Finite Group Databasebeta

← #15867230

Subgroups — #15867230

Order 3328.

950 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718675C211yesmaximal, characteristic
2#13117300C211yesmaximal, characteristic, complemented
3#13115711C211yesmaximal, characteristic
4#13115701C211yesmaximal, characteristic
5#13115576C211yesmaximal, characteristic, complemented
6#13115561C211yesmaximal, characteristic, complemented
7#13115536C211yesmaximal, characteristic, complemented
8#13115532C211yesmaximal, characteristic, complemented
9#13115522C211yesmaximal, characteristic, complemented
10#13115518C211yesmaximal, characteristic, complemented
11#13114734C211yesmaximal, characteristic, complemented
12#13114664C211yesmaximal, characteristic, complemented
13#13114661C211yesmaximal, characteristic, complemented
14C4×#88043C211yesmaximal, characteristic, complemented
15C13×#2293C211yesmaximal, characteristic, complemented
16C2×C4×D4×C13C2211yescharacteristic
17C2×C13×#117—21no—
18C22×#6104C2211yescharacteristic
19C2×C4×D52C2211yescharacteristic
20C2×#88126—21no—
21C13×#390C2211yescharacteristic
22C13×#390C2211yescharacteristic
23C13×#389C2211yescharacteristic
24C13×#389C2211yescharacteristic
25C13×#388—21no—
26C13×#388—21no—
27C4×C13×C4⋊C4C2211yescharacteristic
28C4×C13×C22⋊C4—21no—
29C43×C13C2211yescharacteristic
30C2×#88072C2211yescharacteristic
31C2×#88072C2211yescharacteristic
32C2×#88072C2211yescharacteristic
33#11718675C418yescomplemented
34C2×#88049C2211yescharacteristic
35C2×#88049C2211yescharacteristic
36C2×#88049C2211yescharacteristic
37C2×#88048C2211yescharacteristic
38C2×#88048C2211yescharacteristic
39C2×#88047C2211yescharacteristic
40#11718601—21no—
41#11718601—21no—
42#11718600C2211yescharacteristic
43#11718600C2211yescharacteristic
44C4×#6103—21no—
45C4×C4⋊Dic13C2211yescharacteristic
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×D52C2311yescharacteristic
63C22×C4×D13—21no—
64C4×D4×C13—22no—
65C4×D4×C13C2×C414yes—
66C13×#117—44no—
67C2×C13×C4⋊C4—21no—
68C2×C13×C4⋊C4—21no—
69C2×C13×C4⋊C4C2311yescharacteristic
70C2×C13×C4⋊C4C2311yescharacteristic
71C2×C13×C4⋊C4C2311yescharacteristic
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×C13D411yescharacteristic
79C2×C42×C13D411yescharacteristic
80C2×C42×C13D411yescharacteristic
81C2×C42×C13D411yescharacteristic
82C2×C42×C13C2311yescharacteristic
83C2×C42×C13C2311yescharacteristic
84C2×C42×C13C2311yescharacteristic
85C2×#6104—22no—
86C2×#6104—22no—
87C2×#6104C2×C414yes—
88C2×#6103—21no—
89C2×#6103—21no—
90C2×#6103—21no—
91C2×#6103—21no—
92C2×#6103—21no—
93C2×C4⋊Dic13C2311yescharacteristic
94C2×C4⋊Dic13C2311yescharacteristic
95C2×C4⋊Dic13C2311yescharacteristic
96C2×#6101—21no—
97C2×#6101—21no—
98C2×C4×Dic13—21no—
99C22×#1055C2311yescharacteristic
100C22×#1055C2311yescharacteristic
101C22×#1055C2311yescharacteristic
102C22×#1055C2311yescharacteristic
103C4×D52—22no—
104C4×D52C2×C414yes—
105#88126—44no—
106C13×#95—21no—
107C13×#95—21no—
108C13×#95—21no—
109#88072—22no—
110#88072—22no—
111#88072C2×C414yes—
112#88071—21no—
113#88071—21no—
114#88071—21no—
115#88049—22no—
116#88049—22no—
117#88049C2×C414yes—
118#88048—22no—
119#88048C2×C414yes—
120#88047—22no—
121#88043—22no—
122#88043—22no—
123#88043—22no—
124#88043C2×C414yes—
125C4×#1055—22no—
126C4×#1055—22no—
127#21286—131nomaximal, Sylow
128C24×C13—21no—
129C23×D13—21no—
130C2×D4×C13—21no—
131C2×D4×C13—21no—
132C2×D4×C13—21no—
133C2×D4×C13—21no—
134C2×D4×C13—21no—
135C2×D4×C13C22×C412yes—
136C22×C4×C13—21no—
137C22×C4×C13—24no—
138C22×C4×C13—21no—
139C22×C4×C13—21no—
140C22×C4×C13—42no—
141C22×C4×C13—42no—
142C22×C4×C13C2×D411yescharacteristic
143C22×C4×C13C2×D411yescharacteristic
144C22×C4×C13C2×D411yescharacteristic
145C22×C4×C13C2×D411yescharacteristic
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13C2×D411yescharacteristic
148C22×C4×C13C2411yescharacteristic
149C22×Dic13—21no—
150C22×Dic13—21no—
151C22×Dic13—21no—
152C2×D52—21no—
153C2×D52—21no—
154C2×D52—21no—
155C2×D52—21no—
156C2×D52—21no—
157C2×D52C22×C412yes—
158C2×C4×D13—24no—
159C2×C4×D13—42no—
160C2×C4×D13—42no—
161C13×C4⋊C4—21no—
162C13×C4⋊C4—21no—
163C13×C4⋊C4—21no—
164C13×C4⋊C4—21no—
165C13×C4⋊C4—21no—
166C13×C4⋊C4—42no—
167C13×C4⋊C4—42no—
168C13×C4⋊C4C22×C412yes—
169C13×C22⋊C4—24no—
170C13×C22⋊C4—42no—
171C13×C22⋊C4—42no—
172C13×C22⋊C4—42no—
173C13×C22⋊C4—42no—
174C42×C13—22no—
175C42×C13—22no—
176C42×C13—21no—
177C42×C13—21no—
178C42×C13—21no—
179C42×C13—21no—
180C42×C13—41no—
181C42×C13—41no—
182C42×C13—42no—
183C42×C13C22×C412yes—
184C42×C13#4112yes—
185#6104—28no—
186#6103—24no—
187#6103—42no—
188#6103—42no—
189#6103—42no—
190#6103—42no—
191C4⋊Dic13—21no—
192C4⋊Dic13—21no—
193C4⋊Dic13—21no—
194C4⋊Dic13—21no—
195C4⋊Dic13—21no—
196C4⋊Dic13C22×C412yes—
197#6101—42no—
198#6101—42no—
199C4×Dic13—42no—
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055—21no—
203C2×#1055—21no—
204C2×#1055—21no—
205C2×#1055—21no—
206C2×#1055C22×C412yes—
207C2×#1055C22×C412yes—
208C2×#1055#4112yes—
209C2×#1055#4112yes—
210C2×#1055#4112yes—
211C2×#1055#4112yes—
212C2×#442—131no—
213#2293—131no—
214#2293D1311yescharacteristic, complemented
215#1972—131no—
216#1970—131no—
217#1944—131no—
218#1941—131no—
219#1936—131no—
220#1936—131no—
221#1934—131no—
222#1934—131no—
223#1776—131no—
224#1762—131no—
225#1762—131no—
226C4×#97—131no—
227C23×C13—22no—
228C23×C13—41no—
229C23×C13—41no—
230C23×C13—41no—
231C23×C13—41no—
232C23×C13—41no—
233C23×C13—41no—
234C23×C13C22×D411yescharacteristic
235C22×D13—22no—
236C22×D13—41no—
237C22×D13—41no—
238C22×D13—41no—
239C22×D13—41no—
240C22×D13—41no—
241C22×D13—41no—
242D4×C13—22no—
243D4×C13—22no—
244D4×C13—41no—
245D4×C13—41no—
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—21no—
253C2×C4×C13—21no—
254C2×C4×C13—22no—
255C2×C4×C13—21no—
256C2×C4×C13—21no—
257C2×C4×C13—21no—
258C2×C4×C13—21no—
259C2×C4×C13—21no—
260C2×C4×C13—21no—
261C2×C4×C13—48no—
262C2×C4×C13—41no—
263C2×C4×C13—41no—
264C2×C4×C13—41no—
265C2×C4×C13—41no—
266C2×C4×C13—41no—
267C2×C4×C13—41no—
268C2×C4×C13—41no—
269C2×C4×C13—41no—
270C2×C4×C13C4×D412yes—
271C2×C4×C13C4×D412yes—
272C2×C4×C13AGL(1,ℤ/8)12yes—
273C2×C4×C13AGL(1,ℤ/8)12yes—
274C2×C4×C13C23×C411yescharacteristic
275C2×C4×C13C2×#4111yescharacteristic
276C2×C4×C13C2×#4111yescharacteristic
277C2×C4×C13C2×#4111yescharacteristic
278C2×C4×C13C2×#4111yescharacteristic
279C2×C4×C13C2×#4111yescharacteristic
280C2×Dic13—22no—
281C2×Dic13—41no—
282C2×Dic13—41no—
283C2×Dic13—41no—
284C2×Dic13—41no—
285C2×Dic13—41no—
286C2×Dic13—41no—
287C2×Dic13—41no—
288C2×Dic13—41no—
289D52—22no—
290D52—22no—
291D52—41no—
292D52—41no—
293C4×D13—48no—
294#1055—22no—
295#1055—22no—
296#1055—22no—
297#1055#11714yescomplemented
298C22×D8—131no—
299C2×C4×D4—131no—
300C2×C4×D4C2×D1311yescharacteristic
301C2×#117—21no—
302C2×#117—261no—
303#442—138no—
304C2×#107—131no—
305C2×#106—131no—
306C2×#106—131no—
307C2×#102—131no—
308C2×#102—131no—
309C2×#102—131no—
310C2×#102—131no—
311C2×#102—131no—
312C2×#102—131no—
313C2×#97—131no—
314C2×#97—131no—
315C2×#97—131no—
316C2×#97—131no—
317C2×C4×C8—131no—
318C2×C4×C8—131no—
319#390—131no—
320#390—131no—
321#390C2×D1311yescharacteristic
322#390C2×D1311yescharacteristic
323#389—131no—
324#389—131no—
325#389C2×D1311yescharacteristic
326#389C2×D1311yescharacteristic
327#388—21no—
328#388—21no—
329#388—261no—
330#388—261no—
331C4×C4⋊C4—131no—
332C4×C4⋊C4C2×D1311yescharacteristic
333C4×C22⋊C4—21no—
334C4×C22⋊C4—261no—
335C43C2×D1311yescharacteristic
336#340—131no—
337#340—131no—
338#340—131no—
339#340—131no—
340#340—131no—
341#340—131no—
342C22×C13—42no—
343C22×C13—42no—
344C22×C13—42no—
345C22×C13—81no—
346C22×C13—81no—
347C22×C13—81no—
348C22×C13—81no—
349C22×C13C2×C4×D411yescharacteristic
350C22×C13#53211yescharacteristic
351C22×C13#53211yescharacteristic
352C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
353C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
354C22×C13#57511yescharacteristic
355C22×C13#57511yescharacteristic
356C2×D13—42no—
357C2×D13—42no—
358C2×D13—42no—
359C2×D13—81no—
360C2×D13—81no—
361C2×D13—81no—
362C2×D13—81no—
363C4×C13—22no—
364C4×C13—22no—
365C4×C13—22no—
366C4×C13—22no—
367C4×C13—41no—
368C4×C13—41no—
369C4×C13—42no—
370C4×C13—81no—
371C4×C13—81no—
372C4×C13C2×#11711yescharacteristic
373C4×C13C4×#4111yescharacteristic
374C4×C13#52911yescharacteristic
375C4×C13#52911yescharacteristic
376Dic13—42no—
377Dic13—81no—
378Dic13—81no—
379C22×D4—131no—
380C22×D4C22×D1311yescharacteristic
381C23×C4—21no—
382C23×C4—261no—
383C2×D8—134no—
384C2×D8—262no—
385C2×D8—262no—
386C22×C8—131no—
387C22×C8—131no—
388C22×C8—131no—
389C22×C8—131no—
390C4×D4—22no—
391C4×D4—134no—
392C4×D4—262no—
393C4×D4C4×D1314yes—
394#117—44no—
395#117—524no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—131no—
399C2×C4⋊C4—131no—
400C2×C4⋊C4—131no—
401C2×C4⋊C4—261no—
402C2×C4⋊C4—261no—
403C2×C4⋊C4C22×D1311yescharacteristic
404C2×C4⋊C4C22×D1311yescharacteristic
405C2×C4⋊C4C22×D1311yescharacteristic
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—261no—
412C2×C22⋊C4—261no—
413C2×C22⋊C4—261no—
414C2×C22⋊C4—261no—
415C2×C22⋊C4—261no—
416C2×C42—21no—
417C2×C42—261no—
418C2×C42C22⋊D1311yescharacteristic
419C2×C42C22⋊D1311yescharacteristic
420C2×C42C22⋊D1311yescharacteristic
421C2×C42C22⋊D1311yescharacteristic
422C2×C42C22×D1311yescharacteristic
423C2×C42C22×D1311yescharacteristic
424C2×C42C22×D1311yescharacteristic
425#107—262no—
426#106—134no—
427#106—262no—
428#102—134no—
429#102—134no—
430#102—262no—
431#102—262no—
432#102—262no—
433#102—262no—
434#97—134no—
435#97—262no—
436#97—262no—
437#97—262no—
438C4×C8—262no—
439C4×C8—262no—
440#95—21no—
441#95—21no—
442#95—21no—
443#95—261no—
444#95—261no—
445#95—261no—
446C2×C13—82no—
447C2×C13#229311yescharacteristic
448C2×C13C4×AGL(1,ℤ/8)11yescharacteristic
449C2×C13C4×AGL(1,ℤ/8)11yescharacteristic
450C2×C13#318011yescharacteristic
451C2×C13#318011yescharacteristic
452C2×C13#318311yescharacteristic
453C2×C13#318411yescharacteristic
454D13—82no—
455C24—21no—
456C24—261no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—132no—
463C2×D4—261no—
464C2×D4—261no—
465C2×D4—261no—
466C2×D4—261no—
467C2×D4—261no—
468C2×D4C2×C4×D1312yes—
469C22×C4—21no—
470C22×C4—24no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—42no—
474C22×C4—42no—
475C22×C4—261no—
476C22×C4—264no—
477C22×C4—261no—
478C22×C4—261no—
479C22×C4—522no—
480C22×C4—522no—
481C22×C4C2×C22⋊D1311yescharacteristic
482C22×C4C2×C22⋊D1311yescharacteristic
483C22×C4C2×C22⋊D1311yescharacteristic
484C22×C4C2×C22⋊D1311yescharacteristic
485C22×C4C2×C22⋊D1311yescharacteristic
486C22×C4C2×C22⋊D1311yescharacteristic
487C22×C4C23×D1311yescharacteristic
488D8—268no—
489C2×C8—132no—
490C2×C8—132no—
491C2×C8—132no—
492C2×C8—132no—
493C2×C8—132no—
494C2×C8—132no—
495C2×C8—261no—
496C2×C8—261no—
497C2×C8—261no—
498C2×C8—261no—
499C2×C8—261no—
500C2×C8—261no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—42no—
507C4⋊C4—42no—
508C4⋊C4—132no—
509C4⋊C4—261no—
510C4⋊C4—261no—
511C4⋊C4—261no—
512C4⋊C4—261no—
513C4⋊C4—261no—
514C4⋊C4—522no—
515C4⋊C4—522no—
516C4⋊C4C2×C4×D1312yes—
517C22⋊C4—24no—
518C22⋊C4—42no—
519C22⋊C4—42no—
520C22⋊C4—42no—
521C22⋊C4—42no—
522C22⋊C4—264no—
523C22⋊C4—522no—
524C22⋊C4—522no—
525C22⋊C4—522no—
526C22⋊C4—522no—
527C42—22no—
528C42—22no—
529C42—21no—
530C42—21no—
531C42—21no—
532C42—21no—
533C42—41no—
534C42—41no—
535C42—42no—
536C42—522no—
537C42C2×C4×D1312yes—
538C42#612712yes—
539C13#2128611yescharacteristic, complemented, Sylow
540C23—22no—
541C23—41no—
542C23—41no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23—41no—
547C23—262no—
548C23—521no—
549C23—521no—
550C23—521no—
551C23—521no—
552C23—521no—
553C23—521no—
554C23C22×C22⋊D1311yescharacteristic
555D4—22no—
556D4—22no—
557D4—41no—
558D4—41no—
559D4—262no—
560D4—262no—
561D4—521no—
562D4—521no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—22no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—48no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—262no—
588C2×C4—528no—
589C2×C4—521no—
590C2×C4—521no—
591C2×C4—521no—
592C2×C4—521no—
593C2×C4—521no—
594C2×C4—521no—
595C2×C4—521no—
596C2×C4—521no—
597C2×C4C4×C22⋊D1312yes—
598C2×C4C4×C22⋊D1312yes—
599C2×C4#8818612yes—
600C2×C4#8820312yes—
601C2×C4C22×C4×D1311yescharacteristic
602C2×C4C2×#612711yescharacteristic
603C2×C4#41×D1311yescharacteristic
604C2×C4#41×D1311yescharacteristic
605C2×C4#41×D1311yescharacteristic
606C2×C4#41×D1311yescharacteristic
607C8—134no—
608C8—262no—
609C8—262no—
610C8—262no—
611C22—42no—
612C22—42no—
613C22—42no—
614C22—81no—
615C22—81no—
616C22—81no—
617C22—81no—
618C22—522no—
619C22—522no—
620C22—522no—
621C22—1041no—
622C22—1041no—
623C22—1041no—
624C22—1041no—
625C22C2×C4×C22⋊D1311yescharacteristic
626C22C2×#8818611yescharacteristic
627C22C2×#8820311yescharacteristic
628C22#1171952711yescharacteristic
629C22#1171952711yescharacteristic
630C22#1171953711yescharacteristic
631C22#1171953711yescharacteristic
632C4—22no—
633C4—22no—
634C4—22no—
635C4—22no—
636C4—42no—
637C4—41no—
638C4—41no—
639C4—81no—
640C4—81no—
641C4—522no—
642C4—1041no—
643C4—1041no—
644C4D13×#11711yescharacteristic
645C4#1171922711yescharacteristic
646C4#1171923311yescharacteristic
647C4#1171923311yescharacteristic
648C2—82no—
649C2—1042no—
650C2#1311729511yescharacteristic
651C2C4×#8820311yescharacteristic
652C2C4×#8818611yescharacteristic
653C2#1312552811yescharacteristic
654C2#1312553511yescharacteristic
655C2#1312555911yescharacteristic
656C2#1312557011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#2293C2
socleC23×C13C22×D4
prime radicalC22×#6104C22
cosocleC22×C4×C13C24
hypercenter#2293D13
hypocenterC13#21286
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. #13117300C2semidirect
5. #13115576C2semidirect
6. #13115561C2semidirect
7. #13115536C2semidirect
8. #13115532C2semidirect
9. #13115522C2semidirect
10. #13115518C2semidirect
11. #13114734C2semidirect
12. #13114664C2semidirect
13. #13114661C2semidirect
14. C4×#88043C2semidirect
15. C13×#2293C2semidirect
33. #11718675C4semidirect
214. #2293D13semidirect
297. #1055#117semidirect
539. C13#21286semidirect

Maximal subgroups

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

subgroupindex
C2×#117186752
#131173002
#131157112
#131157012
#131155762
#131155612
#131155362
#131155322
#131155222
#131155182
#131147342
#131146642
#131146612
C4×#880432
C13×#22932
#2128613