Finite Group Databasebeta

← #27195587

Subgroups — #27195587

Order 13184.

442 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 101 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
1#20268302C211yesmaximal, characteristic
2C2×#15692949C212yesmaximal, complemented
3#20267755C211yesmaximal, characteristic, complemented
4#20267551C212yesmaximal, complemented
5C22×C42×C103C211yesmaximal, characteristic, complemented
6C2×#13110105C2211yescharacteristic
7C2×#13110089C2212yes—
8#15693004—21no—
9#15693000C412yescomplemented
10#15692995C412yescomplemented
11#15692990—21no—
12C4×C22⋊D103—22no—
13#15692980C2211yescharacteristic
14#15692949—24no—
15C22⋊(C103⋊C8)—22no—
16C23×C4×C103—21no—
17C23×C4×C103C2211yescharacteristic
18C2×C42×C103—21no—
19C2×C42×C103—24no—
20C2×C42×C103C2212yes—
21#13110105—22no—
22#13110105—22no—
23C2×Dic206C2×C411yescharacteristic, complemented
24C2×D412C2×C411yescharacteristic, complemented
25C2×C22⋊D103—22no—
26C2×C22⋊D103—21no—
27C2×C4×D103—21no—
28#13110089—22no—
29#13110089—22no—
30C2×C103⋊C8—22no—
31C4⋊Dic103C2×C412yescomplemented
32Dic103⋊C4—22no—
33C22⋊Dic103—22no—
34C22⋊Dic103—21no—
35(C2×D103)⋊C4—22no—
36C4×Dic103—21no—
37C24×C103D411yescharacteristic
38C22×C4×C103—24no—
39C22×C4×C103—28no—
40C22×C4×C103—22no—
41C22×C4×C103—22no—
42C22×C4×C103—22no—
43C22×C4×C103C2×C412yes—
44C22×C4×C103D412yes—
45C22×C4×C103D411yescharacteristic
46C22×C4×C103C2311yescharacteristic
47C42×C103—24no—
48C42×C103—22no—
49C42×C103D414yescomplemented
50C23×C103—24no—
51C23×C103—21no—
52C23×C103—21no—
53C23×C103C22⋊C412yes—
54C23×C103C2×D411yescharacteristic
55C22×D103—21no—
56C2×C4×C103—216no—
57C2×C4×C103—28no—
58C2×C4×C103—21no—
59C2×C4×C103—24no—
60C2×C4×C103—21no—
61C2×C4×C103—24no—
62C2×C4×C103—24no—
63C2×C4×C103C22⋊C412yes—
64C2×C4×C103C22×C411yescharacteristic
65C2×C4×C103C2×D412yes—
66C2×C4×C103C2×D411yescharacteristic
67C2×C4×C103#4112yes—
68C22⋊D103—44no—
69C22⋊D103—41no—
70C22⋊D103—41no—
71C2×Dic103—22no—
72C2×Dic103—21no—
73D412—22no—
74C4×D103—42no—
75Dic206—22no—
76C103⋊C8—42no—
77C22×C103—24no—
78C22×C103—24no—
79C22×C103—22no—
80C22×C103—22no—
81C22×C103—22no—
82C22×C103#10414yescomplemented
83C22×C103C2×C22⋊C411yescharacteristic
84C22×C103#12011yescharacteristic
85C22×C103#12311yescharacteristic
86C2×D103—41no—
87C2×D103—42no—
88C4×C103—28no—
89C4×C103—22no—
90C4×C103C4×D412yes—
91C4×C103#12112yes—
92Dic103—41no—
93Dic103—42no—
94C2×C103—21no—
95C2×C103—24no—
96C2×C103—21no—
97C2×C103#38611yescharacteristic
98C2×C103C2×#10412yes—
99D103—81no—
100#1896—1031nomaximal, Sylow
101C103#189611yescharacteristic, complemented, Sylow
102#525—1031no—
103C22×C42D10311yescharacteristic, complemented
104C2×#104—1032no—
105#407—1031no—
106#339—1032no—
107C2×#41—1031no—
108C23×C4—21no—
109C23×C4C2×D10311yescharacteristic
110C2×M16—1032no—
111#123—2061no—
112C22⋊Q8—1032no—
113#121—1032no—
114#120—2061no—
115C4×D4—2062no—
116#117—1031no—
117C2×C42—21no—
118C2×C42—24no—
119C2×C42C2×D10312yes—
120#104—2064no—
121C22⋊C8—2062no—
122C24C22⋊D10311yescharacteristic
123#41—2062no—
124#41—2062no—
125C2×Q8—1031no—
126C2×D4—1031no—
127C2×D4—2062no—
128C2×D4—2061no—
129C22×C4—24no—
130C22×C4—28no—
131C22×C4—22no—
132C22×C4—22no—
133C22×C4—22no—
134C22×C4—2061no—
135C22×C4C4×D10312yes—
136C22×C4D41212yes—
137C22×C4C22⋊D10311yescharacteristic
138C22×C4C22×D10311yescharacteristic
139M16—2062no—
140M16—2062no—
141C2×C8—2062no—
142C4⋊C4—1032no—
143C4⋊C4—2062no—
144C22⋊C4—2062no—
145C22⋊C4—2061no—
146C22⋊C4—2062no—
147C42—24no—
148C42—22no—
149C42—2061no—
150C42C22⋊D10314yescomplemented
151C23—24no—
152C23—21no—
153C23—21no—
154C23—2061no—
155C23(C2×D103)⋊C412yes—
156C23C2×C22⋊D10311yescharacteristic
157Q8—2062no—
158D4—4124no—
159D4—4121no—
160D4—4121no—
161D4—2062no—
162C2×C4—216no—
163C2×C4—28no—
164C2×C4—21no—
165C2×C4—24no—
166C2×C4—21no—
167C2×C4—24no—
168C2×C4—24no—
169C2×C4—4122no—
170C2×C4—2062no—
171C2×C4—2061no—
172C2×C4(C2×D103)⋊C412yes—
173C2×C4C2×C4×D10311yescharacteristic
174C2×C4C2×C22⋊D10312yes—
175C2×C4C2×D41211yescharacteristic
176C2×C4#1311010512yes—
177C8—4122no—
178C22—24no—
179C22—24no—
180C22—22no—
181C22—22no—
182C22—22no—
183C22—4122no—
184C22—4121no—
185C22#1569294914yescomplemented
186C22C2×(C2×D103)⋊C411yescharacteristic
187C22#1569299011yescharacteristic
188C22#1569300411yescharacteristic
189C4—28no—
190C4—22no—
191C4—4122no—
192C4—4121no—
193C4C4×C22⋊D10312yes—
194C4#1569299512yes—
195C2—21no—
196C2—24no—
197C2—21no—
198C2—8241no—
199C2#2026767011yescharacteristic
200C2C2×#1569294912yes—
subgroupG/H
centerC2×C4C2×D412
commutatorC2×C4×C103C22×C4
FrattiniC22×C4C22×D103
FittingC22×C42×C103C2
socleC22×C103C2×C22⋊C4
prime radical#20268302C2
cosocleC22×C4×C103C23
hypercenterC22×C42D103
hypocenterC103#1896
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
2. C2×#15692949C2semidirect
3. #20267755C2semidirect
4. #20267551C2semidirect
5. C22×C42×C103C2semidirect
9. #15693000C4semidirect
10. #15692995C4semidirect
23. C2×Dic206C2×C4semidirect
24. C2×D412C2×C4semidirect
31. C4⋊Dic103C2×C4semidirect
49. C42×C103D4semidirect
82. C22×C103#104semidirect
101. C103#1896semidirect
103. C22×C42D103semidirect
150. C42C22⋊D103semidirect
185. C22#15692949semidirect

Maximal subgroups

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

subgroupindex
#202683022
C2×#156929492
#202677552
#202675512
C22×C42×C1032
#1896103