Finite Group Databasebeta

← #15790163

Subgroups — #15790163

Order 3328.

1422 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#6103C211yesmaximal, characteristic
2#13113096C212yesmaximal, complemented
3#13113095C212yesmaximal, complemented
4#13113084C212yesmaximal
5#13113078C212yesmaximal
6#13113063C211yesmaximal, characteristic, complemented
7#13113061C211yesmaximal, characteristic, complemented
8#13113061C211yesmaximal, characteristic, complemented
9#13113057C211yesmaximal, characteristic
10#13113057C211yesmaximal, characteristic
11C13×C4⋊#95C211yesmaximal, characteristic, complemented
12C23×C4×D13C2211yescharacteristic
13C22×C13×C4⋊C4C2212yes—
14C22×C42×C13C2211yescharacteristic
15C22×#6103C2211yescharacteristic
16C22×#6103C2211yescharacteristic
17C22×#6103C2212yes—
18C22×#6103C2212yes—
19C22×C4×Dic13C2211yescharacteristic
20C2×C13×#95C2211yescharacteristic
21C2×C13×#95C2211yescharacteristic
22C2×C13×#95C2212yes—
23C2×#88071C2212yes—
24C2×#88071C2211yescharacteristic
25C2×#88071C2211yescharacteristic
26C2×#88071C2212yes—
27C2×#88071C2212yes—
28C2×#88071C2212yes—
29C2×#88071C2212yes—
30C2×#88071C2212yes—
31C2×#88071C2212yes—
32C2×#88071C2212yes—
33C2×#88071C2211yescharacteristic
34C2×#88071C2211yescharacteristic
35C4×#6103C418yescomplemented
36C24×D13C2311yescharacteristic
37C23×C4×C13C2312yes—
38C23×C4×C13C2312yes—
39C23×C4×C13C2311yescharacteristic
40C23×C4×C13C2311yescharacteristic
41C23×C4×C13C2311yescharacteristic
42C23×Dic13C2312yes—
43C23×Dic13C2312yes—
44C23×Dic13C2311yescharacteristic
45C23×Dic13C2311yescharacteristic
46C23×Dic13C2311yescharacteristic
47C22×C4×D13—22no—
48C22×C4×D13—22no—
49C22×C4×D13—42no—
50C22×C4×D13—42no—
51C22×C4×D13C2×C414yes—
52C2×C13×C4⋊C4—24no—
53C2×C13×C4⋊C4—42no—
54C2×C13×C4⋊C4—42no—
55C2×C42×C13—42no—
56C2×C42×C13C2×C414yes—
57C2×#6103—24no—
58C2×#6103—24no—
59C2×#6103—24no—
60C2×#6103—24no—
61C2×#6103—42no—
62C2×#6103—42no—
63C2×#6103—42no—
64C2×#6103—42no—
65C2×#6103C2×C414yes—
66C2×#6103C2×C414yes—
67C2×C4×Dic13—42no—
68C2×C4×Dic13C2×C414yes—
69C13×#95—22no—
70C13×#95—22no—
71C13×#95—42no—
72#88071—24no—
73#88071—22no—
74#88071—22no—
75#88071—42no—
76#88071—42no—
77#88071—42no—
78#88071—42no—
79#88071—42no—
80#88071—42no—
81#88071—42no—
82#88071C2×C414yes—
83#88071C2×C414yes—
84#14351—131nomaximal, Sylow
85C24×C13C2411yescharacteristic
86C23×D13—22no—
87C23×D13—21no—
88C23×D13—21no—
89C23×D13—21no—
90C23×D13—21no—
91C23×D13—22no—
92C23×D13—22no—
93C23×D13—21no—
94C23×D13—21no—
95C23×D13C22×C412yes—
96C23×D13#4114yes—
97C22×C4×C13—22no—
98C22×C4×C13—22no—
99C22×C4×C13—22no—
100C22×C4×C13—21no—
101C22×C4×C13—21no—
102C22×C4×C13—22no—
103C22×C4×C13—22no—
104C22×C4×C13—21no—
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—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×C13C22×C412yes—
121C22×C4×C13C22×C412yes—
122C22×C4×C13C22×C412yes—
123C22×C4×C13#4114yes—
124C22×C4×C13#4112yes—
125C22×C4×C13#4112yes—
126C22×Dic13—22no—
127C22×Dic13—22no—
128C22×Dic13—21no—
129C22×Dic13—21no—
130C22×Dic13—21no—
131C22×Dic13—21no—
132C22×Dic13—22no—
133C22×Dic13—22no—
134C22×Dic13—22no—
135C22×Dic13—22no—
136C22×Dic13—21no—
137C22×Dic13—21no—
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×Dic13C22×C412yes—
153C22×Dic13C22×C412yes—
154C22×Dic13C22×C412yes—
155C2×C4×D13—28no—
156C2×C4×D13—44no—
157C2×C4×D13—44no—
158C2×C4×D13—48no—
159C2×C4×D13—48no—
160C13×C4⋊C4—48no—
161C42×C13—44no—
162#6103—28no—
163#6103—28no—
164#6103—48no—
165#6103—48no—
166C4×Dic13—44no—
167C2×C4×C22⋊C4—131no—
168#1443—132no—
169#1442—132no—
170#1440—132no—
171#1439—132no—
172C4⋊#95D1311yescharacteristic, complemented
173#1434—131no—
174#1434—131no—
175#1434—131no—
176C22⋊#95—131no—
177C22⋊#95—131no—
178C23×C13C23×C411yescharacteristic
179C23×C13C2×#4112yes—
180C23×C13C2×#4111yescharacteristic
181C23×C13C2×#4111yescharacteristic
182C23×C13C2×#4112yes—
183C23×C13H(5,𝔽2)12yes—
184C23×C13H(5,𝔽2)12yes—
185C23×C13H(5,𝔽2)11yescharacteristic
186C23×C13H(5,𝔽2)11yescharacteristic
187C23×C132−1+411yescharacteristic
188C23×C132−1+411yescharacteristic
189C22×D13—22no—
190C22×D13—22no—
191C22×D13—22no—
192C22×D13—22no—
193C22×D13—22no—
194C22×D13—22no—
195C22×D13—24no—
196C22×D13—24no—
197C22×D13—24no—
198C22×D13—24no—
199C22×D13—24no—
200C22×D13—24no—
201C22×D13—42no—
202C22×D13—42no—
203C22×D13—42no—
204C22×D13—42no—
205C22×D13—41no—
206C22×D13—42no—
207C22×D13—41no—
208C22×D13—41no—
209C22×D13—41no—
210C22×D13—42no—
211C22×D13#11714yes—
212C2×C4×C13—22no—
213C2×C4×C13—22no—
214C2×C4×C13—22no—
215C2×C4×C13—22no—
216C2×C4×C13—24no—
217C2×C4×C13—24no—
218C2×C4×C13—24no—
219C2×C4×C13—24no—
220C2×C4×C13—22no—
221C2×C4×C13—22no—
222C2×C4×C13—22no—
223C2×C4×C13—42no—
224C2×C4×C13—42no—
225C2×C4×C13—42no—
226C2×C4×C13—42no—
227C2×C4×C13—42no—
228C2×C4×C13—42no—
229C2×C4×C13—42no—
230C2×C4×C13—42no—
231C2×C4×C13—42no—
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#11714yes—
240C2×C4×C13#11714yes—
241C2×Dic13—22no—
242C2×Dic13—22no—
243C2×Dic13—22no—
244C2×Dic13—22no—
245C2×Dic13—22no—
246C2×Dic13—22no—
247C2×Dic13—22no—
248C2×Dic13—22no—
249C2×Dic13—22no—
250C2×Dic13—42no—
251C2×Dic13—42no—
252C2×Dic13—42no—
253C2×Dic13—42no—
254C2×Dic13—42no—
255C2×Dic13—42no—
256C2×Dic13—42no—
257C2×Dic13—42no—
258C2×Dic13—42no—
259C2×Dic13—42no—
260C2×Dic13—42no—
261C2×Dic13—42no—
262C2×Dic13—42no—
263C2×Dic13—42no—
264C2×Dic13—42no—
265C2×Dic13—42no—
266C2×Dic13—42no—
267C2×Dic13—42no—
268C2×Dic13—42no—
269C2×Dic13—42no—
270C4×D13—416no—
271C24×C4—131no—
272C22×C4⋊C4C2×D1312yes—
273C22×C22⋊C4—131no—
274C22×C22⋊C4—131no—
275C22×C22⋊C4—132no—
276C22×C22⋊C4—132no—
277C22×C42—131no—
278C22×C42C2×D1311yescharacteristic
279C4×C22⋊C4—138no—
280C2×#95—131no—
281C2×#95—131no—
282C2×#95—131no—
283C2×#95—131no—
284C2×#95—132no—
285C2×#95—132no—
286C2×#95—132no—
287C2×#95—132no—
288C2×#95—132no—
289C2×#95—132no—
290C2×#95—132no—
291C2×#95—132no—
292C2×#95C2×D1311yescharacteristic
293C2×#95C2×D1311yescharacteristic
294C2×#95C2×D1312yes—
295C22×C13C2×#11711yescharacteristic
296C22×C13C2×#11711yescharacteristic
297C22×C13C2×#11711yescharacteristic
298C22×C13#51811yescharacteristic
299C22×C13#51811yescharacteristic
300C22×C13#52011yescharacteristic
301C22×C13#52011yescharacteristic
302C22×C13#52912yes—
303C22×C13#52912yes—
304C22×C13#53812yes—
305C22×C13#53812yes—
306C22×C13#53812yes—
307C22×C13#53812yes—
308C22×C13#53812yes—
309C22×C13#53912yes—
310C22×C13#53912yes—
311C22×C13#53912yes—
312C22×C13#54011yescharacteristic
313C22×C13#54012yes—
314C22×C13#54111yescharacteristic
315C22×C13#54211yescharacteristic
316C22×C13#54211yescharacteristic
317C22×C13#54212yes—
318C2×D13—24no—
319C2×D13—24no—
320C2×D13—24no—
321C2×D13—42no—
322C2×D13—42no—
323C2×D13—42no—
324C2×D13—42no—
325C2×D13—44no—
326C2×D13—44no—
327C2×D13—44no—
328C2×D13—44no—
329C4×C13—24no—
330C4×C13—24no—
331C4×C13—42no—
332C4×C13—82no—
333C4×C13—82no—
334Dic13—42no—
335Dic13—42no—
336Dic13—42no—
337Dic13—82no—
338Dic13—82no—
339C25—131no—
340C23×C4—131no—
341C23×C4—131no—
342C23×C4—131no—
343C23×C4—134no—
344C23×C4—132no—
345C23×C4—132no—
346C23×C4—262no—
347C23×C4—262no—
348C23×C4—522no—
349C23×C4—522no—
350C23×C4C22×D1312yes—
351C23×C4C22×D1312yes—
352C23×C4C22×D1311yescharacteristic
353C23×C4C22×D1311yescharacteristic
354C23×C4C22×D1311yescharacteristic
355C2×C4⋊C4—24no—
356C2×C4⋊C4—42no—
357C2×C4⋊C4—42no—
358C2×C22⋊C4—134no—
359C2×C22⋊C4—134no—
360C2×C22⋊C4—264no—
361C2×C22⋊C4—264no—
362C2×C22⋊C4—264no—
363C2×C22⋊C4—264no—
364C2×C22⋊C4—522no—
365C2×C22⋊C4—522no—
366C2×C22⋊C4—522no—
367C2×C22⋊C4—522no—
368C2×C42—42no—
369C2×C42—134no—
370C2×C42—522no—
371C2×C42C4×D1314yes—
372#95—22no—
373#95—22no—
374#95—42no—
375#95—134no—
376#95—134no—
377#95—264no—
378#95—262no—
379#95—262no—
380#95—522no—
381#95—522no—
382#95—522no—
383#95—522no—
384#95—522no—
385#95—522no—
386#95—522no—
387C2×C13#228311yescharacteristic
388C2×C13#231211yescharacteristic
389C2×C13#231411yescharacteristic
390C2×C13#231811yescharacteristic
391C2×C13#231811yescharacteristic
392C2×C13#231811yescharacteristic
393C2×C13#231911yescharacteristic
394C2×C13#264812yes—
395C2×C13#264912yes—
396C2×C13#265212yes—
397C2×C13#265312yes—
398D13—44no—
399C24—132no—
400C24—134no—
401C24—262no—
402C24—261no—
403C24—261no—
404C24—261no—
405C24—262no—
406C24—261no—
407C24—261no—
408C24—261no—
409C24—262no—
410C24C23×D1311yescharacteristic
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—22no—
416C22×C4—21no—
417C22×C4—22no—
418C22×C4—21no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—132no—
435C22×C4—132no—
436C22×C4—132no—
437C22×C4—262no—
438C22×C4—261no—
439C22×C4—261no—
440C22×C4—261no—
441C22×C4—262no—
442C22×C4—261no—
443C22×C4—261no—
444C22×C4—261no—
445C22×C4—262no—
446C22×C4—262no—
447C22×C4—262no—
448C22×C4—262no—
449C22×C4—268no—
450C22×C4—262no—
451C22×C4—262no—
452C22×C4—262no—
453C22×C4—262no—
454C22×C4—262no—
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—524no—
465C22×C4—524no—
466C22×C4—528no—
467C22×C4—528no—
468C22×C4C2×C4×D1312yes—
469C22×C4C2×C4×D1312yes—
470C22×C4C2×C4×D1312yes—
471C22×C4#612714yes—
472C22×C4#612912yes—
473C22×C4#613112yes—
474C4⋊C4—48no—
475C22⋊C4—268no—
476C22⋊C4—268no—
477C22⋊C4—528no—
478C22⋊C4—528no—
479C42—44no—
480C42—524no—
481C13#1435111yescharacteristic, complemented, Sylow
482C23—134no—
483C23—262no—
484C23—262no—
485C23—262no—
486C23—262no—
487C23—262no—
488C23—262no—
489C23—264no—
490C23—264no—
491C23—264no—
492C23—264no—
493C23—264no—
494C23—264no—
495C23—521no—
496C23—521no—
497C23—521no—
498C23—521no—
499C23—522no—
500C23—522no—
501C23—522no—
502C23—522no—
503C23—522no—
504C23—522no—
505C23C22×C4×D1311yescharacteristic
506C23C2×#612712yes—
507C23C2×#612911yescharacteristic
508C23#8825111yescharacteristic
509C23#8825111yescharacteristic
510C23#8825112yes—
511C23C2×#613111yescharacteristic
512C23#8825411yescharacteristic
513C23#8825411yescharacteristic
514C23#41×D1312yes—
515C23#8825612yes—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—24no—
519C2×C4—22no—
520C2×C4—24no—
521C2×C4—22no—
522C2×C4—24no—
523C2×C4—24no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—262no—
544C2×C4—262no—
545C2×C4—262no—
546C2×C4—262no—
547C2×C4—262no—
548C2×C4—262no—
549C2×C4—262no—
550C2×C4—262no—
551C2×C4—262no—
552C2×C4—5216no—
553C2×C4—522no—
554C2×C4—522no—
555C2×C4—522no—
556C2×C4—522no—
557C2×C4—522no—
558C2×C4—522no—
559C2×C4—522no—
560C2×C4—522no—
561C2×C4—522no—
562C2×C4—522no—
563C2×C4—522no—
564C2×C4—522no—
565C2×C4—522no—
566C2×C4—522no—
567C2×C4—522no—
568C2×C4—522no—
569C2×C4—522no—
570C2×C4—522no—
571C2×C4—522no—
572C2×C4—522no—
573C2×C4#8812614yes—
574C2×C4#8814614yes—
575C22—264no—
576C22—264no—
577C22—264no—
578C22—522no—
579C22—522no—
580C22—522no—
581C22—524no—
582C22—524no—
583C22—524no—
584C22—524no—
585C22—522no—
586C22C2×#8812611yescharacteristic
587C22#1171919111yescharacteristic
588C22#1171919912yes—
589C22C2×#8814611yescharacteristic
590C22#1171920911yescharacteristic
591C22#1171920911yescharacteristic
592C22#1171922012yes—
593C22D13×#11711yescharacteristic
594C22#1171922611yescharacteristic
595C22#1171926212yes—
596C22#1171926712yes—
597C22#1171928512yes—
598C22#1171928712yes—
599C22#1171931812yes—
600C22#1171932212yes—
601C22#1171934312yes—
602C22#1171934912yes—
603C22#1171938312yes—
604C22#1171939712yes—
605C22#1171942411yescharacteristic
606C22#1171943611yescharacteristic
607C22#1171943811yescharacteristic
608C22#1171943811yescharacteristic
609C4—24no—
610C4—24no—
611C4—42no—
612C4—82no—
613C4—82no—
614C4—522no—
615C4—522no—
616C4—522no—
617C4—1042no—
618C4—1042no—
619C2—524no—
620C2#1311723211yescharacteristic
621C2#1311743311yescharacteristic
622C2#1311744411yescharacteristic
623C2#1311747011yescharacteristic
624C2#1311747111yescharacteristic
625C2#1311747211yescharacteristic
626C2#1311747411yescharacteristic
627C2#1312082812yes—
628C2#1312084512yes—
629C2#1312088812yes—
630C2#1312090512yes—
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×C4⋊#95C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenterC4⋊#95D13
hypocenterC13#14351
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
2. #13113096C2semidirect
3. #13113095C2semidirect
6. #13113063C2semidirect
7. #13113061C2semidirect
8. #13113061C2semidirect
11. C13×C4⋊#95C2semidirect
35. C4×#6103C4semidirect
172. C4⋊#95D13semidirect
481. C13#14351semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#61032
#131130962
#131130952
#131130842
#131130782
#131130632
#131130612
#131130572
C13×C4⋊#952
#1435113