Finite Group Databasebeta

← #46813461

Subgroups — #46813461

Order 34432.

1160 conjugacy classes of subgroups; only the 229 normal subgroups are shown.

normal subgroups only

This group has 1160 conjugacy classes of subgroups — too many to draw. Only its 229 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
1C23×C22⋊D269C211yesmaximal, characteristic
2C2×C22⋊C4×D269C212yesmaximal, complemented
3#31770481C218yesmaximal, complemented
4#31770466C212yesmaximal, complemented
5#31770461C211yesmaximal, characteristic, complemented
6#379×C269C211yesmaximal, characteristic, complemented
7C24×D269C2211yescharacteristic
8C22×C22⋊D269—28no—
9C22×C22⋊D269C418yescomplemented
10C22×C22⋊D269C2214yes—
11C23×Dic269C2211yescharacteristic
12C22×C4×D269C2214yescomplemented
13C2×C22⋊Dic269C2212yes—
14C2×C22⋊Dic269C2214yescomplemented
15C2×#16864379C2214yescomplemented
16C22⋊C4×D269—28no—
17#22575360C2218yescomplemented
18C25×C269C2211yescharacteristic
19C2×C22⋊C4×C269C2212yes—
20C2×C22⋊C4×C269C2214yescomplemented
21C23×D269—44no—
22C23×D269C2×C414yes—
23C23×D269D418yes—
24C23×D269C2312yes—
25C2×C22⋊D269—232no—
26C2×C22⋊D269—28no—
27C2×C22⋊D269—28no—
28C2×C22⋊D269C2×C4116yescomplemented
29C22×Dic269—24no—
30C22×Dic269C2×C414yescomplemented
31C22×Dic269C2314yes—
32C22×Dic269C2312yes—
33C2×C4×D269—28no—
34C2×C4×D269—48no—
35C22⋊Dic269—24no—
36C22⋊Dic269—44no—
37#16864379—28no—
38C24×C269—24no—
39C24×C269—44no—
40C24×C269C2×C414yescomplemented
41C24×C269C2312yes—
42C24×C269C2311yescharacteristic
43C22×C4×C269C2314yes—
44C22⋊C4×C269—24no—
45C22⋊C4×C269—44no—
46C22×D269—28no—
47C22×D269—48no—
48C22×D269—416no—
49C22×D269C22⋊C4116yescomplemented
50C22×D269C22×C414yes—
51C22×D269C2×D414yes—
52C22×D269C2×D414yes—
53C22⋊D269—232no—
54C2×Dic269—28no—
55C2×Dic269—24no—
56C2×Dic269—24no—
57C2×Dic269—28no—
58C2×Dic269C22×C414yes—
59C4×D269—416no—
60C23×C269—24no—
61C23×C269—28no—
62C23×C269—24no—
63C23×C269—24no—
64C23×C269—24no—
65C23×C269—48no—
66C23×C269—416no—
67C23×C269C22×C414yes—
68C23×C269C22×C412yes—
69C23×C269C2×D414yes—
70C23×C269C2411yescharacteristic
71C2×C4×C269—24no—
72C2×C4×C269—28no—
73C22×C269—24no—
74C22×C269—28no—
75C22×C269—24no—
76C22×C269—24no—
77C22×C269—24no—
78C22×C269—416no—
79C22×C269—48no—
80C22×C269C2×C22⋊C414yes—
81C22×C269C23×C411yescharacteristic
82C22×C269C22×D412yes—
83C22×C269H(5,𝔽2)14yes—
84C2×D269—28no—
85C2×D269—28no—
86C2×D269—28no—
87C2×D269—416no—
88C2×D269C2×C22⋊C418yes—
89C4×C269—44no—
90Dic269—24no—
91Dic269—44no—
92C2×C269—24no—
93C2×C269—44no—
94C2×C269C22×C22⋊C411yescharacteristic
95C2×C269#51812yes—
96C2×C269#53414yes—
97D269—28no—
98C269#230811yescharacteristic, complemented, Sylow
99#2308—2691nomaximal, Sylow
100C23×D4—2691no—
101C22×C22⋊C4—2692no—
102#386—2698no—
103#381—2692no—
104#379—2691no—
105#379D26911yescharacteristic, complemented
106C25—2691no—
107C25C2×D26911yescharacteristic
108C22×D4—2698no—
109C22×D4—2694no—
110C22×D4—5388no—
111C23×C4—2691no—
112C23×C4—2694no—
113C2×C22⋊C4—2692no—
114C2×C22⋊C4—2694no—
115C2×C22⋊C4—2694no—
116C2×C22⋊C4—5388no—
117C2×C22⋊C4C2×D26912yes—
118C2×C22⋊C4C2×D26914yescomplemented
119#95—2698no—
120C24—24no—
121C24—44no—
122C24—2692no—
123C24—2694no—
124C24—2698no—
125C24—10764no—
126C24C4×D26914yescomplemented
127C24C22×D26912yes—
128C24C22×D26911yescharacteristic
129C2×D4—26916no—
130C2×D4—53832no—
131C2×D4—5388no—
132C2×D4—5388no—
133C22×C4—2694no—
134C22×C4—2692no—
135C22×C4—2694no—
136C22×C4—5388no—
137C22×C4—5384no—
138C22×C4—10768no—
139C22×C4C22×D26914yes—
140C22⋊C4—24no—
141C22⋊C4—44no—
142C22⋊C4—5388no—
143C22⋊C4—5384no—
144C22⋊C4—10764no—
145C23—24no—
146C23—28no—
147C23—24no—
148C23—24no—
149C23—24no—
150C23—48no—
151C23—416no—
152C23—2694no—
153C23—2694no—
154C23—2694no—
155C23—26916no—
156C23—5388no—
157C23—107616no—
158C23—10768no—
159C23C2×C4×D26914yes—
160C23C2×C4×D26912yes—
161C23D4×D26914yes—
162C23C23×D26911yescharacteristic
163D4—53832no—
164C2×C4—24no—
165C2×C4—28no—
166C2×C4—2694no—
167C2×C4—5388no—
168C2×C4—5384no—
169C2×C4—5384no—
170C2×C4—5388no—
171C2×C4—107616no—
172C22—28no—
173C22—24no—
174C22—24no—
175C22—24no—
176C22—24no—
177C22—416no—
178C22—48no—
179C22—2698no—
180C22—5388no—
181C22—5388no—
182C22—5388no—
183C22—107616no—
184C22C22⋊C4×D26914yes—
185C22C22×C4×D26911yescharacteristic
186C22C2×D4×D26912yes—
187C22#2257549814yes—
188C4—44no—
189C4—5384no—
190C4—10764no—
191C2—24no—
192C2—44no—
193C2—5388no—
194C2C2×C22⋊C4×D26911yescharacteristic
195C2#3177107812yes—
196C2#3177116514yes—
subgroupG/H
center, FrattiniC23C23×D269
commutatorC22×C269C23×C4
Fitting#379×C269C2
socle, cosocleC23×C269C24
prime radicalC23×C22⋊D269C2
hypercenter#379D269
hypocenterC269#2308
LCSG ▷ C22×C269 ▷ C269
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊C4×D269C2semidirect
3. #31770481C2semidirect
4. #31770466C2semidirect
5. #31770461C2semidirect
6. #379×C269C2semidirect
9. C22×C22⋊D269C4semidirect
12. C22×C4×D269C22semidirect
14. C2×C22⋊Dic269C22semidirect
15. C2×#16864379C22semidirect
17. #22575360C22semidirect
20. C2×C22⋊C4×C269C22semidirect
28. C2×C22⋊D269C2×C4semidirect
30. C22×Dic269C2×C4semidirect
40. C24×C269C2×C4semidirect
49. C22×D269C22⋊C4semidirect
98. C269#2308semidirect
105. #379D269semidirect
118. C2×C22⋊C4C2×D269semidirect
126. C24C4×D269semidirect

Maximal subgroups

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

subgroupindex
C23×C22⋊D2692
C2×C22⋊C4×D2692
#317704812
#317704662
#317704612
#379×C2692
#2308269