Finite Group Databasebeta

← #15907757

Subgroups — #15907757

Order 3328.

926 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×C4⋊Dic13C211yesmaximal, characteristic, complemented
2#13116272C212yesmaximal, complemented
3#13116022C212yesmaximal, complemented
4#13115631C211yesmaximal, characteristic, complemented
5#13115597C211yesmaximal, characteristic, complemented
6#13115154C212yesmaximal, complemented
7#13114963C211yesmaximal, characteristic, complemented
8#13114924C212yesmaximal, complemented
9#13114836C211yesmaximal, characteristic, complemented
10C4×#88072C211yesmaximal, characteristic, complemented
11C13×#2537C211yesmaximal, characteristic
12C2×C13×#121—21no—
13C2×C13×#121C2212yes—
14C2×C4×D4×C13C2211yescharacteristic
15C2×C4×D4×C13C2211yescharacteristic
16C2×D4×Dic13—21no—
17C22×C4⋊Dic13C2212yes—
18C13×#394—22no—
19C13×#384C2211yescharacteristic
20C13×#380—21no—
21C13×#380C2212yes—
22C2×#88072C2211yescharacteristic
23C2×#88072C2211yescharacteristic
24C2×#88072C2212yes—
25#11718873C2212yes—
26C2×C22⋊#1055C2212yes—
27C2×C22⋊#1055C2212yes—
28#11718646—21no—
29C2×#88048C2212yes—
30#11718611—22no—
31#11718596C2211yescharacteristic
32C4×C4⋊Dic13C2211yescharacteristic
33C2×C4⋊#1055C2211yescharacteristic
34C2×C4×#1055C2211yescharacteristic
35#11718121C2212yes—
36#11718121C2212yes—
37#11718121C2211yescharacteristic
38#11718121C2211yescharacteristic
39#11718121C2212yes—
40#11718121C2212yes—
41C22×D4×C13—22no—
42C22×D4×C13D411yescharacteristic
43C22×D4×C13C2311yescharacteristic
44C23×C4×C13—21no—
45C23×C4×C13C2312yes—
46C23×Dic13—22no—
47C13×#121—24no—
48C13×#121—42no—
49C13×#121—44no—
50C4×D4×C13—22no—
51C4×D4×C13—22no—
52C4×D4×C13—22no—
53C4×D4×C13—22no—
54C2×C13×C4⋊C4—21no—
55C2×C13×C4⋊C4—21no—
56C2×C13×C4⋊C4D411yescharacteristic
57C2×C13×C4⋊C4C2311yescharacteristic
58C2×C13×C4⋊C4C2312yes—
59C2×C13×C22⋊C4—22no—
60C2×C13×C22⋊C4—22no—
61C2×C13×C22⋊C4—21no—
62C2×C13×C22⋊C4D412yes—
63C2×C42×C13C2311yescharacteristic
64C2×C22⋊Dic13—22no—
65D4×Dic13—44no—
66C2×C4⋊Dic13—24no—
67C2×C4⋊Dic13—22no—
68C2×C4⋊Dic13—21no—
69C2×C4⋊Dic13—21no—
70C2×C4⋊Dic13—42no—
71C2×C4⋊Dic13C2312yes—
72C2×C4⋊Dic13C2311yescharacteristic
73C2×C4⋊Dic13C2311yescharacteristic
74C2×C4×Dic13—21no—
75C22×#1055C2311yescharacteristic
76C22×#1055C2311yescharacteristic
77C22×#1055C2312yes—
78C13×#95—22no—
79#88072—22no—
80#88072—22no—
81#88072—42no—
82#88071—21no—
83#88071—22no—
84C22⋊#1055—42no—
85C22⋊#1055—42no—
86#88048—42no—
87C4⋊#1055—22no—
88C4×#1055—22no—
89#24967—131nomaximal, Sylow
90C24×C13—21no—
91C24×C13C2×D412yes—
92C2×D4×C13—22no—
93C2×D4×C13—22no—
94C2×D4×C13—21no—
95C2×D4×C13—21no—
96C2×D4×C13—21no—
97C2×D4×C13—21no—
98C2×D4×C13—21no—
99C2×D4×C13—44no—
100C2×D4×C13—44no—
101C2×D4×C13—82no—
102C2×D4×C13SD1614yes—
103C2×D4×C13#4112yes—
104C22×C4×C13—22no—
105C22×C4×C13—22no—
106C22×C4×C13—22no—
107C22×C4×C13—22no—
108C22×C4×C13—22no—
109C22×C4×C13—22no—
110C22×C4×C13—21no—
111C22×C4×C13—22no—
112C22×C4×C13—42no—
113C22×C4×C13—42no—
114C22×C4×C13—42no—
115C22×C4×C13C2×D412yes—
116C22×C4×C13C2×D411yescharacteristic
117C22×C4×C13C2×D411yescharacteristic
118C22×C4×C13C2411yescharacteristic
119C22×Dic13—21no—
120C22×Dic13—21no—
121C22×Dic13—22no—
122C22×Dic13—44no—
123C22×Dic13—44no—
124C22×Dic13—82no—
125C13×C4⋊C4—22no—
126C13×C4⋊C4—21no—
127C13×C4⋊C4—21no—
128C13×C4⋊C4—22no—
129C13×C4⋊C4—22no—
130C13×C4⋊C4—42no—
131C13×C4⋊C4—81no—
132C13×C22⋊C4—24no—
133C13×C22⋊C4—44no—
134C13×C22⋊C4—44no—
135C13×C22⋊C4—42no—
136C42×C13#4112yes—
137C42×C13#4112yes—
138C22⋊Dic13—44no—
139C4⋊Dic13—21no—
140C4⋊Dic13—21no—
141C4⋊Dic13—22no—
142C4⋊Dic13—22no—
143C4⋊Dic13—21no—
144C4⋊Dic13—44no—
145C4⋊Dic13—42no—
146C4⋊Dic13—81no—
147C4⋊Dic13#4112yes—
148C4×Dic13—42no—
149C2×#1055—21no—
150C2×#1055—21no—
151C2×#1055—21no—
152C2×#1055—21no—
153C2×#1055—22no—
154C2×#1055—21no—
155C2×#1055—21no—
156C2×#1055—22no—
157C2×#1055—22no—
158#2537D1311yescharacteristic
159D4×C4⋊C4—131no—
160#2077—132no—
161#2034—132no—
162#1954—131no—
163#1948—131no—
164#1874—132no—
165#1834—131no—
166#1824—132no—
167#1802—131no—
168C4×#102—131no—
169C23×C13—22no—
170C23×C13—22no—
171C23×C13—22no—
172C23×C13—22no—
173C23×C13—22no—
174C23×C13—22no—
175C23×C13—22no—
176C23×C13—41no—
177C23×C13—41no—
178C23×C13—41no—
179C23×C13—41no—
180C23×C13—41no—
181C23×C13—41no—
182C23×C13C2×SD1614yes—
183C23×C13C22×D411yescharacteristic
184D4×C13—22no—
185D4×C13—22no—
186D4×C13—28no—
187D4×C13—41no—
188D4×C13—41no—
189D4×C13—88no—
190C2×C4×C13—21no—
191C2×C4×C13—21no—
192C2×C4×C13—22no—
193C2×C4×C13—22no—
194C2×C4×C13—22no—
195C2×C4×C13—42no—
196C2×C4×C13—42no—
197C2×C4×C13—42no—
198C2×C4×C13—42no—
199C2×C4×C13—41no—
200C2×C4×C13—42no—
201C2×C4×C13—41no—
202C2×C4×C13—42no—
203C2×C4×C13—41no—
204C2×C4×C13—42no—
205C2×C4×C13—84no—
206C2×C4×C13#12312yes—
207C2×C4×C13#12312yes—
208C2×C4×C13C2×SD1612yes—
209C2×C4×C13AGL(1,ℤ/8)12yes—
210C2×C4×C13C2×#4111yescharacteristic
211C2×C4×C13C2×#4111yescharacteristic
212C2×C4×C13C2×#4111yescharacteristic
213C2×C4×C13C2×#4111yescharacteristic
214C2×C4×C13H(5,𝔽2)11yescharacteristic
215C2×C4×C13H(5,𝔽2)11yescharacteristic
216C2×Dic13—22no—
217C2×Dic13—41no—
218C2×Dic13—41no—
219C2×Dic13—42no—
220C2×Dic13—41no—
221C2×Dic13—41no—
222C2×Dic13—42no—
223C2×Dic13—42no—
224C2×Dic13—41no—
225C2×Dic13—88no—
226#1055—42no—
227#1055—41no—
228#1055—41no—
229C2×#121—21no—
230C2×#121C2×D1312yes—
231C2×C4×D4—261no—
232C2×C4×D4C2×D1311yescharacteristic
233C2×C4×D4C2×D1311yescharacteristic
234C22×C4⋊C4—132no—
235C2×#106—132no—
236C2×C4⋊C8—131no—
237C2×#102—131no—
238C2×#102—131no—
239C2×#102—132no—
240C2×C22⋊C8—132no—
241C2×C22⋊C8—132no—
242C2×C4×C8—131no—
243#394—22no—
244#389—261no—
245#385—262no—
246#384—131no—
247#384C2×D1311yescharacteristic
248#380—21no—
249#380—132no—
250#380C2×D1312yes—
251C4×C4⋊C4—131no—
252#340—132no—
253#340—131no—
254#340—132no—
255#340—131no—
256#340—132no—
257#340—132no—
258C22×C13—24no—
259C22×C13—24no—
260C22×C13—24no—
261C22×C13—42no—
262C22×C13—42no—
263C22×C13—42no—
264C22×C13—42no—
265C22×C13—42no—
266C22×C13—42no—
267C22×C13—42no—
268C22×C13—81no—
269C22×C13—81no—
270C22×C13—81no—
271C22×C13—81no—
272C22×C13C2×#12311yescharacteristic
273C22×C13#54611yescharacteristic
274C22×C13#54611yescharacteristic
275C22×C13C22×SD1611yescharacteristic
276C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
277C22×C13#57611yescharacteristic
278C22×C13#57811yescharacteristic
279C4×C13—22no—
280C4×C13—42no—
281C4×C13—81no—
282C4×C13—82no—
283C4×C13#48114yes—
284C4×C13#52911yescharacteristic
285C4×C13#54011yescharacteristic
286C4×C13#55311yescharacteristic
287C4×C13#55511yescharacteristic
288Dic13—42no—
289Dic13—81no—
290Dic13—82no—
291C22×D4—22no—
292C22×D4C22⋊D1311yescharacteristic
293C22×D4C22×D1311yescharacteristic
294C23×C4—21no—
295C23×C4—262no—
296C23×C4C22×D1312yes—
297C22×C8—131no—
298C22×C8—131no—
299C22×C8—132no—
300#121—24no—
301#121—42no—
302#121—44no—
303C4×D4—22no—
304C4×D4—22no—
305C4×D4—22no—
306C4×D4—22no—
307C4×D4—524no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—131no—
311C2×C4⋊C4—132no—
312C2×C4⋊C4—131no—
313C2×C4⋊C4—264no—
314C2×C4⋊C4—262no—
315C2×C4⋊C4—261no—
316C2×C4⋊C4—261no—
317C2×C4⋊C4—522no—
318C2×C4⋊C4C22⋊D1311yescharacteristic
319C2×C4⋊C4C22×D1311yescharacteristic
320C2×C4⋊C4C22×D1312yes—
321C2×C22⋊C4—22no—
322C2×C22⋊C4—21no—
323C2×C22⋊C4—22no—
324C2×C22⋊C4—262no—
325C2×C22⋊C4C22⋊D1312yes—
326C2×C42—261no—
327C2×C42C22×D1311yescharacteristic
328#106—522no—
329C4⋊C8—262no—
330#102—262no—
331#102—262no—
332#102—522no—
333C22⋊C8—522no—
334C22⋊C8—522no—
335C4×C8—262no—
336#95—22no—
337#95—261no—
338#95—262no—
339C2×C13—44no—
340C2×C13—82no—
341C2×C13#242011yescharacteristic
342C2×C13C2×#48111yescharacteristic
343C2×C13#309811yescharacteristic
344C2×C13#329511yescharacteristic
345C2×C13#329811yescharacteristic
346C2×C13#332511yescharacteristic
347C2×C13#333011yescharacteristic
348C24—21no—
349C24C2×C22⋊D1312yes—
350C2×D4—22no—
351C2×D4—22no—
352C2×D4—21no—
353C2×D4—21no—
354C2×D4—21no—
355C2×D4—21no—
356C2×D4—21no—
357C2×D4—44no—
358C2×D4—44no—
359C2×D4—82no—
360C2×D4#610514yes—
361C2×D4#612912yes—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—21no—
369C22×C4—22no—
370C22×C4—42no—
371C22×C4—42no—
372C22×C4—42no—
373C22×C4—261no—
374C22×C4—261no—
375C22×C4—262no—
376C22×C4—524no—
377C22×C4—524no—
378C22×C4—1042no—
379C22×C4C2×C22⋊D1312yes—
380C22×C4C2×C22⋊D1311yescharacteristic
381C22×C4C2×C22⋊D1311yescharacteristic
382C22×C4C23×D1311yescharacteristic
383C2×C8—261no—
384C2×C8—261no—
385C2×C8—261no—
386C2×C8—262no—
387C2×C8—261no—
388C2×C8—262no—
389C2×C8—261no—
390C2×C8—261no—
391C2×C8—262no—
392C4⋊C4—22no—
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—22no—
396C4⋊C4—22no—
397C4⋊C4—42no—
398C4⋊C4—81no—
399C4⋊C4—132no—
400C4⋊C4—261no—
401C4⋊C4—261no—
402C4⋊C4—261no—
403C4⋊C4—262no—
404C4⋊C4—262no—
405C4⋊C4—524no—
406C4⋊C4—522no—
407C4⋊C4—1041no—
408C22⋊C4—24no—
409C22⋊C4—44no—
410C22⋊C4—44no—
411C22⋊C4—42no—
412C22⋊C4—524no—
413C42—522no—
414C42#612912yes—
415C42#612912yes—
416C13#2496711yescharacteristic, complemented, Sylow
417C23—22no—
418C23—22no—
419C23—22no—
420C23—22no—
421C23—22no—
422C23—22no—
423C23—22no—
424C23—41no—
425C23—41no—
426C23—41no—
427C23—41no—
428C23—41no—
429C23—41no—
430C23C2×#610514yes—
431C23C22×C22⋊D1311yescharacteristic
432D4—28no—
433D4—22no—
434D4—22no—
435D4—41no—
436D4—41no—
437D4—88no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—41no—
448C2×C4—42no—
449C2×C4—41no—
450C2×C4—42no—
451C2×C4—41no—
452C2×C4—42no—
453C2×C4—84no—
454C2×C4—262no—
455C2×C4—521no—
456C2×C4—521no—
457C2×C4—521no—
458C2×C4—521no—
459C2×C4—522no—
460C2×C4—522no—
461C2×C4—522no—
462C2×C4—521no—
463C2×C4—1048no—
464C2×C4C2×#610512yes—
465C2×C4#8818912yes—
466C2×C4#8818912yes—
467C2×C4#8820312yes—
468C2×C4C2×#612911yescharacteristic
469C2×C4C2×#612911yescharacteristic
470C2×C4C2×#612911yescharacteristic
471C2×C4#8825111yescharacteristic
472C2×C4#41×D1311yescharacteristic
473C2×C4#8825611yescharacteristic
474C8—521no—
475C8—521no—
476C8—522no—
477C22—24no—
478C22—24no—
479C22—24no—
480C22—42no—
481C22—42no—
482C22—42no—
483C22—42no—
484C22—42no—
485C22—42no—
486C22—42no—
487C22—81no—
488C22—81no—
489C22—81no—
490C22—81no—
491C22C22×#610511yescharacteristic
492C22C2×#8818911yescharacteristic
493C22#1171951111yescharacteristic
494C22C2×#8820311yescharacteristic
495C22#1171953411yescharacteristic
496C22#1171954011yescharacteristic
497C22#1171954311yescharacteristic
498C4—22no—
499C4—42no—
500C4—82no—
501C4—81no—
502C4—522no—
503C4—1042no—
504C4—1041no—
505C4#1171869514yes—
506C4#1171930511yescharacteristic
507C4#1171932111yescharacteristic
508C4#1171932311yescharacteristic
509C4#1171932411yescharacteristic
510C2—44no—
511C2—82no—
512C2#1311832411yescharacteristic
513C2C2×#1171869511yescharacteristic
514C2#1312481011yescharacteristic
515C2#1312666011yescharacteristic
516C2#1312669511yescharacteristic
517C2#1312707211yescharacteristic
518C2#1312714111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
Fitting, prime radicalC13×#2537C2
socleC23×C13C22×D4
hypercenter#2537D13
hypocenterC13#24967
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2537

Complements

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

NH ≅ G/Ntype
1. D4×C4⋊Dic13C2semidirect
2. #13116272C2semidirect
3. #13116022C2semidirect
4. #13115631C2semidirect
5. #13115597C2semidirect
6. #13115154C2semidirect
7. #13114963C2semidirect
8. #13114924C2semidirect
9. #13114836C2semidirect
10. C4×#88072C2semidirect
416. C13#24967semidirect

Maximal subgroups

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

subgroupindex
D4×C4⋊Dic132
#131162722
#131160222
#131156312
#131155972
#131151542
#131149632
#131149242
#131148362
C4×#880722
C13×#25372
#2496713