Finite Group Databasebeta

← #13119311

Subgroups — #13119311

Order 1664.

544 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 169 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×#88151C211yesmaximal, characteristic
2C2×C4⋊C4×D13C211yesmaximal, characteristic
3C13×#384C211yesmaximal, characteristic, complemented
4#11718650C214yesmaximal
5#11718645C214yesmaximal, complemented
6#11718637C211yesmaximal, characteristic, complemented
7#11718635C211yesmaximal, characteristic, complemented
8C4×#6103C211yesmaximal, characteristic
9#11718590C211yesmaximal, characteristic, complemented
10C22×C4×D13C2211yescharacteristic
11C22×C4×D13C2212yes—
12C22×Dic26C2211yescharacteristic
13C2×C13×C4⋊C4C2211yescharacteristic
14C2×C13×C4⋊C4C2211yescharacteristic
15C2×C13×C4⋊C4C2214yes—
16C2×C42×C13C2211yescharacteristic
17C2×#6103C2212yes—
18C2×#6103C2212yes—
19C2×C4⋊Dic13C2211yescharacteristic
20C2×C4⋊Dic13C2212yes—
21C2×#6101C2212yes—
22C2×#6101C2214yes—
23C2×C4×Dic13C2211yescharacteristic
24#88151—24no—
25C4⋊C4×D13—24no—
26#88071C2214yes—
27#88071C2212yes—
28#88071C2214yes—
29C23×D13C2311yescharacteristic
30C22×C4×C13C2312yes—
31C22×C4×C13C2312yes—
32C22×C4×C13C2312yes—
33C22×C4×C13C2311yescharacteristic
34C22×Dic13C2312yes—
35C22×Dic13C2312yes—
36C22×Dic13C2311yescharacteristic
37C22×Dic13C2312yes—
38C2×C4×D13—22no—
39C2×C4×D13—22no—
40C2×C4×D13—24no—
41C2×C4×D13—44no—
42C2×C4×D13D414yes—
43C2×Dic26—22no—
44C2×Dic26—22no—
45C2×Dic26—22no—
46C13×C4⋊C4—22no—
47C13×C4⋊C4—22no—
48C13×C4⋊C4—44no—
49C42×C13—22no—
50#6103—24no—
51#6103Q818yescomplemented
52C4⋊Dic13—22no—
53C4⋊Dic13—24no—
54#6101—24no—
55#6101—44no—
56C4×Dic13—22no—
57#2502—131nomaximal, Sylow
58C23×C13C2411yescharacteristic
59C22×D13—21no—
60C22×D13—21no—
61C22×D13—22no—
62C22×D13C2×D412yes—
63C22×D13C2×Q814yes—
64C2×C4×C13—22no—
65C2×C4×C13—22no—
66C2×C4×C13—22no—
67C2×C4×C13—22no—
68C2×C4×C13—24no—
69C2×C4×C13—24no—
70C2×C4×C13C2×D412yes—
71C2×C4×C13C2×Q814yes—
72C2×C4×C13#4112yes—
73C2×C4×C13#4112yes—
74C2×Dic13—22no—
75C2×Dic13—21no—
76C2×Dic13—21no—
77C2×Dic13—22no—
78C2×Dic13—22no—
79C2×Dic13—22no—
80C2×Dic13—22no—
81C2×Dic13—22no—
82C2×Dic13—24no—
83C2×Dic13C2×D412yes—
84C2×Dic13C2×Q814yes—
85C4×D13—28no—
86C4×D13—48no—
87Dic26—44no—
88C2×C22⋊Q8—131no—
89C22×C4⋊C4—131no—
90#398—134no—
91#391—131no—
92#391—131no—
93#385—134no—
94#384—131no—
95#384D1311yescharacteristic, complemented
96C4×C22⋊C4—131no—
97C22×C13C22×D411yescharacteristic
98C22×C13C22×Q812yes—
99C22×C13C2×#4111yescharacteristic
100C22×C13C2×#4111yescharacteristic
101C22×C13H(5,𝔽2)12yes—
102C2×D13—22no—
103C2×D13—22no—
104C2×D13—24no—
105C2×D13—24no—
106C2×D13C4⋊Q814yes—
107C4×C13—24no—
108C4×C13—42no—
109C4×C13—42no—
110C4×C13#12314yes—
111Dic13—22no—
112Dic13—24no—
113Dic13—42no—
114Dic13—42no—
115C22×Q8—131no—
116C23×C4—131no—
117C23×C4—132no—
118C22⋊Q8—264no—
119C2×C4⋊C4—132no—
120C2×C4⋊C4—131no—
121C2×C4⋊C4—132no—
122C2×C4⋊C4—134no—
123C2×C4⋊C4—264no—
124C2×C4⋊C4C2×D1311yescharacteristic
125C2×C4⋊C4C2×D1311yescharacteristic
126C2×C4⋊C4C2×D1314yes—
127C2×C22⋊C4—132no—
128C2×C22⋊C4—132no—
129C2×C42—131no—
130C2×C42C2×D1311yescharacteristic
131#95—132no—
132#95—134no—
133#95—134no—
134C2×C13C2×#12311yescharacteristic
135C2×C13C2×C4⋊Q811yescharacteristic
136C2×C13#53511yescharacteristic
137C2×C13#55412yes—
138C2×C13#55412yes—
139D13—24no—
140C24—131no—
141C2×Q8—262no—
142C2×Q8—262no—
143C2×Q8—262no—
144C22×C4—132no—
145C22×C4—131no—
146C22×C4—134no—
147C22×C4—132no—
148C22×C4—132no—
149C22×C4—264no—
150C22×C4—262no—
151C22×C4—262no—
152C22×C4—524no—
153C22×C4C22×D1312yes—
154C22×C4C22×D1312yes—
155C22×C4C22×D1312yes—
156C22×C4C22×D1311yescharacteristic
157C4⋊C4—22no—
158C4⋊C4—22no—
159C4⋊C4—44no—
160C4⋊C4—264no—
161C4⋊C4—264no—
162C4⋊C4—262no—
163C4⋊C4—524no—
164C22⋊C4—138no—
165C22⋊C4—264no—
166C42—22no—
167C42—262no—
168C13#250211yescharacteristic, complemented, Sylow
169C23—132no—
170C23—134no—
171C23—261no—
172C23—262no—
173C23—261no—
174C23C23×D1311yescharacteristic
175Q8—524no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—24no—
181C2×C4—24no—
182C2×C4—132no—
183C2×C4—134no—
184C2×C4—261no—
185C2×C4—262no—
186C2×C4—262no—
187C2×C4—261no—
188C2×C4—268no—
189C2×C4—262no—
190C2×C4—262no—
191C2×C4—262no—
192C2×C4—264no—
193C2×C4—262no—
194C2×C4—528no—
195C2×C4#612712yes—
196C2×C4D4×D1312yes—
197C2×C4Q8×D1314yes—
198C2×C4#613112yes—
199C22—134no—
200C22—264no—
201C22—262no—
202C22—264no—
203C22—262no—
204C22C2×#612711yescharacteristic
205C22C2×D4×D1311yescharacteristic
206C22#8825112yes—
207C22C2×Q8×D1312yes—
208C22C2×#613111yescharacteristic
209C4—24no—
210C4—42no—
211C4—42no—
212C4—264no—
213C4—262no—
214C4—522no—
215C4—522no—
216C4#8814814yes—
217C2—264no—
218C2C2×#8814811yescharacteristic
219C2#1171921612yes—
220C2#1171942011yescharacteristic
221C2D13×C4⋊Q811yescharacteristic
222C2#1171943512yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#384C2
prime radicalC23×D13C23
hypercenter#384D13
hypocenterC13#2502
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #384

Complements

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

NH ≅ G/Ntype
3. C13×#384C2semidirect
5. #11718645C2semidirect
6. #11718637C2semidirect
7. #11718635C2semidirect
9. #11718590C2semidirect
51. #6103Q8semidirect
95. #384D13semidirect
168. C13#2502semidirect

Maximal subgroups

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

subgroupindex
C2×#881512
C2×C4⋊C4×D132
C13×#3842
#117186502
#117186452
#117186372
#117186352
C4×#61032
#117185902
#250213