Finite Group Databasebeta

← #15896976

Subgroups — #15896976

Order 3328.

1184 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718748C211yesmaximal, characteristic, complemented
2C2×#11718687C211yesmaximal, characteristic, complemented
3#13119737C211yesmaximal, characteristic
4#13116036C212yesmaximal, complemented
5#13115837C212yesmaximal, complemented
6#13115810C211yesmaximal, characteristic, complemented
7#13115635C211yesmaximal, characteristic, complemented
8#13115153C212yesmaximal, complemented
9#13115024C212yesmaximal, complemented
10#13114851C211yesmaximal, characteristic, complemented
11C2×C13×#554C211yesmaximal, characteristic, complemented
12C13×#554—24no—
13C13×#554—24no—
14C2×C13×C4⋊Q8C2211yescharacteristic
15C2×C13×#125—21no—
16C2×C13×C22⋊Q8—22no—
17C2×C13×C22⋊Q8C2212yes—
18C2×C4×Q8×C13C2211yescharacteristic
19C2×C4×D4×C13—21no—
20C2×C4×D4×C13C2211yescharacteristic
21C22×C13×C4⋊C4C2212yes—
22C22×#6106C2211yescharacteristic
23C2×#88184C2212yes—
24C2×C4×D52C2211yescharacteristic
25C2×#88075C2211yescharacteristic
26C2×#88075C2212yes—
27#11718884—21no—
28#11718873C2212yes—
29C2×C22⋊#1055C2212yes—
30C2×C22⋊#1055C2212yes—
31#11718748—24no—
32#11718687—24no—
33#11718654—21no—
34C2×#88049C2211yescharacteristic
35C2×#88049C2212yes—
36C2×#88047C2211yescharacteristic
37C2×#88047C2212yes—
38#11718617—22no—
39#11718597C2211yescharacteristic
40C2×C4⋊#1055C2211yescharacteristic
41C2×#88043C2211yescharacteristic
42#11718121C2212yes—
43#11718121C2212yes—
44#11718121C2212yes—
45C22×Q8×C13—21no—
46C22×Q8×C13C2311yescharacteristic
47C22×D4×C13D411yescharacteristic
48C23×C4×C13—22no—
49C23×C4×C13C2312yes—
50C22×C22⋊D13—22no—
51C22×D52C2311yescharacteristic
52C22×C4×D13—21no—
53C13×C4⋊Q8—22no—
54C13×C4⋊Q8D414yescomplemented
55C13×#125—28no—
56C13×C22⋊Q8—216no—
57C13×C22⋊Q8—24no—
58C13×C22⋊Q8—24no—
59C4×Q8×C13—22no—
60C4×Q8×C13D414yescomplemented
61C4×D4×C13—28no—
62C4×D4×C13—22no—
63C4×D4×C13—22no—
64C2×C13×C4⋊C4—22no—
65C2×C13×C4⋊C4—21no—
66C2×C13×C4⋊C4—21no—
67C2×C13×C4⋊C4—22no—
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—22no—
74C2×C13×C22⋊C4D412yes—
75C2×C42×C13—21no—
76C2×C42×C13C2311yescharacteristic
77C2×C22⋊Dic13—22no—
78C2×#6106—22no—
79C2×#6106—22no—
80C2×#6106—22no—
81#88184—24no—
82#88184—42no—
83C2×#6103—21no—
84C2×#6103—22no—
85C2×C4⋊Dic13C2311yescharacteristic
86C2×C4⋊Dic13C2312yes—
87C22×#1055C2311yescharacteristic
88C22×#1055C2312yes—
89C22×#1055C2311yescharacteristic
90C4×D52—22no—
91C4×D52—22no—
92#88075—22no—
93#88075—42no—
94#88071—21no—
95#88071—21no—
96#88071—22no—
97C22⋊#1055—24no—
98C22⋊#1055—42no—
99#88049—22no—
100#88049—24no—
101#88047—22no—
102#88047—24no—
103C4⋊#1055—22no—
104#88043—22no—
105#24130—131nomaximal, Sylow
106C24×C13C2×D412yes—
107C23×D13—21no—
108C2×Q8×C13—24no—
109C2×Q8×C13—21no—
110C2×Q8×C13—21no—
111C2×Q8×C13—21no—
112C2×Q8×C13—21no—
113C2×Q8×C13—21no—
114C2×Q8×C13—82no—
115C2×Q8×C13C2×D412yes—
116C2×D4×C13—24no—
117C2×D4×C13—22no—
118C22×C4×C13—21no—
119C22×C4×C13—21no—
120C22×C4×C13—22no—
121C22×C4×C13—28no—
122C22×C4×C13—22no—
123C22×C4×C13—22no—
124C22×C4×C13—22no—
125C22×C4×C13—22no—
126C22×C4×C13—22no—
127C22×C4×C13—22no—
128C22×C4×C13—82no—
129C22×C4×C13—82no—
130C22×C4×C13C2×D412yes—
131C22×C4×C13C2×D411yescharacteristic
132C22×C4×C13C2×D411yescharacteristic
133C22×C4×C13C2411yescharacteristic
134C2×C22⋊D13—44no—
135C2×C22⋊D13—44no—
136C2×C22⋊D13—82no—
137C22×Dic13—22no—
138C22×Dic13—21no—
139C2×D52—21no—
140C2×D52—21no—
141C2×D52—21no—
142C2×D52—21no—
143C2×D52—21no—
144C2×D52#4112yes—
145C2×C4×D13—42no—
146C2×C4×D13—82no—
147C13×C4⋊C4—28no—
148C13×C4⋊C4—28no—
149C13×C4⋊C4—24no—
150C13×C4⋊C4—24no—
151C13×C4⋊C4—22no—
152C13×C4⋊C4—21no—
153C13×C4⋊C4—22no—
154C13×C4⋊C4C2×D412yes—
155C13×C4⋊C4C2×D414yes—
156C13×C22⋊C4—28no—
157C13×C22⋊C4—24no—
158C42×C13—24no—
159C42×C13C2×D412yes—
160C42×C13C2×D412yes—
161C22⋊Dic13—82no—
162#6106—28no—
163#6103—44no—
164#6103—42no—
165C4⋊Dic13—21no—
166C4⋊Dic13—21no—
167C4⋊Dic13—22no—
168C4⋊Dic13—22no—
169C2×#1055—21no—
170C2×#1055—21no—
171C2×#1055—21no—
172C2×#1055—22no—
173C2×#1055—22no—
174C2×#1055—21no—
175C2×#1055—22no—
176C2×#1055—21no—
177C2×#1055#4112yes—
178C2×#554D1311yescharacteristic, complemented
179C2×#474—131no—
180C2×#440—131no—
181#2535—131no—
182#2036—132no—
183#2000—132no—
184#1993—131no—
185#1955—131no—
186#1874—132no—
187#1852—132no—
188#1805—131no—
189C23×C13—22no—
190C23×C13—22no—
191C23×C13—22no—
192C23×C13—22no—
193C23×C13—22no—
194C23×C13—22no—
195C23×C13#13714yes—
196C23×C13C22×D411yescharacteristic
197C22×D13—22no—
198C22×D13—41no—
199C22×D13—41no—
200C22×D13—42no—
201C22×D13—42no—
202Q8×C13—22no—
203Q8×C13—22no—
204Q8×C13—41no—
205Q8×C13—41no—
206Q8×C13—84no—
207D4×C13—28no—
208C2×C4×C13—22no—
209C2×C4×C13—22no—
210C2×C4×C13—22no—
211C2×C4×C13—22no—
212C2×C4×C13—22no—
213C2×C4×C13—24no—
214C2×C4×C13—22no—
215C2×C4×C13—22no—
216C2×C4×C13—41no—
217C2×C4×C13—41no—
218C2×C4×C13—42no—
219C2×C4×C13—42no—
220C2×C4×C13—42no—
221C2×C4×C13—42no—
222C2×C4×C13—42no—
223C2×C4×C13—42no—
224C2×C4×C13—42no—
225C2×C4×C13—88no—
226C2×C4×C13#12012yes—
227C2×C4×C13#12012yes—
228C2×C4×C13C22×D411yescharacteristic
229C2×C4×C13C22×D411yescharacteristic
230C2×C4×C13C2×#4111yescharacteristic
231C2×C4×C13C2×#4111yescharacteristic
232C2×C4×C13H(5,𝔽2)11yescharacteristic
233C2×C4×C132−1+411yescharacteristic
234C22⋊D13—88no—
235C2×Dic13—41no—
236C2×Dic13—42no—
237C2×Dic13—42no—
238C2×Dic13—42no—
239C2×Dic13—42no—
240D52—22no—
241D52—22no—
242D52—41no—
243D52—41no—
244C4×D13—84no—
245#1055—22no—
246#1055—41no—
247#1055—42no—
248C22×SD16—131no—
249#554—24no—
250#554—24no—
251C2×C4⋊Q8C2×D1311yescharacteristic
252C2×#125—21no—
253C2×C22⋊Q8—22no—
254C2×C22⋊Q8C2×D1312yes—
255C2×#121—132no—
256C2×C4×Q8C2×D1311yescharacteristic
257C2×C4×D4—21no—
258C2×C4×D4—131no—
259C2×C4×D4C2×D1311yescharacteristic
260C22×C4⋊C4C2×D1312yes—
261#474—264no—
262#440—264no—
263C2×#107—131no—
264C2×#107—132no—
265C2×C4⋊C8—131no—
266C2×#103—131no—
267C2×#103—132no—
268C2×#102—131no—
269C2×#102—132no—
270C2×C22⋊C8—132no—
271C2×C22⋊C8—132no—
272C2×#97—131no—
273#397—261no—
274#392—261no—
275#386—262no—
276#382—131no—
277#380—132no—
278#340—132no—
279#340—132no—
280#340—132no—
281C22×C13—24no—
282C22×C13—24no—
283C22×C13—24no—
284C22×C13—42no—
285C22×C13—42no—
286C22×C13—42no—
287C22×C13—42no—
288C22×C13C2×#12011yescharacteristic
289C22×C13#54611yescharacteristic
290C22×C13#54711yescharacteristic
291C22×C13C2×#13712yes—
292C22×C13#57612yes—
293C2×D13—42no—
294C2×D13—44no—
295C2×D13—82no—
296C2×D13—81no—
297C2×D13—81no—
298C4×C13—22no—
299C4×C13—22no—
300C4×C13—42no—
301C4×C13—42no—
302C4×C13—42no—
303C4×C13—44no—
304C4×C13#52511yescharacteristic
305C4×C13#53711yescharacteristic
306C4×C13#54811yescharacteristic
307C4×C13#55011yescharacteristic
308Dic13—81no—
309Dic13—82no—
310C22×Q8—21no—
311C22×Q8C22×D1311yescharacteristic
312C22×D4—131no—
313C22×D4—262no—
314C22×D4C22⋊D1311yescharacteristic
315C23×C4—22no—
316C23×C4—261no—
317C23×C4C22×D1312yes—
318C2×SD16—262no—
319C2×SD16—262no—
320C2×SD16—262no—
321C22×C8—131no—
322C22×C8—131no—
323C22×C8—132no—
324C4⋊Q8—22no—
325C4⋊Q8C22⋊D1314yescomplemented
326#125—28no—
327C22⋊Q8—216no—
328C22⋊Q8—24no—
329C22⋊Q8—24no—
330#121—264no—
331#121—522no—
332C4×Q8—22no—
333C4×Q8C22⋊D1314yescomplemented
334C4×D4—28no—
335C4×D4—22no—
336C4×D4—22no—
337C4×D4—262no—
338C4×D4—262no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—131no—
346C2×C4⋊C4—132no—
347C2×C4⋊C4C22⋊D1311yescharacteristic
348C2×C4⋊C4C22×D1311yescharacteristic
349C2×C4⋊C4C22×D1312yes—
350C2×C22⋊C4—22no—
351C2×C22⋊C4—261no—
352C2×C22⋊C4—262no—
353C2×C22⋊C4—262no—
354C2×C22⋊C4C22⋊D1312yes—
355C2×C42—21no—
356C2×C42C22×D1311yescharacteristic
357#107—262no—
358#107—264no—
359C4⋊C8—262no—
360#103—262no—
361#103—522no—
362#102—262no—
363#102—264no—
364C22⋊C8—264no—
365C22⋊C8—522no—
366#97—262no—
367#95—262no—
368#95—261no—
369#95—261no—
370C2×C13—44no—
371C2×C13#240711yescharacteristic
372C2×C13#300411yescharacteristic
373C2×C13#300811yescharacteristic
374C2×C13#331412yes—
375C2×C13#334612yes—
376D13—82no—
377C24—261no—
378C24C2×C22⋊D1312yes—
379C2×Q8—24no—
380C2×Q8—21no—
381C2×Q8—21no—
382C2×Q8—21no—
383C2×Q8—21no—
384C2×Q8—21no—
385C2×Q8—82no—
386C2×Q8C2×C22⋊D1312yes—
387C2×D4—24no—
388C2×D4—22no—
389C2×D4—132no—
390C2×D4—261no—
391C2×D4—261no—
392C2×D4—261no—
393C2×D4—261no—
394C2×D4—261no—
395C2×D4—524no—
396C2×D4—524no—
397C2×D4—1042no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—22no—
401C22×C4—28no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—82no—
409C22×C4—82no—
410C22×C4—262no—
411C22×C4—261no—
412C22×C4—522no—
413C22×C4—1042no—
414C22×C4C2×C22⋊D1312yes—
415C22×C4C2×C22⋊D1311yescharacteristic
416C22×C4C2×C22⋊D1311yescharacteristic
417C22×C4C23×D1311yescharacteristic
418SD16—268no—
419C2×C8—132no—
420C2×C8—261no—
421C2×C8—261no—
422C2×C8—262no—
423C2×C8—261no—
424C2×C8—262no—
425C2×C8—261no—
426C2×C8—261no—
427C2×C8—262no—
428C4⋊C4—28no—
429C4⋊C4—28no—
430C4⋊C4—24no—
431C4⋊C4—24no—
432C4⋊C4—22no—
433C4⋊C4—21no—
434C4⋊C4—22no—
435C4⋊C4—262no—
436C4⋊C4—262no—
437C4⋊C4—261no—
438C4⋊C4—261no—
439C4⋊C4C2×C22⋊D1312yes—
440C4⋊C4C2×C22⋊D1314yes—
441C22⋊C4—28no—
442C22⋊C4—24no—
443C22⋊C4—524no—
444C22⋊C4—522no—
445C22⋊C4—1042no—
446C42—24no—
447C42C2×C22⋊D1312yes—
448C42C2×C22⋊D1312yes—
449C13#2413011yescharacteristic, complemented, Sylow
450C23—22no—
451C23—22no—
452C23—22no—
453C23—22no—
454C23—22no—
455C23—22no—
456C23—262no—
457C23—522no—
458C23—521no—
459C23—522no—
460C23—521no—
461C23#8819614yes—
462C23C22×C22⋊D1311yescharacteristic
463Q8—22no—
464Q8—22no—
465Q8—41no—
466Q8—41no—
467Q8—84no—
468D4—28no—
469D4—262no—
470D4—262no—
471D4—521no—
472D4—521no—
473D4—1048no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—24no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—88no—
492C2×C4—522no—
493C2×C4—522no—
494C2×C4—522no—
495C2×C4—522no—
496C2×C4—521no—
497C2×C4—1044no—
498C2×C4#8820712yes—
499C2×C4#8820712yes—
500C2×C4#41×D1311yescharacteristic
501C2×C4#41×D1311yescharacteristic
502C2×C4#8825611yescharacteristic
503C2×C4#8825711yescharacteristic
504C2×C4C22×C22⋊D1311yescharacteristic
505C2×C4C22×C22⋊D1311yescharacteristic
506C8—262no—
507C8—521no—
508C8—522no—
509C22—24no—
510C22—24no—
511C22—24no—
512C22—42no—
513C22—42no—
514C22—42no—
515C22—42no—
516C22—522no—
517C22—524no—
518C22—1041no—
519C22—1042no—
520C22—1041no—
521C22C2×#8819612yes—
522C22#1171952911yescharacteristic
523C22#1171953411yescharacteristic
524C22#1171954012yes—
525C22C2×#8820711yescharacteristic
526C4—22no—
527C4—22no—
528C4—42no—
529C4—44no—
530C4—42no—
531C4—42no—
532C4—1041no—
533C4—1042no—
534C4#1171953311yescharacteristic
535C4#1171953611yescharacteristic
536C4#1171953811yescharacteristic
537C4#1171953911yescharacteristic
538C2—44no—
539C2—1042no—
540C2#1311817511yescharacteristic
541C2#1312407011yescharacteristic
542C2#1312410411yescharacteristic
543C2#1312691112yes—
544C2#1312731512yes—
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#554C2
socleC23×C13C22×D4
prime radical#13119737C2
hypercenterC2×#554D13
hypocenterC13#24130
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. C2×#11718748C2semidirect
2. C2×#11718687C2semidirect
4. #13116036C2semidirect
5. #13115837C2semidirect
6. #13115810C2semidirect
7. #13115635C2semidirect
8. #13115153C2semidirect
9. #13115024C2semidirect
10. #13114851C2semidirect
11. C2×C13×#554C2semidirect
54. C13×C4⋊Q8D4semidirect
60. C4×Q8×C13D4semidirect
178. C2×#554D13semidirect
325. C4⋊Q8C22⋊D13semidirect
333. C4×Q8C22⋊D13semidirect
449. C13#24130semidirect

Maximal subgroups

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

subgroupindex
C2×#117187482
C2×#117186872
#131197372
#131160362
#131158372
#131158102
#131156352
#131151532
#131150242
#131148512
C2×C13×#5542
#2413013