Finite Group Databasebeta

← #27205695

Subgroups — #27205695

Order 13184.

348 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 137 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#20268346C211yesmaximal, characteristic
2#125×D103C211yesmaximal, characteristic
3#20268201C211yesmaximal, characteristic, complemented
4#20268200C211yesmaximal, characteristic, complemented
5#20268197C211yesmaximal, characteristic, complemented
6#20268192C212yesmaximal, complemented
7#20268191C212yesmaximal, complemented
8#20267832C212yesmaximal
9#20267830C212yesmaximal
10#20267743C211yesmaximal, characteristic
11#501×C103C211yesmaximal, characteristic, complemented
12C2×#13110088C2212yes—
13#15693021C2211yescharacteristic
14#15693013C2211yescharacteristic
15#15693012C2211yescharacteristic
16#15693012C2211yescharacteristic
17#15693012C2212yes—
18#15693011—21no—
19#15693011—21no—
20#15693001—21no—
21#15692997—21no—
22Q8×Dic103—21no—
23#15692986—21no—
24#15692979C2212yes—
25C4⋊C4×D103—21no—
26C4⋊C4×D103—21no—
27C4⋊C4×D103C2211yescharacteristic
28C4⋊C4×D103C2211yescharacteristic
29C42×D103C2211yescharacteristic
30#15692955C2212yes—
31#15692954C2212yes—
32#15692954C2212yes—
33#15692953C2212yes—
34#15692952C2212yes—
35#15692952C2212yes—
36#15692932C2211yescharacteristic
37C8×Dic103C2212yes—
38C4⋊Q8×C103C2211yescharacteristic
39#125×C103C2211yescharacteristic
40#107×C103C2212yes—
41#106×C103C2212yes—
42#97×C103C2211yescharacteristic
43C2×Dic206—21no—
44C2×C4×D103—21no—
45C2×C4×D103—21no—
46C2×C4×D103D411yescharacteristic
47C2×C4×D103D411yescharacteristic
48C2×C4×D103C2311yescharacteristic
49#13110088Q818yescomplemented
50C2×C103⋊C8C2312yes—
51C4⋊Dic103—21no—
52C4⋊Dic103—21no—
53C4⋊Dic103—21no—
54C4⋊Dic103—22no—
55C4⋊Dic103C2311yescharacteristic
56C4⋊Dic103C2312yes—
57C4⋊Dic103C2311yescharacteristic
58Dic103⋊C4—21no—
59Dic103⋊C4—21no—
60Dic103⋊C4—21no—
61Dic103⋊C4—21no—
62Dic103⋊C4—21no—
63Dic103⋊C4—21no—
64Dic103⋊C4—22no—
65(C2×D103)⋊C4—22no—
66C4×Dic103—22no—
67C4×Dic103D411yescharacteristic
68C4×Dic103D411yescharacteristic
69C4×Dic103C2311yescharacteristic
70C2×Q8×C103—21no—
71C2×C8×C103C2312yes—
72C4⋊C4×C103—21no—
73C4⋊C4×C103—21no—
74C4⋊C4×C103—21no—
75C4⋊C4×C103C2311yescharacteristic
76C4⋊C4×C103C2312yes—
77C4⋊C4×C103C2311yescharacteristic
78C42×C103C2311yescharacteristic
79C22×D103C2×D411yescharacteristic
80Q8×C103—42no—
81C2×C4×C103—21no—
82C2×C4×C103—21no—
83C2×C4×C103—22no—
84C2×C4×C103C2×D411yescharacteristic
85C2×C4×C103C2×D411yescharacteristic
86C2×C4×C103C2411yescharacteristic
87C2×Dic103—22no—
88C2×Dic103—21no—
89C2×Dic103—21no—
90C2×Dic103C2×D411yescharacteristic
91C2×Dic103C2×D411yescharacteristic
92C2×Dic103C2×D411yescharacteristic
93C4×D103—41no—
94C4×D103—41no—
95C4×D103—42no—
96C4×D103—42no—
97C4×D103C2×Q814yes—
98Dic206—42no—
99C8×C103C2×Q814yes—
100C103⋊C8C2×Q814yes—
101C22×C103C22×D411yescharacteristic
102C2×D103—21no—
103C2×D103—21no—
104C2×D103C4⋊Q812yes—
105C4×C103—21no—
106C4×C103—21no—
107C4×C103—41no—
108C4×C103—41no—
109C4×C103—42no—
110C4×C103C22×Q812yes—
111Dic103—21no—
112Dic103—21no—
113Dic103—42no—
114Dic103—41no—
115Dic103—41no—
116Dic103C4⋊Q812yes—
117C2×C103C2×C4⋊Q811yescharacteristic
118C2×C103#57511yescharacteristic
119C2×C103#57511yescharacteristic
120D103—22no—
121#3166—1031nomaximal, Sylow
122C103#316611yescharacteristic, complemented, Sylow
123#533—1031no—
124C2×#125—1031no—
125#501—1031no—
126#501—1031no—
127#501—1031no—
128#501D10311yescharacteristic, complemented
129#499—1032no—
130#499—1032no—
131#428—1032no—
132#428—1032no—
133C4×M16—1031no—
134C2×M16—1032no—
135C4⋊Q8—1031no—
136C4⋊Q8C2×D10311yescharacteristic
137#125—1031no—
138#125—1031no—
139#125—1032no—
140#125—1031no—
141#125—2061no—
142#125—2061no—
143#125C2×D10311yescharacteristic
144C22⋊Q8—2061no—
145C22⋊Q8—2061no—
146C4×Q8—2061no—
147C4×Q8—2061no—
148#117—1032no—
149C2×C4⋊C4—1031no—
150C2×C4⋊C4—1031no—
151C2×C4⋊C4—2061no—
152C2×C4⋊C4—2061no—
153C2×C42—1031no—
154#107—1032no—
155#107—1032no—
156#107—1032no—
157#107C2×D10312yes—
158#106—1032no—
159#106—1032no—
160#106—1032no—
161#106C2×D10312yes—
162#97—1031no—
163#97C2×D10311yescharacteristic
164C4×C8—1032no—
165C2×Q8—21no—
166C2×Q8—2061no—
167C22×C4—1031no—
168C22×C4—1031no—
169C22×C4—1031no—
170C22×C4—2061no—
171C22×C4—2061no—
172M16—1038no—
173C2×C8—1032no—
174C2×C8C22×D10312yes—
175C4⋊C4—21no—
176C4⋊C4—21no—
177C4⋊C4—21no—
178C4⋊C4—1031no—
179C4⋊C4—1031no—
180C4⋊C4—1032no—
181C4⋊C4—2061no—
182C4⋊C4—2061no—
183C4⋊C4—2061no—
184C4⋊C4—2061no—
185C4⋊C4—2062no—
186C4⋊C4—2061no—
187C4⋊C4—2061no—
188C4⋊C4—2062no—
189C4⋊C4—2061no—
190C4⋊C4—2061no—
191C4⋊C4—2061no—
192C4⋊C4C22×D10311yescharacteristic
193C4⋊C4C22×D10312yes—
194C4⋊C4C22×D10311yescharacteristic
195C22⋊C4—2062no—
196C42—1031no—
197C42—1031no—
198C42—1031no—
199C42—2062no—
200C42C22×D10311yescharacteristic
201C23—1031no—
202Q8—42no—
203Q8—4122no—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—1031no—
208C2×C4—1034no—
209C2×C4—1031no—
210C2×C4—1031no—
211C2×C4—4121no—
212C2×C4—4121no—
213C2×C4—4122no—
214C2×C4—4122no—
215C2×C4—2062no—
216C2×C4—2061no—
217C2×C4—2061no—
218C2×C4D4×D10311yescharacteristic
219C2×C4D4×D10311yescharacteristic
220C2×C4C23×D10311yescharacteristic
221C8—1034no—
222C8Q8×D10314yes—
223C22—1032no—
224C22—2061no—
225C22—2061no—
226C22C2×D4×D10311yescharacteristic
227C4—21no—
228C4—21no—
229C4—41no—
230C4—42no—
231C4—41no—
232C4—1032no—
233C4—4121no—
234C4—4121no—
235C4—4122no—
236C4—2061no—
237C4—2061no—
238C4C2×Q8×D10312yes—
239C2—2062no—
240C2C4⋊Q8×D10311yescharacteristic
241C2#2026858711yescharacteristic
242C2#2026859011yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#501×C103C2
socleC22×C103C22×D4
prime radicalC22×D103C2×D4
hypercenter#501D103
hypocenterC103#3166
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
3. #20268201C2semidirect
4. #20268200C2semidirect
5. #20268197C2semidirect
6. #20268192C2semidirect
7. #20268191C2semidirect
11. #501×C103C2semidirect
49. #13110088Q8semidirect
122. C103#3166semidirect
128. #501D103semidirect

Maximal subgroups

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

subgroupindex
#202683462
#125×D1032
#202682012
#202682002
#202681972
#202681922
#202681912
#202678322
#202678302
#202677432
#501×C1032
#3166103