Finite Group Databasebeta

← C41×#9926 #23786127

Subgroups — C41×#9926 #23786127

Order 10496.

734 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#483C211yesmaximal, characteristic, complemented
2C41×#2626C211yesmaximal, characteristic
3C2×C41×#397C211yesmaximal, characteristic
4C41×#1823C211yesmaximal, characteristic, complemented
5C2×C41×#328C211yesmaximal, characteristic, complemented
6C2×C41×#323C211yesmaximal, characteristic
7C41×#1294C211yesmaximal, characteristic, complemented
8C2×C22⋊Q8×C41C2211yescharacteristic
9C22×C4⋊C4×C41C2211yescharacteristic
10C22×C22⋊C4×C41—21no—
11C22×C22⋊C4×C41C2211yescharacteristic
12C41×#483—22no—
13C41×#483—22no—
14C2×#106×C41—21no—
15C2×#103×C41—21no—
16C2×C22⋊C8×C41C2211yescharacteristic
17C2×C22⋊C8×C41C2211yescharacteristic
18C41×#399—21no—
19C41×#397—22no—
20C41×#397—22no—
21C41×#396—22no—
22C41×#393—21no—
23C41×#385—21no—
24C41×#380C2211yescharacteristic
25C41×#379—21no—
26C2×#95×C41—21no—
27C2×#95×C41C2211yescharacteristic
28C41×#340—22no—
29C41×#328—22no—
30C41×#323—22no—
31C25×C41D411yescharacteristic
32C22×Q8×C41D411yescharacteristic
33C23×C4×C41—21no—
34C23×C4×C41—21no—
35C23×C4×C41D411yescharacteristic
36C23×C4×C41C2311yescharacteristic
37C22×C8×C41—21no—
38C22×C8×C41—21no—
39C22⋊Q8×C41—21no—
40C22⋊Q8×C41—21no—
41C22⋊Q8×C41—21no—
42C22⋊Q8×C41—21no—
43C2×C4⋊C4×C41—21no—
44C2×C4⋊C4×C41—21no—
45C2×C4⋊C4×C41—21no—
46C2×C4⋊C4×C41—21no—
47C2×C4⋊C4×C41—21no—
48C2×C4⋊C4×C41—21no—
49C2×C4⋊C4×C41—22no—
50C2×C4⋊C4×C41D412yes—
51C2×C4⋊C4×C41D411yescharacteristic
52C2×C4⋊C4×C41D412yes—
53C2×C22⋊C4×C41—24no—
54C2×C22⋊C4×C41—21no—
55C2×C22⋊C4×C41—21no—
56C2×C22⋊C4×C41—21no—
57C2×C22⋊C4×C41—21no—
58C2×C22⋊C4×C41—21no—
59C2×C22⋊C4×C41—21no—
60C2×C22⋊C4×C41—21no—
61C2×C22⋊C4×C41—21no—
62C2×C22⋊C4×C41—22no—
63C2×C22⋊C4×C41—22no—
64C2×C22⋊C4×C41—42no—
65C2×C22⋊C4×C41—42no—
66#106×C41—24no—
67#103×C41—24no—
68C22⋊C8×C41—21no—
69C22⋊C8×C41—21no—
70C22⋊C8×C41—21no—
71C22⋊C8×C41D412yes—
72#95×C41—24no—
73#95×C41—22no—
74#95×C41—21no—
75#95×C41—21no—
76#95×C41D412yes—
77C24×C41—21no—
78C24×C41—21no—
79C24×C41—21no—
80C24×C41—21no—
81C24×C41—21no—
82C24×C41—21no—
83C24×C41—42no—
84C24×C41—42no—
85C24×C41SD1612yes—
86C24×C41C2×D411yescharacteristic
87C2×Q8×C41—21no—
88C2×Q8×C41—21no—
89C2×Q8×C41—42no—
90C22×C4×C41—21no—
91C22×C4×C41—22no—
92C22×C4×C41—22no—
93C22×C4×C41—22no—
94C22×C4×C41—21no—
95C22×C4×C41—21no—
96C22×C4×C41—21no—
97C22×C4×C41—21no—
98C22×C4×C41—42no—
99C22×C4×C41—42no—
100C22×C4×C41—42no—
101C22×C4×C41—42no—
102C22×C4×C41—41no—
103C22×C4×C41—41no—
104C22×C4×C41—41no—
105C22×C4×C41—41no—
106C22×C4×C41—41no—
107C22×C4×C41—41no—
108C22×C4×C41—41no—
109C22×C4×C41—41no—
110C22×C4×C41C2×D411yescharacteristic
111C22×C4×C41C2×D411yescharacteristic
112C22×C4×C41C2×D411yescharacteristic
113C22×C4×C41C2×D411yescharacteristic
114C22×C4×C41C2×D411yescharacteristic
115C22×C4×C41#4111yescharacteristic
116C2×C8×C41—22no—
117C2×C8×C41—42no—
118C2×C8×C41—42no—
119C2×C8×C41—41no—
120C4⋊C4×C41—22no—
121C4⋊C4×C41—21no—
122C4⋊C4×C41—22no—
123C4⋊C4×C41—21no—
124C4⋊C4×C41—42no—
125C4⋊C4×C41—41no—
126C4⋊C4×C41—41no—
127C4⋊C4×C41—41no—
128C4⋊C4×C41—41no—
129C4⋊C4×C41—82no—
130C22⋊C4×C41—48no—
131C22⋊C4×C41—41no—
132C22⋊C4×C41—41no—
133C22⋊C4×C41—41no—
134C22⋊C4×C41—41no—
135C22⋊C4×C41—41no—
136C22⋊C4×C41—41no—
137C22⋊C4×C41—41no—
138C22⋊C4×C41—41no—
139C22⋊C4×C41—82no—
140C22⋊C4×C41—82no—
141C23×C41—22no—
142C23×C41—22no—
143C23×C41—22no—
144C23×C41—22no—
145C23×C41—22no—
146C23×C41—44no—
147C23×C41—44no—
148C23×C41—42no—
149C23×C41—42no—
150C23×C41—41no—
151C23×C41—41no—
152C23×C41—41no—
153C23×C41—42no—
154C23×C41—42no—
155C23×C41—41no—
156C23×C41—82no—
157C23×C41—82no—
158C23×C41—81no—
159C23×C41—81no—
160C23×C41#12011yescharacteristic
161C23×C41#12011yescharacteristic
162C23×C41#12111yescharacteristic
163C23×C41C2×SD1611yescharacteristic
164C23×C41#13511yescharacteristic
165C23×C41AGL(1,ℤ/8)11yescharacteristic
166C23×C41#13711yescharacteristic
167Q8×C41—42no—
168Q8×C41—81no—
169C2×C4×C41—22no—
170C2×C4×C41—22no—
171C2×C4×C41—41no—
172C2×C4×C41—41no—
173C2×C4×C41—41no—
174C2×C4×C41—41no—
175C2×C4×C41—42no—
176C2×C4×C41—42no—
177C2×C4×C41—42no—
178C2×C4×C41—41no—
179C2×C4×C41—41no—
180C2×C4×C41—41no—
181C2×C4×C41—42no—
182C2×C4×C41—42no—
183C2×C4×C41—42no—
184C2×C4×C41—42no—
185C2×C4×C41—42no—
186C2×C4×C41—42no—
187C2×C4×C41—42no—
188C2×C4×C41—42no—
189C2×C4×C41—42no—
190C2×C4×C41—42no—
191C2×C4×C41—82no—
192C2×C4×C41—82no—
193C2×C4×C41—81no—
194C2×C4×C41—81no—
195C2×C4×C41—81no—
196C2×C4×C41—81no—
197C2×C4×C41—81no—
198C2×C4×C41#12011yescharacteristic
199C2×C4×C41#12111yescharacteristic
200C2×C4×C41#12111yescharacteristic
201C2×C4×C41#12711yescharacteristic
202C8×C41—42no—
203C8×C41—81no—
204#9926C4111yesmaximal, characteristic, direct product factor, Sylow
205C22×C41—22no—
206C22×C41—22no—
207C22×C41—22no—
208C22×C41—22no—
209C22×C41—21no—
210C22×C41—21no—
211C22×C41—21no—
212C22×C41—21no—
213C22×C41—44no—
214C22×C41—44no—
215C22×C41—42no—
216C22×C41—82no—
217C22×C41—82no—
218C22×C41—82no—
219C22×C41—82no—
220C22×C41—81no—
221C22×C41—81no—
222C22×C41#39211yescharacteristic
223C22×C41#44811yescharacteristic
224C22×C41#44911yescharacteristic
225C22×C41#45011yescharacteristic
226C22×C41#45211yescharacteristic
227C22×C41#45512yes—
228C22×C41#45812yes—
229C22×C41#46511yescharacteristic
230C22×C41#46811yescharacteristic
231C4×C41—21no—
232C4×C41—21no—
233C4×C41—21no—
234C4×C41—21no—
235C4×C41—82no—
236C4×C41—82no—
237C4×C41—82no—
238C4×C41—81no—
239C4×C41—81no—
240C4×C41—81no—
241C2×#483C2×C4111yescharacteristic, complemented
242#2626C2×C4111yescharacteristic
243C2×#397C2×C4111yescharacteristic
244#1823C2×C4111yescharacteristic, complemented
245C2×#328C2×C4111yescharacteristic, complemented
246C2×#323C2×C4111yescharacteristic
247#1294C2×C4111yescharacteristic, complemented
248C2×C41—21no—
249C2×C41—21no—
250C2×C41—21no—
251C2×C41—21no—
252C2×C41—82no—
253C2×C41#160812yes—
254C2×C41#161212yes—
255C2×C41#200011yescharacteristic
256C2×C41#200411yescharacteristic
257C2×C41#202211yescharacteristic
258C2×C22⋊Q8C22×C4111yescharacteristic
259C22×C4⋊C4C22×C4111yescharacteristic
260C22×C22⋊C4—21no—
261C22×C22⋊C4C22×C4111yescharacteristic
262#483—22no—
263#483—22no—
264C2×#106—21no—
265C2×#103—21no—
266C2×C22⋊C8C22×C4111yescharacteristic
267C2×C22⋊C8C22×C4111yescharacteristic
268#399—21no—
269#397—22no—
270#397—22no—
271#396—22no—
272#393—21no—
273#385—21no—
274#380C22×C4111yescharacteristic
275#379—21no—
276C2×#95—21no—
277C2×#95C22×C4111yescharacteristic
278#340—22no—
279#328—22no—
280#323—22no—
281C41#992611yescharacteristic, direct product factor, Sylow
282C25D4×C4111yescharacteristic
283C22×Q8D4×C4111yescharacteristic
284C23×C4—21no—
285C23×C4—21no—
286C23×C4D4×C4111yescharacteristic
287C23×C4C23×C4111yescharacteristic
288C22×C8—21no—
289C22×C8—21no—
290C22⋊Q8—21no—
291C22⋊Q8—21no—
292C22⋊Q8—21no—
293C22⋊Q8—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4D4×C4112yes—
302C2×C4⋊C4D4×C4111yescharacteristic
303C2×C4⋊C4D4×C4112yes—
304C2×C22⋊C4—24no—
305C2×C22⋊C4—21no—
306C2×C22⋊C4—21no—
307C2×C22⋊C4—21no—
308C2×C22⋊C4—21no—
309C2×C22⋊C4—21no—
310C2×C22⋊C4—21no—
311C2×C22⋊C4—21no—
312C2×C22⋊C4—21no—
313C2×C22⋊C4—22no—
314C2×C22⋊C4—22no—
315C2×C22⋊C4—42no—
316C2×C22⋊C4—42no—
317#106—24no—
318#103—24no—
319C22⋊C8—21no—
320C22⋊C8—21no—
321C22⋊C8—21no—
322C22⋊C8D4×C4112yes—
323#95—24no—
324#95—22no—
325#95—21no—
326#95—21no—
327#95D4×C4112yes—
328C24—21no—
329C24—21no—
330C24—21no—
331C24—21no—
332C24—21no—
333C24—21no—
334C24—42no—
335C24—42no—
336C24SD16×C4112yes—
337C24C2×D4×C4111yescharacteristic
338C2×Q8—21no—
339C2×Q8—21no—
340C2×Q8—42no—
341C22×C4—21no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—22no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—42no—
350C22×C4—42no—
351C22×C4—42no—
352C22×C4—42no—
353C22×C4—41no—
354C22×C4—41no—
355C22×C4—41no—
356C22×C4—41no—
357C22×C4—41no—
358C22×C4—41no—
359C22×C4—41no—
360C22×C4—41no—
361C22×C4C2×D4×C4111yescharacteristic
362C22×C4C2×D4×C4111yescharacteristic
363C22×C4C2×D4×C4111yescharacteristic
364C22×C4C2×D4×C4111yescharacteristic
365C22×C4C2×D4×C4111yescharacteristic
366C22×C4#41×C4111yescharacteristic
367C2×C8—22no—
368C2×C8—42no—
369C2×C8—42no—
370C2×C8—41no—
371C4⋊C4—22no—
372C4⋊C4—21no—
373C4⋊C4—22no—
374C4⋊C4—21no—
375C4⋊C4—42no—
376C4⋊C4—41no—
377C4⋊C4—41no—
378C4⋊C4—41no—
379C4⋊C4—41no—
380C4⋊C4—82no—
381C22⋊C4—48no—
382C22⋊C4—41no—
383C22⋊C4—41no—
384C22⋊C4—41no—
385C22⋊C4—41no—
386C22⋊C4—41no—
387C22⋊C4—41no—
388C22⋊C4—41no—
389C22⋊C4—41no—
390C22⋊C4—82no—
391C22⋊C4—82no—
392C23—22no—
393C23—22no—
394C23—22no—
395C23—22no—
396C23—22no—
397C23—44no—
398C23—42no—
399C23—44no—
400C23—42no—
401C23—41no—
402C23—41no—
403C23—41no—
404C23—42no—
405C23—42no—
406C23—41no—
407C23—82no—
408C23—81no—
409C23—82no—
410C23—81no—
411C23#120×C4111yescharacteristic
412C23#120×C4111yescharacteristic
413C23#121×C4111yescharacteristic
414C23C2×SD16×C4111yescharacteristic
415C23#135×C4111yescharacteristic
416C23AGL(1,ℤ/8)×C4111yescharacteristic
417C23#137×C4111yescharacteristic
418Q8—42no—
419Q8—81no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—82no—
443C2×C4—82no—
444C2×C4—81no—
445C2×C4—81no—
446C2×C4—81no—
447C2×C4—81no—
448C2×C4—81no—
449C2×C4#120×C4111yescharacteristic
450C2×C4#121×C4111yescharacteristic
451C2×C4#121×C4111yescharacteristic
452C2×C4#127×C4111yescharacteristic
453C8—42no—
454C8—81no—
455C22—21no—
456C22—21no—
457C22—22no—
458C22—22no—
459C22—22no—
460C22—22no—
461C22—21no—
462C22—21no—
463C22—44no—
464C22—44no—
465C22—42no—
466C22—82no—
467C22—82no—
468C22—82no—
469C22—81no—
470C22—82no—
471C22—81no—
472C22C41×#39211yescharacteristic
473C22C41×#44811yescharacteristic
474C22C41×#44911yescharacteristic
475C22C41×#45011yescharacteristic
476C22C41×#45211yescharacteristic
477C22C41×#45512yes—
478C22C41×#45812yes—
479C22C41×#46511yescharacteristic
480C22C41×#46811yescharacteristic
481C4—21no—
482C4—21no—
483C4—21no—
484C4—21no—
485C4—82no—
486C4—81no—
487C4—82no—
488C4—82no—
489C4—81no—
490C4—81no—
491C2—21no—
492C2—21no—
493C2—21no—
494C2—21no—
495C2—82no—
496C2C41×#160812yes—
497C2C41×#161212yes—
498C2C41×#200011yescharacteristic
499C2C41×#200411yescharacteristic
500C2C41×#202211yescharacteristic
subgroupG/H
center, socleC23×C41#120
commutator, Frattini, cosocleC23×C4C23×C41
prime radicalC25×C41D4
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
1. C2×C41×#483C2semidirect
4. C41×#1823C2semidirect
5. C2×C41×#328C2semidirect
7. C41×#1294C2semidirect
204. #9926C41direct (N × H)
241. C2×#483C2×C41semidirect
244. #1823C2×C41semidirect
245. C2×#328C2×C41semidirect
247. #1294C2×C41semidirect
281. C41#9926direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C41×#4832
C41×#26262
C2×C41×#3972
C41×#18232
C2×C41×#3282
C2×C41×#3232
C41×#12942
#992641