Finite Group Databasebeta

← #13125760

Subgroups — #13125760

Order 1664.

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

normal subgroups only

This group has 428 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
1D13×C4⋊Q8C211yesmaximal, characteristic, complemented
2#11719253C211yesmaximal, characteristic
3C13×#461C211yesmaximal, characteristic, complemented
4#11718836C212yesmaximal, complemented
5#11718831C212yesmaximal, complemented
6#11718744C211yesmaximal, characteristic, complemented
7#11718680C211yesmaximal, characteristic, complemented
8#11718502C211yesmaximal, characteristic, complemented
9#11718494C211yesmaximal, characteristic, complemented
10#11718467C212yesmaximal, complemented
11#11718453C212yesmaximal, complemented
12C2×Q8×D13C2212yes—
13C2×#6127—21no—
14C2×C13×SD16C2212yes—
15C13×C4⋊Q8C2211yescharacteristic
16C4×D4×C13C2211yescharacteristic
17#88198C2212yes—
18C2×#6106C2212yes—
19#88194C2211yescharacteristic
20#88192C2211yescharacteristic
21C2×#6105C2212yes—
22C4×C22⋊D13—21no—
23C2×#6095C2212yes—
24#88149C2211yescharacteristic
25C4⋊C4×D13—21no—
26C4⋊C4×D13—21no—
27#88142—21no—
28#88142—21no—
29#88142C2211yescharacteristic
30#88139—21no—
31#88138—21no—
32C4×D52C2211yescharacteristic
33C42×D13C2211yescharacteristic
34#88123C2211yescharacteristic
35C13×C4⋊C8C2211yescharacteristic
36C13×#103C2212yes—
37#88075C2212yes—
38#88060C2212yes—
39#88056C2212yes—
40C8×Dic13C2212yes—
41#88050C2212yes—
42C4⋊#1055C2211yescharacteristic
43C2×Q8×C13C2312yes—
44C2×D4×C13C2311yescharacteristic
45C22×C4×C13—21no—
46C2×C22⋊D13—21no—
47C2×C22⋊D13—21no—
48C2×C22⋊D13—21no—
49Q8×D13—42no—
50Q8×D13—42no—
51#6127—44no—
52C2×D52—21no—
53C2×D52C2311yescharacteristic
54C2×C4×D13—22no—
55C2×C4×D13—21no—
56C2×C4×D13D411yescharacteristic
57C2×C4×D13D411yescharacteristic
58C2×C4×D13C2311yescharacteristic
59C2×Dic26—21no—
60C2×Dic26—22no—
61C2×Dic26C2312yes—
62C13×SD16—42no—
63C2×C8×C13C2312yes—
64C13×C4⋊C4—21no—
65C13×C4⋊C4—21no—
66C13×C4⋊C4C2311yescharacteristic
67C13×C22⋊C4—21no—
68C42×C13C2311yescharacteristic
69C22⋊Dic13—21no—
70#6106—42no—
71#6105—42no—
72#6103—21no—
73#6103—21no—
74C4⋊Dic13—21no—
75C4⋊Dic13—21no—
76C4⋊Dic13C2311yescharacteristic
77#6101—21no—
78#6101—22no—
79#6101—22no—
80C4×Dic13D411yescharacteristic
81C4×Dic13D411yescharacteristic
82C4×Dic13C2311yescharacteristic
83C2×#1055C2312yes—
84#6095—42no—
85#3206—131nomaximal, Sylow
86C23×C13—21no—
87C22×D13—21no—
88C22×D13C2×D411yescharacteristic
89Q8×C13—22no—
90Q8×C13—22no—
91D4×C13—21no—
92D4×C13—21no—
93C2×C4×C13—22no—
94C2×C4×C13—21no—
95C2×C4×C13—42no—
96C2×C4×C13C2×D411yescharacteristic
97C2×C4×C13C2×D411yescharacteristic
98C2×C4×C13C2411yescharacteristic
99C22⋊D13—42no—
100C22⋊D13—42no—
101C22⋊D13—42no—
102C2×Dic13—22no—
103C2×Dic13—21no—
104C2×Dic13C2×D411yescharacteristic
105C2×Dic13C2×D411yescharacteristic
106C2×Dic13C2×D411yescharacteristic
107D52—21no—
108D52—21no—
109D52—42no—
110C4×D13—21no—
111C4×D13—21no—
112C4×D13—22no—
113C4×D13—44no—
114C4×D13—42no—
115C4×D13SD1614yescomplemented
116Dic26—22no—
117Dic26—22no—
118Dic26—44no—
119Dic26—42no—
120C8×C13—22no—
121#1055—22no—
122#532—131no—
123C2×C4⋊Q8—131no—
124#492—132no—
125#487—132no—
126#461—131no—
127#461—131no—
128#461—131no—
129#461D1311yescharacteristic, complemented
130#448—132no—
131#448—132no—
132#431—131no—
133C22×C13—41no—
134C22×C13—41no—
135C22×C13—41no—
136C22×C13C22×D411yescharacteristic
137C2×D13—21no—
138C2×D13—21no—
139C2×D13—41no—
140C2×D13—41no—
141C2×D13—41no—
142C2×D13C2×SD1612yes—
143C4×C13—21no—
144C4×C13—42no—
145C4×C13—41no—
146C4×C13C2×SD1612yes—
147C4×C13H(5,𝔽2)11yescharacteristic
148C4×C13H(5,𝔽2)11yescharacteristic
149Dic13—21no—
150Dic13—42no—
151Dic13—41no—
152Dic13C2×SD1612yes—
153Dic13#13712yes—
154C2×#41—261no—
155C22×Q8—132no—
156C2×SD16—132no—
157C2×SD16—132no—
158C2×SD16—132no—
159C2×SD16C2×D1312yes—
160C4⋊Q8—131no—
161C4⋊Q8—132no—
162C4⋊Q8—131no—
163C4⋊Q8—261no—
164C4⋊Q8—261no—
165C4⋊Q8C2×D1311yescharacteristic
166#127—131no—
167#124—261no—
168#121—131no—
169#121—131no—
170#121—261no—
171C4×D4—131no—
172C4×D4—261no—
173C4×D4C2×D1311yescharacteristic
174C2×C4⋊C4—261no—
175C2×C4⋊C4—261no—
176C2×C42—131no—
177C4⋊C8—131no—
178C4⋊C8C2×D1311yescharacteristic
179#103—132no—
180#103—132no—
181#103—132no—
182#103C2×D1312yes—
183C22⋊C8—132no—
184C4×C8—132no—
185C2×C13—81no—
186C2×C13#53511yescharacteristic
187C2×C13C22×SD1611yescharacteristic
188C2×C13C2×#13711yescharacteristic
189D13—22no—
190D13—81no—
191#41—524no—
192C2×Q8—132no—
193C2×Q8—261no—
194C2×Q8—262no—
195C2×Q8—522no—
196C2×Q8—522no—
197C2×Q8C22×D1312yes—
198C2×D4—131no—
199C2×D4—261no—
200C2×D4—261no—
201C2×D4—261no—
202C2×D4—261no—
203C2×D4C22×D1311yescharacteristic
204C22×C4—21no—
205C22×C4—131no—
206C22×C4—131no—
207C22×C4—131no—
208C22×C4—262no—
209C22×C4—261no—
210SD16—42no—
211SD16—522no—
212SD16—522no—
213SD16—522no—
214C2×C8—132no—
215C2×C8C22×D1312yes—
216C4⋊C4—21no—
217C4⋊C4—21no—
218C4⋊C4—131no—
219C4⋊C4—262no—
220C4⋊C4—262no—
221C4⋊C4—261no—
222C4⋊C4—261no—
223C4⋊C4—261no—
224C4⋊C4C22×D1311yescharacteristic
225C22⋊C4—21no—
226C22⋊C4—261no—
227C22⋊C4—261no—
228C22⋊C4—261no—
229C42—131no—
230C42—131no—
231C42—131no—
232C42C22×D1311yescharacteristic
233C13#320611yescharacteristic, complemented, Sylow
234C23—21no—
235C23—131no—
236C23—261no—
237Q8—22no—
238Q8—22no—
239Q8—262no—
240Q8—262no—
241Q8—522no—
242Q8—524no—
243D4—21no—
244D4—21no—
245D4—261no—
246D4—261no—
247D4—522no—
248D4—522no—
249D4—522no—
250D4—522no—
251C2×C4—21no—
252C2×C4—22no—
253C2×C4—42no—
254C2×C4—131no—
255C2×C4—131no—
256C2×C4—134no—
257C2×C4—131no—
258C2×C4—262no—
259C2×C4—261no—
260C2×C4—261no—
261C2×C4—261no—
262C2×C4—262no—
263C2×C4—524no—
264C2×C4—522no—
265C2×C4D4×D1311yescharacteristic
266C2×C4D4×D1311yescharacteristic
267C2×C4C23×D1311yescharacteristic
268C8—22no—
269C8—262no—
270C22—41no—
271C22—41no—
272C22—41no—
273C22—132no—
274C22—261no—
275C22—261no—
276C22—521no—
277C22—521no—
278C22—521no—
279C22C2×D4×D1311yescharacteristic
280C4—21no—
281C4—41no—
282C4—42no—
283C4—132no—
284C4—132no—
285C4—261no—
286C4—521no—
287C4—522no—
288C4SD16×D1312yes—
289C4#8825111yescharacteristic
290C4#8825611yescharacteristic
291C2—81no—
292C2—262no—
293C2—1041no—
294C2#1171931211yescharacteristic
295C2C2×SD16×D1311yescharacteristic
296C2D13×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#461C2
socleC22×C13C22×D4
prime radical#11719253C2
hypercenter#461D13
hypocenterC13#3206
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. D13×C4⋊Q8C2semidirect
3. C13×#461C2semidirect
4. #11718836C2semidirect
5. #11718831C2semidirect
6. #11718744C2semidirect
7. #11718680C2semidirect
8. #11718502C2semidirect
9. #11718494C2semidirect
10. #11718467C2semidirect
11. #11718453C2semidirect
115. C4×D13SD16semidirect
129. #461D13semidirect
233. C13#3206semidirect

Maximal subgroups

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

subgroupindex
D13×C4⋊Q82
#117192532
C13×#4612
#117188362
#117188312
#117187442
#117186802
#117185022
#117184942
#117184672
#117184532
#320613