Finite Group Databasebeta

← #15868573

Subgroups — #15868573

Order 3328.

1868 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718879C211yesmaximal, characteristic
2C2×#11718679C212yesmaximal, complemented
3C4×#88178C211yesmaximal, characteristic, complemented
4#13115170C212yesmaximal, complemented
5#13115143C211yesmaximal, characteristic, complemented
6#13115083C212yesmaximal, complemented
7#13115024C211yesmaximal, characteristic, complemented
8#13114767C211yesmaximal, characteristic
9#13114661C212yesmaximal, complemented
10#13114598C211yesmaximal, characteristic, complemented
11C22×C4×D4×C13C211yesmaximal, characteristic
12C23×D4×C13C2211yescharacteristic
13C24×C4×C13—21no—
14C2×C4×D4×C13—28no—
15C2×C4×D4×C13—21no—
16C2×C4×D4×C13—21no—
17C2×C4×D4×C13C2212yes—
18C2×C4×D4×C13C2212yes—
19C22×C13×C4⋊C4C2211yescharacteristic
20C22×C13×C22⋊C4—21no—
21C22×C42×C13C2211yescharacteristic
22C22×#6105C2212yes—
23C2×#88178C2211yescharacteristic
24C2×C4×Dic26C2211yescharacteristic, complemented
25#11718879C418yescomplemented
26C2×#88072C2212yes—
27C2×#88072C2212yes—
28C2×#88072C2212yes—
29#11718873C2211yescharacteristic
30#11718871—21no—
31C4×C22⋊Dic13—21no—
32C2×C22⋊#1055C2211yescharacteristic
33C2×C22⋊#1055C2211yescharacteristic
34#11718679—28no—
35C2×#88050C2212yescomplemented
36C2×#88047C2212yescomplemented
37C4×C4⋊Dic13C2211yescharacteristic, complemented
38#11718594—21no—
39C4×#6101—21no—
40#11718590C2211yescharacteristic, complemented
41#11718589C2211yescharacteristic, complemented
42C2×#88043C2212yescomplemented
43#11718121C2212yescomplemented
44#11718121C2212yescomplemented
45#11718116C2212yescomplemented
46C25×C13—21no—
47C22×D4×C13—24no—
48C22×D4×C13—24no—
49C22×D4×C13—21no—
50C22×D4×C13—22no—
51C22×D4×C13C2×C414yes—
52C22×D4×C13C2312yes—
53C23×C4×C13—28no—
54C23×C4×C13—21no—
55C23×C4×C13—22no—
56C23×C4×C13—22no—
57C23×C4×C13—44no—
58C23×C4×C13—44no—
59C23×C4×C13D411yescharacteristic
60C23×C4×C13D411yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C22×Dic26C2311yescharacteristic
63C4×D4×C13—28no—
64C4×D4×C13—28no—
65C4×D4×C13—24no—
66C4×D4×C13—24no—
67C4×D4×C13—24no—
68C4×D4×C13D418yes—
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4—24no—
71C2×C13×C4⋊C4C2312yes—
72C2×C13×C22⋊C4—28no—
73C2×C13×C22⋊C4—22no—
74C2×C13×C22⋊C4—22no—
75C2×C42×C13—24no—
76C2×C42×C13D411yescharacteristic
77C2×C42×C13D411yescharacteristic
78C2×C42×C13C2311yescharacteristic
79C2×C42×C13C2311yescharacteristic
80C2×C22⋊Dic13—21no—
81C2×C22⋊Dic13—21no—
82C2×#6105—24no—
83C2×#6105—24no—
84C2×#6105C2×C418yescomplemented
85C2×C4⋊Dic13C2311yescharacteristic
86C2×C4⋊Dic13C2311yescharacteristic
87C2×C4⋊Dic13C2311yescharacteristic
88#88178—22no—
89#88178C2×C414yescomplemented
90C2×#6101—21no—
91C2×#6101—21no—
92C2×#6101—21no—
93C2×C4×Dic13—21no—
94C2×C4×Dic13—21no—
95C22×#1055C2312yes—
96C22×#1055C2312yes—
97C4×Dic26—24no—
98#88072—24no—
99#88072—24no—
100#88072C2×C418yescomplemented
101#88071—21no—
102#88071—21no—
103#88071—21no—
104#88071—21no—
105#88071—21no—
106C22⋊#1055—22no—
107C22⋊#1055C2×C414yescomplemented
108#88050—24no—
109#88047—24no—
110#88043—24no—
111#21453—131nomaximal, Sylow
112C24×C13—24no—
113C24×C13—24no—
114C24×C13—24no—
115C24×C13—22no—
116C24×C13—42no—
117C24×C13—42no—
118C24×C13—42no—
119C24×C13—42no—
120C24×C13C2×D411yescharacteristic
121C2×D4×C13—24no—
122C2×D4×C13—24no—
123C2×D4×C13—216no—
124C2×D4×C13—216no—
125C2×D4×C13—24no—
126C2×D4×C13—22no—
127C2×D4×C13—22no—
128C2×D4×C13—22no—
129C2×D4×C13C22×C414yes—
130C2×D4×C13C2×D414yes—
131C2×D4×C13#4114yes—
132C22×C4×C13—22no—
133C22×C4×C13—22no—
134C22×C4×C13—22no—
135C22×C4×C13—22no—
136C22×C4×C13—22no—
137C22×C4×C13—24no—
138C22×C4×C13—28no—
139C22×C4×C13—22no—
140C22×C4×C13—22no—
141C22×C4×C13—22no—
142C22×C4×C13—28no—
143C22×C4×C13—41no—
144C22×C4×C13—432no—
145C22×C4×C13—44no—
146C22×C4×C13—44no—
147C22×C4×C13—44no—
148C22×C4×C13—42no—
149C22×C4×C13—42no—
150C22×C4×C13—44no—
151C22×C4×C13C22×C412yes—
152C22×C4×C13C2×D411yescharacteristic
153C22×C4×C13C2×D411yescharacteristic
154C22×C4×C13C2×D411yescharacteristic
155C22×C4×C13C2×D411yescharacteristic
156C22×C4×C13C2×D411yescharacteristic
157C22×C4×C13#4112yes—
158C22×C4×C13C2411yescharacteristic
159C22×Dic13—21no—
160C22×Dic13—21no—
161C22×Dic13—21no—
162C22×Dic13—21no—
163C2×Dic26—22no—
164C2×Dic26—22no—
165C2×Dic26—21no—
166C2×Dic26C22×C412yescomplemented
167C13×C4⋊C4—24no—
168C13×C4⋊C4—22no—
169C13×C4⋊C4C2×D414yes—
170C13×C22⋊C4—28no—
171C13×C22⋊C4—28no—
172C42×C13—22no—
173C42×C13—22no—
174C42×C13—22no—
175C42×C13C2×D414yes—
176C22⋊Dic13—24no—
177C22⋊Dic13—42no—
178#6105—216no—
179C4⋊Dic13—21no—
180C4⋊Dic13—22no—
181C4⋊Dic13—22no—
182C4⋊Dic13C22×C412yescomplemented
183#6101—24no—
184#6101—42no—
185#6101—42no—
186C4×Dic13—42no—
187C4×Dic13—42no—
188C2×#1055—22no—
189C2×#1055—22no—
190C2×#1055—22no—
191C2×#1055—22no—
192C2×#1055—22no—
193C2×#1055C22×C414yescomplemented
194C22×C4×D4D1311yescharacteristic
195C2×#450—131no—
196C2×#440—132no—
197C4×C22⋊Q8—131no—
198#1877—132no—
199#1872—131no—
200#1862—132no—
201#1852—131no—
202#1786—131no—
203#1762—132no—
204#1749—131no—
205C23×C13—21no—
206C23×C13—21no—
207C23×C13—21no—
208C23×C13—21no—
209C23×C13—216no—
210C23×C13—24no—
211C23×C13—24no—
212C23×C13—24no—
213C23×C13—48no—
214C23×C13—48no—
215C23×C13—48no—
216C23×C13—48no—
217C23×C13—48no—
218C23×C13—42no—
219C23×C13—42no—
220C23×C13—42no—
221C23×C13—42no—
222C23×C13—48no—
223C23×C13C4×D412yes—
224C23×C13AGL(1,ℤ/8)12yes—
225C23×C13#13712yes—
226C23×C13C22×D411yescharacteristic
227D4×C13—216no—
228D4×C13—24no—
229D4×C13—24no—
230D4×C13—24no—
231D4×C13C4×D418yes—
232C2×C4×C13—28no—
233C2×C4×C13—21no—
234C2×C4×C13—21no—
235C2×C4×C13—21no—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
241C2×C4×C13—24no—
242C2×C4×C13—24no—
243C2×C4×C13—21no—
244C2×C4×C13—24no—
245C2×C4×C13—21no—
246C2×C4×C13—21no—
247C2×C4×C13—44no—
248C2×C4×C13—416no—
249C2×C4×C13—416no—
250C2×C4×C13—48no—
251C2×C4×C13—42no—
252C2×C4×C13—42no—
253C2×C4×C13C4×D412yes—
254C2×C4×C13#12012yes—
255C2×C4×C13#12012yes—
256C2×C4×C13AGL(1,ℤ/8)12yes—
257C2×C4×C13C23×C411yescharacteristic
258C2×C4×C13C22×D412yes—
259C2×C4×C13C2×#4112yes—
260C2×C4×C13C2×#4111yescharacteristic
261C2×Dic13—22no—
262C2×Dic13—22no—
263C2×Dic13—41no—
264C2×Dic13—41no—
265C2×Dic13—41no—
266C2×Dic13—41no—
267C2×Dic13—41no—
268C2×Dic13—41no—
269C2×Dic13—41no—
270C2×Dic13—41no—
271C2×Dic13—41no—
272C2×Dic13—41no—
273Dic26—24no—
274Dic26—42no—
275#1055—24no—
276#1055—42no—
277C23×D4C2×D1311yescharacteristic
278C24×C4—21no—
279C22×SD16—132no—
280C2×C22⋊Q8—131no—
281C2×C4×Q8—131no—
282C2×C4×D4—28no—
283C2×C4×D4—21no—
284C2×C4×D4—21no—
285C2×C4×D4C2×D1312yes—
286C2×C4×D4C2×D1312yes—
287C22×C4⋊C4C2×D1311yescharacteristic
288C22×C22⋊C4—21no—
289C22×C42C2×D1311yescharacteristic
290#450—138no—
291#440—268no—
292C2×#107—132no—
293C2×#103—132no—
294C2×#102—132no—
295C2×#102—132no—
296C2×#102—132no—
297C2×C22⋊C8—131no—
298C2×C22⋊C8—131no—
299C2×#97—132no—
300#391—131no—
301#389—131no—
302#387—261no—
303#385—261no—
304#380—131no—
305C4×C4⋊C4—131no—
306C4×C4⋊C4—261no—
307C4×C22⋊C4—261no—
308#340—132no—
309#340—132no—
310#336—132no—
311C22×C13—22no—
312C22×C13—22no—
313C22×C13—22no—
314C22×C13—22no—
315C22×C13—22no—
316C22×C13—22no—
317C22×C13—28no—
318C22×C13—432no—
319C22×C13—44no—
320C22×C13—44no—
321C22×C13—44no—
322C22×C13—44no—
323C22×C13—44no—
324C22×C13—44no—
325C22×C13#44014yescomplemented
326C22×C13C2×C4×D411yescharacteristic
327C22×C13C2×#12011yescharacteristic
328C22×C13#52511yescharacteristic
329C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
330C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
331C22×C13C2×#13711yescharacteristic
332C22×C13#57511yescharacteristic
333C4×C13—22no—
334C4×C13—22no—
335C4×C13—22no—
336C4×C13—22no—
337C4×C13—44no—
338C4×C13—41no—
339C4×C13C2×C4×D412yes—
340C4×C13#52512yes—
341Dic13—42no—
342Dic13—42no—
343Dic13—81no—
344Dic13—81no—
345C25—21no—
346C22×Q8—131no—
347C22×D4—24no—
348C22×D4—24no—
349C22×D4—22no—
350C22×D4—21no—
351C22×D4C4×D1314yes—
352C22×D4C22×D1312yes—
353C23×C4—28no—
354C23×C4—21no—
355C23×C4—22no—
356C23×C4—22no—
357C23×C4—44no—
358C23×C4—44no—
359C23×C4C22⋊D1311yescharacteristic
360C23×C4C22⋊D1311yescharacteristic
361C23×C4C22×D1311yescharacteristic
362C2×SD16—138no—
363C2×SD16—264no—
364C2×SD16—264no—
365C22×C8—132no—
366C22×C8—132no—
367C22⋊Q8—134no—
368C22⋊Q8—262no—
369C4×Q8—264no—
370C4×D4—28no—
371C4×D4—28no—
372C4×D4—24no—
373C4×D4—24no—
374C4×D4—24no—
375C4×D4C22⋊D1318yes—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—24no—
378C2×C4⋊C4—131no—
379C2×C4⋊C4—131no—
380C2×C4⋊C4—131no—
381C2×C4⋊C4—261no—
382C2×C4⋊C4—261no—
383C2×C4⋊C4—261no—
384C2×C4⋊C4C22×D1312yes—
385C2×C22⋊C4—28no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—261no—
389C2×C22⋊C4—261no—
390C2×C42—24no—
391C2×C42—261no—
392C2×C42—261no—
393C2×C42C22⋊D1311yescharacteristic
394C2×C42C22⋊D1311yescharacteristic
395C2×C42C22×D1311yescharacteristic
396C2×C42C22×D1311yescharacteristic
397#107—264no—
398#103—264no—
399#102—138no—
400#102—264no—
401#102—264no—
402C22⋊C8—134no—
403C22⋊C8—262no—
404#97—264no—
405#95—261no—
406#95—261no—
407#95—261no—
408#95—261no—
409#95—261no—
410C2×C13—24no—
411C2×C13—48no—
412C2×C13C4×#12011yescharacteristic
413C2×C13C2×#44011yescharacteristic
414C2×C13C4×AGL(1,ℤ/8)11yescharacteristic
415C2×C13#300311yescharacteristic
416C2×C13#300711yescharacteristic
417C2×C13#311011yescharacteristic
418C2×C13#311411yescharacteristic
419C24—24no—
420C24—24no—
421C24—24no—
422C24—22no—
423C24—42no—
424C24—42no—
425C24—42no—
426C24—42no—
427C24C2×C22⋊D1311yescharacteristic
428C2×Q8—132no—
429C2×Q8—261no—
430C2×Q8—262no—
431C2×Q8—262no—
432C2×D4—24no—
433C2×D4—24no—
434C2×D4—216no—
435C2×D4—216no—
436C2×D4—24no—
437C2×D4—22no—
438C2×D4—22no—
439C2×D4—22no—
440C2×D4C2×C4×D1314yes—
441C2×D4#612714yes—
442C2×D4C2×C22⋊D1314yes—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—24no—
449C22×C4—28no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—28no—
454C22×C4—41no—
455C22×C4—432no—
456C22×C4—44no—
457C22×C4—44no—
458C22×C4—44no—
459C22×C4—42no—
460C22×C4—42no—
461C22×C4—44no—
462C22×C4—261no—
463C22×C4—261no—
464C22×C4—261no—
465C22×C4—261no—
466C22×C4C2×C4×D1312yes—
467C22×C4#612712yes—
468C22×C4C2×C22⋊D1311yescharacteristic
469C22×C4C2×C22⋊D1311yescharacteristic
470C22×C4C2×C22⋊D1311yescharacteristic
471C22×C4C2×C22⋊D1311yescharacteristic
472C22×C4C2×C22⋊D1311yescharacteristic
473C22×C4C23×D1311yescharacteristic
474SD16—2616no—
475C2×C8—134no—
476C2×C8—262no—
477C2×C8—262no—
478C2×C8—262no—
479C2×C8—262no—
480C2×C8—262no—
481C4⋊C4—24no—
482C4⋊C4—22no—
483C4⋊C4—132no—
484C4⋊C4—264no—
485C4⋊C4—261no—
486C4⋊C4—262no—
487C4⋊C4—262no—
488C4⋊C4—522no—
489C4⋊C4—522no—
490C4⋊C4C2×C22⋊D1314yes—
491C22⋊C4—28no—
492C22⋊C4—28no—
493C22⋊C4—264no—
494C22⋊C4—522no—
495C42—22no—
496C42—22no—
497C42—22no—
498C42—522no—
499C42—522no—
500C42C2×C22⋊D1314yes—
501C13#2145311yescharacteristic, complemented, Sylow
502C23—21no—
503C23—21no—
504C23—21no—
505C23—21no—
506C23—216no—
507C23—24no—
508C23—24no—
509C23—24no—
510C23—48no—
511C23—48no—
512C23—48no—
513C23—48no—
514C23—48no—
515C23—48no—
516C23—42no—
517C23—42no—
518C23—42no—
519C23—42no—
520C23C4×C22⋊D1312yes—
521C23#8818612yes—
522C23#8820512yes—
523C23C22×C22⋊D1311yescharacteristic
524Q8—264no—
525Q8—522no—
526D4—216no—
527D4—24no—
528D4—24no—
529D4—24no—
530D4C4×C22⋊D1318yes—
531C2×C4—28no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—24no—
541C2×C4—24no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—24no—
546C2×C4—44no—
547C2×C4—416no—
548C2×C4—416no—
549C2×C4—48no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—262no—
553C2×C4—262no—
554C2×C4—521no—
555C2×C4—521no—
556C2×C4—521no—
557C2×C4—521no—
558C2×C4—521no—
559C2×C4—521no—
560C2×C4—521no—
561C2×C4—521no—
562C2×C4—521no—
563C2×C4—521no—
564C2×C4C4×C22⋊D1312yes—
565C2×C4#8818612yes—
566C2×C4#8820712yes—
567C2×C4#8820712yes—
568C2×C4C22×C4×D1311yescharacteristic
569C2×C4C2×#612712yes—
570C2×C4C2×#612711yescharacteristic
571C2×C4C22×C22⋊D1312yes—
572C8—264no—
573C8—522no—
574C22—22no—
575C22—22no—
576C22—22no—
577C22—22no—
578C22—22no—
579C22—22no—
580C22—28no—
581C22—432no—
582C22—44no—
583C22—44no—
584C22—44no—
585C22—44no—
586C22—44no—
587C22—44no—
588C22#1171867914yescomplemented
589C22C2×C4×C22⋊D1311yescharacteristic
590C22#1171949611yescharacteristic
591C22C2×#8818611yescharacteristic
592C22C2×#8818611yescharacteristic
593C22#1171952711yescharacteristic
594C22C2×#8820511yescharacteristic
595C22C2×#8820711yescharacteristic
596C4—22no—
597C4—22no—
598C4—22no—
599C4—22no—
600C4—41no—
601C4—44no—
602C4—522no—
603C4—522no—
604C4—1041no—
605C4—1041no—
606C4C2×C4×C22⋊D1312yes—
607C4#1171949612yes—
608C2—24no—
609C2—48no—
610C2C4×#8820711yescharacteristic
611C2C2×#1171867911yescharacteristic
612C2C4×#8818611yescharacteristic
613C2#1312406311yescharacteristic
614C2#1312409611yescharacteristic
615C2#1312493511yescharacteristic
616C2#1312497411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC22×C4×D4×C13C2
socleC23×C13C22×D4
prime radicalC23×D4×C13C22
cosocleC22×C4×C13C24
hypercenterC22×C4×D4D13
hypocenterC13#21453
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
2. C2×#11718679C2semidirect
3. C4×#88178C2semidirect
4. #13115170C2semidirect
5. #13115143C2semidirect
6. #13115083C2semidirect
7. #13115024C2semidirect
9. #13114661C2semidirect
10. #13114598C2semidirect
24. C2×C4×Dic26C22semidirect
25. #11718879C4semidirect
35. C2×#88050C22semidirect
36. C2×#88047C22semidirect
37. C4×C4⋊Dic13C22semidirect
40. #11718590C22semidirect
41. #11718589C22semidirect
42. C2×#88043C22semidirect
43. #11718121C22semidirect
44. #11718121C22semidirect
45. #11718116C22semidirect
84. C2×#6105C2×C4semidirect
89. #88178C2×C4semidirect
100. #88072C2×C4semidirect
107. C22⋊#1055C2×C4semidirect
166. C2×Dic26C22×C4semidirect
182. C4⋊Dic13C22×C4semidirect
193. C2×#1055C22×C4semidirect
325. C22×C13#440semidirect
501. C13#21453semidirect
588. C22#11718679semidirect

Maximal subgroups

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

subgroupindex
C2×#117188792
C2×#117186792
C4×#881782
#131151702
#131151432
#131150832
#131150242
#131147672
#131146612
#131145982
C22×C4×D4×C132
#2145313