Finite Group Databasebeta

← #46782002

Subgroups — #46782002

Order 33664.

200 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 53 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#30682661C211yesmaximal, characteristic
2#30682341C211yesmaximal, characteristic, complemented
3#30682140C211yesmaximal, characteristic
4#30681683C211yesmaximal, characteristic, complemented
5Q8⋊(C263⋊C8)C211yesmaximal, characteristic, complemented
6#30681665C211yesmaximal, characteristic
7#475×C263C211yesmaximal, characteristic, complemented
8C2×#16862363—21no—
9#22554470C2211yescharacteristic
10#22554465—22no—
11#22554458—21no—
12#22554446—21no—
13C4×Dic526—21no—
14C4×D1052C2211yescharacteristic
15#22554428—21no—
16#22554403—22no—
17C4⋊(C263⋊C8)C2211yescharacteristic
18#22554394—21no—
19C4×C263⋊C8C2211yescharacteristic
20C4⋊Q8×C263C2211yescharacteristic
21C4×Q8×C263C2211yescharacteristic
22#106×C263—21no—
23C4⋊C8×C263C2211yescharacteristic
24#103×C263—21no—
25C2×Dic526—21no—
26C2×D1052D411yescharacteristic
27C2×C4×D263—21no—
28#16862363—42no—
29C2×C263⋊C8—21no—
30C2×C263⋊C8—21no—
31C4⋊Dic263—21no—
32C4⋊Dic263D411yescharacteristic
33C4⋊Dic263D412yes—
34Dic263⋊C4—22no—
35(C2×D263)⋊C4—22no—
36(C2×D263)⋊C4—22no—
37(C2×D263)⋊C4—21no—
38C4×Dic263—22no—
39C2×Q8×C263—21no—
40C2×Q8×C263D411yescharacteristic
41C2×C8×C263—21no—
42C4⋊C4×C263—21no—
43C4⋊C4×C263—21no—
44C4⋊C4×C263—21no—
45C4⋊C4×C263D411yescharacteristic
46C42×C263—21no—
47C42×C263C2311yescharacteristic
48C22×D263—21no—
49Dic526—41no—
50Dic526—41no—
51D1052—21no—
52D1052—21no—
53C2×Dic263—21no—
54C2×Dic263—22no—
55C4×D263—41no—
56C4×D263—41no—
57C263⋊C8—22no—
58C263⋊C8—41no—
59Q8×C263—21no—
60Q8×C263—21no—
61Q8×C263—41no—
62Q8×C263—41no—
63C2×C4×C263—21no—
64C2×C4×C263—21no—
65C2×C4×C263—41no—
66C2×C4×C263C2×D411yescharacteristic
67C2×C4×C263C2×D411yescharacteristic
68C2×C4×C263C2×D411yescharacteristic
69C8×C263—41no—
70C22×C263#12011yescharacteristic
71C2×D263—41no—
72C2×D263—41no—
73C2×D263—41no—
74C4×C263—21no—
75C4×C263—41no—
76C4×C263—41no—
77C4×C263—81no—
78C4×C263#13511yescharacteristic
79C4×C263#13511yescharacteristic
80C4×C263AGL(1,ℤ/8)11yescharacteristic
81C4×C263#13711yescharacteristic
82Dic263—42no—
83Dic263—41no—
84C2×C263#44911yescharacteristic
85C2×C263#45211yescharacteristic
86C2×C263#45611yescharacteristic
87D263—81no—
88C263#165011yescharacteristic, complemented, Sylow
89#1650—2631nomaximal, Sylow
90#556—2631no—
91#500—2631no—
92#475D26311yescharacteristic, complemented
93#461—2631no—
94#332—2631no—
95Q8⋊C8—2631no—
96D4⋊C8—2631no—
97C2×SD16—5261no—
98C4⋊Q8—2631no—
99C4⋊Q8C2×D26311yescharacteristic
100#126—5262no—
101#124—5261no—
102C22⋊Q8—5261no—
103C4×Q8—5261no—
104C4×Q8C2×D26311yescharacteristic
105C4×D4—2631no—
106#117—5261no—
107#107—5262no—
108#106—21no—
109C4⋊C8—2631no—
110C4⋊C8C2×D26311yescharacteristic
111#103—21no—
112#103—5261no—
113C4×C8—2631no—
114C2×Q8—21no—
115C2×Q8—5261no—
116C2×Q8C22⋊D26311yescharacteristic
117C2×D4—2631no—
118C22×C4—5261no—
119SD16—10522no—
120C2×C8—21no—
121C2×C8—5261no—
122C2×C8—5261no—
123C4⋊C4—21no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4—2631no—
127C4⋊C4—2632no—
128C4⋊C4—5262no—
129C4⋊C4—5261no—
130C4⋊C4C22⋊D26311yescharacteristic
131C22⋊C4—5262no—
132C22⋊C4—5262no—
133C22⋊C4—5261no—
134C42—21no—
135C42—5262no—
136C42C22×D26311yescharacteristic
137C23—5261no—
138Q8—21no—
139Q8—21no—
140Q8—41no—
141Q8—41no—
142Q8—10521no—
143Q8—10521no—
144D4—5261no—
145D4—5261no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—41no—
149C2×C4—5261no—
150C2×C4—5262no—
151C2×C4—10521no—
152C2×C4—10521no—
153C2×C4D4×D26311yescharacteristic
154C2×C4D4×D26311yescharacteristic
155C2×C4C2×C22⋊D26311yescharacteristic
156C8—41no—
157C8—5262no—
158C8—10521no—
159C22—10521no—
160C22—10521no—
161C22—10521no—
162C22#2255443811yescharacteristic
163C4—21no—
164C4—41no—
165C4—41no—
166C4—81no—
167C4—10522no—
168C4—10521no—
169C4#2255449011yescharacteristic
170C4#2255449111yescharacteristic
171C4#2255449711yescharacteristic
172C4#2255450111yescharacteristic
173C2—21041no—
174C2#3068208211yescharacteristic
175C2#3068209811yescharacteristic
176C2#3068211911yescharacteristic
subgroupG/H
centerC22#22554438
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
Fitting#475×C263C2
socleC22×C263#120
prime radicalC2×D1052D4
hypercenter#475D263
hypocenterC263#1650
LCSG ▷ C42×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
2. #30682341C2semidirect
4. #30681683C2semidirect
5. Q8⋊(C263⋊C8)C2semidirect
7. #475×C263C2semidirect
88. C263#1650semidirect
92. #475D263semidirect

Maximal subgroups

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

subgroupindex
#306826612
#306823412
#306821402
#306816832
Q8⋊(C263⋊C8)2
#306816652
#475×C2632
#1650263