Finite Group Databasebeta

← C41×#9445 #23785646

Subgroups — C41×#9445 #23785646

Order 10496.

770 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#2879C211yesmaximal, characteristic, complemented
2C41×#2431C211yesmaximal, characteristic
3C41×#1782C211yesmaximal, characteristic, complemented
4C41×#1510C212yesmaximal, complemented
5C41×#1284C212yesmaximal, complemented
6C22×#41×C41C2211yescharacteristic
7C22×M16×C41—21no—
8C2×#127×C41C411yescharacteristic, complemented
9C2×#124×C41C411yescharacteristic, complemented
10C2×#121×C41C2211yescharacteristic
11C2×#99×C41—21no—
12C2×#99×C41—21no—
13C41×#408—24no—
14C41×#407—21no—
15C41×#407C2212yes—
16C41×#392—21no—
17C41×#392—21no—
18C41×#391C411yescharacteristic, complemented
19C41×#390C411yescharacteristic, complemented
20C41×#386—21no—
21C41×#386—21no—
22C41×#381C2212yes—
23C4×C22⋊C4×C41C2211yescharacteristic
24C41×#327—24no—
25C2×#41×C41—22no—
26C2×#41×C41—22no—
27C2×#41×C41—42no—
28C2×#41×C41—42no—
29C22×Q8×C41C2×C411yescharacteristic
30C22×D4×C41—21no—
31C22×D4×C41—21no—
32C22×D4×C41—21no—
33C22×D4×C41C2×C411yescharacteristic
34C22×D4×C41C2×C411yescharacteristic
35C22×D4×C41D411yescharacteristic
36C22×D4×C41D411yescharacteristic
37C23×C4×C41D411yescharacteristic
38C23×C4×C41D411yescharacteristic
39C23×C4×C41C2311yescharacteristic
40C2×M16×C41—22no—
41C2×M16×C41—22no—
42C2×M16×C41—42no—
43C2×M16×C41—42no—
44C22×C8×C41—22no—
45#127×C41—42no—
46#124×C41—42no—
47#121×C41—22no—
48#121×C41—22no—
49C2×C4⋊C4×C41C2×C411yescharacteristic
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×C42×C41C2×C411yescharacteristic
58C2×C42×C41C2×C411yescharacteristic
59#99×C41—42no—
60#99×C41—42no—
61C22⋊C8×C41—24no—
62C22⋊C8×C41—22no—
63C22⋊C8×C41D414yescomplemented
64#95×C41—21no—
65#95×C41—21no—
66#95×C41—21no—
67#95×C41—22no—
68#95×C41—22no—
69C24×C41—21no—
70C24×C41C22⋊C411yescharacteristic
71C24×C41C22⋊C411yescharacteristic
72C24×C41C2×D411yescharacteristic
73#41×C41—44no—
74#41×C41—44no—
75#41×C41—48no—
76C2×Q8×C41—22no—
77C2×Q8×C41—22no—
78C2×Q8×C41—41no—
79C2×D4×C41—22no—
80C2×D4×C41—22no—
81C2×D4×C41—22no—
82C2×D4×C41—22no—
83C2×D4×C41—22no—
84C2×D4×C41—22no—
85C2×D4×C41—22no—
86C2×D4×C41—41no—
87C2×D4×C41—41no—
88C2×D4×C41—41no—
89C2×D4×C41—41no—
90C2×D4×C41—41no—
91C2×D4×C41—42no—
92C2×D4×C41—42no—
93C2×D4×C41—42no—
94C2×D4×C41—42no—
95C2×D4×C41—42no—
96C2×D4×C41—81no—
97C2×D4×C41—81no—
98C2×D4×C41—81no—
99C2×D4×C41—81no—
100C22×C4×C41—22no—
101C22×C4×C41—22no—
102C22×C4×C41—21no—
103C22×C4×C41—21no—
104C22×C4×C41—21no—
105C22×C4×C41—21no—
106C22×C4×C41—21no—
107C22×C4×C41—21no—
108C22×C4×C41—21no—
109C22×C4×C41—41no—
110C22×C4×C41—41no—
111C22×C4×C41—41no—
112C22×C4×C41—41no—
113C22×C4×C41—42no—
114C22×C4×C41C22⋊C411yescharacteristic
115C22×C4×C41C22⋊C411yescharacteristic
116C22×C4×C41C22×C411yescharacteristic
117C22×C4×C41C2×D411yescharacteristic
118C22×C4×C41C2×D412yes—
119C22×C4×C41#4112yes—
120M16×C41—44no—
121M16×C41—42no—
122M16×C41—42no—
123C2×C8×C41—24no—
124C2×C8×C41—44no—
125C4⋊C4×C41—22no—
126C22⋊C4×C41—42no—
127C22⋊C4×C41—42no—
128C22⋊C4×C41—42no—
129C22⋊C4×C41—41no—
130C22⋊C4×C41—41no—
131C22⋊C4×C41—42no—
132C22⋊C4×C41—42no—
133C22⋊C4×C41—81no—
134C22⋊C4×C41—81no—
135C42×C41—41no—
136C42×C41—41no—
137C23×C41—21no—
138C23×C41—21no—
139C23×C41—21no—
140C23×C41—21no—
141C23×C41—21no—
142C23×C41—21no—
143C23×C41—21no—
144C23×C41—41no—
145C23×C41—41no—
146C23×C41—41no—
147C23×C41—41no—
148C23×C41—41no—
149C23×C41—41no—
150C23×C41—41no—
151C23×C41—41no—
152C23×C41—41no—
153C23×C41—41no—
154C23×C41—41no—
155C23×C41—41no—
156C23×C41—41no—
157C23×C41#9912yes—
158C23×C41C2×C22⋊C411yescharacteristic
159C23×C41#12112yes—
160Q8×C41—44no—
161D4×C41—44no—
162D4×C41—44no—
163D4×C41—44no—
164D4×C41—82no—
165D4×C41—84no—
166D4×C41—84no—
167D4×C41—84no—
168C2×C4×C41—22no—
169C2×C4×C41—22no—
170C2×C4×C41—24no—
171C2×C4×C41—21no—
172C2×C4×C41—21no—
173C2×C4×C41—21no—
174C2×C4×C41—21no—
175C2×C4×C41—21no—
176C2×C4×C41—21no—
177C2×C4×C41—22no—
178C2×C4×C41—21no—
179C2×C4×C41—21no—
180C2×C4×C41—21no—
181C2×C4×C41—42no—
182C2×C4×C41—42no—
183C2×C4×C41—42no—
184C2×C4×C41—42no—
185C2×C4×C41—41no—
186C2×C4×C41—41no—
187C2×C4×C41—41no—
188C2×C4×C41—41no—
189C2×C4×C41—41no—
190C2×C4×C41—41no—
191C2×C4×C41—41no—
192C2×C4×C41—41no—
193C2×C4×C41—82no—
194C2×C4×C41—82no—
195C2×C4×C41—82no—
196C2×C4×C41#9912yes—
197C2×C4×C41C4×D412yes—
198C2×C4×C41#12011yescharacteristic
199C2×C4×C41#12311yescharacteristic
200C8×C41—44no—
201#9445C4111yesmaximal, characteristic, direct product factor, Sylow
202C22×C41—21no—
203C22×C41—21no—
204C22×C41—22no—
205C22×C41—22no—
206C22×C41—22no—
207C22×C41—22no—
208C22×C41—42no—
209C22×C41—42no—
210C22×C41—41no—
211C22×C41—41no—
212C22×C41—41no—
213C22×C41—41no—
214C22×C41—41no—
215C22×C41—81no—
216C22×C41—81no—
217C22×C41—81no—
218C22×C41—81no—
219C22×C41—81no—
220C22×C41—81no—
221C22×C41—81no—
222C22×C41—81no—
223C22×C41—81no—
224C22×C41—81no—
225C22×C41—81no—
226C22×C41#38611yescharacteristic
227C22×C41C2×#9911yescharacteristic
228C22×C41C2×#9911yescharacteristic
229C4×C41—21no—
230C4×C41—21no—
231C4×C41—22no—
232C4×C41—22no—
233C4×C41—42no—
234C4×C41—41no—
235C4×C41—81no—
236C4×C41—81no—
237C4×C41—162no—
238#2879C2×C4111yescharacteristic, complemented
239#2431C2×C4111yescharacteristic
240#1782C2×C4111yescharacteristic, complemented
241#1510C2×C4112yescomplemented
242#1284C2×C4112yescomplemented
243C2×C41—21no—
244C2×C41—21no—
245C2×C41—42no—
246C2×C41—42no—
247C2×C41—81no—
248C2×C41—161no—
249C2×C41#188411yescharacteristic
250C2×C41#189811yescharacteristic
251C2×C41#191011yescharacteristic
252C22×#41C22×C4111yescharacteristic
253C22×M16—21no—
254C2×#127C4×C4111yescharacteristic, complemented
255C2×#124C4×C4111yescharacteristic, complemented
256C2×#121C22×C4111yescharacteristic
257C2×#99—21no—
258C2×#99—21no—
259#408—24no—
260#407—21no—
261#407C22×C4112yes—
262#392—21no—
263#392—21no—
264#391C4×C4111yescharacteristic, complemented
265#390C4×C4111yescharacteristic, complemented
266#386—21no—
267#386—21no—
268#381C22×C4112yes—
269C4×C22⋊C4C22×C4111yescharacteristic
270#327—24no—
271C41#944511yescharacteristic, direct product factor, Sylow
272C2×#41—22no—
273C2×#41—22no—
274C2×#41—42no—
275C2×#41—42no—
276C22×Q8C2×C4×C4111yescharacteristic
277C22×D4—21no—
278C22×D4—21no—
279C22×D4—21no—
280C22×D4C2×C4×C4111yescharacteristic
281C22×D4C2×C4×C4111yescharacteristic
282C22×D4D4×C4111yescharacteristic
283C22×D4D4×C4111yescharacteristic
284C23×C4D4×C4111yescharacteristic
285C23×C4D4×C4111yescharacteristic
286C23×C4C23×C4111yescharacteristic
287C2×M16—22no—
288C2×M16—22no—
289C2×M16—42no—
290C2×M16—42no—
291C22×C8—22no—
292#127—42no—
293#124—42no—
294#121—22no—
295#121—22no—
296C2×C4⋊C4C2×C4×C4111yescharacteristic
297C2×C22⋊C4—21no—
298C2×C22⋊C4—21no—
299C2×C22⋊C4—21no—
300C2×C22⋊C4—21no—
301C2×C22⋊C4—22no—
302C2×C22⋊C4—21no—
303C2×C22⋊C4—21no—
304C2×C42C2×C4×C4111yescharacteristic
305C2×C42C2×C4×C4111yescharacteristic
306#99—42no—
307#99—42no—
308C22⋊C8—24no—
309C22⋊C8—22no—
310C22⋊C8D4×C4114yescomplemented
311#95—21no—
312#95—21no—
313#95—21no—
314#95—22no—
315#95—22no—
316C24—21no—
317C24C22⋊C4×C4111yescharacteristic
318C24C22⋊C4×C4111yescharacteristic
319C24C2×D4×C4111yescharacteristic
320#41—44no—
321#41—44no—
322#41—48no—
323C2×Q8—22no—
324C2×Q8—22no—
325C2×Q8—41no—
326C2×D4—22no—
327C2×D4—22no—
328C2×D4—22no—
329C2×D4—22no—
330C2×D4—22no—
331C2×D4—22no—
332C2×D4—22no—
333C2×D4—41no—
334C2×D4—41no—
335C2×D4—41no—
336C2×D4—41no—
337C2×D4—41no—
338C2×D4—42no—
339C2×D4—42no—
340C2×D4—42no—
341C2×D4—42no—
342C2×D4—42no—
343C2×D4—81no—
344C2×D4—81no—
345C2×D4—81no—
346C2×D4—81no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—41no—
357C22×C4—41no—
358C22×C4—41no—
359C22×C4—41no—
360C22×C4—42no—
361C22×C4C22⋊C4×C4111yescharacteristic
362C22×C4C22⋊C4×C4111yescharacteristic
363C22×C4C22×C4×C4111yescharacteristic
364C22×C4C2×D4×C4111yescharacteristic
365C22×C4C2×D4×C4112yes—
366C22×C4#41×C4112yes—
367M16—44no—
368M16—42no—
369M16—42no—
370C2×C8—24no—
371C2×C8—44no—
372C4⋊C4—22no—
373C22⋊C4—42no—
374C22⋊C4—42no—
375C22⋊C4—42no—
376C22⋊C4—41no—
377C22⋊C4—41no—
378C22⋊C4—42no—
379C22⋊C4—42no—
380C22⋊C4—81no—
381C22⋊C4—81no—
382C42—41no—
383C42—41no—
384C23—21no—
385C23—21no—
386C23—21no—
387C23—21no—
388C23—21no—
389C23—21no—
390C23—21no—
391C23—41no—
392C23—41no—
393C23—41no—
394C23—41no—
395C23—41no—
396C23—41no—
397C23—41no—
398C23—41no—
399C23—41no—
400C23—41no—
401C23—41no—
402C23—41no—
403C23—41no—
404C23#99×C4112yes—
405C23C2×C22⋊C4×C4111yescharacteristic
406C23#121×C4112yes—
407Q8—44no—
408D4—44no—
409D4—44no—
410D4—44no—
411D4—82no—
412D4—84no—
413D4—84no—
414D4—84no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—24no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—22no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—82no—
441C2×C4—82no—
442C2×C4—82no—
443C2×C4#99×C4112yes—
444C2×C4C4×D4×C4112yes—
445C2×C4#120×C4111yescharacteristic
446C2×C4#123×C4111yescharacteristic
447C8—44no—
448C22—21no—
449C22—21no—
450C22—22no—
451C22—22no—
452C22—22no—
453C22—22no—
454C22—42no—
455C22—42no—
456C22—41no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—41no—
461C22—81no—
462C22—81no—
463C22—81no—
464C22—81no—
465C22—81no—
466C22—81no—
467C22—81no—
468C22—81no—
469C22—81no—
470C22—81no—
471C22—81no—
472C22C41×#38611yescharacteristic
473C22C2×#99×C4111yescharacteristic
474C22C2×#99×C4111yescharacteristic
475C4—21no—
476C4—21no—
477C4—22no—
478C4—22no—
479C4—42no—
480C4—41no—
481C4—81no—
482C4—81no—
483C4—162no—
484C2—21no—
485C2—21no—
486C2—42no—
487C2—42no—
488C2—81no—
489C2—161no—
490C2C41×#188411yescharacteristic
491C2C41×#189811yescharacteristic
492C2C41×#191011yescharacteristic
subgroupG/H
center, socleC22×C41#386
commutatorC22×C4C22×C4×C41
Frattini, cosocleC23×C4C23×C41
prime radicalC41×#2431C2
LCSG ▷ C22×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×#2879C2semidirect
3. C41×#1782C2semidirect
4. C41×#1510C2semidirect
5. C41×#1284C2semidirect
8. C2×#127×C41C4semidirect
9. C2×#124×C41C4semidirect
18. C41×#391C4semidirect
19. C41×#390C4semidirect
63. C22⋊C8×C41D4semidirect
201. #9445C41direct (N × H)
238. #2879C2×C41semidirect
240. #1782C2×C41semidirect
241. #1510C2×C41semidirect
242. #1284C2×C41semidirect
254. C2×#127C4×C41semidirect
255. C2×#124C4×C41semidirect
264. #391C4×C41semidirect
265. #390C4×C41semidirect
271. C41#9445direct (N × H)
310. C22⋊C8D4×C41semidirect

Maximal subgroups

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

subgroupindex
C41×#28792
C41×#24312
C41×#17822
C41×#15102
C41×#12842
#944541