Finite Group Databasebeta

← C22×#22575424 #46824104

Subgroups — C22×#22575424 #46824104

Order 34432.

2528 conjugacy classes of subgroups; only the 685 normal subgroups are shown.

normal subgroups only

This group has 2528 conjugacy classes of subgroups — too many to draw. Only its 685 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
1C23×C22⋊D269C212yesmaximal, complemented
2C23×C4×D269C211yesmaximal, characteristic, complemented
3C2×#22575424C2124yesmaximal, direct product factor
4C22×C4⋊Dic269C211yesmaximal, characteristic, complemented
5C22×C22⋊Dic269C212yesmaximal, complemented
6C23×D4×C269C211yesmaximal, characteristic, complemented
7C24×D269C2211yescharacteristic
8C22×C22⋊D269—216no—
9C22×C22⋊D269C22124yescomplemented
10C23×Dic269C2211yescharacteristic
11C23×Dic269C2212yes—
12C22×C4×D269—28no—
13C22×C4×D269C22112yescomplemented
14#22575424C22164yesdirect product factor
15C2×C4⋊Dic269C22112yescomplemented
16C2×C22⋊Dic269C22124yescomplemented
17C25×C269C2212yes—
18C22×D4×C269—28no—
19C22×D4×C269C22112yescomplemented
20C23×C4×C269C2211yescharacteristic
21C23×D269—24no—
22C23×D269—24no—
23C23×D269D418yescomplemented
24C23×D269C2316yes—
25C2×C22⋊D269—296no—
26C2×C22⋊D269C23132yescomplemented
27C22×Dic269—24no—
28C22×Dic269—28no—
29C22×Dic269C2316yes—
30C22×Dic269C23112yes—
31C2×C4×D269—248no—
32C2×C4×D269C23116yescomplemented
33C4⋊Dic269C23116yescomplemented
34C22⋊Dic269C23132yescomplemented
35C24×C269—28no—
36C24×C269—28no—
37C24×C269—28no—
38C24×C269C23112yes—
39C24×C269C2311yescharacteristic
40C2×D4×C269—248no—
41C2×D4×C269C23116yescomplemented
42C22×C4×C269D418yescomplemented
43C22×C4×C269C2316yes—
44C22×D269—232no—
45C22×D269—212no—
46C22×D269—212no—
47C22×D269C2×D4124yescomplemented
48C22×D269C2414yes—
49C22⋊D269—264no—
50C2×Dic269—212no—
51C2×Dic269—224no—
52C2×Dic269C2414yes—
53C2×Dic269C2418yes—
54C4×D269—232no—
55C23×C269—224no—
56C23×C269—224no—
57C23×C269—224no—
58C23×C269—432no—
59C23×C269C2×D414yes—
60C23×C269C2×D414yes—
61C23×C269#4114yes—
62C23×C269C2418yes—
63C23×C269C2413yes—
64D4×C269—232no—
65C2×C4×C269C2×D4124yescomplemented
66C2×C4×C269C2414yes—
67C22×C269—28no—
68C22×C269—28no—
69C22×C269—28no—
70C22×C269—448no—
71C22×C269#121116yescomplemented
72C22×C269C22×D416yes—
73C22×C269C22×D416yes—
74C22×C269C2×#4116yes—
75C22×C269C2511yescharacteristic
76C2×D269—248no—
77C2×D269—24no—
78C2×D269—24no—
79C2×D269C22×D418yescomplemented
80C4×C269C22×D418yescomplemented
81Dic269—24no—
82Dic269—28no—
83C2×C269—48no—
84C2×C269C2×#121112yescomplemented
85C2×C269C23×D411yescharacteristic
86C2×C269C23×D411yescharacteristic
87C2×C269C22×#4111yescharacteristic
88D269—28no—
89C269C22×#12111yescharacteristic, complemented, Sylow
90C22×#121—2691nomaximal, Sylow
91C23×D4—2692no—
92C23×D4D26911yescharacteristic, complemented
93C24×C4—2691no—
94C2×#121—26924no—
95C22×C4⋊C4—2691no—
96C22×C22⋊C4—2692no—
97C25—2691no—
98C25C2×D26912yes—
99C22×D4—28no—
100C22×D4—26924no—
101C22×D4—53816no—
102C22×D4C2×D269112yescomplemented
103C23×C4—2691no—
104C23×C4—2692no—
105C23×C4—26912no—
106C23×C4—5388no—
107C23×C4C2×D26911yescharacteristic
108#121—26964no—
109C2×C4⋊C4—26912no—
110C2×C22⋊C4—26924no—
111C24—28no—
112C24—28no—
113C24—28no—
114C24—2698no—
115C24—2696no—
116C24—5384no—
117C24—5384no—
118C24C22×D269112yes—
119C24C22×D26911yescharacteristic
120C2×D4—248no—
121C2×D4—26932no—
122C2×D4—53896no—
123C2×D4C22×D269116yescomplemented
124C22×C4—2696no—
125C22×C4—26912no—
126C22×C4—26916no—
127C22×C4—5388no—
128C22×C4—5384no—
129C22×C4—53848no—
130C22×C4C22⋊D26918yescomplemented
131C22×C4C22×D26916yes—
132C4⋊C4—26916no—
133C22⋊C4—26932no—
134C23—224no—
135C23—224no—
136C23—224no—
137C23—432no—
138C23—26924no—
139C23—2694no—
140C23—53832no—
141C23—53812no—
142C23—53812no—
143C23D4×D26914yes—
144C23C2×C22⋊D26914yes—
145C23#1686440114yes—
146C23C23×D26918yes—
147C23C23×D26913yes—
148D4—232no—
149D4—53864no—
150C2×C4—2694no—
151C2×C4—2698no—
152C2×C4—53824no—
153C2×C4—53812no—
154C2×C4—53832no—
155C2×C4C2×C22⋊D269124yescomplemented
156C2×C4C23×D26914yes—
157C22—28no—
158C22—28no—
159C22—28no—
160C22—448no—
161C22—2698no—
162C22—5384no—
163C22—5384no—
164C22—53848no—
165C22#22575424116yesdirect product factor
166C22C2×D4×D26916yes—
167C22C22×C22⋊D26916yes—
168C22C2×#1686440116yes—
169C22C24×D26911yescharacteristic
170C4—5388no—
171C4—5384no—
172C4C22×C22⋊D26918yescomplemented
173C2—48no—
174C2—5388no—
175C2C2×#22575424112yesdirect product factor
176C2C22×D4×D26911yescharacteristic
177C2C23×C22⋊D26911yescharacteristic
178C2C22×#1686440111yescharacteristic
subgroupG/H
centerC24C22×D269
commutator, cosocleC22×C269C25
FrattiniC22C24×D269
FittingC23×D4×C269C2
socleC24×C269C23
hypercenterC23×D4D269
hypocenterC269C22×#121
LCSG ▷ C22×C269 ▷ C269
UCSC1 ◁ C24 ◁ C23×D4

Complements

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

NH ≅ G/Ntype
1. C23×C22⋊D269C2semidirect
2. C23×C4×D269C2semidirect
3. C2×#22575424C2direct (N × H)
4. C22×C4⋊Dic269C2semidirect
5. C22×C22⋊Dic269C2semidirect
6. C23×D4×C269C2semidirect
9. C22×C22⋊D269C22semidirect
13. C22×C4×D269C22semidirect
14. #22575424C22direct (N × H)
15. C2×C4⋊Dic269C22semidirect
16. C2×C22⋊Dic269C22semidirect
19. C22×D4×C269C22semidirect
23. C23×D269D4semidirect
26. C2×C22⋊D269C23semidirect
32. C2×C4×D269C23semidirect
33. C4⋊Dic269C23semidirect
34. C22⋊Dic269C23semidirect
41. C2×D4×C269C23semidirect
42. C22×C4×C269D4semidirect
47. C22×D269C2×D4semidirect
65. C2×C4×C269C2×D4semidirect
71. C22×C269#121semidirect
79. C2×D269C22×D4semidirect
80. C4×C269C22×D4semidirect
84. C2×C269C2×#121semidirect
89. C269C22×#121semidirect
92. C23×D4D269semidirect
102. C22×D4C2×D269semidirect
123. C2×D4C22×D269semidirect
130. C22×C4C22⋊D269semidirect
155. C2×C4C2×C22⋊D269semidirect
165. C22#22575424direct (N × H)
172. C4C22×C22⋊D269semidirect
175. C2C2×#22575424direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C22⋊D2692
C23×C4×D2692
C2×#225754242
C22×C4⋊Dic2692
C22×C22⋊Dic2692
C23×D4×C2692
C22×#121269