Finite Group Databasebeta

← #13125962

Subgroups — #13125962

Order 1664.

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

normal subgroups only

This group has 404 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
1#11719301C211yesmaximal, characteristic
2C2×#88142C211yesmaximal, characteristic, complemented
3C13×#481C211yesmaximal, characteristic, complemented
4#11718695C211yesmaximal, characteristic, complemented
5#11718629C211yesmaximal, characteristic, complemented
6#11718531C212yesmaximal, complemented
7#11718516C212yesmaximal, complemented
8#11718422C212yesmaximal, complemented
9#11718421C212yesmaximal, complemented
10#11718396C211yesmaximal, characteristic, complemented
11#11718379C211yesmaximal, characteristic, complemented
12C2×#6129—21no—
13C22×Dic26—21no—
14C13×#121C2211yescharacteristic
15C2×C13×C4⋊C4C2211yescharacteristic
16#88194C2211yescharacteristic
17#88193—21no—
18D4×Dic13C2211yescharacteristic
19#88184C2211yescharacteristic
20C2×C4⋊Dic13C2211yescharacteristic
21C2×#6101—21no—
22C2×C4×Dic13C2211yescharacteristic
23#88147C2211yescharacteristic
24#88142—21no—
25#88142—21no—
26#88142C2212yes—
27#88142C2212yes—
28#88142C2211yescharacteristic
29#88139—21no—
30#88135—21no—
31C13×#106C2212yes—
32C13×#102C2212yes—
33C13×C22⋊C8C2211yescharacteristic
34#88072C2212yes—
35C22⋊#1055C2211yescharacteristic
36#88061C2212yes—
37#88057C2212yes—
38#88054C2212yes—
39C8×Dic13C2212yes—
40#88049C2212yes—
41#88048C2212yes—
42#88048C2212yes—
43C2×D4×C13—21no—
44C2×D4×C13C2311yescharacteristic
45C22×C4×C13—21no—
46C22×C4×C13C2311yescharacteristic
47C2×C22⋊D13—21no—
48C2×C22⋊D13—21no—
49C2×C22⋊D13—21no—
50C22×Dic13—21no—
51C22×Dic13—21no—
52C22×Dic13D411yescharacteristic
53C22×Dic13D411yescharacteristic
54#6129—44no—
55C2×D52C2311yescharacteristic
56C2×C4×D13—21no—
57C2×Dic26—21no—
58C2×Dic26—22no—
59C2×Dic26—22no—
60C2×Dic26—44no—
61C2×C8×C13C2312yes—
62C13×C4⋊C4—21no—
63C13×C4⋊C4C2312yes—
64C13×C4⋊C4C2311yescharacteristic
65C13×C22⋊C4—21no—
66C22⋊Dic13—21no—
67#6103—21no—
68#6103—21no—
69C4⋊Dic13—21no—
70C4⋊Dic13C2312yes—
71C4⋊Dic13C2311yescharacteristic
72#6101—21no—
73#6101—22no—
74#6101—22no—
75C4×Dic13D411yescharacteristic
76C4×Dic13D411yescharacteristic
77C4×Dic13C2311yescharacteristic
78C4×Dic13C2311yescharacteristic
79C2×#1055C2312yes—
80#3227—131nomaximal, Sylow
81C23×C13—21no—
82C23×C13C2×D411yescharacteristic
83C22×D13—21no—
84D4×C13—22no—
85D4×C13—42no—
86C2×C4×C13—22no—
87C2×C4×C13—22no—
88C2×C4×C13—21no—
89C2×C4×C13—42no—
90C2×C4×C13C2×D411yescharacteristic
91C2×C4×C13C2411yescharacteristic
92C22⋊D13—42no—
93C22⋊D13—42no—
94C22⋊D13—42no—
95C2×Dic13—22no—
96C2×Dic13—22no—
97C2×Dic13—21no—
98C2×Dic13—42no—
99C2×Dic13—42no—
100C2×Dic13SD1614yes—
101C2×Dic13C2×D411yescharacteristic
102C2×Dic13C2×D411yescharacteristic
103C2×Dic13C2×D411yescharacteristic
104C2×Dic13C2×D411yescharacteristic
105D52—22no—
106C4×D13—42no—
107Dic26—44no—
108Dic26—42no—
109Dic26—44no—
110C8×C13—22no—
111#1055—22no—
112#532—131no—
113C2×C4⋊Q8—131no—
114#498—132no—
115#486—132no—
116#481—131no—
117#481—131no—
118#481—131no—
119#481D1311yescharacteristic, complemented
120#476—132no—
121#476—132no—
122#431—131no—
123C22×C13—21no—
124C22×C13—21no—
125C22×C13—41no—
126C22×C13—41no—
127C22×C13—41no—
128C22×C13C2×SD1612yes—
129C22×C13C22×D411yescharacteristic
130C2×D13—41no—
131C2×D13—41no—
132C2×D13—41no—
133C4×C13—21no—
134C4×C13—41no—
135C4×C13—42no—
136C4×C132−1+412yes—
137Dic13—21no—
138Dic13—41no—
139Dic13—42no—
140Dic13C2×SD1612yes—
141Dic13C2×SD1612yes—
142Dic13AGL(1,ℤ/8)12yes—
143C2×#41—261no—
144C22×Q8—261no—
145C4⋊Q8—132no—
146C4⋊Q8—132no—
147C4⋊Q8—131no—
148C4⋊Q8—261no—
149C4⋊Q8—261no—
150#127—131no—
151#124—261no—
152#121—131no—
153#121—261no—
154#121C2×D1311yescharacteristic
155C4×D4—131no—
156C4×D4—131no—
157C4×D4—261no—
158C2×C4⋊C4—131no—
159C2×C4⋊C4—261no—
160C2×C4⋊C4C2×D1311yescharacteristic
161C2×C42—131no—
162#106—132no—
163#106—132no—
164#106—132no—
165#106C2×D1312yes—
166C4⋊C8—132no—
167#102—132no—
168#102—132no—
169#102—132no—
170#102C2×D1312yes—
171C22⋊C8—131no—
172C22⋊C8C2×D1311yescharacteristic
173C4×C8—132no—
174C2×C13—22no—
175C2×C13—81no—
176C2×C13#53611yescharacteristic
177C2×C13C22×SD1611yescharacteristic
178C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
179D13—81no—
180#41—524no—
181C2×Q8—261no—
182C2×Q8—262no—
183C2×Q8—262no—
184C2×Q8—524no—
185C2×D4—21no—
186C2×D4—131no—
187C2×D4—261no—
188C2×D4—261no—
189C2×D4—261no—
190C2×D4C22×D1311yescharacteristic
191C22×C4—21no—
192C22×C4—131no—
193C22×C4—131no—
194C22×C4—261no—
195C22×C4—261no—
196C22×C4—261no—
197C22×C4C22×D1311yescharacteristic
198C2×C8—132no—
199C2×C8C22×D1312yes—
200C4⋊C4—21no—
201C4⋊C4—132no—
202C4⋊C4—131no—
203C4⋊C4—262no—
204C4⋊C4—262no—
205C4⋊C4—261no—
206C4⋊C4—261no—
207C4⋊C4C22×D1312yes—
208C4⋊C4C22×D1311yescharacteristic
209C22⋊C4—21no—
210C22⋊C4—261no—
211C22⋊C4—261no—
212C22⋊C4—261no—
213C42—131no—
214C42—131no—
215C42—131no—
216C42—131no—
217C13#322711yescharacteristic, complemented, Sylow
218C23—21no—
219C23—261no—
220C23D4×D1311yescharacteristic
221Q8—524no—
222Q8—522no—
223Q8—524no—
224D4—22no—
225D4—42no—
226D4—262no—
227D4—522no—
228D4—522no—
229D4—522no—
230C2×C4—22no—
231C2×C4—21no—
232C2×C4—22no—
233C2×C4—42no—
234C2×C4—134no—
235C2×C4—131no—
236C2×C4—131no—
237C2×C4—131no—
238C2×C4—131no—
239C2×C4—262no—
240C2×C4—261no—
241C2×C4—262no—
242C2×C4—522no—
243C2×C4—522no—
244C2×C4—522no—
245C2×C4D4×D1311yescharacteristic
246C2×C4C23×D1311yescharacteristic
247C8—22no—
248C8—262no—
249C22—21no—
250C22—21no—
251C22—41no—
252C22—41no—
253C22—41no—
254C22—521no—
255C22—521no—
256C22—521no—
257C22SD16×D1312yes—
258C22C2×D4×D1311yescharacteristic
259C4—21no—
260C4—41no—
261C4—42no—
262C4—132no—
263C4—132no—
264C4—132no—
265C4—261no—
266C4—521no—
267C4—522no—
268C4#8825712yes—
269C2—22no—
270C2—81no—
271C2—1041no—
272C2#1171935311yescharacteristic
273C2C2×SD16×D1311yescharacteristic
274C2D13×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#481C2
socleC22×C13C22×D4
prime radical#11719301C2
hypercenter#481D13
hypocenterC13#3227
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
2. C2×#88142C2semidirect
3. C13×#481C2semidirect
4. #11718695C2semidirect
5. #11718629C2semidirect
6. #11718531C2semidirect
7. #11718516C2semidirect
8. #11718422C2semidirect
9. #11718421C2semidirect
10. #11718396C2semidirect
11. #11718379C2semidirect
119. #481D13semidirect
217. C13#3227semidirect

Maximal subgroups

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

subgroupindex
#117193012
C2×#881422
C13×#4812
#117186952
#117186292
#117185312
#117185162
#117184222
#117184212
#117183962
#117183792
#322713