Finite Group Databasebeta

← #13127431

Subgroups — #13127431

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
1C13×#547C211yesmaximal, characteristic, complemented
2#11719268C211yesmaximal, characteristic, complemented
3#11718748C211yesmaximal, characteristic, complemented
4#11718740C211yesmaximal, characteristic, complemented
5#11718700C212yesmaximal, complemented
6#11718696C212yesmaximal, complemented
7C4×#6104C211yesmaximal, characteristic, complemented
8#11718673C211yesmaximal, characteristic, complemented
9#11718669C211yesmaximal, characteristic, complemented
10#11718629C212yesmaximal, complemented
11#11718625C212yesmaximal, complemented
12C2×C13×#41—21no—
13C13×C4⋊Q8C2211yescharacteristic
14C13×#123—22no—
15C13×C22⋊Q8—21no—
16C13×#121C2212yes—
17C4×D4×C13C2211yescharacteristic
18C4×D4×C13C2211yescharacteristic
19C2×C13×C4⋊C4C2212yes—
20#88192—21no—
21C2×#6104C2211yescharacteristic
22#88184C2212yes—
23#88180C2212yes—
24C2×#6099C2212yes—
25#88146—21no—
26#88139—22no—
27C4×D52C2211yescharacteristic
28#88123C2211yescharacteristic
29#88072C2212yes—
30#88072C2211yescharacteristic
31C22⋊#1055C2212yes—
32#88049C2211yescharacteristic
33#88049C2212yes—
34#88048C2212yes—
35#88048C2212yes—
36#88048C2212yes—
37#88047C2211yescharacteristic
38#88047C2212yes—
39C4⋊#1055C2211yescharacteristic
40C4×#1055C2211yescharacteristic
41C13×#41—44no—
42C2×Q8×C13—21no—
43C2×D4×C13—22no—
44C2×D4×C13D411yescharacteristic
45C2×D4×C13C2311yescharacteristic
46C22×C4×C13—22no—
47C22×C4×C13—21no—
48C22×C4×C13C2312yes—
49C2×C22⋊D13—22no—
50C2×D52C2311yescharacteristic
51C2×C4×D13—21no—
52C2×Dic26—21no—
53C13×C4⋊C4—22no—
54C13×C4⋊C4—21no—
55C13×C4⋊C4D411yescharacteristic
56C13×C4⋊C4C2311yescharacteristic
57C13×C4⋊C4C2312yes—
58C13×C22⋊C4—21no—
59C13×C22⋊C4—22no—
60C13×C22⋊C4D412yes—
61C42×C13C2311yescharacteristic
62C22⋊Dic13—22no—
63#6104—22no—
64#6103—21no—
65#6103—22no—
66C4⋊Dic13—21no—
67C4⋊Dic13C2312yes—
68C4⋊Dic13C2311yescharacteristic
69C4×Dic13—22no—
70#6099—24no—
71C2×#1055C2311yescharacteristic
72C2×#1055C2312yes—
73C2×#1055C2311yescharacteristic
74#3354—131nomaximal, Sylow
75C23×C13—21no—
76C23×C13C2×D412yes—
77C22×D13—21no—
78Q8×C13—42no—
79D4×C13—22no—
80D4×C13—21no—
81D4×C13—21no—
82D4×C13—44no—
83C2×C4×C13—22no—
84C2×C4×C13—22no—
85C2×C4×C13—21no—
86C2×C4×C13—22no—
87C2×C4×C13—44no—
88C2×C4×C13—42no—
89C2×C4×C13C2×D412yes—
90C2×C4×C13C2×D411yescharacteristic
91C2×C4×C13C2×D411yescharacteristic
92C2×C4×C13C2411yescharacteristic
93C22⋊D13—82no—
94C2×Dic13—21no—
95C2×Dic13—22no—
96D52—21no—
97D52—21no—
98C4×D13—42no—
99Dic26—81no—
100#1055—22no—
101#1055—21no—
102#1055#4112yescomplemented
103#555—131no—
104#547D1311yescharacteristic, complemented
105#498—131no—
106#482—132no—
107#481—132no—
108#476—131no—
109#474—131no—
110#469—132no—
111C4×D8—131no—
112#436—131no—
113#428—132no—
114C22×C13—22no—
115C22×C13—22no—
116C22×C13—22no—
117C22×C13—41no—
118C22×C13—41no—
119C22×C13—41no—
120C22×C13C22×D411yescharacteristic
121C2×D13—41no—
122C2×D13—41no—
123C2×D13—41no—
124C4×C13—22no—
125C4×C13—21no—
126C4×C13—41no—
127C4×C13—42no—
128C4×C13AGL(1,ℤ/8)12yes—
129C4×C13C2×#4111yescharacteristic
130C4×C132−1+411yescharacteristic
131Dic13—41no—
132Dic13—42no—
133C2×#41—21no—
134C2×D8—131no—
135C2×M16—132no—
136C4⋊Q8—131no—
137C4⋊Q8C2×D1311yescharacteristic
138#124—262no—
139#123—22no—
140C22⋊Q8—21no—
141#121—132no—
142#121—261no—
143#121C2×D1312yes—
144C4×D4—131no—
145C4×D4C2×D1311yescharacteristic
146C4×D4C2×D1311yescharacteristic
147#117—132no—
148#117—261no—
149C2×C4⋊C4C2×D1312yes—
150#107—131no—
151#107—132no—
152#106—132no—
153#106—132no—
154#106—132no—
155C4⋊C8—131no—
156#102—131no—
157#102—132no—
158#102—131no—
159#102—132no—
160C22⋊C8—132no—
161C4×C8—131no—
162C2×C13—42no—
163C2×C13—81no—
164C2×C13#54711yescharacteristic
165C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
166C2×C13#57711yescharacteristic
167D13—81no—
168#41—44no—
169C2×Q8—21no—
170C2×Q8—261no—
171C2×D4—22no—
172C2×D4—131no—
173C2×D4—262no—
174C2×D4C22⋊D1311yescharacteristic
175C2×D4C22×D1311yescharacteristic
176C22×C4—22no—
177C22×C4—21no—
178C22×C4—261no—
179C22×C4C22×D1312yes—
180D8—262no—
181M16—264no—
182C2×C8—131no—
183C2×C8—131no—
184C2×C8—132no—
185C4⋊C4—22no—
186C4⋊C4—21no—
187C4⋊C4—132no—
188C4⋊C4—131no—
189C4⋊C4—261no—
190C4⋊C4C22⋊D1311yescharacteristic
191C4⋊C4C22×D1311yescharacteristic
192C4⋊C4C22×D1312yes—
193C22⋊C4—21no—
194C22⋊C4—22no—
195C22⋊C4—262no—
196C22⋊C4—262no—
197C22⋊C4—261no—
198C22⋊C4C22⋊D1312yes—
199C42—262no—
200C42C22×D1311yescharacteristic
201C13#335411yescharacteristic, complemented, Sylow
202C23—21no—
203C23—261no—
204C23C2×C22⋊D1312yes—
205Q8—42no—
206Q8—1041no—
207D4—22no—
208D4—21no—
209D4—21no—
210D4—44no—
211D4—261no—
212D4—261no—
213D4—1042no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—44no—
219C2×C4—42no—
220C2×C4—261no—
221C2×C4—262no—
222C2×C4—522no—
223C2×C4C2×C22⋊D1312yes—
224C2×C4C2×C22⋊D1311yescharacteristic
225C2×C4C2×C22⋊D1311yescharacteristic
226C2×C4C23×D1311yescharacteristic
227C8—132no—
228C8—262no—
229C8—261no—
230C22—22no—
231C22—22no—
232C22—22no—
233C22—41no—
234C22—41no—
235C22—41no—
236C22—521no—
237C22—521no—
238C22—521no—
239C22C22×C22⋊D1311yescharacteristic
240C4—22no—
241C4—21no—
242C4—41no—
243C4—42no—
244C4—521no—
245C4—522no—
246C4#8818612yes—
247C4#41×D1311yescharacteristic
248C4#8825711yescharacteristic
249C2—42no—
250C2—81no—
251C2—1041no—
252C2C2×#8818611yescharacteristic
253C2#1171952911yescharacteristic
254C2#1171954211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#547C2
socleC22×C13C22×D4
hypercenter#547D13
hypocenterC13#3354
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. C13×#547C2semidirect
2. #11719268C2semidirect
3. #11718748C2semidirect
4. #11718740C2semidirect
5. #11718700C2semidirect
6. #11718696C2semidirect
7. C4×#6104C2semidirect
8. #11718673C2semidirect
9. #11718669C2semidirect
10. #11718629C2semidirect
11. #11718625C2semidirect
102. #1055#41semidirect
104. #547D13semidirect
201. C13#3354semidirect

Maximal subgroups

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

subgroupindex
C13×#5472
#117192682
#117187482
#117187402
#117187002
#117186962
C4×#61042
#117186732
#117186692
#117186292
#117186252
#335413