Finite Group Databasebeta

← #488×D103 #27205457

Subgroups — #488×D103 #27205457

Order 13184.

412 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 125 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#125×D103C211yesmaximal, characteristic, complemented
2#124×D103C211yesmaximal, characteristic
3#20268148C211yesmaximal, characteristic, complemented
4#20268147C212yesmaximal, complemented
5#20268146C211yesmaximal, characteristic, complemented
6#20268145C211yesmaximal, characteristic, complemented
7#20268144C212yesmaximal, complemented
8#103×D103C212yesmaximal, complemented
9#102×D103C212yesmaximal
10C4×C8×D103C211yesmaximal, characteristic, complemented
11#488×C103C211yesmaximal, characteristic, complemented
12C2×Q8×D103C2211yescharacteristic
13C2×D4×D103C2211yescharacteristic
14C2×C8×D103C2212yes—
15#15693013C2211yescharacteristic, complemented
16#15693012C2212yescomplemented
17#15693011—22no—
18#15693010C2211yescharacteristic
19#15693009C2211yescharacteristic
20#15693008C2211yescharacteristic
21#15693007—22no—
22C4⋊C4×D103—22no—
23C4⋊C4×D103C2212yes—
24C22⋊C4×D103—22no—
25C42×D103C2211yescharacteristic
26#15692946C2212yescomplemented
27#15692945C2212yescomplemented
28#15692944C2212yescomplemented
29#15692943C2212yes—
30#15692942C2212yes—
31#15692941C2212yes—
32C4×C103⋊C8C2211yescharacteristic, complemented
33C8×Dic103C2212yescomplemented
34#125×C103C2211yescharacteristic, complemented
35#124×C103C2211yescharacteristic
36#103×C103C2212yescomplemented
37#102×C103C2212yes—
38C4×C8×C103C2211yescharacteristic, complemented
39C23×D103—21no—
40C2×Dic206—21no—
41C2×Dic206C2311yescharacteristic
42Q8×D103—24no—
43C2×D412C2311yescharacteristic
44C2×C22⋊D103—21no—
45D4×D103—24no—
46C2×C4×D103—21no—
47C2×C4×D103—22no—
48C2×C4×D103D412yes—
49C2×C4×D103C2311yescharacteristic
50C2×C103⋊C8C2312yes—
51C8×D103—24no—
52C4⋊Dic103—22no—
53C4⋊Dic103C2312yes—
54Dic103⋊C4—22no—
55Dic103⋊C4—22no—
56Dic103⋊C4—22no—
57C22⋊Dic103—22no—
58(C2×D103)⋊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×D103—42no—
72C22×D103—44no—
73C22×D103C2×D411yescharacteristic
74Q8×C103—22no—
75D4×C103—22no—
76C2×C4×C103—21no—
77C2×C4×C103—22no—
78C2×C4×C103C2×D412yes—
79C2×C4×C103C2411yescharacteristic
80C22⋊D103—42no—
81C2×Dic103—21no—
82C2×Dic103—22no—
83C2×Dic103C2×D412yes—
84C2×Dic103C2×D411yescharacteristic
85D412—22no—
86C4×D103—24no—
87C4×D103—42no—
88C4×D103—44no—
89C4×D103#4114yes—
90Dic206—22no—
91Dic206—42no—
92C8×C103—22no—
93C103⋊C8—22no—
94C22×C103—41no—
95C22×C103—42no—
96C22×C103C22×D411yescharacteristic
97C2×D103—41no—
98C2×D103—42no—
99C2×D103—84no—
100C2×D103#12412yes—
101C2×D103#13514yes—
102C4×C103—22no—
103C4×C103—41no—
104C4×C103—42no—
105C4×C103C2×#4112yes—
106Dic103—22no—
107Dic103—41no—
108Dic103—42no—
109Dic103#12412yes—
110C2×C103—81no—
111C2×C103C2×#12411yescharacteristic
112C2×C103C2×#13512yes—
113D103—81no—
114D103#48814yesdirect product factor
115C2×#488—1031nomaximal, Sylow
116C103C2×#48811yescharacteristic, complemented, Sylow
117C2×#125—1031no—
118C2×#124—1031no—
119#488—1031no—
120#488—1031no—
121#488—1032no—
122#488—1032no—
123#488—1031no—
124#488D10311yescharacteristic, direct product factor
125C2×#103—1032no—
126C2×#102—1032no—
127C2×C4×C8—1031no—
128C22×Q8—1031no—
129C22×D4—1031no—
130C22×C8—1032no—
131#125—1032no—
132#125—1031no—
133#125—2062no—
134#125C2×D10311yescharacteristic, complemented
135#124—1031no—
136#124—1031no—
137#124—1031no—
138#124—2062no—
139#124C2×D10311yescharacteristic
140C2×C4⋊C4—1032no—
141C2×C4⋊C4—2062no—
142C2×C22⋊C4—2062no—
143C2×C42—1031no—
144#103—1032no—
145#103—1032no—
146#103—1032no—
147#103C2×D10312yescomplemented
148#102—1032no—
149#102—1032no—
150#102—1032no—
151#102C2×D10312yes—
152C4×C8—1032no—
153C4×C8—1031no—
154C4×C8C2×D10311yescharacteristic, complemented
155C24—2061no—
156C2×Q8—1031no—
157C2×Q8—2061no—
158C2×Q8—2064no—
159C2×Q8C22×D10311yescharacteristic
160C2×D4—1031no—
161C2×D4—2064no—
162C2×D4—2061no—
163C2×D4C22×D10311yescharacteristic
164C22×C4—1031no—
165C22×C4—1032no—
166C22×C4—2061no—
167C22×C4—2062no—
168C2×C8—1032no—
169C2×C8—2064no—
170C2×C8C22×D10312yes—
171C4⋊C4—22no—
172C4⋊C4—1032no—
173C4⋊C4—2062no—
174C4⋊C4—2062no—
175C4⋊C4—2062no—
176C4⋊C4—2062no—
177C4⋊C4C22×D10312yes—
178C22⋊C4—22no—
179C22⋊C4—2062no—
180C22⋊C4—2062no—
181C22⋊C4—2062no—
182C42—1032no—
183C42—1031no—
184C42C22×D10311yescharacteristic
185C23—21no—
186C23—1031no—
187C23—4122no—
188C23—4124no—
189C23—2061no—
190Q8—22no—
191Q8—4122no—
192Q8—2062no—
193D4—22no—
194D4—4122no—
195D4—2062no—
196C2×C4—21no—
197C2×C4—22no—
198C2×C4—1031no—
199C2×C4—1034no—
200C2×C4—1032no—
201C2×C4—4122no—
202C2×C4—4124no—
203C2×C4—2064no—
204C2×C4—2061no—
205C2×C4—2062no—
206C2×C4D4×D10312yes—
207C2×C4C23×D10311yescharacteristic
208C8—22no—
209C8—2062no—
210C22—41no—
211C22—42no—
212C22—8244no—
213C22—1032no—
214C22—1034no—
215C22—4121no—
216C22—4122no—
217C22C2×D4×D10311yescharacteristic
218C4—22no—
219C4—41no—
220C4—42no—
221C4—1032no—
222C4—4121no—
223C4—4122no—
224C4—2062no—
225C4#41×D10312yes—
226C2—81no—
227C2—8241no—
228C2—1034no—
229C2#124×D10311yescharacteristic
230C2#135×D10312yes—
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#488×C103C2
socleC22×C103C22×D4
prime radicalC2×D4×D103C22
hypercenter#488D103
hypocenterC103C2×#488
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
1. #125×D103C2semidirect
3. #20268148C2semidirect
4. #20268147C2semidirect
5. #20268146C2semidirect
6. #20268145C2semidirect
7. #20268144C2semidirect
8. #103×D103C2semidirect
10. C4×C8×D103C2semidirect
11. #488×C103C2semidirect
15. #15693013C22semidirect
16. #15693012C22semidirect
26. #15692946C22semidirect
27. #15692945C22semidirect
28. #15692944C22semidirect
32. C4×C103⋊C8C22semidirect
33. C8×Dic103C22semidirect
34. #125×C103C22semidirect
36. #103×C103C22semidirect
38. C4×C8×C103C22semidirect
114. D103#488direct (N × H)
116. C103C2×#488semidirect
124. #488D103direct (N × H)
134. #125C2×D103semidirect
147. #103C2×D103semidirect
154. C4×C8C2×D103semidirect

Maximal subgroups

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

subgroupindex
#125×D1032
#124×D1032
#202681482
#202681472
#202681462
#202681452
#202681442
#103×D1032
#102×D1032
C4×C8×D1032
#488×C1032
C2×#488103