Finite Group Databasebeta

← #13120626

Subgroups — #13120626

Order 1664.

548 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 149 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×C13×#121C211yesmaximal, characteristic
2C2×#88180C211yesmaximal, characteristic, complemented
3#11718883C214yesmaximal, complemented
4#11718882C212yesmaximal, complemented
5#11718873C211yesmaximal, characteristic, complemented
6#11718634C212yesmaximal, complemented
7#11718614C212yesmaximal, complemented
8#11718610C212yesmaximal, complemented
9C22×D4×C13C2211yescharacteristic
10C22×D4×C13C2212yes—
11C23×C4×C13C2211yescharacteristic
12C13×#121—24no—
13C2×C13×C4⋊C4C2211yescharacteristic
14C2×C13×C22⋊C4C2212yes—
15C2×C22⋊Dic13C2212yes—
16C2×C22⋊Dic13C2214yes—
17C2×C22⋊Dic13C2214yes—
18C2×C22⋊Dic13C2212yes—
19#88180—24no—
20C2×C4⋊Dic13C2211yescharacteristic
21C2×C4⋊Dic13C2211yescharacteristic
22C2×C4⋊Dic13C2212yes—
23C2×#6101C2214yes—
24C2×C4×Dic13C2212yes—
25#88071C2212yes—
26#88071C2214yes—
27C24×C13C2312yes—
28C24×C13C2311yescharacteristic
29C2×D4×C13—24no—
30C2×D4×C13—22no—
31C2×D4×C13—24no—
32C2×D4×C13—44no—
33C22×C4×C13—24no—
34C22×C4×C13D414yes—
35C22×C4×C13C2312yes—
36C22×C4×C13C2311yescharacteristic
37C22×C4×C13C2311yescharacteristic
38C22×Dic13C2312yes—
39C22×Dic13C2314yes—
40C22×Dic13C2312yes—
41C13×C4⋊C4—22no—
42C13×C22⋊C4—24no—
43C22⋊Dic13—24no—
44C22⋊Dic13—44no—
45C22⋊Dic13—42no—
46C22⋊Dic13—44no—
47C4⋊Dic13—22no—
48C4⋊Dic13—22no—
49C4⋊Dic13—24no—
50#6101—44no—
51C4×Dic13—24no—
52#2624—131nomaximal, Sylow
53C23×C13—22no—
54C23×C13—21no—
55C23×C13—22no—
56C23×C13—21no—
57C23×C13—22no—
58C23×C13—24no—
59C23×C13—22no—
60C23×C13—24no—
61C23×C13—22no—
62C23×C13C2×D412yes—
63C23×C13C2411yescharacteristic
64D4×C13—48no—
65D4×C13—44no—
66C2×C4×C13—22no—
67C2×C4×C13—28no—
68C2×C4×C13—22no—
69C2×C4×C13—24no—
70C2×C4×C13C2×D412yes—
71C2×C4×C13C2×D412yes—
72C2×C4×C13#4114yes—
73C2×Dic13—22no—
74C2×Dic13—22no—
75C2×Dic13—24no—
76C2×Dic13—22no—
77C2×Dic13—24no—
78C2×Dic13—22no—
79C2×Dic13—22no—
80C2×Dic13—24no—
81C2×Dic13—22no—
82C2×#121D1311yescharacteristic
83C2×#117—131no—
84#399—132no—
85#397—132no—
86#394—134no—
87#390—132no—
88#389—132no—
89#380—131no—
90C22×C13—22no—
91C22×C13—22no—
92C22×C13—22no—
93C22×C13—42no—
94C22×C13—42no—
95C22×C13—42no—
96C22×C13—42no—
97C22×C13—42no—
98C22×C13—44no—
99C22×C13—44no—
100C22×C13C22×D411yescharacteristic
101C22×C13C2×#4112yes—
102C22×C13H(5,𝔽2)12yes—
103C22×C13H(5,𝔽2)11yescharacteristic
104C22×C132−1+411yescharacteristic
105C4×C13—22no—
106C4×C13—42no—
107C4×C13#12314yes—
108Dic13—42no—
109Dic13—42no—
110Dic13—44no—
111C22×D4C2×D1311yescharacteristic
112C22×D4C2×D1312yes—
113C23×C4C2×D1311yescharacteristic
114#121—24no—
115#117—264no—
116C2×C4⋊C4—131no—
117C2×C4⋊C4—131no—
118C2×C4⋊C4—132no—
119C2×C4⋊C4—134no—
120C2×C4⋊C4C2×D1311yescharacteristic
121C2×C22⋊C4—132no—
122C2×C22⋊C4—132no—
123C2×C22⋊C4—134no—
124C2×C22⋊C4—134no—
125C2×C22⋊C4C2×D1312yes—
126C2×C42—132no—
127#95—132no—
128#95—134no—
129C2×C13—42no—
130C2×C13—82no—
131C2×C13C2×#12311yescharacteristic
132C2×C13#53511yescharacteristic
133C2×C13#53711yescharacteristic
134C2×C13#54012yes—
135C2×C13#54212yes—
136C24C22×D1312yes—
137C24C22×D1311yescharacteristic
138C2×D4—24no—
139C2×D4—24no—
140C2×D4—22no—
141C2×D4—44no—
142C22×C4—24no—
143C22×C4—132no—
144C22×C4—134no—
145C22×C4—132no—
146C22×C4C22⋊D1314yes—
147C22×C4C22×D1312yes—
148C22×C4C22×D1311yescharacteristic
149C22×C4C22×D1311yescharacteristic
150C4⋊C4—22no—
151C4⋊C4—264no—
152C4⋊C4—262no—
153C4⋊C4—262no—
154C4⋊C4—524no—
155C22⋊C4—24no—
156C22⋊C4—264no—
157C22⋊C4—524no—
158C22⋊C4—522no—
159C22⋊C4—524no—
160C42—264no—
161C13#262411yescharacteristic, complemented, Sylow
162C23—22no—
163C23—22no—
164C23—21no—
165C23—21no—
166C23—24no—
167C23—24no—
168C23—22no—
169C23—22no—
170C23—22no—
171C23C2×C22⋊D1312yes—
172C23C23×D1311yescharacteristic
173D4—48no—
174D4—44no—
175C2×C4—22no—
176C2×C4—28no—
177C2×C4—24no—
178C2×C4—22no—
179C2×C4—264no—
180C2×C4—262no—
181C2×C4—264no—
182C2×C4—262no—
183C2×C4—262no—
184C2×C4—264no—
185C2×C4—262no—
186C2×C4—262no—
187C2×C4—262no—
188C2×C4#612914yes—
189C2×C4C2×C22⋊D1312yes—
190C2×C4C2×C22⋊D1312yes—
191C22—22no—
192C22—22no—
193C22—22no—
194C22—42no—
195C22—42no—
196C22—42no—
197C22—42no—
198C22—42no—
199C22—44no—
200C22—44no—
201C22C2×#612912yes—
202C22#8825112yes—
203C22#8825611yescharacteristic
204C22#8825711yescharacteristic
205C22C22×C22⋊D1311yescharacteristic
206C4—22no—
207C4—42no—
208C4—522no—
209C4—522no—
210C4—524no—
211C4#8818914yes—
212C2—42no—
213C2—82no—
214C2#1171930812yes—
215C2#1171932412yes—
216C2C2×#8818911yescharacteristic
217C2#1171951011yescharacteristic
218C2#1171953811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
Fitting, prime radicalC2×C13×#121C2
hypercenterC2×#121D13
hypocenterC13#2624
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
2. C2×#88180C2semidirect
3. #11718883C2semidirect
4. #11718882C2semidirect
5. #11718873C2semidirect
6. #11718634C2semidirect
7. #11718614C2semidirect
8. #11718610C2semidirect
161. C13#2624semidirect

Maximal subgroups

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

subgroupindex
C2×C13×#1212
C2×#881802
#117188832
#117188822
#117188732
#117186342
#117186142
#117186102
#262413