Finite Group Databasebeta

← #15793592

Subgroups — #15793592

Order 3328.

1586 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718882C211yesmaximal, characteristic
2C2×#11718642C211yesmaximal, characteristic, complemented
3#13113101C211yesmaximal, characteristic, complemented
4#13113089C211yesmaximal, characteristic, complemented
5#13113085C212yesmaximal, complemented
6#13113081C212yesmaximal, complemented
7#13113081C212yesmaximal, complemented
8#13113081C212yesmaximal, complemented
9#13113077C211yesmaximal, characteristic
10#13113061C211yesmaximal, characteristic, complemented
11C2×C13×#394C211yesmaximal, characteristic
12C23×D4×C13C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C13×C22⋊C4C2212yes—
15C22×C13×C22⋊C4C2212yes—
16C22×C22⋊Dic13C2212yes—
17C22×C22⋊Dic13C2212yes—
18C22×C22⋊Dic13C2212yes—
19C22×C22⋊Dic13C2212yes—
20C22×C4⋊Dic13C2211yescharacteristic
21C22×C4⋊Dic13C2211yescharacteristic
22C22×C4⋊Dic13C2212yes—
23C22×C4×Dic13C2211yescharacteristic
24C13×#394C418yescomplemented
25C2×C13×#95C2211yescharacteristic
26#11718882—24no—
27C2×#88071C2211yescharacteristic
28C2×#88071C2211yescharacteristic
29C2×#88071C2211yescharacteristic
30C2×#88071C2211yescharacteristic
31C2×#88071C2211yescharacteristic
32C2×#88071C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2212yes—
35C2×#88071C2212yes—
36C2×#88071C2212yes—
37#11718642—24no—
38C25×C13C2312yes—
39C22×D4×C13—22no—
40C22×D4×C13—22no—
41C22×D4×C13—42no—
42C22×D4×C13—42no—
43C22×D4×C13C2×C414yes—
44C23×C4×C13C2311yescharacteristic
45C23×C4×C13C2312yes—
46C23×C4×C13C2311yescharacteristic
47C23×C4×C13C2311yescharacteristic
48C23×Dic13C2311yescharacteristic
49C23×Dic13C2312yes—
50C23×Dic13C2311yescharacteristic
51C23×Dic13C2312yes—
52C23×Dic13C2311yescharacteristic
53C23×Dic13C2311yescharacteristic
54C2×C13×C4⋊C4—22no—
55C2×C13×C4⋊C4—22no—
56C2×C13×C4⋊C4C2×C414yes—
57C2×C13×C22⋊C4—42no—
58C2×C13×C22⋊C4—42no—
59C2×C13×C22⋊C4—42no—
60C2×C13×C22⋊C4—42no—
61C2×C13×C22⋊C4C2×C418yes—
62C2×C13×C22⋊C4C2×C418yes—
63C2×C22⋊Dic13—24no—
64C2×C22⋊Dic13—24no—
65C2×C22⋊Dic13—42no—
66C2×C22⋊Dic13—42no—
67C2×C22⋊Dic13—42no—
68C2×C22⋊Dic13—42no—
69C2×C22⋊Dic13—42no—
70C2×C22⋊Dic13—42no—
71C2×C22⋊Dic13—42no—
72C2×C22⋊Dic13—42no—
73C2×C22⋊Dic13—42no—
74C2×C22⋊Dic13—42no—
75C2×C4⋊Dic13—22no—
76C2×C4⋊Dic13—22no—
77C2×C4⋊Dic13—42no—
78C2×C4⋊Dic13—42no—
79C2×C4⋊Dic13—42no—
80C2×C4⋊Dic13—42no—
81C2×C4⋊Dic13—42no—
82C2×C4×Dic13—42no—
83C2×C4×Dic13D414yes—
84C13×#95C2×C414yes—
85#88071—22no—
86#88071—22no—
87#88071—22no—
88#88071—22no—
89#88071—22no—
90#88071—42no—
91#88071—42no—
92#88071—42no—
93#88071—42no—
94#88071—42no—
95#14624—131nomaximal, Sylow
96C24×C13—22no—
97C24×C13—22no—
98C24×C13—22no—
99C24×C13—22no—
100C24×C13—22no—
101C24×C13—22no—
102C24×C13—22no—
103C24×C13—22no—
104C24×C13—22no—
105C24×C13—22no—
106C24×C13—22no—
107C24×C13—22no—
108C24×C13—22no—
109C24×C13—22no—
110C24×C13C22×C414yes—
111C24×C13C2411yescharacteristic
112C2×D4×C13—28no—
113C2×D4×C13—48no—
114C2×D4×C13—44no—
115C2×D4×C13—44no—
116C2×D4×C13—48no—
117C22×C4×C13—22no—
118C22×C4×C13—22no—
119C22×C4×C13—21no—
120C22×C4×C13—21no—
121C22×C4×C13—21no—
122C22×C4×C13—21no—
123C22×C4×C13—21no—
124C22×C4×C13—22no—
125C22×C4×C13—22no—
126C22×C4×C13—22no—
127C22×C4×C13—22no—
128C22×C4×C13—22no—
129C22×C4×C13—22no—
130C22×C4×C13—22no—
131C22×C4×C13—21no—
132C22×C4×C13—21no—
133C22×C4×C13—21no—
134C22×C4×C13—22no—
135C22×C4×C13C22×C414yes—
136C22×C4×C13C22×C412yes—
137C22×C4×C13C22×C412yes—
138C22×C4×C13C22×C412yes—
139C22×C4×C13C2×D412yes—
140C22×C4×C13#4112yes—
141C22×Dic13—21no—
142C22×Dic13—22no—
143C22×Dic13—22no—
144C22×Dic13—22no—
145C22×Dic13—21no—
146C22×Dic13—21no—
147C22×Dic13—22no—
148C22×Dic13—21no—
149C22×Dic13—21no—
150C22×Dic13—21no—
151C22×Dic13—22no—
152C22×Dic13—22no—
153C22×Dic13—22no—
154C22×Dic13—22no—
155C22×Dic13—22no—
156C22×Dic13—22no—
157C22×Dic13—22no—
158C22×Dic13—22no—
159C22×Dic13—22no—
160C22×Dic13—22no—
161C22×Dic13—22no—
162C22×Dic13—21no—
163C22×Dic13—22no—
164C22×Dic13—22no—
165C22×Dic13—22no—
166C22×Dic13—22no—
167C22×Dic13—22no—
168C22×Dic13—21no—
169C22×Dic13—21no—
170C22×Dic13—22no—
171C22×Dic13—21no—
172C22×Dic13—22no—
173C22×Dic13C2×D412yes—
174C22×Dic13C2×D412yes—
175C13×C4⋊C4—28no—
176C13×C22⋊C4—48no—
177C13×C22⋊C4—48no—
178C22⋊Dic13—48no—
179C22⋊Dic13—48no—
180C22⋊Dic13—48no—
181C22⋊Dic13—48no—
182C4⋊Dic13—44no—
183C4⋊Dic13—44no—
184C4⋊Dic13—48no—
185C4×Dic13—44no—
186C2×#394D1311yescharacteristic
187C2×#390—131no—
188C2×#387—131no—
189#1444—131no—
190#1441—131no—
191#1440—132no—
192#1439—132no—
193#1439—132no—
194#1439—132no—
195#1438—131no—
196#1434—131no—
197C23×C13—24no—
198C23×C13—24no—
199C23×C13—24no—
200C23×C13—24no—
201C23×C13—24no—
202C23×C13—24no—
203C23×C13—24no—
204C23×C13—42no—
205C23×C13—42no—
206C23×C13—42no—
207C23×C13—42no—
208C23×C13—42no—
209C23×C13—42no—
210C23×C13—42no—
211C23×C13—42no—
212C23×C13—42no—
213C23×C13—42no—
214C23×C13—42no—
215C23×C13—42no—
216C23×C13—42no—
217C23×C13—42no—
218C23×C13—42no—
219C23×C13—42no—
220C23×C13—42no—
221C23×C13—42no—
222C23×C13—42no—
223C23×C13—42no—
224C23×C13—42no—
225C23×C13—42no—
226C23×C13—42no—
227C23×C13—42no—
228C23×C13—42no—
229C23×C13—42no—
230C23×C13—42no—
231C23×C13—42no—
232C23×C13C23×C411yescharacteristic
233C23×C13C22×D411yescharacteristic
234C23×C13C2×#4111yescharacteristic
235C23×C13H(5,𝔽2)12yes—
236C23×C13H(5,𝔽2)12yes—
237C23×C13H(5,𝔽2)11yescharacteristic
238C23×C13H(5,𝔽2)11yescharacteristic
239C23×C13H(5,𝔽2)11yescharacteristic
240C23×C13H(5,𝔽2)12yes—
241C23×C132−1+412yes—
242C23×C132−1+411yescharacteristic
243D4×C13—416no—
244C2×C4×C13—24no—
245C2×C4×C13—22no—
246C2×C4×C13—22no—
247C2×C4×C13—24no—
248C2×C4×C13—22no—
249C2×C4×C13—22no—
250C2×C4×C13—22no—
251C2×C4×C13—24no—
252C2×C4×C13—24no—
253C2×C4×C13—24no—
254C2×C4×C13—22no—
255C2×C4×C13—24no—
256C2×C4×C13—41no—
257C2×C4×C13—41no—
258C2×C4×C13—41no—
259C2×C4×C13—41no—
260C2×C4×C13—42no—
261C2×C4×C13—41no—
262C2×C4×C13—41no—
263C2×C4×C13—42no—
264C2×C4×C13—42no—
265C2×C4×C13—42no—
266C2×C4×C13—42no—
267C2×C4×C13C4×D414yes—
268C2×Dic13—22no—
269C2×Dic13—22no—
270C2×Dic13—22no—
271C2×Dic13—22no—
272C2×Dic13—22no—
273C2×Dic13—22no—
274C2×Dic13—42no—
275C2×Dic13—42no—
276C2×Dic13—42no—
277C2×Dic13—42no—
278C2×Dic13—41no—
279C2×Dic13—42no—
280C2×Dic13—42no—
281C2×Dic13—42no—
282C2×Dic13—41no—
283C2×Dic13—41no—
284C2×Dic13—41no—
285C2×Dic13—41no—
286C2×Dic13—41no—
287C2×Dic13—42no—
288C2×Dic13—42no—
289C2×Dic13—42no—
290C2×Dic13—42no—
291C2×Dic13—42no—
292C2×Dic13—42no—
293C2×Dic13—42no—
294C2×Dic13—42no—
295C2×Dic13—42no—
296C2×Dic13—42no—
297C2×Dic13—42no—
298C2×Dic13—42no—
299C2×Dic13—42no—
300C2×Dic13—42no—
301C2×Dic13—42no—
302C23×D4C2×D1311yescharacteristic
303C22×C4⋊C4—131no—
304C22×C4⋊C4—131no—
305C22×C4⋊C4—132no—
306C22×C4⋊C4C2×D1311yescharacteristic
307C22×C22⋊C4—132no—
308C22×C22⋊C4—132no—
309C22×C22⋊C4—132no—
310C22×C22⋊C4—132no—
311C22×C22⋊C4C2×D1312yes—
312C22×C22⋊C4C2×D1312yes—
313C22×C42—131no—
314#394Dic1318yescomplemented
315#390—264no—
316#387—264no—
317C2×#95—131no—
318C2×#95—131no—
319C2×#95—131no—
320C2×#95—131no—
321C2×#95—131no—
322C2×#95—132no—
323C2×#95—132no—
324C2×#95—132no—
325C2×#95—132no—
326C2×#95—132no—
327C2×#95C2×D1311yescharacteristic
328C22×C13—44no—
329C22×C13—44no—
330C22×C13—44no—
331C22×C13—44no—
332C22×C13—44no—
333C22×C13—44no—
334C22×C13—44no—
335C22×C13—82no—
336C22×C13—82no—
337C22×C13—82no—
338C22×C13—82no—
339C22×C13—82no—
340C22×C13—82no—
341C22×C13—82no—
342C22×C13—82no—
343C22×C13C2×C4×D411yescharacteristic
344C22×C13#51812yes—
345C22×C13#51811yescharacteristic
346C22×C13#52011yescharacteristic
347C22×C13#52012yes—
348C22×C13#53411yescharacteristic
349C22×C13#53511yescharacteristic
350C22×C13#53511yescharacteristic
351C22×C13#53511yescharacteristic
352C22×C13#53611yescharacteristic
353C22×C13#53711yescharacteristic
354C22×C13#53812yes—
355C22×C13#54011yescharacteristic
356C22×C13#54211yescharacteristic
357C22×C13#54212yes—
358C22×C13#56012yes—
359C22×C13#56012yes—
360C22×C13#56012yes—
361C22×C13#56212yes—
362C22×C13#56212yes—
363C22×C13#56212yes—
364C22×C13#56212yes—
365C22×C13#56312yes—
366C4×C13—24no—
367C4×C13—42no—
368C4×C13—42no—
369C4×C13—44no—
370Dic13—42no—
371Dic13—42no—
372Dic13—82no—
373Dic13—81no—
374Dic13—82no—
375Dic13—81no—
376C25C22×D1312yes—
377C22×D4—22no—
378C22×D4—22no—
379C22×D4—42no—
380C22×D4—42no—
381C22×D4C2×Dic1314yes—
382C23×C4—131no—
383C23×C4—131no—
384C23×C4—131no—
385C23×C4—132no—
386C23×C4—131no—
387C23×C4—132no—
388C23×C4C22×D1311yescharacteristic
389C23×C4C22×D1312yes—
390C23×C4C22×D1311yescharacteristic
391C23×C4C22×D1311yescharacteristic
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—262no—
395C2×C4⋊C4—262no—
396C2×C4⋊C4—522no—
397C2×C4⋊C4—522no—
398C2×C4⋊C4—522no—
399C2×C4⋊C4—522no—
400C2×C4⋊C4—522no—
401C2×C4⋊C4C2×Dic1314yes—
402C2×C22⋊C4—42no—
403C2×C22⋊C4—42no—
404C2×C22⋊C4—42no—
405C2×C22⋊C4—42no—
406C2×C22⋊C4—264no—
407C2×C22⋊C4—264no—
408C2×C22⋊C4—522no—
409C2×C22⋊C4—522no—
410C2×C22⋊C4—522no—
411C2×C22⋊C4—522no—
412C2×C22⋊C4—522no—
413C2×C22⋊C4—522no—
414C2×C22⋊C4—522no—
415C2×C22⋊C4—522no—
416C2×C22⋊C4—522no—
417C2×C22⋊C4—522no—
418C2×C22⋊C4C2×Dic1318yes—
419C2×C22⋊C4C2×Dic1318yes—
420C2×C42—134no—
421C2×C42—522no—
422#95—262no—
423#95—262no—
424#95—262no—
425#95—262no—
426#95—262no—
427#95—522no—
428#95—522no—
429#95—522no—
430#95—522no—
431#95—522no—
432#95C2×Dic1314yes—
433C2×C13—84no—
434C2×C13#232111yescharacteristic
435C2×C13#232411yescharacteristic
436C2×C13#232611yescharacteristic
437C2×C13#237612yes—
438C2×C13#237712yes—
439C2×C13#281311yescharacteristic
440C2×C13#281611yescharacteristic
441C2×C13#281811yescharacteristic
442C2×C13#282011yescharacteristic
443C2×C13#282912yes—
444C2×C13#283012yes—
445C24—22no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24C22×Dic1314yes—
460C24C23×D1311yescharacteristic
461C2×D4—28no—
462C2×D4—48no—
463C2×D4—44no—
464C2×D4—44no—
465C2×D4—48no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—22no—
482C22×C4—21no—
483C22×C4—22no—
484C22×C4—132no—
485C22×C4—132no—
486C22×C4—261no—
487C22×C4—262no—
488C22×C4—262no—
489C22×C4—261no—
490C22×C4—261no—
491C22×C4—262no—
492C22×C4—261no—
493C22×C4—262no—
494C22×C4—261no—
495C22×C4—261no—
496C22×C4—262no—
497C22×C4—262no—
498C22×C4—262no—
499C22×C4—262no—
500C22×C4—262no—
501C22×C4—262no—
502C22×C4—261no—
503C22×C4—262no—
504C22×C4—262no—
505C22×C4—262no—
506C22×C4—262no—
507C22×C4—261no—
508C22×C4—262no—
509C22×C4—262no—
510C22×C4—262no—
511C22×C4—262no—
512C22×C4—261no—
513C22×C4—262no—
514C22×C4—262no—
515C22×C4—262no—
516C22×C4—261no—
517C22×C4—262no—
518C22×C4D4×D1312yes—
519C22×C4#612912yes—
520C22×C4C22×Dic1314yes—
521C22×C4C22×Dic1312yes—
522C22×C4C22×Dic1312yes—
523C22×C4C22×Dic1312yes—
524C4⋊C4—28no—
525C4⋊C4—524no—
526C4⋊C4—524no—
527C4⋊C4—528no—
528C22⋊C4—48no—
529C22⋊C4—48no—
530C22⋊C4—528no—
531C22⋊C4—528no—
532C22⋊C4—528no—
533C22⋊C4—528no—
534C42—524no—
535C13#1462411yescharacteristic, complemented, Sylow
536C23—24no—
537C23—24no—
538C23—24no—
539C23—24no—
540C23—24no—
541C23—24no—
542C23—24no—
543C23—42no—
544C23—42no—
545C23—42no—
546C23—42no—
547C23—42no—
548C23—42no—
549C23—42no—
550C23—42no—
551C23—42no—
552C23—42no—
553C23—42no—
554C23—42no—
555C23—42no—
556C23—42no—
557C23—42no—
558C23—42no—
559C23—42no—
560C23—42no—
561C23—42no—
562C23—42no—
563C23—42no—
564C23—42no—
565C23—42no—
566C23—42no—
567C23—42no—
568C23—42no—
569C23—42no—
570C23—42no—
571C23C2×D4×D1311yescharacteristic
572C23C2×#612911yescharacteristic
573C23#8825112yes—
574C23#8825112yes—
575C23#8825111yescharacteristic
576C23#8825111yescharacteristic
577C23#8825611yescharacteristic
578C23#8825612yes—
579C23#8825711yescharacteristic
580C23#8825712yes—
581C23C23×Dic1311yescharacteristic
582D4—416no—
583C2×C4—24no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—24no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—24no—
591C2×C4—24no—
592C2×C4—24no—
593C2×C4—24no—
594C2×C4—22no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—42no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—262no—
607C2×C4—262no—
608C2×C4—262no—
609C2×C4—262no—
610C2×C4—262no—
611C2×C4—262no—
612C2×C4—522no—
613C2×C4—522no—
614C2×C4—522no—
615C2×C4—522no—
616C2×C4—521no—
617C2×C4—522no—
618C2×C4—521no—
619C2×C4—522no—
620C2×C4—522no—
621C2×C4—521no—
622C2×C4—521no—
623C2×C4—522no—
624C2×C4—522no—
625C2×C4—522no—
626C2×C4—522no—
627C2×C4—522no—
628C2×C4—522no—
629C2×C4—522no—
630C2×C4—522no—
631C2×C4—522no—
632C2×C4—522no—
633C2×C4—522no—
634C2×C4—522no—
635C2×C4—522no—
636C2×C4—522no—
637C2×C4—521no—
638C2×C4—521no—
639C2×C4—522no—
640C2×C4D4×Dic1314yes—
641C22—44no—
642C22—44no—
643C22—44no—
644C22—44no—
645C22—44no—
646C22—44no—
647C22—44no—
648C22—82no—
649C22—82no—
650C22—82no—
651C22—82no—
652C22—82no—
653C22—82no—
654C22—82no—
655C22—82no—
656C22#1171929411yescharacteristic
657C22#1171929711yescharacteristic
658C22#1171929812yes—
659C22#1171930811yescharacteristic
660C22#1171931211yescharacteristic
661C22#1171931311yescharacteristic
662C22#1171932411yescharacteristic
663C22#1171932512yes—
664C22#1171932512yes—
665C22#1171932612yes—
666C22#1171932612yes—
667C22#1171935612yes—
668C22#1171937112yes—
669C22#1171937212yes—
670C22#1171937212yes—
671C22#1171937911yescharacteristic
672C22#1171938011yescharacteristic
673C22#1171938712yes—
674C22C2×D4×Dic1311yescharacteristic
675C22#1171950312yes—
676C22#1171950311yescharacteristic
677C22#1171953211yescharacteristic
678C22#1171953212yes—
679C4—24no—
680C4—44no—
681C4—42no—
682C4—42no—
683C4—522no—
684C4—522no—
685C4—1041no—
686C4—1042no—
687C4—1041no—
688C4—1042no—
689C2—84no—
690C2#1311749711yescharacteristic
691C2#1311753111yescharacteristic
692C2#1311754911yescharacteristic
693C2#1311798412yes—
694C2#1311799312yes—
695C2#1312283711yescharacteristic
696C2#1312286711yescharacteristic
697C2#1312287811yescharacteristic
698C2#1312288911yescharacteristic
699C2#1312297212yes—
700C2#1312298212yes—
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#394C2
socle, cosocleC24×C13C24
prime radicalC23×D4×C13C22
hypercenterC2×#394D13
hypocenterC13#14624
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
2. C2×#11718642C2semidirect
3. #13113101C2semidirect
4. #13113089C2semidirect
5. #13113085C2semidirect
6. #13113081C2semidirect
7. #13113081C2semidirect
8. #13113081C2semidirect
10. #13113061C2semidirect
24. C13×#394C4semidirect
314. #394Dic13semidirect
535. C13#14624semidirect

Maximal subgroups

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

subgroupindex
C2×#117188822
C2×#117186422
#131131012
#131130892
#131130852
#131130812
#131130772
#131130612
C2×C13×#3942
#1462413