Finite Group Databasebeta

← #15793602

Subgroups — #15793602

Order 3328.

1390 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718334C211yesmaximal, characteristic
2C2×#11718590C211yesmaximal, characteristic, complemented
3C2×#11718601C211yesmaximal, characteristic
4#13113106C211yesmaximal, characteristic, complemented
5#13113101C211yesmaximal, characteristic, complemented
6#13113092C212yesmaximal, complemented
7#13113091C212yesmaximal, complemented
8#13113084C212yesmaximal
9#13113082C211yesmaximal, characteristic
10#13113082C212yesmaximal
11C13×#1434C211yesmaximal, characteristic, complemented
12C23×Dic26C2211yescharacteristic
13C22×C42×C13C2211yescharacteristic
14C22×#6103C2211yescharacteristic
15C22×#6103C2211yescharacteristic
16C22×#6103C2211yescharacteristic
17C22×#6103C2212yes—
18C22×#6103C2212yes—
19C22×C4⋊Dic13C2211yescharacteristic
20C22×C4⋊Dic13C2212yes—
21C22×#6101C2211yescharacteristic
22C2×C13×#95C2211yescharacteristic
23C2×C13×#95C2212yes—
24C2×C13×#95C2212yes—
25C2×C13×#95C2211yescharacteristic
26C2×#88071C2212yes—
27C2×#88071C2211yescharacteristic
28C2×#88071C2212yes—
29C2×#88071C2211yescharacteristic
30C2×#88071C2212yes—
31C2×#88071C2212yes—
32C2×#88071C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2212yes—
35#11718601—24no—
36#11718590—24no—
37#11718334C418yescomplemented
38C24×D13C2311yescharacteristic
39C23×C4×C13C2312yes—
40C23×C4×C13C2312yes—
41C23×C4×C13C2311yescharacteristic
42C23×C4×C13C2311yescharacteristic
43C23×C4×C13C2311yescharacteristic
44C23×Dic13C2311yescharacteristic
45C23×Dic13C2312yes—
46C23×Dic13C2311yescharacteristic
47C23×Dic13C2311yescharacteristic
48C23×Dic13C2312yes—
49C22×Dic26—22no—
50C22×Dic26—22no—
51C22×Dic26—42no—
52C22×Dic26—42no—
53C22×Dic26C2×C414yes—
54C2×C42×C13—42no—
55C2×C42×C13D414yes—
56C2×#6103—22no—
57C2×#6103—22no—
58C2×#6103—22no—
59C2×#6103—22no—
60C2×#6103—42no—
61C2×#6103—42no—
62C2×#6103—42no—
63C2×#6103—42no—
64C2×#6103—42no—
65C2×#6103—42no—
66C2×#6103—42no—
67C2×#6103C2×C414yes—
68C2×#6103C2×C418yes—
69C2×C4⋊Dic13—22no—
70C2×C4⋊Dic13—42no—
71C2×C4⋊Dic13—42no—
72C2×C4⋊Dic13—42no—
73C2×C4⋊Dic13—42no—
74C2×#6101—22no—
75C2×#6101—42no—
76C13×#95—22no—
77C13×#95—42no—
78C13×#95—42no—
79C13×#95C2×C414yes—
80#88071—24no—
81#88071—24no—
82#88071—22no—
83#88071—22no—
84#88071—42no—
85#88071—42no—
86#88071—42no—
87#88071—42no—
88#88071C2×C418yes—
89#14625—131nomaximal, Sylow
90C24×C13C2411yescharacteristic
91C23×D13—21no—
92C23×D13—21no—
93C23×D13—22no—
94C23×D13—21no—
95C23×D13—22no—
96C23×D13—22no—
97C23×D13—21no—
98C23×D13—21no—
99C23×D13—21no—
100C23×D13—22no—
101C23×D13C22×C412yes—
102C22×C4×C13—22no—
103C22×C4×C13—22no—
104C22×C4×C13—22no—
105C22×C4×C13—21no—
106C22×C4×C13—22no—
107C22×C4×C13—22no—
108C22×C4×C13—22no—
109C22×C4×C13—22no—
110C22×C4×C13—22no—
111C22×C4×C13—22no—
112C22×C4×C13—21no—
113C22×C4×C13—22no—
114C22×C4×C13—22no—
115C22×C4×C13—21no—
116C22×C4×C13—21no—
117C22×C4×C13—22no—
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×C13C22×C414yes—
126C22×C4×C13C22×C412yes—
127C22×C4×C13C2×D412yes—
128C22×C4×C13C2×D412yes—
129C22×C4×C13C2×D412yes—
130C22×C4×C13#4112yes—
131C22×Dic13—22no—
132C22×Dic13—21no—
133C22×Dic13—21no—
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—22no—
145C22×Dic13—22no—
146C22×Dic13—22no—
147C22×Dic13—22no—
148C22×Dic13—22no—
149C22×Dic13—22no—
150C22×Dic13—21no—
151C22×Dic13—22no—
152C22×Dic13—22no—
153C22×Dic13—22no—
154C22×Dic13—21no—
155C22×Dic13—21no—
156C22×Dic13—22no—
157C22×Dic13—21no—
158C22×Dic13C22×C412yes—
159C22×Dic13C22×C414yes—
160C2×Dic26—28no—
161C2×Dic26—48no—
162C2×Dic26—44no—
163C2×Dic26—44no—
164C2×Dic26—48no—
165C42×C13—44no—
166#6103—28no—
167#6103—48no—
168#6103—44no—
169#6103—44no—
170#6103—48no—
171C4⋊Dic13—44no—
172C4⋊Dic13—48no—
173#6101—44no—
174C2×#393—131no—
175C2×#391—131no—
176C2×#388—131no—
177#1446—131no—
178#1444—131no—
179#1442—132no—
180#1442—132no—
181#1440—132no—
182#1439—131no—
183#1439—132no—
184#1434D1311yescharacteristic, complemented
185C23×C13C23×C411yescharacteristic
186C23×C13C22×D411yescharacteristic
187C23×C13C2×#4111yescharacteristic
188C23×C13H(5,𝔽2)12yes—
189C23×C13H(5,𝔽2)12yes—
190C23×C13H(5,𝔽2)12yes—
191C23×C13H(5,𝔽2)11yescharacteristic
192C23×C132−1+411yescharacteristic
193C23×C132−1+411yescharacteristic
194C23×C132−1+411yescharacteristic
195C23×C132−1+412yes—
196C22×D13—22no—
197C22×D13—24no—
198C22×D13—22no—
199C22×D13—22no—
200C22×D13—24no—
201C22×D13—41no—
202C22×D13—41no—
203C22×D13—41no—
204C22×D13—41no—
205C22×D13—41no—
206C22×D13—41no—
207C22×D13—42no—
208C22×D13—41no—
209C22×D13—41no—
210C22×D13—42no—
211C22×D13—42no—
212C22×D13—42no—
213C22×D13—42no—
214C22×D13—42no—
215C22×D13—42no—
216C22×D13—42no—
217C22×D13—42no—
218C22×D13—42no—
219C2×C4×C13—24no—
220C2×C4×C13—22no—
221C2×C4×C13—22no—
222C2×C4×C13—24no—
223C2×C4×C13—24no—
224C2×C4×C13—24no—
225C2×C4×C13—24no—
226C2×C4×C13—22no—
227C2×C4×C13—22no—
228C2×C4×C13—22no—
229C2×C4×C13—22no—
230C2×C4×C13—22no—
231C2×C4×C13—22no—
232C2×C4×C13—42no—
233C2×C4×C13—42no—
234C2×C4×C13—42no—
235C2×C4×C13—42no—
236C2×C4×C13—42no—
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×C13—42no—
245C2×C4×C13—42no—
246C2×C4×C13—42no—
247C2×C4×C13C4×D414yes—
248C2×Dic13—22no—
249C2×Dic13—24no—
250C2×Dic13—24no—
251C2×Dic13—24no—
252C2×Dic13—24no—
253C2×Dic13—42no—
254C2×Dic13—41no—
255C2×Dic13—42no—
256C2×Dic13—41no—
257C2×Dic13—42no—
258C2×Dic13—42no—
259C2×Dic13—42no—
260C2×Dic13—41no—
261C2×Dic13—41no—
262C2×Dic13—42no—
263C2×Dic13—41no—
264C2×Dic13—42no—
265C2×Dic13—41no—
266C2×Dic13—41no—
267C2×Dic13—42no—
268C2×Dic13—41no—
269C2×Dic13—42no—
270C2×Dic13—42no—
271C2×Dic13—42no—
272C2×Dic13—42no—
273C2×Dic13—42no—
274C2×Dic13—42no—
275C2×Dic13—42no—
276C2×Dic13—42no—
277Dic26—416no—
278C23×Q8—131no—
279C22×C4⋊C4—131no—
280C22×C4⋊C4—131no—
281C22×C4⋊C4—132no—
282C22×C22⋊C4—131no—
283C22×C22⋊C4—132no—
284C22×C22⋊C4—131no—
285C22×C22⋊C4—131no—
286C22×C22⋊C4—132no—
287C22×C42C2×D1311yescharacteristic
288#393—138no—
289#391—264no—
290#388—264no—
291C2×#95—132no—
292C2×#95—132no—
293C2×#95—132no—
294C2×#95—131no—
295C2×#95—131no—
296C2×#95—132no—
297C2×#95—132no—
298C2×#95—132no—
299C2×#95—132no—
300C2×#95C2×D1311yescharacteristic
301C2×#95C2×D1312yes—
302C2×#95C2×D1312yes—
303C2×#95C2×D1311yescharacteristic
304C22×C13C2×C4×D411yescharacteristic
305C22×C13#51812yes—
306C22×C13#51911yescharacteristic
307C22×C13#52012yes—
308C22×C13#52011yescharacteristic
309C22×C13#53411yescharacteristic
310C22×C13#53511yescharacteristic
311C22×C13#53511yescharacteristic
312C22×C13#53611yescharacteristic
313C22×C13#53611yescharacteristic
314C22×C13#53711yescharacteristic
315C22×C13#53812yes—
316C22×C13#54111yescharacteristic
317C22×C13#54212yes—
318C22×C13#54211yescharacteristic
319C22×C13H(3,𝔽4)12yes—
320C22×C13#56212yes—
321C22×C13#56212yes—
322C22×C13#56212yes—
323C22×C13#56212yes—
324C22×C13#56312yes—
325C22×C13#56312yes—
326C22×C13#56312yes—
327C2×D13—42no—
328C2×D13—42no—
329C2×D13—42no—
330C2×D13—44no—
331C2×D13—44no—
332C2×D13—81no—
333C2×D13—81no—
334C2×D13—81no—
335C2×D13—82no—
336C2×D13—82no—
337C2×D13—81no—
338C4×C13—24no—
339C4×C13—42no—
340C4×C13—44no—
341C4×C13—42no—
342C4×C13—82no—
343Dic13—44no—
344Dic13—42no—
345Dic13—81no—
346Dic13—82no—
347Dic13—81no—
348C25—131no—
349C22×Q8—134no—
350C22×Q8—262no—
351C22×Q8—262no—
352C22×Q8—522no—
353C22×Q8—522no—
354C23×C4—131no—
355C23×C4—132no—
356C23×C4—131no—
357C23×C4—132no—
358C23×C4—131no—
359C23×C4C22×D1312yes—
360C23×C4C22×D1312yes—
361C23×C4C22×D1311yescharacteristic
362C23×C4C22×D1311yescharacteristic
363C23×C4C22×D1311yescharacteristic
364C2×C4⋊C4—262no—
365C2×C4⋊C4—262no—
366C2×C4⋊C4—522no—
367C2×C4⋊C4—522no—
368C2×C4⋊C4—522no—
369C2×C4⋊C4—522no—
370C2×C4⋊C4—522no—
371C2×C22⋊C4—134no—
372C2×C22⋊C4—138no—
373C2×C22⋊C4—262no—
374C2×C22⋊C4—262no—
375C2×C22⋊C4—262no—
376C2×C22⋊C4—262no—
377C2×C22⋊C4—522no—
378C2×C22⋊C4—522no—
379C2×C22⋊C4—522no—
380C2×C22⋊C4—522no—
381C2×C22⋊C4—522no—
382C2×C22⋊C4—522no—
383C2×C22⋊C4—522no—
384C2×C42—42no—
385C2×C42D5214yes—
386#95—22no—
387#95—42no—
388#95—42no—
389#95—138no—
390#95—262no—
391#95—262no—
392#95—264no—
393#95—264no—
394#95—522no—
395#95—522no—
396#95—522no—
397#95—522no—
398#95C4×D1314yes—
399C2×C13#232111yescharacteristic
400C2×C13#232311yescharacteristic
401C2×C13#232611yescharacteristic
402C2×C13#237812yes—
403C2×C13#237912yes—
404C2×C13#281411yescharacteristic
405C2×C13#281611yescharacteristic
406C2×C13#281911yescharacteristic
407C2×C13#282111yescharacteristic
408C2×C13#283112yes—
409C2×C13#283212yes—
410D13—82no—
411C24—132no—
412C24—261no—
413C24—261no—
414C24—262no—
415C24—261no—
416C24—261no—
417C24—262no—
418C24—262no—
419C24—262no—
420C24—261no—
421C24—261no—
422C24C23×D1311yescharacteristic
423C2×Q8—268no—
424C2×Q8—528no—
425C2×Q8—524no—
426C2×Q8—524no—
427C2×Q8—528no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—21no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—132no—
452C22×C4—134no—
453C22×C4—262no—
454C22×C4—261no—
455C22×C4—261no—
456C22×C4—262no—
457C22×C4—262no—
458C22×C4—262no—
459C22×C4—262no—
460C22×C4—262no—
461C22×C4—262no—
462C22×C4—262no—
463C22×C4—261no—
464C22×C4—262no—
465C22×C4—261no—
466C22×C4—262no—
467C22×C4—262no—
468C22×C4—261no—
469C22×C4—261no—
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—261no—
479C22×C4—261no—
480C22×C4C2×C4×D1314yes—
481C22×C4C2×C4×D1312yes—
482C22×C4C2×D5212yes—
483C22×C4C2×D5212yes—
484C22×C4C2×D5212yes—
485C22×C4#612712yes—
486C4⋊C4—524no—
487C4⋊C4—524no—
488C4⋊C4—528no—
489C22⋊C4—268no—
490C22⋊C4—528no—
491C22⋊C4—524no—
492C22⋊C4—524no—
493C22⋊C4—528no—
494C42—44no—
495C13#1462511yescharacteristic, complemented, Sylow
496C23—262no—
497C23—264no—
498C23—264no—
499C23—262no—
500C23—262no—
501C23—521no—
502C23—521no—
503C23—521no—
504C23—521no—
505C23—521no—
506C23—521no—
507C23—522no—
508C23—522no—
509C23—521no—
510C23—521no—
511C23—522no—
512C23—522no—
513C23—522no—
514C23—522no—
515C23—522no—
516C23—522no—
517C23—522no—
518C23—522no—
519C23C22×C4×D1311yescharacteristic
520C23C22×D5211yescharacteristic
521C23C2×#612711yescharacteristic
522C23#8825112yes—
523C23#8825111yescharacteristic
524C23#8825411yescharacteristic
525C23#8825612yes—
526C23#8825612yes—
527C23#8825712yes—
528C23#8825711yescharacteristic
529C23#8825711yescharacteristic
530Q8—5216no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—24no—
534C2×C4—24no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—24no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—262no—
560C2×C4—264no—
561C2×C4—264no—
562C2×C4—264no—
563C2×C4—264no—
564C2×C4—522no—
565C2×C4—521no—
566C2×C4—522no—
567C2×C4—521no—
568C2×C4—522no—
569C2×C4—522no—
570C2×C4—522no—
571C2×C4—521no—
572C2×C4—521no—
573C2×C4—522no—
574C2×C4—521no—
575C2×C4—521no—
576C2×C4—522no—
577C2×C4—522no—
578C2×C4—521no—
579C2×C4—521no—
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×C4C4×D5214yes—
589C22—524no—
590C22—524no—
591C22—522no—
592C22—522no—
593C22—522no—
594C22—1041no—
595C22—1041no—
596C22—1041no—
597C22—1041no—
598C22—1042no—
599C22—1042no—
600C22C2×C4×D5211yescharacteristic
601C22#1171919811yescharacteristic
602C22#1171921511yescharacteristic
603C22#1171922812yes—
604C22#1171923011yescharacteristic
605C22#1171923011yescharacteristic
606C22#1171923111yescharacteristic
607C22#1171923111yescharacteristic
608C22#1171923912yes—
609C22#1171925012yes—
610C22#1171925111yescharacteristic
611C22#1171926512yes—
612C22#1171926611yescharacteristic
613C22#1171927711yescharacteristic
614C22#1171928811yescharacteristic
615C22#1171932612yes—
616C22#1171935112yes—
617C22#1171937212yes—
618C22#1171937212yes—
619C22#1171938812yes—
620C22#1171940512yes—
621C22#1171941712yes—
622C22#1171941712yes—
623C4—24no—
624C4—42no—
625C4—42no—
626C4—44no—
627C4—82no—
628C4—524no—
629C4—522no—
630C4—1041no—
631C4—1041no—
632C4—1042no—
633C2—1042no—
634C2#1311749611yescharacteristic
635C2#1311751911yescharacteristic
636C2#1311754711yescharacteristic
637C2#1311800112yes—
638C2#1311800512yes—
639C2#1312285111yescharacteristic
640C2#1312286611yescharacteristic
641C2#1312288211yescharacteristic
642C2#1312289711yescharacteristic
643C2#1312299012yes—
644C2#1312300112yes—
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1434C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenter#1434D13
hypocenterC13#14625
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
2. C2×#11718590C2semidirect
4. #13113106C2semidirect
5. #13113101C2semidirect
6. #13113092C2semidirect
7. #13113091C2semidirect
11. C13×#1434C2semidirect
37. #11718334C4semidirect
184. #1434D13semidirect
495. C13#14625semidirect

Maximal subgroups

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

subgroupindex
C2×#117183342
C2×#117185902
C2×#117186012
#131131062
#131131012
#131130922
#131130912
#131130842
#131130822
C13×#14342
#1462513