Finite Group Databasebeta

← #1910×C269 #46807017

Subgroups — #1910×C269 #46807017

Order 34432.

344 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 108 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
1#568×C269C211yesmaximal, characteristic, complemented
2#535×C269C211yesmaximal, characteristic
3#418×C269C212yesmaximal, complemented
4#410×C269C211yesmaximal, characteristic, complemented
5H(3,ℤ/4)×C269C212yesmaximal, complemented
6C2×#41×C269C2211yescharacteristic
7C22×D4×C269C2211yescharacteristic
8#131×C269—24no—
9C2×M16×C269—22no—
10C2×M16×C269C2212yes—
11#127×C269C412yescomplemented
12#124×C269C412yescomplemented
13#121×C269—22no—
14#120×C269—22no—
15#117×C269C2212yes—
16#117×C269C2211yescharacteristic
17#102×C269—24no—
18#99×C269—22no—
19C24×C269—21no—
20#41×C269—22no—
21#41×C269—22no—
22C2×Q8×C269C2×C411yescharacteristic
23C2×D4×C269—24no—
24C2×D4×C269—22no—
25C2×D4×C269—21no—
26C2×D4×C269—22no—
27C2×D4×C269C2×C412yes—
28C2×D4×C269C2×C411yescharacteristic
29C2×D4×C269D412yes—
30C22×C4×C269D412yes—
31C22×C4×C269C2311yescharacteristic
32M16×C269—24no—
33M16×C269—22no—
34M16×C269—22no—
35C2×C8×C269—24no—
36C2×C8×C269D414yescomplemented
37C4⋊C4×C269—21no—
38C4⋊C4×C269—22no—
39C22⋊C4×C269—21no—
40C22⋊C4×C269—24no—
41C22⋊C4×C269—22no—
42C42×C269—22no—
43C42×C269C2×C412yes—
44C23×C269—22no—
45C23×C269—42no—
46C23×C269—82no—
47C23×C269C22⋊C412yes—
48C23×C269C2×D411yescharacteristic
49Q8×C269—22no—
50D4×C269—24no—
51D4×C269—22no—
52D4×C269—24no—
53D4×C269—41no—
54D4×C269—41no—
55D4×C269—84no—
56C2×C4×C269—22no—
57C2×C4×C269—22no—
58C2×C4×C269—22no—
59C2×C4×C269—42no—
60C2×C4×C269C22⋊C412yes—
61C2×C4×C269C22×C411yescharacteristic
62C2×C4×C269C2×D412yes—
63C2×C4×C269C2×D411yescharacteristic
64C2×C4×C269#4112yes—
65C8×C269—24no—
66C22×C269—22no—
67C22×C269—41no—
68C22×C269—42no—
69C22×C269—44no—
70C22×C269—42no—
71C22×C269—84no—
72C22×C269C2×C22⋊C411yescharacteristic
73C22×C269#12112yes—
74C4×C269—22no—
75C4×C269—42no—
76C4×C269—82no—
77C4×C269C4×D412yes—
78C4×C269#12011yescharacteristic
79C4×C269#12311yescharacteristic
80C2×C269—21no—
81C2×C269—22no—
82C2×C269—42no—
83C2×C269—82no—
84C2×C269#38611yescharacteristic
85C269#191011yescharacteristic, direct product factor, Sylow
86#1910C26911yesmaximal, characteristic, direct product factor, Sylow
87#568C2×C26911yescharacteristic, complemented
88#535C2×C26911yescharacteristic
89#418C2×C26912yescomplemented
90#410C2×C26911yescharacteristic, complemented
91H(3,ℤ/4)C2×C26912yescomplemented
92C2×#41C22×C26911yescharacteristic
93C22×D4C22×C26911yescharacteristic
94#131—24no—
95C2×M16—22no—
96C2×M16C22×C26912yes—
97#127C4×C26912yescomplemented
98#124C4×C26912yescomplemented
99#121—22no—
100#120—22no—
101#117C22×C26912yes—
102#117C22×C26911yescharacteristic
103#102—24no—
104#99—22no—
105C24—21no—
106#41—22no—
107#41—22no—
108C2×Q8C2×C4×C26911yescharacteristic
109C2×D4—24no—
110C2×D4—22no—
111C2×D4—21no—
112C2×D4—22no—
113C2×D4C2×C4×C26912yes—
114C2×D4C2×C4×C26911yescharacteristic
115C2×D4D4×C26912yes—
116C22×C4D4×C26912yes—
117C22×C4C23×C26911yescharacteristic
118M16—24no—
119M16—22no—
120M16—22no—
121C2×C8—24no—
122C2×C8D4×C26914yescomplemented
123C4⋊C4—21no—
124C4⋊C4—22no—
125C22⋊C4—21no—
126C22⋊C4—24no—
127C22⋊C4—22no—
128C42—22no—
129C42C2×C4×C26912yes—
130C23—22no—
131C23—42no—
132C23—82no—
133C23C22⋊C4×C26912yes—
134C23C2×D4×C26911yescharacteristic
135Q8—22no—
136D4—24no—
137D4—22no—
138D4—24no—
139D4—41no—
140D4—41no—
141D4—84no—
142C2×C4—22no—
143C2×C4—22no—
144C2×C4—22no—
145C2×C4—42no—
146C2×C4C22⋊C4×C26912yes—
147C2×C4C22×C4×C26911yescharacteristic
148C2×C4C2×D4×C26912yes—
149C2×C4C2×D4×C26911yescharacteristic
150C2×C4#41×C26912yes—
151C8—24no—
152C22—22no—
153C22—41no—
154C22—42no—
155C22—44no—
156C22—42no—
157C22—84no—
158C22C2×C22⋊C4×C26911yescharacteristic
159C22#121×C26912yes—
160C4—22no—
161C4—42no—
162C4—82no—
163C4C4×D4×C26912yes—
164C4#120×C26911yescharacteristic
165C4#123×C26911yescharacteristic
166C2—21no—
167C2—22no—
168C2—42no—
169C2—82no—
170C2#386×C26911yescharacteristic
subgroupG/H
center, socleC2×C269#386
commutatorC2×C4C22×C4×C269
Frattini, cosocleC22×C4C23×C269
prime radical#535×C269C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C269 ◁ C22×C4×C269 ◁ G

Complements

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

NH ≅ G/Ntype
1. #568×C269C2semidirect
3. #418×C269C2semidirect
4. #410×C269C2semidirect
5. H(3,ℤ/4)×C269C2semidirect
11. #127×C269C4semidirect
12. #124×C269C4semidirect
36. C2×C8×C269D4semidirect
85. C269#1910direct (N × H)
86. #1910C269direct (N × H)
87. #568C2×C269semidirect
89. #418C2×C269semidirect
90. #410C2×C269semidirect
91. H(3,ℤ/4)C2×C269semidirect
97. #127C4×C269semidirect
98. #124C4×C269semidirect
122. C2×C8D4×C269semidirect

Maximal subgroups

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

subgroupindex
#568×C2692
#535×C2692
#418×C2692
#410×C2692
H(3,ℤ/4)×C2692
#1910269