Finite Group Databasebeta

← #13119290

Subgroups — #13119290

Order 1664.

484 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 153 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×C13×C22⋊Q8C211yesmaximal, characteristic
2C2×#88180C211yesmaximal, characteristic
3#11718891C211yesmaximal, characteristic, complemented
4#11718891C211yesmaximal, characteristic, complemented
5C4×C22⋊Dic13C211yesmaximal, characteristic
6#11718639C214yesmaximal, complemented
7#11718638C211yesmaximal, characteristic, complemented
8#11718637C211yesmaximal, characteristic, complemented
9#11718613C214yesmaximal
10C22×Q8×C13C2211yescharacteristic
11C23×C4×C13C2211yescharacteristic
12C13×C22⋊Q8—24no—
13C2×C13×C4⋊C4C2211yescharacteristic
14C2×C13×C4⋊C4C2212yes—
15C2×C13×C22⋊C4C2212yes—
16C2×C22⋊Dic13C2212yes—
17C2×C22⋊Dic13C2212yes—
18#88180—24no—
19C2×C4⋊Dic13C2211yescharacteristic
20C2×C4⋊Dic13C2211yescharacteristic
21C2×#6101C2214yes—
22C2×C4×Dic13C2212yes—
23C2×C4×Dic13C2211yescharacteristic
24C2×C4×Dic13C2211yescharacteristic
25#88071C2214yes—
26#88071C2214yes—
27#88071C2214yes—
28#88071C2212yes—
29C24×C13C2311yescharacteristic
30C2×Q8×C13—22no—
31C2×Q8×C13—22no—
32C2×Q8×C13—22no—
33C22×C4×C13—22no—
34C22×C4×C13—22no—
35C22×C4×C13D414yes—
36C22×C4×C13C2312yes—
37C22×C4×C13C2312yes—
38C22×C4×C13C2311yescharacteristic
39C22×C4×C13C2311yescharacteristic
40C22×Dic13C2312yes—
41C22×Dic13C2312yes—
42C22×Dic13C2312yes—
43C22×Dic13C2312yes—
44C13×C4⋊C4—22no—
45C13×C4⋊C4—24no—
46C13×C22⋊C4—24no—
47C22⋊Dic13—24no—
48C22⋊Dic13—24no—
49C4⋊Dic13—22no—
50C4⋊Dic13—22no—
51#6101—28no—
52C4×Dic13—24no—
53C4×Dic13—22no—
54C4×Dic13—22no—
55#2499—131nomaximal, Sylow
56C23×C13—22no—
57C23×C13—21no—
58C23×C13—21no—
59C23×C13—22no—
60C23×C13C2×D412yes—
61C23×C13C2411yescharacteristic
62Q8×C13—44no—
63C2×C4×C13—21no—
64C2×C4×C13—21no—
65C2×C4×C13—28no—
66C2×C4×C13—22no—
67C2×C4×C13—22no—
68C2×C4×C13—24no—
69C2×C4×C13—22no—
70C2×C4×C13—22no—
71C2×C4×C13C2×D412yes—
72C2×C4×C13C2×D412yes—
73C2×C4×C13#4112yes—
74C2×C4×C13#4112yes—
75C2×Dic13—22no—
76C2×Dic13—22no—
77C2×Dic13—22no—
78C2×Dic13—22no—
79C2×Dic13—22no—
80C2×Dic13—24no—
81C2×Dic13—22no—
82C2×Dic13—24no—
83C2×Dic13—22no—
84C2×Dic13#4114yes—
85C2×C22⋊Q8D1311yescharacteristic
86C2×#117—131no—
87#397—134no—
88#391—131no—
89#391—131no—
90#387—134no—
91#384—131no—
92#382—131no—
93C4×C22⋊C4—131no—
94C22×C13—22no—
95C22×C13—22no—
96C22×C13—22no—
97C22×C13—42no—
98C22×C13—42no—
99C22×C13C22×D411yescharacteristic
100C22×C13C2×#4111yescharacteristic
101C22×C13C2×#4111yescharacteristic
102C22×C13C2×#4112yes—
103C22×C132−1+412yes—
104C4×C13—22no—
105C4×C13—42no—
106C4×C13—42no—
107C4×C13#12314yes—
108Dic13—24no—
109Dic13—42no—
110Dic13—42no—
111Dic13—42no—
112C22×Q8C2×D1311yescharacteristic
113C23×C4C2×D1311yescharacteristic
114C22⋊Q8—24no—
115#117—264no—
116C2×C4⋊C4—131no—
117C2×C4⋊C4—131no—
118C2×C4⋊C4—134no—
119C2×C4⋊C4C2×D1311yescharacteristic
120C2×C4⋊C4C2×D1312yes—
121C2×C22⋊C4—132no—
122C2×C22⋊C4—132no—
123C2×C22⋊C4C2×D1312yes—
124C2×C42—132no—
125C2×C42—131no—
126C2×C42—131no—
127#95—132no—
128#95—134no—
129#95—134no—
130#95—134no—
131C2×C13—42no—
132C2×C13C2×#12311yescharacteristic
133C2×C13#53211yescharacteristic
134C2×C13#53611yescharacteristic
135C2×C13#55212yes—
136C2×C13#55612yes—
137C24C22×D1311yescharacteristic
138C2×Q8—22no—
139C2×Q8—22no—
140C2×Q8—22no—
141C22×C4—22no—
142C22×C4—22no—
143C22×C4—132no—
144C22×C4—132no—
145C22×C4—132no—
146C22×C4—132no—
147C22×C4C22⋊D1314yes—
148C22×C4C22×D1312yes—
149C22×C4C22×D1312yes—
150C22×C4C22×D1311yescharacteristic
151C22×C4C22×D1311yescharacteristic
152C4⋊C4—22no—
153C4⋊C4—24no—
154C4⋊C4—268no—
155C4⋊C4—262no—
156C4⋊C4—262no—
157C22⋊C4—24no—
158C22⋊C4—264no—
159C22⋊C4—264no—
160C42—262no—
161C42—262no—
162C42—264no—
163C13#249911yescharacteristic, complemented, Sylow
164C23—21no—
165C23—21no—
166C23—22no—
167C23—22no—
168C23C2×C22⋊D1312yes—
169C23C23×D1311yescharacteristic
170Q8—44no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—28no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—24no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—134no—
180C2×C4—262no—
181C2×C4—262no—
182C2×C4—262no—
183C2×C4—264no—
184C2×C4—262no—
185C2×C4—262no—
186C2×C4—264no—
187C2×C4—262no—
188C2×C4—262no—
189C2×C4#612912yes—
190C2×C4#612912yes—
191C2×C4C2×C22⋊D1312yes—
192C2×C4C2×C22⋊D1312yes—
193C22—22no—
194C22—22no—
195C22—22no—
196C22—42no—
197C22—42no—
198C22C2×#612911yescharacteristic
199C22C2×#612911yescharacteristic
200C22#8825412yes—
201C22#41×D1312yes—
202C22C22×C22⋊D1311yescharacteristic
203C4—22no—
204C4—42no—
205C4—42no—
206C4—264no—
207C4—522no—
208C4—522no—
209C4—522no—
210C4#8818914yes—
211C2—42no—
212C2#1171934412yes—
213C2#1171934612yes—
214C2C2×#8818911yescharacteristic
215C2#1171952111yescharacteristic
216C2#1171953711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC2×C13×C22⋊Q8C2
prime radicalC24×C13C23
hypercenterC2×C22⋊Q8D13
hypocenterC13#2499
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. #11718891C2semidirect
4. #11718891C2semidirect
6. #11718639C2semidirect
7. #11718638C2semidirect
8. #11718637C2semidirect
163. C13#2499semidirect

Maximal subgroups

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

subgroupindex
C2×C13×C22⋊Q82
C2×#881802
#117188912
C4×C22⋊Dic132
#117186392
#117186382
#117186372
#117186132
#249913