Finite Group Databasebeta

← C22×D8×D269 #46825599

Subgroups — C22×D8×D269 #46825599

Order 34432.

1976 conjugacy classes of subgroups; only the 565 normal subgroups are shown.

normal subgroups only

This group has 1976 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×D4×D269C212yesmaximal, complemented
2C22×D2152C211yesmaximal, characteristic, complemented
3C22×#16864387C212yesmaximal, complemented
4C2×D8×D269C2124yesmaximal, direct product factor
5C22×C8×D269C211yesmaximal, characteristic, complemented
6C22×D8×C269C211yesmaximal, characteristic, complemented
7C24×D269—22no—
8C22×D1076C2212yescomplemented
9C22×C22⋊D269—22no—
10C2×D4×D269—212no—
11C2×D4×D269C22124yescomplemented
12C22×C4×D269C2211yescharacteristic
13C2×D2152C22112yescomplemented
14C2×#16864387C22124yescomplemented
15D8×D269C22164yesdirect product factor
16C22×#14524130C2211yescharacteristic, complemented
17C2×C8×D269C22112yescomplemented
18C22×D4×C269C2212yescomplemented
19C2×D8×C269C22112yescomplemented
20C22×C8×C269C2211yescharacteristic, complemented
21C23×D269—224no—
22C23×D269—22no—
23C23×D269—416no—
24C23×D269D411yescharacteristic
25C2×D1076—26no—
26C2×D1076C23112yescomplemented
27C2×C22⋊D269—224no—
28D4×D269—248no—
29D4×D269C23132yescomplemented
30C22×Dic269D411yescharacteristic
31C2×C4×D269D416yes—
32C2×C4×D269C2316yes—
33D2152C23116yescomplemented
34#16864387C23132yescomplemented
35C2×#14524130C2316yescomplemented
36C8×D269C23116yescomplemented
37C24×C269—22no—
38C2×D4×C269—26no—
39C2×D4×C269C23112yescomplemented
40C22×C4×C269C2311yescharacteristic
41D8×C269C23116yescomplemented
42C2×C8×C269C2316yescomplemented
43C22×D269—212no—
44C22×D269—232no—
45C22×D269—48no—
46C22×D269—496no—
47C22×D269D818yesdirect product factor
48C22×D269C2×D416yes—
49D1076—212no—
50D1076C2418yescomplemented
51C22⋊D269—232no—
52C2×Dic269C2×D416yes—
53C4×D269C2×D4112yes—
54C4×D269C2414yes—
55#14524130C2414yescomplemented
56C23×C269—212no—
57C23×C269—48no—
58C23×C269C2×D411yescharacteristic
59D4×C269—212no—
60D4×C269C2418yescomplemented
61C2×C4×C269C2×D413yes—
62C2×C4×C269C2413yes—
63C8×C269C2414yescomplemented
64C22×C269—28no—
65C22×C269—424no—
66C22×C269C2×D814yescomplemented
67C22×C269C22×D413yes—
68C2×D269—28no—
69C2×D269—424no—
70C2×D269—464no—
71C2×D269C2×D8124yesdirect product factor
72C2×D269C22×D414yes—
73C4×C269C22×D413yes—
74C4×C269C2511yescharacteristic
75Dic269C22×D414yes—
76C2×C269—48no—
77C2×C269C22×D816yescomplemented
78C2×C269C23×D411yescharacteristic
79D269—48no—
80D269C22×D818yesdirect product factor
81C269C23×D811yescharacteristic, complemented, Sylow
82C23×D8—2691nomaximal, Sylow
83C23×D4—2692no—
84C22×D8—2692no—
85C22×D8—26924no—
86C22×D8—2691no—
87C22×D8D26911yescharacteristic, direct product factor
88C23×C8—2691no—
89C25—5382no—
90C22×D4—26924no—
91C22×D4—2692no—
92C22×D4—53812no—
93C22×D4—5382no—
94C22×D4C2×D26912yescomplemented
95C23×C4—2691no—
96C2×D8—26924no—
97C2×D8—26964no—
98C2×D8—26912no—
99C2×D8C2×D269112yesdirect product factor
100C22×C8—2691no—
101C22×C8—26912no—
102C22×C8C2×D26911yescharacteristic, complemented
103C24—22no—
104C24—2691no—
105C24—53824no—
106C24—5382no—
107C24—107616no—
108C2×D4—26no—
109C2×D4—26932no—
110C2×D4—26912no—
111C2×D4—53848no—
112C2×D4—53824no—
113C2×D4—5386no—
114C2×D4C22×D269112yescomplemented
115C22×C4—2691no—
116C22×C4—2696no—
117C22×C4—2696no—
118C22×C4C22×D26911yescharacteristic
119D8—26932no—
120D8—26916no—
121D8C22×D269116yesdirect product factor
122C2×C8—2696no—
123C2×C8—26916no—
124C2×C8C22×D26916yescomplemented
125C23—212no—
126C23—48no—
127C23—2698no—
128C23—2696no—
129C23—53832no—
130C23—53812no—
131C23—107696no—
132C23—10768no—
133C23D4×D26911yescharacteristic
134D4—212no—
135D4—2698no—
136D4—53832no—
137D4—53812no—
138D4C23×D26918yescomplemented
139C2×C4—2696no—
140C2×C4—26912no—
141C2×C4—2694no—
142C2×C4D4×D26913yes—
143C2×C4C23×D26913yes—
144C8—2694no—
145C8C23×D26914yescomplemented
146C22—28no—
147C22—424no—
148C22—2694no—
149C22—26924no—
150C22—5388no—
151C22—107664no—
152C22—107624no—
153C22D8×D26914yesdirect product factor
154C22C2×D4×D26913yes—
155C4—2694no—
156C4C2×D4×D26913yes—
157C4C24×D26911yescharacteristic
158C2—48no—
159C2—2698no—
160C2—10768no—
161C2C2×D8×D26916yesdirect product factor
162C2C22×D4×D26911yescharacteristic
subgroupG/H
centerC23D4×D269
commutator, cosocleC4×C269C25
FrattiniC4C24×D269
FittingC22×D8×C269C2
socleC23×C269C2×D4
hypercenterC22×D8D269
hypocenterC269C23×D8
LCSG ▷ C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. C22×D4×D269C2semidirect
2. C22×D2152C2semidirect
3. C22×#16864387C2semidirect
4. C2×D8×D269C2direct (N × H)
5. C22×C8×D269C2semidirect
6. C22×D8×C269C2semidirect
8. C22×D1076C22semidirect
11. C2×D4×D269C22semidirect
13. C2×D2152C22semidirect
14. C2×#16864387C22semidirect
15. D8×D269C22direct (N × H)
16. C22×#14524130C22semidirect
17. C2×C8×D269C22semidirect
18. C22×D4×C269C22semidirect
19. C2×D8×C269C22semidirect
20. C22×C8×C269C22semidirect
26. C2×D1076C23semidirect
29. D4×D269C23semidirect
33. D2152C23semidirect
34. #16864387C23semidirect
35. C2×#14524130C23semidirect
36. C8×D269C23semidirect
39. C2×D4×C269C23semidirect
41. D8×C269C23semidirect
42. C2×C8×C269C23semidirect
47. C22×D269D8direct (N × H)
50. D1076C24semidirect
55. #14524130C24semidirect
60. D4×C269C24semidirect
63. C8×C269C24semidirect
66. C22×C269C2×D8semidirect
71. C2×D269C2×D8direct (N × H)
77. C2×C269C22×D8semidirect
80. D269C22×D8direct (N × H)
81. C269C23×D8semidirect
87. C22×D8D269direct (N × H)
94. C22×D4C2×D269semidirect
99. C2×D8C2×D269direct (N × H)
102. C22×C8C2×D269semidirect
114. C2×D4C22×D269semidirect
121. D8C22×D269direct (N × H)
124. C2×C8C22×D269semidirect
138. D4C23×D269semidirect
145. C8C23×D269semidirect
153. C22D8×D269direct (N × H)
161. C2C2×D8×D269direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D4×D2692
C22×D21522
C22×#168643872
C2×D8×D2692
C22×C8×D2692
C22×D8×C2692
C23×D8269