Finite Group Databasebeta

← #46783183

Subgroups — #46783183

Order 33664.

412 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 105 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
1C22×#16862360C211yesmaximal, characteristic, complemented
2C2×#22554444C211yesmaximal, characteristic
3C2×#22554390C212yesmaximal, complemented
4#30681700C212yesmaximal, complemented
5#380×C263C211yesmaximal, characteristic, complemented
6C22×D1052C2211yescharacteristic
7C22×C22⋊D263—21no—
8C2×#16862360—24no—
9C2×#16862360—22no—
10C22×C263⋊C8C2212yes—
11#22554444—22no—
12#22554444C414yescomplemented
13C2×C4⋊Dic263C2211yescharacteristic
14C2×(C2×D263)⋊C4—21no—
15#22554390—24no—
16C23×C4×C263C2211yescharacteristic
17C2×C4⋊C4×C263C2212yes—
18C2×C22⋊C4×C263—21no—
19#95×C263—21no—
20C23×D263—21no—
21C2×D1052—22no—
22C2×D1052—21no—
23C2×D1052—22no—
24C2×D1052C2×C412yes—
25C2×C22⋊D263—24no—
26C2×C22⋊D263—44no—
27C22×Dic263—21no—
28#16862360—28no—
29C2×C263⋊C8—22no—
30C2×C263⋊C8—22no—
31C2×C263⋊C8D414yescomplemented
32C4⋊Dic263—21no—
33C4⋊Dic263C2×C412yes—
34(C2×D263)⋊C4—24no—
35C24×C263D411yescharacteristic
36C22×C4×C263—22no—
37C22×C4×C263—22no—
38C22×C4×C263—22no—
39C22×C4×C263C2×C412yes—
40C22×C4×C263D411yescharacteristic
41C22×C4×C263D412yes—
42C22×C4×C263C2311yescharacteristic
43C4⋊C4×C263—22no—
44C4⋊C4×C263—22no—
45C22⋊C4×C263—42no—
46C22×D263—22no—
47C22×D263—42no—
48C22×D263—42no—
49C22×D263—41no—
50C22×D263—41no—
51D1052—24no—
52D1052—41no—
53D1052—41no—
54C22⋊D263—48no—
55C2×Dic263—22no—
56C2×Dic263—42no—
57C263⋊C8—24no—
58C23×C263—22no—
59C23×C263—21no—
60C23×C263—22no—
61C23×C263—21no—
62C23×C263C22⋊C412yes—
63C23×C263C2×D411yescharacteristic
64C2×C4×C263—22no—
65C2×C4×C263—24no—
66C2×C4×C263—22no—
67C2×C4×C263—22no—
68C2×C4×C263—42no—
69C2×C4×C263—42no—
70C2×C4×C263—42no—
71C2×C4×C263C22⋊C412yes—
72C2×C4×C263C22×C411yescharacteristic
73C2×C4×C263C2×D412yes—
74C2×C4×C263C2×D411yescharacteristic
75C2×C4×C263#4112yes—
76C22×C263—22no—
77C22×C263—22no—
78C22×C263—22no—
79C22×C263—42no—
80C22×C263—42no—
81C22×C263C2×C22⋊C411yescharacteristic
82C22×C263#12112yes—
83C22×C263AGL(1,ℤ/8)12yes—
84C22×C263AGL(1,ℤ/8)11yescharacteristic
85C22×C263#13711yescharacteristic
86C2×D263—42no—
87C2×D263—42no—
88C2×D263—42no—
89C2×D263—82no—
90C2×D263—82no—
91C4×C263—22no—
92C4×C263—82no—
93C4×C263C4×D412yes—
94C4×C263#12011yescharacteristic
95C4×C263#12311yescharacteristic
96Dic263—42no—
97C2×C263—42no—
98C2×C263#38611yescharacteristic
99C2×C263#41711yescharacteristic
100C2×C263#41811yescharacteristic
101C2×C263#46812yes—
102C2×C263#46912yes—
103D263—82no—
104C263#189511yescharacteristic, complemented, Sylow
105#1895—2631nomaximal, Sylow
106C22×M16—2631no—
107C2×#121—2631no—
108C2×#102—2632no—
109#380D26311yescharacteristic, complemented
110#340—2632no—
111C22×D4—2631no—
112C22×D4—5261no—
113C23×C4C2×D26311yescharacteristic
114C2×M16—5264no—
115C2×M16—5262no—
116C22×C8—2632no—
117#121—2634no—
118#121—5262no—
119C2×C4⋊C4—2631no—
120C2×C4⋊C4C2×D26312yes—
121C2×C22⋊C4—21no—
122C2×C22⋊C4—5261no—
123#102—5264no—
124#95—21no—
125C24—5261no—
126C24C22⋊D26311yescharacteristic
127C2×D4—2632no—
128C2×D4—5264no—
129C2×D4—5262no—
130C2×D4—5261no—
131C2×D4—5262no—
132C2×D4—10524no—
133C22×C4—22no—
134C22×C4—22no—
135C22×C4—22no—
136C22×C4—5261no—
137C22×C4C4×D26312yes—
138C22×C4C22⋊D26311yescharacteristic
139C22×C4D105212yes—
140C22×C4C22×D26311yescharacteristic
141M16—5268no—
142C2×C8—2634no—
143C2×C8—5262no—
144C2×C8—5262no—
145C4⋊C4—22no—
146C4⋊C4—22no—
147C4⋊C4—2632no—
148C4⋊C4—5261no—
149C22⋊C4—42no—
150C22⋊C4—5264no—
151C23—22no—
152C23—22no—
153C23—21no—
154C23—21no—
155C23—5262no—
156C23—10522no—
157C23—10522no—
158C23—10521no—
159C23—10521no—
160C23(C2×D263)⋊C412yes—
161C23C2×C22⋊D26311yescharacteristic
162D4—5264no—
163D4—10528no—
164D4—10521no—
165D4—10521no—
166C2×C4—22no—
167C2×C4—24no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—42no—
171C2×C4—42no—
172C2×C4—42no—
173C2×C4—5262no—
174C2×C4—10522no—
175C2×C4(C2×D263)⋊C412yes—
176C2×C4C2×C4×D26311yescharacteristic
177C2×C4D4×D26312yes—
178C2×C4C2×D105211yescharacteristic
179C2×C4#1686237512yes—
180C8—5264no—
181C22—22no—
182C22—22no—
183C22—22no—
184C22—42no—
185C22—42no—
186C22—10522no—
187C22—10522no—
188C22—10522no—
189C22—21042no—
190C22—21042no—
191C22C2×(C2×D263)⋊C411yescharacteristic
192C22#2255444212yes—
193C22#2255449512yes—
194C22#2255449611yescharacteristic
195C22#2255450111yescharacteristic
196C4—22no—
197C4—82no—
198C4—10522no—
199C4(C22⋊D263)⋊C412yes—
200C4#2255444011yescharacteristic
201C4#2255445411yescharacteristic
202C2—42no—
203C2—21042no—
204C2#3068181511yescharacteristic
205C2#3068193711yescharacteristic
206C2#3068194211yescharacteristic
207C2#3068218612yes—
208C2#3068218912yes—
subgroupG/H
centerC23C2×C22⋊D263
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
Fitting#380×C263C2
socleC23×C263C2×D4
prime radicalC2×#22554444C2
cosocleC22×C4×C263C23
hypercenter#380D263
hypocenterC263#1895
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C23 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
1. C22×#16862360C2semidirect
3. C2×#22554390C2semidirect
4. #30681700C2semidirect
5. #380×C263C2semidirect
12. #22554444C4semidirect
31. C2×C263⋊C8D4semidirect
104. C263#1895semidirect
109. #380D263semidirect

Maximal subgroups

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

subgroupindex
C22×#168623602
C2×#225544442
C2×#225543902
#306817002
#380×C2632
#1895263