Finite Group Databasebeta

← #27205986

Subgroups — #27205986

Order 13184.

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

normal subgroups only

This group has 418 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#20268302C212yesmaximal, complemented
2#20268133C212yesmaximal, complemented
3#20268116C212yesmaximal, complemented
4#20268049C211yesmaximal, characteristic, complemented
5#20268044C211yesmaximal, characteristic, complemented
6#20268037C212yesmaximal, complemented
7#20267955C212yesmaximal, complemented
8#20267938C212yesmaximal, complemented
9#407×C103C211yesmaximal, characteristic, complemented
10C2×#13110105C2212yes—
11C2×Dic412C2211yescharacteristic, complemented
12C2×#13110094C2212yescomplemented
13C2×D824C2211yescharacteristic, complemented
14#15693004—22no—
15#15693000C2212yes—
16#15693000C2212yes—
17#15692995C2212yes—
18#15692995C2212yes—
19#15692990—22no—
20C4×C22⋊D103—22no—
21C4×C22⋊D103—22no—
22#15692980C2212yes—
23#15692955C2212yescomplemented
24#15692953C2211yescharacteristic, complemented
25#15692953C2211yescharacteristic, complemented
26#15692946C2212yescomplemented
27#15692946C2212yescomplemented
28#15692943C2212yescomplemented
29#15692943C2212yescomplemented
30C23×C4×C103C2211yescharacteristic
31C2×M16×C103C2211yescharacteristic
32C2×M16×C103C2211yescharacteristic
33C22⋊C8×C103C2212yes—
34C22⋊C8×C103C2212yes—
35#13110105—42no—
36#13110105—42no—
37C2×Dic206C2312yes—
38C2×D412C2312yes—
39C2×C22⋊D103—22no—
40C2×C22⋊D103—22no—
41C2×C22⋊D103—22no—
42C2×C4×D103—22no—
43Dic412—41no—
44#13110094—42no—
45D824—41no—
46C4⋊Dic103C2312yes—
47C4⋊Dic103C2312yes—
48Dic103⋊C4—22no—
49Dic103⋊C4—22no—
50C22⋊Dic103—22no—
51C22⋊Dic103—22no—
52C22⋊Dic103—22no—
53(C2×D103)⋊C4—22no—
54(C2×D103)⋊C4—22no—
55C4×Dic103—22no—
56C24×C103D411yescharacteristic
57C22×C4×C103—41no—
58C22×C4×C103—41no—
59C22×C4×C103D411yescharacteristic
60C22×C4×C103D412yes—
61C22×C4×C103C2312yes—
62C22×C4×C103C2311yescharacteristic
63M16×C103—41no—
64M16×C103—41no—
65C2×C8×C103C2311yescharacteristic
66C2×C8×C103C2312yes—
67C2×C8×C103C2311yescharacteristic
68C23×C103—41no—
69C23×C103—42no—
70C23×C103C2×D412yes—
71C23×C103C2×D411yescharacteristic
72C22×D103—22no—
73C2×C4×C103—21no—
74C2×C4×C103—21no—
75C2×C4×C103—22no—
76C2×C4×C103—22no—
77C2×C4×C103—41no—
78C2×C4×C103—42no—
79C2×C4×C103C2×D412yes—
80C2×C4×C103C2×D411yescharacteristic
81C2×C4×C103C2411yescharacteristic
82C22⋊D103—44no—
83C22⋊D103—44no—
84C22⋊D103—44no—
85C2×Dic103—22no—
86C2×Dic103—22no—
87C2×Dic103—22no—
88D412—22no—
89D412—22no—
90C4×D103—44no—
91Dic206—22no—
92Dic206—22no—
93C8×C103—21no—
94C8×C103—22no—
95C8×C103—21no—
96C22×C103—22no—
97C22×C103—21no—
98C22×C103—22no—
99C22×C103—22no—
100C22×C103—22no—
101C22×C103—44no—
102C22×C103C22×D411yescharacteristic
103C2×D103—42no—
104C2×D103—42no—
105C2×D103—42no—
106C4×C103—22no—
107C4×C103—21no—
108C4×C103H(5,𝔽2)11yescharacteristic
109C4×C103H(5,𝔽2)11yescharacteristic
110Dic103—42no—
111Dic103—42no—
112Dic103—42no—
113C2×C103—42no—
114C2×C103—41no—
115C2×C103#53411yescharacteristic
116C2×C103#57512yes—
117D103—82no—
118#3197—1031nomaximal, Sylow
119C103#319711yescharacteristic, complemented, Sylow
120#525—1032no—
121#485—1032no—
122#482—1032no—
123#470—1031no—
124#469—1031no—
125#468—1032no—
126#452—1032no—
127#449—1032no—
128#407D10311yescharacteristic, complemented
129C2×#41—1032no—
130C23×C4C2×D10311yescharacteristic
131C2×Q16—1031no—
132C2×SD16—1032no—
133C2×D8—1031no—
134C2×M16C2×D10311yescharacteristic
135C2×M16C2×D10311yescharacteristic
136#123—2062no—
137C22⋊Q8—1032no—
138C22⋊Q8—1032no—
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#106—1031no—
148#103—1032no—
149#103—1032no—
150#102—1032no—
151#102—1032no—
152C22⋊C8C2×D10312yes—
153C22⋊C8C2×D10312yes—
154C24D41211yescharacteristic
155#41—4122no—
156#41—4122no—
157C2×Q8—1032no—
158C2×D4—1032no—
159C2×D4—2062no—
160C2×D4—2062no—
161C2×D4—2062no—
162C22×C4—41no—
163C22×C4—41no—
164C22×C4—2062no—
165C22×C4D41211yescharacteristic
166C22×C4D41212yes—
167C22×C4C22×D10312yes—
168C22×C4C22×D10311yescharacteristic
169Q16—4121no—
170SD16—4122no—
171D8—4121no—
172M16—41no—
173M16—41no—
174C2×C8C22×D10311yescharacteristic
175C2×C8C22×D10312yes—
176C2×C8C22×D10311yescharacteristic
177C4⋊C4—1032no—
178C4⋊C4—1032no—
179C4⋊C4—2062no—
180C4⋊C4—2062no—
181C22⋊C4—2062no—
182C22⋊C4—2062no—
183C22⋊C4—2062no—
184C22⋊C4—2062no—
185C22⋊C4—2062no—
186C42—2062no—
187C23—41no—
188C23—42no—
189C23—2062no—
190C23C2×D41211yescharacteristic
191C23C2×D41212yes—
192Q8—2062no—
193Q8—2062no—
194D4—4124no—
195D4—4124no—
196D4—4124no—
197D4—2062no—
198D4—2062no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—41no—
204C2×C4—42no—
205C2×C4—4124no—
206C2×C4—2062no—
207C2×C4—2062no—
208C2×C4—2062no—
209C2×C4C2×D41212yes—
210C2×C4C2×D41211yescharacteristic
211C2×C4C23×D10311yescharacteristic
212C8—21no—
213C8—22no—
214C8—21no—
215C22—22no—
216C22—22no—
217C22—22no—
218C22—22no—
219C22—21no—
220C22—44no—
221C22—4122no—
222C22—4122no—
223C22—4122no—
224C22C22×D41211yescharacteristic
225C4—22no—
226C4—21no—
227C4—4122no—
228C4—4122no—
229C4—4122no—
230C4#1569306611yescharacteristic
231C4#1569306611yescharacteristic
232C2—41no—
233C2—42no—
234C2—8242no—
235C2#2026835311yescharacteristic
236C2#2026859112yes—
subgroupG/H
centerC22C22×D412
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#407×C103C2
socleC22×C103C22×D4
hypercenter#407D103
hypocenterC103#3197
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
1. #20268302C2semidirect
2. #20268133C2semidirect
3. #20268116C2semidirect
4. #20268049C2semidirect
5. #20268044C2semidirect
6. #20268037C2semidirect
7. #20267955C2semidirect
8. #20267938C2semidirect
9. #407×C103C2semidirect
11. C2×Dic412C22semidirect
12. C2×#13110094C22semidirect
13. C2×D824C22semidirect
23. #15692955C22semidirect
24. #15692953C22semidirect
25. #15692953C22semidirect
26. #15692946C22semidirect
27. #15692946C22semidirect
28. #15692943C22semidirect
29. #15692943C22semidirect
119. C103#3197semidirect
128. #407D103semidirect

Maximal subgroups

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

subgroupindex
#202683022
#202681332
#202681162
#202680492
#202680442
#202680372
#202679552
#202679382
#407×C1032
#3197103