Finite Group Databasebeta

← #15766274

Subgroups — #15766274

Order 3328.

708 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13115643C211yesmaximal, characteristic, complemented
2#13115594C211yesmaximal, characteristic, complemented
3#13114836C211yesmaximal, characteristic, complemented
4C2×#11718136C211yesmaximal, characteristic, complemented
5C2×D4⋊#1055C211yesmaximal, characteristic, complemented
6#13112677C211yesmaximal, characteristic, complemented
7C13×#2541C211yesmaximal, characteristic
8C2×C13×#127—21no—
9C2×C13×#127C2211yescharacteristic
10C2×C13×#121—21no—
11C2×C13×#121—21no—
12C2×C4×D4×C13C2211yescharacteristic
13C13×#392—22no—
14C13×#390—21no—
15C4×C13×C4⋊C4C2211yescharacteristic
16C2×#88072—21no—
17C2×#88072—22no—
18C2×#88047—21no—
19#11718596C2211yescharacteristic
20C2×C4⋊#1055C2211yescharacteristic
21C2×C4⋊#1055C2211yescharacteristic
22C2×C4×#1055C2211yescharacteristic
23#11718136—22no—
24D4⋊#1055—22no—
25#11718121—21no—
26#11718121—21no—
27C22×D4×C13—22no—
28C22×D4×C13—22no—
29C22×D4×C13—21no—
30C22×D4×C13—21no—
31C22×D4×C13D411yescharacteristic
32C22×D4×C13D412yes—
33C23×C4×C13—21no—
34C13×#127—21no—
35C13×#127—21no—
36C13×#127—21no—
37C13×#127—21no—
38C13×#127—42no—
39C13×#127—42no—
40C13×#121—42no—
41C13×#121—42no—
42C13×#121—42no—
43C13×#121—42no—
44C4×D4×C13—21no—
45C4×D4×C13—21no—
46C4×D4×C13—21no—
47C4×D4×C13—21no—
48C2×C13×C4⋊C4D411yescharacteristic
49C2×C13×C4⋊C4D411yescharacteristic
50C2×C13×C4⋊C4D411yescharacteristic
51C2×C13×C22⋊C4—22no—
52C2×C13×C22⋊C4—22no—
53C2×C13×C22⋊C4—21no—
54C2×C42×C13—21no—
55C2×C42×C13C2311yescharacteristic
56C2×C4⋊Dic13—21no—
57C2×C4⋊Dic13—21no—
58C2×C4⋊Dic13—21no—
59C22×#1055—21no—
60C22×#1055—21no—
61C22×#1055—21no—
62C13×#95—21no—
63#88072—44no—
64#88072—42no—
65#88047—42no—
66C4⋊#1055—21no—
67C4⋊#1055—21no—
68C4⋊#1055—21no—
69C4⋊#1055D412yescomplemented
70C4×#1055—21no—
71C4×#1055—21no—
72#10408—131nomaximal, Sylow
73C24×C13—21no—
74C24×C13—22no—
75C2×D4×C13—21no—
76C2×D4×C13—22no—
77C2×D4×C13—21no—
78C2×D4×C13—22no—
79C2×D4×C13—21no—
80C2×D4×C13—21no—
81C2×D4×C13—21no—
82C2×D4×C13—42no—
83C2×D4×C13—42no—
84C2×D4×C13—44no—
85C2×D4×C13—44no—
86C2×D4×C13—44no—
87C2×D4×C13—44no—
88C2×D4×C13—41no—
89C2×D4×C13—41no—
90C2×D4×C13—41no—
91C2×D4×C13—41no—
92C2×D4×C13—41no—
93C2×D4×C13—41no—
94C2×D4×C13—41no—
95C2×D4×C13—41no—
96C2×D4×C13—41no—
97C2×D4×C13—41no—
98C2×D4×C13—41no—
99C2×D4×C13—41no—
100C2×D4×C13—82no—
101C2×D4×C13—82no—
102C2×D4×C13D812yes—
103C22×C4×C13—21no—
104C22×C4×C13—21no—
105C22×C4×C13—21no—
106C22×C4×C13—41no—
107C22×C4×C13—41no—
108C22×C4×C13—41no—
109C22×C4×C13—41no—
110C22×C4×C13—41no—
111C22×C4×C13—41no—
112C22×C4×C13C2×D411yescharacteristic
113C22×C4×C13C2×D411yescharacteristic
114C22×C4×C13C2×D411yescharacteristic
115C22×Dic13—41no—
116C13×C4⋊C4—21no—
117C13×C4⋊C4—21no—
118C13×C4⋊C4—21no—
119C13×C4⋊C4—21no—
120C13×C4⋊C4D812yes—
121C13×C4⋊C4SD1612yes—
122C13×C22⋊C4—44no—
123C13×C22⋊C4—44no—
124C13×C22⋊C4—41no—
125C13×C22⋊C4—41no—
126C42×C13—41no—
127C42×C13—41no—
128C42×C13C2×D411yescharacteristic
129C42×C13#4111yescharacteristic
130C42×C13#4111yescharacteristic
131C42×C13#4111yescharacteristic
132C4⋊Dic13—42no—
133C4⋊Dic13—41no—
134C4⋊Dic13—41no—
135C4⋊Dic13—41no—
136C4⋊Dic13—41no—
137C2×#1055—22no—
138C2×#1055—22no—
139C2×#1055—41no—
140C2×#1055—41no—
141C2×#1055—41no—
142C2×#1055—41no—
143C2×#1055—41no—
144C2×#1055—41no—
145C2×#1055—41no—
146#2541D1311yescharacteristic
147#1957—131no—
148#1947—131no—
149#1802—131no—
150C2×#331—131no—
151C2×D4⋊C8—131no—
152#1279—131no—
153C23×C13—22no—
154C23×C13—41no—
155C23×C13—41no—
156C23×C13—41no—
157C23×C13—41no—
158C23×C13—41no—
159C23×C13—41no—
160C23×C13—42no—
161C23×C13—42no—
162C23×C13—42no—
163C23×C13—42no—
164C23×C13—42no—
165C23×C13—42no—
166C23×C13—42no—
167C23×C13#12011yescharacteristic
168D4×C13—22no—
169D4×C13—22no—
170D4×C13—44no—
171D4×C13—41no—
172D4×C13—41no—
173D4×C13—82no—
174D4×C13—88no—
175D4×C13—88no—
176D4×C13—81no—
177D4×C13—81no—
178D4×C13—81no—
179D4×C13—81no—
180D4×C13—81no—
181D4×C13—81no—
182D4×C13—81no—
183D4×C13—81no—
184C2×C4×C13—21no—
185C2×C4×C13—21no—
186C2×C4×C13—22no—
187C2×C4×C13—22no—
188C2×C4×C13—41no—
189C2×C4×C13—41no—
190C2×C4×C13—41no—
191C2×C4×C13—41no—
192C2×C4×C13—41no—
193C2×C4×C13—41no—
194C2×C4×C13—41no—
195C2×C4×C13—81no—
196C2×C4×C13—81no—
197C2×C4×C13—81no—
198C2×C4×C13—81no—
199C2×C4×C13#12111yescharacteristic
200C2×C4×C13#12111yescharacteristic
201C2×C4×C13#12111yescharacteristic
202C2×C4×C13#12311yescharacteristic
203C2×C4×C13#12311yescharacteristic
204C2×C4×C13#12411yescharacteristic
205C2×C4×C13C2×D811yescharacteristic
206C2×C4×C13C2×D811yescharacteristic
207C2×C4×C13C2×SD1611yescharacteristic
208C2×C4×C13#13511yescharacteristic
209C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
210C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
211C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
212C2×C4×C13#13711yescharacteristic
213C2×Dic13—81no—
214C2×Dic13—81no—
215C2×Dic13—81no—
216#1055—42no—
217#1055—42no—
218#1055—81no—
219C2×#127—21no—
220C2×#127C2×D1311yescharacteristic
221C2×#121—21no—
222C2×#121—21no—
223C2×C4×D4C2×D1311yescharacteristic
224C2×#107—261no—
225C2×C4⋊C8—131no—
226C2×C4⋊C8—131no—
227C2×#102—261no—
228C2×#102—262no—
229C2×C4×C8—131no—
230#392—22no—
231#390—21no—
232#384—131no—
233C4×C4⋊C4C2×D1311yescharacteristic
234#340—261no—
235#340—261no—
236#331—262no—
237D4⋊C8—262no—
238C22×C13—42no—
239C22×C13—42no—
240C22×C13—42no—
241C22×C13—81no—
242C22×C13—81no—
243C22×C13—81no—
244C22×C13—81no—
245C22×C13—82no—
246C22×C13—82no—
247C22×C13—82no—
248C22×C13—82no—
249C22×C13—82no—
250C22×C13—82no—
251C22×C13—82no—
252C22×C13#39411yescharacteristic
253C22×C13#44711yescharacteristic
254C22×C13#44711yescharacteristic
255C22×C13#45011yescharacteristic
256C22×C13#45211yescharacteristic
257C22×C13#45311yescharacteristic
258C22×C13#45511yescharacteristic
259C4×C13—21no—
260C4×C13—21no—
261C4×C13—42no—
262C4×C13—42no—
263C4×C13—81no—
264C4×C13#45911yescharacteristic
265C4×C13#46011yescharacteristic
266C4×C13#46611yescharacteristic
267C4×C13#46811yescharacteristic
268C4×C13#48011yescharacteristic
269C4×C13#48211yescharacteristic
270C4×C13#48611yescharacteristic
271C4×C13#49011yescharacteristic
272Dic13—161no—
273C22×D4—22no—
274C22×D4—22no—
275C22×D4—21no—
276C22×D4—21no—
277C22×D4C22⋊D1311yescharacteristic
278C22×D4C22⋊D1312yes—
279C23×C4—21no—
280C22×C8—261no—
281C22×C8—261no—
282C22×C8—261no—
283#127—21no—
284#127—21no—
285#127—21no—
286#127—21no—
287#127—42no—
288#127—42no—
289#121—42no—
290#121—42no—
291#121—42no—
292#121—42no—
293C4×D4—21no—
294C4×D4—21no—
295C4×D4—21no—
296C4×D4—21no—
297C2×C4⋊C4—261no—
298C2×C4⋊C4—261no—
299C2×C4⋊C4—261no—
300C2×C4⋊C4C22⋊D1311yescharacteristic
301C2×C4⋊C4C22⋊D1311yescharacteristic
302C2×C4⋊C4C22⋊D1311yescharacteristic
303C2×C22⋊C4—22no—
304C2×C22⋊C4—22no—
305C2×C22⋊C4—21no—
306C2×C42—21no—
307C2×C42C22×D1311yescharacteristic
308#107—522no—
309C4⋊C8—132no—
310C4⋊C8—261no—
311C4⋊C8—261no—
312C4⋊C8—261no—
313#102—524no—
314#102—522no—
315C4×C8—261no—
316C4×C8—261no—
317#95—21no—
318C2×C13—82no—
319C2×C13—162no—
320C2×C13#161911yescharacteristic
321C2×C13#163111yescharacteristic
322C2×C13#163911yescharacteristic
323C2×C13#164111yescharacteristic
324C2×C13#203311yescharacteristic
325C2×C13#203711yescharacteristic
326C2×C13#204111yescharacteristic
327C24—21no—
328C24—22no—
329C2×D4—21no—
330C2×D4—21no—
331C2×D4—22no—
332C2×D4—21no—
333C2×D4—22no—
334C2×D4—21no—
335C2×D4—21no—
336C2×D4—42no—
337C2×D4—42no—
338C2×D4—44no—
339C2×D4—44no—
340C2×D4—44no—
341C2×D4—44no—
342C2×D4—41no—
343C2×D4—41no—
344C2×D4—41no—
345C2×D4—41no—
346C2×D4—41no—
347C2×D4—41no—
348C2×D4—41no—
349C2×D4—41no—
350C2×D4—41no—
351C2×D4—41no—
352C2×D4—41no—
353C2×D4—41no—
354C2×D4—82no—
355C2×D4—82no—
356C2×D4#610412yes—
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—41no—
361C22×C4—41no—
362C22×C4—41no—
363C22×C4—41no—
364C22×C4—41no—
365C22×C4—41no—
366C22×C4—521no—
367C22×C4C2×C22⋊D1311yescharacteristic
368C22×C4C2×C22⋊D1311yescharacteristic
369C22×C4C2×C22⋊D1311yescharacteristic
370C2×C8—262no—
371C2×C8—262no—
372C2×C8—521no—
373C2×C8—521no—
374C2×C8—521no—
375C2×C8—521no—
376C2×C8—521no—
377C2×C8—521no—
378C2×C8—521no—
379C4⋊C4—21no—
380C4⋊C4—21no—
381C4⋊C4—21no—
382C4⋊C4—21no—
383C4⋊C4—522no—
384C4⋊C4—521no—
385C4⋊C4—521no—
386C4⋊C4—521no—
387C4⋊C4—521no—
388C4⋊C4#610412yes—
389C4⋊C4#610512yes—
390C22⋊C4—44no—
391C22⋊C4—44no—
392C22⋊C4—41no—
393C22⋊C4—41no—
394C42—41no—
395C42—41no—
396C42D4×D1311yescharacteristic
397C42#612911yescharacteristic
398C42#612911yescharacteristic
399C42#612911yescharacteristic
400C13#1040811yescharacteristic, complemented, Sylow
401C23—22no—
402C23—41no—
403C23—41no—
404C23—41no—
405C23—41no—
406C23—41no—
407C23—41no—
408C23—42no—
409C23—42no—
410C23—42no—
411C23—42no—
412C23—42no—
413C23—42no—
414C23—42no—
415C23#8820711yescharacteristic
416D4—22no—
417D4—22no—
418D4—44no—
419D4—41no—
420D4—41no—
421D4—82no—
422D4—88no—
423D4—88no—
424D4—81no—
425D4—81no—
426D4—81no—
427D4—81no—
428D4—81no—
429D4—81no—
430D4—81no—
431D4—81no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—81no—
444C2×C4—81no—
445C2×C4—81no—
446C2×C4—81no—
447C2×C4—1041no—
448C2×C4—1041no—
449C2×C4—1041no—
450C2×C4C2×#610411yescharacteristic
451C2×C4C2×#610411yescharacteristic
452C2×C4#8818611yescharacteristic
453C2×C4#8818611yescharacteristic
454C2×C4#8818611yescharacteristic
455C2×C4C2×#610511yescharacteristic
456C2×C4#8818911yescharacteristic
457C2×C4#8818911yescharacteristic
458C2×C4#8819011yescharacteristic
459C2×C4#8819211yescharacteristic
460C2×C4#8819311yescharacteristic
461C2×C4#8819311yescharacteristic
462C2×C4#8820411yescharacteristic
463C2×C4#8820511yescharacteristic
464C8—522no—
465C8—522no—
466C8—1041no—
467C22—42no—
468C22—42no—
469C22—42no—
470C22—81no—
471C22—81no—
472C22—81no—
473C22—81no—
474C22—82no—
475C22—82no—
476C22—82no—
477C22—82no—
478C22—82no—
479C22—82no—
480C22—82no—
481C22#1171887811yescharacteristic
482C22#1171887811yescharacteristic
483C22#1171887911yescharacteristic
484C22#1171888311yescharacteristic
485C22#1171890011yescharacteristic
486C22#1171890211yescharacteristic
487C22#1171890311yescharacteristic
488C4—21no—
489C4—21no—
490C4—42no—
491C4—42no—
492C4—81no—
493C4—2081no—
494C4#1171869411yescharacteristic
495C4#1171869611yescharacteristic
496C4#1171869911yescharacteristic
497C4#1171870311yescharacteristic
498C4#1171873111yescharacteristic
499C4#1171873211yescharacteristic
500C4#1171873311yescharacteristic
501C4#1171873611yescharacteristic
502C2—82no—
503C2—162no—
504C2#1311389011yescharacteristic
505C2#1311396311yescharacteristic
506C2#1311401511yescharacteristic
507C2#1311402911yescharacteristic
508C2#1311601511yescharacteristic
509C2#1311604311yescharacteristic
510C2#1311606711yescharacteristic
subgroupG/H
centerC23#88207
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
Fitting, prime radicalC13×#2541C2
socleC23×C13#120
hypercenter#2541D13
hypocenterC13#10408
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2541

Complements

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

NH ≅ G/Ntype
1. #13115643C2semidirect
2. #13115594C2semidirect
3. #13114836C2semidirect
4. C2×#11718136C2semidirect
5. C2×D4⋊#1055C2semidirect
6. #13112677C2semidirect
69. C4⋊#1055D4semidirect
400. C13#10408semidirect

Maximal subgroups

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

subgroupindex
#131156432
#131155942
#131148362
C2×#117181362
C2×D4⋊#10552
#131126772
C13×#25412
#1040813