Finite Group Databasebeta

← #15760342

Subgroups — #15760342

Order 3328.

706 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 706 conjugacy classes of subgroups — too many to draw. Only its 115 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#13123877C211yesmaximal, characteristic, complemented
2#13119782C211yesmaximal, characteristic
3#13113505C212yesmaximal, complemented
4#13112737C212yesmaximal, complemented
5C13×#1800C211yesmaximal, characteristic, complemented
6C2×C4×D4×C13C2211yescharacteristic
7C2×#88194—21no—
8C2×#88184—22no—
9C2×#88128C2211yescharacteristic
10C13×#423C2212yes—
11C2×C13×#100—21no—
12#11718868—22no—
13#11718673—24no—
14#11718649—21no—
15#11718621C414yes—
16C4×C4⋊Dic13C2211yescharacteristic
17#11718586C2212yes—
18C13×#343—21no—
19#11718077—24no—
20C22×D4×C13D411yescharacteristic
21C23×C4×C13D412yes—
22C22×C22⋊D13—24no—
23C22×D52—21no—
24C22×D52—21no—
25C22×D52C2×C412yes—
26C2×C13×M16—22no—
27C4×D4×C13—22no—
28C4×D4×C13—22no—
29C2×C13×C4⋊C4D411yescharacteristic
30C2×C13×C22⋊C4C2×C412yes—
31C2×C42×C13C2311yescharacteristic
32#88194—44no—
33#88184—48no—
34C2×#6103—24no—
35C2×C4⋊Dic13—21no—
36C2×C4×Dic13—21no—
37C2×#6099—24no—
38#88128—22no—
39#88128—22no—
40C13×C4⋊C8—22no—
41C13×C4⋊C8—22no—
42C13×#100—42no—
43#88071C2×C412yes—
44C22⋊#1055—24no—
45C22⋊#1055—22no—
46C4⋊#1055D414yescomplemented
47C4×#1055—22no—
48#9405—131nomaximal, Sylow
49C24×C13C22⋊C412yes—
50C23×D13—22no—
51C2×D4×C13—22no—
52C2×D4×C13—21no—
53C2×D4×C13—22no—
54C2×D4×C13—21no—
55C22×C4×C13—22no—
56C22×C4×C13—22no—
57C22×C4×C13—44no—
58C22×C4×C13C22⋊C412yes—
59C22×C4×C13C22×C411yescharacteristic
60C22×C4×C13C2×D411yescharacteristic
61C22×C4×C13C2×D411yescharacteristic
62C2×C22⋊D13—48no—
63C2×C22⋊D13—48no—
64C2×C22⋊D13—84no—
65C22×Dic13—22no—
66C2×D52—24no—
67C2×D52—44no—
68C2×D52—41no—
69C2×D52—42no—
70C2×D52—41no—
71C2×D52—42no—
72C2×D52—41no—
73C2×D52—41no—
74C2×D52—82no—
75C13×M16—42no—
76C13×M16—42no—
77C2×C8×C13—42no—
78C13×C4⋊C4—22no—
79C13×C22⋊C4—24no—
80C42×C13C2×D412yes—
81C42×C13#4112yes—
82#6103—48no—
83C4⋊Dic13—24no—
84C4×Dic13—42no—
85#6099—84no—
86C2×#1055—24no—
87#2975—131no—
88#2541—131no—
89#1800D1311yescharacteristic, complemented
90#1545—132no—
91#1303—132no—
92C23×C13—22no—
93C23×C13—22no—
94C23×C13—22no—
95C23×C13—42no—
96C23×C13—42no—
97C23×C13C2×C22⋊C411yescharacteristic
98C22×D13—44no—
99C22×D13—44no—
100C22×D13—42no—
101C22×D13—42no—
102C22×D13—42no—
103D4×C13—42no—
104D4×C13—42no—
105C2×C4×C13—22no—
106C2×C4×C13—22no—
107C2×C4×C13—41no—
108C2×C4×C13—44no—
109C2×C4×C13—42no—
110C2×C4×C13—82no—
111C2×C4×C13C4×D412yes—
112C2×C4×C13#12011yescharacteristic
113C2×C4×C13#12112yes—
114C2×C4×C13#12311yescharacteristic
115C2×C4×C13AGL(1,ℤ/8)12yes—
116C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
117C2×C4×C13#13711yescharacteristic
118C22⋊D13—816no—
119C2×Dic13—24no—
120C2×Dic13—42no—
121C2×Dic13—42no—
122D52—82no—
123D52—84no—
124D52—82no—
125D52—82no—
126D52—82no—
127C8×C13—82no—
128#1055—44no—
129C2×#127—131no—
130C2×#127—261no—
131C2×#121—262no—
132C2×C4×D4C2×D1311yescharacteristic
133#436—264no—
134#431—132no—
135#423C2×D1312yes—
136C2×#100—21no—
137#407—262no—
138#392—134no—
139#390—261no—
140C4×C4⋊C4—131no—
141#343—21no—
142#331—264no—
143C22×C13—21no—
144C22×C13—21no—
145C22×C13—44no—
146C22×C13—42no—
147C22×C13—42no—
148C22×C13—42no—
149C22×C13—82no—
150C22×C13#38611yescharacteristic
151C22×C13#41711yescharacteristic
152C22×C13#41811yescharacteristic
153C2×D13—84no—
154C2×D13—84no—
155C2×D13—82no—
156C2×D13—82no—
157C2×D13—82no—
158C4×C13—21no—
159C4×C13—22no—
160C4×C13—42no—
161C4×C13#45312yes—
162C4×C13#46812yes—
163C4×C13#46912yes—
164Dic13—44no—
165C22×D4—132no—
166C22×D4—264no—
167C22×D4—261no—
168C22×D4—261no—
169C22×D4C22⋊D1311yescharacteristic
170C23×C4D5212yes—
171C2×M16—22no—
172C2×M16—264no—
173#127—262no—
174#127—262no—
175#127—524no—
176#121—528no—
177C4×D4—22no—
178C4×D4—22no—
179C2×C4⋊C4—261no—
180C2×C4⋊C4C22⋊D1311yescharacteristic
181C2×C22⋊C4—264no—
182C2×C22⋊C4C4×D1312yes—
183C2×C42—261no—
184C2×C42C22×D1311yescharacteristic
185C4⋊C8—22no—
186C4⋊C8—22no—
187C4⋊C8—134no—
188#100—42no—
189C22⋊C8—264no—
190C22⋊C8—262no—
191C4×C8—262no—
192#95—132no—
193C2×C13—21no—
194C2×C13—21no—
195C2×C13—82no—
196C2×C13#188711yescharacteristic
197C2×C13#189511yescharacteristic
198C2×C13#191411yescharacteristic
199D13—162no—
200C24—262no—
201C24#610312yes—
202C2×D4—21no—
203C2×D4—22no—
204C2×D4—21no—
205C2×D4—22no—
206C2×D4—264no—
207C2×D4—524no—
208C2×D4—528no—
209C2×D4—528no—
210C2×D4—521no—
211C2×D4—521no—
212C2×D4—521no—
213C2×D4—522no—
214C2×D4—521no—
215C2×D4—522no—
216C2×D4—1042no—
217C2×D4—1044no—
218C22×C4—22no—
219C22×C4—22no—
220C22×C4—44no—
221C22×C4—262no—
222C22×C4#610312yes—
223C22×C4C2×C4×D1311yescharacteristic
224C22×C4C2×D5211yescharacteristic
225C22×C4C2×C22⋊D1311yescharacteristic
226M16—42no—
227M16—42no—
228M16—1044no—
229C2×C8—42no—
230C2×C8—264no—
231C4⋊C4—22no—
232C4⋊C4—264no—
233C22⋊C4—24no—
234C22⋊C4—528no—
235C42—522no—
236C42D4×D1312yes—
237C42#612912yes—
238C13#940511yescharacteristic, complemented, Sylow
239C23—22no—
240C23—22no—
241C23—22no—
242C23—42no—
243C23—42no—
244C23—524no—
245C23—524no—
246C23—522no—
247C23—522no—
248C23—522no—
249C23C2×#610311yescharacteristic
250D4—42no—
251D4—42no—
252D4—1044no—
253D4—1042no—
254D4—10416no—
255D4—1042no—
256D4—1042no—
257D4—1042no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—41no—
261C2×C4—44no—
262C2×C4—42no—
263C2×C4—82no—
264C2×C4—264no—
265C2×C4—522no—
266C2×C4—522no—
267C2×C4#8813512yes—
268C2×C4#8813611yescharacteristic
269C2×C4#8814011yescharacteristic
270C2×C4#8818611yescharacteristic
271C2×C4#8819312yes—
272C2×C4#8819611yescharacteristic
273C2×C4#8820312yes—
274C8—82no—
275C8—524no—
276C22—21no—
277C22—21no—
278C22—44no—
279C22—42no—
280C22—42no—
281C22—42no—
282C22—82no—
283C22—1044no—
284C22—1044no—
285C22—1042no—
286C22—1042no—
287C22—1042no—
288C22#1171861911yescharacteristic
289C22#1171862711yescharacteristic
290C22#1171866211yescharacteristic
291C4—21no—
292C4—22no—
293C4—42no—
294C4—524no—
295C4#1171840812yes—
296C4#1171870012yes—
297C4#1171871012yes—
298C2—21no—
299C2—21no—
300C2—82no—
301C2—2082no—
302C2#1311523211yescharacteristic
303C2#1311527211yescharacteristic
304C2#1311538111yescharacteristic
subgroupG/H
centerC22#11718619
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1800C2
socleC22×C13#386
prime radical#13119782C2
cosocleC2×C42×C13C23
hypercenter#1800D13
hypocenterC13#9405
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1800

Complements

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

NH ≅ G/Ntype
1. #13123877C2semidirect
3. #13113505C2semidirect
4. #13112737C2semidirect
5. C13×#1800C2semidirect
46. C4⋊#1055D4semidirect
89. #1800D13semidirect
238. C13#9405semidirect

Maximal subgroups

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

subgroupindex
#131238772
#131197822
#131135052
#131127372
C13×#18002
#940513