Finite Group Databasebeta

← #15789945

Subgroups — #15789945

Order 3328.

1454 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718608C211yesmaximal, characteristic
2C2×#11718635C211yesmaximal, characteristic, complemented
3C2×#11718612C211yesmaximal, characteristic
4#13113106C211yesmaximal, characteristic, complemented
5#13113097C212yesmaximal, complemented
6#13113095C211yesmaximal, characteristic, complemented
7#13113083C212yesmaximal
8#13113073C212yesmaximal
9#13113070C212yesmaximal, complemented
10#95×Dic13C211yesmaximal, characteristic, complemented
11C13×#1439C211yesmaximal, characteristic
12C23×Dic26C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C13×C22⋊C4C2211yescharacteristic
15C22×C13×C22⋊C4C2212yes—
16C22×C22⋊Dic13C2211yescharacteristic
17C22×C22⋊Dic13C2211yescharacteristic
18C22×C22⋊Dic13C2212yes—
19C22×C4⋊Dic13C2211yescharacteristic
20C22×C4×Dic13C2212yes—
21C22×C4×Dic13C2211yescharacteristic
22C2×C13×#95C2212yes—
23C2×C13×#95C2211yescharacteristic
24C2×#88071C2211yescharacteristic
25C2×#88071C2211yescharacteristic
26C2×#88071C2212yes—
27C2×#88071C2212yes—
28C2×#88071C2212yes—
29C2×#88071C2212yes—
30C2×#88071C2212yes—
31C2×#88071C2212yes—
32C2×#88071C2212yes—
33C2×#88071C2211yescharacteristic
34C2×#88071C2212yes—
35#11718635—24no—
36#11718612—24no—
37#11718608C418yescomplemented
38C25×C13C2311yescharacteristic
39C23×C4×C13C2312yes—
40C23×C4×C13C2311yescharacteristic
41C23×C4×C13C2312yes—
42C23×C4×C13C2311yescharacteristic
43C23×Dic13C2311yescharacteristic
44C23×Dic13C2311yescharacteristic
45C23×Dic13C2312yes—
46C23×Dic13C2312yes—
47C23×Dic13C2311yescharacteristic
48C23×Dic13C2311yescharacteristic
49C22×Dic26—22no—
50C22×Dic26—22no—
51C22×Dic26—42no—
52C22×Dic26—42no—
53C22×Dic26C2×C414yes—
54C2×C13×C4⋊C4—22no—
55C2×C13×C4⋊C4—42no—
56C2×C13×C22⋊C4—22no—
57C2×C13×C22⋊C4—22no—
58C2×C13×C22⋊C4—24no—
59C2×C13×C22⋊C4—42no—
60C2×C13×C22⋊C4—42no—
61C2×C13×C22⋊C4C2×C414yes—
62C2×C22⋊Dic13—22no—
63C2×C22⋊Dic13—22no—
64C2×C22⋊Dic13—24no—
65C2×C22⋊Dic13—42no—
66C2×C22⋊Dic13—42no—
67C2×C22⋊Dic13—42no—
68C2×C22⋊Dic13C2×C418yes—
69C2×C4⋊Dic13—22no—
70C2×C4⋊Dic13—24no—
71C2×C4×Dic13—24no—
72C2×C4×Dic13—42no—
73C2×C4×Dic13—42no—
74C2×C4×Dic13—42no—
75C2×C4×Dic13D414yes—
76C13×#95—22no—
77C13×#95—24no—
78#88071—22no—
79#88071—24no—
80#88071—22no—
81#88071—24no—
82#88071—24no—
83#88071—42no—
84#88071—42no—
85#88071—42no—
86#88071—42no—
87#88071C2×C414yes—
88#88071C2×C418yes—
89#14323—131nomaximal, Sylow
90C24×C13—21no—
91C24×C13—22no—
92C24×C13—21no—
93C24×C13—22no—
94C24×C13—22no—
95C24×C13—22no—
96C24×C13—21no—
97C24×C13—21no—
98C24×C13—21no—
99C24×C13—21no—
100C24×C13C22×C412yes—
101C24×C13C2411yescharacteristic
102C22×C4×C13—22no—
103C22×C4×C13—22no—
104C22×C4×C13—21no—
105C22×C4×C13—22no—
106C22×C4×C13—22no—
107C22×C4×C13—22no—
108C22×C4×C13—22no—
109C22×C4×C13—21no—
110C22×C4×C13—22no—
111C22×C4×C13—22no—
112C22×C4×C13—22no—
113C22×C4×C13—22no—
114C22×C4×C13—22no—
115C22×C4×C13—22no—
116C22×C4×C13—22no—
117C22×C4×C13—22no—
118C22×C4×C13—22no—
119C22×C4×C13—22no—
120C22×C4×C13—22no—
121C22×C4×C13C22×C412yes—
122C22×C4×C13C22×C412yes—
123C22×C4×C13C2×D412yes—
124C22×C4×C13#4114yes—
125C22×C4×C13#4112yes—
126C22×Dic13—22no—
127C22×Dic13—21no—
128C22×Dic13—21no—
129C22×Dic13—22no—
130C22×Dic13—22no—
131C22×Dic13—22no—
132C22×Dic13—22no—
133C22×Dic13—22no—
134C22×Dic13—22no—
135C22×Dic13—22no—
136C22×Dic13—22no—
137C22×Dic13—22no—
138C22×Dic13—22no—
139C22×Dic13—22no—
140C22×Dic13—22no—
141C22×Dic13—22no—
142C22×Dic13—22no—
143C22×Dic13—21no—
144C22×Dic13—21no—
145C22×Dic13—21no—
146C22×Dic13—21no—
147C22×Dic13—22no—
148C22×Dic13—22no—
149C22×Dic13—22no—
150C22×Dic13—21no—
151C22×Dic13—22no—
152C22×Dic13—21no—
153C22×Dic13—21no—
154C22×Dic13—21no—
155C22×Dic13C22×C414yes—
156C22×Dic13C22×C414yes—
157C22×Dic13C2×D412yes—
158C22×Dic13C2×D412yes—
159C22×Dic13#4114yes—
160C2×Dic26—28no—
161C2×Dic26—48no—
162C2×Dic26—44no—
163C2×Dic26—44no—
164C2×Dic26—48no—
165C13×C4⋊C4—44no—
166C13×C22⋊C4—28no—
167C13×C22⋊C4—48no—
168C22⋊Dic13—48no—
169C22⋊Dic13—44no—
170C22⋊Dic13—44no—
171C4⋊Dic13—44no—
172C4×Dic13—44no—
173C4×Dic13—48no—
174C2×#393—131no—
175C2×#391—131no—
176C2×#388—131no—
177#1446—131no—
178#1443—132no—
179#1442—131no—
180#1440—132no—
181#1439D1311yescharacteristic
182#1437—132no—
183#1436—132no—
184C4×#95—131no—
185C23×C13—22no—
186C23×C13—24no—
187C23×C13—24no—
188C23×C13—22no—
189C23×C13—22no—
190C23×C13—41no—
191C23×C13—42no—
192C23×C13—41no—
193C23×C13—41no—
194C23×C13—41no—
195C23×C13—41no—
196C23×C13—41no—
197C23×C13—42no—
198C23×C13—42no—
199C23×C13—42no—
200C23×C13—42no—
201C23×C13—42no—
202C23×C13—41no—
203C23×C13—41no—
204C23×C13—42no—
205C23×C13—42no—
206C23×C13—42no—
207C23×C13—42no—
208C23×C13C23×C411yescharacteristic
209C23×C13C22×D411yescharacteristic
210C23×C13C2×#4111yescharacteristic
211C23×C13C2×#4112yes—
212C23×C13C2×#4112yes—
213C23×C13H(5,𝔽2)12yes—
214C23×C13H(5,𝔽2)12yes—
215C23×C13H(5,𝔽2)11yescharacteristic
216C23×C132−1+411yescharacteristic
217C23×C132−1+411yescharacteristic
218C23×C132−1+411yescharacteristic
219C2×C4×C13—24no—
220C2×C4×C13—22no—
221C2×C4×C13—22no—
222C2×C4×C13—24no—
223C2×C4×C13—22no—
224C2×C4×C13—24no—
225C2×C4×C13—24no—
226C2×C4×C13—24no—
227C2×C4×C13—24no—
228C2×C4×C13—41no—
229C2×C4×C13—42no—
230C2×C4×C13—41no—
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×C13C4×D414yes—
243C2×Dic13—22no—
244C2×Dic13—22no—
245C2×Dic13—24no—
246C2×Dic13—24no—
247C2×Dic13—24no—
248C2×Dic13—24no—
249C2×Dic13—24no—
250C2×Dic13—24no—
251C2×Dic13—24no—
252C2×Dic13—24no—
253C2×Dic13—22no—
254C2×Dic13—22no—
255C2×Dic13—22no—
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—42no—
265C2×Dic13—42no—
266C2×Dic13—41no—
267C2×Dic13—41no—
268C2×Dic13—41no—
269C2×Dic13—41no—
270C2×Dic13—41no—
271C2×Dic13—41no—
272C2×Dic13—42no—
273C2×Dic13—42no—
274C2×Dic13—42no—
275C2×Dic13—42no—
276C2×Dic13#12414yes—
277Dic26—416no—
278C23×Q8—131no—
279C22×C4⋊C4—131no—
280C22×C4⋊C4C2×D1311yescharacteristic
281C22×C22⋊C4—132no—
282C22×C22⋊C4—131no—
283C22×C22⋊C4—131no—
284C22×C22⋊C4C2×D1311yescharacteristic
285C22×C22⋊C4C2×D1312yes—
286C22×C42—131no—
287C22×C42—132no—
288#393—138no—
289#391—264no—
290#388—264no—
291C2×#95—131no—
292C2×#95—132no—
293C2×#95—132no—
294C2×#95—132no—
295C2×#95—132no—
296C2×#95—131no—
297C2×#95—131no—
298C2×#95—132no—
299C2×#95—132no—
300C2×#95—132no—
301C2×#95—132no—
302C2×#95C2×D1311yescharacteristic
303C2×#95C2×D1312yes—
304C22×C13—42no—
305C22×C13—42no—
306C22×C13—44no—
307C22×C13—44no—
308C22×C13—42no—
309C22×C13—81no—
310C22×C13—81no—
311C22×C13—82no—
312C22×C13—82no—
313C22×C13—81no—
314C22×C13—81no—
315C22×C13C2×C4×D411yescharacteristic
316C22×C13C4×#4112yes—
317C22×C13#51812yes—
318C22×C13#51911yescharacteristic
319C22×C13#52011yescharacteristic
320C22×C13C2×#12411yescharacteristic
321C22×C13#52912yes—
322C22×C13#53211yescharacteristic
323C22×C13#53411yescharacteristic
324C22×C13#53511yescharacteristic
325C22×C13#53611yescharacteristic
326C22×C13#53711yescharacteristic
327C22×C13#53812yes—
328C22×C13#53812yes—
329C22×C13#53812yes—
330C22×C13#53912yes—
331C22×C13#53912yes—
332C22×C13#54111yescharacteristic
333C22×C13#54211yescharacteristic
334C22×C13#54212yes—
335C22×C13#54212yes—
336C22×C13#54212yes—
337C22×C13#54212yes—
338C4×C13—24no—
339C4×C13—44no—
340C4×C13—42no—
341C4×C13—82no—
342Dic13—24no—
343Dic13—44no—
344Dic13—44no—
345Dic13—42no—
346Dic13—81no—
347Dic13—81no—
348C25C22×D1311yescharacteristic
349C22×Q8—134no—
350C22×Q8—262no—
351C22×Q8—262no—
352C22×Q8—522no—
353C22×Q8—522no—
354C23×C4—131no—
355C23×C4—132no—
356C23×C4—132no—
357C23×C4—131no—
358C23×C4—131no—
359C23×C4—131no—
360C23×C4C22×D1312yes—
361C23×C4C22×D1311yescharacteristic
362C23×C4C22×D1312yes—
363C23×C4C22×D1311yescharacteristic
364C2×C4⋊C4—22no—
365C2×C4⋊C4—42no—
366C2×C4⋊C4—264no—
367C2×C4⋊C4—262no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—42no—
372C2×C22⋊C4—42no—
373C2×C22⋊C4—138no—
374C2×C22⋊C4—262no—
375C2×C22⋊C4—262no—
376C2×C22⋊C4—264no—
377C2×C22⋊C4—522no—
378C2×C22⋊C4—522no—
379C2×C22⋊C4—522no—
380C2×C22⋊C4C4×D1314yes—
381C2×C42—134no—
382C2×C42—264no—
383C2×C42—522no—
384C2×C42—522no—
385C2×C42—522no—
386#95—22no—
387#95—24no—
388#95—134no—
389#95—138no—
390#95—262no—
391#95—264no—
392#95—264no—
393#95—262no—
394#95—264no—
395#95—522no—
396#95—522no—
397#95—522no—
398#95—522no—
399C2×C13—82no—
400C2×C13C4×#12411yescharacteristic
401C2×C13#232111yescharacteristic
402C2×C13#232311yescharacteristic
403C2×C13#233212yes—
404C2×C13#233712yes—
405C2×C13#263911yescharacteristic
406C2×C13#264011yescharacteristic
407C2×C13#265012yes—
408C2×C13#265312yes—
409C2×C13#266211yescharacteristic
410C2×C13#266311yescharacteristic
411C24—21no—
412C24—21no—
413C24—22no—
414C24—21no—
415C24—22no—
416C24—21no—
417C24—22no—
418C24—22no—
419C24—21no—
420C24—21no—
421C24C2×C4×D1312yes—
422C24C23×D1311yescharacteristic
423C2×Q8—268no—
424C2×Q8—528no—
425C2×Q8—524no—
426C2×Q8—528no—
427C2×Q8—524no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—21no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—132no—
448C22×C4—134no—
449C22×C4—134no—
450C22×C4—134no—
451C22×C4—132no—
452C22×C4—261no—
453C22×C4—262no—
454C22×C4—261no—
455C22×C4—262no—
456C22×C4—262no—
457C22×C4—262no—
458C22×C4—262no—
459C22×C4—262no—
460C22×C4—262no—
461C22×C4—262no—
462C22×C4—262no—
463C22×C4—262no—
464C22×C4—261no—
465C22×C4—262no—
466C22×C4—262no—
467C22×C4—262no—
468C22×C4—262no—
469C22×C4—262no—
470C22×C4—261no—
471C22×C4—261no—
472C22×C4—261no—
473C22×C4—262no—
474C22×C4—261no—
475C22×C4—261no—
476C22×C4—262no—
477C22×C4—262no—
478C22×C4—262no—
479C22×C4—261no—
480C22×C4—261no—
481C22×C4C2×C4×D1312yes—
482C22×C4C2×C4×D1312yes—
483C22×C4D4×D1312yes—
484C22×C4#612914yes—
485C22×C4#612912yes—
486C4⋊C4—44no—
487C4⋊C4—524no—
488C22⋊C4—28no—
489C22⋊C4—48no—
490C22⋊C4—524no—
491C22⋊C4—528no—
492C22⋊C4—524no—
493C42—524no—
494C42—528no—
495C13#1432311yescharacteristic, complemented, Sylow
496C23—22no—
497C23—22no—
498C23—22no—
499C23—24no—
500C23—24no—
501C23—41no—
502C23—42no—
503C23—42no—
504C23—41no—
505C23—42no—
506C23—41no—
507C23—42no—
508C23—41no—
509C23—41no—
510C23—42no—
511C23—42no—
512C23—41no—
513C23—42no—
514C23—42no—
515C23—42no—
516C23—41no—
517C23—42no—
518C23—41no—
519C23C22×C4×D1311yescharacteristic
520C23C2×D4×D1311yescharacteristic
521C23C2×#612911yescharacteristic
522C23C2×#612912yes—
523C23#8825111yescharacteristic
524C23#8825112yes—
525C23#8825411yescharacteristic
526C23#41×D1312yes—
527C23#8825612yes—
528C23#8825711yescharacteristic
529C23#8825711yescharacteristic
530Q8—5216no—
531C2×C4—24no—
532C2×C4—22no—
533C2×C4—24no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—24no—
537C2×C4—24no—
538C2×C4—24no—
539C2×C4—24no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—134no—
555C2×C4—262no—
556C2×C4—262no—
557C2×C4—264no—
558C2×C4—264no—
559C2×C4—264no—
560C2×C4—264no—
561C2×C4—264no—
562C2×C4—264no—
563C2×C4—264no—
564C2×C4—264no—
565C2×C4—262no—
566C2×C4—262no—
567C2×C4—262no—
568C2×C4—522no—
569C2×C4—522no—
570C2×C4—522no—
571C2×C4—522no—
572C2×C4—522no—
573C2×C4—522no—
574C2×C4—522no—
575C2×C4—522no—
576C2×C4—522no—
577C2×C4—522no—
578C2×C4—521no—
579C2×C4—521no—
580C2×C4—521no—
581C2×C4—522no—
582C2×C4—521no—
583C2×C4—522no—
584C2×C4—522no—
585C2×C4—521no—
586C2×C4—521no—
587C2×C4—522no—
588C2×C4#8813514yes—
589C22—42no—
590C22—42no—
591C22—44no—
592C22—42no—
593C22—44no—
594C22—81no—
595C22—82no—
596C22—82no—
597C22—81no—
598C22—81no—
599C22—81no—
600C22C2×#8813511yescharacteristic
601C22#1171920911yescharacteristic
602C22#1171922111yescharacteristic
603C22C4×#612912yes—
604C22#1171925012yes—
605C22#1171929711yescharacteristic
606C22#1171929812yes—
607C22#1171930512yes—
608C22#1171930811yescharacteristic
609C22#1171930812yes—
610C22#1171931311yescharacteristic
611C22#1171932212yes—
612C22#1171933011yescharacteristic
613C22#1171933311yescharacteristic
614C22#1171934512yes—
615C22#1171934812yes—
616C22#1171935811yescharacteristic
617C22#1171936212yes—
618C22#1171937012yes—
619C22#1171937412yes—
620C22D13×#12411yescharacteristic
621C22#1171941212yes—
622C22#1171942111yescharacteristic
623C4—24no—
624C4—44no—
625C4—42no—
626C4—82no—
627C4—264no—
628C4—524no—
629C4—524no—
630C4—522no—
631C4—1041no—
632C4—1041no—
633C2—82no—
634C2#1311738311yescharacteristic
635C2#1311749911yescharacteristic
636C2#1311751411yescharacteristic
637C2#1311759312yes—
638C2#1311765012yes—
639C2#1312076311yescharacteristic
640C2#1312077411yescharacteristic
641C2#1312085512yes—
642C2#1312090012yes—
643C2#1312097811yescharacteristic
644C2#1312098911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1439C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenter#1439D13
hypocenterC13#14323
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. C2×#11718635C2semidirect
4. #13113106C2semidirect
5. #13113097C2semidirect
6. #13113095C2semidirect
9. #13113070C2semidirect
10. #95×Dic13C2semidirect
37. #11718608C4semidirect
495. C13#14323semidirect

Maximal subgroups

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

subgroupindex
C2×#117186082
C2×#117186352
C2×#117186122
#131131062
#131130972
#131130952
#131130832
#131130732
#131130702
#95×Dic132
C13×#14392
#1432313