Finite Group Databasebeta

← #15874127

Subgroups — #15874127

Order 3328.

1296 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#121×Dic13C211yesmaximal, characteristic, complemented
2C2×#11718882C211yesmaximal, characteristic, complemented
3#13115713C212yesmaximal, complemented
4#13115535C212yesmaximal, complemented
5#13115465C212yesmaximal, complemented
6#13115186C212yesmaximal, complemented
7#13115154C211yesmaximal, characteristic, complemented
8#13115031C211yesmaximal, characteristic, complemented
9#13114767C211yesmaximal, characteristic, complemented
10#13114600C211yesmaximal, characteristic, complemented
11C2×C13×#447C211yesmaximal, characteristic
12C23×D4×C13C2211yescharacteristic
13C22×C13×D8C2212yes—
14C2×C13×#121C2211yescharacteristic
15C22×C22⋊Dic13—21no—
16C22×C22⋊Dic13—21no—
17C2×D4×Dic13—21no—
18C2×D4×Dic13C2211yescharacteristic, complemented
19C22×C4⋊Dic13C2211yescharacteristic
20C22×C4×Dic13C2211yescharacteristic
21C13×#447C418yescomplemented
22C2×C13×#102C2212yes—
23C2×C13×C22⋊C8C2211yescharacteristic
24#11718882—21no—
25#11718882—21no—
26#11718882C2212yes—
27#11718882C2212yes—
28#11718882C2211yescharacteristic, complemented
29#11718881—21no—
30C2×#88072C2212yes—
31C2×#88072C2212yes—
32C2×#88072C2212yescomplemented
33#11718873C2211yescharacteristic
34C2×C22⋊#1055C2211yescharacteristic
35C2×#88057C2212yescomplemented
36C2×#88055C2212yescomplemented
37#11718646C2211yescharacteristic, complemented
38C4⋊C4×Dic13C2211yescharacteristic, complemented
39#11718612—21no—
40C22⋊C4×Dic13—21no—
41#11718143C2212yescomplemented
42#11718142C2212yescomplemented
43#11718121C2212yescomplemented
44C25×C13—21no—
45C22×D4×C13—21no—
46C22×D4×C13—21no—
47C22×D4×C13—22no—
48C22×D4×C13—42no—
49C22×D4×C13—42no—
50C22×D4×C13C2×C414yescomplemented
51C22×D4×C13C2312yes—
52C22×D4×C13C2311yescharacteristic
53C23×C4×C13C2311yescharacteristic
54C23×Dic13—21no—
55C23×Dic13—21no—
56C23×Dic13D411yescharacteristic
57C23×Dic13D411yescharacteristic
58C2×C13×D8—42no—
59C2×C13×D8—42no—
60C2×C13×D8C2×C418yescomplemented
61C22×C8×C13C2312yes—
62C13×#121—22no—
63C13×#121C2×C414yes—
64C2×C13×C4⋊C4C2311yescharacteristic
65C2×C13×C22⋊C4—21no—
66C2×C22⋊Dic13—21no—
67C2×C22⋊Dic13—21no—
68C2×C22⋊Dic13—21no—
69C2×C22⋊Dic13—22no—
70C2×C22⋊Dic13—22no—
71C2×C22⋊Dic13—22no—
72C2×C22⋊Dic13—22no—
73C2×C22⋊Dic13—21no—
74C2×C22⋊Dic13—44no—
75C2×C22⋊Dic13—44no—
76D4×Dic13—42no—
77D4×Dic13—44no—
78C2×C4⋊Dic13—21no—
79C2×C4⋊Dic13—21no—
80C2×C4⋊Dic13—42no—
81C2×C4⋊Dic13C2312yes—
82C2×C4⋊Dic13C2311yescharacteristic
83C2×C4⋊Dic13C2311yescharacteristic
84C2×C4×Dic13—21no—
85C2×C4×Dic13—42no—
86C2×C4×Dic13D411yescharacteristic
87C2×C4×Dic13D411yescharacteristic
88C2×C4×Dic13C2311yescharacteristic
89C2×C4×Dic13C2311yescharacteristic
90C22×#1055C2312yes—
91C13×#102C2×C418yescomplemented
92C13×C22⋊C8C2×C414yescomplemented
93#88072—42no—
94#88072—42no—
95#88072—42no—
96#88071—21no—
97#88071—21no—
98#88071—21no—
99C22⋊#1055—22no—
100#88057—42no—
101#88055—42no—
102#22046—131nomaximal, Sylow
103C24×C13—24no—
104C24×C13—22no—
105C24×C13—21no—
106C24×C13—42no—
107C24×C13—42no—
108C24×C13—42no—
109C24×C13—42no—
110C24×C13—42no—
111C24×C13—42no—
112C24×C13C2×D411yescharacteristic
113C2×D4×C13—24no—
114C2×D4×C13—24no—
115C2×D4×C13—21no—
116C2×D4×C13—22no—
117C2×D4×C13—22no—
118C2×D4×C13—22no—
119C2×D4×C13—22no—
120C2×D4×C13—22no—
121C2×D4×C13—22no—
122C2×D4×C13—22no—
123C2×D4×C13—48no—
124C2×D4×C13—42no—
125C2×D4×C13—42no—
126C2×D4×C13—48no—
127C2×D4×C13—42no—
128C2×D4×C13—42no—
129C2×D4×C13C22×C414yes—
130C2×D4×C13C22×C412yes—
131C22×C4×C13—22no—
132C22×C4×C13—22no—
133C22×C4×C13—21no—
134C22×C4×C13C22×C412yes—
135C22×C4×C13C2×D411yescharacteristic
136C22×C4×C13#4112yes—
137C22×C4×C13C2411yescharacteristic
138C22×Dic13—22no—
139C22×Dic13—22no—
140C22×Dic13—22no—
141C22×Dic13—21no—
142C22×Dic13—21no—
143C22×Dic13—22no—
144C22×Dic13—41no—
145C22×Dic13—41no—
146C22×Dic13—41no—
147C22×Dic13—42no—
148C22×Dic13—42no—
149C22×Dic13—42no—
150C22×Dic13—42no—
151C22×Dic13—42no—
152C22×Dic13—42no—
153C22×Dic13C2×D411yescharacteristic
154C22×Dic13C2×D411yescharacteristic
155C22×Dic13C2×D411yescharacteristic
156C22×Dic13C2×D411yescharacteristic
157C13×D8—48no—
158C2×C8×C13—22no—
159C2×C8×C13—22no—
160C2×C8×C13C22×C414yes—
161C13×C4⋊C4—21no—
162C13×C4⋊C4C22×C412yes—
163C13×C22⋊C4—24no—
164C22⋊Dic13—42no—
165C22⋊Dic13—42no—
166C22⋊Dic13—42no—
167C22⋊Dic13—44no—
168C22⋊Dic13—44no—
169C22⋊Dic13—44no—
170C22⋊Dic13—42no—
171C22⋊Dic13—44no—
172C4⋊Dic13—22no—
173C4⋊Dic13—22no—
174C4⋊Dic13—22no—
175C4⋊Dic13—22no—
176C4⋊Dic13—42no—
177C4⋊Dic13—42no—
178C4×Dic13—22no—
179C4×Dic13—22no—
180C4×Dic13—41no—
181C4×Dic13—41no—
182C4×Dic13—42no—
183C2×#1055—22no—
184C2×#1055—22no—
185C2×#1055—22no—
186C2×#447D1311yescharacteristic
187C4×#121—131no—
188C2×#390—131no—
189#1972—132no—
190#1936—132no—
191#1926—132no—
192#1879—132no—
193#1874—131no—
194#1853—131no—
195#1786—131no—
196#1749—131no—
197C23×C13—21no—
198C23×C13—21no—
199C23×C13—21no—
200C23×C13—21no—
201C23×C13—22no—
202C23×C13—24no—
203C23×C13—48no—
204C23×C13—48no—
205C23×C13—41no—
206C23×C13—42no—
207C23×C13—42no—
208C23×C13—41no—
209C23×C13—42no—
210C23×C13—42no—
211C23×C13—41no—
212C23×C13—41no—
213C23×C13—41no—
214C23×C13—42no—
215C23×C13—41no—
216C23×C13—42no—
217C23×C13—48no—
218C23×C13—84no—
219C23×C13—84no—
220C23×C13—84no—
221C23×C13—84no—
222C23×C13C4×D412yes—
223C23×C13AGL(1,ℤ/8)12yes—
224C23×C13AGL(1,ℤ/8)12yes—
225C23×C13C22×D411yescharacteristic
226D4×C13—24no—
227D4×C13—24no—
228D4×C13—24no—
229D4×C13—48no—
230D4×C13—48no—
231D4×C13—42no—
232D4×C13—42no—
233D4×C13—42no—
234C2×C4×C13—21no—
235C2×C4×C13—21no—
236C2×C4×C13—24no—
237C2×C4×C13—24no—
238C2×C4×C13—22no—
239C2×C4×C13—41no—
240C2×C4×C13—41no—
241C2×C4×C13C4×D412yes—
242C2×C4×C13C23×C411yescharacteristic
243C2×C4×C13C2×#4111yescharacteristic
244C2×C4×C13H(5,𝔽2)12yes—
245C2×C4×C13H(5,𝔽2)12yes—
246C2×Dic13—21no—
247C2×Dic13—21no—
248C2×Dic13—21no—
249C2×Dic13—21no—
250C2×Dic13—21no—
251C2×Dic13—21no—
252C2×Dic13—21no—
253C2×Dic13—21no—
254C2×Dic13—21no—
255C2×Dic13—21no—
256C2×Dic13—21no—
257C2×Dic13—44no—
258C2×Dic13—44no—
259C2×Dic13—41no—
260C2×Dic13—42no—
261C2×Dic13—41no—
262C2×Dic13—41no—
263C2×Dic13—41no—
264C2×Dic13—42no—
265C2×Dic13—42no—
266C2×Dic13—41no—
267C2×Dic13—41no—
268C2×Dic13—84no—
269C2×Dic13—84no—
270C2×Dic13AGL(1,ℤ/8)12yes—
271C8×C13—24no—
272#1055—42no—
273C23×D4C2×D1311yescharacteristic
274C22×D8C2×D1312yes—
275C2×#121C2×D1311yescharacteristic
276C2×C4×D4—131no—
277C2×C4×D4—261no—
278C22×C4⋊C4—131no—
279C22×C22⋊C4—261no—
280C22×C22⋊C4—261no—
281C22×C42—131no—
282#447Dic1318yescomplemented
283C2×#106—132no—
284C2×#102—132no—
285C2×#102—132no—
286C2×#102—132no—
287C2×#102C2×D1312yes—
288C2×C22⋊C8—131no—
289C2×C22⋊C8C2×D1311yescharacteristic
290C2×#97—132no—
291#390—132no—
292#390—132no—
293#390—131no—
294#390—261no—
295#390—261no—
296#389—131no—
297#388—261no—
298#386—261no—
299#380—131no—
300C4×C4⋊C4—131no—
301C4×C22⋊C4—261no—
302#340—132no—
303#340—132no—
304#336—132no—
305C22×C13—22no—
306C22×C13—22no—
307C22×C13—22no—
308C22×C13—22no—
309C22×C13—22no—
310C22×C13—22no—
311C22×C13—44no—
312C22×C13—42no—
313C22×C13—42no—
314C22×C13—44no—
315C22×C13—42no—
316C22×C13—44no—
317C22×C13—816no—
318C22×C13—81no—
319C22×C13—82no—
320C22×C13—81no—
321C22×C13—82no—
322C22×C13—81no—
323C22×C13—82no—
324C22×C13—81no—
325C22×C13—82no—
326C22×C13#44214yes—
327C22×C13C2×C4×D411yescharacteristic
328C22×C13#53411yescharacteristic
329C22×C13#53511yescharacteristic
330C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
331C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
332C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
333C22×C13#57511yescharacteristic
334C4×C13—22no—
335C4×C13—42no—
336C4×C13#51812yes—
337C4×C13#53812yes—
338Dic13—22no—
339Dic13—41no—
340Dic13—41no—
341Dic13—41no—
342Dic13—81no—
343Dic13—81no—
344Dic13—82no—
345C25—21no—
346C22×D4—21no—
347C22×D4—21no—
348C22×D4—22no—
349C22×D4—42no—
350C22×D4—42no—
351C22×D4C2×Dic1314yescomplemented
352C22×D4C22×D1311yescharacteristic
353C22×D4C22×D1312yes—
354C23×C4—131no—
355C23×C4—131no—
356C23×C4—261no—
357C23×C4—261no—
358C23×C4C22×D1311yescharacteristic
359C2×D8—42no—
360C2×D8—42no—
361C2×D8C2×Dic1318yescomplemented
362C22×C8—132no—
363C22×C8C22×D1312yes—
364#121—22no—
365#121C2×Dic1314yes—
366C4×D4—522no—
367C4×D4—524no—
368C2×C4⋊C4—132no—
369C2×C4⋊C4—131no—
370C2×C4⋊C4—131no—
371C2×C4⋊C4—261no—
372C2×C4⋊C4—261no—
373C2×C4⋊C4—522no—
374C2×C4⋊C4C22×D1311yescharacteristic
375C2×C22⋊C4—21no—
376C2×C22⋊C4—262no—
377C2×C22⋊C4—262no—
378C2×C22⋊C4—262no—
379C2×C22⋊C4—262no—
380C2×C22⋊C4—261no—
381C2×C22⋊C4—261no—
382C2×C22⋊C4—261no—
383C2×C22⋊C4—261no—
384C2×C22⋊C4—524no—
385C2×C22⋊C4—524no—
386C2×C42—131no—
387C2×C42—131no—
388C2×C42—131no—
389C2×C42—131no—
390C2×C42—261no—
391C2×C42—522no—
392#106—522no—
393#102—522no—
394#102—522no—
395#102—522no—
396#102C2×Dic1318yescomplemented
397C22⋊C8—262no—
398C22⋊C8C2×Dic1314yescomplemented
399#97—522no—
400#95—261no—
401#95—261no—
402#95—261no—
403C2×C13—24no—
404C2×C13—82no—
405C2×C13—84no—
406C2×C13#232111yescharacteristic
407C2×C13C2×#44211yescharacteristic
408C2×C13C4×AGL(1,ℤ/8)11yescharacteristic
409C2×C13#319211yescharacteristic
410C2×C13#319411yescharacteristic
411C2×C13#321311yescharacteristic
412C2×C13#321711yescharacteristic
413C24—24no—
414C24—21no—
415C24—22no—
416C24—42no—
417C24—42no—
418C24—42no—
419C24—42no—
420C24—42no—
421C24—42no—
422C24D4×D1311yescharacteristic
423C2×D4—24no—
424C2×D4—24no—
425C2×D4—21no—
426C2×D4—22no—
427C2×D4—22no—
428C2×D4—22no—
429C2×D4—22no—
430C2×D4—22no—
431C2×D4—22no—
432C2×D4—22no—
433C2×D4—48no—
434C2×D4—42no—
435C2×D4—42no—
436C2×D4—48no—
437C2×D4—42no—
438C2×D4—42no—
439C2×D4C22×Dic1314yes—
440C2×D4C22×Dic1312yes—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—131no—
445C22×C4—131no—
446C22×C4—131no—
447C22×C4—131no—
448C22×C4—262no—
449C22×C4—262no—
450C22×C4—262no—
451C22×C4—261no—
452C22×C4—261no—
453C22×C4—262no—
454C22×C4—522no—
455C22×C4—521no—
456C22×C4—521no—
457C22×C4—521no—
458C22×C4—522no—
459C22×C4—522no—
460C22×C4—522no—
461C22×C4—522no—
462C22×C4—522no—
463C22×C4D4×D1311yescharacteristic
464C22×C4#612912yes—
465C22×C4C22×Dic1312yes—
466C22×C4C23×D1311yescharacteristic
467D8—48no—
468C2×C8—22no—
469C2×C8—22no—
470C2×C8—262no—
471C2×C8—262no—
472C2×C8—262no—
473C2×C8C22×Dic1314yes—
474C4⋊C4—21no—
475C4⋊C4—262no—
476C4⋊C4—262no—
477C4⋊C4—262no—
478C4⋊C4—262no—
479C4⋊C4—522no—
480C4⋊C4—522no—
481C4⋊C4C22×Dic1312yes—
482C22⋊C4—24no—
483C22⋊C4—524no—
484C22⋊C4—524no—
485C22⋊C4—524no—
486C22⋊C4—524no—
487C22⋊C4—522no—
488C22⋊C4—522no—
489C22⋊C4—522no—
490C22⋊C4—522no—
491C42—262no—
492C42—262no—
493C42—521no—
494C42—521no—
495C42—522no—
496C13#2204611yescharacteristic, complemented, Sylow
497C23—21no—
498C23—21no—
499C23—21no—
500C23—21no—
501C23—22no—
502C23—24no—
503C23—48no—
504C23—48no—
505C23—42no—
506C23—41no—
507C23—41no—
508C23—42no—
509C23—42no—
510C23—41no—
511C23—41no—
512C23—42no—
513C23—41no—
514C23—42no—
515C23—42no—
516C23—41no—
517C23—48no—
518C23—84no—
519C23—84no—
520C23—84no—
521C23—84no—
522C23#8816512yes—
523C23#8816512yes—
524C23D4×Dic1312yes—
525C23C2×D4×D1311yescharacteristic
526D4—24no—
527D4—24no—
528D4—24no—
529D4—48no—
530D4—48no—
531D4—42no—
532D4—42no—
533D4—42no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—24no—
537C2×C4—24no—
538C2×C4—22no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—132no—
542C2×C4—261no—
543C2×C4—261no—
544C2×C4—261no—
545C2×C4—261no—
546C2×C4—261no—
547C2×C4—261no—
548C2×C4—261no—
549C2×C4—261no—
550C2×C4—261no—
551C2×C4—261no—
552C2×C4—261no—
553C2×C4—524no—
554C2×C4—524no—
555C2×C4—521no—
556C2×C4—522no—
557C2×C4—521no—
558C2×C4—522no—
559C2×C4—521no—
560C2×C4—521no—
561C2×C4—521no—
562C2×C4—522no—
563C2×C4—521no—
564C2×C4—1044no—
565C2×C4—1044no—
566C2×C4D4×Dic1312yes—
567C2×C4C2×#612911yescharacteristic
568C2×C4#8825112yes—
569C2×C4#8825112yes—
570C2×C4C23×Dic1311yescharacteristic
571C8—24no—
572C8—522no—
573C22—22no—
574C22—22no—
575C22—22no—
576C22—22no—
577C22—22no—
578C22—22no—
579C22—42no—
580C22—44no—
581C22—44no—
582C22—42no—
583C22—42no—
584C22—44no—
585C22—816no—
586C22—81no—
587C22—82no—
588C22—81no—
589C22—82no—
590C22—81no—
591C22—82no—
592C22—81no—
593C22—82no—
594C22#1171881314yes—
595C22#1171929411yescharacteristic
596C22#1171929711yescharacteristic
597C22C2×#8816511yescharacteristic
598C22C2×#8816511yescharacteristic
599C22D13×AGL(1,ℤ/8)11yescharacteristic
600C22#1171947811yescharacteristic
601C22C2×D4×Dic1311yescharacteristic
602C4—22no—
603C4—42no—
604C4—262no—
605C4—521no—
606C4—521no—
607C4—521no—
608C4—1041no—
609C4—1041no—
610C4—1042no—
611C4#1171929812yes—
612C4#1171950312yes—
613C2—24no—
614C2—84no—
615C2—82no—
616C2#1311749711yescharacteristic
617C2C2×#1171881311yescharacteristic
618C2AGL(1,ℤ/8)×Dic1311yescharacteristic
619C2#1312563411yescharacteristic
620C2#1312564711yescharacteristic
621C2#1312582011yescharacteristic
622C2#1312585211yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
Fitting, prime radicalC2×C13×#447C2
socleC23×C13C22×D4
cosocleC22×C4×C13C24
hypercenterC2×#447D13
hypocenterC13#22046
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#447

Complements

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

NH ≅ G/Ntype
1. #121×Dic13C2semidirect
2. C2×#11718882C2semidirect
3. #13115713C2semidirect
4. #13115535C2semidirect
5. #13115465C2semidirect
6. #13115186C2semidirect
7. #13115154C2semidirect
8. #13115031C2semidirect
9. #13114767C2semidirect
10. #13114600C2semidirect
18. C2×D4×Dic13C22semidirect
21. C13×#447C4semidirect
28. #11718882C22semidirect
32. C2×#88072C22semidirect
35. C2×#88057C22semidirect
36. C2×#88055C22semidirect
37. #11718646C22semidirect
38. C4⋊C4×Dic13C22semidirect
41. #11718143C22semidirect
42. #11718142C22semidirect
43. #11718121C22semidirect
50. C22×D4×C13C2×C4semidirect
60. C2×C13×D8C2×C4semidirect
91. C13×#102C2×C4semidirect
92. C13×C22⋊C8C2×C4semidirect
282. #447Dic13semidirect
351. C22×D4C2×Dic13semidirect
361. C2×D8C2×Dic13semidirect
396. #102C2×Dic13semidirect
398. C22⋊C8C2×Dic13semidirect
496. C13#22046semidirect

Maximal subgroups

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

subgroupindex
#121×Dic132
C2×#117188822
#131157132
#131155352
#131154652
#131151862
#131151542
#131150312
#131147672
#131146002
C2×C13×#4472
#2204613