Finite Group Databasebeta

← #15760316

Subgroups — #15760316

Order 3328.

466 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 109 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#13123919C211yesmaximal, characteristic
2#13120045C211yesmaximal, characteristic
3#13114829C211yesmaximal, characteristic
4#13113517C211yesmaximal, characteristic
5#13112738C211yesmaximal, characteristic
6#13112737C211yesmaximal, characteristic
7C13×#1548C211yesmaximal, characteristic
8C2×C13×C4⋊Q8C2211yescharacteristic
9C2×C4×Dic26C2211yescharacteristic
10C13×#431C2211yescharacteristic
11C13×#423C2211yescharacteristic
12#11718890C414yes—
13C2×#88064—21no—
14#11718637—21no—
15#11718635—21no—
16#11718634—22no—
17C4×C4⋊Dic13C2211yescharacteristic
18#11718586C2211yescharacteristic
19#11718585C2211yescharacteristic
20#11718492—22no—
21#11718380—22no—
22#11718340—22no—
23C13×#333—22no—
24#11718146—21no—
25#11718138—22no—
26C22×Q8×C13C2×C412yes—
27C22×Dic26D411yescharacteristic
28C2×C13×M16—21no—
29C13×C4⋊Q8—21no—
30C13×C4⋊Q8—21no—
31C13×C4⋊Q8—21no—
32C13×C4⋊Q8—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4—21no—
35C2×C42×C13C2311yescharacteristic
36C2×C4⋊Dic13—21no—
37C2×C4⋊Dic13D411yescharacteristic
38C2×#6101—24no—
39C2×#6101C2×C412yes—
40C2×C4×Dic13—21no—
41C2×C4×Dic13D412yes—
42C2×#6099—21no—
43C4×Dic26—21no—
44C4×Dic26—21no—
45C4×Dic26—21no—
46C4×Dic26—21no—
47C13×C4⋊C8—21no—
48C13×C4⋊C8—21no—
49C13×C4⋊C8D412yes—
50C13×C22⋊C8—21no—
51C4×C8×C13—21no—
52#88071—24no—
53#88071C2×C412yes—
54C22⋊#1055—21no—
55#88064—42no—
56#88055—24no—
57#88054—24no—
58C4⋊#1055—21no—
59C4⋊#1055—21no—
60C4⋊#1055D412yes—
61C4×#1055—21no—
62#9400—131nomaximal, Sylow
63C2×Q8×C13—22no—
64C2×Q8×C13—22no—
65C2×Q8×C13—82no—
66C22×C4×C13—22no—
67C22×C4×C13C22×C411yescharacteristic
68C22×C4×C13C2×D411yescharacteristic
69C22×C4×C13C2×D411yescharacteristic
70C22×Dic13—22no—
71C22×Dic13C22⋊C412yes—
72C22×Dic13C22⋊C412yes—
73C2×Dic26—21no—
74C2×Dic26—21no—
75C2×Dic26—21no—
76C2×Dic26—21no—
77C2×Dic26—21no—
78C2×Dic26—21no—
79C13×M16—41no—
80C13×M16—41no—
81C2×C8×C13—22no—
82C2×C8×C13—41no—
83C13×C4⋊C4—41no—
84C13×C4⋊C4—41no—
85C13×C4⋊C4—41no—
86C13×C4⋊C4—41no—
87C42×C13C2×D411yescharacteristic
88C42×C13C2×D411yescharacteristic
89C42×C13#4111yescharacteristic
90C42×C13#4111yescharacteristic
91C4⋊Dic13—24no—
92C4⋊Dic13—21no—
93C4⋊Dic13—21no—
94#6101—22no—
95#6101—22no—
96#6101—84no—
97C4×Dic13—22no—
98C4×Dic13—22no—
99C4×Dic13—41no—
100C4×Dic13—41no—
101#6099—41no—
102#6099—41no—
103C2×#1055—22no—
104C2×#1055—41no—
105#2983—131no—
106#2567—131no—
107#1801—131no—
108#1548—131no—
109#1548D1311yescharacteristic
110#1303—131no—
111#1303—131no—
112C23×C13C2×C22⋊C411yescharacteristic
113Q8×C13—82no—
114Q8×C13—82no—
115C2×C4×C13—22no—
116C2×C4×C13—41no—
117C2×C4×C13—44no—
118C2×C4×C13—42no—
119C2×C4×C13C4×D411yescharacteristic
120C2×C4×C13C4×D411yescharacteristic
121C2×C4×C13#12011yescharacteristic
122C2×C4×C13#12111yescharacteristic
123C2×C4×C13#12111yescharacteristic
124C2×C4×C13#12311yescharacteristic
125C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
126C2×C4×C13#13711yescharacteristic
127C2×C4×C13#13711yescharacteristic
128C2×C4×C13#13711yescharacteristic
129C2×Dic13—24no—
130C2×Dic13—22no—
131C2×Dic13—22no—
132C2×Dic13—22no—
133C2×Dic13—22no—
134C2×Dic13—42no—
135C2×Dic13—42no—
136C2×Dic13—42no—
137Dic26—41no—
138Dic26—41no—
139Dic26—41no—
140Dic26—41no—
141C8×C13—42no—
142C8×C13—81no—
143#1055—42no—
144#1055—81no—
145C2×C4⋊Q8C2×D1311yescharacteristic
146C2×C4×Q8—131no—
147#446—262no—
148#446—262no—
149#432—262no—
150#431—131no—
151#431C2×D1311yescharacteristic
152#423—131no—
153#423C2×D1311yescharacteristic
154C2×#101—261no—
155#395—134no—
156#391—261no—
157#389—262no—
158#384—261no—
159C4×C4⋊C4—131no—
160#343—261no—
161#333—22no—
162#333—262no—
163C22×C13—21no—
164C22×C13—21no—
165C22×C13#38611yescharacteristic
166C22×C13#41711yescharacteristic
167C22×C13#41911yescharacteristic
168C4×C13—21no—
169C4×C13—21no—
170C4×C13—21no—
171C4×C13—82no—
172C4×C13#45612yes—
173C4×C13#46811yescharacteristic
174C4×C13#46811yescharacteristic
175C4×C13#47011yescharacteristic
176C4×C13#47011yescharacteristic
177Dic13—44no—
178Dic13—42no—
179Dic13—42no—
180C22×Q8—131no—
181C22×Q8C4×D1312yes—
182C2×M16—21no—
183C2×M16—261no—
184C4⋊Q8—21no—
185C4⋊Q8—21no—
186C4⋊Q8—21no—
187C4⋊Q8—21no—
188C4×Q8—261no—
189C4×Q8—261no—
190C4×Q8—261no—
191C4×Q8—261no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—132no—
195C2×C4⋊C4—131no—
196C2×C4⋊C4—261no—
197C2×C4⋊C4—264no—
198C2×C42—132no—
199C2×C42—261no—
200C2×C42C22×D1311yescharacteristic
201C4⋊C8—21no—
202C4⋊C8—21no—
203C4⋊C8—132no—
204C4⋊C8—264no—
205C4⋊C8—261no—
206C4⋊C8—261no—
207C4⋊C8C22⋊D1312yes—
208#101—522no—
209C22⋊C8—21no—
210C22⋊C8—261no—
211#97—264no—
212C4×C8—21no—
213C4×C8—261no—
214#95—132no—
215#95—264no—
216C2×C13—21no—
217C2×C13—21no—
218C2×C13#188611yescharacteristic
219C2×C13#189411yescharacteristic
220C2×C13#191411yescharacteristic
221C2×Q8—22no—
222C2×Q8—22no—
223C2×Q8—82no—
224C2×Q8—261no—
225C2×Q8—261no—
226C2×Q8—261no—
227C2×Q8—261no—
228C2×Q8—261no—
229C2×Q8—261no—
230C22×C4—22no—
231C22×C4—132no—
232C22×C4—132no—
233C22×C4—262no—
234C22×C4C2×C4×D1311yescharacteristic
235C22×C4D4×D1311yescharacteristic
236C22×C4D4×D1311yescharacteristic
237M16—41no—
238M16—41no—
239M16—521no—
240M16—521no—
241C2×C8—22no—
242C2×C8—41no—
243C2×C8—262no—
244C2×C8—521no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—264no—
250C4⋊C4—262no—
251C4⋊C4—261no—
252C4⋊C4—262no—
253C4⋊C4—261no—
254C4⋊C4—1044no—
255C42—262no—
256C42—262no—
257C42—521no—
258C42—521no—
259C42#612711yescharacteristic
260C42D4×D1311yescharacteristic
261C42#612911yescharacteristic
262C42C2×C22⋊D1311yescharacteristic
263C13#940011yescharacteristic, complemented, Sylow
264C23C22⋊C4×D1311yescharacteristic
265Q8—82no—
266Q8—82no—
267Q8—521no—
268Q8—521no—
269Q8—521no—
270Q8—521no—
271C2×C4—22no—
272C2×C4—41no—
273C2×C4—44no—
274C2×C4—42no—
275C2×C4—264no—
276C2×C4—262no—
277C2×C4—262no—
278C2×C4—262no—
279C2×C4—262no—
280C2×C4—522no—
281C2×C4—522no—
282C2×C4—522no—
283C2×C4#8813511yescharacteristic
284C2×C4#8813711yescharacteristic
285C2×C4#8813811yescharacteristic
286C2×C4#8816811yescharacteristic
287C2×C4#8816911yescharacteristic
288C2×C4#8817211yescharacteristic
289C2×C4#8817211yescharacteristic
290C2×C4C4×C22⋊D1311yescharacteristic
291C2×C4#8819111yescharacteristic
292C2×C4#8819211yescharacteristic
293C8—42no—
294C8—81no—
295C8—522no—
296C8—1041no—
297C22—21no—
298C22—21no—
299C22#1171846311yescharacteristic
300C22#1171846411yescharacteristic
301C22#1171861711yescharacteristic
302C4—21no—
303C4—21no—
304C4—21no—
305C4—82no—
306C4—524no—
307C4—522no—
308C4—522no—
309C4#1171847311yescharacteristic
310C4#1171847711yescharacteristic
311C4#1171883511yescharacteristic
312C4#1171885011yescharacteristic
313C4#1171886612yes—
314C2—21no—
315C2—21no—
316C2#1311522611yescharacteristic
317C2#1311526611yescharacteristic
318C2#1311538011yescharacteristic
subgroupG/H
centerC22#11718617
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1548C2
socleC22×C13#386
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C42×C13C23
hypercenter#1548D13
hypocenterC13#9400
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1548

Complements

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

NH ≅ G/Ntype
263. C13#9400semidirect

Maximal subgroups

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

subgroupindex
#131239192
#131200452
#131148292
#131135172
#131127382
#131127372
C13×#15482
#940013