Finite Group Databasebeta

← #261×#478 #16800217

Subgroups — #261×#478 #16800217

Order 3328.

948 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#125×#261C211yesmaximal, characteristic, complemented
2C4×D4×#261C211yesmaximal, characteristic
3#13131016C211yesmaximal, characteristic, complemented
4#13130949C211yesmaximal, characteristic, complemented
5#13130900C211yesmaximal, characteristic, complemented
6#13130898C211yesmaximal, characteristic, complemented
7#13130801C211yesmaximal, characteristic
8#13130799C211yesmaximal, characteristic
9#13130706C211yesmaximal, characteristic
10#107×#261C211yesmaximal, characteristic, complemented
11#106×#261C211yesmaximal, characteristic, complemented
12C4⋊C8×#261C211yesmaximal, characteristic, complemented
13#102×#261C211yesmaximal, characteristic
14#102×#261C211yesmaximal, characteristic
15D13×#478C211yesmaximal, characteristic
16C2×D4×#261C2211yescharacteristic
17C2×D4×#261C2211yescharacteristic
18C22×C4×#261—21no—
19D13×#125C2211yescharacteristic
20C4×D4×D13C2211yescharacteristic
21C2×#88115C2211yescharacteristic
22C2×#88115C2211yescharacteristic
23C4×C22⋊#261—21no—
24C2×#88102C2211yescharacteristic
25C2×#88101C2211yescharacteristic
26C2×C8×#261C2211yescharacteristic
27C2×C8×#261C2211yescharacteristic
28#11719083C2211yescharacteristic
29#11719083C2211yescharacteristic
30#11719082—21no—
31#11719082—21no—
32C4⋊C4×#261—21no—
33C4⋊C4×#261—21no—
34C4⋊C4×#261C2211yescharacteristic
35C4⋊C4×#261C2211yescharacteristic
36C4⋊C4×#261C2211yescharacteristic
37C4⋊C4×#261C2211yescharacteristic
38C22⋊C4×#261—21no—
39C22⋊C4×#261—21no—
40#11719060C2211yescharacteristic
41C4×C4⋊#261C2211yescharacteristic
42C42×#261C2211yescharacteristic
43D13⋊(C4⋊C8)C2211yescharacteristic
44C13×#478C411yescharacteristic, complemented
45#11718727C411yescharacteristic, complemented
46#11718670C411yescharacteristic, complemented
47#11718552C411yescharacteristic, complemented
48D13×#107C2211yescharacteristic
49#11718532C411yescharacteristic, complemented
50D13×#106C2211yescharacteristic
51#11718508C411yescharacteristic, complemented
52D13×C4⋊C8C2211yescharacteristic
53D13×#102C2211yescharacteristic
54D13×#102C2211yescharacteristic
55#11718427C411yescharacteristic, complemented
56#11718424C411yescharacteristic, 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
67C23×#261—21no—
68C23×#261—21no—
69C2×D4×D13C2311yescharacteristic
70C22×C4×D13—21no—
71C2×C22⋊#261—21no—
72C2×C22⋊#261—21no—
73D4×#261—22no—
74D4×#261—22no—
75D4×#261—22no—
76D4×#261Q814yes—
77C2×C4⋊#261—21no—
78C2×C4⋊#261—21no—
79C2×C4⋊#261C2311yescharacteristic
80C2×C4⋊#261C2311yescharacteristic
81C2×C4⋊#261C2311yescharacteristic
82C2×C4⋊#261C2311yescharacteristic
83C2×C4×#261—21no—
84C2×C4×#261—21no—
85C2×C4×#261—21no—
86C2×C4×#261—21no—
87C2×C4×#261—21no—
88C2×C4×#261—44no—
89C2×C4×#261D411yescharacteristic
90C2×C4×#261D411yescharacteristic
91C2×C4×#261D411yescharacteristic
92C2×C4×#261D411yescharacteristic
93C2×C4×#261C2311yescharacteristic
94C2×C4×#261C2311yescharacteristic
95C2×D13⋊C8C2311yescharacteristic
96C2×D13⋊C8C2311yescharacteristic
97C13×#125C2×C411yescharacteristic, complemented
98C4×D4×C13C2×C411yescharacteristic
99D4×Dic13C2×C411yescharacteristic
100C4×C22⋊D13—21no—
101C2×C8×D13C2311yescharacteristic
102C2×C8×D13C2311yescharacteristic
103#88147C2×C411yescharacteristic
104C4⋊C4×D13—21no—
105C4⋊C4×D13—21no—
106C4⋊C4×D13C2311yescharacteristic
107C4⋊C4×D13C2311yescharacteristic
108C4⋊C4×D13C2311yescharacteristic
109#88144C2×C411yescharacteristic, complemented
110#88144C2×C411yescharacteristic, complemented
111#88143—21no—
112#88143—21no—
113#88135—21no—
114C22⋊C4×D13—21no—
115C4×D52C2×C411yescharacteristic
116C42×D13C2311yescharacteristic
117#88124C2×C411yescharacteristic, complemented
118#88115—22no—
119#88115—22no—
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(C2×#261)⋊C4—21no—
129#88112—21no—
130C4⋊#1057—21no—
131#88102—22no—
132#88101—22no—
133C8×#261—22no—
134C8×#261—22no—
135C13×#107C2×C411yescharacteristic, complemented
136C13×#106C2×C411yescharacteristic, complemented
137C13×C4⋊C8C2×C411yescharacteristic, complemented
138C13×#102C2×C411yescharacteristic
139C13×#102C2×C411yescharacteristic
140#88072C2×C411yescharacteristic
141#88072C2×C411yescharacteristic
142#88061C2×C411yescharacteristic
143#88061C2×C411yescharacteristic
144#88058C2×C411yescharacteristic, complemented
145#88057C2×C411yescharacteristic, complemented
146#88054C2×C411yescharacteristic, complemented
147#88054C2×C411yescharacteristic, complemented
148#88049C2×C411yescharacteristic
149#88049C2×C411yescharacteristic
150#88048C2×C411yescharacteristic, complemented
151#88048C2×C411yescharacteristic, complemented
152#88047C2×C411yescharacteristic, complemented
153#88047C2×C411yescharacteristic, complemented
154C4⋊#1055C2×C411yescharacteristic, complemented
155C4×#478—131nomaximal, Sylow
156C23×D13—21no—
157C22×#261—24no—
158C22×#261—21no—
159C22×#261—21no—
160C22×#261—24no—
161C22×#261—21no—
162C22×#261—21no—
163C22×#261—42no—
164C22×#261—42no—
165C22×#261—42no—
166C22×#261—42no—
167C22×#261C2×D411yescharacteristic
168C22×#261C2×D411yescharacteristic
169C22×#261C2×D411yescharacteristic
170C22×#261C2×D411yescharacteristic
171C2×D4×C13C22×C411yescharacteristic
172C22×C4×C13—21no—
173C2×C22⋊D13—21no—
174C22×Dic13—21no—
175D4×D13—21no—
176D4×D13—21no—
177D4×D13C2×Q812yes—
178D4×D13#4112yes—
179C2×D52C22×C411yescharacteristic
180C2×C4×D13—21no—
181C2×C4×D13—21no—
182C2×C4×D13—21no—
183C2×C4×D13—21no—
184C2×C4×D13—21no—
185C2×C4×D13—42no—
186C2×C4×D13—42no—
187C2×C4×D13C2×D411yescharacteristic
188C2×C4×D13C2×D411yescharacteristic
189C2×C4×D13C2411yescharacteristic
190C22⋊#261—24no—
191C22⋊#261—24no—
192C2×#1057—21no—
193C2×#1057—21no—
194C4⋊#261—21no—
195C4⋊#261—21no—
196C4⋊#261—21no—
197C4⋊#261—21no—
198C4⋊#261—21no—
199C4⋊#261—21no—
200C4⋊#261—42no—
201C4⋊#261—42no—
202C4⋊#261C2×Q812yes—
203C4⋊#261#4112yes—
204C4×#261—22no—
205C4×#261—22no—
206C4×#261—22no—
207C4×#261—21no—
208C4×#261—21no—
209C4×#261—41no—
210C4×#261—42no—
211C4×#261—42no—
212C4×#261—42no—
213C4×#261—42no—
214C4×#261—42no—
215C4×#261C2×Q812yes—
216C4×#261#4112yes—
217D13⋊C8—21no—
218D13⋊C8—21no—
219D13⋊C8—21no—
220D13⋊C8—21no—
221C2×C8×C13C22×C411yescharacteristic
222C2×C8×C13C22×C411yescharacteristic
223C13×C4⋊C4—21no—
224C13×C4⋊C4—21no—
225C13×C4⋊C4C22×C411yescharacteristic
226C13×C4⋊C4C22×C411yescharacteristic
227C13×C4⋊C4C22×C411yescharacteristic
228C13×C22⋊C4—21no—
229C42×C13C22×C411yescharacteristic
230C22⋊Dic13—21no—
231#6103—21no—
232#6103—21no—
233C4⋊Dic13—21no—
234C4⋊Dic13—21no—
235C4⋊Dic13C22×C411yescharacteristic
236C4⋊Dic13C22×C411yescharacteristic
237C4⋊Dic13C22×C411yescharacteristic
238#6101—21no—
239#6101—21no—
240#6101—21no—
241#6101—21no—
242#6101—21no—
243#6101—21no—
244#6101—21no—
245C4×Dic13C22×C411yescharacteristic
246C4×Dic13#4111yescharacteristic
247C4×Dic13#4111yescharacteristic
248C2×#1055C22×C411yescharacteristic
249C2×#1055C22×C411yescharacteristic
250C8×D13—21no—
251C8×D13—21no—
252C8×D13—21no—
253C8×D13—21no—
254C2×#478—131no—
255C4×#125—131no—
256C42×D4—131no—
257#1989—131no—
258#1949—131no—
259#1921—131no—
260#1919—131no—
261#1864—131no—
262#1862—131no—
263#1804—131no—
264C4×#107—131no—
265C4×#106—131no—
266C4×C4⋊C8—131no—
267C4×#102—131no—
268C4×#102—131no—
269C23×C13—21no—
270C22×D13—21no—
271C22×D13—22no—
272C22×D13—22no—
273C22×D13—41no—
274C22×D13—41no—
275C22×D13—41no—
276C22×D13—41no—
277C22×D13C22×D411yescharacteristic
278C2×#261—21no—
279C2×#261—21no—
280C2×#261—21no—
281C2×#261—21no—
282C2×#261—22no—
283C2×#261—21no—
284C2×#261—22no—
285C2×#261—21no—
286C2×#261—21no—
287C2×#261—48no—
288C2×#261—41no—
289C2×#261—41no—
290C2×#261—41no—
291C2×#261—41no—
292C2×#261—48no—
293C2×#261—41no—
294C2×#261—41no—
295C2×#261—41no—
296C2×#261—41no—
297C2×#261—41no—
298C2×#261—41no—
299C2×#261C22⋊Q812yes—
300C2×#261C22⋊Q812yes—
301C2×#261#13512yes—
302C2×#261#13512yes—
303C2×#261AGL(1,ℤ/8)12yes—
304D4×C13—21no—
305D4×C13C4×Q812yes—
306C2×C4×C13—21no—
307C2×C4×C13—21no—
308C2×C4×C13—21no—
309C2×C4×C13—42no—
310C2×C4×C13C4×D411yescharacteristic
311C2×C4×C13C4×D411yescharacteristic
312C2×C4×C13C23×C411yescharacteristic
313C22⋊D13—22no—
314C22⋊D13—22no—
315C2×Dic13—21no—
316C2×Dic13—21no—
317C2×Dic13—21no—
318C2×Dic13—42no—
319C2×Dic13C4×D411yescharacteristic
320C2×Dic13C4×D411yescharacteristic
321C2×Dic13C2×#4111yescharacteristic
322D52—21no—
323D52C4×Q812yes—
324C4×D13—21no—
325C4×D13—21no—
326C4×D13—21no—
327C4×D13—21no—
328C4×D13—42no—
329C4×D13—42no—
330C4×D13—41no—
331C4×D13—41no—
332C4×D13—41no—
333C4×D13—41no—
334C4×D13—41no—
335C4×D13—41no—
336C4×D13C22×Q811yescharacteristic
337C4×D13C2×#4111yescharacteristic
338C4×D13C2×#4111yescharacteristic
339C4×D13C2×#4111yescharacteristic
340#1057—41no—
341#1057—41no—
342C8×C13—21no—
343C8×C13—21no—
344#1055—21no—
345#1055—21no—
346C2×#125—131no—
347C2×C4×D4—131no—
348C2×C4×D4—131no—
349C2×C4×D4—131no—
350C22×C42—261no—
351#478—131no—
352#478—131no—
353#478—131no—
354#478—131no—
355#478—131no—
356#478—131no—
357#478—131no—
358#478#26111yescharacteristic, direct product factor
359C2×#107—131no—
360C2×#107—131no—
361C2×#106—131no—
362C2×#106—131no—
363C2×C4⋊C8—131no—
364C2×C4⋊C8—131no—
365C2×#102—131no—
366C2×#102—131no—
367C2×#102—131no—
368C2×#102—131no—
369C2×C4×C8—131no—
370C2×C4×C8—131no—
371#389—131no—
372#389—131no—
373#387—261no—
374#387—261no—
375#382—131no—
376C4×C4⋊C4—131no—
377C4×C4⋊C4—131no—
378C4×C4⋊C4—131no—
379C4×C4⋊C4—131no—
380C4×C4⋊C4—131no—
381C4×C4⋊C4—261no—
382C4×C4⋊C4—261no—
383C4×C22⋊C4—261no—
384C4×C22⋊C4—261no—
385C4×C22⋊C4—261no—
386C43—131no—
387#340—131no—
388#340—131no—
389#340—131no—
390#340—131no—
391#340—131no—
392#340—131no—
393#340—131no—
394#340—131no—
395#336—131no—
396#336—131no—
397C22×C13—22no—
398C22×C13—41no—
399C22×C13—41no—
400C22×C13C2×C4×D411yescharacteristic
401C2×D13—22no—
402C2×D13—41no—
403C2×D13—41no—
404C2×D13—42no—
405C2×D13—42no—
406C2×D13—42no—
407C2×D13—42no—
408C2×D13C2×C22⋊Q811yescharacteristic
409C2×D13#52511yescharacteristic
410C2×D13C2×#13511yescharacteristic
411C2×D13C2×#13511yescharacteristic
412C2×D13C2×AGL(1,ℤ/8)11yescharacteristic
413C2×D13#57511yescharacteristic
414#261—22no—
415#261—22no—
416#261—42no—
417#261—41no—
418#261—42no—
419#261—81no—
420#261—81no—
421#261#47814yesdirect product factor
422C4×C13—21no—
423C4×C13—21no—
424C4×C13—41no—
425C4×C13—41no—
426C4×C13—41no—
427C4×C13C2×C4×Q811yescharacteristic
428C4×C13C4×#4111yescharacteristic
429Dic13—21no—
430Dic13—21no—
431Dic13—41no—
432Dic13—41no—
433Dic13—41no—
434Dic13#52911yescharacteristic
435Dic13#53311yescharacteristic
436C22×D4—131no—
437C23×C4—261no—
438C23×C4—261no—
439C23×C4—261no—
440C22×C8—131no—
441C22×C8—131no—
442C22×C8—131no—
443C22×C8—131no—
444#125—131no—
445#125—131no—
446#125—131no—
447#125—261no—
448#125—261no—
449#125C2×#26111yescharacteristic, complemented
450C4×D4—134no—
451C4×D4—131no—
452C4×D4—131no—
453C4×D4—131no—
454C4×D4—261no—
455C4×D4—261no—
456C4×D4—262no—
457C4×D4—262no—
458C4×D4—262no—
459C4×D4C2×#26111yescharacteristic
460C2×C4⋊C4—131no—
461C2×C4⋊C4—131no—
462C2×C4⋊C4—131no—
463C2×C4⋊C4—131no—
464C2×C4⋊C4—131no—
465C2×C4⋊C4—131no—
466C2×C4⋊C4—131no—
467C2×C4⋊C4—261no—
468C2×C4⋊C4—261no—
469C2×C4⋊C4—261no—
470C2×C4⋊C4—261no—
471C2×C22⋊C4—261no—
472C2×C22⋊C4—261no—
473C2×C22⋊C4—261no—
474C2×C42—131no—
475C2×C42—131no—
476C2×C42—131no—
477C2×C42—131no—
478C2×C42—131no—
479C2×C42—131no—
480C2×C42—131no—
481C2×C42—261no—
482C2×C42—261no—
483C2×C42—261no—
484C2×C42—261no—
485C2×C42—261no—
486C2×C42—524no—
487#107—131no—
488#107—131no—
489#107—131no—
490#107—262no—
491#107C2×#26111yescharacteristic, complemented
492#106—131no—
493#106—131no—
494#106—131no—
495#106—262no—
496#106C2×#26111yescharacteristic, complemented
497C4⋊C8—131no—
498C4⋊C8—131no—
499C4⋊C8—131no—
500C4⋊C8—261no—
501C4⋊C8—261no—
502C4⋊C8C2×#26111yescharacteristic, complemented
503#102—131no—
504#102—131no—
505#102—131no—
506#102—131no—
507#102—131no—
508#102—131no—
509#102—262no—
510#102—262no—
511#102C2×#26111yescharacteristic
512#102C2×#26111yescharacteristic
513C4×C8—262no—
514C4×C8—262no—
515#95—261no—
516#95—261no—
517#95—261no—
518#95—261no—
519#95—261no—
520#95—261no—
521#95—261no—
522#95—261no—
523#95—261no—
524C2×C13—42no—
525C2×C13C4×C22⋊Q811yescharacteristic
526C2×C13C4×#13511yescharacteristic
527C2×C13C4×AGL(1,ℤ/8)11yescharacteristic
528D13—42no—
529D13C2×#47811yescharacteristic
530D13#307611yescharacteristic
531D13#310211yescharacteristic
532D13#310511yescharacteristic
533C24—261no—
534C2×D4—132no—
535C2×D4—132no—
536C2×D4—131no—
537C2×D4—261no—
538C2×D4—261no—
539C2×D4—261no—
540C2×D4C22×#26111yescharacteristic
541C22×C4—21no—
542C22×C4—131no—
543C22×C4—131no—
544C22×C4—131no—
545C22×C4—131no—
546C22×C4—131no—
547C22×C4—131no—
548C22×C4—131no—
549C22×C4—261no—
550C22×C4—261no—
551C22×C4—261no—
552C22×C4—261no—
553C22×C4—261no—
554C22×C4—264no—
555C22×C4—261no—
556C22×C4—261no—
557C22×C4—264no—
558C22×C4—261no—
559C22×C4—261no—
560C22×C4—261no—
561C22×C4—522no—
562C22×C4—522no—
563C22×C4—522no—
564C22×C4—522no—
565C22×C4—522no—
566C22×C4—522no—
567C2×C8—131no—
568C2×C8—131no—
569C2×C8—261no—
570C2×C8—261no—
571C2×C8—261no—
572C2×C8—261no—
573C2×C8—261no—
574C2×C8—261no—
575C2×C8—261no—
576C2×C8—261no—
577C2×C8—261no—
578C2×C8—261no—
579C2×C8C22×#26111yescharacteristic
580C2×C8C22×#26111yescharacteristic
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—132no—
584C4⋊C4—132no—
585C4⋊C4—131no—
586C4⋊C4—131no—
587C4⋊C4—131no—
588C4⋊C4—261no—
589C4⋊C4—261no—
590C4⋊C4—261no—
591C4⋊C4—261no—
592C4⋊C4—261no—
593C4⋊C4—261no—
594C4⋊C4—261no—
595C4⋊C4—261no—
596C4⋊C4—261no—
597C4⋊C4—261no—
598C4⋊C4—261no—
599C4⋊C4—261no—
600C4⋊C4—261no—
601C4⋊C4—261no—
602C4⋊C4—261no—
603C4⋊C4—522no—
604C4⋊C4—522no—
605C4⋊C4C22×#26111yescharacteristic
606C4⋊C4C22×#26111yescharacteristic
607C4⋊C4C22×#26111yescharacteristic
608C22⋊C4—21no—
609C22⋊C4—261no—
610C22⋊C4—261no—
611C22⋊C4—264no—
612C22⋊C4—264no—
613C22⋊C4—261no—
614C42—132no—
615C42—132no—
616C42—131no—
617C42—131no—
618C42—131no—
619C42—262no—
620C42—261no—
621C42—261no—
622C42—262no—
623C42—262no—
624C42—522no—
625C42—522no—
626C42—522no—
627C42—521no—
628C42—522no—
629C42—522no—
630C42C22×#26111yescharacteristic
631C13C4×#47811yescharacteristic, complemented, Sylow
632C23—21no—
633C23—131no—
634C23—262no—
635C23—262no—
636C23—261no—
637C23—521no—
638C23—521no—
639C23—521no—
640C23—521no—
641D4—21no—
642D4—132no—
643D4—262no—
644D4—262no—
645D4—261no—
646D4Q8×#26112yes—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—42no—
651C2×C4—132no—
652C2×C4—132no—
653C2×C4—132no—
654C2×C4—131no—
655C2×C4—131no—
656C2×C4—131no—
657C2×C4—131no—
658C2×C4—131no—
659C2×C4—132no—
660C2×C4—132no—
661C2×C4—131no—
662C2×C4—131no—
663C2×C4—261no—
664C2×C4—261no—
665C2×C4—261no—
666C2×C4—261no—
667C2×C4—261no—
668C2×C4—261no—
669C2×C4—261no—
670C2×C4—261no—
671C2×C4—261no—
672C2×C4—261no—
673C2×C4—261no—
674C2×C4—262no—
675C2×C4—262no—
676C2×C4—261no—
677C2×C4—261no—
678C2×C4—261no—
679C2×C4—522no—
680C2×C4—522no—
681C2×C4—521no—
682C2×C4—521no—
683C2×C4—521no—
684C2×C4—521no—
685C2×C4—521no—
686C2×C4—521no—
687C2×C4—528no—
688C2×C4—522no—
689C2×C4—528no—
690C2×C4—521no—
691C2×C4—521no—
692C2×C4—521no—
693C2×C4—521no—
694C2×C4—521no—
695C2×C4—521no—
696C2×C4—521no—
697C2×C4—521no—
698C2×C4—521no—
699C2×C4—521no—
700C2×C4D4×#26111yescharacteristic
701C2×C4D4×#26111yescharacteristic
702C2×C4C23×#26111yescharacteristic
703C8—21no—
704C8—21no—
705C8—261no—
706C8—261no—
707C8—521no—
708C8—521no—
709C22—22no—
710C22—41no—
711C22—41no—
712C22—131no—
713C22—131no—
714C22—131no—
715C22—131no—
716C22—131no—
717C22—131no—
718C22—262no—
719C22—522no—
720C22—522no—
721C22—522no—
722C22—522no—
723C22—521no—
724C22—521no—
725C22C2×D4×#26111yescharacteristic
726C4—21no—
727C4—21no—
728C4—41no—
729C4—41no—
730C4—41no—
731C4—134no—
732C4—131no—
733C4—131no—
734C4—262no—
735C4—262no—
736C4—261no—
737C4—261no—
738C4—521no—
739C4—522no—
740C4—522no—
741C4—521no—
742C4—521no—
743C4—521no—
744C4—1041no—
745C4—1041no—
746C4C2×Q8×#26111yescharacteristic
747C4#41×#26111yescharacteristic
748C2—42no—
749C2—131no—
750C2—131no—
751C2—131no—
752C2—131no—
753C2—522no—
754C2C22⋊Q8×#26111yescharacteristic
755C2#135×#26111yescharacteristic
756C2AGL(1,ℤ/8)×#26111yescharacteristic
subgroupG/H
centerC22C2×D4×#261
commutatorC2×C4×C13C23×C4
FrattiniC2×C4C23×#261
FittingC13×#478C4
socleC22×C13C2×C4×D4
prime radicalC2×D4×D13C23
cosocleC2×C4×D13C24
hypercenter#478#261
hypocenterC13C4×#478
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #125×#261C2semidirect
3. #13131016C2semidirect
4. #13130949C2semidirect
5. #13130900C2semidirect
6. #13130898C2semidirect
10. #107×#261C2semidirect
11. #106×#261C2semidirect
12. C4⋊C8×#261C2semidirect
44. C13×#478C4semidirect
45. #11718727C4semidirect
46. #11718670C4semidirect
47. #11718552C4semidirect
49. #11718532C4semidirect
51. #11718508C4semidirect
55. #11718427C4semidirect
56. #11718424C4semidirect
97. C13×#125C2×C4semidirect
109. #88144C2×C4semidirect
110. #88144C2×C4semidirect
117. #88124C2×C4semidirect
135. C13×#107C2×C4semidirect
136. C13×#106C2×C4semidirect
137. C13×C4⋊C8C2×C4semidirect
144. #88058C2×C4semidirect
145. #88057C2×C4semidirect
146. #88054C2×C4semidirect
147. #88054C2×C4semidirect
150. #88048C2×C4semidirect
151. #88048C2×C4semidirect
152. #88047C2×C4semidirect
153. #88047C2×C4semidirect
154. C4⋊#1055C2×C4semidirect
358. #478#261direct (N × H)
421. #261#478direct (N × H)
449. #125C2×#261semidirect
491. #107C2×#261semidirect
496. #106C2×#261semidirect
502. C4⋊C8C2×#261semidirect
631. C13C4×#478semidirect

Maximal subgroups

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

subgroupindex
#125×#2612
C4×D4×#2612
#131310162
#131309492
#131309002
#131308982
#131308012
#131307992
#131307062
#107×#2612
#106×#2612
C4⋊C8×#2612
#102×#2612
D13×#4782
C4×#47813