Finite Group Databasebeta

← #13125901

Subgroups — #13125901

Order 1664.

396 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 109 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#11719436C211yesmaximal, characteristic, complemented
2#11719420C211yesmaximal, characteristic
3C13×#492C211yesmaximal, characteristic, complemented
4#11718834C212yesmaximal, complemented
5#11718830C212yesmaximal, complemented
6#11718827C212yesmaximal, complemented
7#11718824C212yesmaximal, complemented
8#11718747C211yesmaximal, characteristic, complemented
9#11718732C211yesmaximal, characteristic, complemented
10#11718358C211yesmaximal, characteristic, complemented
11#11718351C211yesmaximal, characteristic, complemented
12C2×#6129C2211yescharacteristic
13C2×D4×D13C2211yescharacteristic
14C2×C13×SD16C2212yes—
15C2×C13×SD16C2212yescomplemented
16C13×C4⋊Q8C2211yescharacteristic, complemented
17C13×#127C2211yescharacteristic
18#88200C2212yes—
19Q8×Dic13C2212yescomplemented
20C2×#6107C2212yescomplemented
21C2×#6106C2212yes—
22#88194C2211yescharacteristic
23#88193—22no—
24#88191—22no—
25#88190C2211yescharacteristic
26#88152—22no—
27#88143—22no—
28#88129C2211yescharacteristic
29#88126C2211yescharacteristic
30#88124C2211yescharacteristic, complemented
31C4×C8×C13C2211yescharacteristic, complemented
32#88072C2212yes—
33#88072C2212yescomplemented
34#88061C2212yes—
35#88060C2212yes—
36#88056C2212yescomplemented
37#88054C2212yescomplemented
38#88043C2211yescharacteristic, complemented
39C23×D13—21no—
40C2×Q8×C13C2312yes—
41C2×D4×C13—22no—
42C2×D4×C13C2311yescharacteristic
43C2×D4×C13C2311yescharacteristic
44C2×C22⋊D13—21no—
45C2×C22⋊D13—21no—
46C2×C22⋊D13—22no—
47C22×Dic13—21no—
48#6129—42no—
49D4×D13—42no—
50C2×D52C2311yescharacteristic
51C2×C4×D13C2311yescharacteristic
52C2×Dic26C2311yescharacteristic
53C13×SD16—42no—
54C13×SD16—42no—
55C2×C8×C13C2312yes—
56C13×C4⋊C4—22no—
57C42×C13C2311yescharacteristic
58C22⋊Dic13—22no—
59#6107—42no—
60#6106—42no—
61#6103—22no—
62#6103—22no—
63#6103D412yes—
64C4⋊Dic13—22no—
65C4⋊Dic13C2312yes—
66#6101—22no—
67#6101—22no—
68#6101D412yes—
69C4×Dic13—22no—
70C4×Dic13C2311yescharacteristic
71C2×#1055C2312yes—
72#3222—131nomaximal, Sylow
73C23×C13—21no—
74C23×C13—21no—
75C22×D13—21no—
76C22×D13—42no—
77C22×D13—82no—
78C22×D13C2×D411yescharacteristic
79Q8×C13—22no—
80Q8×C13—22no—
81D4×C13—22no—
82D4×C13—22no—
83D4×C13—82no—
84C2×C4×C13—22no—
85C2×C4×C13C2×D412yes—
86C2×C4×C13C2411yescharacteristic
87C22⋊D13—42no—
88C22⋊D13—42no—
89C22⋊D13—82no—
90C2×Dic13—22no—
91C2×Dic13—21no—
92C2×Dic13—42no—
93C2×Dic13C2×D412yes—
94C2×Dic13C2×D411yescharacteristic
95D52—22no—
96C4×D13—22no—
97Dic26—22no—
98C8×C13—22no—
99#1055—22no—
100#541—131no—
101#535—131no—
102#497—131no—
103#492D1311yescharacteristic, complemented
104#490—131no—
105#488—131no—
106#464—132no—
107#460—132no—
108#452—132no—
109#450—132no—
110#433—131no—
111C22×C13—41no—
112C22×C13—41no—
113C22×C13—42no—
114C22×C13—42no—
115C22×C13C22×D411yescharacteristic
116C2×D13—21no—
117C2×D13—22no—
118C2×D13—41no—
119C2×D13—42no—
120C2×D13—84no—
121C4×C13—22no—
122C4×C13—42no—
123C4×C13H(5,𝔽2)12yes—
124Dic13—21no—
125Dic13—22no—
126Dic13—41no—
127Dic13—42no—
128C2×#41—131no—
129C22×D4—131no—
130C2×Q16—132no—
131C2×SD16—132no—
132C2×SD16C2×D1312yes—
133C2×SD16C2×D1312yescomplemented
134C4⋊Q8C2×D1311yescharacteristic, complemented
135#127—131no—
136#127C2×D1311yescharacteristic
137#126—262no—
138#125—131no—
139#125—262no—
140#124—131no—
141#124—131no—
142C22⋊Q8—132no—
143#121—262no—
144#120—262no—
145C4×Q8—132no—
146#117—131no—
147C4⋊C8—132no—
148#103—132no—
149#102—132no—
150#102—132no—
151#102—132no—
152C22⋊C8—132no—
153#97—131no—
154C4×C8C2×D1311yescharacteristic, complemented
155C2×C13—81no—
156C2×C13—81no—
157C2×C13#53511yescharacteristic
158C2×C13#57712yes—
159D13—41no—
160D13—81no—
161C24—261no—
162#41—522no—
163C2×Q8—131no—
164C2×Q8C22×D1312yes—
165C2×D4—22no—
166C2×D4—131no—
167C2×D4—261no—
168C2×D4—262no—
169C2×D4—261no—
170C2×D4—522no—
171C2×D4C22×D1311yescharacteristic
172C2×D4C22×D1311yescharacteristic
173C22×C4—131no—
174C22×C4—261no—
175Q16—522no—
176SD16—42no—
177SD16—42no—
178SD16—522no—
179C2×C8—132no—
180C2×C8C22×D1312yes—
181C4⋊C4—22no—
182C4⋊C4—132no—
183C4⋊C4—132no—
184C4⋊C4—262no—
185C4⋊C4—262no—
186C4⋊C4—262no—
187C22⋊C4—132no—
188C22⋊C4—262no—
189C22⋊C4—262no—
190C22⋊C4—262no—
191C42—131no—
192C42—262no—
193C42C22×D1311yescharacteristic
194C13#322211yescharacteristic, complemented, Sylow
195C23—21no—
196C23—21no—
197C23—131no—
198C23—261no—
199C23—522no—
200C23—1042no—
201Q8—22no—
202Q8—22no—
203Q8—262no—
204D4—22no—
205D4—22no—
206D4—82no—
207D4—262no—
208D4—522no—
209D4—522no—
210D4—1042no—
211C2×C4—22no—
212C2×C4—132no—
213C2×C4—131no—
214C2×C4—262no—
215C2×C4—262no—
216C2×C4—261no—
217C2×C4—522no—
218C2×C4D4×D1312yes—
219C2×C4C23×D1311yescharacteristic
220C8—22no—
221C8—262no—
222C22—42no—
223C22—42no—
224C22—41no—
225C22—41no—
226C22—262no—
227C22—261no—
228C22—522no—
229C22—521no—
230C22—1044no—
231C22C2×D4×D1311yescharacteristic
232C4—22no—
233C4—42no—
234C4—262no—
235C4—261no—
236C4—522no—
237C4—521no—
238C4#8825112yes—
239C2—81no—
240C2—81no—
241C2—521no—
242C2—1041no—
243C2#1171942011yescharacteristic
244C2#1171946712yes—
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#492C2
socleC22×C13C22×D4
prime radical#11719420C2
hypercenter#492D13
hypocenterC13#3222
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
1. #11719436C2semidirect
3. C13×#492C2semidirect
4. #11718834C2semidirect
5. #11718830C2semidirect
6. #11718827C2semidirect
7. #11718824C2semidirect
8. #11718747C2semidirect
9. #11718732C2semidirect
10. #11718358C2semidirect
11. #11718351C2semidirect
15. C2×C13×SD16C22semidirect
16. C13×C4⋊Q8C22semidirect
19. Q8×Dic13C22semidirect
20. C2×#6107C22semidirect
30. #88124C22semidirect
31. C4×C8×C13C22semidirect
33. #88072C22semidirect
36. #88056C22semidirect
37. #88054C22semidirect
38. #88043C22semidirect
103. #492D13semidirect
133. C2×SD16C2×D13semidirect
134. C4⋊Q8C2×D13semidirect
154. C4×C8C2×D13semidirect
194. C13#3222semidirect

Maximal subgroups

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

subgroupindex
#117194362
#117194202
C13×#4922
#117188342
#117188302
#117188272
#117188242
#117187472
#117187322
#117183582
#117183512
#322213