Finite Group Databasebeta

← #15867295

Subgroups — #15867295

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
1C2×#11718371C211yesmaximal, characteristic
2#13117488C211yesmaximal, characteristic, complemented
3#13117480C211yesmaximal, 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
13C4×#88056C211yesmaximal, characteristic, complemented
14C4×#88061C211yesmaximal, characteristic
15C13×#1726C211yesmaximal, characteristic, complemented
16C22×#6095C2211yescharacteristic
17C2×C4×D52C2211yescharacteristic
18C2×C4×Dic26C2211yescharacteristic
19C2×C13×#97C2211yescharacteristic
20C2×C13×#97C2211yescharacteristic
21C2×C13×#97C2211yescharacteristic
22C2×C4×C8×C13C2211yescharacteristic
23C2×C4×C8×C13C2211yescharacteristic
24C2×C4×C8×C13C2211yescharacteristic
25C13×#376C2211yescharacteristic
26C2×#88061C2211yescharacteristic
27C2×#88061C2211yescharacteristic
28C2×#88061C2211yescharacteristic
29C2×#88058C2211yescharacteristic
30C2×#88058C2211yescharacteristic
31C2×#88057C2211yescharacteristic
32C2×#88056C2211yescharacteristic
33C2×#88056C2211yescharacteristic
34C2×#88056C2211yescharacteristic
35#11718600C2211yescharacteristic
36#11718600C2211yescharacteristic
37C4×C4⋊Dic13C2211yescharacteristic
38C4×C4⋊Dic13C2211yescharacteristic
39#11718590C2211yescharacteristic
40#11718590C2211yescharacteristic
41#11718589C2211yescharacteristic
42#11718589C2211yescharacteristic
43#11718589C2211yescharacteristic
44#11718589C2211yescharacteristic
45#11718371C418yescomplemented
46#11718330—21no—
47#11718330—21no—
48#11718328—21no—
49#11718325—21no—
50#11718313—21no—
51#11718313—21no—
52#11718312—21no—
53#11718311—21no—
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×C13C2311yescharacteristic
68C2×C42×C13C2311yescharacteristic
69C2×C42×C13C2311yescharacteristic
70C2×#6103—21no—
71C2×#6103—21no—
72C2×#6103—21no—
73C2×#6103—21no—
74C2×#6103—21no—
75C2×C4⋊Dic13C2311yescharacteristic
76C2×C4⋊Dic13C2311yescharacteristic
77C2×C4⋊Dic13C2311yescharacteristic
78C2×C4⋊Dic13C2311yescharacteristic
79C2×C4⋊Dic13C2311yescharacteristic
80C2×C4⋊Dic13C2311yescharacteristic
81C2×#6101—21no—
82C2×#6101—21no—
83C2×#6101—21no—
84C2×#6101—21no—
85C2×#6101—21no—
86C2×C4×Dic13—21no—
87C2×C4×Dic13—21no—
88C2×C4×Dic13—21no—
89C2×#6095—22no—
90C2×#6095—22no—
91C2×#6095C2×C414yes—
92C4×D52—22no—
93C4×D52C2×C414yes—
94C4×Dic26—22no—
95C4×Dic26C2×C414yes—
96C13×#97—22no—
97C13×#97—22no—
98C13×#97C2×C414yes—
99C4×C8×C13—22no—
100C4×C8×C13—22no—
101C4×C8×C13—22no—
102C13×#95D411yescharacteristic
103C13×#95D411yescharacteristic
104C13×#95D411yescharacteristic
105C13×#95D411yescharacteristic
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#88071—21no—
115#88071—21no—
116#88061—22no—
117#88061—22no—
118#88061C2×C414yes—
119#88058—22no—
120#88058C2×C414yes—
121#88057—22no—
122#88056—22no—
123#88056—22no—
124#88056C2×C414yes—
125#21291—131nomaximal, Sylow
126C23×D13—21no—
127C22×C4×C13C2×D411yescharacteristic
128C22×C4×C13C2×D411yescharacteristic
129C22×C4×C13C2×D411yescharacteristic
130C22×C4×C13C2×D411yescharacteristic
131C22×C4×C13C2×D411yescharacteristic
132C22×C4×C13C2×D411yescharacteristic
133C22×C4×C13C2411yescharacteristic
134C22×Dic13—21no—
135C22×Dic13—21no—
136C22×Dic13—21no—
137C22×Dic13—21no—
138C22×Dic13—21no—
139C22×Dic13—21no—
140C22×Dic13—21no—
141C2×D52—21no—
142C2×D52—21no—
143C2×D52—21no—
144C2×D52—21no—
145C2×D52—21no—
146C2×D52C22×C412yes—
147C2×C4×D13—24no—
148C2×C4×D13—81no—
149C2×C4×D13—81no—
150C2×Dic26—21no—
151C2×Dic26—21no—
152C2×Dic26—21no—
153C2×Dic26—21no—
154C2×Dic26—21no—
155C2×Dic26C22×C412yes—
156C2×C8×C13—21no—
157C2×C8×C13—21no—
158C2×C8×C13—21no—
159C2×C8×C13—21no—
160C2×C8×C13—21no—
161C2×C8×C13—21no—
162C2×C8×C13C22×C412yes—
163C2×C8×C13C22×C412yes—
164C2×C8×C13#4112yes—
165C2×C8×C13#4112yes—
166C2×C8×C13#4112yes—
167C2×C8×C13#4112yes—
168C42×C13—21no—
169C42×C13—21no—
170C42×C13—21no—
171C42×C13—21no—
172C42×C13C22×C412yes—
173C42×C13#4112yes—
174#6103—24no—
175#6103—81no—
176#6103—81no—
177#6103—81no—
178#6103—81no—
179C4⋊Dic13—21no—
180C4⋊Dic13—21no—
181C4⋊Dic13—21no—
182C4⋊Dic13—21no—
183C4⋊Dic13—21no—
184C4⋊Dic13—21no—
185C4⋊Dic13—21no—
186C4⋊Dic13—21no—
187C4⋊Dic13—21no—
188C4⋊Dic13—21no—
189C4⋊Dic13C22×C412yes—
190C4⋊Dic13C22×C412yes—
191#6101—24no—
192#6101—81no—
193#6101—81no—
194#6101—81no—
195#6101—81no—
196C4×Dic13—24no—
197C4×Dic13—81no—
198C4×Dic13—81no—
199#6095—28no—
200C2×#440—131no—
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#1726D1311yescharacteristic, complemented
215C23×C13C22×D411yescharacteristic
216C22×D13—22no—
217C22×D13—41no—
218C22×D13—41no—
219C22×D13—41no—
220C22×D13—41no—
221C22×D13—41no—
222C22×D13—41no—
223C2×C4×C13—21no—
224C2×C4×C13—21no—
225C2×C4×C13—21no—
226C2×C4×C13—21no—
227C2×C4×C13—21no—
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×C13C4×D412yes—
240C2×C4×C13C4×D412yes—
241C2×C4×C13C23×C411yescharacteristic
242C2×C4×C13C2×#4111yescharacteristic
243C2×C4×C13C2×#4111yescharacteristic
244C2×C4×C13C2×#4111yescharacteristic
245C2×C4×C13C2×#4111yescharacteristic
246C2×C4×C13C2×#4111yescharacteristic
247C2×Dic13—22no—
248C2×Dic13—22no—
249C2×Dic13—22no—
250C2×Dic13—41no—
251C2×Dic13—41no—
252C2×Dic13—41no—
253C2×Dic13—41no—
254C2×Dic13—41no—
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—
268D52—22no—
269D52—22no—
270D52—41no—
271D52—41no—
272C4×D13—84no—
273Dic26—22no—
274Dic26—22no—
275Dic26—41no—
276Dic26—41no—
277C8×C13—22no—
278C8×C13—22no—
279C8×C13—22no—
280C8×C13#11714yes—
281C22×SD16—131no—
282C2×C4×Q8—131no—
283C2×C4×D4—131no—
284#440—138no—
285C2×#107—131no—
286C2×#107—131no—
287C2×#106—131no—
288C2×#103—131no—
289C2×#103—131no—
290C2×#103—131no—
291C2×#102—131no—
292C2×#102—131no—
293C2×#102—131no—
294C2×#97C2×D1311yescharacteristic
295C2×#97C2×D1311yescharacteristic
296C2×#97C2×D1311yescharacteristic
297C2×C4×C8C2×D1311yescharacteristic
298C2×C4×C8C2×D1311yescharacteristic
299C2×C4×C8C2×D1311yescharacteristic
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#376C2×D1311yescharacteristic
319#340—131no—
320#340—131no—
321#340—131no—
322#340—131no—
323#340—131no—
324#340—131no—
325C22×C13C2×C4×D411yescharacteristic
326C22×C13#53211yescharacteristic
327C22×C13#53211yescharacteristic
328C22×C13#57611yescharacteristic
329C22×C13#57711yescharacteristic
330C22×C13#57711yescharacteristic
331C22×C13#57811yescharacteristic
332C2×D13—42no—
333C2×D13—42no—
334C2×D13—42no—
335C2×D13—81no—
336C2×D13—81no—
337C2×D13—81no—
338C2×D13—81no—
339C4×C13—22no—
340C4×C13—22no—
341C4×C13—41no—
342C4×C13—41no—
343C4×C13—41no—
344C4×C13—41no—
345C4×C13C2×#11711yescharacteristic
346C4×C13C4×#4111yescharacteristic
347C4×C13#52911yescharacteristic
348C4×C13#52911yescharacteristic
349Dic13—42no—
350Dic13—42no—
351Dic13—42no—
352Dic13—81no—
353Dic13—81no—
354Dic13—81no—
355Dic13—81no—
356C22×Q8—131no—
357C22×D4—131no—
358C23×C4—261no—
359C2×SD16—134no—
360C2×SD16—262no—
361C2×SD16—262no—
362C22×C8C22×D1311yescharacteristic
363C22×C8C22×D1311yescharacteristic
364C22×C8C22×D1311yescharacteristic
365C22×C8C22×D1311yescharacteristic
366C4×Q8—134no—
367C4×Q8—262no—
368C4×D4—134no—
369C4×D4—262no—
370C2×C4⋊C4—131no—
371C2×C4⋊C4—131no—
372C2×C4⋊C4—131no—
373C2×C4⋊C4—131no—
374C2×C4⋊C4—131no—
375C2×C4⋊C4—131no—
376C2×C4⋊C4—261no—
377C2×C4⋊C4—261no—
378C2×C4⋊C4—261no—
379C2×C4⋊C4—261no—
380C2×C4⋊C4—261no—
381C2×C22⋊C4—261no—
382C2×C22⋊C4—261no—
383C2×C22⋊C4—261no—
384C2×C22⋊C4—261no—
385C2×C22⋊C4—261no—
386C2×C42—261no—
387C2×C42—261no—
388C2×C42—261no—
389C2×C42C22×D1311yescharacteristic
390C2×C42C22×D1311yescharacteristic
391C2×C42C22×D1311yescharacteristic
392#107—134no—
393#107—262no—
394#106—262no—
395#103—134no—
396#103—262no—
397#103—262no—
398#102—134no—
399#102—262no—
400#102—262no—
401#97—22no—
402#97—22no—
403#97C4×D1314yes—
404C4×C8—22no—
405C4×C8—22no—
406C4×C8—22no—
407#95—261no—
408#95—261no—
409#95—261no—
410#95—261no—
411#95—261no—
412#95—261no—
413#95—261no—
414#95—261no—
415#95—261no—
416#95—261no—
417#95D5211yescharacteristic
418#95D5211yescharacteristic
419#95D5211yescharacteristic
420#95D5211yescharacteristic
421C2×C13#229311yescharacteristic
422C2×C13#294611yescharacteristic
423C2×C13#294711yescharacteristic
424C2×C13#317411yescharacteristic
425C2×C13#317511yescharacteristic
426C2×C13#317811yescharacteristic
427C2×C13#317911yescharacteristic
428D13—82no—
429C24—261no—
430C2×Q8—132no—
431C2×Q8—261no—
432C2×Q8—261no—
433C2×Q8—261no—
434C2×Q8—261no—
435C2×Q8—261no—
436C2×D4—132no—
437C2×D4—261no—
438C2×D4—261no—
439C2×D4—261no—
440C2×D4—261no—
441C2×D4—261no—
442C22×C4—261no—
443C22×C4—261no—
444C22×C4—261no—
445C22×C4—264no—
446C22×C4—261no—
447C22×C4—261no—
448C22×C4—261no—
449C22×C4—261no—
450C22×C4—1041no—
451C22×C4—1041no—
452C22×C4C2×D5211yescharacteristic
453C22×C4C2×D5211yescharacteristic
454C22×C4C2×D5211yescharacteristic
455C22×C4C2×D5211yescharacteristic
456C22×C4C2×D5211yescharacteristic
457C22×C4C2×D5211yescharacteristic
458C22×C4C23×D1311yescharacteristic
459SD16—268no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8C2×C4×D1312yes—
467C2×C8C2×C4×D1312yes—
468C2×C8#612712yes—
469C2×C8#612712yes—
470C2×C8#612712yes—
471C2×C8#612712yes—
472C4⋊C4—132no—
473C4⋊C4—132no—
474C4⋊C4—264no—
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—261no—
484C4⋊C4—261no—
485C4⋊C4—1041no—
486C4⋊C4—1041no—
487C4⋊C4—1041no—
488C4⋊C4—1041no—
489C22⋊C4—264no—
490C22⋊C4—1041no—
491C22⋊C4—1041no—
492C22⋊C4—1041no—
493C22⋊C4—1041no—
494C42—21no—
495C42—21no—
496C42—21no—
497C42—21no—
498C42—264no—
499C42—1041no—
500C42—1041no—
501C42C2×C4×D1312yes—
502C42#612712yes—
503C13#2129111yescharacteristic, complemented, Sylow
504C23—262no—
505C23—521no—
506C23—521no—
507C23—521no—
508C23—521no—
509C23—521no—
510C23—521no—
511C23C22×D5211yescharacteristic
512Q8—262no—
513Q8—262no—
514Q8—521no—
515Q8—521no—
516D4—262no—
517D4—262no—
518D4—521no—
519D4—521no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—262no—
537C2×C4—262no—
538C2×C4—262no—
539C2×C4—521no—
540C2×C4—521no—
541C2×C4—521no—
542C2×C4—521no—
543C2×C4—521no—
544C2×C4—521no—
545C2×C4—521no—
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—1044no—
558C2×C4C4×D5212yes—
559C2×C4C4×D5212yes—
560C2×C4C22×C4×D1311yescharacteristic
561C2×C4C2×#612711yescharacteristic
562C2×C4C2×#612711yescharacteristic
563C2×C4C2×#612711yescharacteristic
564C2×C4C2×#612711yescharacteristic
565C2×C4C2×#612711yescharacteristic
566C8—22no—
567C8—22no—
568C8—22no—
569C8#8812614yes—
570C22—522no—
571C22—522no—
572C22—522no—
573C22—1041no—
574C22—1041no—
575C22—1041no—
576C22—1041no—
577C22C2×C4×D5211yescharacteristic
578C22#1171918211yescharacteristic
579C22#1171918211yescharacteristic
580C22#1171945611yescharacteristic
581C22#1171945611yescharacteristic
582C22#1171945711yescharacteristic
583C22#1171945811yescharacteristic
584C4—22no—
585C4—22no—
586C4—41no—
587C4—41no—
588C4—41no—
589C4—41no—
590C4—522no—
591C4—522no—
592C4—522no—
593C4—1041no—
594C4—1041no—
595C4—1041no—
596C4—1041no—
597C4C2×#8812611yescharacteristic
598C4C4×#612711yescharacteristic
599C4#1171918411yescharacteristic
600C4#1171918411yescharacteristic
601C2—1042no—
602C2#1311730011yescharacteristic
603C2#1312367011yescharacteristic
604C2#1312368111yescharacteristic
605C2#1312546411yescharacteristic
606C2#1312547511yescharacteristic
607C2#1312550411yescharacteristic
608C2#1312551911yescharacteristic
subgroupG/H
centerC23C22×D52
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1726C2
socleC23×C13C22×D4
prime radicalC22×D52C23
cosocleC22×C4×C13C24
hypercenter#1726D13
hypocenterC13#21291
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ #376 ◁ #1726

Complements

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

NH ≅ G/Ntype
2. #13117488C2semidirect
6. #13115574C2semidirect
7. #13115569C2semidirect
9. #13115526C2semidirect
11. #13115512C2semidirect
12. #13114733C2semidirect
13. C4×#88056C2semidirect
15. C13×#1726C2semidirect
45. #11718371C4semidirect
214. #1726D13semidirect
503. C13#21291semidirect

Maximal subgroups

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

subgroupindex
C2×#117183712
#131174882
#131174802
#131157172
#131156902
#131155742
#131155692
#131155332
#131155262
#131155192
#131155122
#131147332
C4×#880562
C4×#880612
C13×#17262
#2129113