Finite Group Databasebeta

← #13118107

Subgroups — #13118107

Order 1664.

528 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 159 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×Q8×Dic13C211yesmaximal, characteristic, complemented
2C2×#88146C211yesmaximal, characteristic
3C13×#395C211yesmaximal, characteristic, complemented
4#11718892C211yesmaximal, characteristic
5#11718655C212yesmaximal
6#11718647C211yesmaximal, characteristic, complemented
7C4⋊C4×Dic13C212yesmaximal, complemented
8#11718338C211yesmaximal, characteristic
9#11718327C212yesmaximal
10#11718322C212yesmaximal, complemented
11#11718310C211yesmaximal, characteristic, complemented
12C22×Q8×C13C2211yescharacteristic
13C22×C4×D13C2211yescharacteristic
14C2×C13×C4⋊C4C2211yescharacteristic
15C2×C13×C4⋊C4C2212yes—
16Q8×Dic13—24no—
17C2×#6103C2211yescharacteristic
18C2×#6103C2211yescharacteristic
19C2×#6103C2212yes—
20C2×#6103C2212yes—
21C2×C4⋊Dic13C2211yescharacteristic
22C2×C4⋊Dic13C2212yes—
23C2×C4⋊Dic13C2211yescharacteristic
24C2×C4⋊Dic13C2212yes—
25C2×#6101C2212yes—
26C2×C4×Dic13C2211yescharacteristic
27C2×C4×Dic13C2212yes—
28C2×C4×Dic13C2212yes—
29C2×C4×Dic13C2211yescharacteristic
30#88146—24no—
31C13×#95C2211yescharacteristic
32C13×#95C2212yes—
33#88071C2211yescharacteristic
34#88071C2212yes—
35#88071C2212yes—
36#88071C2212yes—
37C23×D13C2311yescharacteristic
38C2×Q8×C13—22no—
39C2×Q8×C13—24no—
40C22×C4×C13C2311yescharacteristic
41C22×C4×C13C2311yescharacteristic
42C22×C4×C13C2311yescharacteristic
43C22×C4×C13C2312yes—
44C22×C4×C13C2312yes—
45C22×Dic13C2312yes—
46C22×Dic13C2312yes—
47C22×Dic13C2311yescharacteristic
48C22×Dic13C2311yescharacteristic
49C22×Dic13C2311yescharacteristic
50C2×C4×D13—22no—
51C2×C4×D13—22no—
52C2×C4×D13Q814yescomplemented
53C13×C4⋊C4—22no—
54C13×C4⋊C4—24no—
55#6103—22no—
56#6103—24no—
57#6103—24no—
58#6103—22no—
59C4⋊Dic13—22no—
60C4⋊Dic13—24no—
61C4⋊Dic13—22no—
62C4⋊Dic13—24no—
63#6101—24no—
64C4×Dic13—22no—
65C4×Dic13—24no—
66C4×Dic13—24no—
67C4×Dic13D414yes—
68#2396—131nomaximal, Sylow
69C23×C13C2411yescharacteristic
70C22×D13—21no—
71C22×D13—22no—
72C22×D13—22no—
73C22×D13—21no—
74C22×D13C2×Q812yes—
75Q8×C13—28no—
76C2×C4×C13—22no—
77C2×C4×C13—21no—
78C2×C4×C13—22no—
79C2×C4×C13—22no—
80C2×C4×C13—21no—
81C2×C4×C13—22no—
82C2×C4×C13—22no—
83C2×C4×C13—21no—
84C2×C4×C13—22no—
85C2×C4×C13C2×D412yes—
86C2×C4×C13C2×Q812yes—
87C2×C4×C13#4114yes—
88C2×C4×C13#4114yes—
89C2×Dic13—22no—
90C2×Dic13—22no—
91C2×Dic13—21no—
92C2×Dic13—22no—
93C2×Dic13—22no—
94C2×Dic13—22no—
95C2×Dic13—22no—
96C2×Dic13—22no—
97C2×Dic13—22no—
98C2×Dic13C2×D412yes—
99C2×Dic13C2×D412yes—
100C2×Dic13C2×Q812yes—
101C2×Dic13#4112yes—
102C4×D13—28no—
103C2×C4×Q8—131no—
104C2×#117—131no—
105#400—131no—
106#399—131no—
107#398—132no—
108#396—132no—
109#395D1311yescharacteristic, complemented
110#393—131no—
111C4×C4⋊C4—132no—
112C4×C4⋊C4—131no—
113C4×C22⋊C4—132no—
114C22×C13C22×D411yescharacteristic
115C22×C13C22×Q811yescharacteristic
116C22×C13C2×#4112yes—
117C22×C13C2×#4112yes—
118C22×C13C2×#4111yescharacteristic
119C2×D13—22no—
120C2×D13—24no—
121C2×D13—41no—
122C2×D13—42no—
123C2×D13—41no—
124C4×C13—22no—
125C4×C13—22no—
126C4×C13—24no—
127C4×C13—24no—
128C4×C13—41no—
129Dic13—22no—
130Dic13—42no—
131Dic13—42no—
132Dic13—41no—
133Dic13C22⋊Q814yes—
134C22×Q8C2×D1311yescharacteristic
135C23×C4—131no—
136C4×Q8—264no—
137#117—264no—
138C2×C4⋊C4—131no—
139C2×C4⋊C4—132no—
140C2×C4⋊C4—131no—
141C2×C4⋊C4—132no—
142C2×C4⋊C4—132no—
143C2×C4⋊C4C2×D1311yescharacteristic
144C2×C4⋊C4C2×D1312yes—
145C2×C22⋊C4—131no—
146C2×C22⋊C4—131no—
147C2×C22⋊C4—132no—
148C2×C22⋊C4—132no—
149C2×C42—131no—
150C2×C42—131no—
151C2×C42—132no—
152C2×C42—132no—
153#95—132no—
154#95—132no—
155#95—131no—
156#95—132no—
157#95C2×D1312yes—
158#95C2×D1311yescharacteristic
159C2×C13C2×C22⋊Q811yescharacteristic
160C2×C13#52511yescharacteristic
161C2×C13#52912yes—
162C2×C13#53211yescharacteristic
163C2×C13#53312yes—
164D13—42no—
165C24—131no—
166C2×Q8—22no—
167C2×Q8—24no—
168C22×C4—131no—
169C22×C4—131no—
170C22×C4—134no—
171C22×C4—132no—
172C22×C4—131no—
173C22×C4—132no—
174C22×C4—262no—
175C22×C4—262no—
176C22×C4C22×D1311yescharacteristic
177C22×C4C22×D1311yescharacteristic
178C22×C4C22×D1312yes—
179C22×C4C22×D1311yescharacteristic
180C22×C4C22×D1312yes—
181C4⋊C4—22no—
182C4⋊C4—24no—
183C4⋊C4—262no—
184C4⋊C4—264no—
185C4⋊C4—262no—
186C4⋊C4—264no—
187C4⋊C4—264no—
188C22⋊C4—262no—
189C22⋊C4—262no—
190C22⋊C4—264no—
191C22⋊C4—264no—
192C42—134no—
193C42—262no—
194C42—264no—
195C42—264no—
196C13#239611yescharacteristic, complemented, Sylow
197C23—132no—
198C23—261no—
199C23—262no—
200C23—262no—
201C23—261no—
202C23C23×D1311yescharacteristic
203Q8—28no—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—132no—
214C2×C4—132no—
215C2×C4—132no—
216C2×C4—132no—
217C2×C4—268no—
218C2×C4—262no—
219C2×C4—261no—
220C2×C4—262no—
221C2×C4—262no—
222C2×C4—262no—
223C2×C4—262no—
224C2×C4—262no—
225C2×C4—262no—
226C2×C4—262no—
227C2×C4D4×D1312yes—
228C2×C4#612914yes—
229C2×C4Q8×D1312yes—
230C2×C4#613114yes—
231C22—264no—
232C22—262no—
233C22—521no—
234C22—521no—
235C22—522no—
236C22C2×D4×D1311yescharacteristic
237C22C2×#612912yes—
238C22C2×Q8×D1311yescharacteristic
239C22C2×#613112yes—
240C22#41×D1311yescharacteristic
241C4—22no—
242C4—24no—
243C4—24no—
244C4—22no—
245C4—41no—
246C4—134no—
247C4—262no—
248C4—521no—
249C4—522no—
250C4—522no—
251C2—522no—
252C2#1171929111yescharacteristic
253C2#1171932912yes—
254C2D13×C22⋊Q811yescharacteristic
255C2#1171943011yescharacteristic
256C2#1171943312yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#395C2
prime radicalC23×D13C23
hypercenter#395D13
hypocenterC13#2396
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
1. C2×Q8×Dic13C2semidirect
3. C13×#395C2semidirect
6. #11718647C2semidirect
7. C4⋊C4×Dic13C2semidirect
10. #11718322C2semidirect
11. #11718310C2semidirect
52. C2×C4×D13Q8semidirect
109. #395D13semidirect
196. C13#2396semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×Dic132
C2×#881462
C13×#3952
#117188922
#117186552
#117186472
C4⋊C4×Dic132
#117183382
#117183272
#117183222
#117183102
#239613