Finite Group Databasebeta

← #13125439

Subgroups — #13125439

Order 1664.

364 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 119 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#11719433C211yesmaximal, characteristic, complemented
2#11719385C211yesmaximal, characteristic
3C13×#497C211yesmaximal, characteristic, complemented
4#11718850C212yesmaximal, complemented
5Q16×Dic13C212yesmaximal, complemented
6#11718835C212yesmaximal
7SD16×Dic13C212yesmaximal, complemented
8#11718743C211yesmaximal, characteristic, complemented
9#11718716C211yesmaximal, characteristic, complemented
10#11718368C211yesmaximal, characteristic, complemented
11#11718363C211yesmaximal, characteristic, complemented
12C2×C13×Q16C2212yes—
13C2×C13×SD16C2212yes—
14C13×C4⋊Q8C2211yescharacteristic
15C13×#124C2211yescharacteristic
16#88200C2212yes—
17#88200C2211yescharacteristic
18Q8×Dic13C2212yes—
19Q8×Dic13C2211yescharacteristic
20#88192C2211yescharacteristic
21D4×Dic13C2211yescharacteristic
22C2×#6094C2212yes—
23#88151—21no—
24#88146—21no—
25#88144—21no—
26#88141—21no—
27#88137—21no—
28#88135—21no—
29#88133—21no—
30#88131—21no—
31C42×D13C2211yescharacteristic
32#88124C2211yescharacteristic
33#88123C2211yescharacteristic
34C13×#97C2211yescharacteristic
35#88075C2212yes—
36#88075C2212yes—
37#88075C2212yes—
38#88072C2212yes—
39#88058C2212yes—
40#88057C2212yes—
41C8×Dic13C2212yes—
42#88043C2211yescharacteristic
43C2×Q8×C13C2311yescharacteristic
44C2×Q8×C13C2312yes—
45C2×D4×C13C2311yescharacteristic
46C2×C22⋊D13—21no—
47C22×Dic13—21no—
48C2×C4×D13D411yescharacteristic
49C2×C4×D13D411yescharacteristic
50C2×C4×D13C2311yescharacteristic
51C2×Dic26—21no—
52C13×Q16—24no—
53C13×SD16—24no—
54C2×C8×C13C2312yes—
55C13×C4⋊C4—21no—
56C13×C4⋊C4—21no—
57C13×C22⋊C4—21no—
58C13×C22⋊C4—21no—
59C42×C13C2311yescharacteristic
60C22⋊Dic13—21no—
61C22⋊Dic13—21no—
62#6103—21no—
63#6103—22no—
64C4⋊Dic13—21no—
65C4⋊Dic13—21no—
66C4⋊Dic13—22no—
67C4⋊Dic13C2312yes—
68C4⋊Dic13C2311yescharacteristic
69C4⋊Dic13C2311yescharacteristic
70#6101—21no—
71#6101—21no—
72#6101—21no—
73#6101—22no—
74C4×Dic13—21no—
75C4×Dic13—22no—
76C4×Dic13D411yescharacteristic
77C4×Dic13D411yescharacteristic
78C4×Dic13C2311yescharacteristic
79C2×#1055C2312yes—
80#6094—24no—
81#3172—131nomaximal, Sylow
82C23×C13—21no—
83C22×D13C2×D411yescharacteristic
84Q8×C13—22no—
85Q8×C13—22no—
86Q8×C13—22no—
87D4×C13—22no—
88C2×C4×C13—21no—
89C2×C4×C13—22no—
90C2×C4×C13C2×D411yescharacteristic
91C2×C4×C13C2×D411yescharacteristic
92C2×C4×C13C2411yescharacteristic
93C22⋊D13—42no—
94C2×Dic13—21no—
95C2×Dic13—22no—
96C2×Dic13—21no—
97C2×Dic13—42no—
98C2×Dic13C2×D411yescharacteristic
99C2×Dic13C2×D411yescharacteristic
100C2×Dic13C2×D411yescharacteristic
101C4×D13—22no—
102C4×D13—22no—
103C4×D13—41no—
104Dic26—42no—
105C8×C13#4114yes—
106#1055—22no—
107#533—131no—
108#529—131no—
109#501—131no—
110#497D1311yescharacteristic, complemented
111#491—131no—
112#489—131no—
113#470—132no—
114#468—132no—
115C4×Q16—132no—
116C4×SD16—132no—
117C4×M16—131no—
118C22×C13—41no—
119C22×C13—41no—
120C22×C13—41no—
121C22×C13C22×D411yescharacteristic
122C2×D13—21no—
123C2×D13—21no—
124C2×D13—21no—
125C4×C13—21no—
126C4×C13—21no—
127C4×C13—41no—
128C4×C13—42no—
129C4×C13C2×#4112yes—
130Dic13—21no—
131Dic13—21no—
132Dic13—41no—
133Dic13—42no—
134Dic13—41no—
135Dic13#13712yes—
136C2×Q16C2×D1312yes—
137C2×SD16C2×D1312yes—
138C2×M16—132no—
139C4⋊Q8—131no—
140C4⋊Q8C2×D1311yescharacteristic
141#126—261no—
142#125—131no—
143#125—261no—
144#124C2×D1311yescharacteristic
145#123—261no—
146C22⋊Q8—131no—
147C22⋊Q8—132no—
148C22⋊Q8—261no—
149#121—131no—
150C4×Q8—131no—
151C4×Q8—132no—
152C4×Q8—261no—
153C4×D4—131no—
154C4×D4—261no—
155#117—261no—
156#117—261no—
157C2×C42—131no—
158#107—132no—
159#106—132no—
160#103—132no—
161#103—132no—
162#103—132no—
163#102—132no—
164#97—131no—
165#97C2×D1311yescharacteristic
166C4×C8—132no—
167C2×C13—81no—
168C2×C13#53211yescharacteristic
169C2×C13C2×#13711yescharacteristic
170C2×C13#57511yescharacteristic
171D13—41no—
172C2×Q8—261no—
173C2×Q8C22×D1311yescharacteristic
174C2×Q8C22×D1312yes—
175C2×D4—261no—
176C2×D4C22×D1311yescharacteristic
177C22×C4—131no—
178C22×C4—131no—
179C22×C4—131no—
180C22×C4—261no—
181Q16—24no—
182SD16—24no—
183M16—264no—
184C2×C8—132no—
185C2×C8C22×D1312yes—
186C4⋊C4—21no—
187C4⋊C4—21no—
188C4⋊C4—132no—
189C4⋊C4—131no—
190C4⋊C4—131no—
191C4⋊C4—261no—
192C4⋊C4—262no—
193C4⋊C4—261no—
194C4⋊C4—262no—
195C4⋊C4—261no—
196C4⋊C4—261no—
197C4⋊C4—261no—
198C22⋊C4—21no—
199C22⋊C4—21no—
200C22⋊C4—262no—
201C22⋊C4—261no—
202C22⋊C4—261no—
203C22⋊C4—261no—
204C42—131no—
205C42—131no—
206C42—131no—
207C42—261no—
208C42—262no—
209C42C22×D1311yescharacteristic
210C13#317211yescharacteristic, complemented, Sylow
211C23—21no—
212C23—131no—
213Q8—22no—
214Q8—22no—
215Q8—22no—
216Q8—522no—
217D4—22no—
218D4—522no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—131no—
222C2×C4—131no—
223C2×C4—131no—
224C2×C4—262no—
225C2×C4—262no—
226C2×C4—261no—
227C2×C4—262no—
228C2×C4—261no—
229C2×C4—521no—
230C2×C4—522no—
231C2×C4D4×D1311yescharacteristic
232C2×C4D4×D1311yescharacteristic
233C2×C4C23×D1311yescharacteristic
234C8—262no—
235C8#612914yes—
236C22—41no—
237C22—41no—
238C22—41no—
239C22—261no—
240C22—261no—
241C22—261no—
242C22C2×D4×D1311yescharacteristic
243C4—21no—
244C4—21no—
245C4—41no—
246C4—42no—
247C4—132no—
248C4—261no—
249C4—261no—
250C4—521no—
251C4—521no—
252C4—522no—
253C4C2×#612912yes—
254C2—81no—
255C2—521no—
256C2#1171942111yescharacteristic
257C2D13×#13711yescharacteristic
258C2#1171948211yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#497C2
socleC22×C13C22×D4
prime radical#88192C22
hypercenter#497D13
hypocenterC13#3172
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

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

NH ≅ G/Ntype
1. #11719433C2semidirect
3. C13×#497C2semidirect
4. #11718850C2semidirect
5. Q16×Dic13C2semidirect
7. SD16×Dic13C2semidirect
8. #11718743C2semidirect
9. #11718716C2semidirect
10. #11718368C2semidirect
11. #11718363C2semidirect
110. #497D13semidirect
210. C13#3172semidirect

Maximal subgroups

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

subgroupindex
#117194332
#117193852
C13×#4972
#117188502
Q16×Dic132
#117188352
SD16×Dic132
#117187432
#117187162
#117183682
#117183632
#317213