Finite Group Databasebeta

← C41×#18228 #23794429

Subgroups — C41×#18228 #23794429

Order 10496.

1300 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3537C211yesmaximal, characteristic, complemented
2C41×#3006C211yesmaximal, characteristic, complemented
3C41×#3002C211yesmaximal, characteristic, complemented
4C41×#2615C211yesmaximal, characteristic, complemented
5C41×#1606C212yesmaximal, complemented
6C41×#1601C212yesmaximal, complemented
7C41×#1600C212yesmaximal, complemented
8C41×#1595C212yesmaximal, complemented
9C41×#1519C211yesmaximal, characteristic, complemented
10C41×#1513C211yesmaximal, characteristic, complemented
11C41×#1471C211yesmaximal, characteristic, complemented
12C22×#41×C41C2211yescharacteristic, complemented
13C2×AGL(1,ℤ/8)×C41—21no—
14C2×#135×C41—21no—
15C41×#560—22no—
16C41×#553—21no—
17C41×#553—21no—
18D42×C41—22no—
19D42×C41—21no—
20D42×C41—21no—
21C41×#540—21no—
22C41×#538—21no—
23C41×#538C2212yes—
24C41×#535—21no—
25C41×#534—21no—
26C41×#534C2212yes—
27C41×#525C2211yescharacteristic
28C2×#121×C41—21no—
29C2×#121×C41C2211yescharacteristic
30C2×#121×C41C2211yescharacteristic
31C41×#452—21no—
32C41×#451C2211yescharacteristic, complemented
33C41×#450C2211yescharacteristic, complemented
34C41×#449—21no—
35C41×#449—22no—
36C41×#448C2211yescharacteristic, complemented
37C41×#448C2212yescomplemented
38C41×#447C2211yescharacteristic, complemented
39C41×#447C2212yescomplemented
40C41×#417—21no—
41C41×#416—21no—
42C41×#407C2211yescharacteristic, complemented
43C2×C22⋊C8×C41C2211yescharacteristic, complemented
44C41×#393C2212yescomplemented
45C41×#392—22no—
46C41×#392C2212yescomplemented
47C41×#380—21no—
48C41×#380C2211yescharacteristic, complemented
49C41×#328C2212yescomplemented
50C41×#327C2212yescomplemented
51C41×#327C2212yescomplemented
52C41×#327C2212yescomplemented
53C41×#323C2212yescomplemented
54C41×#323C2212yescomplemented
55C2×#41×C41—21no—
56C2×#41×C41—21no—
57C2×#41×C41—21no—
58C2×#41×C41—21no—
59C2×#41×C41—44no—
60C2×#41×C41D411yescharacteristic, complemented
61C22×Q8×C41C2311yescharacteristic
62C22×D4×C41—22no—
63C22×D4×C41—21no—
64C22×D4×C41—21no—
65C22×D4×C41—22no—
66C22×D4×C41—21no—
67C22×D4×C41—22no—
68C22×D4×C41D411yescharacteristic
69C22×D4×C41D412yes—
70C22×D4×C41D411yescharacteristic, complemented
71C22×D4×C41C2311yescharacteristic
72C23×C4×C41—21no—
73C23×C4×C41C2311yescharacteristic
74AGL(1,ℤ/8)×C41—44no—
75#135×C41—44no—
76C2×Q16×C41—21no—
77C2×SD16×C41—21no—
78C2×SD16×C41—21no—
79C2×SD16×C41—22no—
80C2×D8×C41—21no—
81C2×D8×C41—22no—
82C2×M16×C41—21no—
83C22×C8×C41—21no—
84#127×C41—22no—
85#127×C41—21no—
86#126×C41—22no—
87#126×C41—22no—
88#125×C41—21no—
89#124×C41—22no—
90#123×C41—22no—
91#123×C41—21no—
92#123×C41—22no—
93#123×C41—22no—
94#123×C41—22no—
95C22⋊Q8×C41D411yescharacteristic, complemented
96C22⋊Q8×C41C2311yescharacteristic
97#121×C41—22no—
98#121×C41—21no—
99#121×C41—21no—
100#121×C41—22no—
101#121×C41—22no—
102#121×C41—22no—
103#121×C41—22no—
104#121×C41—21no—
105#121×C41—21no—
106#121×C41—21no—
107#121×C41—21no—
108#121×C41—21no—
109#121×C41—21no—
110#121×C41—22no—
111#121×C41—44no—
112#121×C41D412yescomplemented
113#121×C41D411yescharacteristic, complemented
114#121×C41C2312yes—
115#121×C41C2311yescharacteristic
116#120×C41—22no—
117#120×C41—22no—
118#120×C41—22no—
119#120×C41—21no—
120#120×C41—22no—
121#120×C41—22no—
122#120×C41—22no—
123C4×D4×C41—22no—
124C4×D4×C41—21no—
125C4×D4×C41—21no—
126C4×D4×C41—21no—
127C4×D4×C41—21no—
128C4×D4×C41—22no—
129#117×C41—21no—
130#117×C41D411yescharacteristic, complemented
131C2×C4⋊C4×C41—21no—
132C2×C4⋊C4×C41D411yescharacteristic
133C2×C4⋊C4×C41D411yescharacteristic, complemented
134C2×C22⋊C4×C41—21no—
135C2×C22⋊C4×C41—22no—
136C2×C22⋊C4×C41—21no—
137C2×C22⋊C4×C41—22no—
138C2×C22⋊C4×C41C2312yes—
139#103×C41—21no—
140#103×C41—21no—
141#103×C41—22no—
142#102×C41—21no—
143#102×C41—21no—
144#102×C41—22no—
145C22⋊C8×C41—21no—
146C22⋊C8×C41—21no—
147C22⋊C8×C41C2311yescharacteristic
148C22⋊C8×C41C2311yescharacteristic
149C22⋊C8×C41C2312yes—
150#95×C41—22no—
151#95×C41C2312yes—
152C24×C41—22no—
153C24×C41—21no—
154C24×C41—21no—
155C24×C41C2×D412yes—
156C24×C41C2×D411yescharacteristic
157#41×C41—24no—
158#41×C41—24no—
159#41×C41—42no—
160#41×C41—42no—
161#41×C41—42no—
162#41×C41—42no—
163#41×C41—42no—
164#41×C41—42no—
165#41×C41—42no—
166C2×Q8×C41—21no—
167C2×Q8×C41—21no—
168C2×Q8×C41—42no—
169C2×Q8×C41C2×D411yescharacteristic
170C2×D4×C41—22no—
171C2×D4×C41—21no—
172C2×D4×C41—21no—
173C2×D4×C41—22no—
174C2×D4×C41—22no—
175C2×D4×C41—22no—
176C2×D4×C41—22no—
177C2×D4×C41—22no—
178C2×D4×C41—22no—
179C2×D4×C41—21no—
180C2×D4×C41—22no—
181C2×D4×C41—22no—
182C2×D4×C41—21no—
183C2×D4×C41—21no—
184C2×D4×C41—21no—
185C2×D4×C41—21no—
186C2×D4×C41—21no—
187C2×D4×C41—42no—
188C2×D4×C41—42no—
189C2×D4×C41—42no—
190C2×D4×C41—42no—
191C2×D4×C41—42no—
192C2×D4×C41—41no—
193C2×D4×C41—41no—
194C2×D4×C41—44no—
195C2×D4×C41—82no—
196C2×D4×C41—82no—
197C2×D4×C41—82no—
198C2×D4×C41—82no—
199C2×D4×C41—81no—
200C2×D4×C41—81no—
201C2×D4×C41—82no—
202C2×D4×C41—82no—
203C2×D4×C41—84no—
204C2×D4×C41C2×D411yescharacteristic
205C2×D4×C41C2×D412yes—
206C22×C4×C41—24no—
207C22×C4×C41—21no—
208C22×C4×C41—22no—
209C22×C4×C41—22no—
210C22×C4×C41—21no—
211C22×C4×C41—21no—
212C22×C4×C41—22no—
213C22×C4×C41—42no—
214C22×C4×C41—42no—
215C22×C4×C41—41no—
216C22×C4×C41—41no—
217C22×C4×C41C2×D411yescharacteristic
218C22×C4×C41C2×D411yescharacteristic
219C22×C4×C41C2×D411yescharacteristic
220C22×C4×C41C2×D412yes—
221C22×C4×C41C2×D411yescharacteristic
222C22×C4×C41C2×D411yescharacteristic
223C22×C4×C41C2411yescharacteristic
224Q16×C41—42no—
225SD16×C41—42no—
226SD16×C41—42no—
227SD16×C41—44no—
228D8×C41—42no—
229D8×C41—44no—
230M16×C41—42no—
231C2×C8×C41—21no—
232C2×C8×C41—21no—
233C2×C8×C41—22no—
234C2×C8×C41—42no—
235C4⋊C4×C41—22no—
236C4⋊C4×C41—22no—
237C4⋊C4×C41—21no—
238C4⋊C4×C41—21no—
239C4⋊C4×C41—21no—
240C4⋊C4×C41—21no—
241C4⋊C4×C41—21no—
242C4⋊C4×C41—42no—
243C4⋊C4×C41C2×D412yes—
244C4⋊C4×C41C2×D411yescharacteristic
245C4⋊C4×C41C2×D411yescharacteristic
246C22⋊C4×C41—22no—
247C22⋊C4×C41—22no—
248C22⋊C4×C41—22no—
249C22⋊C4×C41—22no—
250C22⋊C4×C41—22no—
251C22⋊C4×C41—21no—
252C22⋊C4×C41—21no—
253C22⋊C4×C41—21no—
254C22⋊C4×C41—22no—
255C22⋊C4×C41—21no—
256C22⋊C4×C41—22no—
257C22⋊C4×C41—22no—
258C22⋊C4×C41—22no—
259C22⋊C4×C41—21no—
260C22⋊C4×C41—44no—
261C22⋊C4×C41—81no—
262C22⋊C4×C41—82no—
263C42×C41—22no—
264C42×C41—21no—
265C23×C41—21no—
266C23×C41—21no—
267C23×C41—22no—
268C23×C41—22no—
269C23×C41—22no—
270C23×C41—21no—
271C23×C41—22no—
272C23×C41—22no—
273C23×C41—41no—
274C23×C41—41no—
275C23×C41—41no—
276C23×C41—41no—
277C23×C41—41no—
278C23×C41—42no—
279C23×C41—42no—
280C23×C41—42no—
281C23×C41—41no—
282C23×C41—41no—
283C23×C41—41no—
284C23×C41—81no—
285C23×C41—81no—
286C23×C41—82no—
287C23×C41—82no—
288C23×C41—82no—
289C23×C41#12011yescharacteristic
290C23×C41#12011yescharacteristic
291C23×C41C22×D411yescharacteristic
292Q8×C41—22no—
293Q8×C41—22no—
294Q8×C41—41no—
295Q8×C41—41no—
296Q8×C41—41no—
297D4×C41—22no—
298D4×C41—22no—
299D4×C41—42no—
300D4×C41—41no—
301D4×C41—41no—
302D4×C41—41no—
303D4×C41—44no—
304D4×C41—42no—
305D4×C41—44no—
306D4×C41—44no—
307D4×C41—42no—
308D4×C41—41no—
309D4×C41—42no—
310D4×C41—41no—
311D4×C41—42no—
312D4×C41—42no—
313D4×C41—81no—
314D4×C41—82no—
315D4×C41—82no—
316D4×C41—81no—
317D4×C41—82no—
318D4×C41—82no—
319D4×C41—82no—
320D4×C41—82no—
321D4×C41—82no—
322D4×C41—88no—
323C2×C4×C41—22no—
324C2×C4×C41—22no—
325C2×C4×C41—22no—
326C2×C4×C41—22no—
327C2×C4×C41—21no—
328C2×C4×C41—22no—
329C2×C4×C41—22no—
330C2×C4×C41—21no—
331C2×C4×C41—21no—
332C2×C4×C41—41no—
333C2×C4×C41—41no—
334C2×C4×C41—41no—
335C2×C4×C41—44no—
336C2×C4×C41—41no—
337C2×C4×C41—41no—
338C2×C4×C41—44no—
339C2×C4×C41—42no—
340C2×C4×C41—42no—
341C2×C4×C41—42no—
342C2×C4×C41—42no—
343C2×C4×C41—42no—
344C2×C4×C41—81no—
345C2×C4×C41—82no—
346C2×C4×C41—82no—
347C2×C4×C41#12011yescharacteristic
348C2×C4×C41#12011yescharacteristic
349C2×C4×C41C22×D411yescharacteristic
350C2×C4×C41C22×D411yescharacteristic
351C8×C41—41no—
352C8×C41—41no—
353C8×C41—42no—
354#18228C4111yesmaximal, characteristic, direct product factor, Sylow
355C22×C41—21no—
356C22×C41—21no—
357C22×C41—21no—
358C22×C41—21no—
359C22×C41—21no—
360C22×C41—21no—
361C22×C41—21no—
362C22×C41—21no—
363C22×C41—42no—
364C22×C41—42no—
365C22×C41—42no—
366C22×C41—42no—
367C22×C41—41no—
368C22×C41—42no—
369C22×C41—42no—
370C22×C41—41no—
371C22×C41—42no—
372C22×C41—41no—
373C22×C41—42no—
374C22×C41—42no—
375C22×C41—81no—
376C22×C41—81no—
377C22×C41—82no—
378C22×C41—82no—
379C22×C41—81no—
380C22×C41—81no—
381C22×C41—81no—
382C22×C41—81no—
383C22×C41—162no—
384C22×C41—164no—
385C22×C41C2×#12011yescharacteristic
386C22×C41#57611yescharacteristic
387C22×C41#57711yescharacteristic
388C4×C41—21no—
389C4×C41—21no—
390C4×C41—21no—
391C4×C41—42no—
392C4×C41—41no—
393C4×C41—42no—
394C4×C41—41no—
395C4×C41—42no—
396C4×C41—41no—
397C4×C41—82no—
398C4×C41B(4,𝔽2)12yes—
399#3537C2×C4111yescharacteristic, complemented
400#3006C2×C4111yescharacteristic, complemented
401#3002C2×C4111yescharacteristic, complemented
402#2615C2×C4111yescharacteristic, complemented
403#1606C2×C4112yescomplemented
404#1601C2×C4112yescomplemented
405#1600C2×C4112yescomplemented
406#1595C2×C4112yescomplemented
407#1519C2×C4111yescharacteristic, complemented
408#1513C2×C4111yescharacteristic, complemented
409#1471C2×C4111yescharacteristic, complemented
410C2×C41—21no—
411C2×C41—21no—
412C2×C41—41no—
413C2×C41—41no—
414C2×C41—82no—
415C2×C41—82no—
416C2×C41—82no—
417C2×C41—81no—
418C2×C41#301211yescharacteristic
419C2×C41#301911yescharacteristic
420C2×C41C2×B(4,𝔽2)11yescharacteristic
421C22×#41C22×C4111yescharacteristic, complemented
422C2×AGL(1,ℤ/8)—21no—
423C2×#135—21no—
424#560—22no—
425#553—21no—
426#553—21no—
427D42—22no—
428D42—21no—
429D42—21no—
430#540—21no—
431#538—21no—
432#538C22×C4112yes—
433#535—21no—
434#534—21no—
435#534C22×C4112yes—
436#525C22×C4111yescharacteristic
437C2×#121—21no—
438C2×#121C22×C4111yescharacteristic
439C2×#121C22×C4111yescharacteristic
440#452—21no—
441#451C22×C4111yescharacteristic, complemented
442#450C22×C4111yescharacteristic, complemented
443#449—21no—
444#449—22no—
445#448C22×C4111yescharacteristic, complemented
446#448C22×C4112yescomplemented
447#447C22×C4111yescharacteristic, complemented
448#447C22×C4112yescomplemented
449#417—21no—
450#416—21no—
451#407C22×C4111yescharacteristic, complemented
452C2×C22⋊C8C22×C4111yescharacteristic, complemented
453#393C22×C4112yescomplemented
454#392—22no—
455#392C22×C4112yescomplemented
456#380—21no—
457#380C22×C4111yescharacteristic, complemented
458#328C22×C4112yescomplemented
459#327C22×C4112yescomplemented
460#327C22×C4112yescomplemented
461#327C22×C4112yescomplemented
462#323C22×C4112yescomplemented
463#323C22×C4112yescomplemented
464C41#1822811yescharacteristic, direct product factor, Sylow
465C2×#41—21no—
466C2×#41—21no—
467C2×#41—21no—
468C2×#41—21no—
469C2×#41—44no—
470C2×#41D4×C4111yescharacteristic, complemented
471C22×Q8C23×C4111yescharacteristic
472C22×D4—22no—
473C22×D4—21no—
474C22×D4—21no—
475C22×D4—22no—
476C22×D4—21no—
477C22×D4—22no—
478C22×D4D4×C4111yescharacteristic
479C22×D4D4×C4112yes—
480C22×D4D4×C4111yescharacteristic, complemented
481C22×D4C23×C4111yescharacteristic
482C23×C4—21no—
483C23×C4C23×C4111yescharacteristic
484AGL(1,ℤ/8)—44no—
485#135—44no—
486C2×Q16—21no—
487C2×SD16—21no—
488C2×SD16—21no—
489C2×SD16—22no—
490C2×D8—21no—
491C2×D8—22no—
492C2×M16—21no—
493C22×C8—21no—
494#127—22no—
495#127—21no—
496#126—22no—
497#126—22no—
498#125—21no—
499#124—22no—
500#123—22no—
501#123—21no—
502#123—22no—
503#123—22no—
504#123—22no—
505C22⋊Q8D4×C4111yescharacteristic, complemented
506C22⋊Q8C23×C4111yescharacteristic
507#121—22no—
508#121—21no—
509#121—21no—
510#121—22no—
511#121—22no—
512#121—22no—
513#121—22no—
514#121—21no—
515#121—21no—
516#121—21no—
517#121—21no—
518#121—21no—
519#121—21no—
520#121—22no—
521#121—44no—
522#121D4×C4112yescomplemented
523#121D4×C4111yescharacteristic, complemented
524#121C23×C4112yes—
525#121C23×C4111yescharacteristic
526#120—22no—
527#120—22no—
528#120—22no—
529#120—21no—
530#120—22no—
531#120—22no—
532#120—22no—
533C4×D4—22no—
534C4×D4—21no—
535C4×D4—21no—
536C4×D4—21no—
537C4×D4—21no—
538C4×D4—22no—
539#117—21no—
540#117D4×C4111yescharacteristic, complemented
541C2×C4⋊C4—21no—
542C2×C4⋊C4D4×C4111yescharacteristic
543C2×C4⋊C4D4×C4111yescharacteristic, complemented
544C2×C22⋊C4—21no—
545C2×C22⋊C4—22no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—22no—
548C2×C22⋊C4C23×C4112yes—
549#103—21no—
550#103—21no—
551#103—22no—
552#102—21no—
553#102—21no—
554#102—22no—
555C22⋊C8—21no—
556C22⋊C8—21no—
557C22⋊C8C23×C4111yescharacteristic
558C22⋊C8C23×C4111yescharacteristic
559C22⋊C8C23×C4112yes—
560#95—22no—
561#95C23×C4112yes—
562C24—22no—
563C24—21no—
564C24—21no—
565C24C2×D4×C4112yes—
566C24C2×D4×C4111yescharacteristic
567#41—24no—
568#41—24no—
569#41—42no—
570#41—42no—
571#41—42no—
572#41—42no—
573#41—42no—
574#41—42no—
575#41—42no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—42no—
579C2×Q8C2×D4×C4111yescharacteristic
580C2×D4—22no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—22no—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—21no—
590C2×D4—22no—
591C2×D4—22no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—42no—
598C2×D4—42no—
599C2×D4—42no—
600C2×D4—42no—
601C2×D4—42no—
602C2×D4—41no—
603C2×D4—41no—
604C2×D4—44no—
605C2×D4—82no—
606C2×D4—82no—
607C2×D4—82no—
608C2×D4—82no—
609C2×D4—81no—
610C2×D4—81no—
611C2×D4—82no—
612C2×D4—82no—
613C2×D4—84no—
614C2×D4C2×D4×C4111yescharacteristic
615C2×D4C2×D4×C4112yes—
616C22×C4—24no—
617C22×C4—21no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—22no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4—41no—
626C22×C4—41no—
627C22×C4C2×D4×C4111yescharacteristic
628C22×C4C2×D4×C4111yescharacteristic
629C22×C4C2×D4×C4111yescharacteristic
630C22×C4C2×D4×C4112yes—
631C22×C4C2×D4×C4111yescharacteristic
632C22×C4C2×D4×C4111yescharacteristic
633C22×C4C24×C4111yescharacteristic
634Q16—42no—
635SD16—42no—
636SD16—42no—
637SD16—44no—
638D8—42no—
639D8—44no—
640M16—42no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—22no—
644C2×C8—42no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—42no—
653C4⋊C4C2×D4×C4112yes—
654C4⋊C4C2×D4×C4111yescharacteristic
655C4⋊C4C2×D4×C4111yescharacteristic
656C22⋊C4—22no—
657C22⋊C4—22no—
658C22⋊C4—22no—
659C22⋊C4—22no—
660C22⋊C4—22no—
661C22⋊C4—21no—
662C22⋊C4—21no—
663C22⋊C4—21no—
664C22⋊C4—22no—
665C22⋊C4—21no—
666C22⋊C4—22no—
667C22⋊C4—22no—
668C22⋊C4—22no—
669C22⋊C4—21no—
670C22⋊C4—44no—
671C22⋊C4—81no—
672C22⋊C4—82no—
673C42—22no—
674C42—21no—
675C23—21no—
676C23—21no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—21no—
681C23—22no—
682C23—22no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—81no—
695C23—81no—
696C23—82no—
697C23—82no—
698C23—82no—
699C23#120×C4111yescharacteristic
700C23#120×C4111yescharacteristic
701C23C22×D4×C4111yescharacteristic
702Q8—22no—
703Q8—22no—
704Q8—41no—
705Q8—41no—
706Q8—41no—
707D4—22no—
708D4—22no—
709D4—42no—
710D4—41no—
711D4—41no—
712D4—41no—
713D4—44no—
714D4—42no—
715D4—44no—
716D4—44no—
717D4—42no—
718D4—41no—
719D4—42no—
720D4—41no—
721D4—42no—
722D4—42no—
723D4—81no—
724D4—82no—
725D4—82no—
726D4—81no—
727D4—82no—
728D4—82no—
729D4—82no—
730D4—82no—
731D4—82no—
732D4—88no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—21no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—44no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—44no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—81no—
755C2×C4—82no—
756C2×C4—82no—
757C2×C4#120×C4111yescharacteristic
758C2×C4#120×C4111yescharacteristic
759C2×C4C22×D4×C4111yescharacteristic
760C2×C4C22×D4×C4111yescharacteristic
761C8—41no—
762C8—41no—
763C8—42no—
764C22—21no—
765C22—21no—
766C22—21no—
767C22—21no—
768C22—21no—
769C22—21no—
770C22—21no—
771C22—21no—
772C22—42no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—41no—
777C22—42no—
778C22—42no—
779C22—41no—
780C22—42no—
781C22—41no—
782C22—42no—
783C22—42no—
784C22—81no—
785C22—81no—
786C22—82no—
787C22—82no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22—81no—
792C22—162no—
793C22—164no—
794C22C2×#120×C4111yescharacteristic
795C22C41×#57611yescharacteristic
796C22C41×#57711yescharacteristic
797C4—21no—
798C4—21no—
799C4—21no—
800C4—42no—
801C4—41no—
802C4—42no—
803C4—41no—
804C4—42no—
805C4—41no—
806C4—82no—
807C4C41×B(4,𝔽2)12yes—
808C2—21no—
809C2—21no—
810C2—41no—
811C2—41no—
812C2—82no—
813C2—82no—
814C2—82no—
815C2—81no—
816C2C41×#301211yescharacteristic
817C2C41×#301911yescharacteristic
818C2C2×C41×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC22×C41C2×#120
commutator, Frattini, cosocleC22×C4C24×C41
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C41 ◁ C23×C4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C41×#3537C2semidirect
2. C41×#3006C2semidirect
3. C41×#3002C2semidirect
4. C41×#2615C2semidirect
5. C41×#1606C2semidirect
6. C41×#1601C2semidirect
7. C41×#1600C2semidirect
8. C41×#1595C2semidirect
9. C41×#1519C2semidirect
10. C41×#1513C2semidirect
11. C41×#1471C2semidirect
12. C22×#41×C41C22semidirect
32. C41×#451C22semidirect
33. C41×#450C22semidirect
36. C41×#448C22semidirect
37. C41×#448C22semidirect
38. C41×#447C22semidirect
39. C41×#447C22semidirect
42. C41×#407C22semidirect
43. C2×C22⋊C8×C41C22semidirect
44. C41×#393C22semidirect
46. C41×#392C22semidirect
48. C41×#380C22semidirect
49. C41×#328C22semidirect
50. C41×#327C22semidirect
51. C41×#327C22semidirect
52. C41×#327C22semidirect
53. C41×#323C22semidirect
54. C41×#323C22semidirect
60. C2×#41×C41D4semidirect
70. C22×D4×C41D4semidirect
95. C22⋊Q8×C41D4semidirect
112. #121×C41D4semidirect
113. #121×C41D4semidirect
130. #117×C41D4semidirect
133. C2×C4⋊C4×C41D4semidirect
354. #18228C41direct (N × H)
399. #3537C2×C41semidirect
400. #3006C2×C41semidirect
401. #3002C2×C41semidirect
402. #2615C2×C41semidirect
403. #1606C2×C41semidirect
404. #1601C2×C41semidirect
405. #1600C2×C41semidirect
406. #1595C2×C41semidirect
407. #1519C2×C41semidirect
408. #1513C2×C41semidirect
409. #1471C2×C41semidirect
421. C22×#41C22×C41semidirect
441. #451C22×C41semidirect
442. #450C22×C41semidirect
445. #448C22×C41semidirect
446. #448C22×C41semidirect
447. #447C22×C41semidirect
448. #447C22×C41semidirect
451. #407C22×C41semidirect
452. C2×C22⋊C8C22×C41semidirect
453. #393C22×C41semidirect
455. #392C22×C41semidirect
457. #380C22×C41semidirect
458. #328C22×C41semidirect
459. #327C22×C41semidirect
460. #327C22×C41semidirect
461. #327C22×C41semidirect
462. #323C22×C41semidirect
463. #323C22×C41semidirect
464. C41#18228direct (N × H)
470. C2×#41D4×C41semidirect
480. C22×D4D4×C41semidirect
505. C22⋊Q8D4×C41semidirect
522. #121D4×C41semidirect
523. #121D4×C41semidirect
540. #117D4×C41semidirect
543. C2×C4⋊C4D4×C41semidirect

Maximal subgroups

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

subgroupindex
C41×#35372
C41×#30062
C41×#30022
C41×#26152
C41×#16062
C41×#16012
C41×#16002
C41×#15952
C41×#15192
C41×#15132
C41×#14712
#1822841