Finite Group Databasebeta

← C41×#23525 #23799726

Subgroups — C41×#23525 #23799726

Order 10496.

1332 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#575C211yesmaximal, characteristic
2C2×C41×#430C211yesmaximal, characteristic, complemented
3C2×C41×#421C211yesmaximal, characteristic, complemented
4C41×#2896C211yesmaximal, characteristic, complemented
5C2×C41×#413C211yesmaximal, characteristic, complemented
6C2×C41×#413C211yesmaximal, characteristic, complemented
7C41×#2049C214yesmaximal, complemented
8C41×#2048C214yesmaximal, complemented
9C2×C41×#344C211yesmaximal, characteristic, complemented
10C22×#41×C41C2211yescharacteristic
11C22×#41×C41C2211yescharacteristic
12C41×#575—22no—
13C41×#575—22no—
14C41×#575—22no—
15C41×#575—22no—
16C2×#137×C41—21no—
17C2×#137×C41C2212yes—
18C2×AGL(1,ℤ/8)×C41—21no—
19C2×AGL(1,ℤ/8)×C41C2212yes—
20C2×#135×C41—22no—
21C22×M16×C41C2211yescharacteristic
22C22×M16×C41C2211yescharacteristic
23C22×M16×C41C2211yescharacteristic
24C22×M16×C41C2211yescharacteristic
25C2×#117×C41C2211yescharacteristic
26C41×#430—22no—
27C41×#430C2214yescomplemented
28C2×#108×C41—22no—
29C41×#421—22no—
30C41×#421C2214yes—
31C2×#104×C41—22no—
32C41×#419C2212yescomplemented
33C41×#418C2212yescomplemented
34C41×#417—22no—
35C41×#416—22no—
36C41×#413—22no—
37C41×#413—22no—
38C41×#413—22no—
39C41×#413C2214yes—
40C2×#101×C41—21no—
41C2×#101×C41C2212yescomplemented
42C2×#100×C41—21no—
43C2×#100×C41C2212yescomplemented
44C41×#344C2214yescomplemented
45C2×#41×C41—21no—
46C2×#41×C41—21no—
47C2×#41×C41—21no—
48C2×#41×C41—21no—
49C2×#41×C41—21no—
50C2×#41×C41—21no—
51C2×#41×C41—21no—
52C2×#41×C41—21no—
53C2×#41×C41—21no—
54C2×#41×C41—21no—
55C2×#41×C41—21no—
56C2×#41×C41—21no—
57C2×#41×C41—21no—
58C2×#41×C41—21no—
59C2×#41×C41—21no—
60C2×#41×C41—21no—
61C2×#41×C41—21no—
62C2×#41×C41—21no—
63C2×#41×C41—21no—
64C2×#41×C41—21no—
65C2×#41×C41D412yes—
66C2×#41×C41D412yes—
67C2×#41×C41D412yes—
68C2×#41×C41C2312yes—
69C22×Q8×C41D411yescharacteristic
70C22×Q8×C41C2311yescharacteristic
71C22×D4×C41—21no—
72C22×D4×C41—21no—
73C22×D4×C41D411yescharacteristic
74C22×D4×C41C2311yescharacteristic
75C23×C4×C41—21no—
76C23×C4×C41—21no—
77C23×C4×C41C2311yescharacteristic
78#137×C41—24no—
79#137×C41—24no—
80#137×C41—24no—
81#137×C41—24no—
82AGL(1,ℤ/8)×C41—24no—
83AGL(1,ℤ/8)×C41—24no—
84AGL(1,ℤ/8)×C41—24no—
85AGL(1,ℤ/8)×C41—24no—
86#135×C41—28no—
87#135×C41—28no—
88C2×Q16×C41—22no—
89C2×SD16×C41—22no—
90C2×SD16×C41—22no—
91C2×D8×C41—22no—
92C2×M16×C41—21no—
93C2×M16×C41—21no—
94C2×M16×C41—21no—
95C2×M16×C41—21no—
96C2×M16×C41—21no—
97C2×M16×C41—21no—
98C2×M16×C41—21no—
99C2×M16×C41—21no—
100C2×M16×C41—21no—
101C2×M16×C41—21no—
102C2×M16×C41—21no—
103C2×M16×C41—21no—
104C2×M16×C41—21no—
105C2×M16×C41—21no—
106C2×M16×C41—21no—
107C2×M16×C41—21no—
108C2×M16×C41D412yes—
109C2×M16×C41D412yes—
110C2×M16×C41D412yes—
111C2×M16×C41D412yes—
112C2×M16×C41C2312yes—
113C2×M16×C41C2312yes—
114C2×M16×C41C2312yes—
115C2×M16×C41C2312yes—
116C22×C8×C41—21no—
117C22×C8×C41—21no—
118C22×C8×C41—21no—
119C22×C8×C41—21no—
120#117×C41—21no—
121#117×C41—21no—
122#117×C41—21no—
123#117×C41C2312yes—
124C2×C4⋊C4×C41—21no—
125C2×C22⋊C4×C41—21no—
126C2×C42×C41—21no—
127#108×C41—28no—
128#104×C41—28no—
129#103×C41—24no—
130#102×C41—24no—
131#101×C41—24no—
132#101×C41—24no—
133#100×C41—24no—
134#100×C41—24no—
135C24×C41—21no—
136C24×C41—21no—
137C24×C41#4111yescharacteristic
138#41×C41—22no—
139#41×C41—22no—
140#41×C41—22no—
141#41×C41—22no—
142#41×C41—22no—
143#41×C41—22no—
144#41×C41—22no—
145#41×C41—22no—
146#41×C41—22no—
147#41×C41—22no—
148#41×C41—22no—
149#41×C41—22no—
150#41×C41—22no—
151#41×C41—22no—
152#41×C41—22no—
153#41×C41—22no—
154#41×C41—41no—
155#41×C41—41no—
156#41×C41—41no—
157#41×C41—41no—
158#41×C41—41no—
159#41×C41—41no—
160#41×C41—41no—
161#41×C41—41no—
162#41×C41—41no—
163#41×C41—41no—
164#41×C41—41no—
165#41×C41—41no—
166#41×C41—41no—
167#41×C41—41no—
168#41×C41—41no—
169#41×C41—41no—
170C2×Q8×C41—21no—
171C2×Q8×C41—21no—
172C2×Q8×C41—21no—
173C2×Q8×C41—21no—
174C2×Q8×C41—21no—
175C2×Q8×C41—21no—
176C2×Q8×C41—21no—
177C2×Q8×C41—21no—
178C2×Q8×C41—21no—
179C2×Q8×C41—21no—
180C2×Q8×C41C2×D412yes—
181C2×Q8×C41C2×D412yes—
182C2×D4×C41—22no—
183C2×D4×C41—22no—
184C2×D4×C41—22no—
185C2×D4×C41—22no—
186C2×D4×C41—21no—
187C2×D4×C41—21no—
188C2×D4×C41—21no—
189C2×D4×C41—21no—
190C2×D4×C41—21no—
191C2×D4×C41—21no—
192C2×D4×C41—21no—
193C2×D4×C41—21no—
194C2×D4×C41—21no—
195C2×D4×C41—21no—
196C2×D4×C41—41no—
197C2×D4×C41—41no—
198C2×D4×C41—41no—
199C2×D4×C41—41no—
200C2×D4×C41—41no—
201C2×D4×C41—41no—
202C2×D4×C41—41no—
203C2×D4×C41—41no—
204C2×D4×C41C2×D412yes—
205C2×D4×C41C2×D412yes—
206C22×C4×C41—21no—
207C22×C4×C41—21no—
208C22×C4×C41—22no—
209C22×C4×C41—22no—
210C22×C4×C41—22no—
211C22×C4×C41—22no—
212C22×C4×C41—41no—
213C22×C4×C41—41no—
214C22×C4×C41—41no—
215C22×C4×C41—41no—
216C22×C4×C41—41no—
217C22×C4×C41—41no—
218C22×C4×C41—41no—
219C22×C4×C41—41no—
220C22×C4×C41—41no—
221C22×C4×C41C2×D411yescharacteristic
222C22×C4×C41C2×D411yescharacteristic
223C22×C4×C41C2×D411yescharacteristic
224C22×C4×C41C2×D411yescharacteristic
225C22×C4×C41C2×D411yescharacteristic
226C22×C4×C41C2×D411yescharacteristic
227C22×C4×C41C2×D411yescharacteristic
228C22×C4×C41C2×D411yescharacteristic
229C22×C4×C41#4111yescharacteristic
230C22×C4×C41#4111yescharacteristic
231C22×C4×C41#4111yescharacteristic
232C22×C4×C41#4111yescharacteristic
233C22×C4×C41#4111yescharacteristic
234C22×C4×C41C2411yescharacteristic
235Q16×C41—28no—
236SD16×C41—28no—
237SD16×C41—28no—
238D8×C41—28no—
239M16×C41—22no—
240M16×C41—22no—
241M16×C41—22no—
242M16×C41—22no—
243M16×C41—22no—
244M16×C41—22no—
245M16×C41—22no—
246M16×C41—22no—
247M16×C41—22no—
248M16×C41—22no—
249M16×C41—41no—
250M16×C41—41no—
251M16×C41—41no—
252M16×C41—41no—
253M16×C41C2×D414yes—
254M16×C41C2×D414yes—
255C2×C8×C41—22no—
256C2×C8×C41—22no—
257C2×C8×C41—22no—
258C2×C8×C41—22no—
259C2×C8×C41—22no—
260C2×C8×C41—22no—
261C2×C8×C41—22no—
262C2×C8×C41—22no—
263C2×C8×C41—41no—
264C2×C8×C41—41no—
265C2×C8×C41—41no—
266C2×C8×C41—41no—
267C4⋊C4×C41—22no—
268C4⋊C4×C41—41no—
269C22⋊C4×C41—22no—
270C22⋊C4×C41—41no—
271C42×C41—22no—
272C42×C41—41no—
273C23×C41—22no—
274C23×C41—22no—
275C23×C41—41no—
276C23×C41—41no—
277C23×C41—41no—
278C23×C41—41no—
279C23×C41—81no—
280C23×C41—82no—
281C23×C41—82no—
282C23×C41#12111yescharacteristic
283C23×C41#12111yescharacteristic
284C23×C41#12311yescharacteristic
285C23×C41#12311yescharacteristic
286C23×C41#12411yescharacteristic
287C23×C41#12411yescharacteristic
288C23×C41C2×#4111yescharacteristic
289Q8×C41—22no—
290Q8×C41—22no—
291Q8×C41—22no—
292Q8×C41—22no—
293Q8×C41—41no—
294Q8×C41—41no—
295Q8×C41—41no—
296Q8×C41—41no—
297D4×C41—22no—
298D4×C41—22no—
299D4×C41—22no—
300D4×C41—22no—
301D4×C41—42no—
302D4×C41—42no—
303D4×C41—42no—
304D4×C41—42no—
305D4×C41—42no—
306D4×C41—42no—
307D4×C41—42no—
308D4×C41—42no—
309D4×C41—41no—
310D4×C41—41no—
311D4×C41—41no—
312D4×C41—41no—
313C2×C4×C41—22no—
314C2×C4×C41—22no—
315C2×C4×C41—41no—
316C2×C4×C41—41no—
317C2×C4×C41—41no—
318C2×C4×C41—41no—
319C2×C4×C41—42no—
320C2×C4×C41—42no—
321C2×C4×C41—42no—
322C2×C4×C41—42no—
323C2×C4×C41—42no—
324C2×C4×C41—42no—
325C2×C4×C41—42no—
326C2×C4×C41—42no—
327C2×C4×C41—42no—
328C2×C4×C41—82no—
329C2×C4×C41#12011yescharacteristic
330C2×C4×C41#12011yescharacteristic
331C2×C4×C41#12011yescharacteristic
332C2×C4×C41#12011yescharacteristic
333C2×C4×C41#12111yescharacteristic
334C2×C4×C41#12111yescharacteristic
335C2×C4×C41#12111yescharacteristic
336C2×C4×C41#12111yescharacteristic
337C2×C4×C41#12111yescharacteristic
338C2×C4×C41#12111yescharacteristic
339C2×C4×C41#12111yescharacteristic
340C2×C4×C41#12111yescharacteristic
341C2×C4×C41#12111yescharacteristic
342C2×C4×C41#12111yescharacteristic
343C2×C4×C41#12311yescharacteristic
344C2×C4×C41#12311yescharacteristic
345C2×C4×C41#12311yescharacteristic
346C2×C4×C41#12311yescharacteristic
347C2×C4×C41#12311yescharacteristic
348C2×C4×C41#12311yescharacteristic
349C2×C4×C41#12411yescharacteristic
350C2×C4×C41#12411yescharacteristic
351C2×C4×C41C22×D411yescharacteristic
352C2×C4×C41C22×D411yescharacteristic
353C2×C4×C41C22×D411yescharacteristic
354C2×C4×C41C22×D411yescharacteristic
355C2×C4×C41C2×#4111yescharacteristic
356C2×C4×C41C2×#4111yescharacteristic
357C8×C41—24no—
358C8×C41—24no—
359C8×C41—42no—
360C8×C41—42no—
361#23525C4111yesmaximal, characteristic, direct product factor, Sylow
362C22×C41—41no—
363C22×C41—41no—
364C22×C41—41no—
365C22×C41—41no—
366C22×C41—41no—
367C22×C41—41no—
368C22×C41—41no—
369C22×C41—42no—
370C22×C41—42no—
371C22×C41—82no—
372C22×C41—82no—
373C22×C41—82no—
374C22×C41—82no—
375C22×C41—82no—
376C22×C41—82no—
377C22×C41#39411yescharacteristic
378C22×C41#39411yescharacteristic
379C22×C41#39411yescharacteristic
380C22×C41#39411yescharacteristic
381C22×C41C2×#12111yescharacteristic
382C22×C41C2×#12311yescharacteristic
383C22×C41C2×#12411yescharacteristic
384C4×C41—42no—
385C4×C41—42no—
386C4×C41—82no—
387C4×C41#39411yescharacteristic
388C4×C41#39411yescharacteristic
389C4×C41#39411yescharacteristic
390C4×C41#39411yescharacteristic
391C4×C41C2×#12011yescharacteristic
392C4×C41C2×#12111yescharacteristic
393C4×C41C2×#12111yescharacteristic
394C4×C41C2×#12311yescharacteristic
395C2×#575C2×C4111yescharacteristic
396C2×#430C2×C4111yescharacteristic, complemented
397C2×#421C2×C4111yescharacteristic, complemented
398#2896C2×C4111yescharacteristic, complemented
399C2×#413C2×C4111yescharacteristic, complemented
400C2×#413C2×C4111yescharacteristic, complemented
401#2049C2×C4114yescomplemented
402#2048C2×C4114yescomplemented
403C2×#344C2×C4111yescharacteristic, complemented
404C2×C41—21no—
405C2×C41—21no—
406C2×C41—21no—
407C2×C41—21no—
408C2×C41—21no—
409C2×C41—21no—
410C2×C41—21no—
411C2×C41—82no—
412C2×C41—82no—
413C2×C41C2×#39411yescharacteristic
414C22×#41C22×C4111yescharacteristic
415C22×#41C22×C4111yescharacteristic
416#575—22no—
417#575—22no—
418#575—22no—
419#575—22no—
420C2×#137—21no—
421C2×#137C22×C4112yes—
422C2×AGL(1,ℤ/8)—21no—
423C2×AGL(1,ℤ/8)C22×C4112yes—
424C2×#135—22no—
425C22×M16C22×C4111yescharacteristic
426C22×M16C22×C4111yescharacteristic
427C22×M16C22×C4111yescharacteristic
428C22×M16C22×C4111yescharacteristic
429C2×#117C22×C4111yescharacteristic
430#430—22no—
431#430C22×C4114yescomplemented
432C2×#108—22no—
433#421—22no—
434#421C22×C4114yes—
435C2×#104—22no—
436#419C22×C4112yescomplemented
437#418C22×C4112yescomplemented
438#417—22no—
439#416—22no—
440#413—22no—
441#413—22no—
442#413—22no—
443#413C22×C4114yes—
444C2×#101—21no—
445C2×#101C22×C4112yescomplemented
446C2×#100—21no—
447C2×#100C22×C4112yescomplemented
448#344C22×C4114yescomplemented
449C41#2352511yescharacteristic, direct product factor, Sylow
450C2×#41—21no—
451C2×#41—21no—
452C2×#41—21no—
453C2×#41—21no—
454C2×#41—21no—
455C2×#41—21no—
456C2×#41—21no—
457C2×#41—21no—
458C2×#41—21no—
459C2×#41—21no—
460C2×#41—21no—
461C2×#41—21no—
462C2×#41—21no—
463C2×#41—21no—
464C2×#41—21no—
465C2×#41—21no—
466C2×#41—21no—
467C2×#41—21no—
468C2×#41—21no—
469C2×#41—21no—
470C2×#41D4×C4112yes—
471C2×#41D4×C4112yes—
472C2×#41D4×C4112yes—
473C2×#41C23×C4112yes—
474C22×Q8D4×C4111yescharacteristic
475C22×Q8C23×C4111yescharacteristic
476C22×D4—21no—
477C22×D4—21no—
478C22×D4D4×C4111yescharacteristic
479C22×D4C23×C4111yescharacteristic
480C23×C4—21no—
481C23×C4—21no—
482C23×C4C23×C4111yescharacteristic
483#137—24no—
484#137—24no—
485#137—24no—
486#137—24no—
487AGL(1,ℤ/8)—24no—
488AGL(1,ℤ/8)—24no—
489AGL(1,ℤ/8)—24no—
490AGL(1,ℤ/8)—24no—
491#135—28no—
492#135—28no—
493C2×Q16—22no—
494C2×SD16—22no—
495C2×SD16—22no—
496C2×D8—22no—
497C2×M16—21no—
498C2×M16—21no—
499C2×M16—21no—
500C2×M16—21no—
501C2×M16—21no—
502C2×M16—21no—
503C2×M16—21no—
504C2×M16—21no—
505C2×M16—21no—
506C2×M16—21no—
507C2×M16—21no—
508C2×M16—21no—
509C2×M16—21no—
510C2×M16—21no—
511C2×M16—21no—
512C2×M16—21no—
513C2×M16D4×C4112yes—
514C2×M16D4×C4112yes—
515C2×M16D4×C4112yes—
516C2×M16D4×C4112yes—
517C2×M16C23×C4112yes—
518C2×M16C23×C4112yes—
519C2×M16C23×C4112yes—
520C2×M16C23×C4112yes—
521C22×C8—21no—
522C22×C8—21no—
523C22×C8—21no—
524C22×C8—21no—
525#117—21no—
526#117—21no—
527#117—21no—
528#117C23×C4112yes—
529C2×C4⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C42—21no—
532#108—28no—
533#104—28no—
534#103—24no—
535#102—24no—
536#101—24no—
537#101—24no—
538#100—24no—
539#100—24no—
540C24—21no—
541C24—21no—
542C24#41×C4111yescharacteristic
543#41—22no—
544#41—22no—
545#41—22no—
546#41—22no—
547#41—22no—
548#41—22no—
549#41—22no—
550#41—22no—
551#41—22no—
552#41—22no—
553#41—22no—
554#41—22no—
555#41—22no—
556#41—22no—
557#41—22no—
558#41—22no—
559#41—41no—
560#41—41no—
561#41—41no—
562#41—41no—
563#41—41no—
564#41—41no—
565#41—41no—
566#41—41no—
567#41—41no—
568#41—41no—
569#41—41no—
570#41—41no—
571#41—41no—
572#41—41no—
573#41—41no—
574#41—41no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8C2×D4×C4112yes—
586C2×Q8C2×D4×C4112yes—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—22no—
590C2×D4—22no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—41no—
602C2×D4—41no—
603C2×D4—41no—
604C2×D4—41no—
605C2×D4—41no—
606C2×D4—41no—
607C2×D4—41no—
608C2×D4—41no—
609C2×D4C2×D4×C4112yes—
610C2×D4C2×D4×C4112yes—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—41no—
618C22×C4—41no—
619C22×C4—41no—
620C22×C4—41no—
621C22×C4—41no—
622C22×C4—41no—
623C22×C4—41no—
624C22×C4—41no—
625C22×C4—41no—
626C22×C4C2×D4×C4111yescharacteristic
627C22×C4C2×D4×C4111yescharacteristic
628C22×C4C2×D4×C4111yescharacteristic
629C22×C4C2×D4×C4111yescharacteristic
630C22×C4C2×D4×C4111yescharacteristic
631C22×C4C2×D4×C4111yescharacteristic
632C22×C4C2×D4×C4111yescharacteristic
633C22×C4C2×D4×C4111yescharacteristic
634C22×C4#41×C4111yescharacteristic
635C22×C4#41×C4111yescharacteristic
636C22×C4#41×C4111yescharacteristic
637C22×C4#41×C4111yescharacteristic
638C22×C4#41×C4111yescharacteristic
639C22×C4C24×C4111yescharacteristic
640Q16—28no—
641SD16—28no—
642SD16—28no—
643D8—28no—
644M16—22no—
645M16—22no—
646M16—22no—
647M16—22no—
648M16—22no—
649M16—22no—
650M16—22no—
651M16—22no—
652M16—22no—
653M16—22no—
654M16—41no—
655M16—41no—
656M16—41no—
657M16—41no—
658M16C2×D4×C4114yes—
659M16C2×D4×C4114yes—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—22no—
663C2×C8—22no—
664C2×C8—22no—
665C2×C8—22no—
666C2×C8—22no—
667C2×C8—22no—
668C2×C8—41no—
669C2×C8—41no—
670C2×C8—41no—
671C2×C8—41no—
672C4⋊C4—22no—
673C4⋊C4—41no—
674C22⋊C4—22no—
675C22⋊C4—41no—
676C42—22no—
677C42—41no—
678C23—22no—
679C23—22no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—81no—
685C23—82no—
686C23—82no—
687C23#121×C4111yescharacteristic
688C23#121×C4111yescharacteristic
689C23#123×C4111yescharacteristic
690C23#123×C4111yescharacteristic
691C23#124×C4111yescharacteristic
692C23#124×C4111yescharacteristic
693C23C2×#41×C4111yescharacteristic
694Q8—22no—
695Q8—22no—
696Q8—22no—
697Q8—22no—
698Q8—41no—
699Q8—41no—
700Q8—41no—
701Q8—41no—
702D4—22no—
703D4—22no—
704D4—22no—
705D4—22no—
706D4—42no—
707D4—42no—
708D4—42no—
709D4—42no—
710D4—42no—
711D4—42no—
712D4—42no—
713D4—42no—
714D4—41no—
715D4—41no—
716D4—41no—
717D4—41no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—82no—
734C2×C4#120×C4111yescharacteristic
735C2×C4#120×C4111yescharacteristic
736C2×C4#120×C4111yescharacteristic
737C2×C4#120×C4111yescharacteristic
738C2×C4#121×C4111yescharacteristic
739C2×C4#121×C4111yescharacteristic
740C2×C4#121×C4111yescharacteristic
741C2×C4#121×C4111yescharacteristic
742C2×C4#121×C4111yescharacteristic
743C2×C4#121×C4111yescharacteristic
744C2×C4#121×C4111yescharacteristic
745C2×C4#121×C4111yescharacteristic
746C2×C4#121×C4111yescharacteristic
747C2×C4#121×C4111yescharacteristic
748C2×C4#123×C4111yescharacteristic
749C2×C4#123×C4111yescharacteristic
750C2×C4#123×C4111yescharacteristic
751C2×C4#123×C4111yescharacteristic
752C2×C4#123×C4111yescharacteristic
753C2×C4#123×C4111yescharacteristic
754C2×C4#124×C4111yescharacteristic
755C2×C4#124×C4111yescharacteristic
756C2×C4C22×D4×C4111yescharacteristic
757C2×C4C22×D4×C4111yescharacteristic
758C2×C4C22×D4×C4111yescharacteristic
759C2×C4C22×D4×C4111yescharacteristic
760C2×C4C2×#41×C4111yescharacteristic
761C2×C4C2×#41×C4111yescharacteristic
762C8—24no—
763C8—24no—
764C8—42no—
765C8—42no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—42no—
774C22—42no—
775C22—82no—
776C22—82no—
777C22—82no—
778C22—82no—
779C22—82no—
780C22—82no—
781C22C41×#39411yescharacteristic
782C22C41×#39411yescharacteristic
783C22C41×#39411yescharacteristic
784C22C41×#39411yescharacteristic
785C22C2×#121×C4111yescharacteristic
786C22C2×#123×C4111yescharacteristic
787C22C2×#124×C4111yescharacteristic
788C4—42no—
789C4—42no—
790C4—82no—
791C4C41×#39411yescharacteristic
792C4C41×#39411yescharacteristic
793C4C41×#39411yescharacteristic
794C4C41×#39411yescharacteristic
795C4C2×#120×C4111yescharacteristic
796C4C2×#121×C4111yescharacteristic
797C4C2×#121×C4111yescharacteristic
798C4C2×#123×C4111yescharacteristic
799C2—21no—
800C2—21no—
801C2—21no—
802C2—21no—
803C2—21no—
804C2—21no—
805C2—21no—
806C2—82no—
807C2—82no—
808C2C2×C41×#39411yescharacteristic
subgroupG/H
centerC4×C41#394
commutator, Frattini, cosocleC22×C4C24×C41
socleC2×C41C2×#394
prime radicalC2×C41×#575C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C41 ◁ C23×C4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C41×#430C2semidirect
3. C2×C41×#421C2semidirect
4. C41×#2896C2semidirect
5. C2×C41×#413C2semidirect
6. C2×C41×#413C2semidirect
7. C41×#2049C2semidirect
8. C41×#2048C2semidirect
9. C2×C41×#344C2semidirect
27. C41×#430C22semidirect
32. C41×#419C22semidirect
33. C41×#418C22semidirect
41. C2×#101×C41C22semidirect
43. C2×#100×C41C22semidirect
44. C41×#344C22semidirect
361. #23525C41direct (N × H)
396. C2×#430C2×C41semidirect
397. C2×#421C2×C41semidirect
398. #2896C2×C41semidirect
399. C2×#413C2×C41semidirect
400. C2×#413C2×C41semidirect
401. #2049C2×C41semidirect
402. #2048C2×C41semidirect
403. C2×#344C2×C41semidirect
431. #430C22×C41semidirect
436. #419C22×C41semidirect
437. #418C22×C41semidirect
445. C2×#101C22×C41semidirect
447. C2×#100C22×C41semidirect
448. #344C22×C41semidirect
449. C41#23525direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C41×#5752
C2×C41×#4302
C2×C41×#4212
C41×#28962
C2×C41×#4132
C41×#20492
C41×#20482
C2×C41×#3442
#2352541