Finite Group Databasebeta

← C41×#13080 #23789281

Subgroups — C41×#13080 #23789281

Order 10496.

864 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#100×C41C211yesmaximal, characteristic
2C41×#2405C211yesmaximal, characteristic
3C2×C41×#352C212yesmaximal, complemented
4C41×#1781C211yesmaximal, characteristic
5C41×#1390C212yesmaximal, complemented
6C23×D4×C41C2211yescharacteristic
7C22×M16×C41—21no—
8C2×#123×C41C411yescharacteristic, complemented
9C2×#123×C41C2211yescharacteristic
10C22×C22⋊C4×C41C411yescharacteristic, complemented
11C2×#100×C41—21no—
12C2×#100×C41—24no—
13C2×#100×C41C2212yes—
14C2×#99×C41—21no—
15C2×#99×C41C2212yes—
16C41×#394—21no—
17C41×#394—21no—
18C41×#386C411yescharacteristic, complemented
19C41×#386C2211yescharacteristic
20C41×#385—21no—
21C41×#379—21no—
22C41×#379—21no—
23C41×#379C411yescharacteristic, complemented
24C41×#352—24no—
25C25×C41C2×C411yescharacteristic
26C25×C41D411yescharacteristic
27C22×D4×C41—22no—
28C22×D4×C41—22no—
29C22×D4×C41—42no—
30C22×D4×C41—41no—
31C22×D4×C41—41no—
32C22×D4×C41C2×C411yescharacteristic
33C22×D4×C41D411yescharacteristic
34C22×D4×C41D411yescharacteristic
35C22×D4×C41C2311yescharacteristic
36C23×C4×C41C2×C411yescharacteristic
37C23×C4×C41C2×C411yescharacteristic
38C23×C4×C41D411yescharacteristic
39C2×M16×C41—24no—
40C2×M16×C41—22no—
41C2×M16×C41—41no—
42C2×M16×C41—42no—
43C22×C8×C41—41no—
44#123×C41—22no—
45#123×C41—22no—
46#123×C41—42no—
47C2×C4⋊C4×C41—21no—
48C2×C4⋊C4×C41—21no—
49C2×C22⋊C4×C41—21no—
50C2×C22⋊C4×C41—21no—
51C2×C22⋊C4×C41—21no—
52C2×C22⋊C4×C41—21no—
53C2×C22⋊C4×C41—21no—
54C2×C22⋊C4×C41—22no—
55C2×C22⋊C4×C41—21no—
56C2×C22⋊C4×C41—21no—
57C2×C22⋊C4×C41—21no—
58C2×C22⋊C4×C41—41no—
59C2×C22⋊C4×C41—41no—
60C2×C22⋊C4×C41—41no—
61C2×C22⋊C4×C41—41no—
62C2×C22⋊C4×C41C2×C411yescharacteristic
63C2×C22⋊C4×C41C2×C411yescharacteristic
64#100×C41—24no—
65#100×C41—22no—
66#100×C41D414yes—
67#99×C41—22no—
68#99×C41—22no—
69#99×C41—42no—
70#95×C41—21no—
71#95×C41—21no—
72C24×C41—21no—
73C24×C41—21no—
74C24×C41—21no—
75C24×C41—21no—
76C24×C41—22no—
77C24×C41—22no—
78C24×C41—41no—
79C24×C41—41no—
80C24×C41—42no—
81C24×C41—42no—
82C24×C41—81no—
83C24×C41—81no—
84C24×C41C22⋊C411yescharacteristic
85C24×C41C22⋊C411yescharacteristic
86C24×C41C22⋊C411yescharacteristic
87C24×C41C22×C411yescharacteristic
88C24×C41C2×D411yescharacteristic
89C2×D4×C41—22no—
90C2×D4×C41—22no—
91C2×D4×C41—22no—
92C2×D4×C41—22no—
93C2×D4×C41—21no—
94C2×D4×C41—21no—
95C2×D4×C41—41no—
96C2×D4×C41—41no—
97C2×D4×C41—41no—
98C2×D4×C41—41no—
99C2×D4×C41—41no—
100C2×D4×C41—41no—
101C2×D4×C41—44no—
102C2×D4×C41—44no—
103C2×D4×C41—44no—
104C2×D4×C41—44no—
105C2×D4×C41C2×D412yes—
106C2×D4×C41#4112yes—
107C22×C4×C41—21no—
108C22×C4×C41—21no—
109C22×C4×C41—22no—
110C22×C4×C41—21no—
111C22×C4×C41—21no—
112C22×C4×C41—21no—
113C22×C4×C41—21no—
114C22×C4×C41—21no—
115C22×C4×C41—21no—
116C22×C4×C41—22no—
117C22×C4×C41—41no—
118C22×C4×C41—41no—
119C22×C4×C41—41no—
120C22×C4×C41—42no—
121C22×C4×C41—81no—
122C22×C4×C41C22⋊C411yescharacteristic
123C22×C4×C41C2×D411yescharacteristic
124M16×C41—24no—
125M16×C41—44no—
126M16×C41—42no—
127C2×C8×C41—44no—
128C2×C8×C41—42no—
129C4⋊C4×C41—42no—
130C4⋊C4×C41—41no—
131C4⋊C4×C41—41no—
132C22⋊C4×C41—22no—
133C22⋊C4×C41—42no—
134C22⋊C4×C41—42no—
135C22⋊C4×C41—42no—
136C22⋊C4×C41—41no—
137C22⋊C4×C41—41no—
138C22⋊C4×C41—42no—
139C22⋊C4×C41—41no—
140C22⋊C4×C41—42no—
141C22⋊C4×C41—42no—
142C22⋊C4×C41—81no—
143C22⋊C4×C41—81no—
144C22⋊C4×C41—81no—
145C22⋊C4×C41—82no—
146C22⋊C4×C41—82no—
147C23×C41—22no—
148C23×C41—21no—
149C23×C41—21no—
150C23×C41—21no—
151C23×C41—21no—
152C23×C41—21no—
153C23×C41—21no—
154C23×C41—21no—
155C23×C41—21no—
156C23×C41—21no—
157C23×C41—21no—
158C23×C41—21no—
159C23×C41—21no—
160C23×C41—41no—
161C23×C41—42no—
162C23×C41—42no—
163C23×C41—42no—
164C23×C41—42no—
165C23×C41—41no—
166C23×C41—41no—
167C23×C41—41no—
168C23×C41—41no—
169C23×C41—41no—
170C23×C41—41no—
171C23×C41—42no—
172C23×C41—42no—
173C23×C41—41no—
174C23×C41—41no—
175C23×C41—42no—
176C23×C41—42no—
177C23×C41—81no—
178C23×C41—81no—
179C23×C41—81no—
180C23×C41—81no—
181C23×C41—84no—
182C23×C41—84no—
183C23×C41—84no—
184C23×C41—84no—
185C23×C41#9911yescharacteristic
186C23×C41#9911yescharacteristic
187C23×C41C2×C22⋊C411yescharacteristic
188C23×C41C4×D412yes—
189C23×C41#12112yes—
190D4×C41—42no—
191D4×C41—42no—
192D4×C41—44no—
193D4×C41—44no—
194D4×C41—42no—
195D4×C41—42no—
196C2×C4×C41—22no—
197C2×C4×C41—22no—
198C2×C4×C41—22no—
199C2×C4×C41—22no—
200C2×C4×C41—21no—
201C2×C4×C41—21no—
202C2×C4×C41—21no—
203C2×C4×C41—21no—
204C2×C4×C41—41no—
205C2×C4×C41—41no—
206C2×C4×C41—41no—
207C2×C4×C41—41no—
208C2×C4×C41—41no—
209C2×C4×C41—41no—
210C2×C4×C41—41no—
211C2×C4×C41—41no—
212C2×C4×C41—41no—
213C2×C4×C41—41no—
214C2×C4×C41—41no—
215C2×C4×C41—41no—
216C2×C4×C41—82no—
217C2×C4×C41—82no—
218C2×C4×C41—82no—
219C2×C4×C41—82no—
220C2×C4×C41—82no—
221C2×C4×C41#9912yes—
222C2×C4×C41#12011yescharacteristic
223C2×C4×C41#12311yescharacteristic
224C8×C41—44no—
225#13080C4111yesmaximal, characteristic, direct product factor, Sylow
226C22×C41—21no—
227C22×C41—21no—
228C22×C41—21no—
229C22×C41—21no—
230C22×C41—21no—
231C22×C41—21no—
232C22×C41—21no—
233C22×C41—22no—
234C22×C41—22no—
235C22×C41—42no—
236C22×C41—42no—
237C22×C41—42no—
238C22×C41—42no—
239C22×C41—42no—
240C22×C41—42no—
241C22×C41—41no—
242C22×C41—41no—
243C22×C41—41no—
244C22×C41—41no—
245C22×C41—41no—
246C22×C41—41no—
247C22×C41—41no—
248C22×C41—41no—
249C22×C41—41no—
250C22×C41—41no—
251C22×C41—81no—
252C22×C41—84no—
253C22×C41—84no—
254C22×C41—81no—
255C22×C41—81no—
256C22×C41—81no—
257C22×C41—84no—
258C22×C41—84no—
259C22×C41#35212yescomplemented
260C22×C41#38611yescharacteristic
261C22×C41C2×#9911yescharacteristic
262C22×C41C2×#9911yescharacteristic
263C4×C41—21no—
264C4×C41—22no—
265C4×C41—21no—
266C4×C41—81no—
267C4×C41—81no—
268C4×C41—81no—
269C4×C41—81no—
270C4×C41—162no—
271C22×#100C2×C4111yescharacteristic
272#2405C2×C4111yescharacteristic
273C2×#352C2×C4112yescomplemented
274#1781C2×C4111yescharacteristic
275#1390C2×C4112yescomplemented
276C2×C41—21no—
277C2×C41—21no—
278C2×C41—22no—
279C2×C41—42no—
280C2×C41—41no—
281C2×C41—42no—
282C2×C41—81no—
283C2×C41—81no—
284C2×C41#189811yescharacteristic
285C2×C41C2×#35211yescharacteristic
286C2×C41#212111yescharacteristic
287C23×D4C22×C4111yescharacteristic
288C22×M16—21no—
289C2×#123C4×C4111yescharacteristic, complemented
290C2×#123C22×C4111yescharacteristic
291C22×C22⋊C4C4×C4111yescharacteristic, complemented
292C2×#100—21no—
293C2×#100—24no—
294C2×#100C22×C4112yes—
295C2×#99—21no—
296C2×#99C22×C4112yes—
297#394—21no—
298#394—21no—
299#386C4×C4111yescharacteristic, complemented
300#386C22×C4111yescharacteristic
301#385—21no—
302#379—21no—
303#379—21no—
304#379C4×C4111yescharacteristic, complemented
305#352—24no—
306C41#1308011yescharacteristic, direct product factor, Sylow
307C25C2×C4×C4111yescharacteristic
308C25D4×C4111yescharacteristic
309C22×D4—22no—
310C22×D4—22no—
311C22×D4—42no—
312C22×D4—41no—
313C22×D4—41no—
314C22×D4C2×C4×C4111yescharacteristic
315C22×D4D4×C4111yescharacteristic
316C22×D4D4×C4111yescharacteristic
317C22×D4C23×C4111yescharacteristic
318C23×C4C2×C4×C4111yescharacteristic
319C23×C4C2×C4×C4111yescharacteristic
320C23×C4D4×C4111yescharacteristic
321C2×M16—24no—
322C2×M16—22no—
323C2×M16—41no—
324C2×M16—42no—
325C22×C8—41no—
326#123—22no—
327#123—22no—
328#123—42no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C22⋊C4—21no—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—21no—
334C2×C22⋊C4—21no—
335C2×C22⋊C4—21no—
336C2×C22⋊C4—22no—
337C2×C22⋊C4—21no—
338C2×C22⋊C4—21no—
339C2×C22⋊C4—21no—
340C2×C22⋊C4—41no—
341C2×C22⋊C4—41no—
342C2×C22⋊C4—41no—
343C2×C22⋊C4—41no—
344C2×C22⋊C4C2×C4×C4111yescharacteristic
345C2×C22⋊C4C2×C4×C4111yescharacteristic
346#100—24no—
347#100—22no—
348#100D4×C4114yes—
349#99—22no—
350#99—22no—
351#99—42no—
352#95—21no—
353#95—21no—
354C24—21no—
355C24—21no—
356C24—21no—
357C24—21no—
358C24—22no—
359C24—22no—
360C24—41no—
361C24—41no—
362C24—42no—
363C24—42no—
364C24—81no—
365C24—81no—
366C24C22⋊C4×C4111yescharacteristic
367C24C22⋊C4×C4111yescharacteristic
368C24C22⋊C4×C4111yescharacteristic
369C24C22×C4×C4111yescharacteristic
370C24C2×D4×C4111yescharacteristic
371C2×D4—22no—
372C2×D4—22no—
373C2×D4—22no—
374C2×D4—22no—
375C2×D4—21no—
376C2×D4—21no—
377C2×D4—41no—
378C2×D4—41no—
379C2×D4—41no—
380C2×D4—41no—
381C2×D4—41no—
382C2×D4—41no—
383C2×D4—44no—
384C2×D4—44no—
385C2×D4—44no—
386C2×D4—44no—
387C2×D4C2×D4×C4112yes—
388C2×D4#41×C4112yes—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—22no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—22no—
399C22×C4—41no—
400C22×C4—41no—
401C22×C4—41no—
402C22×C4—42no—
403C22×C4—81no—
404C22×C4C22⋊C4×C4111yescharacteristic
405C22×C4C2×D4×C4111yescharacteristic
406M16—24no—
407M16—44no—
408M16—42no—
409C2×C8—44no—
410C2×C8—42no—
411C4⋊C4—42no—
412C4⋊C4—41no—
413C4⋊C4—41no—
414C22⋊C4—22no—
415C22⋊C4—42no—
416C22⋊C4—42no—
417C22⋊C4—42no—
418C22⋊C4—41no—
419C22⋊C4—41no—
420C22⋊C4—42no—
421C22⋊C4—41no—
422C22⋊C4—42no—
423C22⋊C4—42no—
424C22⋊C4—81no—
425C22⋊C4—81no—
426C22⋊C4—81no—
427C22⋊C4—82no—
428C22⋊C4—82no—
429C23—22no—
430C23—21no—
431C23—21no—
432C23—21no—
433C23—21no—
434C23—21no—
435C23—21no—
436C23—21no—
437C23—21no—
438C23—21no—
439C23—21no—
440C23—21no—
441C23—21no—
442C23—41no—
443C23—42no—
444C23—42no—
445C23—42no—
446C23—42no—
447C23—41no—
448C23—41no—
449C23—41no—
450C23—41no—
451C23—41no—
452C23—41no—
453C23—42no—
454C23—42no—
455C23—41no—
456C23—41no—
457C23—42no—
458C23—42no—
459C23—81no—
460C23—81no—
461C23—81no—
462C23—81no—
463C23—84no—
464C23—84no—
465C23—84no—
466C23—84no—
467C23#99×C4111yescharacteristic
468C23#99×C4111yescharacteristic
469C23C2×C22⋊C4×C4111yescharacteristic
470C23C4×D4×C4112yes—
471C23#121×C4112yes—
472D4—42no—
473D4—42no—
474D4—44no—
475D4—44no—
476D4—42no—
477D4—42no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—82no—
499C2×C4—82no—
500C2×C4—82no—
501C2×C4—82no—
502C2×C4—82no—
503C2×C4#99×C4112yes—
504C2×C4#120×C4111yescharacteristic
505C2×C4#123×C4111yescharacteristic
506C8—44no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—21no—
513C22—21no—
514C22—22no—
515C22—22no—
516C22—42no—
517C22—42no—
518C22—42no—
519C22—42no—
520C22—42no—
521C22—42no—
522C22—41no—
523C22—41no—
524C22—41no—
525C22—41no—
526C22—41no—
527C22—41no—
528C22—41no—
529C22—41no—
530C22—41no—
531C22—41no—
532C22—81no—
533C22—84no—
534C22—84no—
535C22—81no—
536C22—81no—
537C22—81no—
538C22—84no—
539C22—84no—
540C22C41×#35212yescomplemented
541C22C41×#38611yescharacteristic
542C22C2×#99×C4111yescharacteristic
543C22C2×#99×C4111yescharacteristic
544C4—21no—
545C4—22no—
546C4—21no—
547C4—81no—
548C4—81no—
549C4—81no—
550C4—81no—
551C4—162no—
552C2—21no—
553C2—21no—
554C2—22no—
555C2—42no—
556C2—41no—
557C2—42no—
558C2—81no—
559C2—81no—
560C2C41×#189811yescharacteristic
561C2C2×C41×#35211yescharacteristic
562C2C41×#212111yescharacteristic
subgroupG/H
center, socleC22×C41C2×#99
commutatorC24C22×C4×C41
Frattini, cosocleC22×D4C23×C41
prime radicalC23×D4×C41C22
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C41 ◁ C24×C41 ◁ C23×D4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C41×#352C2semidirect
5. C41×#1390C2semidirect
8. C2×#123×C41C4semidirect
10. C22×C22⋊C4×C41C4semidirect
18. C41×#386C4semidirect
23. C41×#379C4semidirect
225. #13080C41direct (N × H)
259. C22×C41#352semidirect
273. C2×#352C2×C41semidirect
275. #1390C2×C41semidirect
289. C2×#123C4×C41semidirect
291. C22×C22⋊C4C4×C41semidirect
299. #386C4×C41semidirect
304. #379C4×C41semidirect
306. C41#13080direct (N × H)
540. C22C41×#352semidirect

Maximal subgroups

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

subgroupindex
C22×#100×C412
C41×#24052
C2×C41×#3522
C41×#17812
C41×#13902
#1308041