Finite Group Databasebeta

← #15753803

Subgroups — #15753803

Order 3328.

712 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13114598C211yesmaximal, characteristic, complemented
2C2×#11718129C212yesmaximal
3#13113063C211yesmaximal, characteristic, complemented
4#13112714C212yesmaximal, complemented
5C4×C13×#121C211yesmaximal, characteristic
6C2×C13×#121C2211yescharacteristic
7C2×C4×D4×C13—21no—
8C2×C4×D4×C13C411yescharacteristic, complemented
9C22×C42×C13C2211yescharacteristic
10C13×#390C411yescharacteristic, complemented
11C13×#389C411yescharacteristic, complemented
12C13×#388—21no—
13C13×#386—21no—
14C13×#380C2211yescharacteristic
15C4×C13×C4⋊C4C411yescharacteristic, complemented
16C4×C13×C22⋊C4—21no—
17C2×#88071—21no—
18C2×#88071—21no—
19C2×#88071C2212yes—
20C2×C22⋊#1055C2212yes—
21C2×#88043—21no—
22#11718129C418yescomplemented
23#11718116—21no—
24C22×D4×C13—21no—
25C22×D4×C13C2×C411yescharacteristic
26C23×C4×C13—21no—
27C23×C4×C13D411yescharacteristic
28C23×C4×C13D411yescharacteristic
29C23×C4×C13C2311yescharacteristic
30C23×Dic13—22no—
31C13×#121—22no—
32C13×#121C2×C414yes—
33C4×D4×C13—42no—
34C4×D4×C13—44no—
35C2×C13×C4⋊C4—21no—
36C2×C13×C4⋊C4C2×C411yescharacteristic
37C2×C13×C4⋊C4C2×C411yescharacteristic
38C2×C13×C4⋊C4C2×C411yescharacteristic
39C2×C13×C22⋊C4—21no—
40C2×C13×C22⋊C4—21no—
41C2×C13×C22⋊C4—21no—
42C2×C13×C22⋊C4—21no—
43C2×C13×C22⋊C4—21no—
44C2×C42×C13—21no—
45C2×C42×C13—42no—
46C2×C42×C13C2×C411yescharacteristic
47C2×C42×C13C2×C411yescharacteristic
48C2×C42×C13D411yescharacteristic
49C2×C42×C13D411yescharacteristic
50C22×#1055—22no—
51C13×#95—21no—
52C13×#95—21no—
53C13×#95—21no—
54#88071—22no—
55#88071—42no—
56#88071—42no—
57#88071C2×C414yescomplemented
58C22⋊#1055—22no—
59C22⋊#1055C2×C414yescomplemented
60#88043—42no—
61#8216—131nomaximal, Sylow
62C24×C13—21no—
63C24×C13C2×D411yescharacteristic
64C2×D4×C13—24no—
65C2×D4×C13—21no—
66C2×D4×C13—41no—
67C2×D4×C13—41no—
68C2×D4×C13—42no—
69C2×D4×C13—41no—
70C2×D4×C13—41no—
71C2×D4×C13C4212yes—
72C22×C4×C13—21no—
73C22×C4×C13—21no—
74C22×C4×C13—22no—
75C22×C4×C13—21no—
76C22×C4×C13—22no—
77C22×C4×C13—21no—
78C22×C4×C13—21no—
79C22×C4×C13—41no—
80C22×C4×C13—41no—
81C22×C4×C13—41no—
82C22×C4×C13—41no—
83C22×C4×C13—41no—
84C22×C4×C13—42no—
85C22×C4×C13—42no—
86C22×C4×C13—42no—
87C22×C4×C13C22⋊C411yescharacteristic
88C22×C4×C13C22⋊C411yescharacteristic
89C22×C4×C13C22⋊C411yescharacteristic
90C22×C4×C13C22⋊C411yescharacteristic
91C22×C4×C13C22×C412yes—
92C22×C4×C13C22×C411yescharacteristic
93C22×C4×C13C2×D411yescharacteristic
94C22×C4×C13#4112yes—
95C22×Dic13—24no—
96C22×Dic13—42no—
97C22×Dic13—42no—
98C22×Dic13—42no—
99C22×Dic13—42no—
100C22×Dic13—42no—
101C22×Dic13—42no—
102C13×C4⋊C4—21no—
103C13×C4⋊C4—41no—
104C13×C4⋊C4—41no—
105C13×C4⋊C4—42no—
106C13×C4⋊C4C4212yes—
107C13×C22⋊C4—24no—
108C13×C22⋊C4—42no—
109C13×C22⋊C4—42no—
110C13×C22⋊C4—42no—
111C13×C22⋊C4—42no—
112C42×C13—22no—
113C42×C13—22no—
114C42×C13—41no—
115C42×C13—41no—
116C42×C13—42no—
117C2×#1055—24no—
118C2×#1055—42no—
119C2×#1055—42no—
120C4×#121D1311yescharacteristic
121#1749—131no—
122C2×#327—132no—
123#1434—131no—
124#1294—132no—
125C23×C13—21no—
126C23×C13—21no—
127C23×C13—21no—
128C23×C13—21no—
129C23×C13—22no—
130C23×C13—41no—
131C23×C13—41no—
132C23×C13—41no—
133C23×C13—41no—
134C23×C13—41no—
135C23×C13—41no—
136C23×C13C2×C22⋊C411yescharacteristic
137C23×C13C4×D412yes—
138C23×C13AGL(1,ℤ/8)11yescharacteristic
139C23×C13AGL(1,ℤ/8)12yes—
140C23×C13#13711yescharacteristic
141D4×C13—42no—
142D4×C13—42no—
143D4×C13—44no—
144D4×C13—44no—
145C2×C4×C13—21no—
146C2×C4×C13—21no—
147C2×C4×C13—21no—
148C2×C4×C13—21no—
149C2×C4×C13—21no—
150C2×C4×C13—21no—
151C2×C4×C13—22no—
152C2×C4×C13—21no—
153C2×C4×C13—21no—
154C2×C4×C13—21no—
155C2×C4×C13—21no—
156C2×C4×C13—21no—
157C2×C4×C13—21no—
158C2×C4×C13—21no—
159C2×C4×C13—21no—
160C2×C4×C13—21no—
161C2×C4×C13—42no—
162C2×C4×C13—42no—
163C2×C4×C13—44no—
164C2×C4×C13—42no—
165C2×C4×C13—42no—
166C2×C4×C13—41no—
167C2×C4×C13—41no—
168C2×C4×C13—41no—
169C2×C4×C13—41no—
170C2×C4×C13—41no—
171C2×C4×C13—41no—
172C2×C4×C13—41no—
173C2×C4×C13—41no—
174C2×C4×C13—84no—
175C2×C4×C13#9912yes—
176C2×C4×C13C2×C4211yescharacteristic
177C2×C4×C13#11711yescharacteristic
178C2×C4×C13C4×D412yes—
179C2×Dic13—44no—
180C2×Dic13—44no—
181C2×Dic13—44no—
182C2×Dic13—82no—
183C2×Dic13—82no—
184C2×Dic13—82no—
185C2×Dic13—82no—
186#1055—44no—
187C2×#121C2×D1311yescharacteristic
188C2×C4×D4—21no—
189C2×C4×D4Dic1311yescharacteristic, complemented
190C22×C42C2×D1311yescharacteristic
191C2×C22⋊C8—132no—
192C2×#97—261no—
193#390Dic1311yescharacteristic, complemented
194#389Dic1311yescharacteristic, complemented
195#388—21no—
196#386—21no—
197#380C2×D1311yescharacteristic
198C4×C4⋊C4Dic1311yescharacteristic, complemented
199C4×C22⋊C4—21no—
200C2×#95—132no—
201C2×#95—261no—
202C2×#95—261no—
203#336—261no—
204#327—138no—
205C22×C13—22no—
206C22×C13—22no—
207C22×C13—22no—
208C22×C13—21no—
209C22×C13—21no—
210C22×C13—21no—
211C22×C13—21no—
212C22×C13—22no—
213C22×C13—42no—
214C22×C13—42no—
215C22×C13—42no—
216C22×C13—81no—
217C22×C13—81no—
218C22×C13—81no—
219C22×C13—81no—
220C22×C13C4×C22⋊C411yescharacteristic
221C22×C13C2×#9911yescharacteristic
222C22×C13#41011yescharacteristic
223C22×C13#41711yescharacteristic
224C22×C13#41811yescharacteristic
225C22×C13#42111yescharacteristic
226C22×C13#42111yescharacteristic
227C22×C13#44012yes—
228C22×C13#44212yes—
229C4×C13—22no—
230C4×C13—21no—
231C4×C13—21no—
232C4×C13—22no—
233C4×C13—42no—
234C4×C13—41no—
235C4×C13—41no—
236C4×C13—41no—
237C4×C13—81no—
238C4×C13—81no—
239Dic13—84no—
240C22×D4—21no—
241C22×D4C2×Dic1311yescharacteristic
242C23×C4—21no—
243C23×C4—262no—
244C23×C4C22⋊D1311yescharacteristic
245C23×C4C22⋊D1311yescharacteristic
246C23×C4C22×D1311yescharacteristic
247C22×C8—262no—
248#121—22no—
249#121C4×D1314yes—
250C4×D4—42no—
251C4×D4—44no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4C2×Dic1311yescharacteristic
254C2×C4⋊C4C2×Dic1311yescharacteristic
255C2×C4⋊C4C2×Dic1311yescharacteristic
256C2×C22⋊C4—21no—
257C2×C22⋊C4—21no—
258C2×C22⋊C4—21no—
259C2×C22⋊C4—21no—
260C2×C22⋊C4—21no—
261C2×C42—21no—
262C2×C42—42no—
263C2×C42C2×Dic1311yescharacteristic
264C2×C42C2×Dic1311yescharacteristic
265C2×C42C22⋊D1311yescharacteristic
266C2×C42C22⋊D1311yescharacteristic
267C22⋊C8—134no—
268C22⋊C8—262no—
269#97—522no—
270#95—21no—
271#95—21no—
272#95—21no—
273#95—134no—
274#95—262no—
275#95—522no—
276#95—522no—
277C2×C13—22no—
278C2×C13—22no—
279C2×C13—82no—
280C2×C13#151011yescharacteristic
281C2×C13#151211yescharacteristic
282C2×C13#151311yescharacteristic
283C2×C13#151411yescharacteristic
284C2×C13C4×#9911yescharacteristic
285C2×C13#175911yescharacteristic
286C2×C13#176211yescharacteristic
287C24—21no—
288C24C2×C22⋊D1311yescharacteristic
289C2×D4—24no—
290C2×D4—21no—
291C2×D4—41no—
292C2×D4—41no—
293C2×D4—42no—
294C2×D4—41no—
295C2×D4—41no—
296C2×D4C4×Dic1312yes—
297C22×C4—22no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—22no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—42no—
310C22×C4—42no—
311C22×C4—42no—
312C22×C4—264no—
313C22×C4—522no—
314C22×C4—522no—
315C22×C4—522no—
316C22×C4—522no—
317C22×C4—522no—
318C22×C4—522no—
319C22×C4C22⋊Dic1311yescharacteristic
320C22×C4C22⋊Dic1311yescharacteristic
321C22×C4C22⋊Dic1311yescharacteristic
322C22×C4C22⋊Dic1311yescharacteristic
323C22×C4C2×C4×D1312yes—
324C22×C4#612712yes—
325C22×C4C22×Dic1311yescharacteristic
326C22×C4C2×C22⋊D1311yescharacteristic
327C2×C8—264no—
328C2×C8—522no—
329C2×C8—522no—
330C4⋊C4—21no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—42no—
334C4⋊C4C4×Dic1312yes—
335C22⋊C4—24no—
336C22⋊C4—42no—
337C22⋊C4—42no—
338C22⋊C4—42no—
339C22⋊C4—42no—
340C42—22no—
341C42—22no—
342C42—41no—
343C42—41no—
344C42—42no—
345C13#821611yescharacteristic, complemented, Sylow
346C23—21no—
347C23—21no—
348C23—21no—
349C23—21no—
350C23—22no—
351C23—41no—
352C23—41no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23—41no—
357C23C4×C22⋊D1312yes—
358C23#8818612yes—
359C23#8820311yescharacteristic
360C23#8820511yescharacteristic
361C23C2×C22⋊Dic1311yescharacteristic
362D4—42no—
363D4—42no—
364D4—44no—
365D4—44no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—22no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—44no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—84no—
396C2×C4—524no—
397C2×C4—524no—
398C2×C4—524no—
399C2×C4—1042no—
400C2×C4—1042no—
401C2×C4—1042no—
402C2×C4—1042no—
403C2×C4#8807412yes—
404C2×C4C2×C4×Dic1311yescharacteristic
405C2×C4#8818011yescharacteristic
406C2×C4C4×C22⋊D1312yes—
407C8—524no—
408C22—22no—
409C22—22no—
410C22—22no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—22no—
416C22—42no—
417C22—42no—
418C22—42no—
419C22—81no—
420C22—81no—
421C22—81no—
422C22—81no—
423C22#1171867512yes—
424C22#1171867912yes—
425C22C4×C22⋊Dic1311yescharacteristic
426C22#1171887611yescharacteristic
427C22C2×#8807411yescharacteristic
428C22#1171889311yescharacteristic
429C22#1171889711yescharacteristic
430C22#1171889711yescharacteristic
431C22#1171890111yescharacteristic
432C4—22no—
433C4—21no—
434C4—21no—
435C4—22no—
436C4—41no—
437C4—41no—
438C4—41no—
439C4—42no—
440C4—81no—
441C4—81no—
442C4—1044no—
443C2—22no—
444C2—22no—
445C2—82no—
446C2#1311336511yescharacteristic
447C2#1311337411yescharacteristic
448C2#1311337911yescharacteristic
449C2#1311338311yescharacteristic
450C2C4×#8807411yescharacteristic
451C2#1311464611yescharacteristic
452C2#1311466111yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic13
commutatorC2×C4×C13C2×C42
FrattiniC23×C4C22×D13
FittingC4×C13×#121C2
socleC23×C13C2×C22⋊C4
prime radicalC2×C13×#121C22
cosocleC23×C4×C13C23
hypercenterC4×#121D13
hypocenterC13#8216
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×#121

Complements

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

NH ≅ G/Ntype
1. #13114598C2semidirect
3. #13113063C2semidirect
4. #13112714C2semidirect
8. C2×C4×D4×C13C4semidirect
10. C13×#390C4semidirect
11. C13×#389C4semidirect
15. C4×C13×C4⋊C4C4semidirect
22. #11718129C4semidirect
57. #88071C2×C4semidirect
59. C22⋊#1055C2×C4semidirect
189. C2×C4×D4Dic13semidirect
193. #390Dic13semidirect
194. #389Dic13semidirect
198. C4×C4⋊C4Dic13semidirect
345. C13#8216semidirect

Maximal subgroups

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

subgroupindex
#131145982
C2×#117181292
#131130632
#131127142
C4×C13×#1212
#821613