Finite Group Databasebeta

← D13×#399 #13118082

Subgroups — D13×#399 #13118082

Order 1664.

908 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 908 conjugacy classes of subgroups — too many to draw. Only its 203 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×C4⋊C4×D13C213yesmaximal, complemented
2C2×C22⋊C4×D13C213yesmaximal
3C13×#399C211yesmaximal, characteristic, complemented
4#11718653C213yesmaximal, complemented
5#11718610C213yesmaximal, complemented
6#11718338C211yesmaximal, characteristic, complemented
7D13×#95C211yesmaximal, characteristic, complemented
8C24×D13C2211yescharacteristic
9C22×C4×D13C2213yes—
10C22×C4×D13C2213yes—
11C2×C13×C4⋊C4C2213yescomplemented
12C2×C13×C22⋊C4C2213yes—
13C2×C22⋊Dic13C2213yes—
14C2×#6103C2213yes—
15C2×#6103C2213yes—
16C2×C4⋊Dic13C2213yescomplemented
17C2×#6101C2216yescomplemented
18C4⋊C4×D13—212no—
19C22⋊C4×D13—212no—
20C13×#95C2211yescharacteristic, complemented
21#88071C2213yescomplemented
22C24×C13C2311yescharacteristic
23C23×D13—26no—
24C23×D13—26no—
25C23×D13Q814yes—
26C23×D13C2311yescharacteristic
27C23×D13C2311yescharacteristic
28C22×C4×C13C2313yes—
29C22×C4×C13C2313yes—
30C22×Dic13C2313yes—
31C22×Dic13C2313yes—
32C2×C4×D13—212no—
33C2×C4×D13—26no—
34C2×C4×D13—212no—
35C2×C4×D13D4112yes—
36C13×C4⋊C4—26no—
37C13×C22⋊C4—26no—
38C22⋊Dic13—26no—
39#6103—26no—
40#6103—26no—
41C4⋊Dic13—26no—
42#6101—212no—
43C2×#399—131nomaximal, Sylow
44C23×C13—23no—
45C23×C13—23no—
46C23×C13C2×Q812yes—
47C23×C13C2411yescharacteristic
48C22×D13—23no—
49C22×D13—23no—
50C22×D13—224no—
51C22×D13—412no—
52C22×D13—44no—
53C22×D13C2×D416yes—
54C22×D13C2×Q812yes—
55C22×D13C2×Q812yes—
56C22×D13#4116yes—
57C2×C4×C13—26no—
58C2×C4×C13—26no—
59C2×C4×C13—23no—
60C2×C4×C13C2×D416yes—
61C2×Dic13—26no—
62C2×Dic13—26no—
63C2×Dic13—23no—
64C2×Dic13C2×D416yes—
65C4×D13—224no—
66C4×D13—412no—
67C22×C4⋊C4—133no—
68C22×C22⋊C4—133no—
69#399—133no—
70#399—133no—
71#399—131no—
72#399D1311yescharacteristic, direct product factor
73C2×#95—131no—
74C22×C13—26no—
75C22×C13—43no—
76C22×C13—41no—
77C22×C13C22×D413yes—
78C22×C13C22×Q811yescharacteristic
79C22×C13C2×#4113yes—
80C2×D13—26no—
81C2×D13—43no—
82C2×D13—41no—
83C2×D13—416no—
84C2×D13C22⋊Q8112yes—
85C2×D13#123112yes—
86C2×D13#12714yes—
87C4×C13—26no—
88C4×C13—43no—
89Dic13—26no—
90Dic13—43no—
91C25—131no—
92C23×C4—133no—
93C23×C4—133no—
94C2×C4⋊C4—136no—
95C2×C4⋊C4—133no—
96C2×C4⋊C4—2612no—
97C2×C4⋊C4C2×D1313yescomplemented
98C2×C22⋊C4—133no—
99C2×C22⋊C4—133no—
100C2×C22⋊C4—133no—
101C2×C22⋊C4—2612no—
102C2×C22⋊C4C2×D1313yes—
103#95—133no—
104#95C2×D1311yescharacteristic, complemented
105C2×C13—42no—
106C2×C13C2×C22⋊Q813yes—
107C2×C13C2×#12313yes—
108C2×C13C2×#12711yescharacteristic
109D13—42no—
110D13#39918yesdirect product factor
111C24—131no—
112C24—134no—
113C24—131no—
114C24—266no—
115C24—266no—
116C24C22×D1311yescharacteristic
117C22×C4—133no—
118C22×C4—1312no—
119C22×C4—133no—
120C22×C4—2612no—
121C22×C4—266no—
122C22×C4—2612no—
123C22×C4C22×D1313yes—
124C22×C4C22×D1313yes—
125C4⋊C4—26no—
126C4⋊C4—2612no—
127C4⋊C4—266no—
128C22⋊C4—26no—
129C22⋊C4—266no—
130C22⋊C4—266no—
131C22⋊C4—266no—
132C13C2×#39911yescharacteristic, complemented, Sylow
133C23—23no—
134C23—23no—
135C23—136no—
136C23—132no—
137C23—136no—
138C23—132no—
139C23—2624no—
140C23—263no—
141C23—263no—
142C23—5212no—
143C23—524no—
144C23Q8×D1312yes—
145C23C23×D1311yescharacteristic
146C2×C4—26no—
147C2×C4—23no—
148C2×C4—26no—
149C2×C4—136no—
150C2×C4—2624no—
151C2×C4—266no—
152C2×C4—263no—
153C2×C4—266no—
154C2×C4—5212no—
155C2×C4D4×D1316yes—
156C22—26no—
157C22—43no—
158C22—41no—
159C22—1312no—
160C22—1312no—
161C22—134no—
162C22—266no—
163C22—5216no—
164C22—523no—
165C22—521no—
166C22C2×D4×D1313yes—
167C22C2×Q8×D1311yescharacteristic
168C22#41×D1313yes—
169C4—26no—
170C4—43no—
171C4—266no—
172C4—523no—
173C2—42no—
174C2—138no—
175C2—522no—
176C2D13×C22⋊Q813yes—
177C2D13×#12313yes—
178C2D13×#12711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#399C2
prime radicalC24×D13C22
hypercenter#399D13
hypocenterC13C2×#399
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊C4×D13C2semidirect
3. C13×#399C2semidirect
4. #11718653C2semidirect
5. #11718610C2semidirect
6. #11718338C2semidirect
7. D13×#95C2semidirect
11. C2×C13×C4⋊C4C22semidirect
16. C2×C4⋊Dic13C22semidirect
17. C2×#6101C22semidirect
20. C13×#95C22semidirect
21. #88071C22semidirect
72. #399D13direct (N × H)
97. C2×C4⋊C4C2×D13semidirect
104. #95C2×D13semidirect
110. D13#399direct (N × H)
132. C13C2×#399semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×D132
C2×C22⋊C4×D132
C13×#3992
#117186532
#117186102
#117183382
D13×#952
C2×#39913