Finite Group Databasebeta

← C41×#9923 #23786124

Subgroups — C41×#9923 #23786124

Order 10496.

982 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#450C211yesmaximal, characteristic
2C41×#2627C211yesmaximal, characteristic, complemented
3C2×C41×#394C211yesmaximal, characteristic
4C41×#1786C211yesmaximal, characteristic
5C2×C41×#328C211yesmaximal, characteristic, complemented
6C2×C41×#324C211yesmaximal, characteristic, complemented
7C41×#1294C211yesmaximal, characteristic, complemented
8C23×D4×C41C2211yescharacteristic
9C22×SD16×C41—21no—
10C2×C22⋊Q8×C41C2211yescharacteristic
11C22×C4⋊C4×C41C2211yescharacteristic
12C22×C22⋊C4×C41—21no—
13C22×C22⋊C4×C41—21no—
14C41×#450—22no—
15C41×#450—22no—
16C2×#102×C41—21no—
17C2×#102×C41—22no—
18C2×C22⋊C8×C41C2211yescharacteristic
19C2×C22⋊C8×C41C2211yescharacteristic
20C41×#400—21no—
21C41×#398—22no—
22C41×#395—21no—
23C41×#394—22no—
24C41×#394—22no—
25C41×#385—21no—
26C41×#381—21no—
27C41×#380C2211yescharacteristic
28C2×#95×C41C2211yescharacteristic
29C41×#328—22no—
30C41×#324—22no—
31C25×C41—21no—
32C22×Q8×C41D411yescharacteristic
33C22×D4×C41—21no—
34C22×D4×C41—21no—
35C22×D4×C41—21no—
36C22×D4×C41—21no—
37C22×D4×C41—21no—
38C22×D4×C41—44no—
39C22×D4×C41D412yes—
40C23×C4×C41—21no—
41C23×C4×C41D411yescharacteristic
42C23×C4×C41D411yescharacteristic
43C23×C4×C41C2311yescharacteristic
44C2×SD16×C41—24no—
45C2×SD16×C41—44no—
46C22×C8×C41—21no—
47C22×C8×C41—21no—
48C22⋊Q8×C41—21no—
49C22⋊Q8×C41—21no—
50C22⋊Q8×C41—21no—
51C22⋊Q8×C41—21no—
52C2×C4⋊C4×C41—21no—
53C2×C4⋊C4×C41—21no—
54C2×C4⋊C4×C41—21no—
55C2×C4⋊C4×C41—21no—
56C2×C4⋊C4×C41—21no—
57C2×C4⋊C4×C41—21no—
58C2×C4⋊C4×C41—21no—
59C2×C4⋊C4×C41—22no—
60C2×C4⋊C4×C41D411yescharacteristic
61C2×C4⋊C4×C41D412yes—
62C2×C22⋊C4×C41—24no—
63C2×C22⋊C4×C41—24no—
64C2×C22⋊C4×C41—21no—
65C2×C22⋊C4×C41—21no—
66C2×C22⋊C4×C41—42no—
67C2×C22⋊C4×C41—44no—
68C2×C22⋊C4×C41—42no—
69#102×C41—24no—
70#102×C41—44no—
71C22⋊C8×C41—21no—
72C22⋊C8×C41—21no—
73C22⋊C8×C41—21no—
74C22⋊C8×C41D412yes—
75#95×C41—22no—
76#95×C41—22no—
77#95×C41—22no—
78#95×C41—21no—
79#95×C41—21no—
80#95×C41D412yes—
81C24×C41—24no—
82C24×C41—22no—
83C24×C41—42no—
84C24×C41—42no—
85C24×C41—42no—
86C24×C41—41no—
87C24×C41—41no—
88C24×C41—41no—
89C24×C41—41no—
90C24×C41—41no—
91C24×C41—41no—
92C24×C41C2×D411yescharacteristic
93C2×Q8×C41—21no—
94C2×Q8×C41—21no—
95C2×Q8×C41—42no—
96C2×D4×C41—24no—
97C2×D4×C41—24no—
98C2×D4×C41—22no—
99C2×D4×C41—22no—
100C2×D4×C41—42no—
101C2×D4×C41—42no—
102C2×D4×C41—44no—
103C2×D4×C41—44no—
104C2×D4×C41—44no—
105C2×D4×C41—44no—
106C2×D4×C41—41no—
107C2×D4×C41—41no—
108C22×C4×C41—21no—
109C22×C4×C41—21no—
110C22×C4×C41—21no—
111C22×C4×C41—21no—
112C22×C4×C41—21no—
113C22×C4×C41—21no—
114C22×C4×C41—22no—
115C22×C4×C41—21no—
116C22×C4×C41—21no—
117C22×C4×C41—22no—
118C22×C4×C41—21no—
119C22×C4×C41—21no—
120C22×C4×C41—21no—
121C22×C4×C41—42no—
122C22×C4×C41—42no—
123C22×C4×C41—42no—
124C22×C4×C41—42no—
125C22×C4×C41—41no—
126C22×C4×C41—41no—
127C22×C4×C41SD1612yescomplemented
128C22×C4×C41C2×D411yescharacteristic
129C22×C4×C41C2×D411yescharacteristic
130C22×C4×C41C2×D411yescharacteristic
131C22×C4×C41C2×D411yescharacteristic
132C22×C4×C41C2×D411yescharacteristic
133C22×C4×C41#4111yescharacteristic
134SD16×C41—48no—
135C2×C8×C41—22no—
136C2×C8×C41—42no—
137C2×C8×C41—42no—
138C2×C8×C41—41no—
139C4⋊C4×C41—21no—
140C4⋊C4×C41—21no—
141C4⋊C4×C41—42no—
142C4⋊C4×C41—41no—
143C4⋊C4×C41—41no—
144C4⋊C4×C41—41no—
145C4⋊C4×C41—41no—
146C4⋊C4×C41—41no—
147C4⋊C4×C41—41no—
148C4⋊C4×C41—82no—
149C22⋊C4×C41—48no—
150C22⋊C4×C41—48no—
151C22⋊C4×C41—41no—
152C22⋊C4×C41—41no—
153C22⋊C4×C41—41no—
154C22⋊C4×C41—41no—
155C23×C41—22no—
156C23×C41—22no—
157C23×C41—24no—
158C23×C41—42no—
159C23×C41—44no—
160C23×C41—44no—
161C23×C41—44no—
162C23×C41—44no—
163C23×C41—44no—
164C23×C41—42no—
165C23×C41—42no—
166C23×C41—42no—
167C23×C41—42no—
168C23×C41—42no—
169C23×C41—44no—
170C23×C41—82no—
171C23×C41—82no—
172C23×C41—82no—
173C23×C41—82no—
174C23×C41—82no—
175C23×C41—81no—
176C23×C41—81no—
177C23×C41—82no—
178C23×C41—81no—
179C23×C41—81no—
180C23×C41#12011yescharacteristic
181C23×C41#12011yescharacteristic
182C23×C41#12111yescharacteristic
183C23×C41C2×SD1611yescharacteristic
184C23×C41#13511yescharacteristic
185C23×C41AGL(1,ℤ/8)11yescharacteristic
186C23×C41#13711yescharacteristic
187Q8×C41—42no—
188Q8×C41—81no—
189D4×C41—24no—
190D4×C41—24no—
191D4×C41—42no—
192D4×C41—44no—
193D4×C41—42no—
194D4×C41—44no—
195C2×C4×C41—22no—
196C2×C4×C41—22no—
197C2×C4×C41—22no—
198C2×C4×C41—22no—
199C2×C4×C41—22no—
200C2×C4×C41—41no—
201C2×C4×C41—41no—
202C2×C4×C41—41no—
203C2×C4×C41—41no—
204C2×C4×C41—41no—
205C2×C4×C41—41no—
206C2×C4×C41—41no—
207C2×C4×C41—41no—
208C2×C4×C41—42no—
209C2×C4×C41—42no—
210C2×C4×C41—42no—
211C2×C4×C41—41no—
212C2×C4×C41—41no—
213C2×C4×C41—41no—
214C2×C4×C41—42no—
215C2×C4×C41—42no—
216C2×C4×C41—42no—
217C2×C4×C41—42no—
218C2×C4×C41—42no—
219C2×C4×C41—42no—
220C2×C4×C41—42no—
221C2×C4×C41—82no—
222C2×C4×C41—82no—
223C2×C4×C41—81no—
224C2×C4×C41#12011yescharacteristic
225C2×C4×C41#12111yescharacteristic
226C2×C4×C41#12111yescharacteristic
227C2×C4×C41#12711yescharacteristic
228C8×C41—42no—
229C8×C41—81no—
230#9923C4111yesmaximal, characteristic, direct product factor, Sylow
231C22×C41—22no—
232C22×C41—22no—
233C22×C41—22no—
234C22×C41—22no—
235C22×C41—21no—
236C22×C41—21no—
237C22×C41—21no—
238C22×C41—21no—
239C22×C41—44no—
240C22×C41—44no—
241C22×C41—44no—
242C22×C41—82no—
243C22×C41—82no—
244C22×C41—84no—
245C22×C41—84no—
246C22×C41—84no—
247C22×C41—84no—
248C22×C41—82no—
249C22×C41—82no—
250C22×C41#39211yescharacteristic
251C22×C41#44811yescharacteristic
252C22×C41#44911yescharacteristic
253C22×C41#45011yescharacteristic
254C22×C41#45211yescharacteristic
255C22×C41#45412yes—
256C22×C41B(4,𝔽2)12yes—
257C22×C41#46511yescharacteristic
258C22×C41#46811yescharacteristic
259C4×C41—21no—
260C4×C41—21no—
261C4×C41—21no—
262C4×C41—21no—
263C4×C41—42no—
264C4×C41—82no—
265C4×C41—82no—
266C4×C41—81no—
267C4×C41—81no—
268C4×C41—81no—
269C2×#450C2×C4111yescharacteristic
270#2627C2×C4111yescharacteristic, complemented
271C2×#394C2×C4111yescharacteristic
272#1786C2×C4111yescharacteristic
273C2×#328C2×C4111yescharacteristic, complemented
274C2×#324C2×C4111yescharacteristic, complemented
275#1294C2×C4111yescharacteristic, complemented
276C2×C41—21no—
277C2×C41—21no—
278C2×C41—21no—
279C2×C41—21no—
280C2×C41—84no—
281C2×C41#159712yes—
282C2×C41#159912yes—
283C2×C41#200011yescharacteristic
284C2×C41#200311yescharacteristic
285C2×C41#202111yescharacteristic
286C23×D4C22×C4111yescharacteristic
287C22×SD16—21no—
288C2×C22⋊Q8C22×C4111yescharacteristic
289C22×C4⋊C4C22×C4111yescharacteristic
290C22×C22⋊C4—21no—
291C22×C22⋊C4—21no—
292#450—22no—
293#450—22no—
294C2×#102—21no—
295C2×#102—22no—
296C2×C22⋊C8C22×C4111yescharacteristic
297C2×C22⋊C8C22×C4111yescharacteristic
298#400—21no—
299#398—22no—
300#395—21no—
301#394—22no—
302#394—22no—
303#385—21no—
304#381—21no—
305#380C22×C4111yescharacteristic
306C2×#95C22×C4111yescharacteristic
307#328—22no—
308#324—22no—
309C41#992311yescharacteristic, direct product factor, Sylow
310C25—21no—
311C22×Q8D4×C4111yescharacteristic
312C22×D4—21no—
313C22×D4—21no—
314C22×D4—21no—
315C22×D4—21no—
316C22×D4—21no—
317C22×D4—44no—
318C22×D4D4×C4112yes—
319C23×C4—21no—
320C23×C4D4×C4111yescharacteristic
321C23×C4D4×C4111yescharacteristic
322C23×C4C23×C4111yescharacteristic
323C2×SD16—24no—
324C2×SD16—44no—
325C22×C8—21no—
326C22×C8—21no—
327C22⋊Q8—21no—
328C22⋊Q8—21no—
329C22⋊Q8—21no—
330C22⋊Q8—21no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4D4×C4111yescharacteristic
340C2×C4⋊C4D4×C4112yes—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—21no—
344C2×C22⋊C4—21no—
345C2×C22⋊C4—42no—
346C2×C22⋊C4—44no—
347C2×C22⋊C4—42no—
348#102—24no—
349#102—44no—
350C22⋊C8—21no—
351C22⋊C8—21no—
352C22⋊C8—21no—
353C22⋊C8D4×C4112yes—
354#95—22no—
355#95—22no—
356#95—22no—
357#95—21no—
358#95—21no—
359#95D4×C4112yes—
360C24—24no—
361C24—22no—
362C24—42no—
363C24—42no—
364C24—42no—
365C24—41no—
366C24—41no—
367C24—41no—
368C24—41no—
369C24—41no—
370C24—41no—
371C24C2×D4×C4111yescharacteristic
372C2×Q8—21no—
373C2×Q8—21no—
374C2×Q8—42no—
375C2×D4—24no—
376C2×D4—24no—
377C2×D4—22no—
378C2×D4—22no—
379C2×D4—42no—
380C2×D4—42no—
381C2×D4—44no—
382C2×D4—44no—
383C2×D4—44no—
384C2×D4—44no—
385C2×D4—41no—
386C2×D4—41no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—22no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—42no—
401C22×C4—42no—
402C22×C4—42no—
403C22×C4—42no—
404C22×C4—41no—
405C22×C4—41no—
406C22×C4SD16×C4112yescomplemented
407C22×C4C2×D4×C4111yescharacteristic
408C22×C4C2×D4×C4111yescharacteristic
409C22×C4C2×D4×C4111yescharacteristic
410C22×C4C2×D4×C4111yescharacteristic
411C22×C4C2×D4×C4111yescharacteristic
412C22×C4#41×C4111yescharacteristic
413SD16—48no—
414C2×C8—22no—
415C2×C8—42no—
416C2×C8—42no—
417C2×C8—41no—
418C4⋊C4—21no—
419C4⋊C4—21no—
420C4⋊C4—42no—
421C4⋊C4—41no—
422C4⋊C4—41no—
423C4⋊C4—41no—
424C4⋊C4—41no—
425C4⋊C4—41no—
426C4⋊C4—41no—
427C4⋊C4—82no—
428C22⋊C4—48no—
429C22⋊C4—48no—
430C22⋊C4—41no—
431C22⋊C4—41no—
432C22⋊C4—41no—
433C22⋊C4—41no—
434C23—22no—
435C23—22no—
436C23—24no—
437C23—42no—
438C23—44no—
439C23—44no—
440C23—44no—
441C23—44no—
442C23—44no—
443C23—42no—
444C23—42no—
445C23—42no—
446C23—42no—
447C23—42no—
448C23—44no—
449C23—82no—
450C23—82no—
451C23—82no—
452C23—82no—
453C23—82no—
454C23—81no—
455C23—81no—
456C23—82no—
457C23—81no—
458C23—81no—
459C23#120×C4111yescharacteristic
460C23#120×C4111yescharacteristic
461C23#121×C4111yescharacteristic
462C23C2×SD16×C4111yescharacteristic
463C23#135×C4111yescharacteristic
464C23AGL(1,ℤ/8)×C4111yescharacteristic
465C23#137×C4111yescharacteristic
466Q8—42no—
467Q8—81no—
468D4—24no—
469D4—24no—
470D4—42no—
471D4—44no—
472D4—42no—
473D4—44no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—82no—
501C2×C4—82no—
502C2×C4—81no—
503C2×C4#120×C4111yescharacteristic
504C2×C4#121×C4111yescharacteristic
505C2×C4#121×C4111yescharacteristic
506C2×C4#127×C4111yescharacteristic
507C8—42no—
508C8—81no—
509C22—21no—
510C22—21no—
511C22—22no—
512C22—22no—
513C22—22no—
514C22—22no—
515C22—21no—
516C22—21no—
517C22—44no—
518C22—44no—
519C22—44no—
520C22—82no—
521C22—82no—
522C22—84no—
523C22—84no—
524C22—84no—
525C22—84no—
526C22—82no—
527C22—82no—
528C22C41×#39211yescharacteristic
529C22C41×#44811yescharacteristic
530C22C41×#44911yescharacteristic
531C22C41×#45011yescharacteristic
532C22C41×#45211yescharacteristic
533C22C41×#45412yes—
534C22C41×B(4,𝔽2)12yes—
535C22C41×#46511yescharacteristic
536C22C41×#46811yescharacteristic
537C4—21no—
538C4—21no—
539C4—21no—
540C4—21no—
541C4—42no—
542C4—82no—
543C4—81no—
544C4—81no—
545C4—82no—
546C4—81no—
547C2—21no—
548C2—21no—
549C2—21no—
550C2—21no—
551C2—84no—
552C2C41×#159712yes—
553C2C41×#159912yes—
554C2C41×#200011yescharacteristic
555C2C41×#200311yescharacteristic
556C2C41×#202111yescharacteristic
subgroupG/H
center, socleC23×C41#120
commutator, Frattini, cosocleC23×C4C23×C41
prime radicalC23×D4×C41C22
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C41 ◁ C23×C4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C41×#2627C2semidirect
5. C2×C41×#328C2semidirect
6. C2×C41×#324C2semidirect
7. C41×#1294C2semidirect
127. C22×C4×C41SD16semidirect
230. #9923C41direct (N × H)
270. #2627C2×C41semidirect
273. C2×#328C2×C41semidirect
274. C2×#324C2×C41semidirect
275. #1294C2×C41semidirect
309. C41#9923direct (N × H)
406. C22×C4SD16×C41semidirect

Maximal subgroups

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

subgroupindex
C2×C41×#4502
C41×#26272
C2×C41×#3942
C41×#17862
C2×C41×#3282
C2×C41×#3242
C41×#12942
#992341