Finite Group Databasebeta

← #15878371

Subgroups — #15878371

Order 3328.

1490 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719256C211yesmaximal, characteristic
2C2×D4×#1055C211yesmaximal, characteristic, complemented
3C2×#11718663C212yesmaximal, complemented
4#13115759C211yesmaximal, characteristic, complemented
5#13115637C211yesmaximal, characteristic, complemented
6#13115257C212yesmaximal, complemented
7#13115148C212yesmaximal, complemented
8#13114833C211yesmaximal, characteristic, complemented
9#13114774C212yesmaximal, complemented
10C4×#88049C211yesmaximal, characteristic, complemented
11C13×#2354C211yesmaximal, characteristic, complemented
12C22×#6127C2212yes—
13C2×C4×D4×C13C2211yescharacteristic
14C2×C13×#117C2212yes—
15C2×#88192—21no—
16C2×#88178C2212yes—
17C23×#1055C2212yes—
18#11719256—24no—
19#11719256C418yescomplemented
20C2×C4⋊C4×D13—21no—
21C2×#88137—22no—
22C2×C4×D52C2211yescharacteristic
23C2×#88123C2211yescharacteristic
24C13×#390—21no—
25C13×#388—22no—
26C13×#384C2211yescharacteristic
27C13×#380C2212yes—
28C4×C13×C4⋊C4—21no—
29C4×C13×C4⋊C4C2211yescharacteristic
30C2×C22⋊#1055C2212yes—
31D4×#1055—24no—
32#11718663—28no—
33C2×#88050C2212yes—
34C2×#88050C2212yes—
35C2×#88050C2212yes—
36C2×#88050C2212yes—
37C2×#88049C2212yes—
38C2×#88049C2211yescharacteristic
39C2×#88049C2211yescharacteristic
40C2×C4⋊#1055C2211yescharacteristic
41C2×C4×#1055C2211yescharacteristic
42#11718121C2211yescharacteristic
43#11718121C2212yes—
44#11718121C2211yescharacteristic
45C22×D4×C13D411yescharacteristic
46C23×C4×C13C2312yes—
47C22×C22⋊D13—22no—
48C2×#6127—24no—
49C2×#6127—24no—
50C2×#6127—24no—
51C2×#6127—42no—
52C2×#6127—42no—
53C2×#6127C2×C418yes—
54C22×D52C2311yescharacteristic
55C22×C4×D13—21no—
56C22×C4×D13—22no—
57C22×Dic26C2312yes—
58C4×D4×C13C2×C414yes—
59C4×D4×C13D414yes—
60C13×#117—24no—
61C13×#117—42no—
62C2×C13×C4⋊C4—21no—
63C2×C13×C4⋊C4—21no—
64C2×C13×C4⋊C4D411yescharacteristic
65C2×C13×C4⋊C4C2311yescharacteristic
66C2×C13×C4⋊C4C2312yes—
67C2×C13×C4⋊C4C2311yescharacteristic
68C2×C13×C22⋊C4—22no—
69C2×C13×C22⋊C4—22no—
70C2×C13×C22⋊C4D412yes—
71C2×C42×C13—21no—
72C2×C42×C13—22no—
73C2×C42×C13C2311yescharacteristic
74C2×C22⋊Dic13—22no—
75#88192—28no—
76C2×#6103—21no—
77C2×C4⋊Dic13—21no—
78C2×C4⋊Dic13—21no—
79C2×C4⋊Dic13C2311yescharacteristic
80#88178—24no—
81#88178C2×C418yes—
82C2×#6101—22no—
83C22×#1055—24no—
84C22×#1055—24no—
85C22×#1055—42no—
86C22×#1055C2312yes—
87C22×#1055C2311yescharacteristic
88C22×#1055C2311yescharacteristic
89C4⋊C4×D13—28no—
90#88137—216no—
91C4×D52—22no—
92C4×D52C2×C414yes—
93#88123—22no—
94#88123C2×C414yes—
95C13×#95—22no—
96C13×#95—21no—
97C22⋊#1055—24no—
98#88050—24no—
99#88050—24no—
100#88050—42no—
101#88050—42no—
102#88049—24no—
103#88049—22no—
104#88049D414yescomplemented
105C4⋊#1055—22no—
106C4×#1055—22no—
107#22417—131nomaximal, Sylow
108C24×C13C2×D412yes—
109C23×D13—21no—
110C2×D4×C13—22no—
111C2×D4×C13—22no—
112C2×D4×C13C22⋊C414yes—
113C22×C4×C13—22no—
114C22×C4×C13—22no—
115C22×C4×C13—22no—
116C22×C4×C13—22no—
117C22×C4×C13—21no—
118C22×C4×C13—21no—
119C22×C4×C13—22no—
120C22×C4×C13C22×C414yes—
121C22×C4×C13C2×D414yes—
122C22×C4×C13C2×D412yes—
123C22×C4×C13C2×D411yescharacteristic
124C22×C4×C13C2×D411yescharacteristic
125C22×C4×C13C2411yescharacteristic
126C2×C22⋊D13—28no—
127C2×C22⋊D13—44no—
128C2×C22⋊D13—44no—
129C22×Dic13—21no—
130C22×Dic13—22no—
131#6127—216no—
132#6127—48no—
133#6127—48no—
134#6127—48no—
135C2×D52—21no—
136C2×D52—21no—
137C2×D52—21no—
138C2×D52C22×C412yes—
139C2×D52C2×D412yes—
140C2×D52#4112yes—
141C2×C4×D13—24no—
142C2×C4×D13—28no—
143C2×C4×D13—44no—
144C2×C4×D13—44no—
145C2×C4×D13—42no—
146C2×C4×D13—42no—
147C2×Dic26—22no—
148C2×Dic26—22no—
149C2×Dic26—22no—
150C2×Dic26—22no—
151C2×Dic26—22no—
152C2×Dic26C22×C414yes—
153C13×C4⋊C4—21no—
154C13×C4⋊C4—22no—
155C13×C4⋊C4—21no—
156C13×C4⋊C4—22no—
157C13×C4⋊C4—21no—
158C13×C4⋊C4—42no—
159C13×C4⋊C4—81no—
160C13×C4⋊C4C22⋊C414yes—
161C13×C4⋊C4C2×D412yes—
162C13×C22⋊C4—44no—
163C13×C22⋊C4—82no—
164C13×C22⋊C4C22⋊C418yes—
165C42×C13—44no—
166C42×C13—42no—
167C42×C13C22×C412yes—
168C42×C13C2×D412yes—
169C22⋊Dic13—28no—
170#6103—24no—
171C4⋊Dic13—24no—
172C4⋊Dic13—24no—
173C4⋊Dic13—21no—
174C4⋊Dic13C22×C412yes—
175#6101—28no—
176C2×#1055—21no—
177C2×#1055—21no—
178C2×#1055—21no—
179C2×#1055—22no—
180C2×#1055—22no—
181C2×#1055—21no—
182C2×#1055—22no—
183C2×#1055—21no—
184C2×#1055—48no—
185C2×#1055C2×D412yes—
186C2×#547—131no—
187C2×C8×D4—131no—
188C2×#416—132no—
189#2354D1311yescharacteristic, complemented
190#1981—131no—
191#1956—131no—
192#1892—132no—
193#1873—132no—
194#1802—131no—
195#1788—132no—
196C4×#102—131no—
197C23×C13—22no—
198C23×C13—22no—
199C23×C13—22no—
200C23×C13—22no—
201C23×C13—22no—
202C23×C13—22no—
203C23×C13C2×C22⋊C414yes—
204C23×C13C22×D411yescharacteristic
205C22×D13—22no—
206C22×D13—22no—
207C22×D13—22no—
208C22×D13—41no—
209C22×D13—41no—
210C22×D13—41no—
211C22×D13—41no—
212D4×C13—28no—
213C2×C4×C13—22no—
214C2×C4×C13—22no—
215C2×C4×C13—21no—
216C2×C4×C13—21no—
217C2×C4×C13—24no—
218C2×C4×C13—24no—
219C2×C4×C13—24no—
220C2×C4×C13—24no—
221C2×C4×C13—22no—
222C2×C4×C13—41no—
223C2×C4×C13—41no—
224C2×C4×C13—42no—
225C2×C4×C13—41no—
226C2×C4×C13—41no—
227C2×C4×C13—42no—
228C2×C4×C13—41no—
229C2×C4×C13—42no—
230C2×C4×C13C2×C22⋊C414yes—
231C2×C4×C13C2×C22⋊C412yes—
232C2×C4×C13C2×C22⋊C412yes—
233C2×C4×C13#13512yes—
234C2×C4×C13#13512yes—
235C2×C4×C13C23×C411yescharacteristic
236C2×C4×C13C22×D411yescharacteristic
237C2×C4×C13C22×D411yescharacteristic
238C2×C4×C13C2×#4111yescharacteristic
239C2×C4×C13H(5,𝔽2)11yescharacteristic
240C2×C4×C13H(5,𝔽2)11yescharacteristic
241C22⋊D13—416no—
242C2×Dic13—22no—
243C2×Dic13—24no—
244C2×Dic13—42no—
245C2×Dic13—42no—
246C2×Dic13—41no—
247C2×Dic13—41no—
248D52—22no—
249D52—22no—
250D52—22no—
251D52C4×D414yes—
252C4×D13—416no—
253C4×D13—48no—
254Dic26—24no—
255Dic26—24no—
256Dic26—42no—
257Dic26—42no—
258#1055—22no—
259#1055—42no—
260#1055—41no—
261C22×#41—132no—
262C23×C8—132no—
263#547—138no—
264#547—264no—
265C2×C4⋊Q8—131no—
266C2×#123—262no—
267C2×C22⋊Q8—132no—
268C2×#121—261no—
269C2×C4×D4—131no—
270C2×C4×D4C2×D1311yescharacteristic
271C2×#117C2×D1312yes—
272C22×C4⋊C4—261no—
273C8×D4—264no—
274C2×C4⋊C8—131no—
275#416—268no—
276C2×#103—132no—
277C2×#103—132no—
278C2×#103—132no—
279C2×#103—132no—
280C2×#102—131no—
281C2×#102—132no—
282C2×#102—131no—
283C2×C22⋊C8—132no—
284C2×C4×C8—131no—
285#390—21no—
286#388—22no—
287#384C2×D1311yescharacteristic
288#380C2×D1312yes—
289C4×C4⋊C4—21no—
290C4×C4⋊C4C2×D1311yescharacteristic
291#340—132no—
292#340—131no—
293#340—131no—
294C22×C13—24no—
295C22×C13—24no—
296C22×C13—24no—
297C22×C13—42no—
298C22×C13—42no—
299C22×C13—42no—
300C22×C13—42no—
301C22×C13C22×C22⋊C411yescharacteristic
302C22×C13D4211yescharacteristic
303C22×C13#54611yescharacteristic
304C22×C13C2×#13511yescharacteristic
305C22×C13C2×#13511yescharacteristic
306C22×C13#57711yescharacteristic
307C22×C13#57811yescharacteristic
308C2×D13—24no—
309C2×D13—42no—
310C2×D13—42no—
311C2×D13—42no—
312C2×D13—42no—
313C2×D13—42no—
314C2×D13—42no—
315C4×C13—24no—
316C4×C13—22no—
317C4×C13—42no—
318C4×C13—82no—
319C4×C13—81no—
320C4×C13#41614yescomplemented
321C4×C13C2×C4×D411yescharacteristic
322C4×C13#51811yescharacteristic
323C4×C13D4211yescharacteristic
324C4×C13#54611yescharacteristic
325Dic13—44no—
326Dic13—42no—
327C2×#41—138no—
328C2×#41—264no—
329C2×#41—264no—
330C2×#41—264no—
331C2×#41—522no—
332C2×#41—522no—
333C22×Q8—132no—
334C22×D4—131no—
335C22×D4—262no—
336C22×D4C22⋊D1311yescharacteristic
337C23×C4—261no—
338C23×C4—262no—
339C23×C4C22×D1312yes—
340C22×C8—131no—
341C22×C8—132no—
342C22×C8—131no—
343C22×C8—264no—
344C22×C8—264no—
345C22×C8—522no—
346C4⋊Q8—134no—
347C4⋊Q8—262no—
348#123—2616no—
349C22⋊Q8—138no—
350C22⋊Q8—264no—
351#121—268no—
352C4×D4—134no—
353C4×D4—262no—
354C4×D4C4×D1314yes—
355C4×D4D5214yes—
356#117—24no—
357#117—42no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—131no—
361C2×C4⋊C4—261no—
362C2×C4⋊C4—262no—
363C2×C4⋊C4—261no—
364C2×C4⋊C4—268no—
365C2×C4⋊C4C22⋊D1311yescharacteristic
366C2×C4⋊C4C22×D1312yes—
367C2×C4⋊C4C22×D1311yescharacteristic
368C2×C4⋊C4C22×D1311yescharacteristic
369C2×C22⋊C4—22no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—262no—
372C2×C22⋊C4—261no—
373C2×C22⋊C4C22⋊D1312yes—
374C2×C42—22no—
375C2×C42—21no—
376C2×C42C22×D1311yescharacteristic
377C4⋊C8—262no—
378#103—264no—
379#103—264no—
380#103—522no—
381#103—522no—
382#102—134no—
383#102—264no—
384#102—262no—
385C22⋊C8—264no—
386C4×C8—262no—
387#95—22no—
388#95—21no—
389C2×C13—44no—
390C2×C13D4×C22⋊C411yescharacteristic
391C2×C13C2×#41611yescharacteristic
392C2×C13#289811yescharacteristic
393C2×C13#328311yescharacteristic
394C2×C13#328411yescharacteristic
395C2×C13#330211yescharacteristic
396C2×C13#330311yescharacteristic
397D13—44no—
398C24—261no—
399C24C2×C22⋊D1312yes—
400#41—2616no—
401#41—528no—
402#41—528no—
403#41—528no—
404C2×Q8—134no—
405C2×Q8—262no—
406C2×Q8—262no—
407C2×Q8—262no—
408C2×Q8—262no—
409C2×Q8—262no—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4—132no—
413C2×D4—132no—
414C2×D4—132no—
415C2×D4—268no—
416C2×D4—261no—
417C2×D4—261no—
418C2×D4—261no—
419C2×D4—524no—
420C2×D4—524no—
421C2×D4#610314yes—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—22no—
429C22×C4—261no—
430C22×C4—262no—
431C22×C4—264no—
432C22×C4—268no—
433C22×C4—524no—
434C22×C4—524no—
435C22×C4—522no—
436C22×C4—522no—
437C22×C4C2×C4×D1314yes—
438C22×C4C2×D5214yes—
439C22×C4C2×C22⋊D1312yes—
440C22×C4C2×C22⋊D1311yescharacteristic
441C22×C4C2×C22⋊D1311yescharacteristic
442C22×C4C23×D1311yescharacteristic
443C2×C8—132no—
444C2×C8—261no—
445C2×C8—261no—
446C2×C8—261no—
447C2×C8—262no—
448C2×C8—262no—
449C2×C8—261no—
450C2×C8—261no—
451C2×C8—262no—
452C2×C8—528no—
453C4⋊C4—21no—
454C4⋊C4—22no—
455C4⋊C4—22no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—42no—
459C4⋊C4—81no—
460C4⋊C4—132no—
461C4⋊C4—264no—
462C4⋊C4—268no—
463C4⋊C4—264no—
464C4⋊C4—261no—
465C4⋊C4#610314yes—
466C4⋊C4D4×D1312yes—
467C22⋊C4—44no—
468C22⋊C4—82no—
469C22⋊C4—268no—
470C22⋊C4—264no—
471C22⋊C4#610318yes—
472C42—44no—
473C42—42no—
474C42C2×C4×D1312yes—
475C42C2×D5212yes—
476C13#2241711yescharacteristic, complemented, Sylow
477C23—22no—
478C23—22no—
479C23—22no—
480C23—22no—
481C23—22no—
482C23—22no—
483C23—262no—
484C23—262no—
485C23—262no—
486C23—521no—
487C23—521no—
488C23—521no—
489C23—521no—
490C23C2×#610314yes—
491C23C22×C22⋊D1311yescharacteristic
492Q8—264no—
493Q8—264no—
494Q8—522no—
495Q8—522no—
496D4—28no—
497D4—134no—
498D4—262no—
499D4—262no—
500D4—262no—
501D4—5216no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—24no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—24no—
510C2×C4—22no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—42no—
514C2×C4—41no—
515C2×C4—42no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—42no—
519C2×C4—262no—
520C2×C4—264no—
521C2×C4—5216no—
522C2×C4—522no—
523C2×C4—521no—
524C2×C4—521no—
525C2×C4—522no—
526C2×C4—528no—
527C2×C4C2×#610312yes—
528C2×C4C2×#610314yes—
529C2×C4C2×#610312yes—
530C2×C4#8820412yes—
531C2×C4#8820412yes—
532C2×C4C22×C4×D1311yescharacteristic
533C2×C4C22×D5211yescharacteristic
534C2×C4C2×D4×D1311yescharacteristic
535C2×C4#8825111yescharacteristic
536C2×C4#41×D1311yescharacteristic
537C2×C4#8825611yescharacteristic
538C8—262no—
539C8—522no—
540C8—521no—
541C22—24no—
542C22—24no—
543C22—24no—
544C22—42no—
545C22—42no—
546C22—42no—
547C22—42no—
548C22—264no—
549C22—522no—
550C22—522no—
551C22—522no—
552C22—522no—
553C22—522no—
554C22—522no—
555C22C22×#610311yescharacteristic
556C22D4×C22⋊D1311yescharacteristic
557C22C2×#8820411yescharacteristic
558C22C2×#8820411yescharacteristic
559C22#1171953411yescharacteristic
560C22#1171954111yescharacteristic
561C22#1171954311yescharacteristic
562C4—22no—
563C4—24no—
564C4—42no—
565C4—81no—
566C4—82no—
567C4—522no—
568C4—524no—
569C4#1171866314yescomplemented
570C4C4×D4×D1311yescharacteristic
571C4#1171925011yescharacteristic
572C4D4×D5211yescharacteristic
573C4#1171925911yescharacteristic
574C2—44no—
575C2—524no—
576C2D4×#610311yescharacteristic
577C2C2×#1171866311yescharacteristic
578C2#1312336611yescharacteristic
579C2#1312655411yescharacteristic
580C2#1312656611yescharacteristic
581C2#1312674711yescharacteristic
582C2#1312675811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#2354C2
socleC23×C13C22×D4
prime radicalC2×#11719256C2
cosocleC22×C4×C13C24
hypercenter#2354D13
hypocenterC13#22417
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2354

Complements

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

NH ≅ G/Ntype
2. C2×D4×#1055C2semidirect
3. C2×#11718663C2semidirect
4. #13115759C2semidirect
5. #13115637C2semidirect
6. #13115257C2semidirect
7. #13115148C2semidirect
8. #13114833C2semidirect
9. #13114774C2semidirect
10. C4×#88049C2semidirect
11. C13×#2354C2semidirect
19. #11719256C4semidirect
104. #88049D4semidirect
189. #2354D13semidirect
320. C4×C13#416semidirect
476. C13#22417semidirect
569. C4#11718663semidirect

Maximal subgroups

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

subgroupindex
C2×#117192562
C2×D4×#10552
C2×#117186632
#131157592
#131156372
#131152572
#131151482
#131148332
#131147742
C4×#880492
C13×#23542
#2241713