Finite Group Databasebeta

← #27208277

Subgroups — #27208277

Order 13184.

364 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 113 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#135×D103C212yesmaximal, complemented
2#20268233C212yesmaximal, complemented
3#20268230C212yesmaximal, complemented
4#20268228C212yesmaximal, complemented
5#20268225C212yesmaximal, complemented
6#20268223C211yesmaximal, characteristic, complemented
7#20268221C212yesmaximal, complemented
8C2×#15692960C211yesmaximal, characteristic, complemented
9#508×C103C211yesmaximal, characteristic, complemented
10#41×D103—22no—
11#15693044C2212yes—
12#15693043C2212yescomplemented
13#15693042—22no—
14#15693041—22no—
15#15693040C2212yes—
16Q16×D103C2212yescomplemented
17SD16×D103—22no—
18D8×D103C2212yescomplemented
19C2×C8×D103C2211yescharacteristic
20Dic824C2211yescharacteristic, complemented
21#15692967C2212yescomplemented
22#15692966C2212yescomplemented
23#15692965C2212yescomplemented
24#15692964C2212yescomplemented
25D1648C2211yescharacteristic, complemented
26#15692962C2212yescomplemented
27#15692960C2212yescomplemented
28#15692960C2212yescomplemented
29C2×C103⋊C16C2211yescharacteristic, complemented
30#135×C103C2212yescomplemented
31Q32×C103C2211yescharacteristic, complemented
32SD32×C103C2212yescomplemented
33D16×C103C2211yescharacteristic, complemented
34C2×C16×C103C2211yescharacteristic, complemented
35#13110106—22no—
36#13110105—22no—
37#13110105—42no—
38#13110104—22no—
39#13110104—42no—
40Q8×D103—22no—
41D4×D103—22no—
42D4×D103—42no—
43C2×C4×D103—42no—
44C2×C4×D103D411yescharacteristic
45Dic412C2312yes—
46#13110095—22no—
47#13110094—22no—
48#13110093—22no—
49#13110092—22no—
50D824C2312yes—
51#13110090—22no—
52C2×C103⋊C8D411yescharacteristic
53C8×D103D412yes—
54C8×D103C2312yes—
55C103⋊C16C2312yes—
56#41×C103—22no—
57Q16×C103C2312yes—
58SD16×C103—22no—
59D8×C103C2312yes—
60C2×C8×C103C2311yescharacteristic
61C16×C103C2311yescharacteristic
62C16×C103C2311yescharacteristic
63C22×D103—42no—
64C22×D103D811yescharacteristic
65Q8×C103—22no—
66D4×C103—22no—
67D4×C103—42no—
68C2×C4×C103—42no—
69C2×C4×C103C2×D411yescharacteristic
70C22⋊D103—42no—
71C22⋊D103—42no—
72C22⋊D103—42no—
73C2×Dic103—42no—
74C2×Dic103D811yescharacteristic
75D412—22no—
76D412—42no—
77C4×D103—42no—
78C4×D103—42no—
79C4×D103—42no—
80C4×D103D812yes—
81C4×D103C2×D412yes—
82Dic206—22no—
83Dic206—42no—
84C8×C103C2×D411yescharacteristic
85C8×C103C2411yescharacteristic
86C103⋊C8C2×D412yes—
87C22×C103—42no—
88C22×C103C2×D811yescharacteristic
89C2×D103—41no—
90C2×D103—42no—
91C2×D103—84no—
92C2×D103C2×D812yes—
93C4×C103—42no—
94C4×C103C2×D811yescharacteristic
95C4×C103C22×D411yescharacteristic
96Dic103—42no—
97Dic103C2×D812yes—
98C2×C103—21no—
99C2×C103—82no—
100C2×C103C22×D811yescharacteristic
101D103—22no—
102D103—82no—
103#3414—1031nomaximal, Sylow
104C103#341411yescharacteristic, complemented, Sylow
105C2×#135—1032no—
106#510—1032no—
107#510—1032no—
108#509—1032no—
109#509—1032no—
110#508—1032no—
111#508—1031no—
112#508D10311yescharacteristic, complemented
113C2×M32—1031no—
114C2×#41—2062no—
115#135—1032no—
116#135—1032no—
117#135—1032no—
118#135—2062no—
119#135—2062no—
120#135C2×D10312yescomplemented
121C2×Q16—1032no—
122C2×SD16—2062no—
123C2×D8—1032no—
124C22×C8—1031no—
125Q32—1032no—
126Q32—1031no—
127Q32C2×D10311yescharacteristic, complemented
128SD32—1032no—
129SD32—1032no—
130SD32—1032no—
131SD32C2×D10312yescomplemented
132D16—1032no—
133D16—1031no—
134D16C2×D10311yescharacteristic, complemented
135M32—1032no—
136M32—1032no—
137C2×C16—1031no—
138C2×C16C2×D10311yescharacteristic, complemented
139#41—22no—
140#41—4122no—
141#41—4122no—
142#41—2062no—
143#41—2062no—
144#41—2062no—
145C2×Q8—2062no—
146C2×D4—4122no—
147C2×D4—2062no—
148C22×C4—1031no—
149C22×C4—4122no—
150Q16—1032no—
151Q16—2062no—
152Q16C22×D10312yes—
153SD16—22no—
154SD16—2062no—
155SD16—2062no—
156SD16—2062no—
157D8—1032no—
158D8—2062no—
159D8C22×D10312yes—
160C2×C8—1031no—
161C2×C8—1032no—
162C2×C8—1032no—
163C2×C8C22×D10311yescharacteristic
164C16—1032no—
165C16C22×D10311yescharacteristic
166C16C22×D10311yescharacteristic
167C23—1031no—
168C23—4122no—
169Q8—22no—
170Q8—4122no—
171Q8—2062no—
172D4—22no—
173D4—42no—
174D4—4122no—
175D4—4122no—
176D4—4122no—
177D4—4122no—
178D4—2062no—
179C2×C4—42no—
180C2×C4—1031no—
181C2×C4—1032no—
182C2×C4—1032no—
183C2×C4—4122no—
184C2×C4—4122no—
185C2×C4—4122no—
186C2×C4—4122no—
187C2×C4D4×D10311yescharacteristic
188C8—1032no—
189C8D4×D10311yescharacteristic
190C8C23×D10311yescharacteristic
191C22—42no—
192C22—8244no—
193C22—1032no—
194C22—4121no—
195C22—4122no—
196C22D8×D10311yescharacteristic
197C4—42no—
198C4—1032no—
199C4—4122no—
200C4D8×D10311yescharacteristic
201C4C2×D4×D10311yescharacteristic
202C2—21no—
203C2—82no—
204C2—8242no—
205C2—2062no—
206C2C2×D8×D10311yescharacteristic
subgroupG/H
centerC4D8×D103
commutator, cosocleC8×C103C24
FrattiniC8C23×D103
Fitting#508×C103C2
socleC2×C103C22×D8
hypercenter#508D103
hypocenterC103#3414
LCSG ▷ C8×C103 ▷ C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8 ◁ #508

Complements

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

NH ≅ G/Ntype
1. #135×D103C2semidirect
2. #20268233C2semidirect
3. #20268230C2semidirect
4. #20268228C2semidirect
5. #20268225C2semidirect
6. #20268223C2semidirect
7. #20268221C2semidirect
8. C2×#15692960C2semidirect
9. #508×C103C2semidirect
12. #15693043C22semidirect
16. Q16×D103C22semidirect
18. D8×D103C22semidirect
20. Dic824C22semidirect
21. #15692967C22semidirect
22. #15692966C22semidirect
23. #15692965C22semidirect
24. #15692964C22semidirect
25. D1648C22semidirect
26. #15692962C22semidirect
27. #15692960C22semidirect
28. #15692960C22semidirect
29. C2×C103⋊C16C22semidirect
30. #135×C103C22semidirect
31. Q32×C103C22semidirect
32. SD32×C103C22semidirect
33. D16×C103C22semidirect
34. C2×C16×C103C22semidirect
104. C103#3414semidirect
112. #508D103semidirect
120. #135C2×D103semidirect
127. Q32C2×D103semidirect
131. SD32C2×D103semidirect
134. D16C2×D103semidirect
138. C2×C16C2×D103semidirect

Maximal subgroups

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

subgroupindex
#135×D1032
#202682332
#202682302
#202682282
#202682252
#202682232
#202682212
C2×#156929602
#508×C1032
#3414103