Finite Group Databasebeta

← #15895077

Subgroups — #15895077

Order 3328.

1494 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
1C2×#11718701C211yesmaximal, characteristic, complemented
2C22×#88050C211yesmaximal, characteristic, complemented
3#13118201C211yesmaximal, characteristic, complemented
4#13115974C212yesmaximal, complemented
5#13115839C212yesmaximal, complemented
6#13115265C211yesmaximal, characteristic, complemented
7#13115170C212yesmaximal, complemented
8#13115143C212yesmaximal, complemented
9#13115129C211yesmaximal, characteristic, complemented
10#13114922C211yesmaximal, characteristic, complemented
11C2×C13×#547C211yesmaximal, characteristic
12C22×C13×#41—21no—
13C23×Dic26C2211yescharacteristic
14C13×#547—24no—
15C13×#547—24no—
16C2×C13×C4⋊Q8C2211yescharacteristic
17C2×C13×#123—21no—
18C2×C13×#123—21no—
19C2×C13×C22⋊Q8—21no—
20C2×C13×#121C2211yescharacteristic
21C2×C13×#121C2211yescharacteristic
22C2×C4×D4×C13C2211yescharacteristic
23C2×C4×D4×C13C2211yescharacteristic
24C22×C13×C4⋊C4C2211yescharacteristic
25C22×C13×C4⋊C4C2211yescharacteristic
26C22×#6105C2212yes—
27C2×#88178C2212yes—
28C23×#1055C2211yescharacteristic
29#11718881—21no—
30C2×#88072C2212yes—
31#11718873C2211yescharacteristic
32C2×C22⋊#1055C2211yescharacteristic
33C2×C22⋊#1055C2212yes—
34#11718701—24no—
35#11718640—21no—
36C2×#88050—24no—
37C2×#88050C2212yes—
38C2×#88050C2212yes—
39C2×#88050C2212yes—
40#11718608—21no—
41#11718607—21no—
42#11718590C2212yes—
43#11718121C2212yes—
44#11718121C2212yes—
45#11718121C2212yes—
46#11718116C2212yes—
47C2×C13×#41—28no—
48C2×C13×#41—44no—
49C2×C13×#41—44no—
50C22×Q8×C13—21no—
51C22×D4×C13—21no—
52C22×D4×C13—21no—
53C22×D4×C13D411yescharacteristic
54C22×D4×C13C2311yescharacteristic
55C23×C4×C13—21no—
56C23×C4×C13—21no—
57C23×C4×C13—21no—
58C23×C4×C13C2311yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C23×Dic13—21no—
61C22×Dic26—22no—
62C22×Dic26—24no—
63C22×Dic26—22no—
64C22×Dic26—21no—
65C22×Dic26—42no—
66C22×Dic26C2312yes—
67C13×C4⋊Q8—22no—
68C13×C4⋊Q8—22no—
69C13×#123—28no—
70C13×#123—28no—
71C13×C22⋊Q8—28no—
72C13×#121—22no—
73C13×#121—22no—
74C13×#121—22no—
75C13×#121D414yes—
76C4×D4×C13—22no—
77C4×D4×C13—22no—
78C4×D4×C13—22no—
79C4×D4×C13—22no—
80C2×C13×C4⋊C4—21no—
81C2×C13×C4⋊C4—21no—
82C2×C13×C4⋊C4—22no—
83C2×C13×C4⋊C4—21no—
84C2×C13×C4⋊C4—22no—
85C2×C13×C4⋊C4—22no—
86C2×C13×C4⋊C4D411yescharacteristic
87C2×C13×C4⋊C4D414yes—
88C2×C13×C4⋊C4C2311yescharacteristic
89C2×C13×C4⋊C4C2311yescharacteristic
90C2×C13×C4⋊C4C2311yescharacteristic
91C2×C13×C22⋊C4—21no—
92C2×C13×C22⋊C4—21no—
93C2×C13×C22⋊C4—21no—
94C2×C13×C22⋊C4D411yescharacteristic
95C2×C13×C22⋊C4D411yescharacteristic
96C2×C42×C13C2311yescharacteristic
97C2×C22⋊Dic13—22no—
98C2×C22⋊Dic13—21no—
99C2×#6105—24no—
100C2×#6105—24no—
101C2×#6105—42no—
102C2×C4⋊Dic13C2312yes—
103#88178—24no—
104#88178—42no—
105C2×#6101—22no—
106C22×#1055—22no—
107C22×#1055—42no—
108C22×#1055C2312yes—
109C22×#1055C2312yes—
110#88072—42no—
111#88071—22no—
112#88071—22no—
113#88071—21no—
114C22⋊#1055—22no—
115C22⋊#1055—42no—
116#88050—24no—
117#88050—24no—
118#88050—24no—
119#23961—131nomaximal, Sylow
120C24×C13—21no—
121C24×C13C2×D411yescharacteristic
122C24×C13C2×D411yescharacteristic
123C13×#41—432no—
124C2×Q8×C13—24no—
125C2×Q8×C13—42no—
126C2×Q8×C13—42no—
127C2×D4×C13—22no—
128C2×D4×C13—22no—
129C2×D4×C13—24no—
130C2×D4×C13—24no—
131C2×D4×C13—21no—
132C2×D4×C13—22no—
133C2×D4×C13—22no—
134C2×D4×C13—42no—
135C2×D4×C13—42no—
136C2×D4×C13—42no—
137C2×D4×C13—42no—
138C2×D4×C13SD1614yescomplemented
139C2×D4×C13C2×D412yes—
140C22×C4×C13—22no—
141C22×C4×C13—22no—
142C22×C4×C13—24no—
143C22×C4×C13—24no—
144C22×C4×C13—24no—
145C22×C4×C13—21no—
146C22×C4×C13—21no—
147C22×C4×C13—21no—
148C22×C4×C13—21no—
149C22×C4×C13—21no—
150C22×C4×C13—22no—
151C22×C4×C13—22no—
152C22×C4×C13—42no—
153C22×C4×C13—42no—
154C22×C4×C13—42no—
155C22×C4×C13—42no—
156C22×C4×C13—42no—
157C22×C4×C13—42no—
158C22×C4×C13C2×D411yescharacteristic
159C22×C4×C13C2×D411yescharacteristic
160C22×C4×C13C2×D411yescharacteristic
161C22×C4×C13C2×D412yes—
162C22×C4×C13C2×D412yes—
163C22×C4×C13C2×D411yescharacteristic
164C22×C4×C13C2411yescharacteristic
165C22×Dic13—22no—
166C22×Dic13—22no—
167C22×Dic13—44no—
168C22×Dic13—42no—
169C2×Dic26—28no—
170C2×Dic26—22no—
171C2×Dic26—22no—
172C2×Dic26—22no—
173C2×Dic26—22no—
174C2×Dic26—22no—
175C2×Dic26—48no—
176C2×Dic26—44no—
177C2×Dic26—44no—
178C2×Dic26—42no—
179C2×Dic26#4114yescomplemented
180C13×C4⋊C4—24no—
181C13×C4⋊C4—24no—
182C13×C4⋊C4—24no—
183C13×C4⋊C4—22no—
184C13×C4⋊C4—21no—
185C13×C4⋊C4—21no—
186C13×C4⋊C4—21no—
187C13×C4⋊C4C2×D412yes—
188C13×C4⋊C4C2×D412yes—
189C13×C4⋊C4C2×D412yes—
190C13×C22⋊C4—24no—
191C13×C22⋊C4—24no—
192C13×C22⋊C4—22no—
193C13×C22⋊C4—24no—
194C13×C22⋊C4—22no—
195C42×C13—21no—
196C42×C13—21no—
197C22⋊Dic13—44no—
198C22⋊Dic13—42no—
199#6105—48no—
200C4⋊Dic13—22no—
201C4⋊Dic13—22no—
202#6101—44no—
203C2×#1055—22no—
204C2×#1055—22no—
205C2×#1055—22no—
206C2×#1055—22no—
207C2×#1055—22no—
208C2×#1055—22no—
209C2×#1055—44no—
210C2×#547D1311yescharacteristic
211C2×#448—131no—
212C22×#103—131no—
213#2409—131no—
214#2024—132no—
215#2000—132no—
216#1893—131no—
217#1877—132no—
218#1872—132no—
219#1869—131no—
220#1823—131no—
221C23×C13—22no—
222C23×C13—22no—
223C23×C13—21no—
224C23×C13—22no—
225C23×C13—21no—
226C23×C13—22no—
227C23×C13—22no—
228C23×C13—42no—
229C23×C13—41no—
230C23×C13—41no—
231C23×C13—42no—
232C23×C13#12012yes—
233C23×C13C2×SD1612yes—
234C23×C13C2×SD1612yes—
235C23×C13AGL(1,ℤ/8)12yes—
236C23×C13C22×D411yescharacteristic
237Q8×C13—48no—
238D4×C13—28no—
239D4×C13—24no—
240D4×C13—48no—
241D4×C13—48no—
242D4×C13—41no—
243D4×C13—41no—
244C2×C4×C13—21no—
245C2×C4×C13—22no—
246C2×C4×C13—21no—
247C2×C4×C13—22no—
248C2×C4×C13—22no—
249C2×C4×C13—24no—
250C2×C4×C13—21no—
251C2×C4×C13—21no—
252C2×C4×C13—22no—
253C2×C4×C13—22no—
254C2×C4×C13—22no—
255C2×C4×C13—22no—
256C2×C4×C13—22no—
257C2×C4×C13—48no—
258C2×C4×C13—48no—
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—48no—
266C2×C4×C13—41no—
267C2×C4×C13—41no—
268C2×C4×C13—42no—
269C2×C4×C13#12012yes—
270C2×C4×C13C2×SD1612yes—
271C2×C4×C13C22×D411yescharacteristic
272C2×C4×C13C22×D411yescharacteristic
273C2×C4×C13C2×#4112yes—
274C2×C4×C13H(5,𝔽2)12yes—
275C2×Dic13—24no—
276C2×Dic13—48no—
277C2×Dic13—42no—
278C2×Dic13—42no—
279C2×Dic13—42no—
280C2×Dic13—42no—
281C2×Dic13—42no—
282Dic26—24no—
283Dic26—24no—
284Dic26—48no—
285Dic26—42no—
286Dic26—42no—
287#1055—42no—
288#1055—42no—
289C22×#41—21no—
290C23×Q8—131no—
291C22×SD16—132no—
292C23×C8—131no—
293#547—24no—
294#547—24no—
295C2×C4⋊Q8C2×D1311yescharacteristic
296C2×#123—21no—
297C2×#123—21no—
298C2×C22⋊Q8—21no—
299C2×C22⋊Q8—132no—
300C2×#121C2×D1311yescharacteristic
301C2×#121C2×D1311yescharacteristic
302C2×C4×D4C2×D1311yescharacteristic
303C2×C4×D4C2×D1311yescharacteristic
304C22×C4⋊C4C2×D1311yescharacteristic
305C22×C4⋊C4C2×D1311yescharacteristic
306#448—264no—
307C2×#103—132no—
308C2×#103—132no—
309C2×#103—132no—
310C2×#103—264no—
311C2×#102—132no—
312C2×C22⋊C8—131no—
313C2×C22⋊C8—132no—
314#395—261no—
315#393—261no—
316#391—132no—
317#386—261no—
318#385—261no—
319#380—131no—
320#340—132no—
321#340—132no—
322#340—132no—
323#336—132no—
324C22×C13—22no—
325C22×C13—22no—
326C22×C13—24no—
327C22×C13—24no—
328C22×C13—22no—
329C22×C13—24no—
330C22×C13—41no—
331C22×C13—41no—
332C22×C13—42no—
333C22×C13—42no—
334C22×C13—42no—
335C22×C13—42no—
336C22×C13—82no—
337C22×C13—82no—
338C22×C13#45014yes—
339C22×C13C2×#12011yescharacteristic
340C22×C13#54612yes—
341C22×C13C22×SD1611yescharacteristic
342C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
343C22×C13#57812yes—
344C4×C13—22no—
345C4×C13—22no—
346C4×C13—41no—
347C4×C13—42no—
348C4×C13—42no—
349C4×C13—42no—
350C4×C13—41no—
351C4×C13#52511yescharacteristic
352C4×C13#53511yescharacteristic
353C4×C13#54612yes—
354Dic13—44no—
355Dic13—82no—
356C2×#41—28no—
357C2×#41—44no—
358C2×#41—44no—
359C22×Q8—21no—
360C22×Q8—132no—
361C22×Q8—264no—
362C22×Q8—261no—
363C22×Q8—262no—
364C22×Q8—262no—
365C22×Q8—522no—
366C22×D4—21no—
367C22×D4—21no—
368C22×D4C22⋊D1311yescharacteristic
369C22×D4C22×D1311yescharacteristic
370C23×C4—21no—
371C23×C4—21no—
372C23×C4—21no—
373C23×C4—261no—
374C23×C4C22×D1311yescharacteristic
375C23×C4C22×D1311yescharacteristic
376C2×SD16—264no—
377C2×SD16—264no—
378C2×SD16—522no—
379C22×C8—132no—
380C22×C8—132no—
381C22×C8—262no—
382C22×C8—522no—
383C4⋊Q8—22no—
384C4⋊Q8—22no—
385#123—28no—
386#123—28no—
387C22⋊Q8—28no—
388C22⋊Q8—264no—
389C22⋊Q8—522no—
390#121—22no—
391#121—22no—
392#121—22no—
393#121C22⋊D1314yes—
394C4×D4—22no—
395C4×D4—22no—
396C4×D4—22no—
397C4×D4—22no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—132no—
405C2×C4⋊C4—262no—
406C2×C4⋊C4C22⋊D1311yescharacteristic
407C2×C4⋊C4C22⋊D1314yes—
408C2×C4⋊C4C22×D1311yescharacteristic
409C2×C4⋊C4C22×D1311yescharacteristic
410C2×C4⋊C4C22×D1311yescharacteristic
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—262no—
415C2×C22⋊C4—261no—
416C2×C22⋊C4C22⋊D1311yescharacteristic
417C2×C22⋊C4C22⋊D1311yescharacteristic
418C2×C42C22×D1311yescharacteristic
419#103—264no—
420#103—264no—
421#103—264no—
422#102—522no—
423C22⋊C8—262no—
424C22⋊C8—522no—
425#95—261no—
426#95—262no—
427#95—262no—
428C2×C13—24no—
429C2×C13—42no—
430C2×C13—82no—
431C2×C13#240411yescharacteristic
432C2×C13C2×#45011yescharacteristic
433C2×C13#301111yescharacteristic
434C2×C13#329812yes—
435C2×C13#330812yes—
436C24—21no—
437C24C2×C22⋊D1311yescharacteristic
438C24C2×C22⋊D1311yescharacteristic
439#41—432no—
440C2×Q8—24no—
441C2×Q8—42no—
442C2×Q8—42no—
443C2×Q8—134no—
444C2×Q8—268no—
445C2×Q8—262no—
446C2×Q8—262no—
447C2×Q8—262no—
448C2×Q8—262no—
449C2×Q8—262no—
450C2×Q8—524no—
451C2×Q8—528no—
452C2×Q8—524no—
453C2×Q8—522no—
454C2×D4—22no—
455C2×D4—22no—
456C2×D4—24no—
457C2×D4—24no—
458C2×D4—22no—
459C2×D4—22no—
460C2×D4—21no—
461C2×D4—42no—
462C2×D4—42no—
463C2×D4—42no—
464C2×D4—42no—
465C2×D4#610514yescomplemented
466C2×D4C2×C22⋊D1312yes—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—24no—
470C22×C4—24no—
471C22×C4—24no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—42no—
480C22×C4—42no—
481C22×C4—42no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—262no—
486C22×C4—262no—
487C22×C4—524no—
488C22×C4—522no—
489C22×C4C2×C22⋊D1311yescharacteristic
490C22×C4C2×C22⋊D1311yescharacteristic
491C22×C4C2×C22⋊D1311yescharacteristic
492C22×C4C2×C22⋊D1311yescharacteristic
493C22×C4C2×C22⋊D1312yes—
494C22×C4C2×C22⋊D1312yes—
495C22×C4C23×D1311yescharacteristic
496SD16—528no—
497C2×C8—262no—
498C2×C8—262no—
499C2×C8—262no—
500C2×C8—262no—
501C2×C8—262no—
502C2×C8—262no—
503C2×C8—524no—
504C4⋊C4—24no—
505C4⋊C4—24no—
506C4⋊C4—24no—
507C4⋊C4—22no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—262no—
512C4⋊C4—262no—
513C4⋊C4—524no—
514C4⋊C4C2×C22⋊D1312yes—
515C4⋊C4C2×C22⋊D1312yes—
516C4⋊C4C2×C22⋊D1312yes—
517C22⋊C4—24no—
518C22⋊C4—24no—
519C22⋊C4—22no—
520C22⋊C4—24no—
521C22⋊C4—22no—
522C22⋊C4—524no—
523C22⋊C4—522no—
524C42—21no—
525C42—21no—
526C13#2396111yescharacteristic, complemented, Sylow
527C23—22no—
528C23—22no—
529C23—21no—
530C23—22no—
531C23—22no—
532C23—21no—
533C23—22no—
534C23—41no—
535C23—41no—
536C23—42no—
537C23—42no—
538C23#8818612yes—
539C23C2×#610512yes—
540C23C2×#610512yes—
541C23#8820712yes—
542C23C22×C22⋊D1311yescharacteristic
543Q8—48no—
544Q8—264no—
545Q8—264no—
546Q8—528no—
547Q8—522no—
548Q8—522no—
549D4—28no—
550D4—24no—
551D4—48no—
552D4—48no—
553D4—41no—
554D4—41no—
555C2×C4—21no—
556C2×C4—22no—
557C2×C4—21no—
558C2×C4—22no—
559C2×C4—24no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—48no—
569C2×C4—48no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—48no—
577C2×C4—41no—
578C2×C4—42no—
579C2×C4—41no—
580C2×C4—264no—
581C2×C4—528no—
582C2×C4—522no—
583C2×C4—522no—
584C2×C4—522no—
585C2×C4—522no—
586C2×C4—522no—
587C2×C4C2×#610512yes—
588C2×C4#8820712yes—
589C2×C4#41×D1312yes—
590C2×C4#8825612yes—
591C2×C4C22×C22⋊D1311yescharacteristic
592C2×C4C22×C22⋊D1311yescharacteristic
593C8—522no—
594C8—522no—
595C22—22no—
596C22—24no—
597C22—24no—
598C22—22no—
599C22—24no—
600C22—22no—
601C22—41no—
602C22—42no—
603C22—41no—
604C22—42no—
605C22—42no—
606C22—42no—
607C22—82no—
608C22—82no—
609C22#1171887914yes—
610C22C2×#8818611yescharacteristic
611C22C22×#610511yescharacteristic
612C22#1171953412yes—
613C22#1171954312yes—
614C22C2×#8820711yescharacteristic
615C4—22no—
616C4—22no—
617C4—41no—
618C4—42no—
619C4—42no—
620C4—42no—
621C4—41no—
622C4—524no—
623C4—1042no—
624C4#1171953311yescharacteristic
625C4#1171953412yes—
626C4#1171953511yescharacteristic
627C2—24no—
628C2—42no—
629C2—82no—
630C2#1311815111yescharacteristic
631C2C2×#1171887911yescharacteristic
632C2#1312413111yescharacteristic
633C2#1312669512yes—
634C2#1312682112yes—
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
Fitting, prime radicalC2×C13×#547C2
socleC23×C13C22×D4
hypercenterC2×#547D13
hypocenterC13#23961
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C2×#11718701C2semidirect
2. C22×#88050C2semidirect
3. #13118201C2semidirect
4. #13115974C2semidirect
5. #13115839C2semidirect
6. #13115265C2semidirect
7. #13115170C2semidirect
8. #13115143C2semidirect
9. #13115129C2semidirect
10. #13114922C2semidirect
138. C2×D4×C13SD16semidirect
179. C2×Dic26#41semidirect
465. C2×D4#6105semidirect
526. C13#23961semidirect

Maximal subgroups

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

subgroupindex
C2×#117187012
C22×#880502
#131182012
#131159742
#131158392
#131152652
#131151702
#131151432
#131151292
#131149222
C2×C13×#5472
#2396113