Finite Group Databasebeta

← #27204749

Subgroups — #27204749

Order 13184.

500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 141 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
1C22×#13110088C211yesmaximal, characteristic, complemented
2#20268298C212yesmaximal, complemented
3#20268046C212yesmaximal, complemented
4#20268041C212yesmaximal, complemented
5#20268034C214yesmaximal, complemented
6#20267829C211yesmaximal, characteristic, complemented
7#20267787C212yesmaximal, complemented
8C2×#135×C103C211yesmaximal, characteristic, complemented
9C22×C4×D103C2211yescharacteristic
10C2×#13110088—24no—
11C2×#13110088C2212yes—
12C2×#13110088C2212yes—
13C22×C103⋊C8C2211yescharacteristic
14#15693002—22no—
15#15692997C2214yes—
16#15692992C2214yes—
17#15692989—22no—
18C4×C22⋊D103—24no—
19#15692980C2212yes—
20#15692955C2212yescomplemented
21#15692953C2212yescomplemented
22#15692945C2214yescomplemented
23#15692942C2214yescomplemented
24C2×#41×C103C2212yes—
25#135×C103—24no—
26C2×Q16×C103C2211yescharacteristic, complemented
27C2×SD16×C103C2212yescomplemented
28C2×D8×C103C2211yescharacteristic, complemented
29C22×C8×C103C2211yescharacteristic
30C23×D103D411yescharacteristic
31C2×C22⋊D103—24no—
32C22×Dic103D411yescharacteristic
33C2×C4×D103—22no—
34C2×C4×D103—22no—
35C2×C4×D103D412yes—
36C2×C4×D103C2312yes—
37#13110088—24no—
38#13110088—24no—
39C2×C103⋊C8—22no—
40C2×C103⋊C8C2312yes—
41C4⋊Dic103C2314yes—
42Dic103⋊C4—24no—
43C22⋊Dic103—22no—
44C22⋊Dic103—24no—
45(C2×D103)⋊C4—24no—
46C4×Dic103—22no—
47#41×C103—24no—
48#41×C103—24no—
49C2×Q8×C103C2312yes—
50C2×D4×C103—22no—
51C2×D4×C103C2312yes—
52C22×C4×C103—22no—
53C22×C4×C103C2311yescharacteristic
54Q16×C103—22no—
55SD16×C103—24no—
56D8×C103—22no—
57C2×C8×C103D414yescomplemented
58C2×C8×C103C2311yescharacteristic
59C2×C8×C103C2311yescharacteristic
60C23×C103—22no—
61C23×C103C2×D411yescharacteristic
62C22×D103—22no—
63C22×D103—42no—
64C22×D103C2×D412yes—
65Q8×C103—22no—
66Q8×C103—22no—
67D4×C103—22no—
68D4×C103—22no—
69D4×C103—44no—
70C2×C4×C103—22no—
71C2×C4×C103—44no—
72C2×C4×C103C2×D411yescharacteristic
73C2×C4×C103C2×D412yes—
74C2×C4×C103#4112yes—
75C2×C4×C103C2411yescharacteristic
76C22⋊D103—48no—
77C2×Dic103—22no—
78C2×Dic103—24no—
79C2×Dic103C2×D412yes—
80C4×D103—24no—
81C4×D103—22no—
82C4×D103—22no—
83C8×C103C2×D412yes—
84C8×C103C2×D412yes—
85C103⋊C8—22no—
86C22×C103—22no—
87C22×C103—42no—
88C22×C103—44no—
89C22×C103#12112yes—
90C22×C103C22×D411yescharacteristic
91C2×D103—22no—
92C2×D103—24no—
93C2×D103—44no—
94C4×C103—42no—
95C4×C103#12112yes—
96C4×C103C22×D411yescharacteristic
97C4×C103C2×#4111yescharacteristic
98Dic103—22no—
99Dic103—44no—
100C2×C103—22no—
101C2×C103—82no—
102C2×C103C2×#12111yescharacteristic
103C2×C103#57512yes—
104D103—42no—
105#3054—1031nomaximal, Sylow
106C103#305411yescharacteristic, complemented, Sylow
107C2×#135D10311yescharacteristic, complemented
108C22×M16—1031no—
109#525—1032no—
110#470—1032no—
111#469—1032no—
112#468—1034no—
113#427—1031no—
114#416—1032no—
115C2×#41C2×D10312yes—
116C23×C4—1031no—
117#135—24no—
118C2×Q16C2×D10311yescharacteristic, complemented
119C2×SD16C2×D10312yescomplemented
120C2×D8C2×D10311yescharacteristic, complemented
121C2×M16—1032no—
122C2×M16—1032no—
123C2×M16—2064no—
124C22×C8—1031no—
125C22×C8C2×D10311yescharacteristic
126#123—2062no—
127C22⋊Q8—1034no—
128#121—1034no—
129#120—2062no—
130C4×D4—2064no—
131#117—1032no—
132#107—1032no—
133#106—1032no—
134#103—1034no—
135#102—1034no—
136C24—1031no—
137#41—24no—
138#41—24no—
139C2×Q8C22×D10312yes—
140C2×D4—22no—
141C2×D4—2064no—
142C2×D4C22×D10312yes—
143C22×C4—22no—
144C22×C4—1031no—
145C22×C4—1032no—
146C22×C4—1032no—
147C22×C4—2062no—
148C22×C4—2062no—
149C22×C4C22×D10311yescharacteristic
150Q16—22no—
151SD16—24no—
152D8—22no—
153M16—2064no—
154M16—2064no—
155C2×C8—1032no—
156C2×C8—2062no—
157C2×C8C22⋊D10314yescomplemented
158C2×C8C22×D10311yescharacteristic
159C2×C8C22×D10311yescharacteristic
160C4⋊C4—1034no—
161C4⋊C4—2064no—
162C22⋊C4—2064no—
163C22⋊C4—2064no—
164C22⋊C4—2062no—
165C42—2062no—
166C23—22no—
167C23—1032no—
168C23—4122no—
169C23—2062no—
170C23D4×D10311yescharacteristic
171Q8—22no—
172Q8—22no—
173D4—22no—
174D4—22no—
175D4—44no—
176D4—4128no—
177C2×C4—22no—
178C2×C4—44no—
179C2×C4—1032no—
180C2×C4—2064no—
181C2×C4—2062no—
182C2×C4—2062no—
183C2×C4—2062no—
184C2×C4—2064no—
185C2×C4D4×D10311yescharacteristic
186C2×C4C2×C22⋊D10312yes—
187C2×C4#1311010412yes—
188C2×C4C23×D10311yescharacteristic
189C8—2062no—
190C8C2×C22⋊D10312yes—
191C8C2×C22⋊D10312yes—
192C22—22no—
193C22—44no—
194C22—42no—
195C22—4124no—
196C22—2064no—
197C22—2062no—
198C22#1569299212yes—
199C22C2×D4×D10311yescharacteristic
200C4—42no—
201C4—4124no—
202C4—2062no—
203C4#1569299212yes—
204C4C22×C22⋊D10311yescharacteristic
205C4C2×#1311010411yescharacteristic
206C2—22no—
207C2—82no—
208C2—4122no—
209C2C2×#1569299211yescharacteristic
210C2#2026858812yes—
subgroupG/H
centerC2×C4D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
FittingC2×#135×C103C2
socleC22×C103C22×D4
hypercenterC2×#135D103
hypocenterC103#3054
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C22×#13110088C2semidirect
2. #20268298C2semidirect
3. #20268046C2semidirect
4. #20268041C2semidirect
5. #20268034C2semidirect
6. #20267829C2semidirect
7. #20267787C2semidirect
8. C2×#135×C103C2semidirect
20. #15692955C22semidirect
21. #15692953C22semidirect
22. #15692945C22semidirect
23. #15692942C22semidirect
26. C2×Q16×C103C22semidirect
27. C2×SD16×C103C22semidirect
28. C2×D8×C103C22semidirect
57. C2×C8×C103D4semidirect
106. C103#3054semidirect
107. C2×#135D103semidirect
118. C2×Q16C2×D103semidirect
119. C2×SD16C2×D103semidirect
120. C2×D8C2×D103semidirect
157. C2×C8C22⋊D103semidirect

Maximal subgroups

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

subgroupindex
C22×#131100882
#202682982
#202680462
#202680412
#202680342
#202678292
#202677872
C2×#135×C1032
#3054103