Finite Group Databasebeta

← #15792977

Subgroups — #15792977

Order 3328.

1966 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718612C212yesmaximal, complemented
2C2×#11718881C212yesmaximal
3#13113104C211yesmaximal, characteristic, complemented
4#13113093C212yesmaximal, complemented
5#13113081C212yesmaximal, complemented
6#13113068C211yesmaximal, characteristic, complemented
7#13113058C212yesmaximal, complemented
8#13113058C212yesmaximal, complemented
9C2×C13×#394C211yesmaximal, characteristic
10C23×D4×C13C2211yescharacteristic
11C24×Dic13C2212yes—
12C22×C13×C4⋊C4C2211yescharacteristic
13C22×C13×C22⋊C4C2212yes—
14C22×C13×C22⋊C4C2212yes—
15C22×C22⋊Dic13C2212yes—
16C22×C22⋊Dic13C2212yes—
17C22×C22⋊Dic13C2212yes—
18C22×C4⋊Dic13C2212yes—
19C22×C4×Dic13C2211yescharacteristic
20C13×#394C418yescomplemented
21C2×C13×#95C2211yescharacteristic
22#11718881—28no—
23C2×#88071C2212yes—
24C2×#88071C2212yes—
25C2×#88071C2212yes—
26C2×#88071C2212yes—
27C2×#88071C2212yes—
28C2×#88071C2212yes—
29C2×#88071C2212yes—
30C2×#88071C2211yescharacteristic
31C2×#88071C2211yescharacteristic
32C2×#88071C2211yescharacteristic
33#11718612—28no—
34C25×C13C2312yes—
35C22×D4×C13—24no—
36C22×D4×C13—24no—
37C22×D4×C13—41no—
38C22×D4×C13—41no—
39C22×D4×C13C2×C414yes—
40C23×C4×C13C2311yescharacteristic
41C23×C4×C13C2312yes—
42C23×C4×C13C2311yescharacteristic
43C23×C4×C13C2311yescharacteristic
44C23×Dic13—24no—
45C23×Dic13—24no—
46C23×Dic13—24no—
47C23×Dic13—42no—
48C23×Dic13—42no—
49C23×Dic13—42no—
50C23×Dic13—42no—
51C23×Dic13C2312yes—
52C23×Dic13C2312yes—
53C23×Dic13C2312yes—
54C23×Dic13C2312yes—
55C2×C13×C4⋊C4—41no—
56C2×C13×C4⋊C4—41no—
57C2×C13×C4⋊C4C2×C414yescomplemented
58C2×C13×C22⋊C4—24no—
59C2×C13×C22⋊C4—24no—
60C2×C13×C22⋊C4—42no—
61C2×C13×C22⋊C4—42no—
62C2×C13×C22⋊C4C2×C418yescomplemented
63C2×C13×C22⋊C4C2×C418yescomplemented
64C2×C22⋊Dic13—24no—
65C2×C22⋊Dic13—24no—
66C2×C22⋊Dic13—24no—
67C2×C22⋊Dic13—24no—
68C2×C22⋊Dic13—42no—
69C2×C22⋊Dic13—42no—
70C2×C22⋊Dic13—42no—
71C2×C22⋊Dic13—42no—
72C2×C22⋊Dic13D418yes—
73C2×C4⋊Dic13—24no—
74C2×C4⋊Dic13—42no—
75C2×C4⋊Dic13—42no—
76C2×C4×Dic13—24no—
77C2×C4×Dic13—41no—
78C13×#95C2×C414yescomplemented
79#88071—24no—
80#88071—24no—
81#88071—24no—
82#88071—24no—
83#88071—24no—
84#88071—42no—
85#88071—41no—
86#88071—41no—
87#88071—42no—
88#88071—41no—
89#14571—131nomaximal, Sylow
90C24×C13—22no—
91C24×C13—22no—
92C24×C13—22no—
93C24×C13—22no—
94C24×C13—22no—
95C24×C13—22no—
96C24×C13—22no—
97C24×C13—22no—
98C24×C13—22no—
99C24×C13—22no—
100C24×C13—22no—
101C24×C13—22no—
102C24×C13C22×C414yes—
103C24×C13C2×D414yes—
104C24×C13#4114yes—
105C24×C13C2411yescharacteristic
106C2×D4×C13—216no—
107C2×D4×C13—44no—
108C2×D4×C13—44no—
109C2×D4×C13—48no—
110C2×D4×C13—44no—
111C22×C4×C13—22no—
112C22×C4×C13—22no—
113C22×C4×C13—22no—
114C22×C4×C13—22no—
115C22×C4×C13—22no—
116C22×C4×C13—22no—
117C22×C4×C13—22no—
118C22×C4×C13—22no—
119C22×C4×C13—22no—
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—21no—
127C22×C4×C13—21no—
128C22×C4×C13—22no—
129C22×C4×C13C22×C414yes—
130C22×C4×C13C22×C412yes—
131C22×C4×C13C22×C412yes—
132C22×C4×C13C22×C412yes—
133C22×Dic13—22no—
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—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—48no—
159C22×Dic13—48no—
160C22×Dic13—48no—
161C22×Dic13—48no—
162C22×Dic13—48no—
163C22×Dic13—48no—
164C22×Dic13—48no—
165C22×Dic13C2×D414yes—
166C22×Dic13C2×D414yes—
167C22×Dic13#4114yes—
168C13×C4⋊C4—44no—
169C13×C22⋊C4—216no—
170C13×C22⋊C4—48no—
171C22⋊Dic13—48no—
172C22⋊Dic13—48no—
173C22⋊Dic13—48no—
174C4⋊Dic13—48no—
175C4×Dic13—44no—
176C2×#394D1311yescharacteristic
177C2×#388—132no—
178C2×#386—132no—
179#1445—131no—
180#1442—132no—
181#1439—132no—
182#1436—131no—
183C22⋊#95—132no—
184C22⋊#95—132no—
185C23×C13—24no—
186C23×C13—24no—
187C23×C13—24no—
188C23×C13—24no—
189C23×C13—24no—
190C23×C13—24no—
191C23×C13—24no—
192C23×C13—24no—
193C23×C13—24no—
194C23×C13—24no—
195C23×C13—24no—
196C23×C13—24no—
197C23×C13—24no—
198C23×C13—24no—
199C23×C13—24no—
200C23×C13—24no—
201C23×C13—24no—
202C23×C13—24no—
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—42no—
212C23×C13—42no—
213C23×C13—42no—
214C23×C13—42no—
215C23×C13—42no—
216C23×C13—42no—
217C23×C13—42no—
218C23×C13—42no—
219C23×C13C4×D418yes—
220C23×C13C23×C411yescharacteristic
221C23×C13C22×D412yes—
222C23×C13C2×#4112yes—
223C23×C13C2×#4112yes—
224C23×C13H(5,𝔽2)12yes—
225C23×C13H(5,𝔽2)11yescharacteristic
226C23×C13H(5,𝔽2)11yescharacteristic
227C23×C13H(5,𝔽2)12yes—
228C23×C132−1+412yes—
229D4×C13—416no—
230C2×C4×C13—24no—
231C2×C4×C13—24no—
232C2×C4×C13—24no—
233C2×C4×C13—22no—
234C2×C4×C13—22no—
235C2×C4×C13—24no—
236C2×C4×C13—22no—
237C2×C4×C13—22no—
238C2×C4×C13—22no—
239C2×C4×C13—24no—
240C2×C4×C13—42no—
241C2×C4×C13—42no—
242C2×C4×C13—42no—
243C2×C4×C13—42no—
244C2×C4×C13—42no—
245C2×C4×C13—42no—
246C2×C4×C13—41no—
247C2×C4×C13—41no—
248C2×C4×C13—42no—
249C2×C4×C13—42no—
250C2×C4×C13—41no—
251C2×C4×C13—41no—
252C2×Dic13—24no—
253C2×Dic13—24no—
254C2×Dic13—24no—
255C2×Dic13—24no—
256C2×Dic13—24no—
257C2×Dic13—24no—
258C2×Dic13—24no—
259C2×Dic13—24no—
260C2×Dic13—24no—
261C2×Dic13—432no—
262C2×Dic13—42no—
263C2×Dic13—42no—
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—
281C23×D4C2×D1311yescharacteristic
282C24×C4—132no—
283C22×C4⋊C4—132no—
284C22×C4⋊C4C2×D1311yescharacteristic
285C22×C22⋊C4—132no—
286C22×C22⋊C4—132no—
287C22×C22⋊C4—132no—
288C22×C22⋊C4C2×D1312yes—
289C22×C22⋊C4C2×D1312yes—
290C22×C42—131no—
291#394Dic1318yescomplemented
292#388—268no—
293#386—268no—
294C2×#95—132no—
295C2×#95—132no—
296C2×#95—132no—
297C2×#95—132no—
298C2×#95—132no—
299C2×#95—131no—
300C2×#95—132no—
301C2×#95—131no—
302C2×#95—132no—
303C2×#95—131no—
304C2×#95C2×D1311yescharacteristic
305C22×C13—28no—
306C22×C13—28no—
307C22×C13—28no—
308C22×C13—44no—
309C22×C13—44no—
310C22×C13—44no—
311C22×C13—44no—
312C22×C13—44no—
313C22×C13—44no—
314C22×C13—44no—
315C22×C13—44no—
316C22×C13—44no—
317C22×C13—44no—
318C22×C13—44no—
319C22×C13—44no—
320C22×C13C2×C4×D412yes—
321C22×C13C4×#4111yescharacteristic
322C22×C13#51811yescharacteristic
323C22×C13#51811yescharacteristic
324C22×C13#52012yes—
325C22×C13#53412yes—
326C22×C13#53712yes—
327C22×C13#53812yes—
328C22×C13#53812yes—
329C22×C13#53912yes—
330C22×C13#54012yes—
331C22×C13D4211yescharacteristic
332C22×C13#54612yes—
333C22×C13#54612yes—
334C22×C13#54712yes—
335C22×C13#55111yescharacteristic
336C22×C13#55112yes—
337C22×C13#55212yes—
338C22×C13H(3,𝔽4)11yescharacteristic
339C22×C13#56212yes—
340C22×C13#56311yescharacteristic
341C4×C13—44no—
342C4×C13—42no—
343C4×C13—42no—
344C4×C13—42no—
345Dic13—44no—
346Dic13—44no—
347Dic13—44no—
348Dic13—82no—
349C25C22×D1312yes—
350C22×D4—24no—
351C22×D4—24no—
352C22×D4—41no—
353C22×D4—41no—
354C22×D4C2×Dic1314yes—
355C23×C4—132no—
356C23×C4—132no—
357C23×C4—132no—
358C23×C4—132no—
359C23×C4—264no—
360C23×C4—264no—
361C23×C4—264no—
362C23×C4—522no—
363C23×C4—522no—
364C23×C4—522no—
365C23×C4—522no—
366C23×C4C22×D1312yes—
367C23×C4C22×D1311yescharacteristic
368C23×C4C22×D1311yescharacteristic
369C23×C4C22×D1311yescharacteristic
370C2×C4⋊C4—41no—
371C2×C4⋊C4—41no—
372C2×C4⋊C4—264no—
373C2×C4⋊C4—522no—
374C2×C4⋊C4—522no—
375C2×C4⋊C4C2×Dic1314yescomplemented
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—42no—
379C2×C22⋊C4—42no—
380C2×C22⋊C4—138no—
381C2×C22⋊C4—264no—
382C2×C22⋊C4—264no—
383C2×C22⋊C4—264no—
384C2×C22⋊C4—264no—
385C2×C22⋊C4—522no—
386C2×C22⋊C4—522no—
387C2×C22⋊C4—522no—
388C2×C22⋊C4—522no—
389C2×C22⋊C4C2×Dic1318yescomplemented
390C2×C22⋊C4C2×Dic1318yescomplemented
391C2×C42—264no—
392C2×C42—521no—
393#95—264no—
394#95—264no—
395#95—264no—
396#95—264no—
397#95—264no—
398#95—522no—
399#95—521no—
400#95—521no—
401#95—521no—
402#95—522no—
403#95C2×Dic1314yescomplemented
404C2×C13—48no—
405C2×C13#232512yes—
406C2×C13#233311yescharacteristic
407C2×C13#235811yescharacteristic
408C2×C13#235912yes—
409C2×C13#237911yescharacteristic
410C2×C13#267112yes—
411C2×C13#268412yes—
412C2×C13#269512yes—
413C2×C13#274312yes—
414C24—22no—
415C24—22no—
416C24—22no—
417C24—22no—
418C24—22no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24D4×D1314yes—
427C24#612914yes—
428C24C22×Dic1314yes—
429C24C23×D1311yescharacteristic
430C2×D4—216no—
431C2×D4—44no—
432C2×D4—44no—
433C2×D4—44no—
434C2×D4—48no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—134no—
454C22×C4—134no—
455C22×C4—134no—
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—262no—
465C22×C4—262no—
466C22×C4—262no—
467C22×C4—262no—
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—528no—
482C22×C4—528no—
483C22×C4—528no—
484C22×C4—528no—
485C22×C4—528no—
486C22×C4—528no—
487C22×C4—528no—
488C22×C4C22×Dic1314yes—
489C22×C4C22×Dic1312yes—
490C22×C4C22×Dic1312yes—
491C22×C4C22×Dic1312yes—
492C4⋊C4—44no—
493C4⋊C4—528no—
494C22⋊C4—216no—
495C22⋊C4—48no—
496C22⋊C4—528no—
497C22⋊C4—528no—
498C22⋊C4—528no—
499C42—524no—
500C13#1457111yescharacteristic, complemented, Sylow
501C23—24no—
502C23—24no—
503C23—24no—
504C23—24no—
505C23—24no—
506C23—24no—
507C23—24no—
508C23—24no—
509C23—24no—
510C23—24no—
511C23—24no—
512C23—24no—
513C23—24no—
514C23—24no—
515C23—24no—
516C23—24no—
517C23—24no—
518C23—24no—
519C23—42no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23—42no—
524C23—42no—
525C23—42no—
526C23—42no—
527C23—42no—
528C23—42no—
529C23—42no—
530C23—42no—
531C23—42no—
532C23—42no—
533C23—42no—
534C23—42no—
535C23D4×Dic1318yes—
536C23C2×D4×D1312yes—
537C23C2×#612912yes—
538C23#8825111yescharacteristic
539C23#8825111yescharacteristic
540C23#8825112yes—
541C23#41×D1312yes—
542C23#8825612yes—
543C23#8825712yes—
544C23C23×Dic1311yescharacteristic
545D4—416no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—24no—
549C2×C4—22no—
550C2×C4—24no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—24no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—264no—
569C2×C4—264no—
570C2×C4—264no—
571C2×C4—264no—
572C2×C4—264no—
573C2×C4—264no—
574C2×C4—264no—
575C2×C4—264no—
576C2×C4—264no—
577C2×C4—5232no—
578C2×C4—522no—
579C2×C4—522no—
580C2×C4—522no—
581C2×C4—522no—
582C2×C4—522no—
583C2×C4—522no—
584C2×C4—522no—
585C2×C4—522no—
586C2×C4—522no—
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—
597C22—28no—
598C22—28no—
599C22—28no—
600C22—44no—
601C22—44no—
602C22—44no—
603C22—44no—
604C22—44no—
605C22—44no—
606C22—44no—
607C22—44no—
608C22—44no—
609C22—44no—
610C22—44no—
611C22—44no—
612C22#1171929211yescharacteristic
613C22#1171929511yescharacteristic
614C22#1171929612yes—
615C22#1171930212yes—
616C22#1171930712yes—
617C22#1171931012yes—
618C22#1171931812yes—
619C22#1171932012yes—
620C22#1171932212yes—
621C22#1171935512yes—
622C22#1171935912yes—
623C22#1171936012yes—
624C22#1171936312yes—
625C22#1171937711yescharacteristic
626C22#1171938811yescharacteristic
627C22#1171938912yes—
628C22C2×D4×Dic1312yes—
629C22#1171950311yescharacteristic
630C22#1171950311yescharacteristic
631C22#41×Dic1311yescharacteristic
632C22#1171953212yes—
633C4—44no—
634C4—42no—
635C4—42no—
636C4—42no—
637C4—524no—
638C4—524no—
639C4—524no—
640C4—1042no—
641C2—48no—
642C2#1311754112yes—
643C2#1311760311yescharacteristic
644C2#1311782011yescharacteristic
645C2#1311783212yes—
646C2#1311801011yescharacteristic
647C2#1312106512yes—
648C2#1312121112yes—
649C2#1312137012yes—
650C2#1312197712yes—
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#394C2
socle, cosocleC24×C13C24
prime radicalC23×D4×C13C22
hypercenterC2×#394D13
hypocenterC13#14571
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. C2×#11718612C2semidirect
3. #13113104C2semidirect
4. #13113093C2semidirect
5. #13113081C2semidirect
6. #13113068C2semidirect
7. #13113058C2semidirect
8. #13113058C2semidirect
20. C13×#394C4semidirect
57. C2×C13×C4⋊C4C2×C4semidirect
62. C2×C13×C22⋊C4C2×C4semidirect
63. C2×C13×C22⋊C4C2×C4semidirect
78. C13×#95C2×C4semidirect
291. #394Dic13semidirect
375. C2×C4⋊C4C2×Dic13semidirect
389. C2×C22⋊C4C2×Dic13semidirect
390. C2×C22⋊C4C2×Dic13semidirect
403. #95C2×Dic13semidirect
500. C13#14571semidirect

Maximal subgroups

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

subgroupindex
C2×#117186122
C2×#117188812
#131131042
#131130932
#131130812
#131130682
#131130582
C2×C13×#3942
#1457113