Finite Group Databasebeta

← #49123842

Subgroups — #49123842

Order 36224.

1104 conjugacy classes of subgroups; only the 229 normal subgroups are shown.

normal subgroups only

This group has 1104 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⋊D283C211yesmaximal, characteristic
2C2×#22583566C212yesmaximal, complemented
3#31826365C218yesmaximal, complemented
4#31826321C211yesmaximal, characteristic, complemented
5#31826320C212yesmaximal, complemented
6#379×C283C211yesmaximal, characteristic, complemented
7C24×D283C2211yescharacteristic
8C22×C22⋊D283—28no—
9C22×C22⋊D283C418yescomplemented
10C22×C22⋊D283C2214yes—
11C23×Dic283C2211yescharacteristic
12#22583566—28no—
13C2×Dic283⋊C4C2214yescomplemented
14C2×C22⋊Dic283C2212yes—
15C2×C22⋊Dic283C2214yescomplemented
16C2×(C2×D283)⋊C4C2218yescomplemented
17C2×C4×Dic283C2214yescomplemented
18C25×C283C2211yescharacteristic
19C2×C22⋊C4×C283C2212yes—
20C2×C22⋊C4×C283C2214yescomplemented
21C23×D283—24no—
22C23×D283—44no—
23C23×D283C2×C414yes—
24C23×D283C2312yes—
25C2×C22⋊D283—232no—
26C2×C22⋊D283—28no—
27C2×C22⋊D283—28no—
28C2×C22⋊D283C2×C4116yes—
29C22×Dic283C2×C414yes—
30C22×Dic283D418yes—
31C22×Dic283C2314yes—
32C22×Dic283C2312yes—
33Dic283⋊C4—28no—
34C22⋊Dic283—24no—
35C22⋊Dic283—44no—
36(C2×D283)⋊C4—48no—
37C4×Dic283—28no—
38C24×C283—24no—
39C24×C283—44no—
40C24×C283C2×C414yes—
41C24×C283C2312yes—
42C24×C283C2311yescharacteristic
43C22×C4×C283C2314yes—
44C22⋊C4×C283—24no—
45C22⋊C4×C283—44no—
46C22×D283—28no—
47C22×D283—24no—
48C22×D283—28no—
49C22×D283—48no—
50C22×D283—416no—
51C22×D283C22×C414yes—
52C22⋊D283—232no—
53C2×Dic283—24no—
54C2×Dic283—28no—
55C2×Dic283C22⋊C4116yescomplemented
56C2×Dic283C22×C414yes—
57C2×Dic283C2×D414yes—
58C2×Dic283C2×D414yes—
59C23×C283—24no—
60C23×C283—28no—
61C23×C283—24no—
62C23×C283—24no—
63C23×C283—24no—
64C23×C283—48no—
65C23×C283—416no—
66C23×C283C22×C414yes—
67C23×C283C22×C412yes—
68C23×C283C2×D414yes—
69C23×C283C2411yescharacteristic
70C2×C4×C283—24no—
71C2×C4×C283—28no—
72C22×C283—24no—
73C22×C283—28no—
74C22×C283—24no—
75C22×C283—24no—
76C22×C283—24no—
77C22×C283—416no—
78C22×C283—48no—
79C22×C283C2×C22⋊C414yes—
80C22×C283C23×C411yescharacteristic
81C22×C283C22×D412yes—
82C22×C283H(5,𝔽2)14yes—
83C2×D283—24no—
84C2×D283—28no—
85C2×D283—416no—
86C2×D283—48no—
87C4×C283—44no—
88Dic283—44no—
89Dic283C2×C22⋊C418yes—
90C2×C283—24no—
91C2×C283—44no—
92C2×C283C22×C22⋊C411yescharacteristic
93C2×C283#51812yes—
94C2×C283#53514yes—
95D283—44no—
96C283#230911yescharacteristic, complemented, Sylow
97#2309—2831nomaximal, Sylow
98C23×D4—2831no—
99C2×#117—2832no—
100#390—2838no—
101#379—2831no—
102#379—2832no—
103#379D28311yescharacteristic, complemented
104C25—2831no—
105C25C2×D28311yescharacteristic
106C22×D4—2838no—
107C22×D4—2834no—
108C22×D4—5668no—
109C23×C4—2831no—
110#117—5668no—
111C2×C4⋊C4—2834no—
112C2×C22⋊C4—2832no—
113C2×C22⋊C4—2834no—
114C2×C22⋊C4—2838no—
115C2×C22⋊C4C2×D28312yes—
116C2×C22⋊C4C2×D28314yescomplemented
117C2×C42—2834no—
118C24—24no—
119C24—44no—
120C24—2832no—
121C24—2834no—
122C24—5664no—
123C24—11324no—
124C24C4×D28314yes—
125C24C22×D28312yes—
126C24C22×D28311yescharacteristic
127C2×D4—28316no—
128C2×D4—56632no—
129C2×D4—5668no—
130C2×D4—5668no—
131C22×C4—2834no—
132C22×C4—2838no—
133C22×C4—2832no—
134C22×C4—2834no—
135C22×C4C22×D28314yes—
136C4⋊C4—5668no—
137C22⋊C4—24no—
138C22⋊C4—44no—
139C22⋊C4—5664no—
140C22⋊C4—11328no—
141C22⋊C4—11324no—
142C42—5668no—
143C23—24no—
144C23—28no—
145C23—24no—
146C23—24no—
147C23—24no—
148C23—48no—
149C23—416no—
150C23—2834no—
151C23—5668no—
152C23—5664no—
153C23—5668no—
154C23—11328no—
155C23—113216no—
156C23C2×C4×D28314yes—
157C23C2×C4×D28312yes—
158C23D4×D28314yes—
159C23C23×D28311yescharacteristic
160D4—56632no—
161C2×C4—24no—
162C2×C4—28no—
163C2×C4—28316no—
164C2×C4—2834no—
165C2×C4—2834no—
166C2×C4—2834no—
167C2×C4—5664no—
168C2×C4—5668no—
169C22—28no—
170C22—24no—
171C22—24no—
172C22—24no—
173C22—24no—
174C22—416no—
175C22—48no—
176C22—5664no—
177C22—5668no—
178C22—113216no—
179C22—11328no—
180C22C22⋊C4×D28314yes—
181C22C22×C4×D28311yescharacteristic
182C22C2×D4×D28312yes—
183C22#2258365514yes—
184C4—44no—
185C4—2838no—
186C4—11324no—
187C2—24no—
188C2—44no—
189C2—11324no—
190C2C2×C22⋊C4×D28311yescharacteristic
191C2#3182693812yes—
192C2#3182703014yes—
subgroupG/H
center, FrattiniC23C23×D283
commutatorC22×C283C23×C4
Fitting#379×C283C2
socle, cosocleC23×C283C24
prime radicalC23×C22⋊D283C2
hypercenter#379D283
hypocenterC283#2309
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
2. C2×#22583566C2semidirect
3. #31826365C2semidirect
4. #31826321C2semidirect
5. #31826320C2semidirect
6. #379×C283C2semidirect
9. C22×C22⋊D283C4semidirect
13. C2×Dic283⋊C4C22semidirect
15. C2×C22⋊Dic283C22semidirect
16. C2×(C2×D283)⋊C4C22semidirect
17. C2×C4×Dic283C22semidirect
20. C2×C22⋊C4×C283C22semidirect
55. C2×Dic283C22⋊C4semidirect
96. C283#2309semidirect
103. #379D283semidirect
116. C2×C22⋊C4C2×D283semidirect

Maximal subgroups

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

subgroupindex
C23×C22⋊D2832
C2×#225835662
#318263652
#318263212
#318263202
#379×C2832
#2309283