Finite Group Databasebeta

← #13124780

Subgroups — #13124780

Order 1664.

410 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 137 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#11718886C212yesmaximal, complemented
4#11718868C211yesmaximal, characteristic
5#11718706C214yesmaximal, complemented
6#11718705C212yesmaximal, complemented
7#11718704C212yesmaximal, complemented
8#11718625C212yesmaximal, complemented
9C22×Q8×C13C2211yescharacteristic
10C23×C4×C13C2211yescharacteristic
11C13×C22⋊Q8—21no—
12C13×C22⋊Q8—21no—
13C13×C22⋊Q8C2212yes—
14C13×C22⋊Q8C2212yes—
15C2×C13×C4⋊C4—21no—
16C2×C13×C4⋊C4C2211yescharacteristic
17C2×C13×C22⋊C4—21no—
18C2×C22⋊Dic13—21no—
19#88180—21no—
20#88180—21no—
21#88180C2212yes—
22#88180C2212yes—
23C2×C4⋊Dic13C2211yescharacteristic
24C2×C4⋊Dic13C2211yescharacteristic
25C2×C4×Dic13—21no—
26C2×#6099C2212yes—
27#88075C2214yescomplemented
28#88075C2214yescomplemented
29C22⋊#1055C2212yes—
30C22⋊#1055C2212yes—
31#88048C2214yescomplemented
32#88047C2214yescomplemented
33C24×C13D411yescharacteristic
34C2×Q8×C13—21no—
35C2×Q8×C13—24no—
36C2×Q8×C13C2312yes—
37C22×C4×C13—24no—
38C22×C4×C13—21no—
39C22×C4×C13—21no—
40C22×C4×C13D411yescharacteristic
41C22×C4×C13D411yescharacteristic
42C22×C4×C13D411yescharacteristic
43C22×C4×C13C2311yescharacteristic
44C22×C4×C13C2311yescharacteristic
45C22×C4×C13C2311yescharacteristic
46C22×Dic13—21no—
47C22×Dic13—21no—
48C13×C4⋊C4—22no—
49C13×C4⋊C4—22no—
50C13×C4⋊C4—21no—
51C13×C4⋊C4C2312yes—
52C13×C22⋊C4—22no—
53C13×C22⋊C4—22no—
54C22⋊Dic13—22no—
55C22⋊Dic13—22no—
56C4⋊Dic13—21no—
57C4⋊Dic13—21no—
58C4⋊Dic13C2312yes—
59C4⋊Dic13C2312yes—
60C4×Dic13—22no—
61C4×Dic13—22no—
62#6099—24no—
63C2×#1055C2314yes—
64#3095—131nomaximal, Sylow
65C23×C13—22no—
66C23×C13—22no—
67C23×C13—41no—
68C23×C13C2×D411yescharacteristic
69C23×C13C2×D411yescharacteristic
70C23×C13C2×D411yescharacteristic
71Q8×C13—24no—
72Q8×C13—42no—
73C2×C4×C13—22no—
74C2×C4×C13—22no—
75C2×C4×C13—22no—
76C2×C4×C13—22no—
77C2×C4×C13—22no—
78C2×C4×C13—22no—
79C2×C4×C13—22no—
80C2×C4×C13—42no—
81C2×C4×C13—42no—
82C2×C4×C13C2×D411yescharacteristic
83C2×C4×C13C2×D411yescharacteristic
84C2×C4×C13C2×D411yescharacteristic
85C2×C4×C13#4114yes—
86C2×C4×C13C2411yescharacteristic
87C2×Dic13—22no—
88C2×Dic13—22no—
89C2×Dic13—42no—
90C2×Dic13—42no—
91#1055—24no—
92C2×C22⋊Q8D1311yescharacteristic
93C2×#117—131no—
94#485—134no—
95#484—132no—
96#483—132no—
97#428—132no—
98#419—132no—
99#407—131no—
100C22×C13—21no—
101C22×C13—21no—
102C22×C13—21no—
103C22×C13—21no—
104C22×C13—21no—
105C22×C13—21no—
106C22×C13—21no—
107C22×C13—44no—
108C22×C13#12312yes—
109C22×C13#13712yes—
110C22×C13C22×D411yescharacteristic
111C4×C13—21no—
112C4×C13—21no—
113C4×C13—42no—
114C4×C13—42no—
115C4×C13#12312yes—
116C4×C13C2×#4112yes—
117Dic13—42no—
118Dic13—42no—
119C22×Q8C2×D1311yescharacteristic
120C23×C4C2×D1311yescharacteristic
121C2×M16—132no—
122C22⋊Q8—21no—
123C22⋊Q8—21no—
124C22⋊Q8C2×D1312yes—
125C22⋊Q8C2×D1312yes—
126#117—132no—
127#117—132no—
128#117—261no—
129#117—261no—
130C2×C4⋊C4—21no—
131C2×C4⋊C4—131no—
132C2×C4⋊C4—131no—
133C2×C4⋊C4C2×D1311yescharacteristic
134C2×C22⋊C4—21no—
135C2×C22⋊C4—261no—
136C2×C42—261no—
137#107—134no—
138#106—134no—
139#103—134no—
140#103—134no—
141C22⋊C8—132no—
142C22⋊C8—132no—
143C2×C13—22no—
144C2×C13—22no—
145C2×C13—41no—
146C2×C13C2×#12311yescharacteristic
147C2×C13C2×#13711yescharacteristic
148C2×C13#57511yescharacteristic
149C24C22⋊D1311yescharacteristic
150C2×Q8—21no—
151C2×Q8—24no—
152C2×Q8C22×D1312yes—
153C22×C4—24no—
154C22×C4—21no—
155C22×C4—21no—
156C22×C4—261no—
157C22×C4—261no—
158C22×C4C22⋊D1311yescharacteristic
159C22×C4C22⋊D1311yescharacteristic
160C22×C4C22⋊D1311yescharacteristic
161C22×C4C22×D1311yescharacteristic
162C22×C4C22×D1311yescharacteristic
163C22×C4C22×D1311yescharacteristic
164M16—264no—
165C2×C8—134no—
166C4⋊C4—22no—
167C4⋊C4—22no—
168C4⋊C4—21no—
169C4⋊C4—132no—
170C4⋊C4—132no—
171C4⋊C4—261no—
172C4⋊C4—261no—
173C4⋊C4C22×D1312yes—
174C22⋊C4—22no—
175C22⋊C4—22no—
176C22⋊C4—262no—
177C22⋊C4—262no—
178C42—262no—
179C42—262no—
180C13#309511yescharacteristic, complemented, Sylow
181C23—22no—
182C23—22no—
183C23—41no—
184C23C2×C22⋊D1311yescharacteristic
185C23C2×C22⋊D1311yescharacteristic
186C23C2×C22⋊D1311yescharacteristic
187Q8—24no—
188Q8—42no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—42no—
197C2×C4—42no—
198C2×C4—262no—
199C2×C4—262no—
200C2×C4—522no—
201C2×C4—522no—
202C2×C4#612914yes—
203C2×C4C2×C22⋊D1311yescharacteristic
204C2×C4C2×C22⋊D1311yescharacteristic
205C2×C4C2×C22⋊D1311yescharacteristic
206C2×C4C23×D1311yescharacteristic
207C8—264no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22—21no—
212C22—21no—
213C22—21no—
214C22—21no—
215C22—44no—
216C22#8818912yes—
217C22#8819612yes—
218C22C22×C22⋊D1311yescharacteristic
219C4—21no—
220C4—21no—
221C4—42no—
222C4—42no—
223C4—522no—
224C4—522no—
225C4#8818912yes—
226C4C2×#612912yes—
227C2—22no—
228C2—22no—
229C2—41no—
230C2C2×#8818911yescharacteristic
231C2C2×#8819611yescharacteristic
232C2#1171952711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC2×C13×C22⋊Q8C2
socleC22×C13C22×D4
prime radicalC24×C13D4
hypercenterC2×C22⋊Q8D13
hypocenterC13#3095
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. #11718886C2semidirect
5. #11718706C2semidirect
6. #11718705C2semidirect
7. #11718704C2semidirect
8. #11718625C2semidirect
27. #88075C22semidirect
28. #88075C22semidirect
31. #88048C22semidirect
32. #88047C22semidirect
180. C13#3095semidirect

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
#117188862
#117188682
#117187062
#117187052
#117187042
#117186252
#309513