Finite Group Databasebeta

← #46781766

Subgroups — #46781766

Order 33664.

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

normal subgroups only

This group has 288 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#30682500C211yesmaximal, characteristic
2#30682256C212yesmaximal, complemented
3#30681671C212yesmaximal, complemented
4#30681662C211yesmaximal, characteristic, complemented
5#399×C263C211yesmaximal, characteristic, complemented
6C22×C22⋊D263—21no—
7#22554454—22no—
8#22554444—21no—
9#22554444C2212yes—
10#22554440—22no—
11#22554401—22no—
12#22554390—22no—
13C22⋊(C263⋊C8)C2212yescomplemented
14C2×C4⋊C4×C263—21no—
15C2×C4⋊C4×C263C2211yescharacteristic, complemented
16C2×C22⋊C4×C263—21no—
17C2×C22⋊C4×C263C2211yescharacteristic
18#95×C263C2211yescharacteristic, complemented
19C23×D263—21no—
20C2×D1052—21no—
21C2×D1052D412yes—
22C2×C22⋊D263—22no—
23C2×C22⋊D263—22no—
24C2×C22⋊D263—42no—
25C2×C22⋊D263—42no—
26C22×Dic263—21no—
27C2×C263⋊C8—22no—
28C4⋊Dic263—21no—
29C4⋊Dic263D412yes—
30(C2×D263)⋊C4—22no—
31(C2×D263)⋊C4—22no—
32C24×C263D411yescharacteristic
33C22×C4×C263—21no—
34C22×C4×C263—21no—
35C22×C4×C263D411yescharacteristic
36C22×C4×C263C2311yescharacteristic
37C4⋊C4×C263—22no—
38C4⋊C4×C263—42no—
39C22⋊C4×C263—22no—
40C22⋊C4×C263—42no—
41C22×D263—22no—
42C22×D263—42no—
43C22×D263—81no—
44C22×D263—81no—
45D1052—42no—
46D1052—81no—
47C22⋊D263—44no—
48C22⋊D263—42no—
49C22⋊D263—42no—
50C2×Dic263—22no—
51C2×Dic263—42no—
52C263⋊C8—42no—
53C23×C263—21no—
54C23×C263—21no—
55C23×C263—41no—
56C23×C263—41no—
57C23×C263SD1612yes—
58C23×C263C2×D411yescharacteristic
59C2×C4×C263—22no—
60C2×C4×C263—21no—
61C2×C4×C263—41no—
62C2×C4×C263—41no—
63C2×C4×C263—41no—
64C2×C4×C263—41no—
65C2×C4×C263—41no—
66C2×C4×C263—41no—
67C2×C4×C263—41no—
68C2×C4×C263C2×D412yes—
69C22×C263—21no—
70C22×C263—21no—
71C22×C263—22no—
72C22×C263—42no—
73C22×C263—41no—
74C22×C263—41no—
75C22×C263—81no—
76C22×C263#12011yescharacteristic
77C22×C263C2×SD1611yescharacteristic
78C22×C263AGL(1,ℤ/8)11yescharacteristic
79C2×D263—42no—
80C2×D263—42no—
81C2×D263—42no—
82C2×D263—84no—
83C4×C263—22no—
84C4×C263—42no—
85C4×C263—41no—
86C4×C263—81no—
87Dic263—42no—
88C2×C263—21no—
89C2×C263—21no—
90C2×C263—42no—
91C2×C263#45011yescharacteristic
92C2×C263#45311yescharacteristic
93C2×C263#45811yescharacteristic
94D263—82no—
95C263#161311yescharacteristic, complemented, Sylow
96#1613—2631nomaximal, Sylow
97#534—2631no—
98#481—2632no—
99#399D26311yescharacteristic, complemented
100#327—2632no—
101#323—2631no—
102C22×D4—5261no—
103#123—5262no—
104#121—2632no—
105#121—5261no—
106#120—5262no—
107C2×C4⋊C4—21no—
108C2×C4⋊C4C2×D26311yescharacteristic, complemented
109C2×C22⋊C4—21no—
110C2×C22⋊C4C2×D26311yescharacteristic
111#106—5262no—
112#102—5262no—
113C22⋊C8—2632no—
114#95C2×D26311yescharacteristic, complemented
115C24—5261no—
116C24C22⋊D26311yescharacteristic
117C2×D4—2632no—
118C2×D4—5261no—
119C2×D4—5262no—
120C2×D4—5262no—
121C2×D4—10522no—
122C2×D4—10522no—
123C22×C4—21no—
124C22×C4—21no—
125C22×C4—5261no—
126C22×C4C22⋊D26311yescharacteristic
127C22×C4C22×D26311yescharacteristic
128C2×C8—5262no—
129C4⋊C4—22no—
130C4⋊C4—42no—
131C4⋊C4—2632no—
132C4⋊C4—5261no—
133C22⋊C4—22no—
134C22⋊C4—42no—
135C22⋊C4—5262no—
136C22⋊C4—5262no—
137C23—21no—
138C23—21no—
139C23—41no—
140C23—41no—
141C23—5262no—
142C23—10522no—
143C23—21041no—
144C23—21041no—
145C23#1686236312yes—
146C23C2×C22⋊D26311yescharacteristic
147D4—10522no—
148D4—10524no—
149D4—10522no—
150D4—10522no—
151D4—21041no—
152C2×C4—22no—
153C2×C4—21no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—5262no—
162C2×C4—10522no—
163C2×C4D4×D26312yes—
164C8—10522no—
165C22—21no—
166C22—21no—
167C22—22no—
168C22—42no—
169C22—41no—
170C22—41no—
171C22—81no—
172C22—10522no—
173C22—10522no—
174C22—10522no—
175C22—21044no—
176C22#2255443811yescharacteristic
177C22C2×#1686236311yescharacteristic
178C22#2255449511yescharacteristic
179C4—22no—
180C4—42no—
181C4—41no—
182C4—81no—
183C4—10522no—
184C2—21no—
185C2—21no—
186C2—42no—
187C2—21042no—
188C2#3068208811yescharacteristic
189C2#3068210511yescharacteristic
190C2#3068212711yescharacteristic
subgroupG/H
centerC22#22554438
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
Fitting#399×C263C2
socleC22×C263#120
prime radical#30682500C2
hypercenter#399D263
hypocenterC263#1613
LCSG ▷ C22×C4×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C22×C4 ◁ #399

Complements

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

NH ≅ G/Ntype
2. #30682256C2semidirect
3. #30681671C2semidirect
4. #30681662C2semidirect
5. #399×C263C2semidirect
13. C22⋊(C263⋊C8)C22semidirect
15. C2×C4⋊C4×C263C22semidirect
18. #95×C263C22semidirect
95. C263#1613semidirect
99. #399D263semidirect
108. C2×C4⋊C4C2×D263semidirect
114. #95C2×D263semidirect

Maximal subgroups

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

subgroupindex
#306825002
#306822562
#306816712
#306816622
#399×C2632
#1613263