Finite Group Databasebeta

← #497×D103 #27205580

Subgroups — #497×D103 #27205580

Order 13184.

564 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 145 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
1C2×Q16×D103C212yesmaximal, complemented
2C2×SD16×D103C212yesmaximal
3C4⋊Q8×D103C211yesmaximal, characteristic, complemented
4#124×D103C211yesmaximal, characteristic
5#20268186C211yesmaximal, characteristic, complemented
6#20268185C211yesmaximal, characteristic, complemented
7#20268184C212yesmaximal, complemented
8#20268183C211yesmaximal, characteristic, complemented
9#20268182C212yesmaximal, complemented
10#97×D103C211yesmaximal, characteristic, complemented
11#497×C103C211yesmaximal, characteristic, complemented
12C2×Q8×D103C2211yescharacteristic
13C2×Q8×D103C2212yes—
14C2×D4×D103C2211yescharacteristic
15C2×Dic412C2212yescomplemented
16C2×#13110095C2212yescomplemented
17C2×#13110095C2212yescomplemented
18Q16×D103—28no—
19C2×#13110094C2212yes—
20C2×#13110093C2212yes—
21C2×#13110092C2212yes—
22SD16×D103—28no—
23C2×C8×D103C2212yes—
24#15693021C2211yescharacteristic, complemented
25#15693020—22no—
26#15693019C2212yescomplemented
27#15693010C2211yescharacteristic
28#15693009C2211yescharacteristic
29#15693008C2211yescharacteristic
30#15693007—22no—
31C4⋊C4×D103—22no—
32C22⋊C4×D103—22no—
33C42×D103C2211yescharacteristic
34#15692932C2211yescharacteristic, complemented
35#15692931C2212yescomplemented
36C2×Q16×C103C2212yescomplemented
37C2×SD16×C103C2212yes—
38C4⋊Q8×C103C2211yescharacteristic, complemented
39#124×C103C2211yescharacteristic
40#97×C103C2211yescharacteristic, complemented
41C23×D103—21no—
42C2×Dic206—21no—
43C2×Dic206—22no—
44C2×Dic206C2311yescharacteristic
45C2×Dic206C2312yes—
46Q8×D103—24no—
47Q8×D103—24no—
48Q8×D103—24no—
49C2×D412C2311yescharacteristic
50C2×C22⋊D103—21no—
51D4×D103—24no—
52C2×C4×D103—21no—
53C2×C4×D103—22no—
54C2×C4×D103D412yes—
55C2×C4×D103C2311yescharacteristic
56Dic412—24no—
57#13110095—24no—
58#13110095—24no—
59#13110094—24no—
60#13110093—24no—
61#13110092—24no—
62C2×C103⋊C8C2312yes—
63C8×D103D418yes—
64C4⋊Dic103—22no—
65Dic103⋊C4—24no—
66C22⋊Dic103—22no—
67(C2×D103)⋊C4—22no—
68(C2×D103)⋊C4—22no—
69C4×Dic103D412yes—
70C4×Dic103C2311yescharacteristic
71C2×Q8×C103C2311yescharacteristic
72C2×Q8×C103C2312yes—
73C2×D4×C103C2311yescharacteristic
74Q16×C103—24no—
75SD16×C103—24no—
76C2×C8×C103C2312yes—
77C4⋊C4×C103—22no—
78C22⋊C4×C103—22no—
79C42×C103C2311yescharacteristic
80C23×C103—21no—
81C22×D103—21no—
82C22×D103—42no—
83C22×D103—44no—
84C22×D103C2×D411yescharacteristic
85Q8×C103—22no—
86Q8×C103—22no—
87Q8×C103—22no—
88D4×C103—22no—
89C2×C4×C103—21no—
90C2×C4×C103—22no—
91C2×C4×C103C2×D412yes—
92C2×C4×C103C2411yescharacteristic
93C22⋊D103—42no—
94C2×Dic103—21no—
95C2×Dic103—22no—
96C2×Dic103C2×D412yes—
97C2×Dic103C2×D411yescharacteristic
98D412—22no—
99C4×D103—24no—
100C4×D103—42no—
101C4×D103—44no—
102C4×D103C2×D414yes—
103Dic206—22no—
104Dic206—22no—
105Dic206—22no—
106Dic206—44no—
107Dic206—42no—
108C8×C103C2×D414yes—
109C103⋊C8C2×D414yes—
110C22×C103—41no—
111C22×C103—42no—
112C22×C103C22×D411yescharacteristic
113C2×D103—41no—
114C2×D103—42no—
115C2×D103—84no—
116C2×D103#12712yes—
117C2×D103#13714yes—
118C4×C103—22no—
119C4×C103—41no—
120C4×C103—42no—
121C4×C103C22×D412yes—
122Dic103—22no—
123Dic103—42no—
124Dic103—41no—
125Dic103#12712yes—
126C2×C103—81no—
127C2×C103C2×#12711yescharacteristic
128C2×C103C2×#13712yes—
129D103—81no—
130D103#49714yesdirect product factor
131C2×#497—1031nomaximal, Sylow
132C103C2×#49711yescharacteristic, complemented, Sylow
133C22×Q16—1032no—
134C22×SD16—1032no—
135C2×C4⋊Q8—1031no—
136C2×#124—1031no—
137#497—1032no—
138#497—1032no—
139#497—1031no—
140#497—1031no—
141#497—1031no—
142#497D10311yescharacteristic, direct product factor
143C2×#97—1031no—
144C22×Q8—1031no—
145C22×Q8—1032no—
146C22×D4—1031no—
147C2×Q16—1032no—
148C2×Q16—1032no—
149C2×Q16—1032no—
150C2×Q16—2068no—
151C2×Q16C2×D10312yescomplemented
152C2×SD16—1032no—
153C2×SD16—1032no—
154C2×SD16—1032no—
155C2×SD16—2068no—
156C2×SD16C2×D10312yes—
157C22×C8—1032no—
158C4⋊Q8—1032no—
159C4⋊Q8—1031no—
160C4⋊Q8—2062no—
161C4⋊Q8C2×D10311yescharacteristic, complemented
162#124—1031no—
163#124—1031no—
164#124—1031no—
165#124—2062no—
166#124C2×D10311yescharacteristic
167C2×C4⋊C4—2062no—
168C2×C22⋊C4—2062no—
169C2×C42—1031no—
170#97—1032no—
171#97—1031no—
172#97C2×D10311yescharacteristic, complemented
173C24—2061no—
174C2×Q8—1031no—
175C2×Q8—1032no—
176C2×Q8—2061no—
177C2×Q8—2062no—
178C2×Q8—2064no—
179C2×Q8—2064no—
180C2×Q8—2064no—
181C2×Q8C22×D10311yescharacteristic
182C2×Q8C22×D10312yes—
183C2×D4—1031no—
184C2×D4—2064no—
185C2×D4—2061no—
186C2×D4C22×D10311yescharacteristic
187C22×C4—1031no—
188C22×C4—1032no—
189C22×C4—2061no—
190C22×C4—2062no—
191Q16—24no—
192Q16—2064no—
193Q16—2064no—
194Q16—2064no—
195SD16—24no—
196SD16—2064no—
197SD16—2064no—
198SD16—2064no—
199C2×C8—1032no—
200C2×C8—1038no—
201C2×C8C22×D10312yes—
202C4⋊C4—22no—
203C4⋊C4—2064no—
204C4⋊C4—2062no—
205C22⋊C4—22no—
206C22⋊C4—2062no—
207C22⋊C4—2062no—
208C22⋊C4—2062no—
209C42—1032no—
210C42—1031no—
211C42C22×D10311yescharacteristic
212C23—21no—
213C23—1031no—
214C23—4122no—
215C23—4124no—
216C23—2061no—
217Q8—22no—
218Q8—22no—
219Q8—22no—
220Q8—4122no—
221Q8—4124no—
222Q8—2062no—
223Q8—2062no—
224Q8—2062no—
225D4—22no—
226D4—4122no—
227D4—2062no—
228C2×C4—21no—
229C2×C4—22no—
230C2×C4—1031no—
231C2×C4—1034no—
232C2×C4—1032no—
233C2×C4—4122no—
234C2×C4—4124no—
235C2×C4—2064no—
236C2×C4—2061no—
237C2×C4—2062no—
238C2×C4D4×D10312yes—
239C2×C4C23×D10311yescharacteristic
240C8—1034no—
241C8D4×D10314yes—
242C22—42no—
243C22—41no—
244C22—8244no—
245C22—1034no—
246C22—1032no—
247C22—4122no—
248C22—4121no—
249C22C2×D4×D10311yescharacteristic
250C4—22no—
251C4—41no—
252C4—42no—
253C4—1032no—
254C4—4121no—
255C4—4122no—
256C4—2062no—
257C4C2×D4×D10312yes—
258C2—81no—
259C2—8241no—
260C2—1034no—
261C2#127×D10311yescharacteristic
262C2#137×D10312yes—
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#497×C103C2
socleC22×C103C22×D4
prime radicalC2×D4×D103C22
hypercenter#497D103
hypocenterC103C2×#497
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

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

NH ≅ G/Ntype
1. C2×Q16×D103C2semidirect
3. C4⋊Q8×D103C2semidirect
5. #20268186C2semidirect
6. #20268185C2semidirect
7. #20268184C2semidirect
8. #20268183C2semidirect
9. #20268182C2semidirect
10. #97×D103C2semidirect
11. #497×C103C2semidirect
15. C2×Dic412C22semidirect
16. C2×#13110095C22semidirect
17. C2×#13110095C22semidirect
24. #15693021C22semidirect
26. #15693019C22semidirect
34. #15692932C22semidirect
35. #15692931C22semidirect
36. C2×Q16×C103C22semidirect
38. C4⋊Q8×C103C22semidirect
40. #97×C103C22semidirect
130. D103#497direct (N × H)
132. C103C2×#497semidirect
142. #497D103direct (N × H)
151. C2×Q16C2×D103semidirect
161. C4⋊Q8C2×D103semidirect
172. #97C2×D103semidirect

Maximal subgroups

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

subgroupindex
C2×Q16×D1032
C2×SD16×D1032
C4⋊Q8×D1032
#124×D1032
#202681862
#202681852
#202681842
#202681832
#202681822
#97×D1032
#497×C1032
C2×#497103