Finite Group Databasebeta

← #15789951

Subgroups — #15789951

Order 3328.

1390 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718654C211yesmaximal, characteristic
2C2×#11718601C211yesmaximal, characteristic
3#13113104C211yesmaximal, characteristic, complemented
4#13113095C212yesmaximal, complemented
5#13113095C211yesmaximal, characteristic, complemented
6#13113078C211yesmaximal, characteristic
7#13113078C212yesmaximal
8#13113072C212yesmaximal
9#13113071C212yesmaximal, complemented
10C4×#88071C211yesmaximal, characteristic, complemented
11C2×C13×#389C211yesmaximal, characteristic, complemented
12C22×C13×C4⋊C4C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C13×C4⋊C4C2212yes—
15C22×C42×C13C2211yescharacteristic
16C22×#6103C2211yescharacteristic
17C22×#6103C2211yescharacteristic
18C22×#6103C2211yescharacteristic
19C22×#6103C2212yes—
20C22×#6103C2212yes—
21C22×#6101C2211yescharacteristic
22C22×C4×Dic13C2212yes—
23C13×#389—24no—
24C2×C13×#95C2212yes—
25C2×#88071C2211yescharacteristic
26C2×#88071C2211yescharacteristic
27C2×#88071C2212yes—
28C2×#88071C2212yes—
29C2×#88071C2211yescharacteristic
30C2×#88071C2212yes—
31C2×#88071C2212yes—
32C2×#88071C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2211yescharacteristic
35C2×#88071C2212yes—
36#11718654C418yescomplemented
37#11718601—24no—
38C24×D13C2311yescharacteristic
39C23×C4×C13C2312yes—
40C23×C4×C13C2312yes—
41C23×C4×C13C2311yescharacteristic
42C23×C4×C13C2311yescharacteristic
43C23×C4×C13C2311yescharacteristic
44C23×Dic13C2311yescharacteristic
45C23×Dic13C2311yescharacteristic
46C23×Dic13C2312yes—
47C23×Dic13C2311yescharacteristic
48C23×Dic13C2312yes—
49C2×C13×C4⋊C4—22no—
50C2×C13×C4⋊C4—22no—
51C2×C13×C4⋊C4—24no—
52C2×C13×C4⋊C4—22no—
53C2×C13×C4⋊C4—42no—
54C2×C13×C4⋊C4—42no—
55C2×C13×C4⋊C4—42no—
56C2×C13×C4⋊C4C2×C414yes—
57C2×C42×C13—42no—
58C2×C42×C13D414yes—
59C2×#6103—22no—
60C2×#6103—22no—
61C2×#6103—22no—
62C2×#6103—22no—
63C2×#6103—24no—
64C2×#6103—24no—
65C2×#6103—42no—
66C2×#6103—42no—
67C2×#6103—42no—
68C2×#6103—42no—
69C2×#6103—42no—
70C2×#6103C2×C414yes—
71C2×#6103C2×C418yes—
72C2×#6101—22no—
73C2×#6101—24no—
74C2×C4×Dic13—24no—
75C2×C4×Dic13—42no—
76C2×C4×Dic13—42no—
77C13×#95—24no—
78#88071—22no—
79#88071—22no—
80#88071—22no—
81#88071—24no—
82#88071—24no—
83#88071—42no—
84#88071—42no—
85#88071—42no—
86#88071—42no—
87#88071C2×C418yes—
88#88071C2×C414yes—
89#14324—131nomaximal, Sylow
90C24×C13C2411yescharacteristic
91C23×D13—21no—
92C23×D13—21no—
93C23×D13—22no—
94C23×D13—22no—
95C23×D13—21no—
96C23×D13—22no—
97C23×D13—21no—
98C23×D13—21no—
99C23×D13—22no—
100C23×D13—21no—
101C23×D13C22×C412yes—
102C22×C4×C13—21no—
103C22×C4×C13—22no—
104C22×C4×C13—22no—
105C22×C4×C13—22no—
106C22×C4×C13—21no—
107C22×C4×C13—22no—
108C22×C4×C13—22no—
109C22×C4×C13—22no—
110C22×C4×C13—22no—
111C22×C4×C13—22no—
112C22×C4×C13—22no—
113C22×C4×C13—22no—
114C22×C4×C13—21no—
115C22×C4×C13—21no—
116C22×C4×C13—22no—
117C22×C4×C13—22no—
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×C13C22×C414yes—
125C22×C4×C13C22×C412yes—
126C22×C4×C13C2×D412yes—
127C22×C4×C13C2×D412yes—
128C22×C4×C13C2×D412yes—
129C22×C4×C13#4112yes—
130C22×C4×C13#4114yes—
131C22×Dic13—21no—
132C22×Dic13—22no—
133C22×Dic13—22no—
134C22×Dic13—22no—
135C22×Dic13—22no—
136C22×Dic13—22no—
137C22×Dic13—22no—
138C22×Dic13—21no—
139C22×Dic13—22no—
140C22×Dic13—22no—
141C22×Dic13—22no—
142C22×Dic13—22no—
143C22×Dic13—22no—
144C22×Dic13—22no—
145C22×Dic13—22no—
146C22×Dic13—22no—
147C22×Dic13—21no—
148C22×Dic13—21no—
149C22×Dic13—22no—
150C22×Dic13—22no—
151C22×Dic13—21no—
152C22×Dic13—21no—
153C22×Dic13—21no—
154C22×Dic13—22no—
155C22×Dic13—22no—
156C22×Dic13—21no—
157C22×Dic13C22×C412yes—
158C22×Dic13C22×C414yes—
159C22×Dic13#4114yes—
160C13×C4⋊C4—28no—
161C13×C4⋊C4—44no—
162C13×C4⋊C4—48no—
163C42×C13—44no—
164#6103—28no—
165#6103—48no—
166#6103—48no—
167#6103—44no—
168#6103—44no—
169#6101—44no—
170C4×Dic13—48no—
171C2×#397—131no—
172C2×#389D1311yescharacteristic, complemented
173C2×#388—131no—
174#1445—131no—
175#1442—131no—
176#1442—132no—
177#1439—131no—
178#1439—132no—
179#1437—132no—
180#1436—132no—
181C4×#95—131no—
182C23×C13C23×C411yescharacteristic
183C23×C13C22×D411yescharacteristic
184C23×C13C2×#4111yescharacteristic
185C23×C13C2×#4112yes—
186C23×C13C2×#4112yes—
187C23×C13H(5,𝔽2)11yescharacteristic
188C23×C13H(5,𝔽2)11yescharacteristic
189C23×C13H(5,𝔽2)12yes—
190C23×C13H(5,𝔽2)11yescharacteristic
191C23×C132−1+412yes—
192C23×C132−1+411yescharacteristic
193C22×D13—22no—
194C22×D13—24no—
195C22×D13—22no—
196C22×D13—24no—
197C22×D13—22no—
198C22×D13—41no—
199C22×D13—42no—
200C22×D13—41no—
201C22×D13—41no—
202C22×D13—41no—
203C22×D13—41no—
204C22×D13—41no—
205C22×D13—42no—
206C22×D13—42no—
207C22×D13—42no—
208C22×D13—42no—
209C22×D13—42no—
210C22×D13—41no—
211C22×D13—42no—
212C22×D13—42no—
213C22×D13—41no—
214C22×D13—42no—
215C22×D13—42no—
216C2×C4×C13—24no—
217C2×C4×C13—22no—
218C2×C4×C13—22no—
219C2×C4×C13—22no—
220C2×C4×C13—22no—
221C2×C4×C13—24no—
222C2×C4×C13—24no—
223C2×C4×C13—24no—
224C2×C4×C13—24no—
225C2×C4×C13—24no—
226C2×C4×C13—24no—
227C2×C4×C13—22no—
228C2×C4×C13—22no—
229C2×C4×C13—22no—
230C2×C4×C13—42no—
231C2×C4×C13—42no—
232C2×C4×C13—42no—
233C2×C4×C13—42no—
234C2×C4×C13—42no—
235C2×C4×C13—42no—
236C2×C4×C13—42no—
237C2×C4×C13—42no—
238C2×C4×C13—42no—
239C2×C4×C13—42no—
240C2×C4×C13—42no—
241C2×C4×C13—42no—
242C2×C4×C13—42no—
243C2×C4×C13C4×D414yes—
244C2×C4×C13#12414yes—
245C2×Dic13—22no—
246C2×Dic13—24no—
247C2×Dic13—24no—
248C2×Dic13—24no—
249C2×Dic13—24no—
250C2×Dic13—24no—
251C2×Dic13—24no—
252C2×Dic13—24no—
253C2×Dic13—41no—
254C2×Dic13—42no—
255C2×Dic13—41no—
256C2×Dic13—42no—
257C2×Dic13—42no—
258C2×Dic13—42no—
259C2×Dic13—42no—
260C2×Dic13—42no—
261C2×Dic13—42no—
262C2×Dic13—42no—
263C2×Dic13—42no—
264C2×Dic13—41no—
265C2×Dic13—41no—
266C2×Dic13—41no—
267C2×Dic13—41no—
268C2×Dic13—41no—
269C2×Dic13—41no—
270C2×Dic13—42no—
271C2×Dic13—42no—
272C2×Dic13—42no—
273C2×Dic13—42no—
274C22×C4⋊C4—131no—
275C22×C4⋊C4C2×D1311yescharacteristic
276C22×C4⋊C4C2×D1311yescharacteristic
277C22×C4⋊C4C2×D1312yes—
278C22×C22⋊C4—131no—
279C22×C22⋊C4—132no—
280C22×C22⋊C4—131no—
281C22×C22⋊C4—132no—
282C22×C22⋊C4—131no—
283C22×C42—132no—
284C22×C42C2×D1311yescharacteristic
285#397—138no—
286#389—24no—
287#388—264no—
288C2×#95—131no—
289C2×#95—132no—
290C2×#95—132no—
291C2×#95—131no—
292C2×#95—132no—
293C2×#95—131no—
294C2×#95—131no—
295C2×#95—132no—
296C2×#95—132no—
297C2×#95—132no—
298C2×#95—132no—
299C2×#95C2×D1312yes—
300C22×C13C2×C4×D411yescharacteristic
301C22×C13C4×#4112yes—
302C22×C13#51811yescharacteristic
303C22×C13#52012yes—
304C22×C13#52011yescharacteristic
305C22×C13C2×#12411yescharacteristic
306C22×C13#52912yes—
307C22×C13#53211yescharacteristic
308C22×C13#53411yescharacteristic
309C22×C13#53511yescharacteristic
310C22×C13#53611yescharacteristic
311C22×C13#53711yescharacteristic
312C22×C13#53812yes—
313C22×C13#53812yes—
314C22×C13#53912yes—
315C22×C13#53912yes—
316C22×C13#53912yes—
317C22×C13#54011yescharacteristic
318C22×C13#54012yes—
319C22×C13#54112yes—
320C22×C13#54212yes—
321C22×C13#54212yes—
322C22×C13#54211yescharacteristic
323C2×D13—42no—
324C2×D13—42no—
325C2×D13—44no—
326C2×D13—44no—
327C2×D13—42no—
328C2×D13—81no—
329C2×D13—81no—
330C2×D13—82no—
331C2×D13—82no—
332C2×D13—81no—
333C2×D13—81no—
334C4×C13—24no—
335C4×C13—24no—
336C4×C13—44no—
337C4×C13—42no—
338C4×C13—82no—
339Dic13—44no—
340Dic13—44no—
341Dic13—42no—
342Dic13—81no—
343Dic13—81no—
344C25—131no—
345C23×C4—131no—
346C23×C4—132no—
347C23×C4—132no—
348C23×C4—131no—
349C23×C4—131no—
350C23×C4C22×D1312yes—
351C23×C4C22×D1312yes—
352C23×C4C22×D1311yescharacteristic
353C23×C4C22×D1311yescharacteristic
354C23×C4C22×D1311yescharacteristic
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—24no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—42no—
360C2×C4⋊C4—42no—
361C2×C4⋊C4—42no—
362C2×C4⋊C4—264no—
363C2×C4⋊C4—262no—
364C2×C4⋊C4C4×D1314yes—
365C2×C22⋊C4—134no—
366C2×C22⋊C4—138no—
367C2×C22⋊C4—262no—
368C2×C22⋊C4—262no—
369C2×C22⋊C4—264no—
370C2×C22⋊C4—264no—
371C2×C22⋊C4—262no—
372C2×C22⋊C4—262no—
373C2×C22⋊C4—522no—
374C2×C22⋊C4—522no—
375C2×C22⋊C4—522no—
376C2×C22⋊C4—522no—
377C2×C22⋊C4—522no—
378C2×C42—42no—
379C2×C42—264no—
380C2×C42—522no—
381C2×C42—522no—
382C2×C42C22⋊D1314yes—
383#95—24no—
384#95—138no—
385#95—134no—
386#95—264no—
387#95—264no—
388#95—262no—
389#95—262no—
390#95—262no—
391#95—522no—
392#95—522no—
393#95—522no—
394#95—522no—
395C2×C13C4×#12411yescharacteristic
396C2×C13#232211yescharacteristic
397C2×C13#232411yescharacteristic
398C2×C13#233412yes—
399C2×C13#233512yes—
400C2×C13#263911yescharacteristic
401C2×C13#264011yescharacteristic
402C2×C13#264912yes—
403C2×C13#265412yes—
404C2×C13#266111yescharacteristic
405C2×C13#266411yescharacteristic
406D13—82no—
407C24—132no—
408C24—261no—
409C24—262no—
410C24—261no—
411C24—261no—
412C24—262no—
413C24—262no—
414C24—262no—
415C24—261no—
416C24—261no—
417C24—261no—
418C24C23×D1311yescharacteristic
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—134no—
442C22×C4—132no—
443C22×C4—134no—
444C22×C4—262no—
445C22×C4—261no—
446C22×C4—262no—
447C22×C4—262no—
448C22×C4—262no—
449C22×C4—262no—
450C22×C4—262no—
451C22×C4—262no—
452C22×C4—262no—
453C22×C4—262no—
454C22×C4—262no—
455C22×C4—262no—
456C22×C4—262no—
457C22×C4—262no—
458C22×C4—262no—
459C22×C4—261no—
460C22×C4—261no—
461C22×C4—261no—
462C22×C4—262no—
463C22×C4—262no—
464C22×C4—262no—
465C22×C4—262no—
466C22×C4—261no—
467C22×C4—261no—
468C22×C4—261no—
469C22×C4—261no—
470C22×C4C2×C4×D1314yes—
471C22×C4C2×C4×D1312yes—
472C22×C4#612712yes—
473C22×C4#613114yes—
474C22×C4C2×C22⋊D1312yes—
475C22×C4C2×C22⋊D1312yes—
476C22×C4C2×C22⋊D1312yes—
477C4⋊C4—28no—
478C4⋊C4—44no—
479C4⋊C4—48no—
480C4⋊C4—524no—
481C22⋊C4—268no—
482C22⋊C4—528no—
483C22⋊C4—524no—
484C22⋊C4—528no—
485C22⋊C4—524no—
486C42—44no—
487C42—528no—
488C13#1432411yescharacteristic, complemented, Sylow
489C23—264no—
490C23—262no—
491C23—262no—
492C23—262no—
493C23—264no—
494C23—522no—
495C23—522no—
496C23—522no—
497C23—521no—
498C23—521no—
499C23—521no—
500C23—521no—
501C23—521no—
502C23—521no—
503C23—521no—
504C23—521no—
505C23—522no—
506C23—522no—
507C23—522no—
508C23—522no—
509C23—522no—
510C23—522no—
511C23—522no—
512C23C22×C4×D1311yescharacteristic
513C23C2×#612711yescharacteristic
514C23#8825111yescharacteristic
515C23#8825111yescharacteristic
516C23#8825112yes—
517C23C2×#613112yes—
518C23#8825412yes—
519C23#41×D1312yes—
520C23#8825611yescharacteristic
521C23#8825711yescharacteristic
522C23C22×C22⋊D1311yescharacteristic
523C2×C4—24no—
524C2×C4—24no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—24no—
530C2×C4—24no—
531C2×C4—24no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—264no—
551C2×C4—262no—
552C2×C4—264no—
553C2×C4—264no—
554C2×C4—264no—
555C2×C4—264no—
556C2×C4—264no—
557C2×C4—264no—
558C2×C4—522no—
559C2×C4—522no—
560C2×C4—522no—
561C2×C4—521no—
562C2×C4—522no—
563C2×C4—521no—
564C2×C4—522no—
565C2×C4—522no—
566C2×C4—522no—
567C2×C4—522no—
568C2×C4—522no—
569C2×C4—522no—
570C2×C4—522no—
571C2×C4—521no—
572C2×C4—521no—
573C2×C4—521no—
574C2×C4—521no—
575C2×C4—521no—
576C2×C4—521no—
577C2×C4—522no—
578C2×C4—522no—
579C2×C4C4×C22⋊D1314yes—
580C2×C4#8820114yes—
581C22—522no—
582C22—522no—
583C22—524no—
584C22—524no—
585C22—522no—
586C22—1041no—
587C22—1041no—
588C22—1042no—
589C22—1042no—
590C22—1041no—
591C22—1041no—
592C22#1171920912yes—
593C22#1171922012yes—
594C22#1171925011yescharacteristic
595C22#1171925111yescharacteristic
596C22#1171926611yescharacteristic
597C22#1171926711yescharacteristic
598C22C4×#613112yes—
599C22#1171928512yes—
600C22#1171931812yes—
601C22#1171932012yes—
602C22#1171934912yes—
603C22#1171935012yes—
604C22#1171939712yes—
605C22#1171940112yes—
606C22#1171943812yes—
607C22#1171943812yes—
608C22C2×C4×C22⋊D1311yescharacteristic
609C22#1171950911yescharacteristic
610C22#1171951011yescharacteristic
611C22C2×#8820111yescharacteristic
612C22#1171952111yescharacteristic
613C22#1171953711yescharacteristic
614C22#1171953811yescharacteristic
615C4—24no—
616C4—24no—
617C4—44no—
618C4—42no—
619C4—82no—
620C4—524no—
621C4—524no—
622C4—522no—
623C4—1041no—
624C4—1041no—
625C2—1042no—
626C2C4×#8820111yescharacteristic
627C2#1311750511yescharacteristic
628C2#1311752311yescharacteristic
629C2#1311761012yes—
630C2#1311762912yes—
631C2#1312077011yescharacteristic
632C2#1312077711yescharacteristic
633C2#1312084512yes—
634C2#1312092012yes—
635C2#1312096511yescharacteristic
636C2#1312099711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#389C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenterC2×#389D13
hypocenterC13#14324
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
3. #13113104C2semidirect
4. #13113095C2semidirect
5. #13113095C2semidirect
9. #13113071C2semidirect
10. C4×#88071C2semidirect
11. C2×C13×#389C2semidirect
36. #11718654C4semidirect
172. C2×#389D13semidirect
488. C13#14324semidirect

Maximal subgroups

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

subgroupindex
C2×#117186542
C2×#117186012
#131131042
#131130952
#131130782
#131130722
#131130712
C4×#880712
C2×C13×#3892
#1432413