Finite Group Databasebeta

← #15779488

Subgroups — #15779488

Order 3328.

408 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 135 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
1C2×#11718786C211yesmaximal, characteristic
2C2×#11718105C212yesmaximal, complemented
3#13114869C211yesmaximal, characteristic
4#13112945C212yesmaximal, complemented
5C2×C13×#349C211yesmaximal, characteristic
6C22×C13×M16C2211yescharacteristic
7C22×#6099—21no—
8C2×C13×M32C2212yes—
9#11718873—21no—
10#11718786—24no—
11C2×#88059—21no—
12C2×#88059C2212yes—
13C2×#88058C2211yescharacteristic
14C2×#88057C2211yescharacteristic
15C13×#349C414yescomplemented
16#11718143—21no—
17#11718105—24no—
18C23×C4×C13D411yescharacteristic
19C2×C13×M16—22no—
20C2×C13×M16—22no—
21C2×C13×M16C2×C412yes—
22C2×C13×M16Q812yes—
23C22×C8×C13D411yescharacteristic
24C22×C8×C13C2311yescharacteristic
25C2×C22⋊Dic13—41no—
26C2×C4⋊Dic13—21no—
27C2×C4⋊Dic13—21no—
28C2×#6099—24no—
29C2×#6099—22no—
30C2×#6099—41no—
31C2×#6099—42no—
32C22×#1055—41no—
33C13×M32—22no—
34C13×M32C2×C414yes—
35C2×C13×C16—22no—
36#88071—41no—
37#88059—24no—
38#88059—22no—
39#88059D414yes—
40#88058—22no—
41#88057—22no—
42#12931—131nomaximal, Sylow
43C24×C13SD1611yescharacteristic
44C22×C4×C13—21no—
45C22×C4×C13—21no—
46C22×C4×C13—21no—
47C22×C4×C13—21no—
48C22×C4×C13C4⋊C412yes—
49C22×C4×C13SD1611yescharacteristic
50C22×C4×C13SD1612yes—
51C22×C4×C13C2×D411yescharacteristic
52C22×Dic13—41no—
53C22×Dic13—41no—
54C13×M16—24no—
55C13×M16—24no—
56C2×C8×C13—21no—
57C2×C8×C13—21no—
58C2×C8×C13C4⋊C412yes—
59C2×C8×C13C22×C411yescharacteristic
60C2×C8×C13C2×D412yes—
61C2×C8×C13C2×Q811yescharacteristic
62C2×C8×C13#4112yes—
63C22⋊Dic13—82no—
64C4⋊Dic13—41no—
65C4⋊Dic13—41no—
66C4⋊Dic13—41no—
67C4⋊Dic13—41no—
68#6099—24no—
69#6099—44no—
70#6099—42no—
71C2×#1055—44no—
72C2×#1055—42no—
73C13×C16—24no—
74C2×#430—131no—
75C2×#365—132no—
76C2×#349D1311yescharacteristic
77#1809—131no—
78#1387—132no—
79C23×C13—21no—
80C23×C13—21no—
81C23×C13—41no—
82C23×C13—41no—
83C23×C13#10612yes—
84C23×C13C2×SD1611yescharacteristic
85C2×C4×C13—21no—
86C2×C4×C13—21no—
87C2×C4×C13—22no—
88C2×C4×C13—22no—
89C2×C4×C13—22no—
90C2×C4×C13—22no—
91C2×C4×C13#10612yes—
92C2×C4×C13C2×C4⋊C411yescharacteristic
93C2×C4×C13#12011yescharacteristic
94C2×C4×C13#12311yescharacteristic
95C2×C4×C13C2×SD1611yescharacteristic
96C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
97C2×C4×C13#13711yescharacteristic
98C2×Dic13—81no—
99C2×Dic13—81no—
100C2×Dic13—81no—
101C2×Dic13—81no—
102C2×Dic13—81no—
103C2×Dic13—81no—
104C8×C13—22no—
105C8×C13C4×D412yes—
106C8×C13C22⋊Q812yes—
107#1055—44no—
108C22×M16—261no—
109C22×M16C2×D1311yescharacteristic
110C2×M32C2×D1312yes—
111#430—264no—
112C2×#108—132no—
113C2×#108—261no—
114C2×#107—131no—
115C2×#106—131no—
116#380—261no—
117#365—264no—
118#349Dic1314yescomplemented
119#340—261no—
120C22×C13—21no—
121C22×C13—21no—
122C22×C13—22no—
123C22×C13—42no—
124C22×C13—41no—
125C22×C13—41no—
126C22×C13—81no—
127C22×C13C2×#10611yescharacteristic
128C22×C13#44811yescharacteristic
129C22×C13#48111yescharacteristic
130C4×C13—22no—
131C4×C13#38511yescharacteristic
132C4×C13#42811yescharacteristic
133C4×C13#45011yescharacteristic
134C4×C13#48311yescharacteristic
135Dic13—161no—
136Dic13—161no—
137C23×C4D5211yescharacteristic
138C2×M16—22no—
139C2×M16—22no—
140C2×M16—264no—
141C2×M16—262no—
142C2×M16—521no—
143C2×M16—522no—
144C2×M16Dic2612yes—
145C2×M16C2×Dic1312yes—
146C22×C8—521no—
147C22×C8D5211yescharacteristic
148C22×C8C22×D1311yescharacteristic
149C2×C4⋊C4—261no—
150C2×C4⋊C4—261no—
151C2×C22⋊C4—521no—
152M32—22no—
153M32C2×Dic1314yes—
154C2×C16—22no—
155#108—134no—
156#108—264no—
157#108—262no—
158#107—262no—
159#106—262no—
160#95—521no—
161C2×C13—21no—
162C2×C13—21no—
163C2×C13—42no—
164C2×C13#185311yescharacteristic
165C2×C13#223811yescharacteristic
166C2×C13#223911yescharacteristic
167C24#609511yescharacteristic
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—21no—
172C22×C4—521no—
173C22×C4—521no—
174C22×C4#609512yes—
175C22×C4#609511yescharacteristic
176C22×C4C4⋊Dic1312yes—
177C22×C4C2×D5211yescharacteristic
178M16—24no—
179M16—24no—
180M16—264no—
181M16—524no—
182M16—522no—
183C2×C8—21no—
184C2×C8—21no—
185C2×C8—524no—
186C2×C8—522no—
187C2×C8C4⋊Dic1312yes—
188C2×C8C2×Dic2611yescharacteristic
189C2×C8D4×D1312yes—
190C2×C8#612912yes—
191C2×C8C22×Dic1311yescharacteristic
192C4⋊C4—521no—
193C4⋊C4—521no—
194C4⋊C4—521no—
195C4⋊C4—521no—
196C22⋊C4—1042no—
197C16—24no—
198C13#1293111yescharacteristic, complemented, Sylow
199C23—21no—
200C23—21no—
201C23—41no—
202C23—41no—
203C23#8805712yes—
204C23C2×#609511yescharacteristic
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—1041no—
212C2×C4—1041no—
213C2×C4—1041no—
214C2×C4—1041no—
215C2×C4—1041no—
216C2×C4—1041no—
217C2×C4#8805712yes—
218C2×C4#8813611yescharacteristic
219C2×C4#8814011yescharacteristic
220C2×C4C2×#609511yescharacteristic
221C2×C4#8816211yescharacteristic
222C2×C4#8816311yescharacteristic
223C2×C4C2×C4⋊Dic1311yescharacteristic
224C8—22no—
225C8—524no—
226C8#8813212yes—
227C8D4×Dic1312yes—
228C22—21no—
229C22—21no—
230C22—22no—
231C22—42no—
232C22—41no—
233C22—41no—
234C22—81no—
235C22#1171839611yescharacteristic
236C22#1171839911yescharacteristic
237C22C2×#8805711yescharacteristic
238C4—22no—
239C4—2081no—
240C4—2081no—
241C4#1171838211yescharacteristic
242C4#1171839211yescharacteristic
243C4#1171861111yescharacteristic
244C4#1171878211yescharacteristic
245C2—21no—
246C2—21no—
247C2—42no—
248C2#1311503111yescharacteristic
249C2#1311705111yescharacteristic
250C2#1311705611yescharacteristic
subgroupG/H
centerC22#11718396
commutatorC2×C8×C13C22×C4
FrattiniC22×C8C22×D13
FittingC2×C13×#349C2
socleC22×C13#481
prime radicalC24×C13SD16
cosocleC22×C8×C13C23
hypercenterC2×#349D13
hypocenterC13#12931
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×M16 ◁ C2×#349

Complements

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

NH ≅ G/Ntype
2. C2×#11718105C2semidirect
4. #13112945C2semidirect
15. C13×#349C4semidirect
118. #349Dic13semidirect
198. C13#12931semidirect

Maximal subgroups

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

subgroupindex
C2×#117187862
C2×#117181052
#131148692
#131129452
C2×C13×#3492
#1293113