Finite Group Databasebeta

← #15760469

Subgroups — #15760469

Order 3328.

422 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 89 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#13125383C211yesmaximal, characteristic
2#13118016C211yesmaximal, characteristic
3#13113554C211yesmaximal, characteristic
4#13113387C211yesmaximal, characteristic
5#13112702C211yesmaximal, characteristic
6#13112700C211yesmaximal, characteristic
7C13×#1515C211yesmaximal, characteristic
8C13×#533C2211yescharacteristic
9C2×#88123C2211yescharacteristic
10C13×#432C2211yescharacteristic
11C13×#383C2211yescharacteristic
12#11718740C412yescomplemented
13#11718739C412yescomplemented
14#11718726—22no—
15#11718656—22no—
16#11718598C2211yescharacteristic
17#11718587C2211yescharacteristic
18C4×#6099C2211yescharacteristic
19#11718315—22no—
20#11718314—22no—
21#11718307—22no—
22C13×#328—22no—
23#11718130—22no—
24#11718074—22no—
25C22×Dic26—21no—
26C13×C4⋊Q8C2×C411yescharacteristic
27C13×C4⋊Q8C2×C411yescharacteristic
28C13×#125—21no—
29C13×C22⋊Q8—21no—
30C13×C22⋊Q8—21no—
31C4×Q8×C13—21no—
32C4×Q8×C13—21no—
33C13×#117—21no—
34C2×C42×C13C2311yescharacteristic
35C2×C4⋊Dic13—21no—
36C2×C4⋊Dic13D412yes—
37C2×#6101—22no—
38C2×C4×Dic13—22no—
39C2×#6099—21no—
40#88123—21no—
41#88123—21no—
42#88123C2×C412yes—
43#88123D412yes—
44C13×C4⋊C8—21no—
45C13×C22⋊C8—21no—
46C13×#97—21no—
47C13×#95—21no—
48C13×#95—21no—
49C13×#95D412yes—
50#88071—24no—
51#88071—21no—
52#88071—21no—
53#88071D412yes—
54C22⋊#1055—21no—
55#88048—24no—
56#88047—24no—
57C4⋊#1055—21no—
58#88043—21no—
59#88043—21no—
60C4×#1055C2×C412yes—
61#9427—131nomaximal, Sylow
62C2×Q8×C13—21no—
63C2×Q8×C13—21no—
64C22×C4×C13—22no—
65C22×C4×C13C2×D411yescharacteristic
66C22×C4×C13C2×D411yescharacteristic
67C22×C4×C13C2×D411yescharacteristic
68C22×Dic13—22no—
69C22×Dic13—22no—
70C2×Dic26—22no—
71C2×Dic26—22no—
72C2×Dic26—81no—
73C2×Dic26—81no—
74C2×C8×C13—41no—
75C13×C4⋊C4—21no—
76C13×C4⋊C4—21no—
77C13×C4⋊C4—21no—
78C13×C4⋊C4—21no—
79C13×C4⋊C4—41no—
80C13×C4⋊C4—41no—
81C13×C22⋊C4—41no—
82C42×C13—41no—
83C42×C13C22×C411yescharacteristic
84C42×C13C2×D411yescharacteristic
85C42×C13#4111yescharacteristic
86C42×C13#4111yescharacteristic
87C4⋊Dic13—22no—
88C4⋊Dic13—22no—
89C4⋊Dic13—22no—
90C4⋊Dic13C22⋊C414yes—
91#6101—82no—
92C4×Dic13—82no—
93#6099—24no—
94C2×#1055—22no—
95C2×#1055—41no—
96#3165—131no—
97#2381—131no—
98#1556—131no—
99#1515—131no—
100#1515D1311yescharacteristic
101#1288—131no—
102#1288—131no—
103C23×C13#12011yescharacteristic
104Q8×C13—81no—
105Q8×C13—81no—
106C2×C4×C13—22no—
107C2×C4×C13—41no—
108C2×C4×C13—41no—
109C2×C4×C13—42no—
110C2×C4×C13—42no—
111C2×C4×C13—41no—
112C2×C4×C13—41no—
113C2×C4×C13—42no—
114C2×C4×C13C2×C22⋊C411yescharacteristic
115C2×C4×C13C4×D411yescharacteristic
116C2×C4×C13C4×D411yescharacteristic
117C2×C4×C13#12111yescharacteristic
118C2×C4×C13#12111yescharacteristic
119C2×C4×C13#12311yescharacteristic
120C2×Dic13—24no—
121C2×Dic13—42no—
122C2×Dic13—42no—
123C2×Dic13—42no—
124C2×Dic13—42no—
125C2×Dic13—42no—
126Dic26—82no—
127Dic26—82no—
128C8×C13—81no—
129#1055—24no—
130#1055—81no—
131#533C2×D1311yescharacteristic
132C2×C4⋊Q8—131no—
133#501—262no—
134#500—132no—
135#498—132no—
136#432—131no—
137#432C2×D1311yescharacteristic
138#428—262no—
139C4×M16—131no—
140#391—262no—
141#387—262no—
142#387—262no—
143#383—131no—
144#383C2×D1311yescharacteristic
145#332—262no—
146#328—22no—
147#328—262no—
148C22×C13—21no—
149C22×C13—21no—
150C22×C13#38611yescharacteristic
151C22×C13#45612yes—
152C4×C13—21no—
153C4×C13—21no—
154C4×C13—21no—
155C4×C13—21no—
156C4×C13—21no—
157C4×C13—21no—
158C4×C13—82no—
159C4×C13—81no—
160C4×C13—81no—
161Dic13—44no—
162Dic13—82no—
163C22×Q8—261no—
164C2×M16—261no—
165C4⋊Q8—132no—
166C4⋊Q8—132no—
167C4⋊Q8—261no—
168C4⋊Q8—261no—
169C4⋊Q8C4×D1311yescharacteristic
170C4⋊Q8C4×D1311yescharacteristic
171#125—21no—
172C22⋊Q8—21no—
173C22⋊Q8—21no—
174C4×Q8—21no—
175C4×Q8—21no—
176#117—21no—
177C2×C4⋊C4—132no—
178C2×C4⋊C4—261no—
179C2×C4⋊C4—262no—
180C2×C42—262no—
181C2×C42C22×D1311yescharacteristic
182#107—264no—
183#106—264no—
184C4⋊C8—21no—
185C4⋊C8—261no—
186C22⋊C8—21no—
187C22⋊C8—261no—
188#97—21no—
189#97—261no—
190#97—261no—
191C4×C8—132no—
192#95—21no—
193#95—21no—
194#95—132no—
195#95—264no—
196#95—261no—
197#95—261no—
198#95C22⋊D1312yes—
199C2×C13—22no—
200C2×C13#188611yescharacteristic
201C2×C13#190411yescharacteristic
202C2×C13#190511yescharacteristic
203C2×Q8—21no—
204C2×Q8—21no—
205C2×Q8—262no—
206C2×Q8—262no—
207C2×Q8—1041no—
208C2×Q8—1041no—
209C22×C4—22no—
210C22×C4—262no—
211C22×C4—262no—
212C22×C4D4×D1311yescharacteristic
213C22×C4D4×D1311yescharacteristic
214C22×C4C2×C22⋊D1311yescharacteristic
215M16—264no—
216C2×C8—41no—
217C2×C8—262no—
218C2×C8—521no—
219C4⋊C4—21no—
220C4⋊C4—21no—
221C4⋊C4—21no—
222C4⋊C4—21no—
223C4⋊C4—41no—
224C4⋊C4—41no—
225C4⋊C4—134no—
226C4⋊C4—262no—
227C4⋊C4—262no—
228C4⋊C4—262no—
229C4⋊C4—1042no—
230C22⋊C4—41no—
231C42—41no—
232C42—1042no—
233C42C2×C4×D1311yescharacteristic
234C42#612711yescharacteristic
235C42D4×D1311yescharacteristic
236C42#612911yescharacteristic
237C13#942711yescharacteristic, complemented, Sylow
238C23#8819111yescharacteristic
239Q8—81no—
240Q8—81no—
241Q8—1042no—
242Q8—1042no—
243C2×C4—22no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—264no—
252C2×C4—522no—
253C2×C4—522no—
254C2×C4—522no—
255C2×C4—522no—
256C2×C4—522no—
257C2×C4C22⋊C4×D1311yescharacteristic
258C2×C4#8813511yescharacteristic
259C2×C4#8813711yescharacteristic
260C2×C4#8813811yescharacteristic
261C2×C4C4×C22⋊D1311yescharacteristic
262C2×C4#8819211yescharacteristic
263C8—81no—
264C8—264no—
265C8—1041no—
266C22—21no—
267C22—21no—
268C22#1171861711yescharacteristic
269C22#1171886612yes—
270C4—21no—
271C4—21no—
272C4—21no—
273C4—21no—
274C4—21no—
275C4—21no—
276C4—82no—
277C4—81no—
278C4—81no—
279C4—524no—
280C4—1042no—
281C2—22no—
282C2#1311522611yescharacteristic
283C2#1311532611yescharacteristic
284C2#1311532711yescharacteristic
subgroupG/H
centerC22#11718617
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1515C2
socleC22×C13#386
prime radicalC23×C13#120
cosocleC2×C42×C13C23
hypercenter#1515D13
hypocenterC13#9427
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1515

Complements

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

NH ≅ G/Ntype
12. #11718740C4semidirect
13. #11718739C4semidirect
237. C13#9427semidirect

Maximal subgroups

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

subgroupindex
#131253832
#131180162
#131135542
#131133872
#131127022
#131127002
C13×#15152
#942713