Finite Group Databasebeta

← #15867299

Subgroups — #15867299

Order 3328.

814 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13117487C211yesmaximal, characteristic, complemented
2#13117479C211yesmaximal, characteristic
3#13115719C211yesmaximal, characteristic
4#13115692C211yesmaximal, characteristic
5#13115575C211yesmaximal, characteristic, complemented
6#13115570C211yesmaximal, characteristic, complemented
7#13115535C211yesmaximal, characteristic
8#13115528C211yesmaximal, characteristic, complemented
9#13115521C211yesmaximal, characteristic
10#13115514C211yesmaximal, characteristic, complemented
11#13114733C211yesmaximal, characteristic, complemented
12C4×#88075C211yesmaximal, characteristic, complemented
13C4×#88072C211yesmaximal, characteristic
14#13114524C211yesmaximal, characteristic, complemented
15C2×C13×#440C211yesmaximal, characteristic
16C22×C13×SD16C2211yescharacteristic
17C2×C4×Q8×C13C2211yescharacteristic
18C2×C4×D4×C13C2211yescharacteristic
19C13×#440C418yescomplemented
20C2×C13×#107C2211yescharacteristic
21C2×C13×#103C2211yescharacteristic
22C2×C13×#102C2211yescharacteristic
23C2×C13×#97C2211yescharacteristic
24#11718891C2211yescharacteristic
25#11718891C2211yescharacteristic
26C2×#88075C2211yescharacteristic
27C2×#88075C2211yescharacteristic
28#11718882C2211yescharacteristic
29#11718882C2211yescharacteristic
30C2×#88072C2211yescharacteristic
31C2×#88072C2211yescharacteristic
32#11718873—21no—
33#11718872—21no—
34C2×#88058C2211yescharacteristic
35C2×#88057C2211yescharacteristic
36C2×#88055C2211yescharacteristic
37C2×#88055C2211yescharacteristic
38C2×C8×Dic13C2211yescharacteristic
39C2×C8×Dic13C2211yescharacteristic
40#11718646C2211yescharacteristic
41#11718646C2211yescharacteristic
42#11718646C2211yescharacteristic
43#11718646C2211yescharacteristic
44#11718642—21no—
45#11718642—21no—
46#11718612—21no—
47#11718612—21no—
48#11718598—21no—
49#11718597—21no—
50C4×C4⋊Dic13C2211yescharacteristic
51C4×C4⋊Dic13C2211yescharacteristic
52#11718593C2211yescharacteristic
53C2×C4×#1055C2211yescharacteristic
54#11718143C2211yescharacteristic
55#11718143C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60C22×Q8×C13C2311yescharacteristic
61C22×D4×C13C2311yescharacteristic
62C23×C4×C13—21no—
63C2×C13×SD16—22no—
64C2×C13×SD16—22no—
65C2×C13×SD16C2×C414yes—
66C22×C8×C13C2311yescharacteristic
67C22×C8×C13C2311yescharacteristic
68C4×Q8×C13—22no—
69C4×Q8×C13C2×C414yes—
70C4×D4×C13—22no—
71C4×D4×C13C2×C414yes—
72C2×C13×C4⋊C4—21no—
73C2×C13×C4⋊C4C2311yescharacteristic
74C2×C13×C4⋊C4C2311yescharacteristic
75C2×C13×C22⋊C4—21no—
76C2×C42×C13—21no—
77C2×C42×C13C2311yescharacteristic
78C2×C22⋊Dic13—21no—
79C2×C22⋊Dic13—21no—
80C2×C22⋊Dic13—21no—
81C2×C22⋊Dic13—21no—
82C2×C4⋊Dic13—21no—
83C2×C4⋊Dic13—21no—
84C2×C4⋊Dic13—21no—
85C2×C4⋊Dic13—21no—
86C2×C4⋊Dic13C2311yescharacteristic
87C2×C4⋊Dic13C2311yescharacteristic
88C2×C4⋊Dic13C2311yescharacteristic
89C2×C4⋊Dic13C2311yescharacteristic
90C2×C4×Dic13—21no—
91C2×C4×Dic13—21no—
92C2×C4×Dic13C2311yescharacteristic
93C2×C4×Dic13C2311yescharacteristic
94C22×#1055C2311yescharacteristic
95C22×#1055C2311yescharacteristic
96C13×#107C2×C414yes—
97C13×#103C2×C414yes—
98C13×#102C2×C414yes—
99C13×#97C2×C414yes—
100#88075—22no—
101#88075—22no—
102#88072—22no—
103#88072—22no—
104#88071—21no—
105#88071—21no—
106#88071—21no—
107#88071—21no—
108#88071—21no—
109#88071—21no—
110#88071—21no—
111#88071—21no—
112#88071—21no—
113#88071—21no—
114#88071D411yescharacteristic
115#88071D411yescharacteristic
116#88071D411yescharacteristic
117#88071D411yescharacteristic
118#88058—22no—
119#88057—22no—
120#88055—22no—
121#88055—22no—
122C8×Dic13—22no—
123C8×Dic13—22no—
124C4×#1055—22no—
125#21291—131nomaximal, Sylow
126C24×C13—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—
133C2×D4×C13—21no—
134C2×D4×C13—21no—
135C2×D4×C13—21no—
136C2×D4×C13—21no—
137C2×D4×C13—21no—
138C2×D4×C13C22×C412yes—
139C22×C4×C13—21no—
140C22×C4×C13—21no—
141C22×C4×C13—21no—
142C22×C4×C13—24no—
143C22×C4×C13—81no—
144C22×C4×C13—81no—
145C22×C4×C13C2×D411yescharacteristic
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13C2411yescharacteristic
148C22×Dic13—21no—
149C22×Dic13—21no—
150C22×Dic13—21no—
151C22×Dic13—21no—
152C22×Dic13C2×D411yescharacteristic
153C22×Dic13C2×D411yescharacteristic
154C22×Dic13C2×D411yescharacteristic
155C22×Dic13C2×D411yescharacteristic
156C13×SD16—28no—
157C2×C8×C13—21no—
158C2×C8×C13—21no—
159C2×C8×C13C22×C412yes—
160C2×C8×C13C22×C412yes—
161C2×C8×C13#4112yes—
162C2×C8×C13#4112yes—
163C13×C4⋊C4—24no—
164C13×C4⋊C4—21no—
165C13×C4⋊C4—21no—
166C13×C4⋊C4C22×C412yes—
167C13×C4⋊C4C22×C412yes—
168C13×C22⋊C4—24no—
169C42×C13—24no—
170C42×C13C22×C412yes—
171C42×C13#4112yes—
172C22⋊Dic13—81no—
173C22⋊Dic13—81no—
174C22⋊Dic13—81no—
175C22⋊Dic13—81no—
176C4⋊Dic13—21no—
177C4⋊Dic13—21no—
178C4⋊Dic13—21no—
179C4⋊Dic13—21no—
180C4⋊Dic13—21no—
181C4⋊Dic13—21no—
182C4⋊Dic13—21no—
183C4⋊Dic13—21no—
184C4⋊Dic13—81no—
185C4⋊Dic13—81no—
186C4⋊Dic13—81no—
187C4⋊Dic13—81no—
188C4×Dic13—21no—
189C4×Dic13—21no—
190C4×Dic13—21no—
191C4×Dic13—21no—
192C4×Dic13—81no—
193C4×Dic13—81no—
194C2×#1055—21no—
195C2×#1055—21no—
196C2×#1055—21no—
197C2×#1055—21no—
198C2×#1055#4112yes—
199C2×#1055#4112yes—
200C2×#440D1311yescharacteristic
201#2320—131no—
202#2319—131no—
203#1973—131no—
204#1968—131no—
205#1943—131no—
206#1942—131no—
207#1936—131no—
208#1935—131no—
209#1934—131no—
210#1933—131no—
211#1776—131no—
212C4×#103—131no—
213C4×#102—131no—
214#1726—131no—
215C23×C13—22no—
216C23×C13—41no—
217C23×C13—41no—
218C23×C13—41no—
219C23×C13—41no—
220C23×C13—41no—
221C23×C13—41no—
222C23×C13C22×D411yescharacteristic
223Q8×C13—22no—
224Q8×C13—22no—
225Q8×C13—41no—
226Q8×C13—41no—
227D4×C13—22no—
228D4×C13—22no—
229D4×C13—41no—
230D4×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—22no—
238C2×C4×C13—41no—
239C2×C4×C13—41no—
240C2×C4×C13—41no—
241C2×C4×C13—41no—
242C2×C4×C13—41no—
243C2×C4×C13—41no—
244C2×C4×C13—84no—
245C2×C4×C13C4×D412yes—
246C2×C4×C13C4×D412yes—
247C2×C4×C13C23×C411yescharacteristic
248C2×C4×C13C2×#4111yescharacteristic
249C2×C4×C13C2×#4111yescharacteristic
250C2×C4×C13C2×#4111yescharacteristic
251C2×C4×C13C2×#4111yescharacteristic
252C2×C4×C13C2×#4111yescharacteristic
253C2×Dic13—21no—
254C2×Dic13—21no—
255C2×Dic13—21no—
256C2×Dic13—21no—
257C2×Dic13—21no—
258C2×Dic13—21no—
259C2×Dic13—21no—
260C2×Dic13—21no—
261C2×Dic13—21no—
262C2×Dic13—21no—
263C2×Dic13—21no—
264C2×Dic13—21no—
265C2×Dic13—41no—
266C2×Dic13—41no—
267C2×Dic13—41no—
268C2×Dic13—41no—
269C2×Dic13—41no—
270C2×Dic13—41no—
271C2×Dic13—41no—
272C2×Dic13—41no—
273C2×Dic13—41no—
274C2×Dic13—41no—
275C2×Dic13—41no—
276C2×Dic13—41no—
277C8×C13—22no—
278C8×C13#11714yes—
279#1055—22no—
280#1055—22no—
281C22×SD16C2×D1311yescharacteristic
282C2×C4×Q8C2×D1311yescharacteristic
283C2×C4×D4C2×D1311yescharacteristic
284#440Dic1318yescomplemented
285C2×#107—131no—
286C2×#107C2×D1311yescharacteristic
287C2×#106—131no—
288C2×#103—131no—
289C2×#103—131no—
290C2×#103C2×D1311yescharacteristic
291C2×#102—131no—
292C2×#102—131no—
293C2×#102C2×D1311yescharacteristic
294C2×#97—131no—
295C2×#97—131no—
296C2×#97C2×D1311yescharacteristic
297C2×C4×C8—131no—
298C2×C4×C8—131no—
299C2×C4×C8—131no—
300#391—131no—
301#391—131no—
302#390—131no—
303#390—131no—
304#389—131no—
305#389—131no—
306#389—131no—
307#389—131no—
308#388—261no—
309#388—261no—
310#387—261no—
311#387—261no—
312#383—261no—
313#382—261no—
314#381—261no—
315#380—261no—
316C4×C4⋊C4—131no—
317C4×C4⋊C4—131no—
318#376—131no—
319#340—131no—
320#340—131no—
321#340—131no—
322#340—131no—
323#340—131no—
324#340—131no—
325C22×C13—42no—
326C22×C13—42no—
327C22×C13—42no—
328C22×C13—81no—
329C22×C13—81no—
330C22×C13—81no—
331C22×C13—81no—
332C22×C13C2×C4×D411yescharacteristic
333C22×C13#53211yescharacteristic
334C22×C13#53211yescharacteristic
335C22×C13#57611yescharacteristic
336C22×C13#57711yescharacteristic
337C22×C13#57711yescharacteristic
338C22×C13#57811yescharacteristic
339C4×C13—22no—
340C4×C13—22no—
341C4×C13—42no—
342C4×C13—42no—
343C4×C13—42no—
344C4×C13C2×#11711yescharacteristic
345C4×C13C4×#4111yescharacteristic
346C4×C13#52911yescharacteristic
347C4×C13#52911yescharacteristic
348Dic13—41no—
349Dic13—41no—
350Dic13—41no—
351Dic13—41no—
352Dic13—81no—
353Dic13—81no—
354Dic13—81no—
355Dic13—81no—
356C22×Q8C22×D1311yescharacteristic
357C22×D4C22×D1311yescharacteristic
358C23×C4—21no—
359C2×SD16—22no—
360C2×SD16—22no—
361C2×SD16C2×Dic1314yes—
362C22×C8—131no—
363C22×C8—131no—
364C22×C8C22×D1311yescharacteristic
365C22×C8C22×D1311yescharacteristic
366C4×Q8—22no—
367C4×Q8C2×Dic1314yes—
368C4×D4—22no—
369C4×D4C2×Dic1314yes—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—131no—
372C2×C4⋊C4—131no—
373C2×C4⋊C4—131no—
374C2×C4⋊C4—131no—
375C2×C4⋊C4—261no—
376C2×C4⋊C4—261no—
377C2×C4⋊C4—261no—
378C2×C4⋊C4—261no—
379C2×C4⋊C4C22×D1311yescharacteristic
380C2×C4⋊C4C22×D1311yescharacteristic
381C2×C22⋊C4—21no—
382C2×C22⋊C4—261no—
383C2×C22⋊C4—261no—
384C2×C22⋊C4—261no—
385C2×C22⋊C4—261no—
386C2×C42—21no—
387C2×C42—131no—
388C2×C42—131no—
389C2×C42—261no—
390C2×C42—261no—
391C2×C42C22×D1311yescharacteristic
392#107—262no—
393#107C2×Dic1314yes—
394#106—262no—
395#103—262no—
396#103—262no—
397#103C2×Dic1314yes—
398#102—262no—
399#102—262no—
400#102C2×Dic1314yes—
401#97—262no—
402#97—262no—
403#97C2×Dic1314yes—
404C4×C8—262no—
405C4×C8—262no—
406C4×C8—262no—
407#95—131no—
408#95—131no—
409#95—131no—
410#95—131no—
411#95—261no—
412#95—261no—
413#95—261no—
414#95—261no—
415#95—261no—
416#95—261no—
417#95—261no—
418#95—261no—
419#95—261no—
420#95—261no—
421C2×C13—82no—
422C2×C13#229311yescharacteristic
423C2×C13#294611yescharacteristic
424C2×C13#294711yescharacteristic
425C2×C13#317411yescharacteristic
426C2×C13#317511yescharacteristic
427C2×C13#317811yescharacteristic
428C2×C13#317911yescharacteristic
429C24—21no—
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8C22×Dic1312yes—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4C22×Dic1312yes—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—24no—
446C22×C4—81no—
447C22×C4—81no—
448C22×C4—131no—
449C22×C4—131no—
450C22×C4—131no—
451C22×C4—131no—
452C22×C4—261no—
453C22×C4—261no—
454C22×C4—261no—
455C22×C4—261no—
456C22×C4D4×D1311yescharacteristic
457C22×C4D4×D1311yescharacteristic
458C22×C4C23×D1311yescharacteristic
459SD16—28no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—132no—
463C2×C8—132no—
464C2×C8—261no—
465C2×C8—261no—
466C2×C8—261no—
467C2×C8—261no—
468C2×C8#612712yes—
469C2×C8#612712yes—
470C2×C8C22×Dic1312yes—
471C2×C8C22×Dic1312yes—
472C4⋊C4—24no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—261no—
476C4⋊C4—261no—
477C4⋊C4—261no—
478C4⋊C4—261no—
479C4⋊C4—261no—
480C4⋊C4—261no—
481C4⋊C4—261no—
482C4⋊C4—261no—
483C4⋊C4—1041no—
484C4⋊C4—1041no—
485C4⋊C4—1041no—
486C4⋊C4—1041no—
487C4⋊C4C22×Dic1312yes—
488C4⋊C4C22×Dic1312yes—
489C22⋊C4—24no—
490C22⋊C4—1041no—
491C22⋊C4—1041no—
492C22⋊C4—1041no—
493C22⋊C4—1041no—
494C42—24no—
495C42—261no—
496C42—261no—
497C42—261no—
498C42—261no—
499C42—1041no—
500C42—1041no—
501C42#612912yes—
502C42C22×Dic1312yes—
503C13#2129111yescharacteristic, complemented, Sylow
504C23—22no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23—41no—
511C23C2×D4×D1311yescharacteristic
512Q8—22no—
513Q8—22no—
514Q8—41no—
515Q8—41no—
516D4—22no—
517D4—22no—
518D4—41no—
519D4—41no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—84no—
534C2×C4—261no—
535C2×C4—261no—
536C2×C4—261no—
537C2×C4—261no—
538C2×C4—261no—
539C2×C4—261no—
540C2×C4—261no—
541C2×C4—261no—
542C2×C4—261no—
543C2×C4—261no—
544C2×C4—261no—
545C2×C4—261no—
546C2×C4—521no—
547C2×C4—521no—
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×C4D4×Dic1312yes—
559C2×C4D4×Dic1312yes—
560C2×C4C2×#612711yescharacteristic
561C2×C4C2×#612711yescharacteristic
562C2×C4C2×#612911yescharacteristic
563C2×C4#41×D1311yescharacteristic
564C2×C4#41×D1311yescharacteristic
565C2×C4C23×Dic1311yescharacteristic
566C8—22no—
567C8—262no—
568C8—262no—
569C8#8818014yes—
570C22—42no—
571C22—42no—
572C22—42no—
573C22—81no—
574C22—81no—
575C22—81no—
576C22—81no—
577C22#1171925311yescharacteristic
578C22#1171925311yescharacteristic
579C22#1171947911yescharacteristic
580C22#1171948011yescharacteristic
581C22#1171948311yescharacteristic
582C22#1171948411yescharacteristic
583C22C2×D4×Dic1311yescharacteristic
584C4—22no—
585C4—22no—
586C4—42no—
587C4—42no—
588C4—42no—
589C4—521no—
590C4—521no—
591C4—521no—
592C4—521no—
593C4—1041no—
594C4—1041no—
595C4—1041no—
596C4—1041no—
597C4#1171926211yescharacteristic
598C4#1171926211yescharacteristic
599C4C2×#8818011yescharacteristic
600C4#41×Dic1311yescharacteristic
601C2—82no—
602C2#1311730111yescharacteristic
603C2#1312366911yescharacteristic
604C2#1312368011yescharacteristic
605C2#1312546211yescharacteristic
606C2#1312547311yescharacteristic
607C2#1312550211yescharacteristic
608C2#1312551711yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC2×C13×#440C2
socleC23×C13C22×D4
prime radicalC22×D4×C13C23
cosocleC22×C4×C13C24
hypercenterC2×#440D13
hypocenterC13#21291
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
1. #13117487C2semidirect
5. #13115575C2semidirect
6. #13115570C2semidirect
8. #13115528C2semidirect
10. #13115514C2semidirect
11. #13114733C2semidirect
12. C4×#88075C2semidirect
14. #13114524C2semidirect
19. C13×#440C4semidirect
284. #440Dic13semidirect
503. C13#21291semidirect

Maximal subgroups

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

subgroupindex
#131174872
#131174792
#131157192
#131156922
#131155752
#131155702
#131155352
#131155282
#131155212
#131155142
#131147332
C4×#880752
C4×#880722
#131145242
C2×C13×#4402
#2129113