Finite Group Databasebeta

← #15870320

Subgroups — #15870320

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#13124751C211yesmaximal, characteristic
2#13123539C211yesmaximal, characteristic
3#13123254C211yesmaximal, characteristic, complemented
4#13115485C211yesmaximal, characteristic, complemented
5#13115485C211yesmaximal, characteristic, complemented
6#13115436C211yesmaximal, characteristic, complemented
7#13115436C211yesmaximal, characteristic, complemented
8#13115136C211yesmaximal, characteristic
9#13115043C211yesmaximal, characteristic, complemented
10#13114936C211yesmaximal, characteristic, complemented
11#13114720C211yesmaximal, characteristic, complemented
12#13114715C211yesmaximal, characteristic, complemented
13#13114680C211yesmaximal, characteristic, complemented
14#13114673C211yesmaximal, characteristic, complemented
15C13×#1753C211yesmaximal, characteristic, complemented
16C22×C13×M16C2211yescharacteristic
17#11719496C2211yescharacteristic
18C2×#88180C2211yescharacteristic
19C22×#6099C2211yescharacteristic
20C2×#88155C2211yescharacteristic
21C2×C13×C22⋊C8C2211yescharacteristic
22C2×C13×#97C2211yescharacteristic
23C2×C4×C8×C13C2211yescharacteristic
24C4×C13×C22⋊C4C2211yescharacteristic
25#11718868C2211yescharacteristic
26#11718789—21no—
27#11718789—21no—
28#11718788—21no—
29#11718788—21no—
30#11718783—21no—
31#11718783—21no—
32M16×Dic13—21no—
33M16×Dic13—21no—
34#11718774C2211yescharacteristic
35#11718774C2211yescharacteristic
36#11718771C2211yescharacteristic
37C2×#88059C2211yescharacteristic
38C2×#88059C2211yescharacteristic
39#11718767C2211yescharacteristic
40#11718767C2211yescharacteristic
41#11718763C2211yescharacteristic
42#11718762C2211yescharacteristic
43#11718762C2211yescharacteristic
44#11718762C2211yescharacteristic
45#11718762C2211yescharacteristic
46#11718762C2211yescharacteristic
47C2×#88045C2211yescharacteristic
48C2×#88045C2211yescharacteristic
49#11718398C411yescharacteristic, complemented
50#11718398C411yescharacteristic, complemented
51#11718397C411yescharacteristic, complemented
52#11718396C411yescharacteristic, complemented
53#11718384C411yescharacteristic, complemented
54#11718384C411yescharacteristic, complemented
55#11718383C411yescharacteristic, complemented
56#11718382C411yescharacteristic, complemented
57C13×#336C2211yescharacteristic
58C13×#336C2211yescharacteristic
59#11718144C2211yescharacteristic
60#11718144C2211yescharacteristic
61#11718115C2211yescharacteristic
62#11718115C2211yescharacteristic
63#11718115C2211yescharacteristic
64#11718115C2211yescharacteristic
65#11718115C2211yescharacteristic
66#11718115C2211yescharacteristic
67C23×C4×C13C2311yescharacteristic
68C2×#6127C2311yescharacteristic
69C2×C13×M16—22no—
70C2×C13×M16—22no—
71C2×C13×M16D411yescharacteristic
72C2×C13×M16D411yescharacteristic
73C2×C13×M16D411yescharacteristic
74C2×C13×M16D411yescharacteristic
75C22×C8×C13C2311yescharacteristic
76C22×C8×C13C2311yescharacteristic
77C22×C8×C13C2311yescharacteristic
78C22×C8×C13C2311yescharacteristic
79C2×C13×C22⋊C4—21no—
80C2×C42×C13C2311yescharacteristic
81C2×C42×C13C2311yescharacteristic
82#88207—21no—
83C2×C22⋊Dic13—21no—
84#88184C2×C411yescharacteristic
85#88184C2×C411yescharacteristic
86#88183—21no—
87C4×C22⋊D13—21no—
88C4×C22⋊D13—21no—
89#88180—21no—
90#88180—21no—
91#88180C2×C411yescharacteristic
92#88180C2×C411yescharacteristic
93#88180C2311yescharacteristic
94#88180C2311yescharacteristic
95#88180C2311yescharacteristic
96C2×C4⋊Dic13C2×C411yescharacteristic
97C2×C4⋊Dic13C2×C411yescharacteristic
98#88178C2×C411yescharacteristic
99#88178C2×C411yescharacteristic
100C2×C4×Dic13—21no—
101C2×#6099—21no—
102C2×#6099—22no—
103C2×#6099—22no—
104C2×#6099C2311yescharacteristic
105C2×#6099C2311yescharacteristic
106C2×#6099C2311yescharacteristic
107C2×#6099C2311yescharacteristic
108C22×#1055—21no—
109#88155—22no—
110#88155—22no—
111C2×#6094—21no—
112C2×C8×D13—21no—
113C13×C22⋊C8C2×C411yescharacteristic
114C13×C22⋊C8C2×C411yescharacteristic
115C13×C22⋊C8C2×C411yescharacteristic
116C13×C22⋊C8C2×C411yescharacteristic
117C13×#97—22no—
118C4×C8×C13—22no—
119C13×#95—21no—
120C22⋊#1055—21no—
121C22⋊#1055—21no—
122#88061C2×C411yescharacteristic
123#88061C2×C411yescharacteristic
124#88061C2×C411yescharacteristic
125#88061C2×C411yescharacteristic
126#88060—21no—
127#88060—21no—
128#88059—22no—
129#88059—22no—
130#88058C2×C411yescharacteristic
131#88058C2×C411yescharacteristic
132#88058C2×C411yescharacteristic
133#88058C2×C411yescharacteristic
134#88057C2×C411yescharacteristic
135#88057C2×C411yescharacteristic
136#88057C2×C411yescharacteristic
137#88057C2×C411yescharacteristic
138#88056C2×C411yescharacteristic
139#88056C2×C411yescharacteristic
140#88056C2×C411yescharacteristic
141#88056C2×C411yescharacteristic
142#88055—21no—
143#88055—21no—
144#88055—21no—
145#88055—21no—
146#88055—21no—
147#88054—21no—
148#88054—21no—
149C8×Dic13—21no—
150C8×Dic13—21no—
151C8×Dic13—21no—
152C8×Dic13—21no—
153C8×Dic13—21no—
154#88045—22no—
155#88045—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×C13C22×C411yescharacteristic
165C22×C4×C13C22×C411yescharacteristic
166C22×C4×C13C2×D411yescharacteristic
167C22×C4×C13C2×D411yescharacteristic
168C22×C4×C13#4111yescharacteristic
169C22×C4×C13C2411yescharacteristic
170C2×C22⋊D13—21no—
171C2×C22⋊D13—21no—
172C2×C22⋊D13—21no—
173C22×Dic13—21no—
174C22×Dic13—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—22no—
183C13×M16—22no—
184C13×M16—22no—
185C13×M16—22no—
186C2×C8×C13—21no—
187C2×C8×C13—21no—
188C2×C8×C13—21no—
189C2×C8×C13—21no—
190C2×C8×C13—21no—
191C2×C8×C13—21no—
192C2×C8×C13C22×C411yescharacteristic
193C2×C8×C13C22×C411yescharacteristic
194C2×C8×C13C22×C411yescharacteristic
195C2×C8×C13C22×C411yescharacteristic
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×C22⋊C4—42no—
203C42×C13—21no—
204C42×C13—21no—
205C42×C13—21no—
206C42×C13—21no—
207C22⋊Dic13—21no—
208C22⋊Dic13—21no—
209C22⋊Dic13—21no—
210C22⋊Dic13—21no—
211C22⋊Dic13—21no—
212C22⋊Dic13—21no—
213C22⋊Dic13—21no—
214#6103—21no—
215#6103—21no—
216C4⋊Dic13—21no—
217C4⋊Dic13—21no—
218C4⋊Dic13C22×C411yescharacteristic
219C4⋊Dic13C22×C411yescharacteristic
220C4⋊Dic13C22×C411yescharacteristic
221C4⋊Dic13C22×C411yescharacteristic
222C4⋊Dic13C22×C411yescharacteristic
223C4⋊Dic13C22×C411yescharacteristic
224#6101—21no—
225#6101—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—21no—
235#6099—21no—
236#6099—21no—
237#6099—21no—
238#6099#4112yes—
239#6099#4112yes—
240C2×#1055—24no—
241C2×#1055—21no—
242C2×#1055—21no—
243C2×#1055—21no—
244C2×#1055—21no—
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#1826—131no—
257#1773—131no—
258#1772—131no—
259#1765—131no—
260#1764—131no—
261#1753D1311yescharacteristic, complemented
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—41no—
282C2×C4×C13—41no—
283C2×C4×C13—41no—
284C2×C4×C13—41no—
285C2×C4×C13—41no—
286C2×C4×C13C4×D411yescharacteristic
287C2×C4×C13C4×D411yescharacteristic
288C2×C4×C13C23×C411yescharacteristic
289C2×C4×C13C22×D411yescharacteristic
290C2×C4×C13C2×#4111yescharacteristic
291C2×C4×C13C2×#4111yescharacteristic
292C2×C4×C13C2×#4111yescharacteristic
293C2×C4×C13C2×#4111yescharacteristic
294C22⋊D13—41no—
295C22⋊D13—41no—
296C22⋊D13—81no—
297C22⋊D13—81no—
298C2×Dic13—21no—
299C2×Dic13—21no—
300C2×Dic13—21no—
301C2×Dic13—21no—
302C2×Dic13—21no—
303C2×Dic13—21no—
304C2×Dic13—21no—
305C2×Dic13—81no—
306C2×Dic13—81no—
307D52—21no—
308D52—21no—
309C4×D13—41no—
310C4×D13—41no—
311Dic26—21no—
312Dic26—21no—
313C8×C13—21no—
314C8×C13—21no—
315C8×C13—21no—
316C8×C13—21no—
317C8×C13—21no—
318C8×C13—21no—
319C8×C13#12312yes—
320C8×C13#12312yes—
321#1055—22no—
322#1055—22no—
323#1055—41no—
324#1055—41no—
325C2×#131—131no—
326C22×M16—131no—
327C22×M16C2×D1311yescharacteristic
328#525—131no—
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×#104—131no—
348C2×#104—131no—
349#416—131no—
350#416—131no—
351#408—131no—
352#407—131no—
353C2×C22⋊C8C2×D1311yescharacteristic
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×#97C2×D1311yescharacteristic
364C2×C4×C8C2×D1311yescharacteristic
365C4×C22⋊C4C2×D1311yescharacteristic
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#336C2×D1311yescharacteristic
375#336C2×D1311yescharacteristic
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—81no—
396C4×C13C4×#4111yescharacteristic
397C4×C13C4×#4111yescharacteristic
398C4×C13C2×#12311yescharacteristic
399C4×C13#52511yescharacteristic
400Dic13—41no—
401Dic13—41no—
402Dic13—41no—
403Dic13—41no—
404Dic13—41no—
405Dic13—41no—
406Dic13—41no—
407C2×#41—131no—
408C23×C4C22×D1311yescharacteristic
409#131—262no—
410#131—262no—
411C2×M16—22no—
412C2×M16—22no—
413C2×M16—131no—
414C2×M16—131no—
415C2×M16—131no—
416C2×M16—131no—
417C2×M16—262no—
418C2×M16—262no—
419C2×M16—261no—
420C2×M16—261no—
421C2×M16D5211yescharacteristic
422C2×M16D5211yescharacteristic
423C2×M16D5211yescharacteristic
424C2×M16D5211yescharacteristic
425C22×C8—261no—
426C22×C8—261no—
427C22×C8C22×D1311yescharacteristic
428C22×C8C22×D1311yescharacteristic
429C22×C8C22×D1311yescharacteristic
430C22×C8C22×D1311yescharacteristic
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—131no—
440#117—131no—
441#117—131no—
442#117—131no—
443#117—131no—
444#117—261no—
445#117—261no—
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—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—261no—
476C22⋊C8—261no—
477C22⋊C8—261no—
478C22⋊C8—261no—
479C22⋊C8C4×D1311yescharacteristic
480C22⋊C8C4×D1311yescharacteristic
481C22⋊C8C4×D1311yescharacteristic
482C22⋊C8C4×D1311yescharacteristic
483#97—22no—
484#97—261no—
485#97—261no—
486#97—261no—
487#97—261no—
488#97—261no—
489C4×C8—22no—
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#612711yescharacteristic
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—261no—
521C22×C4—261no—
522C22×C4—261no—
523C22×C4C2×C4×D1311yescharacteristic
524C22×C4C2×C4×D1311yescharacteristic
525C22×C4C2×D5211yescharacteristic
526C22×C4C2×D5211yescharacteristic
527C22×C4#612711yescharacteristic
528C22×C4C23×D1311yescharacteristic
529M16—22no—
530M16—22no—
531M16—22no—
532M16—22no—
533M16—132no—
534M16—132no—
535M16—264no—
536M16—261no—
537M16—261no—
538M16—261no—
539M16—261no—
540M16—261no—
541M16—261no—
542M16—522no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—264no—
550C2×C8—261no—
551C2×C8—261no—
552C2×C8—261no—
553C2×C8—261no—
554C2×C8—522no—
555C2×C8C2×C4×D1311yescharacteristic
556C2×C8C2×C4×D1311yescharacteristic
557C2×C8C2×C4×D1311yescharacteristic
558C2×C8C2×C4×D1311yescharacteristic
559C2×C8C2×D5211yescharacteristic
560C2×C8C2×D5211yescharacteristic
561C2×C8C2×D5211yescharacteristic
562C2×C8C2×D5211yescharacteristic
563C2×C8#612912yes—
564C2×C8#612912yes—
565C4⋊C4—131no—
566C4⋊C4—131no—
567C4⋊C4—131no—
568C4⋊C4—131no—
569C4⋊C4—131no—
570C4⋊C4—131no—
571C4⋊C4—261no—
572C4⋊C4—261no—
573C4⋊C4—261no—
574C4⋊C4—261no—
575C22⋊C4—42no—
576C22⋊C4—261no—
577C22⋊C4—261no—
578C22⋊C4—261no—
579C22⋊C4—261no—
580C22⋊C4—261no—
581C22⋊C4—261no—
582C22⋊C4—261no—
583C22⋊C4—261no—
584C22⋊C4—261no—
585C42—21no—
586C42—21no—
587C42—21no—
588C42—21no—
589C42—261no—
590C42—261no—
591C42—261no—
592C42—261no—
593C42—261no—
594C13#2159411yescharacteristic, complemented, Sylow
595C23—21no—
596C23—21no—
597C23—41no—
598C23—41no—
599C23—261no—
600C23C4×D5211yescharacteristic
601C23C4×D5211yescharacteristic
602C23C2×#612711yescharacteristic
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—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—261no—
628C2×C4—261no—
629C2×C4—261no—
630C2×C4—261no—
631C2×C4—261no—
632C2×C4—261no—
633C2×C4—261no—
634C2×C4—521no—
635C2×C4—521no—
636C2×C4—1041no—
637C2×C4—1041no—
638C2×C4C4×D5211yescharacteristic
639C2×C4C4×D5211yescharacteristic
640C2×C4C22×C4×D1311yescharacteristic
641C2×C4C22×D5211yescharacteristic
642C2×C4C2×#612911yescharacteristic
643C2×C4C2×#612911yescharacteristic
644C2×C4#41×D1311yescharacteristic
645C2×C4#41×D1311yescharacteristic
646C8—21no—
647C8—21no—
648C8—21no—
649C8—21no—
650C8—21no—
651C8—21no—
652C8—262no—
653C8—262no—
654C8—521no—
655C8—521no—
656C8#8814012yes—
657C8#8814012yes—
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×C4×D5211yescharacteristic
672C22#1171924311yescharacteristic
673C22#1171924311yescharacteristic
674C4—21no—
675C4—21no—
676C4—42no—
677C4—81no—
678C4—521no—
679C4—521no—
680C4—521no—
681C4—521no—
682C4—521no—
683C4—521no—
684C4—521no—
685C4C2×#8814011yescharacteristic
686C4#1171922911yescharacteristic
687C4C4×#612911yescharacteristic
688C4C4×#612911yescharacteristic
689C2—21no—
690C2—21no—
691C2—41no—
692C2—41no—
693C2—1041no—
694C2C4×#8814011yescharacteristic
695C2#1312374711yescharacteristic
696C2#1312375411yescharacteristic
subgroupG/H
centerC2×C4C22×D52
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1753C2
socleC22×C13C2×C4×D4
prime radical#11719496C22
cosocleC22×C4×C13C24
hypercenter#1753D13
hypocenterC13#21594
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×M16 ◁ #1753

Complements

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

NH ≅ G/Ntype
3. #13123254C2semidirect
4. #13115485C2semidirect
5. #13115485C2semidirect
6. #13115436C2semidirect
7. #13115436C2semidirect
9. #13115043C2semidirect
10. #13114936C2semidirect
11. #13114720C2semidirect
12. #13114715C2semidirect
13. #13114680C2semidirect
14. #13114673C2semidirect
15. C13×#1753C2semidirect
49. #11718398C4semidirect
50. #11718398C4semidirect
51. #11718397C4semidirect
52. #11718396C4semidirect
53. #11718384C4semidirect
54. #11718384C4semidirect
55. #11718383C4semidirect
56. #11718382C4semidirect
261. #1753D13semidirect
594. C13#21594semidirect

Maximal subgroups

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

subgroupindex
#131247512
#131235392
#131232542
#131154852
#131154362
#131151362
#131150432
#131149362
#131147202
#131147152
#131146802
#131146732
C13×#17532
#2159413