Finite Group Databasebeta

← #11929245

Subgroups — #11929245

Order 1248.

332 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 108 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×#64625C211yesmaximal, characteristic, complemented
2C2×C13×#67C211yesmaximal, characteristic, complemented
3C2×C3×C22⋊D13C211yesmaximal, characteristic, complemented
4#10597756C212yesmaximal, complemented
5D3×C22⋊D13C212yesmaximal, complemented
6#67×D13C212yesmaximal, complemented
7#10597748C212yesmaximal, complemented
8#10597746C212yesmaximal, complemented
9#10597745C212yesmaximal, complemented
10#88251—31nomaximal, Hall
11C23×C3×C13C2211yescharacteristic, complemented
12C22×D39C2211yescharacteristic, complemented
13C22×D3×C13C2211yescharacteristic, complemented
14C22×C3×D13C2211yescharacteristic, complemented
15C2×D3×D13C2212yescomplemented
16#64625C2212yescomplemented
17#64625C2212yescomplemented
18C2×Dic39C2211yescharacteristic, complemented
19C13×#67C2212yescomplemented
20C13×#67C2212yescomplemented
21C2×Dic3×C13C2211yescharacteristic, complemented
22C3×C22⋊D13C2212yescomplemented
23C3×C22⋊D13C2212yescomplemented
24C2×C3×Dic13C2211yescharacteristic, complemented
25#64605C2212yescomplemented
26#64604C2212yescomplemented
27#64603C2212yescomplemented
28#64602C2212yescomplemented
29#64601C2212yescomplemented
30D3×Dic13C2212yescomplemented
31Dic3×D13C2212yescomplemented
32C2×D4×C13—31no—
33C2×C22⋊D13—31no—
34C2×C22⋊D13—32no—
35C2×C22⋊D13D311yescharacteristic, complemented
36#6129—32no—
37#6129—32no—
38D4×D13—32no—
39D4×D13—32no—
40#6127—32no—
41C22×C3×C13—41no—
42C22×C3×C13C2311yescharacteristic
43C22×C3×C13C2311yescharacteristic
44C22×C3×C13C2311yescharacteristic
45C2×D39—41no—
46C2×D39C2312yes—
47C2×D3×C13—41no—
48C2×D3×C13C2312yes—
49C2×C3×D13—41no—
50C2×C3×D13C2312yes—
51D3×D13—42no—
52Dic39C2312yes—
53C3×Dic13C2312yes—
54Dic3×C13C2312yes—
55C23×C13—31no—
56C23×C13C2×D311yescharacteristic, complemented
57C22×D13—31no—
58C22×D13—32no—
59C22×D13C2×D311yescharacteristic, complemented
60D4×C13—32no—
61D4×C13—32no—
62C2×C4×C13—31no—
63C22⋊D13—32no—
64C22⋊D13—32no—
65C22⋊D13—32no—
66C22⋊D13—32no—
67C22⋊D13C2×D312yescomplemented
68C22⋊D13C2×D312yescomplemented
69C2×Dic13—31no—
70C2×Dic13—32no—
71C2×Dic13C2×D311yescharacteristic, complemented
72D52—32no—
73C4×D13—32no—
74C4×D13—32no—
75Dic26—32no—
76#1004—131nomaximal, Hall
77C2×C3×C13—21no—
78C2×C3×C13—21no—
79C2×C3×C13—21no—
80C2×C3×C13C2411yescharacteristic
81D39—22no—
82C3×D13—22no—
83D3×C13—22no—
84C22×C13—32no—
85C22×C13—41no—
86C22×C13—121no—
87C22×C13C22×D311yescharacteristic
88C22×C13C22×D311yescharacteristic
89C22×C13C22×D311yescharacteristic
90C2×D13—32no—
91C2×D13—41no—
92C2×D13—122no—
93C2×D13—121no—
94C2×D13C22×D312yes—
95C4×C13—32no—
96Dic13—32no—
97Dic13C22×D312yes—
98C2×C3×D4—131no—
99C2×#67—131no—
100C2×#67—132no—
101C2×#67D1311yescharacteristic, complemented
102#237—132no—
103#237—132no—
104D3×D4—132no—
105D3×D4—132no—
106#235—132no—
107C3×C13H(5,𝔽2)11yescharacteristic, complemented, Hall
108H(5,𝔽2)—391noSylow
109C2×C13—21no—
110C2×C13—21no—
111C2×C13—21no—
112C2×C13—62no—
113C2×C13C23×D311yescharacteristic
114D13—22no—
115D13—62no—
116C23×C3—131no—
117C23×C3C2×D1311yescharacteristic, complemented
118C22×D3—131no—
119C22×D3—132no—
120C22×D3C2×D1311yescharacteristic, complemented
121C3×D4—132no—
122C3×D4—132no—
123C2×C3×C4—131no—
124#67—132no—
125#67—132no—
126#67—132no—
127#67—132no—
128#67C2×D1312yescomplemented
129#67C2×D1312yescomplemented
130C2×Dic3—131no—
131C2×Dic3—132no—
132C2×Dic3C2×D1311yescharacteristic, complemented
133D12—132no—
134C4×D3—132no—
135C4×D3—132no—
136Dic6—132no—
137#41—392no—
138#41—392no—
139#41—392no—
140C2×D4—31no—
141C2×D4—131no—
142C2×D4—392no—
143C2×D4—392no—
144C2×D4—392no—
145C2×D4—391no—
146C13#100411yescharacteristic, complemented, Sylow
147C22×C3—41no—
148C22×C3—132no—
149C22×C3—521no—
150C22×C3C22×D1311yescharacteristic
151C22×C3C22×D1311yescharacteristic
152C22×C3C22×D1311yescharacteristic
153C2×D3—41no—
154C2×D3—132no—
155C2×D3—522no—
156C2×D3—521no—
157C2×D3C22×D1312yes—
158C3×C4—132no—
159Dic3—132no—
160Dic3C22×D1312yes—
161C23—31no—
162C23—131no—
163C23—392no—
164C23—391no—
165C23D3×D1311yescharacteristic, complemented
166Q8—392no—
167D4—32no—
168D4—32no—
169D4—132no—
170D4—132no—
171D4—392no—
172D4—392no—
173D4—392no—
174D4—392no—
175D4—392no—
176C2×C4—31no—
177C2×C4—131no—
178C2×C4—392no—
179C2×C4—392no—
180C2×C4—392no—
181C2×C4—391no—
182C2×C3—21no—
183C2×C3—21no—
184C2×C3—21no—
185C2×C3—262no—
186C2×C3C23×D1311yescharacteristic
187D3—22no—
188D3—262no—
189C22—32no—
190C22—41no—
191C22—121no—
192C22—132no—
193C22—392no—
194C22—521no—
195C22—1561no—
196C22—1562no—
197C22C2×D3×D1311yescharacteristic
198C22C2×D3×D1311yescharacteristic
199C22C2×D3×D1311yescharacteristic
200C4—32no—
201C4—132no—
202C4—392no—
203C3#8825111yescharacteristic, complemented, Sylow
204C2—21no—
205C2—21no—
206C2—21no—
207C2—62no—
208C2—262no—
209C2—782no—
210C2C22×D3×D1311yescharacteristic
subgroupG/H
center, FrattiniC2C22×D3×D13
commutator, socle, cosocleC2×C3×C13C24
FittingC23×C3×C13C22
hypercenterC23D3×D13
hypocenterC3×C13H(5,𝔽2)
LCSG ▷ C2×C3×C13 ▷ C3×C13
UCSC1 ◁ C2 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C2×#64625C2semidirect
2. C2×C13×#67C2semidirect
3. C2×C3×C22⋊D13C2semidirect
4. #10597756C2semidirect
5. D3×C22⋊D13C2semidirect
6. #67×D13C2semidirect
7. #10597748C2semidirect
8. #10597746C2semidirect
9. #10597745C2semidirect
11. C23×C3×C13C22semidirect
12. C22×D39C22semidirect
13. C22×D3×C13C22semidirect
14. C22×C3×D13C22semidirect
15. C2×D3×D13C22semidirect
16. #64625C22semidirect
17. #64625C22semidirect
18. C2×Dic39C22semidirect
19. C13×#67C22semidirect
20. C13×#67C22semidirect
21. C2×Dic3×C13C22semidirect
22. C3×C22⋊D13C22semidirect
23. C3×C22⋊D13C22semidirect
24. C2×C3×Dic13C22semidirect
25. #64605C22semidirect
26. #64604C22semidirect
27. #64603C22semidirect
28. #64602C22semidirect
29. #64601C22semidirect
30. D3×Dic13C22semidirect
31. Dic3×D13C22semidirect
35. C2×C22⋊D13D3semidirect
56. C23×C13C2×D3semidirect
59. C22×D13C2×D3semidirect
67. C22⋊D13C2×D3semidirect
68. C22⋊D13C2×D3semidirect
71. C2×Dic13C2×D3semidirect
101. C2×#67D13semidirect
107. C3×C13H(5,𝔽2)semidirect
117. C23×C3C2×D13semidirect
120. C22×D3C2×D13semidirect
128. #67C2×D13semidirect
129. #67C2×D13semidirect
132. C2×Dic3C2×D13semidirect
146. C13#1004semidirect
165. C23D3×D13semidirect
203. C3#88251semidirect

Maximal subgroups

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

subgroupindex
C2×#646252
C2×C13×#672
C2×C3×C22⋊D132
#105977562
D3×C22⋊D132
#67×D132
#105977482
#105977462
#105977452
#882513
#100413