Finite Group Databasebeta

← #15793968

Subgroups — #15793968

Order 3328.

1334 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88143C211yesmaximal, characteristic
2C2×#11718638C211yesmaximal, characteristic
3C2×#11718311C211yesmaximal, characteristic
4#13113102C212yesmaximal
5#13113102C212yesmaximal
6#13113090C211yesmaximal, characteristic
7#13113089C211yesmaximal, characteristic
8#13113088C212yesmaximal
9#13113087C212yesmaximal
10#13113086C211yesmaximal, characteristic
11C13×#1441C211yesmaximal, characteristic
12C22×C13×C4⋊C4C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C4⋊Dic13C2211yescharacteristic
15C22×C4⋊Dic13C2211yescharacteristic
16C22×#6101C2211yescharacteristic
17C22×#6101C2211yescharacteristic
18C22×#6101C2211yescharacteristic
19C22×#6101C2211yescharacteristic
20C22×#6101C2212yes—
21C22×C4×Dic13C2211yescharacteristic
22C2×#88143—24no—
23C2×#88143—24no—
24C2×#88143C418yescomplemented
25C2×C13×#95C2211yescharacteristic
26C2×C13×#95C2212yes—
27C2×C13×#95C2212yes—
28C2×#88071C2212yes—
29C2×#88071C2211yescharacteristic
30C2×#88071C2212yes—
31C2×#88071C2212yes—
32C2×#88071C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2212yes—
35C2×#88071C2212yes—
36C2×#88071C2212yes—
37C2×#88071C2212yes—
38#11718638—24no—
39#11718311—24no—
40C23×C4×C13C2312yes—
41C23×C4×C13C2312yes—
42C23×C4×C13C2311yescharacteristic
43C23×C4×C13C2311yescharacteristic
44C23×C4×C13C2311yescharacteristic
45C23×Dic13C2312yes—
46C23×Dic13C2312yes—
47C23×Dic13C2311yescharacteristic
48C23×Dic13C2311yescharacteristic
49C23×Dic13C2311yescharacteristic
50C23×Dic13C2311yescharacteristic
51C2×C13×C4⋊C4—22no—
52C2×C13×C4⋊C4—22no—
53C2×C13×C4⋊C4—22no—
54C2×C13×C4⋊C4—42no—
55C2×C13×C4⋊C4C2×C414yes—
56C2×C4⋊Dic13—22no—
57C2×C4⋊Dic13—22no—
58C2×C4⋊Dic13—22no—
59C2×C4⋊Dic13—42no—
60C2×C4⋊Dic13C2×C414yes—
61C2×#6101—22no—
62C2×#6101—22no—
63C2×#6101—22no—
64C2×#6101—22no—
65C2×#6101—22no—
66C2×#6101—22no—
67C2×#6101—22no—
68C2×#6101—22no—
69C2×#6101—24no—
70C2×#6101—42no—
71C2×#6101—42no—
72C2×#6101C2×C414yes—
73C2×#6101C2×C414yes—
74C2×#6101C2×C414yes—
75C2×#6101C2×C414yes—
76C2×C4×Dic13C2×C414yes—
77C2×C4×Dic13D414yes—
78C2×C4×Dic13D414yes—
79#88143—232no—
80C13×#95—22no—
81C13×#95—42no—
82C13×#95—42no—
83#88071—22no—
84#88071—24no—
85#88071—24no—
86#88071—24no—
87#88071—42no—
88#88071—42no—
89#88071—42no—
90#88071—42no—
91#88071—42no—
92#88071—42no—
93#14664—131nomaximal, Sylow
94C24×C13C2411yescharacteristic
95C22×C4×C13—22no—
96C22×C4×C13—22no—
97C22×C4×C13—21no—
98C22×C4×C13—21no—
99C22×C4×C13—21no—
100C22×C4×C13—21no—
101C22×C4×C13—21no—
102C22×C4×C13—22no—
103C22×C4×C13—21no—
104C22×C4×C13—21no—
105C22×C4×C13—21no—
106C22×C4×C13—22no—
107C22×C4×C13—22no—
108C22×C4×C13—22no—
109C22×C4×C13—22no—
110C22×C4×C13—22no—
111C22×C4×C13—22no—
112C22×C4×C13—22no—
113C22×C4×C13—22no—
114C22×C4×C13—22no—
115C22×C4×C13—22no—
116C22×C4×C13—22no—
117C22×C4×C13—22no—
118C22×C4×C13—22no—
119C22×C4×C13—22no—
120C22×C4×C13—22no—
121C22×C4×C13C22×C412yes—
122C22×C4×C13C22×C412yes—
123C22×C4×C13C22×C412yes—
124C22×C4×C13C2×D412yes—
125C22×C4×C13C2×D412yes—
126C22×Dic13—21no—
127C22×Dic13—21no—
128C22×Dic13—22no—
129C22×Dic13—22no—
130C22×Dic13—21no—
131C22×Dic13—21no—
132C22×Dic13—21no—
133C22×Dic13—21no—
134C22×Dic13—21no—
135C22×Dic13—21no—
136C22×Dic13—22no—
137C22×Dic13—21no—
138C22×Dic13—21no—
139C22×Dic13—21no—
140C22×Dic13—22no—
141C22×Dic13—21no—
142C22×Dic13—22no—
143C22×Dic13—22no—
144C22×Dic13—22no—
145C22×Dic13—22no—
146C22×Dic13—22no—
147C22×Dic13—22no—
148C22×Dic13—22no—
149C22×Dic13—22no—
150C22×Dic13—22no—
151C22×Dic13—22no—
152C22×Dic13—22no—
153C22×Dic13—22no—
154C22×Dic13—22no—
155C22×Dic13—22no—
156C22×Dic13C22×C412yes—
157C22×Dic13C22×C412yes—
158C22×Dic13C22×C412yes—
159C22×Dic13C22×C412yes—
160C22×Dic13C2×D412yes—
161C22×Dic13C2×D412yes—
162C22×Dic13C2×D412yes—
163C22×Dic13C2×D412yes—
164C13×C4⋊C4—28no—
165C13×C4⋊C4—44no—
166C4⋊Dic13—28no—
167C4⋊Dic13—44no—
168#6101—28no—
169#6101—28no—
170#6101—28no—
171#6101—28no—
172#6101—48no—
173C4×Dic13C22⋊C4116yes—
174C22×#125—131no—
175C2×#382—131no—
176C2×#382—131no—
177#1445—132no—
178#1445—132no—
179#1441—132no—
180#1441—131no—
181#1441—132no—
182#1441—131no—
183#1441—131no—
184#1441D1311yescharacteristic
185C23×C13C23×C411yescharacteristic
186C23×C13C22×D411yescharacteristic
187C23×C13C22×D411yescharacteristic
188C23×C13H(5,𝔽2)11yescharacteristic
189C23×C13H(5,𝔽2)12yes—
190C23×C13H(5,𝔽2)11yescharacteristic
191C23×C132−1+412yes—
192C23×C132−1+412yes—
193C23×C132−1+411yescharacteristic
194C23×C132−1+411yescharacteristic
195C23×C132−1+412yes—
196C2×C4×C13—24no—
197C2×C4×C13—22no—
198C2×C4×C13—22no—
199C2×C4×C13—24no—
200C2×C4×C13—22no—
201C2×C4×C13—22no—
202C2×C4×C13—22no—
203C2×C4×C13—22no—
204C2×C4×C13—24no—
205C2×C4×C13—41no—
206C2×C4×C13—41no—
207C2×C4×C13—41no—
208C2×C4×C13—41no—
209C2×C4×C13—42no—
210C2×C4×C13—41no—
211C2×C4×C13—41no—
212C2×C4×C13—42no—
213C2×C4×C13—42no—
214C2×C4×C13—42no—
215C2×C4×C13—42no—
216C2×C4×C13—42no—
217C2×C4×C13—42no—
218C2×C4×C13—42no—
219C2×C4×C13—42no—
220C2×C4×C13—42no—
221C2×C4×C13—42no—
222C2×C4×C13—42no—
223C2×C4×C13—42no—
224C2×C4×C13—42no—
225C2×C4×C13—42no—
226C2×C4×C13C2×C22⋊C414yes—
227C2×Dic13—24no—
228C2×Dic13—22no—
229C2×Dic13—22no—
230C2×Dic13—22no—
231C2×Dic13—22no—
232C2×Dic13—24no—
233C2×Dic13—22no—
234C2×Dic13—22no—
235C2×Dic13—22no—
236C2×Dic13—22no—
237C2×Dic13—22no—
238C2×Dic13—22no—
239C2×Dic13—22no—
240C2×Dic13—22no—
241C2×Dic13—24no—
242C2×Dic13—41no—
243C2×Dic13—41no—
244C2×Dic13—41no—
245C2×Dic13—41no—
246C2×Dic13—42no—
247C2×Dic13—41no—
248C2×Dic13—41no—
249C2×Dic13—42no—
250C2×Dic13—42no—
251C2×Dic13—42no—
252C2×Dic13—42no—
253C2×Dic13—42no—
254C2×Dic13—42no—
255C2×Dic13—42no—
256C2×Dic13—42no—
257C2×Dic13—42no—
258C2×Dic13—42no—
259C2×Dic13—42no—
260C2×Dic13—42no—
261C2×Dic13—42no—
262C2×Dic13—42no—
263C2×Dic13C2×C22⋊C414yes—
264C2×Dic13C2×C22⋊C414yes—
265C2×#125—138no—
266C2×#125—264no—
267C2×#125—264no—
268C22×C4⋊C4—131no—
269C22×C4⋊C4—131no—
270C22×C4⋊C4—131no—
271C22×C4⋊C4—131no—
272C22×C4⋊C4—131no—
273C22×C4⋊C4—132no—
274C22×C4⋊C4—131no—
275C22×C4⋊C4C2×D1311yescharacteristic
276C22×C4⋊C4C2×D1311yescharacteristic
277C22×C42—131no—
278#382—264no—
279#382—264no—
280C2×#95—132no—
281C2×#95—131no—
282C2×#95—132no—
283C2×#95—132no—
284C2×#95—132no—
285C2×#95—132no—
286C2×#95—132no—
287C2×#95—132no—
288C2×#95—132no—
289C2×#95—132no—
290C2×#95C2×D1311yescharacteristic
291C2×#95C2×D1312yes—
292C2×#95C2×D1312yes—
293C22×C13C22×C22⋊C411yescharacteristic
294C22×C13#51912yes—
295C22×C13#52011yescharacteristic
296C22×C13#52011yescharacteristic
297C22×C13#52012yes—
298C22×C13#53511yescharacteristic
299C22×C13#53511yescharacteristic
300C22×C13#53611yescharacteristic
301C22×C13#53612yes—
302C22×C13#53611yescharacteristic
303C22×C13#53611yescharacteristic
304C22×C13#53611yescharacteristic
305C22×C13#53712yes—
306C22×C13#53711yescharacteristic
307C22×C13#53711yescharacteristic
308C22×C13#56212yes—
309C22×C13#56212yes—
310C22×C13#56312yes—
311C22×C13#56312yes—
312C22×C13#56312yes—
313C22×C13#56312yes—
314C22×C13#56412yes—
315C22×C13#56412yes—
316C4×C13—24no—
317C4×C13—42no—
318C4×C13—42no—
319C4×C13—82no—
320C4×C13—82no—
321Dic13—24no—
322Dic13—24no—
323Dic13—42no—
324Dic13—42no—
325Dic13—82no—
326Dic13—82no—
327C23×C4—131no—
328C23×C4—131no—
329C23×C4—131no—
330C23×C4—131no—
331C23×C4—132no—
332C23×C4—132no—
333C23×C4C22×D1312yes—
334C23×C4C22×D1312yes—
335C23×C4C22×D1311yescharacteristic
336C23×C4C22×D1311yescharacteristic
337C23×C4C22×D1311yescharacteristic
338#125—2632no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—42no—
343C2×C4⋊C4—134no—
344C2×C4⋊C4—134no—
345C2×C4⋊C4—134no—
346C2×C4⋊C4—134no—
347C2×C4⋊C4—134no—
348C2×C4⋊C4—262no—
349C2×C4⋊C4—262no—
350C2×C4⋊C4—262no—
351C2×C4⋊C4—262no—
352C2×C4⋊C4—262no—
353C2×C4⋊C4—262no—
354C2×C4⋊C4—262no—
355C2×C4⋊C4—262no—
356C2×C4⋊C4—262no—
357C2×C4⋊C4—262no—
358C2×C4⋊C4—264no—
359C2×C4⋊C4—262no—
360C2×C4⋊C4—522no—
361C2×C4⋊C4—522no—
362C2×C4⋊C4—522no—
363C2×C4⋊C4C4×D1314yes—
364C2×C42—134no—
365C2×C42—134no—
366C2×C42—134no—
367#95—22no—
368#95—42no—
369#95—42no—
370#95—264no—
371#95—264no—
372#95—264no—
373#95—262no—
374#95—522no—
375#95—522no—
376#95—522no—
377#95—522no—
378#95—522no—
379#95—522no—
380C2×C13#231011yescharacteristic
381C2×C13#231111yescharacteristic
382C2×C13#231111yescharacteristic
383C2×C13#238212yes—
384C2×C13#238212yes—
385C2×C13#282012yes—
386C2×C13#282011yescharacteristic
387C2×C13#282011yescharacteristic
388C2×C13#282212yes—
389C2×C13#282211yescharacteristic
390C2×C13#282211yescharacteristic
391C24C23×D1311yescharacteristic
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—22no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—132no—
419C22×C4—132no—
420C22×C4—132no—
421C22×C4—132no—
422C22×C4—132no—
423C22×C4—132no—
424C22×C4—132no—
425C22×C4—132no—
426C22×C4—261no—
427C22×C4—262no—
428C22×C4—261no—
429C22×C4—261no—
430C22×C4—261no—
431C22×C4—262no—
432C22×C4—261no—
433C22×C4—261no—
434C22×C4—261no—
435C22×C4—261no—
436C22×C4—261no—
437C22×C4—262no—
438C22×C4—261no—
439C22×C4—261no—
440C22×C4—261no—
441C22×C4—262no—
442C22×C4—262no—
443C22×C4—262no—
444C22×C4—262no—
445C22×C4—262no—
446C22×C4—262no—
447C22×C4—262no—
448C22×C4—262no—
449C22×C4—262no—
450C22×C4—262no—
451C22×C4—262no—
452C22×C4—262no—
453C22×C4—262no—
454C22×C4—262no—
455C22×C4—262no—
456C22×C4C2×C4×D1312yes—
457C22×C4C2×C4×D1312yes—
458C22×C4C2×C4×D1312yes—
459C22×C4D4×D1312yes—
460C22×C4D4×D1312yes—
461C4⋊C4—28no—
462C4⋊C4—44no—
463C4⋊C4—268no—
464C4⋊C4—268no—
465C4⋊C4—268no—
466C4⋊C4—268no—
467C4⋊C4—268no—
468C4⋊C4—524no—
469C4⋊C4—528no—
470C42—1316no—
471C13#1466411yescharacteristic, complemented, Sylow
472C23C22×C4×D1311yescharacteristic
473C23C2×D4×D1311yescharacteristic
474C23C2×D4×D1311yescharacteristic
475C23#8825112yes—
476C23#8825111yescharacteristic
477C23#8825412yes—
478C23#8825411yescharacteristic
479C23#8825611yescharacteristic
480C23#8825711yescharacteristic
481C23#8825712yes—
482C23#8825712yes—
483C2×C4—24no—
484C2×C4—22no—
485C2×C4—24no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—24no—
492C2×C4—41no—
493C2×C4—42no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—134no—
514C2×C4—134no—
515C2×C4—262no—
516C2×C4—262no—
517C2×C4—262no—
518C2×C4—264no—
519C2×C4—262no—
520C2×C4—262no—
521C2×C4—264no—
522C2×C4—262no—
523C2×C4—262no—
524C2×C4—262no—
525C2×C4—262no—
526C2×C4—262no—
527C2×C4—262no—
528C2×C4—262no—
529C2×C4—264no—
530C2×C4—521no—
531C2×C4—522no—
532C2×C4—521no—
533C2×C4—521no—
534C2×C4—521no—
535C2×C4—521no—
536C2×C4—521no—
537C2×C4—522no—
538C2×C4—522no—
539C2×C4—522no—
540C2×C4—522no—
541C2×C4—522no—
542C2×C4—522no—
543C2×C4—522no—
544C2×C4—522no—
545C2×C4—522no—
546C2×C4—522no—
547C2×C4—522no—
548C2×C4—522no—
549C2×C4—522no—
550C2×C4—522no—
551C2×C4C22⋊C4×D1314yes—
552C22C2×C22⋊C4×D1311yescharacteristic
553C22#1171920911yescharacteristic
554C22#1171922811yescharacteristic
555C22#1171925112yes—
556C22#1171927712yes—
557C22#1171929711yescharacteristic
558C22#1171930212yes—
559C22#1171931211yescharacteristic
560C22#1171931311yescharacteristic
561C22#1171932612yes—
562C22#1171933312yes—
563C22#1171933311yescharacteristic
564C22#1171933411yescharacteristic
565C22#1171935112yes—
566C22#1171935212yes—
567C22#1171935311yescharacteristic
568C22#1171935612yes—
569C22#1171938011yescharacteristic
570C22C13⋊#56412yes—
571C22C13⋊#56412yes—
572C22#1171941712yes—
573C22#1171942911yescharacteristic
574C22#1171944012yes—
575C4—24no—
576C4—42no—
577C4—42no—
578C4—82no—
579C4—82no—
580C4—264no—
581C4—264no—
582C4—522no—
583C4—522no—
584C4—1042no—
585C4—1042no—
586C2#1311741911yescharacteristic
587C2#1311742311yescharacteristic
588C2#1311742511yescharacteristic
589C2#1311801812yes—
590C2#1311802012yes—
591C2#1312288512yes—
592C2#1312288911yescharacteristic
593C2#1312289111yescharacteristic
594C2#1312290212yes—
595C2#1312290511yescharacteristic
596C2#1312290611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1441C2
socle, prime radical, cosocleC24×C13C24
hypercenter#1441D13
hypocenterC13#14664
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
24. C2×#88143C4semidirect
471. C13#14664semidirect

Maximal subgroups

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

subgroupindex
C22×#881432
C2×#117186382
C2×#117183112
#131131022
#131130902
#131130892
#131130882
#131130872
#131130862
C13×#14412
#1466413