Finite Group Databasebeta

← #27197720

Subgroups — #27197720

Order 13184.

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⋊D103C211yesmaximal, characteristic
2C2×C22⋊C4×D103C212yesmaximal, complemented
3#20267667C218yesmaximal, complemented
4#20267652C212yesmaximal, complemented
5#20267647C211yesmaximal, characteristic, complemented
6#379×C103C211yesmaximal, characteristic, complemented
7C24×D103C2211yescharacteristic
8C22×C22⋊D103—28no—
9C22×C22⋊D103C418yescomplemented
10C22×C22⋊D103C2214yes—
11C23×Dic103C2211yescharacteristic
12C22×C4×D103C2214yescomplemented
13C2×C22⋊Dic103C2212yes—
14C2×C22⋊Dic103C2214yescomplemented
15C2×(C2×D103)⋊C4C2214yescomplemented
16C22⋊C4×D103—28no—
17C103⋊#95C2218yescomplemented
18C25×C103C2211yescharacteristic
19C2×C22⋊C4×C103C2212yes—
20C2×C22⋊C4×C103C2214yescomplemented
21C23×D103—44no—
22C23×D103C2×C414yes—
23C23×D103D418yes—
24C23×D103C2312yes—
25C2×C22⋊D103—232no—
26C2×C22⋊D103—28no—
27C2×C22⋊D103—28no—
28C2×C22⋊D103C2×C4116yescomplemented
29C22×Dic103—24no—
30C22×Dic103C2×C414yescomplemented
31C22×Dic103C2314yes—
32C22×Dic103C2312yes—
33C2×C4×D103—28no—
34C2×C4×D103—48no—
35C22⋊Dic103—24no—
36C22⋊Dic103—44no—
37(C2×D103)⋊C4—28no—
38C24×C103—24no—
39C24×C103—44no—
40C24×C103C2×C414yescomplemented
41C24×C103C2312yes—
42C24×C103C2311yescharacteristic
43C22×C4×C103C2314yes—
44C22⋊C4×C103—24no—
45C22⋊C4×C103—44no—
46C23×C103—24no—
47C23×C103—28no—
48C23×C103—24no—
49C23×C103—24no—
50C23×C103—24no—
51C23×C103—48no—
52C23×C103—416no—
53C23×C103C22×C414yes—
54C23×C103C22×C412yes—
55C23×C103C2×D414yes—
56C23×C103C2411yescharacteristic
57C22×D103—28no—
58C22×D103—48no—
59C22×D103—416no—
60C22×D103C22⋊C4116yescomplemented
61C22×D103C22×C414yes—
62C22×D103C2×D414yes—
63C22×D103C2×D414yes—
64C2×C4×C103—24no—
65C2×C4×C103—28no—
66C22⋊D103—232no—
67C2×Dic103—28no—
68C2×Dic103—24no—
69C2×Dic103—24no—
70C2×Dic103—28no—
71C2×Dic103C22×C414yes—
72C4×D103—416no—
73C22×C103—24no—
74C22×C103—28no—
75C22×C103—24no—
76C22×C103—24no—
77C22×C103—24no—
78C22×C103—416no—
79C22×C103—48no—
80C22×C103C2×C22⋊C414yes—
81C22×C103C23×C411yescharacteristic
82C22×C103C22×D412yes—
83C22×C103H(5,𝔽2)14yes—
84C2×D103—28no—
85C2×D103—28no—
86C2×D103—28no—
87C2×D103—416no—
88C2×D103C2×C22⋊C418yes—
89C4×C103—44no—
90Dic103—24no—
91Dic103—44no—
92C2×C103—24no—
93C2×C103—44no—
94C2×C103C22×C22⋊C411yescharacteristic
95C2×C103#51812yes—
96C2×C103#53414yes—
97D103—28no—
98#2308—1031nomaximal, Sylow
99C103#230811yescharacteristic, complemented, Sylow
100C23×D4—1031no—
101C22×C22⋊C4—1032no—
102#386—1038no—
103#381—1032no—
104#379—1031no—
105#379D10311yescharacteristic, complemented
106C25—1031no—
107C25C2×D10311yescharacteristic
108C22×D4—1038no—
109C22×D4—1034no—
110C22×D4—2068no—
111C23×C4—1031no—
112C23×C4—1034no—
113C2×C22⋊C4—1034no—
114C2×C22⋊C4—1032no—
115C2×C22⋊C4—1034no—
116C2×C22⋊C4—2068no—
117C2×C22⋊C4C2×D10312yes—
118C2×C22⋊C4C2×D10314yescomplemented
119#95—1038no—
120C24—24no—
121C24—44no—
122C24—1034no—
123C24—1038no—
124C24—1032no—
125C24—4124no—
126C24C4×D10314yescomplemented
127C24C22×D10312yes—
128C24C22×D10311yescharacteristic
129C2×D4—10316no—
130C2×D4—2068no—
131C2×D4—2068no—
132C2×D4—20632no—
133C22×C4—1034no—
134C22×C4—1032no—
135C22×C4—1034no—
136C22×C4—4128no—
137C22×C4—2068no—
138C22×C4—2064no—
139C22×C4C22×D10314yes—
140C22⋊C4—24no—
141C22⋊C4—44no—
142C22⋊C4—4124no—
143C22⋊C4—2068no—
144C22⋊C4—2064no—
145C23—24no—
146C23—24no—
147C23—24no—
148C23—24no—
149C23—28no—
150C23—48no—
151C23—416no—
152C23—10316no—
153C23—1034no—
154C23—1034no—
155C23—1034no—
156C23—41216no—
157C23—4128no—
158C23—2068no—
159C23C2×C4×D10314yes—
160C23C2×C4×D10312yes—
161C23D4×D10314yes—
162C23C23×D10311yescharacteristic
163D4—20632no—
164C2×C4—24no—
165C2×C4—28no—
166C2×C4—1034no—
167C2×C4—41216no—
168C2×C4—2064no—
169C2×C4—2068no—
170C2×C4—2064no—
171C2×C4—2068no—
172C22—28no—
173C22—24no—
174C22—24no—
175C22—24no—
176C22—24no—
177C22—416no—
178C22—48no—
179C22—1038no—
180C22—41216no—
181C22—2068no—
182C22—2068no—
183C22—2068no—
184C22C22⋊C4×D10314yes—
185C22C22×C4×D10311yescharacteristic
186C22C2×D4×D10312yes—
187C22#1569306614yes—
188C4—44no—
189C4—4124no—
190C4—2064no—
191C2—24no—
192C2—44no—
193C2—2068no—
194C2C2×C22⋊C4×D10311yescharacteristic
195C2#2026826412yes—
196C2#2026835114yes—
subgroupG/H
center, FrattiniC23C23×D103
commutatorC22×C103C23×C4
Fitting#379×C103C2
socle, cosocleC23×C103C24
prime radicalC23×C22⋊D103C2
hypercenter#379D103
hypocenterC103#2308
LCSG ▷ C22×C103 ▷ C103
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊C4×D103C2semidirect
3. #20267667C2semidirect
4. #20267652C2semidirect
5. #20267647C2semidirect
6. #379×C103C2semidirect
9. C22×C22⋊D103C4semidirect
12. C22×C4×D103C22semidirect
14. C2×C22⋊Dic103C22semidirect
15. C2×(C2×D103)⋊C4C22semidirect
17. C103⋊#95C22semidirect
20. C2×C22⋊C4×C103C22semidirect
28. C2×C22⋊D103C2×C4semidirect
30. C22×Dic103C2×C4semidirect
40. C24×C103C2×C4semidirect
60. C22×D103C22⋊C4semidirect
99. C103#2308semidirect
105. #379D103semidirect
118. C2×C22⋊C4C2×D103semidirect
126. C24C4×D103semidirect

Maximal subgroups

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

subgroupindex
C23×C22⋊D1032
C2×C22⋊C4×D1032
#202676672
#202676522
#202676472
#379×C1032
#2308103