Finite Group Databasebeta

← #15898994

Subgroups — #15898994

Order 3328.

1150 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718745C211yesmaximal, characteristic, complemented
2C2×#11718748C211yesmaximal, characteristic, complemented
3C4×#88184C211yesmaximal, characteristic
4#13116171C212yesmaximal, complemented
5#13115979C212yesmaximal, complemented
6#13115789C211yesmaximal, characteristic, complemented
7#13115785C211yesmaximal, characteristic, complemented
8#13115158C212yesmaximal
9#13115035C212yesmaximal, complemented
10#13114816C211yesmaximal, characteristic, complemented
11C2×C13×#533C211yesmaximal, characteristic, complemented
12C13×#533—24no—
13C13×#533—24no—
14C2×C13×C4⋊Q8C2211yescharacteristic
15C2×C13×C4⋊Q8C2211yescharacteristic
16C2×C13×#125C2212yes—
17C2×C13×C22⋊Q8—21no—
18C2×C13×C22⋊Q8—21no—
19C2×C4×Q8×C13—21no—
20C2×C4×Q8×C13—21no—
21C2×C13×#117C2212yes—
22C22×C42×C13C2211yescharacteristic
23C2×#88184C2211yescharacteristic
24C2×C4×C22⋊D13—21no—
25C2×C4×D52C2211yescharacteristic
26#11718874—21no—
27#11718873C2211yescharacteristic
28C2×C22⋊#1055C2212yes—
29#11718748—24no—
30#11718745—24no—
31C2×#88049C2212yes—
32C2×#88049C2212yes—
33C2×#88048C2212yes—
34C2×#88047C2212yes—
35#11718601—21no—
36#11718600C2211yescharacteristic
37C4×#6103—21no—
38C4×C4⋊Dic13C2211yescharacteristic
39#11718589C2211yescharacteristic
40C2×C4⋊#1055C2211yescharacteristic
41C2×C4⋊#1055C2211yescharacteristic
42#11718121C2212yes—
43#11718121C2212yes—
44#11718121C2212yes—
45#11718121C2212yes—
46#11718116C2212yes—
47C22×Q8×C13—21no—
48C22×Q8×C13—21no—
49C23×C4×C13D411yescharacteristic
50C23×C4×C13D411yescharacteristic
51C23×C4×C13C2311yescharacteristic
52C22×C22⋊D13—21no—
53C22×D52C2311yescharacteristic
54C22×C4×D13—21no—
55C13×C4⋊Q8—22no—
56C13×C4⋊Q8—22no—
57C13×C4⋊Q8D414yescomplemented
58C13×C4⋊Q8D414yescomplemented
59C13×#125—24no—
60C13×#125—24no—
61C13×C22⋊Q8—28no—
62C13×C22⋊Q8—28no—
63C4×Q8×C13—28no—
64C4×Q8×C13—28no—
65C13×#117—24no—
66C13×#117—24no—
67C2×C13×C4⋊C4—22no—
68C2×C13×C4⋊C4—22no—
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4—21no—
71C2×C13×C4⋊C4C2312yes—
72C2×C13×C4⋊C4C2312yes—
73C2×C13×C22⋊C4—22no—
74C2×C42×C13—22no—
75C2×C42×C13—22no—
76C2×C42×C13—22no—
77C2×C42×C13D411yescharacteristic
78C2×C42×C13D411yescharacteristic
79C2×C42×C13C2311yescharacteristic
80C2×C42×C13C2311yescharacteristic
81C2×C22⋊Dic13—21no—
82#88184—22no—
83#88184Q814yescomplemented
84C4×C22⋊D13—44no—
85C2×#6103—21no—
86C2×#6103—21no—
87C2×#6103—21no—
88C2×#6103—21no—
89C2×C4⋊Dic13C2311yescharacteristic
90C2×C4⋊Dic13C2311yescharacteristic
91C2×C4⋊Dic13C2311yescharacteristic
92C2×#6101—21no—
93C2×C4×Dic13—21no—
94C22×#1055C2312yes—
95C22×#1055C2312yes—
96C4×D52—22no—
97C4×D52—22no—
98#88071—21no—
99#88071—21no—
100#88071—21no—
101C22⋊#1055—24no—
102#88049—24no—
103#88049—24no—
104#88048—24no—
105#88047—24no—
106C4⋊#1055—22no—
107C4⋊#1055—22no—
108#24300—131nomaximal, Sylow
109C24×C13C2×D411yescharacteristic
110C23×D13—21no—
111C2×Q8×C13—24no—
112C2×Q8×C13—24no—
113C2×Q8×C13—42no—
114C2×Q8×C13—42no—
115C2×Q8×C13—42no—
116C2×Q8×C13—42no—
117C22×C4×C13—21no—
118C22×C4×C13—21no—
119C22×C4×C13—21no—
120C22×C4×C13—21no—
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—41no—
128C22×C4×C13—41no—
129C22×C4×C13C2×D411yescharacteristic
130C22×C4×C13C2×D411yescharacteristic
131C22×C4×C13C2×D411yescharacteristic
132C22×C4×C13C2×D411yescharacteristic
133C22×C4×C13C2×D411yescharacteristic
134C22×C4×C13C2×Q812yes—
135C22×C4×C13#4112yes—
136C22×C4×C13C2411yescharacteristic
137C2×C22⋊D13—24no—
138C2×C22⋊D13—42no—
139C2×C22⋊D13—42no—
140C22×Dic13—21no—
141C22×Dic13—21no—
142C22×Dic13—21no—
143C2×D52—21no—
144C2×D52—21no—
145C2×D52—21no—
146C2×D52—21no—
147C2×D52—21no—
148C2×D52C2×Q812yes—
149C2×C4×D13—42no—
150C2×C4×D13—42no—
151C2×C4×D13—42no—
152C13×C4⋊C4—28no—
153C13×C4⋊C4—28no—
154C13×C4⋊C4—24no—
155C13×C4⋊C4—24no—
156C13×C4⋊C4—22no—
157C13×C4⋊C4—22no—
158C13×C4⋊C4C2×D414yes—
159C13×C4⋊C4C2×D414yes—
160C13×C22⋊C4—28no—
161C42×C13—28no—
162C42×C13—22no—
163C42×C13—22no—
164C42×C13—21no—
165C42×C13—21no—
166C42×C13C2×D412yes—
167C42×C13C2×D412yes—
168C22⋊Dic13—42no—
169#6103—24no—
170#6103—42no—
171#6103—42no—
172#6103—42no—
173C4⋊Dic13—21no—
174C4⋊Dic13—21no—
175C4⋊Dic13—21no—
176C4⋊Dic13—21no—
177C4⋊Dic13—21no—
178C4⋊Dic13C2×Q812yes—
179#6101—42no—
180C4×Dic13—42no—
181C2×#1055—22no—
182C2×#1055—22no—
183C2×#1055—22no—
184C2×#1055—22no—
185C2×#1055—22no—
186C2×#1055—22no—
187C2×#533D1311yescharacteristic, complemented
188C2×#476—131no—
189C2×#474—131no—
190C4×#121—131no—
191#2059—132no—
192#2025—132no—
193#1988—131no—
194#1987—131no—
195#1875—132no—
196#1854—132no—
197#1797—131no—
198C23×C13—21no—
199C23×C13—21no—
200C23×C13—21no—
201C23×C13—21no—
202C23×C13—21no—
203C23×C13—21no—
204C23×C13C22⋊Q812yes—
205C23×C13C22×D411yescharacteristic
206C22×D13—22no—
207C22×D13—41no—
208C22×D13—41no—
209C22×D13—41no—
210C22×D13—41no—
211C22×D13—41no—
212C22×D13—41no—
213Q8×C13—48no—
214Q8×C13—48no—
215C2×C4×C13—21no—
216C2×C4×C13—21no—
217C2×C4×C13—21no—
218C2×C4×C13—21no—
219C2×C4×C13—22no—
220C2×C4×C13—22no—
221C2×C4×C13—22no—
222C2×C4×C13—22no—
223C2×C4×C13—21no—
224C2×C4×C13—21no—
225C2×C4×C13—24no—
226C2×C4×C13—24no—
227C2×C4×C13—21no—
228C2×C4×C13—21no—
229C2×C4×C13—21no—
230C2×C4×C13—21no—
231C2×C4×C13—44no—
232C2×C4×C13—42no—
233C2×C4×C13—42no—
234C2×C4×C13—42no—
235C2×C4×C13—42no—
236C2×C4×C13—44no—
237C2×C4×C13#12012yes—
238C2×C4×C13#12012yes—
239C2×C4×C13C22⋊Q812yes—
240C2×C4×C13#13512yes—
241C2×C4×C13AGL(1,ℤ/8)12yes—
242C2×C4×C13C22×D411yescharacteristic
243C2×C4×C13C22×D411yescharacteristic
244C2×C4×C13C22×Q811yescharacteristic
245C2×C4×C13C2×#4111yescharacteristic
246C2×C4×C132−1+411yescharacteristic
247C2×C4×C132−1+411yescharacteristic
248C22⋊D13—48no—
249C2×Dic13—22no—
250C2×Dic13—41no—
251C2×Dic13—41no—
252C2×Dic13—41no—
253C2×Dic13—41no—
254C2×Dic13—41no—
255C2×Dic13—41no—
256C2×Dic13—41no—
257C2×Dic13—41no—
258D52—22no—
259D52—22no—
260D52—41no—
261D52—41no—
262C4×D13—84no—
263#1055—42no—
264#1055—42no—
265#533—24no—
266#533—24no—
267C2×C4⋊Q8C2×D1311yescharacteristic
268C2×C4⋊Q8C2×D1311yescharacteristic
269C2×#125C2×D1312yes—
270C2×C22⋊Q8—21no—
271C2×C22⋊Q8—21no—
272C2×#121—131no—
273C2×C4×Q8—21no—
274C2×C4×Q8—21no—
275C2×C4×D4—131no—
276C2×C4×D4—261no—
277C2×#117C2×D1312yes—
278C22×C42C2×D1311yescharacteristic
279#476—264no—
280#474—264no—
281C2×#107—132no—
282C2×#106—132no—
283C2×C4⋊C8—131no—
284C2×C4⋊C8—131no—
285C2×#102—132no—
286C2×#102—132no—
287C2×C22⋊C8—132no—
288#390—131no—
289#389—131no—
290#388—261no—
291#386—261no—
292#380—131no—
293C4×C4⋊C4—131no—
294C4×C22⋊C4—261no—
295#340—132no—
296#340—132no—
297#340—132no—
298#340—132no—
299#336—132no—
300C22×C13—22no—
301C22×C13—22no—
302C22×C13—22no—
303C22×C13—41no—
304C22×C13—41no—
305C22×C13—41no—
306C22×C13—41no—
307C22×C13C2×#12011yescharacteristic
308C22×C13C2×C22⋊Q811yescharacteristic
309C22×C13#53611yescharacteristic
310C22×C13C2×#13511yescharacteristic
311C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
312C22×C13#57511yescharacteristic
313C22×C13#57511yescharacteristic
314C2×D13—42no—
315C2×D13—42no—
316C2×D13—42no—
317C2×D13—81no—
318C2×D13—81no—
319C2×D13—81no—
320C2×D13—81no—
321C4×C13—22no—
322C4×C13—22no—
323C4×C13—41no—
324C4×C13—44no—
325C4×C13—41no—
326C4×C13—44no—
327C4×C13#44914yes—
328C4×C13#54811yescharacteristic
329C4×C13#54811yescharacteristic
330C4×C13D4×Q811yescharacteristic
331C4×C13D4×Q811yescharacteristic
332Dic13—42no—
333Dic13—81no—
334Dic13—81no—
335C22×Q8—21no—
336C22×Q8—21no—
337C22×D4—131no—
338C22×D4—261no—
339C23×C4—261no—
340C23×C4C22⋊D1311yescharacteristic
341C23×C4C22⋊D1311yescharacteristic
342C23×C4C22×D1311yescharacteristic
343C22×C8—132no—
344C22×C8—132no—
345C4⋊Q8—22no—
346C4⋊Q8—22no—
347C4⋊Q8C22⋊D1314yescomplemented
348C4⋊Q8C22⋊D1314yescomplemented
349#125—24no—
350#125—24no—
351C22⋊Q8—28no—
352C22⋊Q8—28no—
353#121—134no—
354#121—262no—
355C4×Q8—28no—
356C4×Q8—28no—
357C4×D4—262no—
358C4×D4—262no—
359C4×D4—524no—
360#117—24no—
361#117—24no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—131no—
367C2×C4⋊C4—131no—
368C2×C4⋊C4—131no—
369C2×C4⋊C4—261no—
370C2×C4⋊C4C22×D1312yes—
371C2×C4⋊C4C22×D1312yes—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—261no—
374C2×C22⋊C4—261no—
375C2×C22⋊C4—261no—
376C2×C22⋊C4—261no—
377C2×C22⋊C4—261no—
378C2×C42—22no—
379C2×C42—22no—
380C2×C42—22no—
381C2×C42—261no—
382C2×C42C22⋊D1311yescharacteristic
383C2×C42C22⋊D1311yescharacteristic
384C2×C42C22×D1311yescharacteristic
385C2×C42C22×D1311yescharacteristic
386#107—264no—
387#106—264no—
388C4⋊C8—262no—
389C4⋊C8—262no—
390#102—264no—
391#102—264no—
392C22⋊C8—264no—
393#95—261no—
394#95—261no—
395#95—261no—
396C2×C13—42no—
397C2×C13#240911yescharacteristic
398C2×C13C2×#44911yescharacteristic
399C2×C13#300511yescharacteristic
400C2×C13#307611yescharacteristic
401C2×C13#307711yescharacteristic
402C2×C13#323311yescharacteristic
403C2×C13#323511yescharacteristic
404D13—82no—
405C24—261no—
406C24C2×C22⋊D1311yescharacteristic
407C2×Q8—24no—
408C2×Q8—24no—
409C2×Q8—42no—
410C2×Q8—42no—
411C2×Q8—42no—
412C2×Q8—42no—
413C2×D4—132no—
414C2×D4—264no—
415C2×D4—261no—
416C2×D4—261no—
417C2×D4—261no—
418C2×D4—261no—
419C2×D4—261no—
420C2×D4—522no—
421C2×D4—522no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—41no—
433C22×C4—41no—
434C22×C4—261no—
435C22×C4—261no—
436C22×C4—261no—
437C22×C4—522no—
438C22×C4—522no—
439C22×C4—522no—
440C22×C4Q8×D1312yes—
441C22×C4#613112yes—
442C22×C4C2×C22⋊D1311yescharacteristic
443C22×C4C2×C22⋊D1311yescharacteristic
444C22×C4C2×C22⋊D1311yescharacteristic
445C22×C4C2×C22⋊D1311yescharacteristic
446C22×C4C2×C22⋊D1311yescharacteristic
447C22×C4C23×D1311yescharacteristic
448C2×C8—262no—
449C2×C8—262no—
450C2×C8—262no—
451C2×C8—262no—
452C2×C8—262no—
453C2×C8—262no—
454C4⋊C4—28no—
455C4⋊C4—28no—
456C4⋊C4—24no—
457C4⋊C4—24no—
458C4⋊C4—22no—
459C4⋊C4—22no—
460C4⋊C4—132no—
461C4⋊C4—261no—
462C4⋊C4—261no—
463C4⋊C4—261no—
464C4⋊C4—261no—
465C4⋊C4—261no—
466C4⋊C4—522no—
467C4⋊C4C2×C22⋊D1314yes—
468C4⋊C4C2×C22⋊D1314yes—
469C22⋊C4—28no—
470C22⋊C4—264no—
471C22⋊C4—522no—
472C22⋊C4—522no—
473C22⋊C4—522no—
474C22⋊C4—522no—
475C42—28no—
476C42—22no—
477C42—22no—
478C42—21no—
479C42—21no—
480C42—522no—
481C42C2×C22⋊D1312yes—
482C42C2×C22⋊D1312yes—
483C13#2430011yescharacteristic, complemented, Sylow
484C23—21no—
485C23—21no—
486C23—21no—
487C23—21no—
488C23—21no—
489C23—21no—
490C23—262no—
491C23—521no—
492C23—521no—
493C23—521no—
494C23—521no—
495C23—521no—
496C23—521no—
497C23#8820012yes—
498C23C22×C22⋊D1311yescharacteristic
499Q8—48no—
500Q8—48no—
501D4—262no—
502D4—262no—
503D4—528no—
504D4—521no—
505D4—521no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—24no—
521C2×C4—24no—
522C2×C4—44no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—44no—
528C2×C4—262no—
529C2×C4—521no—
530C2×C4—521no—
531C2×C4—521no—
532C2×C4—521no—
533C2×C4—521no—
534C2×C4—521no—
535C2×C4—521no—
536C2×C4—521no—
537C2×C4—1044no—
538C2×C4#8820012yes—
539C2×C4#8820312yes—
540C2×C4#8820412yes—
541C2×C4#8820712yes—
542C2×C4#8820712yes—
543C2×C4C2×Q8×D1311yescharacteristic
544C2×C4C2×#613111yescharacteristic
545C2×C4#8825411yescharacteristic
546C2×C4#8825411yescharacteristic
547C2×C4C22×C22⋊D1311yescharacteristic
548C2×C4C22×C22⋊D1311yescharacteristic
549C8—522no—
550C8—522no—
551C22—22no—
552C22—22no—
553C22—22no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22—522no—
559C22—522no—
560C22—522no—
561C22—1041no—
562C22—1041no—
563C22—1041no—
564C22—1041no—
565C22C2×#8820011yescharacteristic
566C22#1171952111yescharacteristic
567C22C2×#8820311yescharacteristic
568C22C2×#8820411yescharacteristic
569C22#1171952711yescharacteristic
570C22#1171952711yescharacteristic
571C22C2×#8820711yescharacteristic
572C4—22no—
573C4—22no—
574C4—41no—
575C4—44no—
576C4—41no—
577C4—44no—
578C4—522no—
579C4—1041no—
580C4—1041no—
581C4#1171889914yes—
582C4Q8×C22⋊D1311yescharacteristic
583C4Q8×C22⋊D1311yescharacteristic
584C4#1171952211yescharacteristic
585C4#1171952211yescharacteristic
586C2—42no—
587C2—1042no—
588C2#1311819511yescharacteristic
589C2C2×#1171889911yescharacteristic
590C2#1312407811yescharacteristic
591C2#1312461811yescharacteristic
592C2#1312462911yescharacteristic
593C2#1312601511yescharacteristic
594C2#1312603411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#533C2
socleC23×C13C22×D4
prime radicalC2×#88184C22
hypercenterC2×#533D13
hypocenterC13#24300
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. C2×#11718745C2semidirect
2. C2×#11718748C2semidirect
4. #13116171C2semidirect
5. #13115979C2semidirect
6. #13115789C2semidirect
7. #13115785C2semidirect
9. #13115035C2semidirect
10. #13114816C2semidirect
11. C2×C13×#533C2semidirect
57. C13×C4⋊Q8D4semidirect
58. C13×C4⋊Q8D4semidirect
83. #88184Q8semidirect
187. C2×#533D13semidirect
347. C4⋊Q8C22⋊D13semidirect
348. C4⋊Q8C22⋊D13semidirect
483. C13#24300semidirect

Maximal subgroups

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

subgroupindex
C2×#117187452
C2×#117187482
C4×#881842
#131161712
#131159792
#131157892
#131157852
#131151582
#131150352
#131148162
C2×C13×#5332
#2430013