Finite Group Databasebeta

← #13120660

Subgroups — #13120660

Order 1664.

488 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 157 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×#88126C211yesmaximal, characteristic
2C2×#88123C211yesmaximal, characteristic, complemented
3C13×#382C211yesmaximal, characteristic, complemented
4#11718648C212yesmaximal
5#11718646C212yesmaximal, complemented
6#11718338C212yesmaximal
7#11718334C212yesmaximal
8#11718320C212yesmaximal, complemented
9#11718317C212yesmaximal, complemented
10C22×C4×D13C2211yescharacteristic
11C22×Dic26C2212yes—
12C2×C13×C4⋊C4C2212yes—
13C2×C42×C13C2211yescharacteristic
14C2×#6103C2211yescharacteristic
15C2×#6103C2211yescharacteristic
16C2×#6103C2214yes—
17C2×C4⋊Dic13C2212yes—
18C2×C4⋊Dic13C2212yes—
19C2×C4⋊Dic13C2214yes—
20C2×#6101C2211yescharacteristic
21C2×#6101C2211yescharacteristic
22C2×C4×Dic13C2211yescharacteristic
23#88126—24no—
24#88123—24no—
25C13×#95C2212yes—
26C13×#95C2212yes—
27#88071C2214yes—
28#88071C2214yes—
29C23×D13C2311yescharacteristic
30C22×C4×C13C2314yes—
31C22×C4×C13C2311yescharacteristic
32C22×C4×C13C2311yescharacteristic
33C22×C4×C13C2311yescharacteristic
34C22×Dic13C2311yescharacteristic
35C22×Dic13C2314yes—
36C22×Dic13C2311yescharacteristic
37C22×Dic13C2311yescharacteristic
38C2×C4×D13—22no—
39C2×C4×D13—22no—
40C2×C4×D13Q814yescomplemented
41C2×Dic26—24no—
42C2×Dic26—44no—
43C13×C4⋊C4—24no—
44C42×C13D414yes—
45#6103—22no—
46#6103—22no—
47#6103—44no—
48C4⋊Dic13—24no—
49C4⋊Dic13—24no—
50C4⋊Dic13—44no—
51#6101—22no—
52#6101—22no—
53C4×Dic13—22no—
54#2628—131nomaximal, Sylow
55C23×C13C2411yescharacteristic
56C22×D13—21no—
57C22×D13—21no—
58C22×D13—22no—
59C22×D13—22no—
60C22×D13C2×Q812yes—
61C2×C4×C13—22no—
62C2×C4×C13—22no—
63C2×C4×C13—24no—
64C2×C4×C13—24no—
65C2×C4×C13—24no—
66C2×C4×C13C2×D412yes—
67C2×C4×C13C2×D412yes—
68C2×C4×C13C2×D412yes—
69C2×C4×C13C2×Q812yes—
70C2×C4×C13#4112yes—
71C2×Dic13—21no—
72C2×Dic13—21no—
73C2×Dic13—21no—
74C2×Dic13—21no—
75C2×Dic13—24no—
76C2×Dic13—22no—
77C2×Dic13—24no—
78C2×Dic13—24no—
79C2×Dic13—22no—
80C2×Dic13C2×Q812yes—
81C4×D13—28no—
82Dic26—48no—
83C2×C4⋊Q8—131no—
84C2×#117—131no—
85#400—132no—
86#399—132no—
87#395—132no—
88#393—132no—
89#389—132no—
90#382D1311yescharacteristic, complemented
91#380—132no—
92C22×C13C22×D411yescharacteristic
93C22×C13C22×Q811yescharacteristic
94C22×C13C2×#4111yescharacteristic
95C22×C13H(5,𝔽2)12yes—
96C22×C132−1+412yes—
97C2×D13—22no—
98C2×D13—24no—
99C2×D13—41no—
100C2×D13—41no—
101C2×D13—42no—
102C4×C13—22no—
103C4×C13—22no—
104C4×C13—44no—
105C4×C13C22⋊Q814yes—
106Dic13—22no—
107Dic13—44no—
108Dic13—41no—
109Dic13—41no—
110C22×Q8—132no—
111C23×C4—131no—
112C4⋊Q8—264no—
113#117—264no—
114C2×C4⋊C4—131no—
115C2×C4⋊C4—131no—
116C2×C4⋊C4—132no—
117C2×C4⋊C4—132no—
118C2×C4⋊C4—134no—
119C2×C4⋊C4C2×D1312yes—
120C2×C22⋊C4—131no—
121C2×C22⋊C4—131no—
122C2×C22⋊C4—134no—
123C2×C42—131no—
124C2×C42C2×D1311yescharacteristic
125#95—134no—
126#95—134no—
127#95C2×D1312yes—
128#95C2×D1312yes—
129C2×C13C2×C22⋊Q811yescharacteristic
130C2×C13#53511yescharacteristic
131C2×C13#53611yescharacteristic
132C2×C13#54212yes—
133C2×C13#54412yes—
134D13—42no—
135C24—131no—
136C2×Q8—264no—
137C2×Q8—524no—
138C22×C4—131no—
139C22×C4—134no—
140C22×C4—131no—
141C22×C4—134no—
142C22×C4—131no—
143C22×C4—262no—
144C22×C4—262no—
145C22×C4C22×D1314yes—
146C22×C4C22×D1311yescharacteristic
147C22×C4C22×D1311yescharacteristic
148C22×C4C22×D1311yescharacteristic
149C4⋊C4—24no—
150C4⋊C4—262no—
151C4⋊C4—262no—
152C4⋊C4—264no—
153C4⋊C4—264no—
154C4⋊C4—524no—
155C22⋊C4—262no—
156C22⋊C4—262no—
157C22⋊C4—524no—
158C42—262no—
159C42D5214yes—
160C13#262811yescharacteristic, complemented, Sylow
161C23—132no—
162C23—261no—
163C23—261no—
164C23—262no—
165C23—262no—
166C23C23×D1311yescharacteristic
167Q8—528no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—24no—
171C2×C4—24no—
172C2×C4—24no—
173C2×C4—132no—
174C2×C4—261no—
175C2×C4—261no—
176C2×C4—268no—
177C2×C4—261no—
178C2×C4—261no—
179C2×C4—264no—
180C2×C4—264no—
181C2×C4—262no—
182C2×C4—264no—
183C2×C4—262no—
184C2×C4C2×D5212yes—
185C2×C4C2×D5212yes—
186C2×C4C2×D5212yes—
187C2×C4#612912yes—
188C2×C4Q8×D1312yes—
189C22—262no—
190C22—264no—
191C22—521no—
192C22—521no—
193C22—522no—
194C22C22×D5211yescharacteristic
195C22C2×#612911yescharacteristic
196C22C2×Q8×D1311yescharacteristic
197C22#8825612yes—
198C22#8825712yes—
199C4—22no—
200C4—22no—
201C4—44no—
202C4—262no—
203C4—521no—
204C4—524no—
205C4—521no—
206C4#8815114yes—
207C2—522no—
208C2C2×#8815111yescharacteristic
209C2#1171923011yescharacteristic
210C2#1171923111yescharacteristic
211C2#1171938712yes—
212C2#1171939412yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#382C2
prime radicalC23×D13C23
hypercenter#382D13
hypocenterC13#2628
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
2. C2×#88123C2semidirect
3. C13×#382C2semidirect
5. #11718646C2semidirect
8. #11718320C2semidirect
9. #11718317C2semidirect
40. C2×C4×D13Q8semidirect
90. #382D13semidirect
160. C13#2628semidirect

Maximal subgroups

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

subgroupindex
C2×#881262
C2×#881232
C13×#3822
#117186482
#117186462
#117183382
#117183342
#117183202
#117183172
#262813