Finite Group Databasebeta

← #16804992

Subgroups — #16804992

Order 3328.

878 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131365C211yesmaximal, characteristic, complemented
2#13131349C211yesmaximal, characteristic
3#13131020C211yesmaximal, characteristic, complemented
4#13130949C211yesmaximal, characteristic, complemented
5#13130942C211yesmaximal, characteristic, complemented
6#13130939C211yesmaximal, characteristic, complemented
7#13130899C211yesmaximal, characteristic, complemented
8#13130898C211yesmaximal, characteristic, complemented
9#13130801C211yesmaximal, characteristic
10#13130799C211yesmaximal, characteristic
11#13130637C211yesmaximal, characteristic, complemented
12#13130607C211yesmaximal, characteristic
13#13130606C211yesmaximal, characteristic
14#102×#261C211yesmaximal, characteristic
15D13×#476C211yesmaximal, characteristic
16C2×Q8×#261—21no—
17C2×D4×#261C2211yescharacteristic
18C2×D4×#261C2211yescharacteristic
19D13×C4⋊Q8C2211yescharacteristic
20C4×D4×D13C2211yescharacteristic
21(C2×#261)⋊Q8—21no—
22C2×#88115C2211yescharacteristic
23C2×#88115C2211yescharacteristic
24#11719136—21no—
25C2×(C2×#261)⋊C4—21no—
26C2×#88102C2211yescharacteristic
27C2×#88101C2211yescharacteristic
28C2×#88100C2211yescharacteristic
29C2×C8×#261C2211yescharacteristic
30#11719083C2211yescharacteristic
31#11719083C2211yescharacteristic
32#11719083C2211yescharacteristic
33#11719083C2211yescharacteristic
34#11719082—21no—
35#11719082—21no—
36C4⋊C4×#261C2211yescharacteristic
37C4⋊C4×#261C2211yescharacteristic
38#11719070—21no—
39#11719070—21no—
40#11719060C2211yescharacteristic
41C4×C4⋊#261C2211yescharacteristic
42C4×C4⋊#261C2211yescharacteristic
43#11719047C2211yescharacteristic
44C13×#476C411yescharacteristic, complemented
45#11718745C411yescharacteristic, complemented
46#11718669C411yescharacteristic, complemented
47#11718531C411yescharacteristic, complemented
48#11718531C411yescharacteristic, complemented
49D13×#106C2211yescharacteristic
50D13×#106C2211yescharacteristic
51#11718503C411yescharacteristic, complemented
52D13×C4⋊C8C2211yescharacteristic
53D13×#102C2211yescharacteristic
54D13×#102C2211yescharacteristic
55#11718422C411yescharacteristic, complemented
56#11718422C411yescharacteristic, 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×Q8×D13—21no—
70C2×D4×D13C2311yescharacteristic
71C22×C4×D13—21no—
72C2×C22⋊#261—21no—
73C2×C22⋊#261—21no—
74Q8×#261—44no—
75D4×#261—22no—
76D4×#261—22no—
77D4×#261—41no—
78D4×#261—41no—
79C2×C4⋊#261—21no—
80C2×C4⋊#261—21no—
81C2×C4⋊#261—21no—
82C2×C4⋊#261—21no—
83C2×C4⋊#261D411yescharacteristic
84C2×C4⋊#261D411yescharacteristic
85C2×C4⋊#261C2311yescharacteristic
86C2×C4⋊#261C2311yescharacteristic
87C2×C4⋊#261C2311yescharacteristic
88C2×C4⋊#261C2311yescharacteristic
89C2×C4×#261—21no—
90C2×C4×#261—21no—
91C2×C4×#261—21no—
92C2×C4×#261C2311yescharacteristic
93C2×C4×#261C2311yescharacteristic
94C2×D13⋊C8C2311yescharacteristic
95C2×D13⋊C8C2311yescharacteristic
96C13×C4⋊Q8C2×C411yescharacteristic, complemented
97C4×D4×C13C2×C411yescharacteristic
98#88198—21no—
99D4×Dic13C2×C411yescharacteristic
100C4×C22⋊D13—21no—
101C2×C8×D13C2311yescharacteristic
102C2×C8×D13C2311yescharacteristic
103#88147C2×C411yescharacteristic
104C4⋊C4×D13—21no—
105C4⋊C4×D13C2311yescharacteristic
106C4⋊C4×D13C2311yescharacteristic
107C4⋊C4×D13C2311yescharacteristic
108#88142—21no—
109#88142C2×C411yescharacteristic, complemented
110#88142C2×C411yescharacteristic, complemented
111#88135—21no—
112C22⋊C4×D13—21no—
113C4×D52C2×C411yescharacteristic
114C42×D13C2311yescharacteristic
115#88123C2×C411yescharacteristic, complemented
116#88115—22no—
117#88115Q814yescomplemented
118(C2×#261)⋊C4—21no—
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)⋊C4D411yescharacteristic
128(C2×#261)⋊C4D411yescharacteristic
129#88110—21no—
130#88110—21no—
131#88102—41no—
132#88101—41no—
133#88100—41no—
134C8×#261—41no—
135C13×#106C2×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#88057C2×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#88048C2×C411yescharacteristic, complemented
153#88048C2×C411yescharacteristic, complemented
154C4⋊#1055C2×C411yescharacteristic, complemented
155#22975—131nomaximal, Sylow
156C23×D13—21no—
157C22×#261—21no—
158C22×#261—21no—
159C22×#261—21no—
160C22×#261—21no—
161C22×#261—42no—
162C22×#261—42no—
163C22×#261—42no—
164C22×#261—42no—
165C22×#261—81no—
166C22×#261—81no—
167C22×#261C2×D411yescharacteristic
168C22×#261C2×D411yescharacteristic
169C22×#261C2×D411yescharacteristic
170C22×#261C2×D411yescharacteristic
171C2×Q8×C13—21no—
172C2×D4×C13C22×C411yescharacteristic
173C22×C4×C13—21no—
174C2×C22⋊D13—21no—
175C22×Dic13—21no—
176Q8×D13—42no—
177Q8×D13—42no—
178D4×D13—21no—
179D4×D13—21no—
180D4×D13C2×Q812yes—
181D4×D13#4112yes—
182C2×D52C22×C411yescharacteristic
183C2×C4×D13—21no—
184C2×C4×D13—21no—
185C2×C4×D13—21no—
186C2×C4×D13—21no—
187C2×C4×D13—21no—
188C2×C4×D13—81no—
189C2×C4×D13—81no—
190C2×C4×D13C2×D411yescharacteristic
191C2×C4×D13C2×D411yescharacteristic
192C2×C4×D13C2411yescharacteristic
193C2×Dic26—21no—
194C2×Dic26—21no—
195C2×Dic26—21no—
196C22⋊#261—42no—
197C22⋊#261—42no—
198C2×#1057—21no—
199C2×#1057—21no—
200C4⋊#261—22no—
201C4⋊#261—21no—
202C4⋊#261—21no—
203C4⋊#261—21no—
204C4⋊#261—21no—
205C4⋊#261—21no—
206C4⋊#261—21no—
207C4⋊#261—21no—
208C4⋊#261—41no—
209C4⋊#261—42no—
210C4⋊#261—42no—
211C4⋊#261—81no—
212C4⋊#261—81no—
213C4⋊#261C2×Q812yes—
214C4×#261—21no—
215C4×#261—21no—
216C4×#261—21no—
217C4×#261—21no—
218C4×#261—42no—
219C4×#261—42no—
220C4×#261—42no—
221D13⋊C8—21no—
222D13⋊C8—21no—
223D13⋊C8—21no—
224D13⋊C8C2×Q812yes—
225C2×C8×C13C22×C411yescharacteristic
226C2×C8×C13C22×C411yescharacteristic
227C13×C4⋊C4—21no—
228C13×C4⋊C4C22×C411yescharacteristic
229C13×C4⋊C4C22×C411yescharacteristic
230C13×C4⋊C4C22×C411yescharacteristic
231C13×C22⋊C4—21no—
232C42×C13C22×C411yescharacteristic
233C22⋊Dic13—21no—
234#6103—21no—
235#6103—21no—
236C4⋊Dic13—21no—
237C4⋊Dic13C22×C411yescharacteristic
238C4⋊Dic13C22×C411yescharacteristic
239C4⋊Dic13C22×C411yescharacteristic
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×#476—131no—
255#2365—131no—
256#2349—131no—
257#1993—131no—
258#1949—131no—
259#1944—131no—
260#1941—131no—
261#1920—131no—
262#1919—131no—
263#1864—131no—
264#1862—131no—
265#1771—131no—
266#1762—131no—
267#1762—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—21no—
283C2×#261—22no—
284C2×#261—21no—
285C2×#261—21no—
286C2×#261—21no—
287C2×#261—21no—
288C2×#261—21no—
289C2×#261—21no—
290C2×#261—41no—
291C2×#261—41no—
292C2×#261—41no—
293C2×#261—41no—
294C2×#261—41no—
295C2×#261—41no—
296C2×#261—41no—
297C2×#261—41no—
298C2×#261—41no—
299C2×#261—41no—
300C2×#261—41no—
301C2×#261—84no—
302C2×#261—84no—
303C2×#261AGL(1,ℤ/8)12yes—
304Q8×C13—42no—
305D4×C13—21no—
306D4×C13C4×Q812yescomplemented
307C2×C4×C13—21no—
308C2×C4×C13—21no—
309C2×C4×C13—21no—
310C2×C4×C13—81no—
311C2×C4×C13C4×D411yescharacteristic
312C2×C4×C13C4×D411yescharacteristic
313C2×C4×C13C23×C411yescharacteristic
314C22⋊D13—22no—
315C22⋊D13—22no—
316C2×Dic13—21no—
317C2×Dic13—21no—
318C2×Dic13—21no—
319C2×Dic13—81no—
320C2×Dic13C4×D411yescharacteristic
321C2×Dic13C4×D411yescharacteristic
322C2×Dic13C2×#4111yescharacteristic
323D52—21no—
324D52C4×Q812yescomplemented
325C4×D13—21no—
326C4×D13—21no—
327C4×D13—21no—
328C4×D13—21no—
329C4×D13—41no—
330C4×D13—41no—
331C4×D13—41no—
332C4×D13—41no—
333C4×D13—41no—
334C4×D13—41no—
335C4×D13—81no—
336C4×D13—81no—
337C4×D13C22×Q811yescharacteristic
338C4×D13C2×#4111yescharacteristic
339C4×D13H(5,𝔽2)11yescharacteristic
340C4×D132−1+411yescharacteristic
341Dic26—42no—
342Dic26—42no—
343Dic26—42no—
344#1057—22no—
345#1057—41no—
346C8×C13—21no—
347C8×C13—21no—
348#1055—21no—
349#1055—21no—
350C2×C4⋊Q8—131no—
351C2×C4×Q8—261no—
352C2×C4×D4—131no—
353C2×C4×D4—131no—
354C2×C4×D4—131no—
355#476—131no—
356#476—131no—
357#476—131no—
358#476—131no—
359#476—131no—
360#476—131no—
361#476—131no—
362#476#26111yescharacteristic, complemented
363C2×#107—131no—
364C2×#106—131no—
365C2×#106—131no—
366C2×#106—131no—
367C2×C4⋊C8—131no—
368C2×#102—131no—
369C2×#102—131no—
370C2×#102—131no—
371C2×#102—131no—
372C2×#97—131no—
373C2×#97—131no—
374C2×C4×C8—131no—
375#391—261no—
376#389—131no—
377#389—131no—
378#389—131no—
379#389—131no—
380#387—261no—
381#387—261no—
382#385—261no—
383#385—261no—
384#382—131no—
385#380—261no—
386C4×C4⋊C4—131no—
387C4×C4⋊C4—131no—
388C4×C4⋊C4—131no—
389C4×C4⋊C4—131no—
390C2×#95—261no—
391#340—131no—
392#340—131no—
393#340—131no—
394#340—131no—
395#340—131no—
396#340—131no—
397#340—131no—
398#340—131no—
399#336—131no—
400#336—131no—
401C22×C13—22no—
402C22×C13—41no—
403C22×C13—41no—
404C22×C13C2×C4×D411yescharacteristic
405C2×D13—22no—
406C2×D13—41no—
407C2×D13—41no—
408C2×D13—42no—
409C2×D13—42no—
410C2×D13—42no—
411C2×D13—42no—
412C2×D13#54611yescharacteristic
413C2×D13D4×Q811yescharacteristic
414C2×D13C2×AGL(1,ℤ/8)11yescharacteristic
415C2×D13#57511yescharacteristic
416C2×D13#57711yescharacteristic
417C2×D13#57711yescharacteristic
418#261—22no—
419#261—42no—
420#261—41no—
421#261—41no—
422#261—41no—
423#261—81no—
424#261—81no—
425#261—81no—
426C4×C13—21no—
427C4×C13—21no—
428C4×C13—41no—
429C4×C13—41no—
430C4×C13—41no—
431C4×C13C2×C4×Q811yescharacteristic
432C4×C13#52011yescharacteristic
433Dic13—21no—
434Dic13—21no—
435Dic13—41no—
436Dic13—41no—
437Dic13—41no—
438Dic13#55211yescharacteristic
439Dic13#55411yescharacteristic
440C22×Q8—261no—
441C22×D4—131no—
442C23×C4—261no—
443C23×C4—261no—
444C23×C4—261no—
445C22×C8—131no—
446C22×C8—131no—
447C22×C8—131no—
448C22×C8—131no—
449C4⋊Q8—131no—
450C4⋊Q8—131no—
451C4⋊Q8—131no—
452C4⋊Q8—261no—
453C4⋊Q8—261no—
454C4⋊Q8C2×#26111yescharacteristic, complemented
455C4×Q8—524no—
456C4×D4—131no—
457C4×D4—131no—
458C4×D4—131no—
459C4×D4—261no—
460C4×D4—261no—
461C4×D4—262no—
462C4×D4—262no—
463C4×D4—521no—
464C4×D4—521no—
465C4×D4C2×#26111yescharacteristic
466C2×C4⋊C4—131no—
467C2×C4⋊C4—131no—
468C2×C4⋊C4—131no—
469C2×C4⋊C4—131no—
470C2×C4⋊C4—131no—
471C2×C4⋊C4—131no—
472C2×C4⋊C4—131no—
473C2×C4⋊C4—131no—
474C2×C4⋊C4—131no—
475C2×C4⋊C4—261no—
476C2×C4⋊C4—261no—
477C2×C4⋊C4—261no—
478C2×C4⋊C4—261no—
479C2×C4⋊C4—261no—
480C2×C22⋊C4—261no—
481C2×C22⋊C4—261no—
482C2×C22⋊C4—261no—
483C2×C42—131no—
484C2×C42—131no—
485C2×C42—131no—
486C2×C42—261no—
487C2×C42—261no—
488C2×C42—261no—
489#107—521no—
490#106—131no—
491#106—131no—
492#106—131no—
493#106—131no—
494#106—131no—
495#106—131no—
496#106—521no—
497#106C2×#26111yescharacteristic, complemented
498#106C2×#26111yescharacteristic, complemented
499C4⋊C8—131no—
500C4⋊C8—131no—
501C4⋊C8—131no—
502C4⋊C8C2×#26111yescharacteristic, complemented
503#102—134no—
504#102—131no—
505#102—131no—
506#102—131no—
507#102—131no—
508#102—131no—
509#102—131no—
510#102—262no—
511#102C2×#26111yescharacteristic
512#102C2×#26111yescharacteristic
513#97—261no—
514#97—261no—
515#97—521no—
516C4×C8—521no—
517#95—131no—
518#95—131no—
519#95—261no—
520#95—261no—
521#95—261no—
522#95—261no—
523#95—261no—
524#95—261no—
525#95—261no—
526#95—261no—
527#95—261no—
528C2×C13—42no—
529C2×C13#236011yescharacteristic
530C2×C13C4×AGL(1,ℤ/8)11yescharacteristic
531C2×C13#294911yescharacteristic
532D13—42no—
533D13#330611yescharacteristic
534D13#331111yescharacteristic
535D13#338411yescharacteristic
536D13#338811yescharacteristic
537C24—261no—
538C2×Q8—21no—
539C2×Q8—261no—
540C2×Q8—261no—
541C2×Q8—261no—
542C2×Q8—522no—
543C2×Q8—522no—
544C2×D4—132no—
545C2×D4—132no—
546C2×D4—131no—
547C2×D4—261no—
548C2×D4—261no—
549C2×D4—261no—
550C2×D4C22×#26111yescharacteristic
551C22×C4—21no—
552C22×C4—131no—
553C22×C4—131no—
554C22×C4—131no—
555C22×C4—131no—
556C22×C4—131no—
557C22×C4—131no—
558C22×C4—131no—
559C22×C4—261no—
560C22×C4—261no—
561C22×C4—261no—
562C22×C4—261no—
563C22×C4—261no—
564C22×C4—261no—
565C22×C4—261no—
566C22×C4—261no—
567C22×C4—261no—
568C22×C4—261no—
569C22×C4—522no—
570C22×C4—522no—
571C22×C4—522no—
572C22×C4—522no—
573C22×C4—1041no—
574C22×C4—1041no—
575C22×C4—1041no—
576C22×C4—1041no—
577C2×C8—132no—
578C2×C8—131no—
579C2×C8—131no—
580C2×C8—261no—
581C2×C8—261no—
582C2×C8—261no—
583C2×C8—261no—
584C2×C8—261no—
585C2×C8—261no—
586C2×C8—261no—
587C2×C8—261no—
588C2×C8—261no—
589C2×C8C22×#26111yescharacteristic
590C2×C8C22×#26111yescharacteristic
591C4⋊C4—21no—
592C4⋊C4—132no—
593C4⋊C4—131no—
594C4⋊C4—131no—
595C4⋊C4—131no—
596C4⋊C4—261no—
597C4⋊C4—261no—
598C4⋊C4—261no—
599C4⋊C4—261no—
600C4⋊C4—261no—
601C4⋊C4—262no—
602C4⋊C4—261no—
603C4⋊C4—261no—
604C4⋊C4—261no—
605C4⋊C4—261no—
606C4⋊C4—261no—
607C4⋊C4—261no—
608C4⋊C4—261no—
609C4⋊C4—261no—
610C4⋊C4—522no—
611C4⋊C4—521no—
612C4⋊C4—522no—
613C4⋊C4—1041no—
614C4⋊C4—1041no—
615C4⋊C4C22×#26111yescharacteristic
616C4⋊C4C22×#26111yescharacteristic
617C4⋊C4C22×#26111yescharacteristic
618C22⋊C4—21no—
619C22⋊C4—261no—
620C22⋊C4—261no—
621C22⋊C4—261no—
622C22⋊C4—522no—
623C22⋊C4—522no—
624C42—131no—
625C42—131no—
626C42—131no—
627C42—261no—
628C42—261no—
629C42—261no—
630C42—261no—
631C42—522no—
632C42—522no—
633C42—522no—
634C42C22×#26111yescharacteristic
635C13#2297511yescharacteristic, complemented, Sylow
636C23—21no—
637C23—131no—
638C23—262no—
639C23—262no—
640C23—261no—
641C23—521no—
642C23—521no—
643C23—521no—
644C23—521no—
645Q8—42no—
646Q8—522no—
647Q8—522no—
648Q8—522no—
649D4—21no—
650D4—132no—
651D4—262no—
652D4—262no—
653D4—261no—
654D4Q8×#26112yescomplemented
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—81no—
659C2×C4—131no—
660C2×C4—131no—
661C2×C4—131no—
662C2×C4—131no—
663C2×C4—131no—
664C2×C4—132no—
665C2×C4—131no—
666C2×C4—131no—
667C2×C4—261no—
668C2×C4—261no—
669C2×C4—261no—
670C2×C4—261no—
671C2×C4—261no—
672C2×C4—261no—
673C2×C4—261no—
674C2×C4—261no—
675C2×C4—261no—
676C2×C4—261no—
677C2×C4—262no—
678C2×C4—261no—
679C2×C4—261no—
680C2×C4—261no—
681C2×C4—261no—
682C2×C4—261no—
683C2×C4—261no—
684C2×C4—261no—
685C2×C4—261no—
686C2×C4—521no—
687C2×C4—521no—
688C2×C4—521no—
689C2×C4—521no—
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×C4—521no—
701C2×C4—521no—
702C2×C4—521no—
703C2×C4—1041no—
704C2×C4—1041no—
705C2×C4—1041no—
706C2×C4—1044no—
707C2×C4—1044no—
708C2×C4D4×#26111yescharacteristic
709C2×C4D4×#26111yescharacteristic
710C2×C4C23×#26111yescharacteristic
711C8—21no—
712C8—21no—
713C8—262no—
714C8—261no—
715C8—261no—
716C8—521no—
717C22—22no—
718C22—41no—
719C22—41no—
720C22—131no—
721C22—131no—
722C22—131no—
723C22—131no—
724C22—131no—
725C22—131no—
726C22—262no—
727C22—522no—
728C22—522no—
729C22—522no—
730C22—522no—
731C22—521no—
732C22—521no—
733C22C2×D4×#26111yescharacteristic
734C4—21no—
735C4—21no—
736C4—41no—
737C4—41no—
738C4—41no—
739C4—131no—
740C4—131no—
741C4—262no—
742C4—261no—
743C4—261no—
744C4—521no—
745C4—521no—
746C4—521no—
747C4—522no—
748C4—521no—
749C4—521no—
750C4—521no—
751C4—1041no—
752C4—1041no—
753C4—1041no—
754C4C2×Q8×#26111yescharacteristic
755C4#1171963111yescharacteristic
756C2—42no—
757C2—131no—
758C2—131no—
759C2—131no—
760C2—131no—
761C2—522no—
762C2#1313136011yescharacteristic
763C2AGL(1,ℤ/8)×#26111yescharacteristic
764C2#1313159611yescharacteristic
subgroupG/H
centerC22C2×D4×#261
commutatorC2×C4×C13C23×C4
FrattiniC2×C4C23×#261
FittingC13×#476C4
socleC22×C13C2×C4×D4
prime radicalC2×D4×D13C23
cosocleC2×C4×D13C24
hypercenter#476#261
hypocenterC13#22975
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #13131365C2semidirect
3. #13131020C2semidirect
4. #13130949C2semidirect
5. #13130942C2semidirect
6. #13130939C2semidirect
7. #13130899C2semidirect
8. #13130898C2semidirect
11. #13130637C2semidirect
44. C13×#476C4semidirect
45. #11718745C4semidirect
46. #11718669C4semidirect
47. #11718531C4semidirect
48. #11718531C4semidirect
51. #11718503C4semidirect
55. #11718422C4semidirect
56. #11718422C4semidirect
96. C13×C4⋊Q8C2×C4semidirect
109. #88142C2×C4semidirect
110. #88142C2×C4semidirect
115. #88123C2×C4semidirect
117. #88115Q8semidirect
135. C13×#106C2×C4semidirect
136. C13×#106C2×C4semidirect
137. C13×C4⋊C8C2×C4semidirect
144. #88057C2×C4semidirect
145. #88057C2×C4semidirect
146. #88054C2×C4semidirect
147. #88054C2×C4semidirect
150. #88048C2×C4semidirect
151. #88048C2×C4semidirect
152. #88048C2×C4semidirect
153. #88048C2×C4semidirect
154. C4⋊#1055C2×C4semidirect
306. D4×C13C4×Q8semidirect
324. D52C4×Q8semidirect
362. #476#261semidirect
454. C4⋊Q8C2×#261semidirect
497. #106C2×#261semidirect
498. #106C2×#261semidirect
502. C4⋊C8C2×#261semidirect
635. C13#22975semidirect
654. D4Q8×#261semidirect

Maximal subgroups

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

subgroupindex
#131313652
#131313492
#131310202
#131309492
#131309422
#131309392
#131308992
#131308982
#131308012
#131307992
#131306372
#131306072
#131306062
#102×#2612
D13×#4762
#2297513