Finite Group Databasebeta

← #15780288

Subgroups — #15780288

Order 3328.

558 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88038C211yesmaximal, characteristic, complemented
2C2×#11718818C211yesmaximal, characteristic
3C2×#11718154C211yesmaximal, characteristic, complemented
4#13114862C211yesmaximal, characteristic, complemented
5#13112928C211yesmaximal, characteristic, complemented
6#13112927C211yesmaximal, characteristic, complemented
7C2×C13×#357C211yesmaximal, characteristic, complemented
8C22×C13×D8C2211yescharacteristic
9C2×#88192—21no—
10C22×C8×D13C2211yescharacteristic
11C22×C13×C16C2211yescharacteristic
12C2×C13×#107C2211yescharacteristic
13C2×#88072—21no—
14#11718818—22no—
15#11718818C414yescomplemented
16C2×#88058C2211yescharacteristic
17C2×#88058C2211yescharacteristic
18C22×#6090C2211yescharacteristic
19#11718648—21no—
20C2×#88038—22no—
21C2×#88038—22no—
22C2×#88038—22no—
23C13×#357—22no—
24#11718154—22no—
25#11718121—21no—
26C22×D4×C13—21no—
27C22×C22⋊D13—41no—
28C22×C4×D13D411yescharacteristic
29C2×C13×D8—21no—
30C2×C13×D8—21no—
31C2×C13×D8—21no—
32C2×C13×D8—21no—
33C2×C13×D8—21no—
34C2×C13×D8C2×C412yes—
35C22×C8×C13C2311yescharacteristic
36C2×C13×C4⋊C4—21no—
37C2×C22⋊Dic13—41no—
38#88192—24no—
39#88192—42no—
40C2×#6103—41no—
41C2×C4⋊Dic13—21no—
42C2×C4⋊Dic13—21no—
43C22×#1055D411yescharacteristic
44C2×C8×D13—21no—
45C2×C8×D13—21no—
46C2×C8×D13—21no—
47C2×C8×D13—21no—
48C2×C8×D13C2×C412yes—
49C2×C8×D13D412yes—
50C2×C13×C16—21no—
51C2×C13×C16—21no—
52C2×C13×C16D412yescomplemented
53C13×#107—21no—
54C13×#107—21no—
55#88072—24no—
56#88071—41no—
57#88058—21no—
58#88058—21no—
59#88058—21no—
60#88058C2×C412yes—
61C2×#6090—21no—
62C2×#6090—21no—
63C2×#6090D412yescomplemented
64#88038—28no—
65#13061—131nomaximal, Sylow
66C24×C13—41no—
67C23×D13D811yescharacteristic
68C2×D4×C13—22no—
69C2×D4×C13—41no—
70C2×D4×C13—41no—
71C2×D4×C13—41no—
72C2×D4×C13—41no—
73C2×D4×C13—41no—
74C22×C4×C13—41no—
75C22×C4×C13C2×D411yescharacteristic
76C2×C22⋊D13—44no—
77C2×C22⋊D13—82no—
78C2×C22⋊D13—82no—
79C22×Dic13—41no—
80C22×Dic13—41no—
81C22×Dic13D811yescharacteristic
82C2×C4×D13—21no—
83C2×C4×D13—21no—
84C2×C4×D13—21no—
85C2×C4×D13—21no—
86C2×C4×D13C22⋊C412yes—
87C2×C4×D13SD1612yes—
88C13×D8—22no—
89C13×D8—22no—
90C13×D8—41no—
91C13×D8—41no—
92C2×C8×C13C22×C411yescharacteristic
93C2×C8×C13C2×D411yescharacteristic
94C2×C8×C13C2×D411yescharacteristic
95C2×C8×C13C2×D411yescharacteristic
96C2×C8×C13#4111yescharacteristic
97C2×C8×C13#4111yescharacteristic
98C13×C4⋊C4—41no—
99C13×C4⋊C4—41no—
100C22⋊Dic13—44no—
101#6103—82no—
102C4⋊Dic13—22no—
103C4⋊Dic13—41no—
104C4⋊Dic13—41no—
105C4⋊Dic13—41no—
106C2×#1055—21no—
107C2×#1055—21no—
108C2×#1055C22⋊C412yes—
109C8×D13—22no—
110C8×D13—22no—
111C8×D13—22no—
112C8×D13—22no—
113C13×C16—22no—
114#6090—22no—
115C22×M32—131no—
116C2×#466—131no—
117C2×#357—131no—
118C2×#357D1311yescharacteristic, complemented
119#1808—131no—
120#1380—131no—
121#1380—131no—
122C23×C13—42no—
123C23×C13—81no—
124C23×C13—81no—
125C23×C13—81no—
126C23×C13—81no—
127C23×C13—81no—
128C23×C13—81no—
129C23×C13C2×D811yescharacteristic
130C22×D13—21no—
131C22×D13—21no—
132C22×D13—21no—
133C22×D13—21no—
134C22×D13—21no—
135C22×D13—21no—
136C22×D13#10212yes—
137D4×C13—42no—
138D4×C13—42no—
139D4×C13—81no—
140D4×C13—81no—
141C2×C4×C13—81no—
142C2×C4×C13—81no—
143C2×C4×C13—81no—
144C2×C4×C13C2×C22⋊C411yescharacteristic
145C2×C4×C13#12111yescharacteristic
146C2×C4×C13#12111yescharacteristic
147C2×C4×C13C2×SD1611yescharacteristic
148C2×C4×C13#13511yescharacteristic
149C2×C4×C13#13511yescharacteristic
150C22⋊D13—88no—
151C2×Dic13—21no—
152C2×Dic13—21no—
153C2×Dic13—42no—
154C2×Dic13—81no—
155C2×Dic13—81no—
156C2×Dic13—81no—
157C2×Dic13—81no—
158C2×Dic13—81no—
159C2×Dic13#10212yes—
160C4×D13—22no—
161C4×D13—22no—
162C4×D13—22no—
163C4×D13—22no—
164C8×C13C4×D411yescharacteristic
165C8×C13C4×D411yescharacteristic
166C8×C13#12011yescharacteristic
167C8×C13#12311yescharacteristic
168#1055—22no—
169C22×D8C2×D1311yescharacteristic
170C23×C8—131no—
171C2×#121—261no—
172C2×M32—262no—
173C2×M32—262no—
174C2×M32—262no—
175C22×C16—131no—
176C22×C16C2×D1311yescharacteristic
177#466—134no—
178#466—262no—
179C2×#107—131no—
180C2×#107—131no—
181C2×#107C2×D1311yescharacteristic
182C2×#102—261no—
183#380—261no—
184#357—22no—
185#357—262no—
186#340—261no—
187C22×C13—82no—
188C22×C13—82no—
189C22×C13—82no—
190C22×C13—161no—
191C22×C13—161no—
192C22×C13—161no—
193C22×C13—161no—
194C22×C13C2×#10211yescharacteristic
195C22×C13#46611yescharacteristic
196C22×C13#46611yescharacteristic
197C22×C13#50911yescharacteristic
198C22×C13#50911yescharacteristic
199C22×C13#50911yescharacteristic
200C22×C13#51011yescharacteristic
201C2×D13—22no—
202C2×D13—22no—
203C2×D13—22no—
204C2×D13—41no—
205C2×D13—41no—
206C2×D13—41no—
207C2×D13—41no—
208C4×C13—161no—
209C4×C13#38611yescharacteristic
210C4×C13#41611yescharacteristic
211C4×C13#46511yescharacteristic
212C4×C13#46511yescharacteristic
213Dic13—22no—
214Dic13—82no—
215Dic13—161no—
216C22×D4—21no—
217C22×D4—521no—
218C23×C4—131no—
219C2×D8—21no—
220C2×D8—21no—
221C2×D8—21no—
222C2×D8—21no—
223C2×D8—21no—
224C2×D8C4×D1312yes—
225C22×C8—131no—
226C22×C8—132no—
227C22×C8—132no—
228C22×C8—261no—
229C22×C8—261no—
230C22×C8—261no—
231C22×C8—261no—
232C22×C8C22×D1311yescharacteristic
233#121—264no—
234#121—522no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—261no—
237C2×C4⋊C4—261no—
238C2×C22⋊C4—521no—
239C2×C22⋊C4—521no—
240M32—268no—
241C2×C16—21no—
242C2×C16—21no—
243C2×C16—132no—
244C2×C16—261no—
245C2×C16—261no—
246C2×C16C22⋊D1312yescomplemented
247#107—21no—
248#107—21no—
249#107—132no—
250#107—261no—
251#107—261no—
252#107—261no—
253#102—264no—
254#95—521no—
255C2×C13—162no—
256C2×C13#189311yescharacteristic
257C2×C13#213911yescharacteristic
258C2×C13#214011yescharacteristic
259C2×C13#221811yescharacteristic
260C2×C13#221811yescharacteristic
261C2×C13#222011yescharacteristic
262C2×C13#222011yescharacteristic
263D13—42no—
264C24—41no—
265C24—131no—
266C2×D4—22no—
267C2×D4—41no—
268C2×D4—41no—
269C2×D4—41no—
270C2×D4—41no—
271C2×D4—41no—
272C2×D4—524no—
273C2×D4—1042no—
274C2×D4—1042no—
275C22×C4—41no—
276C22×C4—131no—
277C22×C4—132no—
278C22×C4—132no—
279C22×C4—261no—
280C22×C4—261no—
281C22×C4—261no—
282C22×C4—261no—
283C22×C4—521no—
284C22×C4—521no—
285C22×C4D4×D1311yescharacteristic
286D8—22no—
287D8—22no—
288D8—41no—
289D8—41no—
290C2×C8—132no—
291C2×C8—261no—
292C2×C8—261no—
293C2×C8—262no—
294C2×C8—262no—
295C2×C8—262no—
296C2×C8—262no—
297C2×C8C2×C4×D1311yescharacteristic
298C2×C8#612711yescharacteristic
299C2×C8D4×D1311yescharacteristic
300C2×C8D4×D1311yescharacteristic
301C2×C8#612911yescharacteristic
302C2×C8C2×C22⋊D1311yescharacteristic
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—262no—
306C4⋊C4—521no—
307C4⋊C4—521no—
308C4⋊C4—521no—
309C22⋊C4—524no—
310C22⋊C4—1042no—
311C16—22no—
312C16—262no—
313C13#1306111yescharacteristic, complemented, Sylow
314C23—42no—
315C23—81no—
316C23—81no—
317C23—81no—
318C23—81no—
319C23—81no—
320C23—81no—
321C23—132no—
322C23—261no—
323C23—261no—
324C23—261no—
325C23—261no—
326C23—261no—
327C23—261no—
328C23D8×D1311yescharacteristic
329D4—42no—
330D4—42no—
331D4—81no—
332D4—81no—
333D4—1048no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4—132no—
338C2×C4—261no—
339C2×C4—261no—
340C2×C4—262no—
341C2×C4—262no—
342C2×C4—262no—
343C2×C4—262no—
344C2×C4—522no—
345C2×C4—1041no—
346C2×C4—1041no—
347C2×C4—1041no—
348C2×C4—1041no—
349C2×C4—1041no—
350C2×C4C22⋊C4×D1311yescharacteristic
351C2×C4#8813811yescharacteristic
352C2×C4#8816611yescharacteristic
353C2×C4SD16×D1311yescharacteristic
354C2×C4#8817011yescharacteristic
355C2×C4#8819211yescharacteristic
356C8—262no—
357C8#8813511yescharacteristic
358C8#8813711yescharacteristic
359C8C4×C22⋊D1311yescharacteristic
360C8#8819111yescharacteristic
361C22—82no—
362C22—82no—
363C22—82no—
364C22—161no—
365C22—161no—
366C22—161no—
367C22—161no—
368C22—262no—
369C22—262no—
370C22—262no—
371C22—521no—
372C22—521no—
373C22—521no—
374C22—521no—
375C22D13×#10211yescharacteristic
376C22#1171843611yescharacteristic
377C22#1171857211yescharacteristic
378C22#1171857211yescharacteristic
379C22#1171857511yescharacteristic
380C22#1171857611yescharacteristic
381C22#1171881811yescharacteristic
382C4—161no—
383C4—262no—
384C4—1042no—
385C4—2081no—
386C4#1171843311yescharacteristic
387C4#1171843911yescharacteristic
388C4#1171861711yescharacteristic
389C4#1171883211yescharacteristic
390C2—162no—
391C2—522no—
392C2#1311526111yescharacteristic
393C2#1311654511yescharacteristic
394C2#1311655011yescharacteristic
395C2#1311693611yescharacteristic
396C2#1311693811yescharacteristic
397C2#1311694611yescharacteristic
398C2#1311694811yescharacteristic
subgroupG/H
centerC23D8×D13
commutatorC2×C8×C13C22×C4
FrattiniC22×C8C22×D13
FittingC2×C13×#357C2
socleC23×C13C2×D8
prime radicalC2×#11718818C2
cosocleC22×C8×C13C23
hypercenterC2×#357D13
hypocenterC13#13061
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#357

Complements

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

NH ≅ G/Ntype
1. C22×#88038C2semidirect
3. C2×#11718154C2semidirect
4. #13114862C2semidirect
5. #13112928C2semidirect
6. #13112927C2semidirect
7. C2×C13×#357C2semidirect
15. #11718818C4semidirect
52. C2×C13×C16D4semidirect
63. C2×#6090D4semidirect
118. C2×#357D13semidirect
246. C2×C16C22⋊D13semidirect
313. C13#13061semidirect

Maximal subgroups

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

subgroupindex
C22×#880382
C2×#117188182
C2×#117181542
#131148622
#131129282
#131129272
C2×C13×#3572
#1306113