Finite Group Databasebeta

← #46781884

Subgroups — #46781884

Order 33664.

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

normal subgroups only

This group has 214 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#30682648C211yesmaximal, characteristic
2#30682318C211yesmaximal, characteristic, complemented
3#30682233C211yesmaximal, characteristic, complemented
4#30682229C211yesmaximal, characteristic
5#30681686C211yesmaximal, characteristic, complemented
6#30681667C211yesmaximal, characteristic
7Q8⋊C8×C263C211yesmaximal, characteristic, complemented
8C2×Dic1052—22no—
9#22554470C2211yescharacteristic
10#22554470C2211yescharacteristic
11#22554462—21no—
12#22554448—22no—
13#22554446—21no—
14C4×D1052—21no—
15C4×D1052C2211yescharacteristic
16C4⋊C4×D263—21no—
17#22554403—21no—
18#22554402—21no—
19C4⋊(C263⋊C8)C2211yescharacteristic
20#22554394—21no—
21#22554392—21no—
22C4×Q8×C263C2211yescharacteristic
23C4⋊C8×C263C2211yescharacteristic
24C4×C8×C263C2211yescharacteristic
25C2×Dic526—21no—
26C2×Dic526D412yes—
27C2×D1052D411yescharacteristic
28C2×C4×D263—22no—
29C2×C4×D263—21no—
30Dic1052—44no—
31C2×C263⋊C8—21no—
32C4⋊Dic263—21no—
33C4⋊Dic263—21no—
34C4⋊Dic263—21no—
35C4⋊Dic263—21no—
36C4⋊Dic263D411yescharacteristic
37Dic263⋊C4—22no—
38Dic263⋊C4—22no—
39(C2×D263)⋊C4—22no—
40(C2×D263)⋊C4—21no—
41C2×Q8×C263D411yescharacteristic
42C2×C8×C263—21no—
43C2×C8×C263—21no—
44C4⋊C4×C263—21no—
45C4⋊C4×C263D411yescharacteristic
46C42×C263—21no—
47C42×C263C2311yescharacteristic
48C22×D263—21no—
49Dic526—42no—
50Dic526—42no—
51D1052—21no—
52D1052Q1612yescomplemented
53C2×Dic263—21no—
54C2×Dic263—22no—
55C2×Dic263—41no—
56C4×D263—41no—
57C4×D263—41no—
58C4×D263—82no—
59C263⋊C8—41no—
60Q8×C263—21no—
61Q8×C263—21no—
62C2×C4×C263—21no—
63C2×C4×C263—21no—
64C2×C4×C263C2×D411yescharacteristic
65C2×C4×C263C2×D411yescharacteristic
66C2×C4×C263C2×D411yescharacteristic
67C8×C263—22no—
68C8×C263—41no—
69C22×C263#12011yescharacteristic
70C2×D263—22no—
71C2×D263—41no—
72C2×D263—41no—
73C4×C263—21no—
74C4×C263—41no—
75C4×C263—41no—
76C4×C263C2×Q1611yescharacteristic
77C4×C263#13511yescharacteristic
78C4×C263#13711yescharacteristic
79C4×C263#13711yescharacteristic
80Dic263—41no—
81Dic263—42no—
82Dic263—81no—
83C2×C263#45111yescharacteristic
84C2×C263#45211yescharacteristic
85C2×C263#45311yescharacteristic
86D263—42no—
87C263#163211yescharacteristic, complemented, Sylow
88#1632—2631nomaximal, Sylow
89#554—2631no—
90#494—2631no—
91#477—2631no—
92#476—2631no—
93#333—2631no—
94Q8⋊C8D26311yescharacteristic, complemented
95D4⋊C8—2631no—
96C2×Q16—5262no—
97C4⋊Q8—2631no—
98C4⋊Q8—2631no—
99#125—5261no—
100C22⋊Q8—5262no—
101C22⋊Q8—5261no—
102C4×Q8C2×D26311yescharacteristic
103C4×D4—2631no—
104C4×D4—5261no—
105C2×C4⋊C4—5261no—
106#107—5261no—
107#106—5261no—
108C4⋊C8—2631no—
109C4⋊C8C2×D26311yescharacteristic
110#103—5261no—
111#102—5261no—
112C4×C8C2×D26311yescharacteristic
113C2×Q8—2632no—
114C2×Q8—5261no—
115C2×Q8D105211yescharacteristic
116C2×D4—2631no—
117C22×C4—5262no—
118C22×C4—5261no—
119Q16—10524no—
120C2×C8—21no—
121C2×C8—21no—
122C2×C8—5261no—
123C4⋊C4—21no—
124C4⋊C4—2631no—
125C4⋊C4—5262no—
126C4⋊C4—5262no—
127C4⋊C4—5261no—
128C4⋊C4—5261no—
129C4⋊C4—5261no—
130C4⋊C4—5261no—
131C4⋊C4D105211yescharacteristic
132C22⋊C4—5262no—
133C22⋊C4—5261no—
134C42—21no—
135C42C22×D26311yescharacteristic
136C23—5261no—
137Q8—21no—
138Q8—21no—
139Q8—10522no—
140Q8—10522no—
141D4—2632no—
142D4—5261no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—5261no—
146C2×C4—5262no—
147C2×C4—10521no—
148C2×C4—10521no—
149C2×C4—10521no—
150C2×C4—21042no—
151C2×C4D4×D26311yescharacteristic
152C2×C4D4×D26311yescharacteristic
153C2×C4C2×D105211yescharacteristic
154C8—22no—
155C8—41no—
156C8—10521no—
157C22—5262no—
158C22—10521no—
159C22—10521no—
160C22#2255444011yescharacteristic
161C4—21no—
162C4—41no—
163C4—41no—
164C4—10521no—
165C4—10522no—
166C4—21041no—
167C4Q16×D26311yescharacteristic
168C4#2255449211yescharacteristic
169C4#2255449911yescharacteristic
170C4#2255450311yescharacteristic
171C2—10522no—
172C2#3068209511yescharacteristic
173C2#3068210211yescharacteristic
174C2#3068210711yescharacteristic
subgroupG/H
centerC22#22554440
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
FittingQ8⋊C8×C263C2
socleC22×C263#120
prime radicalC2×D1052D4
hypercenterQ8⋊C8D263
hypocenterC263#1632
LCSG ▷ C42×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
2. #30682318C2semidirect
3. #30682233C2semidirect
5. #30681686C2semidirect
7. Q8⋊C8×C263C2semidirect
52. D1052Q16semidirect
87. C263#1632semidirect
94. Q8⋊C8D263semidirect

Maximal subgroups

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

subgroupindex
#306826482
#306823182
#306822332
#306822292
#306816862
#306816672
Q8⋊C8×C2632
#1632263