Finite Group Databasebeta

← #13119291

Subgroups — #13119291

Order 1664.

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

normal subgroups only

This group has 484 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×#88146C211yesmaximal, characteristic
3C13×#391C211yesmaximal, characteristic, complemented
4#11718891C211yesmaximal, characteristic, complemented
5#11718638C211yesmaximal, characteristic, complemented
6C4×#6103C211yesmaximal, characteristic
7#11718596C211yesmaximal, characteristic, complemented
8#11718335C214yesmaximal
9#11718315C214yesmaximal, complemented
10C22×Q8×C13C2211yescharacteristic
11C22×C4×D13C2211yescharacteristic
12C2×C13×C4⋊C4C2211yescharacteristic
13C2×C42×C13C2211yescharacteristic
14#88200—24no—
15C2×#6103C2212yes—
16C2×#6103C2212yes—
17C2×#6103C2212yes—
18C2×C4⋊Dic13C2211yescharacteristic
19C2×C4⋊Dic13C2211yescharacteristic
20C2×C4⋊Dic13C2214yes—
21C2×#6101C2212yes—
22C2×C4×Dic13C2212yes—
23C2×C4×Dic13C2211yescharacteristic
24#88146—24no—
25C13×#95C2214yes—
26#88071C2212yes—
27#88071C2214yes—
28#88071C2214yes—
29C23×D13C2311yescharacteristic
30C2×Q8×C13—22no—
31C2×Q8×C13—22no—
32C2×Q8×C13—22no—
33C22×C4×C13C2312yes—
34C22×C4×C13C2312yes—
35C22×C4×C13C2312yes—
36C22×C4×C13C2311yescharacteristic
37C22×Dic13C2312yes—
38C22×Dic13C2312yes—
39C22×Dic13C2312yes—
40C22×Dic13C2311yescharacteristic
41C2×C4×D13—22no—
42C2×C4×D13—22no—
43C2×C4×D13D414yes—
44C13×C4⋊C4—22no—
45C42×C13—22no—
46#6103—24no—
47#6103—24no—
48#6103—24no—
49C4⋊Dic13—22no—
50C4⋊Dic13—22no—
51C4⋊Dic13—28no—
52#6101—24no—
53C4×Dic13—22no—
54C4×Dic13—24no—
55#2499—131nomaximal, Sylow
56C23×C13C2411yescharacteristic
57C22×D13—22no—
58C22×D13—21no—
59C22×D13—21no—
60C22×D13—22no—
61C22×D13C2×D412yes—
62Q8×C13—44no—
63C2×C4×C13—22no—
64C2×C4×C13—22no—
65C2×C4×C13—22no—
66C2×C4×C13—22no—
67C2×C4×C13—22no—
68C2×C4×C13—22no—
69C2×C4×C13—24no—
70C2×C4×C13C2×D412yes—
71C2×C4×C13#4114yes—
72C2×C4×C13#4112yes—
73C2×C4×C13#4112yes—
74C2×Dic13—21no—
75C2×Dic13—21no—
76C2×Dic13—22no—
77C2×Dic13—22no—
78C2×Dic13—22no—
79C2×Dic13—24no—
80C2×Dic13—24no—
81C2×Dic13—22no—
82C2×Dic13—22no—
83C2×Dic13C2×D412yes—
84C4×D13—28no—
85C2×C22⋊Q8—131no—
86C2×#117—131no—
87#397—134no—
88#391—131no—
89#391D1311yescharacteristic, complemented
90#387—134no—
91#384—131no—
92#382—131no—
93C4×C22⋊C4—131no—
94C22×C13C22×D411yescharacteristic
95C22×C13C2×#4111yescharacteristic
96C22×C13C2×#4111yescharacteristic
97C22×C13C2×#4112yes—
98C22×C132−1+412yes—
99C2×D13—22no—
100C2×D13—22no—
101C2×D13—22no—
102C2×D13—42no—
103C2×D13—42no—
104C4×C13—24no—
105C4×C13—42no—
106C4×C13—42no—
107C4×C13#12314yes—
108Dic13—22no—
109Dic13—42no—
110Dic13—42no—
111Dic13—42no—
112C22×Q8C2×D1311yescharacteristic
113C23×C4—131no—
114C22⋊Q8—264no—
115#117—264no—
116C2×C4⋊C4—131no—
117C2×C4⋊C4—132no—
118C2×C4⋊C4—131no—
119C2×C4⋊C4—134no—
120C2×C4⋊C4C2×D1311yescharacteristic
121C2×C22⋊C4—132no—
122C2×C22⋊C4—132no—
123C2×C22⋊C4—132no—
124C2×C42—132no—
125C2×C42—131no—
126C2×C42C2×D1311yescharacteristic
127#95—132no—
128#95—134no—
129#95—134no—
130#95C2×D1314yes—
131C2×C13C2×#12311yescharacteristic
132C2×C13#53211yescharacteristic
133C2×C13#53611yescharacteristic
134C2×C13#55212yes—
135C2×C13#55612yes—
136D13—42no—
137C24—131no—
138C2×Q8—22no—
139C2×Q8—22no—
140C2×Q8—22no—
141C22×C4—131no—
142C22×C4—134no—
143C22×C4—132no—
144C22×C4—132no—
145C22×C4—132no—
146C22×C4—262no—
147C22×C4—262no—
148C22×C4C22×D1312yes—
149C22×C4C22×D1312yes—
150C22×C4C22×D1312yes—
151C22×C4C22×D1311yescharacteristic
152C4⋊C4—22no—
153C4⋊C4—264no—
154C4⋊C4—262no—
155C4⋊C4—262no—
156C4⋊C4—268no—
157C22⋊C4—264no—
158C22⋊C4—264no—
159C22⋊C4—264no—
160C42—22no—
161C42—264no—
162C42—262no—
163C13#249911yescharacteristic, complemented, Sylow
164C23—132no—
165C23—261no—
166C23—261no—
167C23—262no—
168C23—262no—
169C23C23×D1311yescharacteristic
170Q8—44no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—24no—
178C2×C4—132no—
179C2×C4—261no—
180C2×C4—261no—
181C2×C4—268no—
182C2×C4—262no—
183C2×C4—262no—
184C2×C4—262no—
185C2×C4—262no—
186C2×C4—264no—
187C2×C4—264no—
188C2×C4—262no—
189C2×C4#612712yes—
190C2×C4D4×D1312yes—
191C2×C4#612912yes—
192C2×C4#613114yes—
193C22—262no—
194C22—262no—
195C22—262no—
196C22—522no—
197C22—522no—
198C22C2×#612711yescharacteristic
199C22C2×D4×D1311yescharacteristic
200C22C2×#612911yescharacteristic
201C22C2×#613112yes—
202C22#8825712yes—
203C4—24no—
204C4—42no—
205C4—42no—
206C4—262no—
207C4—522no—
208C4—522no—
209C4—522no—
210C4#8813714yes—
211C2—522no—
212C2C2×#8813711yescharacteristic
213C2#1171928912yes—
214C2#1171934712yes—
215C2#1171938011yescharacteristic
216C2#1171943011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#391C2
prime radicalC23×D13C23
hypercenter#391D13
hypocenterC13#2499
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
3. C13×#391C2semidirect
4. #11718891C2semidirect
5. #11718638C2semidirect
7. #11718596C2semidirect
9. #11718315C2semidirect
89. #391D13semidirect
163. C13#2499semidirect

Maximal subgroups

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

subgroupindex
C2×#882002
C2×#881462
C13×#3912
#117188912
#117186382
C4×#61032
#117185962
#117183352
#117183152
#249913