Finite Group Databasebeta

← #13119484

Subgroups — #13119484

Order 1664.

412 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 129 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
1C13×#385C211yesmaximal, characteristic
2C4×C22⋊Dic13C212yesmaximal
3#11718642C212yesmaximal, complemented
4#11718639C212yesmaximal, complemented
5#11718614C211yesmaximal, characteristic
6#11718613C212yesmaximal
7#11718610C211yesmaximal, characteristic
8#11718316C212yesmaximal, complemented
9#11718311C212yesmaximal, complemented
10C23×C4×C13C2211yescharacteristic
11C2×C13×C4⋊C4C2212yes—
12C2×C13×C22⋊C4C2211yescharacteristic
13C2×C13×C22⋊C4C2211yescharacteristic
14C2×C22⋊Dic13C2212yes—
15C2×C22⋊Dic13C2212yes—
16C2×C4⋊Dic13C2211yescharacteristic
17C2×C4⋊Dic13C2211yescharacteristic
18C2×#6101C2212yes—
19C2×#6101C2212yes—
20C2×C4×Dic13C2212yes—
21C2×C4×Dic13C2212yes—
22C13×#95C2212yes—
23#88071C2211yescharacteristic
24#88071C2212yes—
25#88071C2212yes—
26#88071C2212yes—
27#88071C2212yes—
28#88071C2212yes—
29#88071C2211yescharacteristic
30#88071C2212yes—
31C24×C13C2311yescharacteristic
32C22×C4×C13—24no—
33C22×C4×C13—41no—
34C22×C4×C13C2312yes—
35C22×C4×C13C2311yescharacteristic
36C22×C4×C13C2311yescharacteristic
37C22×C4×C13C2312yes—
38C22×Dic13C2312yes—
39C22×Dic13C2312yes—
40C22×Dic13C2312yes—
41C22×Dic13C2312yes—
42C13×C4⋊C4—24no—
43C13×C22⋊C4—22no—
44C13×C22⋊C4—41no—
45C22⋊Dic13—24no—
46C22⋊Dic13—24no—
47C4⋊Dic13—41no—
48C4⋊Dic13—41no—
49#6101—24no—
50#6101—24no—
51C4×Dic13—24no—
52C4×Dic13—42no—
53#2517—131nomaximal, Sylow
54C23×C13—22no—
55C23×C13—22no—
56C23×C13—21no—
57C23×C13—21no—
58C23×C13#4112yes—
59C23×C13C2411yescharacteristic
60C2×C4×C13—22no—
61C2×C4×C13—22no—
62C2×C4×C13—22no—
63C2×C4×C13—22no—
64C2×C4×C13—22no—
65C2×C4×C13—22no—
66C2×C4×C13—22no—
67C2×C4×C13—21no—
68C2×C4×C13—21no—
69C2×C4×C13—44no—
70C2×C4×C13#4114yes—
71C2×Dic13—22no—
72C2×Dic13—22no—
73C2×Dic13—22no—
74C2×Dic13—22no—
75C2×Dic13—22no—
76C2×Dic13—22no—
77C2×Dic13—22no—
78C2×Dic13—22no—
79C2×Dic13—22no—
80C2×Dic13—22no—
81C2×Dic13—22no—
82C2×Dic13#4114yes—
83#399—131no—
84#397—132no—
85#397—131no—
86#387—132no—
87#387—132no—
88#387—132no—
89#385D1311yescharacteristic
90#382—132no—
91C4×C22⋊C4—132no—
92C22×C13—24no—
93C22×C13—22no—
94C22×C13—41no—
95C22×C13—42no—
96C22×C13—41no—
97C22×C13C2×#4111yescharacteristic
98C22×C13C2×#4112yes—
99C22×C13C2×#4112yes—
100C22×C13H(5,𝔽2)11yescharacteristic
101C22×C132−1+411yescharacteristic
102C4×C13—24no—
103C4×C13—42no—
104C4×C13—41no—
105C4×C13—41no—
106Dic13—24no—
107Dic13—42no—
108Dic13—42no—
109Dic13—42no—
110C23×C4C2×D1311yescharacteristic
111C2×C4⋊C4—132no—
112C2×C4⋊C4—132no—
113C2×C4⋊C4—131no—
114C2×C4⋊C4—131no—
115C2×C4⋊C4C2×D1312yes—
116C2×C22⋊C4—132no—
117C2×C22⋊C4—132no—
118C2×C22⋊C4C2×D1311yescharacteristic
119C2×C22⋊C4C2×D1311yescharacteristic
120C2×C42—132no—
121C2×C42—132no—
122#95—132no—
123#95—132no—
124#95—131no—
125#95—132no—
126#95—132no—
127#95—132no—
128#95—132no—
129#95—131no—
130#95C2×D1312yes—
131C2×C13—42no—
132C2×C13#52912yes—
133C2×C13#53911yescharacteristic
134C2×C13#55111yescharacteristic
135C2×C13#55212yes—
136C2×C13#55911yescharacteristic
137C24C22×D1311yescharacteristic
138C22×C4—24no—
139C22×C4—41no—
140C22×C4—132no—
141C22×C4—132no—
142C22×C4—132no—
143C22×C4—132no—
144C22×C4C22×D1312yes—
145C22×C4C22×D1311yescharacteristic
146C22×C4C22×D1311yescharacteristic
147C22×C4C22×D1312yes—
148C4⋊C4—24no—
149C4⋊C4—264no—
150C4⋊C4—264no—
151C4⋊C4—521no—
152C4⋊C4—521no—
153C22⋊C4—22no—
154C22⋊C4—41no—
155C22⋊C4—264no—
156C22⋊C4—264no—
157C42—264no—
158C42—522no—
159C13#251711yescharacteristic, complemented, Sylow
160C23—22no—
161C23—21no—
162C23—21no—
163C23—22no—
164C23#612712yes—
165C23C23×D1311yescharacteristic
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—44no—
176C2×C4—134no—
177C2×C4—262no—
178C2×C4—262no—
179C2×C4—262no—
180C2×C4—262no—
181C2×C4—262no—
182C2×C4—262no—
183C2×C4—262no—
184C2×C4—262no—
185C2×C4—262no—
186C2×C4—262no—
187C2×C4—262no—
188C2×C4#612914yes—
189C22—22no—
190C22—24no—
191C22—41no—
192C22—42no—
193C22—41no—
194C22C2×#612711yescharacteristic
195C22C2×#612912yes—
196C22#8825111yescharacteristic
197C22#8825411yescharacteristic
198C22#41×D1312yes—
199C4—24no—
200C4—42no—
201C4—41no—
202C4—41no—
203C4—264no—
204C4—522no—
205C4—522no—
206C4—522no—
207C2—42no—
208C2#1171922011yescharacteristic
209C2#1171924312yes—
210C2#1171929211yescharacteristic
211C2#1171934412yes—
212C2#1171936911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#385C2
prime radicalC24×C13C23
hypercenter#385D13
hypocenterC13#2517
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
3. #11718642C2semidirect
4. #11718639C2semidirect
8. #11718316C2semidirect
9. #11718311C2semidirect
159. C13#2517semidirect

Maximal subgroups

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

subgroupindex
C13×#3852
C4×C22⋊Dic132
#117186422
#117186392
#117186142
#117186132
#117186102
#117183162
#117183112
#251713