Finite Group Databasebeta

← D13×#2866 #16068961

Subgroups — D13×#2866 #16068961

Order 3328.

2186 conjugacy classes of subgroups; only the 591 normal subgroups are shown.

normal subgroups only

This group has 2186 conjugacy classes of subgroups — too many to draw. Only its 591 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#13123229C217yesmaximal, complemented
2#13123228C211yesmaximal, characteristic, complemented
3#13123227C217yesmaximal, complemented
4D13×#388C217yesmaximal
5D13×#387C217yesmaximal, complemented
6C43×D13C211yesmaximal, characteristic, complemented
7C13×#2866C211yesmaximal, characteristic, complemented
8C2×C4⋊C4×D13C2217yes—
9C2×C22⋊C4×D13C2217yes—
10C2×C42×D13C2217yes—
11C13×#388C2217yes—
12C13×#387C2217yescomplemented
13C43×C13C2211yescharacteristic, complemented
14#11718651C2217yes—
15#11718642C2217yescomplemented
16#11718639C2217yescomplemented
17#11718612C2217yes—
18#11718606C2217yes—
19#11718605C2217yes—
20#11718601C2217yes—
21#11718594C2217yescomplemented
22C42×Dic13C2217yescomplemented
23#11718331C2217yes—
24#11718330C2217yes—
25D13×#95C2217yes—
26D13×#95C2217yes—
27#11718316C2217yescomplemented
28#11718315C2217yescomplemented
29#11718314C2217yescomplemented
30#11718313C2217yescomplemented
31C24×D13C2311yescharacteristic
32C22×C4×D13C2317yes—
33C22×C4×D13C2317yes—
34C2×C13×C4⋊C4C2317yes—
35C2×C13×C22⋊C4C2317yes—
36C2×C42×C13C2317yes—
37C2×C22⋊Dic13C2317yes—
38C2×#6103C2317yes—
39C2×#6103C2317yes—
40C2×C4⋊Dic13C2317yes—
41C2×#6101C2317yes—
42C2×#6101C2317yes—
43C2×C4×Dic13C2317yes—
44C2×C4×Dic13C2317yes—
45C2×C4×Dic13C2317yes—
46C4⋊C4×D13—228no—
47C22⋊C4×D13—228no—
48C42×D13—228no—
49C13×#95C2317yes—
50C13×#95C2317yes—
51#88071C2317yes—
52#88071C2317yes—
53#88071C2317yes—
54#88071C2317yes—
55#88071C2317yes—
56#88071C2317yes—
57C2×#2866—131nomaximal, Sylow
58C24×C13C2411yescharacteristic
59C23×D13—214no—
60C23×D13C2411yescharacteristic
61C23×D13C2411yescharacteristic
62C22×C4×C13C2417yes—
63C22×C4×C13C2417yes—
64C22×Dic13C2417yes—
65C22×Dic13C2417yes—
66C2×C4×D13—214no—
67C2×C4×D13—214no—
68C2×C4×D13—214no—
69C2×C4×D13—214no—
70C2×C4×D13—214no—
71C2×C4×D13#41128yes—
72C13×C4⋊C4—214no—
73C13×C22⋊C4—214no—
74C42×C13—214no—
75C22⋊Dic13—214no—
76#6103—214no—
77#6103—214no—
78C4⋊Dic13—214no—
79#6101—214no—
80#6101—214no—
81C4×Dic13—214no—
82C4×Dic13—214no—
83C4×Dic13—214no—
84#2866—137no—
85#2866—137no—
86#2866—131no—
87#2866D1311yescharacteristic, direct product factor
88C2×#388—137no—
89C2×#387—137no—
90C2×C43—131no—
91C23×C13—27no—
92C23×C13C2511yescharacteristic
93C22×D13—27no—
94C22×D13—428no—
95C22×D13C2×#41114yes—
96C2×C4×C13—27no—
97C2×C4×C13—27no—
98C2×C4×C13—27no—
99C2×C4×C13—27no—
100C2×C4×C13—27no—
101C2×C4×C13C2×#41114yes—
102C2×Dic13—27no—
103C2×Dic13—27no—
104C2×Dic13—27no—
105C2×Dic13—27no—
106C2×Dic13—27no—
107C2×Dic13C2×#41114yes—
108C4×D13—256no—
109C4×D13—428no—
110C22×C4⋊C4—137no—
111C22×C22⋊C4—137no—
112C22×C42—137no—
113#388—137no—
114#388—137no—
115#388—137no—
116#388—137no—
117#388—137no—
118#388—137no—
119#388—137no—
120#388C2×D1317yes—
121#387—137no—
122#387—137no—
123#387—137no—
124#387—137no—
125#387—137no—
126#387—137no—
127#387—137no—
128#387C2×D1317yescomplemented
129C2×#95—137no—
130C2×#95—137no—
131C43—137no—
132C43C2×D1311yescharacteristic, complemented
133C22×C13—47no—
134C22×C13C22×#4117yes—
135C2×D13—47no—
136C2×D13—88no—
137C2×D13#529128yes—
138C4×C13—214no—
139C4×C13—47no—
140Dic13—214no—
141Dic13—47no—
142C25—131no—
143C23×C4—137no—
144C23×C4—137no—
145C2×C4⋊C4—137no—
146C2×C4⋊C4—137no—
147C2×C4⋊C4—137no—
148C2×C4⋊C4—2628no—
149C2×C4⋊C4C22×D1317yes—
150C2×C22⋊C4—137no—
151C2×C22⋊C4—137no—
152C2×C22⋊C4—137no—
153C2×C22⋊C4—2628no—
154C2×C22⋊C4C22×D1317yes—
155C2×C42—137no—
156C2×C42—137no—
157C2×C42—137no—
158C2×C42—2628no—
159C2×C42C22×D1317yes—
160#95—137no—
161#95—137no—
162#95—137no—
163#95—137no—
164#95—137no—
165#95—137no—
166#95C22×D1317yes—
167#95C22×D1317yes—
168C2×C13—81no—
169C2×C13C2×#52917yes—
170D13—81no—
171D13#286618yesdirect product factor
172C24—131no—
173C24—131no—
174C24—2614no—
175C24C23×D1311yescharacteristic
176C22×C4—137no—
177C22×C4—1328no—
178C22×C4—137no—
179C22×C4—2614no—
180C22×C4—2614no—
181C22×C4—2614no—
182C22×C4—2614no—
183C22×C4—2614no—
184C22×C4C23×D1317yes—
185C22×C4C23×D1317yes—
186C4⋊C4—214no—
187C4⋊C4—2614no—
188C4⋊C4—2614no—
189C4⋊C4—2614no—
190C22⋊C4—214no—
191C22⋊C4—2614no—
192C22⋊C4—2614no—
193C22⋊C4—2614no—
194C42—214no—
195C42—2614no—
196C42—2614no—
197C42—2614no—
198C13C2×#286611yescharacteristic, complemented, Sylow
199C23—27no—
200C23—1314no—
201C23—267no—
202C23—5228no—
203C23C24×D1311yescharacteristic
204C2×C4—27no—
205C2×C4—27no—
206C2×C4—27no—
207C2×C4—27no—
208C2×C4—27no—
209C2×C4—1314no—
210C2×C4—2656no—
211C2×C4—267no—
212C2×C4—267no—
213C2×C4—267no—
214C2×C4—267no—
215C2×C4—267no—
216C2×C4—5228no—
217C2×C4#41×D13114yes—
218C22—47no—
219C22—1328no—
220C22—527no—
221C22—1048no—
222C22C2×#41×D1317yes—
223C4—214no—
224C4—47no—
225C4—2614no—
226C4—527no—
227C2—81no—
228C2—138no—
229C2—1041no—
230C2D13×#52917yes—
subgroupG/H
center, FrattiniC23C24×D13
commutator, socle, cosocleC23×C13C25
FittingC13×#2866C2
prime radicalC24×D13C23
hypercenter#2866D13
hypocenterC13C2×#2866
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #2866

Complements

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

NH ≅ G/Ntype
1. #13123229C2semidirect
2. #13123228C2semidirect
3. #13123227C2semidirect
5. D13×#387C2semidirect
6. C43×D13C2semidirect
7. C13×#2866C2semidirect
12. C13×#387C22semidirect
13. C43×C13C22semidirect
15. #11718642C22semidirect
16. #11718639C22semidirect
21. #11718594C22semidirect
22. C42×Dic13C22semidirect
27. #11718316C22semidirect
28. #11718315C22semidirect
29. #11718314C22semidirect
30. #11718313C22semidirect
87. #2866D13direct (N × H)
128. #387C2×D13semidirect
132. C43C2×D13semidirect
171. D13#2866direct (N × H)
198. C13C2×#2866semidirect

Maximal subgroups

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

subgroupindex
#131232292
#131232282
#131232272
D13×#3882
D13×#3872
C43×D132
C13×#28662
C2×#286613