Finite Group Databasebeta

← #46781909

Subgroups — #46781909

Order 33664.

228 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 57 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#30682603C211yesmaximal, characteristic
2#30682230C211yesmaximal, characteristic, complemented
3#30682225C211yesmaximal, characteristic
4#30681684C211yesmaximal, characteristic, complemented
5#30681670C211yesmaximal, characteristic, complemented
6#30681667C211yesmaximal, characteristic
7#487×C263C211yesmaximal, characteristic, complemented
8C2×Q8×D263—21no—
9#22554469—21no—
10#22554448—22no—
11#22554446—21no—
12C4×Dic526C2211yescharacteristic
13C4×D1052C2211yescharacteristic
14#22554432—21no—
15#22554403—21no—
16#22554401—21no—
17C4⋊(C263⋊C8)C2211yescharacteristic
18C4⋊(C263⋊C8)C2211yescharacteristic
19#22554393—21no—
20#22554390—21no—
21C4⋊Q8×C263C2211yescharacteristic
22C4⋊Q8×C263C2211yescharacteristic
23#103×C263—22no—
24C4×C8×C263C2211yescharacteristic
25C2×Dic526—22no—
26C2×Dic526D411yescharacteristic
27Q8×D263—42no—
28Q8×D263—42no—
29C2×D1052D411yescharacteristic
30C2×C4×D263—22no—
31C2×C4×D263—21no—
32C2×C263⋊C8—21no—
33C2×C263⋊C8—21no—
34C4⋊Dic263D411yescharacteristic
35C4⋊Dic263D411yescharacteristic
36Dic263⋊C4—22no—
37Dic263⋊C4—21no—
38(C2×D263)⋊C4—22no—
39(C2×D263)⋊C4—21no—
40C4×Dic263—21no—
41C2×Q8×C263—21no—
42C2×Q8×C263—21no—
43C2×C8×C263—21no—
44C4⋊C4×C263—21no—
45C4⋊C4×C263—21no—
46C4⋊C4×C263—21no—
47C4⋊C4×C263D412yes—
48C42×C263C2311yescharacteristic
49C22×D263—21no—
50Dic526—21no—
51Dic526—44no—
52Dic526SD1612yes—
53D1052—21no—
54D1052Q1612yes—
55C2×Dic263—21no—
56C2×Dic263—21no—
57C2×Dic263—21no—
58C4×D263—44no—
59C4×D263—41no—
60C4×D263—41no—
61C263⋊C8—41no—
62C263⋊C8—41no—
63Q8×C263—42no—
64Q8×C263—41no—
65Q8×C263—41no—
66C2×C4×C263—22no—
67C2×C4×C263—41no—
68C2×C4×C263C2×D411yescharacteristic
69C2×C4×C263C2×D411yescharacteristic
70C2×C4×C263C2×D411yescharacteristic
71C8×C263—41no—
72C22×C263#12011yescharacteristic
73C2×D263—22no—
74C2×D263—41no—
75C2×D263—41no—
76C4×C263—21no—
77C4×C263—42no—
78C4×C263—81no—
79C4×C263C2×SD1611yescharacteristic
80C4×C263C2×Q1611yescharacteristic
81C4×C263AGL(1,ℤ/8)11yescharacteristic
82C4×C263#13711yescharacteristic
83Dic263—22no—
84Dic263—41no—
85Dic263—41no—
86C2×C263#45011yescharacteristic
87C2×C263#45111yescharacteristic
88C2×C263#45411yescharacteristic
89D263—42no—
90C263#163711yescharacteristic, complemented, Sylow
91#1637—2631nomaximal, Sylow
92D4×Q8—2631no—
93#487D26311yescharacteristic, complemented
94#477—2631no—
95#476—2631no—
96#332—2631no—
97Q8⋊C8—2631no—
98D4⋊C8—2631no—
99C22×Q8—5261no—
100C4⋊Q8—5261no—
101C4⋊Q8C2×D26311yescharacteristic
102C4⋊Q8C2×D26311yescharacteristic
103C22⋊Q8—5261no—
104C22⋊Q8—5262no—
105C4×Q8—2631no—
106C4×D4—2631no—
107C4×D4—5261no—
108#107—5261no—
109#106—5261no—
110C4⋊C8—2631no—
111C4⋊C8—2631no—
112#103—22no—
113#103—5261no—
114#102—5261no—
115C4×C8C2×D26311yescharacteristic
116C2×Q8—21no—
117C2×Q8—21no—
118C2×Q8—2631no—
119C2×Q8—5262no—
120C2×Q8—10522no—
121C2×Q8—10522no—
122C2×D4—2631no—
123C22×C4—5262no—
124C22×C4—5261no—
125C2×C8—21no—
126C2×C8—5261no—
127C2×C8—5261no—
128C4⋊C4—21no—
129C4⋊C4—21no—
130C4⋊C4—21no—
131C4⋊C4—2631no—
132C4⋊C4—2631no—
133C4⋊C4—5262no—
134C4⋊C4—5261no—
135C4⋊C4C22⋊D26312yes—
136C22⋊C4—5262no—
137C22⋊C4—5261no—
138C42—5261no—
139C42C22×D26311yescharacteristic
140C23—5261no—
141Q8—42no—
142Q8—41no—
143Q8—41no—
144Q8—2632no—
145Q8—5261no—
146Q8—10524no—
147D4—2632no—
148D4—5261no—
149C2×C4—22no—
150C2×C4—41no—
151C2×C4—5261no—
152C2×C4—5261no—
153C2×C4—5261no—
154C2×C4—10524no—
155C2×C4—10521no—
156C2×C4—10521no—
157C2×C4D4×D26311yescharacteristic
158C2×C4D4×D26311yescharacteristic
159C2×C4C2×C22⋊D26311yescharacteristic
160C8—41no—
161C8—10521no—
162C8—10521no—
163C22—5262no—
164C22—10521no—
165C22—10521no—
166C22#2255443811yescharacteristic
167C4—21no—
168C4—42no—
169C4—81no—
170C4—5262no—
171C4—10521no—
172C4—10521no—
173C4SD16×D26311yescharacteristic
174C4Q16×D26311yescharacteristic
175C4#2255449711yescharacteristic
176C4#2255450211yescharacteristic
177C2—10522no—
178C2#3068208711yescharacteristic
179C2#3068209211yescharacteristic
180C2#3068211011yescharacteristic
subgroupG/H
centerC22#22554438
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
Fitting#487×C263C2
socleC22×C263#120
prime radicalC2×D1052D4
hypercenter#487D263
hypocenterC263#1637
LCSG ▷ C42×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
2. #30682230C2semidirect
4. #30681684C2semidirect
5. #30681670C2semidirect
7. #487×C263C2semidirect
90. C263#1637semidirect
93. #487D263semidirect

Maximal subgroups

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

subgroupindex
#306826032
#306822302
#306822252
#306816842
#306816702
#306816672
#487×C2632
#1637263