Finite Group Databasebeta

← #13124528

Subgroups — #13124528

Order 1664.

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

normal subgroups only

This group has 472 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
1C2×#88163C211yesmaximal, characteristic, complemented
2C2×#88161C211yesmaximal, characteristic, complemented
3#11719231C211yesmaximal, characteristic, complemented
4#11719215C211yesmaximal, characteristic
5C13×#428C211yesmaximal, characteristic, complemented
6#11718663C211yesmaximal, characteristic, complemented
7C2×#88050C211yesmaximal, characteristic, complemented
8#11718548C212yesmaximal, complemented
9#11718547C212yesmaximal, complemented
10#11718529C212yesmaximal, complemented
11#11718525C212yesmaximal, complemented
12C2×#6127C2211yescharacteristic
13C2×#6127C2211yescharacteristic
14C22×Dic26C2211yescharacteristic
15C2×C13×M16C2211yescharacteristic
16C13×#117C2211yescharacteristic
17C2×C13×C4⋊C4C2211yescharacteristic
18#88184—22no—
19C22×#1055C2211yescharacteristic
20#88163—24no—
21#88161—24no—
22C2×Dic52C2212yes—
23C2×#6095C2212yes—
24C2×#6094C2212yes—
25C2×C8×D13C2212yes—
26#88151—21no—
27#88151C2212yes—
28#88151C2212yes—
29#88151C2212yes—
30#88149—21no—
31#88149C2212yes—
32#88140—22no—
33#88129—21no—
34#88123—21no—
35C13×#107C2212yes—
36C13×#106C2212yes—
37#88050C2211yescharacteristic
38#88050C2211yescharacteristic
39#88050C2212yes—
40#88050C2212yes—
41#88049C2211yescharacteristic
42#88049C2211yescharacteristic
43C22×C4×C13—21no—
44C22×C4×C13C2311yescharacteristic
45C2×C22⋊D13—21no—
46C2×C22⋊D13D412yes—
47C22×Dic13—21no—
48#6127—22no—
49#6127—22no—
50#6127—22no—
51#6127—22no—
52C2×D52—22no—
53C2×D52D411yescharacteristic
54C2×D52C2311yescharacteristic
55C2×C4×D13—21no—
56C2×C4×D13C2312yes—
57C2×Dic26—22no—
58C2×Dic26—22no—
59C2×Dic26—21no—
60C2×Dic26D411yescharacteristic
61C2×Dic26C2312yes—
62C2×Dic26C2311yescharacteristic
63C13×M16D414yescomplemented
64C2×C8×C13C2312yes—
65C13×C4⋊C4—21no—
66C13×C4⋊C4C2311yescharacteristic
67C13×C4⋊C4C2312yes—
68C13×C4⋊C4C2311yescharacteristic
69C13×C22⋊C4—21no—
70C42×C13—21no—
71#6103—22no—
72#6103—22no—
73#6103—22no—
74#6103—22no—
75C4⋊Dic13—22no—
76C4⋊Dic13—22no—
77C4⋊Dic13—22no—
78C2×#1055—22no—
79C2×#1055C2311yescharacteristic
80C2×#1055C2311yescharacteristic
81Dic52—24no—
82#6095—24no—
83#6094—24no—
84C8×D13—24no—
85#3063—131nomaximal, Sylow
86C23×C13C2×D411yescharacteristic
87C22×D13—21no—
88C22×D13C2×D412yes—
89C2×C4×C13—21no—
90C2×C4×C13—21no—
91C2×C4×C13—22no—
92C2×C4×C13—81no—
93C2×C4×C13C2×D411yescharacteristic
94C2×C4×C13C2×D412yes—
95C2×C4×C13#4112yes—
96C2×C4×C13C2411yescharacteristic
97C22⋊D13—24no—
98C22⋊D13—42no—
99C2×Dic13—22no—
100C2×Dic13—21no—
101C2×Dic13—42no—
102C2×Dic13C2×D412yes—
103D52—22no—
104D52—21no—
105D52—21no—
106D52—82no—
107C4×D13—22no—
108C4×D13—22no—
109C4×D13—42no—
110Dic26—22no—
111Dic26—22no—
112Dic26—21no—
113Dic26—22no—
114Dic26—21no—
115Dic26—42no—
116C8×C13C2×D414yes—
117#1055—21no—
118#1055—21no—
119C2×#137—131no—
120C2×#131—131no—
121#537—131no—
122#536—131no—
123#470—132no—
124#468—132no—
125#467—132no—
126#465—132no—
127#428D1311yescharacteristic, complemented
128#416—131no—
129C2×#103—131no—
130C22×C13—21no—
131C22×C13—21no—
132C22×C13#12112yes—
133C22×C13C22×D411yescharacteristic
134C2×D13—22no—
135C2×D13—22no—
136C2×D13—22no—
137C2×D13—41no—
138C2×D13—41no—
139C2×D13—41no—
140C4×C13—42no—
141C4×C13—41no—
142C4×C13—41no—
143C4×C13#12112yes—
144C4×C13C22×D411yescharacteristic
145C4×C13C2×#4111yescharacteristic
146Dic13—22no—
147Dic13—42no—
148Dic13—41no—
149C2×#41—131no—
150C2×#41—131no—
151C22×Q8—131no—
152#137—264no—
153C2×Q16—132no—
154C2×SD16—132no—
155#131—264no—
156C2×M16—132no—
157C2×M16C2×D1311yescharacteristic
158C22×C8—131no—
159C22×C8—132no—
160C4⋊Q8—261no—
161#124—261no—
162#123—262no—
163C22⋊Q8—132no—
164C22⋊Q8—132no—
165C22⋊Q8—132no—
166C22⋊Q8—261no—
167#121—132no—
168#121—261no—
169#121—262no—
170#117C2×D1311yescharacteristic
171C2×C4⋊C4C2×D1311yescharacteristic
172#107C2×D1312yes—
173#106C2×D1312yes—
174#103—132no—
175#103—132no—
176#103—131no—
177#103—131no—
178#102—131no—
179#102—131no—
180C2×C13—22no—
181C2×C13C2×#12111yescharacteristic
182C2×C13#57711yescharacteristic
183C2×C13#57811yescharacteristic
184D13—42no—
185D13—81no—
186#41—262no—
187#41—262no—
188#41—262no—
189#41—262no—
190C2×Q8—131no—
191C2×Q8—132no—
192C2×Q8—131no—
193C2×Q8—261no—
194C2×Q8—262no—
195C2×Q8—262no—
196C2×D4—132no—
197C2×D4—131no—
198C2×D4—131no—
199C2×D4—262no—
200C2×D4—261no—
201C22×C4—21no—
202C22×C4—132no—
203C22×C4—261no—
204C22×C4—261no—
205C22×C4C22×D1311yescharacteristic
206Q16—264no—
207SD16—264no—
208M16—264no—
209M16D5214yescomplemented
210C2×C8—131no—
211C2×C8—131no—
212C2×C8—262no—
213C2×C8—264no—
214C2×C8C22×D1312yes—
215C4⋊C4—21no—
216C4⋊C4—262no—
217C4⋊C4—262no—
218C4⋊C4—262no—
219C4⋊C4C22×D1311yescharacteristic
220C4⋊C4C22×D1311yescharacteristic
221C4⋊C4C22×D1312yes—
222C22⋊C4—21no—
223C22⋊C4—262no—
224C22⋊C4—262no—
225C22⋊C4—262no—
226C22⋊C4—262no—
227C42—21no—
228C13#306311yescharacteristic, complemented, Sylow
229C23—132no—
230C23—261no—
231C23D4×D1311yescharacteristic
232Q8—262no—
233Q8—262no—
234Q8—261no—
235Q8—262no—
236Q8—261no—
237Q8—522no—
238D4—264no—
239D4—262no—
240D4—261no—
241D4—261no—
242D4—522no—
243D4—1042no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—22no—
247C2×C4—81no—
248C2×C4—132no—
249C2×C4—262no—
250C2×C4—262no—
251C2×C4—261no—
252C2×C4—262no—
253C2×C4—522no—
254C2×C4—522no—
255C2×C4C2×D5212yes—
256C2×C4D4×D1311yescharacteristic
257C2×C4#613112yes—
258C2×C4C23×D1311yescharacteristic
259C8—261no—
260C8—261no—
261C8C2×D5214yes—
262C22—21no—
263C22—21no—
264C22—262no—
265C22—262no—
266C22—262no—
267C22—521no—
268C22—521no—
269C22—521no—
270C22#8814912yes—
271C22C2×D4×D1311yescharacteristic
272C4—41no—
273C4—42no—
274C4—41no—
275C4—262no—
276C4—521no—
277C4—522no—
278C4#8814912yes—
279C4C22×D5211yescharacteristic
280C4C2×#613111yescharacteristic
281C2—22no—
282C2—522no—
283C2—1041no—
284C2C2×#8814911yescharacteristic
285C2#1171948011yescharacteristic
286C2#1171948411yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#428C2
socleC22×C13C22×D4
prime radical#11719215C2
hypercenter#428D13
hypocenterC13#3063
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
1. C2×#88163C2semidirect
2. C2×#88161C2semidirect
3. #11719231C2semidirect
5. C13×#428C2semidirect
6. #11718663C2semidirect
7. C2×#88050C2semidirect
8. #11718548C2semidirect
9. #11718547C2semidirect
10. #11718529C2semidirect
11. #11718525C2semidirect
63. C13×M16D4semidirect
127. #428D13semidirect
209. M16D52semidirect
228. C13#3063semidirect

Maximal subgroups

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

subgroupindex
C2×#881632
C2×#881612
#117192312
#117192152
C13×#4282
#117186632
C2×#880502
#117185482
#117185472
#117185292
#117185252
#306313