Finite Group Databasebeta

← #46782032

Subgroups — #46782032

Order 33664.

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

normal subgroups only

This group has 240 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#30682591C211yesmaximal, characteristic
2#30682334C211yesmaximal, characteristic, complemented
3#30682219C211yesmaximal, characteristic, complemented
4#30682144C211yesmaximal, characteristic, complemented
5#30681665C211yesmaximal, characteristic, complemented
6#30681665C211yesmaximal, characteristic, complemented
7#332×C263C211yesmaximal, characteristic, complemented
8C2×#16862377—21no—
9C2×#16862365—21no—
10#22554470C2211yescharacteristic
11#22554455—22no—
12#22554446—21no—
13#22554445—21no—
14C4×D1052C2211yescharacteristic
15C4×D1052C2211yescharacteristic
16C4⋊C4×D263—21no—
17#22554404—21no—
18#22554401—22no—
19#22554395—21no—
20#22554392—21no—
21C4×C263⋊C8C2211yescharacteristic
22C4⋊Q8×C263C2211yescharacteristic
23C4⋊C8×C263C2211yescharacteristic
24C4⋊C8×C263C2211yescharacteristic
25#16862377—42no—
26#16862377—42no—
27C2×Dic526—21no—
28C2×D1052—22no—
29C2×D1052D411yescharacteristic
30C2×D1052D411yescharacteristic
31C2×C4×D263—22no—
32C2×C4×D263—21no—
33C2×C4×D263—21no—
34#16862365—42no—
35C2×C263⋊C8—21no—
36C4⋊Dic263—21no—
37C4⋊Dic263—21no—
38C4⋊Dic263D411yescharacteristic
39C4⋊Dic263D411yescharacteristic
40Dic263⋊C4—22no—
41(C2×D263)⋊C4—22no—
42(C2×D263)⋊C4—21no—
43(C2×D263)⋊C4—21no—
44C2×Q8×C263—21no—
45C2×C8×C263—21no—
46C2×C8×C263—21no—
47C4⋊C4×C263—21no—
48C4⋊C4×C263D412yes—
49C42×C263C2311yescharacteristic
50C22×D263—21no—
51C22×D263—21no—
52Dic526—41no—
53Dic526—41no—
54D1052—21no—
55D1052—21no—
56D1052—21no—
57D1052—44no—
58D1052SD1612yescomplemented
59C2×Dic263—21no—
60C2×Dic263—21no—
61C2×Dic263—41no—
62C4×D263—44no—
63C4×D263—41no—
64C4×D263—41no—
65C4×D263—41no—
66C4×D263—41no—
67C263⋊C8—22no—
68Q8×C263—41no—
69Q8×C263—41no—
70C2×C4×C263—22no—
71C2×C4×C263C2×D411yescharacteristic
72C2×C4×C263C2×D411yescharacteristic
73C2×C4×C263C2×D411yescharacteristic
74C8×C263—41no—
75C8×C263—41no—
76C22×C263#12011yescharacteristic
77C2×D263—22no—
78C2×D263—41no—
79C2×D263—41no—
80C2×D263—41no—
81C2×D263—41no—
82C2×D263—41no—
83C4×C263—21no—
84C4×C263—42no—
85C4×C263C2×SD1611yescharacteristic
86C4×C263#13511yescharacteristic
87C4×C263AGL(1,ℤ/8)11yescharacteristic
88C4×C263AGL(1,ℤ/8)11yescharacteristic
89Dic263—41no—
90Dic263—41no—
91Dic263—81no—
92C2×C263#44911yescharacteristic
93C2×C263#45011yescharacteristic
94C2×C263#45611yescharacteristic
95D263—42no—
96D263—81no—
97C263#165411yescharacteristic, complemented, Sylow
98#1654—2631nomaximal, Sylow
99#547—2631no—
100#498—2631no—
101#474—2631no—
102#461—2631no—
103#332D26311yescharacteristic, complemented
104D4⋊C8—2631no—
105D4⋊C8—2631no—
106C2×#41—5261no—
107C2×SD16—5261no—
108C4⋊Q8—2631no—
109C4⋊Q8C2×D26311yescharacteristic
110#123—5262no—
111C22⋊Q8—5261no—
112#121—5261no—
113C4×D4—2631no—
114C4×D4—2631no—
115C2×C4⋊C4—5261no—
116#107—5261no—
117#106—5262no—
118C4⋊C8C2×D26311yescharacteristic
119C4⋊C8C2×D26311yescharacteristic
120#103—5261no—
121#102—5261no—
122C4×C8—2631no—
123#41—10522no—
124#41—10522no—
125C2×Q8—21no—
126C2×Q8—5261no—
127C2×D4—2631no—
128C2×D4—2631no—
129C2×D4—5262no—
130C22×C4—5262no—
131C22×C4—5261no—
132C22×C4—5261no—
133SD16—10522no—
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—5261no—
137C4⋊C4—21no—
138C4⋊C4—2631no—
139C4⋊C4—2631no—
140C4⋊C4—5262no—
141C4⋊C4—5261no—
142C4⋊C4—5261no—
143C4⋊C4D105212yes—
144C22⋊C4—5262no—
145C22⋊C4—5261no—
146C22⋊C4—5261no—
147C42C22×D26311yescharacteristic
148C23—5261no—
149C23—5261no—
150Q8—41no—
151Q8—41no—
152Q8—10521no—
153Q8—10521no—
154D4—2632no—
155D4—5261no—
156D4—5261no—
157D4—5261no—
158D4—10524no—
159C2×C4—22no—
160C2×C4—5261no—
161C2×C4—5261no—
162C2×C4—10524no—
163C2×C4—10521no—
164C2×C4—10521no—
165C2×C4—10521no—
166C2×C4—10521no—
167C2×C4—10521no—
168C2×C4D4×D26311yescharacteristic
169C2×C4D4×D26311yescharacteristic
170C2×C4C2×D105211yescharacteristic
171C8—41no—
172C8—41no—
173C8—5262no—
174C22—5262no—
175C22—10521no—
176C22—10521no—
177C22—10521no—
178C22—10521no—
179C22—10521no—
180C22#2255444011yescharacteristic
181C4—21no—
182C4—42no—
183C4—10521no—
184C4—10521no—
185C4—21041no—
186C4SD16×D26311yescharacteristic
187C4#2255449311yescharacteristic
188C4#2255449411yescharacteristic
189C4#2255449711yescharacteristic
190C2—10522no—
191C2—21041no—
192C2#3068208611yescharacteristic
193C2#3068209011yescharacteristic
194C2#3068212311yescharacteristic
subgroupG/H
centerC22#22554440
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
Fitting#332×C263C2
socleC22×C263#120
prime radical#30682591C2
hypercenter#332D263
hypocenterC263#1654
LCSG ▷ C42×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #30682334C2semidirect
3. #30682219C2semidirect
4. #30682144C2semidirect
5. #30681665C2semidirect
6. #30681665C2semidirect
7. #332×C263C2semidirect
58. D1052SD16semidirect
97. C263#1654semidirect
103. #332D263semidirect

Maximal subgroups

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

subgroupindex
#306825912
#306823342
#306822192
#306821442
#306816652
#332×C2632
#1654263