Finite Group Databasebeta

← #1885×C263 #46778854

Subgroups — #1885×C263 #46778854

Order 33664.

360 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 112 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
1C2×#124×C263C211yesmaximal, characteristic
2#518×C263C211yesmaximal, characteristic
3#419×C263C212yesmaximal, complemented
4C2×#100×C263C211yesmaximal, characteristic
5#339×C263C212yesmaximal, complemented
6C22×Q8×C263C2211yescharacteristic
7C22×D4×C263C2211yescharacteristic
8C2×M16×C263C2212yes—
9#124×C263—22no—
10#124×C263C414yescomplemented
11C4×D4×C263—24no—
12#117×C263C2212yes—
13C2×C22⋊C4×C263—22no—
14C2×C22⋊C4×C263—22no—
15C2×C42×C263C2211yescharacteristic
16#103×C263—24no—
17#100×C263—22no—
18C24×C263D412yes—
19C2×Q8×C263—21no—
20C2×Q8×C263—22no—
21C2×Q8×C263—22no—
22C2×Q8×C263C2×C412yescomplemented
23C2×D4×C263—22no—
24C2×D4×C263—22no—
25C2×D4×C263C2×C412yes—
26C2×D4×C263D412yes—
27C22×C4×C263—21no—
28C22×C4×C263—21no—
29C22×C4×C263—24no—
30C22×C4×C263C2311yescharacteristic
31M16×C263—22no—
32M16×C263—22no—
33C2×C8×C263—22no—
34C4⋊C4×C263D414yes—
35C22⋊C4×C263—24no—
36C22⋊C4×C263—28no—
37C22⋊C4×C263—22no—
38C42×C263—21no—
39C42×C263—22no—
40C42×C263C2×C412yescomplemented
41C23×C263—22no—
42C23×C263—22no—
43C23×C263—44no—
44C23×C263C22⋊C414yes—
45C23×C263C2×D411yescharacteristic
46Q8×C263—24no—
47Q8×C263—42no—
48D4×C263—24no—
49D4×C263—24no—
50C2×C4×C263—22no—
51C2×C4×C263—22no—
52C2×C4×C263—24no—
53C2×C4×C263—42no—
54C2×C4×C263—41no—
55C2×C4×C263—41no—
56C2×C4×C263—84no—
57C2×C4×C263C22×C411yescharacteristic
58C2×C4×C263C2×D412yes—
59C2×C4×C263C2×D411yescharacteristic
60C2×C4×C263#4112yes—
61C8×C263—42no—
62C22×C263—22no—
63C22×C263—24no—
64C22×C263—44no—
65C22×C263—44no—
66C22×C263—82no—
67C22×C263C2×C22⋊C411yescharacteristic
68C22×C263#12011yescharacteristic
69C22×C263#12311yescharacteristic
70C4×C263—42no—
71C4×C263—42no—
72C4×C263—44no—
73C4×C263C4×D412yes—
74C4×C263#12112yes—
75C2×C263—21no—
76C2×C263—21no—
77C2×C263—44no—
78C2×C263#38611yescharacteristic
79C2×C263#45512yes—
80C263#188511yescharacteristic, direct product factor, Sylow
81#1885C26311yesmaximal, characteristic, direct product factor, Sylow
82C2×#124C2×C26311yescharacteristic
83#518C2×C26311yescharacteristic
84#419C2×C26312yescomplemented
85C2×#100C2×C26311yescharacteristic
86#339C2×C26312yescomplemented
87C22×Q8C22×C26311yescharacteristic
88C22×D4C22×C26311yescharacteristic
89C2×M16C22×C26312yes—
90#124—22no—
91#124C4×C26314yescomplemented
92C4×D4—24no—
93#117C22×C26312yes—
94C2×C22⋊C4—22no—
95C2×C22⋊C4—22no—
96C2×C42C22×C26311yescharacteristic
97#103—24no—
98#100—22no—
99C24D4×C26312yes—
100C2×Q8—21no—
101C2×Q8—22no—
102C2×Q8—22no—
103C2×Q8C2×C4×C26312yescomplemented
104C2×D4—22no—
105C2×D4—22no—
106C2×D4C2×C4×C26312yes—
107C2×D4D4×C26312yes—
108C22×C4—21no—
109C22×C4—21no—
110C22×C4—24no—
111C22×C4C23×C26311yescharacteristic
112M16—22no—
113M16—22no—
114C2×C8—22no—
115C4⋊C4D4×C26314yes—
116C22⋊C4—24no—
117C22⋊C4—28no—
118C22⋊C4—22no—
119C42—21no—
120C42—22no—
121C42C2×C4×C26312yescomplemented
122C23—22no—
123C23—22no—
124C23—44no—
125C23C22⋊C4×C26314yes—
126C23C2×D4×C26311yescharacteristic
127Q8—24no—
128Q8—42no—
129D4—24no—
130D4—24no—
131C2×C4—22no—
132C2×C4—22no—
133C2×C4—24no—
134C2×C4—42no—
135C2×C4—41no—
136C2×C4—41no—
137C2×C4—84no—
138C2×C4C22×C4×C26311yescharacteristic
139C2×C4C2×D4×C26312yes—
140C2×C4C2×D4×C26311yescharacteristic
141C2×C4#41×C26312yes—
142C8—42no—
143C22—22no—
144C22—24no—
145C22—44no—
146C22—44no—
147C22—82no—
148C22C2×C22⋊C4×C26311yescharacteristic
149C22#120×C26311yescharacteristic
150C22#123×C26311yescharacteristic
151C4—42no—
152C4—42no—
153C4—44no—
154C4C4×D4×C26312yes—
155C4#121×C26312yes—
156C2—21no—
157C2—21no—
158C2—44no—
159C2#386×C26311yescharacteristic
160C2#455×C26312yes—
subgroupG/H
center, socleC22×C263#120
commutatorC2×C4C22×C4×C263
Frattini, cosocleC22×C4C23×C263
prime radicalC22×D4×C263C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C263 ◁ C22×C4×C263 ◁ G

Complements

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

NH ≅ G/Ntype
3. #419×C263C2semidirect
5. #339×C263C2semidirect
10. #124×C263C4semidirect
22. C2×Q8×C263C2×C4semidirect
40. C42×C263C2×C4semidirect
80. C263#1885direct (N × H)
81. #1885C263direct (N × H)
84. #419C2×C263semidirect
86. #339C2×C263semidirect
91. #124C4×C263semidirect
103. C2×Q8C2×C4×C263semidirect
121. C42C2×C4×C263semidirect

Maximal subgroups

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

subgroupindex
C2×#124×C2632
#518×C2632
#419×C2632
C2×#100×C2632
#339×C2632
#1885263