Finite Group Databasebeta

← #15867252

Subgroups — #15867252

Order 3328.

874 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718679C211yesmaximal, characteristic
2#13117313C211yesmaximal, characteristic, complemented
3#13115716C211yesmaximal, characteristic
4#13115689C211yesmaximal, characteristic
5#13115571C211yesmaximal, characteristic, complemented
6#13115566C211yesmaximal, characteristic, complemented
7#13115536C211yesmaximal, characteristic
8#13115525C211yesmaximal, characteristic, complemented
9#13115522C211yesmaximal, characteristic
10#13115511C211yesmaximal, characteristic, complemented
11#13114734C211yesmaximal, characteristic, complemented
12#13114669C211yesmaximal, characteristic, complemented
13#13114661C211yesmaximal, characteristic
14C4×#88043C211yesmaximal, characteristic, complemented
15C13×#2293C211yesmaximal, characteristic
16C2×C4×D4×C13C2211yescharacteristic
17C2×C13×#117—21no—
18C22×#6105C2211yescharacteristic
19C2×C4×Dic26C2211yescharacteristic
20C13×#390C2211yescharacteristic
21C13×#390C2211yescharacteristic
22C13×#389C2211yescharacteristic
23C13×#389C2211yescharacteristic
24C13×#388—21no—
25C13×#388—21no—
26C4×C13×C4⋊C4C2211yescharacteristic
27C4×C13×C22⋊C4—21no—
28C43×C13C2211yescharacteristic
29C2×#88072C2211yescharacteristic
30C2×#88072C2211yescharacteristic
31C2×#88072C2211yescharacteristic
32#11718679C418yescomplemented
33C2×#88050C2211yescharacteristic
34C2×#88050C2211yescharacteristic
35C2×#88050C2211yescharacteristic
36C2×#88048C2211yescharacteristic
37C2×#88047C2211yescharacteristic
38C2×#88047C2211yescharacteristic
39C4×C4⋊Dic13C2211yescharacteristic
40#11718594—21no—
41#11718594—21no—
42#11718593—21no—
43C4×#6101—21no—
44#11718590C2211yescharacteristic
45#11718590C2211yescharacteristic
46#11718589C2211yescharacteristic
47#11718589C2211yescharacteristic
48C2×#88043C2211yescharacteristic
49C2×#88043C2211yescharacteristic
50C2×#88043C2211yescharacteristic
51C2×#88043C2211yescharacteristic
52C2×C4×#1055C2211yescharacteristic
53C2×C4×#1055C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60C22×D4×C13C2311yescharacteristic
61C23×C4×C13—21no—
62C22×Dic26C2311yescharacteristic
63C4×D4×C13—22no—
64C4×D4×C13C2×C414yes—
65C13×#117—44no—
66C2×C13×C4⋊C4—21no—
67C2×C13×C4⋊C4—21no—
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×C13D411yescharacteristic
78C2×C42×C13D411yescharacteristic
79C2×C42×C13D411yescharacteristic
80C2×C42×C13D411yescharacteristic
81C2×C42×C13C2311yescharacteristic
82C2×C42×C13C2311yescharacteristic
83C2×C42×C13C2311yescharacteristic
84C2×#6105—22no—
85C2×#6105—22no—
86C2×#6105C2×C414yes—
87C2×C4⋊Dic13C2311yescharacteristic
88C2×C4⋊Dic13C2311yescharacteristic
89C2×C4⋊Dic13C2311yescharacteristic
90C2×#6101—21no—
91C2×#6101—21no—
92C2×#6101—21no—
93C2×C4×Dic13—21no—
94C2×C4×Dic13—21no—
95C22×#1055C2311yescharacteristic
96C22×#1055C2311yescharacteristic
97C22×#1055C2311yescharacteristic
98C22×#1055C2311yescharacteristic
99C4×Dic26—22no—
100C4×Dic26C2×C414yes—
101C13×#95—21no—
102C13×#95—21no—
103C13×#95—21no—
104#88072—22no—
105#88072—22no—
106#88072C2×C414yes—
107#88071—21no—
108#88071—21no—
109#88071—21no—
110#88071—21no—
111#88071—21no—
112#88071—21no—
113#88071—21no—
114#88050—22no—
115#88050—22no—
116#88050C2×C414yes—
117#88048—22no—
118#88047—22no—
119#88047C2×C414yes—
120#88043—22no—
121#88043—22no—
122#88043—22no—
123#88043C2×C414yes—
124C4×#1055—22no—
125C4×#1055—22no—
126#21288—131nomaximal, Sylow
127C24×C13—21no—
128C2×D4×C13—21no—
129C2×D4×C13—21no—
130C2×D4×C13—21no—
131C2×D4×C13—21no—
132C2×D4×C13—21no—
133C2×D4×C13C22×C412yes—
134C22×C4×C13—21no—
135C22×C4×C13—24no—
136C22×C4×C13—21no—
137C22×C4×C13—21no—
138C22×C4×C13—42no—
139C22×C4×C13—42no—
140C22×C4×C13C2×D411yescharacteristic
141C22×C4×C13C2×D411yescharacteristic
142C22×C4×C13C2×D411yescharacteristic
143C22×C4×C13C2×D411yescharacteristic
144C22×C4×C13C2×D411yescharacteristic
145C22×C4×C13C2×D411yescharacteristic
146C22×C4×C13C2411yescharacteristic
147C22×Dic13—21no—
148C22×Dic13—21no—
149C22×Dic13—21no—
150C22×Dic13—21no—
151C2×Dic26—21no—
152C2×Dic26—21no—
153C2×Dic26—21no—
154C2×Dic26—21no—
155C2×Dic26—21no—
156C2×Dic26C22×C412yes—
157C13×C4⋊C4—21no—
158C13×C4⋊C4—21no—
159C13×C4⋊C4—21no—
160C13×C4⋊C4—21no—
161C13×C4⋊C4—21no—
162C13×C4⋊C4—42no—
163C13×C4⋊C4—42no—
164C13×C4⋊C4C22×C412yes—
165C13×C22⋊C4—24no—
166C13×C22⋊C4—42no—
167C13×C22⋊C4—42no—
168C13×C22⋊C4—42no—
169C13×C22⋊C4—42no—
170C42×C13—22no—
171C42×C13—22no—
172C42×C13—21no—
173C42×C13—21no—
174C42×C13—21no—
175C42×C13—21no—
176C42×C13—41no—
177C42×C13—41no—
178C42×C13—42no—
179C42×C13C22×C412yes—
180C42×C13#4112yes—
181#6105—28no—
182C4⋊Dic13—21no—
183C4⋊Dic13—21no—
184C4⋊Dic13—21no—
185C4⋊Dic13—21no—
186C4⋊Dic13—21no—
187C4⋊Dic13C22×C412yes—
188#6101—24no—
189#6101—42no—
190#6101—42no—
191C4×Dic13—24no—
192C4×Dic13—42no—
193C2×#1055—21no—
194C2×#1055—21no—
195C2×#1055—21no—
196C2×#1055—21no—
197C2×#1055—21no—
198C2×#1055—21no—
199C2×#1055C22×C412yes—
200C2×#1055C22×C412yes—
201C2×#1055#4112yes—
202C2×#1055#4112yes—
203C2×#1055#4112yes—
204C2×#1055#4112yes—
205C2×#440—131no—
206#2295—131no—
207#2293D1311yescharacteristic
208#1973—131no—
209#1968—131no—
210#1943—131no—
211#1942—131no—
212#1936—131no—
213#1935—131no—
214#1934—131no—
215#1933—131no—
216#1776—131no—
217#1763—131no—
218#1762—131no—
219C4×#97—131no—
220C23×C13—22no—
221C23×C13—41no—
222C23×C13—41no—
223C23×C13—41no—
224C23×C13—41no—
225C23×C13—41no—
226C23×C13—41no—
227C23×C13C22×D411yescharacteristic
228D4×C13—22no—
229D4×C13—22no—
230D4×C13—41no—
231D4×C13—41no—
232C2×C4×C13—21no—
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—22no—
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—48no—
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—41no—
256C2×C4×C13C4×D412yes—
257C2×C4×C13C4×D412yes—
258C2×C4×C13AGL(1,ℤ/8)12yes—
259C2×C4×C13#13712yes—
260C2×C4×C13C23×C411yescharacteristic
261C2×C4×C13C2×#4111yescharacteristic
262C2×C4×C13C2×#4111yescharacteristic
263C2×C4×C13C2×#4111yescharacteristic
264C2×C4×C13C2×#4111yescharacteristic
265C2×C4×C13C2×#4111yescharacteristic
266C2×Dic13—22no—
267C2×Dic13—22no—
268C2×Dic13—41no—
269C2×Dic13—41no—
270C2×Dic13—41no—
271C2×Dic13—41no—
272C2×Dic13—41no—
273C2×Dic13—41no—
274C2×Dic13—41no—
275C2×Dic13—41no—
276C2×Dic13—41no—
277C2×Dic13—41no—
278Dic26—22no—
279Dic26—22no—
280Dic26—41no—
281Dic26—41no—
282#1055—22no—
283#1055—22no—
284#1055—22no—
285#1055#11714yescomplemented
286C22×SD16—131no—
287C2×C4×Q8—131no—
288C2×C4×D4C2×D1311yescharacteristic
289C2×#117—21no—
290#440—138no—
291C2×#107—131no—
292C2×#107—131no—
293C2×#106—131no—
294C2×#103—131no—
295C2×#103—131no—
296C2×#103—131no—
297C2×#102—131no—
298C2×#102—131no—
299C2×#102—131no—
300C2×#97—131no—
301C2×#97—131no—
302C2×#97—131no—
303C2×#97—131no—
304C2×C4×C8—131no—
305C2×C4×C8—131no—
306#391—131no—
307#391—131no—
308#390C2×D1311yescharacteristic
309#390C2×D1311yescharacteristic
310#389—131no—
311#389—131no—
312#389C2×D1311yescharacteristic
313#389C2×D1311yescharacteristic
314#388—21no—
315#388—21no—
316#387—261no—
317#387—261no—
318C4×C4⋊C4—131no—
319C4×C4⋊C4—261no—
320C4×C4⋊C4C2×D1311yescharacteristic
321C4×C22⋊C4—21no—
322#376—261no—
323C43C2×D1311yescharacteristic
324#340—131no—
325#340—131no—
326#340—131no—
327#340—131no—
328#340—131no—
329#340—131no—
330C22×C13—42no—
331C22×C13—42no—
332C22×C13—42no—
333C22×C13—81no—
334C22×C13—81no—
335C22×C13—81no—
336C22×C13—81no—
337C22×C13C2×C4×D411yescharacteristic
338C22×C13#53211yescharacteristic
339C22×C13#53211yescharacteristic
340C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
341C22×C13C2×#13711yescharacteristic
342C22×C13#57511yescharacteristic
343C22×C13#57511yescharacteristic
344C4×C13—22no—
345C4×C13—22no—
346C4×C13—22no—
347C4×C13—22no—
348C4×C13—41no—
349C4×C13—41no—
350C4×C13—42no—
351C4×C13—81no—
352C4×C13—81no—
353C4×C13C2×#11711yescharacteristic
354C4×C13C4×#4111yescharacteristic
355C4×C13#52911yescharacteristic
356C4×C13#52911yescharacteristic
357Dic13—42no—
358Dic13—42no—
359Dic13—81no—
360Dic13—81no—
361C22×Q8—131no—
362C22×D4C22×D1311yescharacteristic
363C23×C4—21no—
364C2×SD16—134no—
365C2×SD16—262no—
366C2×SD16—262no—
367C22×C8—131no—
368C22×C8—131no—
369C22×C8—131no—
370C22×C8—131no—
371C4×Q8—134no—
372C4×Q8—262no—
373C4×D4—22no—
374C4×D4C4×D1314yes—
375#117—44no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
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×D1311yescharacteristic
385C2×C4⋊C4C22×D1311yescharacteristic
386C2×C4⋊C4C22×D1311yescharacteristic
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C42—21no—
393C2×C42—261no—
394C2×C42—261no—
395C2×C42C22⋊D1311yescharacteristic
396C2×C42C22⋊D1311yescharacteristic
397C2×C42C22⋊D1311yescharacteristic
398C2×C42C22⋊D1311yescharacteristic
399C2×C42C22×D1311yescharacteristic
400C2×C42C22×D1311yescharacteristic
401C2×C42C22×D1311yescharacteristic
402#107—134no—
403#107—262no—
404#106—262no—
405#103—134no—
406#103—262no—
407#103—262no—
408#102—134no—
409#102—262no—
410#102—262no—
411#97—134no—
412#97—262no—
413#97—262no—
414#97—262no—
415C4×C8—262no—
416C4×C8—262no—
417#95—21no—
418#95—21no—
419#95—21no—
420#95—261no—
421#95—261no—
422#95—261no—
423#95—261no—
424#95—261no—
425#95—261no—
426#95—261no—
427C2×C13—82no—
428C2×C13#229311yescharacteristic
429C2×C13C4×AGL(1,ℤ/8)11yescharacteristic
430C2×C13C4×#13711yescharacteristic
431C2×C13#318011yescharacteristic
432C2×C13#318111yescharacteristic
433C2×C13#318211yescharacteristic
434C2×C13#318311yescharacteristic
435C24—21no—
436C2×Q8—132no—
437C2×Q8—261no—
438C2×Q8—261no—
439C2×Q8—261no—
440C2×Q8—261no—
441C2×Q8—261no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4C2×C4×D1312yes—
448C22×C4—21no—
449C22×C4—24no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—42no—
453C22×C4—42no—
454C22×C4—261no—
455C22×C4—261no—
456C22×C4—261no—
457C22×C4—261no—
458C22×C4C2×C22⋊D1311yescharacteristic
459C22×C4C2×C22⋊D1311yescharacteristic
460C22×C4C2×C22⋊D1311yescharacteristic
461C22×C4C2×C22⋊D1311yescharacteristic
462C22×C4C2×C22⋊D1311yescharacteristic
463C22×C4C2×C22⋊D1311yescharacteristic
464C22×C4C23×D1311yescharacteristic
465SD16—268no—
466C2×C8—132no—
467C2×C8—132no—
468C2×C8—132no—
469C2×C8—132no—
470C2×C8—132no—
471C2×C8—132no—
472C2×C8—261no—
473C2×C8—261no—
474C2×C8—261no—
475C2×C8—261no—
476C2×C8—261no—
477C2×C8—261no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—42no—
484C4⋊C4—42no—
485C4⋊C4—132no—
486C4⋊C4—264no—
487C4⋊C4—261no—
488C4⋊C4—261no—
489C4⋊C4—261no—
490C4⋊C4—261no—
491C4⋊C4—261no—
492C4⋊C4—522no—
493C4⋊C4—522no—
494C4⋊C4C2×C4×D1312yes—
495C22⋊C4—24no—
496C22⋊C4—42no—
497C22⋊C4—42no—
498C22⋊C4—42no—
499C22⋊C4—42no—
500C42—22no—
501C42—22no—
502C42—21no—
503C42—21no—
504C42—21no—
505C42—21no—
506C42—41no—
507C42—41no—
508C42—42no—
509C42—264no—
510C42—522no—
511C42C2×C4×D1312yes—
512C42#612712yes—
513C13#2128811yescharacteristic, complemented, Sylow
514C23—22no—
515C23—41no—
516C23—41no—
517C23—41no—
518C23—41no—
519C23—41no—
520C23—41no—
521C23C22×C22⋊D1311yescharacteristic
522Q8—262no—
523Q8—262no—
524Q8—521no—
525Q8—521no—
526D4—22no—
527D4—22no—
528D4—41no—
529D4—41no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—22no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—48no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—262no—
555C2×C4—262no—
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×C4—521no—
565C2×C4—521no—
566C2×C4C4×C22⋊D1312yes—
567C2×C4C4×C22⋊D1312yes—
568C2×C4#8818612yes—
569C2×C4#8820512yes—
570C2×C4C22×C4×D1311yescharacteristic
571C2×C4C2×#612711yescharacteristic
572C2×C4#41×D1311yescharacteristic
573C2×C4#41×D1311yescharacteristic
574C2×C4#41×D1311yescharacteristic
575C2×C4#41×D1311yescharacteristic
576C8—134no—
577C8—262no—
578C8—262no—
579C8—262no—
580C22—42no—
581C22—42no—
582C22—42no—
583C22—81no—
584C22—81no—
585C22—81no—
586C22—81no—
587C22C2×C4×C22⋊D1311yescharacteristic
588C22C2×#8818611yescharacteristic
589C22#1171952711yescharacteristic
590C22#1171952711yescharacteristic
591C22C2×#8820511yescharacteristic
592C22#1171953711yescharacteristic
593C22#1171953711yescharacteristic
594C4—22no—
595C4—22no—
596C4—22no—
597C4—22no—
598C4—42no—
599C4—41no—
600C4—41no—
601C4—81no—
602C4—81no—
603C4—522no—
604C4—522no—
605C4—1041no—
606C4—1041no—
607C4D13×#11711yescharacteristic
608C4#1171922711yescharacteristic
609C4#1171923311yescharacteristic
610C4#1171923311yescharacteristic
611C2—82no—
612C2#1311729511yescharacteristic
613C2C4×#8818611yescharacteristic
614C2C4×#8820511yescharacteristic
615C2#1312552811yescharacteristic
616C2#1312554611yescharacteristic
617C2#1312555011yescharacteristic
618C2#1312555911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#2293C2
socleC23×C13C22×D4
prime radicalC22×D4×C13C23
cosocleC22×C4×C13C24
hypercenter#2293D13
hypocenterC13#21288
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C43 ◁ #2293

Complements

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

NH ≅ G/Ntype
2. #13117313C2semidirect
5. #13115571C2semidirect
6. #13115566C2semidirect
8. #13115525C2semidirect
10. #13115511C2semidirect
11. #13114734C2semidirect
12. #13114669C2semidirect
14. C4×#88043C2semidirect
32. #11718679C4semidirect
285. #1055#117semidirect
513. C13#21288semidirect

Maximal subgroups

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

subgroupindex
C2×#117186792
#131173132
#131157162
#131156892
#131155712
#131155662
#131155362
#131155252
#131155222
#131155112
#131147342
#131146692
#131146612
C4×#880432
C13×#22932
#2128813