Finite Group Databasebeta

← #15872644

Subgroups — #15872644

Order 3328.

1114 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719327C211yesmaximal, characteristic
2C2×#11718380C211yesmaximal, characteristic
3C2×#11718638C211yesmaximal, characteristic
4#13115807C212yesmaximal, complemented
5#13115654C212yesmaximal, complemented
6#13115144C211yesmaximal, characteristic
7#13115143C211yesmaximal, characteristic
8#13115141C211yesmaximal, characteristic
9#13114850C212yesmaximal, complemented
10#13114849C212yesmaximal, complemented
11C13×#1872C211yesmaximal, characteristic
12C2×C13×C22⋊Q8C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C2×Q8×Dic13C2211yescharacteristic
15C2×#88198C2211yescharacteristic
16C22×C4⋊Dic13C2211yescharacteristic
17C2×#88178C2211yescharacteristic
18C22×C4×Dic13C2211yescharacteristic
19#11719327—24no—
20#11719327C418yescomplemented
21C2×#88143—21no—
22C2×#88142C2211yescharacteristic
23C2×#88141—21no—
24C2×#88141C2211yescharacteristic
25C2×#88132—21no—
26C2×#88131—21no—
27C2×C13×#103C2212yes—
28C2×C13×C22⋊C8C2211yescharacteristic
29C2×#88075C2212yes—
30C2×#88071—21no—
31C2×#88071—21no—
32C2×C22⋊#1055C2211yescharacteristic
33C2×#88056C2212yes—
34C2×#88055C2212yes—
35C2×#88054C2212yes—
36#11718638—21no—
37#11718638—21no—
38#11718638C2212yes—
39#11718638C2212yes—
40C2×#88050C2212yes—
41#11718380—24no—
42C13×#340C2212yes—
43#11718143C2212yes—
44#11718121C2212yes—
45#11718121C2212yes—
46C22×Q8×C13C2311yescharacteristic
47C23×C4×C13—21no—
48C23×C4×C13C2311yescharacteristic
49C23×Dic13—21no—
50C23×Dic13D411yescharacteristic
51C23×Dic13D411yescharacteristic
52C22×Dic26—21no—
53C22×Dic26C2311yescharacteristic
54C22×C8×C13C2312yes—
55C13×C22⋊Q8—22no—
56C13×C22⋊Q8C2×C414yes—
57C2×C13×C4⋊C4—21no—
58C2×C13×C4⋊C4—21no—
59C2×C13×C4⋊C4—42no—
60C2×C13×C4⋊C4C2312yes—
61C2×C13×C4⋊C4C2311yescharacteristic
62C2×C13×C22⋊C4—21no—
63C2×C22⋊Dic13—21no—
64Q8×Dic13—22no—
65Q8×Dic13C2×C414yescomplemented
66#88198—22no—
67#88198C2×C414yescomplemented
68C2×C4⋊Dic13—21no—
69C2×C4⋊Dic13—21no—
70C2×C4⋊Dic13—42no—
71C2×C4⋊Dic13C2312yes—
72C2×C4⋊Dic13C2311yescharacteristic
73#88178—22no—
74#88178C2×C414yes—
75C2×#6101—21no—
76C2×#6101—21no—
77C2×#6101—21no—
78C2×#6101—21no—
79C2×#6101—21no—
80C2×C4×Dic13—21no—
81C2×C4×Dic13—21no—
82C2×C4×Dic13C2×C414yes—
83C2×C4×Dic13D411yescharacteristic
84C2×C4×Dic13D411yescharacteristic
85C2×C4×Dic13D414yes—
86C2×C4×Dic13C2311yescharacteristic
87C2×C4×Dic13C2311yescharacteristic
88C22×#1055C2312yes—
89#88143—28no—
90#88142—22no—
91#88142C2×C414yescomplemented
92#88141—28no—
93#88141—22no—
94#88141C2×C414yescomplemented
95#88132—28no—
96#88131—28no—
97C13×#103—42no—
98C13×C22⋊C8—22no—
99#88075—42no—
100#88071—22no—
101#88071—22no—
102#88071—22no—
103#88071—22no—
104C22⋊#1055—22no—
105#88056—42no—
106#88055—24no—
107#88054—24no—
108#88050—42no—
109#21866—131nomaximal, Sylow
110C24×C13C2×D411yescharacteristic
111C2×Q8×C13—21no—
112C2×Q8×C13—22no—
113C2×Q8×C13—22no—
114C2×Q8×C13C22×C412yes—
115C22×C4×C13—22no—
116C22×C4×C13—22no—
117C22×C4×C13—21no—
118C22×C4×C13—21no—
119C22×C4×C13—22no—
120C22×C4×C13—42no—
121C22×C4×C13—42no—
122C22×C4×C13—42no—
123C22×C4×C13C22×C412yes—
124C22×C4×C13C2×D411yescharacteristic
125C22×C4×C13C2×D412yes—
126C22×C4×C13C2411yescharacteristic
127C22×Dic13—22no—
128C22×Dic13—22no—
129C22×Dic13—21no—
130C22×Dic13—21no—
131C22×Dic13—22no—
132C22×Dic13—41no—
133C22×Dic13—41no—
134C22×Dic13—42no—
135C22×Dic13—42no—
136C22×Dic13—42no—
137C22×Dic13C22⋊C414yes—
138C22×Dic13C22⋊C414yes—
139C22×Dic13C2×D411yescharacteristic
140C22×Dic13C2×D411yescharacteristic
141C22×Dic13C2×D411yescharacteristic
142C22×Dic13C2×D411yescharacteristic
143C2×Dic26—22no—
144C2×Dic26—22no—
145C2×Dic26—21no—
146C2×Dic26—24no—
147C2×Dic26—42no—
148C2×Dic26—42no—
149C2×Dic26C22×C412yes—
150C2×C8×C13—22no—
151C2×C8×C13—22no—
152C2×C8×C13—22no—
153C13×C4⋊C4—24no—
154C13×C4⋊C4—21no—
155C13×C4⋊C4—22no—
156C13×C4⋊C4—22no—
157C13×C4⋊C4—42no—
158C13×C4⋊C4C22×C412yes—
159C13×C22⋊C4—24no—
160C22⋊Dic13—24no—
161C4⋊Dic13—21no—
162C4⋊Dic13—24no—
163C4⋊Dic13—22no—
164C4⋊Dic13—22no—
165C4⋊Dic13—42no—
166C4⋊Dic13C22×C412yes—
167#6101—24no—
168#6101—24no—
169#6101—24no—
170#6101—24no—
171#6101—24no—
172C4×Dic13—24no—
173C4×Dic13—24no—
174C4×Dic13C22⋊C414yes—
175C4×Dic13C22⋊C414yes—
176C4×Dic13C22×C412yes—
177C4×Dic13C22×C412yes—
178C4×Dic13C2×D412yes—
179C4×Dic13C2×D412yes—
180C2×#1055—22no—
181C2×#1055—22no—
182C2×#1055—22no—
183C2×#533—131no—
184C2×#432—131no—
185C2×#382—131no—
186#1993—132no—
187#1960—132no—
188#1872—131no—
189#1872—131no—
190#1872—131no—
191#1872D1311yescharacteristic
192#1805—132no—
193#1805—132no—
194C23×C13—21no—
195C23×C13—21no—
196C23×C13—21no—
197C23×C13—21no—
198C23×C13C2×C22⋊C412yes—
199C23×C13#13712yes—
200C23×C13#13712yes—
201C23×C13C22×D411yescharacteristic
202Q8×C13—24no—
203Q8×C13—42no—
204C2×C4×C13—21no—
205C2×C4×C13—21no—
206C2×C4×C13—24no—
207C2×C4×C13—24no—
208C2×C4×C13—22no—
209C2×C4×C13—22no—
210C2×C4×C13—41no—
211C2×C4×C13—41no—
212C2×C4×C13—41no—
213C2×C4×C13—41no—
214C2×C4×C13—42no—
215C2×C4×C13—42no—
216C2×C4×C13—42no—
217C2×C4×C13—84no—
218C2×C4×C13C2×C22⋊C412yes—
219C2×C4×C13C23×C411yescharacteristic
220C2×C4×C13C22×D411yescharacteristic
221C2×C4×C13H(5,𝔽2)12yes—
222C2×C4×C132−1+412yes—
223C2×Dic13—21no—
224C2×Dic13—21no—
225C2×Dic13—21no—
226C2×Dic13—21no—
227C2×Dic13—21no—
228C2×Dic13—21no—
229C2×Dic13—21no—
230C2×Dic13—21no—
231C2×Dic13—28no—
232C2×Dic13—22no—
233C2×Dic13—22no—
234C2×Dic13—44no—
235C2×Dic13—41no—
236C2×Dic13—41no—
237C2×Dic13—41no—
238C2×Dic13—41no—
239C2×Dic13—42no—
240C2×Dic13—42no—
241C2×Dic13—42no—
242C2×Dic13—84no—
243C2×Dic13C2×C22⋊C412yes—
244C2×Dic13C2×C22⋊C412yes—
245C2×Dic13C2×C22⋊C412yes—
246C2×Dic13C2×C22⋊C412yes—
247Dic26—24no—
248Dic26—48no—
249Dic26—42no—
250C8×C13—42no—
251#1055—42no—
252#533—138no—
253#533—264no—
254C2×C4⋊Q8—131no—
255C2×C4⋊Q8—131no—
256C2×#125—261no—
257C2×C22⋊Q8—131no—
258C2×C22⋊Q8—261no—
259C2×C22⋊Q8C2×D1311yescharacteristic
260C2×C4×Q8—131no—
261C2×C4×Q8—131no—
262C2×C4×Q8—261no—
263C2×#117—261no—
264C22×C4⋊C4—131no—
265C22×C4⋊C4C2×D1311yescharacteristic
266C22×C42—131no—
267#432—264no—
268C2×C4⋊C8—132no—
269C2×#103—132no—
270C2×#103—132no—
271C2×#103—132no—
272C2×#103C2×D1312yes—
273C2×C22⋊C8—131no—
274C2×C22⋊C8C2×D1311yescharacteristic
275C2×#97—132no—
276#382—132no—
277#382—132no—
278#382—261no—
279#382—261no—
280C2×#95—261no—
281C2×#95—261no—
282#340—132no—
283#340—132no—
284#340—132no—
285#340C2×D1312yes—
286C22×C13—22no—
287C22×C13—22no—
288C22×C13—22no—
289C22×C13—22no—
290C22×C13—22no—
291C22×C13—22no—
292C22×C13#41914yes—
293C22×C13C22×C22⋊C411yescharacteristic
294C22×C13#53511yescharacteristic
295C22×C13#53611yescharacteristic
296C22×C13C2×#13711yescharacteristic
297C22×C13C2×#13711yescharacteristic
298C22×C13#57511yescharacteristic
299C22×C13#57511yescharacteristic
300C4×C13—22no—
301C4×C13—42no—
302C4×C13—42no—
303C4×C13—82no—
304C4×C13#52012yes—
305C4×C13#53712yes—
306Dic13—22no—
307Dic13—22no—
308Dic13—22no—
309Dic13—22no—
310Dic13—42no—
311Dic13—42no—
312Dic13—82no—
313C22×Q8—131no—
314C22×Q8—261no—
315C22×Q8C22×D1311yescharacteristic
316C23×C4—21no—
317C23×C4—131no—
318C23×C4—131no—
319C23×C4—261no—
320C23×C4C22×D1311yescharacteristic
321C22×C8—132no—
322C22×C8C22×D1312yes—
323C4⋊Q8—134no—
324C4⋊Q8—134no—
325C4⋊Q8—262no—
326C4⋊Q8—262no—
327#125—268no—
328C22⋊Q8—22no—
329C22⋊Q8—134no—
330C22⋊Q8—268no—
331C22⋊Q8—262no—
332C22⋊Q8C4×D1314yes—
333C4×Q8—134no—
334C4×Q8—134no—
335C4×Q8—262no—
336C4×Q8—268no—
337C4×Q8—262no—
338#117—268no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—42no—
342C2×C4⋊C4—131no—
343C2×C4⋊C4—132no—
344C2×C4⋊C4—261no—
345C2×C4⋊C4—261no—
346C2×C4⋊C4—261no—
347C2×C4⋊C4—261no—
348C2×C4⋊C4—261no—
349C2×C4⋊C4—261no—
350C2×C4⋊C4—261no—
351C2×C4⋊C4—522no—
352C2×C4⋊C4C22×D1312yes—
353C2×C4⋊C4C22×D1311yescharacteristic
354C2×C22⋊C4—21no—
355C2×C22⋊C4—261no—
356C2×C42—134no—
357C2×C42—131no—
358C2×C42—131no—
359C2×C42—134no—
360C2×C42—131no—
361C2×C42—131no—
362C2×C42—261no—
363C2×C42—261no—
364C4⋊C8—264no—
365#103—42no—
366#103—522no—
367#103—522no—
368#103—522no—
369C22⋊C8—22no—
370C22⋊C8—262no—
371#97—264no—
372#95—262no—
373#95—262no—
374#95—262no—
375#95—262no—
376C2×C13—24no—
377C2×C13#231111yescharacteristic
378C2×C13C2×#41911yescharacteristic
379C2×C13#289611yescharacteristic
380C2×C13#321511yescharacteristic
381C2×C13#321511yescharacteristic
382C2×C13#323611yescharacteristic
383C2×C13#323611yescharacteristic
384C24D4×D1311yescharacteristic
385C2×Q8—21no—
386C2×Q8—22no—
387C2×Q8—22no—
388C2×Q8—132no—
389C2×Q8—264no—
390C2×Q8—261no—
391C2×Q8—262no—
392C2×Q8—262no—
393C2×Q8—522no—
394C2×Q8—522no—
395C2×Q8C2×C4×D1312yes—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—22no—
401C22×C4—42no—
402C22×C4—42no—
403C22×C4—42no—
404C22×C4—134no—
405C22×C4—131no—
406C22×C4—131no—
407C22×C4—131no—
408C22×C4—131no—
409C22×C4—134no—
410C22×C4—262no—
411C22×C4—262no—
412C22×C4—261no—
413C22×C4—261no—
414C22×C4—262no—
415C22×C4—521no—
416C22×C4—521no—
417C22×C4—522no—
418C22×C4—522no—
419C22×C4—522no—
420C22×C4C2×C4×D1312yes—
421C22×C4D4×D1311yescharacteristic
422C22×C4D4×D1312yes—
423C22×C4C23×D1311yescharacteristic
424C2×C8—22no—
425C2×C8—22no—
426C2×C8—22no—
427C2×C8—262no—
428C2×C8—262no—
429C2×C8—262no—
430C4⋊C4—24no—
431C4⋊C4—21no—
432C4⋊C4—22no—
433C4⋊C4—22no—
434C4⋊C4—42no—
435C4⋊C4—132no—
436C4⋊C4—264no—
437C4⋊C4—264no—
438C4⋊C4—264no—
439C4⋊C4—264no—
440C4⋊C4—264no—
441C4⋊C4—264no—
442C4⋊C4—261no—
443C4⋊C4—262no—
444C4⋊C4—262no—
445C4⋊C4—522no—
446C4⋊C4C2×C4×D1312yes—
447C22⋊C4—24no—
448C22⋊C4—264no—
449C42—134no—
450C42—134no—
451C42—132no—
452C42—132no—
453C42—132no—
454C42—132no—
455C42—264no—
456C42—264no—
457C13#2186611yescharacteristic, complemented, Sylow
458C23—21no—
459C23—21no—
460C23—21no—
461C23—21no—
462C23C22⋊C4×D1312yes—
463C23#8816912yes—
464C23#8817212yes—
465C23C2×D4×D1311yescharacteristic
466Q8—24no—
467Q8—42no—
468Q8—264no—
469Q8—528no—
470Q8—522no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—24no—
474C2×C4—24no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—84no—
485C2×C4—132no—
486C2×C4—132no—
487C2×C4—132no—
488C2×C4—132no—
489C2×C4—261no—
490C2×C4—261no—
491C2×C4—261no—
492C2×C4—261no—
493C2×C4—261no—
494C2×C4—261no—
495C2×C4—261no—
496C2×C4—261no—
497C2×C4—268no—
498C2×C4—262no—
499C2×C4—262no—
500C2×C4—524no—
501C2×C4—521no—
502C2×C4—521no—
503C2×C4—521no—
504C2×C4—521no—
505C2×C4—522no—
506C2×C4—522no—
507C2×C4—522no—
508C2×C4—1044no—
509C2×C4C22⋊C4×D1312yes—
510C2×C4C22×C4×D1311yescharacteristic
511C2×C4C2×D4×D1311yescharacteristic
512C2×C4#8825112yes—
513C2×C4#8825712yes—
514C8—42no—
515C8—522no—
516C22—22no—
517C22—22no—
518C22—22no—
519C22—22no—
520C22—22no—
521C22—22no—
522C22#1171846314yes—
523C22C2×C22⋊C4×D1311yescharacteristic
524C22#1171929711yescharacteristic
525C22#1171935311yescharacteristic
526C22C2×#8816911yescharacteristic
527C22C2×#8817211yescharacteristic
528C22#1171947811yescharacteristic
529C22#1171948211yescharacteristic
530C4—22no—
531C4—42no—
532C4—42no—
533C4—82no—
534C4—262no—
535C4—262no—
536C4—262no—
537C4—262no—
538C4—522no—
539C4—522no—
540C4—1042no—
541C4#1171925112yes—
542C4#1171930212yes—
543C2—24no—
544C2#1311742311yescharacteristic
545C2C2×#1171846311yescharacteristic
546C2#1312335211yescharacteristic
547C2#1312583611yescharacteristic
548C2#1312583811yescharacteristic
549C2#1312603911yescharacteristic
550C2#1312604111yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1872C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
cosocleC22×C4×C13C24
hypercenter#1872D13
hypocenterC13#21866
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1872

Complements

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

NH ≅ G/Ntype
4. #13115807C2semidirect
5. #13115654C2semidirect
9. #13114850C2semidirect
10. #13114849C2semidirect
20. #11719327C4semidirect
65. Q8×Dic13C2×C4semidirect
67. #88198C2×C4semidirect
91. #88142C2×C4semidirect
94. #88141C2×C4semidirect
457. C13#21866semidirect

Maximal subgroups

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

subgroupindex
C2×#117193272
C2×#117183802
C2×#117186382
#131158072
#131156542
#131151442
#131151432
#131151412
#131148502
#131148492
C13×#18722
#2186613