Finite Group Databasebeta

← #15874120

Subgroups — #15874120

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
1C2×#11718697C211yesmaximal, characteristic
2C2×#11718600C211yesmaximal, characteristic, complemented
3#13115711C212yesmaximal, complemented
4#13115532C212yesmaximal, complemented
5#13115463C212yesmaximal, complemented
6#13115184C212yesmaximal, complemented
7#13115154C211yesmaximal, characteristic, complemented
8#13115028C211yesmaximal, characteristic, complemented
9#13114766C211yesmaximal, characteristic, complemented
10#13114598C211yesmaximal, characteristic, complemented
11C4×C13×#121C211yesmaximal, characteristic, complemented
12C23×D52C2211yescharacteristic
13C2×C13×#121C2211yescharacteristic
14C2×C4×D4×C13—21no—
15C2×C4×D4×C13C2211yescharacteristic, complemented
16C22×C42×C13C2211yescharacteristic
17C22×#6104C2212yes—
18C22×#6103—21no—
19C22×#6103—21no—
20C22×C4⋊Dic13C2211yescharacteristic
21C13×#390C2211yescharacteristic, complemented
22C13×#389C2211yescharacteristic, complemented
23C13×#388—21no—
24C13×#386—21no—
25C13×#380C2211yescharacteristic
26C4×C13×C4⋊C4C2211yescharacteristic, complemented
27C4×C13×C22⋊C4—21no—
28C2×#88072C2212yescomplemented
29C2×C22⋊#1055C2211yescharacteristic
30C2×C22⋊#1055C2211yescharacteristic
31#11718697C418yescomplemented
32C2×#88049C2212yes—
33C2×#88049C2212yes—
34C2×#88049C2212yes—
35C2×#88048C2212yescomplemented
36#11718600—21no—
37#11718600—21no—
38#11718600C2212yes—
39#11718600C2212yes—
40C2×#88043C2212yescomplemented
41#11718121C2212yescomplemented
42#11718121C2212yescomplemented
43#11718116C2212yescomplemented
44C24×D13—21no—
45C22×D4×C13—21no—
46C22×D4×C13C2311yescharacteristic
47C23×C4×C13—21no—
48C23×C4×C13D411yescharacteristic
49C23×C4×C13D411yescharacteristic
50C23×C4×C13C2311yescharacteristic
51C23×Dic13—21no—
52C22×D52—21no—
53C22×D52—22no—
54C22×D52—42no—
55C22×D52—42no—
56C22×D52C2×C414yescomplemented
57C22×D52C2312yes—
58C13×#121—22no—
59C13×#121C2×C414yes—
60C4×D4×C13—42no—
61C4×D4×C13—44no—
62C2×C13×C4⋊C4—21no—
63C2×C13×C4⋊C4C2311yescharacteristic
64C2×C13×C4⋊C4C2311yescharacteristic
65C2×C13×C4⋊C4C2311yescharacteristic
66C2×C13×C22⋊C4—21no—
67C2×C13×C22⋊C4—21no—
68C2×C13×C22⋊C4—21no—
69C2×C13×C22⋊C4—21no—
70C2×C13×C22⋊C4—21no—
71C2×C42×C13—21no—
72C2×C42×C13—42no—
73C2×C42×C13D411yescharacteristic
74C2×C42×C13D411yescharacteristic
75C2×C42×C13C2311yescharacteristic
76C2×C42×C13C2311yescharacteristic
77C2×#6104—42no—
78C2×#6104—42no—
79C2×#6104C2×C418yescomplemented
80C2×#6103—22no—
81C2×#6103—22no—
82C2×#6103—22no—
83C2×#6103—22no—
84C2×#6103—44no—
85C2×#6103—44no—
86C2×C4⋊Dic13—21no—
87C2×C4⋊Dic13—42no—
88C2×C4⋊Dic13C2312yes—
89C22×#1055C2312yes—
90C22×#1055C2312yes—
91C13×#95—21no—
92C13×#95—21no—
93C13×#95—21no—
94#88072—42no—
95C22⋊#1055—22no—
96C22⋊#1055C2×C414yescomplemented
97#88049—42no—
98#88049—42no—
99#88049C2×C418yescomplemented
100#88048—42no—
101#88043—42no—
102#22046—131nomaximal, Sylow
103C24×C13—21no—
104C24×C13C2×D411yescharacteristic
105C23×D13—24no—
106C23×D13—22no—
107C23×D13—42no—
108C23×D13—42no—
109C23×D13—42no—
110C23×D13—42no—
111C23×D13—42no—
112C23×D13—42no—
113C2×D4×C13—24no—
114C2×D4×C13—21no—
115C2×D4×C13—22no—
116C2×D4×C13—22no—
117C2×D4×C13—42no—
118C2×D4×C13—42no—
119C2×D4×C13C22×C412yes—
120C22×C4×C13—22no—
121C22×C4×C13—22no—
122C22×C4×C13—22no—
123C22×C4×C13—22no—
124C22×C4×C13—21no—
125C22×C4×C13—22no—
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13—41no—
129C22×C4×C13—41no—
130C22×C4×C13—41no—
131C22×C4×C13—42no—
132C22×C4×C13—42no—
133C22×C4×C13—42no—
134C22×C4×C13C22×C412yes—
135C22×C4×C13C2×D411yescharacteristic
136C22×C4×C13C2×D411yescharacteristic
137C22×C4×C13C2×D411yescharacteristic
138C22×C4×C13C2×D411yescharacteristic
139C22×C4×C13C2×D411yescharacteristic
140C22×C4×C13#4112yes—
141C22×C4×C13C2411yescharacteristic
142C22×Dic13—22no—
143C22×Dic13—42no—
144C22×Dic13—42no—
145C22×Dic13—42no—
146C2×D52—22no—
147C2×D52—22no—
148C2×D52—22no—
149C2×D52—22no—
150C2×D52—24no—
151C2×D52—22no—
152C2×D52—48no—
153C2×D52—42no—
154C2×D52—42no—
155C2×D52—48no—
156C2×D52C22×C414yes—
157C13×C4⋊C4—21no—
158C13×C4⋊C4—22no—
159C13×C4⋊C4—22no—
160C13×C4⋊C4—42no—
161C13×C4⋊C4C22×C412yes—
162C13×C22⋊C4—24no—
163C13×C22⋊C4—42no—
164C13×C22⋊C4—42no—
165C13×C22⋊C4—42no—
166C13×C22⋊C4—42no—
167C42×C13—22no—
168C42×C13—22no—
169C42×C13—41no—
170C42×C13—41no—
171C42×C13—42no—
172#6104—48no—
173#6103—44no—
174#6103—44no—
175#6103—44no—
176#6103—44no—
177C4⋊Dic13—22no—
178C4⋊Dic13—22no—
179C4⋊Dic13—42no—
180C2×#1055—22no—
181C2×#1055—22no—
182C2×#1055—22no—
183C2×#1055—22no—
184C2×#1055—22no—
185C2×#1055C22×C414yes—
186C2×#447—131no—
187C4×#121D1311yescharacteristic, complemented
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—41no—
203C23×C13—41no—
204C23×C13—41no—
205C23×C13—41no—
206C23×C13—41no—
207C23×C13—41no—
208C23×C13C4×D412yes—
209C23×C13AGL(1,ℤ/8)12yes—
210C23×C13AGL(1,ℤ/8)12yes—
211C23×C13C22×D411yescharacteristic
212C22×D13—24no—
213C22×D13—48no—
214C22×D13—48no—
215C22×D13—42no—
216C22×D13—42no—
217C22×D13—42no—
218C22×D13—42no—
219C22×D13—42no—
220C22×D13—42no—
221C22×D13—48no—
222C22×D13—84no—
223C22×D13—84no—
224C22×D13—84no—
225C22×D13—84no—
226D4×C13—24no—
227D4×C13—48no—
228D4×C13—42no—
229C2×C4×C13—21no—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—24no—
234C2×C4×C13—24no—
235C2×C4×C13—22no—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—21no—
245C2×C4×C13—44no—
246C2×C4×C13—44no—
247C2×C4×C13—41no—
248C2×C4×C13—41no—
249C2×C4×C13—41no—
250C2×C4×C13—41no—
251C2×C4×C13—41no—
252C2×C4×C13—41no—
253C2×C4×C13—41no—
254C2×C4×C13—41no—
255C2×C4×C13—84no—
256C2×C4×C13C4×D412yes—
257C2×C4×C13AGL(1,ℤ/8)12yes—
258C2×C4×C13C23×C411yescharacteristic
259C2×C4×C13C2×#4111yescharacteristic
260C2×C4×C13H(5,𝔽2)12yes—
261C2×C4×C13H(5,𝔽2)12yes—
262C2×Dic13—42no—
263C2×Dic13—42no—
264C2×Dic13—42no—
265C2×Dic13—84no—
266D52—24no—
267D52—24no—
268D52—48no—
269D52—42no—
270D52—42no—
271#1055—24no—
272#1055—42no—
273C23×D4—131no—
274C22×D8—132no—
275C2×#121C2×D1311yescharacteristic
276C2×C4×D4—21no—
277C2×C4×D4C2×D1311yescharacteristic, complemented
278C22×C4⋊C4—131no—
279C22×C22⋊C4—261no—
280C22×C22⋊C4—261no—
281C22×C42C2×D1311yescharacteristic
282#447—138no—
283C2×#106—132no—
284C2×#102—132no—
285C2×#102—132no—
286C2×#102—132no—
287C2×#102—132no—
288C2×C22⋊C8—131no—
289C2×C22⋊C8—131no—
290C2×#97—132no—
291#390—132no—
292#390—132no—
293#390—261no—
294#390—261no—
295#390C2×D1311yescharacteristic, complemented
296#389C2×D1311yescharacteristic, complemented
297#388—21no—
298#386—21no—
299#380C2×D1311yescharacteristic
300C4×C4⋊C4C2×D1311yescharacteristic, complemented
301C4×C22⋊C4—21no—
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—42no—
312C22×C13—42no—
313C22×C13—42no—
314C22×C13—81no—
315C22×C13—81no—
316C22×C13—81no—
317C22×C13—81no—
318C22×C13#44214yes—
319C22×C13C2×C4×D411yescharacteristic
320C22×C13#53411yescharacteristic
321C22×C13#53511yescharacteristic
322C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
323C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
324C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
325C22×C13#57511yescharacteristic
326C2×D13—44no—
327C2×D13—44no—
328C2×D13—44no—
329C2×D13—816no—
330C2×D13—82no—
331C2×D13—82no—
332C2×D13—82no—
333C2×D13—82no—
334C4×C13—22no—
335C4×C13—22no—
336C4×C13—41no—
337C4×C13—41no—
338C4×C13—41no—
339C4×C13—42no—
340C4×C13—81no—
341C4×C13—81no—
342C4×C13#51812yes—
343C4×C13#53812yes—
344Dic13—82no—
345C25—261no—
346C22×D4—21no—
347C22×D4—134no—
348C22×D4—132no—
349C22×D4—262no—
350C22×D4—261no—
351C22×D4—522no—
352C22×D4—522no—
353C22×D4C22×D1311yescharacteristic
354C23×C4—21no—
355C23×C4—261no—
356C23×C4C22⋊D1311yescharacteristic
357C23×C4C22⋊D1311yescharacteristic
358C23×C4C22×D1311yescharacteristic
359C2×D8—138no—
360C2×D8—522no—
361C2×D8—522no—
362C22×C8—132no—
363C22×C8—132no—
364#121—22no—
365#121C4×D1314yes—
366C4×D4—42no—
367C4×D4—44no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—132no—
370C2×C4⋊C4—261no—
371C2×C4⋊C4—522no—
372C2×C4⋊C4C22×D1311yescharacteristic
373C2×C4⋊C4C22×D1311yescharacteristic
374C2×C4⋊C4C22×D1311yescharacteristic
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—262no—
381C2×C22⋊C4—262no—
382C2×C22⋊C4—262no—
383C2×C22⋊C4—262no—
384C2×C22⋊C4—524no—
385C2×C22⋊C4—524no—
386C2×C42—21no—
387C2×C42—42no—
388C2×C42C22⋊D1311yescharacteristic
389C2×C42C22⋊D1311yescharacteristic
390C2×C42C22×D1311yescharacteristic
391C2×C42C22×D1311yescharacteristic
392#106—522no—
393#102—138no—
394#102—522no—
395#102—522no—
396#102—522no—
397C22⋊C8—134no—
398C22⋊C8—262no—
399#97—522no—
400#95—21no—
401#95—21no—
402#95—21no—
403C2×C13—24no—
404C2×C13—82no—
405C2×C13#232111yescharacteristic
406C2×C13C2×#44211yescharacteristic
407C2×C13C4×AGL(1,ℤ/8)11yescharacteristic
408C2×C13#319211yescharacteristic
409C2×C13#319411yescharacteristic
410C2×C13#321311yescharacteristic
411C2×C13#321711yescharacteristic
412D13—84no—
413C24—21no—
414C24—264no—
415C24—262no—
416C24—522no—
417C24—522no—
418C24—522no—
419C24—522no—
420C24—522no—
421C24—522no—
422C24C2×C22⋊D1311yescharacteristic
423C2×D4—24no—
424C2×D4—21no—
425C2×D4—22no—
426C2×D4—22no—
427C2×D4—42no—
428C2×D4—42no—
429C2×D4—134no—
430C2×D4—264no—
431C2×D4—262no—
432C2×D4—262no—
433C2×D4—262no—
434C2×D4—262no—
435C2×D4—262no—
436C2×D4—528no—
437C2×D4—522no—
438C2×D4—522no—
439C2×D4—528no—
440C2×D4C2×C4×D1312yes—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—42no—
453C22×C4—42no—
454C22×C4—42no—
455C22×C4—262no—
456C22×C4—522no—
457C22×C4—522no—
458C22×C4—522no—
459C22×C4C2×C4×D1312yes—
460C22×C4#612712yes—
461C22×C4C2×C22⋊D1311yescharacteristic
462C22×C4C2×C22⋊D1311yescharacteristic
463C22×C4C2×C22⋊D1311yescharacteristic
464C22×C4C2×C22⋊D1311yescharacteristic
465C22×C4C2×C22⋊D1311yescharacteristic
466C22×C4C23×D1311yescharacteristic
467D8—528no—
468C2×C8—134no—
469C2×C8—262no—
470C2×C8—262no—
471C2×C8—262no—
472C2×C8—262no—
473C2×C8—262no—
474C4⋊C4—21no—
475C4⋊C4—22no—
476C4⋊C4—22no—
477C4⋊C4—42no—
478C4⋊C4—262no—
479C4⋊C4—262no—
480C4⋊C4—522no—
481C4⋊C4C2×C4×D1312yes—
482C22⋊C4—24no—
483C22⋊C4—42no—
484C22⋊C4—42no—
485C22⋊C4—42no—
486C22⋊C4—42no—
487C22⋊C4—524no—
488C22⋊C4—524no—
489C22⋊C4—524no—
490C22⋊C4—524no—
491C42—22no—
492C42—22no—
493C42—41no—
494C42—41no—
495C42—42no—
496C13#2204611yescharacteristic, complemented, Sylow
497C23—21no—
498C23—21no—
499C23—21no—
500C23—21no—
501C23—22no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—264no—
509C23—528no—
510C23—528no—
511C23—528no—
512C23—522no—
513C23—522no—
514C23—522no—
515C23—522no—
516C23—522no—
517C23—522no—
518C23—1044no—
519C23—1044no—
520C23—1044no—
521C23—1044no—
522C23C4×C22⋊D1312yes—
523C23#8818612yes—
524C23#8820312yes—
525C23C22×C22⋊D1311yescharacteristic
526D4—24no—
527D4—48no—
528D4—42no—
529D4—264no—
530D4—264no—
531D4—528no—
532D4—522no—
533D4—522no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—24no—
539C2×C4—24no—
540C2×C4—22no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—44no—
551C2×C4—44no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—84no—
561C2×C4—522no—
562C2×C4—522no—
563C2×C4—522no—
564C2×C4—1044no—
565C2×C4C4×C22⋊D1312yes—
566C2×C4#8820312yes—
567C2×C4C22×C4×D1311yescharacteristic
568C2×C4C2×#612711yescharacteristic
569C2×C4#8825112yes—
570C2×C4#8825612yes—
571C8—264no—
572C8—522no—
573C22—22no—
574C22—22no—
575C22—22no—
576C22—22no—
577C22—22no—
578C22—22no—
579C22—42no—
580C22—42no—
581C22—42no—
582C22—81no—
583C22—81no—
584C22—81no—
585C22—81no—
586C22—524no—
587C22—524no—
588C22—524no—
589C22—10416no—
590C22—1042no—
591C22—1042no—
592C22—1042no—
593C22—1042no—
594C22#1171867514yes—
595C22C2×C4×C22⋊D1311yescharacteristic
596C22C2×#8818611yescharacteristic
597C22#1171950911yescharacteristic
598C22C2×#8820311yescharacteristic
599C22C2×#8820311yescharacteristic
600C22#1171952711yescharacteristic
601C22#1171953511yescharacteristic
602C4—22no—
603C4—22no—
604C4—41no—
605C4—41no—
606C4—41no—
607C4—42no—
608C4—81no—
609C4—81no—
610C4—1042no—
611C4#1171925012yes—
612C4#1171926512yes—
613C2—24no—
614C2—82no—
615C2—1044no—
616C2#1311749011yescharacteristic
617C2C2×#1171867511yescharacteristic
618C2C4×#8820311yescharacteristic
619C2#1312563311yescharacteristic
620C2#1312564611yescharacteristic
621C2#1312581911yescharacteristic
622C2#1312585111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC4×C13×#121C2
socleC23×C13C22×D4
prime radicalC2×#11718697C2
cosocleC22×C4×C13C24
hypercenterC4×#121D13
hypocenterC13#22046
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×#121

Complements

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

NH ≅ G/Ntype
2. C2×#11718600C2semidirect
3. #13115711C2semidirect
4. #13115532C2semidirect
5. #13115463C2semidirect
6. #13115184C2semidirect
7. #13115154C2semidirect
8. #13115028C2semidirect
9. #13114766C2semidirect
10. #13114598C2semidirect
11. C4×C13×#121C2semidirect
15. C2×C4×D4×C13C22semidirect
21. C13×#390C22semidirect
22. C13×#389C22semidirect
26. C4×C13×C4⋊C4C22semidirect
28. C2×#88072C22semidirect
31. #11718697C4semidirect
35. C2×#88048C22semidirect
40. C2×#88043C22semidirect
41. #11718121C22semidirect
42. #11718121C22semidirect
43. #11718116C22semidirect
56. C22×D52C2×C4semidirect
79. C2×#6104C2×C4semidirect
96. C22⋊#1055C2×C4semidirect
99. #88049C2×C4semidirect
187. C4×#121D13semidirect
277. C2×C4×D4C2×D13semidirect
295. #390C2×D13semidirect
296. #389C2×D13semidirect
300. C4×C4⋊C4C2×D13semidirect
496. C13#22046semidirect

Maximal subgroups

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

subgroupindex
C2×#117186972
C2×#117186002
#131157112
#131155322
#131154632
#131151842
#131151542
#131150282
#131147662
#131145982
C4×C13×#1212
#2204613