Finite Group Databasebeta

← #13120627

Subgroups — #13120627

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×#88184C211yesmaximal, characteristic
2C2×#88180C211yesmaximal, characteristic, complemented
3C13×#380C211yesmaximal, characteristic, complemented
4#11718649C212yesmaximal, complemented
5#11718646C212yesmaximal, complemented
6#11718622C214yesmaximal, complemented
7#11718338C212yesmaximal, complemented
8#11718335C212yesmaximal, complemented
9C23×C4×C13C2211yescharacteristic
10C22×C22⋊D13C2212yes—
11C22×D52C2211yescharacteristic
12C2×C13×C4⋊C4C2212yes—
13C2×C13×C22⋊C4C2212yes—
14C2×C22⋊Dic13C2212yes—
15#88184—24no—
16C2×#6103C2212yes—
17C2×#6103C2214yes—
18C2×#6103C2214yes—
19#88180—24no—
20C2×C4⋊Dic13C2211yescharacteristic
21C2×C4⋊Dic13C2211yescharacteristic
22C2×C4⋊Dic13C2211yescharacteristic
23C2×C4⋊Dic13C2214yes—
24C2×C4×Dic13C2212yes—
25C13×#95C2212yes—
26#88071C2214yes—
27C24×C13C2311yescharacteristic
28C23×D13C2312yes—
29C22×C4×C13—24no—
30C22×C4×C13D414yes—
31C22×C4×C13C2314yes—
32C22×C4×C13C2311yescharacteristic
33C22×C4×C13C2311yescharacteristic
34C2×C22⋊D13—24no—
35C2×C22⋊D13—44no—
36C22×Dic13C2312yes—
37C22×Dic13C2312yes—
38C22×Dic13C2312yes—
39C2×D52—22no—
40C2×D52—24no—
41C13×C4⋊C4—24no—
42C13×C22⋊C4—42no—
43C22⋊Dic13—24no—
44#6103—24no—
45#6103—44no—
46#6103—44no—
47C4⋊Dic13—22no—
48C4⋊Dic13—22no—
49C4⋊Dic13—22no—
50C4⋊Dic13—44no—
51C4×Dic13—24no—
52#2624—131nomaximal, Sylow
53C23×C13—22no—
54C23×C13—21no—
55C23×C13—22no—
56C23×C13—21no—
57C23×C13C2×D412yes—
58C23×C13C2411yescharacteristic
59C22×D13—22no—
60C22×D13—24no—
61C22×D13—22no—
62C22×D13—24no—
63C22×D13—22no—
64C2×C4×C13—22no—
65C2×C4×C13—28no—
66C2×C4×C13—24no—
67C2×C4×C13—24no—
68C2×C4×C13—24no—
69C2×C4×C13C2×D412yes—
70C2×C4×C13C2×D412yes—
71C2×C4×C13#4114yes—
72C22⋊D13—48no—
73C2×Dic13—22no—
74C2×Dic13—22no—
75C2×Dic13—22no—
76C2×Dic13—22no—
77C2×Dic13—24no—
78C2×Dic13—22no—
79C2×Dic13—22no—
80C2×Dic13—22no—
81D52—44no—
82C2×#121—131no—
83C2×#117—131no—
84#399—132no—
85#397—132no—
86#394—134no—
87#390—132no—
88#389—132no—
89#380D1311yescharacteristic, complemented
90C22×C13—22no—
91C22×C13—22no—
92C22×C13—22no—
93C22×C13—42no—
94C22×C13—42no—
95C22×C13C22×D411yescharacteristic
96C22×C13C2×#4112yes—
97C22×C13H(5,𝔽2)11yescharacteristic
98C22×C13H(5,𝔽2)12yes—
99C22×C132−1+411yescharacteristic
100C2×D13—42no—
101C2×D13—42no—
102C2×D13—42no—
103C2×D13—44no—
104C2×D13—44no—
105C4×C13—22no—
106C4×C13—44no—
107C4×C13#12314yes—
108Dic13—42no—
109Dic13—42no—
110Dic13—42no—
111C22×D4—132no—
112C22×D4—131no—
113C23×C4C2×D1311yescharacteristic
114#121—264no—
115#117—264no—
116C2×C4⋊C4—131no—
117C2×C4⋊C4—131no—
118C2×C4⋊C4—131no—
119C2×C4⋊C4—134no—
120C2×C4⋊C4C2×D1312yes—
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—134no—
128#95C2×D1312yes—
129C2×C13—42no—
130C2×C13C2×#12311yescharacteristic
131C2×C13#53511yescharacteristic
132C2×C13#53711yescharacteristic
133C2×C13#54012yes—
134C2×C13#54212yes—
135D13—82no—
136C24—132no—
137C24C22×D1311yescharacteristic
138C2×D4—264no—
139C2×D4—262no—
140C2×D4—264no—
141C2×D4—524no—
142C22×C4—24no—
143C22×C4—132no—
144C22×C4—132no—
145C22×C4—132no—
146C22×C4D5214yes—
147C22×C4C22×D1314yes—
148C22×C4C22×D1311yescharacteristic
149C22×C4C22×D1311yescharacteristic
150C4⋊C4—24no—
151C4⋊C4—262no—
152C4⋊C4—262no—
153C4⋊C4—262no—
154C4⋊C4—524no—
155C22⋊C4—42no—
156C22⋊C4—264no—
157C22⋊C4—264no—
158C22⋊C4—524no—
159C22⋊C4—524no—
160C42—264no—
161C13#262411yescharacteristic, complemented, Sylow
162C23—22no—
163C23—21no—
164C23—21no—
165C23—22no—
166C23—262no—
167C23—264no—
168C23—262no—
169C23—262no—
170C23—264no—
171C23C2×D5212yes—
172C23C23×D1311yescharacteristic
173D4—528no—
174D4—524no—
175C2×C4—22no—
176C2×C4—28no—
177C2×C4—24no—
178C2×C4—24no—
179C2×C4—24no—
180C2×C4—262no—
181C2×C4—262no—
182C2×C4—262no—
183C2×C4—262no—
184C2×C4—262no—
185C2×C4—262no—
186C2×C4—262no—
187C2×C4—264no—
188C2×C4C2×D5212yes—
189C2×C4C2×D5212yes—
190C2×C4#612914yes—
191C22—22no—
192C22—22no—
193C22—22no—
194C22—42no—
195C22—42no—
196C22—522no—
197C22—522no—
198C22—522no—
199C22—524no—
200C22—524no—
201C22C22×D5211yescharacteristic
202C22C2×#612912yes—
203C22#8825111yescharacteristic
204C22#8825411yescharacteristic
205C22#8825612yes—
206C4—22no—
207C4—44no—
208C4—522no—
209C4—522no—
210C4—522no—
211C4#8814014yes—
212C2—42no—
213C2—1042no—
214C2C2×#8814011yescharacteristic
215C2#1171921511yescharacteristic
216C2#1171923011yescharacteristic
217C2#1171932412yes—
218C2#1171934812yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#380C2
prime radicalC2×#88184C2
hypercenter#380D13
hypocenterC13#2624
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
2. C2×#88180C2semidirect
3. C13×#380C2semidirect
4. #11718649C2semidirect
5. #11718646C2semidirect
6. #11718622C2semidirect
7. #11718338C2semidirect
8. #11718335C2semidirect
89. #380D13semidirect
161. C13#2624semidirect

Maximal subgroups

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

subgroupindex
C2×#881842
C2×#881802
C13×#3802
#117186492
#117186462
#117186222
#117183382
#117183352
#262413