Finite Group Databasebeta

← #16021518

Subgroups — #16021518

Order 3328.

2390 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D13×#117C211yesmaximal, characteristic
2#13117446C211yesmaximal, characteristic, complemented
3#13117445C211yesmaximal, characteristic, complemented
4#13117444C211yesmaximal, characteristic, complemented
5#13117443C212yesmaximal, complemented
6#13117441C212yesmaximal, complemented
7#13117435C214yesmaximal, complemented
8#13117430C214yesmaximal
9#13117330C214yesmaximal, complemented
10#13117328C214yesmaximal, complemented
11#13117242C211yesmaximal, characteristic, complemented
12#13117241C211yesmaximal, characteristic, complemented
13#13117218C212yesmaximal
14C4×#88146C212yesmaximal, complemented
15C13×#2314C211yesmaximal, characteristic, complemented
16C23×C4×D13C2211yescharacteristic
17C2×C13×#117C2211yescharacteristic
18C2×#88180C2211yescharacteristic
19D13×#117C4116yescomplemented
20C2×#88146C2212yes—
21C2×#88146C2212yes—
22C2×#88146C2212yes—
23C2×C4⋊C4×D13C2212yes—
24C2×C22⋊C4×D13C2212yes—
25C2×#88131C2212yes—
26C2×#88126C2211yescharacteristic
27C2×#88126C2211yescharacteristic
28C2×C42×D13C2211yescharacteristic
29C2×C42×D13C2211yescharacteristic
30C13×#388C2214yes—
31C13×#387C2214yescomplemented
32C13×#384C2211yescharacteristic, complemented
33C13×#382C2211yescharacteristic, complemented
34C13×#380C2212yes—
35C4×C13×C4⋊C4C2212yescomplemented
36#11718873C2212yes—
37#11718651C2214yes—
38#11718648C2212yes—
39#11718648C2212yes—
40#11718648C2214yes—
41#11718642C2214yescomplemented
42#11718639C2214yescomplemented
43#11718638C2212yescomplemented
44#11718637C2212yescomplemented
45C4⋊C4×Dic13C2212yescomplemented
46C4⋊C4×Dic13C2212yescomplemented
47C4⋊C4×Dic13C2214yescomplemented
48#11718616C2214yes—
49#11718612C2214yes—
50#11718606C2214yes—
51#11718605C2214yes—
52C22⋊C4×Dic13C2214yes—
53#11718601C2214yes—
54C4×#6103C2214yes—
55#11718597C2211yescharacteristic, complemented
56#11718596C2211yescharacteristic, complemented
57C4×C4⋊Dic13C2212yescomplemented
58#11718594C2214yescomplemented
59C42×Dic13C2214yescomplemented
60#11718331C2214yes—
61#11718330C2214yes—
62#11718328C2214yes—
63#11718327C2214yes—
64#11718327C2214yes—
65#11718325C2214yes—
66#11718316C2214yescomplemented
67#11718315C2214yescomplemented
68#11718314C2214yescomplemented
69#11718313C2214yescomplemented
70#11718310C2214yescomplemented
71#11718309C2214yescomplemented
72C24×D13C2311yescharacteristic
73C23×C4×C13C2311yescharacteristic
74C23×Dic13C2311yescharacteristic
75C22×C4×D13—24no—
76C22×C4×D13—24no—
77C22×C4×D13C2×C418yes—
78C22×C4×D13C2311yescharacteristic
79C22×C4×D13C2311yescharacteristic
80C22×C4×D13C2311yescharacteristic
81C22×C4×D13C2312yes—
82C22×C4×D13C2312yes—
83C22×C4×D13C2311yescharacteristic
84C13×#117C2×C418yes—
85C2×C13×C4⋊C4C2312yes—
86C2×C13×C4⋊C4C2312yes—
87C2×C13×C4⋊C4C2314yes—
88C2×C13×C4⋊C4C2312yes—
89C2×C13×C22⋊C4C2314yes—
90C2×C13×C22⋊C4C2312yes—
91C2×C42×C13C2314yes—
92C2×C42×C13C2311yescharacteristic
93C2×C42×C13C2311yescharacteristic
94C2×C22⋊Dic13C2314yes—
95C2×C22⋊Dic13C2312yes—
96C2×#6103C2314yes—
97C2×#6103C2314yes—
98C2×#6103C2314yes—
99C2×#6103C2314yes—
100C2×#6103C2312yes—
101C2×#6103C2312yes—
102#88180C2×C418yes—
103C2×C4⋊Dic13C2312yes—
104C2×C4⋊Dic13C2312yes—
105C2×C4⋊Dic13C2314yes—
106C2×C4⋊Dic13C2312yes—
107C2×#6101C2314yes—
108C2×#6101C2314yes—
109C2×#6101C2312yes—
110C2×#6101C2312yes—
111C2×C4×Dic13C2314yes—
112C2×C4×Dic13C2314yes—
113C2×C4×Dic13C2314yes—
114C2×C4×Dic13C2314yes—
115C2×C4×Dic13C2314yes—
116C2×C4×Dic13C2311yescharacteristic
117C2×C4×Dic13C2311yescharacteristic
118C2×C4×Dic13C2312yes—
119C2×C4×Dic13C2312yes—
120#88146—28no—
121#88146—28no—
122#88146C2×C4116yes—
123C4⋊C4×D13C2×C4116yes—
124C22⋊C4×D13C2×C4116yes—
125#88131C2×C4116yes—
126#88126C2×C418yes—
127#88126C2×C418yes—
128C42×D13C2×C418yes—
129C42×D13C2×C418yes—
130C13×#95C2314yes—
131C13×#95C2314yes—
132C13×#95C2314yes—
133#88071C2314yes—
134#88071C2314yes—
135#88071C2314yes—
136#88071C2314yes—
137#88071C2314yes—
138#88071C2314yes—
139#88071C2314yes—
140#88071C2314yes—
141#88071C2314yes—
142#34048—131nomaximal, Sylow
143C24×C13C2411yescharacteristic
144C23×D13—22no—
145C23×D13—22no—
146C23×D13—42no—
147C23×D13—42no—
148C23×D13C22×C414yes—
149C23×D13C2411yescharacteristic
150C23×D13C2411yescharacteristic
151C22×C4×C13—22no—
152C22×C4×C13—22no—
153C22×C4×C13C22×C414yes—
154C22×C4×C13C2414yes—
155C22×C4×C13C2414yes—
156C22×C4×C13C2411yescharacteristic
157C22×C4×C13C2412yes—
158C22×C4×C13C2412yes—
159C22×C4×C13C2411yescharacteristic
160C22×Dic13—22no—
161C22×Dic13—22no—
162C22×Dic13C22×C414yes—
163C22×Dic13C2414yes—
164C22×Dic13C2414yes—
165C22×Dic13C2411yescharacteristic
166C22×Dic13C2412yes—
167C22×Dic13C2412yes—
168C22×Dic13C2411yescharacteristic
169C2×C4×D13—22no—
170C2×C4×D13—22no—
171C2×C4×D13—22no—
172C2×C4×D13—22no—
173C2×C4×D13—22no—
174C2×C4×D13—22no—
175C2×C4×D13—232no—
176C2×C4×D13—42no—
177C2×C4×D13—42no—
178C2×C4×D13—42no—
179C2×C4×D13—42no—
180C2×C4×D13C22×C414yes—
181C2×C4×D13C22×C414yes—
182C2×C4×D13C22×C414yes—
183C2×C4×D13C22×C418yes—
184C2×C4×D13C22×C418yes—
185C2×C4×D13C22×C414yes—
186C2×C4×D13#4114yes—
187C2×C4×D13#4114yes—
188C13×C4⋊C4—24no—
189C13×C4⋊C4—24no—
190C13×C4⋊C4—44no—
191C13×C4⋊C4C22×C418yes—
192C13×C22⋊C4—44no—
193C13×C22⋊C4C22×C418yes—
194C42×C13—44no—
195C42×C13C22×C414yes—
196C42×C13C22×C414yes—
197C22⋊Dic13—44no—
198C22⋊Dic13C22×C418yes—
199#6103—28no—
200#6103—28no—
201#6103—44no—
202#6103—44no—
203#6103C22×C418yes—
204#6103C22×C418yes—
205C4⋊Dic13—24no—
206C4⋊Dic13—24no—
207C4⋊Dic13—44no—
208C4⋊Dic13C22×C418yes—
209#6101—44no—
210#6101—44no—
211#6101C22×C418yes—
212#6101C22×C418yes—
213C4×Dic13—28no—
214C4×Dic13—28no—
215C4×Dic13—44no—
216C4×Dic13—44no—
217C4×Dic13—44no—
218C4×Dic13C22×C414yes—
219C4×Dic13C22×C414yes—
220C4×Dic13C22×C418yes—
221C4×Dic13C22×C418yes—
222C22×#117—131no—
223#2314—131no—
224#2314—131no—
225#2314—132no—
226#2314—132no—
227#2314—131no—
228#2314D1311yescharacteristic, complemented
229#2313—134no—
230#2312—134no—
231#2298—134no—
232#2298—134no—
233#2285—131no—
234#2285—131no—
235#2280—132no—
236C4×#117—132no—
237C23×C13—21no—
238C23×C13—21no—
239C23×C13—22no—
240C23×C13—22no—
241C23×C13C23×C412yes—
242C23×C13C2511yescharacteristic
243C22×D13—22no—
244C22×D13—22no—
245C22×D13—21no—
246C22×D13—21no—
247C22×D13—22no—
248C22×D13—22no—
249C22×D13—28no—
250C22×D13—48no—
251C22×D13—44no—
252C22×D13—48no—
253C22×D13—44no—
254C22×D13C23×C412yes—
255C22×D13C23×C412yes—
256C22×D13C2×#4112yes—
257C22×D13C2×#4112yes—
258C2×C4×C13—21no—
259C2×C4×C13—21no—
260C2×C4×C13—22no—
261C2×C4×C13—22no—
262C2×C4×C13—22no—
263C2×C4×C13—22no—
264C2×C4×C13—28no—
265C2×C4×C13—24no—
266C2×C4×C13—24no—
267C2×C4×C13—24no—
268C2×C4×C13—24no—
269C2×C4×C13—24no—
270C2×C4×C13—24no—
271C2×C4×C13C23×C414yes—
272C2×C4×C13C23×C414yes—
273C2×C4×C13C23×C412yes—
274C2×C4×C13C23×C412yes—
275C2×C4×C13C2×#4112yes—
276C2×C4×C13C2×#4112yes—
277C2×Dic13—21no—
278C2×Dic13—21no—
279C2×Dic13—22no—
280C2×Dic13—22no—
281C2×Dic13—22no—
282C2×Dic13—22no—
283C2×Dic13—28no—
284C2×Dic13—24no—
285C2×Dic13—24no—
286C2×Dic13—24no—
287C2×Dic13—24no—
288C2×Dic13—24no—
289C2×Dic13—24no—
290C2×Dic13C23×C414yes—
291C2×Dic13C23×C414yes—
292C2×Dic13C23×C412yes—
293C2×Dic13C23×C412yes—
294C2×Dic13C2×#4112yes—
295C2×Dic13C2×#4112yes—
296C4×D13—28no—
297C4×D13—28no—
298C4×D13—28no—
299C4×D13—48no—
300C4×D13—48no—
301C4×D13#117116yes—
302C24×C4—131no—
303C2×#117—131no—
304C2×#117—1316no—
305C2×#117—132no—
306C2×#117—132no—
307C2×#117—132no—
308C2×#117—132no—
309C2×#117—131no—
310C2×#117—131no—
311C2×#117C2×D1311yescharacteristic
312C22×C4⋊C4—132no—
313C22×C22⋊C4—132no—
314C22×C42—131no—
315C22×C42—131no—
316#388—134no—
317#388—134no—
318#388—134no—
319#388—134no—
320#388—134no—
321#388—134no—
322#388—134no—
323#388C2×D1314yes—
324#387—134no—
325#387—134no—
326#387—134no—
327#387—134no—
328#387—134no—
329#387—134no—
330#387—134no—
331#387C2×D1314yescomplemented
332#384—132no—
333#384—131no—
334#384C2×D1311yescharacteristic, complemented
335#382—132no—
336#382—131no—
337#382C2×D1311yescharacteristic, complemented
338#381—134no—
339#380—132no—
340#380—134no—
341#380—132no—
342#380—132no—
343#380—134no—
344#380C2×D1312yes—
345#379—134no—
346C4×C4⋊C4—132no—
347C4×C4⋊C4—132no—
348C4×C4⋊C4—134no—
349C4×C4⋊C4—132no—
350C4×C4⋊C4—134no—
351C4×C4⋊C4C2×D1312yescomplemented
352C4×C22⋊C4—134no—
353C4×C22⋊C4—134no—
354C4×C22⋊C4—134no—
355C4×C22⋊C4—134no—
356#376—134no—
357C43—134no—
358C22×C13—22no—
359C22×C13—24no—
360C22×C13—41no—
361C22×C13—42no—
362C22×C13—41no—
363C22×C13C24×C411yescharacteristic
364C22×C13C22×#4111yescharacteristic
365C22×C13C22×#4111yescharacteristic
366C22×C13#58512yes—
367C22×C13#58512yes—
368C2×D13—24no—
369C2×D13—22no—
370C2×D13—24no—
371C2×D13—22no—
372C2×D13—22no—
373C2×D13—24no—
374C2×D13—416no—
375C2×D13—41no—
376C2×D13—42no—
377C2×D13—41no—
378C2×D13C2×#11714yes—
379C4×C13—22no—
380C4×C13—24no—
381C4×C13—24no—
382C4×C13—44no—
383C4×C13—44no—
384C4×C13C2×#11714yes—
385Dic13—22no—
386Dic13—24no—
387Dic13—24no—
388Dic13—44no—
389Dic13—44no—
390Dic13C2×#11714yes—
391C25—131no—
392C23×C4—131no—
393C23×C4—131no—
394C23×C4—138no—
395C23×C4—131no—
396C23×C4—131no—
397C23×C4—131no—
398C23×C4—132no—
399C23×C4—132no—
400C23×C4—264no—
401C23×C4—264no—
402C23×C4C22×D1311yescharacteristic
403#117—138no—
404#117—1316no—
405#117—1316no—
406#117—138no—
407#117—138no—
408#117—268no—
409#117—268no—
410#117C4×D1318yes—
411C2×C4⋊C4—132no—
412C2×C4⋊C4—132no—
413C2×C4⋊C4—132no—
414C2×C4⋊C4—1316no—
415C2×C4⋊C4—132no—
416C2×C4⋊C4—132no—
417C2×C4⋊C4—134no—
418C2×C4⋊C4—134no—
419C2×C4⋊C4—134no—
420C2×C4⋊C4C22×D1312yes—
421C2×C4⋊C4C22×D1312yes—
422C2×C4⋊C4C22×D1314yes—
423C2×C4⋊C4C22×D1312yes—
424C2×C22⋊C4—132no—
425C2×C22⋊C4—132no—
426C2×C22⋊C4—132no—
427C2×C22⋊C4—1316no—
428C2×C22⋊C4—134no—
429C2×C22⋊C4—134no—
430C2×C22⋊C4—134no—
431C2×C22⋊C4—134no—
432C2×C22⋊C4—134no—
433C2×C22⋊C4C22×D1314yes—
434C2×C22⋊C4C22×D1312yes—
435C2×C42—132no—
436C2×C42—132no—
437C2×C42—131no—
438C2×C42—131no—
439C2×C42—138no—
440C2×C42—138no—
441C2×C42—134no—
442C2×C42—134no—
443C2×C42—134no—
444C2×C42—134no—
445C2×C42—134no—
446C2×C42C22×D1314yes—
447C2×C42C22×D1311yescharacteristic
448C2×C42C22×D1311yescharacteristic
449#95—134no—
450#95—134no—
451#95—134no—
452#95—134no—
453#95—134no—
454#95—134no—
455#95—134no—
456#95—134no—
457#95—134no—
458#95C22×D1314yes—
459#95C22×D1314yes—
460#95C22×D1314yes—
461C2×C13—42no—
462C2×C13C22×#11711yescharacteristic
463C2×C13#342812yes—
464C2×C13#345511yescharacteristic
465C2×C13#345512yes—
466C2×C13#345511yescharacteristic
467D13—24no—
468D13—42no—
469C24—131no—
470C24—131no—
471C24—134no—
472C24—262no—
473C24—262no—
474C24—522no—
475C24—522no—
476C24C23×D1311yescharacteristic
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—131no—
480C22×C4—134no—
481C22×C4—134no—
482C22×C4—134no—
483C22×C4—134no—
484C22×C4—131no—
485C22×C4—132no—
486C22×C4—132no—
487C22×C4—134no—
488C22×C4—134no—
489C22×C4—134no—
490C22×C4—138no—
491C22×C4—138no—
492C22×C4—134no—
493C22×C4—134no—
494C22×C4—262no—
495C22×C4—262no—
496C22×C4—2632no—
497C22×C4—262no—
498C22×C4—262no—
499C22×C4—262no—
500C22×C4—262no—
501C22×C4—262no—
502C22×C4—262no—
503C22×C4—522no—
504C22×C4—522no—
505C22×C4—522no—
506C22×C4—522no—
507C22×C4C2×C4×D1314yes—
508C22×C4C23×D1314yes—
509C22×C4C23×D1314yes—
510C22×C4C23×D1311yescharacteristic
511C22×C4C23×D1312yes—
512C22×C4C23×D1312yes—
513C22×C4C23×D1311yescharacteristic
514C4⋊C4—24no—
515C4⋊C4—24no—
516C4⋊C4—44no—
517C4⋊C4—138no—
518C4⋊C4—138no—
519C4⋊C4—138no—
520C4⋊C4—264no—
521C4⋊C4—264no—
522C4⋊C4—524no—
523C4⋊C4—524no—
524C4⋊C4—524no—
525C4⋊C4C2×C4×D1318yes—
526C22⋊C4—44no—
527C22⋊C4—138no—
528C22⋊C4—138no—
529C22⋊C4—138no—
530C22⋊C4—268no—
531C22⋊C4—268no—
532C22⋊C4—524no—
533C22⋊C4—524no—
534C22⋊C4—524no—
535C22⋊C4C2×C4×D1318yes—
536C42—44no—
537C42—138no—
538C42—138no—
539C42—134no—
540C42—134no—
541C42—268no—
542C42—268no—
543C42—524no—
544C42—524no—
545C42—524no—
546C42C2×C4×D1314yes—
547C42C2×C4×D1314yes—
548C13#3404811yescharacteristic, complemented, Sylow
549C23—21no—
550C23—21no—
551C23—22no—
552C23—22no—
553C23—132no—
554C23—132no—
555C23—132no—
556C23—132no—
557C23—268no—
558C23—262no—
559C23—262no—
560C23—261no—
561C23—261no—
562C23—262no—
563C23—262no—
564C23—528no—
565C23—524no—
566C23—528no—
567C23—524no—
568C23C22×C4×D1312yes—
569C23C24×D1311yescharacteristic
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—28no—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—24no—
580C2×C4—24no—
581C2×C4—24no—
582C2×C4—24no—
583C2×C4—132no—
584C2×C4—132no—
585C2×C4—132no—
586C2×C4—1316no—
587C2×C4—134no—
588C2×C4—134no—
589C2×C4—132no—
590C2×C4—268no—
591C2×C4—268no—
592C2×C4—268no—
593C2×C4—261no—
594C2×C4—261no—
595C2×C4—262no—
596C2×C4—262no—
597C2×C4—262no—
598C2×C4—262no—
599C2×C4—268no—
600C2×C4—264no—
601C2×C4—264no—
602C2×C4—264no—
603C2×C4—264no—
604C2×C4—264no—
605C2×C4—264no—
606C2×C4—528no—
607C2×C4—528no—
608C2×C4C22×C4×D1314yes—
609C2×C4C22×C4×D1314yes—
610C2×C4C22×C4×D1312yes—
611C2×C4C22×C4×D1312yes—
612C2×C4#41×D1312yes—
613C2×C4#41×D1312yes—
614C22—22no—
615C22—24no—
616C22—41no—
617C22—42no—
618C22—41no—
619C22—134no—
620C22—262no—
621C22—264no—
622C22—262no—
623C22—264no—
624C22—262no—
625C22—264no—
626C22—5216no—
627C22—521no—
628C22—522no—
629C22—521no—
630C22C23×C4×D1311yescharacteristic
631C22C2×#41×D1311yescharacteristic
632C22C2×#41×D1311yescharacteristic
633C22#1171965012yes—
634C22#1171965212yes—
635C4—22no—
636C4—24no—
637C4—24no—
638C4—44no—
639C4—44no—
640C4—134no—
641C4—262no—
642C4—264no—
643C4—264no—
644C4—524no—
645C4—524no—
646C4D13×#11714yes—
647C2—42no—
648C2—264no—
649C2—522no—
650C2C2×D13×#11711yescharacteristic
651C2#1312803612yes—
652C2#1312822011yescharacteristic
653C2#1312822312yes—
654C2#1312822711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D13
commutatorC22×C13C24×C4
FittingC13×#2314C2
socle, cosocleC23×C13C25
prime radicalC24×D13C23
hypercenter#2314D13
hypocenterC13#34048
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ #2314

Complements

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

NH ≅ G/Ntype
2. #13117446C2semidirect
3. #13117445C2semidirect
4. #13117444C2semidirect
5. #13117443C2semidirect
6. #13117441C2semidirect
7. #13117435C2semidirect
9. #13117330C2semidirect
10. #13117328C2semidirect
11. #13117242C2semidirect
12. #13117241C2semidirect
14. C4×#88146C2semidirect
15. C13×#2314C2semidirect
19. D13×#117C4semidirect
31. C13×#387C22semidirect
32. C13×#384C22semidirect
33. C13×#382C22semidirect
35. C4×C13×C4⋊C4C22semidirect
41. #11718642C22semidirect
42. #11718639C22semidirect
43. #11718638C22semidirect
44. #11718637C22semidirect
45. C4⋊C4×Dic13C22semidirect
46. C4⋊C4×Dic13C22semidirect
47. C4⋊C4×Dic13C22semidirect
55. #11718597C22semidirect
56. #11718596C22semidirect
57. C4×C4⋊Dic13C22semidirect
58. #11718594C22semidirect
59. C42×Dic13C22semidirect
66. #11718316C22semidirect
67. #11718315C22semidirect
68. #11718314C22semidirect
69. #11718313C22semidirect
70. #11718310C22semidirect
71. #11718309C22semidirect
228. #2314D13semidirect
331. #387C2×D13semidirect
334. #384C2×D13semidirect
337. #382C2×D13semidirect
351. C4×C4⋊C4C2×D13semidirect
548. C13#34048semidirect

Maximal subgroups

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

subgroupindex
C2×D13×#1172
#131174462
#131174452
#131174442
#131174432
#131174412
#131174352
#131174302
#131173302
#131173282
#131172422
#131172412
#131172182
C4×#881462
C13×#23142
#3404813