Finite Group Databasebeta

← #15873448

Subgroups — #15873448

Order 3328.

834 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718494C211yesmaximal, characteristic
2#13117232C211yesmaximal, characteristic
3D13×#382C211yesmaximal, characteristic
4#13115606C211yesmaximal, characteristic, complemented
5#13115604C211yesmaximal, characteristic, complemented
6#13115602C211yesmaximal, characteristic, complemented
7#13115030C211yesmaximal, characteristic
8#13115027C211yesmaximal, characteristic
9#13115025C211yesmaximal, characteristic
10#13115022C211yesmaximal, characteristic
11#13114999C211yesmaximal, characteristic, complemented
12#13114997C211yesmaximal, characteristic, complemented
13#13114965C211yesmaximal, characteristic, complemented
14#13114965C211yesmaximal, characteristic, complemented
15C13×#1949C211yesmaximal, characteristic, complemented
16C2×C4⋊C4×D13C2211yescharacteristic
17C2×C4⋊C4×D13C2211yescharacteristic
18C2×C42×D13C2211yescharacteristic
19C2×C13×#107C2211yescharacteristic
20C2×C13×#106C2211yescharacteristic
21C2×C13×C4⋊C8C2211yescharacteristic
22C13×#382C2211yescharacteristic
23C4×C13×C4⋊C4C2211yescharacteristic
24C2×#88060C2211yescharacteristic
25C2×#88060C2211yescharacteristic
26C2×#88058C2211yescharacteristic
27C2×#88057C2211yescharacteristic
28C2×C8×Dic13C2211yescharacteristic
29C2×C8×Dic13C2211yescharacteristic
30#11718648C2211yescharacteristic
31#11718648C2211yescharacteristic
32#11718638C2211yescharacteristic
33#11718638C2211yescharacteristic
34#11718638C2211yescharacteristic
35#11718638C2211yescharacteristic
36C2×#88048C2211yescharacteristic
37C2×#88048C2211yescharacteristic
38C2×#88047C2211yescharacteristic
39C2×#88047C2211yescharacteristic
40C4×#6103—21no—
41#11718597C2211yescharacteristic
42C4×C4⋊Dic13C2211yescharacteristic
43#11718593—21no—
44C2×C4⋊#1055C2211yescharacteristic
45#11718494C418yescomplemented
46#11718325—21no—
47D13×#95—21no—
48D13×#95—21no—
49#11718312—21no—
50#11718311—21no—
51#11718311—21no—
52C13×#340C2211yescharacteristic
53C13×#340C2211yescharacteristic
54#11718143C2211yescharacteristic
55#11718143C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60C22×C4×D13—21no—
61C22×C4×D13—21no—
62C22×C4×D13D411yescharacteristic
63C22×C4×D13D411yescharacteristic
64C22×C4×D13C2311yescharacteristic
65C22×C8×C13C2311yescharacteristic
66C22×C8×C13C2311yescharacteristic
67C2×C13×C4⋊C4C2311yescharacteristic
68C2×C13×C4⋊C4C2311yescharacteristic
69C2×C13×C4⋊C4C2311yescharacteristic
70C2×C13×C4⋊C4C2311yescharacteristic
71C2×C42×C13—21no—
72C2×C42×C13C2311yescharacteristic
73C2×#6103—21no—
74C2×#6103—21no—
75C2×C4⋊Dic13C2311yescharacteristic
76C2×C4⋊Dic13C2311yescharacteristic
77C2×C4⋊Dic13C2311yescharacteristic
78C2×C4⋊Dic13C2311yescharacteristic
79C2×#6101—21no—
80C2×#6101—21no—
81C2×C4×Dic13—21no—
82C2×C4×Dic13D411yescharacteristic
83C2×C4×Dic13D411yescharacteristic
84C2×C4×Dic13C2311yescharacteristic
85C22×#1055C2311yescharacteristic
86C22×#1055C2311yescharacteristic
87C4⋊C4×D13—41no—
88C4⋊C4×D13—41no—
89C4⋊C4×D13—41no—
90C4⋊C4×D13—41no—
91C42×D13C2×C414yes—
92C42×D13Q814yes—
93C13×#107—41no—
94C13×#106—41no—
95C13×C4⋊C8C2×C414yescomplemented
96C13×#95—21no—
97C13×#95—21no—
98C13×#95—21no—
99#88071—21no—
100#88071—21no—
101#88071—21no—
102#88071—21no—
103#88071—21no—
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#88060C2×C414yes—
113#88060C2×C414yes—
114#88058—41no—
115#88057—41no—
116C8×Dic13C2×C414yescomplemented
117C8×Dic13C2×C414yescomplemented
118#88048—41no—
119#88048—41no—
120#88047—41no—
121#88047—41no—
122C4⋊#1055C2×C414yescomplemented
123#21983—131nomaximal, Sylow
124C23×D13C2×D411yescharacteristic
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13C2×D411yescharacteristic
130C22×C4×C13C2×D411yescharacteristic
131C22×C4×C13C2411yescharacteristic
132C22×Dic13—21no—
133C22×Dic13—21no—
134C22×Dic13—21no—
135C22×Dic13—21no—
136C22×Dic13C2×D411yescharacteristic
137C22×Dic13C2×D411yescharacteristic
138C22×Dic13C2×D411yescharacteristic
139C2×C4×D13—22no—
140C2×C4×D13—22no—
141C2×C4×D13—21no—
142C2×C4×D13—21no—
143C2×C4×D13—21no—
144C2×C4×D13—21no—
145C2×C4×D13—41no—
146C2×C4×D13—41no—
147C2×C4×D13—42no—
148C2×C4×D13—42no—
149C2×C4×D13—42no—
150C2×C4×D13—42no—
151C2×C4×D13—42no—
152C2×C4×D13—42no—
153C2×C4×D13C4⋊C414yes—
154C2×C4×D13C4⋊C414yes—
155C2×C4×D13C22×C412yes—
156C2×C4×D13C2×Q812yes—
157C2×C8×C13—21no—
158C2×C8×C13—21no—
159C2×C8×C13—21no—
160C2×C8×C13—21no—
161C2×C8×C13C22×C412yes—
162C2×C8×C13C22×C412yes—
163C13×C4⋊C4—21no—
164C13×C4⋊C4—21no—
165C13×C4⋊C4—21no—
166C13×C4⋊C4—21no—
167C13×C4⋊C4—21no—
168C13×C4⋊C4—21no—
169C13×C4⋊C4—21no—
170C13×C4⋊C4—21no—
171C42×C13—42no—
172C42×C13C22×C412yes—
173C42×C13C2×Q812yes—
174#6103—42no—
175#6103—42no—
176C4⋊Dic13—21no—
177C4⋊Dic13—21no—
178C4⋊Dic13—21no—
179C4⋊Dic13—21no—
180C4⋊Dic13—21no—
181C4⋊Dic13—21no—
182C4⋊Dic13—21no—
183C4⋊Dic13—21no—
184#6101—42no—
185#6101—42no—
186C4×Dic13—42no—
187C4×Dic13C4⋊C414yes—
188C4×Dic13C4⋊C414yes—
189C4×Dic13C22×C412yes—
190C4×Dic13C2×Q812yes—
191C2×#1055—21no—
192C2×#1055—21no—
193C2×#1055—21no—
194C2×#1055—21no—
195C2×#1055C22×C412yes—
196C2×#1055C22×C412yes—
197C2×#431—131no—
198#2283—131no—
199C2×#382—131no—
200#1949—131no—
201#1949—131no—
202#1949—131no—
203#1949D1311yescharacteristic, complemented
204#1853—131no—
205#1853—131no—
206#1852—131no—
207#1852—131no—
208#1846—131no—
209#1846—131no—
210#1835—131no—
211#1835—131no—
212C23×C13C22×D411yescharacteristic
213C22×D13—21no—
214C22×D13—21no—
215C22×D13—21no—
216C22×D13—21no—
217C22×D13C2×C4⋊C412yes—
218C22×D13#13512yes—
219C22×D13#13512yes—
220C2×C4×C13—21no—
221C2×C4×C13—21no—
222C2×C4×C13—21no—
223C2×C4×C13—21no—
224C2×C4×C13—41no—
225C2×C4×C13—41no—
226C2×C4×C13—41no—
227C2×C4×C13—41no—
228C2×C4×C13—41no—
229C2×C4×C13—41no—
230C2×C4×C13—41no—
231C2×C4×C13—41no—
232C2×C4×C13—41no—
233C2×C4×C13—41no—
234C2×C4×C13—41no—
235C2×C4×C13—41no—
236C2×C4×C13C2×C4⋊C412yes—
237C2×C4×C13C2×C4⋊C412yes—
238C2×C4×C13C23×C411yescharacteristic
239C2×C4×C13C22×Q811yescharacteristic
240C2×C4×C13H(5,𝔽2)11yescharacteristic
241C2×C4×C13H(5,𝔽2)11yescharacteristic
242C2×C4×C132−1+411yescharacteristic
243C2×C4×C132−1+411yescharacteristic
244C2×Dic13—21no—
245C2×Dic13—21no—
246C2×Dic13—21no—
247C2×Dic13—21no—
248C2×Dic13—21no—
249C2×Dic13—21no—
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×Dic13C2×C4⋊C412yes—
263C2×Dic13C2×C4⋊C412yes—
264C2×Dic13C2×C4⋊C412yes—
265C4×D13—28no—
266C4×D13—22no—
267C4×D13—22no—
268C4×D13—22no—
269C4×D13—22no—
270C4×D13—44no—
271C4×D13—84no—
272C4×D13—84no—
273C8×C13—22no—
274C8×C13—22no—
275#1055—22no—
276#1055—22no—
277C22×C4⋊C4—131no—
278C22×C4⋊C4—131no—
279C22×C42—131no—
280#431—138no—
281C2×#107—131no—
282C2×#107—131no—
283C2×#107—131no—
284C2×#107C2×D1311yescharacteristic
285C2×#106—131no—
286C2×#106—131no—
287C2×#106—131no—
288C2×#106C2×D1311yescharacteristic
289C2×C4⋊C8—131no—
290C2×C4⋊C8C2×D1311yescharacteristic
291C2×C22⋊C8—131no—
292C2×C22⋊C8—131no—
293C2×C4×C8—131no—
294C2×C4×C8—131no—
295#383—261no—
296#382—131no—
297#382—131no—
298#382—131no—
299#382—131no—
300#382—131no—
301#382—261no—
302#382—261no—
303#382C2×D1311yescharacteristic
304#381—261no—
305#380—131no—
306#380—131no—
307C4×C4⋊C4—131no—
308C4×C4⋊C4C2×D1311yescharacteristic
309C4×C22⋊C4—261no—
310#376—261no—
311C2×#95—261no—
312C2×#95—261no—
313#340—131no—
314#340—131no—
315#340—131no—
316#340—131no—
317#340—131no—
318#340—131no—
319#340C2×D1311yescharacteristic
320#340C2×D1311yescharacteristic
321C22×C13C22×C4⋊C411yescharacteristic
322C22×C13#53511yescharacteristic
323C22×C13#53611yescharacteristic
324C22×C13C2×#13511yescharacteristic
325C22×C13C2×#13511yescharacteristic
326C22×C13#57511yescharacteristic
327C22×C13#57511yescharacteristic
328C2×D13—22no—
329C2×D13—22no—
330C2×D13—22no—
331C2×D13—22no—
332C2×D13—22no—
333C2×D13—22no—
334C2×D13#42714yes—
335C4×C13—22no—
336C4×C13—22no—
337C4×C13—81no—
338C4×C13—81no—
339C4×C13—81no—
340C4×C13—81no—
341C4×C13#52011yescharacteristic
342C4×C13#52011yescharacteristic
343C4×C13#54411yescharacteristic
344C4×C13#54411yescharacteristic
345Dic13—22no—
346Dic13—22no—
347Dic13—22no—
348Dic13—81no—
349Dic13—81no—
350Dic13—81no—
351Dic13—81no—
352C23×C4—131no—
353C23×C4—131no—
354C23×C4—131no—
355C23×C4—261no—
356C23×C4—261no—
357C22×C8—131no—
358C22×C8—131no—
359C22×C8C22×D1311yescharacteristic
360C22×C8C22×D1311yescharacteristic
361C2×C4⋊C4—131no—
362C2×C4⋊C4—131no—
363C2×C4⋊C4—131no—
364C2×C4⋊C4—131no—
365C2×C4⋊C4—261no—
366C2×C4⋊C4—261no—
367C2×C4⋊C4—521no—
368C2×C4⋊C4—521no—
369C2×C4⋊C4—521no—
370C2×C4⋊C4—521no—
371C2×C4⋊C4C22×D1311yescharacteristic
372C2×C4⋊C4C22×D1311yescharacteristic
373C2×C4⋊C4C22×D1311yescharacteristic
374C2×C4⋊C4C22×D1311yescharacteristic
375C2×C22⋊C4—261no—
376C2×C22⋊C4—261no—
377C2×C42—21no—
378C2×C42—131no—
379C2×C42—131no—
380C2×C42—131no—
381C2×C42—134no—
382C2×C42—134no—
383C2×C42—261no—
384C2×C42C22×D1311yescharacteristic
385#107—41no—
386#107—521no—
387#107—521no—
388#107—521no—
389#106—41no—
390#106—521no—
391#106—521no—
392#106—521no—
393C4⋊C8—134no—
394C4⋊C8C4×D1314yescomplemented
395C22⋊C8—134no—
396C22⋊C8—134no—
397C4×C8—134no—
398C4×C8—134no—
399#95—21no—
400#95—21no—
401#95—21no—
402#95—261no—
403#95—261no—
404#95—261no—
405#95—261no—
406#95—261no—
407#95—261no—
408#95—261no—
409#95—261no—
410#95—261no—
411#95—261no—
412#95—261no—
413#95—261no—
414#95—261no—
415C2×C13#231711yescharacteristic
416C2×C13C2×#42711yescharacteristic
417C2×C13#291111yescharacteristic
418C2×C13#321111yescharacteristic
419C2×C13#321111yescharacteristic
420C2×C13#323211yescharacteristic
421C2×C13#323211yescharacteristic
422D13—24no—
423C24—131no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—131no—
429C22×C4—131no—
430C22×C4—131no—
431C22×C4—134no—
432C22×C4—132no—
433C22×C4—132no—
434C22×C4—134no—
435C22×C4—262no—
436C22×C4—262no—
437C22×C4—261no—
438C22×C4—261no—
439C22×C4—261no—
440C22×C4—261no—
441C22×C4—261no—
442C22×C4—261no—
443C22×C4—261no—
444C22×C4—261no—
445C22×C4—521no—
446C22×C4—521no—
447C22×C4—522no—
448C22×C4—522no—
449C22×C4—522no—
450C22×C4—522no—
451C22×C4—522no—
452C22×C4—522no—
453C22×C4D4×D1311yescharacteristic
454C22×C4D4×D1311yescharacteristic
455C22×C4C23×D1311yescharacteristic
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—132no—
461C2×C8—132no—
462C2×C8—261no—
463C2×C8—261no—
464C2×C8—261no—
465C2×C8—261no—
466C2×C8C2×C4×D1312yes—
467C2×C8C2×C4×D1312yes—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
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—522no—
485C4⋊C4—522no—
486C22⋊C4—522no—
487C22⋊C4—522no—
488C42—42no—
489C42—134no—
490C42—134no—
491C42—132no—
492C42—132no—
493C42—522no—
494C42C2×C4×D1312yes—
495C42Q8×D1312yes—
496C13#2198311yescharacteristic, complemented, Sylow
497C23—132no—
498C23—132no—
499C23—132no—
500C23—261no—
501C23—261no—
502C23—261no—
503C23—261no—
504C23C2×D4×D1311yescharacteristic
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—132no—
522C2×C4—132no—
523C2×C4—132no—
524C2×C4—268no—
525C2×C4—261no—
526C2×C4—261no—
527C2×C4—261no—
528C2×C4—261no—
529C2×C4—261no—
530C2×C4—261no—
531C2×C4—262no—
532C2×C4—262no—
533C2×C4—262no—
534C2×C4—262no—
535C2×C4—524no—
536C2×C4—521no—
537C2×C4—521no—
538C2×C4—521no—
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—1044no—
549C2×C4—1044no—
550C2×C4C4⋊C4×D1312yes—
551C2×C4C4⋊C4×D1312yes—
552C2×C4C22×C4×D1311yescharacteristic
553C2×C4#8825111yescharacteristic
554C2×C4C2×Q8×D1311yescharacteristic
555C2×C4#8825411yescharacteristic
556C2×C4#8825611yescharacteristic
557C2×C4#8825711yescharacteristic
558C8—22no—
559C8—22no—
560C8—262no—
561C8—262no—
562C22—134no—
563C22—262no—
564C22—262no—
565C22—262no—
566C22—262no—
567C22—262no—
568C22—262no—
569C22C2×C4⋊C4×D1311yescharacteristic
570C22#1171931211yescharacteristic
571C22#1171933311yescharacteristic
572C22D13×#13511yescharacteristic
573C22D13×#13511yescharacteristic
574C22#1171947811yescharacteristic
575C22#1171948211yescharacteristic
576C4—22no—
577C4—22no—
578C4—81no—
579C4—81no—
580C4—81no—
581C4—81no—
582C4—262no—
583C4—262no—
584C4—262no—
585C4—1041no—
586C4—1041no—
587C4—1041no—
588C4—1041no—
589C4#1171925111yescharacteristic
590C4#1171927911yescharacteristic
591C4#1171939411yescharacteristic
592C4#1171943411yescharacteristic
593C2—264no—
594C2#1311745811yescharacteristic
595C2D13×#42711yescharacteristic
596C2#1312342311yescharacteristic
597C2#1312579911yescharacteristic
598C2#1312580511yescharacteristic
599C2#1312600211yescharacteristic
600C2#1312600811yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1949C2
socleC23×C13C22×D4
prime radicalC23×D13C2×D4
cosocleC22×C4×C13C24
hypercenter#1949D13
hypocenterC13#21983
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1949

Complements

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

NH ≅ G/Ntype
4. #13115606C2semidirect
5. #13115604C2semidirect
6. #13115602C2semidirect
11. #13114999C2semidirect
12. #13114997C2semidirect
13. #13114965C2semidirect
14. #13114965C2semidirect
15. C13×#1949C2semidirect
45. #11718494C4semidirect
95. C13×C4⋊C8C2×C4semidirect
116. C8×Dic13C2×C4semidirect
117. C8×Dic13C2×C4semidirect
122. C4⋊#1055C2×C4semidirect
203. #1949D13semidirect
394. C4⋊C8C4×D13semidirect
496. C13#21983semidirect

Maximal subgroups

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

subgroupindex
C2×#117184942
#131172322
D13×#3822
#131156062
#131156042
#131156022
#131150302
#131150272
#131150252
#131150222
#131149992
#131149972
#131149652
C13×#19492
#2198313