Finite Group Databasebeta

← #46781915

Subgroups — #46781915

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#30682289C211yesmaximal, characteristic, complemented
3#30682234C211yesmaximal, characteristic, complemented
4#30682228C211yesmaximal, characteristic
5#30681685C211yesmaximal, characteristic, complemented
6#30681670C211yesmaximal, characteristic, complemented
7D4⋊C8×C263C211yesmaximal, characteristic
8C22×Dic526—21no—
9#22554470C2211yescharacteristic
10#22554470C2211yescharacteristic
11#22554469—21no—
12#22554449—21no—
13#22554447—22no—
14C4×Dic526C2211yescharacteristic
15D4×Dic263—21no—
16#22554404—21no—
17#22554401—21no—
18C4⋊(C263⋊C8)C2211yescharacteristic
19#22554395—21no—
20#22554395—22no—
21#22554391—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—
32C2×C263⋊C8—21no—
33C4⋊Dic263—21no—
34C4⋊Dic263—21no—
35C4⋊Dic263—21no—
36C4⋊Dic263D412yes—
37C4⋊Dic263D411yescharacteristic
38Dic263⋊C4—22no—
39Dic263⋊C4—21no—
40C22⋊Dic263—22no—
41C4×Dic263—21no—
42C2×D4×C263D411yescharacteristic
43C22×C4×C263—21no—
44C2×C8×C263—21no—
45C2×C8×C263—21no—
46C4⋊C4×C263D411yescharacteristic
47C22⋊C4×C263—21no—
48C42×C263C2311yescharacteristic
49Dic526—21no—
50Dic526—44no—
51Dic526—41no—
52Dic526—41no—
53Dic526—42no—
54Dic526SD1612yes—
55C2×Dic263—21no—
56C2×Dic263—21no—
57C2×Dic263—22no—
58C2×Dic263—44no—
59C2×Dic263—41no—
60C263⋊C8—41no—
61C23×C263—21no—
62D4×C263—21no—
63D4×C263Q1612yes—
64C2×C4×C263—21no—
65C2×C4×C263—41no—
66C2×C4×C263—41no—
67C2×C4×C263C2×D411yescharacteristic
68C2×C4×C263C2×D411yescharacteristic
69C2×C4×C263C2×D411yescharacteristic
70C8×C263—41no—
71C8×C263—41no—
72C22×C263—22no—
73C22×C263—41no—
74C22×C263—41no—
75C22×C263#12011yescharacteristic
76C4×C263—21no—
77C4×C263—41no—
78C4×C263C2×SD1611yescharacteristic
79C4×C263C2×Q1611yescharacteristic
80C4×C263AGL(1,ℤ/8)11yescharacteristic
81C4×C263#13711yescharacteristic
82Dic263—22no—
83Dic263—42no—
84Dic263—41no—
85Dic263—81no—
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#476—2631no—
96#332—2631no—
97Q8⋊C8—2631no—
98D4⋊C8D26311yescharacteristic
99C22×Q8—5261no—
100C4⋊Q8—2631no—
101C4⋊Q8—2631no—
102C4⋊Q8—5261no—
103C22⋊Q8—5262no—
104C22⋊Q8—5261no—
105C4×Q8—2631no—
106C4×D4—5261no—
107C4×D4C2×D26311yescharacteristic
108#107—5261no—
109#106—5261no—
110C4⋊C8—2631no—
111C4⋊C8C2×D26311yescharacteristic
112#103—5262no—
113#103—5261no—
114#102—5261no—
115C4×C8C2×D26311yescharacteristic
116C2×Q8—2631no—
117C2×Q8—5262no—
118C2×Q8—5261no—
119C2×Q8—5261no—
120C2×Q8—10522no—
121C2×Q8—10522no—
122C2×D4D105211yescharacteristic
123C22×C4—21no—
124C22×C4—5262no—
125C2×C8—21no—
126C2×C8—21no—
127C2×C8—5261no—
128C4⋊C4—2632no—
129C4⋊C4—2631no—
130C4⋊C4—5262no—
131C4⋊C4—5261no—
132C4⋊C4—5261no—
133C4⋊C4—5261no—
134C4⋊C4—5261no—
135C4⋊C4D105211yescharacteristic
136C22⋊C4—21no—
137C22⋊C4—5262no—
138C42—5261no—
139C42C22×D26311yescharacteristic
140C23—21no—
141Q8—2632no—
142Q8—5261no—
143Q8—10522no—
144Q8—10524no—
145Q8—10521no—
146Q8—10521no—
147D4—21no—
148D4Dic105212yes—
149C2×C4—21no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—5261no—
153C2×C4—5261no—
154C2×C4—5262no—
155C2×C4—10524no—
156C2×C4—10521no—
157C2×C4D4×D26311yescharacteristic
158C2×C4D4×D26311yescharacteristic
159C2×C4C2×D105211yescharacteristic
160C8—41no—
161C8—41no—
162C8—10521no—
163C22—22no—
164C22—41no—
165C22—41no—
166C22#2255444011yescharacteristic
167C4—21no—
168C4—41no—
169C4—5262no—
170C4—10521no—
171C4—10522no—
172C4—21041no—
173C4SD16×D26311yescharacteristic
174C4C2×Dic105211yescharacteristic
175C4#2255449411yescharacteristic
176C4#2255450311yescharacteristic
177C2—42no—
178C2#3068209011yescharacteristic
179C2#3068209611yescharacteristic
180C2#3068211211yescharacteristic
subgroupG/H
centerC22#22554440
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
FittingD4⋊C8×C263C2
socleC22×C263#120
prime radicalC2×D4×C263D4
hypercenterD4⋊C8D263
hypocenterC263#1637
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. #30682289C2semidirect
3. #30682234C2semidirect
5. #30681685C2semidirect
6. #30681670C2semidirect
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
#306822892
#306822342
#306822282
#306816852
#306816702
D4⋊C8×C2632
#1637263