Finite Group Databasebeta

← #15896752

Subgroups — #15896752

Order 3328.

1088 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718705C211yesmaximal, characteristic, complemented
2C2×#11718656C211yesmaximal, characteristic, complemented
3#13119144C211yesmaximal, characteristic
4#13116171C212yesmaximal, complemented
5#13116029C212yesmaximal, complemented
6#13115270C211yesmaximal, characteristic, complemented
7#13115134C211yesmaximal, characteristic
8#13115090C212yesmaximal, complemented
9#13115024C212yesmaximal, complemented
10#13114931C211yesmaximal, characteristic, complemented
11C2×C13×#552C211yesmaximal, characteristic
12C13×#552—24no—
13C13×#552—24no—
14C2×C13×#126—21no—
15C2×C13×#125—21no—
16C2×C13×#125C2211yescharacteristic
17C2×C13×#123—21no—
18C2×C13×C22⋊Q8C2211yescharacteristic
19C2×C13×C22⋊Q8C2211yescharacteristic
20C2×C4×Q8×C13C2211yescharacteristic
21C2×C4×D4×C13C2211yescharacteristic
22C2×C13×#117—21no—
23C2×C13×#117C2211yescharacteristic
24C22×C13×C4⋊C4C2211yescharacteristic
25C2×#88189—21no—
26C22×C4⋊Dic13C2211yescharacteristic
27C22×#6099C2211yescharacteristic
28C2×#88075C2212yes—
29C2×#88075C2212yes—
30#11718873C2211yescharacteristic
31#11718873C2212yes—
32C2×C22⋊#1055C2211yescharacteristic
33C2×C22⋊#1055C2212yes—
34#11718705—24no—
35#11718656—24no—
36#11718644—21no—
37C2×#88048C2212yes—
38C2×#88047C2212yes—
39C2×#88047C2212yes—
40#11718614—21no—
41#11718604—21no—
42#11718589C2212yes—
43#11718121C2212yes—
44#11718121C2212yes—
45#11718121C2212yes—
46#11718116C2212yes—
47C22×Q8×C13C2311yescharacteristic
48C22×D4×C13D411yescharacteristic
49C23×C4×C13—21no—
50C23×C4×C13C2311yescharacteristic
51C23×C4×C13C2311yescharacteristic
52C23×Dic13—21no—
53C13×#126—28no—
54C13×#125—28no—
55C13×#125—22no—
56C13×#125—22no—
57C13×#123—28no—
58C13×C22⋊Q8—22no—
59C13×C22⋊Q8—22no—
60C13×C22⋊Q8—22no—
61C13×C22⋊Q8D414yes—
62C4×Q8×C13—22no—
63C4×Q8×C13—22no—
64C4×D4×C13—22no—
65C4×D4×C13—22no—
66C13×#117—28no—
67C13×#117—22no—
68C13×#117D414yes—
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4—21no—
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4—21no—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4—21no—
75C2×C13×C4⋊C4—22no—
76C2×C13×C4⋊C4—22no—
77C2×C13×C4⋊C4D411yescharacteristic
78C2×C13×C4⋊C4C2311yescharacteristic
79C2×C13×C4⋊C4C2311yescharacteristic
80C2×C13×C4⋊C4C2311yescharacteristic
81C2×C13×C22⋊C4—21no—
82C2×C13×C22⋊C4—21no—
83C2×C13×C22⋊C4—21no—
84C2×C13×C22⋊C4D411yescharacteristic
85C2×C13×C22⋊C4D411yescharacteristic
86C2×C42×C13—21no—
87C2×C42×C13—21no—
88C2×C42×C13C2311yescharacteristic
89C2×C22⋊Dic13—21no—
90C2×C22⋊Dic13—22no—
91#88189—44no—
92C2×C4⋊Dic13—22no—
93C2×C4⋊Dic13—22no—
94C2×C4⋊Dic13—21no—
95C2×C4⋊Dic13C2312yes—
96C2×C4⋊Dic13C2312yes—
97C2×#6101—22no—
98C2×#6099—22no—
99C2×#6099—24no—
100C22×#1055C2312yes—
101C22×#1055C2312yes—
102#88075—24no—
103#88075—24no—
104#88071—22no—
105#88071—22no—
106#88071—21no—
107C22⋊#1055—22no—
108C22⋊#1055—24no—
109#88048—24no—
110#88047—24no—
111#88047—24no—
112#24110—131nomaximal, Sylow
113C24×C13C2×D411yescharacteristic
114C24×C13C2×D411yescharacteristic
115C2×Q8×C13—21no—
116C2×Q8×C13—22no—
117C2×Q8×C13—22no—
118C2×Q8×C13C2×D412yes—
119C2×D4×C13—22no—
120C2×D4×C13—22no—
121C2×D4×C13—41no—
122C22×C4×C13—22no—
123C22×C4×C13—22no—
124C22×C4×C13—24no—
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13—21no—
131C22×C4×C13—22no—
132C22×C4×C13—22no—
133C22×C4×C13—42no—
134C22×C4×C13—42no—
135C22×C4×C13C2×D411yescharacteristic
136C22×C4×C13C2×D411yescharacteristic
137C22×C4×C13C2×D411yescharacteristic
138C22×C4×C13C2×D411yescharacteristic
139C22×C4×C13C2×D412yes—
140C22×C4×C13C2×D412yes—
141C22×C4×C13C2411yescharacteristic
142C22×Dic13—22no—
143C22×Dic13—22no—
144C22×Dic13—42no—
145C22×Dic13—42no—
146C22×Dic13—42no—
147C13×C4⋊C4—24no—
148C13×C4⋊C4—24no—
149C13×C4⋊C4—24no—
150C13×C4⋊C4—24no—
151C13×C4⋊C4—24no—
152C13×C4⋊C4—24no—
153C13×C4⋊C4—22no—
154C13×C4⋊C4—21no—
155C13×C4⋊C4—21no—
156C13×C4⋊C4—21no—
157C13×C4⋊C4C2×D412yes—
158C13×C4⋊C4C2×D412yes—
159C13×C4⋊C4C2×D412yes—
160C13×C22⋊C4—24no—
161C13×C22⋊C4—24no—
162C13×C22⋊C4—24no—
163C13×C22⋊C4—22no—
164C13×C22⋊C4—22no—
165C42×C13—24no—
166C42×C13—24no—
167C42×C13—21no—
168C42×C13—21no—
169C22⋊Dic13—42no—
170C22⋊Dic13—44no—
171C4⋊Dic13—22no—
172C4⋊Dic13—22no—
173C4⋊Dic13—22no—
174C4⋊Dic13—22no—
175C4⋊Dic13—42no—
176#6101—44no—
177#6099—28no—
178C2×#1055—22no—
179C2×#1055—22no—
180C2×#1055—22no—
181C2×#1055—22no—
182C2×#1055—22no—
183C2×#1055#4114yes—
184C2×#552D1311yescharacteristic
185C2×#484—131no—
186C2×#428—131no—
187#2486—131no—
188#2059—132no—
189#2035—132no—
190#1894—131no—
191#1870—131no—
192#1863—132no—
193#1852—132no—
194#1825—131no—
195C23×C13—21no—
196C23×C13—22no—
197C23×C13—22no—
198C23×C13—21no—
199C23×C13—21no—
200C23×C13—21no—
201C23×C13—22no—
202C23×C13—22no—
203C23×C13#12012yes—
204C23×C13AGL(1,ℤ/8)12yes—
205C23×C13C22×D411yescharacteristic
206Q8×C13—24no—
207Q8×C13—41no—
208Q8×C13—41no—
209D4×C13—44no—
210C2×C4×C13—22no—
211C2×C4×C13—22no—
212C2×C4×C13—22no—
213C2×C4×C13—24no—
214C2×C4×C13—21no—
215C2×C4×C13—22no—
216C2×C4×C13—22no—
217C2×C4×C13—22no—
218C2×C4×C13—21no—
219C2×C4×C13—21no—
220C2×C4×C13—22no—
221C2×C4×C13—22no—
222C2×C4×C13—21no—
223C2×C4×C13—21no—
224C2×C4×C13—22no—
225C2×C4×C13—48no—
226C2×C4×C13—42no—
227C2×C4×C13—41no—
228C2×C4×C13—41no—
229C2×C4×C13—41no—
230C2×C4×C13—41no—
231C2×C4×C13—42no—
232C2×C4×C13—41no—
233C2×C4×C13—41no—
234C2×C4×C13—42no—
235C2×C4×C13#12012yes—
236C2×C4×C13C22×D411yescharacteristic
237C2×C4×C13C22×D411yescharacteristic
238C2×C4×C13C2×#4112yes—
239C2×C4×C132−1+412yes—
240C2×Dic13—42no—
241C2×Dic13—42no—
242C2×Dic13—42no—
243C2×Dic13—42no—
244C2×Dic13—42no—
245C2×Dic13—42no—
246C2×Dic13—84no—
247#1055—24no—
248#1055—42no—
249C22×M16—131no—
250#552—24no—
251#552—24no—
252C2×#126—21no—
253C2×#125—21no—
254C2×#125C2×D1311yescharacteristic
255C2×#123—21no—
256C2×#123—261no—
257C2×C22⋊Q8C2×D1311yescharacteristic
258C2×C22⋊Q8C2×D1311yescharacteristic
259C2×C4×Q8C2×D1311yescharacteristic
260C2×C4×D4C2×D1311yescharacteristic
261C2×#117—21no—
262C2×#117C2×D1311yescharacteristic
263C22×C4⋊C4—131no—
264C22×C4⋊C4C2×D1311yescharacteristic
265#484—264no—
266#428—264no—
267C2×#107—132no—
268C2×#107—132no—
269C2×#106—132no—
270C2×#103—132no—
271C2×#103—132no—
272C2×C22⋊C8—131no—
273C2×C22⋊C8—132no—
274#398—261no—
275#397—261no—
276#389—132no—
277#381—261no—
278#380—131no—
279#380—132no—
280#340—132no—
281#340—132no—
282#340—132no—
283#336—132no—
284C22×C13—24no—
285C22×C13—22no—
286C22×C13—22no—
287C22×C13—22no—
288C22×C13—22no—
289C22×C13—42no—
290C22×C13—42no—
291C22×C13—42no—
292C22×C13—41no—
293C22×C13—41no—
294C22×C13C2×#12011yescharacteristic
295C22×C13#54712yes—
296C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
297C22×C13#57511yescharacteristic
298C22×C13#57812yes—
299C4×C13—22no—
300C4×C13—41no—
301C4×C13—42no—
302C4×C13—41no—
303C4×C13—42no—
304C4×C13—42no—
305C4×C13—41no—
306C4×C13—42no—
307C4×C13#52511yescharacteristic
308C4×C13#53611yescharacteristic
309C4×C13#54712yes—
310Dic13—82no—
311Dic13—82no—
312C22×Q8C22×D1311yescharacteristic
313C22×D4C22⋊D1311yescharacteristic
314C23×C4—21no—
315C23×C4—261no—
316C23×C4C22×D1311yescharacteristic
317C23×C4C22×D1311yescharacteristic
318C2×M16—264no—
319C2×M16—262no—
320C22×C8—132no—
321C22×C8—132no—
322#126—28no—
323#125—28no—
324#125—22no—
325#125—22no—
326#123—28no—
327#123—524no—
328C22⋊Q8—22no—
329C22⋊Q8—22no—
330C22⋊Q8—22no—
331C22⋊Q8C22⋊D1314yes—
332C4×Q8—22no—
333C4×Q8—22no—
334C4×D4—22no—
335C4×D4—22no—
336#117—28no—
337#117—22no—
338#117C22⋊D1314yes—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—132no—
348C2×C4⋊C4—132no—
349C2×C4⋊C4—262no—
350C2×C4⋊C4—262no—
351C2×C4⋊C4—261no—
352C2×C4⋊C4—262no—
353C2×C4⋊C4C22⋊D1311yescharacteristic
354C2×C4⋊C4C22×D1311yescharacteristic
355C2×C4⋊C4C22×D1311yescharacteristic
356C2×C4⋊C4C22×D1311yescharacteristic
357C2×C22⋊C4—21no—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—261no—
361C2×C22⋊C4—262no—
362C2×C22⋊C4C22⋊D1311yescharacteristic
363C2×C22⋊C4C22⋊D1311yescharacteristic
364C2×C42—21no—
365C2×C42—21no—
366C2×C42C22×D1311yescharacteristic
367#107—264no—
368#107—264no—
369#106—264no—
370#103—264no—
371#103—264no—
372C22⋊C8—264no—
373C22⋊C8—262no—
374#95—262no—
375#95—261no—
376#95—262no—
377C2×C13—42no—
378C2×C13—42no—
379C2×C13#240611yescharacteristic
380C2×C13#300611yescharacteristic
381C2×C13#301111yescharacteristic
382C2×C13#334312yes—
383C2×C13#335212yes—
384C24C2×C22⋊D1311yescharacteristic
385C24C2×C22⋊D1311yescharacteristic
386C2×Q8—21no—
387C2×Q8—22no—
388C2×Q8—22no—
389C2×Q8C2×C22⋊D1312yes—
390C2×D4—22no—
391C2×D4—22no—
392C2×D4—41no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—24no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—42no—
405C22×C4—42no—
406C22×C4—262no—
407C22×C4—262no—
408C22×C4—522no—
409C22×C4—522no—
410C22×C4—522no—
411C22×C4C2×C22⋊D1311yescharacteristic
412C22×C4C2×C22⋊D1311yescharacteristic
413C22×C4C2×C22⋊D1311yescharacteristic
414C22×C4C2×C22⋊D1311yescharacteristic
415C22×C4C2×C22⋊D1312yes—
416C22×C4C2×C22⋊D1312yes—
417C22×C4C23×D1311yescharacteristic
418M16—268no—
419C2×C8—134no—
420C2×C8—262no—
421C2×C8—262no—
422C2×C8—262no—
423C2×C8—262no—
424C2×C8—262no—
425C4⋊C4—24no—
426C4⋊C4—24no—
427C4⋊C4—24no—
428C4⋊C4—24no—
429C4⋊C4—24no—
430C4⋊C4—24no—
431C4⋊C4—22no—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—262no—
436C4⋊C4—262no—
437C4⋊C4—262no—
438C4⋊C4—262no—
439C4⋊C4—524no—
440C4⋊C4—522no—
441C4⋊C4C2×C22⋊D1312yes—
442C4⋊C4C2×C22⋊D1312yes—
443C4⋊C4C2×C22⋊D1312yes—
444C22⋊C4—24no—
445C22⋊C4—24no—
446C22⋊C4—24no—
447C22⋊C4—22no—
448C22⋊C4—22no—
449C22⋊C4—522no—
450C22⋊C4—524no—
451C42—24no—
452C42—24no—
453C42—21no—
454C42—21no—
455C13#2411011yescharacteristic, complemented, Sylow
456C23—21no—
457C23—21no—
458C23—21no—
459C23—22no—
460C23—22no—
461C23—22no—
462C23—22no—
463C23—21no—
464C23#8820312yes—
465C23#8820712yes—
466C23C22×C22⋊D1311yescharacteristic
467Q8—24no—
468Q8—41no—
469Q8—41no—
470D4—44no—
471C2×C4—22no—
472C2×C4—24no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—21no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—22no—
486C2×C4—48no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—522no—
497C2×C4—522no—
498C2×C4—522no—
499C2×C4—522no—
500C2×C4—522no—
501C2×C4—522no—
502C2×C4—1044no—
503C2×C4#8820712yes—
504C2×C4#41×D1312yes—
505C2×C4#8825712yes—
506C2×C4C22×C22⋊D1311yescharacteristic
507C2×C4C22×C22⋊D1311yescharacteristic
508C8—264no—
509C8—522no—
510C22—22no—
511C22—24no—
512C22—22no—
513C22—22no—
514C22—22no—
515C22—41no—
516C22—42no—
517C22—41no—
518C22—42no—
519C22—42no—
520C22C2×#8820311yescharacteristic
521C22#1171952711yescharacteristic
522C22#1171952912yes—
523C22#1171954312yes—
524C22C2×#8820711yescharacteristic
525C4—22no—
526C4—41no—
527C4—42no—
528C4—41no—
529C4—42no—
530C4—41no—
531C4—42no—
532C4—42no—
533C4—1042no—
534C4—1042no—
535C4#1171952912yes—
536C4#1171953011yescharacteristic
537C4#1171953311yescharacteristic
538C2—42no—
539C2—42no—
540C2#1311816711yescharacteristic
541C2#1312408811yescharacteristic
542C2#1312413111yescharacteristic
543C2#1312727612yes—
544C2#1312740512yes—
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#552C2
socleC23×C13C22×D4
prime radicalC22×D4×C13D4
hypercenterC2×#552D13
hypocenterC13#24110
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
1. C2×#11718705C2semidirect
2. C2×#11718656C2semidirect
4. #13116171C2semidirect
5. #13116029C2semidirect
6. #13115270C2semidirect
8. #13115090C2semidirect
9. #13115024C2semidirect
10. #13114931C2semidirect
455. C13#24110semidirect

Maximal subgroups

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

subgroupindex
C2×#117187052
C2×#117186562
#131191442
#131161712
#131160292
#131152702
#131151342
#131150902
#131150242
#131149312
C2×C13×#5522
#2411013