Finite Group Databasebeta

← #13118115

Subgroups — #13118115

Order 1664.

840 conjugacy classes of subgroups; only the 177 normal subgroups are shown.

normal subgroups only

This group has 840 conjugacy classes of subgroups — too many to draw. Only its 177 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
1C2×C4×D4×C13C211yesmaximal, characteristic, complemented
2C2×C4×C22⋊D13C214yesmaximal, complemented
3C2×C4×D52C211yesmaximal, characteristic, complemented
4#11718884C212yesmaximal, complemented
5#11718653C212yesmaximal, complemented
6#11718621C212yesmaximal, complemented
7#11718610C212yesmaximal, complemented
8#11718593C211yesmaximal, characteristic, complemented
9C22×D4×C13C2211yescharacteristic
10C23×C4×C13C2212yes—
11C22×C22⋊D13C2214yes—
12C22×D52C2211yescharacteristic
13C22×C4×D13C2212yes—
14C4×D4×C13—24no—
15C2×C13×C4⋊C4C2211yescharacteristic
16C2×C13×C22⋊C4C2212yes—
17C2×C42×C13C2211yescharacteristic
18C2×C22⋊Dic13C2214yes—
19C4×C22⋊D13—216no—
20C2×#6103C2212yes—
21C2×#6103C2214yes—
22C2×C4⋊Dic13C2211yescharacteristic
23C2×#6101C2214yes—
24C2×C4×Dic13C2212yes—
25C4×D52—24no—
26#88071C2212yes—
27#88071C2212yes—
28C24×C13C2312yes—
29C23×D13C2312yes—
30C2×D4×C13—24no—
31C2×D4×C13—22no—
32C22×C4×C13—28no—
33C22×C4×C13—24no—
34C22×C4×C13C2312yes—
35C22×C4×C13C2311yescharacteristic
36C22×C4×C13C2311yescharacteristic
37C22×C4×C13C2311yescharacteristic
38C2×C22⋊D13—28no—
39C2×C22⋊D13—28no—
40C2×C22⋊D13—28no—
41C22×Dic13C2312yes—
42C22×Dic13C2314yes—
43C2×D52—24no—
44C2×D52—22no—
45C2×C4×D13—24no—
46C2×C4×D13—28no—
47C13×C4⋊C4—22no—
48C13×C22⋊C4—24no—
49C42×C13D414yescomplemented
50C22⋊Dic13—28no—
51#6103—24no—
52#6103—28no—
53C4⋊Dic13—22no—
54#6101—28no—
55C4×Dic13D418yescomplemented
56#2397—131nomaximal, Sylow
57C23×C13—24no—
58C23×C13—22no—
59C23×C13—24no—
60C23×C13—22no—
61C23×C13#4114yes—
62C23×C13C2411yescharacteristic
63C22×D13—22no—
64C22×D13—24no—
65C22×D13—22no—
66C22×D13—24no—
67C22×D13#4114yes—
68D4×C13—28no—
69C2×C4×C13—22no—
70C2×C4×C13—22no—
71C2×C4×C13—24no—
72C2×C4×C13—22no—
73C2×C4×C13—48no—
74C2×C4×C13C2×D412yes—
75C2×C4×C13C2×D412yes—
76C2×C4×C13C2×D414yes—
77C2×C4×C13C2×D412yes—
78C22⋊D13—232no—
79C2×Dic13—24no—
80C2×Dic13—24no—
81C2×Dic13—24no—
82C2×Dic13—22no—
83C2×Dic13C2×D418yes—
84D52—28no—
85C4×D13—48no—
86C2×C4×D4—134no—
87C2×C4×D4—131no—
88C2×C4×D4D1311yescharacteristic, complemented
89#399—132no—
90#399—132no—
91#392—132no—
92#392—132no—
93#376—131no—
94C22×C13—28no—
95C22×C13—24no—
96C22×C13—44no—
97C22×C13—42no—
98C22×C13—42no—
99C22×C13C22×D412yes—
100C22×C13C22×D411yescharacteristic
101C22×C13C2×#4112yes—
102C22×C13C2×#4112yes—
103C2×D13—24no—
104C2×D13—28no—
105C2×D13—42no—
106C2×D13—44no—
107C2×D13—42no—
108C4×C13—22no—
109C4×C13—22no—
110C4×C13—42no—
111C4×C13#12714yes—
112Dic13—28no—
113Dic13—42no—
114C22×D4—134no—
115C22×D4—131no—
116C22×D4C2×D1311yescharacteristic
117C23×C4—132no—
118C23×C4C2×D1312yes—
119C4×D4—24no—
120C4×D4—2616no—
121C4×D4—264no—
122C2×C4⋊C4—134no—
123C2×C4⋊C4—131no—
124C2×C4⋊C4C2×D1311yescharacteristic
125C2×C22⋊C4—134no—
126C2×C22⋊C4—134no—
127C2×C22⋊C4—132no—
128C2×C22⋊C4C2×D1312yes—
129C2×C42—132no—
130C2×C42C2×D1311yescharacteristic
131#95—132no—
132#95—132no—
133C2×C13—44no—
134C2×C13#52511yescharacteristic
135C2×C13#52514yes—
136C2×C13#52511yescharacteristic
137C2×C13C2×#12711yescharacteristic
138D13—44no—
139C24—132no—
140C24C22×D1312yes—
141C2×D4—24no—
142C2×D4—22no—
143C2×D4—264no—
144C2×D4—268no—
145C2×D4—268no—
146C2×D4—268no—
147C2×D4—262no—
148C22×C4—28no—
149C22×C4—24no—
150C22×C4—134no—
151C22×C4—132no—
152C22×C4—268no—
153C22×C4—264no—
154C22×C4C22×D1312yes—
155C22×C4C22×D1311yescharacteristic
156C22×C4C22×D1311yescharacteristic
157C22×C4C22×D1311yescharacteristic
158C4⋊C4—22no—
159C4⋊C4—268no—
160C4⋊C4—262no—
161C22⋊C4—24no—
162C22⋊C4—268no—
163C22⋊C4—268no—
164C22⋊C4—264no—
165C42—138no—
166C42C22⋊D1314yescomplemented
167C13#239711yescharacteristic, complemented, Sylow
168C23—22no—
169C23—24no—
170C23—24no—
171C23—22no—
172C23—134no—
173C23—264no—
174C23—264no—
175C23—262no—
176C23—262no—
177C23#612714yes—
178C23C23×D1311yescharacteristic
179D4—28no—
180D4—268no—
181D4—2632no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—24no—
185C2×C4—22no—
186C2×C4—48no—
187C2×C4—138no—
188C2×C4—264no—
189C2×C4—264no—
190C2×C4—264no—
191C2×C4—262no—
192C2×C4—528no—
193C2×C4D4×D1314yes—
194C2×C4C2×C22⋊D1312yes—
195C2×C4C2×C22⋊D1312yes—
196C2×C4C2×C22⋊D1312yes—
197C22—24no—
198C22—28no—
199C22—44no—
200C22—42no—
201C22—42no—
202C22—268no—
203C22—264no—
204C22—522no—
205C22—524no—
206C22—522no—
207C22C2×#612712yes—
208C22C2×D4×D1312yes—
209C22#41×D1312yes—
210C22C22×C22⋊D1311yescharacteristic
211C4—22no—
212C4—22no—
213C4—42no—
214C4—268no—
215C4—522no—
216C4#8819414yes—
217C2—44no—
218C2—524no—
219C2#1171925214yes—
220C2#1171949611yescharacteristic
221C2C2×#8819411yescharacteristic
222C2#1171953311yescharacteristic
subgroupG/H
centerC22×C4C22×D13
commutator, socle, cosocleC23×C13C24
FrattiniC23C23×D13
FittingC2×C4×D4×C13C2
hypercenterC2×C4×D4D13
hypocenterC13#2397
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×C4×D4×C13C2semidirect
2. C2×C4×C22⋊D13C2semidirect
3. C2×C4×D52C2semidirect
4. #11718884C2semidirect
5. #11718653C2semidirect
6. #11718621C2semidirect
7. #11718610C2semidirect
8. #11718593C2semidirect
49. C42×C13D4semidirect
55. C4×Dic13D4semidirect
88. C2×C4×D4D13semidirect
166. C42C22⋊D13semidirect
167. C13#2397semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×C132
C2×C4×C22⋊D132
C2×C4×D522
#117188842
#117186532
#117186212
#117186102
#117185932
#239713