Finite Group Databasebeta

← #13127433

Subgroups — #13127433

Order 1664.

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

normal subgroups only

This group has 386 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#11719268C211yesmaximal, characteristic, complemented
2#11719256C211yesmaximal, characteristic, complemented
3C4×C13×D8C211yesmaximal, characteristic, complemented
4#11718820C212yesmaximal, complemented
5#11718669C211yesmaximal, characteristic, complemented
6#11718668C211yesmaximal, characteristic, complemented
7#11718542C212yesmaximal, complemented
8#11718440C212yesmaximal, complemented
9#11718438C212yesmaximal, complemented
10#11718349C211yesmaximal, characteristic, complemented
11#11718341C211yesmaximal, characteristic, complemented
12C2×#6127—21no—
13C2×C13×D8C2211yescharacteristic
14C4×D4×C13C2211yescharacteristic
15C4×D4×C13C2211yescharacteristic
16#88192C2212yes—
17#88192C2212yes—
18#88184—21no—
19#88180—21no—
20#88178—21no—
21C2×#6094C2212yes—
22#88146C2212yes—
23C4⋊C4×D13C2212yes—
24#88139—22no—
25#88137—22no—
26C4×D52C2211yescharacteristic
27#88123C2211yescharacteristic
28#88123C2211yescharacteristic
29C13×#107C2211yescharacteristic
30C13×#102C2211yescharacteristic
31C13×#102C2211yescharacteristic
32C4×C8×C13C2211yescharacteristic
33#88072C2212yes—
34#88072C2212yes—
35#88060C2212yes—
36#88057C2212yes—
37#88057C2212yes—
38#88048C2212yes—
39#88047C2212yes—
40C4⋊#1055C2211yescharacteristic
41C2×D4×C13C2311yescharacteristic
42C2×D4×C13C2311yescharacteristic
43C22×C4×C13—21no—
44C22×C4×C13—21no—
45C2×C22⋊D13—22no—
46C2×C22⋊D13—22no—
47#6127—44no—
48C2×D52D411yescharacteristic
49C2×C4×D13—22no—
50C2×C4×D13C2312yes—
51C2×Dic26—21no—
52C2×Dic26—21no—
53C13×D8—22no—
54C2×C8×C13C2311yescharacteristic
55C2×C8×C13C2311yescharacteristic
56C13×C4⋊C4C2311yescharacteristic
57C13×C4⋊C4C2311yescharacteristic
58C13×C22⋊C4—21no—
59C13×C22⋊C4—21no—
60C42×C13C2311yescharacteristic
61C22⋊Dic13—22no—
62C22⋊Dic13—22no—
63#6103—22no—
64#6103D412yes—
65C4⋊Dic13—21no—
66C4⋊Dic13—21no—
67C4⋊Dic13D411yescharacteristic
68C4⋊Dic13C2312yes—
69C4⋊Dic13C2312yes—
70#6101—22no—
71C4×Dic13—22no—
72C2×#1055C2312yes—
73#6094—24no—
74#3354—131nomaximal, Sylow
75C23×C13—21no—
76C23×C13—21no—
77C22×D13C2×D412yes—
78D4×C13—21no—
79D4×C13—21no—
80D4×C13—21no—
81D4×C13—21no—
82C2×C4×C13—21no—
83C2×C4×C13—21no—
84C2×C4×C13—42no—
85C2×C4×C13—42no—
86C2×C4×C13C2×D411yescharacteristic
87C2×C4×C13C2×D411yescharacteristic
88C2×C4×C13C2411yescharacteristic
89C22⋊D13—44no—
90C22⋊D13—82no—
91C2×Dic13—22no—
92C2×Dic13—22no—
93C2×Dic13C2×D412yes—
94D52—22no—
95C4×D13—22no—
96C4×D13—22no—
97C4×D13—44no—
98Dic26—42no—
99Dic26—81no—
100C8×C13—21no—
101C8×C13#4112yescomplemented
102#1055—22no—
103#555—131no—
104#547—131no—
105#498—131no—
106#482—132no—
107#481—132no—
108#476—131no—
109#474—131no—
110#469—132no—
111C4×D8D1311yescharacteristic, complemented
112#436—131no—
113#428—132no—
114C22×C13—41no—
115C22×C13—41no—
116C22×C13—41no—
117C22×C13—41no—
118C22×C13—41no—
119C22×C13—41no—
120C22×C13C22×D411yescharacteristic
121C2×D13—22no—
122C2×D13—22no—
123C2×D13—22no—
124C4×C13—21no—
125C4×C13—41no—
126C4×C13—41no—
127C4×C13AGL(1,ℤ/8)12yes—
128C4×C13C2×#4111yescharacteristic
129C4×C132−1+411yescharacteristic
130Dic13—22no—
131Dic13—42no—
132Dic13—42no—
133C2×#41—261no—
134C2×D8C2×D1311yescharacteristic
135C2×M16—132no—
136C4⋊Q8—131no—
137C4⋊Q8—131no—
138#124—262no—
139#123—262no—
140C22⋊Q8—261no—
141#121—132no—
142#121—132no—
143#121—261no—
144C4×D4—131no—
145C4×D4C2×D1311yescharacteristic
146C4×D4C2×D1311yescharacteristic
147#117—132no—
148#117—261no—
149C2×C4⋊C4—132no—
150#107—132no—
151#107C2×D1311yescharacteristic
152#106—132no—
153#106—132no—
154#106—132no—
155C4⋊C8—131no—
156#102—132no—
157#102—132no—
158#102C2×D1311yescharacteristic
159#102C2×D1311yescharacteristic
160C22⋊C8—132no—
161C4×C8C2×D1311yescharacteristic
162C2×C13—81no—
163C2×C13—81no—
164C2×C13#54711yescharacteristic
165C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
166C2×C13#57711yescharacteristic
167D13—42no—
168#41—524no—
169C2×Q8—261no—
170C2×Q8—261no—
171C2×D4—131no—
172C2×D4—262no—
173C2×D4—262no—
174C2×D4C22×D1311yescharacteristic
175C2×D4C22×D1311yescharacteristic
176C22×C4—21no—
177C22×C4—21no—
178C22×C4—132no—
179C22×C4—262no—
180D8—22no—
181M16—264no—
182C2×C8—132no—
183C2×C8C22×D1311yescharacteristic
184C2×C8C22×D1311yescharacteristic
185C4⋊C4—131no—
186C4⋊C4—132no—
187C4⋊C4—132no—
188C4⋊C4—262no—
189C4⋊C4—261no—
190C4⋊C4—261no—
191C4⋊C4C22×D1311yescharacteristic
192C4⋊C4C22×D1311yescharacteristic
193C22⋊C4—21no—
194C22⋊C4—21no—
195C22⋊C4—132no—
196C22⋊C4—262no—
197C22⋊C4—262no—
198C22⋊C4—262no—
199C42—262no—
200C42C22×D1311yescharacteristic
201C13#335411yescharacteristic, complemented, Sylow
202C23—21no—
203C23—21no—
204C23—132no—
205Q8—522no—
206Q8—1041no—
207D4—21no—
208D4—21no—
209D4—21no—
210D4—21no—
211D4—262no—
212D4—524no—
213D4—1042no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—132no—
219C2×C4—262no—
220C2×C4—262no—
221C2×C4—262no—
222C2×C4—262no—
223C2×C4—524no—
224C2×C4D4×D1311yescharacteristic
225C2×C4D4×D1311yescharacteristic
226C2×C4C23×D1311yescharacteristic
227C8—21no—
228C8—262no—
229C8#612712yescomplemented
230C22—41no—
231C22—41no—
232C22—41no—
233C22—41no—
234C22—41no—
235C22—41no—
236C22—262no—
237C22—262no—
238C22—262no—
239C22C2×D4×D1311yescharacteristic
240C4—21no—
241C4—41no—
242C4—41no—
243C4—262no—
244C4—522no—
245C4—522no—
246C4#8816512yes—
247C4C2×#612711yescharacteristic
248C4#8825711yescharacteristic
249C2—81no—
250C2—81no—
251C2—522no—
252C2#1171925611yescharacteristic
253C2C2×#8816511yescharacteristic
254C2#1171947511yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC4×C13×D8C2
socleC22×C13C22×D4
hypercenterC4×D8D13
hypocenterC13#3354
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #11719268C2semidirect
2. #11719256C2semidirect
3. C4×C13×D8C2semidirect
4. #11718820C2semidirect
5. #11718669C2semidirect
6. #11718668C2semidirect
7. #11718542C2semidirect
8. #11718440C2semidirect
9. #11718438C2semidirect
10. #11718349C2semidirect
11. #11718341C2semidirect
101. C8×C13#41semidirect
111. C4×D8D13semidirect
201. C13#3354semidirect
229. C8#6127semidirect

Maximal subgroups

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

subgroupindex
#117192682
#117192562
C4×C13×D82
#117188202
#117186692
#117186682
#117185422
#117184402
#117184382
#117183492
#117183412
#335413