Finite Group Databasebeta

← #261×#479 #16800218

Subgroups — #261×#479 #16800218

Order 3328.

828 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#125×#261C211yesmaximal, characteristic
2C4×Q8×#261C211yesmaximal, characteristic
3#13131016C211yesmaximal, characteristic
4#13130949C211yesmaximal, characteristic
5#13130899C211yesmaximal, characteristic
6#13130897C211yesmaximal, characteristic
7#13130802C211yesmaximal, characteristic
8#13130800C211yesmaximal, characteristic
9#13130707C211yesmaximal, characteristic
10#107×#261C211yesmaximal, characteristic
11#106×#261C211yesmaximal, characteristic
12C4⋊C8×#261C211yesmaximal, characteristic
13#103×#261C211yesmaximal, characteristic
14#103×#261C211yesmaximal, characteristic
15D13×#479C211yesmaximal, characteristic
16C2×Q8×#261C2211yescharacteristic
17C2×Q8×#261C2211yescharacteristic
18D13×#125C2211yescharacteristic
19C4×Q8×D13C2211yescharacteristic
20C2×#88117C2211yescharacteristic
21C2×#88117C2211yescharacteristic
22C2×#88102C2211yescharacteristic
23C2×#88101C2211yescharacteristic
24C2×C8×#261C2211yescharacteristic
25C2×C8×#261C2211yescharacteristic
26#11719083C2211yescharacteristic
27#11719083C2211yescharacteristic
28#11719082—21no—
29#11719082—21no—
30C4⋊C4×#261—21no—
31C4⋊C4×#261—21no—
32C4⋊C4×#261—21no—
33C4⋊C4×#261—21no—
34C4⋊C4×#261C2211yescharacteristic
35C4⋊C4×#261C2211yescharacteristic
36C4⋊C4×#261C2211yescharacteristic
37C4⋊C4×#261C2211yescharacteristic
38#11719060C2211yescharacteristic
39C4×C4⋊#261—21no—
40C4×C4⋊#261C2211yescharacteristic
41C42×#261—21no—
42C42×#261C2211yescharacteristic
43D13⋊(C4⋊C8)C2211yescharacteristic
44C13×#479C411yescharacteristic, complemented
45#11718724C411yescharacteristic, complemented
46#11718683C411yescharacteristic, complemented
47D13×#107C2211yescharacteristic
48#11718538C411yescharacteristic, complemented
49D13×#106C2211yescharacteristic
50#11718518C411yescharacteristic, complemented
51D13×C4⋊C8C2211yescharacteristic
52#11718490C411yescharacteristic, complemented
53D13×#103C2211yescharacteristic
54D13×#103C2211yescharacteristic
55#11718460C411yescharacteristic, complemented
56#11718457C411yescharacteristic, complemented
57#11718265C2211yescharacteristic
58#11718265C2211yescharacteristic
59(C2×#261)⋊C8C2211yescharacteristic
60(C2×#261)⋊C8C2211yescharacteristic
61#11718246C2211yescharacteristic
62#11718246C2211yescharacteristic
63#11718246C2211yescharacteristic
64#11718246C2211yescharacteristic
65#11718246C2211yescharacteristic
66#11718246C2211yescharacteristic
67C2×Q8×D13C2311yescharacteristic
68Q8×#261—22no—
69Q8×#261—22no—
70Q8×#261—22no—
71Q8×#261Q814yes—
72C2×C4⋊#261—21no—
73C2×C4⋊#261—21no—
74C2×C4⋊#261—21no—
75C2×C4⋊#261—21no—
76C2×C4⋊#261C2311yescharacteristic
77C2×C4⋊#261C2311yescharacteristic
78C2×C4⋊#261C2311yescharacteristic
79C2×C4⋊#261C2311yescharacteristic
80C2×C4×#261—21no—
81C2×C4×#261—21no—
82C2×C4×#261—21no—
83C2×C4×#261—21no—
84C2×C4×#261—21no—
85C2×C4×#261—21no—
86C2×C4×#261—21no—
87C2×C4×#261D411yescharacteristic
88C2×C4×#261D411yescharacteristic
89C2×C4×#261D411yescharacteristic
90C2×C4×#261D411yescharacteristic
91C2×C4×#261C2311yescharacteristic
92C2×C4×#261C2311yescharacteristic
93C2×D13⋊C8C2311yescharacteristic
94C2×D13⋊C8C2311yescharacteristic
95C13×#125C2×C411yescharacteristic
96C4×Q8×C13C2×C411yescharacteristic
97Q8×Dic13C2×C411yescharacteristic
98C2×C8×D13C2311yescharacteristic
99C2×C8×D13C2311yescharacteristic
100C4⋊C4×D13—21no—
101C4⋊C4×D13—21no—
102C4⋊C4×D13—21no—
103C4⋊C4×D13C2311yescharacteristic
104C4⋊C4×D13C2311yescharacteristic
105C4⋊C4×D13C2311yescharacteristic
106#88144C2×C411yescharacteristic
107#88144C2×C411yescharacteristic
108#88143—21no—
109#88143—21no—
110#88141—21no—
111#88141C2×C411yescharacteristic
112C42×D13—21no—
113C42×D13C2311yescharacteristic
114#88124C2×C411yescharacteristic
115C4×Dic26—21no—
116C4×Dic26C2×C411yescharacteristic
117#88117—22no—
118#88117—22no—
119(C2×#261)⋊C4—21no—
120(C2×#261)⋊C4—21no—
121(C2×#261)⋊C4—21no—
122(C2×#261)⋊C4—21no—
123(C2×#261)⋊C4—21no—
124(C2×#261)⋊C4—21no—
125(C2×#261)⋊C4—21no—
126(C2×#261)⋊C4—21no—
127(C2×#261)⋊C4—21no—
128#88112—21no—
129C4⋊#1057—21no—
130#88102—22no—
131#88101—22no—
132C8×#261—22no—
133C8×#261—22no—
134C13×#107C2×C411yescharacteristic
135C13×#106C2×C411yescharacteristic
136C13×C4⋊C8C2×C411yescharacteristic
137C13×#103C2×C411yescharacteristic
138C13×#103C2×C411yescharacteristic
139#88075C2×C411yescharacteristic
140#88075C2×C411yescharacteristic
141#88058C2×C411yescharacteristic
142#88057C2×C411yescharacteristic
143#88056C2×C411yescharacteristic
144#88056C2×C411yescharacteristic
145#88054C2×C411yescharacteristic
146#88054C2×C411yescharacteristic
147#88050C2×C411yescharacteristic
148#88050C2×C411yescharacteristic
149#88048C2×C411yescharacteristic
150#88048C2×C411yescharacteristic
151#88047C2×C411yescharacteristic
152#88047C2×C411yescharacteristic
153C4⋊#1055C2×C411yescharacteristic
154C4×#479—131nomaximal, Sylow
155C22×#261—21no—
156C22×#261—21no—
157C22×#261—21no—
158C22×#261—21no—
159C22×#261C2×D411yescharacteristic
160C22×#261C2×D411yescharacteristic
161C22×#261C2×D411yescharacteristic
162C22×#261C2×D411yescharacteristic
163C2×Q8×C13C22×C411yescharacteristic
164Q8×D13—21no—
165Q8×D13—21no—
166Q8×D13C2×Q812yes—
167Q8×D13#4112yes—
168C2×C4×D13—21no—
169C2×C4×D13—21no—
170C2×C4×D13—21no—
171C2×C4×D13—21no—
172C2×C4×D13C2×D411yescharacteristic
173C2×C4×D13C2×D411yescharacteristic
174C2×C4×D13C2411yescharacteristic
175C2×Dic26—21no—
176C2×Dic26C22×C411yescharacteristic
177C2×#1057—21no—
178C2×#1057—21no—
179C4⋊#261—24no—
180C4⋊#261—24no—
181C4⋊#261—21no—
182C4⋊#261—21no—
183C4⋊#261—21no—
184C4⋊#261—21no—
185C4⋊#261—21no—
186C4⋊#261—21no—
187C4⋊#261—42no—
188C4⋊#261—42no—
189C4⋊#261C2×Q812yes—
190C4⋊#261#4112yes—
191C4×#261—24no—
192C4×#261—24no—
193C4×#261—22no—
194C4×#261—22no—
195C4×#261—22no—
196C4×#261—21no—
197C4×#261—21no—
198C4×#261—41no—
199C4×#261—42no—
200C4×#261—42no—
201C4×#261—42no—
202C4×#261—42no—
203C4×#261—42no—
204C4×#261C2×Q812yes—
205C4×#261#4112yes—
206D13⋊C8—21no—
207D13⋊C8—21no—
208D13⋊C8—21no—
209D13⋊C8—21no—
210C2×C8×C13C22×C411yescharacteristic
211C2×C8×C13C22×C411yescharacteristic
212C13×C4⋊C4—21no—
213C13×C4⋊C4—21no—
214C13×C4⋊C4—21no—
215C13×C4⋊C4C22×C411yescharacteristic
216C13×C4⋊C4C22×C411yescharacteristic
217C13×C4⋊C4C22×C411yescharacteristic
218C42×C13—21no—
219C42×C13C22×C411yescharacteristic
220C4⋊Dic13—21no—
221C4⋊Dic13—21no—
222C4⋊Dic13—21no—
223C4⋊Dic13C22×C411yescharacteristic
224C4⋊Dic13C22×C411yescharacteristic
225C4⋊Dic13C22×C411yescharacteristic
226#6101—21no—
227#6101—21no—
228#6101—21no—
229#6101—21no—
230#6101—21no—
231#6101—21no—
232#6101—21no—
233#6101—21no—
234#6101—21no—
235C4×Dic13—21no—
236C4×Dic13—21no—
237C4×Dic13—21no—
238C4×Dic13C22×C411yescharacteristic
239C4×Dic13#4111yescharacteristic
240C4×Dic13#4111yescharacteristic
241C2×#1055C22×C411yescharacteristic
242C2×#1055C22×C411yescharacteristic
243C8×D13—21no—
244C8×D13—21no—
245C8×D13—21no—
246C8×D13—21no—
247C2×#479—131no—
248C4×#125—131no—
249C42×Q8—131no—
250#1989—131no—
251#1949—131no—
252#1920—131no—
253#1918—131no—
254#1865—131no—
255#1863—131no—
256#1805—131no—
257C4×#107—131no—
258C4×#106—131no—
259C4×C4⋊C8—131no—
260C4×#103—131no—
261C4×#103—131no—
262C22×D13C22×D411yescharacteristic
263C2×#261—21no—
264C2×#261—21no—
265C2×#261—21no—
266C2×#261—21no—
267C2×#261—22no—
268C2×#261—21no—
269C2×#261—22no—
270C2×#261—21no—
271C2×#261—21no—
272C2×#261—41no—
273C2×#261—41no—
274C2×#261—41no—
275C2×#261—41no—
276C2×#261—41no—
277C2×#261—41no—
278C2×#261—41no—
279C2×#261—41no—
280C2×#261—41no—
281C2×#261—41no—
282C2×#261C22⋊Q812yes—
283C2×#261C22⋊Q812yes—
284C2×#261#13512yes—
285C2×#261#13512yes—
286C2×#261#13712yes—
287Q8×C13—21no—
288Q8×C13C4×Q812yes—
289C2×C4×C13—21no—
290C2×C4×C13—21no—
291C2×C4×C13—21no—
292C2×C4×C13—21no—
293C2×C4×C13C4×D411yescharacteristic
294C2×C4×C13C4×D411yescharacteristic
295C2×C4×C13C23×C411yescharacteristic
296C2×Dic13—21no—
297C2×Dic13—21no—
298C2×Dic13—21no—
299C2×Dic13—21no—
300C2×Dic13C4×D411yescharacteristic
301C2×Dic13C4×D411yescharacteristic
302C2×Dic13C2×#4111yescharacteristic
303C4×D13—22no—
304C4×D13—22no—
305C4×D13—21no—
306C4×D13—21no—
307C4×D13—21no—
308C4×D13—21no—
309C4×D13—41no—
310C4×D13—41no—
311C4×D13—41no—
312C4×D13—41no—
313C4×D13—41no—
314C4×D13—41no—
315C4×D13C22×Q811yescharacteristic
316C4×D13C2×#4111yescharacteristic
317C4×D13C2×#4111yescharacteristic
318C4×D13C2×#4111yescharacteristic
319Dic26—21no—
320Dic26—22no—
321Dic26—22no—
322Dic26C4×Q812yes—
323#1057—41no—
324#1057—41no—
325C8×C13—21no—
326C8×C13—21no—
327#1055—21no—
328#1055—21no—
329C2×#125—131no—
330C2×C4×Q8—131no—
331C2×C4×Q8—131no—
332C2×C4×Q8—131no—
333#479—131no—
334#479—131no—
335#479—131no—
336#479—131no—
337#479—131no—
338#479—131no—
339#479—131no—
340#479#26111yescharacteristic, direct product factor
341C2×#107—131no—
342C2×#107—131no—
343C2×#106—131no—
344C2×#106—131no—
345C2×C4⋊C8—131no—
346C2×C4⋊C8—131no—
347C2×#103—131no—
348C2×#103—131no—
349C2×#103—131no—
350C2×#103—131no—
351C2×C4×C8—131no—
352C2×C4×C8—131no—
353#389—131no—
354#389—131no—
355#387—261no—
356#387—261no—
357#382—131no—
358C4×C4⋊C4—131no—
359C4×C4⋊C4—131no—
360C4×C4⋊C4—131no—
361C4×C4⋊C4—131no—
362C4×C4⋊C4—131no—
363C4×C4⋊C4—261no—
364C4×C4⋊C4—261no—
365C4×C4⋊C4—261no—
366C4×C4⋊C4—261no—
367C4×C4⋊C4—261no—
368C43—131no—
369C43—261no—
370#340—131no—
371#340—131no—
372#340—131no—
373#340—131no—
374#340—131no—
375#340—131no—
376#340—131no—
377#340—131no—
378#336—131no—
379#336—131no—
380C22×C13C2×C4×D411yescharacteristic
381C2×D13C2×C22⋊Q811yescharacteristic
382C2×D13#52511yescharacteristic
383C2×D13C2×#13511yescharacteristic
384C2×D13C2×#13511yescharacteristic
385C2×D13C2×#13711yescharacteristic
386C2×D13#57511yescharacteristic
387#261—22no—
388#261—22no—
389#261—42no—
390#261—41no—
391#261—42no—
392#261—81no—
393#261—81no—
394#261#47914yesdirect product factor
395C4×C13—21no—
396C4×C13—21no—
397C4×C13—22no—
398C4×C13—41no—
399C4×C13—41no—
400C4×C13—41no—
401C4×C13C2×C4×Q811yescharacteristic
402C4×C13C4×#4111yescharacteristic
403Dic13—21no—
404Dic13—21no—
405Dic13—22no—
406Dic13—41no—
407Dic13—41no—
408Dic13—41no—
409Dic13#52911yescharacteristic
410Dic13#53311yescharacteristic
411C22×Q8—131no—
412C22×C8—131no—
413C22×C8—131no—
414C22×C8—131no—
415C22×C8—131no—
416#125—131no—
417#125—131no—
418#125—131no—
419#125—261no—
420#125—261no—
421#125C2×#26111yescharacteristic
422C4×Q8—134no—
423C4×Q8—131no—
424C4×Q8—131no—
425C4×Q8—131no—
426C4×Q8—261no—
427C4×Q8—261no—
428C4×Q8—262no—
429C4×Q8—262no—
430C4×Q8—262no—
431C4×Q8C2×#26111yescharacteristic
432C2×C4⋊C4—131no—
433C2×C4⋊C4—131no—
434C2×C4⋊C4—131no—
435C2×C4⋊C4—131no—
436C2×C4⋊C4—131no—
437C2×C4⋊C4—131no—
438C2×C4⋊C4—131no—
439C2×C4⋊C4—261no—
440C2×C4⋊C4—261no—
441C2×C4⋊C4—261no—
442C2×C4⋊C4—261no—
443C2×C4⋊C4—261no—
444C2×C4⋊C4—261no—
445C2×C4⋊C4—261no—
446C2×C42—131no—
447C2×C42—131no—
448C2×C42—131no—
449C2×C42—131no—
450C2×C42—131no—
451C2×C42—131no—
452C2×C42—131no—
453C2×C42—261no—
454C2×C42—261no—
455C2×C42—261no—
456C2×C42—261no—
457C2×C42—261no—
458C2×C42—261no—
459C2×C42—261no—
460C2×C42—261no—
461#107—131no—
462#107—131no—
463#107—131no—
464#107—262no—
465#107C2×#26111yescharacteristic
466#106—131no—
467#106—131no—
468#106—131no—
469#106—262no—
470#106C2×#26111yescharacteristic
471C4⋊C8—131no—
472C4⋊C8—131no—
473C4⋊C8—131no—
474C4⋊C8—261no—
475C4⋊C8—261no—
476C4⋊C8C2×#26111yescharacteristic
477#103—131no—
478#103—131no—
479#103—131no—
480#103—131no—
481#103—131no—
482#103—131no—
483#103—262no—
484#103—262no—
485#103C2×#26111yescharacteristic
486#103C2×#26111yescharacteristic
487C4×C8—262no—
488C4×C8—262no—
489#95—261no—
490#95—261no—
491#95—261no—
492#95—261no—
493#95—261no—
494#95—261no—
495#95—261no—
496#95—261no—
497#95—261no—
498C2×C13C4×C22⋊Q811yescharacteristic
499C2×C13C4×#13511yescharacteristic
500C2×C13C4×#13711yescharacteristic
501D13C2×#47911yescharacteristic
502D13#307611yescharacteristic
503D13#310211yescharacteristic
504D13#310811yescharacteristic
505C2×Q8—132no—
506C2×Q8—132no—
507C2×Q8—131no—
508C2×Q8—261no—
509C2×Q8—261no—
510C2×Q8—261no—
511C2×Q8C22×#26111yescharacteristic
512C22×C4—131no—
513C22×C4—131no—
514C22×C4—131no—
515C22×C4—131no—
516C22×C4—131no—
517C22×C4—131no—
518C22×C4—131no—
519C22×C4—261no—
520C22×C4—261no—
521C22×C4—261no—
522C22×C4—261no—
523C22×C4—261no—
524C22×C4—261no—
525C22×C4—261no—
526C22×C4—261no—
527C2×C8—131no—
528C2×C8—131no—
529C2×C8—261no—
530C2×C8—261no—
531C2×C8—261no—
532C2×C8—261no—
533C2×C8—261no—
534C2×C8—261no—
535C2×C8—261no—
536C2×C8—261no—
537C2×C8—261no—
538C2×C8—261no—
539C2×C8C22×#26111yescharacteristic
540C2×C8C22×#26111yescharacteristic
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—132no—
545C4⋊C4—132no—
546C4⋊C4—131no—
547C4⋊C4—131no—
548C4⋊C4—131no—
549C4⋊C4—261no—
550C4⋊C4—261no—
551C4⋊C4—261no—
552C4⋊C4—261no—
553C4⋊C4—261no—
554C4⋊C4—261no—
555C4⋊C4—261no—
556C4⋊C4—261no—
557C4⋊C4—261no—
558C4⋊C4—261no—
559C4⋊C4—261no—
560C4⋊C4—264no—
561C4⋊C4—261no—
562C4⋊C4—261no—
563C4⋊C4—261no—
564C4⋊C4—261no—
565C4⋊C4—264no—
566C4⋊C4—261no—
567C4⋊C4—261no—
568C4⋊C4—261no—
569C4⋊C4—522no—
570C4⋊C4—522no—
571C4⋊C4C22×#26111yescharacteristic
572C4⋊C4C22×#26111yescharacteristic
573C4⋊C4C22×#26111yescharacteristic
574C42—21no—
575C42—132no—
576C42—132no—
577C42—131no—
578C42—131no—
579C42—131no—
580C42—261no—
581C42—261no—
582C42—261no—
583C42—261no—
584C42—262no—
585C42—262no—
586C42—262no—
587C42—264no—
588C42—264no—
589C42—261no—
590C42—522no—
591C42—522no—
592C42—522no—
593C42—522no—
594C42—521no—
595C42—522no—
596C42C22×#26111yescharacteristic
597C13C4×#47911yescharacteristic, complemented, Sylow
598C23—131no—
599Q8—21no—
600Q8—132no—
601Q8—262no—
602Q8—262no—
603Q8—261no—
604Q8Q8×#26112yes—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—132no—
610C2×C4—132no—
611C2×C4—132no—
612C2×C4—131no—
613C2×C4—131no—
614C2×C4—131no—
615C2×C4—131no—
616C2×C4—131no—
617C2×C4—132no—
618C2×C4—132no—
619C2×C4—131no—
620C2×C4—131no—
621C2×C4—262no—
622C2×C4—262no—
623C2×C4—261no—
624C2×C4—261no—
625C2×C4—261no—
626C2×C4—261no—
627C2×C4—261no—
628C2×C4—261no—
629C2×C4—261no—
630C2×C4—261no—
631C2×C4—261no—
632C2×C4—262no—
633C2×C4—262no—
634C2×C4—261no—
635C2×C4—261no—
636C2×C4—261no—
637C2×C4—261no—
638C2×C4—261no—
639C2×C4—261no—
640C2×C4—521no—
641C2×C4—521no—
642C2×C4—521no—
643C2×C4—521no—
644C2×C4—521no—
645C2×C4—521no—
646C2×C4—521no—
647C2×C4—521no—
648C2×C4—521no—
649C2×C4—521no—
650C2×C4—521no—
651C2×C4—521no—
652C2×C4—521no—
653C2×C4—521no—
654C2×C4—521no—
655C2×C4—521no—
656C2×C4D4×#26111yescharacteristic
657C2×C4D4×#26111yescharacteristic
658C2×C4C23×#26111yescharacteristic
659C8—21no—
660C8—21no—
661C8—261no—
662C8—261no—
663C8—521no—
664C8—521no—
665C22—131no—
666C22—131no—
667C22—131no—
668C22—131no—
669C22—131no—
670C22—131no—
671C22C2×D4×#26111yescharacteristic
672C4—22no—
673C4—21no—
674C4—21no—
675C4—41no—
676C4—41no—
677C4—41no—
678C4—134no—
679C4—131no—
680C4—131no—
681C4—262no—
682C4—262no—
683C4—262no—
684C4—261no—
685C4—261no—
686C4—521no—
687C4—522no—
688C4—522no—
689C4—521no—
690C4—521no—
691C4—521no—
692C4—1041no—
693C4—1041no—
694C4C2×Q8×#26111yescharacteristic
695C4#41×#26111yescharacteristic
696C2—131no—
697C2—131no—
698C2—131no—
699C2—131no—
700C2C22⋊Q8×#26111yescharacteristic
701C2#135×#26111yescharacteristic
702C2#137×#26111yescharacteristic
subgroupG/H
centerC22C2×D4×#261
commutatorC2×C4×C13C23×C4
FrattiniC2×C4C23×#261
FittingC13×#479C4
socleC22×C13C2×C4×D4
prime radicalC22×D13C22×D4
cosocleC2×C4×D13C24
hypercenter#479#261
hypocenterC13C4×#479
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
44. C13×#479C4semidirect
45. #11718724C4semidirect
46. #11718683C4semidirect
48. #11718538C4semidirect
50. #11718518C4semidirect
52. #11718490C4semidirect
55. #11718460C4semidirect
56. #11718457C4semidirect
340. #479#261direct (N × H)
394. #261#479direct (N × H)
597. C13C4×#479semidirect

Maximal subgroups

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

subgroupindex
#125×#2612
C4×Q8×#2612
#131310162
#131309492
#131308992
#131308972
#131308022
#131308002
#131307072
#107×#2612
#106×#2612
C4⋊C8×#2612
#103×#2612
D13×#4792
C4×#47913