Finite Group Databasebeta

← #15792099

Subgroups — #15792099

Order 3328.

1962 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718612C212yesmaximal, complemented
2#13113104C212yesmaximal, complemented
3#13113081C212yesmaximal, complemented
4#13113077C211yesmaximal, characteristic
5#13113077C211yesmaximal, characteristic
6#13113073C212yesmaximal, complemented
7#13113065C212yesmaximal, complemented
8#13113059C212yesmaximal, complemented
9C22×C13×#123C211yesmaximal, characteristic
10C23×D4×C13C2211yescharacteristic
11C24×C4×C13C2211yescharacteristic
12C2×C13×#123—28no—
13C2×C13×#123C418yescomplemented
14C22×C13×C4⋊C4C2212yes—
15C22×C13×C22⋊C4C2212yes—
16C22×C13×C22⋊C4C2211yescharacteristic
17C22×C22⋊Dic13C2212yes—
18C22×C22⋊Dic13C2212yes—
19C22×C22⋊Dic13C2211yescharacteristic
20C22×C22⋊Dic13C2212yes—
21C22×C22⋊Dic13C2211yescharacteristic
22C22×C4⋊Dic13C2212yes—
23C22×C4×Dic13C2212yes—
24C2×#88071C2212yes—
25C2×#88071C2212yes—
26C2×#88071C2211yescharacteristic
27C2×#88071C2212yes—
28C2×#88071C2212yes—
29C2×#88071C2212yes—
30C2×#88071C2212yes—
31C2×#88071C2212yes—
32C2×#88071C2211yescharacteristic
33#11718612—28no—
34C25×C13C2311yescharacteristic
35C25×C13C2311yescharacteristic
36C22×D4×C13—24no—
37C22×D4×C13—42no—
38C22×D4×C13—41no—
39C22×D4×C13—41no—
40C22×D4×C13C2×C414yes—
41C23×C4×C13—24no—
42C23×C4×C13—42no—
43C23×C4×C13—41no—
44C23×C4×C13—41no—
45C23×C4×C13C2×C414yes—
46C23×C4×C13C2312yes—
47C23×C4×C13C2311yescharacteristic
48C23×C4×C13C2312yes—
49C23×Dic13C2312yes—
50C23×Dic13C2312yes—
51C23×Dic13C2312yes—
52C23×Dic13C2312yes—
53C13×#123—232no—
54C2×C13×C4⋊C4—24no—
55C2×C13×C4⋊C4—24no—
56C2×C13×C4⋊C4C2×C418yes—
57C2×C13×C22⋊C4—24no—
58C2×C13×C22⋊C4—24no—
59C2×C13×C22⋊C4C2×C418yes—
60C2×C13×C22⋊C4C2×C414yes—
61C2×C13×C22⋊C4D418yes—
62C2×C22⋊Dic13—24no—
63C2×C22⋊Dic13—24no—
64C2×C22⋊Dic13—24no—
65C2×C22⋊Dic13—24no—
66C2×C22⋊Dic13—24no—
67C2×C22⋊Dic13—24no—
68C2×C22⋊Dic13—41no—
69C2×C22⋊Dic13—42no—
70C2×C22⋊Dic13—42no—
71C2×C22⋊Dic13—42no—
72C2×C22⋊Dic13—42no—
73C2×C22⋊Dic13—41no—
74C2×C22⋊Dic13—42no—
75C2×C4⋊Dic13—24no—
76C2×C4⋊Dic13—24no—
77C2×C4⋊Dic13—42no—
78C2×C4×Dic13—24no—
79C2×C4×Dic13—24no—
80C2×C4×Dic13—42no—
81#88071—24no—
82#88071—24no—
83#88071—41no—
84#88071—42no—
85#88071—42no—
86#88071—42no—
87#88071—42no—
88#88071—41no—
89#88071—42no—
90#14506—131nomaximal, Sylow
91C24×C13—22no—
92C24×C13—22no—
93C24×C13—22no—
94C24×C13—22no—
95C24×C13—21no—
96C24×C13—21no—
97C24×C13—22no—
98C24×C13—22no—
99C24×C13—22no—
100C24×C13—22no—
101C24×C13—22no—
102C24×C13—22no—
103C24×C13—21no—
104C24×C13—21no—
105C24×C13—22no—
106C24×C13C22×C412yes—
107C24×C13C22×C412yes—
108C24×C13C2×D414yes—
109C24×C13C2411yescharacteristic
110C2×D4×C13—28no—
111C2×D4×C13—44no—
112C2×D4×C13—44no—
113C2×D4×C13—48no—
114C2×D4×C13—48no—
115C22×C4×C13—22no—
116C22×C4×C13—22no—
117C22×C4×C13—22no—
118C22×C4×C13—22no—
119C22×C4×C13—28no—
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×C13—22no—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13—44no—
131C22×C4×C13—44no—
132C22×C4×C13—48no—
133C22×C4×C13—48no—
134C22×C4×C13C22×C414yes—
135C22×C4×C13C22×C412yes—
136C22×C4×C13C22×C414yes—
137C22×C4×C13C2×D414yes—
138C22×C4×C13C2×D414yes—
139C22×Dic13—22no—
140C22×Dic13—22no—
141C22×Dic13—22no—
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×Dic13—22no—
157C22×Dic13—22no—
158C22×Dic13—22no—
159C22×Dic13—22no—
160C22×Dic13—22no—
161C22×Dic13—22no—
162C22×Dic13—22no—
163C22×Dic13—22no—
164C22×Dic13—22no—
165C22×Dic13#4114yes—
166C22×Dic13#4114yes—
167C13×C4⋊C4—216no—
168C13×C22⋊C4—216no—
169C13×C22⋊C4C22⋊C4116yescomplemented
170C22⋊Dic13—44no—
171C22⋊Dic13—48no—
172C22⋊Dic13—48no—
173C22⋊Dic13—48no—
174C22⋊Dic13—44no—
175C4⋊Dic13—48no—
176C4×Dic13—48no—
177C22×#123D1311yescharacteristic
178C2×#388—132no—
179#1445—132no—
180#1439—132no—
181#1438—131no—
182#1438—131no—
183#1437—132no—
184C4⋊#95—132no—
185C22⋊#95—132no—
186C23×C13—24no—
187C23×C13—22no—
188C23×C13—22no—
189C23×C13—24no—
190C23×C13—24no—
191C23×C13—24no—
192C23×C13—24no—
193C23×C13—24no—
194C23×C13—24no—
195C23×C13—24no—
196C23×C13—22no—
197C23×C13—24no—
198C23×C13—22no—
199C23×C13—22no—
200C23×C13—24no—
201C23×C13—42no—
202C23×C13—42no—
203C23×C13—42no—
204C23×C13—42no—
205C23×C13—41no—
206C23×C13—42no—
207C23×C13—41no—
208C23×C13—41no—
209C23×C13—42no—
210C23×C13—41no—
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—41no—
222C23×C13—42no—
223C23×C13—41no—
224C23×C13—41no—
225C23×C13—42no—
226C23×C13—41no—
227C23×C13C2×C22⋊C414yes—
228C23×C13C23×C411yescharacteristic
229C23×C13C22×D412yes—
230C23×C13C2×#4112yes—
231C23×C13C2×#4112yes—
232C23×C13H(5,𝔽2)12yes—
233C23×C13H(5,𝔽2)11yescharacteristic
234C23×C13H(5,𝔽2)11yescharacteristic
235C23×C13H(5,𝔽2)12yes—
236C23×C132−1+412yes—
237D4×C13—416no—
238C2×C4×C13—24no—
239C2×C4×C13—24no—
240C2×C4×C13—24no—
241C2×C4×C13—24no—
242C2×C4×C13—24no—
243C2×C4×C13—24no—
244C2×C4×C13—24no—
245C2×C4×C13—22no—
246C2×C4×C13—24no—
247C2×C4×C13—24no—
248C2×C4×C13—22no—
249C2×C4×C13—22no—
250C2×C4×C13—416no—
251C2×C4×C13—42no—
252C2×C4×C13—42no—
253C2×C4×C13—42no—
254C2×C4×C13—42no—
255C2×C4×C13—42no—
256C2×C4×C13—42no—
257C2×C4×C13C2×C22⋊C418yes—
258C2×Dic13—24no—
259C2×Dic13—24no—
260C2×Dic13—24no—
261C2×Dic13—24no—
262C2×Dic13—24no—
263C2×Dic13—24no—
264C2×Dic13—42no—
265C2×Dic13—42no—
266C2×Dic13—42no—
267C2×Dic13—42no—
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×Dic13—42no—
278C2×Dic13—42no—
279C2×Dic13—42no—
280C2×Dic13—42no—
281C2×Dic13—42no—
282C2×Dic13—42no—
283C2×Dic13—42no—
284C2×Dic13—42no—
285C2×Dic13—42no—
286C23×D4C2×D1311yescharacteristic
287C24×C4C2×D1311yescharacteristic
288C2×#123—28no—
289C2×#123Dic1318yescomplemented
290C22×C4⋊C4—132no—
291C22×C4⋊C4C2×D1312yes—
292C22×C22⋊C4—132no—
293C22×C22⋊C4—132no—
294C22×C22⋊C4—131no—
295C22×C22⋊C4—132no—
296C22×C22⋊C4—131no—
297C22×C22⋊C4C2×D1312yes—
298C22×C22⋊C4C2×D1311yescharacteristic
299C22×C42—132no—
300#388—268no—
301C2×#95—132no—
302C2×#95—132no—
303C2×#95—132no—
304C2×#95—132no—
305C2×#95—132no—
306C2×#95—132no—
307C2×#95—131no—
308C2×#95—132no—
309C2×#95—131no—
310C22×C13—24no—
311C22×C13—28no—
312C22×C13—44no—
313C22×C13—42no—
314C22×C13—42no—
315C22×C13—44no—
316C22×C13—44no—
317C22×C13—44no—
318C22×C13—44no—
319C22×C13—42no—
320C22×C13—44no—
321C22×C13—44no—
322C22×C13—42no—
323C22×C13—42no—
324C22×C13—82no—
325C22×C13—82no—
326C22×C13—82no—
327C22×C13—82no—
328C22×C13C22×C22⋊C411yescharacteristic
329C22×C13C4×#4112yes—
330C22×C13#51811yescharacteristic
331C22×C13#51811yescharacteristic
332C22×C13#52012yes—
333C22×C13#53512yes—
334C22×C13#53512yes—
335C22×C13#53812yes—
336C22×C13#53912yes—
337C22×C13#54012yes—
338C22×C13#54212yes—
339C22×C13#54612yes—
340C22×C13#54612yes—
341C22×C13#54712yes—
342C22×C13#54712yes—
343C22×C13#55111yescharacteristic
344C22×C13#55312yes—
345C22×C13#55911yescharacteristic
346C22×C13#56011yescharacteristic
347C22×C13#56212yes—
348C22×C13#56311yescharacteristic
349C4×C13—28no—
350C4×C13—44no—
351C4×C13—42no—
352Dic13—44no—
353Dic13—44no—
354Dic13—82no—
355Dic13—82no—
356C25C22×D1311yescharacteristic
357C25C22×D1311yescharacteristic
358C22×D4—24no—
359C22×D4—41no—
360C22×D4—42no—
361C22×D4—41no—
362C22×D4C2×Dic1314yes—
363C23×C4—24no—
364C23×C4—41no—
365C23×C4—42no—
366C23×C4—41no—
367C23×C4—132no—
368C23×C4—132no—
369C23×C4—132no—
370C23×C4—132no—
371C23×C4C2×Dic1314yes—
372C23×C4C22×D1312yes—
373C23×C4C22×D1311yescharacteristic
374C23×C4C22×D1312yes—
375#123—232no—
376C2×C4⋊C4—24no—
377C2×C4⋊C4—24no—
378C2×C4⋊C4—264no—
379C2×C4⋊C4—264no—
380C2×C4⋊C4—522no—
381C2×C4⋊C4C2×Dic1318yes—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—264no—
385C2×C22⋊C4—264no—
386C2×C22⋊C4—264no—
387C2×C22⋊C4—264no—
388C2×C22⋊C4—264no—
389C2×C22⋊C4—264no—
390C2×C22⋊C4—521no—
391C2×C22⋊C4—522no—
392C2×C22⋊C4—522no—
393C2×C22⋊C4—522no—
394C2×C22⋊C4—522no—
395C2×C22⋊C4—521no—
396C2×C22⋊C4—522no—
397C2×C22⋊C4C2×Dic1318yes—
398C2×C22⋊C4C2×Dic1314yes—
399C2×C22⋊C4C22⋊D1318yes—
400C2×C42—264no—
401C2×C42—264no—
402C2×C42—522no—
403#95—264no—
404#95—264no—
405#95—522no—
406#95—522no—
407#95—522no—
408#95—522no—
409#95—521no—
410#95—522no—
411#95—521no—
412C2×C13—44no—
413C2×C13—82no—
414C2×C13#230911yescharacteristic
415C2×C13#233512yes—
416C2×C13#233912yes—
417C2×C13#237411yescharacteristic
418C2×C13#237611yescharacteristic
419C2×C13#270312yes—
420C2×C13#270612yes—
421C2×C13#271012yes—
422C2×C13#271812yes—
423C24—21no—
424C24—22no—
425C24—21no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—21no—
431C24—22no—
432C24—21no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24C22×Dic1312yes—
439C24C22×Dic1312yes—
440C24C2×C22⋊D1314yes—
441C24C23×D1311yescharacteristic
442C2×D4—28no—
443C2×D4—44no—
444C2×D4—44no—
445C2×D4—48no—
446C2×D4—48no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—28no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—44no—
463C22×C4—44no—
464C22×C4—48no—
465C22×C4—48no—
466C22×C4—134no—
467C22×C4—134no—
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×C4—262no—
479C22×C4—262no—
480C22×C4—262no—
481C22×C4—262no—
482C22×C4—262no—
483C22×C4—262no—
484C22×C4—262no—
485C22×C4—262no—
486C22×C4—262no—
487C22×C4—262no—
488C22×C4—262no—
489C22×C4—262no—
490C22×C4—262no—
491C22×C4—262no—
492C22×C4—262no—
493C22×C4—262no—
494C22×C4C22×Dic1314yes—
495C22×C4C22×Dic1312yes—
496C22×C4C22×Dic1314yes—
497C22×C4C2×C22⋊D1314yes—
498C22×C4C2×C22⋊D1314yes—
499C4⋊C4—216no—
500C4⋊C4—528no—
501C22⋊C4—216no—
502C22⋊C4—524no—
503C22⋊C4—528no—
504C22⋊C4—528no—
505C22⋊C4—528no—
506C22⋊C4—524no—
507C22⋊C4C22⋊Dic13116yescomplemented
508C42—528no—
509C13#1450611yescharacteristic, complemented, Sylow
510C23—22no—
511C23—22no—
512C23—24no—
513C23—24no—
514C23—24no—
515C23—24no—
516C23—24no—
517C23—24no—
518C23—24no—
519C23—24no—
520C23—22no—
521C23—22no—
522C23—24no—
523C23—24no—
524C23—22no—
525C23—41no—
526C23—42no—
527C23—41no—
528C23—42no—
529C23—42no—
530C23—42no—
531C23—42no—
532C23—41no—
533C23—41no—
534C23—42no—
535C23—42no—
536C23—42no—
537C23—42no—
538C23—42no—
539C23—42no—
540C23—42no—
541C23—41no—
542C23—42no—
543C23—41no—
544C23—42no—
545C23—42no—
546C23—42no—
547C23—42no—
548C23—41no—
549C23—41no—
550C23—42no—
551C23C2×C22⋊Dic1314yes—
552C23#8825111yescharacteristic
553C23#8825112yes—
554C23#8825111yescharacteristic
555C23#41×D1312yes—
556C23#41×D1312yes—
557C23#8825612yes—
558C23#8825712yes—
559C23C23×Dic1311yescharacteristic
560C23C22×C22⋊D1312yes—
561D4—416no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—24no—
573C2×C4—22no—
574C2×C4—416no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—264no—
582C2×C4—264no—
583C2×C4—264no—
584C2×C4—264no—
585C2×C4—264no—
586C2×C4—264no—
587C2×C4—522no—
588C2×C4—522no—
589C2×C4—522no—
590C2×C4—522no—
591C2×C4—522no—
592C2×C4—522no—
593C2×C4—522no—
594C2×C4—522no—
595C2×C4—522no—
596C2×C4—522no—
597C2×C4—522no—
598C2×C4—522no—
599C2×C4—522no—
600C2×C4—522no—
601C2×C4—522no—
602C2×C4—522no—
603C2×C4—522no—
604C2×C4—522no—
605C2×C4—522no—
606C2×C4—522no—
607C2×C4—522no—
608C2×C4—522no—
609C2×C4C2×C22⋊Dic1318yes—
610C22—28no—
611C22—24no—
612C22—42no—
613C22—42no—
614C22—44no—
615C22—44no—
616C22—44no—
617C22—44no—
618C22—44no—
619C22—42no—
620C22—42no—
621C22—44no—
622C22—44no—
623C22—42no—
624C22—82no—
625C22—82no—
626C22—82no—
627C22—82no—
628C22#1171935611yescharacteristic
629C22#1171936212yes—
630C22#1171936411yescharacteristic
631C22#1171936512yes—
632C22#1171936612yes—
633C22#1171936712yes—
634C22#1171936812yes—
635C22#1171936911yescharacteristic
636C22#1171937111yescharacteristic
637C22#1171937212yes—
638C22#1171950311yescharacteristic
639C22#1171950311yescharacteristic
640C22#1171951012yes—
641C22#1171951012yes—
642C22#1171952912yes—
643C22#1171952912yes—
644C22#41×Dic1312yes—
645C22#1171953212yes—
646C22#1171953412yes—
647C22#1171953412yes—
648C22C22×C22⋊Dic1311yescharacteristic
649C4—28no—
650C4—44no—
651C4—42no—
652C4—524no—
653C4—524no—
654C4—1042no—
655C4—1042no—
656C2—44no—
657C2—82no—
658C2#1311741811yescharacteristic
659C2#1311763012yes—
660C2#1311766612yes—
661C2#1311797211yescharacteristic
662C2#1311798411yescharacteristic
663C2#1312147312yes—
664C2#1312151812yes—
665C2#1312157412yes—
666C2#1312168212yes—
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC22×C13×#123C2
socle, cosocleC24×C13C24
prime radicalC23×D4×C13C22
hypercenterC22×#123D13
hypocenterC13#14506
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
1. C2×#11718612C2semidirect
2. #13113104C2semidirect
3. #13113081C2semidirect
6. #13113073C2semidirect
7. #13113065C2semidirect
8. #13113059C2semidirect
13. C2×C13×#123C4semidirect
169. C13×C22⋊C4C22⋊C4semidirect
289. C2×#123Dic13semidirect
507. C22⋊C4C22⋊Dic13semidirect
509. C13#14506semidirect

Maximal subgroups

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

subgroupindex
C2×#117186122
#131131042
#131130812
#131130772
#131130732
#131130652
#131130592
C22×C13×#1232
#1450613