Finite Group Databasebeta

← #27197524

Subgroups — #27197524

Order 13184.

1088 conjugacy classes of subgroups; only the 245 normal subgroups are shown.

normal subgroups only

This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 245 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×C4×D103C211yesmaximal, characteristic
2C2×#15692977C212yesmaximal, complemented
3#20267654C211yesmaximal, characteristic, complemented
4#20267650C214yesmaximal, complemented
5#20267646C212yesmaximal
6#20267638C214yesmaximal, complemented
7#381×C103C211yesmaximal, characteristic, complemented
8C24×D103C2211yescharacteristic
9C23×Dic103C2211yescharacteristic
10C22×C4×D103—28no—
11C22×C4×D103C418yescomplemented
12C22×C4×D103C2212yes—
13C22×C4×D103C2212yes—
14#15692977—28no—
15C2×Dic103⋊C4C2214yescomplemented
16C2×C22⋊Dic103C2212yes—
17C2×(C2×D103)⋊C4C2218yes—
18C2×C4×Dic103C2214yescomplemented
19C103⋊#95C2214yescomplemented
20C23×C4×C103C2211yescharacteristic
21C2×C22⋊C4×C103C2212yes—
22#95×C103C2214yescomplemented
23C23×D103—24no—
24C23×D103—28no—
25C23×D103C2×C414yes—
26C23×D103C2312yes—
27C22×Dic103C2×C414yes—
28C22×Dic103D418yes—
29C22×Dic103C2314yes—
30C22×Dic103C2311yescharacteristic
31C22×Dic103C2311yescharacteristic
32C2×C4×D103—232no—
33C2×C4×D103—28no—
34C2×C4×D103—28no—
35C2×C4×D103C2×C418yes—
36C2×C4×D103C2×C418yes—
37Dic103⋊C4—28no—
38C22⋊Dic103—24no—
39(C2×D103)⋊C4—216no—
40C4×Dic103—28no—
41C24×C103C2311yescharacteristic
42C22×C4×C103—24no—
43C22×C4×C103C2×C414yes—
44C22×C4×C103C2314yes—
45C22×C4×C103C2312yes—
46C22⋊C4×C103—24no—
47C23×C103—24no—
48C23×C103C22×C412yes—
49C23×C103C2×D414yes—
50C23×C103C2411yescharacteristic
51C22×D103—232no—
52C22×D103—28no—
53C22×D103—24no—
54C22×D103—24no—
55C22×D103—216no—
56C22×D103C22×C414yes—
57C22×D103#4118yes—
58C2×C4×C103—28no—
59C2×C4×C103—24no—
60C2×C4×C103—24no—
61C2×C4×C103—28no—
62C2×C4×C103C22×C414yes—
63C2×Dic103—24no—
64C2×Dic103—28no—
65C2×Dic103C22⋊C4116yescomplemented
66C2×Dic103C22×C412yes—
67C2×Dic103C22×C412yes—
68C2×Dic103C2×D414yes—
69C2×Dic103C2×D414yes—
70C4×D103—216no—
71C4×D103—216no—
72C22×C103—24no—
73C22×C103—28no—
74C22×C103C2×C22⋊C414yes—
75C22×C103C23×C411yescharacteristic
76C22×C103C22×D412yes—
77C22×C103C2×#4114yes—
78C2×D103—232no—
79C2×D103—24no—
80C2×D103—24no—
81C2×D103—216no—
82C2×D103#11718yescomplemented
83C4×C103—24no—
84C4×C103—44no—
85Dic103—44no—
86Dic103C2×C22⋊C414yes—
87Dic103C2×C22⋊C414yes—
88C2×C103—24no—
89C2×C103C22×C22⋊C411yescharacteristic
90C2×C103C2×#11712yes—
91C2×C103#52514yes—
92D103—28no—
93#2280—1031nomaximal, Sylow
94C103#228011yescharacteristic, complemented, Sylow
95C24×C4—1031no—
96C2×#117—1032no—
97#381—1031no—
98#381D10311yescharacteristic, complemented
99#380—1034no—
100#379—1032no—
101C4×C22⋊C4—1034no—
102C25—1031no—
103C23×C4—1031no—
104C23×C4—1038no—
105C23×C4—1032no—
106C23×C4—1032no—
107C23×C4—2068no—
108C23×C4C2×D10311yescharacteristic
109#117—2068no—
110C2×C4⋊C4—1034no—
111C2×C22⋊C4—1032no—
112C2×C22⋊C4—1038no—
113C2×C22⋊C4C2×D10312yes—
114C2×C42—1034no—
115#95—1034no—
116#95C2×D10314yescomplemented
117C24—1032no—
118C24—1034no—
119C24—2068no—
120C24—2064no—
121C24C22×D10311yescharacteristic
122C22×C4—24no—
123C22×C4—1034no—
124C22×C4—1038no—
125C22×C4—1031no—
126C22×C4—1031no—
127C22×C4—1038no—
128C22×C4—1038no—
129C22×C4—1034no—
130C22×C4—2068no—
131C22×C4—2068no—
132C22×C4—20632no—
133C22×C4C4×D10314yes—
134C22×C4C22×D10314yes—
135C22×C4C22×D10312yes—
136C4⋊C4—2068no—
137C22⋊C4—24no—
138C22⋊C4—20616no—
139C22⋊C4—2064no—
140C42—2068no—
141C23—24no—
142C23—1038no—
143C23—1034no—
144C23—20616no—
145C23—20632no—
146C23—2064no—
147C23—2064no—
148C23—2068no—
149C23C2×C4×D10312yes—
150C23D4×D10314yes—
151C23C23×D10311yescharacteristic
152C2×C4—24no—
153C2×C4—28no—
154C2×C4—24no—
155C2×C4—28no—
156C2×C4—1034no—
157C2×C4—1034no—
158C2×C4—10316no—
159C2×C4—1032no—
160C2×C4—1032no—
161C2×C4—20616no—
162C2×C4—20616no—
163C2×C4—2064no—
164C2×C4—2068no—
165C2×C4C2×C4×D10314yes—
166C22—28no—
167C22—24no—
168C22—1038no—
169C22—20632no—
170C22—20616no—
171C22—2064no—
172C22—2064no—
173C22C22⋊C4×D10314yes—
174C22C22×C4×D10311yescharacteristic
175C22C2×D4×D10312yes—
176C22#41×D10314yes—
177C4—24no—
178C4—44no—
179C4—1034no—
180C4—1034no—
181C4—4124no—
182C2—24no—
183C2—2068no—
184C2C2×C22⋊C4×D10311yescharacteristic
185C2#117×D10312yes—
186C2#2026829914yes—
subgroupG/H
center, FrattiniC23C23×D103
commutatorC22×C103C23×C4
Fitting#381×C103C2
socle, cosocleC23×C103C24
prime radicalC24×D103C22
hypercenter#381D103
hypocenterC103#2280
LCSG ▷ C22×C103 ▷ C103
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
2. C2×#15692977C2semidirect
3. #20267654C2semidirect
4. #20267650C2semidirect
6. #20267638C2semidirect
7. #381×C103C2semidirect
11. C22×C4×D103C4semidirect
15. C2×Dic103⋊C4C22semidirect
18. C2×C4×Dic103C22semidirect
19. C103⋊#95C22semidirect
22. #95×C103C22semidirect
65. C2×Dic103C22⋊C4semidirect
82. C2×D103#117semidirect
94. C103#2280semidirect
98. #381D103semidirect
116. #95C2×D103semidirect

Maximal subgroups

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

subgroupindex
C23×C4×D1032
C2×#156929772
#202676542
#202676502
#202676462
#202676382
#381×C1032
#2280103