Finite Group Databasebeta

← #15879831

Subgroups — #15879831

Order 3328.

1280 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718586C211yesmaximal, characteristic, complemented
2C2×D13×C22⋊C8C211yesmaximal, characteristic
3C2×C4×#6103C211yesmaximal, characteristic
4#13115443C212yesmaximal, complemented
5#13115440C212yesmaximal, complemented
6#13115015C212yesmaximal, complemented
7#13114814C211yesmaximal, characteristic, complemented
8#13114745C211yesmaximal, characteristic
9#13114606C212yesmaximal, complemented
10C22⋊C8×Dic13C211yesmaximal, characteristic, complemented
11C13×#1817C211yesmaximal, characteristic, complemented
12C23×C4×D13C2211yescharacteristic
13C22×C42×C13C2211yescharacteristic
14C22×#6103C411yescharacteristic
15C22×#6103C411yescharacteristic
16C22×C4×Dic13C2211yescharacteristic
17C22×C8×D13C2212yes—
18C2×C13×C22⋊C8C2211yescharacteristic
19C2×C13×C22⋊C8C2211yescharacteristic
20C2×#88071C411yescharacteristic
21C2×#88071C411yescharacteristic
22C2×C22⋊#1055C2211yescharacteristic
23C2×C22⋊#1055C2211yescharacteristic
24C2×#88060C2212yes—
25C2×#88060C2212yes—
26C2×#88060C2212yes—
27C2×#88054C2212yescomplemented
28C2×C8×Dic13C2212yescomplemented
29C4×#6103C411yescharacteristic
30C4×#6103C411yescharacteristic
31C4×#6103C411yescharacteristic
32C4×#6103C411yescharacteristic
33C4×#6103C2211yescharacteristic
34C4×#6103C2211yescharacteristic
35C4×#6103C2211yescharacteristic
36C4×#6103C2211yescharacteristic
37#11718586—24no—
38C2×C4⋊#1055C2212yescomplemented
39C2×C4×#1055C2212yescomplemented
40D13×C22⋊C8—24no—
41C13×#336C2212yescomplemented
42C13×#336C2212yescomplemented
43#11718142C2212yescomplemented
44#11718142C2212yescomplemented
45C24×D13C2×C411yescharacteristic
46C23×C4×C13C2×C411yescharacteristic
47C23×C4×C13C2×C411yescharacteristic
48C23×C4×C13C2311yescharacteristic
49C23×Dic13C2×C411yescharacteristic
50C23×Dic13C2×C411yescharacteristic
51C23×Dic13C2×C411yescharacteristic
52C22×C4×D13—22no—
53C22×C4×D13—22no—
54C22×C4×D13—24no—
55C22×C4×D13—42no—
56C22×C4×D13C2×C411yescharacteristic
57C22×C4×D13C2×C411yescharacteristic
58C22×C4×D13C2311yescharacteristic
59C22×C4×D13C2311yescharacteristic
60C22×C8×C13C2312yes—
61C22×C8×C13C2312yes—
62C2×C42×C13—22no—
63C2×C42×C13—22no—
64C2×C42×C13C2×C411yescharacteristic
65C2×C42×C13C2×C411yescharacteristic
66C2×C42×C13C2311yescharacteristic
67C2×C42×C13C2311yescharacteristic
68C2×#6103—24no—
69C2×#6103C818yescomplemented
70C2×#6103C2×C411yescharacteristic
71C2×#6103C2×C411yescharacteristic
72C2×#6103C2×C411yescharacteristic
73C2×#6103C2×C411yescharacteristic
74C2×#6103C2×C411yescharacteristic
75C2×#6103C2×C411yescharacteristic
76C2×#6103C2×C411yescharacteristic
77C2×#6103C2×C411yescharacteristic
78C2×C4×Dic13—42no—
79C2×C4×Dic13C2×C411yescharacteristic
80C2×C4×Dic13C2×C411yescharacteristic
81C2×C4×Dic13C2311yescharacteristic
82C2×C4×Dic13C2311yescharacteristic
83C22×#1055C2312yes—
84C22×#1055C2312yes—
85C2×C8×D13—24no—
86C2×C8×D13—24no—
87C2×C8×D13—42no—
88C13×C22⋊C8—22no—
89C13×C22⋊C8—22no—
90#88071C2×C411yescharacteristic
91#88071C2×C411yescharacteristic
92#88071C2×C411yescharacteristic
93#88071C2×C411yescharacteristic
94#88071C2×C411yescharacteristic
95#88071C2×C411yescharacteristic
96#88071C2×C411yescharacteristic
97#88071C2×C411yescharacteristic
98C22⋊#1055—22no—
99C22⋊#1055D414yes—
100#88060—24no—
101#88060—24no—
102#88060—42no—
103#88054—42no—
104C8×Dic13—42no—
105C4⋊#1055—24no—
106C4×#1055—24no—
107#22552—131nomaximal, Sylow
108C24×C13C22×C411yescharacteristic
109C23×D13—22no—
110C23×D13—22no—
111C23×D13—22no—
112C23×D13—22no—
113C23×D13—41no—
114C23×D13—41no—
115C23×D13C2×C814yes—
116C23×D13C22×C411yescharacteristic
117C23×D13C22×C411yescharacteristic
118C22×C4×C13—22no—
119C22×C4×C13—22no—
120C22×C4×C13—22no—
121C22×C4×C13—22no—
122C22×C4×C13—22no—
123C22×C4×C13—22no—
124C22×C4×C13—41no—
125C22×C4×C13C2×C814yescomplemented
126C22×C4×C13C22×C411yescharacteristic
127C22×C4×C13C22×C411yescharacteristic
128C22×C4×C13C22×C411yescharacteristic
129C22×C4×C13C22×C411yescharacteristic
130C22×C4×C13C22×C411yescharacteristic
131C22×C4×C13C2×D412yes—
132C22×C4×C13#4112yes—
133C22×C4×C13C2411yescharacteristic
134C22×Dic13—22no—
135C22×Dic13—22no—
136C22×Dic13—22no—
137C22×Dic13—22no—
138C22×Dic13—41no—
139C22×Dic13—41no—
140C22×Dic13—41no—
141C22×Dic13—41no—
142C22×Dic13C2×C814yescomplemented
143C22×Dic13C22×C411yescharacteristic
144C22×Dic13C22×C411yescharacteristic
145C22×Dic13C22×C411yescharacteristic
146C22×Dic13C22×C411yescharacteristic
147C22×Dic13C22×C411yescharacteristic
148C22×Dic13C22×C411yescharacteristic
149C2×C4×D13—21no—
150C2×C4×D13—21no—
151C2×C4×D13—22no—
152C2×C4×D13—22no—
153C2×C4×D13—22no—
154C2×C4×D13—22no—
155C2×C4×D13—21no—
156C2×C4×D13—22no—
157C2×C4×D13—21no—
158C2×C4×D13—22no—
159C2×C4×D13—22no—
160C2×C4×D13—48no—
161C2×C4×D13—48no—
162C2×C4×D13—41no—
163C2×C4×D13—41no—
164C2×C4×D13#4114yes—
165C2×C8×C13—22no—
166C2×C8×C13—22no—
167C2×C8×C13—22no—
168C2×C8×C13—22no—
169C2×C8×C13—22no—
170C2×C8×C13—22no—
171C42×C13—22no—
172C42×C13—22no—
173C42×C13—21no—
174C42×C13—21no—
175C42×C13—21no—
176C42×C13—21no—
177#6103—22no—
178#6103—22no—
179#6103—22no—
180#6103C2×C814yes—
181#6103C2×C814yes—
182#6103C2×C814yescomplemented
183#6103C2×C814yescomplemented
184#6103M1614yes—
185C4×Dic13—22no—
186C4×Dic13—22no—
187C4×Dic13—41no—
188C4×Dic13—41no—
189C2×#1055—22no—
190C2×#1055—22no—
191C2×#1055—22no—
192C2×#1055—22no—
193C2×#1055—22no—
194C2×#1055C2×D414yes—
195C8×D13—48no—
196C2×#431—131no—
197C22×C22⋊C8—131no—
198C2×C4×C22⋊C4—131no—
199#1923—132no—
200#1923—132no—
201#1850—132no—
202#1817D1311yescharacteristic, complemented
203#1797—131no—
204#1779—131no—
205C8×C22⋊C4—132no—
206C4×C22⋊C8—131no—
207C23×C13—21no—
208C23×C13—21no—
209C23×C13—21no—
210C23×C13—21no—
211C23×C13C4×D412yes—
212C23×C13C22×C812yes—
213C23×C13#13112yes—
214C23×C13C23×C411yescharacteristic
215C22×D13—21no—
216C22×D13—21no—
217C22×D13—21no—
218C22×D13—21no—
219C22×D13—21no—
220C22×D13—21no—
221C22×D13—21no—
222C22×D13—21no—
223C22×D13—21no—
224C22×D13—21no—
225C22×D13—28no—
226C22×D13—28no—
227C22×D13—44no—
228C22×D13—44no—
229C22×D13—44no—
230C22×D13—44no—
231C22×D13—44no—
232C22×D13#11712yes—
233C22×D13C22×C812yes—
234C22×D13C22×C812yes—
235C22×D13C2×M1612yes—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—28no—
245C2×C4×C13—24no—
246C2×C4×C13—24no—
247C2×C4×C13—21no—
248C2×C4×C13—21no—
249C2×C4×C13—21no—
250C2×C4×C13—44no—
251C2×C4×C13C4×D412yes—
252C2×C4×C13C22×C812yes—
253C2×C4×C13C22×C812yes—
254C2×C4×C13C2×M1612yes—
255C2×C4×C13C22×D411yescharacteristic
256C2×C4×C13C2×#4112yes—
257C2×C4×C13C2×#4111yescharacteristic
258C2×C4×C13H(5,𝔽2)12yes—
259C2×Dic13—21no—
260C2×Dic13—21no—
261C2×Dic13—21no—
262C2×Dic13—21no—
263C2×Dic13—21no—
264C2×Dic13—21no—
265C2×Dic13—21no—
266C2×Dic13—21no—
267C2×Dic13—21no—
268C2×Dic13—21no—
269C2×Dic13—21no—
270C2×Dic13—21no—
271C2×Dic13—21no—
272C2×Dic13—21no—
273C2×Dic13—44no—
274C2×Dic13—44no—
275C2×Dic13—44no—
276C2×Dic13#11712yes—
277C2×Dic13C22×C812yes—
278C2×Dic13C22×C812yes—
279C2×Dic13C2×M1612yes—
280C4×D13—24no—
281C4×D13—24no—
282C4×D13—44no—
283C4×D13—44no—
284C4×D13—42no—
285C4×D13—42no—
286C8×C13—42no—
287C8×C13—42no—
288#1055—24no—
289#1055—42no—
290C24×C4—131no—
291C23×C8—132no—
292C22×C22⋊C4—131no—
293C22×C22⋊C4—131no—
294C22×C42—131no—
295C22×C42C2×D1311yescharacteristic
296#431—264no—
297C2×C4⋊C8—132no—
298C2×C4⋊C8—132no—
299C2×C22⋊C8—131no—
300C2×C22⋊C8—131no—
301C2×C22⋊C8—132no—
302C2×C22⋊C8—132no—
303C2×C22⋊C8—132no—
304C2×C22⋊C8—264no—
305C2×C22⋊C8C2×D1311yescharacteristic
306C2×C22⋊C8C2×D1311yescharacteristic
307C2×C4×C8—132no—
308C2×C4×C8—132no—
309C4×C22⋊C4—131no—
310C4×C22⋊C4—131no—
311C4×C22⋊C4—131no—
312C4×C22⋊C4—131no—
313C4×C22⋊C4—131no—
314C4×C22⋊C4—131no—
315C4×C22⋊C4—131no—
316C4×C22⋊C4—131no—
317C2×#95—131no—
318C2×#95—131no—
319#336—132no—
320#336—132no—
321#336C2×D1312yescomplemented
322#336C2×D1312yescomplemented
323C22×C13—22no—
324C22×C13—22no—
325C22×C13—22no—
326C22×C13—22no—
327C22×C13—22no—
328C22×C13—22no—
329C22×C13C8×D414yes—
330C22×C13C2×#11711yescharacteristic
331C22×C13C2×C4×D411yescharacteristic
332C22×C13#51811yescharacteristic
333C22×C13C23×C811yescharacteristic
334C22×C13C22×M1611yescharacteristic
335C22×C13C2×#13111yescharacteristic
336C22×C13#56811yescharacteristic
337C2×D13—22no—
338C2×D13—22no—
339C2×D13—22no—
340C2×D13—22no—
341C2×D13—22no—
342C2×D13—22no—
343C2×D13—22no—
344C2×D13—22no—
345C2×D13—22no—
346C2×D13—416no—
347C2×D13—41no—
348C2×D13—41no—
349C2×D13—41no—
350C2×D13—41no—
351C2×D13#43114yescomplemented
352C4×C13—22no—
353C4×C13—22no—
354C4×C13—22no—
355C4×C13—22no—
356C4×C13—41no—
357C4×C13#54612yes—
358C4×C13#55112yes—
359Dic13—22no—
360Dic13—22no—
361Dic13—22no—
362Dic13—22no—
363Dic13—41no—
364Dic13—41no—
365C25—131no—
366C23×C4—131no—
367C23×C4—131no—
368C23×C4—131no—
369C23×C4—131no—
370C23×C4—131no—
371C23×C4—131no—
372C23×C4—131no—
373C23×C4—264no—
374C23×C4—262no—
375C23×C4—262no—
376C23×C4—522no—
377C23×C4C4×D1311yescharacteristic
378C23×C4C4×D1311yescharacteristic
379C23×C4C22×D1311yescharacteristic
380C22×C8—132no—
381C22×C8—132no—
382C22×C8—264no—
383C22×C8—264no—
384C22×C8—522no—
385C22×C8C22×D1312yes—
386C22×C8C22×D1312yes—
387C2×C22⋊C4—138no—
388C2×C22⋊C4—131no—
389C2×C22⋊C4—131no—
390C2×C22⋊C4—131no—
391C2×C22⋊C4—131no—
392C2×C22⋊C4—131no—
393C2×C22⋊C4—131no—
394C2×C22⋊C4—131no—
395C2×C22⋊C4—131no—
396C2×C22⋊C4—264no—
397C2×C42—22no—
398C2×C42—22no—
399C2×C42—131no—
400C2×C42—131no—
401C2×C42—131no—
402C2×C42—131no—
403C2×C42—522no—
404C2×C42C4×D1311yescharacteristic
405C2×C42C4×D1311yescharacteristic
406C2×C42C22×D1311yescharacteristic
407C2×C42C22×D1311yescharacteristic
408C4⋊C8—264no—
409C4⋊C8—522no—
410C22⋊C8—22no—
411C22⋊C8—22no—
412C22⋊C8—134no—
413C22⋊C8—264no—
414C22⋊C8—264no—
415C22⋊C8—262no—
416C22⋊C8—522no—
417C4×C8—264no—
418C4×C8—522no—
419#95—131no—
420#95—131no—
421#95—131no—
422#95—131no—
423#95—131no—
424#95—131no—
425#95—131no—
426#95—131no—
427C2×C13—24no—
428C2×C13#234211yescharacteristic
429C2×C13C2×#43111yescharacteristic
430C2×C13#292411yescharacteristic
431C2×C13C2×C8×D411yescharacteristic
432C2×C13D4×M1611yescharacteristic
433C2×C13#297211yescharacteristic
434C2×C13#297411yescharacteristic
435D13—24no—
436D13—42no—
437C24—131no—
438C24—131no—
439C24—134no—
440C24—262no—
441C24—262no—
442C24—262no—
443C24—262no—
444C24—521no—
445C24—521no—
446C24C2×C4×D1311yescharacteristic
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—41no—
454C22×C4—131no—
455C22×C4—131no—
456C22×C4—131no—
457C22×C4—131no—
458C22×C4—134no—
459C22×C4—134no—
460C22×C4—131no—
461C22×C4—131no—
462C22×C4—262no—
463C22×C4—262no—
464C22×C4—262no—
465C22×C4—262no—
466C22×C4—261no—
467C22×C4—261no—
468C22×C4—262no—
469C22×C4—262no—
470C22×C4—262no—
471C22×C4—262no—
472C22×C4—262no—
473C22×C4—261no—
474C22×C4—261no—
475C22×C4—262no—
476C22×C4—262no—
477C22×C4—521no—
478C22×C4—521no—
479C22×C4—528no—
480C22×C4—528no—
481C22×C4—521no—
482C22×C4—521no—
483C22×C4—521no—
484C22×C4—521no—
485C22×C4C8×D1314yescomplemented
486C22×C4C2×C4×D1311yescharacteristic
487C22×C4C2×C4×D1311yescharacteristic
488C22×C4C2×C4×D1311yescharacteristic
489C22×C4C2×C4×D1311yescharacteristic
490C22×C4C2×C4×D1311yescharacteristic
491C22×C4D4×D1312yes—
492C22×C4#612912yes—
493C22×C4C23×D1311yescharacteristic
494C2×C8—22no—
495C2×C8—22no—
496C2×C8—22no—
497C2×C8—22no—
498C2×C8—22no—
499C2×C8—22no—
500C2×C8—134no—
501C2×C8—262no—
502C2×C8—262no—
503C2×C8—262no—
504C2×C8—262no—
505C2×C8—262no—
506C2×C8—528no—
507C22⋊C4—134no—
508C22⋊C4—134no—
509C22⋊C4—134no—
510C22⋊C4—134no—
511C22⋊C4—134no—
512C22⋊C4—262no—
513C22⋊C4—262no—
514C22⋊C4—262no—
515C42—22no—
516C42—22no—
517C42—21no—
518C42—21no—
519C42—21no—
520C42—21no—
521C42—262no—
522C42—262no—
523C42—521no—
524C42—521no—
525C13#2255211yescharacteristic, complemented, Sylow
526C23—21no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23—132no—
531C23—132no—
532C23—132no—
533C23—132no—
534C23—268no—
535C23—261no—
536C23—261no—
537C23—261no—
538C23—261no—
539C23—261no—
540C23—261no—
541C23—261no—
542C23—261no—
543C23—261no—
544C23—261no—
545C23—268no—
546C23—524no—
547C23—524no—
548C23—524no—
549C23—524no—
550C23—524no—
551C23#8813512yes—
552C23C2×C8×D1312yes—
553C23#8816112yes—
554C23C22×C4×D1311yescharacteristic
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—28no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—44no—
570C2×C4—132no—
571C2×C4—132no—
572C2×C4—132no—
573C2×C4—132no—
574C2×C4—261no—
575C2×C4—261no—
576C2×C4—261no—
577C2×C4—261no—
578C2×C4—261no—
579C2×C4—261no—
580C2×C4—261no—
581C2×C4—261no—
582C2×C4—264no—
583C2×C4—264no—
584C2×C4—261no—
585C2×C4—261no—
586C2×C4—261no—
587C2×C4—261no—
588C2×C4—261no—
589C2×C4—261no—
590C2×C4—524no—
591C2×C4—524no—
592C2×C4—524no—
593C2×C4—524no—
594C2×C4—524no—
595C2×C4—522no—
596C2×C4—522no—
597C2×C4#8813512yes—
598C2×C4C2×C8×D1312yes—
599C2×C4C2×C8×D1312yes—
600C2×C4M16×D1312yes—
601C2×C4C2×D4×D1311yescharacteristic
602C2×C4C2×#612911yescharacteristic
603C2×C4#41×D1312yes—
604C2×C4#8825612yes—
605C8—42no—
606C8—42no—
607C8—264no—
608C8—522no—
609C22—22no—
610C22—22no—
611C22—22no—
612C22—22no—
613C22—22no—
614C22—22no—
615C22—134no—
616C22—262no—
617C22—262no—
618C22—262no—
619C22—262no—
620C22—262no—
621C22—262no—
622C22—262no—
623C22—262no—
624C22—262no—
625C22—5216no—
626C22—521no—
627C22—521no—
628C22—521no—
629C22—521no—
630C22#1171838614yes—
631C22C2×#8813511yescharacteristic
632C22D13×#11711yescharacteristic
633C22#1171922611yescharacteristic
634C22C22×C8×D1311yescharacteristic
635C22C2×M16×D1311yescharacteristic
636C22C2×#8816111yescharacteristic
637C22#1171945011yescharacteristic
638C4—22no—
639C4—22no—
640C4—22no—
641C4—22no—
642C4—41no—
643C4—262no—
644C4—262no—
645C4—262no—
646C4—262no—
647C4—521no—
648C4—521no—
649C4#1171935912yes—
650C4#1171936312yes—
651C2—24no—
652C2—264no—
653C2—522no—
654C2#1311767811yescharacteristic
655C2D13×#43111yescharacteristic
656C2#1312349511yescharacteristic
657C2C2×#1171838611yescharacteristic
658C2#1312356811yescharacteristic
659C2#1312385911yescharacteristic
660C2#1312387311yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D13
commutatorC22×C13C23×C8
FittingC13×#1817C2
socleC23×C13C23×C4
prime radicalC24×D13C2×C4
cosocleC22×C4×C13C24
hypercenter#1817D13
hypocenterC13#22552
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ #1817

Complements

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

NH ≅ G/Ntype
1. C2×#11718586C2semidirect
4. #13115443C2semidirect
5. #13115440C2semidirect
6. #13115015C2semidirect
7. #13114814C2semidirect
9. #13114606C2semidirect
10. C22⋊C8×Dic13C2semidirect
11. C13×#1817C2semidirect
27. C2×#88054C22semidirect
28. C2×C8×Dic13C22semidirect
38. C2×C4⋊#1055C22semidirect
39. C2×C4×#1055C22semidirect
41. C13×#336C22semidirect
42. C13×#336C22semidirect
43. #11718142C22semidirect
44. #11718142C22semidirect
69. C2×#6103C8semidirect
125. C22×C4×C13C2×C8semidirect
142. C22×Dic13C2×C8semidirect
182. #6103C2×C8semidirect
183. #6103C2×C8semidirect
202. #1817D13semidirect
321. #336C2×D13semidirect
322. #336C2×D13semidirect
351. C2×D13#431semidirect
485. C22×C4C8×D13semidirect
525. C13#22552semidirect

Maximal subgroups

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

subgroupindex
C2×#117185862
C2×D13×C22⋊C82
C2×C4×#61032
#131154432
#131154402
#131150152
#131148142
#131147452
#131146062
C22⋊C8×Dic132
C13×#18172
#2255213