Finite Group Databasebeta

← #15895976

Subgroups — #15895976

Order 3328.

1318 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718705C211yesmaximal, characteristic, complemented
2C22×#88075C211yesmaximal, characteristic, complemented
3#13119153C211yesmaximal, characteristic
4#13116079C212yesmaximal, complemented
5#13116036C212yesmaximal, complemented
6#13115260C211yesmaximal, characteristic, complemented
7#13115129C211yesmaximal, characteristic
8#13115090C212yesmaximal, complemented
9#13114771C211yesmaximal, characteristic, complemented
10#13114771C212yesmaximal, complemented
11C2×D4×Q8×C13C211yesmaximal, characteristic
12C23×Q8×C13C2211yescharacteristic
13C23×Q8×C13C2211yescharacteristic
14D4×Q8×C13—24no—
15D4×Q8×C13—24no—
16C2×C13×C4⋊Q8—21no—
17C2×C13×C4⋊Q8C2211yescharacteristic
18C2×C13×C22⋊Q8—21no—
19C2×C13×C22⋊Q8—21no—
20C2×C13×C22⋊Q8C2211yescharacteristic
21C2×C13×C22⋊Q8C2211yescharacteristic
22C2×C4×Q8×C13C2211yescharacteristic
23C2×C4×D4×C13—21no—
24C2×C4×D4×C13C2211yescharacteristic
25C22×C4⋊Dic13C2211yescharacteristic
26C23×#1055C2211yescharacteristic
27C2×#88075—24no—
28C2×#88075C2212yes—
29C2×#88075C2212yes—
30C2×#88075C2212yes—
31C2×#88075C2212yes—
32C2×#88075C2212yes—
33C2×#88075C2212yes—
34#11718881—21no—
35#11718873C2211yescharacteristic
36#11718873C2212yes—
37C2×C22⋊#1055C2211yescharacteristic
38C2×C22⋊#1055C2212yes—
39#11718705—24no—
40#11718647—21no—
41C2×#88047C2212yes—
42#11718610—21no—
43#11718607—21no—
44#11718589C2212yes—
45#11718121C2212yes—
46#11718116C2212yes—
47C22×Q8×C13—22no—
48C22×Q8×C13—22no—
49C22×Q8×C13—21no—
50C22×Q8×C13—21no—
51C22×Q8×C13—22no—
52C22×Q8×C13—24no—
53C22×Q8×C13—24no—
54C22×Q8×C13—42no—
55C22×Q8×C13—42no—
56C22×Q8×C13D414yes—
57C22×Q8×C13C2311yescharacteristic
58C22×Q8×C13C2311yescharacteristic
59C22×Q8×C13C2311yescharacteristic
60C22×D4×C13D411yescharacteristic
61C23×C4×C13—21no—
62C23×C4×C13—21no—
63C23×C4×C13C2311yescharacteristic
64C23×C4×C13C2311yescharacteristic
65C23×Dic13—21no—
66C13×C4⋊Q8—28no—
67C13×C4⋊Q8—22no—
68C13×C4⋊Q8—22no—
69C13×C22⋊Q8—28no—
70C13×C22⋊Q8—28no—
71C13×C22⋊Q8—22no—
72C13×C22⋊Q8—22no—
73C13×C22⋊Q8—22no—
74C13×C22⋊Q8D414yes—
75C4×Q8×C13—22no—
76C4×Q8×C13—22no—
77C4×D4×C13—28no—
78C4×D4×C13—22no—
79C4×D4×C13—22no—
80C2×C13×C4⋊C4—21no—
81C2×C13×C4⋊C4—21no—
82C2×C13×C4⋊C4—21no—
83C2×C13×C4⋊C4—21no—
84C2×C13×C4⋊C4—21no—
85C2×C13×C4⋊C4D411yescharacteristic
86C2×C13×C4⋊C4C2311yescharacteristic
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—21no—
94C2×C22⋊Dic13—22no—
95C2×C4⋊Dic13—22no—
96C2×C4⋊Dic13—22no—
97C2×C4⋊Dic13—21no—
98C2×C4⋊Dic13C2312yes—
99C2×C4⋊Dic13C2312yes—
100C2×#6101—22no—
101C22×#1055—22no—
102C22×#1055—42no—
103C22×#1055C2312yes—
104C22×#1055C2312yes—
105#88075—24no—
106#88075—24no—
107#88075—24no—
108#88075—24no—
109#88075—42no—
110#88075—42no—
111#88071—22no—
112#88071—22no—
113#88071—21no—
114C22⋊#1055—22no—
115C22⋊#1055—42no—
116#88047—24no—
117#24042—131nomaximal, Sylow
118C24×C13C2×D411yescharacteristic
119C24×C13C2×D411yescharacteristic
120C2×Q8×C13—24no—
121C2×Q8×C13—24no—
122C2×Q8×C13—21no—
123C2×Q8×C13—21no—
124C2×Q8×C13—21no—
125C2×Q8×C13—22no—
126C2×Q8×C13—28no—
127C2×Q8×C13—22no—
128C2×Q8×C13—22no—
129C2×Q8×C13—22no—
130C2×Q8×C13—22no—
131C2×Q8×C13—44no—
132C2×Q8×C13—44no—
133C2×Q8×C13—44no—
134C2×Q8×C13—48no—
135C2×Q8×C13—48no—
136C2×Q8×C13—44no—
137C2×Q8×C13—44no—
138C2×Q8×C13C2×D412yes—
139C2×Q8×C13C2×D412yes—
140C2×Q8×C13C2×D412yes—
141C2×Q8×C13#4114yes—
142C2×D4×C13—22no—
143C2×D4×C13—22no—
144C2×D4×C13Q1614yes—
145C22×C4×C13—21no—
146C22×C4×C13—22no—
147C22×C4×C13—22no—
148C22×C4×C13—24no—
149C22×C4×C13—24no—
150C22×C4×C13—21no—
151C22×C4×C13—21no—
152C22×C4×C13—21no—
153C22×C4×C13—21no—
154C22×C4×C13—21no—
155C22×C4×C13—22no—
156C22×C4×C13—22no—
157C22×C4×C13—44no—
158C22×C4×C13—44no—
159C22×C4×C13C2×D411yescharacteristic
160C22×C4×C13C2×D411yescharacteristic
161C22×C4×C13C2×D411yescharacteristic
162C22×C4×C13C2×D412yes—
163C22×C4×C13C2×D412yes—
164C22×C4×C13C2×D411yescharacteristic
165C22×C4×C13C2411yescharacteristic
166C22×Dic13—22no—
167C22×Dic13—22no—
168C22×Dic13—42no—
169C22×Dic13—82no—
170C13×C4⋊C4—24no—
171C13×C4⋊C4—24no—
172C13×C4⋊C4—24no—
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—22no—
181C13×C22⋊C4—22no—
182C42×C13—24no—
183C42×C13—21no—
184C42×C13—21no—
185C22⋊Dic13—42no—
186C22⋊Dic13—82no—
187C4⋊Dic13—22no—
188C4⋊Dic13—22no—
189C4⋊Dic13—22no—
190C4⋊Dic13—22no—
191C4⋊Dic13—42no—
192#6101—82no—
193C2×#1055—22no—
194C2×#1055—22no—
195C2×#1055—22no—
196C2×#1055—22no—
197C2×#1055—22no—
198C2×#1055—22no—
199C2×#1055—44no—
200C2×D4×Q8D1311yescharacteristic
201C2×#484—131no—
202C22×#103—131no—
203#2487—131no—
204#2043—132no—
205#2036—132no—
206#1892—131no—
207#1869—131no—
208#1863—132no—
209#1787—132no—
210#1787—131no—
211C23×C13—22no—
212C23×C13—22no—
213C23×C13—21no—
214C23×C13—22no—
215C23×C13—21no—
216C23×C13—22no—
217C23×C13#12012yes—
218C23×C13C2×Q1612yes—
219C23×C13C2×Q1612yes—
220C23×C13#13712yes—
221C23×C13C22×D411yescharacteristic
222Q8×C13—22no—
223Q8×C13—24no—
224Q8×C13—22no—
225Q8×C13—22no—
226Q8×C13—24no—
227Q8×C13—48no—
228Q8×C13—48no—
229Q8×C13—41no—
230Q8×C13—41no—
231Q8×C13—42no—
232Q8×C13#12314yes—
233D4×C13—28no—
234C2×C4×C13—21no—
235C2×C4×C13—22no—
236C2×C4×C13—22no—
237C2×C4×C13—24no—
238C2×C4×C13—21no—
239C2×C4×C13—22no—
240C2×C4×C13—22no—
241C2×C4×C13—24no—
242C2×C4×C13—21no—
243C2×C4×C13—22no—
244C2×C4×C13—22no—
245C2×C4×C13—22no—
246C2×C4×C13—21no—
247C2×C4×C13—22no—
248C2×C4×C13—22no—
249C2×C4×C13—48no—
250C2×C4×C13—48no—
251C2×C4×C13—42no—
252C2×C4×C13—42no—
253C2×C4×C13—42no—
254C2×C4×C13—41no—
255C2×C4×C13—41no—
256C2×C4×C13—42no—
257C2×C4×C13#12012yes—
258C2×C4×C13C2×Q1612yes—
259C2×C4×C13C22×D411yescharacteristic
260C2×C4×C13C22×D411yescharacteristic
261C2×C4×C13C2×#4112yes—
262C2×C4×C13H(5,𝔽2)12yes—
263C2×Dic13—42no—
264C2×Dic13—42no—
265C2×Dic13—42no—
266C2×Dic13—42no—
267C2×Dic13—42no—
268C2×Dic13—42no—
269C2×Dic13—84no—
270#1055—42no—
271#1055—42no—
272C23×Q8C2×D1311yescharacteristic
273C23×Q8C2×D1311yescharacteristic
274C23×C8—131no—
275D4×Q8—24no—
276D4×Q8—24no—
277C2×C4⋊Q8—21no—
278C2×C4⋊Q8C2×D1311yescharacteristic
279C2×C22⋊Q8—21no—
280C2×C22⋊Q8—21no—
281C2×C22⋊Q8C2×D1311yescharacteristic
282C2×C22⋊Q8C2×D1311yescharacteristic
283C2×C4×Q8C2×D1311yescharacteristic
284C2×C4×D4—21no—
285C2×C4×D4C2×D1311yescharacteristic
286C22×C4⋊C4—131no—
287#484—264no—
288C2×#107—132no—
289C2×#103—132no—
290C2×#103—132no—
291C2×#103—132no—
292C2×#103—132no—
293C2×#103—132no—
294C2×#103—132no—
295C2×#103—264no—
296C2×C22⋊C8—131no—
297C2×C22⋊C8—132no—
298#400—261no—
299#399—261no—
300#389—132no—
301#386—261no—
302#385—261no—
303#380—131no—
304#380—132no—
305#340—132no—
306#336—132no—
307C22×C13—22no—
308C22×C13—22no—
309C22×C13—24no—
310C22×C13—24no—
311C22×C13—22no—
312C22×C13—24no—
313C22×C13—41no—
314C22×C13—41no—
315C22×C13—42no—
316C22×C13#45114yes—
317C22×C13C2×#12011yescharacteristic
318C22×C13#54612yes—
319C22×C13C22×Q1611yescharacteristic
320C22×C13C2×#13711yescharacteristic
321C22×C13#57712yes—
322C4×C13—22no—
323C4×C13—24no—
324C4×C13—22no—
325C4×C13—41no—
326C4×C13—42no—
327C4×C13—42no—
328C4×C13—41no—
329C4×C13—42no—
330C4×C13C2×#12311yescharacteristic
331C4×C13#53411yescharacteristic
332C4×C13#54612yes—
333Dic13—82no—
334Dic13—82no—
335C22×Q8—22no—
336C22×Q8—22no—
337C22×Q8—21no—
338C22×Q8—21no—
339C22×Q8—22no—
340C22×Q8—24no—
341C22×Q8—24no—
342C22×Q8—42no—
343C22×Q8—42no—
344C22×Q8C22⋊D1314yes—
345C22×Q8C22×D1311yescharacteristic
346C22×Q8C22×D1311yescharacteristic
347C22×Q8C22×D1311yescharacteristic
348C22×D4C22⋊D1311yescharacteristic
349C23×C4—21no—
350C23×C4—21no—
351C23×C4—261no—
352C23×C4C22×D1311yescharacteristic
353C23×C4C22×D1311yescharacteristic
354C22×C8—132no—
355C22×C8—132no—
356C22×C8—262no—
357C22×C8—522no—
358C4⋊Q8—28no—
359C4⋊Q8—22no—
360C4⋊Q8—22no—
361C22⋊Q8—28no—
362C22⋊Q8—28no—
363C22⋊Q8—22no—
364C22⋊Q8—22no—
365C22⋊Q8—22no—
366C22⋊Q8C22⋊D1314yes—
367C4×Q8—22no—
368C4×Q8—22no—
369C4×D4—28no—
370C4×D4—22no—
371C4×D4—22no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—132no—
378C2×C4⋊C4—132no—
379C2×C4⋊C4—262no—
380C2×C4⋊C4—262no—
381C2×C4⋊C4—261no—
382C2×C4⋊C4—262no—
383C2×C4⋊C4C22⋊D1311yescharacteristic
384C2×C4⋊C4C22×D1311yescharacteristic
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—261no—
388C2×C22⋊C4—262no—
389C2×C22⋊C4C22⋊D1311yescharacteristic
390C2×C22⋊C4C22⋊D1311yescharacteristic
391C2×C42—21no—
392C2×C42C22×D1311yescharacteristic
393#107—264no—
394#103—264no—
395#103—264no—
396#103—264no—
397#103—264no—
398#103—522no—
399#103—522no—
400C22⋊C8—262no—
401C22⋊C8—522no—
402#95—262no—
403#95—261no—
404#95—262no—
405C2×C13—24no—
406C2×C13—42no—
407C2×C13#240511yescharacteristic
408C2×C13C2×#45111yescharacteristic
409C2×C13#301011yescharacteristic
410C2×C13#329912yes—
411C2×C13#332012yes—
412C24C2×C22⋊D1311yescharacteristic
413C24C2×C22⋊D1311yescharacteristic
414C2×Q8—24no—
415C2×Q8—24no—
416C2×Q8—22no—
417C2×Q8—21no—
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—28no—
421C2×Q8—22no—
422C2×Q8—22no—
423C2×Q8—22no—
424C2×Q8—22no—
425C2×Q8—44no—
426C2×Q8—44no—
427C2×Q8—44no—
428C2×Q8—48no—
429C2×Q8—48no—
430C2×Q8—44no—
431C2×Q8—44no—
432C2×Q8#612914yes—
433C2×Q8C2×C22⋊D1312yes—
434C2×Q8C2×C22⋊D1312yes—
435C2×Q8C2×C22⋊D1312yes—
436C2×D4—22no—
437C2×D4—22no—
438C2×D4#610714yes—
439C22×C4—21no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—24no—
443C22×C4—24no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—44no—
452C22×C4—44no—
453C22×C4—262no—
454C22×C4—262no—
455C22×C4—522no—
456C22×C4—1042no—
457C22×C4C2×C22⋊D1311yescharacteristic
458C22×C4C2×C22⋊D1311yescharacteristic
459C22×C4C2×C22⋊D1311yescharacteristic
460C22×C4C2×C22⋊D1311yescharacteristic
461C22×C4C2×C22⋊D1312yes—
462C22×C4C2×C22⋊D1312yes—
463C22×C4C23×D1311yescharacteristic
464C2×C8—262no—
465C2×C8—262no—
466C2×C8—262no—
467C2×C8—262no—
468C2×C8—262no—
469C2×C8—262no—
470C2×C8—524no—
471C4⋊C4—24no—
472C4⋊C4—24no—
473C4⋊C4—24no—
474C4⋊C4—24no—
475C4⋊C4—24no—
476C4⋊C4—22no—
477C4⋊C4—21no—
478C4⋊C4—262no—
479C4⋊C4—262no—
480C4⋊C4—262no—
481C4⋊C4—262no—
482C4⋊C4—522no—
483C4⋊C4—1042no—
484C4⋊C4C2×C22⋊D1312yes—
485C22⋊C4—24no—
486C22⋊C4—24no—
487C22⋊C4—22no—
488C22⋊C4—22no—
489C22⋊C4—522no—
490C22⋊C4—1042no—
491C42—24no—
492C42—21no—
493C42—21no—
494C13#2404211yescharacteristic, complemented, Sylow
495C23—22no—
496C23—22no—
497C23—22no—
498C23—21no—
499C23—22no—
500C23—21no—
501C23#8819612yes—
502C23C2×#610712yes—
503C23C2×#610712yes—
504C23#8820712yes—
505C23C22×C22⋊D1311yescharacteristic
506Q8—22no—
507Q8—24no—
508Q8—22no—
509Q8—22no—
510Q8—24no—
511Q8—48no—
512Q8—48no—
513Q8—41no—
514Q8—41no—
515Q8—42no—
516Q8#8818914yes—
517D4—28no—
518C2×C4—22no—
519C2×C4—24no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—24no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—21no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—21no—
533C2×C4—48no—
534C2×C4—48no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—42no—
541C2×C4—522no—
542C2×C4—522no—
543C2×C4—522no—
544C2×C4—522no—
545C2×C4—522no—
546C2×C4—522no—
547C2×C4—1044no—
548C2×C4C2×#610712yes—
549C2×C4#8820712yes—
550C2×C4C2×#612912yes—
551C2×C4#8825112yes—
552C2×C4C22×C22⋊D1311yescharacteristic
553C2×C4C22×C22⋊D1311yescharacteristic
554C8—522no—
555C8—522no—
556C22—22no—
557C22—24no—
558C22—24no—
559C22—22no—
560C22—24no—
561C22—22no—
562C22—41no—
563C22—42no—
564C22—41no—
565C22#1171888914yes—
566C22#1171951112yes—
567C22C2×#8819611yescharacteristic
568C22C22×#610711yescharacteristic
569C22#1171954212yes—
570C22C2×#8820711yescharacteristic
571C4—22no—
572C4—22no—
573C4—24no—
574C4—41no—
575C4—42no—
576C4—41no—
577C4—42no—
578C4—42no—
579C4—1042no—
580C4—1042no—
581C4C2×#8818911yescharacteristic
582C4#1171950911yescharacteristic
583C4#1171951112yes—
584C2—24no—
585C2—42no—
586C2#1311815911yescharacteristic
587C2C2×#1171888911yescharacteristic
588C2#1312412211yescharacteristic
589C2#1312671212yes—
590C2#1312700712yes—
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×D4×Q8×C13C2
socleC23×C13C22×D4
prime radicalC22×D4×C13D4
hypercenterC2×D4×Q8D13
hypocenterC13#24042
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#11718705C2semidirect
2. C22×#88075C2semidirect
4. #13116079C2semidirect
5. #13116036C2semidirect
6. #13115260C2semidirect
8. #13115090C2semidirect
9. #13114771C2semidirect
10. #13114771C2semidirect
494. C13#24042semidirect

Maximal subgroups

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

subgroupindex
C2×#117187052
C22×#880752
#131191532
#131160792
#131160362
#131152602
#131151292
#131150902
#131147712
C2×D4×Q8×C132
#2404213