Finite Group Databasebeta

← #15882754

Subgroups — #15882754

Order 3328.

886 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718675C211yesmaximal, characteristic
2#13117783C211yesmaximal, characteristic, complemented
3#13115711C211yesmaximal, characteristic
4#13115701C211yesmaximal, characteristic
5#13115463C211yesmaximal, characteristic, complemented
6#13115460C211yesmaximal, characteristic, complemented
7#13115456C211yesmaximal, characteristic, complemented
8#13115453C211yesmaximal, characteristic, complemented
9#13115005C211yesmaximal, characteristic, complemented
10#13114843C211yesmaximal, characteristic, complemented
11#13114836C211yesmaximal, characteristic, complemented
12#13114734C211yesmaximal, characteristic, complemented
13C4×#88048C211yesmaximal, characteristic, complemented
14#13114711C211yesmaximal, characteristic, complemented
15C13×#2357C211yesmaximal, characteristic, complemented
16C2×C4×D4×C13C2211yescharacteristic
17C22×#6104C2211yescharacteristic
18C2×#88146—21no—
19C2×C4×D52C2211yescharacteristic
20C13×#390C2211yescharacteristic
21C13×#390C2211yescharacteristic
22C13×#388—21no—
23C13×#388—21no—
24C13×#382C2211yescharacteristic
25C13×#381—21no—
26C4×C13×C4⋊C4C2211yescharacteristic
27C4×C13×C4⋊C4C2211yescharacteristic
28C4×C13×C4⋊C4C2211yescharacteristic
29C4×C13×C22⋊C4—21no—
30C2×#88072C2211yescharacteristic
31C2×#88072C2211yescharacteristic
32C2×#88072C2211yescharacteristic
33#11718675C418yescomplemented
34#11718648—21no—
35C2×#88049C2211yescharacteristic
36C2×#88049C2211yescharacteristic
37C2×#88049C2211yescharacteristic
38C2×#88048C2211yescharacteristic
39C2×#88048C2211yescharacteristic
40C2×#88048C2211yescharacteristic
41C2×#88047C2211yescharacteristic
42C2×#88047C2211yescharacteristic
43#11718600C2211yescharacteristic
44#11718600C2211yescharacteristic
45#11718596C2211yescharacteristic
46C4×C4⋊Dic13C2211yescharacteristic
47C4×C4⋊Dic13C2211yescharacteristic
48C2×C4⋊#1055C2211yescharacteristic
49C2×#88043C2211yescharacteristic
50C2×#88043C2211yescharacteristic
51C2×C4×#1055C2211yescharacteristic
52#11718331—21no—
53#11718331—21no—
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718116C2211yescharacteristic
59#11718116C2211yescharacteristic
60C22×D4×C13C2311yescharacteristic
61C23×C4×C13—21no—
62C22×D52C2311yescharacteristic
63C22×C4×D13—21no—
64C4×D4×C13—22no—
65C4×D4×C13C2×C414yes—
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×C42×C13—21no—
77C2×C42×C13—21no—
78C2×C42×C13C2311yescharacteristic
79C2×C42×C13C2311yescharacteristic
80C2×C42×C13C2311yescharacteristic
81C2×#6104—22no—
82C2×#6104—22no—
83C2×#6104C2×C414yes—
84C2×#6103—21no—
85C2×#6103—21no—
86C2×#6103—21no—
87C2×#6103—21no—
88C2×#6103—21no—
89C2×C4⋊Dic13—21no—
90C2×C4⋊Dic13—21no—
91C2×C4⋊Dic13C2311yescharacteristic
92C2×C4⋊Dic13C2311yescharacteristic
93C2×C4⋊Dic13C2311yescharacteristic
94C2×C4×Dic13—21no—
95C2×C4×Dic13—21no—
96C22×#1055C2311yescharacteristic
97C22×#1055C2311yescharacteristic
98C22×#1055C2311yescharacteristic
99C22×#1055C2311yescharacteristic
100#88146—44no—
101C4×D52—22no—
102C4×D52C2×C414yes—
103C13×#95—21no—
104C13×#95—21no—
105C13×#95—21no—
106C13×#95—21no—
107C13×#95D411yescharacteristic
108C13×#95D411yescharacteristic
109#88072—41no—
110#88072—41no—
111#88072C2×C414yes—
112#88071—21no—
113#88071—21no—
114#88049—41no—
115#88049—41no—
116#88049C2×C414yes—
117#88048—22no—
118#88048—41no—
119#88048C2×C414yes—
120#88047—22no—
121#88047—41no—
122C4⋊#1055—22no—
123#88043—22no—
124#88043C2×C414yes—
125C4×#1055—22no—
126#22817—131nomaximal, Sylow
127C24×C13—21no—
128C23×D13—21no—
129C2×D4×C13—21no—
130C2×D4×C13—21no—
131C2×D4×C13—21no—
132C2×D4×C13—21no—
133C2×D4×C13—21no—
134C2×D4×C13C22×C412yes—
135C22×C4×C13—21no—
136C22×C4×C13—24no—
137C22×C4×C13—21no—
138C22×C4×C13—21no—
139C22×C4×C13—81no—
140C22×C4×C13—81no—
141C22×C4×C13C2×D411yescharacteristic
142C22×C4×C13C2×D411yescharacteristic
143C22×C4×C13C2×D411yescharacteristic
144C22×C4×C13C2×D411yescharacteristic
145C22×C4×C13C2×D411yescharacteristic
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13C2411yescharacteristic
148C22×Dic13—21no—
149C22×Dic13—21no—
150C22×Dic13—21no—
151C2×D52—21no—
152C2×D52—21no—
153C2×D52—21no—
154C2×D52—21no—
155C2×D52—21no—
156C2×D52C22×C412yes—
157C2×C4×D13—24no—
158C2×C4×D13—42no—
159C2×C4×D13—42no—
160C13×C4⋊C4—22no—
161C13×C4⋊C4—21no—
162C13×C4⋊C4—21no—
163C13×C4⋊C4—21no—
164C13×C4⋊C4—21no—
165C13×C4⋊C4—21no—
166C13×C4⋊C4—41no—
167C13×C4⋊C4C22×C412yes—
168C13×C22⋊C4—24no—
169C13×C22⋊C4—42no—
170C13×C22⋊C4—42no—
171C13×C22⋊C4—81no—
172C13×C22⋊C4—81no—
173C42×C13—21no—
174C42×C13—21no—
175C42×C13—21no—
176C42×C13—21no—
177C42×C13—81no—
178C42×C13—81no—
179C42×C13C22×C412yes—
180C42×C13#4112yes—
181#6104—28no—
182#6103—24no—
183#6103—42no—
184#6103—42no—
185#6103—81no—
186#6103—81no—
187C4⋊Dic13—21no—
188C4⋊Dic13—21no—
189C4⋊Dic13—21no—
190C4⋊Dic13—21no—
191C4⋊Dic13—21no—
192C4⋊Dic13—42no—
193C4⋊Dic13—81no—
194C4⋊Dic13C22×C412yes—
195C4×Dic13—42no—
196C4×Dic13—42no—
197C2×#1055—21no—
198C2×#1055—21no—
199C2×#1055—21no—
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055—21no—
203C2×#1055—21no—
204C2×#1055—21no—
205C2×#1055C22×C412yes—
206C2×#1055C22×C412yes—
207C2×#1055#4112yes—
208C2×#1055#4112yes—
209C2×#442—131no—
210#2357D1311yescharacteristic, complemented
211#2354—131no—
212#1972—131no—
213#1970—131no—
214#1926—131no—
215#1926—131no—
216#1925—131no—
217#1925—131no—
218#1847—131no—
219#1804—131no—
220#1802—131no—
221#1776—131no—
222C4×#106—131no—
223#1771—131no—
224C23×C13—22no—
225C23×C13—41no—
226C23×C13—41no—
227C23×C13—41no—
228C23×C13—41no—
229C23×C13—41no—
230C23×C13—41no—
231C23×C13C22×D411yescharacteristic
232C22×D13—22no—
233C22×D13—41no—
234C22×D13—41no—
235C22×D13—41no—
236C22×D13—41no—
237C22×D13—41no—
238C22×D13—41no—
239D4×C13—22no—
240D4×C13—22no—
241D4×C13—41no—
242D4×C13—41no—
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—22no—
250C2×C4×C13—21no—
251C2×C4×C13—21no—
252C2×C4×C13—21no—
253C2×C4×C13—21no—
254C2×C4×C13—21no—
255C2×C4×C13—21no—
256C2×C4×C13—21no—
257C2×C4×C13—21no—
258C2×C4×C13—21no—
259C2×C4×C13—41no—
260C2×C4×C13—41no—
261C2×C4×C13—41no—
262C2×C4×C13—41no—
263C2×C4×C13—41no—
264C2×C4×C13—41no—
265C2×C4×C13—41no—
266C2×C4×C13—41no—
267C2×C4×C13—84no—
268C2×C4×C13C4×D412yes—
269C2×C4×C13C4×D412yes—
270C2×C4×C13AGL(1,ℤ/8)12yes—
271C2×C4×C13C23×C411yescharacteristic
272C2×C4×C13C2×#4111yescharacteristic
273C2×C4×C13C2×#4111yescharacteristic
274C2×C4×C13C2×#4111yescharacteristic
275C2×C4×C13H(5,𝔽2)11yescharacteristic
276C2×C4×C132−1+411yescharacteristic
277C2×Dic13—22no—
278C2×Dic13—41no—
279C2×Dic13—41no—
280C2×Dic13—41no—
281C2×Dic13—41no—
282C2×Dic13—41no—
283C2×Dic13—41no—
284C2×Dic13—41no—
285C2×Dic13—41no—
286D52—22no—
287D52—22no—
288D52—41no—
289D52—41no—
290C4×D13—48no—
291#1055—22no—
292#1055—41no—
293#1055—41no—
294#1055#11714yescomplemented
295C22×D8—131no—
296C2×C4×D4—131no—
297C2×C4×D4C2×D1311yescharacteristic
298C2×#117—261no—
299#442—138no—
300C2×#107—131no—
301C2×#107—131no—
302C2×#106—131no—
303C2×#106—131no—
304C2×#106—131no—
305C2×C4⋊C8—131no—
306C2×#102—131no—
307C2×#102—131no—
308C2×#102—131no—
309C2×#102—131no—
310C2×#102—131no—
311C2×#102—131no—
312C2×#97—131no—
313C2×#97—131no—
314C2×C4×C8—131no—
315#390—131no—
316#390—131no—
317#390C2×D1311yescharacteristic
318#390C2×D1311yescharacteristic
319#388—21no—
320#388—21no—
321#388—261no—
322#388—261no—
323#384—131no—
324#382C2×D1311yescharacteristic
325#381—21no—
326#380—261no—
327C4×C4⋊C4—131no—
328C4×C4⋊C4—131no—
329C4×C4⋊C4C2×D1311yescharacteristic
330C4×C4⋊C4C2×D1311yescharacteristic
331C4×C4⋊C4C2×D1311yescharacteristic
332C4×C22⋊C4—21no—
333#340—131no—
334#340—131no—
335#340—131no—
336#340—131no—
337#336—131no—
338#336—131no—
339C22×C13—42no—
340C22×C13—42no—
341C22×C13—42no—
342C22×C13—81no—
343C22×C13—81no—
344C22×C13—81no—
345C22×C13—81no—
346C22×C13C2×C4×D411yescharacteristic
347C22×C13#54711yescharacteristic
348C22×C13#55011yescharacteristic
349C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
350C22×C13#57511yescharacteristic
351C22×C13#57611yescharacteristic
352C22×C13#57711yescharacteristic
353C2×D13—42no—
354C2×D13—42no—
355C2×D13—42no—
356C2×D13—81no—
357C2×D13—81no—
358C2×D13—81no—
359C2×D13—81no—
360C4×C13—22no—
361C4×C13—22no—
362C4×C13—22no—
363C4×C13—41no—
364C4×C13—41no—
365C4×C13—41no—
366C4×C13—42no—
367C4×C13—81no—
368C4×C13—81no—
369C4×C13C2×#11711yescharacteristic
370C4×C13#52011yescharacteristic
371C4×C13#55511yescharacteristic
372C4×C13#55611yescharacteristic
373Dic13—42no—
374Dic13—81no—
375Dic13—81no—
376C22×D4—131no—
377C22×D4C22×D1311yescharacteristic
378C23×C4—21no—
379C23×C4—261no—
380C2×D8—134no—
381C2×D8—262no—
382C2×D8—262no—
383C22×C8—131no—
384C22×C8—131no—
385C22×C8—131no—
386C22×C8—131no—
387C4×D4—22no—
388C4×D4—134no—
389C4×D4—262no—
390C4×D4C4×D1314yes—
391#117—524no—
392C2×C4⋊C4—131no—
393C2×C4⋊C4—131no—
394C2×C4⋊C4—131no—
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—261no—
408C2×C22⋊C4—261no—
409C2×C22⋊C4—261no—
410C2×C22⋊C4—261no—
411C2×C22⋊C4—261no—
412C2×C42—21no—
413C2×C42—21no—
414C2×C42—261no—
415C2×C42—261no—
416C2×C42C22×D1311yescharacteristic
417C2×C42C22×D1311yescharacteristic
418C2×C42C22×D1311yescharacteristic
419#107—262no—
420#107—521no—
421#106—134no—
422#106—262no—
423#106—521no—
424C4⋊C8—262no—
425#102—134no—
426#102—134no—
427#102—521no—
428#102—521no—
429#102—521no—
430#102—521no—
431#97—134no—
432#97—262no—
433C4×C8—262no—
434#95—21no—
435#95—21no—
436#95—21no—
437#95—21no—
438#95—261no—
439#95—261no—
440#95C22⋊D1311yescharacteristic
441#95C22⋊D1311yescharacteristic
442C2×C13—82no—
443C2×C13#235411yescharacteristic
444C2×C13C4×AGL(1,ℤ/8)11yescharacteristic
445C2×C13#294611yescharacteristic
446C2×C13#334511yescharacteristic
447C2×C13#334711yescharacteristic
448C2×C13#339911yescharacteristic
449C2×C13#340111yescharacteristic
450D13—82no—
451C24—21no—
452C24—261no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—132no—
459C2×D4—261no—
460C2×D4—261no—
461C2×D4—261no—
462C2×D4—261no—
463C2×D4—261no—
464C2×D4C2×C4×D1312yes—
465C22×C4—21no—
466C22×C4—24no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—81no—
470C22×C4—81no—
471C22×C4—261no—
472C22×C4—264no—
473C22×C4—261no—
474C22×C4—261no—
475C22×C4—522no—
476C22×C4—522no—
477C22×C4C2×C22⋊D1311yescharacteristic
478C22×C4C2×C22⋊D1311yescharacteristic
479C22×C4C2×C22⋊D1311yescharacteristic
480C22×C4C2×C22⋊D1311yescharacteristic
481C22×C4C2×C22⋊D1311yescharacteristic
482C22×C4C2×C22⋊D1311yescharacteristic
483C22×C4C23×D1311yescharacteristic
484D8—268no—
485C2×C8—132no—
486C2×C8—132no—
487C2×C8—132no—
488C2×C8—132no—
489C2×C8—261no—
490C2×C8—261no—
491C2×C8—261no—
492C2×C8—261no—
493C2×C8—261no—
494C2×C8—261no—
495C2×C8—261no—
496C2×C8—261no—
497C4⋊C4—22no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—41no—
504C4⋊C4—132no—
505C4⋊C4—261no—
506C4⋊C4—261no—
507C4⋊C4—261no—
508C4⋊C4—261no—
509C4⋊C4—261no—
510C4⋊C4—522no—
511C4⋊C4—1041no—
512C4⋊C4C2×C4×D1312yes—
513C22⋊C4—24no—
514C22⋊C4—42no—
515C22⋊C4—42no—
516C22⋊C4—81no—
517C22⋊C4—81no—
518C22⋊C4—264no—
519C22⋊C4—522no—
520C22⋊C4—522no—
521C22⋊C4—1041no—
522C22⋊C4—1041no—
523C42—21no—
524C42—21no—
525C42—21no—
526C42—21no—
527C42—81no—
528C42—81no—
529C42—522no—
530C42—522no—
531C42C2×C4×D1312yes—
532C42#612712yes—
533C13#2281711yescharacteristic, complemented, Sylow
534C23—22no—
535C23—41no—
536C23—41no—
537C23—41no—
538C23—41no—
539C23—41no—
540C23—41no—
541C23—262no—
542C23—521no—
543C23—521no—
544C23—521no—
545C23—521no—
546C23—521no—
547C23—521no—
548C23C22×C22⋊D1311yescharacteristic
549D4—22no—
550D4—22no—
551D4—41no—
552D4—41no—
553D4—262no—
554D4—262no—
555D4—521no—
556D4—521no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—22no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—84no—
582C2×C4—262no—
583C2×C4—528no—
584C2×C4—521no—
585C2×C4—521no—
586C2×C4—521no—
587C2×C4—521no—
588C2×C4—521no—
589C2×C4—521no—
590C2×C4—521no—
591C2×C4—521no—
592C2×C4C4×C22⋊D1312yes—
593C2×C4C4×C22⋊D1312yes—
594C2×C4#8820312yes—
595C2×C4C22×C4×D1311yescharacteristic
596C2×C4C2×#612711yescharacteristic
597C2×C4#41×D1311yescharacteristic
598C2×C4#41×D1311yescharacteristic
599C2×C4#8825611yescharacteristic
600C2×C4#8825711yescharacteristic
601C8—134no—
602C8—262no—
603C8—521no—
604C8—521no—
605C22—42no—
606C22—42no—
607C22—42no—
608C22—81no—
609C22—81no—
610C22—81no—
611C22—81no—
612C22—522no—
613C22—522no—
614C22—522no—
615C22—1041no—
616C22—1041no—
617C22—1041no—
618C22—1041no—
619C22C2×C4×C22⋊D1311yescharacteristic
620C22C2×#8820311yescharacteristic
621C22#1171952711yescharacteristic
622C22#1171952911yescharacteristic
623C22#1171953911yescharacteristic
624C22#1171954011yescharacteristic
625C22#1171954111yescharacteristic
626C4—22no—
627C4—22no—
628C4—22no—
629C4—42no—
630C4—41no—
631C4—41no—
632C4—41no—
633C4—81no—
634C4—81no—
635C4—522no—
636C4—1041no—
637C4—1041no—
638C4D13×#11711yescharacteristic
639C4#1171922811yescharacteristic
640C4#1171923711yescharacteristic
641C4#1171923811yescharacteristic
642C2—82no—
643C2—1042no—
644C2#1311778611yescharacteristic
645C2C4×#8820311yescharacteristic
646C2#1312366811yescharacteristic
647C2#1312730011yescharacteristic
648C2#1312733011yescharacteristic
649C2#1312787411yescharacteristic
650C2#1312789611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#2357C2
socleC23×C13C22×D4
prime radicalC22×#6104C22
cosocleC22×C4×C13C24
hypercenter#2357D13
hypocenterC13#22817
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2357

Complements

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

NH ≅ G/Ntype
2. #13117783C2semidirect
5. #13115463C2semidirect
6. #13115460C2semidirect
7. #13115456C2semidirect
8. #13115453C2semidirect
9. #13115005C2semidirect
10. #13114843C2semidirect
11. #13114836C2semidirect
12. #13114734C2semidirect
13. C4×#88048C2semidirect
14. #13114711C2semidirect
15. C13×#2357C2semidirect
33. #11718675C4semidirect
210. #2357D13semidirect
294. #1055#117semidirect
533. C13#22817semidirect

Maximal subgroups

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

subgroupindex
C2×#117186752
#131177832
#131157112
#131157012
#131154632
#131154602
#131154562
#131154532
#131150052
#131148432
#131148362
#131147342
C4×#880482
#131147112
C13×#23572
#2281713