Finite Group Databasebeta

← #46781345

Subgroups — #46781345

Order 33664.

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

normal subgroups only

This group has 264 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
2C4×#16862360C211yesmaximal, characteristic, complemented
3#30681678C214yesmaximal, complemented
4C2×#124×C263C211yesmaximal, characteristic
5C2×#16862360—21no—
6C4⋊(C263⋊C8)—21no—
7C22⋊(C263⋊C8)—21no—
8#22554381C2212yescomplemented
9#22554381C2212yescomplemented
10C4×C263⋊C8—21no—
11C22×Q8×C263C411yescharacteristic
12C22×D4×C263C411yescharacteristic
13#124×C263—21no—
14#124×C263—21no—
15#124×C263C412yes—
16#124×C263C2212yes—
17C2×C22⋊C4×C263—21no—
18C2×C22⋊C4×C263—21no—
19C2×C42×C263C2211yescharacteristic
20#16862360—24no—
21C2×C263⋊C8—22no—
22C2×C263⋊C8—22no—
23C24×C263—21no—
24C2×Q8×C263—21no—
25C2×Q8×C263—42no—
26C2×Q8×C263C2×C412yes—
27C2×D4×C263—21no—
28C2×D4×C263—42no—
29C2×D4×C263C2×C412yes—
30C22×C4×C263—21no—
31C22×C4×C263C2×C411yescharacteristic
32C22×C4×C263D411yescharacteristic
33C22×C4×C263D411yescharacteristic
34C22⋊C4×C263—22no—
35C22⋊C4×C263—22no—
36C22⋊C4×C263—22no—
37C22⋊C4×C263—22no—
38C42×C263C2×C411yescharacteristic
39C42×C263D411yescharacteristic
40C42×C263D411yescharacteristic
41C42×C263C2311yescharacteristic
42C263⋊C8—24no—
43C263⋊C8—42no—
44C23×C263—22no—
45C23×C263—42no—
46C23×C263—42no—
47C23×C263—42no—
48C23×C263C22⋊C411yescharacteristic
49Q8×C263—42no—
50Q8×C263—42no—
51D4×C263—42no—
52D4×C263—42no—
53C2×C4×C263—22no—
54C2×C4×C263—22no—
55C2×C4×C263—22no—
56C2×C4×C263—41no—
57C2×C4×C263—42no—
58C2×C4×C263C22⋊C411yescharacteristic
59C2×C4×C263C22⋊C411yescharacteristic
60C2×C4×C263C22⋊C411yescharacteristic
61C2×C4×C263C22×C411yescharacteristic
62C2×C4×C263C2×D411yescharacteristic
63C2×C4×C263C2×D411yescharacteristic
64C22×C263—21no—
65C22×C263—21no—
66C22×C263—42no—
67C22×C263—42no—
68C22×C263—42no—
69C22×C263—84no—
70C22×C263#10412yes—
71C22×C263C2×C22⋊C411yescharacteristic
72C4×C263—21no—
73C4×C263—21no—
74C4×C263—21no—
75C4×C263—21no—
76C4×C263—21no—
77C4×C263—42no—
78C4×C263#10012yes—
79C2×C263—22no—
80C2×C263—82no—
81C2×C263C2×#10011yescharacteristic
82C2×C263C2×#10411yescharacteristic
83C2×C263#42111yescharacteristic
84C263#152711yescharacteristic, complemented, Sylow
85#1527—2631nomaximal, Sylow
86C2×#124D26311yescharacteristic
87#432—2631no—
88C4×M16—2631no—
89#329—2634no—
90C22×Q8Dic26311yescharacteristic
91C22×D4Dic26311yescharacteristic
92C2×M16—5261no—
93#124—21no—
94#124—21no—
95#124Dic26312yes—
96#124C2×D26312yes—
97C2×C22⋊C4—21no—
98C2×C22⋊C4—21no—
99C2×C42C2×D26311yescharacteristic
100C4⋊C8—5261no—
101C22⋊C8—5261no—
102#97—2632no—
103#97—2632no—
104C4×C8—5261no—
105C24—21no—
106C2×Q8—21no—
107C2×Q8—42no—
108C2×Q8C2×Dic26312yes—
109C2×D4—21no—
110C2×D4—42no—
111C2×D4C2×Dic26312yes—
112C22×C4—21no—
113C22×C4C2×Dic26311yescharacteristic
114C22×C4C22⋊D26311yescharacteristic
115C22×C4C22⋊D26311yescharacteristic
116M16—5264no—
117C2×C8—5262no—
118C2×C8—5262no—
119C22⋊C4—22no—
120C22⋊C4—22no—
121C22⋊C4—22no—
122C22⋊C4—22no—
123C42C2×Dic26311yescharacteristic
124C42C22⋊D26311yescharacteristic
125C42C22⋊D26311yescharacteristic
126C42C22×D26311yescharacteristic
127C23—22no—
128C23—42no—
129C23—42no—
130C23—42no—
131C23C22⋊Dic26311yescharacteristic
132Q8—42no—
133Q8—42no—
134D4—42no—
135D4—42no—
136C2×C4—22no—
137C2×C4—22no—
138C2×C4—22no—
139C2×C4—41no—
140C2×C4—42no—
141C2×C4C22⋊Dic26311yescharacteristic
142C2×C4C22⋊Dic26311yescharacteristic
143C2×C4C22⋊Dic26311yescharacteristic
144C2×C4C22×Dic26311yescharacteristic
145C2×C4C2×C22⋊D26311yescharacteristic
146C2×C4C2×C22⋊D26311yescharacteristic
147C8—5264no—
148C8—10522no—
149C22—21no—
150C22—21no—
151C22—42no—
152C22—42no—
153C22—42no—
154C22—84no—
155C22#2255439712yes—
156C22C2×C22⋊Dic26311yescharacteristic
157C4—21no—
158C4—21no—
159C4—21no—
160C4—21no—
161C4—21no—
162C4—42no—
163C4#2255438712yes—
164C2—22no—
165C2—82no—
166C2C2×#2255438711yescharacteristic
167C2C2×#2255439711yescharacteristic
168C2#3068195511yescharacteristic
subgroupG/H
centerC22C2×C22⋊Dic263
commutatorC2×C4×C263C22×C4
FrattiniC42C22×D263
FittingC2×#124×C263C2
socleC22×C263C2×C22⋊C4
prime radicalC22×D4×C263C4
cosocleC42×C263C23
hypercenterC2×#124D263
hypocenterC263#1527
LCSG ▷ C2×C4×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. #30681995C2semidirect
2. C4×#16862360C2semidirect
3. #30681678C2semidirect
8. #22554381C22semidirect
9. #22554381C22semidirect
84. C263#1527semidirect

Maximal subgroups

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

subgroupindex
#306819952
C4×#168623602
#306816782
C2×#124×C2632
#1527263