Finite Group Databasebeta

← D13×#2845 #16069506

Subgroups — D13×#2845 #16069506

Order 3328.

1742 conjugacy classes of subgroups; only the 579 normal subgroups are shown.

normal subgroups only

This group has 1742 conjugacy classes of subgroups — too many to draw. Only its 579 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#13123111C213yesmaximal, complemented
2#13123110C2112yesmaximal, complemented
3D13×#398C2112yesmaximal
4D13×#382C213yesmaximal
5C13×#2845C211yesmaximal, characteristic, complemented
6C2×C4⋊C4×D13C2216yes—
7C2×C4⋊C4×D13C22112yes—
8C2×C42×D13C2211yescharacteristic
9C13×#398C22112yes—
10C13×#382C2213yes—
11#11718645C22112yes—
12#11718645C22112yes—
13#11718644C22112yes—
14#11718641C22112yes—
15#11718638C2216yes—
16#11718597C2213yes—
17D13×#95C22112yes—
18D13×#95C2214yes—
19#11718322C22112yes—
20#11718318C22112yes—
21#11718318C22112yes—
22#11718311C22112yes—
23C22×C4×D13C23112yes—
24C22×C4×D13C2313yes—
25C2×C13×C4⋊C4C2316yes—
26C2×C13×C4⋊C4C23112yes—
27C2×C42×C13C2311yescharacteristic
28C2×C4⋊Dic13C2316yes—
29C2×C4⋊Dic13C23112yes—
30C2×#6101C23112yes—
31C2×#6101C23112yes—
32C2×#6101C23112yes—
33C2×C4×Dic13C2313yes—
34C4⋊C4×D13—412no—
35C4⋊C4×D13—424no—
36C42×D13Q818yes—
37C13×#95C23112yes—
38C13×#95C2314yes—
39#88071C23112yes—
40#88071C23112yes—
41#88071C23112yes—
42#88071C23112yes—
43C2×#2845—131nomaximal, Sylow
44C23×D13C2411yescharacteristic
45C22×C4×C13C24112yes—
46C22×C4×C13C2413yes—
47C22×Dic13C24112yes—
48C22×Dic13C2413yes—
49C2×C4×D13—26no—
50C2×C4×D13—26no—
51C2×C4×D13—224no—
52C2×C4×D13—224no—
53C2×C4×D13—224no—
54C2×C4×D13C2×Q8112yes—
55C13×C4⋊C4—46no—
56C13×C4⋊C4—412no—
57C42×C13C2×Q814yes—
58C4⋊Dic13—412no—
59C4⋊Dic13—46no—
60#6101—412no—
61#6101—412no—
62#6101—412no—
63C4×Dic13C2×Q8112yes—
64#2845—1312no—
65#2845—133no—
66#2845D1311yescharacteristic, direct product factor
67C2×#398—1312no—
68C2×#382—133no—
69C23×C13C2511yescharacteristic
70C22×D13C22×Q812yes—
71C22×D13H(5,𝔽2)16yes—
72C22×D132−1+416yes—
73C2×C4×C13—23no—
74C2×C4×C13—23no—
75C2×C4×C13—212no—
76C2×C4×C13—212no—
77C2×C4×C13—212no—
78C2×C4×C13C22×Q816yes—
79C2×Dic13—23no—
80C2×Dic13—23no—
81C2×Dic13—212no—
82C2×Dic13—212no—
83C2×Dic13—212no—
84C2×Dic13C22×Q816yes—
85C4×D13—224no—
86C4×D13—448no—
87C22×C4⋊C4—1312no—
88C22×C4⋊C4—136no—
89C22×C42—131no—
90#398—1312no—
91#398—1312no—
92#398—1312no—
93#398—1312no—
94#398—1312no—
95#398—1312no—
96#398—1312no—
97#398C2×D13112yes—
98#382—136no—
99#382—133no—
100#382—1312no—
101#382C2×D1313yes—
102C2×#95—134no—
103C2×#95—1312no—
104C22×C13C23×Q811yescharacteristic
105C22×C13C2×H(5,𝔽2)13yes—
106C22×C13C2×2−1+413yes—
107C2×D13#544112yes—
108C2×D13#562112yes—
109C2×D13#56414yes—
110C4×C13—26no—
111C4×C13—412no—
112Dic13—26no—
113Dic13—412no—
114C23×C4—133no—
115C23×C4—1312no—
116C2×C4⋊C4—1312no—
117C2×C4⋊C4—1312no—
118C2×C4⋊C4—1312no—
119C2×C4⋊C4—136no—
120C2×C4⋊C4—1312no—
121C2×C4⋊C4—5212no—
122C2×C4⋊C4—5224no—
123C2×C4⋊C4C22×D1316yes—
124C2×C4⋊C4C22×D13112yes—
125C2×C42—133no—
126C2×C42—138no—
127C2×C42C22×D1311yescharacteristic
128#95—1312no—
129#95—1312no—
130#95—1312no—
131#95—1312no—
132#95C22×D13112yes—
133#95C22×D1314yes—
134C2×C13C2×#54413yes—
135C2×C13C2×#56213yes—
136C2×C13C2×#56411yescharacteristic
137D13#284518yesdirect product factor
138C24—131no—
139C22×C4—133no—
140C22×C4—1312no—
141C22×C4—1312no—
142C22×C4—266no—
143C22×C4—266no—
144C22×C4—2624no—
145C22×C4—2624no—
146C22×C4—2624no—
147C22×C4C23×D13112yes—
148C22×C4C23×D1313yes—
149C4⋊C4—46no—
150C4⋊C4—412no—
151C4⋊C4—5212no—
152C4⋊C4—5212no—
153C4⋊C4—5212no—
154C4⋊C4—526no—
155C4⋊C4—5212no—
156C42—1312no—
157C42Q8×D1314yes—
158C13C2×#284511yescharacteristic, complemented, Sylow
159C23—132no—
160C23—136no—
161C23—136no—
162C23C24×D1311yescharacteristic
163C2×C4—23no—
164C2×C4—23no—
165C2×C4—212no—
166C2×C4—212no—
167C2×C4—212no—
168C2×C4—136no—
169C2×C4—2624no—
170C2×C4—263no—
171C2×C4—263no—
172C2×C4—2612no—
173C2×C4—2612no—
174C2×C4—2612no—
175C2×C4—5248no—
176C2×C4C2×Q8×D1316yes—
177C22—134no—
178C22—1312no—
179C22—1312no—
180C22C22×Q8×D1311yescharacteristic
181C22D13×H(5,𝔽2)13yes—
182C22D13×2−1+413yes—
183C4—26no—
184C4—412no—
185C4—266no—
186C4—5212no—
187C2—138no—
188C2D13×#54413yes—
189C2D13×#56213yes—
190C2D13×#56411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D13
commutator, socle, cosocleC23×C13C25
FittingC13×#2845C2
prime radicalC23×D13C24
hypercenter#2845D13
hypocenterC13C2×#2845
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #2845

Complements

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

NH ≅ G/Ntype
1. #13123111C2semidirect
2. #13123110C2semidirect
5. C13×#2845C2semidirect
66. #2845D13direct (N × H)
137. D13#2845direct (N × H)
158. C13C2×#2845semidirect

Maximal subgroups

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

subgroupindex
#131231112
#131231102
D13×#3982
D13×#3822
C13×#28452
C2×#284513