Finite Group Databasebeta

← #15760305

Subgroups — #15760305

Order 3328.

730 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 730 conjugacy classes of subgroups — too many to draw. Only its 139 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#13123860C211yesmaximal, characteristic, complemented
2#13114828C211yesmaximal, characteristic, complemented
3#13113504C212yesmaximal, complemented
4#13112739C212yesmaximal, complemented
5C13×#2541C211yesmaximal, characteristic
6C2×C13×#127—21no—
7C2×C13×#127C2211yescharacteristic
8C2×C13×#121—22no—
9C2×C4×D4×C13C2211yescharacteristic
10C13×#392C414yes—
11C13×#390—21no—
12C4×C13×C4⋊C4C2211yescharacteristic
13C2×#88073—21no—
14C2×C22⋊#1055—22no—
15D4×#1055—24no—
16#11718586C2212yes—
17#11718585C2212yes—
18#11718136—24no—
19#11718122—21no—
20C22×D4×C13—24no—
21C22×D4×C13—21no—
22C22×D4×C13—21no—
23C22×D4×C13C2×C412yes—
24C22×D4×C13D411yescharacteristic
25C23×C4×C13D412yes—
26C13×#127—22no—
27C13×#127—22no—
28C13×#127—42no—
29C13×#127—42no—
30C13×#121—48no—
31C4×D4×C13—22no—
32C4×D4×C13—22no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4D411yescharacteristic
35C2×C13×C22⋊C4—24no—
36C2×C13×C22⋊C4C2×C412yes—
37C2×C42×C13—21no—
38C2×C42×C13C2311yescharacteristic
39C2×#6099—22no—
40C22×#1055—24no—
41C13×#95C2×C412yes—
42#88073—42no—
43C22⋊#1055—24no—
44C22⋊#1055—22no—
45C4⋊#1055—22no—
46C4⋊#1055—22no—
47C4⋊#1055D414yescomplemented
48C4×#1055—22no—
49#9397—131nomaximal, Sylow
50C24×C13—22no—
51C24×C13C22⋊C412yes—
52C2×D4×C13—24no—
53C2×D4×C13—22no—
54C2×D4×C13—22no—
55C2×D4×C13—44no—
56C2×D4×C13—48no—
57C2×D4×C13—48no—
58C2×D4×C13—41no—
59C2×D4×C13—42no—
60C2×D4×C13—41no—
61C2×D4×C13—41no—
62C2×D4×C13—41no—
63C2×D4×C13—42no—
64C2×D4×C13—84no—
65C2×D4×C13—82no—
66C2×D4×C13D812yes—
67C2×D4×C13SD1612yes—
68C22×C4×C13—22no—
69C22×C4×C13—22no—
70C22×C4×C13—22no—
71C22×C4×C13—44no—
72C22×C4×C13C22⋊C412yes—
73C22×C4×C13C22×C411yescharacteristic
74C22×C4×C13C2×D411yescharacteristic
75C22×C4×C13C2×D411yescharacteristic
76C13×C4⋊C4—24no—
77C13×C4⋊C4—22no—
78C13×C22⋊C4—24no—
79C13×C22⋊C4—48no—
80C42×C13—41no—
81C42×C13—41no—
82C42×C13C2×D412yes—
83C42×C13#4112yes—
84#6099—42no—
85#6099—42no—
86C2×#1055—24no—
87C2×#1055—42no—
88C2×#1055—84no—
89#2972—131no—
90#2541D1311yescharacteristic
91#1800—131no—
92#1545—132no—
93#1303—132no—
94C23×C13—22no—
95C23×C13—22no—
96C23×C13—42no—
97C23×C13—42no—
98C23×C13—44no—
99C23×C13—44no—
100C23×C13—42no—
101C23×C13—42no—
102C23×C13—42no—
103C23×C13#10214yes—
104C23×C13C2×C22⋊C411yescharacteristic
105D4×C13—24no—
106D4×C13—24no—
107D4×C13—82no—
108D4×C13—84no—
109D4×C13—816no—
110D4×C13—82no—
111D4×C13—82no—
112D4×C13—82no—
113C2×C4×C13—22no—
114C2×C4×C13—24no—
115C2×C4×C13—22no—
116C2×C4×C13—41no—
117C2×C4×C13—42no—
118C2×C4×C13—42no—
119C2×C4×C13—44no—
120C2×C4×C13—42no—
121C2×C4×C13—82no—
122C2×C4×C13C4×D412yes—
123C2×C4×C13#12011yescharacteristic
124C2×C4×C13#12112yes—
125C2×C4×C13#12311yescharacteristic
126C2×C4×C13C2×D811yescharacteristic
127C2×C4×C13C2×SD1611yescharacteristic
128C2×C4×C13#13512yes—
129#1055—44no—
130#1055—82no—
131C2×#127—21no—
132C2×#127C2×D1311yescharacteristic
133C2×#121—22no—
134C2×C4×D4C2×D1311yescharacteristic
135C8×D4—264no—
136#431—132no—
137#423—132no—
138C2×#100—261no—
139C2×C22⋊C8—262no—
140#392Dic1314yes—
141#390—21no—
142C4×C4⋊C4C2×D1311yescharacteristic
143#343—261no—
144#331—264no—
145C22×C13—21no—
146C22×C13—21no—
147C22×C13—24no—
148C22×C13—44no—
149C22×C13—42no—
150C22×C13—42no—
151C22×C13—82no—
152C22×C13—84no—
153C22×C13—84no—
154C22×C13—82no—
155C22×C13—82no—
156C22×C13—82no—
157C22×C13#38611yescharacteristic
158C22×C13C2×#10211yescharacteristic
159C22×C13#41611yescharacteristic
160C4×C13—21no—
161C4×C13—22no—
162C4×C13—44no—
163C4×C13—42no—
164C4×C13#45312yes—
165C4×C13#46512yes—
166C4×C13#46612yes—
167C22×D4—24no—
168C22×D4—21no—
169C22×D4—21no—
170C22×D4C2×Dic1312yes—
171C22×D4C22⋊D1311yescharacteristic
172C23×C4C22⋊D1312yes—
173C2×M16—262no—
174C22×C8—264no—
175#127—22no—
176#127—22no—
177#127—42no—
178#127—42no—
179#121—48no—
180C4×D4—22no—
181C4×D4—22no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4C22⋊D1311yescharacteristic
184C2×C22⋊C4—24no—
185C2×C22⋊C4C2×Dic1312yes—
186C2×C42—21no—
187C2×C42C22×D1311yescharacteristic
188C4⋊C8—134no—
189C4⋊C8—262no—
190C4⋊C8—262no—
191#100—522no—
192C22⋊C8—264no—
193C22⋊C8—262no—
194C4×C8—262no—
195#95C2×Dic1312yes—
196C2×C13—21no—
197C2×C13—21no—
198C2×C13—44no—
199C2×C13—162no—
200C2×C13#188711yescharacteristic
201C2×C13#189311yescharacteristic
202C2×C13#191411yescharacteristic
203C24—22no—
204C24C22⋊Dic1312yes—
205C2×D4—24no—
206C2×D4—22no—
207C2×D4—22no—
208C2×D4—44no—
209C2×D4—48no—
210C2×D4—48no—
211C2×D4—41no—
212C2×D4—41no—
213C2×D4—41no—
214C2×D4—41no—
215C2×D4—42no—
216C2×D4—42no—
217C2×D4—84no—
218C2×D4—82no—
219C2×D4#610412yes—
220C2×D4#610512yes—
221C22×C4—22no—
222C22×C4—22no—
223C22×C4—22no—
224C22×C4—44no—
225C22×C4C22⋊Dic1312yes—
226C22×C4C22×Dic1311yescharacteristic
227C22×C4C2×C22⋊D1311yescharacteristic
228C22×C4C2×C22⋊D1311yescharacteristic
229M16—522no—
230M16—522no—
231C2×C8—264no—
232C2×C8—522no—
233C2×C8—1044no—
234C4⋊C4—24no—
235C4⋊C4—22no—
236C22⋊C4—24no—
237C22⋊C4—48no—
238C42—41no—
239C42—41no—
240C42D4×D1312yes—
241C42#612912yes—
242C13#939711yescharacteristic, complemented, Sylow
243C23—22no—
244C23—22no—
245C23—42no—
246C23—42no—
247C23—44no—
248C23—44no—
249C23—42no—
250C23—42no—
251C23—42no—
252C23#8807214yes—
253C23C2×C22⋊Dic1311yescharacteristic
254D4—24no—
255D4—24no—
256D4—84no—
257D4—82no—
258D4—816no—
259D4—82no—
260D4—82no—
261D4—82no—
262C2×C4—22no—
263C2×C4—24no—
264C2×C4—22no—
265C2×C4—41no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—44no—
269C2×C4—42no—
270C2×C4—82no—
271C2×C4C2×#610411yescharacteristic
272C2×C4C2×#610511yescharacteristic
273C2×C4D4×Dic1312yes—
274C2×C4#8818911yescharacteristic
275C2×C4#8819111yescharacteristic
276C2×C4#8819312yes—
277C2×C4#8820412yes—
278C8—524no—
279C8—1042no—
280C22—21no—
281C22—21no—
282C22—24no—
283C22—44no—
284C22—42no—
285C22—42no—
286C22—82no—
287C22—84no—
288C22—84no—
289C22—82no—
290C22—82no—
291C22—82no—
292C22C2×#8807211yescharacteristic
293C22#1171888111yescharacteristic
294C22#1171889411yescharacteristic
295C4—21no—
296C4—22no—
297C4—44no—
298C4—42no—
299C4#1171869912yes—
300C4#1171870212yes—
301C4#1171873812yes—
302C2—21no—
303C2—21no—
304C2—44no—
305C2—162no—
306C2#1311523511yescharacteristic
307C2#1311526511yescharacteristic
308C2#1311538411yescharacteristic
subgroupG/H
centerC22#11718881
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
Fitting, prime radicalC13×#2541C2
socleC22×C13#386
cosocleC2×C42×C13C23
hypercenter#2541D13
hypocenterC13#9397
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2541

Complements

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

NH ≅ G/Ntype
1. #13123860C2semidirect
2. #13114828C2semidirect
3. #13113504C2semidirect
4. #13112739C2semidirect
47. C4⋊#1055D4semidirect
242. C13#9397semidirect

Maximal subgroups

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

subgroupindex
#131238602
#131148282
#131135042
#131127392
C13×#25412
#939713