Finite Group Databasebeta

← #46781216

Subgroups — #46781216

Order 33664.

246 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 81 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#30681995C211yesmaximal, characteristic, complemented
2#30681991C211yesmaximal, characteristic, complemented
3D4⋊(C263⋊C8)C214yesmaximal, complemented
4#532×C263C211yesmaximal, characteristic
5C4⋊(C263⋊C8)—21no—
6C4⋊(C263⋊C8)C2212yes—
7C22⋊(C263⋊C8)—21no—
8C22⋊(C263⋊C8)—21no—
9#22554381—21no—
10C4×C263⋊C8C2212yes—
11C2×#41×C263—21no—
12C4⋊Q8×C263C411yescharacteristic
13#127×C263C411yescharacteristic
14#124×C263—21no—
15#121×C263—21no—
16#121×C263C412yes—
17C4×D4×C263—21no—
18C4×D4×C263C2212yes—
19C2×C42×C263C2211yescharacteristic
20C2×C263⋊C8—22no—
21C2×C263⋊C8—22no—
22#41×C263—44no—
23C2×Q8×C263—21no—
24C2×D4×C263—22no—
25C2×D4×C263—21no—
26C2×D4×C263—21no—
27C2×D4×C263C2×C412yes—
28C22×C4×C263—22no—
29C22×C4×C263C2×C411yescharacteristic
30C22×C4×C263D411yescharacteristic
31C22×C4×C263D411yescharacteristic
32C4⋊C4×C263—21no—
33C4⋊C4×C263C2×C412yes—
34C22⋊C4×C263—22no—
35C22⋊C4×C263—22no—
36C42×C263C2×C411yescharacteristic
37C42×C263D411yescharacteristic
38C42×C263D411yescharacteristic
39C42×C263C2311yescharacteristic
40C263⋊C8—42no—
41C263⋊C8—42no—
42C23×C263—22no—
43C23×C263C22⋊C411yescharacteristic
44Q8×C263—42no—
45D4×C263—24no—
46D4×C263—42no—
47D4×C263—42no—
48D4×C263—44no—
49C2×C4×C263—22no—
50C2×C4×C263—22no—
51C2×C4×C263—22no—
52C2×C4×C263—41no—
53C2×C4×C263—44no—
54C2×C4×C263C22⋊C411yescharacteristic
55C2×C4×C263C22⋊C411yescharacteristic
56C2×C4×C263C22⋊C411yescharacteristic
57C2×C4×C263C22×C411yescharacteristic
58C2×C4×C263C2×D411yescharacteristic
59C2×C4×C263C2×D411yescharacteristic
60C22×C263—21no—
61C22×C263—21no—
62C22×C263—21no—
63C22×C263—42no—
64C22×C263—42no—
65C22×C263—42no—
66C22×C263C2×C22⋊C411yescharacteristic
67C4×C263—21no—
68C4×C263—21no—
69C4×C263—21no—
70C4×C263—21no—
71C4×C263—42no—
72C4×C263#13112yes—
73C4×C263AGL(1,ℤ/8)12yes—
74C2×C263—41no—
75C2×C263—82no—
76C2×C263#40811yescharacteristic
77C2×C263#41811yescharacteristic
78C2×C263#42111yescharacteristic
79C263#149611yescharacteristic, complemented, Sylow
80#1496—2631nomaximal, Sylow
81#532D26311yescharacteristic
82#432—2631no—
83#431—2631no—
84D4⋊C8—2634no—
85C2×#41—21no—
86C4⋊Q8Dic26311yescharacteristic
87#127Dic26311yescharacteristic
88#124—21no—
89#121—21no—
90#121Dic26312yes—
91C4×D4—21no—
92C4×D4C2×D26312yes—
93C2×C42C2×D26311yescharacteristic
94C4⋊C8—2632no—
95C4⋊C8—5261no—
96C22⋊C8—5261no—
97C22⋊C8—5261no—
98#97—5261no—
99C4×C8—2632no—
100#41—44no—
101C2×Q8—21no—
102C2×D4—22no—
103C2×D4—21no—
104C2×D4—21no—
105C2×D4C2×Dic26312yes—
106C22×C4—22no—
107C22×C4C2×Dic26311yescharacteristic
108C22×C4C22⋊D26311yescharacteristic
109C22×C4C22⋊D26311yescharacteristic
110C2×C8—5262no—
111C2×C8—5262no—
112C4⋊C4—21no—
113C4⋊C4C2×Dic26312yes—
114C22⋊C4—22no—
115C22⋊C4—22no—
116C42C2×Dic26311yescharacteristic
117C42C22⋊D26311yescharacteristic
118C42C22⋊D26311yescharacteristic
119C42C22×D26311yescharacteristic
120C23—22no—
121C23C22⋊Dic26311yescharacteristic
122Q8—42no—
123D4—24no—
124D4—42no—
125D4—42no—
126D4—44no—
127C2×C4—22no—
128C2×C4—22no—
129C2×C4—22no—
130C2×C4—41no—
131C2×C4—44no—
132C2×C4C22⋊Dic26311yescharacteristic
133C2×C4C22⋊Dic26311yescharacteristic
134C2×C4C22⋊Dic26311yescharacteristic
135C2×C4C22×Dic26311yescharacteristic
136C2×C4C2×C22⋊D26311yescharacteristic
137C2×C4C2×C22⋊D26311yescharacteristic
138C8—10522no—
139C8—10522no—
140C22—21no—
141C22—21no—
142C22—21no—
143C22—42no—
144C22—42no—
145C22—42no—
146C22C2×C22⋊Dic26311yescharacteristic
147C4—21no—
148C4—21no—
149C4—21no—
150C4—21no—
151C4—42no—
152C4#2255447712yes—
153C4#2255449612yes—
154C2—41no—
155C2—82no—
156C2#3068190511yescharacteristic
157C2#3068194311yescharacteristic
158C2#3068195511yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D263
commutatorC2×C4×C263C22×C4
FrattiniC42C22×D263
Fitting, prime radical#532×C263C2
socleC22×C263C2×C22⋊C4
cosocleC42×C263C23
hypercenter#532D263
hypocenterC263#1496
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #532

Complements

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

NH ≅ G/Ntype
1. #30681995C2semidirect
2. #30681991C2semidirect
3. D4⋊(C263⋊C8)C2semidirect
79. C263#1496semidirect

Maximal subgroups

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

subgroupindex
#306819952
#306819912
D4⋊(C263⋊C8)2
#532×C2632
#1496263