Finite Group Databasebeta

← #15794273

Subgroups — #15794273

Order 3328.

1770 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88133C211yesmaximal, characteristic
2C2×#11718312C211yesmaximal, characteristic, complemented
3C2×C42×Dic13C211yesmaximal, characteristic, complemented
4#13113073C212yesmaximal
5#13113073C212yesmaximal
6#13113073C211yesmaximal, characteristic
7#13113071C211yesmaximal, characteristic, complemented
8#13113070C212yesmaximal, complemented
9#13113069C211yesmaximal, characteristic, complemented
10#13113067C212yesmaximal, complemented
11C13×#1437C211yesmaximal, characteristic
12C22×C13×C22⋊C4C2212yes—
13C22×C13×C22⋊C4C2211yescharacteristic
14C22×C42×C13C2211yescharacteristic
15C22×C22⋊Dic13C2212yes—
16C22×C22⋊Dic13C2211yescharacteristic
17C22×C22⋊Dic13C2211yescharacteristic
18C22×C4⋊Dic13C2211yescharacteristic
19C22×#6101C2211yescharacteristic
20C22×#6101C2211yescharacteristic
21C22×C4×Dic13C2212yes—
22C22×C4×Dic13C2212yes—
23C22×C4×Dic13C2211yescharacteristic
24C22×C4×Dic13C2211yescharacteristic
25C2×#88133—24no—
26C2×#88133—24no—
27C2×#88133C418yescomplemented
28C2×C13×#95C2211yescharacteristic
29C2×C13×#95C2212yes—
30C2×#88071C2212yes—
31C2×#88071C2211yescharacteristic
32C2×#88071C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2212yes—
35C2×#88071C2212yes—
36C2×#88071C2212yes—
37C2×#88071C2212yes—
38C42×Dic13—24no—
39#11718312—24no—
40C25×C13C2311yescharacteristic
41C23×C4×C13C2312yes—
42C23×C4×C13C2311yescharacteristic
43C23×C4×C13C2311yescharacteristic
44C23×C4×C13C2312yes—
45C23×Dic13C2312yes—
46C23×Dic13C2311yescharacteristic
47C23×Dic13C2311yescharacteristic
48C23×Dic13C2311yescharacteristic
49C23×Dic13C2311yescharacteristic
50C23×Dic13C2312yes—
51C2×C13×C22⋊C4—22no—
52C2×C13×C22⋊C4—22no—
53C2×C13×C22⋊C4—24no—
54C2×C13×C22⋊C4—24no—
55C2×C13×C22⋊C4—24no—
56C2×C13×C22⋊C4C2×C414yes—
57C2×C42×C13—22no—
58C2×C42×C13—24no—
59C2×C22⋊Dic13—22no—
60C2×C22⋊Dic13—22no—
61C2×C22⋊Dic13—22no—
62C2×C22⋊Dic13—22no—
63C2×C22⋊Dic13—24no—
64C2×C22⋊Dic13—24no—
65C2×C22⋊Dic13—24no—
66C2×C22⋊Dic13C2×C414yes—
67C2×C22⋊Dic13C2×C414yes—
68C2×C4⋊Dic13—22no—
69C2×C4⋊Dic13—22no—
70C2×C4⋊Dic13C2×C414yes—
71C2×#6101—22no—
72C2×#6101—22no—
73C2×#6101—22no—
74C2×#6101—22no—
75C2×#6101C2×C414yes—
76C2×#6101C2×C414yes—
77C2×C4×Dic13—22no—
78C2×C4×Dic13—24no—
79C2×C4×Dic13—24no—
80C2×C4×Dic13—24no—
81C2×C4×Dic13—24no—
82C2×C4×Dic13—24no—
83C2×C4×Dic13—24no—
84C2×C4×Dic13—24no—
85C2×C4×Dic13C2×C414yes—
86C2×C4×Dic13D414yes—
87C2×C4×Dic13D414yes—
88#88133—232no—
89C13×#95—22no—
90C13×#95—24no—
91#88071—22no—
92#88071—24no—
93#88071—24no—
94#88071—24no—
95#88071—24no—
96#88071—24no—
97#88071—24no—
98#88071—24no—
99#14711—131nomaximal, Sylow
100C24×C13—21no—
101C24×C13—21no—
102C24×C13—22no—
103C24×C13—22no—
104C24×C13—22no—
105C24×C13—22no—
106C24×C13—22no—
107C24×C13—22no—
108C24×C13C22×C412yes—
109C24×C13C2411yescharacteristic
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—21no—
117C22×C4×C13—21no—
118C22×C4×C13—22no—
119C22×C4×C13—22no—
120C22×C4×C13—22no—
121C22×C4×C13—22no—
122C22×C4×C13—22no—
123C22×C4×C13—22no—
124C22×C4×C13—22no—
125C22×C4×C13—22no—
126C22×C4×C13—22no—
127C22×C4×C13C22×C412yes—
128C22×C4×C13C22×C412yes—
129C22×C4×C13C2×D412yes—
130C22×C4×C13C2×D412yes—
131C22×C4×C13#4114yes—
132C22×C4×C13#4114yes—
133C22×C4×C13#4114yes—
134C22×Dic13—22no—
135C22×Dic13—22no—
136C22×Dic13—22no—
137C22×Dic13—22no—
138C22×Dic13—22no—
139C22×Dic13—22no—
140C22×Dic13—22no—
141C22×Dic13—22no—
142C22×Dic13—21no—
143C22×Dic13—21no—
144C22×Dic13—21no—
145C22×Dic13—21no—
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×Dic13—22no—
157C22×Dic13C22×C412yes—
158C22×Dic13C22×C412yes—
159C22×Dic13C22×C412yes—
160C22×Dic13C22×C412yes—
161C22×Dic13C2×D412yes—
162C22×Dic13C2×D412yes—
163C22×Dic13C2×D412yes—
164C22×Dic13C2×D412yes—
165C22×Dic13#4114yes—
166C22×Dic13#4114yes—
167C22×Dic13#4114yes—
168C13×C22⋊C4—28no—
169C13×C22⋊C4—48no—
170C42×C13—28no—
171C22⋊Dic13—28no—
172C22⋊Dic13—28no—
173C22⋊Dic13—48no—
174C4⋊Dic13—28no—
175#6101—28no—
176#6101—28no—
177C4×Dic13—216no—
178C4×Dic13—216no—
179C4×Dic13—28no—
180C4×Dic13C22⋊C4116yescomplemented
181C22×#126—131no—
182C2×#383—131no—
183C2×C43—131no—
184#1437—132no—
185#1437—132no—
186#1437—131no—
187#1437D1311yescharacteristic
188#1436—131no—
189#1436—132no—
190#1436—132no—
191#1436—131no—
192C23×C13—22no—
193C23×C13—22no—
194C23×C13—22no—
195C23×C13—24no—
196C23×C13—24no—
197C23×C13—42no—
198C23×C13—41no—
199C23×C13—42no—
200C23×C13—41no—
201C23×C13—42no—
202C23×C13—42no—
203C23×C13—42no—
204C23×C13—42no—
205C23×C13—42no—
206C23×C13—42no—
207C23×C13—42no—
208C23×C13—42no—
209C23×C13—42no—
210C23×C13—42no—
211C23×C13—41no—
212C23×C13—41no—
213C23×C13C23×C411yescharacteristic
214C23×C13C22×D411yescharacteristic
215C23×C13C22×D411yescharacteristic
216C23×C13C2×#4112yes—
217C23×C13C2×#4112yes—
218C23×C13C2×#4112yes—
219C23×C13C2×#4112yes—
220C23×C13C2×#4112yes—
221C23×C13C2×#4112yes—
222C2×C4×C13—24no—
223C2×C4×C13—22no—
224C2×C4×C13—24no—
225C2×C4×C13—24no—
226C2×C4×C13—22no—
227C2×C4×C13—24no—
228C2×C4×C13—24no—
229C2×C4×C13—24no—
230C2×C4×C13—24no—
231C2×C4×C13—24no—
232C2×C4×C13—22no—
233C2×C4×C13—24no—
234C2×C4×C13—42no—
235C2×C4×C13—41no—
236C2×C4×C13—41no—
237C2×C4×C13—42no—
238C2×C4×C13—42no—
239C2×C4×C13—42no—
240C2×C4×C13—42no—
241C2×C4×C13—42no—
242C2×C4×C13—42no—
243C2×C4×C13—42no—
244C2×C4×C13C2×C22⋊C414yes—
245C2×C4×C13#12618yescomplemented
246C2×Dic13—22no—
247C2×Dic13—22no—
248C2×Dic13—24no—
249C2×Dic13—24no—
250C2×Dic13—24no—
251C2×Dic13—24no—
252C2×Dic13—24no—
253C2×Dic13—24no—
254C2×Dic13—24no—
255C2×Dic13—24no—
256C2×Dic13—24no—
257C2×Dic13—24no—
258C2×Dic13—22no—
259C2×Dic13—22no—
260C2×Dic13—22no—
261C2×Dic13—22no—
262C2×Dic13—22no—
263C2×Dic13—22no—
264C2×Dic13—24no—
265C2×Dic13—42no—
266C2×Dic13—41no—
267C2×Dic13—41no—
268C2×Dic13—42no—
269C2×Dic13—42no—
270C2×Dic13—42no—
271C2×Dic13—42no—
272C2×Dic13—42no—
273C2×Dic13—42no—
274C2×Dic13—42no—
275C2×Dic13—42no—
276C2×Dic13—42no—
277C2×Dic13C2×C22⋊C414yes—
278C2×Dic13C2×C22⋊C414yes—
279C2×Dic13#12618yescomplemented
280C2×#126—138no—
281C2×#126—264no—
282C2×#126—264no—
283C22×C4⋊C4—131no—
284C22×C4⋊C4—131no—
285C22×C4⋊C4—131no—
286C22×C22⋊C4—131no—
287C22×C22⋊C4—131no—
288C22×C22⋊C4—132no—
289C22×C22⋊C4C2×D1312yes—
290C22×C22⋊C4C2×D1311yescharacteristic
291C22×C42—131no—
292C22×C42—132no—
293C22×C42—132no—
294C22×C42—131no—
295C22×C42C2×D1311yescharacteristic
296#383—264no—
297C2×#95—132no—
298C2×#95—132no—
299C2×#95—132no—
300C2×#95—132no—
301C2×#95—132no—
302C2×#95—132no—
303C2×#95—132no—
304C2×#95—131no—
305C2×#95C2×D1312yes—
306C2×#95C2×D1311yescharacteristic
307C43—264no—
308C22×C13—44no—
309C22×C13—44no—
310C22×C13—42no—
311C22×C13—42no—
312C22×C13—42no—
313C22×C13—82no—
314C22×C13—82no—
315C22×C13—82no—
316C22×C13—82no—
317C22×C13C22×C22⋊C411yescharacteristic
318C22×C13C4×#4111yescharacteristic
319C22×C13C4×#4111yescharacteristic
320C22×C13C4×#4112yes—
321C22×C13C4×#4112yes—
322C22×C13#52512yes—
323C22×C13#52511yescharacteristic
324C22×C13#52512yes—
325C22×C13#52511yescharacteristic
326C22×C13C2×#12612yes—
327C22×C13C2×#12612yes—
328C22×C13#52912yes—
329C22×C13#52912yes—
330C22×C13#52912yes—
331C22×C13#52912yes—
332C22×C13#52912yes—
333C22×C13#52912yes—
334C22×C13#53212yes—
335C22×C13#53212yes—
336C22×C13#53211yescharacteristic
337C22×C13#53211yescharacteristic
338C4×C13—28no—
339C4×C13—24no—
340C4×C13—42no—
341C4×C13—82no—
342Dic13—28no—
343Dic13—24no—
344Dic13—24no—
345Dic13—42no—
346Dic13—42no—
347Dic13—82no—
348C25C22×D1311yescharacteristic
349C23×C4—131no—
350C23×C4—131no—
351C23×C4—132no—
352C23×C4—131no—
353C23×C4—131no—
354C23×C4—132no—
355C23×C4C22×D1312yes—
356C23×C4C22×D1311yescharacteristic
357C23×C4C22×D1311yescharacteristic
358C23×C4C22×D1312yes—
359#126—2632no—
360C2×C4⋊C4—134no—
361C2×C4⋊C4—134no—
362C2×C4⋊C4—134no—
363C2×C4⋊C4—262no—
364C2×C4⋊C4—262no—
365C2×C4⋊C4—262no—
366C2×C4⋊C4—262no—
367C2×C4⋊C4—262no—
368C2×C4⋊C4—262no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—134no—
375C2×C22⋊C4—134no—
376C2×C22⋊C4—262no—
377C2×C22⋊C4—262no—
378C2×C22⋊C4—262no—
379C2×C22⋊C4—262no—
380C2×C22⋊C4—264no—
381C2×C22⋊C4—264no—
382C2×C22⋊C4—264no—
383C2×C22⋊C4C4×D1314yes—
384C2×C42—22no—
385C2×C42—24no—
386C2×C42—134no—
387C2×C42—134no—
388C2×C42—134no—
389C2×C42—264no—
390C2×C42—264no—
391C2×C42—264no—
392C2×C42—264no—
393C2×C42—264no—
394C2×C42—264no—
395C2×C42—262no—
396C2×C42—264no—
397#95—22no—
398#95—24no—
399#95—264no—
400#95—264no—
401#95—264no—
402#95—264no—
403#95—264no—
404#95—264no—
405#95—262no—
406#95—264no—
407C2×C13—82no—
408C2×C13#229711yescharacteristic
409C2×C13#229711yescharacteristic
410C2×C13#229711yescharacteristic
411C2×C13C4×#12612yes—
412C2×C13C4×#12612yes—
413C2×C13#285212yes—
414C2×C13#285212yes—
415C2×C13#286012yes—
416C2×C13#286012yes—
417C24—22no—
418C24—21no—
419C24—21no—
420C24—22no—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24C2×C4×D1312yes—
426C24C23×D1311yescharacteristic
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—132no—
445C22×C4—132no—
446C22×C4—132no—
447C22×C4—132no—
448C22×C4—132no—
449C22×C4—132no—
450C22×C4—134no—
451C22×C4—134no—
452C22×C4—134no—
453C22×C4—132no—
454C22×C4—132no—
455C22×C4—262no—
456C22×C4—262no—
457C22×C4—262no—
458C22×C4—262no—
459C22×C4—262no—
460C22×C4—262no—
461C22×C4—262no—
462C22×C4—262no—
463C22×C4—262no—
464C22×C4—261no—
465C22×C4—261no—
466C22×C4—261no—
467C22×C4—261no—
468C22×C4—262no—
469C22×C4—262no—
470C22×C4—262no—
471C22×C4—262no—
472C22×C4—262no—
473C22×C4—262no—
474C22×C4—262no—
475C22×C4—262no—
476C22×C4—262no—
477C22×C4—262no—
478C22×C4C2×C4×D1312yes—
479C22×C4C2×C4×D1312yes—
480C22×C4#612714yes—
481C22×C4D4×D1312yes—
482C22×C4D4×D1312yes—
483C22×C4#612914yes—
484C22×C4#612914yes—
485C4⋊C4—268no—
486C4⋊C4—268no—
487C4⋊C4—268no—
488C22⋊C4—28no—
489C22⋊C4—48no—
490C22⋊C4—268no—
491C22⋊C4—268no—
492C22⋊C4—528no—
493C42—28no—
494C42—1316no—
495C42—2616no—
496C42—2616no—
497C42—268no—
498C13#1471111yescharacteristic, complemented, Sylow
499C23—22no—
500C23—22no—
501C23—22no—
502C23—24no—
503C23—24no—
504C23—42no—
505C23—42no—
506C23—42no—
507C23—42no—
508C23—42no—
509C23—42no—
510C23—41no—
511C23—42no—
512C23—42no—
513C23—42no—
514C23—42no—
515C23—41no—
516C23—41no—
517C23—42no—
518C23—42no—
519C23—41no—
520C23C22×C4×D1311yescharacteristic
521C23C2×#612712yes—
522C23C2×D4×D1311yescharacteristic
523C23C2×D4×D1311yescharacteristic
524C23C2×#612912yes—
525C23C2×#612912yes—
526C23#41×D1312yes—
527C23#41×D1312yes—
528C23#41×D1312yes—
529C2×C4—24no—
530C2×C4—24no—
531C2×C4—24no—
532C2×C4—22no—
533C2×C4—24no—
534C2×C4—24no—
535C2×C4—24no—
536C2×C4—24no—
537C2×C4—24no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—24no—
541C2×C4—42no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—134no—
552C2×C4—134no—
553C2×C4—138no—
554C2×C4—262no—
555C2×C4—262no—
556C2×C4—264no—
557C2×C4—264no—
558C2×C4—264no—
559C2×C4—264no—
560C2×C4—264no—
561C2×C4—264no—
562C2×C4—264no—
563C2×C4—264no—
564C2×C4—264no—
565C2×C4—262no—
566C2×C4—264no—
567C2×C4—262no—
568C2×C4—262no—
569C2×C4—262no—
570C2×C4—262no—
571C2×C4—262no—
572C2×C4—264no—
573C2×C4—522no—
574C2×C4—522no—
575C2×C4—521no—
576C2×C4—522no—
577C2×C4—521no—
578C2×C4—522no—
579C2×C4—522no—
580C2×C4—522no—
581C2×C4—522no—
582C2×C4—522no—
583C2×C4—522no—
584C2×C4—522no—
585C2×C4#8813318yescomplemented
586C2×C4C22⋊C4×D1314yes—
587C22—42no—
588C22—42no—
589C22—42no—
590C22—44no—
591C22—44no—
592C22—82no—
593C22—82no—
594C22—82no—
595C22—82no—
596C22C4×#612711yescharacteristic
597C22C2×#8813312yes—
598C22C2×C22⋊C4×D1311yescharacteristic
599C22#1171922711yescharacteristic
600C22#1171923312yes—
601C22C4×#612912yes—
602C22C4×#612912yes—
603C22#1171924312yes—
604C22#1171925212yes—
605C22#1171925312yes—
606C22#1171926212yes—
607C22#1171929111yescharacteristic
608C22#1171930112yes—
609C22#1171930512yes—
610C22#1171931112yes—
611C22#1171935412yes—
612C22#1171936111yescharacteristic
613C22#1171937311yescharacteristic
614C22#1171938512yes—
615C22D13×#12612yes—
616C22#1171942111yescharacteristic
617C4—28no—
618C4—24no—
619C4—42no—
620C4—82no—
621C4—268no—
622C4—264no—
623C4—264no—
624C4—522no—
625C4—522no—
626C4—1042no—
627C2—82no—
628C2#1311732111yescharacteristic
629C2#1311732211yescharacteristic
630C2#1311732311yescharacteristic
631C2C4×#8813312yes—
632C2#1311739012yes—
633C2#1312314912yes—
634C2#1312315012yes—
635C2#1312320012yes—
636C2#1312320212yes—
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1437C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenter#1437D13
hypocenterC13#14711
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
2. C2×#11718312C2semidirect
3. C2×C42×Dic13C2semidirect
7. #13113071C2semidirect
8. #13113070C2semidirect
9. #13113069C2semidirect
10. #13113067C2semidirect
27. C2×#88133C4semidirect
180. C4×Dic13C22⋊C4semidirect
245. C2×C4×C13#126semidirect
279. C2×Dic13#126semidirect
498. C13#14711semidirect
585. C2×C4#88133semidirect

Maximal subgroups

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

subgroupindex
C22×#881332
C2×#117183122
C2×C42×Dic132
#131130732
#131130712
#131130702
#131130692
#131130672
C13×#14372
#1471113