Finite Group Databasebeta

← #15925486

Subgroups — #15925486

Order 3328.

882 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718455C211yesmaximal, characteristic, complemented
2C22×#88058C211yesmaximal, characteristic
3#13118539C211yesmaximal, characteristic
4#13117845C211yesmaximal, characteristic
5#13116372C211yesmaximal, characteristic, complemented
6#13116331C211yesmaximal, characteristic, complemented
7#13116229C211yesmaximal, characteristic, complemented
8#13116163C211yesmaximal, characteristic, complemented
9#13115593C211yesmaximal, characteristic, complemented
10#13115427C211yesmaximal, characteristic, complemented
11#13115144C211yesmaximal, characteristic
12#13115092C211yesmaximal, characteristic, complemented
13#13115023C211yesmaximal, characteristic
14#13115014C211yesmaximal, characteristic
15C13×#1892C211yesmaximal, characteristic
16C23×C8×C13C2211yescharacteristic
17C2×C13×C22⋊Q8C2211yescharacteristic
18C2×Q8×Dic13C2211yescharacteristic
19C22×C4⋊Dic13C2211yescharacteristic
20C22×C4⋊Dic13C2211yescharacteristic
21C2×#88142C2211yescharacteristic
22C2×#88132—21no—
23C2×C13×#103C2211yescharacteristic
24C2×C13×#103C2211yescharacteristic
25C13×#380C2211yescharacteristic
26#11718891C2211yescharacteristic
27C2×#88075C2211yescharacteristic
28C2×#88075C2211yescharacteristic
29C4×C22⋊Dic13C2211yescharacteristic
30C2×C22⋊#1055C2211yescharacteristic
31C2×#88058—24no—
32C2×#88058C2211yescharacteristic
33C2×#88058C2211yescharacteristic
34C2×#88058C2211yescharacteristic
35C2×#88058C2211yescharacteristic
36C2×#88054C2211yescharacteristic
37C2×#88054C2211yescharacteristic
38#11718646—21no—
39#11718646C2211yescharacteristic
40#11718646C2211yescharacteristic
41#11718642—21no—
42#11718637C2211yescharacteristic
43C4⋊C4×Dic13C2211yescharacteristic
44#11718634C2211yescharacteristic
45C2×#88047C2211yescharacteristic
46C2×#88047C2211yescharacteristic
47#11718611—21no—
48#11718607—21no—
49C22⋊C4×Dic13—21no—
50#11718455—24no—
51#11718318—21no—
52#11718317—21no—
53C13×#340C2211yescharacteristic
54C13×#340C2211yescharacteristic
55#11718142C2211yescharacteristic
56#11718142C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60#11718121C2211yescharacteristic
61C22×Q8×C13C2311yescharacteristic
62C23×C4×C13C2311yescharacteristic
63C23×Dic13—21no—
64C23×Dic13—21no—
65C22×Dic26—21no—
66C22×C8×C13—22no—
67C22×C8×C13—22no—
68C22×C8×C13—22no—
69C22×C8×C13C2311yescharacteristic
70C22×C8×C13C2311yescharacteristic
71C13×C22⋊Q8—22no—
72C13×C22⋊Q8Q814yescomplemented
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4C2311yescharacteristic
75C2×C13×C4⋊C4C2311yescharacteristic
76C2×C13×C4⋊C4C2311yescharacteristic
77C2×C13×C22⋊C4—21no—
78C2×C13×C22⋊C4—21no—
79C2×C22⋊Dic13D411yescharacteristic
80C2×C22⋊Dic13D411yescharacteristic
81Q8×Dic13—22no—
82Q8×Dic13—41no—
83C2×C4⋊Dic13—22no—
84C2×C4⋊Dic13—22no—
85C2×C4⋊Dic13—21no—
86C2×C4⋊Dic13—21no—
87C2×C4⋊Dic13—21no—
88C2×C4⋊Dic13—21no—
89C2×C4⋊Dic13—21no—
90C2×C4⋊Dic13—41no—
91C2×C4⋊Dic13—41no—
92C2×C4⋊Dic13C2311yescharacteristic
93C2×C4⋊Dic13C2311yescharacteristic
94C2×C4⋊Dic13C2311yescharacteristic
95C2×C4⋊Dic13C2311yescharacteristic
96C2×#6101—21no—
97C2×#6101—21no—
98C2×#6101—21no—
99C2×#6101—21no—
100C2×C4×Dic13—21no—
101C2×C4×Dic13—21no—
102C2×C4×Dic13C2311yescharacteristic
103C2×C4×Dic13C2311yescharacteristic
104C22×#1055C2311yescharacteristic
105C22×#1055C2311yescharacteristic
106#88142—22no—
107#88142—41no—
108#88132—44no—
109C13×#103—22no—
110C13×#103—22no—
111C13×#95—21no—
112#88075—22no—
113#88075—41no—
114#88071—21no—
115#88071—21no—
116#88071—21no—
117#88071—21no—
118#88071—21no—
119#88071—21no—
120#88071D411yescharacteristic
121#88071D411yescharacteristic
122C22⋊#1055—22no—
123#88058—22no—
124#88058—22no—
125#88058—22no—
126#88058D414yes—
127#88054—22no—
128#88054—22no—
129#88047—22no—
130#88047—41no—
131#26342—131nomaximal, Sylow
132C24×C13C2×D411yescharacteristic
133C2×Q8×C13—21no—
134C2×Q8×C13—21no—
135C2×Q8×C13—21no—
136C2×Q8×C13—21no—
137C2×Q8×C13—21no—
138C2×Q8×C13C2×Q812yes—
139C22×C4×C13—21no—
140C22×C4×C13—21no—
141C22×C4×C13—21no—
142C22×C4×C13—21no—
143C22×C4×C13—21no—
144C22×C4×C13—21no—
145C22×C4×C13—21no—
146C22×C4×C13—21no—
147C22×C4×C13C2×D411yescharacteristic
148C22×C4×C13C2×Q812yes—
149C22×C4×C13#4112yes—
150C22×C4×C13C2411yescharacteristic
151C22×Dic13—21no—
152C22×Dic13—21no—
153C22×Dic13—21no—
154C22×Dic13—21no—
155C22×Dic13—42no—
156C22×Dic13—42no—
157C22×Dic13—42no—
158C22×Dic13—42no—
159C22×Dic13—81no—
160C22×Dic13—81no—
161C22×Dic13C2×D411yescharacteristic
162C22×Dic13C2×D411yescharacteristic
163C22×Dic13C2×D411yescharacteristic
164C22×Dic13C2×D411yescharacteristic
165C2×Dic26—42no—
166C2×Dic26—42no—
167C2×Dic26—81no—
168C2×C8×C13—28no—
169C2×C8×C13—21no—
170C2×C8×C13—21no—
171C2×C8×C13—21no—
172C2×C8×C13—21no—
173C2×C8×C13C2×D412yes—
174C2×C8×C13#4112yes—
175C13×C4⋊C4—24no—
176C13×C4⋊C4—21no—
177C13×C4⋊C4—21no—
178C13×C4⋊C4—21no—
179C13×C4⋊C4—21no—
180C13×C4⋊C4—21no—
181C13×C4⋊C4C2×Q812yes—
182C13×C22⋊C4—24no—
183C13×C22⋊C4—42no—
184C22⋊Dic13—22no—
185C22⋊Dic13Q1614yes—
186C4⋊Dic13—21no—
187C4⋊Dic13—21no—
188C4⋊Dic13—21no—
189C4⋊Dic13—21no—
190C4⋊Dic13—21no—
191C4⋊Dic13—21no—
192C4⋊Dic13—42no—
193C4⋊Dic13—42no—
194C4⋊Dic13—42no—
195C4⋊Dic13—42no—
196C4⋊Dic13—81no—
197C4⋊Dic13C2×D412yes—
198C4⋊Dic13C2×D412yes—
199#6101—42no—
200#6101—42no—
201#6101—42no—
202#6101—81no—
203C4×Dic13—21no—
204C4×Dic13—21no—
205C4×Dic13—21no—
206C4×Dic13—21no—
207C4×Dic13—42no—
208C4×Dic13—81no—
209C2×#1055—21no—
210C2×#1055—21no—
211C2×#1055—21no—
212C2×#1055—21no—
213C2×#1055—21no—
214C2×#1055—21no—
215C2×#477—131no—
216C22×#107—131no—
217#2440—131no—
218#2360—131no—
219#2095—131no—
220#2087—131no—
221#2068—131no—
222#2057—131no—
223#1947—131no—
224#1921—131no—
225#1892D1311yescharacteristic
226#1872—131no—
227#1863—131no—
228#1852—131no—
229#1850—131no—
230C23×C13—21no—
231C23×C13—21no—
232C23×C13—21no—
233C23×C13—21no—
234C23×C13C22⋊Q812yes—
235C23×C13C2×Q1612yes—
236C23×C13AGL(1,ℤ/8)12yes—
237C23×C13C22×D411yescharacteristic
238Q8×C13—22no—
239Q8×C13—22no—
240Q8×C13—41no—
241Q8×C13—41no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—22no—
245C2×C4×C13—22no—
246C2×C4×C13—22no—
247C2×C4×C13—22no—
248C2×C4×C13—22no—
249C2×C4×C13—22no—
250C2×C4×C13—41no—
251C2×C4×C13—41no—
252C2×C4×C13—41no—
253C2×C4×C13—41no—
254C2×C4×C13—41no—
255C2×C4×C13—41no—
256C2×C4×C13—41no—
257C2×C4×C13—41no—
258C2×C4×C13—41no—
259C2×C4×C13—41no—
260C2×C4×C13C22⋊Q812yes—
261C2×C4×C13C22×D411yescharacteristic
262C2×C4×C13C22×Q811yescharacteristic
263C2×C4×C13C2×#4111yescharacteristic
264C2×C4×C13C2×#4111yescharacteristic
265C2×C4×C13H(5,𝔽2)11yescharacteristic
266C2×C4×C132−1+411yescharacteristic
267C2×Dic13—21no—
268C2×Dic13—21no—
269C2×Dic13—21no—
270C2×Dic13—21no—
271C2×Dic13—21no—
272C2×Dic13—22no—
273C2×Dic13—22no—
274C2×Dic13—21no—
275C2×Dic13—21no—
276C2×Dic13—21no—
277C2×Dic13—21no—
278C2×Dic13—21no—
279C2×Dic13—41no—
280C2×Dic13—41no—
281C2×Dic13—41no—
282C2×Dic13—41no—
283C2×Dic13—41no—
284C2×Dic13—41no—
285C2×Dic13—41no—
286C2×Dic13—41no—
287C2×Dic13—41no—
288C2×Dic13—41no—
289C2×Dic13—84no—
290C2×Dic13—84no—
291C2×Dic13C2×Q1612yes—
292C2×Dic13C2×Q1612yes—
293Dic26—84no—
294C8×C13—22no—
295C8×C13—22no—
296#1055—41no—
297#1055—41no—
298C23×C8C2×D1311yescharacteristic
299C2×C4⋊Q8—131no—
300C2×C22⋊Q8—261no—
301C2×C22⋊Q8C2×D1311yescharacteristic
302C2×C4×Q8—131no—
303C22×C4⋊C4—131no—
304C22×C4⋊C4—131no—
305#477—264no—
306C2×#107—131no—
307C2×#107—131no—
308C2×#107—131no—
309C2×#107—131no—
310C2×#107—131no—
311C2×#107—131no—
312C2×#107—264no—
313C2×C4⋊C8—131no—
314C2×C4⋊C8—131no—
315C2×#103—131no—
316C2×#103—131no—
317C2×#103C2×D1311yescharacteristic
318C2×#103C2×D1311yescharacteristic
319C2×C22⋊C8—131no—
320#398—261no—
321#395—261no—
322#391—131no—
323#389—131no—
324#389—131no—
325#389—131no—
326#389—261no—
327#387—261no—
328#385—261no—
329#385—261no—
330#384—131no—
331#380C2×D1311yescharacteristic
332C4×C4⋊C4—131no—
333C4×C22⋊C4—131no—
334C4×C22⋊C4—261no—
335#340—131no—
336#340—131no—
337#340—131no—
338#340—131no—
339#340C2×D1311yescharacteristic
340#340C2×D1311yescharacteristic
341#336—131no—
342#336—131no—
343C22×C13—22no—
344C22×C13—22no—
345C22×C13—22no—
346C22×C13—22no—
347C22×C13—22no—
348C22×C13—22no—
349C22×C13#47714yescomplemented
350C22×C13C2×C22⋊Q811yescharacteristic
351C22×C13D4211yescharacteristic
352C22×C13#54711yescharacteristic
353C22×C13C22×Q1611yescharacteristic
354C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
355C22×C13#57611yescharacteristic
356C22×C13#57811yescharacteristic
357C4×C13—22no—
358C4×C13—42no—
359C4×C13—42no—
360C4×C13—81no—
361C4×C13—81no—
362C4×C13#52511yescharacteristic
363C4×C13#53911yescharacteristic
364C4×C13D4×Q811yescharacteristic
365C4×C13#55411yescharacteristic
366Dic13—22no—
367Dic13—22no—
368Dic13—41no—
369Dic13—41no—
370Dic13—42no—
371Dic13—42no—
372Dic13—81no—
373Dic13—81no—
374C22×Q8—261no—
375C22×Q8C22×D1311yescharacteristic
376C23×C4—261no—
377C23×C4—261no—
378C23×C4C22×D1311yescharacteristic
379C22×C8—22no—
380C22×C8—22no—
381C22×C8—22no—
382C22×C8—131no—
383C22×C8—131no—
384C22×C8C22×D1311yescharacteristic
385C22×C8C22×D1311yescharacteristic
386C4⋊Q8—262no—
387C4⋊Q8—521no—
388C22⋊Q8—22no—
389C22⋊Q8—524no—
390C22⋊Q8Dic2614yescomplemented
391C4×Q8—262no—
392C4×Q8—521no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—131no—
395C2×C4⋊C4—131no—
396C2×C4⋊C4—131no—
397C2×C4⋊C4—131no—
398C2×C4⋊C4—262no—
399C2×C4⋊C4—262no—
400C2×C4⋊C4—261no—
401C2×C4⋊C4—261no—
402C2×C4⋊C4—261no—
403C2×C4⋊C4—261no—
404C2×C4⋊C4—261no—
405C2×C4⋊C4—261no—
406C2×C4⋊C4—261no—
407C2×C4⋊C4—261no—
408C2×C4⋊C4—261no—
409C2×C4⋊C4—521no—
410C2×C4⋊C4—521no—
411C2×C4⋊C4C22×D1311yescharacteristic
412C2×C4⋊C4C22×D1311yescharacteristic
413C2×C4⋊C4C22×D1311yescharacteristic
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—131no—
417C2×C22⋊C4—131no—
418C2×C42—131no—
419C2×C42—131no—
420C2×C42—261no—
421C2×C42—261no—
422#107—134no—
423#107—262no—
424#107—262no—
425#107—262no—
426#107—262no—
427#107—521no—
428C4⋊C8—262no—
429C4⋊C8—262no—
430#103—22no—
431#103—22no—
432#103—262no—
433#103—521no—
434C22⋊C8—262no—
435#95—21no—
436#95—131no—
437#95—131no—
438#95—261no—
439#95—261no—
440#95—261no—
441#95—261no—
442#95—261no—
443#95—261no—
444C2×C13—24no—
445C2×C13#244911yescharacteristic
446C2×C13C2×#47711yescharacteristic
447C2×C13#308311yescharacteristic
448C2×C13#326411yescharacteristic
449C2×C13D4×Q1611yescharacteristic
450C2×C13#333811yescharacteristic
451C2×C13#334311yescharacteristic
452C24D4×D1311yescharacteristic
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—522no—
459C2×Q8—522no—
460C2×Q8—1041no—
461C2×Q8C2×Dic2612yes—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—131no—
471C22×C4—131no—
472C22×C4—131no—
473C22×C4—131no—
474C22×C4—261no—
475C22×C4—261no—
476C22×C4—261no—
477C22×C4—261no—
478C22×C4—522no—
479C22×C4—522no—
480C22×C4—522no—
481C22×C4—522no—
482C22×C4—1041no—
483C22×C4—1041no—
484C22×C4C2×Dic2612yes—
485C22×C4D4×D1311yescharacteristic
486C22×C4#612912yes—
487C22×C4C23×D1311yescharacteristic
488C2×C8—28no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—261no—
494C2×C8—261no—
495C2×C8—261no—
496C2×C8—261no—
497C2×C8—261no—
498C2×C8—261no—
499C2×C8D4×D1312yes—
500C2×C8#612912yes—
501C4⋊C4—24no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—132no—
508C4⋊C4—132no—
509C4⋊C4—261no—
510C4⋊C4—261no—
511C4⋊C4—261no—
512C4⋊C4—261no—
513C4⋊C4—261no—
514C4⋊C4—261no—
515C4⋊C4—522no—
516C4⋊C4—522no—
517C4⋊C4—522no—
518C4⋊C4—522no—
519C4⋊C4—522no—
520C4⋊C4—522no—
521C4⋊C4—522no—
522C4⋊C4—1041no—
523C4⋊C4—1041no—
524C4⋊C4C2×Dic2612yes—
525C22⋊C4—24no—
526C22⋊C4—42no—
527C22⋊C4—134no—
528C22⋊C4—262no—
529C42—261no—
530C42—261no—
531C42—261no—
532C42—261no—
533C42—522no—
534C42—1041no—
535C13#2634211yescharacteristic, complemented, Sylow
536C23—21no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23#8813212yes—
541C23#8816812yes—
542C23Q16×D1312yes—
543C23C2×D4×D1311yescharacteristic
544Q8—22no—
545Q8—22no—
546Q8—41no—
547Q8—41no—
548Q8—1044no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—132no—
568C2×C4—132no—
569C2×C4—261no—
570C2×C4—261no—
571C2×C4—261no—
572C2×C4—261no—
573C2×C4—261no—
574C2×C4—261no—
575C2×C4—261no—
576C2×C4—261no—
577C2×C4—261no—
578C2×C4—262no—
579C2×C4—262no—
580C2×C4—261no—
581C2×C4—521no—
582C2×C4—521no—
583C2×C4—521no—
584C2×C4—521no—
585C2×C4—521no—
586C2×C4—521no—
587C2×C4—521no—
588C2×C4—521no—
589C2×C4—521no—
590C2×C4—521no—
591C2×C4—1044no—
592C2×C4—1044no—
593C2×C4#8813212yes—
594C2×C4C22×Dic2611yescharacteristic
595C2×C4C2×D4×D1311yescharacteristic
596C2×C4C2×#612911yescharacteristic
597C2×C4C2×#612911yescharacteristic
598C2×C4#8825611yescharacteristic
599C2×C4#8825711yescharacteristic
600C8—22no—
601C8—22no—
602C8—521no—
603C8—521no—
604C22—22no—
605C22—22no—
606C22—22no—
607C22—22no—
608C22—22no—
609C22—22no—
610C22#1171845514yescomplemented
611C22C2×#8813211yescharacteristic
612C22#1171931411yescharacteristic
613C22#1171931611yescharacteristic
614C22C2×#8816811yescharacteristic
615C22C2×Q16×D1311yescharacteristic
616C22#1171947411yescharacteristic
617C22#1171947611yescharacteristic
618C4—22no—
619C4—42no—
620C4—42no—
621C4—81no—
622C4—81no—
623C4—262no—
624C4—262no—
625C4—521no—
626C4—521no—
627C4—522no—
628C4—522no—
629C4—1041no—
630C4—1041no—
631C4D4×Dic2611yescharacteristic
632C4#1171924811yescharacteristic
633C4#1171929111yescharacteristic
634C4#1171937011yescharacteristic
635C2—24no—
636C2#1311865111yescharacteristic
637C2C2×#1171845511yescharacteristic
638C2#1312468511yescharacteristic
639C2#1312631311yescharacteristic
640C2#1312658511yescharacteristic
641C2#1312722511yescharacteristic
642C2#1312728211yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#1892C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
hypercenter#1892D13
hypocenterC13#26342
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1892

Complements

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

NH ≅ G/Ntype
1. C2×#11718455C2semidirect
5. #13116372C2semidirect
6. #13116331C2semidirect
7. #13116229C2semidirect
8. #13116163C2semidirect
9. #13115593C2semidirect
10. #13115427C2semidirect
12. #13115092C2semidirect
72. C13×C22⋊Q8Q8semidirect
349. C22×C13#477semidirect
390. C22⋊Q8Dic26semidirect
535. C13#26342semidirect
610. C22#11718455semidirect

Maximal subgroups

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

subgroupindex
C2×#117184552
C22×#880582
#131185392
#131178452
#131163722
#131163312
#131162292
#131161632
#131155932
#131154272
#131151442
#131150922
#131150232
#131150142
C13×#18922
#2634213