Finite Group Databasebeta

← #46782019

Subgroups — #46782019

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#30682336C211yesmaximal, characteristic, complemented
3#30682219C211yesmaximal, characteristic
4#30682148C211yesmaximal, characteristic, complemented
5#30681685C211yesmaximal, characteristic, complemented
6#30681667C211yesmaximal, characteristic
7Q8⋊C8×C263C211yesmaximal, characteristic, complemented
8C2×#16862366—21no—
9#22554470C2211yescharacteristic
10#22554470C2211yescharacteristic
11#22554465—22no—
12#22554458—21no—
13#22554446—21no—
14C4×Dic526—21no—
15C4×D1052C2211yescharacteristic
16#22554428—21no—
17#22554404—21no—
18#22554402—22no—
19C4⋊(C263⋊C8)C2211yescharacteristic
20#22554393—21no—
21#22554392—21no—
22C4×Q8×C263C2211yescharacteristic
23C4⋊C8×C263C2211yescharacteristic
24C4×C8×C263C2211yescharacteristic
25C2×Dic526—21no—
26C2×Dic526—21no—
27C2×D1052D411yescharacteristic
28C2×C4×D263—21no—
29#16862366—42no—
30C2×C263⋊C8—21no—
31C4⋊Dic263—21no—
32C4⋊Dic263—21no—
33C4⋊Dic263—21no—
34C4⋊Dic263D412yes—
35C4⋊Dic263D411yescharacteristic
36Dic263⋊C4—22no—
37(C2×D263)⋊C4—22no—
38(C2×D263)⋊C4—22no—
39(C2×D263)⋊C4—21no—
40C4×Dic263—22no—
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—41no—
50Dic526—41no—
51Dic526—41no—
52Dic526—41no—
53D1052—21no—
54D1052—21no—
55C2×Dic263—21no—
56C2×Dic263—22no—
57C2×Dic263—41no—
58C4×D263—41no—
59C4×D263—41no—
60C263⋊C8—41no—
61Q8×C263—21no—
62Q8×C263—21no—
63C2×C4×C263—21no—
64C2×C4×C263—21no—
65C2×C4×C263C2×D411yescharacteristic
66C2×C4×C263C2×D411yescharacteristic
67C2×C4×C263C2×D411yescharacteristic
68C8×C263—22no—
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#13511yescharacteristic
78C4×C263#13511yescharacteristic
79C4×C263AGL(1,ℤ/8)11yescharacteristic
80C4×C263#13711yescharacteristic
81Dic263—41no—
82Dic263—42no—
83Dic263—81no—
84C2×C263#44911yescharacteristic
85C2×C263#45211yescharacteristic
86C2×C263#45611yescharacteristic
87D263—81no—
88C263#165211yescharacteristic, complemented, Sylow
89#1652—2631nomaximal, Sylow
90#556—2631no—
91#498—2631no—
92#474—2631no—
93#462—2631no—
94#332—2631no—
95Q8⋊C8D26311yescharacteristic, complemented
96D4⋊C8—2631no—
97C2×Q16—5261no—
98C4⋊Q8—2631no—
99C4⋊Q8—2631no—
100#126—5262no—
101#124—5261no—
102C22⋊Q8—5261no—
103C4×Q8—5261no—
104C4×Q8C2×D26311yescharacteristic
105C4×D4—2631no—
106#117—5261no—
107#107—5261no—
108#106—5262no—
109C4⋊C8—2631no—
110C4⋊C8C2×D26311yescharacteristic
111#103—5261no—
112#102—5261no—
113C4×C8C2×D26311yescharacteristic
114C2×Q8—5261no—
115C2×Q8—5261no—
116C2×Q8D105211yescharacteristic
117C2×D4—2631no—
118C22×C4—5261no—
119Q16—10522no—
120C2×C8—21no—
121C2×C8—21no—
122C2×C8—5261no—
123C4⋊C4—21no—
124C4⋊C4—2632no—
125C4⋊C4—2631no—
126C4⋊C4—5262no—
127C4⋊C4—5261no—
128C4⋊C4—5261no—
129C4⋊C4—5261no—
130C4⋊C4D105211yescharacteristic
131C22⋊C4—5262no—
132C22⋊C4—5262no—
133C22⋊C4—5261no—
134C42—21no—
135C42—5262no—
136C42C22×D26311yescharacteristic
137C23—5261no—
138Q8—21no—
139Q8—21no—
140Q8—10521no—
141Q8—10521no—
142Q8—10521no—
143Q8—10521no—
144D4—5261no—
145D4—5261no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—5261no—
149C2×C4—5262no—
150C2×C4—10521no—
151C2×C4—10521no—
152C2×C4—10521no—
153C2×C4D4×D26311yescharacteristic
154C2×C4D4×D26311yescharacteristic
155C2×C4C2×D105211yescharacteristic
156C8—22no—
157C8—41no—
158C8—10521no—
159C22—10521no—
160C22—10521no—
161C22—10521no—
162C22#2255444011yescharacteristic
163C4—21no—
164C4—41no—
165C4—41no—
166C4—10521no—
167C4—10522no—
168C4—21041no—
169C4#2255449111yescharacteristic
170C4#2255449211yescharacteristic
171C4#2255449811yescharacteristic
172C4#2255450211yescharacteristic
173C2—21041no—
174C2#3068208511yescharacteristic
175C2#3068210311yescharacteristic
176C2#3068212211yescharacteristic
subgroupG/H
centerC22#22554440
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
FittingQ8⋊C8×C263C2
socleC22×C263#120
prime radicalC2×D1052D4
hypercenterQ8⋊C8D263
hypocenterC263#1652
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. #30682336C2semidirect
4. #30682148C2semidirect
5. #30681685C2semidirect
7. Q8⋊C8×C263C2semidirect
88. C263#1652semidirect
95. Q8⋊C8D263semidirect

Maximal subgroups

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

subgroupindex
#306826612
#306823362
#306822192
#306821482
#306816852
#306816672
Q8⋊C8×C2632
#1652263