Finite Group Databasebeta

← #15873186

Subgroups — #15873186

Order 3328.

1266 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D13×C22⋊C8C211yesmaximal, characteristic
2C2×#11718648C211yesmaximal, characteristic
3D13×#380C211yesmaximal, characteristic
4#13115026C211yesmaximal, characteristic, complemented
5#13115025C212yesmaximal, complemented
6#13115024C211yesmaximal, characteristic, complemented
7#13115023C211yesmaximal, characteristic, complemented
8#13115022C212yesmaximal, complemented
9#13114864C212yesmaximal, complemented
10#13114862C212yesmaximal, complemented
11C13×#1852C211yesmaximal, characteristic, complemented
12C23×C4×D13C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×#6103—21no—
15C22×C4⋊Dic13C2211yescharacteristic
16C22×C8×D13C2212yes—
17C2×C4⋊C4×D13C2211yescharacteristic
18C2×C4⋊C4×D13C2211yescharacteristic
19C2×C22⋊C4×D13—21no—
20C2×C13×#107C2212yescomplemented
21C2×C13×C22⋊C8C2211yescharacteristic
22C13×#380C2211yescharacteristic
23#11718873C2211yescharacteristic
24C2×#88071—21no—
25C2×C22⋊#1055C2211yescharacteristic
26C2×#88060C2212yes—
27C2×#88058C2212yescomplemented
28#11718648—21no—
29#11718648—21no—
30#11718648C2211yescharacteristic
31#11718648C2211yescharacteristic
32#11718648C2212yes—
33#11718648C2212yes—
34C2×#88047C2212yescomplemented
35C2×#88047C2212yescomplemented
36#11718603—21no—
37D13×C22⋊C8C418yescomplemented
38#11718328—21no—
39D13×#95—21no—
40C13×#340C2212yescomplemented
41#11718143C2212yescomplemented
42#11718121C2212yescomplemented
43#11718121C2212yescomplemented
44C24×D13D411yescharacteristic
45C23×C4×C13—21no—
46C23×C4×C13C2311yescharacteristic
47C23×Dic13—21no—
48C23×Dic13D411yescharacteristic
49C22×C4×D13—21no—
50C22×C4×D13—21no—
51C22×C4×D13—42no—
52C22×C4×D13—42no—
53C22×C4×D13C2×C414yes—
54C22×C4×D13D411yescharacteristic
55C22×C4×D13D411yescharacteristic
56C22×C4×D13Q814yes—
57C22×C4×D13C2311yescharacteristic
58C22×C4×D13C2311yescharacteristic
59C22×C8×C13C2312yes—
60C2×C13×C4⋊C4—21no—
61C2×C13×C4⋊C4—42no—
62C2×C13×C4⋊C4C2311yescharacteristic
63C2×C13×C4⋊C4C2311yescharacteristic
64C2×C13×C4⋊C4C2312yes—
65C2×C13×C22⋊C4—21no—
66C2×C22⋊Dic13—21no—
67C2×#6103—21no—
68C2×#6103—21no—
69C2×#6103—22no—
70C2×#6103—22no—
71C2×#6103—44no—
72C2×C4⋊Dic13—21no—
73C2×C4⋊Dic13—42no—
74C2×C4⋊Dic13C2311yescharacteristic
75C2×C4⋊Dic13C2311yescharacteristic
76C2×C4⋊Dic13C2312yes—
77C2×#6101—21no—
78C2×#6101—21no—
79C22×#1055C2312yes—
80C2×C8×D13—42no—
81C2×C8×D13—42no—
82C2×C8×D13C2×C418yescomplemented
83C4⋊C4×D13—42no—
84C4⋊C4×D13—42no—
85C22⋊C4×D13—44no—
86C13×#107—42no—
87C13×C22⋊C8C2×C414yescomplemented
88C13×#95—21no—
89#88071—21no—
90#88071—21no—
91#88071—21no—
92#88071—22no—
93#88071—22no—
94C22⋊#1055C2×C414yescomplemented
95#88060C2×C418yescomplemented
96#88058—42no—
97#88047—42no—
98#88047—42no—
99#21940—131nomaximal, Sylow
100C24×C13C2×D411yescharacteristic
101C23×D13—41no—
102C23×D13—41no—
103C23×D13—41no—
104C23×D13—41no—
105C23×D13C4⋊C414yes—
106C23×D13D814yes—
107C23×D13Q1614yes—
108C23×D13C2×D411yescharacteristic
109C23×D13C2×D411yescharacteristic
110C22×C4×C13—22no—
111C22×C4×C13—22no—
112C22×C4×C13—22no—
113C22×C4×C13—21no—
114C22×C4×C13—21no—
115C22×C4×C13—42no—
116C22×C4×C13—42no—
117C22×C4×C13—42no—
118C22×C4×C13C22×C412yes—
119C22×C4×C13C2×D411yescharacteristic
120C22×C4×C13C2×Q812yes—
121C22×C4×C13C2411yescharacteristic
122C22×Dic13—21no—
123C22×Dic13—21no—
124C22×Dic13—22no—
125C22×Dic13—41no—
126C22×Dic13—41no—
127C22×Dic13—42no—
128C22×Dic13—42no—
129C22×Dic13—42no—
130C22×Dic13C4⋊C414yes—
131C22×Dic13C2×D411yescharacteristic
132C22×Dic13C2×D411yescharacteristic
133C2×C4×D13—22no—
134C2×C4×D13—22no—
135C2×C4×D13—22no—
136C2×C4×D13—22no—
137C2×C4×D13—48no—
138C2×C4×D13—48no—
139C2×C4×D13—41no—
140C2×C4×D13—41no—
141C2×C4×D13—41no—
142C2×C4×D13—41no—
143C2×C4×D13—42no—
144C2×C4×D13—42no—
145C2×C4×D13—42no—
146C2×C4×D13—42no—
147C2×C4×D13—42no—
148C2×C4×D13—42no—
149C2×C4×D13C4⋊C414yes—
150C2×C4×D13C4⋊C414yes—
151C2×C4×D13C22×C412yes—
152C2×C4×D13C22×C412yes—
153C2×C4×D13C2×Q812yes—
154C2×C4×D13C2×Q812yes—
155C2×C8×C13—22no—
156C2×C8×C13—22no—
157C2×C8×C13C22×C414yes—
158C13×C4⋊C4—22no—
159C13×C4⋊C4—22no—
160C13×C4⋊C4—22no—
161C13×C4⋊C4—22no—
162C13×C4⋊C4—42no—
163C13×C22⋊C4—42no—
164C22⋊Dic13—42no—
165#6103—42no—
166#6103—42no—
167#6103—44no—
168#6103—44no—
169C4⋊Dic13—22no—
170C4⋊Dic13—22no—
171C4⋊Dic13—22no—
172C4⋊Dic13—22no—
173C4⋊Dic13—42no—
174#6101—42no—
175#6101—42no—
176C2×#1055—22no—
177C2×#1055—22no—
178C2×#1055C22×C414yes—
179C8×D13—48no—
180C22×C22⋊C8—131no—
181C2×#380—131no—
182C2×#380—131no—
183#1852—132no—
184#1852—131no—
185#1852—131no—
186#1852—132no—
187#1852—131no—
188#1852D1311yescharacteristic, complemented
189#1808—132no—
190#1808—132no—
191C23×C13—21no—
192C23×C13—21no—
193C23×C13—21no—
194C23×C13—21no—
195C23×C13C2×C4⋊C412yes—
196C23×C13C2×D812yes—
197C23×C13C2×Q1612yes—
198C23×C13C22×D411yescharacteristic
199C22×D13—21no—
200C22×D13—21no—
201C22×D13—21no—
202C22×D13—21no—
203C22×D13—21no—
204C22×D13—21no—
205C22×D13—21no—
206C22×D13—21no—
207C22×D13—44no—
208C22×D13—44no—
209C22×D13—44no—
210C22×D13—44no—
211C22×D13—44no—
212C22×D13—44no—
213C22×D13#107116yescomplemented
214C22×D13C2×C4⋊C412yes—
215C22×D13C2×C4⋊C412yes—
216C22×D13C2×D812yes—
217C22×D13C2×D812yes—
218C22×D13C2×Q1612yes—
219C22×D13C2×Q1612yes—
220C2×C4×C13—21no—
221C2×C4×C13—21no—
222C2×C4×C13—24no—
223C2×C4×C13—24no—
224C2×C4×C13—41no—
225C2×C4×C13—41no—
226C2×C4×C13—42no—
227C2×C4×C13—42no—
228C2×C4×C13—41no—
229C2×C4×C13—41no—
230C2×C4×C13—41no—
231C2×C4×C13—41no—
232C2×C4×C13—42no—
233C2×C4×C13—84no—
234C2×C4×C13C2×C4⋊C412yes—
235C2×C4×C13C23×C411yescharacteristic
236C2×C4×C13C22×Q811yescharacteristic
237C2×C4×C13H(5,𝔽2)12yes—
238C2×C4×C13H(5,𝔽2)12yes—
239C2×Dic13—21no—
240C2×Dic13—21no—
241C2×Dic13—21no—
242C2×Dic13—21no—
243C2×Dic13—44no—
244C2×Dic13—41no—
245C2×Dic13—41no—
246C2×Dic13—42no—
247C2×Dic13—42no—
248C2×Dic13—41no—
249C2×Dic13—41no—
250C2×Dic13—41no—
251C2×Dic13—41no—
252C2×Dic13—42no—
253C2×Dic13—84no—
254C2×Dic13C2×C4⋊C412yes—
255C2×Dic13C2×C4⋊C412yes—
256C4×D13—24no—
257C4×D13—24no—
258C4×D13—24no—
259C4×D13—24no—
260C4×D13—44no—
261C4×D13—44no—
262C4×D13—84no—
263C4×D13—84no—
264C8×C13—24no—
265#1055—24no—
266C24×C4—131no—
267C23×C8—132no—
268C22×C4⋊C4—131no—
269C22×C4⋊C4—131no—
270C22×C4⋊C4—131no—
271C22×C4⋊C4C2×D1311yescharacteristic
272C22×C22⋊C4—261no—
273C22×C22⋊C4—261no—
274C2×#107—132no—
275C2×#107—132no—
276C2×#107—132no—
277C2×#107C2×D1312yescomplemented
278C2×C22⋊C8—131no—
279C2×C22⋊C8—132no—
280C2×C22⋊C8—138no—
281C2×C22⋊C8C2×D1311yescharacteristic
282#380—131no—
283#380—131no—
284#380—131no—
285#380—132no—
286#380—132no—
287#380—261no—
288#380—261no—
289#380—261no—
290#380—261no—
291#380C2×D1311yescharacteristic
292C2×#95—261no—
293C2×#95—261no—
294#340—132no—
295#340—132no—
296#340—132no—
297#340C2×D1312yescomplemented
298C22×C13—22no—
299C22×C13—22no—
300C22×C13—22no—
301C22×C13—22no—
302C22×C13—22no—
303C22×C13—22no—
304C22×C13C2×#10714yes—
305C22×C13C22×C4⋊C411yescharacteristic
306C22×C13#53411yescharacteristic
307C22×C13#53411yescharacteristic
308C22×C13C22×D811yescharacteristic
309C22×C13C22×Q1611yescharacteristic
310C22×C13#57511yescharacteristic
311C22×C13#57511yescharacteristic
312C2×D13—22no—
313C2×D13—22no—
314C2×D13—22no—
315C2×D13—22no—
316C2×D13—22no—
317C2×D13—22no—
318C2×D13—22no—
319C2×D13—22no—
320C2×D13—22no—
321C2×D13—22no—
322C2×D13—22no—
323C2×D13—22no—
324C2×D13—416no—
325C2×D13C2×#10714yes—
326C2×D13C2×#10714yes—
327C4×C13—22no—
328C4×C13—81no—
329C4×C13—81no—
330C4×C13—82no—
331C4×C13#51812yes—
332C4×C13#54312yes—
333Dic13—22no—
334Dic13—22no—
335Dic13—81no—
336Dic13—81no—
337Dic13—82no—
338C25—131no—
339C23×C4—21no—
340C23×C4—131no—
341C23×C4—131no—
342C23×C4—131no—
343C23×C4—134no—
344C23×C4—131no—
345C23×C4—131no—
346C23×C4—134no—
347C23×C4—261no—
348C23×C4—261no—
349C23×C4—261no—
350C23×C4—522no—
351C23×C4—522no—
352C23×C4C22×D1311yescharacteristic
353C22×C8—132no—
354C22×C8—138no—
355C22×C8—522no—
356C22×C8—522no—
357C22×C8C22×D1312yes—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—42no—
360C2×C4⋊C4—131no—
361C2×C4⋊C4—132no—
362C2×C4⋊C4—131no—
363C2×C4⋊C4—261no—
364C2×C4⋊C4—261no—
365C2×C4⋊C4—261no—
366C2×C4⋊C4—522no—
367C2×C4⋊C4—522no—
368C2×C4⋊C4—522no—
369C2×C4⋊C4C22×D1311yescharacteristic
370C2×C4⋊C4C22×D1311yescharacteristic
371C2×C4⋊C4C22×D1312yes—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—261no—
374C2×C22⋊C4—261no—
375C2×C22⋊C4—262no—
376C2×C22⋊C4—262no—
377C2×C22⋊C4—261no—
378C2×C22⋊C4—524no—
379C2×C22⋊C4—524no—
380#107—42no—
381#107—522no—
382#107—522no—
383#107—522no—
384C22⋊C8—134no—
385C22⋊C8—138no—
386C22⋊C8C4×D1314yescomplemented
387#95—21no—
388#95—261no—
389#95—261no—
390#95—262no—
391#95—262no—
392#95—261no—
393C2×C13—24no—
394C2×C13#231511yescharacteristic
395C2×C13C22×#10711yescharacteristic
396C2×C13#291111yescharacteristic
397C2×C13#318611yescharacteristic
398C2×C13#318611yescharacteristic
399C2×C13#318911yescharacteristic
400C2×C13#318911yescharacteristic
401D13—24no—
402D13—24no—
403C24—131no—
404C24—131no—
405C24—134no—
406C24—134no—
407C24—134no—
408C24—521no—
409C24—521no—
410C24—521no—
411C24—521no—
412C24D4×D1311yescharacteristic
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—22no—
418C22×C4—42no—
419C22×C4—42no—
420C22×C4—42no—
421C22×C4—131no—
422C22×C4—131no—
423C22×C4—134no—
424C22×C4—132no—
425C22×C4—132no—
426C22×C4—132no—
427C22×C4—132no—
428C22×C4—134no—
429C22×C4—134no—
430C22×C4—262no—
431C22×C4—262no—
432C22×C4—262no—
433C22×C4—262no—
434C22×C4—261no—
435C22×C4—262no—
436C22×C4—261no—
437C22×C4—528no—
438C22×C4—528no—
439C22×C4—521no—
440C22×C4—521no—
441C22×C4—521no—
442C22×C4—521no—
443C22×C4—522no—
444C22×C4—522no—
445C22×C4—522no—
446C22×C4—522no—
447C22×C4—522no—
448C22×C4—522no—
449C22×C4—521no—
450C22×C4—521no—
451C22×C4—522no—
452C22×C4—522no—
453C22×C4—522no—
454C22×C4C2×C4×D1312yes—
455C22×C4D4×D1311yescharacteristic
456C22×C4Q8×D1312yes—
457C22×C4C23×D1311yescharacteristic
458C2×C8—22no—
459C2×C8—22no—
460C2×C8—134no—
461C2×C8—262no—
462C2×C8—262no—
463C2×C8—528no—
464C2×C8C2×C4×D1314yes—
465C4⋊C4—22no—
466C4⋊C4—22no—
467C4⋊C4—22no—
468C4⋊C4—22no—
469C4⋊C4—42no—
470C4⋊C4—262no—
471C4⋊C4—262no—
472C4⋊C4—262no—
473C4⋊C4—262no—
474C4⋊C4—522no—
475C4⋊C4—522no—
476C4⋊C4—522no—
477C22⋊C4—42no—
478C22⋊C4—522no—
479C22⋊C4—522no—
480C22⋊C4—524no—
481C22⋊C4—524no—
482C22⋊C4—522no—
483C13#2194011yescharacteristic, complemented, Sylow
484C23—21no—
485C23—21no—
486C23—21no—
487C23—21no—
488C23—132no—
489C23—132no—
490C23—132no—
491C23—132no—
492C23—132no—
493C23—132no—
494C23—1316no—
495C23—261no—
496C23—261no—
497C23—261no—
498C23—261no—
499C23—261no—
500C23—261no—
501C23—261no—
502C23—261no—
503C23—524no—
504C23—524no—
505C23—524no—
506C23—524no—
507C23—524no—
508C23—524no—
509C23C4⋊C4×D1312yes—
510C23D8×D1312yes—
511C23Q16×D1312yes—
512C23C2×D4×D1311yescharacteristic
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—24no—
516C2×C4—24no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—42no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—84no—
527C2×C4—132no—
528C2×C4—132no—
529C2×C4—261no—
530C2×C4—261no—
531C2×C4—261no—
532C2×C4—261no—
533C2×C4—264no—
534C2×C4—264no—
535C2×C4—264no—
536C2×C4—264no—
537C2×C4—524no—
538C2×C4—524no—
539C2×C4—524no—
540C2×C4—521no—
541C2×C4—522no—
542C2×C4—521no—
543C2×C4—521no—
544C2×C4—521no—
545C2×C4—522no—
546C2×C4—521no—
547C2×C4—522no—
548C2×C4—521no—
549C2×C4—1044no—
550C2×C4—1044no—
551C2×C4—1044no—
552C2×C4C4⋊C4×D1312yes—
553C2×C4C22×C4×D1311yescharacteristic
554C2×C4#8825112yes—
555C2×C4C2×Q8×D1311yescharacteristic
556C2×C4#8825612yes—
557C8—24no—
558C8—264no—
559C22—22no—
560C22—22no—
561C22—22no—
562C22—22no—
563C22—22no—
564C22—22no—
565C22—134no—
566C22—134no—
567C22—262no—
568C22—262no—
569C22—262no—
570C22—262no—
571C22—262no—
572C22—262no—
573C22—262no—
574C22—262no—
575C22—262no—
576C22—262no—
577C22—262no—
578C22—262no—
579C22—5216no—
580C22D13×#10714yes—
581C22C2×C4⋊C4×D1311yescharacteristic
582C22#1171929411yescharacteristic
583C22#1171935811yescharacteristic
584C22C2×D8×D1311yescharacteristic
585C22C2×Q16×D1311yescharacteristic
586C22#1171947811yescharacteristic
587C22#1171948211yescharacteristic
588C4—22no—
589C4—82no—
590C4—81no—
591C4—81no—
592C4—262no—
593C4—262no—
594C4—1041no—
595C4—1041no—
596C4—1042no—
597C4#1171925012yes—
598C4#1171933912yes—
599C2—24no—
600C2—264no—
601C2—264no—
602C2#1311744711yescharacteristic
603C2C2×D13×#10711yescharacteristic
604C2#1312342311yescharacteristic
605C2#1312558511yescharacteristic
606C2#1312558611yescharacteristic
607C2#1312560911yescharacteristic
608C2#1312561011yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1852C2
socleC23×C13C22×D4
prime radicalC24×D13D4
cosocleC22×C4×C13C24
hypercenter#1852D13
hypocenterC13#21940
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1852

Complements

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

NH ≅ G/Ntype
4. #13115026C2semidirect
5. #13115025C2semidirect
6. #13115024C2semidirect
7. #13115023C2semidirect
8. #13115022C2semidirect
9. #13114864C2semidirect
10. #13114862C2semidirect
11. C13×#1852C2semidirect
20. C2×C13×#107C22semidirect
27. C2×#88058C22semidirect
34. C2×#88047C22semidirect
35. C2×#88047C22semidirect
37. D13×C22⋊C8C4semidirect
40. C13×#340C22semidirect
41. #11718143C22semidirect
42. #11718121C22semidirect
43. #11718121C22semidirect
82. C2×C8×D13C2×C4semidirect
87. C13×C22⋊C8C2×C4semidirect
94. C22⋊#1055C2×C4semidirect
95. #88060C2×C4semidirect
188. #1852D13semidirect
213. C22×D13#107semidirect
277. C2×#107C2×D13semidirect
297. #340C2×D13semidirect
386. C22⋊C8C4×D13semidirect
483. C13#21940semidirect

Maximal subgroups

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

subgroupindex
C2×D13×C22⋊C82
C2×#117186482
D13×#3802
#131150262
#131150252
#131150242
#131150232
#131150222
#131148642
#131148622
C13×#18522
#2194013