Finite Group Databasebeta

← #15904184

Subgroups — #15904184

Order 3328.

868 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718727C211yesmaximal, characteristic, complemented
2C2×#11718587C211yesmaximal, characteristic, complemented
3C4×#88184C211yesmaximal, characteristic
4#13116273C211yesmaximal, characteristic, complemented
5#13116262C211yesmaximal, characteristic, complemented
6#13116025C211yesmaximal, characteristic
7#13116018C211yesmaximal, characteristic
8#13115794C211yesmaximal, characteristic, complemented
9#13115602C211yesmaximal, characteristic, complemented
10#13115576C211yesmaximal, characteristic, complemented
11#13115571C211yesmaximal, characteristic, complemented
12#13115532C211yesmaximal, characteristic, complemented
13#13115532C211yesmaximal, characteristic, complemented
14#13114843C211yesmaximal, characteristic, complemented
15C13×#2851C211yesmaximal, characteristic, complemented
16C2×C13×#125C2211yescharacteristic
17C22×C42×C13C2211yescharacteristic
18C2×#88184C2211yescharacteristic
19C2×C4×C22⋊D13—21no—
20C2×C4×D52C2211yescharacteristic
21C13×#389C2211yescharacteristic
22C13×#389C2211yescharacteristic
23C13×#387—21no—
24C13×#387—21no—
25C13×#385—21no—
26C13×#385—21no—
27C13×#382C2211yescharacteristic
28C13×#380C2211yescharacteristic
29C13×#380C2211yescharacteristic
30#11718874—21no—
31#11718873C2211yescharacteristic
32C2×C22⋊#1055C2211yescharacteristic
33C2×C22⋊#1055C2211yescharacteristic
34#11718727—24no—
35C2×#88049C2211yescharacteristic
36C2×#88049C2211yescharacteristic
37C2×#88049C2211yescharacteristic
38C2×#88049C2211yescharacteristic
39C2×#88048C2211yescharacteristic
40C2×#88048C2211yescharacteristic
41C2×#88047C2211yescharacteristic
42C2×#88047C2211yescharacteristic
43#11718601—21no—
44#11718600C2211yescharacteristic
45C4×#6103—21no—
46C4×C4⋊Dic13C2211yescharacteristic
47#11718589C2211yescharacteristic
48#11718587—24no—
49C2×C4⋊#1055C2211yescharacteristic
50C2×C4⋊#1055C2211yescharacteristic
51C2×#88043C2211yescharacteristic
52C2×#88043C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60#11718121C2211yescharacteristic
61C23×C4×C13D411yescharacteristic
62C23×C4×C13D411yescharacteristic
63C23×C4×C13C2311yescharacteristic
64C22×C22⋊D13—21no—
65C22×D52C2311yescharacteristic
66C22×C4×D13—21no—
67C13×#125—22no—
68C13×#125—22no—
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4—21no—
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4—21no—
73C2×C13×C4⋊C4C2311yescharacteristic
74C2×C13×C4⋊C4C2311yescharacteristic
75C2×C13×C4⋊C4C2311yescharacteristic
76C2×C13×C4⋊C4C2311yescharacteristic
77C2×C13×C22⋊C4—21no—
78C2×C13×C22⋊C4—21no—
79C2×C42×C13—22no—
80C2×C42×C13—22no—
81C2×C42×C13D411yescharacteristic
82C2×C42×C13D411yescharacteristic
83C2×C42×C13C2311yescharacteristic
84C2×C42×C13C2311yescharacteristic
85C2×C22⋊Dic13—21no—
86#88184—22no—
87#88184—22no—
88C4×C22⋊D13—44no—
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×C4×Dic13—21no—
98C22×#1055C2311yescharacteristic
99C22×#1055C2311yescharacteristic
100C22×#1055C2311yescharacteristic
101C22×#1055C2311yescharacteristic
102C4×D52—22no—
103C4×D52—22no—
104C13×#95—21no—
105C13×#95—21no—
106C13×#95—21no—
107C13×#95—21no—
108C13×#95—21no—
109C13×#95—21no—
110#88071—21no—
111#88071—21no—
112#88071—21no—
113C22⋊#1055—22no—
114C22⋊#1055—22no—
115#88049—22no—
116#88049—22no—
117#88049—22no—
118#88049—22no—
119#88048—22no—
120#88048—22no—
121#88047—22no—
122#88047—22no—
123C4⋊#1055—22no—
124C4⋊#1055D414yescomplemented
125#88043—22no—
126#88043—22no—
127#24706—131nomaximal, Sylow
128C24×C13C2×D411yescharacteristic
129C23×D13—21no—
130C22×C4×C13—22no—
131C22×C4×C13—22no—
132C22×C4×C13—22no—
133C22×C4×C13—21no—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—21no—
138C22×C4×C13—21no—
139C22×C4×C13—21no—
140C22×C4×C13—21no—
141C22×C4×C13—21no—
142C22×C4×C13—21no—
143C22×C4×C13—41no—
144C22×C4×C13—41no—
145C22×C4×C13—41no—
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13C2×D411yescharacteristic
148C22×C4×C13C2×D411yescharacteristic
149C22×C4×C13C2×D411yescharacteristic
150C22×C4×C13C2×D411yescharacteristic
151C22×C4×C13C2411yescharacteristic
152C2×C22⋊D13—24no—
153C2×C22⋊D13—42no—
154C2×C22⋊D13—42no—
155C22×Dic13—21no—
156C22×Dic13—21no—
157C22×Dic13—21no—
158C2×D52—21no—
159C2×D52—21no—
160C2×D52—21no—
161C2×D52—21no—
162C2×D52—21no—
163C2×D52#4112yes—
164C2×C4×D13—42no—
165C2×C4×D13—42no—
166C2×C4×D13—42no—
167C13×C4⋊C4—21no—
168C13×C4⋊C4—21no—
169C13×C4⋊C4—21no—
170C13×C4⋊C4—21no—
171C13×C4⋊C4—21no—
172C13×C4⋊C4—21no—
173C13×C4⋊C4—21no—
174C13×C4⋊C4—21no—
175C13×C4⋊C4—42no—
176C13×C4⋊C4—42no—
177C13×C4⋊C4—42no—
178C13×C4⋊C4—42no—
179C13×C22⋊C4—42no—
180C13×C22⋊C4—42no—
181C42×C13—22no—
182C42×C13—22no—
183C42×C13—21no—
184C42×C13—21no—
185C42×C13C2×D412yes—
186C42×C13#4112yes—
187C22⋊Dic13—42no—
188#6103—24no—
189#6103—42no—
190#6103—42no—
191#6103—42no—
192C4⋊Dic13—21no—
193C4⋊Dic13—21no—
194C4⋊Dic13—21no—
195C4⋊Dic13—21no—
196C4⋊Dic13—21no—
197C4⋊Dic13#4112yes—
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×#1055—21no—
207C2×#1055—21no—
208C2×#1055—21no—
209C2×#1055—21no—
210C2×#1055C2×D412yes—
211C2×#1055C2×D412yes—
212C2×#478—131no—
213C2×#432—131no—
214#2851D1311yescharacteristic, complemented
215C4×#121—131no—
216#2077—131no—
217#2075—131no—
218#2034—131no—
219#2033—131no—
220#1989—131no—
221#1949—131no—
222#1944—131no—
223#1943—131no—
224#1936—131no—
225#1936—131no—
226#1804—131no—
227C23×C13—21no—
228C23×C13—21no—
229C23×C13—21no—
230C23×C13—21no—
231C23×C13—21no—
232C23×C13—21no—
233C23×C13AGL(1,ℤ/8)12yes—
234C23×C13C22×D411yescharacteristic
235C22×D13—22no—
236C22×D13—41no—
237C22×D13—41no—
238C22×D13—41no—
239C22×D13—41no—
240C22×D13—41no—
241C22×D13—41no—
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—21no—
253C2×C4×C13—21no—
254C2×C4×C13—21no—
255C2×C4×C13—44no—
256C2×C4×C13—44no—
257C2×C4×C13—41no—
258C2×C4×C13—41no—
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—41no—
268C2×C4×C13—41no—
269C2×C4×C13—41no—
270C2×C4×C13—41no—
271C2×C4×C13—41no—
272C2×C4×C13—41no—
273C2×C4×C13#12112yes—
274C2×C4×C13#12112yes—
275C2×C4×C13C22×D411yescharacteristic
276C2×C4×C13C2×#4111yescharacteristic
277C2×C4×C13C2×#4111yescharacteristic
278C2×C4×C13C2×#4111yescharacteristic
279C2×C4×C132−1+411yescharacteristic
280C2×C4×C132−1+411yescharacteristic
281C22⋊D13—48no—
282C2×Dic13—22no—
283C2×Dic13—41no—
284C2×Dic13—41no—
285C2×Dic13—41no—
286C2×Dic13—41no—
287C2×Dic13—41no—
288C2×Dic13—41no—
289C2×Dic13—41no—
290C2×Dic13—41no—
291D52—22no—
292D52—22no—
293D52—41no—
294D52—41no—
295C4×D13—84no—
296#1055—22no—
297#1055—22no—
298#1055—41no—
299#1055—41no—
300C2×#125C2×D1311yescharacteristic
301C2×#121—131no—
302C2×C4×D4—131no—
303C2×C4×D4—261no—
304C22×C42C2×D1311yescharacteristic
305#478—264no—
306#432—264no—
307C2×#107—131no—
308C2×#107—131no—
309C2×#106—131no—
310C2×#106—131no—
311C2×C4⋊C8—131no—
312C2×C4⋊C8—131no—
313C2×#102—131no—
314C2×#102—131no—
315C2×#102—131no—
316C2×#102—131no—
317C2×C22⋊C8—131no—
318C2×C22⋊C8—131no—
319C2×#97—131no—
320C2×#97—131no—
321#390—131no—
322#389—131no—
323#389C2×D1311yescharacteristic
324#389C2×D1311yescharacteristic
325#388—261no—
326#387—21no—
327#387—21no—
328#386—261no—
329#385—21no—
330#385—21no—
331#382C2×D1311yescharacteristic
332#380—131no—
333#380C2×D1311yescharacteristic
334#380C2×D1311yescharacteristic
335C4×C4⋊C4—131no—
336C4×C22⋊C4—261no—
337#340—131no—
338#340—131no—
339#340—131no—
340#340—131no—
341#340—131no—
342#340—131no—
343#340—131no—
344#340—131no—
345C22×C13—22no—
346C22×C13—22no—
347C22×C13—22no—
348C22×C13—41no—
349C22×C13—41no—
350C22×C13—41no—
351C22×C13—41no—
352C22×C13C2×#12111yescharacteristic
353C22×C13#52511yescharacteristic
354C22×C13#53611yescharacteristic
355C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
356C22×C13#57511yescharacteristic
357C22×C13#57511yescharacteristic
358C22×C13#57511yescharacteristic
359C2×D13—42no—
360C2×D13—42no—
361C2×D13—42no—
362C2×D13—81no—
363C2×D13—81no—
364C2×D13—81no—
365C2×D13—81no—
366C4×C13—22no—
367C4×C13—22no—
368C4×C13—41no—
369C4×C13—41no—
370C4×C13—41no—
371C4×C13—81no—
372C4×C13—81no—
373C4×C13—81no—
374C4×C13—81no—
375C4×C13#54711yescharacteristic
376C4×C13#54811yescharacteristic
377C4×C13#55211yescharacteristic
378C4×C13#55611yescharacteristic
379Dic13—42no—
380Dic13—81no—
381Dic13—81no—
382C22×D4—131no—
383C22×D4—261no—
384C23×C4—261no—
385C23×C4C22⋊D1311yescharacteristic
386C23×C4C22⋊D1311yescharacteristic
387C23×C4C22×D1311yescharacteristic
388C22×C8—131no—
389C22×C8—131no—
390C22×C8—131no—
391C22×C8—131no—
392#125—22no—
393#125—22no—
394#121—262no—
395#121—262no—
396C4×D4—262no—
397C4×D4—262no—
398C4×D4—524no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—131no—
404C2×C4⋊C4—131no—
405C2×C4⋊C4—131no—
406C2×C4⋊C4—261no—
407C2×C4⋊C4C22×D1311yescharacteristic
408C2×C4⋊C4C22×D1311yescharacteristic
409C2×C4⋊C4C22×D1311yescharacteristic
410C2×C4⋊C4C22×D1311yescharacteristic
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—261no—
414C2×C22⋊C4—261no—
415C2×C22⋊C4—261no—
416C2×C22⋊C4—261no—
417C2×C22⋊C4—261no—
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—261no—
421C2×C42C22⋊D1311yescharacteristic
422C2×C42C22⋊D1311yescharacteristic
423C2×C42C22×D1311yescharacteristic
424C2×C42C22×D1311yescharacteristic
425#107—262no—
426#107—262no—
427#106—262no—
428#106—262no—
429C4⋊C8—134no—
430C4⋊C8—262no—
431#102—262no—
432#102—262no—
433#102—262no—
434#102—262no—
435C22⋊C8—262no—
436C22⋊C8—262no—
437#97—262no—
438#97—262no—
439#95—21no—
440#95—21no—
441#95—21no—
442#95—21no—
443#95—21no—
444#95—21no—
445#95—261no—
446#95—261no—
447#95—261no—
448C2×C13—42no—
449C2×C13#241511yescharacteristic
450C2×C13#305411yescharacteristic
451C2×C13#305511yescharacteristic
452C2×C13#311111yescharacteristic
453C2×C13#311411yescharacteristic
454C2×C13#323411yescharacteristic
455C2×C13#324011yescharacteristic
456D13—82no—
457C24—261no—
458C24C2×C22⋊D1311yescharacteristic
459C2×D4—132no—
460C2×D4—264no—
461C2×D4—261no—
462C2×D4—261no—
463C2×D4—261no—
464C2×D4—261no—
465C2×D4—261no—
466C2×D4—522no—
467C2×D4—522no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—41no—
482C22×C4—41no—
483C22×C4—41no—
484C22×C4—261no—
485C22×C4—261no—
486C22×C4—261no—
487C22×C4—522no—
488C22×C4—522no—
489C22×C4—522no—
490C22×C4C2×C22⋊D1311yescharacteristic
491C22×C4C2×C22⋊D1311yescharacteristic
492C22×C4C2×C22⋊D1311yescharacteristic
493C22×C4C2×C22⋊D1311yescharacteristic
494C22×C4C2×C22⋊D1311yescharacteristic
495C22×C4C23×D1311yescharacteristic
496C2×C8—132no—
497C2×C8—132no—
498C2×C8—261no—
499C2×C8—261no—
500C2×C8—261no—
501C2×C8—261no—
502C2×C8—261no—
503C2×C8—261no—
504C2×C8—261no—
505C2×C8—261no—
506C2×C8—261no—
507C2×C8—261no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—42no—
517C4⋊C4—42no—
518C4⋊C4—42no—
519C4⋊C4—42no—
520C4⋊C4—132no—
521C4⋊C4—261no—
522C4⋊C4—261no—
523C4⋊C4—261no—
524C4⋊C4—261no—
525C4⋊C4—261no—
526C4⋊C4—522no—
527C22⋊C4—42no—
528C22⋊C4—42no—
529C22⋊C4—264no—
530C22⋊C4—522no—
531C22⋊C4—522no—
532C22⋊C4—522no—
533C22⋊C4—522no—
534C42—22no—
535C42—22no—
536C42—21no—
537C42—21no—
538C42—522no—
539C42D4×D1312yes—
540C42#612912yes—
541C13#2470611yescharacteristic, complemented, Sylow
542C23—21no—
543C23—21no—
544C23—21no—
545C23—21no—
546C23—21no—
547C23—21no—
548C23—262no—
549C23—521no—
550C23—521no—
551C23—521no—
552C23—521no—
553C23—521no—
554C23—521no—
555C23#8820312yes—
556C23C22×C22⋊D1311yescharacteristic
557D4—262no—
558D4—262no—
559D4—528no—
560D4—521no—
561D4—521no—
562C2×C4—21no—
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—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—44no—
576C2×C4—44no—
577C2×C4—41no—
578C2×C4—41no—
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—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—262no—
594C2×C4—521no—
595C2×C4—521no—
596C2×C4—521no—
597C2×C4—521no—
598C2×C4—521no—
599C2×C4—521no—
600C2×C4—521no—
601C2×C4—521no—
602C2×C4—1044no—
603C2×C4#8819312yes—
604C2×C4#8819312yes—
605C2×C4C2×D4×D1311yescharacteristic
606C2×C4C2×#612911yescharacteristic
607C2×C4#8825411yescharacteristic
608C2×C4#8825411yescharacteristic
609C2×C4#41×D1311yescharacteristic
610C2×C4#41×D1311yescharacteristic
611C8—262no—
612C8—262no—
613C8—521no—
614C8—521no—
615C22—22no—
616C22—22no—
617C22—22no—
618C22—41no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—522no—
623C22—522no—
624C22—522no—
625C22—1041no—
626C22—1041no—
627C22—1041no—
628C22—1041no—
629C22C2×#8819311yescharacteristic
630C22#1171952111yescharacteristic
631C22C2×#8820311yescharacteristic
632C22#1171952711yescharacteristic
633C22#1171952711yescharacteristic
634C22#1171952711yescharacteristic
635C22#1171953311yescharacteristic
636C4—22no—
637C4—22no—
638C4—41no—
639C4—41no—
640C4—41no—
641C4—81no—
642C4—81no—
643C4—81no—
644C4—81no—
645C4—522no—
646C4—1041no—
647C4—1041no—
648C4#1171933611yescharacteristic
649C4#1171933811yescharacteristic
650C4#1171934411yescharacteristic
651C4#1171934611yescharacteristic
652C2—42no—
653C2—1042no—
654C2#1311826611yescharacteristic
655C2#1312444211yescharacteristic
656C2#1312445711yescharacteristic
657C2#1312493911yescharacteristic
658C2#1312497011yescharacteristic
659C2#1312602611yescharacteristic
660C2#1312607611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2851C2
socleC23×C13C22×D4
prime radicalC2×#88184C22
hypercenter#2851D13
hypocenterC13#24706
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2851

Complements

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

NH ≅ G/Ntype
1. C2×#11718727C2semidirect
2. C2×#11718587C2semidirect
4. #13116273C2semidirect
5. #13116262C2semidirect
8. #13115794C2semidirect
9. #13115602C2semidirect
10. #13115576C2semidirect
11. #13115571C2semidirect
12. #13115532C2semidirect
13. #13115532C2semidirect
14. #13114843C2semidirect
15. C13×#2851C2semidirect
124. C4⋊#1055D4semidirect
214. #2851D13semidirect
541. C13#24706semidirect

Maximal subgroups

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

subgroupindex
C2×#117187272
C2×#117185872
C4×#881842
#131162732
#131162622
#131160252
#131160182
#131157942
#131156022
#131155762
#131155712
#131155322
#131148432
C13×#28512
#2470613