Finite Group Databasebeta

← #15919457

Subgroups — #15919457

Order 3328.

1302 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718716C211yesmaximal, characteristic, complemented
2C2×#11718681C211yesmaximal, characteristic, complemented
3#13120009C211yesmaximal, characteristic, complemented
4#13116029C212yesmaximal, complemented
5#13116022C212yesmaximal, complemented
6#13115769C211yesmaximal, characteristic, complemented
7#13115635C211yesmaximal, characteristic, complemented
8#13114776C212yesmaximal, complemented
9#13114771C212yesmaximal, complemented
10#13114666C211yesmaximal, characteristic, complemented
11C2×C13×#548C211yesmaximal, characteristic
12C22×C13×#41C2211yescharacteristic
13C23×Q8×C13C2211yescharacteristic
14C13×#548—24no—
15C13×#548—24no—
16C2×C13×#124—21no—
17C2×C13×#124C2211yescharacteristic
18C2×C13×C22⋊Q8—21no—
19C2×C13×C22⋊Q8C2211yescharacteristic
20C2×C13×#121—21no—
21C2×C13×#121C2211yescharacteristic
22C2×C4×Q8×C13C2211yescharacteristic
23C2×C4×D4×C13—21no—
24C2×C4×D4×C13C2211yescharacteristic
25C2×#88123C2211yescharacteristic
26C2×#88075C2212yes—
27C2×#88075C2212yes—
28C2×#88075C2212yes—
29C2×#88075C2212yes—
30#11718882—21no—
31C2×#88072C2212yes—
32C2×#88072C2212yes—
33#11718873C2212yes—
34#11718873C2212yes—
35C2×C22⋊#1055C2212yes—
36C2×C22⋊#1055C2212yes—
37#11718716—24no—
38#11718681—24no—
39#11718638—21no—
40C2×#88048C2212yes—
41#11718608—21no—
42#11718608—21no—
43C4×C4⋊Dic13C2211yescharacteristic
44C2×C4⋊#1055C2211yescharacteristic
45C2×#88043C2211yescharacteristic
46#11718121C2212yes—
47C2×C13×#41—22no—
48C2×C13×#41—22no—
49C2×C13×#41—24no—
50C2×C13×#41—42no—
51C22×Q8×C13—22no—
52C22×Q8×C13—22no—
53C22×Q8×C13—21no—
54C22×Q8×C13—24no—
55C22×Q8×C13—42no—
56C22×Q8×C13C2311yescharacteristic
57C22×Q8×C13C2311yescharacteristic
58C22×D4×C13—21no—
59C22×D4×C13—21no—
60C22×D4×C13D411yescharacteristic
61C22×D4×C13C2311yescharacteristic
62C23×C4×C13—21no—
63C23×C4×C13—21no—
64C23×C4×C13C2311yescharacteristic
65C23×C4×C13C2311yescharacteristic
66C22×Dic26—21no—
67C13×#124—28no—
68C13×#124—22no—
69C13×#124D414yes—
70C13×C22⋊Q8—28no—
71C13×C22⋊Q8—22no—
72C13×C22⋊Q8—22no—
73C13×#121—28no—
74C13×#121—22no—
75C13×#121—22no—
76C4×Q8×C13—22no—
77C4×Q8×C13D414yes—
78C4×D4×C13—28no—
79C4×D4×C13—22no—
80C4×D4×C13—22no—
81C2×C13×C4⋊C4—21no—
82C2×C13×C4⋊C4—21no—
83C2×C13×C4⋊C4D411yescharacteristic
84C2×C13×C4⋊C4C2311yescharacteristic
85C2×C13×C22⋊C4—21no—
86C2×C13×C22⋊C4—21no—
87C2×C13×C22⋊C4—21no—
88C2×C13×C22⋊C4—21no—
89C2×C13×C22⋊C4D411yescharacteristic
90C2×C13×C22⋊C4D411yescharacteristic
91C2×C42×C13—21no—
92C2×C42×C13C2311yescharacteristic
93C2×C22⋊Dic13—22no—
94C2×C22⋊Dic13—22no—
95C2×C4⋊Dic13—21no—
96C2×C4⋊Dic13C2312yes—
97C2×C4⋊Dic13C2312yes—
98C2×C4×Dic13—21no—
99C22×#1055C2312yes—
100C22×#1055C2312yes—
101#88123—22no—
102#88123—22no—
103#88075—24no—
104#88075—24no—
105#88075—24no—
106#88075—42no—
107#88072—24no—
108#88072—42no—
109#88071—21no—
110#88071—22no—
111#88071—22no—
112C22⋊#1055—42no—
113C22⋊#1055—42no—
114#88048—24no—
115C4⋊#1055—22no—
116#88043—22no—
117#25895—131nomaximal, Sylow
118C24×C13—21no—
119C24×C13C2×D411yescharacteristic
120C24×C13C2×D411yescharacteristic
121C13×#41—48no—
122C13×#41—44no—
123C13×#41—44no—
124C2×Q8×C13—24no—
125C2×Q8×C13—21no—
126C2×Q8×C13—21no—
127C2×Q8×C13—22no—
128C2×Q8×C13—22no—
129C2×Q8×C13—22no—
130C2×Q8×C13—44no—
131C2×Q8×C13—48no—
132C2×Q8×C13—44no—
133C2×Q8×C13—44no—
134C2×Q8×C13C2×D412yes—
135C2×Q8×C13C2×D412yes—
136C2×Q8×C13#4114yes—
137C2×D4×C13—24no—
138C2×D4×C13—24no—
139C2×D4×C13—22no—
140C2×D4×C13—22no—
141C2×D4×C13—21no—
142C2×D4×C13—22no—
143C2×D4×C13—22no—
144C2×D4×C13—41no—
145C2×D4×C13—44no—
146C2×D4×C13—42no—
147C2×D4×C13—42no—
148C2×D4×C13C2×D412yes—
149C22×C4×C13—21no—
150C22×C4×C13—24no—
151C22×C4×C13—24no—
152C22×C4×C13—21no—
153C22×C4×C13—21no—
154C22×C4×C13—21no—
155C22×C4×C13—21no—
156C22×C4×C13—21no—
157C22×C4×C13—21no—
158C22×C4×C13—22no—
159C22×C4×C13—22no—
160C22×C4×C13—22no—
161C22×C4×C13—22no—
162C22×C4×C13—44no—
163C22×C4×C13—44no—
164C22×C4×C13C2×D411yescharacteristic
165C22×C4×C13C2×D411yescharacteristic
166C22×C4×C13C2×D411yescharacteristic
167C22×C4×C13C2×D411yescharacteristic
168C22×C4×C13C2411yescharacteristic
169C22×Dic13—22no—
170C22×Dic13—22no—
171C2×Dic26—42no—
172C2×Dic26—82no—
173C13×C4⋊C4—24no—
174C13×C4⋊C4—24no—
175C13×C4⋊C4—22no—
176C13×C4⋊C4—21no—
177C13×C4⋊C4C2×D412yes—
178C13×C22⋊C4—24no—
179C13×C22⋊C4—24no—
180C13×C22⋊C4—24no—
181C13×C22⋊C4—24no—
182C13×C22⋊C4—22no—
183C13×C22⋊C4—22no—
184C42×C13—24no—
185C42×C13C2×D412yes—
186C42×C13C2×D412yes—
187C22⋊Dic13—82no—
188C22⋊Dic13—82no—
189C4⋊Dic13—22no—
190C4⋊Dic13—22no—
191C4⋊Dic13—22no—
192C4⋊Dic13—22no—
193C4⋊Dic13—42no—
194C4×Dic13—42no—
195C2×#1055—22no—
196C2×#1055—22no—
197C2×#1055—22no—
198C2×#1055—22no—
199C2×#1055—22no—
200C2×#1055—22no—
201C2×#548D1311yescharacteristic
202C2×#489—131no—
203C2×#475—131no—
204#2563—131no—
205#2035—132no—
206#2034—132no—
207#1983—131no—
208#1955—131no—
209#1788—132no—
210#1787—132no—
211#1763—131no—
212C23×C13—21no—
213C23×C13—22no—
214C23×C13—21no—
215C23×C13—22no—
216C23×C13—21no—
217C23×C13—22no—
218C23×C13—22no—
219C23×C13—21no—
220C23×C13—21no—
221C23×C13—22no—
222C23×C13—42no—
223C23×C13—41no—
224C23×C13—41no—
225C23×C13—42no—
226C23×C13#13712yes—
227C23×C13C22×D411yescharacteristic
228Q8×C13—22no—
229Q8×C13—24no—
230Q8×C13—24no—
231Q8×C13—48no—
232Q8×C13—41no—
233Q8×C13—41no—
234Q8×C13#12414yes—
235D4×C13—24no—
236D4×C13—44no—
237D4×C13—48no—
238D4×C13—48no—
239D4×C13—41no—
240D4×C13—41no—
241C2×C4×C13—22no—
242C2×C4×C13—24no—
243C2×C4×C13—21no—
244C2×C4×C13—21no—
245C2×C4×C13—22no—
246C2×C4×C13—22no—
247C2×C4×C13—22no—
248C2×C4×C13—21no—
249C2×C4×C13—21no—
250C2×C4×C13—22no—
251C2×C4×C13—22no—
252C2×C4×C13—48no—
253C2×C4×C13—48no—
254C2×C4×C13—42no—
255C2×C4×C13—41no—
256C2×C4×C13—41no—
257C2×C4×C13—41no—
258C2×C4×C13—41no—
259C2×C4×C13—41no—
260C2×C4×C13—41no—
261C2×C4×C13—42no—
262C2×C4×C13—42no—
263C2×C4×C13#12012yes—
264C2×C4×C13#12012yes—
265C2×C4×C13C22×D411yescharacteristic
266C2×C4×C13C22×D411yescharacteristic
267C2×C4×C13C2×#4112yes—
268C2×C4×C13H(5,𝔽2)12yes—
269C2×Dic13—42no—
270C2×Dic13—42no—
271C2×Dic13—42no—
272C2×Dic13—42no—
273C2×Dic13—42no—
274C2×Dic13—42no—
275Dic26—84no—
276#1055—42no—
277#1055—42no—
278C22×#41C2×D1311yescharacteristic
279C23×Q8C2×D1311yescharacteristic
280#548—24no—
281#548—24no—
282C2×C4⋊Q8—131no—
283C2×#124—21no—
284C2×#124C2×D1311yescharacteristic
285C2×C22⋊Q8—21no—
286C2×C22⋊Q8C2×D1311yescharacteristic
287C2×#121—21no—
288C2×#121C2×D1311yescharacteristic
289C2×C4×Q8C2×D1311yescharacteristic
290C2×C4×D4—21no—
291C2×C4×D4C2×D1311yescharacteristic
292#489—264no—
293#475—264no—
294C2×#106—132no—
295C2×C4⋊C8—131no—
296C2×#103—132no—
297C2×#103—132no—
298C2×#103—132no—
299C2×#103—132no—
300C2×#102—132no—
301C2×#102—132no—
302C2×C22⋊C8—132no—
303C2×C22⋊C8—132no—
304C2×#97—131no—
305#393—261no—
306#393—261no—
307#390—261no—
308#382—261no—
309#380—132no—
310#380—132no—
311C4×C4⋊C4—131no—
312#340—132no—
313C22×C13—22no—
314C22×C13—24no—
315C22×C13—41no—
316C22×C13—41no—
317C22×C13—42no—
318C22×C13—42no—
319C22×C13—41no—
320C22×C13—41no—
321C22×C13—42no—
322C22×C13—41no—
323C22×C13—42no—
324C22×C13—42no—
325C22×C13—42no—
326C22×C13—82no—
327C22×C13—82no—
328C22×C13C2×#12011yescharacteristic
329C22×C13#54612yes—
330C22×C13C2×#13711yescharacteristic
331C22×C13#57511yescharacteristic
332C22×C13#57712yes—
333C4×C13—24no—
334C4×C13—22no—
335C4×C13—22no—
336C4×C13—41no—
337C4×C13—41no—
338C4×C13—42no—
339C4×C13—42no—
340C4×C13C2×#12411yescharacteristic
341C4×C13#53511yescharacteristic
342C4×C13#54612yes—
343Dic13—82no—
344Dic13—82no—
345C2×#41—22no—
346C2×#41—22no—
347C2×#41—24no—
348C2×#41—42no—
349C22×Q8—22no—
350C22×Q8—22no—
351C22×Q8—21no—
352C22×Q8—24no—
353C22×Q8—42no—
354C22×Q8—261no—
355C22×Q8C22×D1311yescharacteristic
356C22×Q8C22×D1311yescharacteristic
357C22×D4—21no—
358C22×D4—21no—
359C22×D4C22⋊D1311yescharacteristic
360C22×D4C22×D1311yescharacteristic
361C23×C4—21no—
362C23×C4—21no—
363C23×C4C22×D1311yescharacteristic
364C23×C4C22×D1311yescharacteristic
365C22×C8—132no—
366C22×C8—132no—
367C4⋊Q8—262no—
368C4⋊Q8—262no—
369#124—28no—
370#124—22no—
371#124C22⋊D1314yes—
372C22⋊Q8—28no—
373C22⋊Q8—22no—
374C22⋊Q8—22no—
375#121—28no—
376#121—22no—
377#121—22no—
378C4×Q8—22no—
379C4×Q8C22⋊D1314yes—
380C4×D4—28no—
381C4×D4—22no—
382C4×D4—22no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—132no—
386C2×C4⋊C4—132no—
387C2×C4⋊C4—261no—
388C2×C4⋊C4C22⋊D1311yescharacteristic
389C2×C4⋊C4C22×D1311yescharacteristic
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—262no—
395C2×C22⋊C4—262no—
396C2×C22⋊C4C22⋊D1311yescharacteristic
397C2×C22⋊C4C22⋊D1311yescharacteristic
398C2×C42—21no—
399C2×C42—261no—
400C2×C42C22×D1311yescharacteristic
401#106—264no—
402C4⋊C8—262no—
403#103—264no—
404#103—264no—
405#103—264no—
406#103—522no—
407#102—264no—
408#102—522no—
409C22⋊C8—522no—
410C22⋊C8—522no—
411#97—262no—
412#95—261no—
413#95—262no—
414#95—262no—
415C2×C13—42no—
416C2×C13—81no—
417C2×C13—82no—
418C2×C13#243511yescharacteristic
419C2×C13#300711yescharacteristic
420C2×C13#301011yescharacteristic
421C2×C13#331612yes—
422C2×C13#332112yes—
423C24—21no—
424C24C2×C22⋊D1311yescharacteristic
425C24C2×C22⋊D1311yescharacteristic
426#41—48no—
427#41—44no—
428#41—44no—
429C2×Q8—24no—
430C2×Q8—22no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—22no—
434C2×Q8—22no—
435C2×Q8—44no—
436C2×Q8—48no—
437C2×Q8—44no—
438C2×Q8—44no—
439C2×Q8—522no—
440C2×Q8—1042no—
441C2×Q8#612914yes—
442C2×Q8C2×C22⋊D1312yes—
443C2×Q8C2×C22⋊D1312yes—
444C2×D4—24no—
445C2×D4—24no—
446C2×D4—22no—
447C2×D4—22no—
448C2×D4—22no—
449C2×D4—22no—
450C2×D4—21no—
451C2×D4—41no—
452C2×D4—44no—
453C2×D4—42no—
454C2×D4—42no—
455C2×D4C2×C22⋊D1312yes—
456C22×C4—21no—
457C22×C4—24no—
458C22×C4—24no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—44no—
470C22×C4—44no—
471C22×C4—262no—
472C22×C4—262no—
473C22×C4C2×C22⋊D1311yescharacteristic
474C22×C4C2×C22⋊D1311yescharacteristic
475C22×C4C2×C22⋊D1311yescharacteristic
476C22×C4C2×C22⋊D1311yescharacteristic
477C22×C4C23×D1311yescharacteristic
478C2×C8—262no—
479C2×C8—262no—
480C2×C8—262no—
481C2×C8—262no—
482C2×C8—262no—
483C2×C8—262no—
484C4⋊C4—24no—
485C4⋊C4—24no—
486C4⋊C4—22no—
487C4⋊C4—21no—
488C4⋊C4—262no—
489C4⋊C4—262no—
490C4⋊C4—262no—
491C4⋊C4—262no—
492C4⋊C4—522no—
493C4⋊C4C2×C22⋊D1312yes—
494C22⋊C4—24no—
495C22⋊C4—24no—
496C22⋊C4—24no—
497C22⋊C4—24no—
498C22⋊C4—22no—
499C22⋊C4—22no—
500C22⋊C4—1042no—
501C22⋊C4—1042no—
502C42—24no—
503C42—522no—
504C42C2×C22⋊D1312yes—
505C42C2×C22⋊D1312yes—
506C13#2589511yescharacteristic, complemented, Sylow
507C23—22no—
508C23—21no—
509C23—22no—
510C23—21no—
511C23—22no—
512C23—21no—
513C23—21no—
514C23—22no—
515C23—21no—
516C23—22no—
517C23—42no—
518C23—41no—
519C23—41no—
520C23—42no—
521C23#8820512yes—
522C23C22×C22⋊D1311yescharacteristic
523Q8—22no—
524Q8—24no—
525Q8—24no—
526Q8—48no—
527Q8—41no—
528Q8—41no—
529Q8—1044no—
530Q8#8819014yes—
531D4—24no—
532D4—44no—
533D4—48no—
534D4—48no—
535D4—41no—
536D4—41no—
537C2×C4—24no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—48no—
549C2×C4—48no—
550C2×C4—42no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—522no—
560C2×C4—522no—
561C2×C4—522no—
562C2×C4—522no—
563C2×C4—522no—
564C2×C4—522no—
565C2×C4#8820712yes—
566C2×C4#8820712yes—
567C2×C4C2×#612912yes—
568C2×C4#8825112yes—
569C2×C4C22×C22⋊D1311yescharacteristic
570C2×C4C22×C22⋊D1311yescharacteristic
571C8—522no—
572C8—522no—
573C22—22no—
574C22—24no—
575C22—41no—
576C22—41no—
577C22—42no—
578C22—41no—
579C22—42no—
580C22—42no—
581C22—41no—
582C22—41no—
583C22—42no—
584C22—42no—
585C22—42no—
586C22—82no—
587C22—82no—
588C22#1171951112yes—
589C22#1171952711yescharacteristic
590C22C2×#8820511yescharacteristic
591C22#1171954212yes—
592C22C2×#8820711yescharacteristic
593C4—22no—
594C4—24no—
595C4—22no—
596C4—42no—
597C4—41no—
598C4—41no—
599C4—42no—
600C4—1042no—
601C4—1042no—
602C4C2×#8819011yescharacteristic
603C4#1171951011yescharacteristic
604C4#1171951112yes—
605C2—42no—
606C2—81no—
607C2—82no—
608C2#1311848311yescharacteristic
609C2#1312409611yescharacteristic
610C2#1312412211yescharacteristic
611C2#1312694712yes—
612C2#1312702212yes—
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
Fitting, prime radicalC2×C13×#548C2
socleC23×C13C22×D4
hypercenterC2×#548D13
hypocenterC13#25895
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C2×#11718716C2semidirect
2. C2×#11718681C2semidirect
3. #13120009C2semidirect
4. #13116029C2semidirect
5. #13116022C2semidirect
6. #13115769C2semidirect
7. #13115635C2semidirect
8. #13114776C2semidirect
9. #13114771C2semidirect
10. #13114666C2semidirect
506. C13#25895semidirect

Maximal subgroups

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

subgroupindex
C2×#117187162
C2×#117186812
#131200092
#131160292
#131160222
#131157692
#131156352
#131147762
#131147712
#131146662
C2×C13×#5482
#2589513