Finite Group Databasebeta

← #46781840

Subgroups — #46781840

Order 33664.

210 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 55 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#30682663C211yesmaximal, characteristic, complemented
2#30682135C211yesmaximal, characteristic
3#30682135C211yesmaximal, characteristic
4#30681684C211yesmaximal, characteristic, complemented
5#30681670C211yesmaximal, characteristic, complemented
6#30681670C211yesmaximal, characteristic, complemented
7#486×C263C211yesmaximal, characteristic
8C2×#16862364—21no—
9C2×#16862364—21no—
10#22554468—21no—
11#22554461—21no—
12#22554460—22no—
13Q8×Dic263—21no—
14C4×Dic526C2211yescharacteristic
15C4×Dic526C2211yescharacteristic
16#22554435—21no—
17C4⋊(C263⋊C8)C2211yescharacteristic
18C4⋊(C263⋊C8)C2211yescharacteristic
19#22554391—21no—
20#22554391—21no—
21C4⋊Q8×C263C2211yescharacteristic
22#127×C263C2211yescharacteristic
23#102×C263—22no—
24C4×C8×C263C2211yescharacteristic
25C2×Dic526D411yescharacteristic
26C2×Dic526D411yescharacteristic
27#16862364—42no—
28#16862364—42no—
29C2×C263⋊C8—21no—
30C2×C263⋊C8—21no—
31C4⋊Dic263—22no—
32C4⋊Dic263D411yescharacteristic
33C4⋊Dic263D411yescharacteristic
34Dic263⋊C4—22no—
35Dic263⋊C4—22no—
36Dic263⋊C4—21no—
37Dic263⋊C4—21no—
38C4×Dic263—22no—
39C4×Dic263—21no—
40C4×Dic263—21no—
41C2×Q8×C263—21no—
42C2×D4×C263—21no—
43C2×D4×C263—21no—
44C2×D4×C263—21no—
45C2×C8×C263—21no—
46C4⋊C4×C263—21no—
47C4⋊C4×C263D412yes—
48C42×C263C2311yescharacteristic
49Dic526—21no—
50Dic526—21no—
51Dic526—21no—
52Dic526SD1612yescomplemented
53C2×Dic263—21no—
54C2×Dic263—21no—
55C2×Dic263—21no—
56C2×Dic263—21no—
57C263⋊C8—41no—
58C263⋊C8—41no—
59C23×C263—41no—
60Q8×C263—41no—
61Q8×C263—41no—
62D4×C263—42no—
63D4×C263—41no—
64D4×C263—41no—
65D4×C263—41no—
66D4×C263—41no—
67C2×C4×C263—22no—
68C2×C4×C263C2×D411yescharacteristic
69C2×C4×C263C2×D411yescharacteristic
70C2×C4×C263C2×D411yescharacteristic
71C8×C263—41no—
72C22×C263—81no—
73C22×C263—81no—
74C22×C263—81no—
75C22×C263#12011yescharacteristic
76C4×C263—21no—
77C4×C263—42no—
78C4×C263C2×SD1611yescharacteristic
79C4×C263#13511yescharacteristic
80C4×C263AGL(1,ℤ/8)11yescharacteristic
81C4×C263#13711yescharacteristic
82Dic263—22no—
83Dic263—41no—
84Dic263—41no—
85Dic263—41no—
86C2×C263—161no—
87C2×C263#44811yescharacteristic
88C2×C263#44911yescharacteristic
89C2×C263#45411yescharacteristic
90C263#162611yescharacteristic, complemented, Sylow
91#1626—2631nomaximal, Sylow
92#557—2631no—
93#486D26311yescharacteristic
94#460—2631no—
95#460—2631no—
96#332—2631no—
97Q8⋊C8—2631no—
98Q8⋊C8—2631no—
99C2×SD16—5261no—
100C2×SD16—5261no—
101C4⋊Q8—5261no—
102C4⋊Q8C2×D26311yescharacteristic
103#127C2×D26311yescharacteristic
104#125—5261no—
105#125—5262no—
106C4×Q8—2631no—
107C4×Q8—2631no—
108C4×Q8—5261no—
109C4×Q8—5261no—
110C4⋊C8—2631no—
111C4⋊C8—2631no—
112#102—22no—
113#102—5261no—
114#102—5261no—
115C4×C8C2×D26311yescharacteristic
116C2×Q8—21no—
117C2×Q8—2631no—
118C2×Q8—2631no—
119C2×D4—21no—
120C2×D4—21no—
121C2×D4—21no—
122SD16—10522no—
123SD16—10522no—
124C2×C8—21no—
125C2×C8—5261no—
126C2×C8—5261no—
127C4⋊C4—21no—
128C4⋊C4—2631no—
129C4⋊C4—2631no—
130C4⋊C4—5262no—
131C4⋊C4—5262no—
132C4⋊C4—5262no—
133C4⋊C4—5261no—
134C4⋊C4—5261no—
135C4⋊C4C22⋊D26312yes—
136C42—5262no—
137C42—5261no—
138C42—5261no—
139C42C22×D26311yescharacteristic
140C23—41no—
141Q8—41no—
142Q8—41no—
143Q8—2632no—
144Q8—5261no—
145Q8—5261no—
146Q8—5261no—
147D4—42no—
148D4—41no—
149D4—41no—
150D4—41no—
151D4—41no—
152C2×C4—22no—
153C2×C4—5261no—
154C2×C4—5261no—
155C2×C4—5261no—
156C2×C4—5261no—
157C2×C4D4×D26311yescharacteristic
158C2×C4D4×D26311yescharacteristic
159C2×C4C2×C22⋊D26311yescharacteristic
160C8—41no—
161C8—10521no—
162C8—10521no—
163C22—81no—
164C22—81no—
165C22—81no—
166C22#2255443811yescharacteristic
167C4—21no—
168C4—42no—
169C4—5262no—
170C4—10521no—
171C4—10521no—
172C4—10521no—
173C4SD16×D26311yescharacteristic
174C4#2255448911yescharacteristic
175C4#2255449411yescharacteristic
176C4#2255449911yescharacteristic
177C2—161no—
178C2#3068207511yescharacteristic
179C2#3068208011yescharacteristic
180C2#3068211011yescharacteristic
subgroupG/H
centerC22#22554438
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
Fitting#486×C263C2
socleC22×C263#120
prime radical#127×C263C22
hypercenter#486D263
hypocenterC263#1626
LCSG ▷ C42×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #30682663C2semidirect
4. #30681684C2semidirect
5. #30681670C2semidirect
6. #30681670C2semidirect
52. Dic526SD16semidirect
90. C263#1626semidirect

Maximal subgroups

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

subgroupindex
#306826632
#306821352
#306816842
#306816702
#486×C2632
#1626263