Finite Group Databasebeta

← #15896850

Subgroups — #15896850

Order 3328.

1350 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718755C211yesmaximal, characteristic, complemented
2C2×C4×#6105C211yesmaximal, characteristic, complemented
3#13119758C211yesmaximal, characteristic, complemented
4#13116022C212yesmaximal, complemented
5#13115839C212yesmaximal, complemented
6#13115798C211yesmaximal, characteristic, complemented
7#13115631C211yesmaximal, characteristic, complemented
8#13115143C212yesmaximal, complemented
9#13115029C212yesmaximal, complemented
10#13114836C211yesmaximal, characteristic, complemented
11C2×C13×#547C211yesmaximal, characteristic
12C22×C13×#41—21no—
13C13×#547—24no—
14C13×#547—24no—
15C2×C13×C4⋊Q8C2211yescharacteristic
16C2×C13×#123—22no—
17C2×C13×C22⋊Q8—21no—
18C2×C13×#121C2212yes—
19C2×C4×D4×C13C2211yescharacteristic
20C2×C4×D4×C13C2211yescharacteristic
21C22×C13×C4⋊C4C2212yes—
22C22×#6105C2211yescharacteristic
23C2×#88178C2212yes—
24C2×C4×Dic26C2211yescharacteristic
25#11718882—21no—
26C2×#88072C2211yescharacteristic
27C2×#88072C2212yes—
28#11718873C2212yes—
29C2×C22⋊#1055C2212yes—
30C2×C22⋊#1055C2212yes—
31#11718755—24no—
32C4×#6105—24no—
33#11718634—21no—
34C2×#88050C2211yescharacteristic
35C2×#88050C2212yes—
36C2×#88048C2211yescharacteristic
37C2×#88048C2212yes—
38#11718609—22no—
39#11718596C2211yescharacteristic
40C2×C4⋊#1055C2211yescharacteristic
41C2×C4×#1055C2211yescharacteristic
42#11718121C2212yes—
43#11718121C2212yes—
44#11718121C2212yes—
45C2×C13×#41—28no—
46C2×C13×#41—44no—
47C2×C13×#41—44no—
48C22×Q8×C13—21no—
49C22×D4×C13—22no—
50C22×D4×C13D411yescharacteristic
51C22×D4×C13C2311yescharacteristic
52C23×C4×C13—22no—
53C23×C4×C13—21no—
54C23×C4×C13C2312yes—
55C22×Dic26C2311yescharacteristic
56C13×C4⋊Q8—22no—
57C13×C4⋊Q8D414yes—
58C13×#123—216no—
59C13×C22⋊Q8—28no—
60C13×#121—24no—
61C13×#121—24no—
62C4×D4×C13—22no—
63C4×D4×C13—22no—
64C4×D4×C13—22no—
65C4×D4×C13D414yes—
66C2×C13×C4⋊C4—22no—
67C2×C13×C4⋊C4—21no—
68C2×C13×C4⋊C4—24no—
69C2×C13×C4⋊C4—24no—
70C2×C13×C4⋊C4D411yescharacteristic
71C2×C13×C4⋊C4C2311yescharacteristic
72C2×C13×C4⋊C4C2312yes—
73C2×C13×C22⋊C4—21no—
74C2×C13×C22⋊C4—22no—
75C2×C13×C22⋊C4D412yes—
76C2×C42×C13C2311yescharacteristic
77C2×C22⋊Dic13—22no—
78C2×C22⋊Dic13—22no—
79C2×#6105—22no—
80C2×#6105—22no—
81C2×#6105—22no—
82C2×C4⋊Dic13—21no—
83C2×C4⋊Dic13—21no—
84C2×C4⋊Dic13C2311yescharacteristic
85C2×C4⋊Dic13C2312yes—
86#88178—24no—
87#88178—42no—
88C2×#6101—21no—
89C2×#6101—22no—
90C2×C4×Dic13—21no—
91C22×#1055C2311yescharacteristic
92C22×#1055C2312yes—
93C22×#1055C2311yescharacteristic
94C4×Dic26—22no—
95C4×Dic26—22no—
96#88072—22no—
97#88072—42no—
98#88071—22no—
99C22⋊#1055—24no—
100C22⋊#1055—42no—
101#88050—22no—
102#88050—24no—
103#88048—22no—
104#88048—24no—
105C4⋊#1055—22no—
106C4×#1055—22no—
107#24120—131nomaximal, Sylow
108C24×C13—21no—
109C24×C13C2×D412yes—
110C13×#41—432no—
111C2×Q8×C13—24no—
112C2×Q8×C13—42no—
113C2×Q8×C13—42no—
114C2×D4×C13—28no—
115C2×D4×C13—22no—
116C2×D4×C13—22no—
117C2×D4×C13—21no—
118C2×D4×C13—21no—
119C2×D4×C13—21no—
120C2×D4×C13—21no—
121C2×D4×C13—21no—
122C2×D4×C13—44no—
123C2×D4×C13—44no—
124C2×D4×C13SD1614yescomplemented
125C2×D4×C13C2×D412yes—
126C22×C4×C13—28no—
127C22×C4×C13—21no—
128C22×C4×C13—22no—
129C22×C4×C13—24no—
130C22×C4×C13—22no—
131C22×C4×C13—22no—
132C22×C4×C13—22no—
133C22×C4×C13—22no—
134C22×C4×C13—22no—
135C22×C4×C13—22no—
136C22×C4×C13—44no—
137C22×C4×C13—44no—
138C22×C4×C13—42no—
139C22×C4×C13—42no—
140C22×C4×C13C2×D412yes—
141C22×C4×C13C2×D411yescharacteristic
142C22×C4×C13C2×D411yescharacteristic
143C22×C4×C13C2411yescharacteristic
144C22×Dic13—21no—
145C22×Dic13—21no—
146C22×Dic13—22no—
147C2×Dic26—21no—
148C2×Dic26—21no—
149C2×Dic26—21no—
150C2×Dic26—21no—
151C2×Dic26—21no—
152C2×Dic26#4112yescomplemented
153C13×C4⋊C4—28no—
154C13×C4⋊C4—24no—
155C13×C4⋊C4—22no—
156C13×C4⋊C4—21no—
157C13×C4⋊C4—22no—
158C13×C4⋊C4C2×D412yes—
159C13×C4⋊C4C2×D414yes—
160C13×C22⋊C4—28no—
161C13×C22⋊C4—24no—
162C13×C22⋊C4—24no—
163C42×C13C2×D412yes—
164C42×C13C2×D412yes—
165C22⋊Dic13—44no—
166C22⋊Dic13—82no—
167#6105—28no—
168C4⋊Dic13—21no—
169C4⋊Dic13—21no—
170C4⋊Dic13—22no—
171C4⋊Dic13—22no—
172C4⋊Dic13—42no—
173C4⋊Dic13—81no—
174#6101—44no—
175#6101—42no—
176C4×Dic13—42no—
177C2×#1055—21no—
178C2×#1055—21no—
179C2×#1055—21no—
180C2×#1055—22no—
181C2×#1055—22no—
182C2×#1055—21no—
183C2×#1055—22no—
184C2×#1055—21no—
185C2×#1055#4112yescomplemented
186C2×#547D1311yescharacteristic
187C2×#475—131no—
188C2×C4×SD16—131no—
189#2538—131no—
190#2034—132no—
191#2000—132no—
192#1990—131no—
193#1954—131no—
194#1872—132no—
195#1853—132no—
196#1802—131no—
197C23×C13—22no—
198C23×C13—22no—
199C23×C13—22no—
200C23×C13—22no—
201C23×C13—22no—
202C23×C13—22no—
203C23×C13—22no—
204C23×C13—41no—
205C23×C13—41no—
206C23×C13—41no—
207C23×C13—41no—
208C23×C13—41no—
209C23×C13—41no—
210C23×C13C2×SD1614yes—
211C23×C13C22×D411yescharacteristic
212Q8×C13—48no—
213D4×C13—22no—
214D4×C13—22no—
215D4×C13—28no—
216D4×C13—416no—
217D4×C13—41no—
218D4×C13—41no—
219C2×C4×C13—21no—
220C2×C4×C13—21no—
221C2×C4×C13—22no—
222C2×C4×C13—22no—
223C2×C4×C13—24no—
224C2×C4×C13—22no—
225C2×C4×C13—22no—
226C2×C4×C13—416no—
227C2×C4×C13—41no—
228C2×C4×C13—42no—
229C2×C4×C13—41no—
230C2×C4×C13—42no—
231C2×C4×C13—42no—
232C2×C4×C13—42no—
233C2×C4×C13—42no—
234C2×C4×C13—42no—
235C2×C4×C13—48no—
236C2×C4×C13#12012yes—
237C2×C4×C13#12012yes—
238C2×C4×C13C2×SD1612yes—
239C2×C4×C13AGL(1,ℤ/8)12yes—
240C2×C4×C13C22×D411yescharacteristic
241C2×C4×C13C22×D411yescharacteristic
242C2×C4×C13C2×#4111yescharacteristic
243C2×C4×C13C2×#4111yescharacteristic
244C2×C4×C13H(5,𝔽2)11yescharacteristic
245C2×C4×C132−1+411yescharacteristic
246C2×Dic13—22no—
247C2×Dic13—41no—
248C2×Dic13—41no—
249C2×Dic13—41no—
250C2×Dic13—42no—
251C2×Dic13—42no—
252C2×Dic13—42no—
253C2×Dic13—41no—
254C2×Dic13—41no—
255Dic26—22no—
256Dic26—22no—
257Dic26—41no—
258Dic26—41no—
259#1055—22no—
260#1055—41no—
261#1055—42no—
262C22×#41—21no—
263C22×SD16—131no—
264#547—24no—
265#547—24no—
266C2×C4⋊Q8C2×D1311yescharacteristic
267C2×#123—22no—
268C2×C22⋊Q8—21no—
269C2×C22⋊Q8—132no—
270C2×#121C2×D1312yes—
271C2×C4×Q8—131no—
272C2×C4×D4C2×D1311yescharacteristic
273C2×C4×D4C2×D1311yescharacteristic
274C22×C4⋊C4C2×D1312yes—
275#475—264no—
276C4×SD16—264no—
277C2×#106—132no—
278C2×#106—131no—
279C2×C4⋊C8—131no—
280C2×#103—132no—
281C2×#103—131no—
282C2×#102—131no—
283C2×#102—132no—
284C2×C22⋊C8—132no—
285C2×C22⋊C8—132no—
286C2×C4×C8—131no—
287#396—262no—
288#390—261no—
289#389—261no—
290#384—131no—
291#380—132no—
292#340—132no—
293#340—132no—
294#340—132no—
295C22×C13—24no—
296C22×C13—24no—
297C22×C13—24no—
298C22×C13—42no—
299C22×C13—42no—
300C22×C13—42no—
301C22×C13—42no—
302C22×C13—42no—
303C22×C13—42no—
304C22×C13—42no—
305C22×C13—81no—
306C22×C13—81no—
307C22×C13—81no—
308C22×C13—81no—
309C22×C13C2×#12011yescharacteristic
310C22×C13#54611yescharacteristic
311C22×C13#54711yescharacteristic
312C22×C13C22×SD1611yescharacteristic
313C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
314C22×C13#57711yescharacteristic
315C22×C13#57811yescharacteristic
316C4×C13—22no—
317C4×C13—42no—
318C4×C13—42no—
319C4×C13—44no—
320C4×C13#45014yes—
321C4×C13#52511yescharacteristic
322C4×C13#53711yescharacteristic
323C4×C13#54811yescharacteristic
324C4×C13#55011yescharacteristic
325Dic13—42no—
326Dic13—82no—
327Dic13—81no—
328C2×#41—28no—
329C2×#41—44no—
330C2×#41—44no—
331C22×Q8—21no—
332C22×Q8—131no—
333C22×D4—22no—
334C22×D4C22⋊D1311yescharacteristic
335C22×D4C22×D1311yescharacteristic
336C23×C4—22no—
337C23×C4—21no—
338C23×C4C22×D1312yes—
339C2×SD16—262no—
340C2×SD16—262no—
341C2×SD16—262no—
342C22×C8—131no—
343C22×C8—131no—
344C22×C8—132no—
345C4⋊Q8—22no—
346C4⋊Q8C22⋊D1314yes—
347#123—216no—
348C22⋊Q8—28no—
349C22⋊Q8—264no—
350C22⋊Q8—522no—
351#121—24no—
352#121—24no—
353C4×Q8—262no—
354C4×Q8—262no—
355C4×D4—22no—
356C4×D4—22no—
357C4×D4—22no—
358C4×D4C22⋊D1314yes—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—24no—
362C2×C4⋊C4—24no—
363C2×C4⋊C4—131no—
364C2×C4⋊C4—132no—
365C2×C4⋊C4—261no—
366C2×C4⋊C4—262no—
367C2×C4⋊C4—261no—
368C2×C4⋊C4—261no—
369C2×C4⋊C4C22⋊D1311yescharacteristic
370C2×C4⋊C4C22×D1311yescharacteristic
371C2×C4⋊C4C22×D1312yes—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—262no—
375C2×C22⋊C4—262no—
376C2×C22⋊C4C22⋊D1312yes—
377C2×C42—261no—
378C2×C42C22×D1311yescharacteristic
379#106—262no—
380#106—264no—
381C4⋊C8—262no—
382#103—262no—
383#103—264no—
384#102—262no—
385#102—522no—
386C22⋊C8—264no—
387C22⋊C8—522no—
388C4×C8—262no—
389#95—262no—
390C2×C13—44no—
391C2×C13—82no—
392C2×C13#240711yescharacteristic
393C2×C13C2×#45011yescharacteristic
394C2×C13#301311yescharacteristic
395C2×C13#329811yescharacteristic
396C2×C13#333211yescharacteristic
397C2×C13#333511yescharacteristic
398C2×C13#335311yescharacteristic
399C24—21no—
400C24C2×C22⋊D1312yes—
401#41—432no—
402C2×Q8—24no—
403C2×Q8—42no—
404C2×Q8—42no—
405C2×Q8—132no—
406C2×Q8—261no—
407C2×Q8—261no—
408C2×Q8—261no—
409C2×Q8—261no—
410C2×Q8—261no—
411C2×D4—28no—
412C2×D4—22no—
413C2×D4—22no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—44no—
420C2×D4—44no—
421C2×D4#610514yescomplemented
422C2×D4C2×C22⋊D1312yes—
423C22×C4—28no—
424C22×C4—21no—
425C22×C4—22no—
426C22×C4—24no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—44no—
434C22×C4—44no—
435C22×C4—42no—
436C22×C4—42no—
437C22×C4—261no—
438C22×C4—261no—
439C22×C4—262no—
440C22×C4C2×C22⋊D1312yes—
441C22×C4C2×C22⋊D1311yescharacteristic
442C22×C4C2×C22⋊D1311yescharacteristic
443C22×C4C23×D1311yescharacteristic
444SD16—268no—
445C2×C8—132no—
446C2×C8—261no—
447C2×C8—261no—
448C2×C8—262no—
449C2×C8—261no—
450C2×C8—262no—
451C2×C8—261no—
452C2×C8—261no—
453C2×C8—262no—
454C4⋊C4—28no—
455C4⋊C4—24no—
456C4⋊C4—22no—
457C4⋊C4—21no—
458C4⋊C4—22no—
459C4⋊C4—262no—
460C4⋊C4—262no—
461C4⋊C4—261no—
462C4⋊C4—261no—
463C4⋊C4—524no—
464C4⋊C4—522no—
465C4⋊C4—522no—
466C4⋊C4—1041no—
467C4⋊C4C2×C22⋊D1312yes—
468C4⋊C4C2×C22⋊D1314yes—
469C22⋊C4—28no—
470C22⋊C4—24no—
471C22⋊C4—24no—
472C22⋊C4—524no—
473C22⋊C4—1042no—
474C42—522no—
475C42C2×C22⋊D1312yes—
476C42C2×C22⋊D1312yes—
477C13#2412011yescharacteristic, complemented, Sylow
478C23—22no—
479C23—22no—
480C23—22no—
481C23—22no—
482C23—22no—
483C23—22no—
484C23—22no—
485C23—41no—
486C23—41no—
487C23—41no—
488C23—41no—
489C23—41no—
490C23—41no—
491C23C2×#610514yes—
492C23C22×C22⋊D1311yescharacteristic
493Q8—48no—
494Q8—262no—
495Q8—262no—
496Q8—521no—
497Q8—521no—
498D4—22no—
499D4—22no—
500D4—28no—
501D4—416no—
502D4—41no—
503D4—41no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—24no—
511C2×C4—416no—
512C2×C4—41no—
513C2×C4—42no—
514C2×C4—41no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—48no—
521C2×C4—262no—
522C2×C4—521no—
523C2×C4—521no—
524C2×C4—522no—
525C2×C4—522no—
526C2×C4—521no—
527C2×C4—522no—
528C2×C4—521no—
529C2×C4—521no—
530C2×C4#8818612yes—
531C2×C4C2×#610512yes—
532C2×C4#8820712yes—
533C2×C4#8820712yes—
534C2×C4#41×D1311yescharacteristic
535C2×C4#41×D1311yescharacteristic
536C2×C4#8825611yescharacteristic
537C2×C4#8825711yescharacteristic
538C2×C4C22×C22⋊D1311yescharacteristic
539C2×C4C22×C22⋊D1311yescharacteristic
540C8—262no—
541C8—521no—
542C8—522no—
543C22—24no—
544C22—24no—
545C22—24no—
546C22—42no—
547C22—42no—
548C22—42no—
549C22—42no—
550C22—42no—
551C22—42no—
552C22—42no—
553C22—81no—
554C22—81no—
555C22—81no—
556C22—81no—
557C22C2×#8818611yescharacteristic
558C22C22×#610511yescharacteristic
559C22#1171952911yescharacteristic
560C22#1171953411yescharacteristic
561C22#1171954211yescharacteristic
562C22#1171954311yescharacteristic
563C22C2×#8820711yescharacteristic
564C4—22no—
565C4—42no—
566C4—44no—
567C4—42no—
568C4—522no—
569C4—1041no—
570C4—1042no—
571C4#1171887914yes—
572C4#1171953311yescharacteristic
573C4#1171953611yescharacteristic
574C4#1171953811yescharacteristic
575C4#1171953911yescharacteristic
576C2—44no—
577C2—82no—
578C2#1311817511yescharacteristic
579C2C2×#1171887911yescharacteristic
580C2#1312415111yescharacteristic
581C2#1312669511yescharacteristic
582C2#1312715711yescharacteristic
583C2#1312719311yescharacteristic
584C2#1312742011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
Fitting, prime radicalC2×C13×#547C2
socleC23×C13C22×D4
hypercenterC2×#547D13
hypocenterC13#24120
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C2×#11718755C2semidirect
2. C2×C4×#6105C2semidirect
3. #13119758C2semidirect
4. #13116022C2semidirect
5. #13115839C2semidirect
6. #13115798C2semidirect
7. #13115631C2semidirect
8. #13115143C2semidirect
9. #13115029C2semidirect
10. #13114836C2semidirect
124. C2×D4×C13SD16semidirect
152. C2×Dic26#41semidirect
185. C2×#1055#41semidirect
421. C2×D4#6105semidirect
477. C13#24120semidirect

Maximal subgroups

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

subgroupindex
C2×#117187552
C2×C4×#61052
#131197582
#131160222
#131158392
#131157982
#131156312
#131151432
#131150292
#131148362
C2×C13×#5472
#2412013