Finite Group Databasebeta

← #15867258

Subgroups — #15867258

Order 3328.

874 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718371C211yesmaximal, characteristic
2#13117313C211yesmaximal, characteristic, complemented
3#13117300C211yesmaximal, characteristic
4#13115717C211yesmaximal, characteristic
5#13115690C211yesmaximal, characteristic
6#13115574C211yesmaximal, characteristic, complemented
7#13115569C211yesmaximal, characteristic, complemented
8#13115533C211yesmaximal, characteristic
9#13115526C211yesmaximal, characteristic, complemented
10#13115519C211yesmaximal, characteristic
11#13115512C211yesmaximal, characteristic, complemented
12#13114733C211yesmaximal, characteristic, complemented
13#13114667C211yesmaximal, characteristic, complemented
14#13114662C211yesmaximal, characteristic
15C4×C13×#97C211yesmaximal, characteristic, complemented
16C22×#6095C2211yescharacteristic
17C2×C4×D52C2211yescharacteristic
18C2×#88126—21no—
19C2×C4×Dic26C2211yescharacteristic
20C2×C13×#97C2211yescharacteristic
21C2×C13×#97C2211yescharacteristic
22C2×C13×#97C2211yescharacteristic
23C2×C13×#97C2211yescharacteristic
24C2×C4×C8×C13C2211yescharacteristic
25C2×C4×C8×C13C2211yescharacteristic
26C43×C13C2211yescharacteristic
27C2×#88061C2211yescharacteristic
28C2×#88061C2211yescharacteristic
29C2×#88061C2211yescharacteristic
30C2×#88058C2211yescharacteristic
31C2×#88058C2211yescharacteristic
32C2×#88057C2211yescharacteristic
33C2×#88056C2211yescharacteristic
34C2×#88056C2211yescharacteristic
35C2×#88056C2211yescharacteristic
36#11718601—21no—
37#11718601—21no—
38#11718600C2211yescharacteristic
39#11718600C2211yescharacteristic
40C4×#6103—21no—
41C4×C4⋊Dic13C2211yescharacteristic
42C4×C4⋊Dic13C2211yescharacteristic
43#11718594—21no—
44#11718594—21no—
45#11718593—21no—
46C4×#6101—21no—
47#11718590C2211yescharacteristic
48#11718590C2211yescharacteristic
49#11718589C2211yescharacteristic
50#11718589C2211yescharacteristic
51#11718589C2211yescharacteristic
52#11718589C2211yescharacteristic
53#11718371C418yescomplemented
54#11718143C2211yescharacteristic
55#11718143C2211yescharacteristic
56#11718143C2211yescharacteristic
57#11718143C2211yescharacteristic
58#11718143C2211yescharacteristic
59#11718143C2211yescharacteristic
60C22×D52C2311yescharacteristic
61C22×C4×D13—21no—
62C22×Dic26C2311yescharacteristic
63C22×C8×C13C2311yescharacteristic
64C22×C8×C13C2311yescharacteristic
65C22×C8×C13C2311yescharacteristic
66C22×C8×C13C2311yescharacteristic
67C2×C42×C13D411yescharacteristic
68C2×C42×C13D411yescharacteristic
69C2×C42×C13D411yescharacteristic
70C2×C42×C13D411yescharacteristic
71C2×C42×C13C2311yescharacteristic
72C2×C42×C13C2311yescharacteristic
73C2×C42×C13C2311yescharacteristic
74C2×#6103—21no—
75C2×#6103—21no—
76C2×#6103—21no—
77C2×#6103—21no—
78C2×#6103—21no—
79C2×C4⋊Dic13C2311yescharacteristic
80C2×C4⋊Dic13C2311yescharacteristic
81C2×C4⋊Dic13C2311yescharacteristic
82C2×C4⋊Dic13C2311yescharacteristic
83C2×C4⋊Dic13C2311yescharacteristic
84C2×C4⋊Dic13C2311yescharacteristic
85C2×#6101—21no—
86C2×#6101—21no—
87C2×#6101—21no—
88C2×#6101—21no—
89C2×#6101—21no—
90C2×C4×Dic13—21no—
91C2×C4×Dic13—21no—
92C2×C4×Dic13—21no—
93C2×#6095—22no—
94C2×#6095—22no—
95C2×#6095C2×C414yes—
96C4×D52—22no—
97C4×D52C2×C414yes—
98#88126—44no—
99C4×Dic26—22no—
100C4×Dic26C2×C414yes—
101C13×#97—22no—
102C13×#97—22no—
103C13×#97—22no—
104C13×#97C2×C414yes—
105C4×C8×C13—22no—
106C4×C8×C13—22no—
107#88071—21no—
108#88071—21no—
109#88071—21no—
110#88071—21no—
111#88071—21no—
112#88071—21no—
113#88071—21no—
114#88071—21no—
115#88071—21no—
116#88071—21no—
117#88061—22no—
118#88061—22no—
119#88061C2×C414yes—
120#88058—22no—
121#88058C2×C414yes—
122#88057—22no—
123#88056—22no—
124#88056—22no—
125#88056C2×C414yes—
126#21288—131nomaximal, Sylow
127C23×D13—21no—
128C22×C4×C13C2×D411yescharacteristic
129C22×C4×C13C2×D411yescharacteristic
130C22×C4×C13C2×D411yescharacteristic
131C22×C4×C13C2×D411yescharacteristic
132C22×C4×C13C2×D411yescharacteristic
133C22×C4×C13C2×D411yescharacteristic
134C22×C4×C13C2411yescharacteristic
135C22×Dic13—21no—
136C22×Dic13—21no—
137C22×Dic13—21no—
138C22×Dic13—21no—
139C22×Dic13—21no—
140C22×Dic13—21no—
141C22×Dic13—21no—
142C2×D52—21no—
143C2×D52—21no—
144C2×D52—21no—
145C2×D52—21no—
146C2×D52—21no—
147C2×D52C22×C412yes—
148C2×C4×D13—24no—
149C2×C4×D13—42no—
150C2×C4×D13—42no—
151C2×Dic26—21no—
152C2×Dic26—21no—
153C2×Dic26—21no—
154C2×Dic26—21no—
155C2×Dic26—21no—
156C2×Dic26C22×C412yes—
157C2×C8×C13—21no—
158C2×C8×C13—21no—
159C2×C8×C13—21no—
160C2×C8×C13—21no—
161C2×C8×C13—21no—
162C2×C8×C13—21no—
163C2×C8×C13C22×C412yes—
164C2×C8×C13C22×C412yes—
165C2×C8×C13#4112yes—
166C2×C8×C13#4112yes—
167C2×C8×C13#4112yes—
168C2×C8×C13#4112yes—
169C42×C13—22no—
170C42×C13—22no—
171C42×C13—21no—
172C42×C13—21no—
173C42×C13—21no—
174C42×C13—21no—
175C42×C13—41no—
176C42×C13—41no—
177C42×C13C22×C412yes—
178C42×C13#4112yes—
179#6103—24no—
180#6103—42no—
181#6103—42no—
182#6103—42no—
183#6103—42no—
184C4⋊Dic13—21no—
185C4⋊Dic13—21no—
186C4⋊Dic13—21no—
187C4⋊Dic13—21no—
188C4⋊Dic13—21no—
189C4⋊Dic13—21no—
190C4⋊Dic13—21no—
191C4⋊Dic13—21no—
192C4⋊Dic13—21no—
193C4⋊Dic13—21no—
194C4⋊Dic13C22×C412yes—
195C4⋊Dic13C22×C412yes—
196#6101—24no—
197#6101—42no—
198#6101—42no—
199#6101—42no—
200#6101—42no—
201C4×Dic13—24no—
202C4×Dic13—42no—
203C4×Dic13—42no—
204#6095—28no—
205C2×#440—131no—
206#2295—131no—
207#2293—131no—
208#1973—131no—
209#1968—131no—
210#1943—131no—
211#1942—131no—
212#1936—131no—
213#1935—131no—
214#1934—131no—
215#1933—131no—
216#1776—131no—
217#1763—131no—
218#1762—131no—
219C4×#97D1311yescharacteristic, complemented
220C23×C13C22×D411yescharacteristic
221C22×D13—22no—
222C22×D13—41no—
223C22×D13—41no—
224C22×D13—41no—
225C22×D13—41no—
226C22×D13—41no—
227C22×D13—41no—
228C2×C4×C13—21no—
229C2×C4×C13—21no—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—21no—
234C2×C4×C13—21no—
235C2×C4×C13—21no—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
241C2×C4×C13—21no—
242C2×C4×C13C4×D412yes—
243C2×C4×C13C4×D412yes—
244C2×C4×C13AGL(1,ℤ/8)12yes—
245C2×C4×C13#13712yes—
246C2×C4×C13C23×C411yescharacteristic
247C2×C4×C13C2×#4111yescharacteristic
248C2×C4×C13C2×#4111yescharacteristic
249C2×C4×C13C2×#4111yescharacteristic
250C2×C4×C13C2×#4111yescharacteristic
251C2×C4×C13C2×#4111yescharacteristic
252C2×Dic13—22no—
253C2×Dic13—22no—
254C2×Dic13—22no—
255C2×Dic13—41no—
256C2×Dic13—41no—
257C2×Dic13—41no—
258C2×Dic13—41no—
259C2×Dic13—41no—
260C2×Dic13—41no—
261C2×Dic13—41no—
262C2×Dic13—41no—
263C2×Dic13—41no—
264C2×Dic13—41no—
265C2×Dic13—41no—
266C2×Dic13—41no—
267C2×Dic13—41no—
268C2×Dic13—41no—
269C2×Dic13—41no—
270C2×Dic13—41no—
271C2×Dic13—41no—
272C2×Dic13—41no—
273D52—22no—
274D52—22no—
275D52—41no—
276D52—41no—
277C4×D13—48no—
278Dic26—22no—
279Dic26—22no—
280Dic26—41no—
281Dic26—41no—
282C8×C13—22no—
283C8×C13—22no—
284C8×C13—22no—
285C8×C13#11714yescomplemented
286C22×SD16—131no—
287C2×C4×Q8—131no—
288C2×C4×D4—131no—
289C2×#117—261no—
290#440—138no—
291C2×#107—131no—
292C2×#107—131no—
293C2×#106—131no—
294C2×#103—131no—
295C2×#103—131no—
296C2×#103—131no—
297C2×#102—131no—
298C2×#102—131no—
299C2×#102—131no—
300C2×#97C2×D1311yescharacteristic
301C2×#97C2×D1311yescharacteristic
302C2×#97C2×D1311yescharacteristic
303C2×#97C2×D1311yescharacteristic
304C2×C4×C8C2×D1311yescharacteristic
305C2×C4×C8C2×D1311yescharacteristic
306#391—131no—
307#391—131no—
308#390—131no—
309#390—131no—
310#389—131no—
311#389—131no—
312#389—131no—
313#389—131no—
314#388—261no—
315#388—261no—
316#387—261no—
317#387—261no—
318C4×C4⋊C4—131no—
319C4×C4⋊C4—131no—
320C4×C4⋊C4—261no—
321C4×C22⋊C4—261no—
322#376—261no—
323C43C2×D1311yescharacteristic
324#340—131no—
325#340—131no—
326#340—131no—
327#340—131no—
328#340—131no—
329#340—131no—
330C22×C13C2×C4×D411yescharacteristic
331C22×C13#53211yescharacteristic
332C22×C13#53211yescharacteristic
333C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
334C22×C13C2×#13711yescharacteristic
335C22×C13#57511yescharacteristic
336C22×C13#57511yescharacteristic
337C2×D13—42no—
338C2×D13—42no—
339C2×D13—42no—
340C2×D13—81no—
341C2×D13—81no—
342C2×D13—81no—
343C2×D13—81no—
344C4×C13—22no—
345C4×C13—22no—
346C4×C13—22no—
347C4×C13—22no—
348C4×C13—41no—
349C4×C13—41no—
350C4×C13C2×#11711yescharacteristic
351C4×C13C4×#4111yescharacteristic
352C4×C13#52911yescharacteristic
353C4×C13#52911yescharacteristic
354Dic13—42no—
355Dic13—42no—
356Dic13—42no—
357Dic13—81no—
358Dic13—81no—
359Dic13—81no—
360Dic13—81no—
361C22×Q8—131no—
362C22×D4—131no—
363C23×C4—261no—
364C2×SD16—134no—
365C2×SD16—262no—
366C2×SD16—262no—
367C22×C8C22×D1311yescharacteristic
368C22×C8C22×D1311yescharacteristic
369C22×C8C22×D1311yescharacteristic
370C22×C8C22×D1311yescharacteristic
371C4×Q8—134no—
372C4×Q8—262no—
373C4×D4—134no—
374C4×D4—262no—
375#117—524no—
376C2×C4⋊C4—131no—
377C2×C4⋊C4—131no—
378C2×C4⋊C4—131no—
379C2×C4⋊C4—131no—
380C2×C4⋊C4—131no—
381C2×C4⋊C4—131no—
382C2×C4⋊C4—261no—
383C2×C4⋊C4—261no—
384C2×C4⋊C4—261no—
385C2×C4⋊C4—261no—
386C2×C4⋊C4—261no—
387C2×C22⋊C4—261no—
388C2×C22⋊C4—261no—
389C2×C22⋊C4—261no—
390C2×C22⋊C4—261no—
391C2×C22⋊C4—261no—
392C2×C42—261no—
393C2×C42—261no—
394C2×C42—261no—
395C2×C42D5211yescharacteristic
396C2×C42D5211yescharacteristic
397C2×C42D5211yescharacteristic
398C2×C42D5211yescharacteristic
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—22no—
412#97—22no—
413#97—22no—
414#97C4×D1314yes—
415C4×C8—22no—
416C4×C8—22no—
417#95—261no—
418#95—261no—
419#95—261no—
420#95—261no—
421#95—261no—
422#95—261no—
423#95—261no—
424#95—261no—
425#95—261no—
426#95—261no—
427C2×C13#229311yescharacteristic
428C2×C13C4×AGL(1,ℤ/8)11yescharacteristic
429C2×C13C4×#13711yescharacteristic
430C2×C13#318011yescharacteristic
431C2×C13#318111yescharacteristic
432C2×C13#318211yescharacteristic
433C2×C13#318311yescharacteristic
434D13—82no—
435C24—261no—
436C2×Q8—132no—
437C2×Q8—261no—
438C2×Q8—261no—
439C2×Q8—261no—
440C2×Q8—261no—
441C2×Q8—261no—
442C2×D4—132no—
443C2×D4—261no—
444C2×D4—261no—
445C2×D4—261no—
446C2×D4—261no—
447C2×D4—261no—
448C22×C4—261no—
449C22×C4—261no—
450C22×C4—261no—
451C22×C4—264no—
452C22×C4—261no—
453C22×C4—261no—
454C22×C4—261no—
455C22×C4—261no—
456C22×C4—522no—
457C22×C4—522no—
458C22×C4C2×D5211yescharacteristic
459C22×C4C2×D5211yescharacteristic
460C22×C4C2×D5211yescharacteristic
461C22×C4C2×D5211yescharacteristic
462C22×C4C2×D5211yescharacteristic
463C22×C4C2×D5211yescharacteristic
464C22×C4C23×D1311yescharacteristic
465SD16—268no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8C2×C4×D1312yes—
473C2×C8C2×C4×D1312yes—
474C2×C8#612712yes—
475C2×C8#612712yes—
476C2×C8#612712yes—
477C2×C8#612712yes—
478C4⋊C4—132no—
479C4⋊C4—132no—
480C4⋊C4—264no—
481C4⋊C4—261no—
482C4⋊C4—261no—
483C4⋊C4—261no—
484C4⋊C4—261no—
485C4⋊C4—261no—
486C4⋊C4—261no—
487C4⋊C4—261no—
488C4⋊C4—261no—
489C4⋊C4—261no—
490C4⋊C4—261no—
491C4⋊C4—522no—
492C4⋊C4—522no—
493C4⋊C4—522no—
494C4⋊C4—522no—
495C22⋊C4—264no—
496C22⋊C4—522no—
497C22⋊C4—522no—
498C22⋊C4—522no—
499C22⋊C4—522no—
500C42—22no—
501C42—22no—
502C42—21no—
503C42—21no—
504C42—21no—
505C42—21no—
506C42—41no—
507C42—41no—
508C42—264no—
509C42—522no—
510C42—522no—
511C42C2×C4×D1312yes—
512C42#612712yes—
513C13#2128811yescharacteristic, complemented, Sylow
514C23—262no—
515C23—521no—
516C23—521no—
517C23—521no—
518C23—521no—
519C23—521no—
520C23—521no—
521C23C22×D5211yescharacteristic
522Q8—262no—
523Q8—262no—
524Q8—521no—
525Q8—521no—
526D4—262no—
527D4—262no—
528D4—521no—
529D4—521no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
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—262no—
545C2×C4—262no—
546C2×C4—262no—
547C2×C4—528no—
548C2×C4—521no—
549C2×C4—521no—
550C2×C4—521no—
551C2×C4—521no—
552C2×C4—521no—
553C2×C4—521no—
554C2×C4—521no—
555C2×C4—521no—
556C2×C4—521no—
557C2×C4—521no—
558C2×C4—521no—
559C2×C4—521no—
560C2×C4—521no—
561C2×C4—521no—
562C2×C4—521no—
563C2×C4—521no—
564C2×C4—521no—
565C2×C4—521no—
566C2×C4C4×D5212yes—
567C2×C4C4×D5212yes—
568C2×C4#8816212yes—
569C2×C4#8816312yes—
570C2×C4C22×C4×D1311yescharacteristic
571C2×C4C2×#612711yescharacteristic
572C2×C4C2×#612711yescharacteristic
573C2×C4C2×#612711yescharacteristic
574C2×C4C2×#612711yescharacteristic
575C2×C4C2×#612711yescharacteristic
576C8—22no—
577C8—22no—
578C8—22no—
579C8#8812614yescomplemented
580C22—522no—
581C22—522no—
582C22—522no—
583C22—1041no—
584C22—1041no—
585C22—1041no—
586C22—1041no—
587C22C2×C4×D5211yescharacteristic
588C22#1171918211yescharacteristic
589C22#1171918211yescharacteristic
590C22C2×#8816211yescharacteristic
591C22C2×#8816311yescharacteristic
592C22#1171945311yescharacteristic
593C22#1171945311yescharacteristic
594C4—22no—
595C4—22no—
596C4—22no—
597C4—22no—
598C4—41no—
599C4—41no—
600C4—522no—
601C4—522no—
602C4—522no—
603C4—1041no—
604C4—1041no—
605C4—1041no—
606C4—1041no—
607C4C2×#8812611yescharacteristic
608C4C4×#612711yescharacteristic
609C4#1171918411yescharacteristic
610C4#1171918411yescharacteristic
611C2—1042no—
612C2#1311730011yescharacteristic
613C2C4×#8816211yescharacteristic
614C2C4×#8816311yescharacteristic
615C2#1312553411yescharacteristic
616C2#1312554511yescharacteristic
617C2#1312555411yescharacteristic
618C2#1312556511yescharacteristic
subgroupG/H
centerC23C22×D52
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC4×C13×#97C2
socleC23×C13C22×D4
prime radicalC22×D52C23
cosocleC22×C4×C13C24
hypercenterC4×#97D13
hypocenterC13#21288
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C43 ◁ C4×#97

Complements

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

NH ≅ G/Ntype
2. #13117313C2semidirect
6. #13115574C2semidirect
7. #13115569C2semidirect
9. #13115526C2semidirect
11. #13115512C2semidirect
12. #13114733C2semidirect
13. #13114667C2semidirect
15. C4×C13×#97C2semidirect
53. #11718371C4semidirect
219. C4×#97D13semidirect
285. C8×C13#117semidirect
513. C13#21288semidirect
579. C8#88126semidirect

Maximal subgroups

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

subgroupindex
C2×#117183712
#131173132
#131173002
#131157172
#131156902
#131155742
#131155692
#131155332
#131155262
#131155192
#131155122
#131147332
#131146672
#131146622
C4×C13×#972
#2128813