Finite Group Databasebeta

← #13129240

Subgroups — #13129240

Order 1664.

1258 conjugacy classes of subgroups; only the 455 normal subgroups are shown.

normal subgroups only

This group has 1258 conjugacy classes of subgroups — too many to draw. Only its 455 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
1C13×H(3,𝔽4)C211yesmaximal, characteristic, complemented
2#11719388C213yesmaximal, complemented
3#11719379C216yesmaximal, complemented
4#11719375C216yesmaximal, complemented
5#11719373C213yesmaximal, complemented
6#11719297C216yesmaximal, complemented
7#11719295C216yesmaximal, complemented
8C22×C22⋊D13C2216yescomplemented
9C2×#6131C2213yescomplemented
10C2×#6129C2213yescomplemented
11C2×D4×D13C2216yescomplemented
12C13×#124C2213yescomplemented
13C13×#124C2216yescomplemented
14C13×#120C2216yescomplemented
15#88207C2212yescomplemented
16#88201C2216yescomplemented
17#88198C2213yescomplemented
18#88194C2213yes—
19#88194C2216yescomplemented
20#88193C22112yescomplemented
21#88191C2216yescomplemented
22#88139C22112yescomplemented
23#88138C22112yescomplemented
24#88138C22112yescomplemented
25#88136C22112yescomplemented
26#88136C2216yescomplemented
27#88135C22112yescomplemented
28#88131C2216yescomplemented
29#88129C2213yescomplemented
30#88128C2212yescomplemented
31#88126C2216yescomplemented
32C42×D13C2211yescharacteristic, complemented
33C24×C13C2312yes—
34C23×D13C2316yes—
35C2×Q8×C13C2313yes—
36C2×D4×C13C2313yes—
37C2×D4×C13C2316yes—
38C2×C22⋊D13—412no—
39C2×C22⋊D13C23112yes—
40C2×C22⋊D13C2316yes—
41C2×C22⋊D13C23112yes—
42C22×Dic13C2316yes—
43#6131—46no—
44#6129—46no—
45D4×D13—412no—
46C2×D52C2316yes—
47C2×D52C2316yes—
48C2×D52C2313yes—
49C2×C4×D13C2313yes—
50C2×C4×D13C2316yes—
51C2×Dic26C2313yes—
52C13×C22⋊C4C2316yes—
53C13×C22⋊C4C23112yes—
54C42×C13C2311yescharacteristic
55C42×C13C2312yes—
56C22⋊Dic13C2316yes—
57#6103C23112yes—
58#6103C23112yes—
59#6101C23112yes—
60C4×Dic13C2313yes—
61C4×Dic13C2316yes—
62#3549—131nomaximal, Sylow
63C23×C13—46no—
64C23×C13C2416yes—
65C22×D13—412no—
66C22×D13—46no—
67C22×D13C2416yes—
68C22×D13C2411yescharacteristic
69Q8×C13—43no—
70D4×C13—46no—
71D4×C13—43no—
72C2×C4×C13C2416yes—
73C2×C4×C13C2413yes—
74C22⋊D13—224no—
75C22⋊D13—46no—
76C22⋊D13—412no—
77C2×Dic13—212no—
78C2×Dic13C2416yes—
79C2×Dic13C2413yes—
80D52—46no—
81D52—43no—
82D52—46no—
83C4×D13—212no—
84C4×D13—26no—
85Dic26—43no—
86H(3,𝔽4)—133no—
87H(3,𝔽4)D1311yescharacteristic, complemented
88#555—136no—
89D42—136no—
90#535—136no—
91#535—136no—
92#532—133no—
93C22×C13—26no—
94C22×C13—212no—
95C22×C13—84no—
96C22×C13C2511yescharacteristic
97C2×D13—23no—
98C2×D13—26no—
99C2×D13—212no—
100C2×D13—812no—
101C4×C13—23no—
102C4×C13—26no—
103Dic13—26no—
104Dic13H(5,𝔽2)16yes—
105C2×#41—133no—
106C2×#41—133no—
107C22×D4—136no—
108C22×D4—136no—
109C4⋊Q8—133no—
110#127—133no—
111#127—136no—
112#127—132no—
113#124—136no—
114#124—1312no—
115#124—133no—
116#124C2×D1313yescomplemented
117#124C2×D1316yescomplemented
118#121—1312no—
119#121—1312no—
120#121—1312no—
121#120—132no—
122#120—136no—
123#120—136no—
124#120—1312no—
125#120C2×D1316yescomplemented
126C4×D4—1312no—
127#117—136no—
128#117—136no—
129C2×C42—131no—
130C2×C13—46no—
131C2×C13C2×H(5,𝔽2)13yes—
132D13—41no—
133D13—46no—
134C24—136no—
135C24C22×D1312yes—
136#41—526no—
137#41—526no—
138C2×Q8—133no—
139C2×Q8C22×D1313yes—
140C2×D4—1312no—
141C2×D4—1312no—
142C2×D4—136no—
143C2×D4—133no—
144C2×D4—136no—
145C2×D4—136no—
146C2×D4—5212no—
147C2×D4—5212no—
148C2×D4C22×D1313yes—
149C2×D4C22×D1316yes—
150C22×C4—136no—
151C22×C4—133no—
152C22×C4—136no—
153C4⋊C4—1312no—
154C22⋊C4—136no—
155C22⋊C4—1312no—
156C22⋊C4—1312no—
157C22⋊C4C22×D1316yes—
158C22⋊C4C22×D13112yes—
159C42—133no—
160C42—136no—
161C42C22×D1311yescharacteristic
162C42C22×D1312yes—
163C13#354911yescharacteristic, complemented, Sylow
164C23—46no—
165C23—136no—
166C23—131no—
167C23—526no—
168C23—5212no—
169C23C23×D1316yes—
170Q8—43no—
171Q8—523no—
172D4—46no—
173D4—43no—
174D4—2624no—
175D4—526no—
176D4—526no—
177D4—523no—
178D4—5212no—
179D4—526no—
180C2×C4—133no—
181C2×C4—136no—
182C2×C4—2612no—
183C2×C4—266no—
184C2×C4—2612no—
185C2×C4C23×D1313yes—
186C2×C4C23×D1316yes—
187C22—26no—
188C22—212no—
189C22—84no—
190C22—263no—
191C22—266no—
192C22—2612no—
193C22—10412no—
194C22C24×D1311yescharacteristic
195C4—26no—
196C4—23no—
197C4—136no—
198C4—266no—
199C2—46no—
200C2—526no—
201C2—521no—
202C2D13×H(5,𝔽2)13yes—
subgroupG/H
center, FrattiniC22C24×D13
commutator, socle, cosocleC22×C13C25
FittingC13×H(3,𝔽4)C2
hypercenterH(3,𝔽4)D13
hypocenterC13#3549
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ H(3,𝔽4)

Complements

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

NH ≅ G/Ntype
1. C13×H(3,𝔽4)C2semidirect
2. #11719388C2semidirect
3. #11719379C2semidirect
4. #11719375C2semidirect
5. #11719373C2semidirect
6. #11719297C2semidirect
7. #11719295C2semidirect
8. C22×C22⋊D13C22semidirect
9. C2×#6131C22semidirect
10. C2×#6129C22semidirect
11. C2×D4×D13C22semidirect
12. C13×#124C22semidirect
13. C13×#124C22semidirect
14. C13×#120C22semidirect
15. #88207C22semidirect
16. #88201C22semidirect
17. #88198C22semidirect
19. #88194C22semidirect
20. #88193C22semidirect
21. #88191C22semidirect
22. #88139C22semidirect
23. #88138C22semidirect
24. #88138C22semidirect
25. #88136C22semidirect
26. #88136C22semidirect
27. #88135C22semidirect
28. #88131C22semidirect
29. #88129C22semidirect
30. #88128C22semidirect
31. #88126C22semidirect
32. C42×D13C22semidirect
87. H(3,𝔽4)D13semidirect
116. #124C2×D13semidirect
117. #124C2×D13semidirect
125. #120C2×D13semidirect
163. C13#3549semidirect

Maximal subgroups

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

subgroupindex
C13×H(3,𝔽4)2
#117193882
#117193792
#117193752
#117193732
#117192972
#117192952
#354913