Finite Group Databasebeta

← #15834155

Subgroups — #15834155

Order 3328.

642 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124879C211yesmaximal, characteristic
2#13123996C211yesmaximal, characteristic, complemented
3#13123873C211yesmaximal, characteristic, complemented
4#13113747C211yesmaximal, characteristic, complemented
5#13113741C211yesmaximal, characteristic, complemented
6#13113676C211yesmaximal, characteristic, complemented
7#13113675C211yesmaximal, characteristic, complemented
8#13113668C211yesmaximal, characteristic, complemented
9#13113662C211yesmaximal, characteristic, complemented
10#13113657C211yesmaximal, characteristic, complemented
11#13113651C211yesmaximal, characteristic, complemented
12#13113622C211yesmaximal, characteristic, complemented
13C2×#11718051C211yesmaximal, characteristic, complemented
14#13113128C211yesmaximal, characteristic, complemented
15C13×#1494C211yesmaximal, characteristic, complemented
16C13×#529C2211yescharacteristic
17C2×C4×D52C2211yescharacteristic
18C13×#432C2211yescharacteristic
19C2×C4×C8×C13C2211yescharacteristic
20#11718727C411yescharacteristic
21#11718727C411yescharacteristic
22#11718718C411yescharacteristic
23#11718718C411yescharacteristic
24#11718707C411yescharacteristic
25#11718705C411yescharacteristic
26#11718697C411yescharacteristic
27#11718695C411yescharacteristic
28C4×#6106C2211yescharacteristic
29C4×#6106C2211yescharacteristic
30#11718685C2211yescharacteristic, complemented
31Q8×#1055C2211yescharacteristic, complemented
32C4×#6104C2211yescharacteristic
33C4×#6104C2211yescharacteristic
34#11718673C2211yescharacteristic, complemented
35#11718672—21no—
36D4×#1055—21no—
37D4×#1055C2211yescharacteristic, complemented
38#11718661—21no—
39#11718660—21no—
40#11718586C2211yescharacteristic
41#11718586C2211yescharacteristic
42C2×C4⋊#1055C2211yescharacteristic
43#11718499C2211yescharacteristic
44#11718499C2211yescharacteristic
45#11718495C2211yescharacteristic
46#11718495C2211yescharacteristic
47#11718387—21no—
48D13×C22⋊C8—21no—
49#11718367—21no—
50#11718367—21no—
51C13×Q8⋊C8C2211yescharacteristic, complemented
52C13×Q8⋊C8C2211yescharacteristic, complemented
53C13×D4⋊C8C2211yescharacteristic, complemented
54C13×D4⋊C8C2211yescharacteristic, complemented
55#11718072C2211yescharacteristic, complemented
56#11718072C2211yescharacteristic, complemented
57#11718071C2211yescharacteristic, complemented
58#11718071C2211yescharacteristic, complemented
59#11718051C2211yescharacteristic
60#11718051C2211yescharacteristic
61#11718051C2211yescharacteristic
62#11718051C2211yescharacteristic
63#11718046C2211yescharacteristic, complemented
64#11718046C2211yescharacteristic, complemented
65#11718046C2211yescharacteristic, complemented
66#11718046C2211yescharacteristic, complemented
67C22×D52C2×C411yescharacteristic
68C22×C4×D13—21no—
69C22×C8×C13—21no—
70C13×#126—21no—
71C13×#125C2×C411yescharacteristic
72C13×#124C2×C411yescharacteristic
73C13×#123—21no—
74C13×C22⋊Q8C2×C411yescharacteristic
75C13×#121C2×C411yescharacteristic
76C4×Q8×C13C2311yescharacteristic
77C4×D4×C13—21no—
78C4×D4×C13C2311yescharacteristic
79C13×#117—21no—
80C2×C42×C13C2311yescharacteristic
81C2×#6106C2×C411yescharacteristic
82C2×#6106C2×C411yescharacteristic
83C2×#6104C2×C411yescharacteristic
84C2×#6104C2×C411yescharacteristic
85C2×#6103—21no—
86C2×C4⋊Dic13C2×C411yescharacteristic
87C2×#6099—21no—
88C22×#1055—21no—
89C22×#1055—21no—
90C2×#6094—21no—
91C2×#6094—21no—
92C2×C8×D13—21no—
93C2×C8×D13—21no—
94C4×D52—21no—
95C4×D52—21no—
96C4×D52C2×C411yescharacteristic
97C4×D52C2×C411yescharacteristic
98C4×D52C2311yescharacteristic
99C4×D52C2311yescharacteristic
100C13×C4⋊C8C2311yescharacteristic
101C13×C4⋊C8C2311yescharacteristic
102C13×C22⋊C8—21no—
103C13×#97—21no—
104C4×C8×C13—21no—
105C4×C8×C13C2311yescharacteristic
106C4×C8×C13C2311yescharacteristic
107#88075C2×C411yescharacteristic
108#88075C2×C411yescharacteristic
109#88072C2×C411yescharacteristic
110#88072C2×C411yescharacteristic
111C22⋊#1055—21no—
112C22⋊#1055—21no—
113C22⋊#1055C2×C411yescharacteristic
114C22⋊#1055C2×C411yescharacteristic
115C22⋊#1055D411yescharacteristic
116C22⋊#1055D411yescharacteristic
117#88060—21no—
118#88060—21no—
119#88060—21no—
120#88060—21no—
121#88049C2×C411yescharacteristic
122#88049C2×C411yescharacteristic
123#88049C2×C411yescharacteristic
124#88049C2×C411yescharacteristic
125#88048C2×C411yescharacteristic
126#88048C2×C411yescharacteristic
127#88047C2×C411yescharacteristic
128#88047C2×C411yescharacteristic
129C4⋊#1055—21no—
130C4⋊#1055—21no—
131C4⋊#1055—21no—
132C4⋊#1055C2×C411yescharacteristic
133C4⋊#1055C2×C411yescharacteristic
134C4⋊#1055D411yescharacteristic
135C4⋊#1055D411yescharacteristic
136C4⋊#1055C2311yescharacteristic
137C4⋊#1055C2311yescharacteristic
138#88043—21no—
139C4×#1055—21no—
140C4×#1055C2311yescharacteristic
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#18020—131nomaximal, Sylow
145C23×D13—21no—
146C2×Q8×C13C22×C411yescharacteristic
147C2×D4×C13—21no—
148C2×D4×C13C22×C411yescharacteristic
149C22×C4×C13—21no—
150C22×C4×C13C22×C411yescharacteristic
151C22×C4×C13C2×D411yescharacteristic
152C22×C4×C13#4111yescharacteristic
153C22×Dic13—21no—
154C2×D52—22no—
155C2×D52—21no—
156C2×D52—41no—
157C2×D52C22×C411yescharacteristic
158C2×D52C22×C411yescharacteristic
159C2×C4×D13—21no—
160C2×C4×D13—21no—
161C2×C4×D13—21no—
162C2×C4×D13—21no—
163C2×C4×D13—81no—
164C2×C4×D13—81no—
165C2×C8×C13—21no—
166C2×C8×C13—21no—
167C2×C8×C13—21no—
168C2×C8×C13—21no—
169C2×C8×C13—42no—
170C13×C4⋊C4—21no—
171C13×C4⋊C4—21no—
172C13×C4⋊C4—21no—
173C13×C4⋊C4—21no—
174C13×C4⋊C4C22×C411yescharacteristic
175C13×C4⋊C4C22×C411yescharacteristic
176C13×C22⋊C4—21no—
177C13×C22⋊C4—21no—
178C13×C22⋊C4—21no—
179C13×C22⋊C4—21no—
180C13×C22⋊C4—21no—
181C42×C13—21no—
182C42×C13C22×C411yescharacteristic
183C42×C13C2×D411yescharacteristic
184C42×C13#4111yescharacteristic
185C42×C13C2411yescharacteristic
186#6106—22no—
187#6106—41no—
188#6104—22no—
189#6104—41no—
190#6103—21no—
191#6103—21no—
192#6103—21no—
193#6103—21no—
194C4⋊Dic13—21no—
195C4⋊Dic13C22×C411yescharacteristic
196C4⋊Dic13C22×C411yescharacteristic
197#6099—81no—
198C2×#1055—21no—
199C2×#1055—21no—
200C2×#1055—81no—
201C2×#1055—81no—
202C2×#1055C22×C411yescharacteristic
203C2×#1055C22×C411yescharacteristic
204C2×#1055C22×C411yescharacteristic
205C2×#1055C22×C411yescharacteristic
206C2×#1055C2×D411yescharacteristic
207C2×#1055C2×D411yescharacteristic
208C2×#1055C2×D411yescharacteristic
209C2×#1055C2×D411yescharacteristic
210#6094—81no—
211#6094—81no—
212C8×D13—81no—
213C8×D13—81no—
214#3105—131no—
215#2994—131no—
216#2974—131no—
217#1594—131no—
218#1592—131no—
219#1583—131no—
220#1582—131no—
221#1581—131no—
222#1581—131no—
223#1580—131no—
224SD16⋊C8—131no—
225#1573—131no—
226#1494D1311yescharacteristic, complemented
227C2×D4⋊C8—131no—
228#1452—131no—
229C23×C13—21no—
230C23×C13C4×D411yescharacteristic
231C22×D13—21no—
232C22×D13—21no—
233C22×D13—42no—
234C22×D13—42no—
235C22×D13—81no—
236Q8×C13—21no—
237Q8×C13—21no—
238D4×C13—21no—
239D4×C13—21no—
240D4×C13—42no—
241C2×C4×C13—22no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—21no—
245C2×C4×C13—21no—
246C2×C4×C13—21no—
247C2×C4×C13—21no—
248C2×C4×C13—21no—
249C2×C4×C13—41no—
250C2×C4×C13—41no—
251C2×C4×C13C4×D411yescharacteristic
252C2×C4×C13C4×D411yescharacteristic
253C2×C4×C13C4×D411yescharacteristic
254C2×C4×C13C23×C411yescharacteristic
255C2×C4×C13C22×D411yescharacteristic
256C2×C4×C13C2×#4111yescharacteristic
257C2×Dic13—21no—
258C2×Dic13—21no—
259C2×Dic13—81no—
260D52—21no—
261D52—21no—
262D52—21no—
263D52—42no—
264D52#13112yes—
265C4×D13—41no—
266C4×D13—41no—
267C4×D13—41no—
268C4×D13—41no—
269C4×D13—81no—
270C4×D13—81no—
271C8×C13—41no—
272C8×C13—41no—
273C8×C13—41no—
274C8×C13—41no—
275#1055—21no—
276#1055—21no—
277#1055—21no—
278#1055—21no—
279#1055—21no—
280#1055—21no—
281#1055—21no—
282#1055—21no—
283#1055—41no—
284#1055—41no—
285#529C2×D1311yescharacteristic
286C2×C4×D4—131no—
287#484—131no—
288#481—131no—
289#478—131no—
290#478—131no—
291#463—131no—
292#463—131no—
293#450—131no—
294#447—131no—
295#446—131no—
296C8×Q8—131no—
297C4×SD16—131no—
298C4×SD16—131no—
299C4×D8—131no—
300C4×D8—131no—
301#436—131no—
302#436—131no—
303#436—131no—
304#435—261no—
305#435—261no—
306#435—261no—
307C8×D4—131no—
308C8×D4—131no—
309C8×D4—131no—
310C8×D4—261no—
311#433—261no—
312#432C2×D1311yescharacteristic
313#431—131no—
314#431—131no—
315#424—261no—
316C2×C4⋊C8—131no—
317#407—261no—
318C2×C22⋊C8—261no—
319C2×C4×C8C2×D1311yescharacteristic
320#335—131no—
321#335—131no—
322#334—131no—
323#334—131no—
324Q8⋊C8C2×D1311yescharacteristic, complemented
325Q8⋊C8C2×D1311yescharacteristic, complemented
326D4⋊C8—131no—
327D4⋊C8—131no—
328D4⋊C8—131no—
329D4⋊C8—131no—
330D4⋊C8C2×D1311yescharacteristic, complemented
331D4⋊C8C2×D1311yescharacteristic, complemented
332#322—131no—
333#322—131no—
334#322—131no—
335#322—131no—
336C22×C13—21no—
337C22×C13—21no—
338C22×C13—41no—
339C22×C13—41no—
340C22×C13—41no—
341C22×C13#44412yes—
342C22×C13C2×C4×D411yescharacteristic
343C2×D13—22no—
344C2×D13—41no—
345C2×D13—41no—
346C2×D13—41no—
347C2×D13—41no—
348C2×D13—41no—
349C2×D13—84no—
350C4×C13—21no—
351C4×C13—21no—
352C4×C13—21no—
353C4×C13—21no—
354C4×C13—41no—
355C4×C13—41no—
356C4×C13—41no—
357C4×C13C2×#13111yescharacteristic
358C4×C13#56811yescharacteristic
359C4×C13#57611yescharacteristic
360C4×C13#57711yescharacteristic
361Dic13—41no—
362Dic13—41no—
363C22×D4—131no—
364C23×C4—261no—
365C2×SD16—131no—
366C2×SD16—131no—
367C2×D8—131no—
368C2×D8—131no—
369C2×M16—261no—
370C2×M16—261no—
371C2×M16—261no—
372C22×C8—21no—
373C22×C8—261no—
374C22×C8—261no—
375C22×C8—261no—
376C22×C8—261no—
377#126—21no—
378#125C4×D1311yescharacteristic
379#124C4×D1311yescharacteristic
380#123—21no—
381C22⋊Q8C4×D1311yescharacteristic
382#121C4×D1311yescharacteristic
383C4×Q8C22×D1311yescharacteristic
384C4×D4—21no—
385C4×D4—131no—
386C4×D4—131no—
387C4×D4—131no—
388C4×D4—131no—
389C4×D4—261no—
390C4×D4—261no—
391C4×D4C22×D1311yescharacteristic
392#117—21no—
393C2×C4⋊C4—131no—
394C2×C22⋊C4—261no—
395C2×C42C22×D1311yescharacteristic
396#107—131no—
397#107—131no—
398#106—131no—
399#106—131no—
400C4⋊C8—131no—
401C4⋊C8—131no—
402C4⋊C8—131no—
403C4⋊C8—131no—
404C4⋊C8—131no—
405C4⋊C8—131no—
406C4⋊C8—261no—
407C4⋊C8—261no—
408C4⋊C8—261no—
409C4⋊C8C22×D1311yescharacteristic
410C4⋊C8C22×D1311yescharacteristic
411#103—131no—
412#103—131no—
413#102—131no—
414#102—131no—
415#102—131no—
416#102—131no—
417#102—131no—
418#102—131no—
419C22⋊C8—21no—
420C22⋊C8—131no—
421C22⋊C8—131no—
422C22⋊C8—131no—
423C22⋊C8—131no—
424C22⋊C8—261no—
425C22⋊C8—261no—
426C22⋊C8—261no—
427C22⋊C8—261no—
428C22⋊C8—261no—
429C22⋊C8—261no—
430#97—21no—
431#97—261no—
432C4×C8—21no—
433C4×C8—131no—
434C4×C8—131no—
435C4×C8—131no—
436C4×C8—131no—
437C4×C8—261no—
438C4×C8C22×D1311yescharacteristic
439C4×C8C22×D1311yescharacteristic
440C2×C13—22no—
441C2×C13—81no—
442C2×C13#293311yescharacteristic
443C2×C13#294611yescharacteristic
444C2×C13C2×#44411yescharacteristic
445D13—42no—
446D13—81no—
447C24—261no—
448C2×Q8C2×C4×D1311yescharacteristic
449C2×D4—21no—
450C2×D4—131no—
451C2×D4—131no—
452C2×D4—262no—
453C2×D4—261no—
454C2×D4—521no—
455C2×D4C2×C4×D1311yescharacteristic
456C22×C4—21no—
457C22×C4—261no—
458C22×C4—261no—
459C22×C4—261no—
460C22×C4—261no—
461C22×C4—261no—
462C22×C4—1041no—
463C22×C4—1041no—
464C22×C4C2×C4×D1311yescharacteristic
465C22×C4D4×D1311yescharacteristic
466C22×C4#612911yescharacteristic
467SD16—262no—
468SD16—521no—
469D8—262no—
470D8—521no—
471M16—1041no—
472M16—1041no—
473M16—1041no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—42no—
479C2×C8—131no—
480C2×C8—131no—
481C2×C8—131no—
482C2×C8—131no—
483C2×C8—131no—
484C2×C8—131no—
485C2×C8—131no—
486C2×C8—131no—
487C2×C8—261no—
488C2×C8—261no—
489C2×C8—1041no—
490C2×C8—1041no—
491C2×C8—1041no—
492C2×C8—1041no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—131no—
498C4⋊C4—131no—
499C4⋊C4—261no—
500C4⋊C4C2×C4×D1311yescharacteristic
501C4⋊C4C2×C4×D1311yescharacteristic
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4—21no—
506C22⋊C4—21no—
507C22⋊C4—261no—
508C22⋊C4—261no—
509C22⋊C4—261no—
510C22⋊C4—261no—
511C42—21no—
512C42C2×C4×D1311yescharacteristic
513C42D4×D1311yescharacteristic
514C42#612911yescharacteristic
515C42C23×D1311yescharacteristic
516C13#1802011yescharacteristic, complemented, Sylow
517C23—21no—
518C23—261no—
519C23—261no—
520C23—522no—
521C23—522no—
522C23—1041no—
523C23#8813511yescharacteristic
524Q8—21no—
525Q8—21no—
526D4—21no—
527D4—21no—
528D4—42no—
529D4—132no—
530D4—261no—
531D4—261no—
532D4—261no—
533D4—522no—
534C2×C4—22no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—261no—
545C2×C4—261no—
546C2×C4—521no—
547C2×C4—521no—
548C2×C4—521no—
549C2×C4—521no—
550C2×C4—1041no—
551C2×C4—1041no—
552C2×C4—1041no—
553C2×C4#8813511yescharacteristic
554C2×C4#8813511yescharacteristic
555C2×C4#8813511yescharacteristic
556C2×C4C22×C4×D1311yescharacteristic
557C2×C4C2×D4×D1311yescharacteristic
558C2×C4C2×#612911yescharacteristic
559C8—41no—
560C8—41no—
561C8—41no—
562C8—41no—
563C8—261no—
564C8—261no—
565C8—261no—
566C8—261no—
567C8—261no—
568C8—261no—
569C8—261no—
570C8—261no—
571C8—521no—
572C8—521no—
573C22—21no—
574C22—21no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—262no—
579C22—521no—
580C22—521no—
581C22—521no—
582C22—521no—
583C22—521no—
584C22—1044no—
585C22#1171848412yes—
586C22C2×#8813511yescharacteristic
587C4—21no—
588C4—21no—
589C4—21no—
590C4—21no—
591C4—41no—
592C4—41no—
593C4—41no—
594C4—521no—
595C4—521no—
596C4D13×#13111yescharacteristic
597C4#1171945511yescharacteristic
598C4#1171947411yescharacteristic
599C4#1171947511yescharacteristic
600C2—22no—
601C2—81no—
602C2—522no—
603C2—1041no—
604C2#1312356611yescharacteristic
605C2#1312367111yescharacteristic
606C2C2×#1171848411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1494C2
socleC22×C13C2×C4×D4
prime radical#11718697C4
cosocleC42×C13C24
hypercenter#1494D13
hypocenterC13#18020
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1494

Complements

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

NH ≅ G/Ntype
2. #13123996C2semidirect
3. #13123873C2semidirect
4. #13113747C2semidirect
5. #13113741C2semidirect
6. #13113676C2semidirect
7. #13113675C2semidirect
8. #13113668C2semidirect
9. #13113662C2semidirect
10. #13113657C2semidirect
11. #13113651C2semidirect
12. #13113622C2semidirect
13. C2×#11718051C2semidirect
14. #13113128C2semidirect
15. C13×#1494C2semidirect
30. #11718685C22semidirect
31. Q8×#1055C22semidirect
34. #11718673C22semidirect
37. D4×#1055C22semidirect
51. C13×Q8⋊C8C22semidirect
52. C13×Q8⋊C8C22semidirect
53. C13×D4⋊C8C22semidirect
54. C13×D4⋊C8C22semidirect
55. #11718072C22semidirect
56. #11718072C22semidirect
57. #11718071C22semidirect
58. #11718071C22semidirect
63. #11718046C22semidirect
64. #11718046C22semidirect
65. #11718046C22semidirect
66. #11718046C22semidirect
226. #1494D13semidirect
324. Q8⋊C8C2×D13semidirect
325. Q8⋊C8C2×D13semidirect
330. D4⋊C8C2×D13semidirect
331. D4⋊C8C2×D13semidirect
516. C13#18020semidirect

Maximal subgroups

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

subgroupindex
#131248792
#131239962
#131238732
#131137472
#131137412
#131136762
#131136752
#131136682
#131136622
#131136572
#131136512
#131136222
C2×#117180512
#131131282
C13×#14942
#1802013