Finite Group Databasebeta

← #27205541

Subgroups — #27205541

Order 13184.

392 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 117 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#20268340C211yesmaximal, characteristic
2#125×D103C211yesmaximal, characteristic, complemented
3#20268158C212yesmaximal, complemented
4#20268154C212yesmaximal, complemented
5#20268148C211yesmaximal, characteristic, complemented
6#20268146C211yesmaximal, characteristic, complemented
7#20268145C211yesmaximal, characteristic, complemented
8#20267791C212yesmaximal, complemented
9#20267789C212yesmaximal, complemented
10C4×#13110088C211yesmaximal, characteristic, complemented
11#488×C103C211yesmaximal, characteristic, complemented
12C2×#13110106C2211yescharacteristic
13C2×#13110104C2211yescharacteristic
14C2×#13110088C2212yes—
15#15693019C2211yescharacteristic
16#15693017C2211yescharacteristic
17#15693013C2211yescharacteristic
18#15693012C2212yes—
19#15693011—22no—
20#15693009C2211yescharacteristic
21#15692994—22no—
22(C22⋊D103)⋊C4—22no—
23C4⋊C4×D103—22no—
24C4⋊C4×D103C2212yes—
25C42×D103C2211yescharacteristic
26#15692946C2212yes—
27#15692945C2212yes—
28#15692944C2212yes—
29#15692943C2212yes—
30#15692942C2212yes—
31#15692941C2212yes—
32#15692931C2212yes—
33C4×C103⋊C8C2211yescharacteristic
34#125×C103C2211yescharacteristic
35#124×C103C2211yescharacteristic
36#103×C103C2212yes—
37#102×C103C2212yes—
38C4×C8×C103C2211yescharacteristic
39#13110106—24no—
40#13110104—24no—
41C2×Dic206C2311yescharacteristic
42C2×D412—21no—
43C2×D412C2311yescharacteristic
44C2×C22⋊D103—21no—
45C2×C22⋊D103—22no—
46C22×Dic103—21no—
47C2×C4×D103—22no—
48C2×C4×D103—21no—
49C2×C4×D103D412yes—
50C2×C4×D103C2311yescharacteristic
51#13110088—24no—
52C2×C103⋊C8C2312yes—
53C4⋊Dic103—22no—
54C4⋊Dic103C2312yes—
55Dic103⋊C4—22no—
56Dic103⋊C4—22no—
57Dic103⋊C4—22no—
58Dic103⋊C4—22no—
59(C2×D103)⋊C4—22no—
60C4×Dic103D412yes—
61C4×Dic103C2311yescharacteristic
62C2×Q8×C103C2311yescharacteristic
63C2×D4×C103C2311yescharacteristic
64C2×C8×C103C2312yes—
65C4⋊C4×C103—22no—
66C4⋊C4×C103C2312yes—
67C22⋊C4×C103—22no—
68C42×C103C2311yescharacteristic
69C23×C103—21no—
70C22×D103—21no—
71C22×D103C2×D411yescharacteristic
72Q8×C103—22no—
73D4×C103—22no—
74C2×C4×C103—21no—
75C2×C4×C103—22no—
76C2×C4×C103C2×D412yes—
77C2×C4×C103C2411yescharacteristic
78C22⋊D103—44no—
79C22⋊D103—42no—
80C2×Dic103—21no—
81C2×Dic103—22no—
82C2×Dic103—42no—
83C2×Dic103C2×D412yes—
84C2×Dic103C2×D411yescharacteristic
85D412—22no—
86D412—42no—
87C4×D103—42no—
88C4×D103—44no—
89C4×D103—42no—
90C4×D103#4114yes—
91Dic206—22no—
92C8×C103—22no—
93C103⋊C8—22no—
94C22×C103—41no—
95C22×C103—42no—
96C22×C103C22×D411yescharacteristic
97C2×D103—22no—
98C2×D103—41no—
99C2×D103—42no—
100C2×D103#12412yes—
101C4×C103—22no—
102C4×C103—41no—
103C4×C103—42no—
104C4×C103C2×#4112yes—
105Dic103—22no—
106Dic103—41no—
107Dic103—42no—
108Dic103#12412yes—
109C2×C103—81no—
110C2×C103C2×#12411yescharacteristic
111C2×C103#57512yes—
112D103—22no—
113D103—81no—
114#3142—1031nomaximal, Sylow
115C103#314211yescharacteristic, complemented, Sylow
116#532—1031no—
117C2×#125—1031no—
118#491—1032no—
119#490—1032no—
120#488—1031no—
121#488—1031no—
122#488—1031no—
123#488D10311yescharacteristic, complemented
124#417—1032no—
125#417—1032no—
126C4×M16—1031no—
127C2×#41—1031no—
128C2×#41—1031no—
129C2×M16—1032no—
130C4⋊Q8—1031no—
131#127—1031no—
132#125—1032no—
133#125—1031no—
134#125—2062no—
135#125C2×D10311yescharacteristic
136#124—1031no—
137#124C2×D10311yescharacteristic
138#121—2062no—
139C4×D4—2062no—
140C2×C4⋊C4—1032no—
141C2×C4⋊C4—2062no—
142C2×C42—1031no—
143#103—1032no—
144#103—1032no—
145#103—1032no—
146#103C2×D10312yes—
147#102—1032no—
148#102—1032no—
149#102—1032no—
150#102C2×D10312yes—
151#97—1032no—
152C4×C8—1031no—
153C4×C8C2×D10311yescharacteristic
154#41—2064no—
155#41—2064no—
156C2×Q8—1031no—
157C2×Q8C22×D10311yescharacteristic
158C2×D4—1031no—
159C2×D4—2061no—
160C2×D4—2062no—
161C2×D4—2061no—
162C2×D4C22×D10311yescharacteristic
163C22×C4—1031no—
164C22×C4—1032no—
165C22×C4—2061no—
166C22×C4—2062no—
167C22×C4—2061no—
168M16—2064no—
169C2×C8—1032no—
170C2×C8C22×D10312yes—
171C4⋊C4—22no—
172C4⋊C4—1032no—
173C4⋊C4—2062no—
174C4⋊C4—2062no—
175C4⋊C4—2062no—
176C4⋊C4—2062no—
177C4⋊C4—2062no—
178C4⋊C4C22×D10312yes—
179C22⋊C4—22no—
180C22⋊C4—2062no—
181C42—1032no—
182C42—1031no—
183C42C22×D10311yescharacteristic
184C23—21no—
185C23—1031no—
186C23—2061no—
187Q8—22no—
188Q8—2062no—
189D4—22no—
190D4—4122no—
191D4—4122no—
192D4—4124no—
193D4—2062no—
194C2×C4—21no—
195C2×C4—22no—
196C2×C4—1031no—
197C2×C4—1034no—
198C2×C4—1032no—
199C2×C4—4122no—
200C2×C4—4122no—
201C2×C4—4124no—
202C2×C4—4122no—
203C2×C4—2061no—
204C2×C4—2062no—
205C2×C4D4×D10312yes—
206C2×C4C23×D10311yescharacteristic
207C8—22no—
208C8—2062no—
209C22—41no—
210C22—42no—
211C22—1032no—
212C22—4121no—
213C22—4122no—
214C22—2062no—
215C22C2×D4×D10311yescharacteristic
216C4—22no—
217C4—41no—
218C4—42no—
219C4—1032no—
220C4—4121no—
221C4—4122no—
222C4—2062no—
223C4#41×D10312yes—
224C2—81no—
225C2—8241no—
226C2—2062no—
227C2#124×D10311yescharacteristic
228C2#2026858812yes—
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#488×C103C2
socleC22×C103C22×D4
prime radical#20268340C2
hypercenter#488D103
hypocenterC103#3142
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
2. #125×D103C2semidirect
3. #20268158C2semidirect
4. #20268154C2semidirect
5. #20268148C2semidirect
6. #20268146C2semidirect
7. #20268145C2semidirect
8. #20267791C2semidirect
9. #20267789C2semidirect
10. C4×#13110088C2semidirect
11. #488×C103C2semidirect
115. C103#3142semidirect
123. #488D103semidirect

Maximal subgroups

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

subgroupindex
#202683402
#125×D1032
#202681582
#202681542
#202681482
#202681462
#202681452
#202677912
#202677892
C4×#131100882
#488×C1032
#3142103