Finite Group Databasebeta

← #15870312

Subgroups — #15870312

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#13123254C211yesmaximal, characteristic, complemented
3#13115481C211yesmaximal, characteristic, complemented
4#13115481C211yesmaximal, characteristic, complemented
5#13115432C211yesmaximal, characteristic, complemented
6#13115432C211yesmaximal, characteristic, complemented
7#13115139C211yesmaximal, characteristic
8#13115040C211yesmaximal, characteristic, complemented
9#13114933C211yesmaximal, characteristic, complemented
10#13114721C211yesmaximal, characteristic, complemented
11#13114716C211yesmaximal, characteristic, complemented
12#13114678C211yesmaximal, characteristic, complemented
13#13114671C211yesmaximal, characteristic, complemented
14#13114617C211yesmaximal, characteristic, complemented
15C13×#2930C211yesmaximal, characteristic
16C2×C13×#131C2211yescharacteristic
17C22×C13×M16C2211yescharacteristic
18C13×#525C2211yescharacteristic
19C2×#88180C2211yescharacteristic
20C22×#6099C2211yescharacteristic
21C13×#436—21no—
22C13×#436—21no—
23C13×#435—21no—
24C13×#435—21no—
25C13×#424C2211yescharacteristic
26C13×#408C2211yescharacteristic
27C13×#407C2211yescharacteristic
28C13×#405C2211yescharacteristic
29C2×#88077C2211yescharacteristic
30C2×#88077C2211yescharacteristic
31#11718894C2211yescharacteristic
32#11718894C2211yescharacteristic
33C4×C22⋊Dic13C2211yescharacteristic
34C2×C22⋊#1055C2211yescharacteristic
35C2×#88062C2211yescharacteristic
36C2×#88062C2211yescharacteristic
37#11718783—21no—
38#11718783—21no—
39M16×Dic13—21no—
40M16×Dic13—21no—
41#11718762C2211yescharacteristic
42#11718762C2211yescharacteristic
43#11718762C2211yescharacteristic
44#11718762C2211yescharacteristic
45C2×#88055C2211yescharacteristic
46C2×C8×Dic13C2211yescharacteristic
47#11718706C411yescharacteristic, complemented
48#11718706C411yescharacteristic, complemented
49#11718705C411yescharacteristic, complemented
50#11718704C411yescharacteristic, complemented
51#11718696C411yescharacteristic, complemented
52#11718696C411yescharacteristic, complemented
53#11718695C411yescharacteristic, complemented
54#11718694C411yescharacteristic, complemented
55#11718659C2211yescharacteristic
56#11718659C2211yescharacteristic
57#11718150C2211yescharacteristic
58#11718150C2211yescharacteristic
59#11718147C2211yescharacteristic
60#11718147C2211yescharacteristic
61#11718147C2211yescharacteristic
62#11718147C2211yescharacteristic
63#11718142C2211yescharacteristic
64#11718142C2211yescharacteristic
65#11718124C2211yescharacteristic
66#11718124C2211yescharacteristic
67C2×C13×#41C2311yescharacteristic
68C23×C4×C13C2311yescharacteristic
69C13×#131—22no—
70C13×#131—22no—
71C2×C13×M16—21no—
72C2×C13×M16—22no—
73C2×C13×M16—22no—
74C2×C13×M16D411yescharacteristic
75C2×C13×M16D411yescharacteristic
76C2×C13×M16D411yescharacteristic
77C2×C13×M16D411yescharacteristic
78C2×C13×M16C2311yescharacteristic
79C2×C13×M16C2311yescharacteristic
80C22×C8×C13—21no—
81C22×C8×C13C2311yescharacteristic
82C22×C8×C13C2311yescharacteristic
83C13×#123—21no—
84C13×C22⋊Q8C2×C411yescharacteristic
85C13×C22⋊Q8C2×C411yescharacteristic
86C13×#121C2×C411yescharacteristic
87C13×#121C2×C411yescharacteristic
88C13×#120—21no—
89C4×D4×C13—21no—
90C4×D4×C13—21no—
91C13×#117C2311yescharacteristic
92C2×C22⋊Dic13—21no—
93C2×C22⋊Dic13—21no—
94#88180—21no—
95#88180—21no—
96#88180C2×C411yescharacteristic
97#88180C2×C411yescharacteristic
98#88180C2311yescharacteristic
99#88180C2311yescharacteristic
100C2×C4⋊Dic13C2×C411yescharacteristic
101C2×C4⋊Dic13C2×C411yescharacteristic
102C2×C4×Dic13—21no—
103C2×C4×Dic13C2311yescharacteristic
104C2×C4×Dic13C2311yescharacteristic
105C2×#6099—21no—
106C2×#6099—22no—
107C2×#6099—22no—
108C2×#6099C2311yescharacteristic
109C2×#6099C2311yescharacteristic
110C22×#1055—21no—
111C22×#1055C2311yescharacteristic
112C22×#1055C2311yescharacteristic
113C13×C4⋊C8—21no—
114C13×C4⋊C8—21no—
115C13×C22⋊C8—21no—
116C13×C22⋊C8—21no—
117C13×C22⋊C8—21no—
118C13×C22⋊C8—21no—
119C13×#97—21no—
120C4×C8×C13—21no—
121#88077—22no—
122#88077—22no—
123#88075C2×C411yescharacteristic
124#88075C2×C411yescharacteristic
125#88075C2×C411yescharacteristic
126#88075C2×C411yescharacteristic
127#88072C2×C411yescharacteristic
128#88072C2×C411yescharacteristic
129#88072C2×C411yescharacteristic
130#88072C2×C411yescharacteristic
131#88071—21no—
132C22⋊#1055C2×C411yescharacteristic
133C22⋊#1055C2×C411yescharacteristic
134C22⋊#1055C2×C411yescharacteristic
135C22⋊#1055C2×C411yescharacteristic
136#88062—22no—
137#88062—22no—
138#88055—21no—
139#88055—21no—
140#88055—21no—
141#88055—21no—
142#88055—22no—
143C8×Dic13—21no—
144C8×Dic13—21no—
145C8×Dic13—21no—
146C8×Dic13—21no—
147C8×Dic13—22no—
148#88048C2×C411yescharacteristic
149#88048C2×C411yescharacteristic
150#88048C2×C411yescharacteristic
151#88048C2×C411yescharacteristic
152#88047C2×C411yescharacteristic
153#88047C2×C411yescharacteristic
154#88047C2×C411yescharacteristic
155#88047C2×C411yescharacteristic
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×C13C22×C411yescharacteristic
173C22×C4×C13C22×C411yescharacteristic
174C22×C4×C13C2×D411yescharacteristic
175C22×C4×C13C2×D411yescharacteristic
176C22×C4×C13#4111yescharacteristic
177C22×C4×C13C2411yescharacteristic
178C22×Dic13—21no—
179C22×Dic13—21no—
180C22×Dic13—21no—
181C22×Dic13—21no—
182C13×M16—22no—
183C13×M16—22no—
184C13×M16—22no—
185C13×M16—22no—
186C13×M16—21no—
187C13×M16—21no—
188C13×M16—21no—
189C13×M16—21no—
190C13×M16—42no—
191C2×C8×C13—21no—
192C2×C8×C13—21no—
193C2×C8×C13—21no—
194C2×C8×C13—21no—
195C2×C8×C13—42no—
196C2×C8×C13C2×D411yescharacteristic
197C2×C8×C13C2×D411yescharacteristic
198C2×C8×C13C2×D411yescharacteristic
199C2×C8×C13C2×D411yescharacteristic
200C2×C8×C13#4112yes—
201C2×C8×C13#4112yes—
202C13×C4⋊C4—21no—
203C13×C4⋊C4—21no—
204C13×C4⋊C4C22×C411yescharacteristic
205C13×C4⋊C4C22×C411yescharacteristic
206C13×C22⋊C4—21no—
207C13×C22⋊C4—21no—
208C13×C22⋊C4—21no—
209C13×C22⋊C4—21no—
210C13×C22⋊C4—21no—
211C42×C13—21no—
212C22⋊Dic13—21no—
213C22⋊Dic13—21no—
214C22⋊Dic13—21no—
215C22⋊Dic13—21no—
216C22⋊Dic13—42no—
217C4⋊Dic13—21no—
218C4⋊Dic13—21no—
219C4⋊Dic13C22×C411yescharacteristic
220C4⋊Dic13C22×C411yescharacteristic
221C4⋊Dic13C22×C411yescharacteristic
222C4⋊Dic13C22×C411yescharacteristic
223C4×Dic13—21no—
224C4×Dic13—21no—
225C4×Dic13—21no—
226C4×Dic13—21no—
227C4×Dic13—21no—
228C4×Dic13—21no—
229C4×Dic13—21no—
230C4×Dic13—21no—
231#6099—24no—
232#6099—21no—
233#6099—21no—
234#6099#4112yes—
235#6099#4112yes—
236C2×#1055—24no—
237C2×#1055—21no—
238C2×#1055—21no—
239C2×#1055—21no—
240C2×#1055—21no—
241C2×#1055—21no—
242C2×#1055—21no—
243C2×#1055C22×C411yescharacteristic
244C2×#1055C22×C411yescharacteristic
245C2×#1055C22×C411yescharacteristic
246C2×#1055C22×C411yescharacteristic
247#3091—131no—
248#2930D1311yescharacteristic
249#2873—131no—
250#1929—131no—
251#1929—131no—
252#1922—131no—
253#1922—131no—
254#1871—131no—
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—21no—
289C2×C4×C13—21no—
290C2×C4×C13—21no—
291C2×C4×C13—41no—
292C2×C4×C13—41no—
293C2×C4×C13C4×D411yescharacteristic
294C2×C4×C13C4×D411yescharacteristic
295C2×C4×C13C23×C411yescharacteristic
296C2×C4×C13C22×D411yescharacteristic
297C2×C4×C13C2×#4111yescharacteristic
298C2×C4×C13C2×#4111yescharacteristic
299C2×C4×C13C2×#4111yescharacteristic
300C2×C4×C13C2×#4111yescharacteristic
301C2×Dic13—22no—
302C2×Dic13—21no—
303C2×Dic13—21no—
304C2×Dic13—21no—
305C2×Dic13—21no—
306C2×Dic13—41no—
307C2×Dic13—41no—
308C2×Dic13—41no—
309C2×Dic13—41no—
310C2×Dic13—41no—
311C2×Dic13—81no—
312C2×Dic13—81no—
313C8×C13—21no—
314C8×C13—21no—
315C8×C13—41no—
316C8×C13—41no—
317C8×C13#12312yes—
318C8×C13#12312yes—
319#1055—21no—
320#1055—21no—
321#1055—21no—
322#1055—21no—
323#1055—22no—
324#1055—22no—
325C2×#131C2×D1311yescharacteristic
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—21no—
339#436—21no—
340#435—21no—
341#435—21no—
342C2×#108—131no—
343C2×#108—131no—
344#427—131no—
345#427—131no—
346#424C2×D1311yescharacteristic
347C2×#104—131no—
348C2×#104—131no—
349#416—131no—
350#416—131no—
351#408C2×D1311yescharacteristic
352#407C2×D1311yescharacteristic
353C2×C22⋊C8—131no—
354#405—131no—
355#405—131no—
356#405—131no—
357#405—131no—
358#405—261no—
359#405—261no—
360#405C2×D1311yescharacteristic
361C4×M16—261no—
362C4×M16—261no—
363C2×#97—131no—
364C2×C4×C8—131no—
365C4×C22⋊C4—131no—
366#341—131no—
367#341—131no—
368#339—131no—
369#339—131no—
370#339—131no—
371#339—131no—
372#339—131no—
373#339—131no—
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—41no—
395C4×C13—41no—
396C4×C13—41no—
397C4×C13C4×#4111yescharacteristic
398C4×C13C4×#4111yescharacteristic
399C4×C13C2×#12311yescharacteristic
400C4×C13#52511yescharacteristic
401Dic13—42no—
402Dic13—41no—
403Dic13—41no—
404Dic13—41no—
405Dic13—41no—
406Dic13—81no—
407C2×#41C22×D1311yescharacteristic
408C23×C4C22×D1311yescharacteristic
409#131—22no—
410#131—22no—
411C2×M16—22no—
412C2×M16—22no—
413C2×M16—21no—
414C2×M16—131no—
415C2×M16—131no—
416C2×M16—262no—
417C2×M16—262no—
418C2×M16—261no—
419C2×M16C22⋊D1311yescharacteristic
420C2×M16C22⋊D1311yescharacteristic
421C2×M16C22⋊D1311yescharacteristic
422C2×M16C22⋊D1311yescharacteristic
423C2×M16C22×D1311yescharacteristic
424C2×M16C22×D1311yescharacteristic
425C22×C8—21no—
426C22×C8—131no—
427C22×C8—131no—
428C22×C8—261no—
429C22×C8C22×D1311yescharacteristic
430C22×C8C22×D1311yescharacteristic
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—261no—
449C2×C22⋊C4—261no—
450C2×C42—131no—
451C2×C42—131no—
452C2×C42—261no—
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—21no—
464C4⋊C8—21no—
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—21no—
478C22⋊C8—21no—
479C22⋊C8—131no—
480C22⋊C8—131no—
481C22⋊C8—131no—
482C22⋊C8—131no—
483#97—21no—
484#97—262no—
485#97—261no—
486#97—261no—
487#97—261no—
488#97—261no—
489C4×C8—21no—
490C4×C8—262no—
491C4×C8—261no—
492C4×C8—261no—
493C4×C8—261no—
494C4×C8—261no—
495#95—261no—
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#612711yescharacteristic
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—261no—
520C22×C4—261no—
521C22×C4—261no—
522C22×C4—261no—
523C22×C4C2×C4×D1311yescharacteristic
524C22×C4C2×C4×D1311yescharacteristic
525C22×C4#612711yescharacteristic
526C22×C4C2×C22⋊D1311yescharacteristic
527C22×C4C2×C22⋊D1311yescharacteristic
528C22×C4C23×D1311yescharacteristic
529M16—22no—
530M16—22no—
531M16—22no—
532M16—22no—
533M16—21no—
534M16—21no—
535M16—21no—
536M16—21no—
537M16—42no—
538M16—132no—
539M16—132no—
540M16—264no—
541M16—261no—
542M16—261no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—42no—
548C2×C8—131no—
549C2×C8—131no—
550C2×C8—131no—
551C2×C8—131no—
552C2×C8—264no—
553C2×C8—261no—
554C2×C8—261no—
555C2×C8—261no—
556C2×C8—261no—
557C2×C8—261no—
558C2×C8—261no—
559C2×C8#612912yes—
560C2×C8#612912yes—
561C2×C8C2×C22⋊D1311yescharacteristic
562C2×C8C2×C22⋊D1311yescharacteristic
563C2×C8C2×C22⋊D1311yescharacteristic
564C2×C8C2×C22⋊D1311yescharacteristic
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—261no—
581C22⋊C4—261no—
582C22⋊C4—261no—
583C22⋊C4—261no—
584C22⋊C4—522no—
585C42—21no—
586C42—261no—
587C42—261no—
588C42—261no—
589C42—261no—
590C42—261no—
591C42—261no—
592C42—261no—
593C42—261no—
594C13#2159411yescharacteristic, complemented, Sylow
595C23—21no—
596C23—21no—
597C23—21no—
598C23—41no—
599C23—41no—
600C23C4×C22⋊D1311yescharacteristic
601C23C4×C22⋊D1311yescharacteristic
602C23C2×#612711yescharacteristic
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—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—262no—
627C2×C4—261no—
628C2×C4—261no—
629C2×C4—261no—
630C2×C4—261no—
631C2×C4—521no—
632C2×C4—521no—
633C2×C4—521no—
634C2×C4—521no—
635C2×C4—521no—
636C2×C4—1041no—
637C2×C4—1041no—
638C2×C4C4×C22⋊D1311yescharacteristic
639C2×C4C4×C22⋊D1311yescharacteristic
640C2×C4C22×C4×D1311yescharacteristic
641C2×C4C2×#612911yescharacteristic
642C2×C4C2×#612911yescharacteristic
643C2×C4#41×D1311yescharacteristic
644C2×C4#41×D1311yescharacteristic
645C2×C4C22×C22⋊D1311yescharacteristic
646C8—21no—
647C8—21no—
648C8—41no—
649C8—41no—
650C8—261no—
651C8—261no—
652C8—261no—
653C8—261no—
654C8—262no—
655C8—262no—
656C8#8818912yes—
657C8#8818912yes—
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—
671C22#1171924311yescharacteristic
672C22#1171924311yescharacteristic
673C22C2×C4×C22⋊D1311yescharacteristic
674C4—21no—
675C4—21no—
676C4—41no—
677C4—41no—
678C4—41no—
679C4—522no—
680C4—521no—
681C4—521no—
682C4—521no—
683C4—521no—
684C4—1041no—
685C4C4×#612911yescharacteristic
686C4C4×#612911yescharacteristic
687C4C2×#8818911yescharacteristic
688C4#1171953311yescharacteristic
689C2—21no—
690C2—21no—
691C2—41no—
692C2—41no—
693C2—81no—
694C2C4×#8818911yescharacteristic
695C2#1312374311yescharacteristic
696C2#1312375111yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#2930C2
socleC22×C13C2×C4×D4
prime radicalC13×#525C22
cosocleC22×C4×C13C24
hypercenter#2930D13
hypocenterC13#21594
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×M16 ◁ #2930

Complements

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

NH ≅ G/Ntype
2. #13123254C2semidirect
3. #13115481C2semidirect
4. #13115481C2semidirect
5. #13115432C2semidirect
6. #13115432C2semidirect
8. #13115040C2semidirect
9. #13114933C2semidirect
10. #13114721C2semidirect
11. #13114716C2semidirect
12. #13114678C2semidirect
13. #13114671C2semidirect
14. #13114617C2semidirect
47. #11718706C4semidirect
48. #11718706C4semidirect
49. #11718705C4semidirect
50. #11718704C4semidirect
51. #11718696C4semidirect
52. #11718696C4semidirect
53. #11718695C4semidirect
54. #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
#131232542
#131154812
#131154322
#131151392
#131150402
#131149332
#131147212
#131147162
#131146782
#131146712
#131146172
C13×#29302
#2159413