Finite Group Databasebeta

← #13125902

Subgroups — #13125902

Order 1664.

396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 117 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
1C13×#541C211yesmaximal, characteristic, complemented
2#11719230C211yesmaximal, characteristic
3#11718747C211yesmaximal, characteristic, complemented
4#11718746C211yesmaximal, characteristic, complemented
5#11718729C211yesmaximal, characteristic, complemented
6#11718728C211yesmaximal, characteristic, complemented
7#11718708C212yesmaximal, complemented
8#11718707C212yesmaximal, complemented
9#11718689C212yesmaximal, complemented
10#11718688C212yesmaximal, complemented
11#11718661C211yesmaximal, characteristic, complemented
12C2×#6127C2211yescharacteristic
13C22×D52C2211yescharacteristic
14C13×C4⋊Q8C2211yescharacteristic, complemented
15C13×#126—22no—
16C13×#125—22no—
17C13×#125C2211yescharacteristic, complemented
18C13×C22⋊Q8C2212yes—
19C4×Q8×C13C2212yescomplemented
20C13×#117C2211yescharacteristic
21C2×#6107C2212yescomplemented
22C2×#6106C2212yes—
23C2×#6106C2212yes—
24C2×#6106C2212yescomplemented
25#88149—22no—
26#88136—22no—
27#88129C2211yescharacteristic
28#88129C2211yescharacteristic
29#88128C2211yescharacteristic
30#88128C2211yescharacteristic
31C22⋊#1055C2212yes—
32#88050C2212yescomplemented
33#88049C2212yes—
34#88049C2212yes—
35#88049C2212yescomplemented
36C4⋊#1055C2212yescomplemented
37#88043C2211yescharacteristic, complemented
38C4×#1055C2211yescharacteristic, complemented
39C23×D13—21no—
40C2×Q8×C13C2312yes—
41C22×C4×C13C2311yescharacteristic
42C2×C22⋊D13—21no—
43#6127—42no—
44C2×D52—21no—
45C2×D52—22no—
46C2×D52—22no—
47C2×D52—42no—
48C2×D52C2311yescharacteristic
49C2×D52C2311yescharacteristic
50C2×D52C2311yescharacteristic
51C2×C4×D13—21no—
52C2×Dic26C2311yescharacteristic
53C13×C4⋊C4—22no—
54C13×C4⋊C4—22no—
55C13×C4⋊C4—22no—
56C13×C4⋊C4—22no—
57C13×C4⋊C4D412yes—
58C13×C4⋊C4C2312yes—
59C13×C22⋊C4—22no—
60C13×C22⋊C4D412yes—
61C42×C13—22no—
62C42×C13C2311yescharacteristic
63C42×C13C2311yescharacteristic
64#6107—42no—
65#6106—42no—
66#6106—42no—
67#6106—42no—
68#6103—22no—
69#6103—22no—
70C2×#1055C2312yes—
71C2×#1055C2312yes—
72#3222—131nomaximal, Sylow
73C23×C13C2×D411yescharacteristic
74C22×D13—21no—
75C22×D13—21no—
76C22×D13—21no—
77C22×D13—42no—
78C22×D13—82no—
79Q8×C13—22no—
80Q8×C13—22no—
81C2×C4×C13—22no—
82C2×C4×C13—22no—
83C2×C4×C13—22no—
84C2×C4×C13C2×D412yes—
85C2×C4×C13C2×D412yes—
86C2×C4×C13C2×D411yescharacteristic
87C2×C4×C13C2411yescharacteristic
88C22⋊D13—42no—
89C2×Dic13—21no—
90D52—22no—
91D52—22no—
92D52—22no—
93D52—42no—
94D52—82no—
95D52—82no—
96C4×D13—42no—
97Dic26—22no—
98#1055—22no—
99#1055—22no—
100#541D1311yescharacteristic, complemented
101#535—131no—
102#497—131no—
103#492—131no—
104#490—131no—
105#488—131no—
106#464—132no—
107#460—132no—
108#452—132no—
109#450—132no—
110#433—131no—
111C22×C13—21no—
112C22×C13—22no—
113C22×C13C22×D411yescharacteristic
114C2×D13—41no—
115C2×D13—41no—
116C2×D13—41no—
117C2×D13—42no—
118C2×D13—42no—
119C2×D13—42no—
120C2×D13—84no—
121C4×C13—21no—
122C4×C13—22no—
123C4×C13—22no—
124C4×C13—42no—
125C4×C13—42no—
126C4×C13H(5,𝔽2)12yes—
127Dic13—41no—
128C2×#41—131no—
129C22×D4—131no—
130C2×Q16—132no—
131C2×SD16—132no—
132C2×SD16—132no—
133C2×SD16—132no—
134C4⋊Q8C2×D1311yescharacteristic, complemented
135#127—131no—
136#127—131no—
137#126—22no—
138#125—22no—
139#125C2×D1311yescharacteristic, complemented
140#124—131no—
141#124—131no—
142C22⋊Q8C2×D1312yes—
143#121—262no—
144#120—262no—
145C4×Q8C2×D1312yescomplemented
146#117C2×D1311yescharacteristic
147C4⋊C8—132no—
148#103—132no—
149#102—132no—
150#102—132no—
151#102—132no—
152C22⋊C8—132no—
153#97—131no—
154C4×C8—131no—
155C2×C13—41no—
156C2×C13#53511yescharacteristic
157C2×C13#57712yes—
158D13—81no—
159D13—81no—
160D13—81no—
161C24—261no—
162#41—522no—
163C2×Q8—131no—
164C2×Q8C22×D1312yes—
165C2×D4—131no—
166C2×D4—131no—
167C2×D4—131no—
168C2×D4—261no—
169C2×D4—261no—
170C2×D4—262no—
171C2×D4—262no—
172C2×D4—522no—
173C22×C4—261no—
174C22×C4C22×D1311yescharacteristic
175Q16—522no—
176SD16—522no—
177SD16—522no—
178SD16—522no—
179C2×C8—132no—
180C2×C8—132no—
181C4⋊C4—22no—
182C4⋊C4—22no—
183C4⋊C4—22no—
184C4⋊C4—22no—
185C4⋊C4C22⋊D1312yes—
186C4⋊C4C22×D1312yes—
187C22⋊C4—22no—
188C22⋊C4—262no—
189C22⋊C4—262no—
190C22⋊C4C22⋊D1312yes—
191C42—22no—
192C42C22×D1311yescharacteristic
193C42C22×D1311yescharacteristic
194C13#322211yescharacteristic, complemented, Sylow
195C23—261no—
196C23—261no—
197C23—261no—
198C23—522no—
199C23—1042no—
200C23C2×C22⋊D1311yescharacteristic
201Q8—22no—
202Q8—22no—
203Q8—262no—
204D4—262no—
205D4—262no—
206D4—262no—
207D4—522no—
208D4—522no—
209D4—1042no—
210D4—1042no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—261no—
215C2×C4—522no—
216C2×C4C2×C22⋊D1312yes—
217C2×C4C2×C22⋊D1312yes—
218C2×C4C2×C22⋊D1311yescharacteristic
219C2×C4C23×D1311yescharacteristic
220C8—262no—
221C8—262no—
222C22—21no—
223C22—22no—
224C22—521no—
225C22—521no—
226C22—521no—
227C22—522no—
228C22—522no—
229C22—522no—
230C22—1044no—
231C22C22×C22⋊D1311yescharacteristic
232C4—21no—
233C4—22no—
234C4—22no—
235C4—42no—
236C4—42no—
237C4—521no—
238C4#8825612yes—
239C2—41no—
240C2—1041no—
241C2—1041no—
242C2—1041no—
243C2#1171953511yescharacteristic
244C2#1171954212yes—
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#541C2
socleC22×C13C22×D4
prime radical#11719230C2
hypercenter#541D13
hypocenterC13#3222
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ #117 ◁ #541

Complements

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

NH ≅ G/Ntype
1. C13×#541C2semidirect
3. #11718747C2semidirect
4. #11718746C2semidirect
5. #11718729C2semidirect
6. #11718728C2semidirect
7. #11718708C2semidirect
8. #11718707C2semidirect
9. #11718689C2semidirect
10. #11718688C2semidirect
11. #11718661C2semidirect
14. C13×C4⋊Q8C22semidirect
17. C13×#125C22semidirect
19. C4×Q8×C13C22semidirect
21. C2×#6107C22semidirect
24. C2×#6106C22semidirect
32. #88050C22semidirect
35. #88049C22semidirect
36. C4⋊#1055C22semidirect
37. #88043C22semidirect
38. C4×#1055C22semidirect
100. #541D13semidirect
134. C4⋊Q8C2×D13semidirect
139. #125C2×D13semidirect
145. C4×Q8C2×D13semidirect
194. C13#3222semidirect

Maximal subgroups

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

subgroupindex
C13×#5412
#117192302
#117187472
#117187462
#117187292
#117187282
#117187082
#117187072
#117186892
#117186882
#117186612
#322213