Finite Group Databasebeta

← #46781783

Subgroups — #46781783

Order 33664.

246 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 246 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#30682519C211yesmaximal, characteristic
2#30682256C212yesmaximal, complemented
3#30681671C212yesmaximal, complemented
4#30681664C211yesmaximal, characteristic, complemented
5#400×C263C211yesmaximal, characteristic, complemented
6C2×#16862376—21no—
7#22554450—22no—
8#22554445—22no—
9#22554444—21no—
10#22554444C2212yes—
11#22554401—22no—
12#22554390—22no—
13C22⋊(C263⋊C8)C2212yes—
14C2×C4⋊C4×C263C2211yescharacteristic
15C2×C4⋊C4×C263C2211yescharacteristic
16#95×C263—21no—
17#95×C263—21no—
18#95×C263C2211yescharacteristic
19#16862376—42no—
20#16862376—42no—
21C2×Dic526—21no—
22C2×D1052—21no—
23C2×D1052—21no—
24C2×D1052D412yes—
25C2×C22⋊D263—22no—
26C2×C4×D263—22no—
27C2×C263⋊C8—22no—
28C4⋊Dic263—21no—
29C4⋊Dic263D412yes—
30(C2×D263)⋊C4—22no—
31(C2×D263)⋊C4—22no—
32C22×C4×C263—21no—
33C22×C4×C263—21no—
34C22×C4×C263D411yescharacteristic
35C22×C4×C263D411yescharacteristic
36C22×C4×C263C2311yescharacteristic
37C4⋊C4×C263—22no—
38C4⋊C4×C263—22no—
39C22×D263—22no—
40Dic526—42no—
41D1052—42no—
42D1052—42no—
43D1052—81no—
44C22⋊D263—42no—
45C22⋊D263—42no—
46C2×Dic263—22no—
47C4×D263—44no—
48C263⋊C8—42no—
49C23×C263C2×D411yescharacteristic
50C2×C4×C263—21no—
51C2×C4×C263—21no—
52C2×C4×C263—21no—
53C2×C4×C263—41no—
54C2×C4×C263—41no—
55C2×C4×C263—41no—
56C2×C4×C263—41no—
57C2×C4×C263—42no—
58C2×C4×C263—41no—
59C2×C4×C263—41no—
60C2×C4×C263SD1612yes—
61C2×C4×C263C2×D412yes—
62C22×C263—21no—
63C22×C263—21no—
64C22×C263#12011yescharacteristic
65C22×C263C2×SD1611yescharacteristic
66C22×C263AGL(1,ℤ/8)11yescharacteristic
67C2×D263—42no—
68C2×D263—42no—
69C2×D263—42no—
70C4×C263—22no—
71C4×C263—22no—
72C4×C263—41no—
73C4×C263—81no—
74C4×C263—81no—
75Dic263—42no—
76C2×C263—21no—
77C2×C263—21no—
78C2×C263#45011yescharacteristic
79C2×C263#45411yescharacteristic
80C2×C263#45811yescharacteristic
81D263—82no—
82C263#161611yescharacteristic, complemented, Sylow
83#1616—2631nomaximal, Sylow
84#537—2631no—
85#481—2632no—
86#400D26311yescharacteristic, complemented
87#327—2632no—
88#324—2631no—
89C2×#41—5261no—
90C22⋊Q8—5262no—
91#121—2632no—
92#121—5262no—
93#121—5261no—
94C2×C4⋊C4C2×D26311yescharacteristic
95C2×C4⋊C4C2×D26311yescharacteristic
96#106—5262no—
97#102—5262no—
98C22⋊C8—2632no—
99#95—21no—
100#95—21no—
101#95C2×D26311yescharacteristic
102#41—10522no—
103#41—10522no—
104C2×Q8—5261no—
105C2×D4—2632no—
106C2×D4—5261no—
107C2×D4—5261no—
108C2×D4—5262no—
109C22×C4—21no—
110C22×C4—21no—
111C22×C4—5262no—
112C22×C4C22⋊D26311yescharacteristic
113C22×C4C22⋊D26311yescharacteristic
114C22×C4C22×D26311yescharacteristic
115C2×C8—5262no—
116C4⋊C4—22no—
117C4⋊C4—22no—
118C4⋊C4—2632no—
119C4⋊C4—5261no—
120C22⋊C4—5262no—
121C22⋊C4—5262no—
122C23—5262no—
123C23C2×C22⋊D26311yescharacteristic
124Q8—10522no—
125D4—10522no—
126D4—10522no—
127D4—10522no—
128D4—10522no—
129D4—21041no—
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—21no—
133C2×C4—41no—
134C2×C4—41no—
135C2×C4—41no—
136C2×C4—41no—
137C2×C4—42no—
138C2×C4—41no—
139C2×C4—41no—
140C2×C4—5262no—
141C2×C4—10524no—
142C2×C4#1686236312yes—
143C2×C4D4×D26312yes—
144C8—10522no—
145C22—21no—
146C22—21no—
147C22—10522no—
148C22—10522no—
149C22—10522no—
150C22#2255443811yescharacteristic
151C22C2×#1686236311yescharacteristic
152C22#2255449511yescharacteristic
153C4—22no—
154C4—22no—
155C4—41no—
156C4—81no—
157C4—81no—
158C4—10522no—
159C2—21no—
160C2—21no—
161C2—21042no—
162C2#3068208811yescharacteristic
163C2#3068211011yescharacteristic
164C2#3068212711yescharacteristic
subgroupG/H
centerC22#22554438
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
Fitting#400×C263C2
socleC22×C263#120
prime radical#30682519C2
hypercenter#400D263
hypocenterC263#1616
LCSG ▷ C22×C4×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C22×C4 ◁ #400

Complements

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

NH ≅ G/Ntype
2. #30682256C2semidirect
3. #30681671C2semidirect
4. #30681664C2semidirect
5. #400×C263C2semidirect
82. C263#1616semidirect
86. #400D263semidirect

Maximal subgroups

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

subgroupindex
#306825192
#306822562
#306816712
#306816642
#400×C2632
#1616263