Finite Group Databasebeta

← #15779918

Subgroups — #15779918

Order 3328.

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

normal subgroups only

This group has 528 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
1#13124417C211yesmaximal, characteristic
2C2×#11718080C212yesmaximal, complemented
3#13116447C211yesmaximal, characteristic, complemented
4#13112943C212yesmaximal, complemented
5C2×C13×#427C211yesmaximal, characteristic, complemented
6C23×C8×C13C2211yescharacteristic
7C2×C13×#117—21no—
8#11719496—21no—
9C2×#88158C2211yescharacteristic
10C13×#427—24no—
11C2×C13×#107—21no—
12C2×C13×#106C2212yes—
13#11718777C412yescomplemented
14#11718776C412yescomplemented
15#11718775—22no—
16#11718774—21no—
17#11718767C2211yescharacteristic
18C2×#88052C2212yes—
19C22⋊#6090—22no—
20#11718080—24no—
21C23×C4×C13D411yescharacteristic
22C2×#6127—21no—
23C22×C8×C13—22no—
24C22×C8×C13—22no—
25C22×C8×C13C2×C412yes—
26C22×C8×C13D412yes—
27C22×C8×C13D411yescharacteristic
28C22×C8×C13C2311yescharacteristic
29C13×#117—24no—
30C13×#117—42no—
31C2×C13×C4⋊C4—22no—
32C2×C13×C22⋊C4—41no—
33C2×C42×C13—41no—
34#88207—41no—
35#88184—22no—
36#88183—41no—
37C4×C22⋊D13—42no—
38#88180—21no—
39#88178—22no—
40C2×Dic52C2×C411yescharacteristic
41#88158—22no—
42#88158—22no—
43C2×D104C2×C411yescharacteristic
44C2×#6095—21no—
45C13×#107—24no—
46C13×#106—22no—
47C13×#106D414yescomplemented
48#88061—22no—
49#88058C2×C412yes—
50#88057—21no—
51#88056—22no—
52#88052—22no—
53#88052—22no—
54C2×#6090—22no—
55#13002—131nomaximal, Sylow
56C24×C13D811yescharacteristic
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13—21no—
60C22×C4×C13—21no—
61C22×C4×C13—42no—
62C22×C4×C13C22⋊C412yes—
63C22×C4×C13D811yescharacteristic
64C22×C4×C13SD1612yes—
65C22×C4×C13C2×D411yescharacteristic
66C2×C22⋊D13—42no—
67C2×C22⋊D13—41no—
68#6127—41no—
69#6127—41no—
70#6127—41no—
71#6127—41no—
72C2×D52—21no—
73C2×C4×D13—41no—
74C2×Dic26—21no—
75C2×C8×C13—21no—
76C2×C8×C13—21no—
77C2×C8×C13—24no—
78C2×C8×C13—24no—
79C2×C8×C13C22⋊C412yes—
80C2×C8×C13C22×C411yescharacteristic
81C2×C8×C13C2×D412yes—
82C2×C8×C13C2×D411yescharacteristic
83C2×C8×C13#4112yes—
84C13×C4⋊C4—24no—
85C13×C4⋊C4—42no—
86C13×C22⋊C4—44no—
87C42×C13—44no—
88C22⋊Dic13—42no—
89C22⋊Dic13—41no—
90#6103—42no—
91C4⋊Dic13—22no—
92#6101—42no—
93C4×Dic13—41no—
94Dic52—22no—
95D104—22no—
96#6095—42no—
97#6090—42no—
98#3050—131no—
99C2×#427D1311yescharacteristic, complemented
100C2×#360—132no—
101#2112—131no—
102#1386—132no—
103C23×C13—21no—
104C23×C13—21no—
105C23×C13—42no—
106C23×C13#10212yes—
107C23×C13C2×D811yescharacteristic
108C22×D13—41no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—22no—
112C2×C4×C13—22no—
113C2×C4×C13—22no—
114C2×C4×C13—22no—
115C2×C4×C13—44no—
116C2×C4×C13—84no—
117C2×C4×C13#10212yes—
118C2×C4×C13C2×C22⋊C411yescharacteristic
119C2×C4×C13#12011yescharacteristic
120C2×C4×C13#12311yescharacteristic
121C2×C4×C13C2×SD1611yescharacteristic
122C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
123C2×C4×C13#13711yescharacteristic
124C22⋊D13—84no—
125C22⋊D13—81no—
126C22⋊D13—81no—
127C2×Dic13—42no—
128C2×Dic13—41no—
129D52—41no—
130D52—41no—
131C4×D13—81no—
132C4×D13—81no—
133Dic26—41no—
134Dic26—41no—
135C8×C13—22no—
136C8×C13C4×D412yes—
137C8×C13#12112yes—
138C2×#135—131no—
139C23×C8C2×D1311yescharacteristic
140#525—261no—
141C2×#117—21no—
142C2×M32—132no—
143#467—132no—
144#466—132no—
145#465—262no—
146#427—24no—
147#427—131no—
148C2×#107—21no—
149C2×#106C2×D1312yes—
150#416—261no—
151#360—264no—
152C22⋊C16—262no—
153C22×C13—22no—
154C22×C13—22no—
155C22×C13—22no—
156C22×C13—22no—
157C22×C13—42no—
158C22×C13—42no—
159C22×C13C2×#10211yescharacteristic
160C22×C13#44711yescharacteristic
161C22×C13#48011yescharacteristic
162C2×D13—81no—
163C2×D13—82no—
164C4×C13—22no—
165C4×C13—84no—
166C4×C13#38611yescharacteristic
167C4×C13#41711yescharacteristic
168C4×C13#44811yescharacteristic
169C4×C13#48111yescharacteristic
170Dic13—81no—
171Dic13—82no—
172C2×#41—261no—
173C23×C4C22⋊D1311yescharacteristic
174#135—262no—
175#135—262no—
176C2×Q16—131no—
177C2×SD16—261no—
178C2×D8—131no—
179C22×C8—22no—
180C22×C8—22no—
181C22×C8C4×D1312yes—
182C22×C8D5212yes—
183C22×C8C22⋊D1311yescharacteristic
184C22×C8C22×D1311yescharacteristic
185#123—521no—
186C22⋊Q8—262no—
187#121—262no—
188#120—521no—
189C4×D4—522no—
190#117—24no—
191#117—42no—
192#117—261no—
193C2×C4⋊C4—22no—
194C2×C22⋊C4—41no—
195C2×C42—41no—
196M32—262no—
197M32—262no—
198C2×C16—262no—
199#107—24no—
200#107—132no—
201#106—22no—
202#106—261no—
203#106C22⋊D1314yescomplemented
204#103—262no—
205#102—262no—
206C2×C13—21no—
207C2×C13—21no—
208C2×C13—42no—
209C2×C13#187411yescharacteristic
210C2×C13#214512yes—
211D13—161no—
212C24#610411yescharacteristic
213#41—521no—
214#41—521no—
215#41—521no—
216#41—521no—
217C2×Q8—261no—
218C2×D4—261no—
219C2×D4—521no—
220C2×D4—522no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—42no—
226C22×C4—521no—
227C22×C4#610312yes—
228C22×C4#610411yescharacteristic
229C22×C4#610612yes—
230C22×C4C2×C22⋊D1311yescharacteristic
231Q16—262no—
232SD16—522no—
233D8—262no—
234C2×C8—21no—
235C2×C8—21no—
236C2×C8—24no—
237C2×C8—24no—
238C2×C8#610312yes—
239C2×C8C2×C4×D1311yescharacteristic
240C2×C8C2×D5211yescharacteristic
241C2×C8#612712yes—
242C2×C8C2×C22⋊D1312yes—
243C4⋊C4—24no—
244C4⋊C4—42no—
245C4⋊C4—262no—
246C4⋊C4—522no—
247C22⋊C4—44no—
248C22⋊C4—521no—
249C22⋊C4—522no—
250C22⋊C4—522no—
251C42—44no—
252C42—521no—
253C16—522no—
254C13#1300211yescharacteristic, complemented, Sylow
255C23—21no—
256C23—21no—
257C23—42no—
258C23—521no—
259C23#8804912yes—
260C23C2×#610411yescharacteristic
261Q8—521no—
262Q8—521no—
263D4—521no—
264D4—521no—
265D4—1044no—
266D4—1041no—
267D4—1041no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—44no—
275C2×C4—84no—
276C2×C4—522no—
277C2×C4—521no—
278C2×C4—1041no—
279C2×C4—1041no—
280C2×C4#8804912yes—
281C2×C4C2×#610311yescharacteristic
282C2×C4#8818311yescharacteristic
283C2×C4#8818611yescharacteristic
284C2×C4C2×#610611yescharacteristic
285C2×C4#8819611yescharacteristic
286C2×C4#8820711yescharacteristic
287C8—22no—
288C8C4×C22⋊D1312yes—
289C8#8818412yes—
290C22—22no—
291C22—22no—
292C22—22no—
293C22—22no—
294C22—42no—
295C22—42no—
296C22—1041no—
297C22—1042no—
298C22C2×#8804911yescharacteristic
299C22#1171862811yescharacteristic
300C22#1171887811yescharacteristic
301C4—22no—
302C4—84no—
303C4—1041no—
304C4—1042no—
305C4#1171862711yescharacteristic
306C4#1171862911yescharacteristic
307C4#1171887411yescharacteristic
308C4#1171888811yescharacteristic
309C2—21no—
310C2—21no—
311C2—42no—
312C2—2081no—
313C2#1311515311yescharacteristic
314C2#1311657112yes—
subgroupG/H
centerC22C2×#88049
commutatorC2×C8×C13C22×C4
FrattiniC22×C8C22×D13
FittingC2×C13×#427C2
socleC22×C13C2×#102
prime radical#13124417C2
cosocleC22×C8×C13C23
hypercenterC2×#427D13
hypocenterC13#13002
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C23×C8 ◁ C2×#427

Complements

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

NH ≅ G/Ntype
2. C2×#11718080C2semidirect
3. #13116447C2semidirect
4. #13112943C2semidirect
5. C2×C13×#427C2semidirect
13. #11718777C4semidirect
14. #11718776C4semidirect
47. C13×#106D4semidirect
99. C2×#427D13semidirect
203. #106C22⋊D13semidirect
254. C13#13002semidirect

Maximal subgroups

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

subgroupindex
#131244172
C2×#117180802
#131164472
#131129432
C2×C13×#4272
#1300213