Finite Group Databasebeta

← #1782×C263 #46778751

Subgroups — #1782×C263 #46778751

Order 33664.

612 conjugacy classes of subgroups; only the 136 normal subgroups are shown.

normal subgroups only

This group has 612 conjugacy classes of subgroups — too many to draw. Only its 136 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×#41×C263C211yesmaximal, characteristic
2C2×#99×C263C214yesmaximal, complemented
3#381×C263C212yesmaximal, complemented
4C2×#41×C263—28no—
5C2×#41×C263—24no—
6C22×Q8×C263C411yescharacteristic, complemented
7C22×D4×C263C411yescharacteristic, complemented
8C22×D4×C263C2212yes—
9C23×C4×C263C412yescomplemented
10C23×C4×C263C2211yescharacteristic
11C2×C22⋊C4×C263C2214yes—
12#99×C263—28no—
13#95×C263—24no—
14C24×C263C2×C412yes—
15C24×C263C2311yescharacteristic
16#41×C263—232no—
17C2×Q8×C263—24no—
18C2×Q8×C263—22no—
19C2×D4×C263—24no—
20C2×D4×C263—24no—
21C2×D4×C263—24no—
22C2×D4×C263—22no—
23C2×D4×C263D418yes—
24C22×C4×C263—24no—
25C22×C4×C263—24no—
26C22×C4×C263—24no—
27C22×C4×C263—24no—
28C22×C4×C263—24no—
29C22×C4×C263C2×C411yescharacteristic
30C22×C4×C263C2×C412yes—
31C22×C4×C263C2×C411yescharacteristic
32C22×C4×C263D414yes—
33C22⋊C4×C263—28no—
34C23×C263—22no—
35C23×C263—22no—
36C23×C263—42no—
37C23×C263—44no—
38C23×C263C22⋊C414yes—
39C23×C263C22×C411yescharacteristic
40C23×C263C2×D412yes—
41C23×C263C2×D414yes—
42Q8×C263—28no—
43D4×C263—28no—
44D4×C263—216no—
45C2×C4×C263—216no—
46C2×C4×C263—22no—
47C2×C4×C263—22no—
48C2×C4×C263—22no—
49C2×C4×C263—22no—
50C2×C4×C263—28no—
51C2×C4×C263—48no—
52C2×C4×C263—44no—
53C2×C4×C263C22⋊C414yes—
54C2×C4×C263C22⋊C412yes—
55C2×C4×C263C22⋊C412yes—
56C22×C263—24no—
57C22×C263—22no—
58C22×C263—24no—
59C22×C263—44no—
60C22×C263—44no—
61C22×C263—44no—
62C22×C263—44no—
63C22×C263C2×C22⋊C412yes—
64C22×C263C2×C22⋊C411yescharacteristic
65C22×C263#12014yes—
66C4×C263—22no—
67C4×C263—24no—
68C4×C263—22no—
69C4×C263—84no—
70C2×C263—24no—
71C2×C263—22no—
72C2×C263—44no—
73C2×C263#37911yescharacteristic
74C2×C263#41012yes—
75C263#178211yescharacteristic, direct product factor, Sylow
76#1782C26311yesmaximal, characteristic, direct product factor, Sylow
77C22×#41C2×C26311yescharacteristic
78C2×#99C2×C26314yescomplemented
79#381C2×C26312yescomplemented
80C2×#41—28no—
81C2×#41—24no—
82C22×Q8C4×C26311yescharacteristic, complemented
83C22×D4C4×C26311yescharacteristic, complemented
84C22×D4C22×C26312yes—
85C23×C4C4×C26312yescomplemented
86C23×C4C22×C26311yescharacteristic
87C2×C22⋊C4C22×C26314yes—
88#99—28no—
89#95—24no—
90C24C2×C4×C26312yes—
91C24C23×C26311yescharacteristic
92#41—232no—
93C2×Q8—24no—
94C2×Q8—22no—
95C2×D4—24no—
96C2×D4—24no—
97C2×D4—24no—
98C2×D4—22no—
99C2×D4D4×C26318yes—
100C22×C4—24no—
101C22×C4—24no—
102C22×C4—24no—
103C22×C4—24no—
104C22×C4—24no—
105C22×C4C2×C4×C26311yescharacteristic
106C22×C4C2×C4×C26312yes—
107C22×C4C2×C4×C26311yescharacteristic
108C22×C4D4×C26314yes—
109C22⋊C4—28no—
110C23—22no—
111C23—22no—
112C23—42no—
113C23—44no—
114C23C22⋊C4×C26314yes—
115C23C22×C4×C26311yescharacteristic
116C23C2×D4×C26312yes—
117C23C2×D4×C26314yes—
118Q8—28no—
119D4—28no—
120D4—216no—
121C2×C4—216no—
122C2×C4—22no—
123C2×C4—22no—
124C2×C4—22no—
125C2×C4—22no—
126C2×C4—28no—
127C2×C4—48no—
128C2×C4—44no—
129C2×C4C22⋊C4×C26312yes—
130C2×C4C22⋊C4×C26314yes—
131C2×C4C22⋊C4×C26312yes—
132C22—24no—
133C22—22no—
134C22—24no—
135C22—44no—
136C22—44no—
137C22—44no—
138C22—44no—
139C22C2×C22⋊C4×C26312yes—
140C22C2×C22⋊C4×C26311yescharacteristic
141C22#120×C26314yes—
142C4—22no—
143C4—24no—
144C4—22no—
145C4—84no—
146C2—24no—
147C2—22no—
148C2—44no—
149C2#379×C26311yescharacteristic
150C2#410×C26312yes—
subgroupG/H
center, socleC22×C263C2×C22⋊C4
commutatorC23C22×C4×C263
Frattini, cosocleC24C23×C263
prime radicalC22×#41×C263C2
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C263 ◁ C23×C4×C263 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#99×C263C2semidirect
3. #381×C263C2semidirect
6. C22×Q8×C263C4semidirect
7. C22×D4×C263C4semidirect
9. C23×C4×C263C4semidirect
75. C263#1782direct (N × H)
76. #1782C263direct (N × H)
78. C2×#99C2×C263semidirect
79. #381C2×C263semidirect
82. C22×Q8C4×C263semidirect
83. C22×D4C4×C263semidirect
85. C23×C4C4×C263semidirect

Maximal subgroups

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

subgroupindex
C22×#41×C2632
C2×#99×C2632
#381×C2632
#1782263