Finite Group Databasebeta

← #15870321

Subgroups — #15870321

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#13124745C211yesmaximal, characteristic
2#13123540C211yesmaximal, characteristic
3#13123254C211yesmaximal, characteristic, complemented
4#13115487C211yesmaximal, characteristic, complemented
5#13115487C211yesmaximal, characteristic, complemented
6#13115438C211yesmaximal, characteristic, complemented
7#13115438C211yesmaximal, characteristic, complemented
8#13115041C211yesmaximal, characteristic, complemented
9#13114936C211yesmaximal, characteristic, complemented
10#13114719C211yesmaximal, characteristic, complemented
11#13114714C211yesmaximal, characteristic, complemented
12#13114681C211yesmaximal, characteristic, complemented
13#13114674C211yesmaximal, characteristic, complemented
14#13114620C211yesmaximal, characteristic, complemented
15C13×#1871C211yesmaximal, characteristic
16C22×C13×M16C2211yescharacteristic
17C13×#525C2211yescharacteristic
18C2×#88202C2211yescharacteristic
19C2×#88180C2211yescharacteristic
20C22×#6099C2211yescharacteristic
21C2×C13×#104C2211yescharacteristic
22C2×C13×#104C2211yescharacteristic
23C4×C13×C22⋊C4C2211yescharacteristic
24#11718895C2211yescharacteristic
25#11718894C2211yescharacteristic
26#11718894C2211yescharacteristic
27#11718868C2211yescharacteristic
28C2×C22⋊#1055C2211yescharacteristic
29C2×#88062C2211yescharacteristic
30C2×#88062C2211yescharacteristic
31#11718783C2211yescharacteristic
32#11718783C2211yescharacteristic
33#11718783C2211yescharacteristic
34#11718783C2211yescharacteristic
35M16×Dic13—21no—
36M16×Dic13—21no—
37#11718762—21no—
38#11718762—21no—
39#11718706C411yescharacteristic, complemented
40#11718706C411yescharacteristic, complemented
41#11718705C411yescharacteristic, complemented
42#11718704C411yescharacteristic, complemented
43#11718696C411yescharacteristic, complemented
44#11718696C411yescharacteristic, complemented
45#11718695C411yescharacteristic, complemented
46#11718694C411yescharacteristic, complemented
47#11718673—21no—
48#11718673—21no—
49#11718672—21no—
50#11718672—21no—
51#11718660C2211yescharacteristic
52#11718659C2211yescharacteristic
53#11718659C2211yescharacteristic
54#11718658C2211yescharacteristic
55C2×#88043C2211yescharacteristic
56C2×C4×#1055C2211yescharacteristic
57C13×#339C2211yescharacteristic
58C13×#339C2211yescharacteristic
59#11718150C2211yescharacteristic
60#11718150C2211yescharacteristic
61#11718116C2211yescharacteristic
62#11718116C2211yescharacteristic
63#11718115C2211yescharacteristic
64#11718115C2211yescharacteristic
65#11718115C2211yescharacteristic
66#11718115C2211yescharacteristic
67C2×C13×#41C2311yescharacteristic
68C23×C4×C13C2311yescharacteristic
69C2×C13×M16—21no—
70C2×C13×M16—22no—
71C2×C13×M16—22no—
72C2×C13×M16C2311yescharacteristic
73C2×C13×M16C2311yescharacteristic
74C22×C8×C13—21no—
75C13×#123—21no—
76C13×C22⋊Q8C2×C411yescharacteristic
77C13×C22⋊Q8C2×C411yescharacteristic
78C13×#121C2×C411yescharacteristic
79C13×#121C2×C411yescharacteristic
80C13×#120—21no—
81C4×D4×C13—21no—
82C4×D4×C13—21no—
83C13×#117C2311yescharacteristic
84C2×C13×C22⋊C4—21no—
85C2×C42×C13C2311yescharacteristic
86C2×C42×C13C2311yescharacteristic
87C2×C22⋊Dic13—21no—
88#88202—22no—
89#88202—22no—
90#88180—21no—
91#88180—21no—
92#88180C2×C411yescharacteristic
93#88180C2×C411yescharacteristic
94#88180C2311yescharacteristic
95#88180C2311yescharacteristic
96C2×C4⋊Dic13C2×C411yescharacteristic
97C2×C4⋊Dic13C2×C411yescharacteristic
98C2×C4×Dic13—21no—
99C2×#6099—21no—
100C2×#6099—22no—
101C2×#6099—22no—
102C2×#6099D411yescharacteristic
103C2×#6099D411yescharacteristic
104C2×#6099D411yescharacteristic
105C2×#6099D411yescharacteristic
106C2×#6099C2311yescharacteristic
107C2×#6099C2311yescharacteristic
108C22×#1055—21no—
109C22×#1055C2311yescharacteristic
110C22×#1055C2311yescharacteristic
111C22×#1055C2311yescharacteristic
112C22×#1055C2311yescharacteristic
113C13×#104—22no—
114C13×#104—22no—
115C13×#95—21no—
116#88075C2×C411yescharacteristic
117#88075C2×C411yescharacteristic
118#88075C2×C411yescharacteristic
119#88075C2×C411yescharacteristic
120#88072C2×C411yescharacteristic
121#88072C2×C411yescharacteristic
122#88072C2×C411yescharacteristic
123#88072C2×C411yescharacteristic
124C22⋊#1055—21no—
125C22⋊#1055—21no—
126C22⋊#1055—21no—
127C22⋊#1055—21no—
128C22⋊#1055C2×C411yescharacteristic
129C22⋊#1055C2×C411yescharacteristic
130C22⋊#1055C2×C411yescharacteristic
131C22⋊#1055C2×C411yescharacteristic
132#88062—22no—
133#88062—22no—
134#88055—21no—
135#88055—21no—
136#88055—21no—
137#88055—21no—
138C8×Dic13—21no—
139C8×Dic13—21no—
140C8×Dic13—21no—
141C8×Dic13—21no—
142#88048C2×C411yescharacteristic
143#88048C2×C411yescharacteristic
144#88048C2×C411yescharacteristic
145#88048C2×C411yescharacteristic
146#88047C2×C411yescharacteristic
147#88047C2×C411yescharacteristic
148#88047C2×C411yescharacteristic
149#88047C2×C411yescharacteristic
150C4⋊#1055—21no—
151C4⋊#1055—21no—
152#88043—21no—
153#88043—22no—
154C4×#1055—21no—
155C4×#1055—22no—
156#21594—131nomaximal, Sylow
157C24×C13#4111yescharacteristic
158C13×#41—21no—
159C13×#41—21no—
160C13×#41—21no—
161C13×#41—21no—
162C2×Q8×C13C22×C411yescharacteristic
163C2×D4×C13—21no—
164C2×D4×C13—21no—
165C2×D4×C13—21no—
166C2×D4×C13C22×C411yescharacteristic
167C22×C4×C13—21no—
168C22×C4×C13—21no—
169C22×C4×C13—21no—
170C22×C4×C13—21no—
171C22×C4×C13—21no—
172C22×C4×C13—21no—
173C22×C4×C13—21no—
174C22×C4×C13C22×C411yescharacteristic
175C22×C4×C13C22×C411yescharacteristic
176C22×C4×C13C2×D411yescharacteristic
177C22×C4×C13C2×D411yescharacteristic
178C22×C4×C13#4111yescharacteristic
179C22×C4×C13C2411yescharacteristic
180C22×Dic13—21no—
181C22×Dic13—21no—
182C13×M16—24no—
183C13×M16—21no—
184C13×M16—21no—
185C13×M16#4112yes—
186C13×M16#4112yes—
187C2×C8×C13—24no—
188C2×C8×C13—21no—
189C2×C8×C13—21no—
190C13×C4⋊C4—21no—
191C13×C4⋊C4—21no—
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—21no—
199C13×C22⋊C4—42no—
200C42×C13—21no—
201C42×C13—21no—
202C42×C13—21no—
203C42×C13—21no—
204C42×C13—21no—
205C22⋊Dic13—21no—
206C22⋊Dic13—21no—
207C22⋊Dic13—21no—
208C22⋊Dic13—21no—
209C4⋊Dic13—21no—
210C4⋊Dic13—21no—
211C4⋊Dic13C22×C411yescharacteristic
212C4⋊Dic13C22×C411yescharacteristic
213C4⋊Dic13C22×C411yescharacteristic
214C4⋊Dic13C22×C411yescharacteristic
215C4×Dic13—21no—
216C4×Dic13—21no—
217C4×Dic13—21no—
218C4×Dic13—21no—
219#6099—22no—
220#6099—22no—
221#6099—22no—
222#6099—22no—
223#6099—21no—
224#6099—21no—
225#6099—21no—
226#6099—21no—
227#6099—42no—
228C2×#1055—21no—
229C2×#1055—21no—
230C2×#1055—21no—
231C2×#1055—21no—
232C2×#1055—21no—
233C2×#1055—21no—
234C2×#1055—21no—
235C2×#1055—21no—
236C2×#1055—42no—
237C2×#1055C22×C411yescharacteristic
238C2×#1055C22×C411yescharacteristic
239C2×#1055C22×C411yescharacteristic
240C2×#1055C22×C411yescharacteristic
241C2×#1055C2×D411yescharacteristic
242C2×#1055C2×D411yescharacteristic
243C2×#1055C2×D411yescharacteristic
244C2×#1055C2×D411yescharacteristic
245C2×#1055#4112yes—
246C2×#1055#4112yes—
247#3091—131no—
248#2930—131no—
249#2873—131no—
250#1929—131no—
251#1929—131no—
252#1922—131no—
253#1922—131no—
254#1871D1311yescharacteristic
255#1855—131no—
256#1826—131no—
257#1773—131no—
258#1772—131no—
259#1765—131no—
260#1764—131no—
261#1753—131no—
262C23×C13—21no—
263C23×C13—21no—
264C23×C13—21no—
265C23×C13—41no—
266C23×C13—41no—
267C23×C13C4×D411yescharacteristic
268C23×C13C4×D411yescharacteristic
269C23×C13C2×#4111yescharacteristic
270Q8×C13—21no—
271Q8×C13—21no—
272D4×C13—21no—
273D4×C13—21no—
274D4×C13—41no—
275D4×C13—41no—
276D4×C13—81no—
277D4×C13—81no—
278C2×C4×C13—21no—
279C2×C4×C13—21no—
280C2×C4×C13—21no—
281C2×C4×C13—21no—
282C2×C4×C13—21no—
283C2×C4×C13—21no—
284C2×C4×C13—21no—
285C2×C4×C13—21no—
286C2×C4×C13—21no—
287C2×C4×C13—21no—
288C2×C4×C13—22no—
289C2×C4×C13—21no—
290C2×C4×C13—21no—
291C2×C4×C13—21no—
292C2×C4×C13—41no—
293C2×C4×C13—41no—
294C2×C4×C13—41no—
295C2×C4×C13—41no—
296C2×C4×C13—41no—
297C2×C4×C13—41no—
298C2×C4×C13—41no—
299C2×C4×C13C4×D411yescharacteristic
300C2×C4×C13C4×D411yescharacteristic
301C2×C4×C13C23×C411yescharacteristic
302C2×C4×C13C22×D411yescharacteristic
303C2×C4×C13C2×#4111yescharacteristic
304C2×C4×C13C2×#4111yescharacteristic
305C2×C4×C13C2×#4111yescharacteristic
306C2×C4×C13C2×#4111yescharacteristic
307C2×Dic13—21no—
308C2×Dic13—21no—
309C2×Dic13—21no—
310C2×Dic13—21no—
311C2×Dic13—81no—
312C2×Dic13—81no—
313C8×C13—22no—
314C8×C13—22no—
315#1055—21no—
316#1055—21no—
317#1055—21no—
318#1055—21no—
319#1055—21no—
320#1055—21no—
321#1055—41no—
322#1055—41no—
323#1055#12312yes—
324#1055#12312yes—
325C2×#131—131no—
326C22×M16—131no—
327C22×M16C2×D1311yescharacteristic
328#525C2×D1311yescharacteristic
329C2×#117—131no—
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×#104C2×D1311yescharacteristic
348C2×#104C2×D1311yescharacteristic
349#416—131no—
350#416—131no—
351#408—131no—
352#407—131no—
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#339—131no—
371#339—131no—
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—41no—
385C22×C13—41no—
386C22×C13—41no—
387C22×C13—81no—
388C22×C13—81no—
389C22×C13C2×C4×D411yescharacteristic
390C22×C13#52911yescharacteristic
391C22×C13#52911yescharacteristic
392C4×C13—21no—
393C4×C13—21no—
394C4×C13—42no—
395C4×C13—41no—
396C4×C13—41no—
397C4×C13—41no—
398C4×C13—81no—
399C4×C13C4×#4111yescharacteristic
400C4×C13C4×#4111yescharacteristic
401C4×C13C2×#12311yescharacteristic
402C4×C13#52511yescharacteristic
403Dic13—41no—
404Dic13—41no—
405Dic13—41no—
406Dic13—41no—
407C2×#41C22×D1311yescharacteristic
408C23×C4C22×D1311yescharacteristic
409#131—262no—
410#131—262no—
411C2×M16—21no—
412C2×M16—22no—
413C2×M16—22no—
414C2×M16—131no—
415C2×M16—131no—
416C2×M16—131no—
417C2×M16—131no—
418C2×M16—131no—
419C2×M16—131no—
420C2×M16—262no—
421C2×M16—262no—
422C2×M16—261no—
423C2×M16C22×D1311yescharacteristic
424C2×M16C22×D1311yescharacteristic
425C22×C8—21no—
426C22×C8—131no—
427C22×C8—131no—
428C22×C8—131no—
429C22×C8—131no—
430C22×C8—261no—
431#123—21no—
432C22⋊Q8C4×D1311yescharacteristic
433C22⋊Q8C4×D1311yescharacteristic
434#121C4×D1311yescharacteristic
435#121C4×D1311yescharacteristic
436#120—21no—
437C4×D4—21no—
438C4×D4—21no—
439#117—131no—
440#117—131no—
441#117—131no—
442#117—131no—
443#117—261no—
444#117—261no—
445#117C22×D1311yescharacteristic
446C2×C4⋊C4—131no—
447C2×C4⋊C4—131no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—261no—
450C2×C42—261no—
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—22no—
466#104—22no—
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—131no—
476C22⋊C8—131no—
477C22⋊C8—131no—
478C22⋊C8—131no—
479C22⋊C8—261no—
480C22⋊C8—261no—
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×C13—81no—
501C2×C13C4×#12311yescharacteristic
502C2×C13#295611yescharacteristic
503C2×C13#295711yescharacteristic
504C24#612911yescharacteristic
505#41—21no—
506#41—21no—
507#41—21no—
508#41—21no—
509C2×Q8C2×C4×D1311yescharacteristic
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4C2×C4×D1311yescharacteristic
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—261no—
522C22×C4—261no—
523C22×C4C2×C4×D1311yescharacteristic
524C22×C4C2×C4×D1311yescharacteristic
525C22×C4D4×D1311yescharacteristic
526C22×C4D4×D1311yescharacteristic
527C22×C4#612911yescharacteristic
528C22×C4C23×D1311yescharacteristic
529M16—24no—
530M16—21no—
531M16—21no—
532M16—262no—
533M16—262no—
534M16—262no—
535M16—262no—
536M16—261no—
537M16—261no—
538M16—261no—
539M16—261no—
540M16—522no—
541M16#612912yes—
542M16#612912yes—
543C2×C8—24no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—131no—
547C2×C8—131no—
548C2×C8—132no—
549C2×C8—132no—
550C2×C8—131no—
551C2×C8—131no—
552C2×C8—131no—
553C2×C8—131no—
554C2×C8—131no—
555C2×C8—131no—
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—131no—
570C4⋊C4—131no—
571C4⋊C4—261no—
572C4⋊C4—261no—
573C4⋊C4C2×C4×D1311yescharacteristic
574C4⋊C4C2×C4×D1311yescharacteristic
575C22⋊C4—21no—
576C22⋊C4—21no—
577C22⋊C4—21no—
578C22⋊C4—21no—
579C22⋊C4—21no—
580C22⋊C4—42no—
581C22⋊C4—261no—
582C22⋊C4—261no—
583C22⋊C4—261no—
584C22⋊C4—261no—
585C42—21no—
586C42—21no—
587C42—21no—
588C42—21no—
589C42—21no—
590C42—261no—
591C42—261no—
592C42—261no—
593C42—261no—
594C13#2159411yescharacteristic, complemented, Sylow
595C23—21no—
596C23—21no—
597C23—21no—
598C23—41no—
599C23—41no—
600C23#8813511yescharacteristic
601C23#8813511yescharacteristic
602C23C2×#612911yescharacteristic
603Q8—21no—
604Q8—21no—
605D4—21no—
606D4—21no—
607D4—41no—
608D4—41no—
609D4—81no—
610D4—81no—
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—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—261no—
633C2×C4—261no—
634C2×C4—261no—
635C2×C4—261no—
636C2×C4—1041no—
637C2×C4—1041no—
638C2×C4#8813511yescharacteristic
639C2×C4#8813511yescharacteristic
640C2×C4C22×C4×D1311yescharacteristic
641C2×C4C2×D4×D1311yescharacteristic
642C2×C4C2×#612911yescharacteristic
643C2×C4C2×#612911yescharacteristic
644C2×C4#41×D1311yescharacteristic
645C2×C4#41×D1311yescharacteristic
646C8—22no—
647C8—22no—
648C8—132no—
649C8—132no—
650C8—261no—
651C8—261no—
652C8—261no—
653C8—261no—
654C8—261no—
655C8—261no—
656C8—521no—
657C8—521no—
658C22—21no—
659C22—21no—
660C22—21no—
661C22—21no—
662C22—21no—
663C22—21no—
664C22—21no—
665C22—21no—
666C22—41no—
667C22—41no—
668C22—41no—
669C22—81no—
670C22—81no—
671C22C2×#8813511yescharacteristic
672C22#1171930511yescharacteristic
673C22#1171930511yescharacteristic
674C4—21no—
675C4—21no—
676C4—42no—
677C4—41no—
678C4—41no—
679C4—41no—
680C4—81no—
681C4—521no—
682C4—521no—
683C4—521no—
684C4—521no—
685C4C4×#612911yescharacteristic
686C4C4×#612911yescharacteristic
687C4#1171929111yescharacteristic
688C4D13×#12311yescharacteristic
689C2—21no—
690C2—21no—
691C2—41no—
692C2—41no—
693C2—81no—
694C2#1311736111yescharacteristic
695C2#1312374211yescharacteristic
696C2#1312374911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1871C2
socleC22×C13C2×C4×D4
prime radicalC13×#525C22
cosocleC22×C4×C13C24
hypercenter#1871D13
hypocenterC13#21594
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1871

Complements

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

NH ≅ G/Ntype
3. #13123254C2semidirect
4. #13115487C2semidirect
5. #13115487C2semidirect
6. #13115438C2semidirect
7. #13115438C2semidirect
8. #13115041C2semidirect
9. #13114936C2semidirect
10. #13114719C2semidirect
11. #13114714C2semidirect
12. #13114681C2semidirect
13. #13114674C2semidirect
14. #13114620C2semidirect
39. #11718706C4semidirect
40. #11718706C4semidirect
41. #11718705C4semidirect
42. #11718704C4semidirect
43. #11718696C4semidirect
44. #11718696C4semidirect
45. #11718695C4semidirect
46. #11718694C4semidirect
594. C13#21594semidirect

Maximal subgroups

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

subgroupindex
#131247452
#131235402
#131232542
#131154872
#131154382
#131150412
#131149362
#131147192
#131147142
#131146812
#131146742
#131146202
C13×#18712
#2159413