Finite Group Databasebeta

← #27205937

Subgroups — #27205937

Order 13184.

424 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 121 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#20268032C211yesmaximal, characteristic, complemented
5#20268027C211yesmaximal, characteristic, complemented
6#20268020C212yesmaximal, complemented
7#20267955C212yesmaximal, complemented
8#20267938C212yesmaximal, complemented
9C2×C22⋊C8×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#15692955C2211yescharacteristic, complemented
24#15692955C2211yescharacteristic, complemented
25#15692953C2212yescomplemented
26#15692946C2212yescomplemented
27#15692946C2212yescomplemented
28#15692943C2212yescomplemented
29#15692943C2212yescomplemented
30C23×C4×C103C2211yescharacteristic
31C22×C8×C103C2211yescharacteristic
32C22×C8×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
63C2×C8×C103—41no—
64C2×C8×C103—41no—
65C2×C8×C103C2311yescharacteristic
66C2×C8×C103C2312yes—
67C2×C8×C103C2311yescharacteristic
68C23×C103—22no—
69C23×C103—41no—
70C23×C103—41no—
71C23×C103C2×D412yes—
72C23×C103C2×D411yescharacteristic
73C22×D103—22no—
74C2×C4×C103—21no—
75C2×C4×C103—21no—
76C2×C4×C103—22no—
77C2×C4×C103—22no—
78C2×C4×C103—41no—
79C2×C4×C103—42no—
80C2×C4×C103C2×D412yes—
81C2×C4×C103C2×D411yescharacteristic
82C2×C4×C103C2411yescharacteristic
83C22⋊D103—44no—
84C22⋊D103—44no—
85C22⋊D103—44no—
86C2×Dic103—22no—
87C2×Dic103—22no—
88C2×Dic103—22no—
89D412—22no—
90D412—22no—
91C4×D103—44no—
92Dic206—22no—
93Dic206—22no—
94C8×C103—21no—
95C8×C103—22no—
96C8×C103—21no—
97C22×C103—21no—
98C22×C103—21no—
99C22×C103—22no—
100C22×C103—22no—
101C22×C103—22no—
102C22×C103—44no—
103C22×C103#13512yes—
104C22×C103C22×D411yescharacteristic
105C2×D103—42no—
106C2×D103—42no—
107C2×D103—42no—
108C4×C103—22no—
109C4×C103—21no—
110C4×C103H(5,𝔽2)11yescharacteristic
111C4×C103H(5,𝔽2)11yescharacteristic
112Dic103—42no—
113Dic103—42no—
114Dic103—42no—
115C2×C103—22no—
116C2×C103—42no—
117C2×C103#53411yescharacteristic
118C2×C103C2×#13511yescharacteristic
119C2×C103#57511yescharacteristic
120D103—82no—
121#3191—1031nomaximal, Sylow
122C103#319111yescharacteristic, complemented, Sylow
123#525—1032no—
124#485—1032no—
125#482—1032no—
126#467—1031no—
127#466—1031no—
128#465—1032no—
129#452—1032no—
130#449—1032no—
131C2×C22⋊C8D10311yescharacteristic, complemented
132C2×#41—1032no—
133C23×C4C2×D10311yescharacteristic
134C2×Q16—1031no—
135C2×SD16—1032no—
136C2×D8—1031no—
137C22×C8C2×D10311yescharacteristic
138C22×C8C2×D10311yescharacteristic
139#123—2062no—
140C22⋊Q8—1032no—
141C22⋊Q8—1032no—
142#121—1032no—
143#121—1032no—
144#120—2062no—
145C4×D4—2062no—
146C4×D4—2062no—
147#117—1032no—
148#107—1031no—
149#107—1031no—
150#106—1032no—
151#103—1032no—
152#103—1032no—
153#102—1032no—
154#102—1032no—
155C22⋊C8C2×D10312yes—
156C22⋊C8C2×D10312yes—
157C24D41211yescharacteristic
158#41—4122no—
159#41—4122no—
160C2×Q8—1032no—
161C2×D4—1032no—
162C2×D4—2062no—
163C2×D4—2062no—
164C2×D4—2062no—
165C22×C4—41no—
166C22×C4—41no—
167C22×C4—2062no—
168C22×C4D41211yescharacteristic
169C22×C4D41212yes—
170C22×C4C22×D10312yes—
171C22×C4C22×D10311yescharacteristic
172Q16—4121no—
173SD16—4122no—
174D8—4121no—
175C2×C8—41no—
176C2×C8—41no—
177C2×C8C22×D10311yescharacteristic
178C2×C8C22×D10312yes—
179C2×C8C22×D10311yescharacteristic
180C4⋊C4—1032no—
181C4⋊C4—1032no—
182C4⋊C4—2062no—
183C4⋊C4—2062no—
184C22⋊C4—2062no—
185C22⋊C4—2062no—
186C22⋊C4—2062no—
187C22⋊C4—2062no—
188C22⋊C4—2062no—
189C42—2062no—
190C23—22no—
191C23—41no—
192C23—41no—
193C23—2062no—
194C23C2×D41212yes—
195C23C2×D41211yescharacteristic
196Q8—2062no—
197Q8—2062no—
198D4—4124no—
199D4—4124no—
200D4—4124no—
201D4—2062no—
202D4—2062no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—41no—
208C2×C4—42no—
209C2×C4—4124no—
210C2×C4—2062no—
211C2×C4—2062no—
212C2×C4—2062no—
213C2×C4C2×D41212yes—
214C2×C4C2×D41211yescharacteristic
215C2×C4C23×D10311yescharacteristic
216C8—21no—
217C8—22no—
218C8—21no—
219C22—21no—
220C22—21no—
221C22—22no—
222C22—22no—
223C22—22no—
224C22—44no—
225C22—4122no—
226C22—4122no—
227C22—4122no—
228C22#1569304312yes—
229C22C22×D41211yescharacteristic
230C4—22no—
231C4—21no—
232C4—4122no—
233C4—4122no—
234C4—4122no—
235C4#1569306611yescharacteristic
236C4#1569306611yescharacteristic
237C2—22no—
238C2—42no—
239C2—8242no—
240C2#2026835311yescharacteristic
241C2C2×#1569304311yescharacteristic
242C2#2026859111yescharacteristic
subgroupG/H
centerC22C22×D412
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
FittingC2×C22⋊C8×C103C2
socleC22×C103C22×D4
hypercenterC2×C22⋊C8D103
hypocenterC103#3191
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
1. #20268302C2semidirect
2. #20268133C2semidirect
3. #20268116C2semidirect
4. #20268032C2semidirect
5. #20268027C2semidirect
6. #20268020C2semidirect
7. #20267955C2semidirect
8. #20267938C2semidirect
9. C2×C22⋊C8×C103C2semidirect
11. C2×Dic412C22semidirect
12. C2×#13110094C22semidirect
13. C2×D824C22semidirect
23. #15692955C22semidirect
24. #15692955C22semidirect
25. #15692953C22semidirect
26. #15692946C22semidirect
27. #15692946C22semidirect
28. #15692943C22semidirect
29. #15692943C22semidirect
122. C103#3191semidirect
131. C2×C22⋊C8D103semidirect

Maximal subgroups

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

subgroupindex
#202683022
#202681332
#202681162
#202680322
#202680272
#202680202
#202679552
#202679382
C2×C22⋊C8×C1032
#3191103