Finite Group Databasebeta

← C41×#9938 #23786139

Subgroups — C41×#9938 #23786139

Order 10496.

1008 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3006C211yesmaximal, characteristic, complemented
2C41×#2539C211yesmaximal, characteristic, complemented
3C41×#2404C211yesmaximal, characteristic, complemented
4C41×#1789C211yesmaximal, characteristic, complemented
5C41×#1510C211yesmaximal, characteristic, complemented
6C41×#1462C211yesmaximal, characteristic, complemented
7C41×#1284C211yesmaximal, characteristic, complemented
8C22×#41×C41C2211yescharacteristic
9C2×AGL(1,ℤ/8)×C41—21no—
10C2×#123×C41—21no—
11C2×#121×C41C2211yescharacteristic
12C2×#120×C41—21no—
13C2×#120×C41—21no—
14C22×C22⋊C4×C41C2211yescharacteristic
15C41×#449—22no—
16C41×#448—21no—
17C41×#447—21no—
18C2×#104×C41—22no—
19C41×#417—21no—
20C41×#407C2211yescharacteristic
21C41×#407C2211yescharacteristic
22C41×#399—21no—
23C41×#393—21no—
24C41×#392—21no—
25C41×#392—21no—
26C41×#390—22no—
27C41×#386—21no—
28C41×#386—22no—
29C41×#381C2211yescharacteristic
30C4×C22⋊C4×C41C2211yescharacteristic
31C41×#327—22no—
32C41×#323—22no—
33C25×C41D411yescharacteristic
34C2×#41×C41—21no—
35C2×#41×C41—21no—
36C2×#41×C41—21no—
37C2×#41×C41—21no—
38C2×#41×C41—44no—
39C22×Q8×C41D411yescharacteristic, complemented
40C22×D4×C41—21no—
41C22×D4×C41—21no—
42C22×D4×C41—22no—
43C22×D4×C41—22no—
44C22×D4×C41D411yescharacteristic, complemented
45C22×D4×C41D411yescharacteristic, complemented
46C23×C4×C41—21no—
47C23×C4×C41D411yescharacteristic
48C23×C4×C41C2311yescharacteristic
49AGL(1,ℤ/8)×C41—44no—
50C2×SD16×C41—22no—
51C2×D8×C41—22no—
52C2×M16×C41—21no—
53C2×M16×C41—21no—
54#123×C41—44no—
55#121×C41—21no—
56#121×C41—21no—
57#121×C41—21no—
58#121×C41—21no—
59#120×C41—44no—
60#120×C41—44no—
61C2×C4⋊C4×C41—22no—
62C2×C4⋊C4×C41D411yescharacteristic, complemented
63C2×C22⋊C4×C41—21no—
64C2×C22⋊C4×C41—22no—
65C2×C22⋊C4×C41—22no—
66C2×C22⋊C4×C41—22no—
67C2×C22⋊C4×C41—21no—
68C2×C22⋊C4×C41—21no—
69C2×C22⋊C4×C41—21no—
70C2×C22⋊C4×C41—21no—
71C2×C22⋊C4×C41—21no—
72C2×C22⋊C4×C41—21no—
73C2×C22⋊C4×C41—21no—
74C2×C22⋊C4×C41—21no—
75C2×C22⋊C4×C41—22no—
76C2×C42×C41D412yescomplemented
77#104×C41—44no—
78#103×C41—22no—
79#102×C41—22no—
80C22⋊C8×C41—21no—
81C22⋊C8×C41—21no—
82C22⋊C8×C41—21no—
83C22⋊C8×C41D412yescomplemented
84#95×C41—22no—
85#95×C41—21no—
86#95×C41—21no—
87#95×C41D412yescomplemented
88C24×C41—21no—
89C24×C41—21no—
90C24×C41—21no—
91C24×C41—21no—
92C24×C41—21no—
93C24×C41—42no—
94C24×C41—42no—
95C24×C41—42no—
96C24×C41C2×D411yescharacteristic
97#41×C41—24no—
98#41×C41—24no—
99#41×C41—42no—
100#41×C41—42no—
101#41×C41—42no—
102#41×C41—42no—
103#41×C41—42no—
104#41×C41—42no—
105C2×Q8×C41—21no—
106C2×Q8×C41—21no—
107C2×Q8×C41—42no—
108C2×D4×C41—24no—
109C2×D4×C41—21no—
110C2×D4×C41—21no—
111C2×D4×C41—21no—
112C2×D4×C41—21no—
113C2×D4×C41—42no—
114C2×D4×C41—44no—
115C2×D4×C41—42no—
116C2×D4×C41—42no—
117C2×D4×C41—41no—
118C2×D4×C41—41no—
119C2×D4×C41—42no—
120C2×D4×C41—44no—
121C2×D4×C41—42no—
122C2×D4×C41—44no—
123C2×D4×C41—44no—
124C2×D4×C41—41no—
125C2×D4×C41—41no—
126C2×D4×C41—82no—
127C2×D4×C41—82no—
128C22×C4×C41—21no—
129C22×C4×C41—22no—
130C22×C4×C41—22no—
131C22×C4×C41—21no—
132C22×C4×C41—21no—
133C22×C4×C41—21no—
134C22×C4×C41—21no—
135C22×C4×C41—42no—
136C22×C4×C41—42no—
137C22×C4×C41—42no—
138C22×C4×C41—41no—
139C22×C4×C41—41no—
140C22×C4×C41—42no—
141C22×C4×C41C2×D411yescharacteristic
142C22×C4×C41C2×D411yescharacteristic
143C22×C4×C41C2×D411yescharacteristic
144C22×C4×C41C2×D411yescharacteristic
145C22×C4×C41C2×D411yescharacteristic
146C22×C4×C41#4111yescharacteristic
147SD16×C41—44no—
148D8×C41—44no—
149M16×C41—42no—
150M16×C41—42no—
151C2×C8×C41—22no—
152C2×C8×C41—41no—
153C4⋊C4×C41—21no—
154C4⋊C4×C41—21no—
155C4⋊C4×C41—44no—
156C22⋊C4×C41—24no—
157C22⋊C4×C41—44no—
158C22⋊C4×C41—44no—
159C22⋊C4×C41—44no—
160C22⋊C4×C41—42no—
161C22⋊C4×C41—41no—
162C22⋊C4×C41—41no—
163C22⋊C4×C41—41no—
164C22⋊C4×C41—41no—
165C22⋊C4×C41—41no—
166C22⋊C4×C41—41no—
167C22⋊C4×C41—82no—
168C42×C41—42no—
169C23×C41—22no—
170C23×C41—22no—
171C23×C41—22no—
172C23×C41—22no—
173C23×C41—22no—
174C23×C41—22no—
175C23×C41—41no—
176C23×C41—42no—
177C23×C41—42no—
178C23×C41—41no—
179C23×C41—42no—
180C23×C41—41no—
181C23×C41—41no—
182C23×C41—41no—
183C23×C41—41no—
184C23×C41—41no—
185C23×C41—42no—
186C23×C41—41no—
187C23×C41—41no—
188C23×C41—42no—
189C23×C41—42no—
190C23×C41—42no—
191C23×C41—41no—
192C23×C41—42no—
193C23×C41—81no—
194C23×C41—81no—
195C23×C41—88no—
196C23×C41#12011yescharacteristic
197C23×C41#12011yescharacteristic
198C23×C41#12111yescharacteristic
199Q8×C41—22no—
200Q8×C41—22no—
201Q8×C41—41no—
202Q8×C41—41no—
203D4×C41—22no—
204D4×C41—22no—
205D4×C41—41no—
206D4×C41—41no—
207D4×C41—42no—
208D4×C41—44no—
209D4×C41—44no—
210D4×C41—81no—
211D4×C41—88no—
212D4×C41—82no—
213D4×C41—88no—
214D4×C41—82no—
215C2×C4×C41—22no—
216C2×C4×C41—22no—
217C2×C4×C41—24no—
218C2×C4×C41—22no—
219C2×C4×C41—41no—
220C2×C4×C41—41no—
221C2×C4×C41—41no—
222C2×C4×C41—41no—
223C2×C4×C41—44no—
224C2×C4×C41—44no—
225C2×C4×C41—41no—
226C2×C4×C41—42no—
227C2×C4×C41—41no—
228C2×C4×C41—42no—
229C2×C4×C41—42no—
230C2×C4×C41—41no—
231C2×C4×C41—42no—
232C2×C4×C41—41no—
233C2×C4×C41—42no—
234C2×C4×C41—41no—
235C2×C4×C41—41no—
236C2×C4×C41—42no—
237C2×C4×C41—42no—
238C2×C4×C41—81no—
239C2×C4×C41#12011yescharacteristic
240C2×C4×C41#12111yescharacteristic
241C2×C4×C41#12111yescharacteristic
242C2×C4×C41#12711yescharacteristic
243C8×C41—42no—
244C8×C41—81no—
245#9938C4111yesmaximal, characteristic, direct product factor, Sylow
246C22×C41—21no—
247C22×C41—21no—
248C22×C41—21no—
249C22×C41—21no—
250C22×C41—21no—
251C22×C41—21no—
252C22×C41—21no—
253C22×C41—44no—
254C22×C41—44no—
255C22×C41—44no—
256C22×C41—44no—
257C22×C41—42no—
258C22×C41—42no—
259C22×C41—82no—
260C22×C41—82no—
261C22×C41—82no—
262C22×C41—82no—
263C22×C41—82no—
264C22×C41—82no—
265C22×C41—82no—
266C22×C41—81no—
267C22×C41—81no—
268C22×C41—81no—
269C22×C41—81no—
270C22×C41—81no—
271C22×C41—81no—
272C22×C41—81no—
273C22×C41#39211yescharacteristic
274C22×C41#45312yes—
275C22×C41B(4,𝔽2)12yes—
276C4×C41—21no—
277C4×C41—21no—
278C4×C41—21no—
279C4×C41—21no—
280C4×C41—44no—
281C4×C41—42no—
282C4×C41—82no—
283C4×C41—81no—
284C4×C41—81no—
285#3006C2×C4111yescharacteristic, complemented
286#2539C2×C4111yescharacteristic, complemented
287#2404C2×C4111yescharacteristic, complemented
288#1789C2×C4111yescharacteristic, complemented
289#1510C2×C4111yescharacteristic, complemented
290#1462C2×C4111yescharacteristic, complemented
291#1284C2×C4111yescharacteristic, complemented
292C2×C41—22no—
293C2×C41—22no—
294C2×C41—41no—
295C2×C41—82no—
296C2×C41—82no—
297C2×C41—161no—
298C2×C41#200211yescharacteristic
299C2×C41#201011yescharacteristic
300C2×C41#202111yescharacteristic
301C22×#41C22×C4111yescharacteristic
302C2×AGL(1,ℤ/8)—21no—
303C2×#123—21no—
304C2×#121C22×C4111yescharacteristic
305C2×#120—21no—
306C2×#120—21no—
307C22×C22⋊C4C22×C4111yescharacteristic
308#449—22no—
309#448—21no—
310#447—21no—
311C2×#104—22no—
312#417—21no—
313#407C22×C4111yescharacteristic
314#407C22×C4111yescharacteristic
315#399—21no—
316#393—21no—
317#392—21no—
318#392—21no—
319#390—22no—
320#386—21no—
321#386—22no—
322#381C22×C4111yescharacteristic
323C4×C22⋊C4C22×C4111yescharacteristic
324#327—22no—
325#323—22no—
326C41#993811yescharacteristic, direct product factor, Sylow
327C25D4×C4111yescharacteristic
328C2×#41—21no—
329C2×#41—21no—
330C2×#41—21no—
331C2×#41—21no—
332C2×#41—44no—
333C22×Q8D4×C4111yescharacteristic, complemented
334C22×D4—21no—
335C22×D4—21no—
336C22×D4—22no—
337C22×D4—22no—
338C22×D4D4×C4111yescharacteristic, complemented
339C22×D4D4×C4111yescharacteristic, complemented
340C23×C4—21no—
341C23×C4D4×C4111yescharacteristic
342C23×C4C23×C4111yescharacteristic
343AGL(1,ℤ/8)—44no—
344C2×SD16—22no—
345C2×D8—22no—
346C2×M16—21no—
347C2×M16—21no—
348#123—44no—
349#121—21no—
350#121—21no—
351#121—21no—
352#121—21no—
353#120—44no—
354#120—44no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4D4×C4111yescharacteristic, complemented
357C2×C22⋊C4—21no—
358C2×C22⋊C4—22no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—22no—
370C2×C42D4×C4112yescomplemented
371#104—44no—
372#103—22no—
373#102—22no—
374C22⋊C8—21no—
375C22⋊C8—21no—
376C22⋊C8—21no—
377C22⋊C8D4×C4112yescomplemented
378#95—22no—
379#95—21no—
380#95—21no—
381#95D4×C4112yescomplemented
382C24—21no—
383C24—21no—
384C24—21no—
385C24—21no—
386C24—21no—
387C24—42no—
388C24—42no—
389C24—42no—
390C24C2×D4×C4111yescharacteristic
391#41—24no—
392#41—24no—
393#41—42no—
394#41—42no—
395#41—42no—
396#41—42no—
397#41—42no—
398#41—42no—
399C2×Q8—21no—
400C2×Q8—21no—
401C2×Q8—42no—
402C2×D4—24no—
403C2×D4—21no—
404C2×D4—21no—
405C2×D4—21no—
406C2×D4—21no—
407C2×D4—42no—
408C2×D4—44no—
409C2×D4—42no—
410C2×D4—42no—
411C2×D4—41no—
412C2×D4—41no—
413C2×D4—42no—
414C2×D4—44no—
415C2×D4—42no—
416C2×D4—44no—
417C2×D4—44no—
418C2×D4—41no—
419C2×D4—41no—
420C2×D4—82no—
421C2×D4—82no—
422C22×C4—21no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—42no—
430C22×C4—42no—
431C22×C4—42no—
432C22×C4—41no—
433C22×C4—41no—
434C22×C4—42no—
435C22×C4C2×D4×C4111yescharacteristic
436C22×C4C2×D4×C4111yescharacteristic
437C22×C4C2×D4×C4111yescharacteristic
438C22×C4C2×D4×C4111yescharacteristic
439C22×C4C2×D4×C4111yescharacteristic
440C22×C4#41×C4111yescharacteristic
441SD16—44no—
442D8—44no—
443M16—42no—
444M16—42no—
445C2×C8—22no—
446C2×C8—41no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—44no—
450C22⋊C4—24no—
451C22⋊C4—44no—
452C22⋊C4—44no—
453C22⋊C4—44no—
454C22⋊C4—42no—
455C22⋊C4—41no—
456C22⋊C4—41no—
457C22⋊C4—41no—
458C22⋊C4—41no—
459C22⋊C4—41no—
460C22⋊C4—41no—
461C22⋊C4—82no—
462C42—42no—
463C23—22no—
464C23—22no—
465C23—22no—
466C23—22no—
467C23—22no—
468C23—22no—
469C23—41no—
470C23—42no—
471C23—42no—
472C23—41no—
473C23—42no—
474C23—41no—
475C23—41no—
476C23—41no—
477C23—41no—
478C23—41no—
479C23—42no—
480C23—41no—
481C23—41no—
482C23—42no—
483C23—42no—
484C23—42no—
485C23—41no—
486C23—42no—
487C23—81no—
488C23—81no—
489C23—88no—
490C23#120×C4111yescharacteristic
491C23#120×C4111yescharacteristic
492C23#121×C4111yescharacteristic
493Q8—22no—
494Q8—22no—
495Q8—41no—
496Q8—41no—
497D4—22no—
498D4—22no—
499D4—41no—
500D4—41no—
501D4—42no—
502D4—44no—
503D4—44no—
504D4—81no—
505D4—88no—
506D4—82no—
507D4—88no—
508D4—82no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—24no—
512C2×C4—22no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—44no—
518C2×C4—44no—
519C2×C4—41no—
520C2×C4—42no—
521C2×C4—41no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—41no—
525C2×C4—42no—
526C2×C4—41no—
527C2×C4—42no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—81no—
533C2×C4#120×C4111yescharacteristic
534C2×C4#121×C4111yescharacteristic
535C2×C4#121×C4111yescharacteristic
536C2×C4#127×C4111yescharacteristic
537C8—42no—
538C8—81no—
539C22—21no—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—21no—
544C22—21no—
545C22—21no—
546C22—44no—
547C22—44no—
548C22—44no—
549C22—44no—
550C22—42no—
551C22—42no—
552C22—82no—
553C22—82no—
554C22—82no—
555C22—82no—
556C22—82no—
557C22—82no—
558C22—82no—
559C22—81no—
560C22—81no—
561C22—81no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22—81no—
566C22C41×#39211yescharacteristic
567C22C41×#45312yes—
568C22C41×B(4,𝔽2)12yes—
569C4—21no—
570C4—21no—
571C4—21no—
572C4—21no—
573C4—44no—
574C4—42no—
575C4—82no—
576C4—81no—
577C4—81no—
578C2—22no—
579C2—22no—
580C2—41no—
581C2—82no—
582C2—82no—
583C2—161no—
584C2C41×#200211yescharacteristic
585C2C41×#201011yescharacteristic
586C2C41×#202111yescharacteristic
subgroupG/H
center, socleC22×C41#392
commutator, Frattini, cosocleC23×C4C23×C41
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C41 ◁ C23×C4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C41×#3006C2semidirect
2. C41×#2539C2semidirect
3. C41×#2404C2semidirect
4. C41×#1789C2semidirect
5. C41×#1510C2semidirect
6. C41×#1462C2semidirect
7. C41×#1284C2semidirect
39. C22×Q8×C41D4semidirect
44. C22×D4×C41D4semidirect
45. C22×D4×C41D4semidirect
62. C2×C4⋊C4×C41D4semidirect
76. C2×C42×C41D4semidirect
83. C22⋊C8×C41D4semidirect
87. #95×C41D4semidirect
245. #9938C41direct (N × H)
285. #3006C2×C41semidirect
286. #2539C2×C41semidirect
287. #2404C2×C41semidirect
288. #1789C2×C41semidirect
289. #1510C2×C41semidirect
290. #1462C2×C41semidirect
291. #1284C2×C41semidirect
326. C41#9938direct (N × H)
333. C22×Q8D4×C41semidirect
338. C22×D4D4×C41semidirect
339. C22×D4D4×C41semidirect
356. C2×C4⋊C4D4×C41semidirect
370. C2×C42D4×C41semidirect
377. C22⋊C8D4×C41semidirect
381. #95D4×C41semidirect

Maximal subgroups

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

subgroupindex
C41×#30062
C41×#25392
C41×#24042
C41×#17892
C41×#15102
C41×#14622
C41×#12842
#993841