Finite Group Databasebeta

← C41×#24407 #23800608

Subgroups — C41×#24407 #23800608

Order 10496.

1476 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3485C211yesmaximal, characteristic
2C2×C41×#458C211yesmaximal, characteristic, complemented
3C2×C41×#410C211yesmaximal, characteristic, complemented
4C41×#2413C212yesmaximal, complemented
5C41×#2406C211yesmaximal, characteristic, complemented
6C41×#2044C212yesmaximal, complemented
7C41×#2022C212yesmaximal, complemented
8C41×#1899C212yesmaximal, complemented
9C41×#1890C211yesmaximal, characteristic, complemented
10C41×#1867C211yesmaximal, characteristic, complemented
11C41×#1790C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C41C2211yescharacteristic
13C22×#41×C41C2211yescharacteristic
14C41×#547—22no—
15C41×#547—22no—
16C41×#546—22no—
17C41×#546—22no—
18C41×#536—21no—
19C41×#534—21no—
20C41×#534C2212yes—
21C41×#525—21no—
22C2×#123×C41—21no—
23C2×#123×C41C2211yescharacteristic
24C2×#123×C41C2212yes—
25C2×#123×C41C2212yes—
26C2×#123×C41C2211yescharacteristic, complemented
27C41×#518C2211yescharacteristic
28C2×#117×C41C2212yescomplemented
29C22×C4⋊C4×C41C2211yescharacteristic, complemented
30C41×#458—24no—
31C41×#410—24no—
32C2×#99×C41C2212yes—
33C2×#99×C41C2211yescharacteristic
34C2×#99×C41C2212yes—
35C2×#99×C41C2211yescharacteristic
36C2×#99×C41C2212yescomplemented
37C41×#398—22no—
38C41×#396—22no—
39C41×#395—21no—
40C41×#394—21no—
41C41×#389—22no—
42C41×#388—22no—
43C41×#386C2212yes—
44C41×#386C2211yescharacteristic
45C41×#386C2211yescharacteristic, complemented
46C41×#385—21no—
47C41×#385—21no—
48C41×#385C2212yescomplemented
49C41×#381C2212yescomplemented
50C41×#381C2211yescharacteristic, complemented
51C41×#342C2212yescomplemented
52C41×#342C2212yescomplemented
53H(5,𝔽2)×C41—22no—
54H(5,𝔽2)×C41—22no—
55H(5,𝔽2)×C41—42no—
56C2×#41×C41—22no—
57C2×#41×C41—22no—
58C2×#41×C41—21no—
59C2×#41×C41—22no—
60C2×#41×C41—22no—
61C2×#41×C41—22no—
62C2×#41×C41—42no—
63C22×Q8×C41D411yescharacteristic
64C22×D4×C41—21no—
65C22×D4×C41—22no—
66C22×D4×C41D411yescharacteristic
67C22×D4×C41C2312yes—
68C22×D4×C41C2311yescharacteristic
69C22×D4×C41C2311yescharacteristic
70C23×C4×C41D411yescharacteristic
71C23×C4×C41D411yescharacteristic
72C23×C4×C41C2311yescharacteristic
73C23×C4×C41C2311yescharacteristic
74C23×C4×C41C2311yescharacteristic
75C4⋊Q8×C41—22no—
76#124×C41—22no—
77#123×C41—22no—
78#123×C41—22no—
79#123×C41—22no—
80#123×C41—22no—
81#123×C41—22no—
82#123×C41—22no—
83#123×C41—22no—
84#123×C41—22no—
85#123×C41—22no—
86#123×C41—22no—
87#123×C41—22no—
88#123×C41—24no—
89#123×C41—42no—
90#123×C41—42no—
91C22⋊Q8×C41—21no—
92C22⋊Q8×C41—21no—
93C22⋊Q8×C41—22no—
94C22⋊Q8×C41—22no—
95#121×C41—21no—
96#121×C41—21no—
97#121×C41—22no—
98#121×C41—22no—
99#121×C41—22no—
100#121×C41—22no—
101#120×C41—22no—
102#120×C41—22no—
103#120×C41—22no—
104C4×D4×C41—22no—
105C4×D4×C41—22no—
106C4×D4×C41—22no—
107C4×D4×C41—22no—
108#117×C41—21no—
109#117×C41—24no—
110#117×C41—42no—
111C2×C4⋊C4×C41—21no—
112C2×C4⋊C4×C41—21no—
113C2×C4⋊C4×C41—21no—
114C2×C4⋊C4×C41—22no—
115C2×C4⋊C4×C41—21no—
116C2×C4⋊C4×C41—22no—
117C2×C4⋊C4×C41—22no—
118C2×C4⋊C4×C41—21no—
119C2×C4⋊C4×C41—22no—
120C2×C4⋊C4×C41—21no—
121C2×C4⋊C4×C41—22no—
122C2×C4⋊C4×C41D412yes—
123C2×C4⋊C4×C41D412yes—
124C2×C22⋊C4×C41—21no—
125C2×C22⋊C4×C41—21no—
126C2×C22⋊C4×C41—21no—
127C2×C22⋊C4×C41—21no—
128C2×C22⋊C4×C41—22no—
129C2×C22⋊C4×C41—21no—
130C2×C22⋊C4×C41—21no—
131C2×C22⋊C4×C41—21no—
132C2×C22⋊C4×C41—22no—
133C2×C22⋊C4×C41D412yes—
134C2×C22⋊C4×C41D412yes—
135C2×C22⋊C4×C41C2312yes—
136C2×C22⋊C4×C41C2311yescharacteristic
137C2×C22⋊C4×C41C2311yescharacteristic
138C2×C22⋊C4×C41C2312yes—
139C2×C22⋊C4×C41C2312yes—
140C2×C42×C41—22no—
141#99×C41—22no—
142#99×C41—24no—
143#99×C41—24no—
144#99×C41—42no—
145#99×C41D414yescomplemented
146#95×C41—21no—
147#95×C41—22no—
148#95×C41—22no—
149#95×C41—21no—
150#95×C41—21no—
151#95×C41—21no—
152#95×C41—22no—
153#95×C41—22no—
154C24×C41—21no—
155C24×C41C2×D412yes—
156C24×C41C2×D411yescharacteristic
157C24×C41C2×D411yescharacteristic
158C24×C41C2411yescharacteristic
159#41×C41—44no—
160#41×C41—44no—
161#41×C41—44no—
162#41×C41—44no—
163#41×C41—44no—
164#41×C41—44no—
165#41×C41—42no—
166#41×C41—42no—
167C2×Q8×C41—21no—
168C2×Q8×C41—22no—
169C2×Q8×C41—22no—
170C2×Q8×C41—41no—
171C2×D4×C41—22no—
172C2×D4×C41—22no—
173C2×D4×C41—22no—
174C2×D4×C41—21no—
175C2×D4×C41—22no—
176C2×D4×C41—21no—
177C2×D4×C41—22no—
178C2×D4×C41—22no—
179C2×D4×C41—22no—
180C2×D4×C41—22no—
181C2×D4×C41—21no—
182C2×D4×C41—22no—
183C2×D4×C41—22no—
184C2×D4×C41—22no—
185C2×D4×C41—22no—
186C2×D4×C41—22no—
187C2×D4×C41—22no—
188C2×D4×C41—22no—
189C2×D4×C41—41no—
190C2×D4×C41—44no—
191C2×D4×C41—44no—
192C2×D4×C41—42no—
193C2×D4×C41—42no—
194C2×D4×C41C2×D412yes—
195C2×D4×C41#4112yes—
196C22×C4×C41—21no—
197C22×C4×C41—21no—
198C22×C4×C41—22no—
199C22×C4×C41—21no—
200C22×C4×C41—22no—
201C22×C4×C41—22no—
202C22×C4×C41—21no—
203C22×C4×C41—22no—
204C22×C4×C41—22no—
205C22×C4×C41—21no—
206C22×C4×C41—21no—
207C22×C4×C41—21no—
208C22×C4×C41—21no—
209C22×C4×C41—21no—
210C22×C4×C41—21no—
211C22×C4×C41—22no—
212C22×C4×C41—22no—
213C22×C4×C41—21no—
214C22×C4×C41—21no—
215C22×C4×C41—22no—
216C22×C4×C41—21no—
217C22×C4×C41—21no—
218C22×C4×C41—21no—
219C22×C4×C41—22no—
220C22×C4×C41—42no—
221C22×C4×C41—41no—
222C22×C4×C41—41no—
223C22×C4×C41C2×D412yes—
224C22×C4×C41C2×D411yescharacteristic
225C22×C4×C41C2×D411yescharacteristic
226C22×C4×C41C2×D411yescharacteristic
227C22×C4×C41C2×D412yes—
228C22×C4×C41C2×D412yes—
229C22×C4×C41C2×D411yescharacteristic
230C22×C4×C41C2×D412yes—
231C22×C4×C41C2×D412yes—
232C4⋊C4×C41—22no—
233C4⋊C4×C41—22no—
234C4⋊C4×C41—21no—
235C4⋊C4×C41—21no—
236C4⋊C4×C41—22no—
237C4⋊C4×C41—22no—
238C4⋊C4×C41—22no—
239C4⋊C4×C41—22no—
240C4⋊C4×C41—44no—
241C4⋊C4×C41—44no—
242C4⋊C4×C41—44no—
243C4⋊C4×C41—42no—
244C4⋊C4×C41—41no—
245C4⋊C4×C41—41no—
246C4⋊C4×C41—42no—
247C4⋊C4×C41—42no—
248C22⋊C4×C41—22no—
249C22⋊C4×C41—22no—
250C22⋊C4×C41—22no—
251C22⋊C4×C41—22no—
252C22⋊C4×C41—22no—
253C22⋊C4×C41—22no—
254C22⋊C4×C41—22no—
255C22⋊C4×C41—22no—
256C22⋊C4×C41—22no—
257C22⋊C4×C41—22no—
258C22⋊C4×C41—22no—
259C22⋊C4×C41—22no—
260C22⋊C4×C41—22no—
261C22⋊C4×C41—21no—
262C22⋊C4×C41—21no—
263C22⋊C4×C41—22no—
264C22⋊C4×C41—22no—
265C22⋊C4×C41—44no—
266C22⋊C4×C41—42no—
267C22⋊C4×C41—42no—
268C22⋊C4×C41—44no—
269C22⋊C4×C41—42no—
270C22⋊C4×C41—42no—
271C22⋊C4×C41C2×D414yes—
272C42×C41—22no—
273C42×C41—44no—
274C23×C41—21no—
275C23×C41—21no—
276C23×C41—22no—
277C23×C41—21no—
278C23×C41—21no—
279C23×C41—21no—
280C23×C41—22no—
281C23×C41—22no—
282C23×C41—41no—
283C23×C41—41no—
284C23×C41—41no—
285C23×C41—41no—
286C23×C41—41no—
287C23×C41—41no—
288C23×C41—42no—
289C23×C41—42no—
290C23×C41—42no—
291C23×C41—81no—
292C23×C41—81no—
293C23×C41#12112yes—
294C23×C41C22×D411yescharacteristic
295C23×C41C22×D412yes—
296C23×C41C22×D411yescharacteristic
297C23×C41C2×#4111yescharacteristic
298C23×C41H(5,𝔽2)12yes—
299Q8×C41—44no—
300Q8×C41—42no—
301D4×C41—24no—
302D4×C41—24no—
303D4×C41—44no—
304D4×C41—42no—
305D4×C41—44no—
306D4×C41—42no—
307D4×C41—42no—
308D4×C41—42no—
309D4×C41—42no—
310D4×C41—42no—
311D4×C41—42no—
312D4×C41—82no—
313D4×C41—82no—
314C2×C4×C41—21no—
315C2×C4×C41—21no—
316C2×C4×C41—21no—
317C2×C4×C41—21no—
318C2×C4×C41—21no—
319C2×C4×C41—21no—
320C2×C4×C41—22no—
321C2×C4×C41—22no—
322C2×C4×C41—22no—
323C2×C4×C41—22no—
324C2×C4×C41—22no—
325C2×C4×C41—24no—
326C2×C4×C41—22no—
327C2×C4×C41—22no—
328C2×C4×C41—21no—
329C2×C4×C41—22no—
330C2×C4×C41—21no—
331C2×C4×C41—21no—
332C2×C4×C41—24no—
333C2×C4×C41—22no—
334C2×C4×C41—22no—
335C2×C4×C41—42no—
336C2×C4×C41—42no—
337C2×C4×C41—42no—
338C2×C4×C41—42no—
339C2×C4×C41—44no—
340C2×C4×C41—42no—
341C2×C4×C41—42no—
342C2×C4×C41—42no—
343C2×C4×C41—41no—
344C2×C4×C41—42no—
345C2×C4×C41—41no—
346C2×C4×C41—42no—
347C2×C4×C41—42no—
348C2×C4×C41—42no—
349C2×C4×C41—41no—
350C2×C4×C41—41no—
351C2×C4×C41—42no—
352C2×C4×C41—41no—
353C2×C4×C41—41no—
354C2×C4×C41—41no—
355C2×C4×C41—41no—
356C2×C4×C41—41no—
357C2×C4×C41—41no—
358C2×C4×C41—41no—
359C2×C4×C41—42no—
360C2×C4×C41—42no—
361C2×C4×C41—42no—
362C2×C4×C41—81no—
363C2×C4×C41—81no—
364C2×C4×C41#12011yescharacteristic
365C2×C4×C41#12011yescharacteristic
366C2×C4×C41#12012yes—
367C2×C4×C41#12112yes—
368#24407C4111yesmaximal, characteristic, direct product factor, Sylow
369C22×C41—22no—
370C22×C41—21no—
371C22×C41—22no—
372C22×C41—21no—
373C22×C41—22no—
374C22×C41—41no—
375C22×C41—41no—
376C22×C41—42no—
377C22×C41—42no—
378C22×C41—42no—
379C22×C41—41no—
380C22×C41—41no—
381C22×C41—41no—
382C22×C41—42no—
383C22×C41—41no—
384C22×C41—42no—
385C22×C41—41no—
386C22×C41—42no—
387C22×C41—81no—
388C22×C41—82no—
389C22×C41—81no—
390C22×C41—82no—
391C22×C41—162no—
392C22×C41C2×#12011yescharacteristic
393C22×C41C2×#12111yescharacteristic
394C22×C41#53411yescharacteristic
395C22×C41D4212yes—
396C22×C41#54612yes—
397C4×C41—21no—
398C4×C41—21no—
399C4×C41—22no—
400C4×C41—22no—
401C4×C41—44no—
402C4×C41—42no—
403C4×C41—41no—
404C4×C41—42no—
405C4×C41—42no—
406C4×C41—42no—
407C4×C41—82no—
408C4×C41—81no—
409C4×C41—81no—
410C4×C41—81no—
411#3485C2×C4111yescharacteristic
412C2×#458C2×C4111yescharacteristic, complemented
413C2×#410C2×C4111yescharacteristic, complemented
414#2413C2×C4112yescomplemented
415#2406C2×C4111yescharacteristic, complemented
416#2044C2×C4112yescomplemented
417#2022C2×C4112yescomplemented
418#1899C2×C4112yescomplemented
419#1890C2×C4111yescharacteristic, complemented
420#1867C2×C4111yescharacteristic, complemented
421#1790C2×C4111yescharacteristic, complemented
422C2×C41—22no—
423C2×C41—21no—
424C2×C41—21no—
425C2×C41—22no—
426C2×C41—42no—
427C2×C41—81no—
428C2×C41—82no—
429C2×C41#241011yescharacteristic
430C2×C41#302511yescharacteristic
431C2×C41#302811yescharacteristic
432C2×H(5,𝔽2)C22×C4111yescharacteristic
433C22×#41C22×C4111yescharacteristic
434#547—22no—
435#547—22no—
436#546—22no—
437#546—22no—
438#536—21no—
439#534—21no—
440#534C22×C4112yes—
441#525—21no—
442C2×#123—21no—
443C2×#123C22×C4111yescharacteristic
444C2×#123C22×C4112yes—
445C2×#123C22×C4112yes—
446C2×#123C22×C4111yescharacteristic, complemented
447#518C22×C4111yescharacteristic
448C2×#117C22×C4112yescomplemented
449C22×C4⋊C4C22×C4111yescharacteristic, complemented
450#458—24no—
451#410—24no—
452C2×#99C22×C4111yescharacteristic
453C2×#99C22×C4112yes—
454C2×#99C22×C4112yes—
455C2×#99C22×C4111yescharacteristic
456C2×#99C22×C4112yescomplemented
457#398—22no—
458#396—22no—
459#395—21no—
460#394—21no—
461#389—22no—
462#388—22no—
463#386C22×C4111yescharacteristic
464#386C22×C4112yes—
465#386C22×C4111yescharacteristic, complemented
466#385—21no—
467#385—21no—
468#385C22×C4112yescomplemented
469#381C22×C4112yescomplemented
470#381C22×C4111yescharacteristic, complemented
471#342C22×C4112yescomplemented
472#342C22×C4112yescomplemented
473C41#2440711yescharacteristic, direct product factor, Sylow
474H(5,𝔽2)—22no—
475H(5,𝔽2)—22no—
476H(5,𝔽2)—42no—
477C2×#41—22no—
478C2×#41—22no—
479C2×#41—21no—
480C2×#41—22no—
481C2×#41—22no—
482C2×#41—22no—
483C2×#41—42no—
484C22×Q8D4×C4111yescharacteristic
485C22×D4—21no—
486C22×D4—22no—
487C22×D4D4×C4111yescharacteristic
488C22×D4C23×C4112yes—
489C22×D4C23×C4111yescharacteristic
490C22×D4C23×C4111yescharacteristic
491C23×C4D4×C4111yescharacteristic
492C23×C4D4×C4111yescharacteristic
493C23×C4C23×C4111yescharacteristic
494C23×C4C23×C4111yescharacteristic
495C23×C4C23×C4111yescharacteristic
496C4⋊Q8—22no—
497#124—22no—
498#123—22no—
499#123—22no—
500#123—22no—
501#123—22no—
502#123—22no—
503#123—22no—
504#123—22no—
505#123—22no—
506#123—22no—
507#123—22no—
508#123—22no—
509#123—24no—
510#123—42no—
511#123—42no—
512C22⋊Q8—21no—
513C22⋊Q8—21no—
514C22⋊Q8—22no—
515C22⋊Q8—22no—
516#121—21no—
517#121—21no—
518#121—22no—
519#121—22no—
520#121—22no—
521#121—22no—
522#120—22no—
523#120—22no—
524#120—22no—
525C4×D4—22no—
526C4×D4—22no—
527C4×D4—22no—
528C4×D4—22no—
529#117—21no—
530#117—24no—
531#117—42no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—22no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—22no—
538C2×C4⋊C4—22no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—22no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—22no—
543C2×C4⋊C4D4×C4112yes—
544C2×C4⋊C4D4×C4112yes—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—22no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—22no—
554C2×C22⋊C4D4×C4112yes—
555C2×C22⋊C4D4×C4112yes—
556C2×C22⋊C4C23×C4112yes—
557C2×C22⋊C4C23×C4111yescharacteristic
558C2×C22⋊C4C23×C4111yescharacteristic
559C2×C22⋊C4C23×C4112yes—
560C2×C22⋊C4C23×C4112yes—
561C2×C42—22no—
562#99—22no—
563#99—24no—
564#99—24no—
565#99—42no—
566#99D4×C4114yescomplemented
567#95—21no—
568#95—22no—
569#95—22no—
570#95—21no—
571#95—21no—
572#95—21no—
573#95—22no—
574#95—22no—
575C24—21no—
576C24C2×D4×C4112yes—
577C24C2×D4×C4111yescharacteristic
578C24C2×D4×C4111yescharacteristic
579C24C24×C4111yescharacteristic
580#41—44no—
581#41—44no—
582#41—44no—
583#41—44no—
584#41—44no—
585#41—44no—
586#41—42no—
587#41—42no—
588C2×Q8—21no—
589C2×Q8—22no—
590C2×Q8—22no—
591C2×Q8—41no—
592C2×D4—22no—
593C2×D4—22no—
594C2×D4—22no—
595C2×D4—21no—
596C2×D4—22no—
597C2×D4—21no—
598C2×D4—22no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—21no—
603C2×D4—22no—
604C2×D4—22no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—22no—
609C2×D4—22no—
610C2×D4—41no—
611C2×D4—44no—
612C2×D4—44no—
613C2×D4—42no—
614C2×D4—42no—
615C2×D4C2×D4×C4112yes—
616C2×D4#41×C4112yes—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—22no—
620C22×C4—21no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—21no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—22no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—22no—
641C22×C4—42no—
642C22×C4—41no—
643C22×C4—41no—
644C22×C4C2×D4×C4112yes—
645C22×C4C2×D4×C4111yescharacteristic
646C22×C4C2×D4×C4111yescharacteristic
647C22×C4C2×D4×C4111yescharacteristic
648C22×C4C2×D4×C4112yes—
649C22×C4C2×D4×C4112yes—
650C22×C4C2×D4×C4111yescharacteristic
651C22×C4C2×D4×C4112yes—
652C22×C4C2×D4×C4112yes—
653C4⋊C4—22no—
654C4⋊C4—22no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—22no—
658C4⋊C4—22no—
659C4⋊C4—22no—
660C4⋊C4—22no—
661C4⋊C4—44no—
662C4⋊C4—44no—
663C4⋊C4—42no—
664C4⋊C4—44no—
665C4⋊C4—41no—
666C4⋊C4—41no—
667C4⋊C4—42no—
668C4⋊C4—42no—
669C22⋊C4—22no—
670C22⋊C4—22no—
671C22⋊C4—22no—
672C22⋊C4—22no—
673C22⋊C4—22no—
674C22⋊C4—22no—
675C22⋊C4—22no—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—22no—
679C22⋊C4—22no—
680C22⋊C4—22no—
681C22⋊C4—22no—
682C22⋊C4—21no—
683C22⋊C4—21no—
684C22⋊C4—22no—
685C22⋊C4—22no—
686C22⋊C4—44no—
687C22⋊C4—42no—
688C22⋊C4—42no—
689C22⋊C4—44no—
690C22⋊C4—42no—
691C22⋊C4—42no—
692C22⋊C4C2×D4×C4114yes—
693C42—22no—
694C42—44no—
695C23—21no—
696C23—21no—
697C23—22no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—22no—
702C23—22no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—81no—
713C23—81no—
714C23#121×C4112yes—
715C23C22×D4×C4111yescharacteristic
716C23C22×D4×C4112yes—
717C23C22×D4×C4111yescharacteristic
718C23C2×#41×C4111yescharacteristic
719C23H(5,𝔽2)×C4112yes—
720Q8—44no—
721Q8—42no—
722D4—24no—
723D4—24no—
724D4—44no—
725D4—42no—
726D4—44no—
727D4—42no—
728D4—42no—
729D4—42no—
730D4—42no—
731D4—42no—
732D4—42no—
733D4—82no—
734D4—82no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—24no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—21no—
750C2×C4—22no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—24no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—44no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—41no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—41no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—42no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—81no—
784C2×C4—81no—
785C2×C4#120×C4111yescharacteristic
786C2×C4#120×C4111yescharacteristic
787C2×C4#120×C4112yes—
788C2×C4#121×C4112yes—
789C22—22no—
790C22—21no—
791C22—22no—
792C22—21no—
793C22—22no—
794C22—41no—
795C22—41no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—42no—
803C22—41no—
804C22—42no—
805C22—41no—
806C22—42no—
807C22—81no—
808C22—82no—
809C22—81no—
810C22—82no—
811C22—162no—
812C22C2×#120×C4111yescharacteristic
813C22C2×#121×C4111yescharacteristic
814C22C41×#53411yescharacteristic
815C22D42×C4112yes—
816C22C41×#54612yes—
817C4—21no—
818C4—21no—
819C4—22no—
820C4—22no—
821C4—44no—
822C4—42no—
823C4—41no—
824C4—42no—
825C4—42no—
826C4—42no—
827C4—82no—
828C4—81no—
829C4—81no—
830C4—81no—
831C2—22no—
832C2—21no—
833C2—21no—
834C2—22no—
835C2—42no—
836C2—81no—
837C2—82no—
838C2C41×#241011yescharacteristic
839C2C41×#302511yescharacteristic
840C2C41×#302811yescharacteristic
subgroupG/H
center, socleC22×C41C2×#120
commutator, Frattini, cosocleC24C24×C41
prime radicalC41×#3485C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C41 ◁ C23×C4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C41×#458C2semidirect
3. C2×C41×#410C2semidirect
4. C41×#2413C2semidirect
5. C41×#2406C2semidirect
6. C41×#2044C2semidirect
7. C41×#2022C2semidirect
8. C41×#1899C2semidirect
9. C41×#1890C2semidirect
10. C41×#1867C2semidirect
11. C41×#1790C2semidirect
26. C2×#123×C41C22semidirect
28. C2×#117×C41C22semidirect
29. C22×C4⋊C4×C41C22semidirect
36. C2×#99×C41C22semidirect
45. C41×#386C22semidirect
48. C41×#385C22semidirect
49. C41×#381C22semidirect
50. C41×#381C22semidirect
51. C41×#342C22semidirect
52. C41×#342C22semidirect
145. #99×C41D4semidirect
368. #24407C41direct (N × H)
412. C2×#458C2×C41semidirect
413. C2×#410C2×C41semidirect
414. #2413C2×C41semidirect
415. #2406C2×C41semidirect
416. #2044C2×C41semidirect
417. #2022C2×C41semidirect
418. #1899C2×C41semidirect
419. #1890C2×C41semidirect
420. #1867C2×C41semidirect
421. #1790C2×C41semidirect
446. C2×#123C22×C41semidirect
448. C2×#117C22×C41semidirect
449. C22×C4⋊C4C22×C41semidirect
456. C2×#99C22×C41semidirect
465. #386C22×C41semidirect
468. #385C22×C41semidirect
469. #381C22×C41semidirect
470. #381C22×C41semidirect
471. #342C22×C41semidirect
472. #342C22×C41semidirect
473. C41#24407direct (N × H)
566. #99D4×C41semidirect

Maximal subgroups

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

subgroupindex
C41×#34852
C2×C41×#4582
C2×C41×#4102
C41×#24132
C41×#24062
C41×#20442
C41×#20222
C41×#18992
C41×#18902
C41×#18672
C41×#17902
#2440741