Finite Group Databasebeta

← #15760345

Subgroups — #15760345

Order 3328.

706 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 706 conjugacy classes of subgroups — too many to draw. Only its 123 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#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—
14#11718868—22no—
15#11718673—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—44no—
29C13×#121—48no—
30C4×D4×C13—22no—
31C4×D4×C13—22no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4D411yescharacteristic
34C2×C13×C22⋊C4—24no—
35C2×C13×C22⋊C4C2×C412yes—
36C2×C42×C13—21no—
37C2×C42×C13C2311yescharacteristic
38C2×#6099—24no—
39C2×#6099—22no—
40C13×#95C2×C412yes—
41#88073—42no—
42C22⋊#1055—24no—
43C22⋊#1055—22no—
44C4⋊#1055—22no—
45C4⋊#1055—22no—
46C4⋊#1055D414yescomplemented
47C4×#1055—22no—
48#9405—131nomaximal, Sylow
49C24×C13—22no—
50C24×C13C22⋊C412yes—
51C2×D4×C13—24no—
52C2×D4×C13—22no—
53C2×D4×C13—21no—
54C2×D4×C13—22no—
55C2×D4×C13—21no—
56C2×D4×C13—44no—
57C2×D4×C13—48no—
58C2×D4×C13—48no—
59C2×D4×C13—41no—
60C2×D4×C13—42no—
61C2×D4×C13—41no—
62C2×D4×C13—42no—
63C2×D4×C13—41no—
64C2×D4×C13—41no—
65C2×D4×C13—84no—
66C2×D4×C13—82no—
67C22×C4×C13—22no—
68C22×C4×C13—22no—
69C22×C4×C13—22no—
70C22×C4×C13—44no—
71C22×C4×C13C22⋊C412yes—
72C22×C4×C13C22×C411yescharacteristic
73C22×C4×C13C2×D411yescharacteristic
74C22×C4×C13C2×D411yescharacteristic
75C13×C4⋊C4—24no—
76C13×C4⋊C4—22no—
77C13×C22⋊C4—24no—
78C13×C22⋊C4—48no—
79C42×C13—42no—
80C42×C13C2×D412yes—
81C42×C13#4112yes—
82#6099—42no—
83#6099—42no—
84#6099—84no—
85C2×#1055—24no—
86C2×#1055—42no—
87#2975—131no—
88#2541D1311yescharacteristic
89#1800—131no—
90#1545—132no—
91#1303—132no—
92C23×C13—22no—
93C23×C13—22no—
94C23×C13—22no—
95C23×C13—42no—
96C23×C13—42no—
97C23×C13—44no—
98C23×C13—44no—
99C23×C13—42no—
100C23×C13—42no—
101C23×C13—42no—
102C23×C13C2×C22⋊C411yescharacteristic
103D4×C13—42no—
104D4×C13—42no—
105D4×C13—82no—
106D4×C13—84no—
107D4×C13—816no—
108D4×C13—82no—
109D4×C13—82no—
110D4×C13—82no—
111C2×C4×C13—22no—
112C2×C4×C13—24no—
113C2×C4×C13—22no—
114C2×C4×C13—41no—
115C2×C4×C13—42no—
116C2×C4×C13—42no—
117C2×C4×C13—44no—
118C2×C4×C13—42no—
119C2×C4×C13—82no—
120C2×C4×C13C4×D412yes—
121C2×C4×C13#12011yescharacteristic
122C2×C4×C13#12112yes—
123C2×C4×C13#12311yescharacteristic
124C2×C4×C13AGL(1,ℤ/8)12yes—
125C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
126C2×C4×C13#13711yescharacteristic
127#1055—44no—
128#1055—82no—
129C2×#127—21no—
130C2×#127C2×D1311yescharacteristic
131C2×#121—22no—
132C2×C4×D4C2×D1311yescharacteristic
133#436—264no—
134#431—132no—
135#423—132no—
136C2×#100—261no—
137#407—262no—
138#392Dic1314yes—
139#390—21no—
140C4×C4⋊C4C2×D1311yescharacteristic
141#343—261no—
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—84no—
151C22×C13—84no—
152C22×C13—82no—
153C22×C13—82no—
154C22×C13—82no—
155C22×C13#38611yescharacteristic
156C22×C13#41711yescharacteristic
157C22×C13#41811yescharacteristic
158C4×C13—21no—
159C4×C13—22no—
160C4×C13—44no—
161C4×C13—42no—
162C4×C13#45312yes—
163C4×C13#46812yes—
164C4×C13#46912yes—
165C22×D4—24no—
166C22×D4—21no—
167C22×D4—21no—
168C22×D4C2×Dic1312yes—
169C22×D4C22⋊D1311yescharacteristic
170C23×C4C22⋊D1312yes—
171C2×M16—264no—
172C2×M16—262no—
173#127—22no—
174#127—22no—
175#127—44no—
176#121—48no—
177C4×D4—22no—
178C4×D4—22no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4C22⋊D1311yescharacteristic
181C2×C22⋊C4—24no—
182C2×C22⋊C4C2×Dic1312yes—
183C2×C42—21no—
184C2×C42C22×D1311yescharacteristic
185C4⋊C8—134no—
186C4⋊C8—262no—
187C4⋊C8—262no—
188#100—522no—
189C22⋊C8—264no—
190C22⋊C8—262no—
191C4×C8—262no—
192#95C2×Dic1312yes—
193C2×C13—21no—
194C2×C13—21no—
195C2×C13—82no—
196C2×C13—162no—
197C2×C13#188711yescharacteristic
198C2×C13#189511yescharacteristic
199C2×C13#191411yescharacteristic
200C24—22no—
201C24C22⋊Dic1312yes—
202C2×D4—22no—
203C2×D4—24no—
204C2×D4—22no—
205C2×D4—21no—
206C2×D4—21no—
207C2×D4—44no—
208C2×D4—48no—
209C2×D4—48no—
210C2×D4—42no—
211C2×D4—41no—
212C2×D4—41no—
213C2×D4—42no—
214C2×D4—41no—
215C2×D4—41no—
216C2×D4—84no—
217C2×D4—82no—
218C22×C4—22no—
219C22×C4—22no—
220C22×C4—22no—
221C22×C4—44no—
222C22×C4C22⋊Dic1312yes—
223C22×C4C22×Dic1311yescharacteristic
224C22×C4C2×C22⋊D1311yescharacteristic
225C22×C4C2×C22⋊D1311yescharacteristic
226M16—522no—
227M16—522no—
228M16—1044no—
229C2×C8—264no—
230C2×C8—522no—
231C4⋊C4—24no—
232C4⋊C4—22no—
233C22⋊C4—24no—
234C22⋊C4—48no—
235C42—42no—
236C42D4×D1312yes—
237C42#612912yes—
238C13#940511yescharacteristic, complemented, Sylow
239C23—22no—
240C23—22no—
241C23—22no—
242C23—42no—
243C23—42no—
244C23—44no—
245C23—44no—
246C23—42no—
247C23—42no—
248C23—42no—
249C23C2×C22⋊Dic1311yescharacteristic
250D4—42no—
251D4—42no—
252D4—84no—
253D4—82no—
254D4—816no—
255D4—82no—
256D4—82no—
257D4—82no—
258C2×C4—22no—
259C2×C4—24no—
260C2×C4—22no—
261C2×C4—41no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—44no—
265C2×C4—42no—
266C2×C4—82no—
267C2×C4#8818612yes—
268C2×C4D4×Dic1312yes—
269C2×C4#8818911yescharacteristic
270C2×C4#8819111yescharacteristic
271C2×C4#8819312yes—
272C2×C4#8820311yescharacteristic
273C2×C4#8820511yescharacteristic
274C8—524no—
275C8—1042no—
276C22—21no—
277C22—21no—
278C22—44no—
279C22—42no—
280C22—42no—
281C22—42no—
282C22—82no—
283C22—84no—
284C22—84no—
285C22—82no—
286C22—82no—
287C22—82no—
288C22#1171887611yescharacteristic
289C22#1171888111yescharacteristic
290C22#1171889311yescharacteristic
291C4—21no—
292C4—22no—
293C4—44no—
294C4—42no—
295C4#1171870012yes—
296C4#1171870312yes—
297C4#1171873812yes—
298C2—21no—
299C2—21no—
300C2—82no—
301C2—162no—
302C2#1311523511yescharacteristic
303C2#1311527511yescharacteristic
304C2#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#9405
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. #13123877C2semidirect
2. #13114828C2semidirect
3. #13113504C2semidirect
4. #13112739C2semidirect
46. C4⋊#1055D4semidirect
238. C13#9405semidirect

Maximal subgroups

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

subgroupindex
#131238772
#131148282
#131135042
#131127392
C13×#25412
#940513