Finite Group Databasebeta

← #15881355

Subgroups — #15881355

Order 3328.

910 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#6107C211yesmaximal, characteristic
2C2×#11718451C211yesmaximal, characteristic
3C2×#11718451C211yesmaximal, characteristic
4#13117755C211yesmaximal, characteristic
5#13117754C211yesmaximal, characteristic
6#13115568C211yesmaximal, characteristic
7#13115566C211yesmaximal, characteristic
8#13115107C211yesmaximal, characteristic
9#13115106C211yesmaximal, characteristic
10#13115101C211yesmaximal, characteristic
11#13114997C211yesmaximal, characteristic
12#13114850C211yesmaximal, characteristic
13#13114849C211yesmaximal, characteristic
14#13114697C211yesmaximal, characteristic
15C13×#1865C211yesmaximal, characteristic
16C2×C4×Q8×C13C2211yescharacteristic
17C2×Q8×Dic13C2211yescharacteristic
18C2×Q8×Dic13C2211yescharacteristic
19C22×#6107C2211yescharacteristic
20C2×#88141C2211yescharacteristic
21C2×#88141C2211yescharacteristic
22C2×C4×Dic26C2211yescharacteristic
23C2×C13×#106C2211yescharacteristic
24C2×C13×#103C2211yescharacteristic
25C2×C13×#103C2211yescharacteristic
26C13×#389C2211yescharacteristic
27C2×#88075C2211yescharacteristic
28C2×#88057C2211yescharacteristic
29C2×#88056C2211yescharacteristic
30C2×#88056C2211yescharacteristic
31C2×#88054C2211yescharacteristic
32C2×C8×Dic13C2211yescharacteristic
33C2×C8×Dic13C2211yescharacteristic
34C4×#6107—24no—
35#11718646C2211yescharacteristic
36#11718638—21no—
37#11718638C2211yescharacteristic
38#11718638C2211yescharacteristic
39C4⋊C4×Dic13—21no—
40#11718634—21no—
41#11718634C2211yescharacteristic
42#11718633—21no—
43C2×#88050C2211yescharacteristic
44C2×#88047C2211yescharacteristic
45C2×#88047C2211yescharacteristic
46C2×#88047C2211yescharacteristic
47C4×#6101—21no—
48C4×#6101C2211yescharacteristic
49#11718589—21no—
50#11718589C2211yescharacteristic
51C2×C4×#1055C2211yescharacteristic
52#11718451—24no—
53#11718451C418yescomplemented
54#11718311—21no—
55#11718308—21no—
56C13×#340C2211yescharacteristic
57C13×#336C2211yescharacteristic
58#11718143C2211yescharacteristic
59#11718142C2211yescharacteristic
60#11718121C2211yescharacteristic
61#11718121C2211yescharacteristic
62C22×Q8×C13C2311yescharacteristic
63C22×Dic26C2311yescharacteristic
64C22×C8×C13C2311yescharacteristic
65C22×C8×C13C2311yescharacteristic
66C4×Q8×C13—22no—
67C4×Q8×C13—41no—
68C2×C13×C4⋊C4—21no—
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4C2311yescharacteristic
71C2×C13×C4⋊C4C2311yescharacteristic
72C2×C13×C4⋊C4C2311yescharacteristic
73C2×C42×C13—21no—
74C2×C42×C13C2311yescharacteristic
75Q8×Dic13—22no—
76Q8×Dic13—22no—
77Q8×Dic13—41no—
78Q8×Dic13C2×C414yes—
79C2×#6107C2×C414yes—
80C2×#6107D414yes—
81C2×#6107Q814yes—
82C2×C4⋊Dic13—21no—
83C2×C4⋊Dic13—21no—
84C2×C4⋊Dic13—21no—
85C2×C4⋊Dic13C2311yescharacteristic
86C2×C4⋊Dic13C2311yescharacteristic
87C2×C4⋊Dic13C2311yescharacteristic
88C2×#6101—21no—
89C2×#6101—21no—
90C2×#6101—21no—
91C2×#6101—21no—
92C2×#6101—21no—
93C2×#6101D411yescharacteristic
94C2×#6101D411yescharacteristic
95C2×C4×Dic13—21no—
96C2×C4×Dic13—21no—
97C2×C4×Dic13—21no—
98C2×C4×Dic13—21no—
99C2×C4×Dic13—21no—
100C2×C4×Dic13C2311yescharacteristic
101C2×C4×Dic13C2311yescharacteristic
102C22×#1055C2311yescharacteristic
103C22×#1055C2311yescharacteristic
104#88141—22no—
105#88141—22no—
106#88141—41no—
107#88141C2×C414yes—
108C4×Dic26—22no—
109C4×Dic26—41no—
110C13×#106—41no—
111C13×#103—22no—
112C13×#103C2×C414yes—
113C13×#95—21no—
114#88075—22no—
115#88071—21no—
116#88071—21no—
117#88071—21no—
118#88071—21no—
119#88071—21no—
120#88071—21no—
121#88071—21no—
122#88071D411yescharacteristic
123#88071D411yescharacteristic
124#88057—41no—
125#88056—22no—
126#88056C2×C414yes—
127#88054—22no—
128C8×Dic13—22no—
129C8×Dic13C2×C414yes—
130#88050—22no—
131#88047—22no—
132#88047—22no—
133#88047C2×C414yes—
134C4×#1055—22no—
135#22685—131nomaximal, Sylow
136C2×Q8×C13—21no—
137C2×Q8×C13—21no—
138C2×Q8×C13—21no—
139C2×Q8×C13C22×C412yes—
140C2×Q8×C13C2×D412yes—
141C2×Q8×C13C2×Q812yes—
142C22×C4×C13—21no—
143C22×C4×C13—21no—
144C22×C4×C13—21no—
145C22×C4×C13—21no—
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13C2×D411yescharacteristic
148C22×C4×C13C2411yescharacteristic
149C22×Dic13—21no—
150C22×Dic13—21no—
151C22×Dic13—21no—
152C22×Dic13—21no—
153C22×Dic13C2×D411yescharacteristic
154C22×Dic13C2×D411yescharacteristic
155C22×Dic13C2×D411yescharacteristic
156C22×Dic13C2×D411yescharacteristic
157C2×Dic26—21no—
158C2×Dic26—21no—
159C2×Dic26—21no—
160C2×Dic26C22×C412yes—
161C2×Dic26C2×D412yes—
162C2×Dic26C2×Q812yes—
163C2×C8×C13—21no—
164C2×C8×C13—21no—
165C2×C8×C13—21no—
166C2×C8×C13—21no—
167C2×C8×C13—21no—
168C2×C8×C13C22×C412yes—
169C13×C4⋊C4—21no—
170C13×C4⋊C4—21no—
171C13×C4⋊C4—21no—
172C13×C4⋊C4—21no—
173C13×C4⋊C4—21no—
174C13×C4⋊C4—42no—
175C13×C4⋊C4—42no—
176C13×C4⋊C4C22×C412yes—
177C42×C13—21no—
178C42×C13—21no—
179C42×C13—42no—
180#6107C4⋊C4116yescomplemented
181C4⋊Dic13—21no—
182C4⋊Dic13—24no—
183C4⋊Dic13—21no—
184C4⋊Dic13—21no—
185C4⋊Dic13—21no—
186C4⋊Dic13—21no—
187C4⋊Dic13—42no—
188C4⋊Dic13—42no—
189C4⋊Dic13C22×C412yes—
190#6101—22no—
191#6101—24no—
192#6101—22no—
193#6101—42no—
194#6101—42no—
195#6101—42no—
196#6101—42no—
197C4×Dic13—21no—
198C4×Dic13—21no—
199C4×Dic13—24no—
200C4×Dic13—24no—
201C4×Dic13—42no—
202C4×Dic13—42no—
203C4×Dic13—42no—
204C4×Dic13C22×C412yes—
205C4×Dic13#4112yes—
206C2×#1055—21no—
207C2×#1055—21no—
208C2×#1055—21no—
209C2×#1055C22×C412yes—
210C2×#1055C2×D412yes—
211C2×#1055C2×Q812yes—
212C2×C4×Q16—131no—
213C2×C4×Q16—131no—
214C2×C4×Q16—131no—
215#2351—131no—
216#2351—131no—
217#1942—131no—
218#1942—131no—
219#1865—131no—
220#1865—131no—
221#1865—131no—
222#1865D1311yescharacteristic
223#1846—131no—
224#1805—131no—
225#1805—131no—
226C8×C4⋊C4—131no—
227C23×C13C22×D411yescharacteristic
228Q8×C13—22no—
229Q8×C13—22no—
230Q8×C13—22no—
231Q8×C13C2×C4⋊C414yes—
232C2×C4×C13—22no—
233C2×C4×C13—21no—
234C2×C4×C13—22no—
235C2×C4×C13—22no—
236C2×C4×C13—21no—
237C2×C4×C13—22no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
241C2×C4×C13—41no—
242C2×C4×C13—41no—
243C2×C4×C13—41no—
244C2×C4×C13—41no—
245C2×C4×C13—41no—
246C2×C4×C13—41no—
247C2×C4×C13—41no—
248C2×C4×C13—41no—
249C2×C4×C13#13512yes—
250C2×C4×C13C23×C411yescharacteristic
251C2×C4×C13C22×D411yescharacteristic
252C2×C4×C13C22×Q811yescharacteristic
253C2×C4×C13C2×#4111yescharacteristic
254C2×C4×C13H(5,𝔽2)11yescharacteristic
255C2×C4×C132−1+411yescharacteristic
256C2×Dic13—22no—
257C2×Dic13—21no—
258C2×Dic13—22no—
259C2×Dic13—22no—
260C2×Dic13—21no—
261C2×Dic13—21no—
262C2×Dic13—21no—
263C2×Dic13—21no—
264C2×Dic13—21no—
265C2×Dic13—22no—
266C2×Dic13—21no—
267C2×Dic13—21no—
268C2×Dic13—21no—
269C2×Dic13—41no—
270C2×Dic13—41no—
271C2×Dic13—41no—
272C2×Dic13—41no—
273C2×Dic13—41no—
274C2×Dic13—41no—
275C2×Dic13—41no—
276C2×Dic13—41no—
277C2×Dic13C4×D412yes—
278C2×Dic13C4×D412yes—
279C2×Dic13#13512yes—
280Dic26—22no—
281Dic26—22no—
282Dic26—22no—
283Dic26C2×C4⋊C414yes—
284C8×C13—22no—
285C8×C13—41no—
286#1055—41no—
287#1055C2×C4⋊C414yes—
288C22×Q16—131no—
289C2×C4×Q8—131no—
290C2×C4×Q8—131no—
291C2×C4×Q8—131no—
292C2×C4×Q8—131no—
293C2×C4×Q8—131no—
294C2×C4×Q8C2×D1311yescharacteristic
295C4×Q16—138no—
296C4×Q16—264no—
297C4×Q16—264no—
298C2×#107—131no—
299C2×#107—131no—
300C2×#107—131no—
301C2×#106—131no—
302C2×#106C2×D1311yescharacteristic
303C2×C4⋊C8—131no—
304C2×#103—131no—
305C2×#103—131no—
306C2×#103—131no—
307C2×#103—131no—
308C2×#103C2×D1311yescharacteristic
309C2×#103C2×D1311yescharacteristic
310C2×C4×C8—131no—
311C2×C4×C8—131no—
312C2×C4×C8—131no—
313#389—131no—
314#389—131no—
315#389—131no—
316#389—261no—
317#389—261no—
318#389—261no—
319#389—261no—
320#389C2×D1311yescharacteristic
321#382—131no—
322#382—131no—
323#382—261no—
324#382—261no—
325C4×C4⋊C4—131no—
326C4×C4⋊C4—261no—
327C4×C4⋊C4—261no—
328#340—131no—
329#340—131no—
330#340—131no—
331#340C2×D1311yescharacteristic
332#336—131no—
333#336C2×D1311yescharacteristic
334C22×C13C2×C4×D411yescharacteristic
335C22×C13D4211yescharacteristic
336C22×C13D4×Q811yescharacteristic
337C22×C13C2×#13511yescharacteristic
338C22×C13C2×#13511yescharacteristic
339C22×C13#57811yescharacteristic
340C22×C13#57811yescharacteristic
341C4×C13—24no—
342C4×C13—22no—
343C4×C13—42no—
344C4×C13—41no—
345C4×C13—81no—
346C4×C13—81no—
347C4×C13C22×C4⋊C411yescharacteristic
348C4×C13#52011yescharacteristic
349C4×C13#54711yescharacteristic
350C4×C13#55411yescharacteristic
351Dic13—24no—
352Dic13—22no—
353Dic13—22no—
354Dic13—22no—
355Dic13—42no—
356Dic13—41no—
357Dic13—81no—
358Dic13—81no—
359C22×Q8—131no—
360C22×Q8C22×D1311yescharacteristic
361C2×Q16—134no—
362C2×Q16—134no—
363C2×Q16—134no—
364C22×C8—131no—
365C22×C8—131no—
366C22×C8C22×D1311yescharacteristic
367C22×C8C22×D1311yescharacteristic
368C4×Q8—22no—
369C4×Q8—41no—
370C4×Q8—134no—
371C4×Q8—134no—
372C4×Q8—262no—
373C4×Q8—262no—
374C4×Q8—262no—
375C4×Q8—262no—
376C4×Q8—262no—
377C4×Q8—521no—
378C4×Q8—521no—
379C4×Q8—521no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—131no—
383C2×C4⋊C4—131no—
384C2×C4⋊C4—131no—
385C2×C4⋊C4—131no—
386C2×C4⋊C4—131no—
387C2×C4⋊C4—261no—
388C2×C4⋊C4—261no—
389C2×C4⋊C4—261no—
390C2×C4⋊C4—261no—
391C2×C4⋊C4—261no—
392C2×C4⋊C4—261no—
393C2×C4⋊C4—261no—
394C2×C4⋊C4—261no—
395C2×C4⋊C4C22×D1311yescharacteristic
396C2×C4⋊C4C22×D1311yescharacteristic
397C2×C4⋊C4C22×D1311yescharacteristic
398C2×C42—21no—
399C2×C42—131no—
400C2×C42—131no—
401C2×C42—261no—
402C2×C42—261no—
403C2×C42—261no—
404C2×C42—261no—
405C2×C42—261no—
406C2×C42C22×D1311yescharacteristic
407#107—134no—
408#107—262no—
409#107—262no—
410#106—41no—
411#106—521no—
412C4⋊C8—262no—
413#103—22no—
414#103—134no—
415#103—262no—
416#103—262no—
417#103—262no—
418#103C4×D1314yes—
419C4×C8—134no—
420C4×C8—262no—
421C4×C8—262no—
422#95—21no—
423#95—131no—
424#95—131no—
425#95—261no—
426#95—261no—
427#95—261no—
428#95—261no—
429#95—261no—
430#95—261no—
431#95—261no—
432C2×C13D4×C4⋊C411yescharacteristic
433C2×C13C4×#13511yescharacteristic
434C2×C13#295011yescharacteristic
435C2×C13#328511yescharacteristic
436C2×C13#328511yescharacteristic
437C2×C13#338311yescharacteristic
438C2×C13#338311yescharacteristic
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—132no—
443C2×Q8—132no—
444C2×Q8—132no—
445C2×Q8—261no—
446C2×Q8—261no—
447C2×Q8—261no—
448C2×Q8C2×C4×D1312yes—
449C2×Q8D4×D1312yes—
450C2×Q8Q8×D1312yes—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—131no—
456C22×C4—131no—
457C22×C4—131no—
458C22×C4—131no—
459C22×C4—261no—
460C22×C4—261no—
461C22×C4—261no—
462C22×C4—261no—
463C22×C4D4×D1311yescharacteristic
464C22×C4D4×D1311yescharacteristic
465C22×C4C23×D1311yescharacteristic
466Q16—1316no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—132no—
473C2×C8—132no—
474C2×C8—132no—
475C2×C8—261no—
476C2×C8—261no—
477C2×C8—261no—
478C2×C8C2×C4×D1312yes—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—42no—
485C4⋊C4—42no—
486C4⋊C4—132no—
487C4⋊C4—262no—
488C4⋊C4—264no—
489C4⋊C4—264no—
490C4⋊C4—262no—
491C4⋊C4—261no—
492C4⋊C4—261no—
493C4⋊C4—261no—
494C4⋊C4—261no—
495C4⋊C4—261no—
496C4⋊C4—522no—
497C4⋊C4—522no—
498C4⋊C4—522no—
499C4⋊C4—522no—
500C4⋊C4—522no—
501C4⋊C4—522no—
502C4⋊C4C2×C4×D1312yes—
503C42—21no—
504C42—21no—
505C42—42no—
506C42—132no—
507C42—132no—
508C42—264no—
509C42—264no—
510C42—261no—
511C42—261no—
512C42—522no—
513C42—522no—
514C42—522no—
515C13#2268511yescharacteristic, complemented, Sylow
516C23C2×D4×D1311yescharacteristic
517Q8—22no—
518Q8—22no—
519Q8—22no—
520Q8—134no—
521Q8—262no—
522Q8—262no—
523Q8—262no—
524Q8C4⋊C4×D1314yes—
525C2×C4—21no—
526C2×C4—22no—
527C2×C4—21no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—22no—
533C2×C4—21no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—132no—
543C2×C4—132no—
544C2×C4—132no—
545C2×C4—261no—
546C2×C4—261no—
547C2×C4—261no—
548C2×C4—261no—
549C2×C4—261no—
550C2×C4—262no—
551C2×C4—261no—
552C2×C4—262no—
553C2×C4—262no—
554C2×C4—261no—
555C2×C4—261no—
556C2×C4—262no—
557C2×C4—261no—
558C2×C4—521no—
559C2×C4—521no—
560C2×C4—521no—
561C2×C4—521no—
562C2×C4—521no—
563C2×C4—521no—
564C2×C4—521no—
565C2×C4—521no—
566C2×C4#8817012yes—
567C2×C4C22×C4×D1311yescharacteristic
568C2×C4C2×D4×D1311yescharacteristic
569C2×C4#8825111yescharacteristic
570C2×C4C2×Q8×D1311yescharacteristic
571C2×C4#41×D1311yescharacteristic
572C2×C4#8825711yescharacteristic
573C8—22no—
574C8—41no—
575C8—134no—
576C8—521no—
577C22C4×D4×D1311yescharacteristic
578C22#1171929511yescharacteristic
579C22#1171933711yescharacteristic
580C22C2×#8817011yescharacteristic
581C22D13×#13511yescharacteristic
582C22#1171948411yescharacteristic
583C22#1171948411yescharacteristic
584C4—24no—
585C4—22no—
586C4—42no—
587C4—41no—
588C4—81no—
589C4—81no—
590C4—262no—
591C4—264no—
592C4—262no—
593C4—262no—
594C4—522no—
595C4—521no—
596C4—1041no—
597C4—1041no—
598C4C2×C4⋊C4×D1311yescharacteristic
599C4#1171925111yescharacteristic
600C4#1171934111yescharacteristic
601C4#1171936011yescharacteristic
602C2#1311773411yescharacteristic
603C2C4×#8817011yescharacteristic
604C2#1312370111yescharacteristic
605C2#1312657011yescharacteristic
606C2#1312657511yescharacteristic
607C2#1312772211yescharacteristic
608C2#1312772611yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1865C2
socle, prime radicalC23×C13C22×D4
cosocleC22×C4×C13C24
hypercenter#1865D13
hypocenterC13#22685
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1865

Complements

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

NH ≅ G/Ntype
53. #11718451C4semidirect
180. #6107C4⋊C4semidirect
515. C13#22685semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#61072
C2×#117184512
#131177552
#131177542
#131155682
#131155662
#131151072
#131151062
#131151012
#131149972
#131148502
#131148492
#131146972
C13×#18652
#2268513