Finite Group Databasebeta

← #15865989

Subgroups — #15865989

Order 3328.

890 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718687C211yesmaximal, characteristic
2#13117198C211yesmaximal, characteristic
3#13115474C211yesmaximal, characteristic, complemented
4#13115467C211yesmaximal, characteristic, complemented
5#13115425C211yesmaximal, characteristic, complemented
6#13115404C211yesmaximal, characteristic, complemented
7#13115173C211yesmaximal, characteristic
8#13115173C211yesmaximal, characteristic
9#13115096C211yesmaximal, characteristic
10#13115082C211yesmaximal, characteristic
11#13114734C211yesmaximal, characteristic, complemented
12C4×#88075C211yesmaximal, characteristic, complemented
13C4×#88049C211yesmaximal, characteristic
14#13114588C211yesmaximal, characteristic, complemented
15C13×#2320C211yesmaximal, characteristic, complemented
16C2×C4×Q8×C13C2211yescharacteristic
17C22×#6106C2211yescharacteristic
18C2×C4×D52C2211yescharacteristic
19C2×C4×D52C2211yescharacteristic
20C2×C4×D52C2211yescharacteristic
21C13×#391C2211yescharacteristic
22C13×#391C2211yescharacteristic
23C13×#389C2211yescharacteristic
24C13×#389C2211yescharacteristic
25C13×#387—21no—
26C13×#387—21no—
27C13×#383—21no—
28C13×#382—21no—
29C4×C13×C4⋊C4C2211yescharacteristic
30C13×#376C2211yescharacteristic
31C2×#88075C2211yescharacteristic
32C2×#88075C2211yescharacteristic
33C2×#88075C2211yescharacteristic
34#11718687C418yescomplemented
35C2×#88049C2211yescharacteristic
36C2×#88049C2211yescharacteristic
37C2×#88049C2211yescharacteristic
38C2×#88048C2211yescharacteristic
39C2×#88047C2211yescharacteristic
40C2×#88047C2211yescharacteristic
41C4×C4⋊Dic13C2211yescharacteristic
42C4×C4⋊Dic13C2211yescharacteristic
43C4×C4⋊Dic13C2211yescharacteristic
44C2×#88043C2211yescharacteristic
45C2×C4×#1055C2211yescharacteristic
46#11718327—21no—
47#11718327—21no—
48#11718327—21no—
49D13×#95—21no—
50#11718121C2211yescharacteristic
51#11718121C2211yescharacteristic
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718116C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59#11718116C2211yescharacteristic
60C22×Q8×C13C2311yescharacteristic
61C22×D52C2311yescharacteristic
62C22×C4×D13—21no—
63C22×C4×D13—21no—
64C22×C4×D13—21no—
65C4×Q8×C13—22no—
66C4×Q8×C13C2×C414yescomplemented
67C2×C13×C4⋊C4—21no—
68C2×C13×C4⋊C4—21no—
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4C2311yescharacteristic
71C2×C13×C4⋊C4C2311yescharacteristic
72C2×C13×C4⋊C4C2311yescharacteristic
73C2×C42×C13—21no—
74C2×C42×C13—21no—
75C2×C42×C13C2311yescharacteristic
76C2×C42×C13C2311yescharacteristic
77C2×C42×C13C2311yescharacteristic
78C2×#6106—22no—
79C2×#6106—22no—
80C2×#6106C2×C414yes—
81C2×#6103—21no—
82C2×#6103—21no—
83C2×#6103—21no—
84C2×C4⋊Dic13C2311yescharacteristic
85C2×C4⋊Dic13C2311yescharacteristic
86C2×C4⋊Dic13C2311yescharacteristic
87C2×C4×Dic13—21no—
88C2×C4×Dic13—21no—
89C2×C4×Dic13—21no—
90C22×#1055C2311yescharacteristic
91C22×#1055C2311yescharacteristic
92C22×#1055C2311yescharacteristic
93C22×#1055C2311yescharacteristic
94C4×D52—22no—
95C4×D52—22no—
96C4×D52—22no—
97C4×D52—22no—
98C4×D52—22no—
99C4×D52C2×C414yes—
100C13×#95—21no—
101C13×#95—21no—
102C13×#95—21no—
103C13×#95—21no—
104C13×#95—21no—
105C13×#95—21no—
106C13×#95—21no—
107C13×#95D411yescharacteristic
108C13×#95D411yescharacteristic
109C13×#95D411yescharacteristic
110C13×#95D411yescharacteristic
111#88075—22no—
112#88075—22no—
113#88075C2×C414yescomplemented
114#88071—21no—
115#88071—21no—
116#88071—21no—
117#88049—22no—
118#88049—22no—
119#88049C2×C414yes—
120#88048—22no—
121#88047—22no—
122#88047C2×C414yescomplemented
123#88043C2×C414yescomplemented
124C4×#1055—22no—
125#21125—131nomaximal, Sylow
126C23×D13—21no—
127C2×Q8×C13—21no—
128C2×Q8×C13—21no—
129C2×Q8×C13—21no—
130C2×Q8×C13—21no—
131C2×Q8×C13—21no—
132C2×Q8×C13C22×C412yes—
133C22×C4×C13—21no—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13C2×D411yescharacteristic
138C22×C4×C13C2×D411yescharacteristic
139C22×C4×C13C2×D411yescharacteristic
140C22×C4×C13C2×D411yescharacteristic
141C22×C4×C13C2×D411yescharacteristic
142C22×C4×C13C2×D411yescharacteristic
143C22×C4×C13C2411yescharacteristic
144C22×Dic13—21no—
145C22×Dic13—21no—
146C22×Dic13—21no—
147C2×D52—21no—
148C2×D52—21no—
149C2×D52—21no—
150C2×D52C22×C412yes—
151C2×D52#4112yes—
152C2×D52#4112yes—
153C2×C4×D13—24no—
154C2×C4×D13—24no—
155C2×C4×D13—24no—
156C2×C4×D13—81no—
157C2×C4×D13—81no—
158C2×C4×D13—81no—
159C2×C4×D13—81no—
160C2×C4×D13—81no—
161C2×C4×D13—81no—
162C13×C4⋊C4—24no—
163C13×C4⋊C4—21no—
164C13×C4⋊C4—21no—
165C13×C4⋊C4—21no—
166C13×C4⋊C4—21no—
167C13×C4⋊C4—21no—
168C13×C4⋊C4—81no—
169C13×C4⋊C4—81no—
170C13×C4⋊C4C22×C412yes—
171C42×C13—24no—
172C42×C13—21no—
173C42×C13—21no—
174C42×C13—21no—
175C42×C13—21no—
176C42×C13—81no—
177C42×C13C22×C412yes—
178C42×C13#4112yes—
179#6106—28no—
180#6103—24no—
181#6103—24no—
182#6103—24no—
183C4⋊Dic13—21no—
184C4⋊Dic13—21no—
185C4⋊Dic13—21no—
186C4⋊Dic13C22×C412yes—
187C4⋊Dic13#4112yes—
188C4⋊Dic13#4112yes—
189C4×Dic13—81no—
190C4×Dic13—81no—
191C4×Dic13—81no—
192C2×#1055—21no—
193C2×#1055—21no—
194C2×#1055—21no—
195C2×#1055—21no—
196C2×#1055—21no—
197C2×#1055—21no—
198C2×#1055—21no—
199C2×#1055—21no—
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055C22×C412yes—
203C2×#1055C22×C412yes—
204C2×#440—131no—
205#2320D1311yescharacteristic, complemented
206#2275—131no—
207#1928—131no—
208#1927—131no—
209#1921—131no—
210#1918—131no—
211#1877—131no—
212#1877—131no—
213#1864—131no—
214#1862—131no—
215#1776—131no—
216C4×#103—131no—
217C4×#102—131no—
218#1746—131no—
219C23×C13C22×D411yescharacteristic
220C22×D13—22no—
221C22×D13—22no—
222C22×D13—22no—
223C22×D13—41no—
224C22×D13—41no—
225C22×D13—41no—
226C22×D13—41no—
227Q8×C13—22no—
228Q8×C13—22no—
229Q8×C13—41no—
230Q8×C13—41no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—21no—
234C2×C4×C13—21no—
235C2×C4×C13—22no—
236C2×C4×C13—22no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—21no—
245C2×C4×C13—21no—
246C2×C4×C13—21no—
247C2×C4×C13—21no—
248C2×C4×C13—21no—
249C2×C4×C13—41no—
250C2×C4×C13—41no—
251C2×C4×C13—41no—
252C2×C4×C13—41no—
253C2×C4×C13—41no—
254C2×C4×C13—41no—
255C2×C4×C13—41no—
256C2×C4×C13—41no—
257C2×C4×C13—41no—
258C2×C4×C13—41no—
259C2×C4×C13C4×D412yes—
260C2×C4×C13C4×D412yes—
261C2×C4×C13C23×C411yescharacteristic
262C2×C4×C13C2×#4111yescharacteristic
263C2×C4×C13C2×#4111yescharacteristic
264C2×C4×C13C2×#4111yescharacteristic
265C2×C4×C13C2×#4111yescharacteristic
266C2×C4×C13C2×#4111yescharacteristic
267C2×Dic13—22no—
268C2×Dic13—22no—
269C2×Dic13—22no—
270C2×Dic13—41no—
271C2×Dic13—41no—
272C2×Dic13—41no—
273C2×Dic13—41no—
274C2×Dic13—41no—
275C2×Dic13—41no—
276D52—22no—
277D52—22no—
278D52—22no—
279D52#11714yes—
280C4×D13—84no—
281C4×D13—84no—
282C4×D13—84no—
283#1055—22no—
284#1055—22no—
285#1055—41no—
286#1055—41no—
287C22×SD16—131no—
288C2×C4×Q8C2×D1311yescharacteristic
289C2×C4×D4—131no—
290C2×C4×D4—131no—
291C2×C4×D4—131no—
292#440—138no—
293C2×#107—131no—
294C2×#107—131no—
295C2×#106—131no—
296C2×#103—131no—
297C2×#103—131no—
298C2×#103—131no—
299C2×#102—131no—
300C2×#102—131no—
301C2×#102—131no—
302C2×#97—131no—
303C2×C4×C8—131no—
304#391C2×D1311yescharacteristic
305#391C2×D1311yescharacteristic
306#389C2×D1311yescharacteristic
307#389C2×D1311yescharacteristic
308#387—21no—
309#387—21no—
310#383—21no—
311#382—21no—
312C4×C4⋊C4—131no—
313C4×C4⋊C4—131no—
314C4×C4⋊C4—131no—
315C4×C4⋊C4C2×D1311yescharacteristic
316C4×C22⋊C4—261no—
317C4×C22⋊C4—261no—
318C4×C22⋊C4—261no—
319#376C2×D1311yescharacteristic
320C2×#95—261no—
321#340—131no—
322#340—131no—
323#340—131no—
324#340—131no—
325#340—131no—
326#340—131no—
327#336—131no—
328#336—131no—
329#336—131no—
330#336—131no—
331C22×C13C2×C4×D411yescharacteristic
332C22×C13#52511yescharacteristic
333C22×C13#52511yescharacteristic
334C22×C13#57611yescharacteristic
335C22×C13#57711yescharacteristic
336C22×C13#57711yescharacteristic
337C22×C13#57811yescharacteristic
338C2×D13—24no—
339C2×D13—42no—
340C2×D13—42no—
341C2×D13—42no—
342C2×D13—42no—
343C2×D13—42no—
344C2×D13—42no—
345C4×C13—22no—
346C4×C13—22no—
347C4×C13—41no—
348C4×C13—41no—
349C4×C13—41no—
350C4×C13—41no—
351C4×C13—42no—
352C4×C13—42no—
353C4×C13—81no—
354C4×C13—81no—
355C4×C13C2×#11711yescharacteristic
356C4×C13C4×#4111yescharacteristic
357C4×C13#52911yescharacteristic
358C4×C13#52911yescharacteristic
359Dic13—42no—
360Dic13—42no—
361Dic13—42no—
362C22×Q8C22×D1311yescharacteristic
363C22×D4—131no—
364C23×C4—261no—
365C23×C4—261no—
366C23×C4—261no—
367C2×SD16—134no—
368C2×SD16—262no—
369C2×SD16—262no—
370C22×C8—131no—
371C22×C8—131no—
372C22×C8—131no—
373C22×C8—131no—
374C4×Q8—22no—
375C4×Q8C4×D1314yescomplemented
376C4×D4—134no—
377C4×D4—262no—
378C4×D4—262no—
379C4×D4—262no—
380C4×D4—262no—
381C4×D4—262no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—131no—
386C2×C4⋊C4—131no—
387C2×C4⋊C4—131no—
388C2×C4⋊C4C22×D1311yescharacteristic
389C2×C4⋊C4C22×D1311yescharacteristic
390C2×C4⋊C4C22×D1311yescharacteristic
391C2×C22⋊C4—261no—
392C2×C22⋊C4—261no—
393C2×C22⋊C4—261no—
394C2×C42—21no—
395C2×C42—21no—
396C2×C42—261no—
397C2×C42—261no—
398C2×C42—261no—
399C2×C42C22×D1311yescharacteristic
400C2×C42C22×D1311yescharacteristic
401C2×C42C22×D1311yescharacteristic
402#107—134no—
403#107—262no—
404#106—262no—
405#103—134no—
406#103—262no—
407#103—262no—
408#102—134no—
409#102—262no—
410#102—262no—
411#97—134no—
412C4×C8—262no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95—21no—
420#95—261no—
421#95—261no—
422#95—261no—
423#95C22⋊D1311yescharacteristic
424#95C22⋊D1311yescharacteristic
425#95C22⋊D1311yescharacteristic
426#95C22⋊D1311yescharacteristic
427C2×C13#229011yescharacteristic
428C2×C13#294611yescharacteristic
429C2×C13#294711yescharacteristic
430C2×C13#311811yescharacteristic
431C2×C13#312011yescharacteristic
432C2×C13#312311yescharacteristic
433C2×C13#312411yescharacteristic
434D13—44no—
435C24—261no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8C2×C4×D1312yes—
442C2×D4—132no—
443C2×D4—132no—
444C2×D4—132no—
445C2×D4—261no—
446C2×D4—261no—
447C2×D4—261no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—264no—
453C22×C4—264no—
454C22×C4—261no—
455C22×C4—261no—
456C22×C4—261no—
457C22×C4—264no—
458C22×C4—1041no—
459C22×C4—1041no—
460C22×C4—1041no—
461C22×C4—1041no—
462C22×C4—1041no—
463C22×C4—1041no—
464C22×C4C2×C22⋊D1311yescharacteristic
465C22×C4C2×C22⋊D1311yescharacteristic
466C22×C4C2×C22⋊D1311yescharacteristic
467C22×C4C2×C22⋊D1311yescharacteristic
468C22×C4C2×C22⋊D1311yescharacteristic
469C22×C4C2×C22⋊D1311yescharacteristic
470C22×C4C23×D1311yescharacteristic
471SD16—268no—
472C2×C8—132no—
473C2×C8—132no—
474C2×C8—261no—
475C2×C8—261no—
476C2×C8—261no—
477C2×C8—261no—
478C2×C8—261no—
479C2×C8—261no—
480C2×C8—261no—
481C2×C8—261no—
482C2×C8—261no—
483C2×C8—261no—
484C4⋊C4—24no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—81no—
491C4⋊C4—81no—
492C4⋊C4—132no—
493C4⋊C4—132no—
494C4⋊C4—132no—
495C4⋊C4—261no—
496C4⋊C4—261no—
497C4⋊C4—261no—
498C4⋊C4C2×C4×D1312yes—
499C22⋊C4—264no—
500C22⋊C4—264no—
501C22⋊C4—264no—
502C42—24no—
503C42—21no—
504C42—21no—
505C42—21no—
506C42—21no—
507C42—81no—
508C42—1041no—
509C42—1041no—
510C42—1041no—
511C42C2×C4×D1312yes—
512C42#612712yes—
513C13#2112511yescharacteristic, complemented, Sylow
514C23—262no—
515C23—262no—
516C23—262no—
517C23—521no—
518C23—521no—
519C23—521no—
520C23—521no—
521C23C22×C22⋊D1311yescharacteristic
522Q8—22no—
523Q8—22no—
524Q8—41no—
525Q8—41no—
526D4—134no—
527D4—262no—
528D4—262no—
529D4—262no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—262no—
559C2×C4—262no—
560C2×C4—262no—
561C2×C4—521no—
562C2×C4—521no—
563C2×C4—521no—
564C2×C4—521no—
565C2×C4—521no—
566C2×C4—521no—
567C2×C4—1044no—
568C2×C4—1044no—
569C2×C4—1044no—
570C2×C4C4×C22⋊D1312yes—
571C2×C4C4×C22⋊D1312yes—
572C2×C4C22×C4×D1311yescharacteristic
573C2×C4C2×#612711yescharacteristic
574C2×C4#41×D1311yescharacteristic
575C2×C4#41×D1311yescharacteristic
576C2×C4#41×D1311yescharacteristic
577C2×C4#41×D1311yescharacteristic
578C8—262no—
579C8—262no—
580C8—521no—
581C8—521no—
582C22—264no—
583C22—522no—
584C22—522no—
585C22—522no—
586C22—522no—
587C22—522no—
588C22—522no—
589C22C2×C4×C22⋊D1311yescharacteristic
590C22#1171953311yescharacteristic
591C22#1171953311yescharacteristic
592C22#1171954011yescharacteristic
593C22#1171954211yescharacteristic
594C22#1171954211yescharacteristic
595C22#1171954311yescharacteristic
596C4—22no—
597C4—22no—
598C4—42no—
599C4—42no—
600C4—41no—
601C4—41no—
602C4—41no—
603C4—41no—
604C4—81no—
605C4—81no—
606C4—522no—
607C4—522no—
608C4—522no—
609C4D13×#11711yescharacteristic
610C4#1171922711yescharacteristic
611C4#1171923311yescharacteristic
612C4#1171923311yescharacteristic
613C2—524no—
614C2#1311727311yescharacteristic
615C2#1312366411yescharacteristic
616C2#1312367911yescharacteristic
617C2#1312501411yescharacteristic
618C2#1312504411yescharacteristic
619C2#1312508311yescharacteristic
620C2#1312509211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#2320C2
socleC23×C13C22×D4
prime radicalC22×D52C23
cosocleC22×C4×C13C24
hypercenter#2320D13
hypocenterC13#21125
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ #376 ◁ #2320

Complements

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

NH ≅ G/Ntype
3. #13115474C2semidirect
4. #13115467C2semidirect
5. #13115425C2semidirect
6. #13115404C2semidirect
11. #13114734C2semidirect
12. C4×#88075C2semidirect
14. #13114588C2semidirect
15. C13×#2320C2semidirect
34. #11718687C4semidirect
66. C4×Q8×C13C2×C4semidirect
113. #88075C2×C4semidirect
122. #88047C2×C4semidirect
123. #88043C2×C4semidirect
205. #2320D13semidirect
375. C4×Q8C4×D13semidirect
513. C13#21125semidirect

Maximal subgroups

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

subgroupindex
C2×#117186872
#131171982
#131154742
#131154672
#131154252
#131154042
#131151732
#131150962
#131150822
#131147342
C4×#880752
C4×#880492
#131145882
C13×#23202
#2112513