Finite Group Databasebeta

← C41×#25563 #23801764

Subgroups — C41×#25563 #23801764

Order 10496.

1608 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3490C211yesmaximal, characteristic, complemented
2C41×#2410C212yesmaximal, complemented
3C41×#2405C211yesmaximal, characteristic, complemented
4C41×#2062C211yesmaximal, characteristic, complemented
5C41×#2044C211yesmaximal, characteristic, complemented
6C41×#2029C211yesmaximal, characteristic, complemented
7C41×#2021C211yesmaximal, characteristic, complemented
8C41×#1898C212yesmaximal, complemented
9C41×#1889C212yesmaximal, complemented
10C41×#1867C212yesmaximal, complemented
11C2×C41×#342C211yesmaximal, characteristic, complemented
12C23×D4×C41C2211yescharacteristic
13C41×#551—22no—
14C41×#551—22no—
15C41×#546—22no—
16C41×#546—22no—
17C41×#543C2211yescharacteristic
18C41×#538—21no—
19C41×#538—21no—
20C41×#534C2211yescharacteristic
21C41×#525—21no—
22C41×#525—21no—
23C2×#123×C41—21no—
24C2×#121×C41—22no—
25C2×#120×C41C2212yes—
26C2×#120×C41C2212yes—
27C41×#518C2212yes—
28C22×C22⋊C4×C41C2211yescharacteristic
29C22×C22⋊C4×C41C2212yes—
30C2×#99×C41C2212yes—
31C2×#99×C41C2212yes—
32C41×#394—21no—
33C41×#394—21no—
34C41×#394—22no—
35C41×#392—22no—
36C41×#386—21no—
37C41×#386—22no—
38C41×#386C2212yes—
39C41×#385C2211yescharacteristic
40C41×#385C2212yes—
41C41×#385C2211yescharacteristic
42C41×#379C2211yescharacteristic
43C41×#379C2212yes—
44C41×#379C2211yescharacteristic
45C41×#379C2211yescharacteristic
46C41×#342C2211yescharacteristic
47C41×#342C2211yescharacteristic
48C41×#342C2212yes—
49C41×#342C2212yes—
50C41×#342C2212yes—
51C25×C41C2311yescharacteristic
52C25×C41C2311yescharacteristic
53C2×#41×C41—21no—
54C2×#41×C41—21no—
55C22×D4×C41—22no—
56C22×D4×C41—21no—
57C22×D4×C41—22no—
58C22×D4×C41—21no—
59C22×D4×C41—22no—
60C22×D4×C41—44no—
61C22×D4×C41D412yescomplemented
62C22×D4×C41D412yescomplemented
63C22×D4×C41C2312yes—
64C23×C4×C41—22no—
65C23×C4×C41D411yescharacteristic, complemented
66C23×C4×C41D411yescharacteristic, complemented
67C23×C4×C41C2311yescharacteristic
68#126×C41—22no—
69#126×C41—22no—
70#124×C41—22no—
71#124×C41—22no—
72#123×C41—22no—
73#123×C41—22no—
74#123×C41—22no—
75#123×C41—22no—
76#123×C41—22no—
77#123×C41—44no—
78C22⋊Q8×C41—21no—
79C22⋊Q8×C41—21no—
80C22⋊Q8×C41—21no—
81C22⋊Q8×C41—21no—
82C22⋊Q8×C41—22no—
83C22⋊Q8×C41—22no—
84#121×C41—21no—
85#121×C41—21no—
86#121×C41—22no—
87#121×C41—22no—
88#121×C41—21no—
89#121×C41—21no—
90#121×C41—48no—
91#120×C41—22no—
92#120×C41—22no—
93#120×C41—22no—
94#120×C41—22no—
95#120×C41—22no—
96#120×C41—24no—
97#120×C41—42no—
98C4×D4×C41—22no—
99C4×D4×C41—22no—
100C4×D4×C41—22no—
101C4×D4×C41—22no—
102C4×D4×C41—22no—
103C4×D4×C41—22no—
104#117×C41—21no—
105#117×C41—21no—
106#117×C41—22no—
107C2×C4⋊C4×C41—22no—
108C2×C4⋊C4×C41—21no—
109C2×C4⋊C4×C41—21no—
110C2×C22⋊C4×C41—22no—
111C2×C22⋊C4×C41—22no—
112C2×C22⋊C4×C41—22no—
113C2×C22⋊C4×C41—24no—
114C2×C22⋊C4×C41—22no—
115C2×C22⋊C4×C41—22no—
116C2×C22⋊C4×C41—21no—
117C2×C22⋊C4×C41—22no—
118C2×C22⋊C4×C41—22no—
119C2×C22⋊C4×C41—21no—
120C2×C22⋊C4×C41—21no—
121C2×C22⋊C4×C41—21no—
122C2×C22⋊C4×C41—22no—
123C2×C22⋊C4×C41—21no—
124C2×C22⋊C4×C41—21no—
125C2×C22⋊C4×C41—42no—
126C2×C22⋊C4×C41D411yescharacteristic, complemented
127C2×C22⋊C4×C41D411yescharacteristic, complemented
128C2×C22⋊C4×C41D412yescomplemented
129C2×C22⋊C4×C41D412yescomplemented
130C2×C22⋊C4×C41C2312yes—
131C2×C22⋊C4×C41C2311yescharacteristic
132C2×C22⋊C4×C41C2311yescharacteristic
133C2×C22⋊C4×C41C2311yescharacteristic
134C2×C22⋊C4×C41C2311yescharacteristic
135C2×C22⋊C4×C41C2312yes—
136C2×C22⋊C4×C41C2312yes—
137#99×C41—24no—
138#99×C41—42no—
139#95×C41—22no—
140#95×C41—21no—
141#95×C41—21no—
142#95×C41—22no—
143C24×C41—22no—
144C24×C41—21no—
145C24×C41—21no—
146C24×C41—21no—
147C24×C41—22no—
148C24×C41—22no—
149C24×C41—21no—
150C24×C41—21no—
151C24×C41—42no—
152C24×C41—42no—
153C24×C41—81no—
154C24×C41—81no—
155C24×C41C2×D412yes—
156C24×C41C2×D411yescharacteristic
157C24×C41C2×D412yes—
158C24×C41C2×D412yes—
159C24×C41C2×D411yescharacteristic
160C24×C41C2411yescharacteristic
161#41×C41—82no—
162#41×C41—82no—
163C2×Q8×C41—21no—
164C2×Q8×C41—21no—
165C2×D4×C41—28no—
166C2×D4×C41—24no—
167C2×D4×C41—22no—
168C2×D4×C41—22no—
169C2×D4×C41—22no—
170C2×D4×C41—22no—
171C2×D4×C41—22no—
172C2×D4×C41—22no—
173C2×D4×C41—22no—
174C2×D4×C41—22no—
175C2×D4×C41—21no—
176C2×D4×C41—21no—
177C2×D4×C41—22no—
178C2×D4×C41—22no—
179C2×D4×C41—44no—
180C2×D4×C41—42no—
181C2×D4×C41—44no—
182C2×D4×C41—42no—
183C2×D4×C41—44no—
184C2×D4×C41—42no—
185C2×D4×C41—44no—
186C2×D4×C41—42no—
187C2×D4×C41—41no—
188C2×D4×C41—41no—
189C2×D4×C41—44no—
190C2×D4×C41—44no—
191C2×D4×C41—82no—
192C2×D4×C41—82no—
193C22×C4×C41—21no—
194C22×C4×C41—21no—
195C22×C4×C41—22no—
196C22×C4×C41—21no—
197C22×C4×C41—22no—
198C22×C4×C41—22no—
199C22×C4×C41—22no—
200C22×C4×C41—21no—
201C22×C4×C41—21no—
202C22×C4×C41—21no—
203C22×C4×C41—21no—
204C22×C4×C41—22no—
205C22×C4×C41—42no—
206C22×C4×C41—44no—
207C22×C4×C41—42no—
208C22×C4×C41—44no—
209C22×C4×C41—81no—
210C22×C4×C41—82no—
211C22×C4×C41C2×D412yes—
212C22×C4×C41C2×D411yescharacteristic
213C22×C4×C41C2×D412yes—
214C22×C4×C41C2×D411yescharacteristic
215C22×C4×C41C2×D411yescharacteristic
216C22×C4×C41C2×D412yes—
217C22×C4×C41C2×D411yescharacteristic
218C4⋊C4×C41—22no—
219C4⋊C4×C41—22no—
220C4⋊C4×C41—21no—
221C4⋊C4×C41—21no—
222C4⋊C4×C41—21no—
223C4⋊C4×C41—21no—
224C4⋊C4×C41—22no—
225C4⋊C4×C41—22no—
226C4⋊C4×C41—44no—
227C4⋊C4×C41—42no—
228C4⋊C4×C41—42no—
229C22⋊C4×C41—22no—
230C22⋊C4×C41—22no—
231C22⋊C4×C41—22no—
232C22⋊C4×C41—22no—
233C22⋊C4×C41—22no—
234C22⋊C4×C41—22no—
235C22⋊C4×C41—22no—
236C22⋊C4×C41—22no—
237C22⋊C4×C41—22no—
238C22⋊C4×C41—22no—
239C22⋊C4×C41—22no—
240C22⋊C4×C41—22no—
241C22⋊C4×C41—22no—
242C22⋊C4×C41—22no—
243C22⋊C4×C41—22no—
244C22⋊C4×C41—22no—
245C22⋊C4×C41—22no—
246C22⋊C4×C41—21no—
247C22⋊C4×C41—22no—
248C22⋊C4×C41—21no—
249C22⋊C4×C41—44no—
250C22⋊C4×C41—44no—
251C22⋊C4×C41—44no—
252C22⋊C4×C41—44no—
253C22⋊C4×C41—42no—
254C22⋊C4×C41—42no—
255C22⋊C4×C41—42no—
256C22⋊C4×C41—81no—
257C22⋊C4×C41—81no—
258C22⋊C4×C41—82no—
259C22⋊C4×C41—81no—
260C22⋊C4×C41#4114yescomplemented
261C42×C41—22no—
262C42×C41—22no—
263C23×C41—21no—
264C23×C41—21no—
265C23×C41—22no—
266C23×C41—22no—
267C23×C41—22no—
268C23×C41—24no—
269C23×C41—21no—
270C23×C41—21no—
271C23×C41—22no—
272C23×C41—22no—
273C23×C41—22no—
274C23×C41—24no—
275C23×C41—22no—
276C23×C41—22no—
277C23×C41—22no—
278C23×C41—41no—
279C23×C41—41no—
280C23×C41—42no—
281C23×C41—41no—
282C23×C41—41no—
283C23×C41—41no—
284C23×C41—42no—
285C23×C41—42no—
286C23×C41—41no—
287C23×C41—41no—
288C23×C41—42no—
289C23×C41—41no—
290C23×C41—42no—
291C23×C41—42no—
292C23×C41—42no—
293C23×C41—42no—
294C23×C41—41no—
295C23×C41—41no—
296C23×C41—41no—
297C23×C41—42no—
298C23×C41—42no—
299C23×C41—84no—
300C23×C41—84no—
301C23×C41—82no—
302C23×C41—82no—
303C23×C41—82no—
304C23×C41—82no—
305C23×C41#12012yes—
306C23×C41#12011yescharacteristic
307C23×C41#12011yescharacteristic
308C23×C41C22×D411yescharacteristic
309C23×C41C22×D412yes—
310C23×C41C2×#4112yes—
311C23×C41H(5,𝔽2)11yescharacteristic
312C23×C412−1+411yescharacteristic
313Q8×C41—81no—
314Q8×C41—81no—
315D4×C41—44no—
316D4×C41—48no—
317D4×C41—44no—
318D4×C41—42no—
319D4×C41—42no—
320D4×C41—42no—
321D4×C41—42no—
322D4×C41—44no—
323D4×C41—44no—
324D4×C41—82no—
325D4×C41—82no—
326D4×C41—81no—
327D4×C41—81no—
328D4×C41—88no—
329C2×C4×C41—24no—
330C2×C4×C41—22no—
331C2×C4×C41—22no—
332C2×C4×C41—21no—
333C2×C4×C41—21no—
334C2×C4×C41—22no—
335C2×C4×C41—22no—
336C2×C4×C41—21no—
337C2×C4×C41—21no—
338C2×C4×C41—24no—
339C2×C4×C41—22no—
340C2×C4×C41—22no—
341C2×C4×C41—42no—
342C2×C4×C41—41no—
343C2×C4×C41—42no—
344C2×C4×C41—42no—
345C2×C4×C41—42no—
346C2×C4×C41—41no—
347C2×C4×C41—42no—
348C2×C4×C41—41no—
349C2×C4×C41—41no—
350C2×C4×C41—42no—
351C2×C4×C41—41no—
352C2×C4×C41—41no—
353C2×C4×C41—42no—
354C2×C4×C41—41no—
355C2×C4×C41—41no—
356C2×C4×C41—42no—
357C2×C4×C41—41no—
358C2×C4×C41—41no—
359C2×C4×C41—42no—
360C2×C4×C41—41no—
361C2×C4×C41—41no—
362C2×C4×C41—42no—
363C2×C4×C41—81no—
364C2×C4×C41—81no—
365C2×C4×C41—82no—
366C2×C4×C41—82no—
367C2×C4×C41—88no—
368#25563C4111yesmaximal, characteristic, direct product factor, Sylow
369C22×C41—21no—
370C22×C41—21no—
371C22×C41—22no—
372C22×C41—21no—
373C22×C41—22no—
374C22×C41—21no—
375C22×C41—21no—
376C22×C41—22no—
377C22×C41—21no—
378C22×C41—22no—
379C22×C41—21no—
380C22×C41—22no—
381C22×C41—42no—
382C22×C41—41no—
383C22×C41—41no—
384C22×C41—44no—
385C22×C41—42no—
386C22×C41—42no—
387C22×C41—44no—
388C22×C41—44no—
389C22×C41—42no—
390C22×C41—42no—
391C22×C41—44no—
392C22×C41—42no—
393C22×C41—42no—
394C22×C41—42no—
395C22×C41—42no—
396C22×C41—82no—
397C22×C41—81no—
398C22×C41—81no—
399C22×C41—82no—
400C22×C41—82no—
401C22×C41—82no—
402C22×C41—82no—
403C22×C41—81no—
404C22×C41—81no—
405C22×C41—82no—
406C22×C41—81no—
407C22×C41—81no—
408C22×C41B(4,𝔽2)12yes—
409C22×C41C2×#12011yescharacteristic
410C22×C41#53211yescharacteristic
411C22×C41#53711yescharacteristic
412C22×C41#54612yes—
413C22×C41#54712yes—
414C4×C41—44no—
415C4×C41—42no—
416C4×C41—42no—
417C4×C41—41no—
418C4×C41—41no—
419C4×C41—42no—
420C4×C41—41no—
421C4×C41—41no—
422C4×C41—42no—
423C4×C41—81no—
424C4×C41—81no—
425C4×C41—82no—
426#3490C2×C4111yescharacteristic, complemented
427#2410C2×C4112yescomplemented
428#2405C2×C4111yescharacteristic, complemented
429#2062C2×C4111yescharacteristic, complemented
430#2044C2×C4111yescharacteristic, complemented
431#2029C2×C4111yescharacteristic, complemented
432#2021C2×C4111yescharacteristic, complemented
433#1898C2×C4112yescomplemented
434#1889C2×C4112yescomplemented
435#1867C2×C4112yescomplemented
436C2×#342C2×C4111yescharacteristic, complemented
437C2×C41—22no—
438C2×C41—21no—
439C2×C41—21no—
440C2×C41—22no—
441C2×C41—22no—
442C2×C41—41no—
443C2×C41—42no—
444C2×C41—82no—
445C2×C41—82no—
446C2×C41#243011yescharacteristic
447C2×C41C2×B(4,𝔽2)11yescharacteristic
448C2×C41#302611yescharacteristic
449C23×D4C22×C4111yescharacteristic
450#551—22no—
451#551—22no—
452#546—22no—
453#546—22no—
454#543C22×C4111yescharacteristic
455#538—21no—
456#538—21no—
457#534C22×C4111yescharacteristic
458#525—21no—
459#525—21no—
460C2×#123—21no—
461C2×#121—22no—
462C2×#120C22×C4112yes—
463C2×#120C22×C4112yes—
464#518C22×C4112yes—
465C22×C22⋊C4C22×C4111yescharacteristic
466C22×C22⋊C4C22×C4112yes—
467C2×#99C22×C4112yes—
468C2×#99C22×C4112yes—
469#394—21no—
470#394—21no—
471#394—22no—
472#392—22no—
473#386—21no—
474#386—22no—
475#386C22×C4112yes—
476#385C22×C4112yes—
477#385C22×C4111yescharacteristic
478#385C22×C4111yescharacteristic
479#379C22×C4111yescharacteristic
480#379C22×C4112yes—
481#379C22×C4111yescharacteristic
482#379C22×C4111yescharacteristic
483#342C22×C4112yes—
484#342C22×C4111yescharacteristic
485#342C22×C4112yes—
486#342C22×C4112yes—
487#342C22×C4111yescharacteristic
488C41#2556311yescharacteristic, direct product factor, Sylow
489C25C23×C4111yescharacteristic
490C25C23×C4111yescharacteristic
491C2×#41—21no—
492C2×#41—21no—
493C22×D4—22no—
494C22×D4—21no—
495C22×D4—22no—
496C22×D4—21no—
497C22×D4—22no—
498C22×D4—44no—
499C22×D4D4×C4112yescomplemented
500C22×D4D4×C4112yescomplemented
501C22×D4C23×C4112yes—
502C23×C4—22no—
503C23×C4D4×C4111yescharacteristic, complemented
504C23×C4D4×C4111yescharacteristic, complemented
505C23×C4C23×C4111yescharacteristic
506#126—22no—
507#126—22no—
508#124—22no—
509#124—22no—
510#123—22no—
511#123—22no—
512#123—22no—
513#123—22no—
514#123—22no—
515#123—44no—
516C22⋊Q8—21no—
517C22⋊Q8—21no—
518C22⋊Q8—21no—
519C22⋊Q8—21no—
520C22⋊Q8—22no—
521C22⋊Q8—22no—
522#121—21no—
523#121—21no—
524#121—22no—
525#121—22no—
526#121—21no—
527#121—21no—
528#121—48no—
529#120—22no—
530#120—22no—
531#120—22no—
532#120—22no—
533#120—22no—
534#120—24no—
535#120—42no—
536C4×D4—22no—
537C4×D4—22no—
538C4×D4—22no—
539C4×D4—22no—
540C4×D4—22no—
541C4×D4—22no—
542#117—21no—
543#117—21no—
544#117—22no—
545C2×C4⋊C4—22no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—22no—
550C2×C22⋊C4—22no—
551C2×C22⋊C4—24no—
552C2×C22⋊C4—22no—
553C2×C22⋊C4—22no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—22no—
556C2×C22⋊C4—22no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—22no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—42no—
564C2×C22⋊C4D4×C4111yescharacteristic, complemented
565C2×C22⋊C4D4×C4111yescharacteristic, complemented
566C2×C22⋊C4D4×C4112yescomplemented
567C2×C22⋊C4D4×C4112yescomplemented
568C2×C22⋊C4C23×C4112yes—
569C2×C22⋊C4C23×C4111yescharacteristic
570C2×C22⋊C4C23×C4111yescharacteristic
571C2×C22⋊C4C23×C4111yescharacteristic
572C2×C22⋊C4C23×C4111yescharacteristic
573C2×C22⋊C4C23×C4112yes—
574C2×C22⋊C4C23×C4112yes—
575#99—24no—
576#99—42no—
577#95—22no—
578#95—21no—
579#95—21no—
580#95—22no—
581C24—22no—
582C24—21no—
583C24—21no—
584C24—21no—
585C24—22no—
586C24—22no—
587C24—21no—
588C24—21no—
589C24—42no—
590C24—42no—
591C24—81no—
592C24—81no—
593C24C2×D4×C4112yes—
594C24C2×D4×C4111yescharacteristic
595C24C2×D4×C4112yes—
596C24C2×D4×C4112yes—
597C24C2×D4×C4111yescharacteristic
598C24C24×C4111yescharacteristic
599#41—82no—
600#41—82no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×D4—28no—
604C2×D4—24no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—22no—
609C2×D4—22no—
610C2×D4—22no—
611C2×D4—22no—
612C2×D4—22no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—22no—
616C2×D4—22no—
617C2×D4—44no—
618C2×D4—42no—
619C2×D4—44no—
620C2×D4—42no—
621C2×D4—44no—
622C2×D4—42no—
623C2×D4—44no—
624C2×D4—42no—
625C2×D4—41no—
626C2×D4—41no—
627C2×D4—44no—
628C2×D4—44no—
629C2×D4—82no—
630C2×D4—82no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—22no—
634C22×C4—21no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—22no—
643C22×C4—42no—
644C22×C4—44no—
645C22×C4—42no—
646C22×C4—44no—
647C22×C4—81no—
648C22×C4—82no—
649C22×C4C2×D4×C4112yes—
650C22×C4C2×D4×C4111yescharacteristic
651C22×C4C2×D4×C4112yes—
652C22×C4C2×D4×C4111yescharacteristic
653C22×C4C2×D4×C4111yescharacteristic
654C22×C4C2×D4×C4112yes—
655C22×C4C2×D4×C4111yescharacteristic
656C4⋊C4—22no—
657C4⋊C4—22no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—44no—
665C4⋊C4—42no—
666C4⋊C4—42no—
667C22⋊C4—22no—
668C22⋊C4—22no—
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—22no—
683C22⋊C4—22no—
684C22⋊C4—21no—
685C22⋊C4—22no—
686C22⋊C4—21no—
687C22⋊C4—44no—
688C22⋊C4—44no—
689C22⋊C4—44no—
690C22⋊C4—44no—
691C22⋊C4—42no—
692C22⋊C4—42no—
693C22⋊C4—42no—
694C22⋊C4—81no—
695C22⋊C4—81no—
696C22⋊C4—82no—
697C22⋊C4—81no—
698C22⋊C4#41×C4114yescomplemented
699C42—22no—
700C42—22no—
701C23—21no—
702C23—21no—
703C23—22no—
704C23—22no—
705C23—22no—
706C23—24no—
707C23—21no—
708C23—21no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—24no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—41no—
717C23—41no—
718C23—42no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—42no—
723C23—42no—
724C23—41no—
725C23—41no—
726C23—42no—
727C23—41no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—42no—
736C23—42no—
737C23—84no—
738C23—84no—
739C23—82no—
740C23—82no—
741C23—82no—
742C23—82no—
743C23#120×C4112yes—
744C23#120×C4111yescharacteristic
745C23#120×C4111yescharacteristic
746C23C22×D4×C4111yescharacteristic
747C23C22×D4×C4112yes—
748C23C2×#41×C4112yes—
749C23H(5,𝔽2)×C4111yescharacteristic
750C232−1+4×C4111yescharacteristic
751Q8—81no—
752Q8—81no—
753D4—44no—
754D4—48no—
755D4—44no—
756D4—42no—
757D4—42no—
758D4—42no—
759D4—42no—
760D4—44no—
761D4—44no—
762D4—82no—
763D4—82no—
764D4—81no—
765D4—81no—
766D4—88no—
767C2×C4—24no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—24no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—42no—
780C2×C4—41no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—41no—
785C2×C4—42no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—42no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—42no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—42no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—42no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—81no—
802C2×C4—81no—
803C2×C4—82no—
804C2×C4—82no—
805C2×C4—88no—
806C22—21no—
807C22—21no—
808C22—22no—
809C22—21no—
810C22—22no—
811C22—21no—
812C22—21no—
813C22—22no—
814C22—21no—
815C22—22no—
816C22—21no—
817C22—22no—
818C22—42no—
819C22—41no—
820C22—41no—
821C22—44no—
822C22—42no—
823C22—42no—
824C22—44no—
825C22—44no—
826C22—42no—
827C22—42no—
828C22—44no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—82no—
834C22—81no—
835C22—81no—
836C22—82no—
837C22—82no—
838C22—82no—
839C22—82no—
840C22—81no—
841C22—81no—
842C22—82no—
843C22—81no—
844C22—81no—
845C22C41×B(4,𝔽2)12yes—
846C22C2×#120×C4111yescharacteristic
847C22C41×#53211yescharacteristic
848C22C41×#53711yescharacteristic
849C22C41×#54612yes—
850C22C41×#54712yes—
851C4—44no—
852C4—42no—
853C4—42no—
854C4—41no—
855C4—41no—
856C4—42no—
857C4—41no—
858C4—41no—
859C4—42no—
860C4—82no—
861C4—81no—
862C4—81no—
863C2—22no—
864C2—21no—
865C2—21no—
866C2—22no—
867C2—22no—
868C2—41no—
869C2—42no—
870C2—82no—
871C2—82no—
872C2C41×#243011yescharacteristic
873C2C2×C41×B(4,𝔽2)11yescharacteristic
874C2C41×#302611yescharacteristic
subgroupG/H
center, socleC22×C41C2×#120
commutator, Frattini, cosocleC24C24×C41
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C41 ◁ C25×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C41×#3490C2semidirect
2. C41×#2410C2semidirect
3. C41×#2405C2semidirect
4. C41×#2062C2semidirect
5. C41×#2044C2semidirect
6. C41×#2029C2semidirect
7. C41×#2021C2semidirect
8. C41×#1898C2semidirect
9. C41×#1889C2semidirect
10. C41×#1867C2semidirect
11. C2×C41×#342C2semidirect
61. C22×D4×C41D4semidirect
62. C22×D4×C41D4semidirect
65. C23×C4×C41D4semidirect
66. C23×C4×C41D4semidirect
126. C2×C22⋊C4×C41D4semidirect
127. C2×C22⋊C4×C41D4semidirect
128. C2×C22⋊C4×C41D4semidirect
129. C2×C22⋊C4×C41D4semidirect
260. C22⋊C4×C41#41semidirect
368. #25563C41direct (N × H)
426. #3490C2×C41semidirect
427. #2410C2×C41semidirect
428. #2405C2×C41semidirect
429. #2062C2×C41semidirect
430. #2044C2×C41semidirect
431. #2029C2×C41semidirect
432. #2021C2×C41semidirect
433. #1898C2×C41semidirect
434. #1889C2×C41semidirect
435. #1867C2×C41semidirect
436. C2×#342C2×C41semidirect
488. C41#25563direct (N × H)
499. C22×D4D4×C41semidirect
500. C22×D4D4×C41semidirect
503. C23×C4D4×C41semidirect
504. C23×C4D4×C41semidirect
564. C2×C22⋊C4D4×C41semidirect
565. C2×C22⋊C4D4×C41semidirect
566. C2×C22⋊C4D4×C41semidirect
567. C2×C22⋊C4D4×C41semidirect
698. C22⋊C4#41×C41semidirect

Maximal subgroups

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

subgroupindex
C41×#34902
C41×#24102
C41×#24052
C41×#20622
C41×#20442
C41×#20292
C41×#20212
C41×#18982
C41×#18892
C41×#18672
C2×C41×#3422
#2556341