Finite Group Databasebeta

← #16023071

Subgroups — #16023071

Order 3328.

2342 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719227C211yesmaximal, characteristic
2#13117806C214yesmaximal, complemented
3#13117798C214yesmaximal, complemented
4#13117775C214yesmaximal, complemented
5#13117771C214yesmaximal, complemented
6#13117446C211yesmaximal, characteristic, complemented
7#13117445C211yesmaximal, characteristic, complemented
8#13117444C211yesmaximal, characteristic, complemented
9#13117425C212yesmaximal
10#13117241C211yesmaximal, characteristic, complemented
11#13117232C212yesmaximal, complemented
12#13117231C212yesmaximal, complemented
13D13×#382C211yesmaximal, characteristic, complemented
14#13117190C212yesmaximal, complemented
15C13×#2314C211yesmaximal, characteristic, complemented
16C22×#6127C2211yescharacteristic
17C2×C13×#117C2211yescharacteristic
18C22×C4×Dic13C2211yescharacteristic
19#11719227C4116yescomplemented
20C2×#88147C2212yes—
21C2×#88146C2212yes—
22C2×C4⋊C4×D13C2212yes—
23C2×#88141C2212yes—
24C2×#88135C2212yes—
25C2×#88135C2212yes—
26C2×#88126C2211yescharacteristic
27C2×#88126C2211yescharacteristic
28C2×C42×D13C2211yescharacteristic
29C2×C42×D13C2211yescharacteristic
30C13×#388C2214yes—
31C13×#387C2214yes—
32C13×#384C2211yescharacteristic
33C13×#382C2211yescharacteristic
34C13×#380C2212yes—
35C4×C13×C4⋊C4C2212yes—
36#11718873C2212yes—
37#11718651C2214yes—
38#11718648C2212yes—
39#11718648C2212yes—
40#11718648C2214yes—
41#11718642C2214yes—
42#11718639C2214yes—
43#11718638C2212yes—
44#11718638C2212yes—
45C4⋊C4×Dic13C2212yes—
46C4⋊C4×Dic13C2212yes—
47C4⋊C4×Dic13C2214yes—
48#11718618C2214yes—
49#11718617C2214yes—
50#11718612C2214yes—
51#11718604C2214yes—
52C22⋊C4×Dic13C2214yes—
53C4×#6103C2214yes—
54C4×#6103C2214yes—
55#11718597C2211yescharacteristic
56#11718596C2211yescharacteristic
57C4×C4⋊Dic13C2212yes—
58#11718593C2214yes—
59C4×#6101C2214yes—
60#11718331C2214yes—
61#11718327C2214yes—
62#11718326C2214yes—
63#11718325C2214yes—
64D13×#95C2214yes—
65#11718316C2214yes—
66#11718312C2214yes—
67#11718312C2214yes—
68#11718311C2214yes—
69#11718310C2214yes—
70#11718309C2214yes—
71#11718307C2214yes—
72C23×C4×C13C2311yescharacteristic
73C22×C22⋊D13C2311yescharacteristic
74C22×C22⋊D13C2311yescharacteristic
75C23×Dic13C2312yes—
76C2×#6127—24no—
77C2×#6127—24no—
78C2×#6127C2×C418yes—
79C22×D52C2311yescharacteristic
80C22×C4×D13C2311yescharacteristic
81C22×C4×D13C2314yes—
82C22×C4×D13C2312yes—
83C22×C4×D13C2312yes—
84C22×C4×D13C2311yescharacteristic
85C22×Dic26C2311yescharacteristic
86C13×#117C2×C418yescomplemented
87C2×C13×C4⋊C4C2312yes—
88C2×C13×C4⋊C4C2312yes—
89C2×C13×C4⋊C4C2314yes—
90C2×C13×C4⋊C4C2312yes—
91C2×C13×C22⋊C4C2314yes—
92C2×C13×C22⋊C4C2312yes—
93C2×C42×C13C2314yes—
94C2×C42×C13C2311yescharacteristic
95C2×C42×C13C2311yescharacteristic
96C2×C22⋊Dic13C2314yes—
97C2×#6103C2314yes—
98C2×#6103C2314yes—
99C2×#6103C2314yes—
100C2×#6103C2312yes—
101C2×#6103C2312yes—
102C2×C4⋊Dic13C2312yes—
103C2×C4⋊Dic13C2312yes—
104C2×C4⋊Dic13C2314yes—
105C2×#6101C2314yes—
106C2×#6101C2312yes—
107C2×#6101C2312yes—
108C2×C4×Dic13C2×C418yescomplemented
109C2×C4×Dic13C2314yes—
110C2×C4×Dic13C2314yes—
111C2×C4×Dic13C2314yes—
112C2×C4×Dic13C2314yes—
113C2×C4×Dic13C2311yescharacteristic
114C2×C4×Dic13C2312yes—
115C2×C4×Dic13C2312yes—
116C2×C4×Dic13C2311yescharacteristic
117C2×C4×Dic13C2312yes—
118#88147C2×C4116yes—
119#88146—28no—
120C4⋊C4×D13—28no—
121#88141C2×C4116yescomplemented
122#88135C2×C4116yes—
123#88135C2×C4116yescomplemented
124#88126C2×C418yes—
125#88126C2×C418yescomplemented
126C42×D13C2×C418yes—
127C42×D13C2×C418yescomplemented
128C13×#95C2314yes—
129C13×#95C2314yes—
130C13×#95C2314yes—
131#88071C2314yes—
132#88071C2314yes—
133#88071C2314yes—
134#88071C2314yes—
135#88071C2314yes—
136#88071C2314yes—
137#88071C2314yes—
138#88071C2314yes—
139#88071C2314yes—
140#88071C2314yes—
141#88071C2314yes—
142#34189—131nomaximal, Sylow
143C24×C13C2411yescharacteristic
144C23×D13C2411yescharacteristic
145C23×D13C2411yescharacteristic
146C22×C4×C13—22no—
147C22×C4×C13—22no—
148C22×C4×C13C22×C414yes—
149C22×C4×C13C2414yes—
150C22×C4×C13C2414yes—
151C22×C4×C13C2411yescharacteristic
152C22×C4×C13C2412yes—
153C22×C4×C13C2412yes—
154C22×C4×C13C2411yescharacteristic
155C2×C22⋊D13—22no—
156C2×C22⋊D13—22no—
157C2×C22⋊D13—22no—
158C2×C22⋊D13—22no—
159C2×C22⋊D13C22×C414yes—
160C2×C22⋊D13C22×C414yes—
161C22×Dic13—42no—
162C22×Dic13—42no—
163C22×Dic13C22×C418yes—
164C22×Dic13C2414yes—
165C22×Dic13C2414yes—
166C22×Dic13C2412yes—
167C22×Dic13C2411yescharacteristic
168C22×Dic13C2412yes—
169C22×Dic13C2411yescharacteristic
170#6127—232no—
171C2×D52—22no—
172C2×D52—22no—
173C2×D52C22×C414yes—
174C2×C4×D13—22no—
175C2×C4×D13—22no—
176C2×C4×D13—28no—
177C2×C4×D13—42no—
178C2×C4×D13—42no—
179C2×C4×D13—42no—
180C2×C4×D13—42no—
181C2×C4×D13—44no—
182C2×C4×D13—44no—
183C2×C4×D13C22×C414yes—
184C2×C4×D13C22×C418yes—
185C2×C4×D13C22×C418yes—
186C2×C4×D13C22×C414yes—
187C2×C4×D13#4114yes—
188C2×C4×D13#4114yes—
189C2×Dic26—22no—
190C2×Dic26—22no—
191C2×Dic26C22×C414yes—
192C13×C4⋊C4—24no—
193C13×C4⋊C4—24no—
194C13×C4⋊C4—44no—
195C13×C4⋊C4C22×C418yes—
196C13×C22⋊C4—44no—
197C13×C22⋊C4C22×C418yes—
198C42×C13—44no—
199C42×C13C22×C414yes—
200C42×C13C22×C414yes—
201C22⋊Dic13—44no—
202#6103—28no—
203#6103—44no—
204#6103—44no—
205#6103C22×C418yes—
206#6103C22×C418yes—
207C4⋊Dic13—24no—
208C4⋊Dic13—24no—
209C4⋊Dic13—44no—
210#6101—28no—
211#6101C22×C418yes—
212#6101C22×C418yes—
213C4×Dic13—28no—
214C4×Dic13—44no—
215C4×Dic13—44no—
216C4×Dic13—44no—
217C4×Dic13C22×C414yes—
218C4×Dic13C22×C418yes—
219C4×Dic13C22×C418yes—
220C4×Dic13C22×C414yes—
221C4×Dic13C22×C418yes—
222C2×C4×#41—131no—
223#2357—134no—
224#2356—134no—
225#2353—134no—
226#2353—134no—
227#2314—131no—
228#2314—131no—
229#2314—131no—
230#2314D1311yescharacteristic, complemented
231#2311—132no—
232#2285—131no—
233#2283—132no—
234#2283—132no—
235C2×#382—131no—
236#2274—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×D13C23×C412yes—
250C22×D13C23×C412yes—
251C22×D13C2×#4112yes—
252C22×D13C2×#4112yes—
253C2×C4×C13—21no—
254C2×C4×C13—21no—
255C2×C4×C13—22no—
256C2×C4×C13—22no—
257C2×C4×C13—22no—
258C2×C4×C13—22no—
259C2×C4×C13—28no—
260C2×C4×C13—24no—
261C2×C4×C13—24no—
262C2×C4×C13—24no—
263C2×C4×C13—24no—
264C2×C4×C13—24no—
265C2×C4×C13—24no—
266C2×C4×C13C23×C412yes—
267C2×C4×C13C23×C414yes—
268C2×C4×C13C23×C414yes—
269C2×C4×C13C23×C412yes—
270C2×C4×C13C2×#4112yes—
271C2×C4×C13C2×#4112yes—
272C22⋊D13—28no—
273C22⋊D13—28no—
274C2×Dic13—21no—
275C2×Dic13—21no—
276C2×Dic13—22no—
277C2×Dic13—22no—
278C2×Dic13—22no—
279C2×Dic13—22no—
280C2×Dic13—24no—
281C2×Dic13—24no—
282C2×Dic13—24no—
283C2×Dic13—24no—
284C2×Dic13—24no—
285C2×Dic13—24no—
286C2×Dic13—48no—
287C2×Dic13C23×C414yes—
288C2×Dic13C23×C414yes—
289C2×Dic13C23×C412yes—
290C2×Dic13C23×C412yes—
291C2×Dic13C2×#4112yes—
292C2×Dic13C2×#4112yes—
293D52—28no—
294C4×D13—28no—
295C4×D13—48no—
296C4×D13—48no—
297C4×D13—88no—
298C4×D13#117116yes—
299Dic26—28no—
300C22×#41—131no—
301C4×#41—1316no—
302C2×C4×Q8—132no—
303C2×C4×D4—132no—
304C2×C4×D4—132no—
305C2×C4×D4—132no—
306C2×#117—132no—
307C2×#117—131no—
308C2×#117—131no—
309C2×#117C2×D1311yescharacteristic
310C22×C4⋊C4—132no—
311C22×C42—131no—
312C22×C42—131no—
313C22×C42—131no—
314#391—134no—
315#390—134no—
316#388—134no—
317#388—134no—
318#388—134no—
319#388C2×D1314yes—
320#387—134no—
321#387—134no—
322#387—134no—
323#387C2×D1314yes—
324#386—134no—
325#386—134no—
326#384—131no—
327#384C2×D1311yescharacteristic
328#383—134no—
329#383—134no—
330#382—132no—
331#382—132no—
332#382—131no—
333#382—134no—
334#382C2×D1311yescharacteristic
335#381—134no—
336#381—134no—
337#380—132no—
338#380—132no—
339#380—132no—
340#380—134no—
341#380C2×D1312yes—
342C4×C4⋊C4—132no—
343C4×C4⋊C4—132no—
344C4×C4⋊C4—134no—
345C4×C4⋊C4—132no—
346C4×C4⋊C4—134no—
347C4×C4⋊C4—134no—
348C4×C4⋊C4C2×D1312yes—
349C4×C22⋊C4—134no—
350C4×C22⋊C4—134no—
351C4×C22⋊C4—134no—
352C4×C22⋊C4—134no—
353#376—134no—
354#376—134no—
355C2×#95—134no—
356C22×C13—22no—
357C22×C13—24no—
358C22×C13—42no—
359C22×C13—41no—
360C22×C13—41no—
361C22×C13C24×C411yescharacteristic
362C22×C13C22×#4111yescharacteristic
363C22×C13C22×#4111yescharacteristic
364C22×C13#58512yes—
365C22×C13#58512yes—
366C2×D13—24no—
367C2×D13—24no—
368C2×D13—22no—
369C2×D13—22no—
370C2×D13—22no—
371C2×D13—24no—
372C2×D13—42no—
373C2×D13—41no—
374C2×D13—41no—
375C2×D13C2×#11714yes—
376C4×C13—22no—
377C4×C13—24no—
378C4×C13—24no—
379C4×C13—44no—
380C4×C13—44no—
381C4×C13C2×#11714yes—
382Dic13—22no—
383Dic13—24no—
384Dic13—24no—
385Dic13—44no—
386Dic13—44no—
387Dic13C2×#11714yes—
388C2×#41—138no—
389C2×#41—264no—
390C2×#41—264no—
391C22×Q8—131no—
392C22×D4—131no—
393C22×D4—131no—
394C22×D4—131no—
395C23×C4—131no—
396C23×C4—132no—
397C23×C4—131no—
398C23×C4—132no—
399C23×C4—132no—
400C23×C4—134no—
401C23×C4C22×D1311yescharacteristic
402C4×Q8—1316no—
403C4×D4—1316no—
404C4×D4—1316no—
405C4×D4—1316no—
406#117—138no—
407#117—138no—
408#117—268no—
409#117C4×D1318yescomplemented
410C2×C4⋊C4—132no—
411C2×C4⋊C4—132no—
412C2×C4⋊C4—134no—
413C2×C4⋊C4—132no—
414C2×C4⋊C4—132no—
415C2×C4⋊C4—134no—
416C2×C4⋊C4—268no—
417C2×C4⋊C4C22×D1312yes—
418C2×C4⋊C4C22×D1312yes—
419C2×C4⋊C4C22×D1314yes—
420C2×C4⋊C4C22×D1312yes—
421C2×C22⋊C4—132no—
422C2×C22⋊C4—132no—
423C2×C22⋊C4—134no—
424C2×C22⋊C4—134no—
425C2×C22⋊C4—134no—
426C2×C22⋊C4—134no—
427C2×C22⋊C4C22×D1314yes—
428C2×C22⋊C4C22×D1312yes—
429C2×C42—138no—
430C2×C42—131no—
431C2×C42—132no—
432C2×C42—132no—
433C2×C42—132no—
434C2×C42—131no—
435C2×C42—138no—
436C2×C42—138no—
437C2×C42—134no—
438C2×C42—134no—
439C2×C42—134no—
440C2×C42—134no—
441C2×C42C22×D1314yes—
442C2×C42C22×D1311yescharacteristic
443C2×C42C22×D1311yescharacteristic
444#95—134no—
445#95—134no—
446#95—134no—
447#95—134no—
448#95—134no—
449#95—134no—
450#95—134no—
451#95—134no—
452#95—134no—
453#95—134no—
454#95—134no—
455#95C22×D1314yes—
456#95C22×D1314yes—
457#95C22×D1314yes—
458C2×C13—42no—
459C2×C13C22×#11711yescharacteristic
460C2×C13#342812yes—
461C2×C13#351012yes—
462C2×C13#351211yescharacteristic
463C2×C13#351211yescharacteristic
464D13—24no—
465D13—42no—
466C24—131no—
467C24—131no—
468C24C23×D1311yescharacteristic
469#41—2632no—
470C2×Q8—134no—
471C2×Q8—262no—
472C2×Q8—262no—
473C2×D4—134no—
474C2×D4—134no—
475C2×D4—134no—
476C2×D4—262no—
477C2×D4—262no—
478C2×D4—262no—
479C2×D4—262no—
480C2×D4—262no—
481C2×D4—262no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—131no—
485C22×C4—134no—
486C22×C4—134no—
487C22×C4—134no—
488C22×C4—132no—
489C22×C4—131no—
490C22×C4—132no—
491C22×C4—138no—
492C22×C4—134no—
493C22×C4—138no—
494C22×C4—138no—
495C22×C4—134no—
496C22×C4—134no—
497C22×C4—268no—
498C22×C4—262no—
499C22×C4—262no—
500C22×C4—522no—
501C22×C4—522no—
502C22×C4—522no—
503C22×C4—522no—
504C22×C4—524no—
505C22×C4—524no—
506C22×C4—522no—
507C22×C4—522no—
508C22×C4C2×C4×D1314yes—
509C22×C4C23×D1314yes—
510C22×C4C23×D1314yes—
511C22×C4C23×D1311yescharacteristic
512C22×C4C23×D1312yes—
513C22×C4C23×D1312yes—
514C22×C4C23×D1311yescharacteristic
515C4⋊C4—24no—
516C4⋊C4—24no—
517C4⋊C4—44no—
518C4⋊C4—138no—
519C4⋊C4—138no—
520C4⋊C4—268no—
521C4⋊C4—264no—
522C4⋊C4—264no—
523C4⋊C4—524no—
524C4⋊C4C2×C4×D1318yes—
525C22⋊C4—44no—
526C22⋊C4—138no—
527C22⋊C4—138no—
528C22⋊C4—268no—
529C22⋊C4—524no—
530C22⋊C4—524no—
531C22⋊C4—524no—
532C22⋊C4C2×C4×D1318yes—
533C42—44no—
534C42—134no—
535C42—134no—
536C42—138no—
537C42—138no—
538C42—138no—
539C42—268no—
540C42—524no—
541C42—524no—
542C42—524no—
543C42C2×C4×D1314yes—
544C42C2×C4×D1314yes—
545C13#3418911yescharacteristic, complemented, Sylow
546C23—21no—
547C23—21no—
548C23—22no—
549C23—22no—
550C23—132no—
551C23—132no—
552C23—132no—
553C23—132no—
554C23—262no—
555C23—262no—
556C23—261no—
557C23—261no—
558C23—262no—
559C23—262no—
560C23C22×C4×D1312yes—
561C23C24×D1311yescharacteristic
562Q8—268no—
563D4—268no—
564D4—268no—
565D4—268no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—28no—
573C2×C4—24no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—132no—
580C2×C4—132no—
581C2×C4—132no—
582C2×C4—1316no—
583C2×C4—134no—
584C2×C4—134no—
585C2×C4—132no—
586C2×C4—261no—
587C2×C4—261no—
588C2×C4—262no—
589C2×C4—262no—
590C2×C4—262no—
591C2×C4—262no—
592C2×C4—268no—
593C2×C4—264no—
594C2×C4—264no—
595C2×C4—264no—
596C2×C4—264no—
597C2×C4—264no—
598C2×C4—264no—
599C2×C4—528no—
600C2×C4—528no—
601C2×C4—528no—
602C2×C4—1048no—
603C2×C4C22×C4×D1312yes—
604C2×C4C22×C4×D1314yes—
605C2×C4C22×C4×D1314yes—
606C2×C4C22×C4×D1312yes—
607C2×C4#41×D1312yes—
608C2×C4#41×D1312yes—
609C22—22no—
610C22—24no—
611C22—42no—
612C22—41no—
613C22—41no—
614C22—134no—
615C22—264no—
616C22—262no—
617C22—262no—
618C22—264no—
619C22—262no—
620C22—264no—
621C22—522no—
622C22—521no—
623C22—521no—
624C22C23×C4×D1311yescharacteristic
625C22C2×#41×D1311yescharacteristic
626C22C2×#41×D1311yescharacteristic
627C22#1171965012yes—
628C22#1171965212yes—
629C4—22no—
630C4—24no—
631C4—24no—
632C4—44no—
633C4—44no—
634C4—134no—
635C4—262no—
636C4—264no—
637C4—264no—
638C4—524no—
639C4—524no—
640C4D13×#11714yes—
641C2—42no—
642C2—264no—
643C2—522no—
644C2C2×D13×#11711yescharacteristic
645C2#1312803612yes—
646C2#1312872812yes—
647C2#1312875511yescharacteristic
648C2#1312875911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D13
commutatorC22×C13C24×C4
FittingC13×#2314C2
socle, cosocleC23×C13C25
prime radicalC22×#6127C22
hypercenter#2314D13
hypocenterC13#34189
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ #2314

Complements

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

NH ≅ G/Ntype
2. #13117806C2semidirect
3. #13117798C2semidirect
4. #13117775C2semidirect
5. #13117771C2semidirect
6. #13117446C2semidirect
7. #13117445C2semidirect
8. #13117444C2semidirect
10. #13117241C2semidirect
11. #13117232C2semidirect
12. #13117231C2semidirect
13. D13×#382C2semidirect
14. #13117190C2semidirect
15. C13×#2314C2semidirect
19. #11719227C4semidirect
86. C13×#117C2×C4semidirect
108. C2×C4×Dic13C2×C4semidirect
121. #88141C2×C4semidirect
123. #88135C2×C4semidirect
125. #88126C2×C4semidirect
127. C42×D13C2×C4semidirect
230. #2314D13semidirect
409. #117C4×D13semidirect
545. C13#34189semidirect

Maximal subgroups

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

subgroupindex
C2×#117192272
#131178062
#131177982
#131177752
#131177712
#131174462
#131174452
#131174442
#131174252
#131172412
#131172322
#131172312
D13×#3822
#131171902
C13×#23142
#3418913