Finite Group Databasebeta

← #15765260

Subgroups — #15765260

Order 3328.

712 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 712 conjugacy classes of subgroups — too many to draw. Only its 131 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
1C2×#11718745C212yesmaximal, complemented
2#13119752C211yesmaximal, characteristic
3C2×#11718051C212yesmaximal, complemented
4#13112719C211yesmaximal, characteristic, complemented
5C13×#1956C211yesmaximal, characteristic, complemented
6C2×C13×C4⋊Q8C2211yescharacteristic
7C2×#88149—22no—
8C2×C4×D52C2212yes—
9C2×C13×#103—22no—
10C2×C4×C8×C13C2211yescharacteristic
11C13×#384C2211yescharacteristic
12#11718745—24no—
13#11718745—24no—
14#11718652—22no—
15#11718648—22no—
16C2×#88049—22no—
17C2×#88048—22no—
18C2×C4⋊#1055C2212yes—
19#11718051—24no—
20C22×Q8×C13—21no—
21C22×D52—22no—
22C22×D52D412yes—
23C22×C4×D13—22no—
24C22×C8×C13—21no—
25C13×C4⋊Q8—22no—
26C13×C4⋊Q8—21no—
27C13×C4⋊Q8D412yescomplemented
28C2×C13×C4⋊C4—22no—
29C2×C13×C4⋊C4—22no—
30C2×C13×C4⋊C4D412yes—
31C2×C42×C13C2311yescharacteristic
32C2×#6103—24no—
33C2×#6103—22no—
34C2×C4⋊Dic13D412yes—
35C22×#1055—22no—
36#88149—44no—
37#88149—44no—
38C4×D52—22no—
39C4×D52—22no—
40C4×D52—22no—
41C4×D52—22no—
42C13×#103—44no—
43C4×C8×C13—22no—
44#88071—22no—
45#88049—28no—
46#88048—28no—
47C4⋊#1055—22no—
48C4⋊#1055D414yescomplemented
49#10235—131nomaximal, Sylow
50C23×D13—22no—
51C2×Q8×C13—22no—
52C2×Q8×C13—42no—
53C2×Q8×C13—42no—
54C2×Q8×C13—41no—
55C22×C4×C13—22no—
56C22×C4×C13—41no—
57C22×C4×C13C2×D412yes—
58C22×C4×C13C2×D411yescharacteristic
59C22×Dic13—22no—
60C2×D52—22no—
61C2×D52—22no—
62C2×D52—22no—
63C2×D52—22no—
64C2×D52—22no—
65C2×D52—48no—
66C2×D52—82no—
67C2×D52SD1614yes—
68C2×C4×D13—42no—
69C2×C4×D13—42no—
70C2×C4×D13—42no—
71C2×C4×D13—42no—
72C2×C4×D13—42no—
73C2×C4×D13—42no—
74C2×C8×C13—22no—
75C2×C8×C13—41no—
76C2×C8×C13—41no—
77C13×C4⋊C4—24no—
78C13×C4⋊C4—42no—
79C13×C4⋊C4—42no—
80C13×C4⋊C4—42no—
81C13×C4⋊C4—42no—
82C42×C13C2×D411yescharacteristic
83C42×C13C2×D412yes—
84C42×C13#4111yescharacteristic
85#6103—48no—
86#6103—42no—
87#6103—42no—
88C4⋊Dic13—22no—
89C4⋊Dic13—22no—
90C2×#1055—24no—
91C2×#1055—42no—
92C2×#1055—42no—
93C2×#476—132no—
94#2537—131no—
95#1956D1311yescharacteristic, complemented
96C2×D4⋊C8—132no—
97#1296—131no—
98C23×C13#12011yescharacteristic
99C22×D13—24no—
100C22×D13—42no—
101C22×D13—42no—
102C22×D13—42no—
103C22×D13—42no—
104C22×D13—42no—
105C22×D13—42no—
106Q8×C13—44no—
107Q8×C13—82no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—42no—
111C2×C4×C13—44no—
112C2×C4×C13—42no—
113C2×C4×C13—81no—
114C2×C4×C13—81no—
115C2×C4×C13#12012yes—
116C2×C4×C13#12111yescharacteristic
117C2×C4×C13#12112yes—
118C2×C4×C13#12711yescharacteristic
119C2×C4×C13C2×SD1612yes—
120C2×C4×C13#13512yes—
121C2×C4×C13AGL(1,ℤ/8)12yes—
122C2×C4×C13#13712yes—
123C2×Dic13—42no—
124C2×Dic13—42no—
125C2×Dic13—42no—
126D52—24no—
127D52—24no—
128D52—42no—
129D52—42no—
130D52—88no—
131C4×D13—82no—
132C4×D13—82no—
133C4×D13—82no—
134C4×D13—82no—
135C8×C13—42no—
136#1055—44no—
137C2×C4⋊Q8C2×D1311yescharacteristic
138C2×#121—262no—
139C2×C4×D4—132no—
140#476—264no—
141#476—264no—
142C2×#106—262no—
143C2×C4⋊C8—132no—
144C2×#103—22no—
145C2×#102—262no—
146C2×C4×C8C2×D1311yescharacteristic
147#394—262no—
148#384C2×D1311yescharacteristic
149#380—262no—
150D4⋊C8—264no—
151C22×C13#39211yescharacteristic
152C22×C13#45012yes—
153C22×C13#45212yes—
154C22×C13#45311yescharacteristic
155C22×C13#45411yescharacteristic
156C2×D13—44no—
157C2×D13—44no—
158C2×D13—44no—
159C2×D13—82no—
160C2×D13—82no—
161C2×D13—82no—
162C2×D13—82no—
163C4×C13—21no—
164C4×C13—21no—
165C4×C13—82no—
166C4×C13—82no—
167C4×C13#44812yes—
168C4×C13#44912yes—
169C4×C13#46512yes—
170C4×C13#46812yes—
171Dic13—82no—
172C22×Q8—21no—
173C22×D4—132no—
174C22×D4—262no—
175C23×C4—262no—
176C22×C8—21no—
177C22×C8—262no—
178C4⋊Q8—21no—
179C4⋊Q8—22no—
180C4⋊Q8D5212yescomplemented
181#121—524no—
182#121—524no—
183C4×D4—262no—
184C4×D4—262no—
185C4×D4—262no—
186C4×D4—262no—
187C2×C4⋊C4—22no—
188C2×C4⋊C4—22no—
189C2×C4⋊C4—132no—
190C2×C4⋊C4C22⋊D1312yes—
191C2×C22⋊C4—264no—
192C2×C22⋊C4—262no—
193C2×C42C22×D1311yescharacteristic
194#106—268no—
195C4⋊C8—134no—
196C4⋊C8—262no—
197#103—44no—
198#102—268no—
199C4×C8—22no—
200#95—262no—
201C2×C13#162911yescharacteristic
202C2×C13#163411yescharacteristic
203C2×C13#163512yes—
204C2×C13#200012yes—
205C2×C13#200611yescharacteristic
206D13—84no—
207C24—262no—
208C2×Q8—22no—
209C2×Q8—42no—
210C2×Q8—42no—
211C2×Q8—41no—
212C2×D4—134no—
213C2×D4—262no—
214C2×D4—262no—
215C2×D4—262no—
216C2×D4—262no—
217C2×D4—262no—
218C2×D4—528no—
219C2×D4—1042no—
220C22×C4—22no—
221C22×C4—41no—
222C22×C4—262no—
223C22×C4—522no—
224C22×C4—522no—
225C22×C4—522no—
226C22×C4—522no—
227C22×C4—522no—
228C22×C4—522no—
229C22×C4D4×D1312yes—
230C22×C4C2×C22⋊D1311yescharacteristic
231C2×C8—22no—
232C2×C8—41no—
233C2×C8—41no—
234C2×C8—264no—
235C2×C8—522no—
236C2×C8—522no—
237C4⋊C4—24no—
238C4⋊C4—42no—
239C4⋊C4—42no—
240C4⋊C4—42no—
241C4⋊C4—42no—
242C4⋊C4—262no—
243C4⋊C4—262no—
244C22⋊C4—528no—
245C22⋊C4—522no—
246C22⋊C4—522no—
247C42C2×D5211yescharacteristic
248C42#612711yescharacteristic
249C42D4×D1312yes—
250C13#1023511yescharacteristic, complemented, Sylow
251C23—264no—
252C23—522no—
253C23—522no—
254C23—522no—
255C23—522no—
256C23—522no—
257C23—522no—
258C23#8819111yescharacteristic
259Q8—44no—
260Q8—82no—
261D4—264no—
262D4—264no—
263D4—522no—
264D4—522no—
265D4—1048no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—42no—
269C2×C4—44no—
270C2×C4—42no—
271C2×C4—81no—
272C2×C4—81no—
273C2×C4—522no—
274C2×C4—522no—
275C2×C4—522no—
276C2×C4—1042no—
277C2×C4—1042no—
278C2×C4—1042no—
279C2×C4—1042no—
280C2×C4#8813612yes—
281C2×C4#8813812yes—
282C2×C4SD16×D1312yes—
283C2×C4#8816812yes—
284C2×C4#8817212yes—
285C2×C4#8817312yes—
286C2×C4#8818411yescharacteristic
287C2×C4#8819411yescharacteristic
288C8—42no—
289C8—524no—
290C22—524no—
291C22—524no—
292C22—524no—
293C22—1042no—
294C22—1042no—
295C22—1042no—
296C22—1042no—
297C22#1171862111yescharacteristic
298C22#1171872311yescharacteristic
299C22#1171873811yescharacteristic
300C22#1171883012yes—
301C22#1171884812yes—
302C4—21no—
303C4—21no—
304C4—82no—
305C4—82no—
306C4—1042no—
307C4#1171846712yes—
308C4#1171846812yes—
309C4#1171847212yes—
310C4#1171847312yes—
311C2—1044no—
312C2#1311395011yescharacteristic
313C2#1311397911yescharacteristic
314C2#1311398412yes—
315C2#1311583812yes—
316C2#1311587711yescharacteristic
subgroupG/H
centerC23#88191
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1956C2
socleC23×C13#120
prime radical#13119752C2
hypercenter#1956D13
hypocenterC13#10235
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1956

Complements

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

NH ≅ G/Ntype
1. C2×#11718745C2semidirect
3. C2×#11718051C2semidirect
4. #13112719C2semidirect
5. C13×#1956C2semidirect
27. C13×C4⋊Q8D4semidirect
48. C4⋊#1055D4semidirect
95. #1956D13semidirect
180. C4⋊Q8D52semidirect
250. C13#10235semidirect

Maximal subgroups

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

subgroupindex
C2×#117187452
#131197522
C2×#117180512
#131127192
C13×#19562
#1023513