Finite Group Databasebeta

← C2×#13120555 #16029832

Subgroups — C2×#13120555 #16029832

Order 3328.

5194 conjugacy classes of subgroups; only the 907 normal subgroups are shown.

normal subgroups only

This group has 5194 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×#88183C213yesmaximal
2#13120555C2116yesmaximal, direct product factor
3C2×#11718890C214yesmaximal, complemented
4C2×#11718892C214yesmaximal, complemented
5C2×#11718872C213yesmaximal, complemented
6C24×Q8×C13C211yesmaximal, characteristic, complemented
7C23×Q8×C13—224no—
8C23×Q8×C13C2214yes—
9C23×Q8×C13C2218yescomplemented
10C24×C4×C13C2213yes—
11C23×C22⋊D13C2211yescharacteristic
12C22×C22⋊Dic13C2213yes—
13C2×#88183—224no—
14C2×#88183C22124yes—
15C22×#6103C2216yes—
16C22×#6101C2216yes—
17#11718892C22132yescomplemented
18#11718890C22132yescomplemented
19#11718872C22124yescomplemented
20C2×#88071C22112yes—
21C25×C13C2311yescharacteristic
22C24×D13C2311yescharacteristic
23C22×Q8×C13—2128no—
24C22×Q8×C13—248no—
25C22×Q8×C13—296no—
26C22×Q8×C13C23116yes—
27C23×C4×C13—224no—
28C23×C4×C13D4124yes—
29C23×C4×C13C2316yes—
30C23×C4×C13C23112yes—
31C22×C22⋊D13—212no—
32C22×C22⋊D13C2314yes—
33C23×Dic13C2311yescharacteristic
34C23×Dic13C2316yes—
35C2×C22⋊Dic13—212no—
36C2×C22⋊Dic13C23112yes—
37#88183—296no—
38C2×#6103—224no—
39C2×#6103C23124yes—
40C2×#6101—224no—
41C2×#6101C23124yes—
42#88071C23148yes—
43C2×#2614—131nomaximal, Sylow
44C24×C13—28no—
45C24×C13C2×D4112yes—
46C24×C13C2412yes—
47C24×C13C2411yescharacteristic
48C23×D13—26no—
49C23×D13—28no—
50C23×D13C2412yes—
51C2×Q8×C13—2128no—
52C2×Q8×C13—2256no—
53C2×Q8×C13—296no—
54C22×C4×C13—296no—
55C22×C4×C13—248no—
56C22×C4×C13—224no—
57C22×C4×C13C2×D4124yes—
58C22×C4×C13C2×D4148yes—
59C22×C4×C13C24112yes—
60C2×C22⋊D13—224no—
61C2×C22⋊D13—416no—
62C22×Dic13—26no—
63C22×Dic13—212no—
64C22×Dic13—224no—
65C22×Dic13C24112yes—
66C22×Dic13C2412yes—
67C22⋊Dic13—224no—
68#6103—248no—
69#6101—248no—
70C24×Q8D1311yescharacteristic, complemented
71C22×#123—133no—
72#2614—1316no—
73C2×#395—134no—
74C2×#393—134no—
75C2×#381—133no—
76C23×C13—248no—
77C23×C13—28no—
78C23×C13#120116yes—
79C23×C13C22×D4112yes—
80C23×C13C22×D416yes—
81C23×C132−1+418yes—
82C23×C13C2511yescharacteristic
83C22×D13—26no—
84C22×D13—28no—
85C22×D13—44no—
86C22×D13—424no—
87Q8×C13—2128no—
88C2×C4×C13—296no—
89C2×C4×C13—248no—
90C2×C4×C13—224no—
91C2×C4×C13C22×D4124yes—
92C22⋊D13—416no—
93C2×Dic13—26no—
94C2×Dic13—212no—
95C2×Dic13—224no—
96C2×Dic13—44no—
97C2×Dic13—424no—
98C23×Q8—224no—
99C23×Q8C2×D1314yes—
100C23×Q8C2×D1318yescomplemented
101C23×D4—131no—
102C24×C4C2×D1313yes—
103C2×#123—1324no—
104C2×#123—2624no—
105C22×C4⋊C4—136no—
106C22×C22⋊C4—133no—
107C22×C22⋊C4—136no—
108#395—1332no—
109#393—1332no—
110#381—1324no—
111C2×#95—1312no—
112C22×C13—232no—
113C22×C13—224no—
114C22×C13C2×#12018yes—
115C22×C13C2×#12014yes—
116C22×C13#536124yes—
117C22×C13C23×D413yes—
118C22×C13C2×2−1+414yes—
119C2×D13—42no—
120C2×D13—412no—
121C2×D13—88no—
122C4×C13—224no—
123Dic13—42no—
124Dic13—412no—
125C25—131no—
126C25C22×D1311yescharacteristic
127C22×Q8—2128no—
128C22×Q8—248no—
129C22×Q8—296no—
130C22×Q8C22×D13116yes—
131C22×D4—134no—
132C22×D4—2612no—
133C23×C4—224no—
134C23×C4—136no—
135C23×C4—131no—
136C23×C4C22⋊D13124yes—
137C23×C4C22×D13112yes—
138C23×C4C22×D1316yes—
139#123—2696no—
140C2×C4⋊C4—1324no—
141C2×C4⋊C4—2624no—
142C2×C22⋊C4—1312no—
143C2×C22⋊C4—1324no—
144C2×C22⋊C4—2612no—
145C2×C22⋊C4—2624no—
146#95—1348no—
147C2×C13—28no—
148C2×C13#261418yescomplemented
149C2×C13C22×#12011yescharacteristic
150C2×C13C2×#53616yes—
151D13—82no—
152C24—28no—
153C24—132no—
154C24—268no—
155C24—266no—
156C24C2×C22⋊D13112yes—
157C24C23×D1312yes—
158C24C23×D1311yescharacteristic
159C2×Q8—2128no—
160C2×Q8—2256no—
161C2×Q8—296no—
162C2×D4—2624no—
163C2×D4—5216no—
164C22×C4—296no—
165C22×C4—248no—
166C22×C4—224no—
167C22×C4—1312no—
168C22×C4—132no—
169C22×C4—2624no—
170C22×C4—2612no—
171C22×C4—266no—
172C22×C4C2×C22⋊D13124yes—
173C22×C4C2×C22⋊D13148yes—
174C22×C4C23×D13112yes—
175C4⋊C4—2648no—
176C22⋊C4—2624no—
177C22⋊C4—2648no—
178C13C2×#261411yescharacteristic, complemented, Sylow
179C23—248no—
180C23—28no—
181C23—268no—
182C23—266no—
183C23—5224no—
184C23—524no—
185C23#88207116yes—
186C23#8825418yes—
187C23C22×C22⋊D13112yes—
188C23C22×C22⋊D1316yes—
189C23C24×D1311yescharacteristic
190Q8—2128no—
191D4—5216no—
192C2×C4—296no—
193C2×C4—248no—
194C2×C4—224no—
195C2×C4—2624no—
196C2×C4—2612no—
197C2×C4—266no—
198C2×C4—5224no—
199C2×C4—524no—
200C2×C4C22×C22⋊D13124yes—
201C22—232no—
202C22—224no—
203C22—522no—
204C22—5212no—
205C22—1048no—
206C22#11719521124yes—
207C22C2×#8820718yes—
208C22C2×#8820714yes—
209C22C2×#8825414yes—
210C22C23×C22⋊D1313yes—
211C4—224no—
212C4—522no—
213C4—5212no—
214C2—28no—
215C2—1042no—
216C2#1312055518yesdirect product factor
217C2C22×#8820711yescharacteristic
218C2C2×#1171952116yes—
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC24×Q8×C13C2
socleC24×C13C24
prime radicalC23×C22⋊D13C22
hypercenterC24×Q8D13
hypocenterC13C2×#2614
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C24×Q8

Complements

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

NH ≅ G/Ntype
2. #13120555C2direct (N × H)
3. C2×#11718890C2semidirect
4. C2×#11718892C2semidirect
5. C2×#11718872C2semidirect
6. C24×Q8×C13C2semidirect
9. C23×Q8×C13C22semidirect
17. #11718892C22semidirect
18. #11718890C22semidirect
19. #11718872C22semidirect
70. C24×Q8D13semidirect
100. C23×Q8C2×D13semidirect
148. C2×C13#2614semidirect
178. C13C2×#2614semidirect
216. C2#13120555direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881832
#131205552
C2×#117188902
C2×#117188922
C2×#117188722
C24×Q8×C132
C2×#261413