Finite Group Databasebeta

← #27205397

Subgroups — #27205397

Order 13184.

394 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 121 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#20268403C211yesmaximal, characteristic, complemented
2#20268265C211yesmaximal, characteristic
3#20268133C212yesmaximal, complemented
4#20268092C212yesmaximal, complemented
5#20267997C212yesmaximal, complemented
6#20267944C212yesmaximal
7#20267893C212yesmaximal, complemented
8C4×#13110094C212yesmaximal, complemented
9#433×C103C211yesmaximal, characteristic, complemented
10C22×D412C2211yescharacteristic
11C2×#13110094C2212yes—
12C2×#13110094C2212yes—
13#15693021C2211yescharacteristic, complemented
14#15693014—22no—
15#15693013C2211yescharacteristic, complemented
16#15693011—22no—
17#15693000C2212yes—
18C4×Dic206C2212yescomplemented
19C4×D412C2212yes—
20C4×D412C2212yes—
21#15692983—22no—
22#15692980C2211yescharacteristic
23C22⋊C4×D103—22no—
24#15692955C2212yescomplemented
25#15692953C2212yescomplemented
26#15692946C2212yescomplemented
27#15692946C2212yescomplemented
28#15692943C2212yes—
29#15692943C2212yes—
30#117×C103C2211yescharacteristic
31C4⋊C8×C103C2212yescomplemented
32C22⋊C8×C103C2212yes—
33#97×C103C2211yescharacteristic, complemented
34C4×C8×C103C2211yescharacteristic, complemented
35C23×D103—21no—
36C2×Dic206C2312yes—
37C2×D412—21no—
38C2×D412—24no—
39C2×D412C2312yes—
40C2×C4×D103—22no—
41C2×C4×D103—22no—
42#13110094—24no—
43#13110094—24no—
44C4⋊Dic103—22no—
45C4⋊Dic103C2312yes—
46C4⋊Dic103C2312yes—
47Dic103⋊C4—22no—
48Dic103⋊C4—22no—
49Dic103⋊C4—22no—
50C22⋊Dic103—21no—
51C22⋊Dic103—22no—
52(C2×D103)⋊C4—22no—
53(C2×D103)⋊C4—22no—
54C4×Dic103—21no—
55C4×Dic103—22no—
56C22×C4×C103C2311yescharacteristic
57C2×C8×C103C2312yes—
58C2×C8×C103C2312yes—
59C4⋊C4×C103D412yes—
60C22⋊C4×C103D412yes—
61C42×C103C2311yescharacteristic
62C42×C103C2311yescharacteristic
63C23×C103C2×D411yescharacteristic
64C22×D103—22no—
65C22×D103—24no—
66C22×D103—82no—
67C2×C4×C103—22no—
68C2×C4×C103C2×D412yes—
69C2×C4×C103C2×D412yes—
70C2×C4×C103C2×D411yescharacteristic
71C2×C4×C103C2411yescharacteristic
72C2×Dic103—22no—
73C2×Dic103—22no—
74C2×Dic103—22no—
75D412—24no—
76D412—22no—
77D412#4114yes—
78C4×D103—82no—
79C4×D103—82no—
80Dic206—22no—
81Dic206—22no—
82C8×C103—22no—
83C8×C103—22no—
84C22×C103—21no—
85C22×C103—22no—
86C22×C103C22×D411yescharacteristic
87C2×D103—24no—
88C2×D103—42no—
89C2×D103—42no—
90C2×D103—84no—
91C4×C103—21no—
92C4×C103—22no—
93C4×C103—22no—
94C4×C103C2×#4112yes—
95Dic103—42no—
96Dic103—42no—
97Dic103—42no—
98C2×C103—41no—
99C2×C103#52511yescharacteristic
100C2×C103#57712yes—
101D103—44no—
102#3123—1031nomaximal, Sylow
103C103#312311yescharacteristic, complemented, Sylow
104#541—1031no—
105#518—1031no—
106#485—1032no—
107#478—1032no—
108#461—1032no—
109#450—1032no—
110#440—1032no—
111C4×SD16—1032no—
112#433D10311yescharacteristic, complemented
113C22×D4—1031no—
114C2×SD16—1032no—
115C2×SD16—1032no—
116C4⋊Q8—1031no—
117#126—2062no—
118#125—1031no—
119#125—2062no—
120C22⋊Q8—1032no—
121C4×Q8—1032no—
122C4×D4—1032no—
123C4×D4—1032no—
124C4×D4—2062no—
125#117—1031no—
126#117C2×D10311yescharacteristic
127C2×C22⋊C4—2062no—
128#107—1032no—
129#106—1032no—
130C4⋊C8C2×D10312yescomplemented
131#103—1032no—
132#103—1032no—
133#102—1032no—
134#102—1032no—
135C22⋊C8C2×D10312yes—
136#97C2×D10311yescharacteristic, complemented
137C4×C8C2×D10311yescharacteristic, complemented
138C24—2061no—
139C2×Q8—1032no—
140C2×D4—1032no—
141C2×D4—2064no—
142C2×D4—2061no—
143C22×C4—2062no—
144C22×C4—2062no—
145C22×C4C22×D10311yescharacteristic
146SD16—2064no—
147SD16—2064no—
148C2×C8C22×D10312yes—
149C2×C8C22×D10312yes—
150C4⋊C4—1032no—
151C4⋊C4—1032no—
152C4⋊C4—2062no—
153C4⋊C4—2062no—
154C4⋊C4—2062no—
155C4⋊C4—2062no—
156C4⋊C4D41212yes—
157C22⋊C4—2061no—
158C22⋊C4—2062no—
159C22⋊C4—2062no—
160C22⋊C4—2062no—
161C22⋊C4D41212yes—
162C42—2061no—
163C42—2062no—
164C42C22×D10311yescharacteristic
165C42C22×D10311yescharacteristic
166C23—8242no—
167C23—2064no—
168C23—2062no—
169C23C2×D41211yescharacteristic
170Q8—2062no—
171Q8—2062no—
172D4—1034no—
173D4—2064no—
174D4—2062no—
175C2×C4—22no—
176C2×C4—8242no—
177C2×C4—8242no—
178C2×C4—2062no—
179C2×C4—2062no—
180C2×C4—2062no—
181C2×C4C2×D41212yes—
182C2×C4C2×D41211yescharacteristic
183C2×C4C2×D41212yes—
184C2×C4C23×D10311yescharacteristic
185C8—22no—
186C8—22no—
187C22—21no—
188C22—22no—
189C22—8244no—
190C22—4122no—
191C22—4122no—
192C22—2064no—
193C22C22×D41211yescharacteristic
194C4—21no—
195C4—22no—
196C4—22no—
197C4—4122no—
198C4—4122no—
199C4—4122no—
200C4#41×D10312yes—
201C2—41no—
202C2—4124no—
203C2#2026830311yescharacteristic
204C2#2026860312yes—
subgroupG/H
centerC22C22×D412
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#433×C103C2
socleC22×C103C22×D4
prime radicalC22×D412C22
hypercenter#433D103
hypocenterC103#3123
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #20268403C2semidirect
3. #20268133C2semidirect
4. #20268092C2semidirect
5. #20267997C2semidirect
7. #20267893C2semidirect
8. C4×#13110094C2semidirect
9. #433×C103C2semidirect
13. #15693021C22semidirect
15. #15693013C22semidirect
18. C4×Dic206C22semidirect
24. #15692955C22semidirect
25. #15692953C22semidirect
26. #15692946C22semidirect
27. #15692946C22semidirect
31. C4⋊C8×C103C22semidirect
33. #97×C103C22semidirect
34. C4×C8×C103C22semidirect
103. C103#3123semidirect
112. #433D103semidirect
130. C4⋊C8C2×D103semidirect
136. #97C2×D103semidirect
137. C4×C8C2×D103semidirect

Maximal subgroups

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

subgroupindex
#202684032
#202682652
#202681332
#202680922
#202679972
#202679442
#202678932
C4×#131100942
#433×C1032
#3123103