Finite Group Databasebeta

← #15833551

Subgroups — #15833551

Order 3328.

622 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#13123985C211yesmaximal, characteristic, complemented
2#13123912C211yesmaximal, characteristic, complemented
3#13113750C211yesmaximal, characteristic, complemented
4#13113739C211yesmaximal, characteristic, complemented
5#13113727C211yesmaximal, characteristic, complemented
6#13113721C211yesmaximal, characteristic, complemented
7#13113660C211yesmaximal, characteristic, complemented
8SD16⋊#1055C211yesmaximal, characteristic, complemented
9SD16×#1055C211yesmaximal, characteristic, complemented
10D8×#1055C211yesmaximal, characteristic, complemented
11#13113603C211yesmaximal, characteristic, complemented
12#13113296C211yesmaximal, characteristic, complemented
13#13113287C211yesmaximal, characteristic, complemented
14M16×#1055C211yesmaximal, characteristic, complemented
15C13×#3171C211yesmaximal, characteristic
16C13×#532C2211yescharacteristic
17C13×#529C2211yescharacteristic
18C13×#501C411yescharacteristic
19C13×#496C411yescharacteristic
20C13×#490C411yescharacteristic
21C13×#489C411yescharacteristic
22C13×#469C411yescharacteristic
23C13×#469C411yescharacteristic
24C13×#468C411yescharacteristic
25C13×#468C411yescharacteristic
26C4×C13×SD16C2211yescharacteristic
27C4×C13×SD16C2211yescharacteristic
28C4×C13×D8C2211yescharacteristic
29C4×C13×D8C2211yescharacteristic
30C4×C13×M16C2211yescharacteristic
31#11718895—21no—
32#11718895—21no—
33#11718685C2211yescharacteristic
34Q8×#1055C2211yescharacteristic
35#11718673—21no—
36#11718673C2211yescharacteristic
37#11718673C2211yescharacteristic
38#11718673C2211yescharacteristic
39#11718672—21no—
40#11718672—21no—
41#11718672—21no—
42D4×#1055C2211yescharacteristic
43D4×#1055C2211yescharacteristic
44D4×#1055C2211yescharacteristic
45#11718661—21no—
46#11718660—21no—
47#11718587C2211yescharacteristic
48#11718586C2211yescharacteristic
49#11718585C2211yescharacteristic
50C2×C4×#1055C2211yescharacteristic
51Q8⋊#1055C2211yescharacteristic
52Q8⋊#1055C2211yescharacteristic
53D4⋊#1055C2211yescharacteristic
54D4⋊#1055C2211yescharacteristic
55D4⋊#1055C2211yescharacteristic
56D4⋊#1055C2211yescharacteristic
57D4⋊#1055C2211yescharacteristic
58D4⋊#1055C2211yescharacteristic
59#11718050C2211yescharacteristic
60#11718050C2211yescharacteristic
61#11718049C2211yescharacteristic
62#11718049C2211yescharacteristic
63#11718047C2211yescharacteristic
64#11718047C2211yescharacteristic
65C8×#1055C2211yescharacteristic
66C8×#1055C2211yescharacteristic
67C2×C13×#41—21no—
68C2×C13×SD16C2×C411yescharacteristic
69C2×C13×SD16C2×C411yescharacteristic
70C2×C13×D8C2×C411yescharacteristic
71C2×C13×D8C2×C411yescharacteristic
72C2×C13×M16C2×C411yescharacteristic
73C2×C13×M16C2×C411yescharacteristic
74C13×C4⋊Q8C2×C411yescharacteristic
75C13×#127C2×C411yescharacteristic
76C13×#126—21no—
77C13×#125C2×C411yescharacteristic
78C13×#124—21no—
79C13×#124C2×C411yescharacteristic
80C13×#123—21no—
81C13×C22⋊Q8C2×C411yescharacteristic
82C13×#121—21no—
83C13×#121C2×C411yescharacteristic
84C13×#121C2×C411yescharacteristic
85C13×#121C2×C411yescharacteristic
86C4×Q8×C13C2311yescharacteristic
87C4×D4×C13—21no—
88C4×D4×C13—21no—
89C4×D4×C13C2311yescharacteristic
90C4×D4×C13C2311yescharacteristic
91C4×D4×C13C2311yescharacteristic
92C13×#117—21no—
93C2×C42×C13C2311yescharacteristic
94C2×#6099—21no—
95C2×#6099—21no—
96C2×#6099—21no—
97C2×#6099—21no—
98C22×#1055—21no—
99C22×#1055—21no—
100C22×#1055—21no—
101C22×#1055—21no—
102C13×#107C2×C411yescharacteristic
103C13×#107C2×C411yescharacteristic
104C13×#106C2×C411yescharacteristic
105C13×#106C2×C411yescharacteristic
106C13×#103C2×C411yescharacteristic
107C13×#103C2×C411yescharacteristic
108C13×#102C2×C411yescharacteristic
109C13×#102C2×C411yescharacteristic
110C13×#102C2×C411yescharacteristic
111C13×#102C2×C411yescharacteristic
112C13×#102C2×C411yescharacteristic
113C13×#102C2×C411yescharacteristic
114C13×#97C2×C411yescharacteristic
115C13×#97C2×C411yescharacteristic
116C4×C8×C13C2311yescharacteristic
117C4×C8×C13C2311yescharacteristic
118C22⋊#1055—21no—
119C22⋊#1055—21no—
120C22⋊#1055—21no—
121C22⋊#1055—21no—
122C22⋊#1055—21no—
123C22⋊#1055—21no—
124C22⋊#1055—21no—
125C22⋊#1055D411yescharacteristic
126C22⋊#1055D411yescharacteristic
127C4⋊#1055—21no—
128C4⋊#1055—21no—
129C4⋊#1055—21no—
130C4⋊#1055D411yescharacteristic
131C4⋊#1055D411yescharacteristic
132C4⋊#1055C2311yescharacteristic
133C4⋊#1055C2311yescharacteristic
134C4⋊#1055C2311yescharacteristic
135C4⋊#1055C2311yescharacteristic
136#88043—21no—
137#88043—21no—
138C4×#1055—21no—
139C4×#1055—21no—
140C4×#1055C2311yescharacteristic
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#17968—131nomaximal, Sylow
145C13×#41—81no—
146C13×#41—81no—
147C2×Q8×C13—21no—
148C2×Q8×C13C22×C411yescharacteristic
149C2×D4×C13—21no—
150C2×D4×C13—21no—
151C2×D4×C13—21no—
152C2×D4×C13—21no—
153C2×D4×C13—21no—
154C2×D4×C13C22×C411yescharacteristic
155C2×D4×C13C22×C411yescharacteristic
156C2×D4×C13C22×C411yescharacteristic
157C22×C4×C13—21no—
158C22×C4×C13—21no—
159C22×C4×C13—21no—
160C22×C4×C13C22×C411yescharacteristic
161C22×C4×C13C2×D411yescharacteristic
162C22×C4×C13#4111yescharacteristic
163C13×SD16—22no—
164C13×SD16—22no—
165C13×D8—22no—
166C13×D8—22no—
167C13×M16—22no—
168C13×M16—22no—
169C2×C8×C13C22×C411yescharacteristic
170C2×C8×C13C22×C411yescharacteristic
171C2×C8×C13C22×C411yescharacteristic
172C2×C8×C13C22×C411yescharacteristic
173C13×C4⋊C4—21no—
174C13×C4⋊C4—21no—
175C13×C4⋊C4—21no—
176C13×C4⋊C4—21no—
177C13×C4⋊C4—21no—
178C13×C4⋊C4C22×C411yescharacteristic
179C13×C4⋊C4C22×C411yescharacteristic
180C13×C4⋊C4C22×C411yescharacteristic
181C13×C4⋊C4C22×C411yescharacteristic
182C13×C22⋊C4—21no—
183C13×C22⋊C4—21no—
184C13×C22⋊C4—21no—
185C13×C22⋊C4—21no—
186C13×C22⋊C4—21no—
187C13×C22⋊C4—21no—
188C13×C22⋊C4—21no—
189C13×C22⋊C4—21no—
190C13×C22⋊C4—21no—
191C42×C13—21no—
192C42×C13C22×C411yescharacteristic
193C42×C13C2×D411yescharacteristic
194C42×C13#4111yescharacteristic
195C42×C13C2411yescharacteristic
196#6099—81no—
197#6099—81no—
198#6099—81no—
199#6099—81no—
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055—21no—
203C2×#1055—21no—
204C2×#1055—21no—
205C2×#1055—21no—
206C2×#1055—42no—
207C2×#1055—81no—
208C2×#1055—81no—
209C2×#1055—81no—
210C2×#1055C2×D411yescharacteristic
211C2×#1055C2×D411yescharacteristic
212C2×#1055C2×D411yescharacteristic
213C2×#1055C2×D411yescharacteristic
214#3171D1311yescharacteristic
215#2993—131no—
216#2981—131no—
217#1594—131no—
218#1592—131no—
219#1590—131no—
220#1589—131no—
221#1580—131no—
222SD16⋊C8—131no—
223C8×SD16—131no—
224C8×D8—131no—
225#1569—131no—
226#1494—131no—
227#1492—131no—
228C8×M16—131no—
229C23×C13—21no—
230C23×C13—21no—
231C23×C13—21no—
232C23×C13C4×D411yescharacteristic
233Q8×C13—21no—
234Q8×C13—21no—
235Q8×C13—81no—
236D4×C13—21no—
237D4×C13—21no—
238D4×C13—21no—
239D4×C13—21no—
240D4×C13—21no—
241D4×C13—21no—
242D4×C13—81no—
243D4×C13—81no—
244D4×C13—81no—
245D4×C13—81no—
246D4×C13—81no—
247C2×C4×C13—21no—
248C2×C4×C13—21no—
249C2×C4×C13—21no—
250C2×C4×C13—21no—
251C2×C4×C13—21no—
252C2×C4×C13—21no—
253C2×C4×C13—21no—
254C2×C4×C13—21no—
255C2×C4×C13—21no—
256C2×C4×C13—41no—
257C2×C4×C13—41no—
258C2×C4×C13—41no—
259C2×C4×C13—41no—
260C2×C4×C13—41no—
261C2×C4×C13—41no—
262C2×C4×C13—41no—
263C2×C4×C13C4×D411yescharacteristic
264C2×C4×C13C4×D411yescharacteristic
265C2×C4×C13C4×D411yescharacteristic
266C2×C4×C13C23×C411yescharacteristic
267C2×C4×C13C22×D411yescharacteristic
268C2×C4×C13C2×#4111yescharacteristic
269C8×C13—21no—
270C8×C13—21no—
271C8×C13#13112yes—
272C8×C13#13112yes—
273#1055—22no—
274#1055—21no—
275#1055—21no—
276#1055—21no—
277#1055—21no—
278#1055—41no—
279#1055—41no—
280#1055—41no—
281#1055—41no—
282#1055—41no—
283#532C2×D1311yescharacteristic
284#529C2×D1311yescharacteristic
285#501Dic1311yescharacteristic
286#496Dic1311yescharacteristic
287#490Dic1311yescharacteristic
288#489Dic1311yescharacteristic
289#469Dic1311yescharacteristic
290#469Dic1311yescharacteristic
291#468Dic1311yescharacteristic
292#468Dic1311yescharacteristic
293#446—131no—
294C8×Q8—131no—
295C4×SD16C2×D1311yescharacteristic
296C4×SD16C2×D1311yescharacteristic
297C4×D8C2×D1311yescharacteristic
298C4×D8C2×D1311yescharacteristic
299#436—131no—
300#436—131no—
301#436—131no—
302#436—261no—
303#435—261no—
304#435—261no—
305#435—261no—
306C8×D4—131no—
307C8×D4—131no—
308C8×D4—131no—
309#433—261no—
310#432—131no—
311#431—131no—
312#424—261no—
313#423—131no—
314#408—261no—
315#408—261no—
316C4×M16C2×D1311yescharacteristic
317C2×C4×C8—131no—
318#335—131no—
319#335—131no—
320#334—131no—
321#334—131no—
322Q8⋊C8—131no—
323Q8⋊C8—131no—
324D4⋊C8—131no—
325D4⋊C8—131no—
326D4⋊C8—131no—
327D4⋊C8—131no—
328D4⋊C8—131no—
329D4⋊C8—131no—
330#322—131no—
331#322—131no—
332C82—131no—
333C82—131no—
334C22×C13—21no—
335C22×C13—21no—
336C22×C13—21no—
337C22×C13—41no—
338C22×C13—41no—
339C22×C13—41no—
340C22×C13—41no—
341C22×C13—41no—
342C22×C13—41no—
343C22×C13—41no—
344C22×C13—41no—
345C22×C13—41no—
346C22×C13C2×C4×D411yescharacteristic
347C4×C13—21no—
348C4×C13—21no—
349C4×C13—21no—
350C4×C13—21no—
351C4×C13—41no—
352C4×C13—41no—
353C4×C13—41no—
354C4×C13—41no—
355C4×C13—41no—
356C4×C13C2×#13111yescharacteristic
357C4×C13C2×#13111yescharacteristic
358C4×C13#57611yescharacteristic
359C4×C13#57711yescharacteristic
360C2×#41—21no—
361C2×SD16C2×Dic1311yescharacteristic
362C2×SD16C2×Dic1311yescharacteristic
363C2×D8C2×Dic1311yescharacteristic
364C2×D8C2×Dic1311yescharacteristic
365C2×M16—261no—
366C2×M16—261no—
367C2×M16—261no—
368C2×M16—261no—
369C2×M16C2×Dic1311yescharacteristic
370C2×M16C2×Dic1311yescharacteristic
371C22×C8—261no—
372C22×C8—261no—
373C22×C8—261no—
374C22×C8—261no—
375C4⋊Q8C2×Dic1311yescharacteristic
376#127C2×Dic1311yescharacteristic
377#126—21no—
378#125C2×Dic1311yescharacteristic
379#124—21no—
380#124C2×Dic1311yescharacteristic
381#123—21no—
382C22⋊Q8C2×Dic1311yescharacteristic
383#121—21no—
384#121C2×Dic1311yescharacteristic
385#121C2×Dic1311yescharacteristic
386#121C2×Dic1311yescharacteristic
387C4×Q8C22×D1311yescharacteristic
388C4×D4—21no—
389C4×D4—21no—
390C4×D4C22×D1311yescharacteristic
391C4×D4C22×D1311yescharacteristic
392C4×D4C22×D1311yescharacteristic
393#117—21no—
394C2×C42C22×D1311yescharacteristic
395#107C2×Dic1311yescharacteristic
396#107C2×Dic1311yescharacteristic
397#106C2×Dic1311yescharacteristic
398#106C2×Dic1311yescharacteristic
399C4⋊C8—131no—
400C4⋊C8—131no—
401C4⋊C8—131no—
402C4⋊C8—131no—
403C4⋊C8—131no—
404C4⋊C8—131no—
405C4⋊C8—261no—
406C4⋊C8—261no—
407C4⋊C8—261no—
408#103C2×Dic1311yescharacteristic
409#103C2×Dic1311yescharacteristic
410#102C2×Dic1311yescharacteristic
411#102C2×Dic1311yescharacteristic
412#102C2×Dic1311yescharacteristic
413#102C2×Dic1311yescharacteristic
414#102C2×Dic1311yescharacteristic
415#102C2×Dic1311yescharacteristic
416C22⋊C8—131no—
417C22⋊C8—131no—
418C22⋊C8—261no—
419C22⋊C8—261no—
420C22⋊C8—261no—
421C22⋊C8—261no—
422C22⋊C8—261no—
423C22⋊C8—261no—
424C22⋊C8—261no—
425#97—261no—
426#97—261no—
427#97C2×Dic1311yescharacteristic
428#97C2×Dic1311yescharacteristic
429C4×C8—131no—
430C4×C8—131no—
431C4×C8—131no—
432C4×C8—131no—
433C4×C8—261no—
434C4×C8—261no—
435C4×C8C22×D1311yescharacteristic
436C4×C8C22×D1311yescharacteristic
437C2×C13—41no—
438C2×C13—81no—
439C2×C13—81no—
440C2×C13—81no—
441C2×C13#293111yescharacteristic
442C2×C13#294611yescharacteristic
443C2×C13#295611yescharacteristic
444#41—81no—
445#41—81no—
446C2×Q8—21no—
447C2×Q8C22×Dic1311yescharacteristic
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4C22×Dic1311yescharacteristic
454C2×D4C22×Dic1311yescharacteristic
455C2×D4C22×Dic1311yescharacteristic
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4D4×D1311yescharacteristic
460C22×C4#612911yescharacteristic
461C22×C4C22×Dic1311yescharacteristic
462SD16—22no—
463SD16—22no—
464D8—22no—
465D8—22no—
466M16—22no—
467M16—22no—
468M16—1041no—
469M16—1041no—
470M16—1041no—
471M16—1041no—
472C2×C8—131no—
473C2×C8—131no—
474C2×C8—131no—
475C2×C8—131no—
476C2×C8—261no—
477C2×C8—261no—
478C2×C8—261no—
479C2×C8—261no—
480C2×C8—261no—
481C2×C8—261no—
482C2×C8—522no—
483C2×C8—1041no—
484C2×C8—1041no—
485C2×C8—1041no—
486C2×C8C22×Dic1311yescharacteristic
487C2×C8C22×Dic1311yescharacteristic
488C2×C8C22×Dic1311yescharacteristic
489C2×C8C22×Dic1311yescharacteristic
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4C22×Dic1311yescharacteristic
496C4⋊C4C22×Dic1311yescharacteristic
497C4⋊C4C22×Dic1311yescharacteristic
498C4⋊C4C22×Dic1311yescharacteristic
499C22⋊C4—21no—
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4—21no—
506C22⋊C4—21no—
507C22⋊C4—21no—
508C42—21no—
509C42D4×D1311yescharacteristic
510C42#612911yescharacteristic
511C42C22×Dic1311yescharacteristic
512C42C23×D1311yescharacteristic
513C13#1796811yescharacteristic, complemented, Sylow
514C23—21no—
515C23—21no—
516C23—21no—
517C23D4×Dic1311yescharacteristic
518Q8—21no—
519Q8—21no—
520Q8—81no—
521D4—21no—
522D4—21no—
523D4—21no—
524D4—21no—
525D4—21no—
526D4—21no—
527D4—81no—
528D4—81no—
529D4—81no—
530D4—81no—
531D4—81no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4D4×Dic1311yescharacteristic
549C2×C4D4×Dic1311yescharacteristic
550C2×C4D4×Dic1311yescharacteristic
551C2×C4C2×D4×D1311yescharacteristic
552C2×C4C2×#612911yescharacteristic
553C2×C4C23×Dic1311yescharacteristic
554C8—21no—
555C8—21no—
556C8—262no—
557C8—261no—
558C8—261no—
559C8—261no—
560C8—261no—
561C8—521no—
562C8—521no—
563C8—521no—
564C8—521no—
565C8—521no—
566C8#8820212yes—
567C8#8820212yes—
568C22—21no—
569C22—21no—
570C22—21no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22C2×D4×Dic1311yescharacteristic
581C4—21no—
582C4—21no—
583C4—21no—
584C4—21no—
585C4—41no—
586C4—41no—
587C4—41no—
588C4—41no—
589C4—41no—
590C4#1171947911yescharacteristic
591C4#1171948011yescharacteristic
592C4C2×#8820211yescharacteristic
593C4C2×#8820211yescharacteristic
594C2—41no—
595C2—81no—
596C2—81no—
597C2—81no—
598C2#1312354811yescharacteristic
599C2#1312366911yescharacteristic
600C2#1312374611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
Fitting, prime radicalC13×#3171C2
socleC22×C13C2×C4×D4
cosocleC42×C13C24
hypercenter#3171D13
hypocenterC13#17968
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3171

Complements

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

NH ≅ G/Ntype
1. #13123985C2semidirect
2. #13123912C2semidirect
3. #13113750C2semidirect
4. #13113739C2semidirect
5. #13113727C2semidirect
6. #13113721C2semidirect
7. #13113660C2semidirect
8. SD16⋊#1055C2semidirect
9. SD16×#1055C2semidirect
10. D8×#1055C2semidirect
11. #13113603C2semidirect
12. #13113296C2semidirect
13. #13113287C2semidirect
14. M16×#1055C2semidirect
513. C13#17968semidirect

Maximal subgroups

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

subgroupindex
#131239852
#131239122
#131137502
#131137392
#131137272
#131137212
#131136602
SD16⋊#10552
SD16×#10552
D8×#10552
#131136032
#131132962
#131132872
M16×#10552
C13×#31712
#1796813