Finite Group Databasebeta

← #46781844

Subgroups — #46781844

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#30682286C211yesmaximal, characteristic
3#30682139C211yesmaximal, characteristic
4#30682139C211yesmaximal, characteristic
5#30681668C211yesmaximal, characteristic, complemented
6#30681668C211yesmaximal, characteristic, complemented
7#332×C263C211yesmaximal, characteristic, complemented
8C2×#16862365—21no—
9C2×#16862365—21no—
10#22554468—21no—
11#22554467C2211yescharacteristic
12#22554461—21no—
13#22554460—22no—
14Q8×Dic263—21no—
15C4×Dic526C2211yescharacteristic
16C4×Dic526C2211yescharacteristic
17#22554435—21no—
18#22554392—21no—
19#22554392—21no—
20#22554390—22no—
21C4×C263⋊C8C2211yescharacteristic
22C4⋊Q8×C263C2211yescharacteristic
23C4⋊C8×C263C2211yescharacteristic
24C4⋊C8×C263C2211yescharacteristic
25C2×Dic526D411yescharacteristic
26C2×Dic526D411yescharacteristic
27C2×D1052—21no—
28C2×D1052—21no—
29C2×D1052—21no—
30#16862365—42no—
31#16862365—42no—
32C2×C263⋊C8—21no—
33C4⋊Dic263—22no—
34C4⋊Dic263D411yescharacteristic
35C4⋊Dic263D411yescharacteristic
36Dic263⋊C4—22no—
37Dic263⋊C4—22no—
38Dic263⋊C4—21no—
39Dic263⋊C4—21no—
40C4×Dic263—22no—
41C4×Dic263—21no—
42C4×Dic263—21no—
43C2×Q8×C263—21no—
44C2×C8×C263—21no—
45C2×C8×C263—21no—
46C4⋊C4×C263—21no—
47C4⋊C4×C263D412yes—
48C42×C263C2311yescharacteristic
49C22×D263—41no—
50Dic526—21no—
51Dic526—21no—
52Dic526—21no—
53Dic526SD1612yescomplemented
54D1052—42no—
55D1052—41no—
56D1052—41no—
57D1052—41no—
58D1052—41no—
59C2×Dic263—21no—
60C2×Dic263—21no—
61C2×Dic263—21no—
62C2×Dic263—21no—
63C263⋊C8—41no—
64Q8×C263—41no—
65Q8×C263—41no—
66C2×C4×C263—22no—
67C2×C4×C263C2×D411yescharacteristic
68C2×C4×C263C2×D411yescharacteristic
69C2×C4×C263C2×D411yescharacteristic
70C8×C263—41no—
71C8×C263—41no—
72C22×C263#12011yescharacteristic
73C2×D263—81no—
74C2×D263—81no—
75C2×D263—81no—
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#44811yescharacteristic
87C2×C263#44911yescharacteristic
88C2×C263#45411yescharacteristic
89D263—161no—
90C263#162611yescharacteristic, complemented, Sylow
91#1626—2631nomaximal, Sylow
92#557—2631no—
93#486—2631no—
94#460—2631no—
95#460—2631no—
96#332D26311yescharacteristic, complemented
97Q8⋊C8—2631no—
98Q8⋊C8—2631no—
99C2×SD16—5261no—
100C2×SD16—5261no—
101C4⋊Q8—5261no—
102C4⋊Q8C2×D26311yescharacteristic
103#127—2631no—
104#125—5261no—
105#125—5262no—
106C4×Q8—2631no—
107C4×Q8—2631no—
108C4×Q8—5261no—
109C4×Q8—5261no—
110C4⋊C8C2×D26311yescharacteristic
111C4⋊C8C2×D26311yescharacteristic
112#102—5261no—
113#102—5261no—
114#102—5262no—
115C4×C8—2631no—
116C2×Q8—21no—
117C2×Q8—2631no—
118C2×Q8—2631no—
119C2×D4—5261no—
120C2×D4—5261no—
121C2×D4—5261no—
122SD16—10522no—
123SD16—10522no—
124C2×C8—21no—
125C2×C8—21no—
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⋊C4D105212yes—
136C42—5262no—
137C42—5261no—
138C42—5261no—
139C42C22×D26311yescharacteristic
140C23—10521no—
141Q8—41no—
142Q8—41no—
143Q8—2632no—
144Q8—5261no—
145Q8—5261no—
146Q8—5261no—
147D4—10522no—
148D4—10521no—
149D4—10521no—
150D4—10521no—
151D4—10521no—
152C2×C4—22no—
153C2×C4—5261no—
154C2×C4—5261no—
155C2×C4—5261no—
156C2×C4—5261no—
157C2×C4D4×D26311yescharacteristic
158C2×C4D4×D26311yescharacteristic
159C2×C4C2×D105211yescharacteristic
160C8—41no—
161C8—41no—
162C8—10521no—
163C22—21041no—
164C22—21041no—
165C22—21041no—
166C22#2255444011yescharacteristic
167C4—21no—
168C4—42no—
169C4—5262no—
170C4—10521no—
171C4—10521no—
172C4—10521no—
173C4SD16×D26311yescharacteristic
174C4#2255449111yescharacteristic
175C4#2255449411yescharacteristic
176C4#2255450211yescharacteristic
177C2—42081no—
178C2#3068207811yescharacteristic
179C2#3068208411yescharacteristic
180C2#3068211311yescharacteristic
subgroupG/H
centerC22#22554440
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
Fitting#332×C263C2
socleC22×C263#120
prime radical#22554467C22
hypercenter#332D263
hypocenterC263#1626
LCSG ▷ C42×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
1. #30682663C2semidirect
5. #30681668C2semidirect
6. #30681668C2semidirect
7. #332×C263C2semidirect
53. Dic526SD16semidirect
90. C263#1626semidirect
96. #332D263semidirect

Maximal subgroups

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

subgroupindex
#306826632
#306822862
#306821392
#306816682
#332×C2632
#1626263