Finite Group Databasebeta

← #1518×C263 #46778487

Subgroups — #1518×C263 #46778487

Order 33664.

220 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 104 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#533×C263C211yesmaximal, characteristic
2#431×C263C211yesmaximal, characteristic
3#382×C263C211yesmaximal, characteristic
4#328×C263C214yesmaximal
5C4⋊Q8×C263C411yescharacteristic, complemented
6C4⋊Q8×C263C411yescharacteristic, complemented
7#125×C263—21no—
8C22⋊Q8×C263—21no—
9C22⋊Q8×C263C2212yes—
10C4×Q8×C263—21no—
11C4×Q8×C263C412yescomplemented
12#117×C263—21no—
13C2×C4⋊C4×C263—21no—
14C2×C42×C263C2211yescharacteristic
15C4⋊C8×C263—21no—
16C22⋊C8×C263C2212yes—
17C4×C8×C263—21no—
18#95×C263—21no—
19#95×C263C2212yes—
20C2×Q8×C263—21no—
21C2×Q8×C263C2×C412yes—
22C22×C4×C263—22no—
23C22×C4×C263D411yescharacteristic
24C22×C4×C263D411yescharacteristic
25C22×C4×C263C2311yescharacteristic
26C2×C8×C263—22no—
27C4⋊C4×C263—21no—
28C4⋊C4×C263—21no—
29C4⋊C4×C263—21no—
30C4⋊C4×C263—22no—
31C4⋊C4×C263—22no—
32C4⋊C4×C263—42no—
33C4⋊C4×C263C2×C412yes—
34C22⋊C4×C263—22no—
35C42×C263—22no—
36C42×C263C2×C411yescharacteristic
37C42×C263C2×C411yescharacteristic
38C42×C263D411yescharacteristic
39C42×C263D411yescharacteristic
40C23×C263C2×D411yescharacteristic
41Q8×C263—42no—
42Q8×C263—42no—
43C2×C4×C263—22no—
44C2×C4×C263—22no—
45C2×C4×C263—41no—
46C2×C4×C263—41no—
47C2×C4×C263—42no—
48C2×C4×C263—42no—
49C2×C4×C263—42no—
50C2×C4×C263C22⋊C411yescharacteristic
51C2×C4×C263C22⋊C411yescharacteristic
52C2×C4×C263C22⋊C411yescharacteristic
53C2×C4×C263C22⋊C411yescharacteristic
54C2×C4×C263SD1612yes—
55C2×C4×C263Q1612yes—
56C2×C4×C263C22×C411yescharacteristic
57C2×C4×C263C2×D411yescharacteristic
58C8×C263—42no—
59C22×C263—21no—
60C22×C263—21no—
61C22×C263C2×C22⋊C411yescharacteristic
62C22×C263C2×SD1611yescharacteristic
63C22×C263C2×Q1611yescharacteristic
64C4×C263—21no—
65C4×C263—21no—
66C4×C263—21no—
67C4×C263—21no—
68C4×C263—42no—
69C4×C263—42no—
70C4×C263—82no—
71C4×C263#10312yes—
72C4×C263#10312yes—
73C2×C263—21no—
74C2×C263—21no—
75C2×C263#41011yescharacteristic
76C2×C263C2×#10311yescharacteristic
77C2×C263#42111yescharacteristic
78C263#151811yescharacteristic, direct product factor, Sylow
79#1518C26311yesmaximal, characteristic, direct product factor, Sylow
80#533C2×C26311yescharacteristic
81#431C2×C26311yescharacteristic
82#382C2×C26311yescharacteristic
83#328C2×C26314yes—
84C4⋊Q8C4×C26311yescharacteristic, complemented
85C4⋊Q8C4×C26311yescharacteristic, complemented
86#125—21no—
87C22⋊Q8—21no—
88C22⋊Q8C22×C26312yes—
89C4×Q8—21no—
90C4×Q8C4×C26312yescomplemented
91#117—21no—
92C2×C4⋊C4—21no—
93C2×C42C22×C26311yescharacteristic
94C4⋊C8—21no—
95C22⋊C8C22×C26312yes—
96C4×C8—21no—
97#95—21no—
98#95C22×C26312yes—
99C2×Q8—21no—
100C2×Q8C2×C4×C26312yes—
101C22×C4—22no—
102C22×C4D4×C26311yescharacteristic
103C22×C4D4×C26311yescharacteristic
104C22×C4C23×C26311yescharacteristic
105C2×C8—22no—
106C4⋊C4—21no—
107C4⋊C4—21no—
108C4⋊C4—21no—
109C4⋊C4—22no—
110C4⋊C4—22no—
111C4⋊C4—42no—
112C4⋊C4C2×C4×C26312yes—
113C22⋊C4—22no—
114C42—22no—
115C42C2×C4×C26311yescharacteristic
116C42C2×C4×C26311yescharacteristic
117C42D4×C26311yescharacteristic
118C42D4×C26311yescharacteristic
119C23C2×D4×C26311yescharacteristic
120Q8—42no—
121Q8—42no—
122C2×C4—22no—
123C2×C4—22no—
124C2×C4—41no—
125C2×C4—41no—
126C2×C4—42no—
127C2×C4—42no—
128C2×C4—42no—
129C2×C4C22⋊C4×C26311yescharacteristic
130C2×C4C22⋊C4×C26311yescharacteristic
131C2×C4C22⋊C4×C26311yescharacteristic
132C2×C4C22⋊C4×C26311yescharacteristic
133C2×C4SD16×C26312yes—
134C2×C4Q16×C26312yes—
135C2×C4C22×C4×C26311yescharacteristic
136C2×C4C2×D4×C26311yescharacteristic
137C8—42no—
138C22—21no—
139C22—21no—
140C22C2×C22⋊C4×C26311yescharacteristic
141C22C2×SD16×C26311yescharacteristic
142C22C2×Q16×C26311yescharacteristic
143C4—21no—
144C4—21no—
145C4—21no—
146C4—21no—
147C4—42no—
148C4—42no—
149C4—82no—
150C4#103×C26312yes—
151C4#103×C26312yes—
152C2—21no—
153C2—21no—
154C2#410×C26311yescharacteristic
155C2C2×#103×C26311yescharacteristic
156C2#421×C26311yescharacteristic
subgroupG/H
center, socleC22×C263C2×C22⋊C4
commutatorC2×C4C22×C4×C263
Frattini, cosocleC22×C4C23×C263
prime radicalC23×C263C2×D4
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C263 ◁ C2×C42×C263 ◁ G

Complements

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

NH ≅ G/Ntype
5. C4⋊Q8×C263C4semidirect
6. C4⋊Q8×C263C4semidirect
11. C4×Q8×C263C4semidirect
78. C263#1518direct (N × H)
79. #1518C263direct (N × H)
84. C4⋊Q8C4×C263semidirect
85. C4⋊Q8C4×C263semidirect
90. C4×Q8C4×C263semidirect

Maximal subgroups

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

subgroupindex
#533×C2632
#431×C2632
#382×C2632
#328×C2632
#1518263