Finite Group Databasebeta

← #15870311

Subgroups — #15870311

Order 3328.

768 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124749C211yesmaximal, characteristic
2#13123535C211yesmaximal, characteristic
3#13123255C211yesmaximal, characteristic, complemented
4#13115482C211yesmaximal, characteristic, complemented
5#13115482C211yesmaximal, characteristic, complemented
6#13115433C211yesmaximal, characteristic, complemented
7#13115433C211yesmaximal, characteristic, complemented
8#13115136C211yesmaximal, characteristic
9#13115040C211yesmaximal, characteristic, complemented
10#13114719C211yesmaximal, characteristic, complemented
11#13114714C211yesmaximal, characteristic, complemented
12#13114677C211yesmaximal, characteristic, complemented
13#13114670C211yesmaximal, characteristic, complemented
14#13114620C211yesmaximal, characteristic, complemented
15C13×#1826C211yesmaximal, characteristic, complemented
16C2×C13×#117C2211yescharacteristic
17#11719496C2211yescharacteristic
18C22×#6099C2211yescharacteristic
19C22×#6099C2211yescharacteristic
20C2×#88161C2211yescharacteristic
21C13×#407C2211yescharacteristic
22C4×C13×C22⋊C4C2211yescharacteristic
23C2×C22⋊#1055C2211yescharacteristic
24#11718790C2211yescharacteristic
25C2×#88062C2211yescharacteristic
26C2×#88062C2211yescharacteristic
27#11718783C2211yescharacteristic
28#11718780C2211yescharacteristic
29#11718664C411yescharacteristic, complemented
30#11718664C411yescharacteristic, complemented
31#11718663C2211yescharacteristic
32#11718663C2211yescharacteristic
33#11718659C2211yescharacteristic
34#11718659C2211yescharacteristic
35#11718658—21no—
36#11718658—21no—
37#11718658C2211yescharacteristic
38#11718658C2211yescharacteristic
39#11718658C2211yescharacteristic
40#11718658C2211yescharacteristic
41#11718657C411yescharacteristic, complemented
42#11718657C411yescharacteristic, complemented
43#11718632C411yescharacteristic, complemented
44#11718631C411yescharacteristic, complemented
45#11718629C411yescharacteristic, complemented
46#11718628C411yescharacteristic, complemented
47C2×#88045C2211yescharacteristic
48C2×#88045C2211yescharacteristic
49C4×#6099—21no—
50C4×#6099—21no—
51C2×#88043C2211yescharacteristic
52C2×C4×#1055C2211yescharacteristic
53#11718390—21no—
54#11718390—21no—
55#11718389—21no—
56#11718389—21no—
57C13×#339C2211yescharacteristic
58C13×#339C2211yescharacteristic
59C13×#339C2211yescharacteristic
60C13×#339C2211yescharacteristic
61#11718150C2211yescharacteristic
62#11718150C2211yescharacteristic
63#11718116C2211yescharacteristic
64#11718116C2211yescharacteristic
65#11718115C2211yescharacteristic
66#11718115C2211yescharacteristic
67C23×C4×C13C2311yescharacteristic
68C2×#6127C2311yescharacteristic
69C2×C13×M16C2311yescharacteristic
70C2×C13×M16C2311yescharacteristic
71C13×#117—21no—
72C13×#117—21no—
73C13×#117C2×C411yescharacteristic
74C13×#117C2×C411yescharacteristic
75C13×#117C2311yescharacteristic
76C13×#117C2311yescharacteristic
77C2×C13×C4⋊C4C2×C411yescharacteristic
78C2×C13×C4⋊C4C2×C411yescharacteristic
79C2×C13×C22⋊C4—21no—
80C2×C13×C22⋊C4—21no—
81C2×C42×C13—21no—
82C2×C42×C13C2311yescharacteristic
83C2×C42×C13C2311yescharacteristic
84#88207—21no—
85#88184C2×C411yescharacteristic
86#88184C2×C411yescharacteristic
87#88183—21no—
88C4×C22⋊D13—21no—
89C4×C22⋊D13—21no—
90#88180C2311yescharacteristic
91#88178C2×C411yescharacteristic
92#88178C2×C411yescharacteristic
93C2×#6099—21no—
94C2×#6099—22no—
95C2×#6099—22no—
96C2×#6099—22no—
97C2×#6099—22no—
98C2×#6099D411yescharacteristic
99C2×#6099D411yescharacteristic
100C2×#6099D411yescharacteristic
101C2×#6099D411yescharacteristic
102C2×#6099C2311yescharacteristic
103C2×#6099C2311yescharacteristic
104C22×#1055—21no—
105C22×#1055C2311yescharacteristic
106C22×#1055C2311yescharacteristic
107C22×#1055C2311yescharacteristic
108C22×#1055C2311yescharacteristic
109#88161—22no—
110#88161—22no—
111C2×#6094—21no—
112C2×C8×D13—21no—
113C13×C22⋊C8—21no—
114C13×C22⋊C8—21no—
115C13×#95—21no—
116C22⋊#1055C2×C411yescharacteristic
117C22⋊#1055C2×C411yescharacteristic
118C22⋊#1055C2×C411yescharacteristic
119C22⋊#1055C2×C411yescharacteristic
120#88062—22no—
121#88062—22no—
122#88060—21no—
123#88060—21no—
124#88055—21no—
125#88054—21no—
126#88054—21no—
127C8×Dic13—21no—
128#88050C2×C411yescharacteristic
129#88050C2×C411yescharacteristic
130#88050C2×C411yescharacteristic
131#88050C2×C411yescharacteristic
132#88049C2×C411yescharacteristic
133#88049C2×C411yescharacteristic
134#88049C2×C411yescharacteristic
135#88049C2×C411yescharacteristic
136#88048C2×C411yescharacteristic
137#88048C2×C411yescharacteristic
138#88048C2×C411yescharacteristic
139#88048C2×C411yescharacteristic
140#88047C2×C411yescharacteristic
141#88047C2×C411yescharacteristic
142#88047C2×C411yescharacteristic
143#88047C2×C411yescharacteristic
144#88045—22no—
145#88045—22no—
146#88043—21no—
147#88043—21no—
148#88043—21no—
149#88043—21no—
150#88043—22no—
151C4×#1055—21no—
152C4×#1055—21no—
153C4×#1055—21no—
154C4×#1055—21no—
155C4×#1055—22no—
156#21594—131nomaximal, Sylow
157C24×C13#4111yescharacteristic
158C22×C4×C13—21no—
159C22×C4×C13—21no—
160C22×C4×C13—21no—
161C22×C4×C13—21no—
162C22×C4×C13—21no—
163C22×C4×C13—21no—
164C22×C4×C13—21no—
165C22×C4×C13—21no—
166C22×C4×C13C22×C411yescharacteristic
167C22×C4×C13C22×C411yescharacteristic
168C22×C4×C13C2×D411yescharacteristic
169C22×C4×C13C2×D411yescharacteristic
170C22×C4×C13#4111yescharacteristic
171C22×C4×C13C2411yescharacteristic
172C2×C22⋊D13—21no—
173C2×C22⋊D13—21no—
174C2×C22⋊D13—21no—
175#6127—21no—
176#6127—21no—
177#6127—21no—
178#6127—21no—
179C2×D52C22×C411yescharacteristic
180C2×C4×D13—21no—
181C2×Dic26C22×C411yescharacteristic
182C13×M16—21no—
183C13×M16—21no—
184C13×M16—21no—
185C13×M16—21no—
186C2×C8×C13—21no—
187C2×C8×C13—21no—
188C13×C4⋊C4—21no—
189C13×C4⋊C4—21no—
190C13×C4⋊C4C22×C411yescharacteristic
191C13×C4⋊C4C22×C411yescharacteristic
192C13×C4⋊C4C22×C411yescharacteristic
193C13×C4⋊C4C22×C411yescharacteristic
194C13×C22⋊C4—21no—
195C13×C22⋊C4—21no—
196C13×C22⋊C4—21no—
197C13×C22⋊C4—21no—
198C13×C22⋊C4—42no—
199C42×C13—21no—
200C42×C13—21no—
201C42×C13—21no—
202C42×C13—21no—
203C42×C13—21no—
204C42×C13—21no—
205C42×C13—21no—
206C42×C13—21no—
207C22⋊Dic13—21no—
208C22⋊Dic13—21no—
209C22⋊Dic13—21no—
210#6103—21no—
211#6103—21no—
212C4⋊Dic13C22×C411yescharacteristic
213C4⋊Dic13C22×C411yescharacteristic
214#6101—21no—
215#6101—21no—
216C4×Dic13—21no—
217#6099—24no—
218#6099—21no—
219#6099—21no—
220#6099—22no—
221#6099—22no—
222#6099—22no—
223#6099—22no—
224#6099#4112yes—
225#6099#4112yes—
226C2×#1055—24no—
227C2×#1055—21no—
228C2×#1055—21no—
229C2×#1055—21no—
230C2×#1055—21no—
231C2×#1055—21no—
232C2×#1055—21no—
233C2×#1055—21no—
234C2×#1055—21no—
235C2×#1055C22×C411yescharacteristic
236C2×#1055C22×C411yescharacteristic
237C2×#1055C22×C411yescharacteristic
238C2×#1055C22×C411yescharacteristic
239C2×#1055C2×D411yescharacteristic
240C2×#1055C2×D411yescharacteristic
241C2×#1055C2×D411yescharacteristic
242C2×#1055C2×D411yescharacteristic
243C2×#1055#4112yes—
244C2×#1055#4112yes—
245#6094—42no—
246C8×D13—42no—
247#3091—131no—
248#2930—131no—
249#2873—131no—
250#1929—131no—
251#1929—131no—
252#1922—131no—
253#1922—131no—
254#1871—131no—
255#1855—131no—
256#1826D1311yescharacteristic, complemented
257#1773—131no—
258#1772—131no—
259#1765—131no—
260#1764—131no—
261#1753—131no—
262C23×C13—21no—
263C23×C13—21no—
264C23×C13—41no—
265C23×C13—41no—
266C23×C13C4×D411yescharacteristic
267C23×C13C4×D411yescharacteristic
268C23×C13C2×#4111yescharacteristic
269C22×D13—21no—
270C2×C4×C13—21no—
271C2×C4×C13—21no—
272C2×C4×C13—21no—
273C2×C4×C13—21no—
274C2×C4×C13—21no—
275C2×C4×C13—21no—
276C2×C4×C13—21no—
277C2×C4×C13—21no—
278C2×C4×C13—21no—
279C2×C4×C13—21no—
280C2×C4×C13—22no—
281C2×C4×C13—21no—
282C2×C4×C13—21no—
283C2×C4×C13—21no—
284C2×C4×C13—21no—
285C2×C4×C13—41no—
286C2×C4×C13—41no—
287C2×C4×C13—41no—
288C2×C4×C13—41no—
289C2×C4×C13—41no—
290C2×C4×C13—81no—
291C2×C4×C13—81no—
292C2×C4×C13C4×D411yescharacteristic
293C2×C4×C13C4×D411yescharacteristic
294C2×C4×C13C23×C411yescharacteristic
295C2×C4×C13C22×D411yescharacteristic
296C2×C4×C13C2×#4111yescharacteristic
297C2×C4×C13C2×#4111yescharacteristic
298C2×C4×C13C2×#4111yescharacteristic
299C2×C4×C13C2×#4111yescharacteristic
300C22⋊D13—41no—
301C22⋊D13—41no—
302C22⋊D13—81no—
303C22⋊D13—81no—
304C2×Dic13—21no—
305C2×Dic13—21no—
306C2×Dic13—21no—
307D52—21no—
308D52—21no—
309C4×D13—41no—
310C4×D13—41no—
311Dic26—21no—
312Dic26—21no—
313C8×C13—41no—
314C8×C13—41no—
315#1055—21no—
316#1055—21no—
317#1055—21no—
318#1055—21no—
319#1055—21no—
320#1055—21no—
321#1055—22no—
322#1055—22no—
323#1055#12312yes—
324#1055#12312yes—
325C2×#131—131no—
326C22×M16—131no—
327C22×M16—131no—
328#525—131no—
329C2×#117C2×D1311yescharacteristic
330#485—131no—
331#485—131no—
332#484—131no—
333#483—131no—
334#482—131no—
335#482—131no—
336#481—131no—
337#480—131no—
338#436—261no—
339#436—261no—
340#435—261no—
341#435—261no—
342C2×#108—131no—
343C2×#108—131no—
344#427—131no—
345#427—131no—
346#424—131no—
347C2×#104—131no—
348C2×#104—131no—
349#416—131no—
350#416—131no—
351#408—131no—
352#407C2×D1311yescharacteristic
353C2×C22⋊C8—131no—
354#405—131no—
355#405—131no—
356#405—131no—
357#405—131no—
358#405—131no—
359#405—261no—
360#405—261no—
361C4×M16—261no—
362C4×M16—261no—
363C2×#97—131no—
364C2×C4×C8—131no—
365C4×C22⋊C4C2×D1311yescharacteristic
366#341—131no—
367#341—131no—
368#339—131no—
369#339—131no—
370#339C2×D1311yescharacteristic
371#339C2×D1311yescharacteristic
372#339C2×D1311yescharacteristic
373#339C2×D1311yescharacteristic
374#336—131no—
375#336—131no—
376C22×C13—21no—
377C22×C13—21no—
378C22×C13—21no—
379C22×C13—21no—
380C22×C13—21no—
381C22×C13—21no—
382C22×C13—21no—
383C22×C13—21no—
384C22×C13—81no—
385C22×C13—81no—
386C22×C13C2×C4×D411yescharacteristic
387C22×C13#52911yescharacteristic
388C22×C13#52911yescharacteristic
389C2×D13—41no—
390C2×D13—41no—
391C2×D13—41no—
392C4×C13—21no—
393C4×C13—21no—
394C4×C13—42no—
395C4×C13—41no—
396C4×C13—41no—
397C4×C13—41no—
398C4×C13—41no—
399C4×C13—81no—
400C4×C13C4×#4111yescharacteristic
401C4×C13C4×#4111yescharacteristic
402C4×C13C2×#12311yescharacteristic
403C4×C13#52511yescharacteristic
404Dic13—41no—
405Dic13—41no—
406Dic13—41no—
407C2×#41—131no—
408C23×C4C22×D1311yescharacteristic
409#131—262no—
410#131—262no—
411C2×M16—131no—
412C2×M16—131no—
413C2×M16—131no—
414C2×M16—131no—
415C2×M16—131no—
416C2×M16—131no—
417C2×M16—261no—
418C2×M16—262no—
419C2×M16—262no—
420C2×M16—262no—
421C2×M16—262no—
422C2×M16—261no—
423C2×M16C22×D1311yescharacteristic
424C2×M16C22×D1311yescharacteristic
425C22×C8—131no—
426C22×C8—131no—
427C22×C8—131no—
428C22×C8—131no—
429C22×C8—261no—
430C22×C8—261no—
431#123—261no—
432C22⋊Q8—131no—
433C22⋊Q8—131no—
434#121—131no—
435#121—131no—
436#120—261no—
437C4×D4—261no—
438C4×D4—261no—
439#117—21no—
440#117—21no—
441#117—131no—
442#117C4×D1311yescharacteristic
443#117C4×D1311yescharacteristic
444#117C22×D1311yescharacteristic
445#117C22×D1311yescharacteristic
446C2×C4⋊C4C4×D1311yescharacteristic
447C2×C4⋊C4C4×D1311yescharacteristic
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C42—21no—
451C2×C42C22×D1311yescharacteristic
452C2×C42C22×D1311yescharacteristic
453#108—262no—
454#108—262no—
455#107—131no—
456#107—131no—
457#107—131no—
458#107—131no—
459#106—131no—
460#106—131no—
461#106—131no—
462#106—131no—
463C4⋊C8—261no—
464C4⋊C8—261no—
465#104—262no—
466#104—262no—
467#103—131no—
468#103—131no—
469#103—131no—
470#103—131no—
471#102—131no—
472#102—131no—
473#102—131no—
474#102—131no—
475C22⋊C8—21no—
476C22⋊C8—21no—
477C22⋊C8—131no—
478C22⋊C8—131no—
479C22⋊C8—131no—
480C22⋊C8—131no—
481C22⋊C8—261no—
482C22⋊C8—261no—
483#97—262no—
484#97—261no—
485#97—261no—
486#97—261no—
487#97—261no—
488#97—261no—
489C4×C8—262no—
490C4×C8—261no—
491C4×C8—261no—
492C4×C8—261no—
493C4×C8—261no—
494C4×C8—261no—
495#95—21no—
496C2×C13—21no—
497C2×C13—21no—
498C2×C13—41no—
499C2×C13—41no—
500C2×C13C4×#12311yescharacteristic
501C2×C13#295611yescharacteristic
502C2×C13#295711yescharacteristic
503D13—81no—
504C24#612911yescharacteristic
505#41—261no—
506#41—261no—
507#41—261no—
508#41—261no—
509C2×Q8—131no—
510C2×D4—131no—
511C2×D4—261no—
512C2×D4—261no—
513C2×D4—261no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—261no—
523C22×C4C2×C4×D1311yescharacteristic
524C22×C4C2×C4×D1311yescharacteristic
525C22×C4D4×D1311yescharacteristic
526C22×C4D4×D1311yescharacteristic
527C22×C4#612911yescharacteristic
528C22×C4C23×D1311yescharacteristic
529M16—21no—
530M16—21no—
531M16—21no—
532M16—21no—
533M16—132no—
534M16—132no—
535M16—262no—
536M16—262no—
537M16—262no—
538M16—262no—
539M16—264no—
540M16—261no—
541M16—261no—
542M16—522no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—131no—
546C2×C8—131no—
547C2×C8—132no—
548C2×C8—132no—
549C2×C8—131no—
550C2×C8—131no—
551C2×C8—131no—
552C2×C8—131no—
553C2×C8—131no—
554C2×C8—131no—
555C2×C8—264no—
556C2×C8—261no—
557C2×C8—261no—
558C2×C8—261no—
559C2×C8—261no—
560C2×C8—261no—
561C2×C8—261no—
562C2×C8—261no—
563C2×C8—261no—
564C2×C8—522no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—131no—
568C4⋊C4—131no—
569C4⋊C4—261no—
570C4⋊C4—261no—
571C4⋊C4C2×C4×D1311yescharacteristic
572C4⋊C4C2×C4×D1311yescharacteristic
573C4⋊C4C2×C4×D1311yescharacteristic
574C4⋊C4C2×C4×D1311yescharacteristic
575C22⋊C4—21no—
576C22⋊C4—21no—
577C22⋊C4—21no—
578C22⋊C4—21no—
579C22⋊C4—42no—
580C22⋊C4—261no—
581C22⋊C4—261no—
582C22⋊C4—261no—
583C22⋊C4—261no—
584C22⋊C4—261no—
585C42—21no—
586C42—21no—
587C42—21no—
588C42—21no—
589C42—21no—
590C42—21no—
591C42—21no—
592C42—21no—
593C42—261no—
594C13#2159411yescharacteristic, complemented, Sylow
595C23—21no—
596C23—21no—
597C23—41no—
598C23—41no—
599C23—261no—
600C23#8813511yescharacteristic
601C23#8813511yescharacteristic
602C23C2×#612911yescharacteristic
603Q8—261no—
604Q8—261no—
605D4—261no—
606D4—261no—
607D4—521no—
608D4—521no—
609D4—1041no—
610D4—1041no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—22no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—81no—
632C2×C4—81no—
633C2×C4—261no—
634C2×C4—261no—
635C2×C4—261no—
636C2×C4—521no—
637C2×C4—521no—
638C2×C4#8813511yescharacteristic
639C2×C4#8813511yescharacteristic
640C2×C4C22×C4×D1311yescharacteristic
641C2×C4C2×D4×D1311yescharacteristic
642C2×C4#41×D1311yescharacteristic
643C2×C4#41×D1311yescharacteristic
644C2×C4#41×D1311yescharacteristic
645C2×C4#41×D1311yescharacteristic
646C8—41no—
647C8—41no—
648C8—132no—
649C8—132no—
650C8—261no—
651C8—261no—
652C8—261no—
653C8—261no—
654C8—261no—
655C8—261no—
656C8—262no—
657C8—262no—
658C22—21no—
659C22—21no—
660C22—21no—
661C22—21no—
662C22—21no—
663C22—21no—
664C22—21no—
665C22—21no—
666C22—81no—
667C22—81no—
668C22—521no—
669C22—521no—
670C22—521no—
671C22C2×#8813511yescharacteristic
672C22#1171935411yescharacteristic
673C22#1171935411yescharacteristic
674C4—21no—
675C4—21no—
676C4—42no—
677C4—41no—
678C4—41no—
679C4—41no—
680C4—41no—
681C4—81no—
682C4—521no—
683C4—521no—
684C4—521no—
685C4#1171922711yescharacteristic
686C4#1171922711yescharacteristic
687C4D13×#12311yescharacteristic
688C4#1171936111yescharacteristic
689C2—21no—
690C2—21no—
691C2—41no—
692C2—41no—
693C2—1041no—
694C2#1311735311yescharacteristic
695C2#1312374211yescharacteristic
696C2#1312374911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1826C2
socleC22×C13C2×C4×D4
prime radical#11719496C22
cosocleC22×C4×C13C24
hypercenter#1826D13
hypocenterC13#21594
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1826

Complements

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

NH ≅ G/Ntype
3. #13123255C2semidirect
4. #13115482C2semidirect
5. #13115482C2semidirect
6. #13115433C2semidirect
7. #13115433C2semidirect
9. #13115040C2semidirect
10. #13114719C2semidirect
11. #13114714C2semidirect
12. #13114677C2semidirect
13. #13114670C2semidirect
14. #13114620C2semidirect
15. C13×#1826C2semidirect
29. #11718664C4semidirect
30. #11718664C4semidirect
41. #11718657C4semidirect
42. #11718657C4semidirect
43. #11718632C4semidirect
44. #11718631C4semidirect
45. #11718629C4semidirect
46. #11718628C4semidirect
256. #1826D13semidirect
594. C13#21594semidirect

Maximal subgroups

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

subgroupindex
#131247492
#131235352
#131232552
#131154822
#131154332
#131151362
#131150402
#131147192
#131147142
#131146772
#131146702
#131146202
C13×#18262
#2159413