Finite Group Databasebeta

← #15936112

Subgroups — #15936112

Order 3328.

762 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13117892C211yesmaximal, characteristic, complemented
2#13116380C211yesmaximal, characteristic, complemented
3#13116153C211yesmaximal, characteristic
4#13116082C211yesmaximal, characteristic, complemented
5#13115918C211yesmaximal, characteristic
6#13115689C211yesmaximal, characteristic
7#13115470C211yesmaximal, characteristic, complemented
8#13115460C211yesmaximal, characteristic
9#13115411C211yesmaximal, characteristic, complemented
10#13115395C211yesmaximal, characteristic, complemented
11#13115194C211yesmaximal, characteristic
12#13115194C211yesmaximal, characteristic
13#13114838C211yesmaximal, characteristic, complemented
14C4×#88050C211yesmaximal, characteristic, complemented
15C13×#2512C211yesmaximal, characteristic
16C2×C13×#126—21no—
17C22×#6105C2211yescharacteristic
18C22×#6105C2211yescharacteristic
19C2×#88123C2211yescharacteristic
20C2×C4×Dic26C2211yescharacteristic
21C2×C4×Dic26C2211yescharacteristic
22C13×#397—21no—
23C13×#396—21no—
24C13×#390C2211yescharacteristic
25C13×#390C2211yescharacteristic
26C13×#390C2211yescharacteristic
27C13×#389C2211yescharacteristic
28C13×#388—21no—
29C13×#384C2211yescharacteristic
30C4×C13×C4⋊C4C2211yescharacteristic
31C4×C13×C4⋊C4C2211yescharacteristic
32C2×#88072C2211yescharacteristic
33C2×#88072C2211yescharacteristic
34C4⋊C4×Dic13—21no—
35#11718634—21no—
36C2×#88050C2211yescharacteristic
37C2×#88050C2211yescharacteristic
38C2×#88050C2211yescharacteristic
39C2×#88050C2211yescharacteristic
40C2×#88050C2211yescharacteristic
41C2×#88050C2211yescharacteristic
42C2×#88048C2211yescharacteristic
43C2×#88048C2211yescharacteristic
44C4×C4⋊Dic13C2211yescharacteristic
45#11718590C2211yescharacteristic
46#11718590C2211yescharacteristic
47C2×C4⋊#1055C2211yescharacteristic
48C2×C4×#1055C2211yescharacteristic
49#11718315—21no—
50#11718315—21no—
51#11718121C2211yescharacteristic
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718116C2211yescharacteristic
56#11718116C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59C22×D4×C13C2311yescharacteristic
60C22×Dic26C2311yescharacteristic
61C22×Dic26C2311yescharacteristic
62C13×#126—44no—
63C2×C13×C4⋊C4—21no—
64C2×C13×C4⋊C4—21no—
65C2×C13×C4⋊C4—21no—
66C2×C13×C4⋊C4D411yescharacteristic
67C2×C13×C4⋊C4D411yescharacteristic
68C2×C13×C4⋊C4C2311yescharacteristic
69C2×C13×C4⋊C4C2311yescharacteristic
70C2×C13×C4⋊C4C2311yescharacteristic
71C2×C13×C22⋊C4—21no—
72C2×C13×C22⋊C4—21no—
73C2×C13×C22⋊C4—21no—
74C2×C13×C22⋊C4—21no—
75C2×C13×C22⋊C4—21no—
76C2×C13×C22⋊C4—21no—
77C2×C42×C13—21no—
78C2×C42×C13C2311yescharacteristic
79C2×C42×C13C2311yescharacteristic
80C2×C42×C13C2311yescharacteristic
81C2×#6105—22no—
82C2×#6105—22no—
83C2×#6105—22no—
84C2×#6105—41no—
85C2×#6105—41no—
86C2×#6105—41no—
87C2×C4⋊Dic13—21no—
88C2×C4⋊Dic13—21no—
89C2×C4⋊Dic13C2311yescharacteristic
90C2×C4⋊Dic13C2311yescharacteristic
91C2×#6101—21no—
92C2×#6101—21no—
93C2×C4×Dic13—21no—
94C2×C4×Dic13—21no—
95C2×C4×Dic13—21no—
96C22×#1055C2311yescharacteristic
97C22×#1055C2311yescharacteristic
98C22×#1055C2311yescharacteristic
99C22×#1055C2311yescharacteristic
100#88123—22no—
101#88123—22no—
102C4×Dic26—22no—
103C4×Dic26—22no—
104C4×Dic26—41no—
105C4×Dic26—41no—
106C13×#95—21no—
107C13×#95—21no—
108C13×#95D411yescharacteristic
109C13×#95D411yescharacteristic
110#88072—22no—
111#88072—41no—
112#88071—21no—
113#88071—21no—
114#88071—21no—
115#88071—21no—
116#88071—21no—
117#88050—22no—
118#88050—22no—
119#88050—22no—
120#88050—41no—
121#88050—41no—
122#88050—41no—
123#88048—22no—
124#88048—41no—
125C4⋊#1055—41no—
126C4×#1055—41no—
127#27066—131nomaximal, Sylow
128C24×C13—21no—
129C2×D4×C13—21no—
130C2×D4×C13—21no—
131C2×D4×C13—21no—
132C2×D4×C13—21no—
133C2×D4×C13—21no—
134C2×D4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—21no—
138C22×C4×C13C2×D411yescharacteristic
139C22×C4×C13C2×D411yescharacteristic
140C22×C4×C13C2×D411yescharacteristic
141C22×C4×C13C2×D411yescharacteristic
142C22×C4×C13C2×D411yescharacteristic
143C22×C4×C13C2×D411yescharacteristic
144C22×C4×C13C2411yescharacteristic
145C22×Dic13—21no—
146C22×Dic13—21no—
147C22×Dic13—21no—
148C22×Dic13—21no—
149C2×Dic26—21no—
150C2×Dic26—21no—
151C2×Dic26—21no—
152C2×Dic26—21no—
153C2×Dic26—21no—
154C2×Dic26—21no—
155C2×Dic26—21no—
156C2×Dic26—21no—
157C2×Dic26—21no—
158C2×Dic26—21no—
159C2×Dic26#4112yes—
160C2×Dic26#4112yes—
161C13×C4⋊C4—21no—
162C13×C4⋊C4—21no—
163C13×C4⋊C4—21no—
164C13×C4⋊C4—21no—
165C13×C4⋊C4—21no—
166C13×C4⋊C4—21no—
167C13×C4⋊C4—41no—
168C13×C4⋊C4—42no—
169C13×C4⋊C4—42no—
170C13×C4⋊C4—81no—
171C13×C4⋊C4SD1614yescomplemented
172C13×C22⋊C4—42no—
173C13×C22⋊C4—42no—
174C13×C22⋊C4—42no—
175C13×C22⋊C4—42no—
176C13×C22⋊C4—81no—
177C13×C22⋊C4—81no—
178C42×C13—21no—
179C42×C13—21no—
180C42×C13—21no—
181C42×C13—21no—
182C42×C13—21no—
183C42×C13—21no—
184C42×C13—42no—
185#6105—44no—
186#6105—44no—
187C4⋊Dic13—24no—
188C4⋊Dic13—24no—
189C4⋊Dic13—21no—
190C4⋊Dic13—21no—
191C4⋊Dic13—21no—
192C4⋊Dic13#4112yes—
193#6101—42no—
194#6101—42no—
195C4×Dic13—42no—
196C4×Dic13—42no—
197C4×Dic13—42no—
198C2×#1055—21no—
199C2×#1055—21no—
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055—21no—
203C2×#1055—21no—
204C2×#1055—21no—
205C2×#1055—21no—
206C2×#1055—21no—
207C2×#1055—21no—
208C2×#1055—21no—
209C2×#1055#4112yes—
210#2512D1311yescharacteristic
211#2365—131no—
212#2096—131no—
213#2055—131no—
214#2043—131no—
215#2013—131no—
216#1968—131no—
217#1927—131no—
218#1926—131no—
219#1919—131no—
220#1916—131no—
221#1880—131no—
222#1880—131no—
223#1803—131no—
224C4×#103—131no—
225C23×C13—41no—
226C23×C13—41no—
227C23×C13—41no—
228C23×C13—41no—
229C23×C13—41no—
230C23×C13—41no—
231C23×C13—41no—
232C23×C13C22×D411yescharacteristic
233D4×C13—41no—
234D4×C13—41no—
235D4×C13—41no—
236D4×C13—41no—
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—21no—
246C2×C4×C13—21no—
247C2×C4×C13—21no—
248C2×C4×C13—21no—
249C2×C4×C13—21no—
250C2×C4×C13—21no—
251C2×C4×C13—21no—
252C2×C4×C13—41no—
253C2×C4×C13—41no—
254C2×C4×C13—41no—
255C2×C4×C13—41no—
256C2×C4×C13—41no—
257C2×C4×C13—41no—
258C2×C4×C13—41no—
259C2×C4×C13—41no—
260C2×C4×C13—41no—
261C2×C4×C13C2×SD1612yes—
262C2×C4×C13C2×SD1612yes—
263C2×C4×C13C2×SD1612yes—
264C2×C4×C13C2×#4111yescharacteristic
265C2×C4×C13C2×#4111yescharacteristic
266C2×C4×C13C2×#4111yescharacteristic
267C2×C4×C13C2×#4111yescharacteristic
268C2×C4×C13H(5,𝔽2)11yescharacteristic
269C2×C4×C13H(5,𝔽2)11yescharacteristic
270C2×Dic13—22no—
271C2×Dic13—22no—
272C2×Dic13—22no—
273C2×Dic13—41no—
274C2×Dic13—41no—
275C2×Dic13—41no—
276C2×Dic13—41no—
277C2×Dic13—41no—
278C2×Dic13—41no—
279C2×Dic13—41no—
280C2×Dic13—41no—
281C2×Dic13—41no—
282Dic26—22no—
283Dic26—22no—
284Dic26—22no—
285Dic26—22no—
286Dic26—41no—
287Dic26—41no—
288Dic26—41no—
289Dic26—41no—
290#1055—22no—
291#1055—41no—
292#1055—41no—
293#1055—41no—
294C22×SD16—131no—
295C22×SD16—131no—
296C2×C4⋊Q8—131no—
297C2×#126—21no—
298C2×C4×Q8—131no—
299C2×C4×Q8—131no—
300C2×#106—131no—
301C2×#106—131no—
302C2×C4⋊C8—131no—
303C2×#103—131no—
304C2×#103—131no—
305C2×#103—131no—
306C2×#103—131no—
307C2×#103—131no—
308C2×#103—131no—
309C2×#102—131no—
310C2×#102—131no—
311C2×C4×C8—131no—
312#397—21no—
313#396—21no—
314#391—131no—
315#391—131no—
316#390C2×D1311yescharacteristic
317#390C2×D1311yescharacteristic
318#390C2×D1311yescharacteristic
319#389—261no—
320#389C2×D1311yescharacteristic
321#388—21no—
322#387—261no—
323#387—261no—
324#384C2×D1311yescharacteristic
325C4×C4⋊C4—131no—
326C4×C4⋊C4—261no—
327C4×C4⋊C4C2×D1311yescharacteristic
328C4×C4⋊C4C2×D1311yescharacteristic
329#340—131no—
330#340—131no—
331#340—131no—
332#340—131no—
333#336—131no—
334#336—131no—
335#336—131no—
336#336—131no—
337C22×C13—81no—
338C22×C13—81no—
339C22×C13—81no—
340C22×C13—81no—
341C22×C13—81no—
342C22×C13—81no—
343C22×C13—81no—
344C22×C13#52511yescharacteristic
345C22×C13#54611yescharacteristic
346C22×C13#55011yescharacteristic
347C22×C13C22×SD1611yescharacteristic
348C22×C13#57511yescharacteristic
349C22×C13#57711yescharacteristic
350C22×C13#57811yescharacteristic
351C4×C13—22no—
352C4×C13—22no—
353C4×C13—22no—
354C4×C13—41no—
355C4×C13—41no—
356C4×C13—41no—
357C4×C13—81no—
358C4×C13—81no—
359C4×C13—81no—
360C4×C13#52911yescharacteristic
361C4×C13#53811yescharacteristic
362C4×C13#55111yescharacteristic
363C4×C13#55311yescharacteristic
364Dic13—42no—
365Dic13—42no—
366Dic13—42no—
367Dic13—81no—
368C22×Q8—131no—
369C22×Q8—131no—
370C22×D4C22×D1311yescharacteristic
371C2×SD16—262no—
372C2×SD16—262no—
373C2×SD16—262no—
374C2×SD16—521no—
375C2×SD16—521no—
376C2×SD16—521no—
377C22×C8—131no—
378C22×C8—131no—
379C22×C8—131no—
380C22×C8—131no—
381C4⋊Q8—262no—
382C4⋊Q8—262no—
383#126—44no—
384C4×Q8—262no—
385C4×Q8—262no—
386C4×Q8—521no—
387C4×Q8—521no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—131no—
392C2×C4⋊C4—131no—
393C2×C4⋊C4—261no—
394C2×C4⋊C4—261no—
395C2×C4⋊C4—261no—
396C2×C4⋊C4—261no—
397C2×C4⋊C4C22⋊D1311yescharacteristic
398C2×C4⋊C4C22⋊D1311yescharacteristic
399C2×C4⋊C4C22×D1311yescharacteristic
400C2×C4⋊C4C22×D1311yescharacteristic
401C2×C4⋊C4C22×D1311yescharacteristic
402C2×C22⋊C4—21no—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C42—21no—
409C2×C42—261no—
410C2×C42—261no—
411C2×C42—261no—
412C2×C42C22×D1311yescharacteristic
413C2×C42C22×D1311yescharacteristic
414C2×C42C22×D1311yescharacteristic
415#106—262no—
416#106—521no—
417C4⋊C8—521no—
418#103—262no—
419#103—262no—
420#103—262no—
421#103—521no—
422#103—521no—
423#103—521no—
424#102—262no—
425#102—521no—
426C4×C8—521no—
427#95—21no—
428#95—21no—
429#95—261no—
430#95—261no—
431#95—261no—
432#95—261no—
433#95—261no—
434#95C22⋊D1311yescharacteristic
435#95C22⋊D1311yescharacteristic
436C2×C13—161no—
437C2×C13#246711yescharacteristic
438C2×C13#310311yescharacteristic
439C2×C13#312111yescharacteristic
440C2×C13#329811yescharacteristic
441C2×C13#330711yescharacteristic
442C2×C13#339211yescharacteristic
443C2×C13#340211yescharacteristic
444C24—21no—
445C2×Q8—132no—
446C2×Q8—132no—
447C2×Q8—261no—
448C2×Q8—261no—
449C2×Q8—261no—
450C2×Q8—261no—
451C2×Q8—261no—
452C2×Q8—261no—
453C2×Q8—261no—
454C2×Q8—261no—
455C2×Q8—261no—
456C2×Q8—261no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—261no—
467C22×C4—261no—
468C22×C4—261no—
469C22×C4—261no—
470C22×C4C2×C22⋊D1311yescharacteristic
471C22×C4C2×C22⋊D1311yescharacteristic
472C22×C4C2×C22⋊D1311yescharacteristic
473C22×C4C2×C22⋊D1311yescharacteristic
474C22×C4C2×C22⋊D1311yescharacteristic
475C22×C4C2×C22⋊D1311yescharacteristic
476C22×C4C23×D1311yescharacteristic
477SD16—524no—
478SD16—524no—
479C2×C8—132no—
480C2×C8—261no—
481C2×C8—261no—
482C2×C8—261no—
483C2×C8—261no—
484C2×C8—261no—
485C2×C8—261no—
486C2×C8—261no—
487C2×C8—261no—
488C2×C8—261no—
489C2×C8—261no—
490C2×C8—261no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—41no—
498C4⋊C4—42no—
499C4⋊C4—42no—
500C4⋊C4—81no—
501C4⋊C4—132no—
502C4⋊C4—264no—
503C4⋊C4—264no—
504C4⋊C4—261no—
505C4⋊C4—261no—
506C4⋊C4—261no—
507C4⋊C4—522no—
508C4⋊C4—522no—
509C4⋊C4#610514yescomplemented
510C22⋊C4—42no—
511C22⋊C4—42no—
512C22⋊C4—42no—
513C22⋊C4—42no—
514C22⋊C4—81no—
515C22⋊C4—81no—
516C42—21no—
517C42—21no—
518C42—21no—
519C42—21no—
520C42—21no—
521C42—21no—
522C42—42no—
523C42—522no—
524C42—522no—
525C42—522no—
526C13#2706611yescharacteristic, complemented, Sylow
527C23—41no—
528C23—41no—
529C23—41no—
530C23—41no—
531C23—41no—
532C23—41no—
533C23—41no—
534C23C22×C22⋊D1311yescharacteristic
535Q8—262no—
536Q8—262no—
537Q8—262no—
538Q8—262no—
539Q8—521no—
540Q8—521no—
541Q8—521no—
542Q8—521no—
543D4—41no—
544D4—41no—
545D4—41no—
546D4—41no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—262no—
572C2×C4—262no—
573C2×C4—262no—
574C2×C4—521no—
575C2×C4—521no—
576C2×C4—521no—
577C2×C4—521no—
578C2×C4—521no—
579C2×C4—521no—
580C2×C4—521no—
581C2×C4—521no—
582C2×C4—521no—
583C2×C4C2×#610512yes—
584C2×C4C2×#610512yes—
585C2×C4C2×#610512yes—
586C2×C4#41×D1311yescharacteristic
587C2×C4#41×D1311yescharacteristic
588C2×C4#41×D1311yescharacteristic
589C2×C4#41×D1311yescharacteristic
590C2×C4#8825611yescharacteristic
591C2×C4#8825611yescharacteristic
592C8—262no—
593C8—521no—
594C8—521no—
595C8—521no—
596C22—81no—
597C22—81no—
598C22—81no—
599C22—81no—
600C22—81no—
601C22—81no—
602C22—81no—
603C22C22×#610511yescharacteristic
604C22#1171952711yescharacteristic
605C22#1171953311yescharacteristic
606C22#1171953411yescharacteristic
607C22#1171953911yescharacteristic
608C22#1171954111yescharacteristic
609C22#1171954311yescharacteristic
610C4—22no—
611C4—22no—
612C4—22no—
613C4—41no—
614C4—41no—
615C4—41no—
616C4—81no—
617C4—81no—
618C4—81no—
619C4—522no—
620C4—522no—
621C4—522no—
622C4—1041no—
623C4#1171940911yescharacteristic
624C4#1171941011yescharacteristic
625C4#1171941111yescharacteristic
626C4#1171941411yescharacteristic
627C2—161no—
628C2#1311888311yescharacteristic
629C2#1312486311yescharacteristic
630C2#1312505911yescharacteristic
631C2#1312669511yescharacteristic
632C2#1312680611yescharacteristic
633C2#1312781711yescharacteristic
634C2#1312791111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2512C2
socleC23×C13C22×D4
prime radicalC22×D4×C13C23
hypercenter#2512D13
hypocenterC13#27066
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2512

Complements

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

NH ≅ G/Ntype
1. #13117892C2semidirect
2. #13116380C2semidirect
4. #13116082C2semidirect
7. #13115470C2semidirect
9. #13115411C2semidirect
10. #13115395C2semidirect
13. #13114838C2semidirect
14. C4×#88050C2semidirect
171. C13×C4⋊C4SD16semidirect
509. C4⋊C4#6105semidirect
526. C13#27066semidirect

Maximal subgroups

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

subgroupindex
#131178922
#131163802
#131161532
#131160822
#131159182
#131156892
#131154702
#131154602
#131154112
#131153952
#131151942
#131148382
C4×#880502
C13×#25122
#2706613