Finite Group Databasebeta

← #15833100

Subgroups — #15833100

Order 3328.

620 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123985C211yesmaximal, characteristic, complemented
2#13123947C211yesmaximal, characteristic, complemented
3#13113708C211yesmaximal, characteristic, complemented
4#13113701C211yesmaximal, characteristic, complemented
5#13113680C211yesmaximal, characteristic, complemented
6#13113673C211yesmaximal, characteristic, complemented
7#13113660C211yesmaximal, characteristic, complemented
8#13113655C211yesmaximal, characteristic, complemented
9SD16×#1055C211yesmaximal, characteristic, complemented
10SD16×#1055C211yesmaximal, characteristic, complemented
11#13113607C211yesmaximal, characteristic, complemented
12#13113275C211yesmaximal, characteristic, complemented
13#13113249C211yesmaximal, characteristic, complemented
14#13113131C211yesmaximal, characteristic, complemented
15C13×#3102C211yesmaximal, characteristic
16C13×#529C2211yescharacteristic
17C4×C13×#41C2211yescharacteristic
18C13×#485C411yescharacteristic
19C13×#482C411yescharacteristic
20C13×#479C411yescharacteristic
21C13×#478C411yescharacteristic
22C13×#464C411yescharacteristic
23C13×#463C411yescharacteristic
24C13×#452C411yescharacteristic
25C13×#449C411yescharacteristic
26C4×C13×Q16C2211yescharacteristic
27C4×C13×SD16C2211yescharacteristic
28C4×C13×SD16C2211yescharacteristic
29C4×C13×D8C2211yescharacteristic
30C13×#431C2211yescharacteristic
31#11718685C2211yescharacteristic
32Q8×#1055C2211yescharacteristic
33Q8×#1055C2211yescharacteristic
34Q8×#1055C2211yescharacteristic
35#11718673—21no—
36#11718673C2211yescharacteristic
37#11718672—21no—
38D4×#1055—21no—
39D4×#1055—21no—
40D4×#1055C2211yescharacteristic
41D4×#1055C2211yescharacteristic
42D4×#1055C2211yescharacteristic
43#11718661—21no—
44#11718660—21no—
45#11718586—21no—
46#11718586C2211yescharacteristic
47#11718585C2211yescharacteristic
48C2×C4⋊#1055—21no—
49C2×C4⋊#1055C2211yescharacteristic
50C4×#6099C2211yescharacteristic
51Q8⋊#1055C2211yescharacteristic
52Q8⋊#1055C2211yescharacteristic
53Q8⋊#1055C2211yescharacteristic
54Q8⋊#1055C2211yescharacteristic
55D4⋊#1055C2211yescharacteristic
56D4⋊#1055C2211yescharacteristic
57D4⋊#1055C2211yescharacteristic
58D4⋊#1055C2211yescharacteristic
59#11718049C2211yescharacteristic
60#11718049C2211yescharacteristic
61#11718049C2211yescharacteristic
62#11718049C2211yescharacteristic
63#11718047C2211yescharacteristic
64#11718046C2211yescharacteristic
65#11718046C2211yescharacteristic
66C8×#1055C2211yescharacteristic
67C2×C13×#41C2×C411yescharacteristic
68C2×C13×Q16C2×C411yescharacteristic
69C2×C13×SD16C2×C411yescharacteristic
70C2×C13×SD16C2×C411yescharacteristic
71C2×C13×D8C2×C411yescharacteristic
72C13×#126—21no—
73C13×#125C2×C411yescharacteristic
74C13×#124C2×C411yescharacteristic
75C13×#123—21no—
76C13×C22⋊Q8C2×C411yescharacteristic
77C13×#121C2×C411yescharacteristic
78C4×Q8×C13C2×C411yescharacteristic
79C4×Q8×C13C2311yescharacteristic
80C4×Q8×C13C2311yescharacteristic
81C4×D4×C13—21no—
82C4×D4×C13—21no—
83C4×D4×C13—21no—
84C4×D4×C13C2×C411yescharacteristic
85C4×D4×C13C2311yescharacteristic
86C4×D4×C13C2311yescharacteristic
87C13×#117—21no—
88C13×#117—21no—
89C13×#117C2×C411yescharacteristic
90C2×C42×C13—21no—
91C2×C42×C13C2311yescharacteristic
92C2×#6099—21no—
93C2×#6099—21no—
94C2×#6099—21no—
95C22×#1055—21no—
96C22×#1055—21no—
97C22×#1055—21no—
98C22×#1055—21no—
99C13×#107C2×C411yescharacteristic
100C13×#107C2×C411yescharacteristic
101C13×#106C2×C411yescharacteristic
102C13×#106C2×C411yescharacteristic
103C13×C4⋊C8C2×C411yescharacteristic
104C13×C4⋊C8C2×C411yescharacteristic
105C13×#103C2×C411yescharacteristic
106C13×#103C2×C411yescharacteristic
107C13×#103C2×C411yescharacteristic
108C13×#103C2×C411yescharacteristic
109C13×#102C2×C411yescharacteristic
110C13×#102C2×C411yescharacteristic
111C13×#102C2×C411yescharacteristic
112C13×#102C2×C411yescharacteristic
113C13×C22⋊C8C2×C411yescharacteristic
114C13×C22⋊C8C2×C411yescharacteristic
115C4×C8×C13C2311yescharacteristic
116C4×C8×C13C2311yescharacteristic
117C22⋊#1055—21no—
118C22⋊#1055—21no—
119C22⋊#1055—21no—
120C22⋊#1055—21no—
121C22⋊#1055D411yescharacteristic
122C22⋊#1055D411yescharacteristic
123C4⋊#1055—21no—
124C4⋊#1055—21no—
125C4⋊#1055—21no—
126C4⋊#1055—21no—
127C4⋊#1055—21no—
128C4⋊#1055—21no—
129C4⋊#1055D411yescharacteristic
130C4⋊#1055D411yescharacteristic
131C4⋊#1055C2311yescharacteristic
132C4⋊#1055C2311yescharacteristic
133C4⋊#1055C2311yescharacteristic
134C4⋊#1055C2311yescharacteristic
135#88043—21no—
136#88043—21no—
137C4×#1055—21no—
138C4×#1055—21no—
139C4×#1055—21no—
140C4×#1055C2311yescharacteristic
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#17927—131nomaximal, Sylow
145C13×#41—22no—
146C13×#41—22no—
147C2×Q8×C13C22×C411yescharacteristic
148C2×Q8×C13C22×C411yescharacteristic
149C2×D4×C13—21no—
150C2×D4×C13—21no—
151C2×D4×C13C22×C411yescharacteristic
152C2×D4×C13C22×C411yescharacteristic
153C22×C4×C13—21no—
154C22×C4×C13—21no—
155C22×C4×C13—21no—
156C22×C4×C13—21no—
157C22×C4×C13C22×C411yescharacteristic
158C22×C4×C13C2×D411yescharacteristic
159C22×C4×C13#4111yescharacteristic
160C13×Q16—22no—
161C13×SD16—22no—
162C13×SD16—22no—
163C13×D8—22no—
164C2×C8×C13C22×C411yescharacteristic
165C2×C8×C13C22×C411yescharacteristic
166C2×C8×C13C22×C411yescharacteristic
167C2×C8×C13C22×C411yescharacteristic
168C13×C4⋊C4—21no—
169C13×C4⋊C4—21no—
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×C4⋊C4C22×C411yescharacteristic
177C13×C4⋊C4C22×C411yescharacteristic
178C13×C22⋊C4—21no—
179C13×C22⋊C4—21no—
180C13×C22⋊C4—21no—
181C13×C22⋊C4—21no—
182C13×C22⋊C4—21no—
183C13×C22⋊C4—21no—
184C13×C22⋊C4—21no—
185C13×C22⋊C4—21no—
186C42×C13—21no—
187C42×C13—21no—
188C42×C13—21no—
189C42×C13—21no—
190C42×C13C22×C411yescharacteristic
191C42×C13C2×D411yescharacteristic
192C42×C13#4111yescharacteristic
193C42×C13C2411yescharacteristic
194#6099—42no—
195#6099—81no—
196#6099—81no—
197C2×#1055—21no—
198C2×#1055—21no—
199C2×#1055—21no—
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055—21no—
203C2×#1055—81no—
204C2×#1055—81no—
205C2×#1055—81no—
206C2×#1055—81no—
207C2×#1055C2×D411yescharacteristic
208C2×#1055C2×D411yescharacteristic
209C2×#1055C2×D411yescharacteristic
210C2×#1055C2×D411yescharacteristic
211#3102D1311yescharacteristic
212#2993—131no—
213#2988—131no—
214#1587—131no—
215#1586—131no—
216#1583—131no—
217#1582—131no—
218#1580—131no—
219#1579—131no—
220C8×SD16—131no—
221C8×SD16—131no—
222#1570—131no—
223#1489—131no—
224#1483—131no—
225#1453—131no—
226C23×C13—21no—
227C23×C13—21no—
228C23×C13C4×D411yescharacteristic
229Q8×C13—21no—
230Q8×C13—21no—
231Q8×C13—21no—
232Q8×C13#13112yes—
233D4×C13—24no—
234D4×C13—21no—
235D4×C13—21no—
236D4×C13—21no—
237D4×C13—81no—
238D4×C13#13112yes—
239C2×C4×C13—24no—
240C2×C4×C13—21no—
241C2×C4×C13—21no—
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—21no—
250C2×C4×C13—41no—
251C2×C4×C13—41no—
252C2×C4×C13—41no—
253C2×C4×C13—41no—
254C2×C4×C13—41no—
255C2×C4×C13—81no—
256C2×C4×C13C4×D411yescharacteristic
257C2×C4×C13C4×D411yescharacteristic
258C2×C4×C13C4×D411yescharacteristic
259C2×C4×C13C23×C411yescharacteristic
260C2×C4×C13C22×D411yescharacteristic
261C2×C4×C13C2×#4111yescharacteristic
262C8×C13—21no—
263C8×C13—21no—
264C8×C13—21no—
265C8×C13—21no—
266#1055—22no—
267#1055—21no—
268#1055—21no—
269#1055—21no—
270#1055—21no—
271#1055—41no—
272#1055—41no—
273#1055—41no—
274#1055—41no—
275#1055—41no—
276#529C2×D1311yescharacteristic
277C4×#41C2×D1311yescharacteristic
278#485Dic1311yescharacteristic
279#482Dic1311yescharacteristic
280#479Dic1311yescharacteristic
281#478Dic1311yescharacteristic
282#464Dic1311yescharacteristic
283#463Dic1311yescharacteristic
284#452Dic1311yescharacteristic
285#449Dic1311yescharacteristic
286#446—131no—
287C8×Q8—131no—
288C8×Q8—131no—
289C8×Q8—131no—
290C4×Q16C2×D1311yescharacteristic
291C4×SD16C2×D1311yescharacteristic
292C4×SD16C2×D1311yescharacteristic
293C4×D8C2×D1311yescharacteristic
294#436—131no—
295#436—261no—
296#435—261no—
297C8×D4—131no—
298C8×D4—131no—
299C8×D4—131no—
300C8×D4—261no—
301C8×D4—261no—
302#433—261no—
303#431—131no—
304#431—261no—
305#431C2×D1311yescharacteristic
306#424—261no—
307#423—131no—
308C2×C4⋊C8—131no—
309C2×C4⋊C8—261no—
310C4×M16—131no—
311#334—131no—
312#334—131no—
313#334—131no—
314#334—131no—
315Q8⋊C8—131no—
316Q8⋊C8—131no—
317Q8⋊C8—131no—
318Q8⋊C8—131no—
319D4⋊C8—131no—
320D4⋊C8—131no—
321D4⋊C8—131no—
322D4⋊C8—131no—
323#322—131no—
324#322—131no—
325#322—131no—
326C82—131no—
327C22×C13—21no—
328C22×C13—22no—
329C22×C13—21no—
330C22×C13—21no—
331C22×C13—41no—
332C22×C13—41no—
333C22×C13—41no—
334C22×C13—41no—
335C22×C13—41no—
336C22×C13C2×C4×D411yescharacteristic
337C4×C13—21no—
338C4×C13—22no—
339C4×C13—21no—
340C4×C13—21no—
341C4×C13—21no—
342C4×C13—41no—
343C4×C13—41no—
344C4×C13—41no—
345C4×C13—41no—
346C4×C13—41no—
347C4×C13C2×#13111yescharacteristic
348C4×C13C2×#13111yescharacteristic
349C4×C13#57711yescharacteristic
350C4×C13#57711yescharacteristic
351C2×#41C2×Dic1311yescharacteristic
352C2×Q16C2×Dic1311yescharacteristic
353C2×SD16C2×Dic1311yescharacteristic
354C2×SD16C2×Dic1311yescharacteristic
355C2×D8C2×Dic1311yescharacteristic
356C2×M16—261no—
357C2×M16—261no—
358C2×M16—261no—
359C22×C8—261no—
360C22×C8—261no—
361C22×C8—261no—
362C22×C8—261no—
363#126—21no—
364#125C2×Dic1311yescharacteristic
365#124C2×Dic1311yescharacteristic
366#123—21no—
367C22⋊Q8C2×Dic1311yescharacteristic
368#121C2×Dic1311yescharacteristic
369C4×Q8C2×Dic1311yescharacteristic
370C4×Q8C22×D1311yescharacteristic
371C4×Q8C22×D1311yescharacteristic
372C4×D4—21no—
373C4×D4—21no—
374C4×D4—21no—
375C4×D4C2×Dic1311yescharacteristic
376C4×D4C22×D1311yescharacteristic
377C4×D4C22×D1311yescharacteristic
378#117—21no—
379#117—21no—
380#117C2×Dic1311yescharacteristic
381C2×C42—21no—
382C2×C42C22×D1311yescharacteristic
383#107C2×Dic1311yescharacteristic
384#107C2×Dic1311yescharacteristic
385#106C2×Dic1311yescharacteristic
386#106C2×Dic1311yescharacteristic
387C4⋊C8—131no—
388C4⋊C8—131no—
389C4⋊C8—131no—
390C4⋊C8—131no—
391C4⋊C8—131no—
392C4⋊C8—131no—
393C4⋊C8—261no—
394C4⋊C8—261no—
395C4⋊C8—261no—
396C4⋊C8—261no—
397C4⋊C8—261no—
398C4⋊C8—261no—
399C4⋊C8C2×Dic1311yescharacteristic
400C4⋊C8C2×Dic1311yescharacteristic
401#103C2×Dic1311yescharacteristic
402#103C2×Dic1311yescharacteristic
403#103C2×Dic1311yescharacteristic
404#103C2×Dic1311yescharacteristic
405#102C2×Dic1311yescharacteristic
406#102C2×Dic1311yescharacteristic
407#102C2×Dic1311yescharacteristic
408#102C2×Dic1311yescharacteristic
409C22⋊C8—131no—
410C22⋊C8—131no—
411C22⋊C8—261no—
412C22⋊C8—261no—
413C22⋊C8—261no—
414C22⋊C8—261no—
415C22⋊C8C2×Dic1311yescharacteristic
416C22⋊C8C2×Dic1311yescharacteristic
417#97—261no—
418#97—261no—
419C4×C8—131no—
420C4×C8—131no—
421C4×C8—131no—
422C4×C8—131no—
423C4×C8—261no—
424C4×C8—261no—
425C4×C8—261no—
426C4×C8C22×D1311yescharacteristic
427C4×C8C22×D1311yescharacteristic
428C2×C13—41no—
429C2×C13—42no—
430C2×C13—81no—
431C2×C13#292911yescharacteristic
432C2×C13#295211yescharacteristic
433C2×C13#295611yescharacteristic
434#41—22no—
435#41—22no—
436C2×Q8C22×Dic1311yescharacteristic
437C2×Q8C22×Dic1311yescharacteristic
438C2×D4—21no—
439C2×D4—21no—
440C2×D4C22×Dic1311yescharacteristic
441C2×D4C22×Dic1311yescharacteristic
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4D4×D1311yescharacteristic
447C22×C4#612911yescharacteristic
448C22×C4C22×Dic1311yescharacteristic
449Q16—22no—
450SD16—22no—
451SD16—22no—
452D8—22no—
453M16—522no—
454M16—1041no—
455M16—1041no—
456C2×C8—131no—
457C2×C8—131no—
458C2×C8—131no—
459C2×C8—131no—
460C2×C8—261no—
461C2×C8—261no—
462C2×C8—261no—
463C2×C8—261no—
464C2×C8—261no—
465C2×C8—261no—
466C2×C8—1041no—
467C2×C8—1041no—
468C2×C8—1041no—
469C2×C8—1041no—
470C2×C8C22×Dic1311yescharacteristic
471C2×C8C22×Dic1311yescharacteristic
472C2×C8C22×Dic1311yescharacteristic
473C2×C8C22×Dic1311yescharacteristic
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4C22×Dic1311yescharacteristic
481C4⋊C4C22×Dic1311yescharacteristic
482C4⋊C4C22×Dic1311yescharacteristic
483C4⋊C4C22×Dic1311yescharacteristic
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—21no—
489C22⋊C4—21no—
490C22⋊C4—21no—
491C22⋊C4—21no—
492C42—21no—
493C42—21no—
494C42—21no—
495C42—21no—
496C42D4×D1311yescharacteristic
497C42#612911yescharacteristic
498C42C22×Dic1311yescharacteristic
499C42C23×D1311yescharacteristic
500C13#1792711yescharacteristic, complemented, Sylow
501C23—21no—
502C23—21no—
503C23D4×Dic1311yescharacteristic
504Q8—21no—
505Q8—21no—
506Q8—21no—
507Q8#8820212yes—
508D4—24no—
509D4—21no—
510D4—21no—
511D4—21no—
512D4—81no—
513D4#8820212yes—
514C2×C4—24no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—81no—
531C2×C4D4×Dic1311yescharacteristic
532C2×C4D4×Dic1311yescharacteristic
533C2×C4D4×Dic1311yescharacteristic
534C2×C4C2×D4×D1311yescharacteristic
535C2×C4C2×#612911yescharacteristic
536C2×C4C23×Dic1311yescharacteristic
537C8—21no—
538C8—21no—
539C8—21no—
540C8—21no—
541C8—262no—
542C8—261no—
543C8—261no—
544C8—261no—
545C8—261no—
546C8—521no—
547C8—521no—
548C8—521no—
549C8—521no—
550C8—521no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—22no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22C2×D4×Dic1311yescharacteristic
561C4—21no—
562C4—21no—
563C4—21no—
564C4—21no—
565C4—22no—
566C4—41no—
567C4—41no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4#1171947511yescharacteristic
572C4#1171947511yescharacteristic
573C4C2×#8820211yescharacteristic
574C4C2×#8820211yescharacteristic
575C2—41no—
576C2—42no—
577C2—81no—
578C2#1312353111yescharacteristic
579C2#1312372011yescharacteristic
580C2#1312374611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#3102C2
socleC22×C13C2×C4×D4
prime radicalC13×#449C4
cosocleC42×C13C24
hypercenter#3102D13
hypocenterC13#17927
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3102

Complements

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

NH ≅ G/Ntype
1. #13123985C2semidirect
2. #13123947C2semidirect
3. #13113708C2semidirect
4. #13113701C2semidirect
5. #13113680C2semidirect
6. #13113673C2semidirect
7. #13113660C2semidirect
8. #13113655C2semidirect
9. SD16×#1055C2semidirect
10. SD16×#1055C2semidirect
11. #13113607C2semidirect
12. #13113275C2semidirect
13. #13113249C2semidirect
14. #13113131C2semidirect
500. C13#17927semidirect

Maximal subgroups

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

subgroupindex
#131239852
#131239472
#131137082
#131137012
#131136802
#131136732
#131136602
#131136552
SD16×#10552
#131136072
#131132752
#131132492
#131131312
C13×#31022
#1792713