Finite Group Databasebeta

← #46781911

Subgroups — #46781911

Order 33664.

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

normal subgroups only

This group has 228 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#30682288C211yesmaximal, characteristic, complemented
3#30682230C211yesmaximal, characteristic, complemented
4#30681683C211yesmaximal, characteristic, complemented
5#30681668C211yesmaximal, characteristic, complemented
6D4⋊(C263⋊C8)C211yesmaximal, characteristic
7#476×C263C211yesmaximal, characteristic
8C22×Dic526—21no—
9#22554470C2211yescharacteristic
10#22554469—21no—
11#22554449—21no—
12#22554447—22no—
13C4×Dic526C2211yescharacteristic
14D4×Dic263—21no—
15#22554403—21no—
16C4⋊(C263⋊C8)C2211yescharacteristic
17#22554394—22no—
18#22554393—21no—
19C4×C263⋊C8C2211yescharacteristic
20C4⋊Q8×C263C2211yescharacteristic
21C4×D4×C263C2211yescharacteristic
22#106×C263—21no—
23C4⋊C8×C263C2211yescharacteristic
24#102×C263—21no—
25C2×Dic526—22no—
26C2×Dic526—21no—
27C2×Dic526—42no—
28C2×Dic526—42no—
29C2×Dic526D411yescharacteristic
30C22×Dic263—22no—
31C2×C263⋊C8—21no—
32C2×C263⋊C8—21no—
33C4⋊Dic263—21no—
34C4⋊Dic263D412yes—
35C4⋊Dic263D411yescharacteristic
36Dic263⋊C4—22no—
37Dic263⋊C4—21no—
38C22⋊Dic263—22no—
39C4×Dic263—21no—
40C2×Q8×C263—21no—
41C2×D4×C263D411yescharacteristic
42C22×C4×C263—21no—
43C2×C8×C263—21no—
44C4⋊C4×C263—21no—
45C4⋊C4×C263—21no—
46C4⋊C4×C263D411yescharacteristic
47C22⋊C4×C263—21no—
48C42×C263C2311yescharacteristic
49Dic526—21no—
50Dic526—44no—
51Dic526—41no—
52Dic526—41no—
53Dic526SD1612yes—
54C2×Dic263—21no—
55C2×Dic263—21no—
56C2×Dic263—22no—
57C2×Dic263—44no—
58C263⋊C8—41no—
59C263⋊C8—41no—
60C23×C263—21no—
61Q8×C263—42no—
62D4×C263—21no—
63D4×C263Q1612yes—
64C2×C4×C263—21no—
65C2×C4×C263—41no—
66C2×C4×C263—41no—
67C2×C4×C263—41no—
68C2×C4×C263C2×D411yescharacteristic
69C2×C4×C263C2×D411yescharacteristic
70C2×C4×C263C2×D411yescharacteristic
71C8×C263—41no—
72C22×C263—22no—
73C22×C263—41no—
74C22×C263—41no—
75C22×C263#12011yescharacteristic
76C4×C263—21no—
77C4×C263—41no—
78C4×C263—81no—
79C4×C263C2×SD1611yescharacteristic
80C4×C263C2×Q1611yescharacteristic
81C4×C263AGL(1,ℤ/8)11yescharacteristic
82C4×C263#13711yescharacteristic
83Dic263—22no—
84Dic263—42no—
85Dic263—41no—
86C2×C263—42no—
87C2×C263#45011yescharacteristic
88C2×C263#45111yescharacteristic
89C2×C263#45411yescharacteristic
90C263#163711yescharacteristic, complemented, Sylow
91#1637—2631nomaximal, Sylow
92D4×Q8—2631no—
93#487—2631no—
94#477—2631no—
95#476D26311yescharacteristic
96#332—2631no—
97Q8⋊C8—2631no—
98D4⋊C8—2631no—
99C22×Q8—5261no—
100C4⋊Q8—2631no—
101C4⋊Q8—5261no—
102C4⋊Q8C2×D26311yescharacteristic
103C22⋊Q8—5262no—
104C22⋊Q8—5261no—
105C4×Q8—2631no—
106C4×D4—5261no—
107C4×D4C2×D26311yescharacteristic
108#107—5261no—
109#106—21no—
110C4⋊C8—2631no—
111C4⋊C8C2×D26311yescharacteristic
112#103—5261no—
113#103—5262no—
114#102—21no—
115C4×C8—2631no—
116C2×Q8—21no—
117C2×Q8—2631no—
118C2×Q8—5262no—
119C2×Q8—5261no—
120C2×Q8—10522no—
121C2×Q8—10522no—
122C2×D4C22⋊D26311yescharacteristic
123C22×C4—21no—
124C22×C4—5262no—
125C2×C8—21no—
126C2×C8—5261no—
127C2×C8—5261no—
128C4⋊C4—21no—
129C4⋊C4—21no—
130C4⋊C4—2632no—
131C4⋊C4—2631no—
132C4⋊C4—5262no—
133C4⋊C4—5261no—
134C4⋊C4—5261no—
135C4⋊C4C22⋊D26311yescharacteristic
136C22⋊C4—21no—
137C22⋊C4—5262no—
138C42—5261no—
139C42C22×D26311yescharacteristic
140C23—21no—
141Q8—42no—
142Q8—2632no—
143Q8—5261no—
144Q8—10524no—
145Q8—10521no—
146Q8—10521no—
147D4—21no—
148D4#1686236612yes—
149C2×C4—21no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—5261no—
154C2×C4—5261no—
155C2×C4—5262no—
156C2×C4—10524no—
157C2×C4D4×D26311yescharacteristic
158C2×C4D4×D26311yescharacteristic
159C2×C4C2×C22⋊D26311yescharacteristic
160C8—41no—
161C8—10521no—
162C8—10521no—
163C22—22no—
164C22—41no—
165C22—41no—
166C22#2255443811yescharacteristic
167C4—21no—
168C4—41no—
169C4—81no—
170C4—5262no—
171C4—10522no—
172C4—10521no—
173C4SD16×D26311yescharacteristic
174C4C2×#1686236611yescharacteristic
175C4#2255449711yescharacteristic
176C4#2255450011yescharacteristic
177C2—42no—
178C2#3068208711yescharacteristic
179C2#3068209311yescharacteristic
180C2#3068210911yescharacteristic
subgroupG/H
centerC22#22554438
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
Fitting#476×C263C2
socleC22×C263#120
prime radicalC2×D4×C263D4
hypercenter#476D263
hypocenterC263#1637
LCSG ▷ C42×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
2. #30682288C2semidirect
3. #30682230C2semidirect
4. #30681683C2semidirect
5. #30681668C2semidirect
90. C263#1637semidirect

Maximal subgroups

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

subgroupindex
D4×Dic5262
#306822882
#306822302
#306816832
#306816682
D4⋊(C263⋊C8)2
#476×C2632
#1637263