Finite Group Databasebeta

← #13120607

Subgroups — #13120607

Order 1664.

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

normal subgroups only

This group has 528 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×#88200C211yesmaximal, characteristic
2C2×#88198C211yesmaximal, characteristic, complemented
3C2×#88151C211yesmaximal, characteristic
4C2×#88126C211yesmaximal, characteristic
5C13×#391C211yesmaximal, characteristic, complemented
6#11718638C211yesmaximal, characteristic, complemented
7#11718590C211yesmaximal, characteristic, complemented
8#11718336C214yesmaximal
9#11718318C214yesmaximal, complemented
10C22×Q8×C13C2211yescharacteristic
11C22×C4×D13C2211yescharacteristic
12C22×Dic26C2211yescharacteristic
13C2×C13×C4⋊C4C2211yescharacteristic
14C2×C42×C13C2211yescharacteristic
15#88200—24no—
16#88198—24no—
17C2×#6103C2212yes—
18C2×#6103C2212yes—
19C2×#6103C2212yes—
20C2×C4⋊Dic13C2212yes—
21C2×C4⋊Dic13C2211yescharacteristic
22C2×#6101C2212yes—
23C2×#6101C2214yes—
24C2×#6101C2212yes—
25C2×C4×Dic13C2211yescharacteristic
26#88151—24no—
27#88126—24no—
28C13×#95C2214yes—
29#88071C2214yes—
30#88071C2214yes—
31C23×D13C2311yescharacteristic
32C2×Q8×C13—22no—
33C2×Q8×C13—22no—
34C2×Q8×C13—22no—
35C22×C4×C13C2312yes—
36C22×C4×C13C2312yes—
37C22×C4×C13C2312yes—
38C22×C4×C13C2311yescharacteristic
39C22×Dic13C2312yes—
40C22×Dic13C2312yes—
41C22×Dic13C2312yes—
42C22×Dic13C2311yescharacteristic
43C2×C4×D13—22no—
44C2×C4×D13—22no—
45C2×C4×D13D414yes—
46C2×Dic26—22no—
47C2×Dic26—22no—
48C2×Dic26—22no—
49C13×C4⋊C4—22no—
50C42×C13—22no—
51#6103—24no—
52#6103—24no—
53#6103—24no—
54C4⋊Dic13—22no—
55C4⋊Dic13—24no—
56#6101—24no—
57#6101—28no—
58#6101—24no—
59C4×Dic13D414yes—
60#2621—131nomaximal, Sylow
61C23×C13C2411yescharacteristic
62C22×D13—21no—
63C22×D13—21no—
64C22×D13—22no—
65C22×D13—22no—
66C22×D13C2×D412yes—
67Q8×C13—44no—
68C2×C4×C13—22no—
69C2×C4×C13—22no—
70C2×C4×C13—22no—
71C2×C4×C13—22no—
72C2×C4×C13—22no—
73C2×C4×C13—22no—
74C2×C4×C13—22no—
75C2×C4×C13—24no—
76C2×C4×C13C2×D412yes—
77C2×C4×C13C2×D412yes—
78C2×C4×C13#4112yes—
79C2×Dic13—21no—
80C2×Dic13—21no—
81C2×Dic13—22no—
82C2×Dic13—22no—
83C2×Dic13—22no—
84C2×Dic13—22no—
85C2×Dic13—22no—
86C2×Dic13—22no—
87C2×Dic13—24no—
88C2×Dic13C2×D414yes—
89C2×Dic13C2×D412yes—
90C4×D13—28no—
91Dic26—44no—
92C2×C4⋊Q8—131no—
93C2×C22⋊Q8—131no—
94C2×C22⋊Q8—131no—
95C2×#117—131no—
96#398—134no—
97#397—134no—
98#391—131no—
99#391D1311yescharacteristic, complemented
100#382—131no—
101C22×C13C22×D411yescharacteristic
102C22×C13C22×D411yescharacteristic
103C22×C13C2×#4111yescharacteristic
104C22×C132−1+412yes—
105C22×C132−1+412yes—
106C2×D13—22no—
107C2×D13—22no—
108C2×D13—22no—
109C2×D13—42no—
110C2×D13—42no—
111C4×C13—42no—
112C4×C13—42no—
113C4×C13—42no—
114C4×C13#12114yes—
115Dic13—22no—
116Dic13—24no—
117Dic13—42no—
118Dic13—42no—
119C22×Q8—131no—
120C22×Q8C2×D1311yescharacteristic
121C23×C4—131no—
122C4⋊Q8—264no—
123C22⋊Q8—264no—
124C22⋊Q8—264no—
125#117—264no—
126C2×C4⋊C4—132no—
127C2×C4⋊C4—132no—
128C2×C4⋊C4—131no—
129C2×C4⋊C4—132no—
130C2×C4⋊C4—134no—
131C2×C4⋊C4C2×D1311yescharacteristic
132C2×C22⋊C4—132no—
133C2×C22⋊C4—132no—
134C2×C22⋊C4—132no—
135C2×C42—131no—
136C2×C42C2×D1311yescharacteristic
137#95—134no—
138#95—134no—
139#95C2×D1314yes—
140C2×C13C2×#12111yescharacteristic
141C2×C13#53611yescharacteristic
142C2×C13#53612yes—
143C2×C13#53611yescharacteristic
144C2×C13#54112yes—
145D13—42no—
146C24—131no—
147C2×Q8—22no—
148C2×Q8—22no—
149C2×Q8—22no—
150C2×Q8—262no—
151C2×Q8—262no—
152C2×Q8—262no—
153C22×C4—132no—
154C22×C4—131no—
155C22×C4—134no—
156C22×C4—132no—
157C22×C4—132no—
158C22×C4—262no—
159C22×C4—262no—
160C22×C4C22×D1312yes—
161C22×C4C22×D1312yes—
162C22×C4C22×D1312yes—
163C22×C4C22×D1311yescharacteristic
164C4⋊C4—22no—
165C4⋊C4—264no—
166C4⋊C4—264no—
167C4⋊C4—264no—
168C4⋊C4—268no—
169C4⋊C4—262no—
170C22⋊C4—264no—
171C22⋊C4—264no—
172C22⋊C4—264no—
173C42—22no—
174C42—134no—
175C13#262111yescharacteristic, complemented, Sylow
176C23—132no—
177C23—261no—
178C23—261no—
179C23—262no—
180C23—262no—
181C23C23×D1311yescharacteristic
182Q8—44no—
183Q8—524no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—24no—
192C2×C4—134no—
193C2×C4—132no—
194C2×C4—261no—
195C2×C4—261no—
196C2×C4—262no—
197C2×C4—262no—
198C2×C4—268no—
199C2×C4—262no—
200C2×C4—262no—
201C2×C4—262no—
202C2×C4—262no—
203C2×C4—264no—
204C2×C4#612712yes—
205C2×C4D4×D1312yes—
206C2×C4D4×D1312yes—
207C22—262no—
208C22—262no—
209C22—262no—
210C22—522no—
211C22—522no—
212C22C2×#612711yescharacteristic
213C22C2×D4×D1311yescharacteristic
214C22C2×D4×D1311yescharacteristic
215C22#8825412yes—
216C22#8825712yes—
217C4—42no—
218C4—42no—
219C4—42no—
220C4—262no—
221C4—264no—
222C4—522no—
223C4—522no—
224C4#8813814yes—
225C2—522no—
226C2C2×#8813811yescharacteristic
227C2#1171928812yes—
228C2#1171933312yes—
229C2#1171938011yescharacteristic
230C2#1171942911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#391C2
prime radicalC23×D13C23
hypercenter#391D13
hypocenterC13#2621
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
2. C2×#88198C2semidirect
5. C13×#391C2semidirect
6. #11718638C2semidirect
7. #11718590C2semidirect
9. #11718318C2semidirect
99. #391D13semidirect
175. C13#2621semidirect

Maximal subgroups

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

subgroupindex
C2×#882002
C2×#881982
C2×#881512
C2×#881262
C13×#3912
#117186382
#117185902
#117183362
#117183182
#262113