Finite Group Databasebeta

← C41×#18224 #23794425

Subgroups — C41×#18224 #23794425

Order 10496.

1370 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3534C211yesmaximal, characteristic, complemented
2C41×#3003C211yesmaximal, characteristic, complemented
3C2×C41×#447C211yesmaximal, characteristic, complemented
4C41×#2613C211yesmaximal, characteristic, complemented
5C41×#1600C212yesmaximal, complemented
6C41×#1598C212yesmaximal, complemented
7C41×#1597C212yesmaximal, complemented
8C41×#1595C212yesmaximal, complemented
9C41×#1516C211yesmaximal, characteristic, complemented
10C41×#1510C211yesmaximal, characteristic, complemented
11C41×#1468C211yesmaximal, characteristic, complemented
12C23×D4×C41C2211yescharacteristic, complemented
13C2×AGL(1,ℤ/8)×C41—21no—
14C22×D8×C41—21no—
15C41×#562—21no—
16C41×#560—21no—
17C41×#553—21no—
18C41×#551—21no—
19C41×#546—21no—
20C41×#546—21no—
21C41×#546—21no—
22D42×C41—21no—
23C41×#540—21no—
24C41×#539—21no—
25C41×#539C2211yescharacteristic, complemented
26C41×#538—21no—
27C41×#538C2211yescharacteristic, complemented
28C41×#537C2211yescharacteristic, complemented
29C41×#534—21no—
30C41×#534C2211yescharacteristic, complemented
31C41×#525C2211yescharacteristic
32C2×#123×C41C2211yescharacteristic
33C2×#121×C41C2211yescharacteristic
34C2×#120×C41—21no—
35C41×#450—21no—
36C41×#450C2212yescomplemented
37C41×#447—21no—
38C41×#447—21no—
39C41×#447—21no—
40C41×#447C2212yes—
41C41×#447C2212yescomplemented
42C41×#447C2212yescomplemented
43C41×#418—21no—
44C2×#102×C41—21no—
45C41×#407C2211yescharacteristic, complemented
46C2×C22⋊C8×C41C2211yescharacteristic, complemented
47C41×#394—21no—
48C41×#394C2212yescomplemented
49C41×#392—21no—
50C41×#392C2212yescomplemented
51C41×#381C2211yescharacteristic, complemented
52C41×#379—21no—
53C41×#328C2212yescomplemented
54C41×#327C2212yescomplemented
55C41×#327C2212yescomplemented
56C41×#327C2212yescomplemented
57C41×#324C2212yescomplemented
58C41×#323C2212yescomplemented
59C25×C41—21no—
60C2×#41×C41—21no—
61C2×#41×C41D411yescharacteristic, complemented
62C22×D4×C41—21no—
63C22×D4×C41—21no—
64C22×D4×C41—21no—
65C22×D4×C41—22no—
66C22×D4×C41—21no—
67C22×D4×C41—21no—
68C22×D4×C41—21no—
69C22×D4×C41—21no—
70C22×D4×C41—21no—
71C22×D4×C41—44no—
72C22×D4×C41D411yescharacteristic
73C22×D4×C41D411yescharacteristic, complemented
74C22×D4×C41C2312yes—
75C23×C4×C41C2311yescharacteristic
76AGL(1,ℤ/8)×C41—44no—
77C2×SD16×C41—22no—
78C2×D8×C41—22no—
79C2×D8×C41—22no—
80C2×D8×C41—22no—
81C2×D8×C41—44no—
82C2×M16×C41—21no—
83C22×C8×C41—21no—
84#127×C41—21no—
85#126×C41—21no—
86#126×C41—21no—
87#126×C41—21no—
88#126×C41—21no—
89#125×C41—21no—
90#125×C41—21no—
91#124×C41—21no—
92#124×C41—21no—
93#124×C41—21no—
94#123×C41—21no—
95#123×C41—21no—
96#123×C41—21no—
97#123×C41—21no—
98#123×C41—21no—
99#123×C41—21no—
100#123×C41—21no—
101#123×C41—21no—
102#123×C41—21no—
103#123×C41—21no—
104#123×C41—21no—
105#123×C41—21no—
106#123×C41—21no—
107#123×C41—21no—
108C22⋊Q8×C41—21no—
109C22⋊Q8×C41—21no—
110C22⋊Q8×C41—21no—
111C22⋊Q8×C41—21no—
112C22⋊Q8×C41—21no—
113C22⋊Q8×C41D411yescharacteristic, complemented
114C22⋊Q8×C41C2311yescharacteristic
115#121×C41—21no—
116#121×C41—21no—
117#121×C41—21no—
118#121×C41—21no—
119#121×C41—21no—
120#121×C41—21no—
121#121×C41—21no—
122#121×C41—21no—
123#121×C41—21no—
124#121×C41—21no—
125#121×C41—21no—
126#121×C41—21no—
127#121×C41—21no—
128#121×C41—21no—
129#121×C41—21no—
130#121×C41D411yescharacteristic, complemented
131#121×C41D411yescharacteristic, complemented
132#121×C41D411yescharacteristic, complemented
133#121×C41C2311yescharacteristic
134#121×C41C2311yescharacteristic
135#121×C41C2311yescharacteristic
136#120×C41—21no—
137#120×C41—21no—
138#120×C41—21no—
139#120×C41—21no—
140#120×C41—21no—
141#120×C41—21no—
142#120×C41—21no—
143#120×C41—21no—
144#120×C41—44no—
145C4×D4×C41—21no—
146C4×D4×C41—21no—
147C4×D4×C41—21no—
148C4×D4×C41—21no—
149C4×D4×C41—21no—
150C4×D4×C41—21no—
151C4×D4×C41—21no—
152C4×D4×C41—21no—
153#117×C41—21no—
154#117×C41D411yescharacteristic, complemented
155C2×C4⋊C4×C41D411yescharacteristic
156C2×C4⋊C4×C41D411yescharacteristic, complemented
157C2×C4⋊C4×C41C2311yescharacteristic
158C2×C22⋊C4×C41—21no—
159C2×C22⋊C4×C41—21no—
160C2×C22⋊C4×C41—21no—
161C2×C22⋊C4×C41—21no—
162C2×C22⋊C4×C41—22no—
163C2×C22⋊C4×C41—22no—
164C2×C22⋊C4×C41—22no—
165C2×C22⋊C4×C41D411yescharacteristic
166C2×C22⋊C4×C41D411yescharacteristic
167C2×C22⋊C4×C41C2311yescharacteristic
168#102×C41—22no—
169#102×C41—22no—
170#102×C41—22no—
171#102×C41—22no—
172C22⋊C8×C41—21no—
173C22⋊C8×C41—21no—
174C22⋊C8×C41C2312yes—
175C22⋊C8×C41C2312yes—
176#95×C41—21no—
177#95×C41C2312yes—
178C24×C41—24no—
179C24×C41—21no—
180C24×C41—22no—
181C24×C41—21no—
182C24×C41—42no—
183C24×C41—41no—
184C24×C41—41no—
185C24×C41—82no—
186C24×C41—82no—
187C24×C41C2×D411yescharacteristic
188C24×C41C2×D411yescharacteristic
189#41×C41—42no—
190#41×C41—82no—
191C2×Q8×C41—21no—
192C2×Q8×C41C2×D411yescharacteristic
193C2×D4×C41—24no—
194C2×D4×C41—24no—
195C2×D4×C41—21no—
196C2×D4×C41—21no—
197C2×D4×C41—21no—
198C2×D4×C41—21no—
199C2×D4×C41—21no—
200C2×D4×C41—21no—
201C2×D4×C41—21no—
202C2×D4×C41—21no—
203C2×D4×C41—21no—
204C2×D4×C41—21no—
205C2×D4×C41—21no—
206C2×D4×C41—21no—
207C2×D4×C41—21no—
208C2×D4×C41—21no—
209C2×D4×C41—21no—
210C2×D4×C41—21no—
211C2×D4×C41—21no—
212C2×D4×C41—22no—
213C2×D4×C41—22no—
214C2×D4×C41—42no—
215C2×D4×C41—42no—
216C2×D4×C41—42no—
217C2×D4×C41—44no—
218C2×D4×C41—44no—
219C2×D4×C41—44no—
220C2×D4×C41—44no—
221C2×D4×C41—42no—
222C2×D4×C41—44no—
223C2×D4×C41—41no—
224C2×D4×C41—41no—
225C2×D4×C41—82no—
226C2×D4×C41—82no—
227C2×D4×C41—82no—
228C2×D4×C41—82no—
229C2×D4×C41—82no—
230C2×D4×C41C2×D411yescharacteristic
231C2×D4×C41C2×D411yescharacteristic
232C2×D4×C41C2×D411yescharacteristic
233C22×C4×C41—21no—
234C22×C4×C41—21no—
235C22×C4×C41—21no—
236C22×C4×C41—21no—
237C22×C4×C41—21no—
238C22×C4×C41—21no—
239C22×C4×C41—21no—
240C22×C4×C41—22no—
241C22×C4×C41—42no—
242C22×C4×C41C2×D411yescharacteristic
243C22×C4×C41C2×D411yescharacteristic
244C22×C4×C41C2×D411yescharacteristic
245C22×C4×C41C2×D411yescharacteristic
246C22×C4×C41C2×D411yescharacteristic
247C22×C4×C41C2×D411yescharacteristic
248C22×C4×C41C2×D411yescharacteristic
249C22×C4×C41C2×D411yescharacteristic
250C22×C4×C41C2411yescharacteristic
251SD16×C41—44no—
252D8×C41—44no—
253D8×C41—44no—
254D8×C41—44no—
255M16×C41—42no—
256C2×C8×C41—22no—
257C2×C8×C41—22no—
258C2×C8×C41—42no—
259C4⋊C4×C41—21no—
260C4⋊C4×C41—21no—
261C4⋊C4×C41—21no—
262C4⋊C4×C41—21no—
263C4⋊C4×C41—21no—
264C4⋊C4×C41—21no—
265C4⋊C4×C41—21no—
266C4⋊C4×C41—21no—
267C4⋊C4×C41—21no—
268C4⋊C4×C41—21no—
269C4⋊C4×C41—21no—
270C4⋊C4×C41—21no—
271C4⋊C4×C41—21no—
272C4⋊C4×C41C2×D411yescharacteristic
273C4⋊C4×C41C2×D411yescharacteristic
274C4⋊C4×C41C2×D411yescharacteristic
275C4⋊C4×C41C2×D411yescharacteristic
276C22⋊C4×C41—21no—
277C22⋊C4×C41—21no—
278C22⋊C4×C41—21no—
279C22⋊C4×C41—21no—
280C22⋊C4×C41—21no—
281C22⋊C4×C41—21no—
282C22⋊C4×C41—21no—
283C22⋊C4×C41—21no—
284C22⋊C4×C41—21no—
285C22⋊C4×C41—21no—
286C22⋊C4×C41—21no—
287C22⋊C4×C41—21no—
288C22⋊C4×C41—21no—
289C22⋊C4×C41—21no—
290C22⋊C4×C41—21no—
291C22⋊C4×C41—21no—
292C22⋊C4×C41—21no—
293C22⋊C4×C41—21no—
294C22⋊C4×C41—21no—
295C22⋊C4×C41—21no—
296C22⋊C4×C41—21no—
297C22⋊C4×C41—21no—
298C22⋊C4×C41—21no—
299C22⋊C4×C41—21no—
300C22⋊C4×C41—21no—
301C22⋊C4×C41—44no—
302C22⋊C4×C41—42no—
303C22⋊C4×C41—82no—
304C22⋊C4×C41—82no—
305C42×C41—21no—
306C42×C41—21no—
307C42×C41—21no—
308C23×C41—22no—
309C23×C41—22no—
310C23×C41—24no—
311C23×C41—21no—
312C23×C41—21no—
313C23×C41—21no—
314C23×C41—21no—
315C23×C41—22no—
316C23×C41—41no—
317C23×C41—42no—
318C23×C41—42no—
319C23×C41—44no—
320C23×C41—42no—
321C23×C41—41no—
322C23×C41—41no—
323C23×C41—42no—
324C23×C41—42no—
325C23×C41—42no—
326C23×C41—44no—
327C23×C41—42no—
328C23×C41—81no—
329C23×C41—81no—
330C23×C41—82no—
331C23×C41—82no—
332C23×C41—82no—
333C23×C41—82no—
334C23×C41—88no—
335C23×C41—81no—
336C23×C41—81no—
337C23×C41—81no—
338C23×C41—88no—
339C23×C41#12011yescharacteristic
340C23×C41#12011yescharacteristic
341C23×C41C22×D411yescharacteristic
342Q8×C41—41no—
343Q8×C41—81no—
344D4×C41—24no—
345D4×C41—24no—
346D4×C41—41no—
347D4×C41—41no—
348D4×C41—41no—
349D4×C41—42no—
350D4×C41—42no—
351D4×C41—44no—
352D4×C41—44no—
353D4×C41—42no—
354D4×C41—42no—
355D4×C41—42no—
356D4×C41—42no—
357D4×C41—42no—
358D4×C41—81no—
359D4×C41—81no—
360D4×C41—81no—
361D4×C41—81no—
362D4×C41—81no—
363D4×C41—81no—
364D4×C41—81no—
365D4×C41—81no—
366D4×C41—81no—
367D4×C41—81no—
368D4×C41—81no—
369D4×C41—81no—
370D4×C41—88no—
371C2×C4×C41—22no—
372C2×C4×C41—22no—
373C2×C4×C41—21no—
374C2×C4×C41—21no—
375C2×C4×C41—21no—
376C2×C4×C41—21no—
377C2×C4×C41—21no—
378C2×C4×C41—21no—
379C2×C4×C41—21no—
380C2×C4×C41—21no—
381C2×C4×C41—22no—
382C2×C4×C41—41no—
383C2×C4×C41—41no—
384C2×C4×C41—41no—
385C2×C4×C41—41no—
386C2×C4×C41—41no—
387C2×C4×C41—41no—
388C2×C4×C41—42no—
389C2×C4×C41—42no—
390C2×C4×C41—42no—
391C2×C4×C41—81no—
392C2×C4×C41—81no—
393C2×C4×C41—81no—
394C2×C4×C41—81no—
395C2×C4×C41—81no—
396C2×C4×C41—81no—
397C2×C4×C41—81no—
398C2×C4×C41#12011yescharacteristic
399C2×C4×C41#12011yescharacteristic
400C2×C4×C41C22×D411yescharacteristic
401C2×C4×C41C22×D411yescharacteristic
402C8×C41—42no—
403C8×C41—42no—
404#18224C4111yesmaximal, characteristic, direct product factor, Sylow
405C22×C41—21no—
406C22×C41—21no—
407C22×C41—21no—
408C22×C41—21no—
409C22×C41—21no—
410C22×C41—21no—
411C22×C41—21no—
412C22×C41—44no—
413C22×C41—44no—
414C22×C41—44no—
415C22×C41—41no—
416C22×C41—41no—
417C22×C41—41no—
418C22×C41—41no—
419C22×C41—41no—
420C22×C41—41no—
421C22×C41—41no—
422C22×C41—41no—
423C22×C41—41no—
424C22×C41—41no—
425C22×C41—44no—
426C22×C41—41no—
427C22×C41—41no—
428C22×C41—82no—
429C22×C41—82no—
430C22×C41—82no—
431C22×C41—88no—
432C22×C41—88no—
433C22×C41—82no—
434C22×C41—82no—
435C22×C41—162no—
436C22×C41—162no—
437C22×C41B(4,𝔽2)12yes—
438C22×C41C2×#12011yescharacteristic
439C22×C41#57612yes—
440C4×C41—21no—
441C4×C41—21no—
442C4×C41—21no—
443C4×C41—21no—
444C4×C41—41no—
445C4×C41—41no—
446C4×C41—41no—
447C4×C41—41no—
448C4×C41—41no—
449C4×C41—41no—
450C4×C41—41no—
451C4×C41—41no—
452C4×C41—82no—
453#3534C2×C4111yescharacteristic, complemented
454#3003C2×C4111yescharacteristic, complemented
455C2×#447C2×C4111yescharacteristic, complemented
456#2613C2×C4111yescharacteristic, complemented
457#1600C2×C4112yescomplemented
458#1598C2×C4112yescomplemented
459#1597C2×C4112yescomplemented
460#1595C2×C4112yescomplemented
461#1516C2×C4111yescharacteristic, complemented
462#1510C2×C4111yescharacteristic, complemented
463#1468C2×C4111yescharacteristic, complemented
464C2×C41—22no—
465C2×C41—22no—
466C2×C41—41no—
467C2×C41—84no—
468C2×C41—81no—
469C2×C41—81no—
470C2×C41—81no—
471C2×C41—81no—
472C2×C41#300811yescharacteristic
473C2×C41#302111yescharacteristic
474C2×C41C2×B(4,𝔽2)11yescharacteristic
475C23×D4C22×C4111yescharacteristic, complemented
476C2×AGL(1,ℤ/8)—21no—
477C22×D8—21no—
478#562—21no—
479#560—21no—
480#553—21no—
481#551—21no—
482#546—21no—
483#546—21no—
484#546—21no—
485D42—21no—
486#540—21no—
487#539—21no—
488#539C22×C4111yescharacteristic, complemented
489#538—21no—
490#538C22×C4111yescharacteristic, complemented
491#537C22×C4111yescharacteristic, complemented
492#534—21no—
493#534C22×C4111yescharacteristic, complemented
494#525C22×C4111yescharacteristic
495C2×#123C22×C4111yescharacteristic
496C2×#121C22×C4111yescharacteristic
497C2×#120—21no—
498#450—21no—
499#450C22×C4112yescomplemented
500#447—21no—
501#447—21no—
502#447—21no—
503#447C22×C4112yes—
504#447C22×C4112yescomplemented
505#447C22×C4112yescomplemented
506#418—21no—
507C2×#102—21no—
508#407C22×C4111yescharacteristic, complemented
509C2×C22⋊C8C22×C4111yescharacteristic, complemented
510#394—21no—
511#394C22×C4112yescomplemented
512#392—21no—
513#392C22×C4112yescomplemented
514#381C22×C4111yescharacteristic, complemented
515#379—21no—
516#328C22×C4112yescomplemented
517#327C22×C4112yescomplemented
518#327C22×C4112yescomplemented
519#327C22×C4112yescomplemented
520#324C22×C4112yescomplemented
521#323C22×C4112yescomplemented
522C41#1822411yescharacteristic, direct product factor, Sylow
523C25—21no—
524C2×#41—21no—
525C2×#41D4×C4111yescharacteristic, complemented
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—21no—
529C22×D4—22no—
530C22×D4—21no—
531C22×D4—21no—
532C22×D4—21no—
533C22×D4—21no—
534C22×D4—21no—
535C22×D4—44no—
536C22×D4D4×C4111yescharacteristic
537C22×D4D4×C4111yescharacteristic, complemented
538C22×D4C23×C4112yes—
539C23×C4C23×C4111yescharacteristic
540AGL(1,ℤ/8)—44no—
541C2×SD16—22no—
542C2×D8—22no—
543C2×D8—22no—
544C2×D8—22no—
545C2×D8—44no—
546C2×M16—21no—
547C22×C8—21no—
548#127—21no—
549#126—21no—
550#126—21no—
551#126—21no—
552#126—21no—
553#125—21no—
554#125—21no—
555#124—21no—
556#124—21no—
557#124—21no—
558#123—21no—
559#123—21no—
560#123—21no—
561#123—21no—
562#123—21no—
563#123—21no—
564#123—21no—
565#123—21no—
566#123—21no—
567#123—21no—
568#123—21no—
569#123—21no—
570#123—21no—
571#123—21no—
572C22⋊Q8—21no—
573C22⋊Q8—21no—
574C22⋊Q8—21no—
575C22⋊Q8—21no—
576C22⋊Q8—21no—
577C22⋊Q8D4×C4111yescharacteristic, complemented
578C22⋊Q8C23×C4111yescharacteristic
579#121—21no—
580#121—21no—
581#121—21no—
582#121—21no—
583#121—21no—
584#121—21no—
585#121—21no—
586#121—21no—
587#121—21no—
588#121—21no—
589#121—21no—
590#121—21no—
591#121—21no—
592#121—21no—
593#121—21no—
594#121D4×C4111yescharacteristic, complemented
595#121D4×C4111yescharacteristic, complemented
596#121D4×C4111yescharacteristic, complemented
597#121C23×C4111yescharacteristic
598#121C23×C4111yescharacteristic
599#121C23×C4111yescharacteristic
600#120—21no—
601#120—21no—
602#120—21no—
603#120—21no—
604#120—21no—
605#120—21no—
606#120—21no—
607#120—21no—
608#120—44no—
609C4×D4—21no—
610C4×D4—21no—
611C4×D4—21no—
612C4×D4—21no—
613C4×D4—21no—
614C4×D4—21no—
615C4×D4—21no—
616C4×D4—21no—
617#117—21no—
618#117D4×C4111yescharacteristic, complemented
619C2×C4⋊C4D4×C4111yescharacteristic
620C2×C4⋊C4D4×C4111yescharacteristic, complemented
621C2×C4⋊C4C23×C4111yescharacteristic
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—22no—
627C2×C22⋊C4—22no—
628C2×C22⋊C4—22no—
629C2×C22⋊C4D4×C4111yescharacteristic
630C2×C22⋊C4D4×C4111yescharacteristic
631C2×C22⋊C4C23×C4111yescharacteristic
632#102—22no—
633#102—22no—
634#102—22no—
635#102—22no—
636C22⋊C8—21no—
637C22⋊C8—21no—
638C22⋊C8C23×C4112yes—
639C22⋊C8C23×C4112yes—
640#95—21no—
641#95C23×C4112yes—
642C24—24no—
643C24—21no—
644C24—22no—
645C24—21no—
646C24—42no—
647C24—41no—
648C24—41no—
649C24—82no—
650C24—82no—
651C24C2×D4×C4111yescharacteristic
652C24C2×D4×C4111yescharacteristic
653#41—42no—
654#41—82no—
655C2×Q8—21no—
656C2×Q8C2×D4×C4111yescharacteristic
657C2×D4—24no—
658C2×D4—24no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—22no—
677C2×D4—22no—
678C2×D4—42no—
679C2×D4—42no—
680C2×D4—42no—
681C2×D4—44no—
682C2×D4—44no—
683C2×D4—44no—
684C2×D4—44no—
685C2×D4—42no—
686C2×D4—44no—
687C2×D4—41no—
688C2×D4—41no—
689C2×D4—82no—
690C2×D4—82no—
691C2×D4—82no—
692C2×D4—82no—
693C2×D4—82no—
694C2×D4C2×D4×C4111yescharacteristic
695C2×D4C2×D4×C4111yescharacteristic
696C2×D4C2×D4×C4111yescharacteristic
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—22no—
705C22×C4—42no—
706C22×C4C2×D4×C4111yescharacteristic
707C22×C4C2×D4×C4111yescharacteristic
708C22×C4C2×D4×C4111yescharacteristic
709C22×C4C2×D4×C4111yescharacteristic
710C22×C4C2×D4×C4111yescharacteristic
711C22×C4C2×D4×C4111yescharacteristic
712C22×C4C2×D4×C4111yescharacteristic
713C22×C4C2×D4×C4111yescharacteristic
714C22×C4C24×C4111yescharacteristic
715SD16—44no—
716D8—44no—
717D8—44no—
718D8—44no—
719M16—42no—
720C2×C8—22no—
721C2×C8—22no—
722C2×C8—42no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4C2×D4×C4111yescharacteristic
737C4⋊C4C2×D4×C4111yescharacteristic
738C4⋊C4C2×D4×C4111yescharacteristic
739C4⋊C4C2×D4×C4111yescharacteristic
740C22⋊C4—21no—
741C22⋊C4—21no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—21no—
745C22⋊C4—21no—
746C22⋊C4—21no—
747C22⋊C4—21no—
748C22⋊C4—21no—
749C22⋊C4—21no—
750C22⋊C4—21no—
751C22⋊C4—21no—
752C22⋊C4—21no—
753C22⋊C4—21no—
754C22⋊C4—21no—
755C22⋊C4—21no—
756C22⋊C4—21no—
757C22⋊C4—21no—
758C22⋊C4—21no—
759C22⋊C4—21no—
760C22⋊C4—21no—
761C22⋊C4—21no—
762C22⋊C4—21no—
763C22⋊C4—21no—
764C22⋊C4—21no—
765C22⋊C4—44no—
766C22⋊C4—42no—
767C22⋊C4—82no—
768C22⋊C4—82no—
769C42—21no—
770C42—21no—
771C42—21no—
772C23—22no—
773C23—22no—
774C23—24no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—22no—
780C23—41no—
781C23—42no—
782C23—42no—
783C23—44no—
784C23—42no—
785C23—41no—
786C23—41no—
787C23—42no—
788C23—42no—
789C23—42no—
790C23—44no—
791C23—42no—
792C23—81no—
793C23—81no—
794C23—82no—
795C23—82no—
796C23—82no—
797C23—82no—
798C23—88no—
799C23—81no—
800C23—81no—
801C23—81no—
802C23—88no—
803C23#120×C4111yescharacteristic
804C23#120×C4111yescharacteristic
805C23C22×D4×C4111yescharacteristic
806Q8—41no—
807Q8—81no—
808D4—24no—
809D4—24no—
810D4—41no—
811D4—41no—
812D4—41no—
813D4—42no—
814D4—42no—
815D4—44no—
816D4—44no—
817D4—42no—
818D4—42no—
819D4—42no—
820D4—42no—
821D4—42no—
822D4—81no—
823D4—81no—
824D4—81no—
825D4—81no—
826D4—81no—
827D4—81no—
828D4—81no—
829D4—81no—
830D4—81no—
831D4—81no—
832D4—81no—
833D4—81no—
834D4—88no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—22no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—81no—
856C2×C4—81no—
857C2×C4—81no—
858C2×C4—81no—
859C2×C4—81no—
860C2×C4—81no—
861C2×C4—81no—
862C2×C4#120×C4111yescharacteristic
863C2×C4#120×C4111yescharacteristic
864C2×C4C22×D4×C4111yescharacteristic
865C2×C4C22×D4×C4111yescharacteristic
866C8—42no—
867C8—42no—
868C22—21no—
869C22—21no—
870C22—21no—
871C22—21no—
872C22—21no—
873C22—21no—
874C22—21no—
875C22—44no—
876C22—44no—
877C22—44no—
878C22—41no—
879C22—41no—
880C22—41no—
881C22—41no—
882C22—41no—
883C22—41no—
884C22—41no—
885C22—41no—
886C22—41no—
887C22—41no—
888C22—44no—
889C22—41no—
890C22—41no—
891C22—82no—
892C22—82no—
893C22—82no—
894C22—88no—
895C22—88no—
896C22—82no—
897C22—82no—
898C22—162no—
899C22—162no—
900C22C41×B(4,𝔽2)12yes—
901C22C2×#120×C4111yescharacteristic
902C22C41×#57612yes—
903C4—21no—
904C4—21no—
905C4—21no—
906C4—21no—
907C4—41no—
908C4—41no—
909C4—41no—
910C4—41no—
911C4—41no—
912C4—41no—
913C4—41no—
914C4—41no—
915C4—82no—
916C2—22no—
917C2—22no—
918C2—41no—
919C2—84no—
920C2—81no—
921C2—81no—
922C2—81no—
923C2—81no—
924C2C41×#300811yescharacteristic
925C2C41×#302111yescharacteristic
926C2C2×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×#3534C2semidirect
2. C41×#3003C2semidirect
3. C2×C41×#447C2semidirect
4. C41×#2613C2semidirect
5. C41×#1600C2semidirect
6. C41×#1598C2semidirect
7. C41×#1597C2semidirect
8. C41×#1595C2semidirect
9. C41×#1516C2semidirect
10. C41×#1510C2semidirect
11. C41×#1468C2semidirect
12. C23×D4×C41C22semidirect
25. C41×#539C22semidirect
27. C41×#538C22semidirect
28. C41×#537C22semidirect
30. C41×#534C22semidirect
36. C41×#450C22semidirect
41. C41×#447C22semidirect
42. C41×#447C22semidirect
45. C41×#407C22semidirect
46. C2×C22⋊C8×C41C22semidirect
48. C41×#394C22semidirect
50. C41×#392C22semidirect
51. C41×#381C22semidirect
53. C41×#328C22semidirect
54. C41×#327C22semidirect
55. C41×#327C22semidirect
56. C41×#327C22semidirect
57. C41×#324C22semidirect
58. C41×#323C22semidirect
61. C2×#41×C41D4semidirect
73. C22×D4×C41D4semidirect
113. C22⋊Q8×C41D4semidirect
130. #121×C41D4semidirect
131. #121×C41D4semidirect
132. #121×C41D4semidirect
154. #117×C41D4semidirect
156. C2×C4⋊C4×C41D4semidirect
404. #18224C41direct (N × H)
453. #3534C2×C41semidirect
454. #3003C2×C41semidirect
455. C2×#447C2×C41semidirect
456. #2613C2×C41semidirect
457. #1600C2×C41semidirect
458. #1598C2×C41semidirect
459. #1597C2×C41semidirect
460. #1595C2×C41semidirect
461. #1516C2×C41semidirect
462. #1510C2×C41semidirect
463. #1468C2×C41semidirect
475. C23×D4C22×C41semidirect
488. #539C22×C41semidirect
490. #538C22×C41semidirect
491. #537C22×C41semidirect
493. #534C22×C41semidirect
499. #450C22×C41semidirect
504. #447C22×C41semidirect
505. #447C22×C41semidirect
508. #407C22×C41semidirect
509. C2×C22⋊C8C22×C41semidirect
511. #394C22×C41semidirect
513. #392C22×C41semidirect
514. #381C22×C41semidirect
516. #328C22×C41semidirect
517. #327C22×C41semidirect
518. #327C22×C41semidirect
519. #327C22×C41semidirect
520. #324C22×C41semidirect
521. #323C22×C41semidirect
522. C41#18224direct (N × H)
525. C2×#41D4×C41semidirect
537. C22×D4D4×C41semidirect
577. C22⋊Q8D4×C41semidirect
594. #121D4×C41semidirect
595. #121D4×C41semidirect
596. #121D4×C41semidirect
618. #117D4×C41semidirect
620. 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×#35342
C41×#30032
C2×C41×#4472
C41×#26132
C41×#16002
C41×#15982
C41×#15972
C41×#15952
C41×#15162
C41×#15102
C41×#14682
#1822441