Finite Group Databasebeta

← #13126576

Subgroups — #13126576

Order 1664.

482 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 123 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×Q16×D13C211yesmaximal, characteristic, complemented
2C2×#88166C211yesmaximal, characteristic, complemented
3#11719382C212yesmaximal, complemented
4C13×#495C211yesmaximal, characteristic, complemented
5#11718849C211yesmaximal, characteristic, complemented
6#11718834C212yesmaximal, complemented
7#11718831C212yesmaximal, complemented
8#11718818C211yesmaximal, characteristic, complemented
9#11718715C212yesmaximal, complemented
10C4×Dic52C211yesmaximal, characteristic, complemented
11C8×D52C211yesmaximal, characteristic, complemented
12C2×Q8×D13C2212yes—
13C2×#6129C2212yes—
14C2×C13×Q16C2211yescharacteristic
15C2×C13×SD16C2212yes—
16C2×C13×D8C2211yescharacteristic
17C13×#124C2212yes—
18#88200C2212yes—
19C2×#6107C2212yes—
20#88192C2212yes—
21C2×#6105C2212yes—
22Q16×D13—24no—
23#88166—24no—
24C2×Dic52C2211yescharacteristic
25C2×C8×D13C2211yescharacteristic
26C2×C8×D13C2211yescharacteristic
27#88139—22no—
28#88138—22no—
29#88135—22no—
30#88132—22no—
31C4×D52C2211yescharacteristic
32C4×Dic26C2212yes—
33C4×C8×C13C2211yescharacteristic
34#88075C2212yes—
35#88072C2212yes—
36#88060C2211yescharacteristic
37#88060C2211yescharacteristic
38#88058C2211yescharacteristic
39#88056C2212yes—
40C4⋊#1055C2211yescharacteristic
41C2×Q8×C13C2312yes—
42C2×D4×C13C2312yes—
43C2×C22⋊D13—22no—
44C2×C22⋊D13—22no—
45C22×Dic13—22no—
46Q8×D13—24no—
47Q8×D13—42no—
48#6129—24no—
49#6129—42no—
50C2×D52D411yescharacteristic
51C2×C4×D13—22no—
52C2×C4×D13C2311yescharacteristic
53C2×C4×D13C2311yescharacteristic
54C2×Dic26—22no—
55C2×Dic26C2312yes—
56C13×Q16—22no—
57C13×SD16—42no—
58C13×D8—22no—
59C2×C8×C13C2311yescharacteristic
60C2×C8×C13C2311yescharacteristic
61C13×C22⋊C4—22no—
62C13×C22⋊C4—22no—
63C42×C13C2311yescharacteristic
64C22⋊Dic13—22no—
65#6107—24no—
66#6105—24no—
67#6103—22no—
68#6103D411yescharacteristic
69#6103D411yescharacteristic
70C4⋊Dic13D411yescharacteristic
71C4⋊Dic13C2312yes—
72#6101—22no—
73#6101—22no—
74C4×Dic13—22no—
75C2×#1055C2311yescharacteristic
76C2×#1055C2311yescharacteristic
77Dic52D414yescomplemented
78C8×D13—22no—
79C8×D13—22no—
80#3285—131nomaximal, Sylow
81C23×C13—22no—
82C22×D13C2×D411yescharacteristic
83C22×D13C2×D411yescharacteristic
84Q8×C13—22no—
85Q8×C13—22no—
86D4×C13—22no—
87D4×C13—22no—
88C2×C4×C13—22no—
89C2×C4×C13C2×D411yescharacteristic
90C2×C4×C13C2×D411yescharacteristic
91C2×C4×C13C2411yescharacteristic
92C22⋊D13—44no—
93C22⋊D13—44no—
94C2×Dic13—22no—
95C2×Dic13—22no—
96C2×Dic13—44no—
97C2×Dic13C2×D411yescharacteristic
98C2×Dic13C2×D411yescharacteristic
99D52—22no—
100C4×D13—21no—
101C4×D13—21no—
102C4×D13—21no—
103C4×D13—21no—
104C4×D13—44no—
105Dic26—22no—
106Dic26—44no—
107Dic26C2×D414yes—
108C8×C13—21no—
109C8×C13C2×D412yes—
110#1055—21no—
111#1055—21no—
112C2×#135—131no—
113C22×Q16—131no—
114#548—132no—
115#495D1311yescharacteristic, complemented
116#467—131no—
117#466—131no—
118#464—132no—
119#452—132no—
120#448—132no—
121C4×Q16—131no—
122C8×D4—131no—
123C22×C13—42no—
124C22×C13—42no—
125C22×C13—42no—
126C22×C13C22×D411yescharacteristic
127C2×D13—21no—
128C2×D13—21no—
129C2×D13—21no—
130C2×D13—21no—
131C2×D13—21no—
132C2×D13#13512yescomplemented
133C4×C13—21no—
134C4×C13—21no—
135C4×C13—42no—
136C4×C13C22×D411yescharacteristic
137C4×C13H(5,𝔽2)11yescharacteristic
138Dic13—24no—
139Dic13—21no—
140Dic13—21no—
141Dic13—42no—
142C2×#41—132no—
143C22×Q8—132no—
144#135—264no—
145C2×Q16—132no—
146C2×Q16—131no—
147C2×Q16—264no—
148C2×Q16C2×D1311yescharacteristic
149C2×SD16—132no—
150C2×SD16C2×D1312yes—
151C2×D8C2×D1311yescharacteristic
152C22×C8—131no—
153C22×C8—131no—
154#124—262no—
155#124C2×D1312yes—
156C22⋊Q8—132no—
157C22⋊Q8—262no—
158#121—132no—
159#121—262no—
160C4×Q8—132no—
161C4×D4—131no—
162C4×D4—262no—
163#107—131no—
164C4⋊C8—131no—
165#103—132no—
166#103—132no—
167#102—132no—
168C22⋊C8—131no—
169C22⋊C8—131no—
170C4×C8C2×D1311yescharacteristic
171C2×C13—82no—
172C2×C13D4211yescharacteristic
173C2×C13C2×#13511yescharacteristic
174C2×C13#57811yescharacteristic
175D13—22no—
176D13—41no—
177#41—264no—
178#41—522no—
179C2×Q8—132no—
180C2×Q8—262no—
181C2×Q8—264no—
182C2×Q8—522no—
183C2×Q8C22×D1312yes—
184C2×D4—131no—
185C2×D4—262no—
186C2×D4—262no—
187C2×D4C22×D1312yes—
188C22×C4—131no—
189C22×C4—131no—
190C22×C4—262no—
191C22×C4—262no—
192Q16—22no—
193Q16—134no—
194Q16—264no—
195SD16—42no—
196SD16—264no—
197D8—22no—
198C2×C8—131no—
199C2×C8—131no—
200C2×C8—262no—
201C2×C8—262no—
202C2×C8C22×D1311yescharacteristic
203C2×C8C22×D1311yescharacteristic
204C4⋊C4—131no—
205C4⋊C4—132no—
206C4⋊C4—262no—
207C4⋊C4—262no—
208C22⋊C4—22no—
209C22⋊C4—22no—
210C22⋊C4—131no—
211C22⋊C4—131no—
212C22⋊C4—262no—
213C22⋊C4—262no—
214C42—262no—
215C42C22×D1311yescharacteristic
216C13#328511yescharacteristic, complemented, Sylow
217C23—22no—
218C23—131no—
219C23—131no—
220Q8—22no—
221Q8—22no—
222Q8—134no—
223Q8—262no—
224Q8—524no—
225D4—22no—
226D4—22no—
227D4—262no—
228D4—524no—
229D4—524no—
230C2×C4—22no—
231C2×C4—131no—
232C2×C4—131no—
233C2×C4—262no—
234C2×C4—261no—
235C2×C4—261no—
236C2×C4—261no—
237C2×C4—261no—
238C2×C4—262no—
239C2×C4—524no—
240C2×C4—524no—
241C2×C4D4×D1311yescharacteristic
242C2×C4D4×D1311yescharacteristic
243C2×C4C23×D1311yescharacteristic
244C8—21no—
245C8—261no—
246C8—261no—
247C8D4×D1312yes—
248C22—42no—
249C22—42no—
250C22—42no—
251C22—132no—
252C22—261no—
253C22—261no—
254C22—261no—
255C22—261no—
256C22—261no—
257C22C2×D4×D1311yescharacteristic
258C4—21no—
259C4—21no—
260C4—42no—
261C4—261no—
262C4—261no—
263C4—264no—
264C4—522no—
265C4C2×D4×D1311yescharacteristic
266C4#8825111yescharacteristic
267C2—82no—
268C2—262no—
269C2—521no—
270C2#1171942211yescharacteristic
271C2D13×#13511yescharacteristic
272C2#1171947611yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#495C2
socleC22×C13C22×D4
hypercenter#495D13
hypocenterC13#3285
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #495

Complements

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

NH ≅ G/Ntype
1. C2×Q16×D13C2semidirect
2. C2×#88166C2semidirect
3. #11719382C2semidirect
4. C13×#495C2semidirect
5. #11718849C2semidirect
6. #11718834C2semidirect
7. #11718831C2semidirect
8. #11718818C2semidirect
9. #11718715C2semidirect
10. C4×Dic52C2semidirect
11. C8×D52C2semidirect
77. Dic52D4semidirect
115. #495D13semidirect
132. C2×D13#135semidirect
216. C13#3285semidirect

Maximal subgroups

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

subgroupindex
C2×Q16×D132
C2×#881662
#117193822
C13×#4952
#117188492
#117188342
#117188312
#117188182
#117187152
C4×Dic522
C8×D522
#328513