Finite Group Databasebeta

← #15868584

Subgroups — #15868584

Order 3328.

1520 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718888C211yesmaximal, characteristic
2C2×#11718687C212yesmaximal, complemented
3C4×#88184C211yesmaximal, characteristic
4#13115191C212yesmaximal, complemented
5#13115153C211yesmaximal, characteristic
6#13115090C212yesmaximal, complemented
7#13115024C211yesmaximal, characteristic, complemented
8#13114771C211yesmaximal, characteristic, complemented
9#13114666C212yesmaximal, complemented
10#13114598C211yesmaximal, characteristic, complemented
11C22×C4×Q8×C13C211yesmaximal, characteristic, complemented
12C23×Q8×C13C2211yescharacteristic
13C2×C4×Q8×C13—28no—
14C2×C4×Q8×C13—21no—
15C2×C4×Q8×C13—21no—
16C2×C4×Q8×C13C2212yes—
17C2×C4×Q8×C13C2212yes—
18C22×C13×C4⋊C4—21no—
19C22×C13×C4⋊C4C2211yescharacteristic
20C22×C42×C13—21no—
21C22×C42×C13C2211yescharacteristic
22C22×#6106C2212yes—
23C2×#88184C2211yescharacteristic
24C2×C4×C22⋊D13—21no—
25C2×C4×D52C2211yescharacteristic
26#11718888C418yescomplemented
27C2×#88075C2212yes—
28C2×#88075C2212yes—
29C2×#88075C2212yes—
30#11718874—21no—
31#11718873C2211yescharacteristic
32C2×C22⋊#1055C2211yescharacteristic
33C2×C22⋊#1055C2211yescharacteristic
34#11718687—28no—
35C2×#88049C2212yes—
36C2×#88047C2212yes—
37#11718601—21no—
38#11718600C2211yescharacteristic
39C4×#6103—21no—
40C4×C4⋊Dic13C2211yescharacteristic
41#11718589C2211yescharacteristic
42C2×#88043C2212yes—
43#11718121C2212yes—
44#11718121C2212yes—
45#11718116C2212yes—
46C22×Q8×C13—24no—
47C22×Q8×C13—24no—
48C22×Q8×C13—21no—
49C22×Q8×C13—22no—
50C22×Q8×C13C2×C414yescomplemented
51C22×Q8×C13C2312yes—
52C23×C4×C13—21no—
53C23×C4×C13—21no—
54C23×C4×C13D411yescharacteristic
55C23×C4×C13D411yescharacteristic
56C23×C4×C13C2311yescharacteristic
57C22×C22⋊D13—21no—
58C22×D52C2311yescharacteristic
59C22×C4×D13—21no—
60C4×Q8×C13—28no—
61C4×Q8×C13—28no—
62C4×Q8×C13—24no—
63C4×Q8×C13—24no—
64C4×Q8×C13—24no—
65C4×Q8×C13D418yescomplemented
66C2×C13×C4⋊C4—28no—
67C2×C13×C4⋊C4—22no—
68C2×C13×C4⋊C4—22no—
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4—24no—
71C2×C13×C4⋊C4C2312yes—
72C2×C42×C13—28no—
73C2×C42×C13—22no—
74C2×C42×C13—22no—
75C2×C42×C13—24no—
76C2×C42×C13D411yescharacteristic
77C2×C42×C13D411yescharacteristic
78C2×C42×C13C2311yescharacteristic
79C2×C42×C13C2311yescharacteristic
80C2×C22⋊Dic13—21no—
81C2×#6106—24no—
82C2×#6106—24no—
83C2×#6106C2×C418yescomplemented
84#88184—22no—
85#88184C2×C414yes—
86C4×C22⋊D13—44no—
87C2×#6103—21no—
88C2×#6103—21no—
89C2×#6103—21no—
90C2×#6103—21no—
91C2×C4⋊Dic13C2311yescharacteristic
92C2×C4⋊Dic13C2311yescharacteristic
93C2×C4⋊Dic13C2311yescharacteristic
94C2×#6101—21no—
95C2×C4×Dic13—21no—
96C22×#1055C2312yes—
97C22×#1055C2312yes—
98C4×D52—24no—
99#88075—24no—
100#88075—24no—
101#88075C2×C418yescomplemented
102#88071—21no—
103#88071—21no—
104#88071—21no—
105C22⋊#1055—22no—
106C22⋊#1055C2×C414yescomplemented
107#88049—24no—
108#88047—24no—
109#88043—24no—
110#21454—131nomaximal, Sylow
111C24×C13C2×D411yescharacteristic
112C23×D13—21no—
113C2×Q8×C13—24no—
114C2×Q8×C13—216no—
115C2×Q8×C13—24no—
116C2×Q8×C13—216no—
117C2×Q8×C13—24no—
118C2×Q8×C13—22no—
119C2×Q8×C13—22no—
120C2×Q8×C13—22no—
121C2×Q8×C13C22×C414yes—
122C2×Q8×C13C2×D414yes—
123C2×Q8×C13#4114yes—
124C22×C4×C13—24no—
125C22×C4×C13—24no—
126C22×C4×C13—24no—
127C22×C4×C13—22no—
128C22×C4×C13—22no—
129C22×C4×C13—22no—
130C22×C4×C13—22no—
131C22×C4×C13—22no—
132C22×C4×C13—22no—
133C22×C4×C13—24no—
134C22×C4×C13—22no—
135C22×C4×C13—22no—
136C22×C4×C13—22no—
137C22×C4×C13—41no—
138C22×C4×C13—42no—
139C22×C4×C13—42no—
140C22×C4×C13C22×C412yes—
141C22×C4×C13C2×D411yescharacteristic
142C22×C4×C13C2×D411yescharacteristic
143C22×C4×C13C2×D411yescharacteristic
144C22×C4×C13C2×D411yescharacteristic
145C22×C4×C13C2×D411yescharacteristic
146C22×C4×C13#4112yes—
147C22×C4×C13C2411yescharacteristic
148C2×C22⋊D13—24no—
149C2×C22⋊D13—42no—
150C2×C22⋊D13—42no—
151C22×Dic13—21no—
152C22×Dic13—21no—
153C22×Dic13—21no—
154C2×D52—22no—
155C2×D52—22no—
156C2×D52—21no—
157C2×D52C22×C412yes—
158C2×C4×D13—42no—
159C2×C4×D13—42no—
160C2×C4×D13—42no—
161C13×C4⋊C4—28no—
162C13×C4⋊C4—24no—
163C13×C4⋊C4—28no—
164C13×C4⋊C4—22no—
165C13×C4⋊C4C2×D414yes—
166C42×C13—28no—
167C42×C13—28no—
168C42×C13—22no—
169C42×C13—22no—
170C42×C13—22no—
171C42×C13C2×D414yes—
172C22⋊Dic13—42no—
173#6106—216no—
174#6103—24no—
175#6103—42no—
176#6103—42no—
177#6103—42no—
178C4⋊Dic13—21no—
179C4⋊Dic13—22no—
180C4⋊Dic13—22no—
181C4⋊Dic13C22×C412yes—
182#6101—42no—
183C4×Dic13—42no—
184C2×#1055—22no—
185C2×#1055—22no—
186C2×#1055—22no—
187C2×#1055—22no—
188C2×#1055—22no—
189C2×#1055C22×C414yes—
190C22×C4×Q8D1311yescharacteristic, complemented
191C2×#448—131no—
192C2×#440—132no—
193C4×#121—131no—
194#1880—132no—
195#1874—131no—
196#1863—132no—
197#1852—131no—
198#1787—131no—
199#1763—132no—
200#1749—131no—
201C23×C13—21no—
202C23×C13—21no—
203C23×C13—21no—
204C23×C13—21no—
205C23×C13C4×D412yes—
206C23×C13AGL(1,ℤ/8)12yes—
207C23×C13#13712yes—
208C23×C13C22×D411yescharacteristic
209C22×D13—22no—
210C22×D13—41no—
211C22×D13—41no—
212C22×D13—41no—
213C22×D13—41no—
214C22×D13—41no—
215C22×D13—41no—
216Q8×C13—216no—
217Q8×C13—24no—
218Q8×C13—24no—
219Q8×C13—24no—
220Q8×C13C4×D418yescomplemented
221C2×C4×C13—28no—
222C2×C4×C13—216no—
223C2×C4×C13—24no—
224C2×C4×C13—21no—
225C2×C4×C13—24no—
226C2×C4×C13—21no—
227C2×C4×C13—24no—
228C2×C4×C13—21no—
229C2×C4×C13—21no—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—21no—
234C2×C4×C13—24no—
235C2×C4×C13—24no—
236C2×C4×C13—21no—
237C2×C4×C13—24no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—44no—
241C2×C4×C13—48no—
242C2×C4×C13—42no—
243C2×C4×C13—42no—
244C2×C4×C13C4×D412yes—
245C2×C4×C13#12012yes—
246C2×C4×C13#12012yes—
247C2×C4×C13#13712yes—
248C2×C4×C13C23×C411yescharacteristic
249C2×C4×C13C22×D412yes—
250C2×C4×C13C2×#4112yes—
251C2×C4×C13C2×#4111yescharacteristic
252C22⋊D13—48no—
253C2×Dic13—22no—
254C2×Dic13—41no—
255C2×Dic13—41no—
256C2×Dic13—41no—
257C2×Dic13—41no—
258C2×Dic13—41no—
259C2×Dic13—41no—
260C2×Dic13—41no—
261C2×Dic13—41no—
262D52—24no—
263D52—42no—
264C4×D13—84no—
265#1055—24no—
266#1055—42no—
267C23×Q8C2×D1311yescharacteristic
268C22×SD16—132no—
269C2×#121—131no—
270C2×C4×Q8—28no—
271C2×C4×Q8—21no—
272C2×C4×Q8—21no—
273C2×C4×Q8C2×D1312yes—
274C2×C4×Q8C2×D1312yes—
275C2×C4×D4—131no—
276C2×C4×D4—261no—
277C22×C4⋊C4—21no—
278C22×C4⋊C4C2×D1311yescharacteristic
279C22×C42—21no—
280C22×C42C2×D1311yescharacteristic
281#448—138no—
282#440—268no—
283C2×#107—132no—
284C2×#103—132no—
285C2×#103—132no—
286C2×#103—132no—
287C2×#102—132no—
288C2×C22⋊C8—131no—
289C2×C22⋊C8—131no—
290C2×#97—132no—
291#390—131no—
292#389—131no—
293#388—261no—
294#386—261no—
295#380—131no—
296C4×C4⋊C4—131no—
297C4×C22⋊C4—261no—
298#340—132no—
299#340—132no—
300#336—132no—
301C22×C13—22no—
302C22×C13—22no—
303C22×C13—22no—
304C22×C13—22no—
305C22×C13—22no—
306C22×C13—22no—
307C22×C13#44014yescomplemented
308C22×C13C2×C4×D411yescharacteristic
309C22×C13C2×#12011yescharacteristic
310C22×C13#52511yescharacteristic
311C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
312C22×C13C2×#13711yescharacteristic
313C22×C13C2×#13711yescharacteristic
314C22×C13#57511yescharacteristic
315C2×D13—42no—
316C2×D13—42no—
317C2×D13—42no—
318C2×D13—81no—
319C2×D13—81no—
320C2×D13—81no—
321C2×D13—81no—
322C4×C13—22no—
323C4×C13—22no—
324C4×C13—22no—
325C4×C13—28no—
326C4×C13—22no—
327C4×C13—41no—
328C4×C13—44no—
329C4×C13C2×C4×D412yes—
330C4×C13#52512yes—
331Dic13—42no—
332Dic13—81no—
333Dic13—81no—
334C22×Q8—24no—
335C22×Q8—24no—
336C22×Q8—22no—
337C22×Q8—21no—
338C22×Q8C4×D1314yescomplemented
339C22×Q8C22×D1312yes—
340C22×D4—131no—
341C22×D4—261no—
342C23×C4—21no—
343C23×C4—21no—
344C23×C4—261no—
345C23×C4C22⋊D1311yescharacteristic
346C23×C4C22⋊D1311yescharacteristic
347C23×C4C22×D1311yescharacteristic
348C2×SD16—138no—
349C2×SD16—264no—
350C2×SD16—264no—
351C22×C8—132no—
352C22×C8—132no—
353#121—134no—
354#121—262no—
355C4×Q8—28no—
356C4×Q8—28no—
357C4×Q8—24no—
358C4×Q8—24no—
359C4×Q8—24no—
360C4×Q8C22⋊D1318yescomplemented
361C4×D4—264no—
362C4×D4—524no—
363C2×C4⋊C4—28no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—24no—
368C2×C4⋊C4—131no—
369C2×C4⋊C4—131no—
370C2×C4⋊C4—131no—
371C2×C4⋊C4—261no—
372C2×C4⋊C4C22×D1312yes—
373C2×C22⋊C4—261no—
374C2×C22⋊C4—261no—
375C2×C22⋊C4—261no—
376C2×C22⋊C4—261no—
377C2×C22⋊C4—261no—
378C2×C42—28no—
379C2×C42—22no—
380C2×C42—22no—
381C2×C42—24no—
382C2×C42—261no—
383C2×C42C22⋊D1311yescharacteristic
384C2×C42C22⋊D1311yescharacteristic
385C2×C42C22×D1311yescharacteristic
386C2×C42C22×D1311yescharacteristic
387#107—264no—
388#103—138no—
389#103—264no—
390#103—264no—
391#102—264no—
392C22⋊C8—134no—
393C22⋊C8—262no—
394#97—264no—
395#95—261no—
396#95—261no—
397#95—261no—
398C2×C13—24no—
399C2×C13C4×#12011yescharacteristic
400C2×C13C2×#44011yescharacteristic
401C2×C13C4×#13711yescharacteristic
402C2×C13#300411yescharacteristic
403C2×C13#300611yescharacteristic
404C2×C13#311211yescharacteristic
405C2×C13#311711yescharacteristic
406D13—82no—
407C24—261no—
408C24C2×C22⋊D1311yescharacteristic
409C2×Q8—24no—
410C2×Q8—216no—
411C2×Q8—24no—
412C2×Q8—216no—
413C2×Q8—24no—
414C2×Q8—22no—
415C2×Q8—22no—
416C2×Q8—22no—
417C2×Q8C2×C4×D1314yes—
418C2×Q8#612714yes—
419C2×Q8C2×C22⋊D1314yes—
420C2×D4—132no—
421C2×D4—264no—
422C2×D4—262no—
423C2×D4—261no—
424C2×D4—262no—
425C2×D4—522no—
426C2×D4—522no—
427C22×C4—24no—
428C22×C4—24no—
429C22×C4—24no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—24no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—41no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—261no—
444C22×C4—261no—
445C22×C4—261no—
446C22×C4—522no—
447C22×C4—522no—
448C22×C4—522no—
449C22×C4C2×C4×D1312yes—
450C22×C4#612712yes—
451C22×C4C2×C22⋊D1311yescharacteristic
452C22×C4C2×C22⋊D1311yescharacteristic
453C22×C4C2×C22⋊D1311yescharacteristic
454C22×C4C2×C22⋊D1311yescharacteristic
455C22×C4C2×C22⋊D1311yescharacteristic
456C22×C4C23×D1311yescharacteristic
457SD16—2616no—
458C2×C8—134no—
459C2×C8—262no—
460C2×C8—262no—
461C2×C8—262no—
462C2×C8—262no—
463C2×C8—262no—
464C4⋊C4—28no—
465C4⋊C4—24no—
466C4⋊C4—28no—
467C4⋊C4—22no—
468C4⋊C4—132no—
469C4⋊C4—261no—
470C4⋊C4—262no—
471C4⋊C4—262no—
472C4⋊C4—522no—
473C4⋊C4C2×C22⋊D1314yes—
474C22⋊C4—264no—
475C22⋊C4—522no—
476C22⋊C4—522no—
477C22⋊C4—522no—
478C22⋊C4—522no—
479C42—28no—
480C42—28no—
481C42—22no—
482C42—22no—
483C42—22no—
484C42—522no—
485C42C2×C22⋊D1314yes—
486C13#2145411yescharacteristic, complemented, Sylow
487C23—21no—
488C23—21no—
489C23—21no—
490C23—21no—
491C23—262no—
492C23—521no—
493C23—521no—
494C23—521no—
495C23—521no—
496C23—521no—
497C23—521no—
498C23C4×C22⋊D1312yes—
499C23#8819612yes—
500C23#8820312yes—
501C23C22×C22⋊D1311yescharacteristic
502Q8—216no—
503Q8—24no—
504Q8—24no—
505Q8—24no—
506Q8C4×C22⋊D1318yescomplemented
507D4—264no—
508D4—528no—
509D4—522no—
510C2×C4—28no—
511C2×C4—216no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—24no—
522C2×C4—21no—
523C2×C4—24no—
524C2×C4—24no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—24no—
529C2×C4—44no—
530C2×C4—48no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—262no—
534C2×C4—521no—
535C2×C4—521no—
536C2×C4—521no—
537C2×C4—521no—
538C2×C4—521no—
539C2×C4—521no—
540C2×C4—521no—
541C2×C4—521no—
542C2×C4—1044no—
543C2×C4C4×C22⋊D1312yes—
544C2×C4#8819612yes—
545C2×C4#8820712yes—
546C2×C4#8820712yes—
547C2×C4C22×C4×D1311yescharacteristic
548C2×C4C2×#612712yes—
549C2×C4C2×#612711yescharacteristic
550C2×C4C22×C22⋊D1312yes—
551C8—264no—
552C8—522no—
553C22—22no—
554C22—22no—
555C22—22no—
556C22—22no—
557C22—22no—
558C22—22no—
559C22—522no—
560C22—522no—
561C22—522no—
562C22—1041no—
563C22—1041no—
564C22—1041no—
565C22—1041no—
566C22#1171868714yescomplemented
567C22C2×C4×C22⋊D1311yescharacteristic
568C22#1171949611yescharacteristic
569C22C2×#8819611yescharacteristic
570C22C2×#8819611yescharacteristic
571C22C2×#8820311yescharacteristic
572C22#1171952711yescharacteristic
573C22C2×#8820711yescharacteristic
574C4—28no—
575C4—22no—
576C4—22no—
577C4—22no—
578C4—22no—
579C4—41no—
580C4—44no—
581C4—522no—
582C4—1041no—
583C4—1041no—
584C4C2×C4×C22⋊D1312yes—
585C4#1171949612yes—
586C2—24no—
587C2—1042no—
588C2C4×#8820711yescharacteristic
589C2C2×#1171868711yescharacteristic
590C2C4×#8819611yescharacteristic
591C2#1312407011yescharacteristic
592C2#1312408811yescharacteristic
593C2#1312495811yescharacteristic
594C2#1312500711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC22×C4×Q8×C13C2
socleC23×C13C22×D4
prime radicalC2×#88184C22
cosocleC22×C4×C13C24
hypercenterC22×C4×Q8D13
hypocenterC13#21454
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ C22×C4×Q8

Complements

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

NH ≅ G/Ntype
2. C2×#11718687C2semidirect
4. #13115191C2semidirect
6. #13115090C2semidirect
7. #13115024C2semidirect
8. #13114771C2semidirect
9. #13114666C2semidirect
10. #13114598C2semidirect
11. C22×C4×Q8×C13C2semidirect
26. #11718888C4semidirect
50. C22×Q8×C13C2×C4semidirect
65. C4×Q8×C13D4semidirect
83. C2×#6106C2×C4semidirect
101. #88075C2×C4semidirect
106. C22⋊#1055C2×C4semidirect
190. C22×C4×Q8D13semidirect
220. Q8×C13C4×D4semidirect
307. C22×C13#440semidirect
338. C22×Q8C4×D13semidirect
360. C4×Q8C22⋊D13semidirect
486. C13#21454semidirect
506. Q8C4×C22⋊D13semidirect
566. C22#11718687semidirect

Maximal subgroups

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

subgroupindex
C2×#117188882
C2×#117186872
C4×#881842
#131151912
#131151532
#131150902
#131150242
#131147712
#131146662
#131145982
C22×C4×Q8×C132
#2145413