Finite Group Databasebeta

← #27204508

Subgroups — #27204508

Order 13184.

698 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 698 conjugacy classes of subgroups — too many to draw. Only its 161 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#20268589C212yesmaximal, complemented
2#20268365C211yesmaximal, characteristic, complemented
3#20267974C214yesmaximal, complemented
4#20267964C214yesmaximal, complemented
5#20267808C212yesmaximal, complemented
6C2×#15692940C211yesmaximal, characteristic, complemented
7C2×2−1+4×C103C211yesmaximal, characteristic, complemented
8C2×#13110105C2211yescharacteristic
9#15693052—22no—
10#15693051C2214yescomplemented
11#15693047—22no—
12#15693046C2214yescomplemented
13#15693041—24no—
14C2×#13110089C2212yes—
15#15693019C2212yescomplemented
16#15693010C2212yescomplemented
17#15693004—22no—
18#15692997—22no—
19#15692980C2211yescharacteristic
20#15692948C2218yescomplemented
21#15692940C2214yescomplemented
222−1+4×C103—24no—
232−1+4×C103—22no—
242−1+4×C103C2214yes—
25C2×#41×C103—22no—
26C2×#41×C103—22no—
27C2×#41×C103C2212yes—
28C22×Q8×C103—22no—
29C22×Q8×C103C2211yescharacteristic
30#13110105—22no—
31#13110105—22no—
32C2×Dic206C2311yescharacteristic
33C2×D412C2311yescharacteristic
34C2×C22⋊D103—21no—
35C2×C4×D103—21no—
36#13110095—24no—
37#13110093—24no—
38#13110092—24no—
39#13110090—24no—
40#13110089—22no—
41#13110089C2314yes—
42C2×C103⋊C8—22no—
43C4⋊Dic103—21no—
44Dic103⋊C4—24no—
45C22⋊Dic103—21no—
46(C2×D103)⋊C4—24no—
47C4×Dic103C2312yes—
48#41×C103—28no—
49#41×C103—28no—
50#41×C103—28no—
51#41×C103—28no—
52#41×C103—22no—
53#41×C103—22no—
54#41×C103D414yes—
55#41×C103C2314yes—
56C2×Q8×C103—22no—
57C2×Q8×C103—28no—
58C2×Q8×C103—28no—
59C2×Q8×C103—22no—
60C2×Q8×C103—22no—
61C2×Q8×C103D412yes—
62C2×Q8×C103D412yes—
63C2×Q8×C103C2312yes—
64C2×D4×C103—22no—
65C2×D4×C103—22no—
66C2×D4×C103D412yes—
67C22×C4×C103—24no—
68C22×C4×C103—22no—
69C22×C4×C103D412yes—
70C22×C4×C103C2311yescharacteristic
71C23×C103—22no—
72C23×C103C2×D411yescharacteristic
73C22×D103—21no—
74Q8×C103—28no—
75Q8×C103—22no—
76Q8×C103—24no—
77Q8×C103—24no—
78Q8×C103C2×D414yes—
79D4×C103—28no—
80D4×C103—24no—
81D4×C103—24no—
82D4×C103—22no—
83D4×C103C2×D414yes—
84C2×C4×C103—216no—
85C2×C4×C103—22no—
86C2×C4×C103—22no—
87C2×C4×C103—22no—
88C2×C4×C103—24no—
89C2×C4×C103—24no—
90C2×C4×C103C2×D414yes—
91C2×C4×C103C2×D411yescharacteristic
92C2×C4×C103C2×D412yes—
93C2×C4×C103C2×D412yes—
94C2×C4×C103C2411yescharacteristic
95C22⋊D103—41no—
96C22⋊D103—41no—
97C2×Dic103—22no—
98C2×Dic103—21no—
99D412—22no—
100C4×D103—42no—
101Dic206—22no—
102C103⋊C8—24no—
103C22×C103—24no—
104C22×C103—41no—
105C22×C103—44no—
106C22×C103#12011yescharacteristic
107C22×C103#12011yescharacteristic
108C22×C103C22×D411yescharacteristic
109C2×D103—42no—
110C2×D103—41no—
111C4×C103—24no—
112C4×C103—24no—
113C4×C103#12012yes—
114C4×C103C22×D412yes—
115Dic103—42no—
116Dic103—41no—
117C2×C103—21no—
118C2×C103—21no—
119C2×C103—21no—
120C2×C103—44no—
121C2×C103C2×#12011yescharacteristic
122D103—81no—
123#3020—1031nomaximal, Sylow
124C103#302011yescharacteristic, complemented, Sylow
125C2×2−1+4D10311yescharacteristic, complemented
126#575—1032no—
127#536—1031no—
128#456—1034no—
129#454—1034no—
130#421—1032no—
131C2×#101—1031no—
1322−1+4—24no—
1332−1+4—22no—
1342−1+4C2×D10314yes—
135C2×#41—22no—
136C2×#41—22no—
137C2×#41—1031no—
138C2×#41C2×D10312yes—
139C22×Q8—22no—
140C22×Q8C2×D10311yescharacteristic
141#137—1034no—
142#137—2062no—
143AGL(1,ℤ/8)—1034no—
144AGL(1,ℤ/8)—2062no—
145#135—2064no—
146C2×M16—1032no—
147C4⋊Q8—1032no—
148#124—1032no—
149#123—2062no—
150C22⋊Q8—2062no—
151#117—1031no—
152#104—1038no—
153#101—1034no—
154#41—28no—
155#41—28no—
156#41—28no—
157#41—28no—
158#41—22no—
159#41—22no—
160#41—2062no—
161#41—2062no—
162#41C22⋊D10314yes—
163#41C22×D10314yes—
164C2×Q8—22no—
165C2×Q8—28no—
166C2×Q8—28no—
167C2×Q8—22no—
168C2×Q8—22no—
169C2×Q8—1031no—
170C2×Q8C22⋊D10312yes—
171C2×Q8C22⋊D10312yes—
172C2×Q8C22×D10312yes—
173C2×D4—22no—
174C2×D4—22no—
175C2×D4—1031no—
176C2×D4—2061no—
177C2×D4C22⋊D10312yes—
178C22×C4—24no—
179C22×C4—22no—
180C22×C4—2061no—
181C22×C4C22⋊D10312yes—
182C22×C4C22×D10311yescharacteristic
183Q16—2064no—
184SD16—2064no—
185SD16—2064no—
186D8—2064no—
187M16—1034no—
188M16—2062no—
189C2×C8—2062no—
190C4⋊C4—2064no—
191C4⋊C4—2061no—
192C22⋊C4—2061no—
193C22⋊C4—2064no—
194C42—1032no—
195C23—22no—
196C23—2061no—
197C23C2×C22⋊D10311yescharacteristic
198Q8—28no—
199Q8—24no—
200Q8—22no—
201Q8—24no—
202Q8—2062no—
203Q8C2×C22⋊D10314yes—
204D4—28no—
205D4—24no—
206D4—24no—
207D4—22no—
208D4—4121no—
209D4—4121no—
210D4—2062no—
211D4C2×C22⋊D10314yes—
212C2×C4—216no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—24no—
217C2×C4—24no—
218C2×C4—4122no—
219C2×C4—2062no—
220C2×C4—2061no—
221C2×C4C2×C22⋊D10314yes—
222C2×C4C2×C22⋊D10312yes—
223C2×C4C2×C22⋊D10312yes—
224C2×C4C2×C22⋊D10311yescharacteristic
225C2×C4C23×D10311yescharacteristic
226C8—2064no—
227C22—24no—
228C22—41no—
229C22—44no—
230C22—4122no—
231C22—4121no—
232C22#1569299011yescharacteristic
233C22#1569299011yescharacteristic
234C22C22×C22⋊D10311yescharacteristic
235C4—24no—
236C4—24no—
237C4—4122no—
238C4—4121no—
239C4#1569299012yes—
240C4C22×C22⋊D10312yes—
241C2—21no—
242C2—21no—
243C2—21no—
244C2—44no—
245C2—8241no—
246C2C2×#1569299011yescharacteristic
subgroupG/H
centerC2C2×#15692990
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
FittingC2×2−1+4×C103C2
socleC2×C103C2×#120
hypercenterC2×2−1+4D103
hypocenterC103#3020
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×2−1+4

Complements

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

NH ≅ G/Ntype
1. #20268589C2semidirect
2. #20268365C2semidirect
3. #20267974C2semidirect
4. #20267964C2semidirect
5. #20267808C2semidirect
6. C2×#15692940C2semidirect
7. C2×2−1+4×C103C2semidirect
10. #15693051C22semidirect
12. #15693046C22semidirect
15. #15693019C22semidirect
16. #15693010C22semidirect
20. #15692948C22semidirect
21. #15692940C22semidirect
124. C103#3020semidirect
125. C2×2−1+4D103semidirect

Maximal subgroups

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

subgroupindex
#202685892
#202683652
#202679742
#202679642
#202678082
C2×#156929402
C2×2−1+4×C1032
#3020103