Finite Group Databasebeta

← #46782012

Subgroups — #46782012

Order 33664.

234 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 59 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
1D4×Dic526C211yesmaximal, characteristic
2#30682336C211yesmaximal, characteristic, complemented
3#30682224C211yesmaximal, characteristic, complemented
4#30682143C211yesmaximal, characteristic
5#30681685C211yesmaximal, characteristic, complemented
6#30681670C211yesmaximal, characteristic, complemented
7D4⋊C8×C263C211yesmaximal, characteristic
8C22×Dic526—21no—
9C2×#16862364—21no—
10#22554470C2211yescharacteristic
11#22554470C2211yescharacteristic
12#22554469—21no—
13#22554449—21no—
14#22554447—22no—
15C4×Dic526C2211yescharacteristic
16D4×Dic263—21no—
17#22554402—21no—
18#22554402—22no—
19C4⋊(C263⋊C8)C2211yescharacteristic
20#22554395—21no—
21#22554393—21no—
22C4×D4×C263C2211yescharacteristic
23C4⋊C8×C263C2211yescharacteristic
24C4×C8×C263C2211yescharacteristic
25C2×Dic526—22no—
26C2×Dic526—21no—
27C2×Dic526—21no—
28C2×Dic526—42no—
29C2×Dic526—42no—
30C2×Dic526D411yescharacteristic
31C22×Dic263—22no—
32#16862364—42no—
33C2×C263⋊C8—21no—
34C4⋊Dic263—21no—
35C4⋊Dic263—21no—
36C4⋊Dic263—21no—
37C4⋊Dic263D411yescharacteristic
38C4⋊Dic263D412yes—
39Dic263⋊C4—22no—
40Dic263⋊C4—21no—
41C22⋊Dic263—22no—
42C4×Dic263—21no—
43C2×D4×C263D411yescharacteristic
44C22×C4×C263—21no—
45C2×C8×C263—21no—
46C2×C8×C263—21no—
47C4⋊C4×C263D411yescharacteristic
48C22⋊C4×C263—21no—
49C42×C263C2311yescharacteristic
50Dic526—21no—
51Dic526—44no—
52Dic526—41no—
53Dic526—41no—
54Dic526—41no—
55Dic526—41no—
56Dic526SD1612yescomplemented
57C2×Dic263—21no—
58C2×Dic263—21no—
59C2×Dic263—22no—
60C2×Dic263—44no—
61C2×Dic263—41no—
62C263⋊C8—41no—
63C23×C263—21no—
64D4×C263—21no—
65D4×C263SD1612yes—
66C2×C4×C263—21no—
67C2×C4×C263—41no—
68C2×C4×C263—41no—
69C2×C4×C263C2×D411yescharacteristic
70C2×C4×C263C2×D411yescharacteristic
71C2×C4×C263C2×D411yescharacteristic
72C8×C263—22no—
73C8×C263—41no—
74C22×C263—22no—
75C22×C263—41no—
76C22×C263—41no—
77C22×C263#12011yescharacteristic
78C4×C263—21no—
79C4×C263—41no—
80C4×C263C2×SD1611yescharacteristic
81C4×C263C2×SD1611yescharacteristic
82C4×C263AGL(1,ℤ/8)11yescharacteristic
83C4×C263#13711yescharacteristic
84Dic263—22no—
85Dic263—42no—
86Dic263—41no—
87Dic263—81no—
88C2×C263—42no—
89C2×C263#44811yescharacteristic
90C2×C263#45011yescharacteristic
91C2×C263#45611yescharacteristic
92C263#165111yescharacteristic, complemented, Sylow
93#1651—2631nomaximal, Sylow
94D4×Q8—2631no—
95#498—2631no—
96#475—2631no—
97#461—2631no—
98#332—2631no—
99Q8⋊C8—2631no—
100D4⋊C8D26311yescharacteristic
101C22×Q8—5261no—
102C2×SD16—5261no—
103C4⋊Q8—2631no—
104C4⋊Q8—2631no—
105C4⋊Q8—5261no—
106C22⋊Q8—5262no—
107C22⋊Q8—5261no—
108C4×Q8—2631no—
109C4×D4—5261no—
110C4×D4C2×D26311yescharacteristic
111#106—5261no—
112#106—5262no—
113C4⋊C8—2631no—
114C4⋊C8C2×D26311yescharacteristic
115#103—5261no—
116#103—5261no—
117C4×C8C2×D26311yescharacteristic
118C2×Q8—2631no—
119C2×Q8—5262no—
120C2×Q8—5261no—
121C2×Q8—5261no—
122C2×Q8—10522no—
123C2×Q8—10522no—
124C2×D4D105211yescharacteristic
125C22×C4—21no—
126C22×C4—5262no—
127SD16—10522no—
128C2×C8—21no—
129C2×C8—21no—
130C2×C8—5261no—
131C4⋊C4—2631no—
132C4⋊C4—2632no—
133C4⋊C4—5262no—
134C4⋊C4—5261no—
135C4⋊C4—5261no—
136C4⋊C4—5261no—
137C4⋊C4—5261no—
138C4⋊C4D105211yescharacteristic
139C22⋊C4—21no—
140C22⋊C4—5262no—
141C42—5261no—
142C42C22×D26311yescharacteristic
143C23—21no—
144Q8—2632no—
145Q8—5261no—
146Q8—10524no—
147Q8—10521no—
148Q8—10521no—
149Q8—10521no—
150Q8—10521no—
151D4—21no—
152D4#1686236512yes—
153C2×C4—21no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—5261no—
157C2×C4—5261no—
158C2×C4—5262no—
159C2×C4—10524no—
160C2×C4—10521no—
161C2×C4D4×D26311yescharacteristic
162C2×C4D4×D26311yescharacteristic
163C2×C4C2×D105211yescharacteristic
164C8—22no—
165C8—41no—
166C8—10521no—
167C22—22no—
168C22—41no—
169C22—41no—
170C22#2255444011yescharacteristic
171C4—21no—
172C4—41no—
173C4—5262no—
174C4—10521no—
175C4—10522no—
176C4—21041no—
177C4SD16×D26311yescharacteristic
178C4C2×#1686236511yescharacteristic
179C4#2255449411yescharacteristic
180C4#2255450311yescharacteristic
181C2—42no—
182C2#3068207911yescharacteristic
183C2#3068209011yescharacteristic
184C2#3068212211yescharacteristic
subgroupG/H
centerC22#22554440
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
FittingD4⋊C8×C263C2
socleC22×C263#120
prime radicalC2×D4×C263D4
hypercenterD4⋊C8D263
hypocenterC263#1651
LCSG ▷ C42×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #30682336C2semidirect
3. #30682224C2semidirect
5. #30681685C2semidirect
6. #30681670C2semidirect
56. Dic526SD16semidirect
92. C263#1651semidirect

Maximal subgroups

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

subgroupindex
D4×Dic5262
#306823362
#306822242
#306821432
#306816852
#306816702
D4⋊C8×C2632
#1651263