Finite Group Databasebeta

← #15757984

Subgroups — #15757984

Order 3328.

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

normal subgroups only

This group has 696 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
1#13117434C211yesmaximal, characteristic
2#13114922C212yesmaximal, complemented
3C2×#11718117C211yesmaximal, characteristic
4#13112715C212yesmaximal, complemented
5C2×C13×#397C211yesmaximal, characteristic
6C22×C13×C4⋊C4C2211yescharacteristic
7C22×C13×C22⋊C4—21no—
8C22×C13×C22⋊C4C2211yescharacteristic
9C13×#397—22no—
10C13×#397C414yescomplemented
11C2×C13×#95—21no—
12C2×C13×#95C2211yescharacteristic
13#11718908—21no—
14#11718873C2212yes—
15C4×C22⋊Dic13—21no—
16C2×C22⋊#1055C2212yes—
17#11718612—24no—
18#11718121—24no—
19#11718117—22no—
20C25×C13D411yescharacteristic
21C23×C4×C13—21no—
22C23×C4×C13—21no—
23C23×C4×C13D411yescharacteristic
24C23×C4×C13C2311yescharacteristic
25C2×C13×C4⋊C4—22no—
26C2×C13×C4⋊C4—22no—
27C2×C13×C4⋊C4—21no—
28C2×C13×C4⋊C4C2×C412yes—
29C2×C13×C22⋊C4—22no—
30C2×C13×C22⋊C4—22no—
31C2×C13×C22⋊C4—24no—
32C2×C13×C22⋊C4—44no—
33C2×C13×C22⋊C4C2×C412yes—
34C2×C13×C22⋊C4D412yes—
35C2×C22⋊Dic13—22no—
36C2×C22⋊Dic13—22no—
37C2×C22⋊Dic13—22no—
38C2×C4⋊Dic13D414yes—
39C2×C4×Dic13—22no—
40C22×#1055—22no—
41C13×#95—24no—
42C13×#95—21no—
43C13×#95C2×C412yes—
44#88071—22no—
45#88071—22no—
46C22⋊#1055—22no—
47C22⋊#1055—22no—
48#9028—131nomaximal, Sylow
49C24×C13—21no—
50C24×C13—22no—
51C24×C13—21no—
52C24×C13—22no—
53C24×C13—42no—
54C24×C13—42no—
55C24×C13C22⋊C412yes—
56C24×C13C2×D411yescharacteristic
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13—22no—
60C22×C4×C13—22no—
61C22×C4×C13—42no—
62C22×C4×C13—42no—
63C22×C4×C13—42no—
64C22×C4×C13—42no—
65C22×C4×C13—41no—
66C22×C4×C13—41no—
67C22×C4×C13—42no—
68C22×C4×C13—42no—
69C22×C4×C13—42no—
70C22×C4×C13C22⋊C412yes—
71C22×C4×C13C22×C411yescharacteristic
72C22×C4×C13C2×D412yes—
73C22×C4×C13C2×D411yescharacteristic
74C22×C4×C13#4112yes—
75C22×Dic13—24no—
76C13×C4⋊C4—24no—
77C13×C4⋊C4—42no—
78C13×C22⋊C4—24no—
79C13×C22⋊C4—24no—
80C13×C22⋊C4—48no—
81C22⋊Dic13—42no—
82C22⋊Dic13—42no—
83C22⋊Dic13—82no—
84C22⋊Dic13—82no—
85C4⋊Dic13—44no—
86C4×Dic13—82no—
87C2×#1055—44no—
88C2×#1055—42no—
89C2×#397D1311yescharacteristic
90#2312—131no—
91#1823—132no—
92C2×#323—131no—
93#1294—132no—
94C23×C13—22no—
95C23×C13—22no—
96C23×C13—22no—
97C23×C13—22no—
98C23×C13—22no—
99C23×C13—42no—
100C23×C13—42no—
101C23×C13—48no—
102C23×C13—42no—
103C23×C13—42no—
104C23×C13—42no—
105C23×C13—42no—
106C23×C13—81no—
107C23×C13—81no—
108C23×C13—84no—
109C23×C13C2×C22⋊C411yescharacteristic
110C23×C13#12011yescharacteristic
111C23×C13#12311yescharacteristic
112C23×C13#13512yes—
113C23×C13AGL(1,ℤ/8)12yes—
114C2×C4×C13—24no—
115C2×C4×C13—22no—
116C2×C4×C13—41no—
117C2×C4×C13—41no—
118C2×C4×C13—42no—
119C2×C4×C13—42no—
120C2×C4×C13—42no—
121C2×C4×C13—42no—
122C2×C4×C13—42no—
123C2×C4×C13—42no—
124C2×C4×C13—42no—
125C2×C4×C13—42no—
126C2×C4×C13—42no—
127C2×C4×C13—81no—
128C2×C4×C13—84no—
129C2×C4×C13—82no—
130C2×C4×C13—82no—
131C2×C4×C13C4×D412yes—
132C2×C4×C13#12112yes—
133C2×Dic13—44no—
134C2×Dic13—44no—
135C2×Dic13—44no—
136#1055—82no—
137C22×C4⋊C4C2×D1311yescharacteristic
138C22×C22⋊C4—21no—
139C22×C22⋊C4C2×D1311yescharacteristic
140C2×C22⋊C8—132no—
141#397—22no—
142#397Dic1314yescomplemented
143#388—264no—
144#380—132no—
145#379—261no—
146C4×C22⋊C4—261no—
147C2×#95—21no—
148C2×#95C2×D1311yescharacteristic
149#340—264no—
150#323—262no—
151C22×C13—24no—
152C22×C13—24no—
153C22×C13—21no—
154C22×C13—21no—
155C22×C13—21no—
156C22×C13—21no—
157C22×C13—44no—
158C22×C13—42no—
159C22×C13—42no—
160C22×C13—42no—
161C22×C13—82no—
162C22×C13—84no—
163C22×C13—84no—
164C22×C13#38611yescharacteristic
165C22×C13#41611yescharacteristic
166C22×C13#41811yescharacteristic
167C22×C13#44912yes—
168C22×C13#45512yes—
169C22×C13#45812yes—
170C22×C13#48212yes—
171C4×C13—22no—
172C4×C13—22no—
173C4×C13—42no—
174C4×C13—82no—
175C4×C13—82no—
176Dic13—84no—
177C25C22⋊D1311yescharacteristic
178C23×C4—21no—
179C23×C4—21no—
180C23×C4C22⋊D1311yescharacteristic
181C23×C4C22×D1311yescharacteristic
182C22×C8—262no—
183C2×C4⋊C4—22no—
184C2×C4⋊C4—22no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—134no—
187C2×C4⋊C4C2×Dic1312yes—
188C2×C22⋊C4—22no—
189C2×C22⋊C4—22no—
190C2×C22⋊C4—24no—
191C2×C22⋊C4—44no—
192C2×C22⋊C4—262no—
193C2×C22⋊C4—262no—
194C2×C22⋊C4—262no—
195C2×C22⋊C4C2×Dic1312yes—
196C2×C22⋊C4C22⋊D1312yes—
197C2×C42—262no—
198C22⋊C8—262no—
199C22⋊C8—262no—
200#95—24no—
201#95—21no—
202#95—262no—
203#95—262no—
204#95C2×Dic1312yes—
205C2×C13—21no—
206C2×C13—21no—
207C2×C13—22no—
208C2×C13—82no—
209C2×C13#161214yes—
210C2×C13#187511yescharacteristic
211C2×C13#188511yescharacteristic
212C2×C13#189011yescharacteristic
213C24—22no—
214C24—21no—
215C24—21no—
216C24—22no—
217C24—42no—
218C24—42no—
219C24C22⋊Dic1312yes—
220C24C2×C22⋊D1311yescharacteristic
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—22no—
224C22×C4—22no—
225C22×C4—42no—
226C22×C4—42no—
227C22×C4—42no—
228C22×C4—42no—
229C22×C4—42no—
230C22×C4—42no—
231C22×C4—41no—
232C22×C4—41no—
233C22×C4—42no—
234C22×C4—264no—
235C22×C4C22⋊Dic1312yes—
236C22×C4D4×D1312yes—
237C22×C4#612912yes—
238C22×C4C22×Dic1311yescharacteristic
239C22×C4C2×C22⋊D1311yescharacteristic
240C2×C8—524no—
241C2×C8—522no—
242C4⋊C4—24no—
243C4⋊C4—42no—
244C4⋊C4—524no—
245C22⋊C4—24no—
246C22⋊C4—24no—
247C22⋊C4—48no—
248C22⋊C4—522no—
249C22⋊C4—522no—
250C22⋊C4—1042no—
251C22⋊C4—1042no—
252C42—1042no—
253C13#902811yescharacteristic, complemented, Sylow
254C23—22no—
255C23—22no—
256C23—22no—
257C23—22no—
258C23—22no—
259C23—42no—
260C23—42no—
261C23—48no—
262C23—42no—
263C23—42no—
264C23—42no—
265C23—42no—
266C23—81no—
267C23—81no—
268C23—84no—
269C23#8818612yes—
270C23#8818911yescharacteristic
271C23#8819111yescharacteristic
272C23#8820412yes—
273C23C2×C22⋊Dic1311yescharacteristic
274C2×C4—24no—
275C2×C4—22no—
276C2×C4—42no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—81no—
288C2×C4—84no—
289C2×C4—82no—
290C2×C4—82no—
291C2×C4—524no—
292C2×C4—524no—
293C2×C4—524no—
294C2×C4D4×Dic1312yes—
295C2×C4#8819312yes—
296C8—1042no—
297C22—21no—
298C22—21no—
299C22—21no—
300C22—21no—
301C22—24no—
302C22—24no—
303C22—44no—
304C22—42no—
305C22—42no—
306C22—42no—
307C22—82no—
308C22—84no—
309C22—84no—
310C22#1171869612yes—
311C22#1171869812yes—
312C22#1171871412yes—
313C22#1171872212yes—
314C22#1171887611yescharacteristic
315C22#1171888111yescharacteristic
316C22#1171889411yescharacteristic
317C4—22no—
318C4—22no—
319C4—42no—
320C4—82no—
321C4—82no—
322C4—1044no—
323C2—21no—
324C2—22no—
325C2—21no—
326C2—82no—
327C2#1311384814yes—
328C2#1311515911yescharacteristic
329C2#1311522511yescharacteristic
330C2#1311525011yescharacteristic
subgroupG/H
centerC23#88191
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC2×C13×#397C2
socleC23×C13#120
prime radicalC25×C13D4
cosocleC23×C4×C13C23
hypercenterC2×#397D13
hypocenterC13#9028
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#397

Complements

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

NH ≅ G/Ntype
2. #13114922C2semidirect
4. #13112715C2semidirect
10. C13×#397C4semidirect
142. #397Dic13semidirect
253. C13#9028semidirect

Maximal subgroups

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

subgroupindex
#131174342
#131149222
C2×#117181172
#131127152
C2×C13×#3972
#902813