Finite Group Databasebeta

← #15920586

Subgroups — #15920586

Order 3328.

774 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
1#13118532C211yesmaximal, characteristic
2#13117715C211yesmaximal, characteristic
3#13116396C211yesmaximal, characteristic, complemented
4#13116340C211yesmaximal, characteristic, complemented
5#13116335C211yesmaximal, characteristic, complemented
6#13116167C211yesmaximal, characteristic, complemented
7#13115786C211yesmaximal, characteristic, complemented
8#13115596C211yesmaximal, characteristic, complemented
9#13115416C211yesmaximal, characteristic, complemented
10#13115412C211yesmaximal, characteristic, complemented
11#13115013C211yesmaximal, characteristic
12#13114927C211yesmaximal, characteristic
13#13114859C211yesmaximal, characteristic
14C2×#11718121C211yesmaximal, characteristic
15C13×#1853C211yesmaximal, characteristic
16C22×C13×C4⋊C4C2211yescharacteristic
17C22×C4⋊Dic13C2211yescharacteristic
18C2×#88178—21no—
19C23×#1055C2211yescharacteristic
20C2×#88142C2211yescharacteristic
21C2×C13×#106C2211yescharacteristic
22C2×C13×#106C2211yescharacteristic
23C2×C13×C22⋊C8C2211yescharacteristic
24C13×#380C2211yescharacteristic
25#11718873C2211yescharacteristic
26#11718871—21no—
27C4×C22⋊Dic13C2211yescharacteristic
28C2×#88054C2211yescharacteristic
29C2×#88054C2211yescharacteristic
30#11718646C2211yescharacteristic
31#11718645—21no—
32#11718640—21no—
33#11718637C2211yescharacteristic
34C4⋊C4×Dic13C2211yescharacteristic
35C4⋊C4×Dic13C2211yescharacteristic
36#11718634C2211yescharacteristic
37#11718634C2211yescharacteristic
38#11718634C2211yescharacteristic
39C2×#88048C2211yescharacteristic
40C2×#88048C2211yescharacteristic
41#11718603—21no—
42C22⋊C4×Dic13—21no—
43#11718314—21no—
44#11718314—21no—
45C13×#340C2211yescharacteristic
46C13×#340C2211yescharacteristic
47#11718143C2211yescharacteristic
48#11718143C2211yescharacteristic
49#11718143C2211yescharacteristic
50#11718143C2211yescharacteristic
51#11718142C2211yescharacteristic
52#11718142C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59C23×C4×C13—21no—
60C23×C4×C13C2311yescharacteristic
61C23×Dic13—21no—
62C22×Dic26—21no—
63C22×C8×C13C2311yescharacteristic
64C22×C8×C13C2311yescharacteristic
65C2×C13×C4⋊C4—22no—
66C2×C13×C4⋊C4—21no—
67C2×C13×C4⋊C4—41no—
68C2×C13×C4⋊C4C2311yescharacteristic
69C2×C13×C4⋊C4C2311yescharacteristic
70C2×C13×C4⋊C4C2311yescharacteristic
71C2×C13×C4⋊C4C2311yescharacteristic
72C2×C13×C22⋊C4—21no—
73C2×C22⋊Dic13—21no—
74C2×C22⋊Dic13D411yescharacteristic
75C2×C22⋊Dic13D411yescharacteristic
76C2×C4⋊Dic13—21no—
77C2×C4⋊Dic13—22no—
78C2×C4⋊Dic13—21no—
79C2×C4⋊Dic13Q814yescomplemented
80C2×C4⋊Dic13C2311yescharacteristic
81C2×C4⋊Dic13C2311yescharacteristic
82C2×C4⋊Dic13C2311yescharacteristic
83C2×C4⋊Dic13C2311yescharacteristic
84#88178—44no—
85C2×#6101—21no—
86C2×#6101—21no—
87C2×#6101—21no—
88C2×#6101—21no—
89C2×#6101—21no—
90C2×#6101—21no—
91C2×C4×Dic13—21no—
92C2×C4×Dic13—21no—
93C2×C4×Dic13C2311yescharacteristic
94C2×C4×Dic13C2311yescharacteristic
95C22×#1055—22no—
96C22×#1055—22no—
97C22×#1055—41no—
98C22×#1055C2311yescharacteristic
99C22×#1055C2311yescharacteristic
100#88142—22no—
101#88142—41no—
102C13×#106—22no—
103C13×#106—41no—
104C13×C22⋊C8—22no—
105C13×#95—21no—
106#88071—21no—
107#88071—21no—
108#88071—21no—
109#88071—21no—
110#88071—21no—
111#88071—21no—
112#88071—21no—
113#88071D411yescharacteristic
114#88071D411yescharacteristic
115#88054—22no—
116#88054—41no—
117#88048—22no—
118#88048—41no—
119#25992—131nomaximal, Sylow
120C24×C13C2×D411yescharacteristic
121C22×C4×C13—21no—
122C22×C4×C13—21no—
123C22×C4×C13—21no—
124C22×C4×C13—21no—
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13—42no—
130C22×C4×C13—42no—
131C22×C4×C13—81no—
132C22×C4×C13C2×D411yescharacteristic
133C22×C4×C13C2×Q812yes—
134C22×C4×C13#4112yes—
135C22×C4×C13C2411yescharacteristic
136C22×Dic13—21no—
137C22×Dic13—21no—
138C22×Dic13—24no—
139C22×Dic13—21no—
140C22×Dic13—21no—
141C22×Dic13—81no—
142C22×Dic13—81no—
143C22×Dic13C2×D411yescharacteristic
144C22×Dic13C2×D411yescharacteristic
145C22×Dic13C2×D411yescharacteristic
146C22×Dic13C2×D411yescharacteristic
147C2×Dic26—42no—
148C2×Dic26—42no—
149C2×Dic26—81no—
150C2×C8×C13—21no—
151C2×C8×C13—21no—
152C2×C8×C13—21no—
153C2×C8×C13—21no—
154C2×C8×C13—21no—
155C2×C8×C13—21no—
156C13×C4⋊C4—21no—
157C13×C4⋊C4—21no—
158C13×C4⋊C4—21no—
159C13×C4⋊C4—21no—
160C13×C4⋊C4—21no—
161C13×C4⋊C4—21no—
162C13×C4⋊C4—21no—
163C13×C4⋊C4—42no—
164C13×C4⋊C4#4112yes—
165C13×C22⋊C4—42no—
166C22⋊Dic13—22no—
167C22⋊Dic13—42no—
168C22⋊Dic13SD1614yes—
169C4⋊Dic13—24no—
170C4⋊Dic13—21no—
171C4⋊Dic13—21no—
172C4⋊Dic13—21no—
173C4⋊Dic13—21no—
174C4⋊Dic13—21no—
175C4⋊Dic13—21no—
176C4⋊Dic13—42no—
177C4⋊Dic13C2×Q812yes—
178C4⋊Dic13C2×Q812yes—
179#6101—42no—
180#6101—42no—
181#6101—42no—
182#6101—81no—
183#6101—81no—
184#6101—81no—
185C4×Dic13—21no—
186C4×Dic13—21no—
187C4×Dic13—21no—
188C4×Dic13—21no—
189C4×Dic13—81no—
190C4×Dic13—81no—
191C2×#1055—21no—
192C2×#1055—21no—
193C2×#1055—21no—
194C2×#1055—21no—
195C2×#1055—21no—
196C2×#1055—44no—
197C2×#1055#4112yes—
198#2440—131no—
199#2345—131no—
200#2099—131no—
201#2088—131no—
202#2088—131no—
203#2058—131no—
204#1988—131no—
205#1948—131no—
206#1919—131no—
207#1919—131no—
208#1853D1311yescharacteristic
209#1850—131no—
210#1824—131no—
211#1807—131no—
212C2×#340—131no—
213C23×C13—21no—
214C23×C13—21no—
215C23×C13—21no—
216C23×C13—21no—
217C23×C13C22⋊Q812yes—
218C23×C13C2×SD1612yes—
219C23×C13#13712yes—
220C23×C13C22×D411yescharacteristic
221C2×C4×C13—21no—
222C2×C4×C13—21no—
223C2×C4×C13—22no—
224C2×C4×C13—22no—
225C2×C4×C13—22no—
226C2×C4×C13—22no—
227C2×C4×C13—22no—
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×C13—41no—
237C2×C4×C13—41no—
238C2×C4×C13—41no—
239C2×C4×C13—84no—
240C2×C4×C13C22⋊Q812yes—
241C2×C4×C13C22×Q811yescharacteristic
242C2×C4×C13C2×#4111yescharacteristic
243C2×C4×C13C2×#4111yescharacteristic
244C2×C4×C13C2×#4111yescharacteristic
245C2×C4×C13H(5,𝔽2)11yescharacteristic
246C2×C4×C132−1+411yescharacteristic
247C2×Dic13—21no—
248C2×Dic13—21no—
249C2×Dic13—21no—
250C2×Dic13—21no—
251C2×Dic13—22no—
252C2×Dic13—22no—
253C2×Dic13—21no—
254C2×Dic13—21no—
255C2×Dic13—21no—
256C2×Dic13—21no—
257C2×Dic13—21no—
258C2×Dic13—21no—
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—84no—
270C2×Dic13C2×SD1612yes—
271C2×Dic13C2×SD1612yes—
272Dic26—84no—
273C8×C13—41no—
274C8×C13—41no—
275#1055—22no—
276#1055—41no—
277C23×C8—131no—
278C2×C4⋊Q8—131no—
279C2×C22⋊Q8—261no—
280C22×C4⋊C4—131no—
281C22×C4⋊C4C2×D1311yescharacteristic
282C2×#106—131no—
283C2×#106—131no—
284C2×#106C2×D1311yescharacteristic
285C2×#106C2×D1311yescharacteristic
286C2×C4⋊C8—131no—
287C2×C4⋊C8—131no—
288C2×C22⋊C8C2×D1311yescharacteristic
289#398—261no—
290#395—261no—
291#389—131no—
292#389—131no—
293#389—131no—
294#389—131no—
295#387—261no—
296#387—261no—
297#385—261no—
298#384—131no—
299#380—131no—
300#380—261no—
301#380C2×D1311yescharacteristic
302C4×C4⋊C4—131no—
303C4×C4⋊C4—131no—
304C4×C22⋊C4—131no—
305C4×C22⋊C4—261no—
306#340—131no—
307#340—131no—
308#340—131no—
309#340—131no—
310#340—131no—
311#340—131no—
312#340—131no—
313#340—131no—
314#340—131no—
315#340—131no—
316#340C2×D1311yescharacteristic
317#340C2×D1311yescharacteristic
318#336—131no—
319#336—131no—
320C22×C13—22no—
321C22×C13—22no—
322C22×C13—22no—
323C22×C13—22no—
324C22×C13—22no—
325C22×C13—22no—
326C22×C13#47514yes—
327C22×C13C2×C22⋊Q811yescharacteristic
328C22×C13#54611yescharacteristic
329C22×C13#54711yescharacteristic
330C22×C13C22×SD1611yescharacteristic
331C22×C13C2×#13711yescharacteristic
332C22×C13#57611yescharacteristic
333C22×C13#57711yescharacteristic
334C4×C13—22no—
335C4×C13—42no—
336C4×C13—81no—
337C4×C13—81no—
338C4×C13—81no—
339C4×C13#53311yescharacteristic
340C4×C13#54411yescharacteristic
341C4×C13#55111yescharacteristic
342C4×C13#55211yescharacteristic
343Dic13—22no—
344Dic13—22no—
345Dic13—42no—
346Dic13—42no—
347Dic13—41no—
348Dic13—41no—
349Dic13—81no—
350Dic13—81no—
351C22×Q8—261no—
352C23×C4—21no—
353C23×C4—261no—
354C23×C4C22×D1311yescharacteristic
355C22×C8—131no—
356C22×C8—131no—
357C22×C8—262no—
358C22×C8—262no—
359C22×C8—521no—
360C22×C8C22×D1311yescharacteristic
361C22×C8C22×D1311yescharacteristic
362C4⋊Q8—262no—
363C4⋊Q8—521no—
364C22⋊Q8—524no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—41no—
368C2×C4⋊C4—134no—
369C2×C4⋊C4—131no—
370C2×C4⋊C4—131no—
371C2×C4⋊C4—131no—
372C2×C4⋊C4—131no—
373C2×C4⋊C4—262no—
374C2×C4⋊C4—261no—
375C2×C4⋊C4—261no—
376C2×C4⋊C4—261no—
377C2×C4⋊C4—261no—
378C2×C4⋊C4—261no—
379C2×C4⋊C4—261no—
380C2×C4⋊C4—261no—
381C2×C4⋊C4—261no—
382C2×C4⋊C4C22×D1311yescharacteristic
383C2×C4⋊C4C22×D1311yescharacteristic
384C2×C4⋊C4C22×D1311yescharacteristic
385C2×C4⋊C4C22×D1311yescharacteristic
386C2×C22⋊C4—21no—
387C2×C22⋊C4—131no—
388C2×C22⋊C4—131no—
389C2×C22⋊C4—261no—
390C2×C42—131no—
391C2×C42—131no—
392C2×C42—261no—
393C2×C42—261no—
394#106—22no—
395#106—41no—
396#106—262no—
397#106—521no—
398C4⋊C8—262no—
399C4⋊C8—521no—
400C22⋊C8—22no—
401#95—21no—
402#95—131no—
403#95—131no—
404#95—261no—
405#95—261no—
406#95—261no—
407#95—261no—
408#95—261no—
409#95—261no—
410#95—261no—
411C2×C13—24no—
412C2×C13#243811yescharacteristic
413C2×C13C2×#47511yescharacteristic
414C2×C13#308111yescharacteristic
415C2×C13#329511yescharacteristic
416C2×C13#332011yescharacteristic
417C2×C13#333511yescharacteristic
418C2×C13#334611yescharacteristic
419C24D4×D1311yescharacteristic
420C2×Q8—522no—
421C2×Q8—522no—
422C2×Q8—1041no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—42no—
432C22×C4—42no—
433C22×C4—81no—
434C22×C4—131no—
435C22×C4—131no—
436C22×C4—131no—
437C22×C4—131no—
438C22×C4—261no—
439C22×C4—261no—
440C22×C4—264no—
441C22×C4—261no—
442C22×C4—261no—
443C22×C4—1041no—
444C22×C4—1041no—
445C22×C4#612712yes—
446C22×C4D4×D1311yescharacteristic
447C22×C4Q8×D1312yes—
448C22×C4C23×D1311yescharacteristic
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—132no—
456C2×C8—261no—
457C2×C8—261no—
458C2×C8—261no—
459C2×C8—261no—
460C2×C8—261no—
461C2×C8—524no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—42no—
470C4⋊C4—132no—
471C4⋊C4—132no—
472C4⋊C4—264no—
473C4⋊C4—261no—
474C4⋊C4—261no—
475C4⋊C4—261no—
476C4⋊C4—261no—
477C4⋊C4—261no—
478C4⋊C4—261no—
479C4⋊C4—522no—
480C4⋊C4—522no—
481C4⋊C4—522no—
482C4⋊C4—522no—
483C4⋊C4—1041no—
484C4⋊C4—1041no—
485C4⋊C4—1041no—
486C4⋊C4#612912yes—
487C22⋊C4—42no—
488C22⋊C4—134no—
489C22⋊C4—262no—
490C22⋊C4—522no—
491C42—261no—
492C42—261no—
493C42—261no—
494C42—261no—
495C42—1041no—
496C42—1041no—
497C13#2599211yescharacteristic, complemented, Sylow
498C23—21no—
499C23—21no—
500C23—21no—
501C23—21no—
502C23#8815012yes—
503C23SD16×D1312yes—
504C23#8816912yes—
505C23C2×D4×D1311yescharacteristic
506Q8—1044no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—84no—
526C2×C4—132no—
527C2×C4—132no—
528C2×C4—261no—
529C2×C4—261no—
530C2×C4—261no—
531C2×C4—261no—
532C2×C4—261no—
533C2×C4—261no—
534C2×C4—262no—
535C2×C4—262no—
536C2×C4—261no—
537C2×C4—261no—
538C2×C4—261no—
539C2×C4—261no—
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—1044no—
551C2×C4#8815012yes—
552C2×C4C2×#612711yescharacteristic
553C2×C4C2×#612911yescharacteristic
554C2×C4#8825111yescharacteristic
555C2×C4C2×Q8×D1311yescharacteristic
556C2×C4#41×D1311yescharacteristic
557C2×C4#8825711yescharacteristic
558C8—41no—
559C8—41no—
560C8—262no—
561C8—521no—
562C22—22no—
563C22—22no—
564C22—22no—
565C22—22no—
566C22—22no—
567C22—22no—
568C22#1171851514yes—
569C22C2×#8815011yescharacteristic
570C22#1171929611yescharacteristic
571C22#1171936011yescharacteristic
572C22C2×SD16×D1311yescharacteristic
573C22C2×#8816911yescharacteristic
574C22#1171947911yescharacteristic
575C22#1171948311yescharacteristic
576C4—22no—
577C4—42no—
578C4—81no—
579C4—81no—
580C4—81no—
581C4—262no—
582C4—262no—
583C4—522no—
584C4—522no—
585C4—521no—
586C4—521no—
587C4—1041no—
588C4—1041no—
589C4#1171924611yescharacteristic
590C4#1171926111yescharacteristic
591C4#1171932711yescharacteristic
592C4#1171932811yescharacteristic
593C2—24no—
594C2#1311851611yescharacteristic
595C2C2×#1171851511yescharacteristic
596C2#1312466511yescharacteristic
597C2#1312665311yescharacteristic
598C2#1312701111yescharacteristic
599C2#1312718611yescharacteristic
600C2#1312731911yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#1853C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
hypercenter#1853D13
hypocenterC13#25992
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1853

Complements

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

NH ≅ G/Ntype
3. #13116396C2semidirect
4. #13116340C2semidirect
5. #13116335C2semidirect
6. #13116167C2semidirect
7. #13115786C2semidirect
8. #13115596C2semidirect
9. #13115416C2semidirect
10. #13115412C2semidirect
79. C2×C4⋊Dic13Q8semidirect
497. C13#25992semidirect

Maximal subgroups

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

subgroupindex
#131185322
#131177152
#131163962
#131163402
#131163352
#131161672
#131157862
#131155962
#131154162
#131154122
#131150132
#131149272
#131148592
C2×#117181212
C13×#18532
#2599213