Finite Group Databasebeta

← #27195582

Subgroups — #27195582

Order 13184.

412 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 109 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
1C2×#15692995C211yesmaximal, characteristic
2C2×#15692943C212yesmaximal, complemented
3#20267651C211yesmaximal, characteristic, complemented
4#20267554C212yesmaximal, complemented
5C22×M16×C103C211yesmaximal, characteristic, complemented
6C22×D412C2211yescharacteristic
7C22×C22⋊D103—21no—
8#15692995—22no—
9#15692995C414yescomplemented
10C2×C4⋊Dic103C2212yes—
11C2×C4⋊Dic103C2211yescharacteristic
12C2×C22⋊Dic103—21no—
13C2×(C2×D103)⋊C4—21no—
14#15692943—24no—
15C103⋊#95—21no—
16C23×C4×C103C2211yescharacteristic
17C2×M16×C103—22no—
18C2×M16×C103—24no—
19C22×C8×C103C2212yes—
20C23×D103—21no—
21C2×D412—22no—
22C2×D412—22no—
23C2×D412—21no—
24C2×D412C2×C412yes—
25C2×C22⋊D103—24no—
26C2×C22⋊D103—44no—
27C22×Dic103—21no—
28C22×Dic103—22no—
29C4⋊Dic103—21no—
30C4⋊Dic103—22no—
31C4⋊Dic103—22no—
32C4⋊Dic103C2×C412yes—
33C22⋊Dic103—42no—
34(C2×D103)⋊C4—24no—
35C24×C103D411yescharacteristic
36C22×C4×C103—22no—
37C22×C4×C103—22no—
38C22×C4×C103C2×C412yes—
39C22×C4×C103D411yescharacteristic
40C22×C4×C103D412yes—
41C22×C4×C103C2311yescharacteristic
42M16×C103—28no—
43C2×C8×C103—22no—
44C2×C8×C103—22no—
45C2×C8×C103D414yescomplemented
46C23×C103—22no—
47C23×C103—21no—
48C23×C103—22no—
49C23×C103—21no—
50C23×C103C22⋊C412yes—
51C23×C103C2×D411yescharacteristic
52C22×D103—22no—
53C22×D103—42no—
54C22×D103—42no—
55C22×D103—41no—
56C22×D103—41no—
57C2×C4×C103—22no—
58C2×C4×C103—24no—
59C2×C4×C103—22no—
60C2×C4×C103—22no—
61C2×C4×C103C22⋊C412yes—
62C2×C4×C103C22×C411yescharacteristic
63C2×C4×C103C2×D412yes—
64C2×C4×C103C2×D411yescharacteristic
65C2×C4×C103#4112yes—
66C22⋊D103—48no—
67C2×Dic103—22no—
68C2×Dic103—42no—
69C2×Dic103—42no—
70C2×Dic103—42no—
71C2×Dic103—42no—
72D412—24no—
73D412—41no—
74D412—41no—
75C8×C103—24no—
76C22×C103—22no—
77C22×C103—22no—
78C22×C103—22no—
79C22×C103—42no—
80C22×C103—42no—
81C22×C103C2×C22⋊C411yescharacteristic
82C22×C103#12112yes—
83C22×C103AGL(1,ℤ/8)11yescharacteristic
84C22×C103AGL(1,ℤ/8)12yes—
85C22×C103#13711yescharacteristic
86C2×D103—42no—
87C2×D103—42no—
88C2×D103—42no—
89C2×D103—82no—
90C2×D103—82no—
91C4×C103—22no—
92C4×C103C4×D412yes—
93C4×C103#12011yescharacteristic
94C4×C103#12311yescharacteristic
95Dic103—42no—
96Dic103—82no—
97C2×C103—42no—
98C2×C103#38611yescharacteristic
99C2×C103#41711yescharacteristic
100C2×C103#41811yescharacteristic
101C2×C103#46812yes—
102C2×C103#46912yes—
103D103—82no—
104#1895—1031nomaximal, Sylow
105C103#189511yescharacteristic, complemented, Sylow
106C22×M16D10311yescharacteristic, complemented
107C2×#121—1031no—
108C2×#102—1032no—
109#380—1031no—
110#340—1032no—
111C22×D4—1031no—
112C22×D4—2061no—
113C23×C4C2×D10311yescharacteristic
114C2×M16—22no—
115C2×M16—24no—
116C22×C8C2×D10312yes—
117#121—1034no—
118#121—2062no—
119C2×C4⋊C4—1031no—
120C2×C4⋊C4—1032no—
121C2×C22⋊C4—2061no—
122C2×C22⋊C4—2061no—
123#102—2064no—
124#95—2061no—
125C24—2061no—
126C24D41211yescharacteristic
127C2×D4—1032no—
128C2×D4—4124no—
129C2×D4—2064no—
130C2×D4—2061no—
131C2×D4—2062no—
132C2×D4—2062no—
133C22×C4—22no—
134C22×C4—22no—
135C22×C4—2062no—
136C22×C4—2061no—
137C22×C4C4×D10312yes—
138C22×C4D41211yescharacteristic
139C22×C4C22⋊D10312yes—
140C22×C4C22×D10311yescharacteristic
141M16—28no—
142C2×C8—22no—
143C2×C8—22no—
144C2×C8C22⋊D10314yescomplemented
145C4⋊C4—1032no—
146C4⋊C4—2062no—
147C4⋊C4—2062no—
148C4⋊C4—2061no—
149C22⋊C4—4122no—
150C22⋊C4—2064no—
151C23—22no—
152C23—21no—
153C23—22no—
154C23—21no—
155C23—4122no—
156C23—4122no—
157C23—4121no—
158C23—4121no—
159C23—2062no—
160C23(C2×D103)⋊C412yes—
161C23C2×D41211yescharacteristic
162D4—4128no—
163D4—4121no—
164D4—4121no—
165D4—2064no—
166C2×C4—22no—
167C2×C4—24no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—4122no—
171C2×C4—4122no—
172C2×C4—4122no—
173C2×C4—4122no—
174C2×C4—2062no—
175C2×C4(C2×D103)⋊C412yes—
176C2×C4C2×C4×D10311yescharacteristic
177C2×C4C2×C22⋊D10312yes—
178C2×C4C2×C22⋊D10311yescharacteristic
179C2×C4#1311010512yes—
180C8—24no—
181C22—22no—
182C22—22no—
183C22—22no—
184C22—42no—
185C22—42no—
186C22—8242no—
187C22—8242no—
188C22—4122no—
189C22—4122no—
190C22—4122no—
191C22C2×(C2×D103)⋊C411yescharacteristic
192C22#1569299512yes—
193C22#1569304912yes—
194C22#1569304911yescharacteristic
195C22#1569305411yescharacteristic
196C4—22no—
197C4—8242no—
198C4—4122no—
199C4C4×C22⋊D10312yes—
200C4#1569299011yescharacteristic
201C4#1569300411yescharacteristic
202C2—42no—
203C2—8242no—
204C2#2026767011yescharacteristic
205C2#2026779311yescharacteristic
206C2#2026779711yescharacteristic
207C2#2026803712yes—
208C2#2026804412yes—
subgroupG/H
centerC23C2×D412
commutatorC2×C4×C103C22×C4
FrattiniC22×C4C22×D103
FittingC22×M16×C103C2
socleC23×C103C2×D4
prime radicalC2×#15692995C2
cosocleC22×C4×C103C23
hypercenterC22×M16D103
hypocenterC103#1895
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×M16

Complements

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

NH ≅ G/Ntype
2. C2×#15692943C2semidirect
3. #20267651C2semidirect
4. #20267554C2semidirect
5. C22×M16×C103C2semidirect
9. #15692995C4semidirect
45. C2×C8×C103D4semidirect
105. C103#1895semidirect
106. C22×M16D103semidirect
144. C2×C8C22⋊D103semidirect

Maximal subgroups

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

subgroupindex
C2×#156929952
C2×#156929432
#202676512
#202675542
C22×M16×C1032
#1895103