Finite Group Databasebeta

← #27205987

Subgroups — #27205987

Order 13184.

418 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 109 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#20268304C212yesmaximal, complemented
2#20268130C212yesmaximal, complemented
3#20268117C212yesmaximal, complemented
4#20268044C211yesmaximal, characteristic, complemented
5#20268039C212yesmaximal, complemented
6#20267952C212yesmaximal, complemented
7#20267939C212yesmaximal, complemented
8#20267754C211yesmaximal, characteristic, complemented
9#470×C103C211yesmaximal, characteristic, complemented
10C2×#13110106C2212yes—
11C22×C4×D103C2211yescharacteristic
12C2×#13110092C2212yescomplemented
13C2×D824C2211yescharacteristic, complemented
14C2×#13110089C2211yescharacteristic
15#15693006—22no—
16#15692997C2212yes—
17#15692996C2212yes—
18#15692995C2212yes—
19#15692991—22no—
20#15692983—22no—
21(C22⋊D103)⋊C4—22no—
22#15692979C2212yes—
23#15692954C2212yescomplemented
24#15692953C2211yescharacteristic, complemented
25#15692945C2212yescomplemented
26#15692943C2212yescomplemented
27#15692941C2212yescomplemented
28(C2×D103)⋊C8C2212yes—
29(C2×D103)⋊C8C2212yes—
30C2×Q16×C103C2211yescharacteristic, complemented
31C2×M16×C103C2211yescharacteristic
32C22⋊Q8×C103C2212yes—
33#106×C103C2211yescharacteristic, complemented
34#103×C103C2212yescomplemented
35C23×D103D411yescharacteristic
36#13110106—42no—
37#13110106—42no—
38C2×D412—22no—
39C2×D412—22no—
40C2×D412C2312yes—
41C2×C22⋊D103—22no—
42C22×Dic103D411yescharacteristic
43C2×C4×D103—22no—
44C2×C4×D103—41no—
45C2×C4×D103—41no—
46C2×C4×D103D412yes—
47C2×C4×D103C2312yes—
48#13110092—42no—
49D824—41no—
50#13110089—41no—
51C2×C103⋊C8C2312yes—
52C4⋊Dic103C2312yes—
53Dic103⋊C4—22no—
54(C2×D103)⋊C4—22no—
55(C2×D103)⋊C4—22no—
56(C2×D103)⋊C4—22no—
57(C2×D103)⋊C4—22no—
58C4×Dic103—22no—
59C2×Q8×C103C2312yes—
60C22×C4×C103C2311yescharacteristic
61Q16×C103—41no—
62M16×C103—41no—
63C2×C8×C103C2311yescharacteristic
64C2×C8×C103C2311yescharacteristic
65C4⋊C4×C103—22no—
66C4⋊C4×C103C2312yes—
67C22⋊C4×C103—22no—
68C23×C103C2×D411yescharacteristic
69C22×D103—22no—
70C22×D103—41no—
71C22×D103—42no—
72C22×D103C2×D412yes—
73Q8×C103—22no—
74Q8×C103—22no—
75C2×C4×C103—21no—
76C2×C4×C103—21no—
77C2×C4×C103—22no—
78C2×C4×C103—22no—
79C2×C4×C103C2×D411yescharacteristic
80C2×C4×C103C2411yescharacteristic
81C22⋊D103—44no—
82C2×Dic103—22no—
83C2×Dic103—41no—
84C2×Dic103C2×D412yes—
85D412—22no—
86D412—22no—
87D412—44no—
88D412—44no—
89C4×D103—22no—
90C4×D103—22no—
91C4×D103—42no—
92C4×D103—44no—
93C8×C103—21no—
94C8×C103—21no—
95C103⋊C8—22no—
96C22×C103—21no—
97C22×C103—22no—
98C22×C103C22×D411yescharacteristic
99C2×D103—22no—
100C2×D103—22no—
101C2×D103—22no—
102C2×D103—44no—
103C2×D103—42no—
104C2×D103—42no—
105C2×D103—42no—
106C4×C103—21no—
107C4×C103—42no—
108C4×C103—42no—
109C4×C103H(5,𝔽2)11yescharacteristic
110C4×C103H(5,𝔽2)11yescharacteristic
111Dic103—22no—
112Dic103—42no—
113C2×C103—41no—
114C2×C103#53411yescharacteristic
115C2×C103#57512yes—
116D103—42no—
117D103—82no—
118#3197—1031nomaximal, Sylow
119C103#319711yescharacteristic, complemented, Sylow
120#525—1032no—
121#485—1032no—
122#482—1032no—
123#470D10311yescharacteristic, complemented
124#469—1031no—
125#468—1032no—
126#452—1032no—
127#449—1032no—
128#407—1031no—
129C2×#41—1032no—
130C23×C4—1031no—
131C2×Q16C2×D10311yescharacteristic, complemented
132C2×SD16—1032no—
133C2×D8—1031no—
134C2×M16—1031no—
135C2×M16C2×D10311yescharacteristic
136#123—2062no—
137C22⋊Q8—1032no—
138C22⋊Q8C2×D10312yes—
139#121—1032no—
140#121—1032no—
141#120—2062no—
142C4×D4—2062no—
143C4×D4—2062no—
144#117—1032no—
145#107—1032no—
146#106—1031no—
147#106C2×D10311yescharacteristic, complemented
148#103—1032no—
149#103C2×D10312yescomplemented
150#102—1032no—
151#102—1032no—
152C22⋊C8—1032no—
153C22⋊C8—1032no—
154C24—1031no—
155#41—4122no—
156#41—4122no—
157C2×Q8C22×D10312yes—
158C2×D4—1032no—
159C2×D4—2062no—
160C2×D4—2062no—
161C2×D4—2062no—
162C22×C4—1031no—
163C22×C4—1032no—
164C22×C4—1032no—
165C22×C4—4121no—
166C22×C4—4121no—
167C22×C4—2062no—
168C22×C4C22×D10311yescharacteristic
169Q16—41no—
170SD16—4122no—
171D8—4121no—
172M16—41no—
173M16—4121no—
174C2×C8—1032no—
175C2×C8C22×D10311yescharacteristic
176C2×C8C22×D10311yescharacteristic
177C4⋊C4—22no—
178C4⋊C4—1032no—
179C4⋊C4—2062no—
180C4⋊C4C22×D10312yes—
181C22⋊C4—22no—
182C22⋊C4—2062no—
183C22⋊C4—2062no—
184C22⋊C4—2062no—
185C22⋊C4—2062no—
186C42—2062no—
187C23—1032no—
188C23—4121no—
189C23—4122no—
190C23—2062no—
191C23D4×D10311yescharacteristic
192Q8—22no—
193Q8—22no—
194D4—4124no—
195D4—4124no—
196D4—4124no—
197D4—2062no—
198D4—2062no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—1032no—
204C2×C4—4122no—
205C2×C4—4124no—
206C2×C4—4121no—
207C2×C4—2062no—
208C2×C4—2062no—
209C2×C4—2062no—
210C2×C4D4×D10311yescharacteristic
211C2×C4C23×D10311yescharacteristic
212C8—21no—
213C8—21no—
214C8—2062no—
215C22—22no—
216C22—21no—
217C22—4124no—
218C22—4122no—
219C22—4122no—
220C22—4122no—
221C22—2062no—
222C22—2062no—
223C22—2062no—
224C22C2×D4×D10311yescharacteristic
225C4—21no—
226C4—42no—
227C4—42no—
228C4—4122no—
229C4—2062no—
230C4#1569306611yescharacteristic
231C4#1569306711yescharacteristic
232C2—41no—
233C2—8242no—
234C2—4122no—
235C2#2026834911yescharacteristic
236C2#2026859012yes—
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#470×C103C2
socleC22×C103C22×D4
hypercenter#470D103
hypocenterC103#3197
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
1. #20268304C2semidirect
2. #20268130C2semidirect
3. #20268117C2semidirect
4. #20268044C2semidirect
5. #20268039C2semidirect
6. #20267952C2semidirect
7. #20267939C2semidirect
8. #20267754C2semidirect
9. #470×C103C2semidirect
12. C2×#13110092C22semidirect
13. C2×D824C22semidirect
23. #15692954C22semidirect
24. #15692953C22semidirect
25. #15692945C22semidirect
26. #15692943C22semidirect
27. #15692941C22semidirect
30. C2×Q16×C103C22semidirect
33. #106×C103C22semidirect
34. #103×C103C22semidirect
119. C103#3197semidirect
123. #470D103semidirect
131. C2×Q16C2×D103semidirect
147. #106C2×D103semidirect
149. #103C2×D103semidirect

Maximal subgroups

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

subgroupindex
#202683042
#202681302
#202681172
#202680442
#202680392
#202679522
#202679392
#202677542
#470×C1032
#3197103