Finite Group Databasebeta

← #15904223

Subgroups — #15904223

Order 3328.

912 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718668C211yesmaximal, characteristic, complemented
2C2×#11718587C211yesmaximal, characteristic, complemented
3#13123188C211yesmaximal, characteristic, complemented
4#13116267C212yesmaximal, complemented
5#13116022C212yesmaximal
6#13115788C211yesmaximal, characteristic, complemented
7#13115599C211yesmaximal, characteristic, complemented
8#13115576C212yesmaximal, complemented
9#13115536C212yesmaximal, complemented
10#13114836C211yesmaximal, characteristic, complemented
11C4×C13×#121C211yesmaximal, characteristic
12C2×C13×#121C2211yescharacteristic
13C2×C4×D4×C13—21no—
14C2×C4×D4×C13C2211yescharacteristic
15C22×C42×C13C2211yescharacteristic
16C2×#88178—21no—
17C2×#88123C2211yescharacteristic
18C13×#390C2211yescharacteristic
19C13×#389C2211yescharacteristic
20C13×#388—21no—
21C13×#386—21no—
22C13×#380C2211yescharacteristic
23C4×C13×C4⋊C4C2211yescharacteristic
24C4×C13×C22⋊C4—21no—
25C2×#88072C2212yes—
26C2×#88072C2212yes—
27#11718873—21no—
28#11718873C2212yes—
29C2×C22⋊#1055C2212yes—
30#11718668—24no—
31C2×#88048C2212yes—
32C2×#88047C2212yes—
33#11718596C2211yescharacteristic
34#11718590—21no—
35#11718589—21no—
36#11718589C2212yes—
37#11718587—24no—
38C2×C4⋊#1055C2211yescharacteristic
39C2×C4⋊#1055C2211yescharacteristic
40C2×#88043C2212yes—
41#11718121C2212yes—
42#11718121C2212yes—
43#11718121C2212yes—
44#11718121C2212yes—
45C22×D4×C13—21no—
46C22×D4×C13C2311yescharacteristic
47C23×C4×C13—21no—
48C23×C4×C13D411yescharacteristic
49C23×C4×C13D411yescharacteristic
50C23×C4×C13C2311yescharacteristic
51C22×Dic26—21no—
52C13×#121—22no—
53C13×#121—22no—
54C4×D4×C13—22no—
55C4×D4×C13—22no—
56C4×D4×C13—44no—
57C2×C13×C4⋊C4—21no—
58C2×C13×C4⋊C4C2311yescharacteristic
59C2×C13×C4⋊C4C2311yescharacteristic
60C2×C13×C4⋊C4C2311yescharacteristic
61C2×C13×C22⋊C4—21no—
62C2×C13×C22⋊C4—21no—
63C2×C13×C22⋊C4—21no—
64C2×C13×C22⋊C4—21no—
65C2×C13×C22⋊C4—21no—
66C2×C42×C13—22no—
67C2×C42×C13—22no—
68C2×C42×C13—21no—
69C2×C42×C13D411yescharacteristic
70C2×C42×C13D411yescharacteristic
71C2×C42×C13C2311yescharacteristic
72C2×C42×C13C2311yescharacteristic
73C2×C22⋊Dic13—22no—
74C2×C4⋊Dic13—21no—
75C2×C4⋊Dic13—21no—
76C2×C4⋊Dic13—21no—
77C2×C4⋊Dic13C2312yes—
78C2×C4⋊Dic13C2312yes—
79#88178—44no—
80C2×#6101—22no—
81C22×#1055C2312yes—
82C22×#1055C2312yes—
83#88123—22no—
84#88123—22no—
85C13×#95—21no—
86C13×#95—21no—
87C13×#95—21no—
88#88072—24no—
89#88072—24no—
90#88071—22no—
91#88071—22no—
92C22⋊#1055—24no—
93#88048—24no—
94#88047—24no—
95C4⋊#1055—22no—
96C4⋊#1055D414yescomplemented
97#88043—24no—
98#24709—131nomaximal, Sylow
99C24×C13—21no—
100C24×C13C2×D411yescharacteristic
101C2×D4×C13—24no—
102C2×D4×C13—21no—
103C2×D4×C13—21no—
104C2×D4×C13—21no—
105C2×D4×C13—21no—
106C2×D4×C13—21no—
107C2×D4×C13—42no—
108C2×D4×C13—42no—
109C2×D4×C13#4112yes—
110C22×C4×C13—22no—
111C22×C4×C13—21no—
112C22×C4×C13—22no—
113C22×C4×C13—22no—
114C22×C4×C13—22no—
115C22×C4×C13—22no—
116C22×C4×C13—21no—
117C22×C4×C13—21no—
118C22×C4×C13—21no—
119C22×C4×C13—21no—
120C22×C4×C13—21no—
121C22×C4×C13—21no—
122C22×C4×C13—21no—
123C22×C4×C13—21no—
124C22×C4×C13—41no—
125C22×C4×C13—42no—
126C22×C4×C13—42no—
127C22×C4×C13—42no—
128C22×C4×C13C2×D411yescharacteristic
129C22×C4×C13C2×D411yescharacteristic
130C22×C4×C13C2×D411yescharacteristic
131C22×C4×C13C2×D411yescharacteristic
132C22×C4×C13C2×D411yescharacteristic
133C22×C4×C13C2411yescharacteristic
134C22×Dic13—22no—
135C22×Dic13—22no—
136C2×Dic26—42no—
137C2×Dic26—42no—
138C2×Dic26—42no—
139C13×C4⋊C4—21no—
140C13×C4⋊C4—21no—
141C13×C4⋊C4—21no—
142C13×C4⋊C4—21no—
143C13×C4⋊C4—21no—
144C13×C4⋊C4—42no—
145C13×C4⋊C4#4112yes—
146C13×C22⋊C4—24no—
147C13×C22⋊C4—42no—
148C13×C22⋊C4—42no—
149C13×C22⋊C4—42no—
150C13×C22⋊C4—42no—
151C42×C13—22no—
152C42×C13—22no—
153C42×C13—21no—
154C42×C13—21no—
155C42×C13—42no—
156C42×C13C2×D412yes—
157C42×C13#4112yes—
158C22⋊Dic13—44no—
159C4⋊Dic13—22no—
160C4⋊Dic13—22no—
161C4⋊Dic13—22no—
162C4⋊Dic13—22no—
163C4⋊Dic13—42no—
164C4⋊Dic13—42no—
165C4⋊Dic13—42no—
166#6101—44no—
167C2×#1055—22no—
168C2×#1055—22no—
169C2×#1055—22no—
170C2×#1055—22no—
171C2×#1055—22no—
172C2×#1055C2×D414yes—
173C2×#474—131no—
174C2×#432—131no—
175#2857—131no—
176C4×#121D1311yescharacteristic
177#2076—132no—
178#2034—132no—
179#1988—131no—
180#1948—131no—
181#1944—132no—
182#1936—132no—
183#1802—131no—
184C23×C13—21no—
185C23×C13—21no—
186C23×C13—21no—
187C23×C13—21no—
188C23×C13—21no—
189C23×C13—21no—
190C23×C13—22no—
191C23×C13—41no—
192C23×C13—41no—
193C23×C13—41no—
194C23×C13—41no—
195C23×C13—41no—
196C23×C13—41no—
197C23×C13#13712yes—
198C23×C13C22×D411yescharacteristic
199D4×C13—22no—
200D4×C13—22no—
201D4×C13—48no—
202D4×C13—41no—
203D4×C13—41no—
204C2×C4×C13—21no—
205C2×C4×C13—21no—
206C2×C4×C13—21no—
207C2×C4×C13—21no—
208C2×C4×C13—21no—
209C2×C4×C13—21no—
210C2×C4×C13—22no—
211C2×C4×C13—21no—
212C2×C4×C13—21no—
213C2×C4×C13—21no—
214C2×C4×C13—21no—
215C2×C4×C13—21no—
216C2×C4×C13—44no—
217C2×C4×C13—41no—
218C2×C4×C13—41no—
219C2×C4×C13—41no—
220C2×C4×C13—41no—
221C2×C4×C13—41no—
222C2×C4×C13—41no—
223C2×C4×C13—44no—
224C2×C4×C13—41no—
225C2×C4×C13—41no—
226C2×C4×C13—41no—
227C2×C4×C13—41no—
228C2×C4×C13—41no—
229C2×C4×C13—41no—
230C2×C4×C13—84no—
231C2×C4×C13#12112yes—
232C2×C4×C13#12112yes—
233C2×C4×C13AGL(1,ℤ/8)12yes—
234C2×C4×C13AGL(1,ℤ/8)12yes—
235C2×C4×C13C22×D411yescharacteristic
236C2×C4×C13C2×#4111yescharacteristic
237C2×C4×C13C2×#4111yescharacteristic
238C2×C4×C13C2×#4111yescharacteristic
239C2×C4×C132−1+411yescharacteristic
240C2×C4×C132−1+411yescharacteristic
241C2×Dic13—42no—
242C2×Dic13—42no—
243C2×Dic13—42no—
244C2×Dic13—42no—
245C2×Dic13—42no—
246C2×Dic13—42no—
247Dic26—84no—
248#1055—24no—
249#1055—42no—
250C2×C4⋊Q8—131no—
251C2×C22⋊Q8—261no—
252C2×#121C2×D1311yescharacteristic
253C2×C4×D4—21no—
254C2×C4×D4C2×D1311yescharacteristic
255C22×C42C2×D1311yescharacteristic
256#474—264no—
257#432—264no—
258C2×#107—132no—
259C2×#106—132no—
260C2×C4⋊C8—131no—
261C2×C4⋊C8—131no—
262C2×#102—132no—
263C2×#102—132no—
264C2×C22⋊C8—132no—
265C2×#97—132no—
266#391—261no—
267#390C2×D1311yescharacteristic
268#389—132no—
269#389—261no—
270#389C2×D1311yescharacteristic
271#388—21no—
272#386—21no—
273#384—131no—
274#380—132no—
275#380—261no—
276#380C2×D1311yescharacteristic
277C4×C4⋊C4C2×D1311yescharacteristic
278C4×C22⋊C4—21no—
279#340—132no—
280#340—132no—
281#340—132no—
282#340—132no—
283C22×C13—22no—
284C22×C13—22no—
285C22×C13—22no—
286C22×C13—41no—
287C22×C13—41no—
288C22×C13—41no—
289C22×C13—41no—
290C22×C13—42no—
291C22×C13—42no—
292C22×C13—42no—
293C22×C13—81no—
294C22×C13—81no—
295C22×C13—81no—
296C22×C13—81no—
297C22×C13C2×#12111yescharacteristic
298C22×C13#52511yescharacteristic
299C22×C13#53611yescharacteristic
300C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
301C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
302C22×C13C2×#13711yescharacteristic
303C22×C13#57511yescharacteristic
304C4×C13—22no—
305C4×C13—42no—
306C4×C13—41no—
307C4×C13—41no—
308C4×C13—41no—
309C4×C13—81no—
310C4×C13—81no—
311C4×C13#46914yes—
312C4×C13#54711yescharacteristic
313C4×C13#54811yescharacteristic
314C4×C13#55211yescharacteristic
315C4×C13#55611yescharacteristic
316Dic13—82no—
317Dic13—82no—
318C22×Q8—261no—
319C22×D4—21no—
320C22×D4C22×D1311yescharacteristic
321C23×C4—21no—
322C23×C4C22⋊D1311yescharacteristic
323C23×C4C22⋊D1311yescharacteristic
324C23×C4C22×D1311yescharacteristic
325C22×C8—132no—
326C22×C8—132no—
327C4⋊Q8—262no—
328C4⋊Q8—262no—
329C22⋊Q8—524no—
330#121—22no—
331#121—22no—
332C4×D4—22no—
333C4×D4—22no—
334C4×D4—44no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—132no—
337C2×C4⋊C4—132no—
338C2×C4⋊C4—262no—
339C2×C4⋊C4—261no—
340C2×C4⋊C4—261no—
341C2×C4⋊C4—261no—
342C2×C4⋊C4C22×D1311yescharacteristic
343C2×C4⋊C4C22×D1311yescharacteristic
344C2×C4⋊C4C22×D1311yescharacteristic
345C2×C22⋊C4—21no—
346C2×C22⋊C4—21no—
347C2×C22⋊C4—21no—
348C2×C22⋊C4—21no—
349C2×C22⋊C4—21no—
350C2×C22⋊C4—262no—
351C2×C42—22no—
352C2×C42—22no—
353C2×C42—21no—
354C2×C42C22⋊D1311yescharacteristic
355C2×C42C22⋊D1311yescharacteristic
356C2×C42C22×D1311yescharacteristic
357C2×C42C22×D1311yescharacteristic
358#107—264no—
359#106—264no—
360C4⋊C8—134no—
361C4⋊C8—262no—
362#102—264no—
363#102—264no—
364C22⋊C8—264no—
365#97—264no—
366#95—21no—
367#95—21no—
368#95—21no—
369#95—262no—
370#95—262no—
371C2×C13—42no—
372C2×C13—82no—
373C2×C13#241511yescharacteristic
374C2×C13C2×#46911yescharacteristic
375C2×C13#305611yescharacteristic
376C2×C13#311011yescharacteristic
377C2×C13#311511yescharacteristic
378C2×C13#323511yescharacteristic
379C2×C13#323911yescharacteristic
380C24—21no—
381C24C2×C22⋊D1311yescharacteristic
382C2×Q8—522no—
383C2×Q8—522no—
384C2×Q8—522no—
385C2×D4—24no—
386C2×D4—21no—
387C2×D4—21no—
388C2×D4—21no—
389C2×D4—21no—
390C2×D4—21no—
391C2×D4—42no—
392C2×D4—42no—
393C2×D4#612712yes—
394C22×C4—22no—
395C22×C4—21no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—41no—
409C22×C4—42no—
410C22×C4—42no—
411C22×C4—42no—
412C22×C4—262no—
413C22×C4—262no—
414C22×C4C2×C22⋊D1311yescharacteristic
415C22×C4C2×C22⋊D1311yescharacteristic
416C22×C4C2×C22⋊D1311yescharacteristic
417C22×C4C2×C22⋊D1311yescharacteristic
418C22×C4C2×C22⋊D1311yescharacteristic
419C22×C4C23×D1311yescharacteristic
420C2×C8—134no—
421C2×C8—262no—
422C2×C8—262no—
423C2×C8—262no—
424C2×C8—262no—
425C2×C8—262no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4—21no—
430C4⋊C4—21no—
431C4⋊C4—42no—
432C4⋊C4—262no—
433C4⋊C4—262no—
434C4⋊C4—262no—
435C4⋊C4—262no—
436C4⋊C4—524no—
437C4⋊C4—522no—
438C4⋊C4—522no—
439C4⋊C4—522no—
440C4⋊C4#612712yes—
441C22⋊C4—24no—
442C22⋊C4—42no—
443C22⋊C4—42no—
444C22⋊C4—42no—
445C22⋊C4—42no—
446C22⋊C4—524no—
447C42—22no—
448C42—22no—
449C42—21no—
450C42—21no—
451C42—42no—
452C42D4×D1312yes—
453C42#612912yes—
454C13#2470911yescharacteristic, complemented, Sylow
455C23—21no—
456C23—21no—
457C23—21no—
458C23—21no—
459C23—21no—
460C23—21no—
461C23—22no—
462C23—41no—
463C23—41no—
464C23—41no—
465C23—41no—
466C23—41no—
467C23—41no—
468C23#8820512yes—
469C23C22×C22⋊D1311yescharacteristic
470Q8—1044no—
471D4—22no—
472D4—22no—
473D4—48no—
474D4—41no—
475D4—41no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—22no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—44no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—44no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—84no—
503C2×C4—522no—
504C2×C4—522no—
505C2×C4—522no—
506C2×C4—522no—
507C2×C4—522no—
508C2×C4—522no—
509C2×C4#8818612yes—
510C2×C4#8819312yes—
511C2×C4#8819312yes—
512C2×C4#8820312yes—
513C2×C4C2×#612711yescharacteristic
514C2×C4C2×#612711yescharacteristic
515C2×C4C2×D4×D1311yescharacteristic
516C2×C4C2×#612911yescharacteristic
517C2×C4#8825711yescharacteristic
518C2×C4#8825711yescharacteristic
519C8—264no—
520C8—522no—
521C22—22no—
522C22—22no—
523C22—22no—
524C22—41no—
525C22—41no—
526C22—41no—
527C22—41no—
528C22—42no—
529C22—42no—
530C22—42no—
531C22—81no—
532C22—81no—
533C22—81no—
534C22—81no—
535C22#1171949611yescharacteristic
536C22C2×#8818611yescharacteristic
537C22C2×#8819311yescharacteristic
538C22C2×#8820311yescharacteristic
539C22#1171952711yescharacteristic
540C22C2×#8820511yescharacteristic
541C22#1171953011yescharacteristic
542C4—22no—
543C4—41no—
544C4—42no—
545C4—41no—
546C4—41no—
547C4—81no—
548C4—81no—
549C4—1042no—
550C4—1042no—
551C4#1171870014yes—
552C4#1171924611yescharacteristic
553C4#1171924711yescharacteristic
554C4#1171925611yescharacteristic
555C4#1171925711yescharacteristic
556C2—42no—
557C2—82no—
558C2#1311826511yescharacteristic
559C2C2×#1171870011yescharacteristic
560C2#1312446811yescharacteristic
561C2#1312493511yescharacteristic
562C2#1312498711yescharacteristic
563C2#1312603011yescharacteristic
564C2#1312606311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC4×C13×#121C2
socleC23×C13C22×D4
prime radicalC2×C13×#121C22
hypercenterC4×#121D13
hypocenterC13#24709
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×#121

Complements

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

NH ≅ G/Ntype
1. C2×#11718668C2semidirect
2. C2×#11718587C2semidirect
3. #13123188C2semidirect
4. #13116267C2semidirect
6. #13115788C2semidirect
7. #13115599C2semidirect
8. #13115576C2semidirect
9. #13115536C2semidirect
10. #13114836C2semidirect
96. C4⋊#1055D4semidirect
454. C13#24709semidirect

Maximal subgroups

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

subgroupindex
C2×#117186682
C2×#117185872
#131231882
#131162672
#131160222
#131157882
#131155992
#131155762
#131155362
#131148362
C4×C13×#1212
#2470913