Finite Group Databasebeta

← #13124471

Subgroups — #13124471

Order 1664.

492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 141 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
1C22×C13×SD16C211yesmaximal, characteristic, complemented
2#11719521C211yesmaximal, characteristic, complemented
3#11719510C211yesmaximal, characteristic
4C2×#88155C211yesmaximal, characteristic, complemented
5#11718886C211yesmaximal, characteristic, complemented
6#11718876C211yesmaximal, characteristic, complemented
7#11718835C214yesmaximal, complemented
8#11718832C214yesmaximal, complemented
9#11718767C211yesmaximal, characteristic, complemented
10C22×Q8×C13C2211yescharacteristic
11C22×D4×C13C2211yescharacteristic
12C2×#6127C2211yescharacteristic
13C2×C13×SD16—24no—
14C2×C13×SD16C2212yes—
15C2×C13×SD16C2212yes—
16C22×C8×C13C2211yescharacteristic
17#88207—22no—
18#88201—21no—
19#88200C2214yescomplemented
20#88198—21no—
21#88194—21no—
22#88192C2214yes—
23#88190—21no—
24#88183—22no—
25#88180C2211yescharacteristic
26#88180C2211yescharacteristic
27C2×#6099C2211yescharacteristic
28#88155—24no—
29C2×#6094C2212yescomplemented
30C2×C8×D13C2212yescomplemented
31#88075C2214yescomplemented
32#88072C2214yes—
33#88058C2212yescomplemented
34#88057C2212yescomplemented
35C24×C13—21no—
36C2×Q8×C13—21no—
37C2×Q8×C13—22no—
38C2×Q8×C13—22no—
39C2×Q8×C13C2312yes—
40C2×D4×C13—22no—
41C2×D4×C13—21no—
42C2×D4×C13—22no—
43C2×D4×C13C2312yes—
44C22×C4×C13—21no—
45C22×C4×C13C2311yescharacteristic
46C2×C22⋊D13—24no—
47C2×C22⋊D13D412yes—
48#6127—22no—
49#6127—22no—
50C2×D52D411yescharacteristic
51C2×C4×D13C2312yes—
52C2×Dic26D411yescharacteristic
53C13×SD16—24no—
54C13×SD16—24no—
55C2×C8×C13D414yescomplemented
56C2×C8×C13C2311yescharacteristic
57C2×C8×C13C2311yescharacteristic
58C22⋊Dic13—21no—
59C22⋊Dic13—21no—
60C22⋊Dic13—24no—
61#6103—24no—
62C4⋊Dic13C2312yes—
63C4⋊Dic13C2312yes—
64#6101—24no—
65C4×Dic13—21no—
66C4×Dic13—21no—
67#6099—22no—
68C2×#1055C2312yes—
69#6094—24no—
70C8×D13—24no—
71#3057—131nomaximal, Sylow
72C23×C13—22no—
73C23×C13—42no—
74C23×C13—82no—
75C23×C13C2×D411yescharacteristic
76C22×D13C2×D412yes—
77Q8×C13—22no—
78Q8×C13—22no—
79Q8×C13—42no—
80D4×C13—22no—
81D4×C13—22no—
82D4×C13—42no—
83C2×C4×C13—22no—
84C2×C4×C13—42no—
85C2×C4×C13C2×D411yescharacteristic
86C2×C4×C13C2×D412yes—
87C2×C4×C13#4112yes—
88C2×C4×C13C2411yescharacteristic
89C22⋊D13—24no—
90C22⋊D13—84no—
91C2×Dic13—22no—
92C2×Dic13—22no—
93C2×Dic13C2×D412yes—
94D52—22no—
95C4×D13—22no—
96C4×D13—22no—
97Dic26—22no—
98C8×C13C2×D412yes—
99C8×C13C2×D412yes—
100#1055—22no—
101C22×SD16D1311yescharacteristic, complemented
102C2×#131—131no—
103#536—131no—
104#535—131no—
105#468—134no—
106#465—134no—
107#427—131no—
108#419—131no—
109#418—131no—
110C22×C13—22no—
111C22×C13—42no—
112C22×C13—44no—
113C22×C13—84no—
114C22×C13#12112yes—
115C22×C13C22×D411yescharacteristic
116C2×D13—22no—
117C2×D13—24no—
118C4×C13—42no—
119C4×C13#12112yes—
120C4×C13C22×D411yescharacteristic
121C4×C13C2×#4111yescharacteristic
122Dic13—22no—
123Dic13—42no—
124Dic13—42no—
125C2×#41—131no—
126C22×Q8C2×D1311yescharacteristic
127C22×D4C2×D1311yescharacteristic
128C2×SD16—24no—
129C2×SD16C2×D1312yes—
130C2×SD16C2×D1312yes—
131#131—264no—
132C2×M16—131no—
133C2×M16—132no—
134C22×C8—132no—
135C22×C8C2×D1311yescharacteristic
136C4⋊Q8—261no—
137#127—261no—
138#124—261no—
139#124—261no—
140#123—262no—
141C22⋊Q8—134no—
142#121—134no—
143#120—262no—
144#117—131no—
145#117—131no—
146#107—132no—
147#106—132no—
148#103—134no—
149#102—134no—
150C2×C13—22no—
151C2×C13—82no—
152C2×C13C2×#12111yescharacteristic
153C2×C13#57712yes—
154D13—42no—
155C24—21no—
156#41—262no—
157#41—262no—
158C2×Q8—21no—
159C2×Q8—22no—
160C2×Q8—22no—
161C2×Q8—131no—
162C2×Q8C22×D1312yes—
163C2×D4—21no—
164C2×D4—22no—
165C2×D4—22no—
166C2×D4—132no—
167C2×D4—131no—
168C2×D4—264no—
169C2×D4C22×D1312yes—
170C22×C4—21no—
171C22×C4—132no—
172C22×C4C22×D1311yescharacteristic
173SD16—24no—
174SD16—24no—
175M16—262no—
176M16—264no—
177C2×C8—132no—
178C2×C8—264no—
179C2×C8C22⋊D1314yescomplemented
180C2×C8C22×D1311yescharacteristic
181C2×C8C22×D1311yescharacteristic
182C4⋊C4—132no—
183C4⋊C4—132no—
184C4⋊C4—264no—
185C22⋊C4—264no—
186C22⋊C4—264no—
187C22⋊C4—261no—
188C22⋊C4—261no—
189C42—261no—
190C42—261no—
191C13#305711yescharacteristic, complemented, Sylow
192C23—22no—
193C23—42no—
194C23—82no—
195C23—132no—
196C23D4×D1311yescharacteristic
197Q8—22no—
198Q8—22no—
199Q8—42no—
200Q8—262no—
201D4—22no—
202D4—22no—
203D4—42no—
204D4—264no—
205D4—262no—
206D4—1044no—
207C2×C4—22no—
208C2×C4—42no—
209C2×C4—132no—
210C2×C4—262no—
211C2×C4—262no—
212C2×C4—262no—
213C2×C4—262no—
214C2×C4D4×D1311yescharacteristic
215C2×C4#612912yes—
216C2×C4C2×C22⋊D1312yes—
217C2×C4C23×D1311yescharacteristic
218C8—262no—
219C8C2×C22⋊D1312yes—
220C8C2×C22⋊D1312yes—
221C22—22no—
222C22—44no—
223C22—42no—
224C22—84no—
225C22—264no—
226C22—262no—
227C22#8819212yes—
228C22C2×D4×D1311yescharacteristic
229C4—42no—
230C4—262no—
231C4—522no—
232C4—522no—
233C4#8819212yes—
234C4C2×#612911yescharacteristic
235C4C22×C22⋊D1311yescharacteristic
236C2—22no—
237C2—82no—
238C2—522no—
239C2#1171946712yes—
240C2C2×#8819211yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC22×C13×SD16C2
socleC22×C13C22×D4
prime radical#11719510C2
hypercenterC22×SD16D13
hypocenterC13#3057
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C22×C13×SD16C2semidirect
2. #11719521C2semidirect
4. C2×#88155C2semidirect
5. #11718886C2semidirect
6. #11718876C2semidirect
7. #11718835C2semidirect
8. #11718832C2semidirect
9. #11718767C2semidirect
19. #88200C22semidirect
29. C2×#6094C22semidirect
30. C2×C8×D13C22semidirect
31. #88075C22semidirect
33. #88058C22semidirect
34. #88057C22semidirect
55. C2×C8×C13D4semidirect
101. C22×SD16D13semidirect
179. C2×C8C22⋊D13semidirect
191. C13#3057semidirect

Maximal subgroups

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

subgroupindex
C22×C13×SD162
#117195212
#117195102
C2×#881552
#117188862
#117188762
#117188352
#117188322
#117187672
#305713