Finite Group Databasebeta

← #16788499

Subgroups — #16788499

Order 3328.

306 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 92 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
1D13⋊(C4⋊C16)C211yesmaximal, characteristic
2#13130384C211yesmaximal, characteristic
3#13129855C212yesmaximal, complemented
4#13129854C212yesmaximal, complemented
5#13125349C211yesmaximal, characteristic
6#11719393—21no—
7C2×D13⋊C16—21no—
8#11719051—21no—
9C13×#499C411yescharacteristic
10#11718725—21no—
11#11718541C411yescharacteristic
12#11718541C411yescharacteristic
13#11718535C2211yescharacteristic
14#11718535C2211yescharacteristic
15#11718521—21no—
16#11718516—21no—
17C4×C8×D13C2211yescharacteristic
18#11718344C411yescharacteristic
19#11718260C2212yes—
20#11718256C2212yes—
21#11718253—21no—
22C4⋊#6092—21no—
23C13×#125—21no—
24C2×C8×D13C2×C411yescharacteristic
25C2×C8×D13D411yescharacteristic
26#88150—41no—
27#88150—41no—
28#88146—21no—
29#88146—21no—
30#88142—21no—
31#88142—21no—
32#88141—41no—
33#88141—41no—
34C42×D13D411yescharacteristic
35#88124—21no—
36#88111—41no—
37C4⋊#1057—22no—
38C4×#1057—41no—
39C2×#6092—22no—
40D13⋊C16—42no—
41C13×#107C2×C411yescharacteristic
42C13×#107C2×C411yescharacteristic
43C13×#106—21no—
44C4×C8×C13C2×C411yescharacteristic
45#88058C2×C411yescharacteristic
46#88058C2×C411yescharacteristic
47#88057—21no—
48C8×Dic13D411yescharacteristic
49C8×Dic13C2311yescharacteristic
50#88048—21no—
51#88048—21no—
52#88047—21no—
53#88047—21no—
54C4×#1055D411yescharacteristic
55#11939—131nomaximal, Sylow
56C2×C4×D13C22⋊C411yescharacteristic
57C2×C4×D13D811yescharacteristic
58C2×C4×D13SD1611yescharacteristic
59C2×Dic26—41no—
60C2×Dic26—41no—
61C2×#1057—42no—
62C2×C8×C13C22⋊C411yescharacteristic
63C2×C8×C13C22×C411yescharacteristic
64C13×C4⋊C4—21no—
65C13×C4⋊C4—21no—
66C13×C4⋊C4—41no—
67C13×C4⋊C4—41no—
68C42×C13C22⋊C411yescharacteristic
69#6103—41no—
70#6103—41no—
71C4⋊Dic13—21no—
72C4⋊Dic13—21no—
73#6101—41no—
74#6101—41no—
75#6101—41no—
76#6101—41no—
77C4×Dic13—41no—
78C4×Dic13—41no—
79C4×Dic13D811yescharacteristic
80C4×Dic13SD1611yescharacteristic
81C4×Dic13C2×D411yescharacteristic
82C2×#1055C22⋊C411yescharacteristic
83C2×#1055C2×D411yescharacteristic
84C8×D13—22no—
85C8×D13SD1612yes—
86C8×D13Q1612yes—
87#6092—42no—
88#3160—131no—
89C2×C4⋊C16—131no—
90#1564—131no—
91#1365—132no—
92#1364—132no—
93C22×D13#10211yescharacteristic
94C2×C4×C13—41no—
95C2×C4×C13—41no—
96C2×C4×C13#10211yescharacteristic
97C2×C4×C13#10211yescharacteristic
98C2×C4×C13C2×C22⋊C411yescharacteristic
99C2×Dic13—41no—
100C2×Dic13—41no—
101C2×Dic13#10211yescharacteristic
102C2×Dic13C2×D811yescharacteristic
103C2×Dic13C2×SD1611yescharacteristic
104C4×D13—22no—
105C4×D13—41no—
106C4×D13#10112yes—
107C4×D13#10312yes—
108Dic26—82no—
109Dic26—82no—
110#1057—82no—
111C8×C13—21no—
112C8×C13#10312yes—
113#1055—21no—
114#1055C2×SD1611yescharacteristic
115#1055C2×Q1611yescharacteristic
116#533—261no—
117C22×C16—261no—
118#500—131no—
119#500—131no—
120#499—131no—
121#499—261no—
122#499#26111yescharacteristic
123#498—261no—
124#431—261no—
125#427—131no—
126#427—131no—
127#427—261no—
128C2×C4×C8—131no—
129C4⋊C16—132no—
130C4⋊C16—261no—
131#335—132no—
132#334—261no—
133C22×C13C2×#10211yescharacteristic
134C2×D13—21no—
135C2×D13—21no—
136C2×D13#33212yes—
137C4×C13—21no—
138C4×C13—21no—
139C4×C13—81no—
140C4×C13—81no—
141C4×C13C2×#10111yescharacteristic
142C4×C13C2×#10311yescharacteristic
143Dic13—21no—
144Dic13—81no—
145Dic13—81no—
146Dic13#33212yes—
147Dic13#50812yes—
148C22×C8—131no—
149C22×C8—131no—
150C4⋊Q8—261no—
151C4⋊Q8—261no—
152#125—21no—
153#125—261no—
154C22⋊Q8—521no—
155C22⋊Q8—521no—
156C4×Q8—521no—
157C4×Q8—521no—
158#117—261no—
159#117—261no—
160C2×C42—131no—
161C2×C16—262no—
162C2×C16—522no—
163#107—131no—
164#107—131no—
165#107—261no—
166#107—261no—
167#107C2×#26111yescharacteristic
168#107C2×#26111yescharacteristic
169#106—21no—
170#106—261no—
171#106—261no—
172#106—261no—
173C4⋊C8—262no—
174C22⋊C8—521no—
175C4×C8—131no—
176C4×C8—131no—
177C4×C8—131no—
178C4×C8—521no—
179C4×C8C2×#26111yescharacteristic
180C2×C13C2×#33211yescharacteristic
181C2×C13#213811yescharacteristic
182C2×C13#214811yescharacteristic
183D13—22no—
184C2×Q8—521no—
185C2×Q8—521no—
186C22×C4—131no—
187C22×C4—131no—
188C22×C4—131no—
189C2×C8—131no—
190C2×C8—132no—
191C2×C8—132no—
192C2×C8—131no—
193C2×C8—262no—
194C2×C8—522no—
195C2×C8C22⋊#26111yescharacteristic
196C2×C8C22×#26111yescharacteristic
197C4⋊C4—21no—
198C4⋊C4—21no—
199C4⋊C4—41no—
200C4⋊C4—41no—
201C4⋊C4—261no—
202C4⋊C4—261no—
203C4⋊C4—521no—
204C4⋊C4—521no—
205C4⋊C4—521no—
206C4⋊C4—521no—
207C22⋊C4—521no—
208C22⋊C4—521no—
209C42—131no—
210C42—131no—
211C42—131no—
212C42—521no—
213C42—521no—
214C42C22⋊#26111yescharacteristic
215C16—522no—
216C13#1193911yescharacteristic, complemented, Sylow
217C23—131no—
218Q8—1042no—
219Q8—1042no—
220C2×C4—41no—
221C2×C4—41no—
222C2×C4—131no—
223C2×C4—131no—
224C2×C4—132no—
225C2×C4—132no—
226C2×C4—131no—
227C2×C4—262no—
228C2×C4—521no—
229C2×C4—521no—
230C2×C4—521no—
231C2×C4#8811511yescharacteristic
232C2×C4#8811511yescharacteristic
233C2×C4C2×C22⋊#26111yescharacteristic
234C8—21no—
235C8—131no—
236C8—131no—
237C8—261no—
238C8—1042no—
239C8#8811712yes—
240C22—132no—
241C22—261no—
242C22—261no—
243C22C2×#8811511yescharacteristic
244C4—21no—
245C4—21no—
246C4—81no—
247C4—81no—
248C4—132no—
249C4—132no—
250C4—261no—
251C4—1041no—
252C4—1041no—
253C4C2×#8811711yescharacteristic
254C4D13⋊#10111yescharacteristic
255C2—262no—
256C2D13⋊#33211yescharacteristic
257C2#1313114311yescharacteristic
258C2#1313116411yescharacteristic
subgroupG/H
centerC22C2×#88115
commutatorC2×C8×C13C22×C4
FrattiniC2×C8C22×#261
FittingC13×#499C4
socleC22×C13C2×#102
prime radicalC22×D13#102
cosocleC8×Dic13C23
hypercenter#499#261
hypocenterC13#11939
LCSG ▷ C2×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #499

Complements

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

NH ≅ G/Ntype
3. #13129855C2semidirect
4. #13129854C2semidirect
216. C13#11939semidirect

Maximal subgroups

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

subgroupindex
D13⋊(C4⋊C16)2
#131303842
#131298552
#131298542
#131253492
#1193913