Finite Group Databasebeta

← #13119153

Subgroups — #13119153

Order 1664.

584 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 181 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
2C22×C4⋊Dic13C211yesmaximal, characteristic, complemented
3#11718881C212yesmaximal
4#11718873C212yesmaximal, complemented
5#11718873C211yesmaximal, characteristic, complemented
6#11718647C212yesmaximal, complemented
7#11718610C212yesmaximal, complemented
8#11718607C212yesmaximal, complemented
9#11718589C212yesmaximal, complemented
10C22×D4×C13C2211yescharacteristic
11C23×C4×C13C2211yescharacteristic
12C23×C4×C13C2211yescharacteristic
13C23×Dic13C2212yes—
14C4×D4×C13—24no—
15C2×C13×C4⋊C4C2211yescharacteristic
16C2×C13×C22⋊C4C2211yescharacteristic
17C2×C13×C22⋊C4C2211yescharacteristic
18C2×C42×C13C2211yescharacteristic
19C2×C22⋊Dic13C2212yes—
20C2×C22⋊Dic13C2214yes—
21C2×C4⋊Dic13—24no—
22C2×C4⋊Dic13C2212yes—
23C2×C4⋊Dic13C2212yes—
24C2×C4⋊Dic13C2212yes—
25C2×#6101C2214yes—
26#88071C2214yes—
27#88071C2214yes—
28#88071C2212yes—
29C24×C13C2311yescharacteristic
30C24×C13C2311yescharacteristic
31C2×D4×C13—22no—
32C2×D4×C13—22no—
33C2×D4×C13Q814yes—
34C22×C4×C13—24no—
35C22×C4×C13—22no—
36C22×C4×C13—24no—
37C22×C4×C13D414yes—
38C22×C4×C13C2311yescharacteristic
39C22×C4×C13C2311yescharacteristic
40C22×C4×C13C2311yescharacteristic
41C22×C4×C13C2311yescharacteristic
42C22×C4×C13C2311yescharacteristic
43C22×Dic13—24no—
44C22×Dic13—44no—
45C22×Dic13C2314yes—
46C22×Dic13C2314yes—
47C13×C4⋊C4—22no—
48C13×C22⋊C4—22no—
49C13×C22⋊C4—22no—
50C42×C13—22no—
51C22⋊Dic13—24no—
52C22⋊Dic13—44no—
53C4⋊Dic13—24no—
54C4⋊Dic13—24no—
55C4⋊Dic13—24no—
56#6101—44no—
57#2487—131nomaximal, Sylow
58C23×C13—22no—
59C23×C13—22no—
60C23×C13—21no—
61C23×C13—22no—
62C23×C13—21no—
63C23×C13—22no—
64C23×C13C2×D412yes—
65C23×C13C2×Q812yes—
66C23×C13C2×Q812yes—
67C23×C13#4112yes—
68C23×C13C2411yescharacteristic
69D4×C13—28no—
70C2×C4×C13—21no—
71C2×C4×C13—22no—
72C2×C4×C13—21no—
73C2×C4×C13—28no—
74C2×C4×C13—21no—
75C2×C4×C13—21no—
76C2×C4×C13—22no—
77C2×C4×C13—22no—
78C2×C4×C13—44no—
79C2×C4×C13C2×D412yes—
80C2×C4×C13C2×D412yes—
81C2×C4×C13C2×Q812yes—
82C2×C4×C13#4114yes—
83C2×Dic13—24no—
84C2×Dic13—24no—
85C2×Dic13—24no—
86C2×Dic13—24no—
87C2×Dic13—24no—
88C2×Dic13—24no—
89C2×Dic13—48no—
90C2×C4×D4D1311yescharacteristic
91C22×C4⋊C4—131no—
92#400—132no—
93#399—132no—
94#389—132no—
95#386—132no—
96#385—132no—
97#380—132no—
98#380—131no—
99C22×C13—22no—
100C22×C13—22no—
101C22×C13—24no—
102C22×C13—24no—
103C22×C13—22no—
104C22×C13—24no—
105C22×C13—41no—
106C22×C13—41no—
107C22×C13—42no—
108C22×C13C22⋊Q814yes—
109C22×C13C22×D411yescharacteristic
110C22×C13C22×Q811yescharacteristic
111C22×C13C2×#4111yescharacteristic
112C22×C13C2×#4112yes—
113C22×C13H(5,𝔽2)12yes—
114C4×C13—22no—
115C4×C13—22no—
116C4×C13—41no—
117C4×C13—41no—
118C4×C13#12314yes—
119Dic13—44no—
120Dic13—44no—
121C22×D4C2×D1311yescharacteristic
122C23×C4—132no—
123C23×C4C2×D1311yescharacteristic
124C23×C4C2×D1311yescharacteristic
125C4×D4—24no—
126C2×C4⋊C4—132no—
127C2×C4⋊C4—132no—
128C2×C4⋊C4—132no—
129C2×C4⋊C4—134no—
130C2×C4⋊C4—264no—
131C2×C4⋊C4C2×D1311yescharacteristic
132C2×C22⋊C4—132no—
133C2×C22⋊C4—134no—
134C2×C22⋊C4C2×D1311yescharacteristic
135C2×C22⋊C4C2×D1311yescharacteristic
136C2×C42C2×D1311yescharacteristic
137#95—134no—
138#95—132no—
139#95—134no—
140C2×C13—24no—
141C2×C13—42no—
142C2×C13C2×C22⋊Q811yescharacteristic
143C2×C13C2×#12311yescharacteristic
144C2×C13#53511yescharacteristic
145C2×C13#55312yes—
146C2×C13#55412yes—
147C24C22×D1311yescharacteristic
148C24C22×D1311yescharacteristic
149C2×D4—22no—
150C2×D4—22no—
151C2×D4Dic2614yes—
152C22×C4—24no—
153C22×C4—24no—
154C22×C4—22no—
155C22×C4—134no—
156C22×C4—134no—
157C22×C4—264no—
158C22×C4—524no—
159C22×C4C22⋊D1314yes—
160C22×C4C22×D1311yescharacteristic
161C22×C4C22×D1311yescharacteristic
162C22×C4C22×D1311yescharacteristic
163C22×C4C22×D1311yescharacteristic
164C22×C4C22×D1311yescharacteristic
165C4⋊C4—22no—
166C4⋊C4—264no—
167C4⋊C4—264no—
168C4⋊C4—264no—
169C4⋊C4—524no—
170C22⋊C4—22no—
171C22⋊C4—22no—
172C22⋊C4—264no—
173C22⋊C4—524no—
174C42—22no—
175C13#248711yescharacteristic, complemented, Sylow
176C23—22no—
177C23—22no—
178C23—21no—
179C23—22no—
180C23—22no—
181C23—21no—
182C23C2×Dic2612yes—
183C23C2×Dic2612yes—
184C23#612712yes—
185C23C2×C22⋊D1312yes—
186C23C23×D1311yescharacteristic
187D4—28no—
188C2×C4—21no—
189C2×C4—22no—
190C2×C4—21no—
191C2×C4—28no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—44no—
197C2×C4—264no—
198C2×C4—264no—
199C2×C4—264no—
200C2×C4—264no—
201C2×C4—264no—
202C2×C4—264no—
203C2×C4—528no—
204C2×C4C2×Dic2612yes—
205C2×C4#612914yes—
206C2×C4C2×C22⋊D1312yes—
207C2×C4C2×C22⋊D1312yes—
208C22—22no—
209C22—24no—
210C22—24no—
211C22—22no—
212C22—22no—
213C22—24no—
214C22—41no—
215C22—42no—
216C22—41no—
217C22#8817814yes—
218C22C22×Dic2611yescharacteristic
219C22C2×#612711yescharacteristic
220C22C2×#612912yes—
221C22#8825612yes—
222C22C22×C22⋊D1311yescharacteristic
223C4—22no—
224C4—22no—
225C4—41no—
226C4—41no—
227C4—524no—
228C4—524no—
229C4#8818914yes—
230C2—24no—
231C2—42no—
232C2#1171924812yes—
233C2#1171927012yes—
234C2C2×#8817811yescharacteristic
235C2C2×#8818911yescharacteristic
236C2#1171953511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC2×C4×D4×C13C2
prime radicalC22×D4×C13C22
hypercenterC2×C4×D4D13
hypocenterC13#2487
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊Dic13C2semidirect
4. #11718873C2semidirect
5. #11718873C2semidirect
6. #11718647C2semidirect
7. #11718610C2semidirect
8. #11718607C2semidirect
9. #11718589C2semidirect
175. C13#2487semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×C132
C22×C4⋊Dic132
#117188812
#117188732
#117186472
#117186102
#117186072
#117185892
#248713