Finite Group Databasebeta

← #15766869

Subgroups — #15766869

Order 3328.

344 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 83 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#13125984C211yesmaximal, characteristic
2#13115825C211yesmaximal, characteristic
3#13113625C211yesmaximal, characteristic
4#13113574C211yesmaximal, characteristic
5#13113507C211yesmaximal, characteristic
6#13112726C211yesmaximal, characteristic
7C13×#1485C211yesmaximal, characteristic
8C13×#533C2211yescharacteristic
9C2×#88123C2211yescharacteristic
10C13×#431C2211yescharacteristic
11C4×C13×M16C2211yescharacteristic
12#11718742—21no—
13#11718739—21no—
14#11718705—22no—
15#11718682—21no—
16#11718682—21no—
17#11718586C2211yescharacteristic
18#11718585C2211yescharacteristic
19#11718585C2211yescharacteristic
20C13×Q8⋊C8—22no—
21#11718146—22no—
22#11718139—21no—
23#11718139—21no—
24#11718078—22no—
25#11718050—21no—
26#11718049—21no—
27C22×Dic26—21no—
28C2×C13×M16—21no—
29C13×C4⋊Q8D411yescharacteristic
30C13×C4⋊Q8D411yescharacteristic
31C13×#125—21no—
32C13×C22⋊Q8—21no—
33C13×C22⋊Q8—21no—
34C4×Q8×C13—21no—
35C4×Q8×C13—21no—
36C13×#117—21no—
37C2×C42×C13C2311yescharacteristic
38C2×C4⋊Dic13—21no—
39C2×C4⋊Dic13D412yes—
40C2×#6099—21no—
41C2×#6099—21no—
42#88123—21no—
43#88123—21no—
44#88123—21no—
45#88123—21no—
46C13×C4⋊C8D412yes—
47C13×C22⋊C8—21no—
48C13×#97—21no—
49C4×C8×C13—21no—
50C4×C8×C13—21no—
51#88075—22no—
52#88075—22no—
53C22⋊#1055—21no—
54#88047—22no—
55#88047—22no—
56C4⋊#1055—21no—
57C4⋊#1055—21no—
58C4⋊#1055—21no—
59C4⋊#1055—21no—
60C4⋊#1055D411yescharacteristic
61C4⋊#1055D411yescharacteristic
62C4×#1055—21no—
63#10495—131nomaximal, Sylow
64C2×Q8×C13—21no—
65C2×Q8×C13—21no—
66C22×C4×C13C2×D411yescharacteristic
67C22×C4×C13#4111yescharacteristic
68C22×C4×C13#4111yescharacteristic
69C22×Dic13—22no—
70C2×Dic26—41no—
71C2×Dic26—41no—
72C2×Dic26—81no—
73C2×Dic26—81no—
74C13×M16—22no—
75C13×M16—41no—
76C2×C8×C13—22no—
77C2×C8×C13—41no—
78C13×C4⋊C4—21no—
79C13×C4⋊C4—21no—
80C13×C4⋊C4—21no—
81C13×C4⋊C4—21no—
82C13×C4⋊C4—41no—
83C13×C4⋊C4—41no—
84C13×C22⋊C4—41no—
85C42×C13—41no—
86C42×C13C2×D411yescharacteristic
87C42×C13C2×D411yescharacteristic
88C42×C13C2×D411yescharacteristic
89C42×C13#4111yescharacteristic
90C4⋊Dic13—22no—
91C4⋊Dic13—22no—
92C4⋊Dic13—41no—
93C4⋊Dic13—41no—
94#6099—42no—
95#6099—81no—
96C2×#1055—21no—
97C2×#1055—21no—
98C2×#1055—41no—
99C2×#1055—41no—
100#3230—131no—
101#1997—131no—
102#1574—131no—
103#1561—131no—
104#1546—131no—
105#1485D1311yescharacteristic
106#1299—131no—
107C23×C13#12311yescharacteristic
108Q8×C13—41no—
109Q8×C13—41no—
110Q8×C13—41no—
111Q8×C13—41no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—22no—
117C2×C4×C13—41no—
118C2×C4×C13—41no—
119C2×C4×C13#12011yescharacteristic
120C2×C4×C13#12111yescharacteristic
121C2×C4×C13#12111yescharacteristic
122C2×C4×C13#12111yescharacteristic
123C2×C4×C13#12311yescharacteristic
124C2×C4×C13#12411yescharacteristic
125C2×Dic13—42no—
126C2×Dic13—82no—
127Dic26—82no—
128Dic26—81no—
129Dic26—81no—
130C8×C13—42no—
131C8×C13—42no—
132#1055—41no—
133#1055—41no—
134#1055—81no—
135#1055—81no—
136#533C2×D1311yescharacteristic
137C2×C4⋊Q8—131no—
138#500—261no—
139#487—261no—
140#484—262no—
141#477—261no—
142#477—261no—
143#431—131no—
144#431C2×D1311yescharacteristic
145#423—131no—
146#423—131no—
147C4×M16C2×D1311yescharacteristic
148#343—262no—
149#335—261no—
150#334—261no—
151#332—261no—
152#332—261no—
153#332—262no—
154Q8⋊C8—22no—
155C22×C13—21no—
156C22×C13—21no—
157C22×C13—21no—
158C22×C13#39411yescharacteristic
159C4×C13—21no—
160C4×C13—21no—
161C4×C13—21no—
162C4×C13—81no—
163C4×C13—81no—
164C4×C13#45411yescharacteristic
165C4×C13#45611yescharacteristic
166C4×C13#47111yescharacteristic
167C4×C13#47211yescharacteristic
168C4×C13#47312yes—
169Dic13—82no—
170C22×Q8—261no—
171C2×M16—21no—
172C2×M16—261no—
173C2×M16—261no—
174C4⋊Q8—261no—
175C4⋊Q8—261no—
176C4⋊Q8—261no—
177C4⋊Q8—261no—
178C4⋊Q8D5211yescharacteristic
179C4⋊Q8D5211yescharacteristic
180#125—21no—
181C22⋊Q8—21no—
182C22⋊Q8—21no—
183C4×Q8—21no—
184C4×Q8—21no—
185#117—21no—
186C2×C4⋊C4—132no—
187C2×C4⋊C4—261no—
188C2×C42C22×D1311yescharacteristic
189#107—262no—
190#107—262no—
191C4⋊C8—131no—
192C4⋊C8—131no—
193C4⋊C8—261no—
194C4⋊C8—261no—
195C4⋊C8—261no—
196C4⋊C8—261no—
197C4⋊C8C22⋊D1312yes—
198#103—262no—
199#103—262no—
200C22⋊C8—21no—
201C22⋊C8—261no—
202#97—21no—
203C4×C8—21no—
204C4×C8—21no—
205C4×C8—261no—
206C2×C13—41no—
207C2×C13#203811yescharacteristic
208C2×C13#204711yescharacteristic
209C2×C13#205111yescharacteristic
210C2×Q8—21no—
211C2×Q8—21no—
212C2×Q8—521no—
213C2×Q8—521no—
214C2×Q8—1041no—
215C2×Q8—1041no—
216C22×C4—262no—
217C22×C4#612711yescharacteristic
218C22×C4D4×D1311yescharacteristic
219C22×C4#612911yescharacteristic
220M16—22no—
221M16—41no—
222M16—522no—
223M16—1041no—
224C2×C8—22no—
225C2×C8—41no—
226C2×C8—261no—
227C2×C8—261no—
228C2×C8—521no—
229C2×C8—521no—
230C4⋊C4—21no—
231C4⋊C4—21no—
232C4⋊C4—21no—
233C4⋊C4—21no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—262no—
237C4⋊C4—262no—
238C4⋊C4—521no—
239C4⋊C4—521no—
240C22⋊C4—41no—
241C42—41no—
242C42C2×D5211yescharacteristic
243C42D4×D1311yescharacteristic
244C42#612911yescharacteristic
245C42C2×C22⋊D1311yescharacteristic
246C13#1049511yescharacteristic, complemented, Sylow
247C23#8813711yescharacteristic
248Q8—41no—
249Q8—41no—
250Q8—41no—
251Q8—41no—
252Q8—1042no—
253Q8—1041no—
254Q8—1041no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—22no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—522no—
263C2×C4—1042no—
264C2×C4#8813611yescharacteristic
265C2×C4#8813911yescharacteristic
266C2×C4#8814011yescharacteristic
267C2×C4#8818411yescharacteristic
268C2×C4#8819211yescharacteristic
269C2×C4#8819311yescharacteristic
270C8—42no—
271C8—42no—
272C8—521no—
273C8—521no—
274C8—1041no—
275C8—1041no—
276C22—21no—
277C22—21no—
278C22—21no—
279C22#1171862211yescharacteristic
280C4—21no—
281C4—21no—
282C4—21no—
283C4—81no—
284C4—81no—
285C4—1042no—
286C4#1171848711yescharacteristic
287C4#1171848811yescharacteristic
288C4#1171880211yescharacteristic
289C4#1171880311yescharacteristic
290C4#1171886512yes—
291C2—41no—
292C2#1311605211yescharacteristic
293C2#1311610311yescharacteristic
294C2#1311612711yescharacteristic
subgroupG/H
centerC22#11718622
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1485C2
socleC22×C13#394
prime radicalC23×C13#123
hypercenter#1485D13
hypocenterC13#10495
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1485

Complements

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

NH ≅ G/Ntype
246. C13#10495semidirect

Maximal subgroups

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

subgroupindex
#131259842
#131158252
#131136252
#131135742
#131135072
#131127262
C13×#14852
#1049513