic269—21no—
45C22×Dic269D411yescharacteristic
46C2×C4×D269—212no—
47C2×C4×D269D416yes—
48C2×C4×D269C2316yes—
49#16864391C23116yescomplemented
50#16864390C23116yescomplemented
51#16864389C23116yescomplemented
52C2×#14524130C2316yescomplemented
53C8×D269C23116yescomplemented
54C24×C269—21no—
55C2×Q8×C269—23no—
56C2×Q8×C269C2316yescomplemented
57C2×D4×C269—23no—
58C2×D4×C269C2316yes—
59C22×C4×C269—21no—
60C22×C4×C269C2311yescharacteristic
61SD16×C269C23116yescomplemented
62C2×C8×C269C2316yescomplemented
63C22×D269—26no—
64C22×D269—216no—
65C22×D269—44no—
66C22×D269—448no—
67C22×D269SD1618yesdirect product factor
68C22×D269C2×D416yes—
69Dic538—26no—
70Dic538—216no—
71Dic538C2414yescomplemented
72D1076—26no—
73D1076C2414yes—
74C22⋊D269—216no—
75C2×Dic269—26no—
76C2×Dic269C2×D416yes—
77C4×D269—216no—
78C4×D269C2×D4112yes—
79C4×D269C2414yes—
80#14524130C2414yescomplemented
81C23×C269—26no—
82C23×C269—44no—
83C23×C269C2×D411yescharacteristic
84Q8×C269—26no—
85Q8×C269C2414yescomplemented
86D4×C269—26no—
87D4×C269C2414yes—
88C2×C4×C269—26no—
89C2×C4×C269C2×D413yes—
90C2×C4×C269C2413yes—
91C8×C269C2414yescomplemented
92C22×C269—24no—
93C22×C269—412no—
94C22×C269C2×SD1614yescomplemented
95C22×C269C22×D413yes—
96C2×D269—24no—
97C2×D269—412no—
98C2×D269—432no—
99C2×D269C2×SD16124yesdirect product factor
100C2×D269C22×D414yes—
101C4×C269—24no—
102C4×C269C22×D413yes—
103C4×C269C2511yescharacteristic
104Dic269—24no—
105Dic269C22×D414yes—
106C2×C269—44no—
107C2×C269C22×SD1616yescomplemented
108C2×C269C23×D411yescharacteristic
109D269—44no—
110D269C22×SD1618yesdirect product factor
111C269C23×SD1611yescharacteristic, complemented, Sylow
112C23×SD16—2691nomaximal, Sylow
113C23×Q8—2691no—
114C23×D4—2691no—
115C22×SD16—2691no—
116C22×SD16—2691no—
117C22×SD16—26924no—
118C22×SD16—2691no—
119C22×SD16D26911yescharacteristic, direct product factor
120C23×C8—2691no—
121C25—5381no—
122C22×Q8—26912no—
123C22×Q8—2691no—
124C22×Q8—5381no—
125C22×Q8—5386no—
126C22×Q8C2×D26911yescharacteristic, complemented
127C22×D4—26912no—
128C22×D4—2691no—
129C22×D4—5386no—
130C22×D4—5381no—
131C22×D4C2×D26911yescharacteristic
132C23×C4—2691no—
133C23×C4—5381no—
134C2×SD16—26912no—
135C2×SD16—26912no—
136C2×SD16—26964no—
137C2×SD16—26912no—
138C2×SD16C2×D269112yesdirect product factor
139C22×C8—2691no—
140C22×C8—26912no—
141C22×C8C2×D26911yescharacteristic, complemented
142C24—21no—
143C24—2691no—
144C24—53812no—
145C24—5381no—
146C24—10768no—
147C2×Q8—23no—
148C2×Q8—26916no—
149C2×Q8—2696no—
150C2×Q8—53812no—
151C2×Q8—53824no—
152C2×Q8—5383no—
153C2×Q8C22×D26916yescomplemented
154C2×D4—23no—
155C2×D4—26916no—
156C2×D4—2696no—
157C2×D4—53824no—
158C2×D4—53812no—
159C2×D4—5383no—
160C2×D4C22×D26916yes—
161C22×C4—21no—
162C22×C4—2691no—
163C22×C4—2696no—
164C22×C4—2696no—
165C22×C4—53812no—
166C22×C4—5381no—
167C22×C4C22×D26911yescharacteristic
168SD16—26916no—
169SD16—26916no—
170SD16—26916no—
171SD16C22×D269116yesdirect product factor
172C2×C8—2696no—
173C2×C8—26916no—
174C2×C8C22×D26916yescomplemented
175C23—26no—
176C23—44no—
177C23—2698no—
178C23—2696no—
179C23—53816no—
180C23—5386no—
181C23—107648no—
182C23—10764no—
183C23D4×D26911yescharacteristic
184Q8—26no—
185Q8—2694no—
186Q8—53816no—
187Q8—5386no—
188Q8C23×D26914yescomplemented
189D4—26no—
190D4—2694no—
191D4—53816no—
192D4—5386no—
193D4C23×D26914yes—
194C2×C4—26no—
195C2×C4—2696no—
196C2×C4—26912no—
197C2×C4—2694no—
198C2×C4—53816no—
199C2×C4—5386no—
200C2×C4D4×D26913yes—
201C2×C4C23×D26913yes—
202C8—2694no—
203C8C23×D26914yescomplemented
204C22—24no—
205C22—412no—
206C22—2694no—
207C22—26924no—
208C22—5384no—
209C22—107632no—
210C22—107612no—
211C22SD16×D26914yesdirect product factor
212C22C2×D4×D26913yes—
213C4—24no—
214C4—2694no—
215C4—5384no—
216C4C2×D4×D26913yes—
217C4C24×D26911yescharacteristic
218C2—44no—
219C2—2698no—
220C2—10764no—
221C2C2×SD16×D26916yesdirect product factor
222C2C22×D4×D26911yescharacteristic
subgroupG/H
centerC23D4×D269
commutator, cosocleC4×C269C25
FrattiniC4C24×D269
FittingC22×SD16×C269C2
socleC23×C269C2×D4
prime radicalC22×D4×D269C2
hypercenterC22×SD16D269
hypocenterC269C23×SD16
LCSG ▷ C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C22×Q8×D269C2semidirect
3. C22×#16864391C2semidirect
4. C22×#16864390C2semidirect
5. C22×#16864389C2semidirect
6. C2×SD16×D269C2direct (N × H)
7. C22×C8×D269C2semidirect
8. C22×SD16×C269C2semidirect
11. C22×Dic538C22semidirect
13. C2×Q8×D269C22semidirect
20. C2×#16864391C22semidirect
21. C2×#16864390C22semidirect
22. C2×#16864389C22semidirect
23. SD16×D269C22direct (N × H)
24. C22×#14524130C22semidirect
25. C2×C8×D269C22semidirect
26. C22×Q8×C269C22semidirect
28. C2×SD16×C269C22semidirect
29. C22×C8×C269C22semidirect
36. C2×Dic538C23semidirect
38. Q8×D269C23semidirect
49. #16864391C23semidirect
50. #16864390C23semidirect
51. #16864389C23semidirect
52. C2×#14524130C23semidirect
53. C8×D269C23semidirect
56. C2×Q8×C269C23semidirect
61. SD16×C269C23semidirect
62. C2×C8×C269C23semidirect
67. C22×D269SD16direct (N × H)
71. Dic538C24semidirect
80. #14524130C24semidirect
85. Q8×C269C24semidirect
91. C8×C269C24semidirect
94. C22×C269C2×SD16semidirect
99. C2×D269C2×SD16direct (N × H)
107. C2×C269C22×SD16semidirect
110. D269C22×SD16direct (N × H)
111. C269C23×SD16semidirect
119. C22×SD16D269direct (N × H)
126. C22×Q8C2×D269semidirect
138. C2×SD16C2×D269direct (N × H)
141. C22×C8C2×D269semidirect
153. C2×Q8C22×D269semidirect
171. SD16C22×D269direct (N × H)
174. C2×C8C22×D269semidirect
188. Q8C23×D269semidirect
203. C8C23×D269semidirect
211. C22SD16×D269direct (N × H)
221. C2C2×SD16×D269direct (N × H)

Maximal subgroups

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

subgroupindex
C22×Q8×D2692
C22×D4×D2692
C22×#168643912
C22×#168643902
C22×#168643892
C2×SD16×D2692
C22×C8×D2692
C22×SD16×C2692
C23×SD16269