Finite Group Databasebeta

← D13×#1711 #15850593

Subgroups — D13×#1711 #15850593

Order 3328.

802 conjugacy classes of subgroups; only the 179 normal subgroups are shown.

normal subgroups only

This group has 802 conjugacy classes of subgroups — too many to draw. Only its 179 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
1D13×#487C213yesmaximal, complemented
2D13×#486C213yesmaximal
3#13114449C213yesmaximal, complemented
4#13114448C211yesmaximal, characteristic, complemented
5#13114447C213yesmaximal, complemented
6C82×D13C211yesmaximal, characteristic, complemented
7C13×#1711C211yesmaximal, characteristic, complemented
8D13×C4⋊Q8C2213yes—
9D13×#127C2211yescharacteristic
10C13×#487C2213yescomplemented
11C13×#486C2213yes—
12#11718754C2213yescomplemented
13#11718749C2213yes—
14#11718742C2213yescomplemented
15#11718731C2213yes—
16D13×#103—26no—
17#11718453—26no—
18D13×#102—26no—
19#11718421—26no—
20#11718355C2213yes—
21C4×C8×D13C2213yes—
22#11718342C2213yescomplemented
23C82×C13C2211yescharacteristic, complemented
24C8×#1055C2213yescomplemented
25C2×Q8×D13—23no—
26C2×D4×D13—23no—
27C13×C4⋊Q8C2313yes—
28C13×#127C2311yescharacteristic
29#88198—23no—
30#88194—23no—
31C2×C8×D13D416yes—
32C4⋊C4×D13—23no—
33C4⋊C4×D13—23no—
34#88142—23no—
35#88142—23no—
36#88128C2311yescharacteristic
37C42×D13C2311yescharacteristic
38#88123C2313yes—
39C13×#103—26no—
40C13×#102—26no—
41C4×C8×C13C2313yes—
42#88075—26no—
43#88072—26no—
44#88061—26no—
45#88056—26no—
46C8×Dic13D416yes—
47#88050—26no—
48#88049—26no—
49C4×#1055C2313yes—
50C2×#1711—131nomaximal, Sylow
51C23×D13—41no—
52C2×Q8×C13—23no—
53C2×D4×C13—23no—
54C2×C22⋊D13—43no—
55Q8×D13—412no—
56D4×D13—412no—
57C2×D52—23no—
58C2×C4×D13—43no—
59C2×C4×D13C2×D413yes—
60C2×Dic26—23no—
61C2×Dic26—43no—
62C2×C8×C13C2×D416yes—
63C13×C4⋊C4—23no—
64C13×C4⋊C4—23no—
65C42×C13C2411yescharacteristic
66C4⋊Dic13—23no—
67C4⋊Dic13—23no—
68#6101—43no—
69#6101—43no—
70C4×Dic13C2×D413yes—
71C2×#1055C2×D416yes—
72C8×D13—212no—
73C2×#487—133no—
74C2×#486—133no—
75#1711—133no—
76#1711—133no—
77#1711—131no—
78#1711D1311yescharacteristic, direct product factor
79C2×C82—131no—
80C23×C13—41no—
81C22×D13—41no—
82C22×D13—86no—
83C22×D13#12711yescharacteristic
84Q8×C13—46no—
85D4×C13—46no—
86C2×C4×C13—43no—
87C2×C4×C13C22×D413yes—
88C22⋊D13—86no—
89C2×Dic13—43no—
90C2×Dic13#12713yes—
91D52—46no—
92C4×D13—86no—
93C4×D13#135112yes—
94Dic26—46no—
95Dic26—86no—
96C8×C13—26no—
97#1055—26no—
98C2×C4⋊Q8—133no—
99C2×#127—131no—
100#487—133no—
101#487—133no—
102#487—133no—
103#487—266no—
104#487C2×D1313yescomplemented
105#486—133no—
106#486—133no—
107#486—133no—
108#486—266no—
109#486C2×D1313yes—
110C2×#103—266no—
111C2×#102—266no—
112C2×C4×C8—133no—
113C82—133no—
114C82C2×D1311yescharacteristic, complemented
115C22×C13—83no—
116C22×C13C2×#12711yescharacteristic
117C2×D13—83no—
118C2×D13—164no—
119C2×D13#49516yes—
120C4×C13—83no—
121C4×C13C2×#13516yes—
122Dic13—83no—
123Dic13#49516yes—
124C22×Q8—263no—
125C22×D4—263no—
126C22×C8—136no—
127C4⋊Q8—133no—
128C4⋊Q8—263no—
129C4⋊Q8—263no—
130C4⋊Q8—263no—
131C4⋊Q8C22×D1313yes—
132#127—131no—
133#127—263no—
134#127C22×D1311yescharacteristic
135C2×C4⋊C4—263no—
136C2×C4⋊C4—263no—
137C2×C42—131no—
138#103—26no—
139#103—266no—
140#103—266no—
141#103—266no—
142#102—26no—
143#102—266no—
144#102—266no—
145#102—266no—
146C4×C8—136no—
147C4×C8—133no—
148C4×C8C22×D1313yes—
149C2×C13—161no—
150C2×C13C2×#49513yes—
151D13—161no—
152D13#171114yesdirect product factor
153C24—521no—
154C2×Q8—23no—
155C2×Q8—263no—
156C2×Q8—523no—
157C2×Q8—5212no—
158C2×D4—23no—
159C2×D4—263no—
160C2×D4—5212no—
161C2×D4—523no—
162C22×C4—133no—
163C22×C4—523no—
164C2×C8—136no—
165C2×C8—2612no—
166C2×C8D4×D1316yes—
167C4⋊C4—23no—
168C4⋊C4—23no—
169C4⋊C4—263no—
170C4⋊C4—263no—
171C4⋊C4—523no—
172C4⋊C4—523no—
173C42—133no—
174C42C23×D1311yescharacteristic
175C13C2×#171111yescharacteristic, complemented, Sylow
176C23—41no—
177C23—131no—
178C23—521no—
179C23—1046no—
180Q8—46no—
181Q8—526no—
182Q8—1046no—
183D4—46no—
184D4—526no—
185D4—1046no—
186C2×C4—43no—
187C2×C4—133no—
188C2×C4—1312no—
189C2×C4—523no—
190C2×C4—1046no—
191C2×C4C2×D4×D1313yes—
192C8—26no—
193C8—266no—
194C22—83no—
195C22—136no—
196C22—1043no—
197C22—2084no—
198C22D13×#12711yescharacteristic
199C4—83no—
200C4—136no—
201C4—1043no—
202C4D13×#13516yes—
203C2—134no—
204C2—161no—
205C2—2081no—
206C2D13×#49513yes—
subgroupG/H
centerC22D13×#127
commutator, cosocleC42×C13C24
FrattiniC42C23×D13
FittingC13×#1711C2
socleC22×C13C2×#127
prime radicalD13×#127C22
hypercenter#1711D13
hypocenterC13C2×#1711
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #1711

Complements

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

NH ≅ G/Ntype
1. D13×#487C2semidirect
3. #13114449C2semidirect
4. #13114448C2semidirect
5. #13114447C2semidirect
6. C82×D13C2semidirect
7. C13×#1711C2semidirect
10. C13×#487C22semidirect
12. #11718754C22semidirect
14. #11718742C22semidirect
22. #11718342C22semidirect
23. C82×C13C22semidirect
24. C8×#1055C22semidirect
78. #1711D13direct (N × H)
104. #487C2×D13semidirect
114. C82C2×D13semidirect
152. D13#1711direct (N × H)
175. C13C2×#1711semidirect

Maximal subgroups

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

subgroupindex
D13×#4872
D13×#4862
#131144492
#131144482
#131144472
C82×D132
C13×#17112
C2×#171113