Finite Group Databasebeta

← #2099×C263 #46779068

Subgroups — #2099×C263 #46779068

Order 33664.

214 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 100 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#389×C263C211yesmaximal, characteristic
2#384×C263C211yesmaximal, characteristic
3#340×C263C212yesmaximal
4#340×C263C212yesmaximal
5#336×C263C211yesmaximal, characteristic
6C22×C8×C263C2212yes—
7C2×C4⋊C4×C263—21no—
8C2×C4⋊C4×C263—21no—
9C2×C4⋊C4×C263—21no—
10C2×C4⋊C4×C263C2212yes—
11C2×C4⋊C4×C263C2211yescharacteristic
12C2×C4⋊C4×C263C2211yescharacteristic
13C2×C42×C263C2211yescharacteristic
14#95×C263—21no—
15C22×C4×C263—21no—
16C22×C4×C263—21no—
17C22×C4×C263—22no—
18C22×C4×C263D411yescharacteristic
19C22×C4×C263D411yescharacteristic
20C22×C4×C263C2311yescharacteristic
21C2×C8×C263—22no—
22C2×C8×C263—22no—
23C2×C8×C263—22no—
24C4⋊C4×C263—21no—
25C4⋊C4×C263—22no—
26C4⋊C4×C263—24no—
27C4⋊C4×C263—42no—
28C4⋊C4×C263—42no—
29C4⋊C4×C263—42no—
30C4⋊C4×C263Q812yes—
31C42×C263—22no—
32C23×C263C2×D411yescharacteristic
33C2×C4×C263—21no—
34C2×C4×C263—21no—
35C2×C4×C263—21no—
36C2×C4×C263—21no—
37C2×C4×C263—22no—
38C2×C4×C263—41no—
39C2×C4×C263—41no—
40C2×C4×C263—41no—
41C2×C4×C263—42no—
42C2×C4×C263—41no—
43C2×C4×C263—42no—
44C2×C4×C263—42no—
45C2×C4×C263—41no—
46C2×C4×C263D812yes—
47C2×C4×C263SD1612yes—
48C2×C4×C263C2×Q811yescharacteristic
49C2×C4×C263#4112yes—
50C2×C4×C263#4112yes—
51C2×C4×C263#4111yescharacteristic
52C8×C263—42no—
53C22×C263C22⋊Q811yescharacteristic
54C22×C263#12311yescharacteristic
55C22×C263#12411yescharacteristic
56C22×C263C2×D811yescharacteristic
57C22×C263C2×SD1611yescharacteristic
58C22×C263#13711yescharacteristic
59C22×C263#13711yescharacteristic
60C4×C263—22no—
61C4×C263—22no—
62C4×C263—42no—
63C4×C263—81no—
64C4×C263—82no—
65C4×C263#12512yes—
66C4×C263#12612yes—
67C2×C263#40011yescharacteristic
68C2×C263#47411yescharacteristic
69C2×C263#47511yescharacteristic
70C2×C263#48011yescharacteristic
71C2×C263#48311yescharacteristic
72C2×C263#48611yescharacteristic
73C2×C263#49111yescharacteristic
74C263#209911yescharacteristic, direct product factor, Sylow
75#2099C26311yesmaximal, characteristic, direct product factor, Sylow
76#389C2×C26311yescharacteristic
77#384C2×C26311yescharacteristic
78#340C2×C26312yes—
79#340C2×C26312yes—
80#336C2×C26311yescharacteristic
81C22×C8C22×C26312yes—
82C2×C4⋊C4—21no—
83C2×C4⋊C4—21no—
84C2×C4⋊C4—21no—
85C2×C4⋊C4C22×C26312yes—
86C2×C4⋊C4C22×C26311yescharacteristic
87C2×C4⋊C4C22×C26311yescharacteristic
88C2×C42C22×C26311yescharacteristic
89#95—21no—
90C22×C4—21no—
91C22×C4—21no—
92C22×C4—22no—
93C22×C4D4×C26311yescharacteristic
94C22×C4D4×C26311yescharacteristic
95C22×C4C23×C26311yescharacteristic
96C2×C8—22no—
97C2×C8—22no—
98C2×C8—22no—
99C4⋊C4—21no—
100C4⋊C4—22no—
101C4⋊C4—24no—
102C4⋊C4—42no—
103C4⋊C4—42no—
104C4⋊C4—42no—
105C4⋊C4Q8×C26312yes—
106C42—22no—
107C23C2×D4×C26311yescharacteristic
108C2×C4—21no—
109C2×C4—21no—
110C2×C4—21no—
111C2×C4—21no—
112C2×C4—22no—
113C2×C4—41no—
114C2×C4—41no—
115C2×C4—41no—
116C2×C4—41no—
117C2×C4—42no—
118C2×C4—41no—
119C2×C4—42no—
120C2×C4—42no—
121C2×C4D8×C26312yes—
122C2×C4SD16×C26312yes—
123C2×C4C2×Q8×C26311yescharacteristic
124C2×C4#41×C26312yes—
125C2×C4#41×C26312yes—
126C2×C4#41×C26311yescharacteristic
127C8—42no—
128C22C22⋊Q8×C26311yescharacteristic
129C22#123×C26311yescharacteristic
130C22#124×C26311yescharacteristic
131C22C2×D8×C26311yescharacteristic
132C22C2×SD16×C26311yescharacteristic
133C22#137×C26311yescharacteristic
134C22#137×C26311yescharacteristic
135C4—22no—
136C4—22no—
137C4—42no—
138C4—81no—
139C4—82no—
140C4#125×C26312yes—
141C4#126×C26312yes—
142C2#400×C26311yescharacteristic
143C2#474×C26311yescharacteristic
144C2#475×C26311yescharacteristic
145C2#480×C26311yescharacteristic
146C2#483×C26311yescharacteristic
147C2#486×C26311yescharacteristic
148C2#491×C26311yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C263C2×D4
commutator, Frattini, cosocleC22×C4C23×C263
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C263 ◁ C2×C42×C263 ◁ G

Complements

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

NH ≅ G/Ntype
74. C263#2099direct (N × H)
75. #2099C263direct (N × H)

Maximal subgroups

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

subgroupindex
#389×C2632
#384×C2632
#340×C2632
#336×C2632
#2099263