Finite Group Databasebeta

← #13126754

Subgroups — #13126754

Order 1664.

386 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 123 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#11719256C211yesmaximal, characteristic
2#11719247C211yesmaximal, characteristic, complemented
3C8×D4×C13C211yesmaximal, characteristic, complemented
4#11718777C212yesmaximal, complemented
5#11718774C212yesmaximal, complemented
6#11718510C211yesmaximal, characteristic, complemented
7#11718507C211yesmaximal, characteristic, complemented
8#11718394C212yesmaximal, complemented
9#11718384C212yesmaximal, complemented
10C4×#6095C211yesmaximal, characteristic, complemented
11#11718342C211yesmaximal, characteristic, complemented
12C2×#6127C2212yes—
13C22×C8×C13C2212yes—
14C4×D4×C13C2211yescharacteristic
15#88192—21no—
16#88190—21no—
17#88180C2212yes—
18#88178C2212yes—
19#88178C2212yes—
20C2×Dic52C2212yes—
21C2×#6095C2211yescharacteristic
22C4⋊C4×D13—21no—
23#88141—21no—
24#88137—22no—
25#88133—22no—
26C4×D52C2211yescharacteristic
27#88123C2211yescharacteristic
28#88123C2211yescharacteristic
29C4×Dic26C2211yescharacteristic
30C13×C4⋊C8C2211yescharacteristic
31C13×C22⋊C8C2212yes—
32C4×C8×C13C2211yescharacteristic
33#88061C2212yes—
34#88061C2211yescharacteristic
35#88058C2212yes—
36#88057C2211yescharacteristic
37#88056C2212yes—
38#88056C2212yes—
39#88056C2211yescharacteristic
40#88056C2212yes—
41C2×D4×C13D411yescharacteristic
42C22×C4×C13C2312yes—
43C2×C22⋊D13—22no—
44#6127—24no—
45#6127—42no—
46C2×D52C2311yescharacteristic
47C2×C4×D13—21no—
48C2×C4×D13—22no—
49C2×Dic26—21no—
50C2×Dic26C2311yescharacteristic
51C2×Dic26C2312yes—
52C2×C8×C13—42no—
53C2×C8×C13C2311yescharacteristic
54C2×C8×C13C2311yescharacteristic
55C2×C8×C13C2312yes—
56C13×C4⋊C4D411yescharacteristic
57C13×C22⋊C4D412yes—
58C42×C13C2311yescharacteristic
59C22⋊Dic13—22no—
60C22⋊Dic13—22no—
61C22⋊Dic13—22no—
62#6103—21no—
63C4⋊Dic13—21no—
64C4⋊Dic13—21no—
65C4⋊Dic13—21no—
66C4⋊Dic13C2311yescharacteristic
67C4⋊Dic13C2312yes—
68C4⋊Dic13C2311yescharacteristic
69#6101—21no—
70#6101—22no—
71#6101—22no—
72C4×Dic13—21no—
73C4×Dic13—22no—
74Dic52—42no—
75#6095—22no—
76#3302—131nomaximal, Sylow
77C23×C13C2×D412yes—
78C22×D13—21no—
79D4×C13—22no—
80C2×C4×C13—22no—
81C2×C4×C13—22no—
82C2×C4×C13C2×D412yes—
83C2×C4×C13C2×D411yescharacteristic
84C2×C4×C13C2×D411yescharacteristic
85C2×C4×C13C2411yescharacteristic
86C22⋊D13—44no—
87C2×Dic13—21no—
88C2×Dic13—21no—
89C2×Dic13—22no—
90C2×Dic13—21no—
91C2×Dic13—22no—
92D52—21no—
93D52#4112yes—
94C4×D13—44no—
95C4×D13—42no—
96Dic26—21no—
97Dic26—22no—
98Dic26—21no—
99Dic26—22no—
100Dic26—42no—
101C8×C13—21no—
102C8×C13—22no—
103C8×C13—21no—
104#556—131no—
105#547—131no—
106#487—131no—
107#485—132no—
108#474—131no—
109#467—132no—
110#462—131no—
111#452—132no—
112C4×SD16—131no—
113C8×D4D1311yescharacteristic, complemented
114#416—132no—
115C22×C13—22no—
116C22×C13—22no—
117C22×C13—22no—
118C22×C13C22×D411yescharacteristic
119C2×D13—22no—
120C2×D13—41no—
121C2×D13—41no—
122C4×C13—22no—
123C4×C13—21no—
124C4×C13#13512yes—
125C4×C13C2×#4111yescharacteristic
126C4×C13H(5,𝔽2)11yescharacteristic
127Dic13—42no—
128Dic13—41no—
129Dic13—42no—
130Dic13—41no—
131Dic13—41no—
132C2×#41—132no—
133C2×Q16—132no—
134C2×SD16—131no—
135C22×C8C2×D1312yes—
136C4⋊Q8—131no—
137C4⋊Q8—131no—
138#126—262no—
139#124—261no—
140#123—262no—
141C22⋊Q8—132no—
142C22⋊Q8—132no—
143#121—261no—
144C4×Q8—131no—
145C4×Q8—261no—
146C4×D4—131no—
147C4×D4C2×D1311yescharacteristic
148#117—132no—
149C2×C4⋊C4—261no—
150#107—132no—
151#106—131no—
152C4⋊C8C2×D1311yescharacteristic
153#103—132no—
154#103—132no—
155#103—131no—
156#103—132no—
157#102—131no—
158#102—132no—
159C22⋊C8C2×D1312yes—
160C4×C8C2×D1311yescharacteristic
161C2×C13—42no—
162C2×C13#54611yescharacteristic
163C2×C13C2×#13511yescharacteristic
164C2×C13#57811yescharacteristic
165D13—42no—
166#41—264no—
167#41—522no—
168C2×Q8—132no—
169C2×Q8—131no—
170C2×Q8—261no—
171C2×D4—131no—
172C2×D4—262no—
173C2×D4D5211yescharacteristic
174C22×C4—261no—
175C22×C4—262no—
176C22×C4C22×D1312yes—
177Q16—522no—
178SD16—262no—
179C2×C8—42no—
180C2×C8C22×D1311yescharacteristic
181C2×C8C22×D1311yescharacteristic
182C2×C8C22×D1312yes—
183C4⋊C4—131no—
184C4⋊C4—132no—
185C4⋊C4—131no—
186C4⋊C4—261no—
187C4⋊C4—262no—
188C4⋊C4—261no—
189C4⋊C4—262no—
190C4⋊C4—261no—
191C4⋊C4—261no—
192C4⋊C4D5211yescharacteristic
193C22⋊C4—262no—
194C22⋊C4—262no—
195C22⋊C4—262no—
196C22⋊C4—261no—
197C22⋊C4D5212yes—
198C42—262no—
199C42—261no—
200C42C22×D1311yescharacteristic
201C13#330211yescharacteristic, complemented, Sylow
202C23—261no—
203C23C2×D5212yes—
204Q8—261no—
205Q8—262no—
206Q8—261no—
207Q8—262no—
208Q8—522no—
209D4—22no—
210D4—132no—
211D4—261no—
212D4—524no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—261no—
216C2×C4—262no—
217C2×C4—261no—
218C2×C4—261no—
219C2×C4—262no—
220C2×C4—524no—
221C2×C4—522no—
222C2×C4C2×D5212yes—
223C2×C4C2×D5211yescharacteristic
224C2×C4C2×D5211yescharacteristic
225C2×C4C23×D1311yescharacteristic
226C8—21no—
227C8—22no—
228C8—21no—
229C22—22no—
230C22—22no—
231C22—22no—
232C22—262no—
233C22—521no—
234C22—521no—
235C22C22×D5211yescharacteristic
236C4—21no—
237C4—22no—
238C4—521no—
239C4—522no—
240C4—521no—
241C4—522no—
242C4—521no—
243C4#8815812yes—
244C4#8825111yescharacteristic
245C4#41×D1311yescharacteristic
246C2—42no—
247C2—522no—
248C2#1171925911yescharacteristic
249C2C2×#8815811yescharacteristic
250C2#1171945811yescharacteristic
subgroupG/H
centerC22C22×D52
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC8×D4×C13C2
socleC22×C13C22×D4
prime radical#11719256C2
hypercenterC8×D4D13
hypocenterC13#3302
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
2. #11719247C2semidirect
3. C8×D4×C13C2semidirect
4. #11718777C2semidirect
5. #11718774C2semidirect
6. #11718510C2semidirect
7. #11718507C2semidirect
8. #11718394C2semidirect
9. #11718384C2semidirect
10. C4×#6095C2semidirect
11. #11718342C2semidirect
113. C8×D4D13semidirect
201. C13#3302semidirect

Maximal subgroups

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

subgroupindex
#117192562
#117192472
C8×D4×C132
#117187772
#117187742
#117185102
#117185072
#117183942
#117183842
C4×#60952
#117183422
#330213