Finite Group Databasebeta

← #15917617

Subgroups — #15917617

Order 3328.

1102 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×#11718726C211yesmaximal, characteristic, complemented
2C2×#11718668C211yesmaximal, characteristic, complemented
3#13120009C211yesmaximal, characteristic, complemented
4#13116022C212yesmaximal, complemented
5#13116015C212yesmaximal, complemented
6#13115794C211yesmaximal, characteristic, complemented
7#13115635C211yesmaximal, characteristic, complemented
8#13115035C212yesmaximal, complemented
9#13115024C212yesmaximal, complemented
10#13114661C211yesmaximal, characteristic, complemented
11C2×C13×#553C211yesmaximal, characteristic
12C13×#553—24no—
13C13×#553—24no—
14C2×C13×#126—21no—
15C2×C13×#125C2211yescharacteristic
16C2×C13×#123—21no—
17C2×C13×#121—21no—
18C2×C13×#121C2211yescharacteristic
19C2×C13×#121C2211yescharacteristic
20C2×C4×D4×C13—21no—
21C2×C4×D4×C13C2211yescharacteristic
22C2×C4×D4×C13C2211yescharacteristic
23C2×C13×#117C2211yescharacteristic
24C22×C13×C4⋊C4C2211yescharacteristic
25C2×#88123C2211yescharacteristic
26#11718882—21no—
27C2×#88072C2212yes—
28C2×#88072C2212yes—
29#11718873C2212yes—
30#11718873C2212yes—
31C2×C22⋊#1055C2212yes—
32C2×C22⋊#1055C2212yes—
33#11718726—24no—
34#11718668—24no—
35#11718638—21no—
36C2×#88048C2212yes—
37C2×#88047C2212yes—
38C2×#88047C2212yes—
39#11718608—21no—
40#11718608—21no—
41C4×C4⋊Dic13C2211yescharacteristic
42C2×C4⋊#1055C2211yescharacteristic
43C2×#88043C2211yescharacteristic
44#11718121C2212yes—
45#11718121C2212yes—
46#11718121C2212yes—
47C22×D4×C13—21no—
48C22×D4×C13—21no—
49C22×D4×C13D411yescharacteristic
50C22×D4×C13C2311yescharacteristic
51C23×C4×C13—21no—
52C23×C4×C13—21no—
53C23×C4×C13C2311yescharacteristic
54C23×C4×C13C2311yescharacteristic
55C22×Dic26—21no—
56C13×#126—28no—
57C13×#125—22no—
58C13×#125D414yes—
59C13×#123—28no—
60C13×#121—28no—
61C13×#121—22no—
62C13×#121—22no—
63C13×#121—22no—
64C13×#121—22no—
65C4×D4×C13—28no—
66C4×D4×C13—22no—
67C4×D4×C13—22no—
68C4×D4×C13—22no—
69C4×D4×C13D414yes—
70C13×#117—22no—
71C13×#117—22no—
72C2×C13×C4⋊C4—21no—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4—21no—
75C2×C13×C4⋊C4—22no—
76C2×C13×C4⋊C4—22no—
77C2×C13×C4⋊C4D411yescharacteristic
78C2×C13×C4⋊C4C2311yescharacteristic
79C2×C13×C4⋊C4C2311yescharacteristic
80C2×C13×C4⋊C4C2311yescharacteristic
81C2×C13×C22⋊C4—21no—
82C2×C13×C22⋊C4—21no—
83C2×C13×C22⋊C4—21no—
84C2×C13×C22⋊C4—21no—
85C2×C13×C22⋊C4D411yescharacteristic
86C2×C13×C22⋊C4D411yescharacteristic
87C2×C42×C13—21no—
88C2×C42×C13C2311yescharacteristic
89C2×C22⋊Dic13—22no—
90C2×C22⋊Dic13—22no—
91C2×C4⋊Dic13—21no—
92C2×C4⋊Dic13C2312yes—
93C2×C4⋊Dic13C2312yes—
94C2×C4×Dic13—21no—
95C22×#1055C2312yes—
96C22×#1055C2312yes—
97#88123—22no—
98#88123—22no—
99#88072—24no—
100#88072—24no—
101#88071—21no—
102#88071—22no—
103#88071—22no—
104C22⋊#1055—24no—
105C22⋊#1055—24no—
106#88048—24no—
107#88047—24no—
108#88047—24no—
109C4⋊#1055—22no—
110#88043—22no—
111#25713—131nomaximal, Sylow
112C24×C13—21no—
113C24×C13C2×D411yescharacteristic
114C24×C13C2×D411yescharacteristic
115C2×D4×C13—24no—
116C2×D4×C13—22no—
117C2×D4×C13—24no—
118C2×D4×C13—22no—
119C2×D4×C13—21no—
120C2×D4×C13—22no—
121C2×D4×C13—22no—
122C2×D4×C13—41no—
123C2×D4×C13—42no—
124C2×D4×C13—42no—
125C2×D4×C13—82no—
126C2×D4×C13C2×D412yes—
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13—24no—
131C22×C4×C13—21no—
132C22×C4×C13—21no—
133C22×C4×C13—21no—
134C22×C4×C13—21no—
135C22×C4×C13—22no—
136C22×C4×C13—22no—
137C22×C4×C13—22no—
138C22×C4×C13—22no—
139C22×C4×C13—24no—
140C22×C4×C13—82no—
141C22×C4×C13—82no—
142C22×C4×C13C2×D411yescharacteristic
143C22×C4×C13C2×D411yescharacteristic
144C22×C4×C13C2×D411yescharacteristic
145C22×C4×C13C2×D411yescharacteristic
146C22×C4×C13C2411yescharacteristic
147C22×Dic13—22no—
148C22×Dic13—22no—
149C2×Dic26—42no—
150C2×Dic26—82no—
151C13×C4⋊C4—24no—
152C13×C4⋊C4—24no—
153C13×C4⋊C4—24no—
154C13×C4⋊C4—22no—
155C13×C4⋊C4—21no—
156C13×C4⋊C4—21no—
157C13×C4⋊C4—21no—
158C13×C4⋊C4C2×D412yes—
159C13×C4⋊C4C2×D412yes—
160C13×C4⋊C4C2×D412yes—
161C13×C22⋊C4—24no—
162C13×C22⋊C4—24no—
163C13×C22⋊C4—24no—
164C13×C22⋊C4—24no—
165C13×C22⋊C4—22no—
166C13×C22⋊C4—22no—
167C42×C13—24no—
168C42×C13C2×D412yes—
169C42×C13C2×D412yes—
170C22⋊Dic13—82no—
171C22⋊Dic13—82no—
172C4⋊Dic13—22no—
173C4⋊Dic13—22no—
174C4⋊Dic13—22no—
175C4⋊Dic13—22no—
176C4⋊Dic13—42no—
177C4×Dic13—42no—
178C2×#1055—22no—
179C2×#1055—22no—
180C2×#1055—22no—
181C2×#1055—22no—
182C2×#1055—22no—
183C2×#1055#4114yes—
184C2×#553D1311yescharacteristic
185C2×#501—131no—
186C2×#474—131no—
187#2563—131no—
188#2034—132no—
189#2033—132no—
190#1989—131no—
191#1955—131no—
192#1854—132no—
193#1852—132no—
194#1762—131no—
195C23×C13—21no—
196C23×C13—22no—
197C23×C13—21no—
198C23×C13—22no—
199C23×C13—21no—
200C23×C13—22no—
201C23×C13—22no—
202C23×C13—21no—
203C23×C13—21no—
204C23×C13—22no—
205C23×C13—42no—
206C23×C13—41no—
207C23×C13—41no—
208C23×C13—42no—
209C23×C13#13712yes—
210C23×C13C22×D411yescharacteristic
211D4×C13—22no—
212D4×C13—22no—
213D4×C13—44no—
214D4×C13—48no—
215D4×C13—42no—
216D4×C13—84no—
217C2×C4×C13—21no—
218C2×C4×C13—21no—
219C2×C4×C13—22no—
220C2×C4×C13—21no—
221C2×C4×C13—22no—
222C2×C4×C13—22no—
223C2×C4×C13—21no—
224C2×C4×C13—22no—
225C2×C4×C13—22no—
226C2×C4×C13—22no—
227C2×C4×C13—41no—
228C2×C4×C13—41no—
229C2×C4×C13—42no—
230C2×C4×C13—42no—
231C2×C4×C13—41no—
232C2×C4×C13—41no—
233C2×C4×C13—41no—
234C2×C4×C13—41no—
235C2×C4×C13—42no—
236C2×C4×C13—42no—
237C2×C4×C13—84no—
238C2×C4×C13—84no—
239C2×C4×C13#12012yes—
240C2×C4×C13#12012yes—
241C2×C4×C13C22×D411yescharacteristic
242C2×C4×C13C22×D411yescharacteristic
243C2×C4×C13C2×#4112yes—
244C2×C4×C132−1+412yes—
245C2×Dic13—42no—
246C2×Dic13—42no—
247C2×Dic13—42no—
248C2×Dic13—42no—
249C2×Dic13—42no—
250C2×Dic13—42no—
251Dic26—84no—
252#1055—24no—
253#1055—42no—
254#553—24no—
255#553—24no—
256C2×C4⋊Q8—131no—
257C2×#126—21no—
258C2×#125C2×D1311yescharacteristic
259C2×#123—21no—
260C2×#121—21no—
261C2×#121C2×D1311yescharacteristic
262C2×#121C2×D1311yescharacteristic
263C2×C4×D4—21no—
264C2×C4×D4C2×D1311yescharacteristic
265C2×C4×D4C2×D1311yescharacteristic
266C2×#117C2×D1311yescharacteristic
267C22×C4⋊C4C2×D1311yescharacteristic
268#501—264no—
269#474—264no—
270C2×#107—132no—
271C2×#107—132no—
272C2×#106—132no—
273C2×C4⋊C8—131no—
274C2×#102—132no—
275C2×#102—132no—
276C2×C22⋊C8—132no—
277C2×C22⋊C8—132no—
278C2×#97—131no—
279#393—261no—
280#393—261no—
281#390—261no—
282#382—261no—
283#380—132no—
284#380—132no—
285C4×C4⋊C4—131no—
286#340—132no—
287#340—132no—
288#340—132no—
289C22×C13—24no—
290C22×C13—22no—
291C22×C13—42no—
292C22×C13—41no—
293C22×C13—41no—
294C22×C13—42no—
295C22×C13—42no—
296C22×C13—41no—
297C22×C13—42no—
298C22×C13—41no—
299C22×C13—42no—
300C22×C13—42no—
301C22×C13—41no—
302C22×C13—82no—
303C22×C13—82no—
304C22×C13C2×#12011yescharacteristic
305C22×C13#54712yes—
306C22×C13C2×#13711yescharacteristic
307C22×C13#57511yescharacteristic
308C22×C13#57612yes—
309C4×C13—22no—
310C4×C13—22no—
311C4×C13—41no—
312C4×C13—41no—
313C4×C13—42no—
314C4×C13—42no—
315C4×C13—42no—
316C4×C13#53211yescharacteristic
317C4×C13#53611yescharacteristic
318C4×C13#54812yes—
319Dic13—82no—
320Dic13—82no—
321C22×Q8—261no—
322C22×D4—21no—
323C22×D4—21no—
324C22×D4C22⋊D1311yescharacteristic
325C22×D4C22×D1311yescharacteristic
326C23×C4—21no—
327C23×C4—21no—
328C23×C4C22×D1311yescharacteristic
329C23×C4C22×D1311yescharacteristic
330C22×C8—132no—
331C22×C8—132no—
332C4⋊Q8—262no—
333C4⋊Q8—262no—
334#126—28no—
335#125—22no—
336#125C22⋊D1314yes—
337#123—28no—
338#121—28no—
339#121—22no—
340#121—22no—
341#121—22no—
342#121—22no—
343C4×D4—28no—
344C4×D4—22no—
345C4×D4—22no—
346C4×D4—22no—
347C4×D4C22⋊D1314yes—
348#117—22no—
349#117—22no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—132no—
356C2×C4⋊C4—132no—
357C2×C4⋊C4—261no—
358C2×C4⋊C4C22⋊D1311yescharacteristic
359C2×C4⋊C4C22×D1311yescharacteristic
360C2×C4⋊C4C22×D1311yescharacteristic
361C2×C4⋊C4C22×D1311yescharacteristic
362C2×C22⋊C4—21no—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—262no—
367C2×C22⋊C4—262no—
368C2×C22⋊C4C22⋊D1311yescharacteristic
369C2×C22⋊C4C22⋊D1311yescharacteristic
370C2×C42—21no—
371C2×C42—261no—
372C2×C42C22×D1311yescharacteristic
373#107—264no—
374#107—264no—
375#106—264no—
376C4⋊C8—262no—
377#102—264no—
378#102—264no—
379C22⋊C8—264no—
380C22⋊C8—264no—
381#97—262no—
382#95—261no—
383#95—262no—
384#95—262no—
385C2×C13—42no—
386C2×C13—81no—
387C2×C13—82no—
388C2×C13#243211yescharacteristic
389C2×C13#300711yescharacteristic
390C2×C13#300811yescharacteristic
391C2×C13#334612yes—
392C2×C13#334712yes—
393C24—21no—
394C24C2×C22⋊D1311yescharacteristic
395C24C2×C22⋊D1311yescharacteristic
396C2×Q8—522no—
397C2×Q8—1042no—
398C2×D4—24no—
399C2×D4—22no—
400C2×D4—24no—
401C2×D4—22no—
402C2×D4—22no—
403C2×D4—22no—
404C2×D4—21no—
405C2×D4—41no—
406C2×D4—42no—
407C2×D4—42no—
408C2×D4—82no—
409C2×D4C2×C22⋊D1312yes—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—24no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—24no—
423C22×C4—82no—
424C22×C4—82no—
425C22×C4—262no—
426C22×C4—262no—
427C22×C4C2×C22⋊D1311yescharacteristic
428C22×C4C2×C22⋊D1311yescharacteristic
429C22×C4C2×C22⋊D1311yescharacteristic
430C22×C4C2×C22⋊D1311yescharacteristic
431C22×C4C23×D1311yescharacteristic
432C2×C8—134no—
433C2×C8—262no—
434C2×C8—262no—
435C2×C8—262no—
436C2×C8—262no—
437C2×C8—262no—
438C4⋊C4—24no—
439C4⋊C4—24no—
440C4⋊C4—24no—
441C4⋊C4—22no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—262no—
446C4⋊C4—262no—
447C4⋊C4—262no—
448C4⋊C4—262no—
449C4⋊C4—522no—
450C4⋊C4C2×C22⋊D1312yes—
451C4⋊C4C2×C22⋊D1312yes—
452C4⋊C4C2×C22⋊D1312yes—
453C22⋊C4—24no—
454C22⋊C4—24no—
455C22⋊C4—24no—
456C22⋊C4—24no—
457C22⋊C4—22no—
458C22⋊C4—22no—
459C22⋊C4—1042no—
460C22⋊C4—1042no—
461C42—24no—
462C42—522no—
463C42C2×C22⋊D1312yes—
464C42C2×C22⋊D1312yes—
465C13#2571311yescharacteristic, complemented, Sylow
466C23—21no—
467C23—22no—
468C23—22no—
469C23—21no—
470C23—21no—
471C23—21no—
472C23—22no—
473C23—22no—
474C23—21no—
475C23—22no—
476C23—41no—
477C23—41no—
478C23—42no—
479C23—42no—
480C23#8820512yes—
481C23C22×C22⋊D1311yescharacteristic
482Q8—1044no—
483D4—22no—
484D4—22no—
485D4—44no—
486D4—48no—
487D4—42no—
488D4—84no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—21no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—21no—
498C2×C4—22no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—84no—
510C2×C4—84no—
511C2×C4—522no—
512C2×C4—522no—
513C2×C4—522no—
514C2×C4—522no—
515C2×C4—522no—
516C2×C4—522no—
517C2×C4#8820712yes—
518C2×C4#8820712yes—
519C2×C4#41×D1312yes—
520C2×C4#8825712yes—
521C2×C4C22×C22⋊D1311yescharacteristic
522C2×C4C22×C22⋊D1311yescharacteristic
523C8—264no—
524C8—522no—
525C22—22no—
526C22—24no—
527C22—41no—
528C22—42no—
529C22—41no—
530C22—41no—
531C22—42no—
532C22—42no—
533C22—41no—
534C22—42no—
535C22—42no—
536C22—41no—
537C22—42no—
538C22—82no—
539C22—82no—
540C22#1171952711yescharacteristic
541C22C2×#8820511yescharacteristic
542C22#1171952912yes—
543C22#1171954012yes—
544C22C2×#8820711yescharacteristic
545C4—22no—
546C4—22no—
547C4—42no—
548C4—42no—
549C4—42no—
550C4—41no—
551C4—41no—
552C4—1042no—
553C4—1042no—
554C4#1171953011yescharacteristic
555C4#1171953612yes—
556C4#1171953711yescharacteristic
557C2—42no—
558C2—81no—
559C2—82no—
560C2#1311846011yescharacteristic
561C2#1312409611yescharacteristic
562C2#1312410411yescharacteristic
563C2#1312732112yes—
564C2#1312733012yes—
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
Fitting, prime radicalC2×C13×#553C2
socleC23×C13C22×D4
hypercenterC2×#553D13
hypocenterC13#25713
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. C2×#11718726C2semidirect
2. C2×#11718668C2semidirect
3. #13120009C2semidirect
4. #13116022C2semidirect
5. #13116015C2semidirect
6. #13115794C2semidirect
7. #13115635C2semidirect
8. #13115035C2semidirect
9. #13115024C2semidirect
10. #13114661C2semidirect
465. C13#25713semidirect

Maximal subgroups

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

subgroupindex
C2×#117187262
C2×#117186682
#131200092
#131160222
#131160152
#131157942
#131156352
#131150352
#131150242
#131146612
C2×C13×#5532
#2571313