Finite Group Databasebeta

← #13125910

Subgroups — #13125910

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
1#11719230C211yesmaximal, characteristic
2#11719223C211yesmaximal, characteristic, complemented
3C13×#433C211yesmaximal, characteristic, complemented
4#11718509C212yesmaximal, complemented
5#11718506C212yesmaximal, complemented
6#11718394C212yesmaximal, complemented
7#11718392C212yesmaximal, complemented
8#11718376C211yesmaximal, characteristic, complemented
9#11718374C211yesmaximal, characteristic, complemented
10#11718358C211yesmaximal, characteristic, complemented
11#11718354C211yesmaximal, characteristic, complemented
12C2×#6127C2211yescharacteristic
13C22×D52C2211yescharacteristic
14C13×#117C2211yescharacteristic
15#88178C2212yes—
16C2×Dic52C2212yescomplemented
17C2×#6095C2212yes—
18C2×#6095C2212yes—
19C2×#6095C2212yescomplemented
20#88149—22no—
21#88143—22no—
22#88136—22no—
23#88133—22no—
24#88129C2211yescharacteristic
25#88129C2211yescharacteristic
26#88128C2211yescharacteristic
27#88128C2211yescharacteristic
28#88124C2211yescharacteristic, complemented
29#88123C2211yescharacteristic, complemented
30C4×Dic26C2212yescomplemented
31C13×C4⋊C8C2212yescomplemented
32C13×C22⋊C8C2212yes—
33C13×#97C2211yescharacteristic, complemented
34C4×C8×C13C2211yescharacteristic, complemented
35#88061C2212yes—
36#88061C2212yes—
37#88061C2212yescomplemented
38#88056C2212yescomplemented
39C23×D13—21no—
40C22×C4×C13C2311yescharacteristic
41C2×C22⋊D13—21no—
42#6127—42no—
43C2×D52—21no—
44C2×D52—22no—
45C2×D52—22no—
46C2×D52—42no—
47C2×D52C2311yescharacteristic
48C2×D52C2311yescharacteristic
49C2×D52C2311yescharacteristic
50C2×C4×D13—21no—
51C2×Dic26C2312yes—
52C2×Dic26C2311yescharacteristic
53C2×C8×C13C2312yes—
54C2×C8×C13C2312yes—
55C13×C4⋊C4D412yes—
56C13×C22⋊C4D412yes—
57C42×C13C2311yescharacteristic
58C42×C13C2311yescharacteristic
59C22⋊Dic13—22no—
60#6103—22no—
61#6103—22no—
62C4⋊Dic13—22no—
63C4⋊Dic13C2312yes—
64#6101—22no—
65#6101—22no—
66#6101—22no—
67C4×Dic13—22no—
68Dic52—42no—
69#6095—42no—
70#6095—42no—
71#6095—42no—
72#3222—131nomaximal, Sylow
73C23×C13C2×D411yescharacteristic
74C22×D13—21no—
75C22×D13—21no—
76C22×D13—21no—
77C22×D13—42no—
78C22×D13—82no—
79C2×C4×C13—22no—
80C2×C4×C13C2×D412yes—
81C2×C4×C13C2×D411yescharacteristic
82C2×C4×C13C2×D412yes—
83C2×C4×C13C2411yescharacteristic
84C22⋊D13—42no—
85C2×Dic13—22no—
86C2×Dic13—22no—
87C2×Dic13—21no—
88D52—22no—
89D52—22no—
90D52—22no—
91D52—42no—
92D52—82no—
93D52—82no—
94C4×D13—42no—
95Dic26—22no—
96Dic26—22no—
97Dic26—22no—
98C8×C13—22no—
99C8×C13—22no—
100#541—131no—
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#433D1311yescharacteristic, complemented
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×C13H(5,𝔽2)12yes—
125Dic13—41no—
126Dic13—42no—
127Dic13—42no—
128C2×#41—131no—
129C22×D4—131no—
130C2×Q16—132no—
131C2×SD16—132no—
132C2×SD16—132no—
133C2×SD16—132no—
134C4⋊Q8—131no—
135#127—131no—
136#127—131no—
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#117C2×D1311yescharacteristic
147C4⋊C8C2×D1312yescomplemented
148#103—132no—
149#102—132no—
150#102—132no—
151#102—132no—
152C22⋊C8C2×D1312yes—
153#97C2×D1311yescharacteristic, complemented
154C4×C8C2×D1311yescharacteristic, complemented
155C2×C13—41no—
156C2×C13#53511yescharacteristic
157C2×C13#57712yes—
158D13—81no—
159D13—81no—
160D13—81no—
161C24—261no—
162#41—522no—
163C2×Q8—131no—
164C2×Q8—132no—
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×C8C22×D1312yes—
180C2×C8C22×D1312yes—
181C4⋊C4—132no—
182C4⋊C4—262no—
183C4⋊C4—262no—
184C4⋊C4—262no—
185C4⋊C4—262no—
186C4⋊C4D5212yes—
187C22⋊C4—262no—
188C22⋊C4—262no—
189C22⋊C4—262no—
190C22⋊C4D5212yes—
191C42—262no—
192C42C22×D1311yescharacteristic
193C42C22×D1311yescharacteristic
194C13#322211yescharacteristic, complemented, Sylow
195C23—261no—
196C23—261no—
197C23—261no—
198C23—522no—
199C23—1042no—
200C23C2×D5211yescharacteristic
201Q8—262no—
202Q8—262no—
203Q8—262no—
204D4—262no—
205D4—262no—
206D4—262no—
207D4—522no—
208D4—522no—
209D4—1042no—
210D4—1042no—
211C2×C4—22no—
212C2×C4—262no—
213C2×C4—262no—
214C2×C4—261no—
215C2×C4—522no—
216C2×C4C2×D5212yes—
217C2×C4C2×D5212yes—
218C2×C4C2×D5211yescharacteristic
219C2×C4C23×D1311yescharacteristic
220C8—22no—
221C8—22no—
222C22—22no—
223C22—21no—
224C22—522no—
225C22—522no—
226C22—522no—
227C22—521no—
228C22—521no—
229C22—521no—
230C22—1044no—
231C22C22×D5211yescharacteristic
232C4—22no—
233C4—22no—
234C4—21no—
235C4—522no—
236C4—521no—
237C4—522no—
238C4#8825612yes—
239C2—41no—
240C2—1041no—
241C2—1041no—
242C2—1041no—
243C2#1171923011yescharacteristic
244C2#1171945612yes—
subgroupG/H
centerC22C22×D52
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#433C2
socleC22×C13C22×D4
prime radical#11719230C2
hypercenter#433D13
hypocenterC13#3222
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
2. #11719223C2semidirect
3. C13×#433C2semidirect
4. #11718509C2semidirect
5. #11718506C2semidirect
6. #11718394C2semidirect
7. #11718392C2semidirect
8. #11718376C2semidirect
9. #11718374C2semidirect
10. #11718358C2semidirect
11. #11718354C2semidirect
16. C2×Dic52C22semidirect
19. C2×#6095C22semidirect
28. #88124C22semidirect
29. #88123C22semidirect
30. C4×Dic26C22semidirect
31. C13×C4⋊C8C22semidirect
33. C13×#97C22semidirect
34. C4×C8×C13C22semidirect
37. #88061C22semidirect
38. #88056C22semidirect
110. #433D13semidirect
147. C4⋊C8C2×D13semidirect
153. #97C2×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
#117192302
#117192232
C13×#4332
#117185092
#117185062
#117183942
#117183922
#117183762
#117183742
#117183582
#117183542
#322213