Finite Group Databasebeta

← C2×#13120938 #16029461

Subgroups — C2×#13120938 #16029461

Order 3328.

4886 conjugacy classes of subgroups; only the 907 normal subgroups are shown.

normal subgroups only

This group has 4886 conjugacy classes of subgroups — too many to draw. Only its 907 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
1C22×#88184C216yesmaximal, complemented
2#13120938C2116yesmaximal, direct product factor
3C2×#11718338C214yesmaximal, complemented
4C2×#11718332C214yesmaximal, complemented
5C22×C13×#95C211yesmaximal, characteristic, complemented
6C24×C4×C13C2213yes—
7C23×C22⋊D13C2214yes—
8C23×D52C2216yes—
9C2×#88184—248no—
10C2×#88184C22148yescomplemented
11C22×#6103C22112yes—
12C22×C4⋊Dic13C2216yes—
13C2×C13×#95C2214yes—
14C2×C13×#95C2218yescomplemented
15#11718338C22132yescomplemented
16#11718332C22132yescomplemented
17C25×C13C2311yescharacteristic
18C24×D13C2314yes—
19C23×C4×C13—412no—
20C23×C4×C13D4124yescomplemented
21C23×C4×C13C2316yes—
22C23×C4×C13C23112yes—
23C22×C22⋊D13—248no—
24C22×C22⋊D13C23116yes—
25C23×Dic13C2314yes—
26C22×D52—224no—
27C22×D52—424no—
28C22×D52C23124yes—
29#88184—2192no—
30C2×#6103—248no—
31C2×#6103C23148yes—
32C2×C4⋊Dic13—224no—
33C2×C4⋊Dic13C23124yes—
34C13×#95C23116yes—
35C2×#2656—131nomaximal, Sylow
36C24×C13—26no—
37C24×C13—22no—
38C24×C13C2×D4112yes—
39C24×C13C2412yes—
40C24×C13C2411yescharacteristic
41C23×D13—224no—
42C23×D13—224no—
43C23×D13—28no—
44C23×D13C2418yes—
45C22×C4×C13—224no—
46C22×C4×C13—448no—
47C22×C4×C13—424no—
48C22×C4×C13C2×D4124yes—
49C22×C4×C13C2×D4148yescomplemented
50C22×C4×C13C24112yes—
51C2×C22⋊D13—296no—
52C2×C22⋊D13—464no—
53C22×Dic13—224no—
54C22×Dic13C2418yes—
55C2×D52—248no—
56C2×D52—448no—
57C2×D52—496no—
58#6103—296no—
59C4⋊Dic13—248no—
60C22×#121—136no—
61#2656—1316no—
62C2×#399—134no—
63C2×#392—134no—
64C22×#95D1311yescharacteristic, complemented
65C23×C13—224no—
66C23×C13—224no—
67C23×C13—26no—
68C23×C13—22no—
69C23×C13#127116yes—
70C23×C13C22×D4112yes—
71C23×C13C22×D416yes—
72C23×C13H(5,𝔽2)16yes—
73C23×C132−1+412yes—
74C23×C13C2511yescharacteristic
75C22×D13—224no—
76C22×D13—224no—
77C22×D13—28no—
78C22×D13—416no—
79C22×D13—448no—
80C22×D13—448no—
81C2×C4×C13—248no—
82C2×C4×C13—224no—
83C2×C4×C13—448no—
84C2×C4×C13C22×D4124yes—
85C22⋊D13—464no—
86C2×Dic13—224no—
87C2×Dic13—416no—
88D52—496no—
89C23×D4—134no—
90C23×D4—136no—
91C24×C4C2×D1313yes—
92C2×#121—1348no—
93C2×#121—2648no—
94C22×C4⋊C4—136no—
95C22×C22⋊C4—1312no—
96#399—1332no—
97#392—1332no—
98C2×#95C2×D1314yes—
99C2×#95C2×D1318yescomplemented
100C22×C13—232no—
101C22×C13—212no—
102C22×C13—212no—
103C22×C13C2×#12718yes—
104C22×C13C2×#12714yes—
105C22×C13#534112yes—
106C22×C13#537112yes—
107C22×C13C23×D413yes—
108C22×C13C2×H(5,𝔽2)13yes—
109C22×C13C2×2−1+411yescharacteristic
110C2×D13—48no—
111C2×D13—424no—
112C2×D13—424no—
113C2×D13—832no—
114C4×C13—224no—
115Dic13—48no—
116C25—134no—
117C25C22×D1311yescharacteristic
118C22×D4—1316no—
119C22×D4—1324no—
120C22×D4—2648no—
121C22×D4—2624no—
122C22×D4—5224no—
123C23×C4—412no—
124C23×C4—134no—
125C23×C4D52124yescomplemented
126C23×C4C22×D1316yes—
127C23×C4C22×D13112yes—
128#121—26192no—
129C2×C4⋊C4—1324no—
130C2×C4⋊C4—2624no—
131C2×C22⋊C4—1348no—
132C2×C22⋊C4—2648no—
133#95C22×D13116yes—
134C2×C13—28no—
135C2×C13#265618yescomplemented
136C2×C13C22×#12711yescharacteristic
137C2×C13C2×#53413yes—
138C2×C13C2×#53713yes—
139D13—88no—
140C24—26no—
141C24—22no—
142C24—138no—
143C24—2624no—
144C24—2624no—
145C24—268no—
146C24C2×D52112yes—
147C24C23×D1312yes—
148C24C23×D1311yescharacteristic
149C2×D4—2696no—
150C2×D4—2648no—
151C2×D4—5248no—
152C2×D4—5296no—
153C2×D4—5264no—
154C22×C4—224no—
155C22×C4—448no—
156C22×C4—424no—
157C22×C4—138no—
158C22×C4—2624no—
159C22×C4C2×D52124yes—
160C22×C4C2×D52148yescomplemented
161C22×C4C23×D13112yes—
162C4⋊C4—2648no—
163C22⋊C4—2696no—
164C13C2×#265611yescharacteristic, complemented, Sylow
165C23—224no—
166C23—224no—
167C23—26no—
168C23—22no—
169C23—2624no—
170C23—2624no—
171C23—268no—
172C23—5216no—
173C23—5248no—
174C23—5248no—
175C23#88128116yes—
176C23C22×D52112yes—
177C23C22×D5216yes—
178C23#8825116yes—
179C23#8825412yes—
180C23C24×D1311yescharacteristic
181D4—5296no—
182D4—5264no—
183C2×C4—248no—
184C2×C4—224no—
185C2×C4—448no—
186C2×C4—2624no—
187C2×C4—5216no—
188C2×C4C22×D52124yes—
189C22—232no—
190C22—212no—
191C22—212no—
192C22—528no—
193C22—5224no—
194C22—5224no—
195C22—10432no—
196C22C2×#8812818yes—
197C22C2×#8812814yes—
198C22#11719198112yes—
199C22#11719215112yes—
200C22C23×D5213yes—
201C22C2×#8825113yes—
202C22C2×#8825411yescharacteristic
203C4—224no—
204C4—528no—
205C2—28no—
206C2—1048no—
207C2#1312093818yesdirect product factor
208C2C22×#8812811yescharacteristic
209C2C2×#1171919813yes—
210C2C2×#1171921513yes—
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC22×C13×#95C2
socleC24×C13C24
hypercenterC22×#95D13
hypocenterC13C2×#2656
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×#95

Complements

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

NH ≅ G/Ntype
1. C22×#88184C2semidirect
2. #13120938C2direct (N × H)
3. C2×#11718338C2semidirect
4. C2×#11718332C2semidirect
5. C22×C13×#95C2semidirect
10. C2×#88184C22semidirect
14. C2×C13×#95C22semidirect
15. #11718338C22semidirect
16. #11718332C22semidirect
20. C23×C4×C13D4semidirect
49. C22×C4×C13C2×D4semidirect
64. C22×#95D13semidirect
99. C2×#95C2×D13semidirect
125. C23×C4D52semidirect
135. C2×C13#2656semidirect
160. C22×C4C2×D52semidirect
164. C13C2×#2656semidirect
207. C2#13120938direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881842
#131209382
C2×#117183382
C2×#117183322
C22×C13×#952
C2×#265613