Finite Group Databasebeta

← C22×#22575479 #46825618

Subgroups — C22×#22575479 #46825618

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×#16864402C211yesmaximal, characteristic, complemented
2C2×#22575479C2124yesmaximal, direct product factor
3C22×#16864390C212yesmaximal, complemented
4C22×#16864387C212yesmaximal, complemented
5C22×#16864386C211yesmaximal, characteristic, complemented
6C23×D4×C269C211yesmaximal, characteristic, complemented
7C2×#16864402—26no—
8C2×#16864402C22112yescomplemented
9C22×Dic538C2211yescharacteristic, complemented
10C22×D1076C2211yescharacteristic, complemented
11C22×C22⋊D269—21no—
12C22×C4×D269—21no—
13#22575479C22164yesdirect product factor
14C2×#16864390C22124yescomplemented
15C2×#16864387C22124yescomplemented
16C2×#16864386C22112yescomplemented
17C22×#14524130C2212yescomplemented
18C25×C269—21no—
19C22×D4×C269—21no—
20C22×D4×C269—26no—
21C22×D4×C269C2212yes—
22C22×D4×C269C22112yescomplemented
23C23×C4×C269C2211yescharacteristic
24C23×D269—21no—
25#16864402—224no—
26#16864402C23116yescomplemented
27C2×Dic538—23no—
28C2×Dic538C2316yescomplemented
29C2×D1076—23no—
30C2×D1076C2316yescomplemented
31C2×C22⋊D269—212no—
32C22×Dic269—21no—
33C2×C4×D269—212no—
34#16864390C23132yescomplemented
35#16864387C23132yescomplemented
36#16864386C23116yescomplemented
37C2×#14524130C23112yescomplemented
38C24×C269—22no—
39C24×C269—212no—
40C24×C269—48no—
41C24×C269D411yescharacteristic
42C2×D4×C269—26no—
43C2×D4×C269—212no—
44C2×D4×C269—224no—
45C2×D4×C269C23112yes—
46C2×D4×C269C23116yescomplemented
47C22×C4×C269D411yescharacteristic
48C22×C4×C269D416yes—
49C22×C4×C269C2311yescharacteristic
50C22×C4×C269C2316yes—
51C22×D269—26no—
52C22×D269—44no—
53Dic538—26no—
54Dic538C2414yescomplemented
55D1076—26no—
56D1076C2414yescomplemented
57C22⋊D269—216no—
58C2×Dic269—26no—
59C4×D269—216no—
60#14524130C2418yescomplemented
61C23×C269—24no—
62C23×C269—212no—
63C23×C269—216no—
64C23×C269—448no—
65C23×C269—48no—
66C23×C269C2×D416yes—
67C23×C269C2×D411yescharacteristic
68D4×C269—212no—
69D4×C269—216no—
70D4×C269C2418yes—
71C2×C4×C269C2×D416yes—
72C2×C4×C269C2×D413yes—
73C2×C4×C269C2×D4112yes—
74C2×C4×C269C2413yes—
75C2×C4×C269C2414yes—
76C22×C269—212no—
77C22×C269—28no—
78C22×C269—432no—
79C22×C269—424no—
80C22×C269AGL(1,ℤ/8)14yescomplemented
81C22×C269C22×D414yes—
82C22×C269C22×D413yes—
83C2×D269—24no—
84C2×D269—412no—
85C4×C269C22×D414yes—
86C4×C269C22×D413yes—
87C4×C269C2511yescharacteristic
88Dic269—24no—
89C2×C269—24no—
90C2×C269—48no—
91C2×C269C2×AGL(1,ℤ/8)16yescomplemented
92C2×C269C23×D411yescharacteristic
93D269—44no—
94C269C22×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
95C22×AGL(1,ℤ/8)—2691nomaximal, Sylow
96C22×#41—2691no—
97C23×D4D26911yescharacteristic, complemented
98C2×AGL(1,ℤ/8)—26924no—
99C22×SD16—2692no—
100C22×D8—2692no—
101C22×M16—2691no—
102C25—21no—
103C2×#41—26912no—
104C2×#41—5386no—
105C22×Q8—2691no—
106C22×D4—26no—
107C22×D4—21no—
108C22×D4—2691no—
109C22×D4—5381no—
110C22×D4C2×D26912yes—
111C22×D4C2×D269112yescomplemented
112C23×C4—5381no—
113C23×C4C2×D26911yescharacteristic
114AGL(1,ℤ/8)—26964no—
115C2×SD16—26924no—
116C2×D8—26924no—
117C2×M16—26912no—
118C22×C8—2692no—
119C24—212no—
120C24—22no—
121C24—48no—
122C24—5381no—
123C24C22⋊D26911yescharacteristic
124#41—26916no—
125#41—53824no—
126C2×Q8—2696no—
127C2×Q8—5383no—
128C2×D4—26no—
129C2×D4—212no—
130C2×D4—224no—
131C2×D4—2696no—
132C2×D4—53812no—
133C2×D4—5383no—
134C2×D4C22×D269112yes—
135C2×D4C22×D269116yescomplemented
136C22×C4—5381no—
137C22×C4—53812no—
138C22×C4C22⋊D26916yes—
139C22×C4C22⋊D26911yescharacteristic
140C22×C4C22×D26916yes—
141C22×C4C22×D26911yescharacteristic
142SD16—26932no—
143D8—26932no—
144M16—26916no—
145C2×C8—26912no—
146C23—24no—
147C23—212no—
148C23—216no—
149C23—448no—
150C23—48no—
151C23—5386no—
152C23—10764no—
153C23C2×C22⋊D26916yes—
154C23C2×C22⋊D26911yescharacteristic
155Q8—2694no—
156Q8—5386no—
157D4—212no—
158D4—216no—
159D4—2694no—
160D4—53816no—
161D4—5386no—
162D4C23×D26918yes—
163C2×C4—5386no—
164C2×C4—53816no—
165C2×C4C2×C22⋊D26916yes—
166C2×C4C2×C22⋊D26913yes—
167C2×C4C2×C22⋊D269112yes—
168C2×C4C23×D26913yes—
169C2×C4C23×D26914yes—
170C8—2698no—
171C22—212no—
172C22—28no—
173C22—432no—
174C22—424no—
175C22—5384no—
176C22—107612no—
177C22#2257547914yesdirect product factor
178C22C22×C22⋊D26914yes—
179C22C22×C22⋊D26913yes—
180C4—5384no—
181C4C22×C22⋊D26914yes—
182C4C22×C22⋊D26913yes—
183C4C24×D26911yescharacteristic
184C2—24no—
185C2—48no—
186C2—10764no—
187C2C2×#2257547916yesdirect product factor
188C2C23×C22⋊D26911yescharacteristic
subgroupG/H
centerC23C2×C22⋊D269
commutator, cosocleC4×C269C25
FrattiniC4C24×D269
FittingC23×D4×C269C2
socleC23×C269C2×D4
hypercenterC23×D4D269
hypocenterC269C22×AGL(1,ℤ/8)
LCSG ▷ C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×D4

Complements

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

NH ≅ G/Ntype
1. C22×#16864402C2semidirect
2. C2×#22575479C2direct (N × H)
3. C22×#16864390C2semidirect
4. C22×#16864387C2semidirect
5. C22×#16864386C2semidirect
6. C23×D4×C269C2semidirect
8. C2×#16864402C22semidirect
9. C22×Dic538C22semidirect
10. C22×D1076C22semidirect
13. #22575479C22direct (N × H)
14. C2×#16864390C22semidirect
15. C2×#16864387C22semidirect
16. C2×#16864386C22semidirect
17. C22×#14524130C22semidirect
22. C22×D4×C269C22semidirect
26. #16864402C23semidirect
28. C2×Dic538C23semidirect
30. C2×D1076C23semidirect
34. #16864390C23semidirect
35. #16864387C23semidirect
36. #16864386C23semidirect
37. C2×#14524130C23semidirect
46. C2×D4×C269C23semidirect
54. Dic538C24semidirect
56. D1076C24semidirect
60. #14524130C24semidirect
80. C22×C269AGL(1,ℤ/8)semidirect
91. C2×C269C2×AGL(1,ℤ/8)semidirect
94. C269C22×AGL(1,ℤ/8)semidirect
97. C23×D4D269semidirect
111. C22×D4C2×D269semidirect
135. C2×D4C22×D269semidirect
177. C22#22575479direct (N × H)
187. C2C2×#22575479direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#168644022
C2×#225754792
C22×#168643902
C22×#168643872
C22×#168643862
C23×D4×C2692
C22×AGL(1,ℤ/8)269