Finite Group Databasebeta

← C41×#24031 #23800232

Subgroups — C41×#24031 #23800232

Order 10496.

1334 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3488C211yesmaximal, characteristic
2C41×#3093C211yesmaximal, characteristic, complemented
3C41×#2896C211yesmaximal, characteristic, complemented
4C41×#2500C211yesmaximal, characteristic, complemented
5C41×#2040C211yesmaximal, characteristic, complemented
6C41×#2039C211yesmaximal, characteristic, complemented
7C41×#2037C211yesmaximal, characteristic, complemented
8C41×#2037C211yesmaximal, characteristic, complemented
9C41×#1900C211yesmaximal, characteristic, complemented
10C41×#1871C211yesmaximal, characteristic, complemented
11C41×#1860C211yesmaximal, characteristic, complemented
12C41×#1859C211yesmaximal, characteristic, complemented
13C41×#1792C211yesmaximal, characteristic, complemented
14C41×#1792C211yesmaximal, characteristic, complemented
15C41×#1789C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C41C2211yescharacteristic
17C22×#41×C41C2211yescharacteristic
18C22×M16×C41C2211yescharacteristic, complemented
19C41×#550—21no—
20C41×#548—21no—
21C41×#546—21no—
22C41×#546—22no—
23D42×C41—22no—
24D42×C41—21no—
25C41×#537—21no—
26C41×#537C2211yescharacteristic
27C41×#535—21no—
28C41×#535C2211yescharacteristic
29C41×#525—21no—
30C41×#525C2211yescharacteristic
31C2×#121×C41—21no—
32C2×#121×C41C2211yescharacteristic
33C41×#520C2211yescharacteristic
34C2×#117×C41C2211yescharacteristic, complemented
35C41×#485—21no—
36C41×#485—21no—
37C41×#482—21no—
38C41×#482—21no—
39C41×#428C2211yescharacteristic, complemented
40C41×#428C2211yescharacteristic, complemented
41C2×#104×C41C2211yescharacteristic
42C2×#104×C41C2211yescharacteristic
43C2×#104×C41C2211yescharacteristic, complemented
44C2×#104×C41C2211yescharacteristic, complemented
45C2×#104×C41C2211yescharacteristic, complemented
46C2×#104×C41C2211yescharacteristic, complemented
47C41×#419—21no—
48C41×#418—21no—
49C41×#417C2211yescharacteristic
50C41×#417C2211yescharacteristic
51C41×#417C2211yescharacteristic, complemented
52C41×#417C2211yescharacteristic, complemented
53C41×#417C2211yescharacteristic, complemented
54C41×#417C2211yescharacteristic, complemented
55C41×#416—21no—
56C41×#416—21no—
57C2×#100×C41C2211yescharacteristic, complemented
58C2×#100×C41C2211yescharacteristic, complemented
59C41×#407C2211yescharacteristic, complemented
60C41×#394—22no—
61C41×#390C2211yescharacteristic, complemented
62C41×#390C2211yescharacteristic, complemented
63C41×#388—22no—
64C41×#384C2211yescharacteristic, complemented
65C41×#382C2211yescharacteristic, complemented
66C4×C22⋊C4×C41C2211yescharacteristic, complemented
67C41×#343C2211yescharacteristic, complemented
68C41×#343C2211yescharacteristic, complemented
69C41×#339C2211yescharacteristic, complemented
70C41×#339C2211yescharacteristic, complemented
71H(5,𝔽2)×C41—22no—
72H(5,𝔽2)×C41—22no—
73H(5,𝔽2)×C41—41no—
74H(5,𝔽2)×C41—41no—
75C2×#41×C41—21no—
76C2×#41×C41—21no—
77C2×#41×C41—21no—
78C2×#41×C41—21no—
79C2×#41×C41—22no—
80C2×#41×C41—22no—
81C2×#41×C41—41no—
82C2×#41×C41—41no—
83C2×#41×C41D411yescharacteristic
84C2×#41×C41D411yescharacteristic
85C2×#41×C41C2311yescharacteristic
86C2×#41×C41C2311yescharacteristic
87C2×#41×C41C2311yescharacteristic
88C22×Q8×C41D411yescharacteristic
89C22×D4×C41—21no—
90C22×D4×C41—22no—
91C22×D4×C41—22no—
92C22×D4×C41—21no—
93C22×D4×C41—21no—
94C22×D4×C41D411yescharacteristic
95C22×D4×C41D412yes—
96C22×D4×C41C2311yescharacteristic
97C23×C4×C41—21no—
98C23×C4×C41C2311yescharacteristic
99C2×M16×C41—21no—
100C2×M16×C41—41no—
101C2×M16×C41—41no—
102C2×M16×C41C2311yescharacteristic
103C2×M16×C41C2311yescharacteristic
104C2×M16×C41C2311yescharacteristic
105C2×M16×C41C2311yescharacteristic
106C22×C8×C41—21no—
107#127×C41—22no—
108#127×C41—21no—
109#124×C41—22no—
110#124×C41—21no—
111#123×C41—22no—
112#123×C41—21no—
113C22⋊Q8×C41—22no—
114C22⋊Q8×C41—21no—
115C22⋊Q8×C41—21no—
116C22⋊Q8×C41D411yescharacteristic
117C22⋊Q8×C41D411yescharacteristic
118#121×C41—22no—
119#121×C41—22no—
120#121×C41—22no—
121#121×C41—22no—
122#121×C41—22no—
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—22no—
130#121×C41—21no—
131#121×C41—21no—
132#121×C41D411yescharacteristic
133#121×C41D411yescharacteristic
134#120×C41—22no—
135#120×C41—22no—
136#120×C41—22no—
137#120×C41—21no—
138#120×C41—22no—
139C4×Q8×C41—21no—
140C4×D4×C41—22no—
141C4×D4×C41—22no—
142C4×D4×C41—21no—
143C4×D4×C41—22no—
144C4×D4×C41—21no—
145C4×D4×C41—21no—
146#117×C41—21no—
147#117×C41—21no—
148#117×C41—21no—
149#117×C41—21no—
150#117×C41—21no—
151#117×C41C2311yescharacteristic
152C2×C4⋊C4×C41—21no—
153C2×C4⋊C4×C41—22no—
154C2×C4⋊C4×C41C2311yescharacteristic
155C2×C4⋊C4×C41C2311yescharacteristic
156C2×C4⋊C4×C41C2311yescharacteristic
157C2×C22⋊C4×C41—22no—
158C2×C22⋊C4×C41—21no—
159C2×C22⋊C4×C41—21no—
160C2×C22⋊C4×C41—22no—
161C2×C22⋊C4×C41—22no—
162C2×C22⋊C4×C41D412yes—
163C2×C42×C41—21no—
164C2×C42×C41C2311yescharacteristic
165C2×C42×C41C2311yescharacteristic
166#107×C41—21no—
167#107×C41—21no—
168#106×C41—21no—
169#106×C41—21no—
170#104×C41—22no—
171#104×C41—22no—
172#104×C41—41no—
173#104×C41—41no—
174#104×C41—41no—
175#104×C41—41no—
176#103×C41—21no—
177#103×C41—21no—
178#103×C41—21no—
179#103×C41—21no—
180#103×C41—21no—
181#103×C41—21no—
182#102×C41—21no—
183#102×C41—21no—
184#102×C41—21no—
185#102×C41—21no—
186#102×C41—21no—
187#102×C41—21no—
188#100×C41—41no—
189#100×C41—41no—
190C22⋊C8×C41—21no—
191C22⋊C8×C41—21no—
192#95×C41—21no—
193#95×C41—22no—
194C24×C41—22no—
195C24×C41—21no—
196C24×C41C2×D412yes—
197C24×C41C2×D411yescharacteristic
198#41×C41—21no—
199#41×C41—21no—
200#41×C41—22no—
201#41×C41—22no—
202#41×C41—21no—
203#41×C41—21no—
204#41×C41—21no—
205#41×C41—21no—
206#41×C41—21no—
207#41×C41—21no—
208#41×C41—21no—
209#41×C41—21no—
210#41×C41—42no—
211#41×C41—42no—
212#41×C41—41no—
213#41×C41—41no—
214#41×C41—42no—
215#41×C41—42no—
216#41×C41—42no—
217#41×C41—42no—
218#41×C41—42no—
219#41×C41—42no—
220#41×C41#4112yes—
221#41×C41#4112yes—
222C2×Q8×C41—21no—
223C2×Q8×C41—22no—
224C2×Q8×C41—41no—
225C2×Q8×C41C2×D411yescharacteristic
226C2×Q8×C41C2×D411yescharacteristic
227C2×Q8×C41C2×D411yescharacteristic
228C2×D4×C41—21no—
229C2×D4×C41—22no—
230C2×D4×C41—22no—
231C2×D4×C41—22no—
232C2×D4×C41—22no—
233C2×D4×C41—21no—
234C2×D4×C41—21no—
235C2×D4×C41—21no—
236C2×D4×C41—21no—
237C2×D4×C41—21no—
238C2×D4×C41—22no—
239C2×D4×C41—22no—
240C2×D4×C41—22no—
241C2×D4×C41—21no—
242C2×D4×C41—22no—
243C2×D4×C41—21no—
244C2×D4×C41—21no—
245C2×D4×C41—21no—
246C2×D4×C41—21no—
247C2×D4×C41—21no—
248C2×D4×C41—21no—
249C2×D4×C41—21no—
250C2×D4×C41—41no—
251C2×D4×C41—42no—
252C2×D4×C41—42no—
253C2×D4×C41—42no—
254C2×D4×C41—42no—
255C2×D4×C41—44no—
256C2×D4×C41—44no—
257C2×D4×C41—42no—
258C2×D4×C41—42no—
259C2×D4×C41—82no—
260C2×D4×C41—84no—
261C2×D4×C41C2×D411yescharacteristic
262C2×D4×C41C2×D411yescharacteristic
263C2×D4×C41C2×D411yescharacteristic
264C22×C4×C41—21no—
265C22×C4×C41—21no—
266C22×C4×C41—21no—
267C22×C4×C41—21no—
268C22×C4×C41—21no—
269C22×C4×C41—22no—
270C22×C4×C41—21no—
271C22×C4×C41—21no—
272C22×C4×C41—22no—
273C22×C4×C41—21no—
274C22×C4×C41—21no—
275C22×C4×C41—21no—
276C22×C4×C41—21no—
277C22×C4×C41—21no—
278C22×C4×C41—21no—
279C22×C4×C41—21no—
280C22×C4×C41—42no—
281C22×C4×C41—42no—
282C22×C4×C41C2×D411yescharacteristic
283C22×C4×C41C2×D411yescharacteristic
284C22×C4×C41C2×D411yescharacteristic
285C22×C4×C41C2×D411yescharacteristic
286C22×C4×C41C2×D411yescharacteristic
287C22×C4×C41C2×D412yes—
288C22×C4×C41C2411yescharacteristic
289M16×C41—21no—
290M16×C41—21no—
291M16×C41—21no—
292M16×C41—21no—
293M16×C41—21no—
294M16×C41—21no—
295M16×C41—21no—
296M16×C41—21no—
297M16×C41—42no—
298C2×C8×C41—21no—
299C2×C8×C41—21no—
300C2×C8×C41—21no—
301C2×C8×C41—21no—
302C2×C8×C41—42no—
303C4⋊C4×C41—22no—
304C4⋊C4×C41—22no—
305C4⋊C4×C41—21no—
306C4⋊C4×C41—21no—
307C4⋊C4×C41—21no—
308C4⋊C4×C41—21no—
309C4⋊C4×C41—21no—
310C4⋊C4×C41—21no—
311C4⋊C4×C41—21no—
312C4⋊C4×C41—21no—
313C4⋊C4×C41—82no—
314C4⋊C4×C41C2×D411yescharacteristic
315C4⋊C4×C41C2×D411yescharacteristic
316C22⋊C4×C41—22no—
317C22⋊C4×C41—22no—
318C22⋊C4×C41—22no—
319C22⋊C4×C41—22no—
320C22⋊C4×C41—22no—
321C22⋊C4×C41—21no—
322C22⋊C4×C41—21no—
323C22⋊C4×C41—21no—
324C22⋊C4×C41—21no—
325C22⋊C4×C41—22no—
326C22⋊C4×C41—22no—
327C22⋊C4×C41—21no—
328C22⋊C4×C41—42no—
329C22⋊C4×C41—44no—
330C22⋊C4×C41—41no—
331C22⋊C4×C41—41no—
332C22⋊C4×C41—82no—
333C42×C41—22no—
334C42×C41—21no—
335C42×C41—21no—
336C42×C41—21no—
337C42×C41—21no—
338C42×C41—21no—
339C42×C41—41no—
340C42×C41—41no—
341C23×C41—21no—
342C23×C41—21no—
343C23×C41—21no—
344C23×C41—22no—
345C23×C41—21no—
346C23×C41—21no—
347C23×C41—22no—
348C23×C41—22no—
349C23×C41—41no—
350C23×C41—41no—
351C23×C41—42no—
352C23×C41—42no—
353C23×C41—44no—
354C23×C41—42no—
355C23×C41—42no—
356C23×C41—81no—
357C23×C41—82no—
358C23×C41—82no—
359C23×C41#12011yescharacteristic
360C23×C41#12011yescharacteristic
361C23×C41C22×D411yescharacteristic
362Q8×C41—21no—
363Q8×C41—21no—
364Q8×C41—21no—
365Q8×C41—21no—
366Q8×C41—21no—
367Q8×C41—42no—
368Q8×C41#12312yes—
369D4×C41—22no—
370D4×C41—22no—
371D4×C41—21no—
372D4×C41—21no—
373D4×C41—21no—
374D4×C41—21no—
375D4×C41—21no—
376D4×C41—42no—
377D4×C41—42no—
378D4×C41—44no—
379D4×C41—42no—
380D4×C41—44no—
381D4×C41—44no—
382D4×C41—42no—
383D4×C41—41no—
384D4×C41—41no—
385D4×C41—41no—
386D4×C41—41no—
387D4×C41—41no—
388D4×C41—41no—
389D4×C41—41no—
390D4×C41—41no—
391D4×C41—81no—
392D4×C41—82no—
393D4×C41—82no—
394D4×C41—82no—
395D4×C41—82no—
396D4×C41#12312yes—
397C2×C4×C41—21no—
398C2×C4×C41—21no—
399C2×C4×C41—21no—
400C2×C4×C41—21no—
401C2×C4×C41—21no—
402C2×C4×C41—21no—
403C2×C4×C41—21no—
404C2×C4×C41—21no—
405C2×C4×C41—21no—
406C2×C4×C41—21no—
407C2×C4×C41—21no—
408C2×C4×C41—22no—
409C2×C4×C41—22no—
410C2×C4×C41—22no—
411C2×C4×C41—21no—
412C2×C4×C41—22no—
413C2×C4×C41—21no—
414C2×C4×C41—21no—
415C2×C4×C41—21no—
416C2×C4×C41—42no—
417C2×C4×C41—42no—
418C2×C4×C41—42no—
419C2×C4×C41—44no—
420C2×C4×C41—41no—
421C2×C4×C41—41no—
422C2×C4×C41—41no—
423C2×C4×C41—41no—
424C2×C4×C41—41no—
425C2×C4×C41—41no—
426C2×C4×C41—42no—
427C2×C4×C41—41no—
428C2×C4×C41—42no—
429C2×C4×C41—41no—
430C2×C4×C41—42no—
431C2×C4×C41—41no—
432C2×C4×C41—41no—
433C2×C4×C41—41no—
434C2×C4×C41—82no—
435C2×C4×C41#12011yescharacteristic
436C2×C4×C41#12011yescharacteristic
437C2×C4×C41C22×D411yescharacteristic
438C2×C4×C41C22×D411yescharacteristic
439C2×C4×C41C2×#4111yescharacteristic
440C2×C4×C41C2×#4111yescharacteristic
441C2×C4×C41H(5,𝔽2)11yescharacteristic
442C2×C4×C41H(5,𝔽2)11yescharacteristic
443C8×C41—41no—
444C8×C41—41no—
445C8×C41—41no—
446C8×C41—41no—
447#24031C4111yesmaximal, characteristic, direct product factor, Sylow
448C22×C41—21no—
449C22×C41—21no—
450C22×C41—21no—
451C22×C41—21no—
452C22×C41—22no—
453C22×C41—21no—
454C22×C41—21no—
455C22×C41—21no—
456C22×C41—21no—
457C22×C41—41no—
458C22×C41—41no—
459C22×C41—41no—
460C22×C41—41no—
461C22×C41—42no—
462C22×C41—41no—
463C22×C41—42no—
464C22×C41—41no—
465C22×C41—42no—
466C22×C41—41no—
467C22×C41—41no—
468C22×C41—81no—
469C22×C41—81no—
470C22×C41—82no—
471C22×C41—82no—
472C22×C41—84no—
473C22×C41—164no—
474C22×C41C2×#12011yescharacteristic
475C22×C41#54611yescharacteristic
476C22×C41#54611yescharacteristic
477C4×C41—21no—
478C4×C41—21no—
479C4×C41—22no—
480C4×C41—42no—
481C4×C41—41no—
482C4×C41—41no—
483C4×C41—41no—
484C4×C41—42no—
485C4×C41—41no—
486C4×C41—81no—
487C4×C41—81no—
488C4×C41—81no—
489C4×C41C2×#12311yescharacteristic
490C4×C41#53411yescharacteristic
491C4×C41#54611yescharacteristic
492C4×C41#54611yescharacteristic
493#3488C2×C4111yescharacteristic
494#3093C2×C4111yescharacteristic, complemented
495#2896C2×C4111yescharacteristic, complemented
496#2500C2×C4111yescharacteristic, complemented
497#2040C2×C4111yescharacteristic, complemented
498#2039C2×C4111yescharacteristic, complemented
499#2037C2×C4111yescharacteristic, complemented
500#2037C2×C4111yescharacteristic, complemented
501#1900C2×C4111yescharacteristic, complemented
502#1871C2×C4111yescharacteristic, complemented
503#1860C2×C4111yescharacteristic, complemented
504#1859C2×C4111yescharacteristic, complemented
505#1792C2×C4111yescharacteristic, complemented
506#1792C2×C4111yescharacteristic, complemented
507#1789C2×C4111yescharacteristic, complemented
508C2×C41—21no—
509C2×C41—21no—
510C2×C41—41no—
511C2×C41—41no—
512C2×C41—42no—
513C2×C41—81no—
514C2×C41—82no—
515C2×C41—81no—
516C2×C41#240511yescharacteristic
517C2×C41#301811yescharacteristic
518C2×C41#301911yescharacteristic
519C2×H(5,𝔽2)C22×C4111yescharacteristic
520C22×#41C22×C4111yescharacteristic
521C22×M16C22×C4111yescharacteristic, complemented
522#550—21no—
523#548—21no—
524#546—21no—
525#546—22no—
526D42—22no—
527D42—21no—
528#537—21no—
529#537C22×C4111yescharacteristic
530#535—21no—
531#535C22×C4111yescharacteristic
532#525—21no—
533#525C22×C4111yescharacteristic
534C2×#121—21no—
535C2×#121C22×C4111yescharacteristic
536#520C22×C4111yescharacteristic
537C2×#117C22×C4111yescharacteristic, complemented
538#485—21no—
539#485—21no—
540#482—21no—
541#482—21no—
542#428C22×C4111yescharacteristic, complemented
543#428C22×C4111yescharacteristic, complemented
544C2×#104C22×C4111yescharacteristic
545C2×#104C22×C4111yescharacteristic
546C2×#104C22×C4111yescharacteristic, complemented
547C2×#104C22×C4111yescharacteristic, complemented
548C2×#104C22×C4111yescharacteristic, complemented
549C2×#104C22×C4111yescharacteristic, complemented
550#419—21no—
551#418—21no—
552#417C22×C4111yescharacteristic
553#417C22×C4111yescharacteristic
554#417C22×C4111yescharacteristic, complemented
555#417C22×C4111yescharacteristic, complemented
556#417C22×C4111yescharacteristic, complemented
557#417C22×C4111yescharacteristic, complemented
558#416—21no—
559#416—21no—
560C2×#100C22×C4111yescharacteristic, complemented
561C2×#100C22×C4111yescharacteristic, complemented
562#407C22×C4111yescharacteristic, complemented
563#394—22no—
564#390C22×C4111yescharacteristic, complemented
565#390C22×C4111yescharacteristic, complemented
566#388—22no—
567#384C22×C4111yescharacteristic, complemented
568#382C22×C4111yescharacteristic, complemented
569C4×C22⋊C4C22×C4111yescharacteristic, complemented
570#343C22×C4111yescharacteristic, complemented
571#343C22×C4111yescharacteristic, complemented
572#339C22×C4111yescharacteristic, complemented
573#339C22×C4111yescharacteristic, complemented
574C41#2403111yescharacteristic, direct product factor, Sylow
575H(5,𝔽2)—22no—
576H(5,𝔽2)—22no—
577H(5,𝔽2)—41no—
578H(5,𝔽2)—41no—
579C2×#41—21no—
580C2×#41—21no—
581C2×#41—21no—
582C2×#41—21no—
583C2×#41—22no—
584C2×#41—22no—
585C2×#41—41no—
586C2×#41—41no—
587C2×#41D4×C4111yescharacteristic
588C2×#41D4×C4111yescharacteristic
589C2×#41C23×C4111yescharacteristic
590C2×#41C23×C4111yescharacteristic
591C2×#41C23×C4111yescharacteristic
592C22×Q8D4×C4111yescharacteristic
593C22×D4—21no—
594C22×D4—22no—
595C22×D4—22no—
596C22×D4—21no—
597C22×D4—21no—
598C22×D4D4×C4111yescharacteristic
599C22×D4D4×C4112yes—
600C22×D4C23×C4111yescharacteristic
601C23×C4—21no—
602C23×C4C23×C4111yescharacteristic
603C2×M16—21no—
604C2×M16—41no—
605C2×M16—41no—
606C2×M16C23×C4111yescharacteristic
607C2×M16C23×C4111yescharacteristic
608C2×M16C23×C4111yescharacteristic
609C2×M16C23×C4111yescharacteristic
610C22×C8—21no—
611#127—22no—
612#127—21no—
613#124—22no—
614#124—21no—
615#123—22no—
616#123—21no—
617C22⋊Q8—22no—
618C22⋊Q8—21no—
619C22⋊Q8—21no—
620C22⋊Q8D4×C4111yescharacteristic
621C22⋊Q8D4×C4111yescharacteristic
622#121—22no—
623#121—22no—
624#121—22no—
625#121—22no—
626#121—22no—
627#121—21no—
628#121—21no—
629#121—21no—
630#121—21no—
631#121—21no—
632#121—21no—
633#121—22no—
634#121—21no—
635#121—21no—
636#121D4×C4111yescharacteristic
637#121D4×C4111yescharacteristic
638#120—22no—
639#120—22no—
640#120—22no—
641#120—21no—
642#120—22no—
643C4×Q8—21no—
644C4×D4—22no—
645C4×D4—22no—
646C4×D4—21no—
647C4×D4—22no—
648C4×D4—21no—
649C4×D4—21no—
650#117—21no—
651#117—21no—
652#117—21no—
653#117—21no—
654#117—21no—
655#117C23×C4111yescharacteristic
656C2×C4⋊C4—21no—
657C2×C4⋊C4—22no—
658C2×C4⋊C4C23×C4111yescharacteristic
659C2×C4⋊C4C23×C4111yescharacteristic
660C2×C4⋊C4C23×C4111yescharacteristic
661C2×C22⋊C4—22no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—22no—
665C2×C22⋊C4—22no—
666C2×C22⋊C4D4×C4112yes—
667C2×C42—21no—
668C2×C42C23×C4111yescharacteristic
669C2×C42C23×C4111yescharacteristic
670#107—21no—
671#107—21no—
672#106—21no—
673#106—21no—
674#104—22no—
675#104—22no—
676#104—41no—
677#104—41no—
678#104—41no—
679#104—41no—
680#103—21no—
681#103—21no—
682#103—21no—
683#103—21no—
684#103—21no—
685#103—21no—
686#102—21no—
687#102—21no—
688#102—21no—
689#102—21no—
690#102—21no—
691#102—21no—
692#100—41no—
693#100—41no—
694C22⋊C8—21no—
695C22⋊C8—21no—
696#95—21no—
697#95—22no—
698C24—22no—
699C24—21no—
700C24C2×D4×C4112yes—
701C24C2×D4×C4111yescharacteristic
702#41—21no—
703#41—21no—
704#41—22no—
705#41—22no—
706#41—21no—
707#41—21no—
708#41—21no—
709#41—21no—
710#41—21no—
711#41—21no—
712#41—21no—
713#41—21no—
714#41—42no—
715#41—42no—
716#41—41no—
717#41—41no—
718#41—42no—
719#41—42no—
720#41—42no—
721#41—42no—
722#41—42no—
723#41—42no—
724#41#41×C4112yes—
725#41#41×C4112yes—
726C2×Q8—21no—
727C2×Q8—22no—
728C2×Q8—41no—
729C2×Q8C2×D4×C4111yescharacteristic
730C2×Q8C2×D4×C4111yescharacteristic
731C2×Q8C2×D4×C4111yescharacteristic
732C2×D4—21no—
733C2×D4—22no—
734C2×D4—22no—
735C2×D4—22no—
736C2×D4—22no—
737C2×D4—21no—
738C2×D4—21no—
739C2×D4—21no—
740C2×D4—21no—
741C2×D4—21no—
742C2×D4—22no—
743C2×D4—22no—
744C2×D4—22no—
745C2×D4—21no—
746C2×D4—22no—
747C2×D4—21no—
748C2×D4—21no—
749C2×D4—21no—
750C2×D4—21no—
751C2×D4—21no—
752C2×D4—21no—
753C2×D4—21no—
754C2×D4—41no—
755C2×D4—42no—
756C2×D4—42no—
757C2×D4—42no—
758C2×D4—42no—
759C2×D4—44no—
760C2×D4—44no—
761C2×D4—42no—
762C2×D4—42no—
763C2×D4—82no—
764C2×D4—84no—
765C2×D4C2×D4×C4111yescharacteristic
766C2×D4C2×D4×C4111yescharacteristic
767C2×D4C2×D4×C4111yescharacteristic
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—22no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—22no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—42no—
785C22×C4—42no—
786C22×C4C2×D4×C4111yescharacteristic
787C22×C4C2×D4×C4111yescharacteristic
788C22×C4C2×D4×C4111yescharacteristic
789C22×C4C2×D4×C4111yescharacteristic
790C22×C4C2×D4×C4111yescharacteristic
791C22×C4C2×D4×C4112yes—
792C22×C4C24×C4111yescharacteristic
793M16—21no—
794M16—21no—
795M16—21no—
796M16—21no—
797M16—21no—
798M16—21no—
799M16—21no—
800M16—21no—
801M16—42no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8—42no—
807C4⋊C4—22no—
808C4⋊C4—22no—
809C4⋊C4—21no—
810C4⋊C4—21no—
811C4⋊C4—21no—
812C4⋊C4—21no—
813C4⋊C4—21no—
814C4⋊C4—21no—
815C4⋊C4—21no—
816C4⋊C4—21no—
817C4⋊C4—82no—
818C4⋊C4C2×D4×C4111yescharacteristic
819C4⋊C4C2×D4×C4111yescharacteristic
820C22⋊C4—22no—
821C22⋊C4—22no—
822C22⋊C4—22no—
823C22⋊C4—22no—
824C22⋊C4—22no—
825C22⋊C4—21no—
826C22⋊C4—21no—
827C22⋊C4—21no—
828C22⋊C4—21no—
829C22⋊C4—22no—
830C22⋊C4—22no—
831C22⋊C4—21no—
832C22⋊C4—42no—
833C22⋊C4—44no—
834C22⋊C4—41no—
835C22⋊C4—41no—
836C22⋊C4—82no—
837C42—22no—
838C42—21no—
839C42—21no—
840C42—21no—
841C42—21no—
842C42—21no—
843C42—41no—
844C42—41no—
845C23—21no—
846C23—21no—
847C23—21no—
848C23—22no—
849C23—21no—
850C23—21no—
851C23—22no—
852C23—22no—
853C23—41no—
854C23—41no—
855C23—42no—
856C23—42no—
857C23—44no—
858C23—42no—
859C23—42no—
860C23—81no—
861C23—82no—
862C23—82no—
863C23#120×C4111yescharacteristic
864C23#120×C4111yescharacteristic
865C23C22×D4×C4111yescharacteristic
866Q8—21no—
867Q8—21no—
868Q8—21no—
869Q8—21no—
870Q8—21no—
871Q8—42no—
872Q8#123×C4112yes—
873D4—22no—
874D4—22no—
875D4—21no—
876D4—21no—
877D4—21no—
878D4—21no—
879D4—21no—
880D4—42no—
881D4—42no—
882D4—44no—
883D4—42no—
884D4—44no—
885D4—44no—
886D4—42no—
887D4—41no—
888D4—41no—
889D4—41no—
890D4—41no—
891D4—41no—
892D4—41no—
893D4—41no—
894D4—41no—
895D4—82no—
896D4—81no—
897D4—82no—
898D4—82no—
899D4—82no—
900D4#123×C4112yes—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—21no—
916C2×C4—22no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—21no—
920C2×C4—42no—
921C2×C4—42no—
922C2×C4—42no—
923C2×C4—44no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—42no—
931C2×C4—41no—
932C2×C4—42no—
933C2×C4—41no—
934C2×C4—42no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—82no—
939C2×C4#120×C4111yescharacteristic
940C2×C4#120×C4111yescharacteristic
941C2×C4C22×D4×C4111yescharacteristic
942C2×C4C22×D4×C4111yescharacteristic
943C2×C4C2×#41×C4111yescharacteristic
944C2×C4C2×#41×C4111yescharacteristic
945C2×C4H(5,𝔽2)×C4111yescharacteristic
946C2×C4H(5,𝔽2)×C4111yescharacteristic
947C8—41no—
948C8—41no—
949C8—41no—
950C8—41no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—22no—
956C22—21no—
957C22—21no—
958C22—21no—
959C22—21no—
960C22—41no—
961C22—41no—
962C22—41no—
963C22—41no—
964C22—42no—
965C22—41no—
966C22—42no—
967C22—41no—
968C22—42no—
969C22—41no—
970C22—41no—
971C22—81no—
972C22—81no—
973C22—82no—
974C22—82no—
975C22—84no—
976C22—164no—
977C22C2×#120×C4111yescharacteristic
978C22C41×#54611yescharacteristic
979C22C41×#54611yescharacteristic
980C4—21no—
981C4—21no—
982C4—22no—
983C4—42no—
984C4—41no—
985C4—41no—
986C4—41no—
987C4—42no—
988C4—41no—
989C4—81no—
990C4—81no—
991C4—81no—
992C4C2×#123×C4111yescharacteristic
993C4C41×#53411yescharacteristic
994C4C41×#54611yescharacteristic
995C4C41×#54611yescharacteristic
996C2—21no—
997C2—21no—
998C2—41no—
999C2—41no—
1000C2—42no—
1001C2—81no—
1002C2—82no—
1003C2—81no—
1004C2C41×#240511yescharacteristic
1005C2C41×#301811yescharacteristic
1006C2C41×#301911yescharacteristic
subgroupG/H
center, socleC22×C41C2×#120
commutator, Frattini, cosocleC22×C4C24×C41
prime radicalC41×#3488C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C41 ◁ C23×C4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C41×#3093C2semidirect
3. C41×#2896C2semidirect
4. C41×#2500C2semidirect
5. C41×#2040C2semidirect
6. C41×#2039C2semidirect
7. C41×#2037C2semidirect
8. C41×#2037C2semidirect
9. C41×#1900C2semidirect
10. C41×#1871C2semidirect
11. C41×#1860C2semidirect
12. C41×#1859C2semidirect
13. C41×#1792C2semidirect
14. C41×#1792C2semidirect
15. C41×#1789C2semidirect
18. C22×M16×C41C22semidirect
34. C2×#117×C41C22semidirect
39. C41×#428C22semidirect
40. C41×#428C22semidirect
43. C2×#104×C41C22semidirect
44. C2×#104×C41C22semidirect
45. C2×#104×C41C22semidirect
46. C2×#104×C41C22semidirect
51. C41×#417C22semidirect
52. C41×#417C22semidirect
53. C41×#417C22semidirect
54. C41×#417C22semidirect
57. C2×#100×C41C22semidirect
58. C2×#100×C41C22semidirect
59. C41×#407C22semidirect
61. C41×#390C22semidirect
62. C41×#390C22semidirect
64. C41×#384C22semidirect
65. C41×#382C22semidirect
66. C4×C22⋊C4×C41C22semidirect
67. C41×#343C22semidirect
68. C41×#343C22semidirect
69. C41×#339C22semidirect
70. C41×#339C22semidirect
447. #24031C41direct (N × H)
494. #3093C2×C41semidirect
495. #2896C2×C41semidirect
496. #2500C2×C41semidirect
497. #2040C2×C41semidirect
498. #2039C2×C41semidirect
499. #2037C2×C41semidirect
500. #2037C2×C41semidirect
501. #1900C2×C41semidirect
502. #1871C2×C41semidirect
503. #1860C2×C41semidirect
504. #1859C2×C41semidirect
505. #1792C2×C41semidirect
506. #1792C2×C41semidirect
507. #1789C2×C41semidirect
521. C22×M16C22×C41semidirect
537. C2×#117C22×C41semidirect
542. #428C22×C41semidirect
543. #428C22×C41semidirect
546. C2×#104C22×C41semidirect
547. C2×#104C22×C41semidirect
548. C2×#104C22×C41semidirect
549. C2×#104C22×C41semidirect
554. #417C22×C41semidirect
555. #417C22×C41semidirect
556. #417C22×C41semidirect
557. #417C22×C41semidirect
560. C2×#100C22×C41semidirect
561. C2×#100C22×C41semidirect
562. #407C22×C41semidirect
564. #390C22×C41semidirect
565. #390C22×C41semidirect
567. #384C22×C41semidirect
568. #382C22×C41semidirect
569. C4×C22⋊C4C22×C41semidirect
570. #343C22×C41semidirect
571. #343C22×C41semidirect
572. #339C22×C41semidirect
573. #339C22×C41semidirect
574. C41#24031direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#34882
C41×#30932
C41×#28962
C41×#25002
C41×#20402
C41×#20392
C41×#20372
C41×#19002
C41×#18712
C41×#18602
C41×#18592
C41×#17922
C41×#17892
#2403141