Finite Group Databasebeta

← #46783280

Subgroups — #46783280

Order 33664.

362 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 93 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#30682413C211yesmaximal, characteristic, complemented
2#30681955C212yesmaximal, complemented
3C2×#22554387C211yesmaximal, characteristic, complemented
4#30681694C212yesmaximal, complemented
5#535×C263C211yesmaximal, characteristic
6C2×#16862360C2212yes—
7D4×Dic263—24no—
8#22554429C2212yes—
9C2×C22⋊Dic263—22no—
10#22554397—24no—
11#22554387—22no—
12C2×#41×C263C2211yescharacteristic
13C22×D4×C263C2211yescharacteristic
14#127×C263C412yescomplemented
15#124×C263C412yescomplemented
16#121×C263—22no—
17#120×C263—22no—
18#117×C263C2211yescharacteristic
19C22×Dic263—24no—
20#16862360—22no—
21#16862360—22no—
22C2×C263⋊C8—22no—
23C4⋊Dic263—22no—
24C22⋊Dic263—24no—
25C22⋊Dic263—22no—
26C4×Dic263D414yescomplemented
27C24×C263D412yes—
28#41×C263—22no—
29#41×C263—22no—
30C2×Q8×C263C2×C411yescharacteristic, complemented
31C2×D4×C263—21no—
32C2×D4×C263—24no—
33C2×D4×C263—22no—
34C2×D4×C263—22no—
35C2×D4×C263C2×C412yes—
36C2×D4×C263C2×C411yescharacteristic, complemented
37C2×D4×C263D412yes—
38C22×C4×C263—21no—
39C22×C4×C263C2311yescharacteristic
40C4⋊C4×C263—21no—
41C22⋊C4×C263—24no—
42C22⋊C4×C263—21no—
43C42×C263C2×C412yescomplemented
44C2×Dic263—24no—
45C2×Dic263—84no—
46C263⋊C8—42no—
47C23×C263—22no—
48C23×C263—22no—
49C23×C263—21no—
50C23×C263—82no—
51C23×C263C22⋊C414yes—
52C23×C263C2×D411yescharacteristic
53Q8×C263—22no—
54D4×C263—24no—
55D4×C263—22no—
56D4×C263—24no—
57D4×C263—41no—
58D4×C263—41no—
59D4×C263—84no—
60C2×C4×C263—22no—
61C2×C4×C263—21no—
62C2×C4×C263—42no—
63C2×C4×C263C22×C411yescharacteristic
64C2×C4×C263C2×D412yes—
65C2×C4×C263C2×D411yescharacteristic
66C2×C4×C263#4112yes—
67C22×C263—24no—
68C22×C263—41no—
69C22×C263—44no—
70C22×C263—44no—
71C22×C263—42no—
72C22×C263—41no—
73C22×C263—82no—
74C22×C263C2×C22⋊C411yescharacteristic
75C22×C263#12011yescharacteristic
76C22×C263#12311yescharacteristic
77C4×C263—42no—
78C4×C263—41no—
79C4×C263C4×D412yes—
80C4×C263#12112yes—
81Dic263—44no—
82C2×C263—21no—
83C2×C263—21no—
84C2×C263—21no—
85C2×C263—44no—
86C2×C263—81no—
87C2×C263#38611yescharacteristic
88C263#191111yescharacteristic, complemented, Sylow
89#1911—2631nomaximal, Sylow
90#535D26311yescharacteristic
91#518—2631no—
92#421—2632no—
93C2×#100—2631no—
94H(3,ℤ/4)—2632no—
95C2×#41C2×D26311yescharacteristic
96C22×D4C2×D26311yescharacteristic
97C2×M16—2632no—
98#127Dic26312yescomplemented
99#124Dic26312yescomplemented
100#121—22no—
101#120—22no—
102C4×D4—5264no—
103#117—2632no—
104#117C2×D26311yescharacteristic
105C2×C22⋊C4—5262no—
106#104—5264no—
107#100—5262no—
108C24C22⋊D26312yes—
109#41—22no—
110#41—22no—
111C2×Q8C2×Dic26311yescharacteristic, complemented
112C2×D4—21no—
113C2×D4—24no—
114C2×D4—22no—
115C2×D4—22no—
116C2×D4C2×Dic26312yes—
117C2×D4C2×Dic26311yescharacteristic, complemented
118C2×D4C22⋊D26312yes—
119C22×C4—21no—
120C22×C4—5264no—
121C22×C4C22×D26311yescharacteristic
122M16—5262no—
123M16—5262no—
124C2×C8—5262no—
125C4⋊C4—21no—
126C4⋊C4—5262no—
127C22⋊C4—24no—
128C22⋊C4—21no—
129C22⋊C4—5264no—
130C22⋊C4—5262no—
131C42—2634no—
132C42C2×Dic26312yescomplemented
133C23—22no—
134C23—22no—
135C23—21no—
136C23—82no—
137C23C22⋊Dic26314yes—
138C23C2×C22⋊D26311yescharacteristic
139Q8—22no—
140D4—24no—
141D4—22no—
142D4—24no—
143D4—41no—
144D4—41no—
145D4—84no—
146C2×C4—22no—
147C2×C4—21no—
148C2×C4—42no—
149C2×C4—5264no—
150C2×C4—21044no—
151C2×C4C22×Dic26311yescharacteristic
152C2×C4D4×D26312yes—
153C2×C4C2×C22⋊D26311yescharacteristic
154C2×C4#1686237512yes—
155C8—10522no—
156C22—24no—
157C22—41no—
158C22—44no—
159C22—44no—
160C22—42no—
161C22—41no—
162C22—82no—
163C22C2×C22⋊Dic26311yescharacteristic
164C22#2255443811yescharacteristic
165C22#2255445111yescharacteristic
166C4—42no—
167C4—41no—
168C4—10524no—
169C4D4×Dic26312yes—
170C4#2255444212yes—
171C2—21no—
172C2—21no—
173C2—21no—
174C2—44no—
175C2—81no—
176C2#3068181811yescharacteristic
subgroupG/H
centerC2#30681818
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
Fitting, prime radical#535×C263C2
socleC2×C263#386
cosocleC22×C4×C263C23
hypercenter#535D263
hypocenterC263#1911
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C2 ◁ C22×C4 ◁ #535

Complements

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

NH ≅ G/Ntype
1. #30682413C2semidirect
2. #30681955C2semidirect
3. C2×#22554387C2semidirect
4. #30681694C2semidirect
14. #127×C263C4semidirect
15. #124×C263C4semidirect
26. C4×Dic263D4semidirect
30. C2×Q8×C263C2×C4semidirect
36. C2×D4×C263C2×C4semidirect
43. C42×C263C2×C4semidirect
88. C263#1911semidirect
98. #127Dic263semidirect
99. #124Dic263semidirect
111. C2×Q8C2×Dic263semidirect
117. C2×D4C2×Dic263semidirect
132. C42C2×Dic263semidirect

Maximal subgroups

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

subgroupindex
#306824132
#306819552
C2×#225543872
#306816942
#535×C2632
#1911263