Finite Group Databasebeta

← C41×#19314 #23795515

Subgroups — C41×#19314 #23795515

Order 10496.

630 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3165C211yesmaximal, characteristic, complemented
2C41×#3116C211yesmaximal, characteristic
3C41×#3039C211yesmaximal, characteristic
4C41×#2970C211yesmaximal, characteristic
5C41×#1694C212yesmaximal, complemented
6C41×#1692C212yesmaximal, complemented
7C41×#1673C212yesmaximal, complemented
8C41×#1671C212yesmaximal, complemented
9C41×#1569C211yesmaximal, characteristic, complemented
10C41×#1559C211yesmaximal, characteristic, complemented
11C41×#1556C211yesmaximal, characteristic, complemented
12C2×#137×C41—21no—
13C41×#533C2211yescharacteristic
14C2×C4⋊Q8×C41C2211yescharacteristic
15C4×#41×C41C2211yescharacteristic
16C41×#501—21no—
17C41×#501—21no—
18C41×#500C2212yes—
19C41×#498C2212yes—
20C41×#485—21no—
21C41×#477C2211yescharacteristic
22C41×#476C2211yescharacteristic
23C41×#462—21no—
24C41×#462C2212yes—
25C41×#462C2211yescharacteristic
26C41×#461—21no—
27C41×#461C2212yes—
28C41×#461C2211yescharacteristic
29C41×#452—21no—
30C41×#446C2212yes—
31C41×#441—21no—
32C41×#440—21no—
33C41×#435—22no—
34C8×D4×C41C2212yes—
35C41×#432—21no—
36C41×#432C2211yescharacteristic
37C41×#432C2211yescharacteristic
38C41×#428—22no—
39C41×#423C2211yescharacteristic
40C41×#419—21no—
41C4×M16×C41C2211yescharacteristic
42C2×#97×C41—21no—
43C41×#335C2212yes—
44C41×#334C2212yes—
45C41×#333C2212yes—
46C41×#332C2212yes—
47C41×#332C2212yes—
48C41×#332C2212yes—
49C2×#41×C41D411yescharacteristic
50C22×Q8×C41—21no—
51#137×C41—44no—
52C2×Q16×C41—22no—
53C2×Q16×C41—21no—
54C2×SD16×C41—22no—
55C2×SD16×C41—21no—
56C2×M16×C41—21no—
57C2×M16×C41D412yes—
58C22×C8×C41—22no—
59C4⋊Q8×C41—21no—
60C4⋊Q8×C41—21no—
61C4⋊Q8×C41—21no—
62C4⋊Q8×C41C2311yescharacteristic
63C4⋊Q8×C41C2312yes—
64C4⋊Q8×C41C2311yescharacteristic
65#125×C41—21no—
66C22⋊Q8×C41—21no—
67C22⋊Q8×C41—21no—
68C4×Q8×C41—21no—
69C4×Q8×C41—21no—
70C4×Q8×C41D411yescharacteristic
71C4×Q8×C41C2311yescharacteristic
72C4×D4×C41—21no—
73C4×D4×C41—21no—
74C4×D4×C41D411yescharacteristic
75C4×D4×C41C2311yescharacteristic
76#117×C41—21no—
77#117×C41—21no—
78#117×C41D411yescharacteristic
79C2×C4⋊C4×C41—21no—
80C2×C4⋊C4×C41—21no—
81C2×C42×C41—21no—
82C2×C42×C41C2311yescharacteristic
83#107×C41—22no—
84#107×C41—22no—
85#107×C41—21no—
86#106×C41—22no—
87#106×C41—22no—
88#106×C41—21no—
89C4⋊C8×C41—22no—
90C4⋊C8×C41—21no—
91C4⋊C8×C41C2312yes—
92C4⋊C8×C41C2311yescharacteristic
93C4⋊C8×C41C2311yescharacteristic
94C4⋊C8×C41C2312yes—
95#103×C41—21no—
96#103×C41—22no—
97#103×C41—22no—
98#103×C41—21no—
99#103×C41—21no—
100#102×C41—21no—
101C22⋊C8×C41—21no—
102C22⋊C8×C41—21no—
103C22⋊C8×C41—22no—
104#97×C41—22no—
105#97×C41—21no—
106#97×C41—21no—
107#97×C41D411yescharacteristic
108#97×C41D411yescharacteristic
109C4×C8×C41C2312yes—
110#41×C41—22no—
111#41×C41—41no—
112C2×Q8×C41—21no—
113C2×Q8×C41—22no—
114C2×Q8×C41—21no—
115C2×Q8×C41—42no—
116C2×Q8×C41—42no—
117C2×Q8×C41—41no—
118C2×Q8×C41C2×D411yescharacteristic
119C2×D4×C41—21no—
120C2×D4×C41C2×D411yescharacteristic
121C22×C4×C41—21no—
122C22×C4×C41—21no—
123C22×C4×C41—21no—
124C22×C4×C41—41no—
125C22×C4×C41C2×D411yescharacteristic
126C22×C4×C41C2×D411yescharacteristic
127C22×C4×C41#4111yescharacteristic
128Q16×C41—42no—
129Q16×C41—44no—
130SD16×C41—42no—
131SD16×C41—44no—
132M16×C41—24no—
133M16×C41—42no—
134C2×C8×C41—22no—
135C2×C8×C41—21no—
136C2×C8×C41—21no—
137C2×C8×C41—22no—
138C2×C8×C41—44no—
139C2×C8×C41C2×D412yes—
140C2×C8×C41C2×D412yes—
141C4⋊C4×C41—21no—
142C4⋊C4×C41—21no—
143C4⋊C4×C41—21no—
144C4⋊C4×C41—21no—
145C4⋊C4×C41—22no—
146C4⋊C4×C41—21no—
147C4⋊C4×C41—22no—
148C4⋊C4×C41—21no—
149C4⋊C4×C41—41no—
150C4⋊C4×C41—41no—
151C4⋊C4×C41—41no—
152C4⋊C4×C41—41no—
153C4⋊C4×C41C2×D411yescharacteristic
154C4⋊C4×C41C2×D411yescharacteristic
155C22⋊C4×C41—21no—
156C22⋊C4×C41—21no—
157C22⋊C4×C41—21no—
158C22⋊C4×C41—41no—
159C42×C41—21no—
160C42×C41—21no—
161C42×C41—21no—
162C42×C41—41no—
163C42×C41C2×D411yescharacteristic
164C42×C41C2×D411yescharacteristic
165C42×C41#4111yescharacteristic
166C42×C41C2411yescharacteristic
167C23×C41—21no—
168C23×C41#12111yescharacteristic
169Q8×C41—21no—
170Q8×C41—21no—
171Q8×C41—42no—
172Q8×C41—41no—
173Q8×C41—41no—
174Q8×C41—42no—
175Q8×C41—81no—
176Q8×C41—82no—
177D4×C41—21no—
178D4×C41—42no—
179D4×C41AGL(1,ℤ/8)12yes—
180C2×C4×C41—21no—
181C2×C4×C41—22no—
182C2×C4×C41—21no—
183C2×C4×C41—21no—
184C2×C4×C41—21no—
185C2×C4×C41—21no—
186C2×C4×C41—41no—
187C2×C4×C41—42no—
188C2×C4×C41—42no—
189C2×C4×C41—41no—
190C2×C4×C41—41no—
191C2×C4×C41—42no—
192C2×C4×C41—81no—
193C2×C4×C41—82no—
194C2×C4×C41#12111yescharacteristic
195C2×C4×C41#12111yescharacteristic
196C2×C4×C41#12111yescharacteristic
197C2×C4×C41C22×D411yescharacteristic
198C2×C4×C41C22×D411yescharacteristic
199C2×C4×C41C2×#4111yescharacteristic
200C8×C41—22no—
201C8×C41—42no—
202C8×C41—41no—
203C8×C41—42no—
204C8×C41—41no—
205C8×C41#13714yescomplemented
206#19314C4111yesmaximal, characteristic, direct product factor, Sylow
207C22×C41—21no—
208C22×C41—21no—
209C22×C41—22no—
210C22×C41—21no—
211C22×C41—41no—
212C22×C41—41no—
213C22×C41C2×#12111yescharacteristic
214C4×C41—21no—
215C4×C41—21no—
216C4×C41—21no—
217C4×C41—21no—
218C4×C41—41no—
219C4×C41—41no—
220C4×C41—41no—
221C4×C41—82no—
222C4×C41—81no—
223C4×C41—81no—
224C4×C41C2×AGL(1,ℤ/8)11yescharacteristic
225C4×C41C2×#13712yes—
226C4×C41#57511yescharacteristic
227#3165C2×C4111yescharacteristic, complemented
228#3116C2×C4111yescharacteristic
229#3039C2×C4111yescharacteristic
230#2970C2×C4111yescharacteristic
231#1694C2×C4112yescomplemented
232#1692C2×C4112yescomplemented
233#1673C2×C4112yescomplemented
234#1671C2×C4112yescomplemented
235#1569C2×C4111yescharacteristic, complemented
236#1559C2×C4111yescharacteristic, complemented
237#1556C2×C4111yescharacteristic, complemented
238C2×C41—41no—
239C2×C41—42no—
240C2×C41#303911yescharacteristic
241C2×C41#305511yescharacteristic
242C2×C41#306911yescharacteristic
243C2×#137—21no—
244#533C22×C4111yescharacteristic
245C2×C4⋊Q8C22×C4111yescharacteristic
246C4×#41C22×C4111yescharacteristic
247#501—21no—
248#501—21no—
249#500C22×C4112yes—
250#498C22×C4112yes—
251#485—21no—
252#477C22×C4111yescharacteristic
253#476C22×C4111yescharacteristic
254#462—21no—
255#462C22×C4111yescharacteristic
256#462C22×C4112yes—
257#461—21no—
258#461C22×C4111yescharacteristic
259#461C22×C4112yes—
260#452—21no—
261#446C22×C4112yes—
262#441—21no—
263#440—21no—
264#435—22no—
265C8×D4C22×C4112yes—
266#432—21no—
267#432C22×C4111yescharacteristic
268#432C22×C4111yescharacteristic
269#428—22no—
270#423C22×C4111yescharacteristic
271#419—21no—
272C4×M16C22×C4111yescharacteristic
273C2×#97—21no—
274#335C22×C4112yes—
275#334C22×C4112yes—
276#333C22×C4112yes—
277#332C22×C4112yes—
278#332C22×C4112yes—
279#332C22×C4112yes—
280C41#1931411yescharacteristic, direct product factor, Sylow
281C2×#41D4×C4111yescharacteristic
282C22×Q8—21no—
283#137—44no—
284C2×Q16—22no—
285C2×Q16—21no—
286C2×SD16—22no—
287C2×SD16—21no—
288C2×M16—21no—
289C2×M16D4×C4112yes—
290C22×C8—22no—
291C4⋊Q8—21no—
292C4⋊Q8—21no—
293C4⋊Q8—21no—
294C4⋊Q8C23×C4112yes—
295C4⋊Q8C23×C4111yescharacteristic
296C4⋊Q8C23×C4111yescharacteristic
297#125—21no—
298C22⋊Q8—21no—
299C22⋊Q8—21no—
300C4×Q8—21no—
301C4×Q8—21no—
302C4×Q8D4×C4111yescharacteristic
303C4×Q8C23×C4111yescharacteristic
304C4×D4—21no—
305C4×D4—21no—
306C4×D4D4×C4111yescharacteristic
307C4×D4C23×C4111yescharacteristic
308#117—21no—
309#117—21no—
310#117D4×C4111yescharacteristic
311C2×C4⋊C4—21no—
312C2×C4⋊C4—21no—
313C2×C42—21no—
314C2×C42C23×C4111yescharacteristic
315#107—22no—
316#107—22no—
317#107—21no—
318#106—22no—
319#106—22no—
320#106—21no—
321C4⋊C8—22no—
322C4⋊C8—21no—
323C4⋊C8C23×C4112yes—
324C4⋊C8C23×C4111yescharacteristic
325C4⋊C8C23×C4111yescharacteristic
326C4⋊C8C23×C4112yes—
327#103—21no—
328#103—22no—
329#103—22no—
330#103—21no—
331#103—21no—
332#102—21no—
333C22⋊C8—21no—
334C22⋊C8—21no—
335C22⋊C8—22no—
336#97—22no—
337#97—21no—
338#97—21no—
339#97D4×C4111yescharacteristic
340#97D4×C4111yescharacteristic
341C4×C8C23×C4112yes—
342#41—22no—
343#41—41no—
344C2×Q8—21no—
345C2×Q8—22no—
346C2×Q8—21no—
347C2×Q8—42no—
348C2×Q8—42no—
349C2×Q8—41no—
350C2×Q8C2×D4×C4111yescharacteristic
351C2×D4—21no—
352C2×D4C2×D4×C4111yescharacteristic
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—41no—
357C22×C4C2×D4×C4111yescharacteristic
358C22×C4C2×D4×C4111yescharacteristic
359C22×C4#41×C4111yescharacteristic
360Q16—42no—
361Q16—44no—
362SD16—42no—
363SD16—44no—
364M16—24no—
365M16—42no—
366C2×C8—22no—
367C2×C8—21no—
368C2×C8—21no—
369C2×C8—22no—
370C2×C8—44no—
371C2×C8C2×D4×C4112yes—
372C2×C8C2×D4×C4112yes—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4—21no—
377C4⋊C4—22no—
378C4⋊C4—21no—
379C4⋊C4—22no—
380C4⋊C4—21no—
381C4⋊C4—41no—
382C4⋊C4—41no—
383C4⋊C4—41no—
384C4⋊C4—41no—
385C4⋊C4C2×D4×C4111yescharacteristic
386C4⋊C4C2×D4×C4111yescharacteristic
387C22⋊C4—21no—
388C22⋊C4—21no—
389C22⋊C4—21no—
390C22⋊C4—41no—
391C42—21no—
392C42—21no—
393C42—21no—
394C42—41no—
395C42C2×D4×C4111yescharacteristic
396C42C2×D4×C4111yescharacteristic
397C42#41×C4111yescharacteristic
398C42C24×C4111yescharacteristic
399C23—21no—
400C23#121×C4111yescharacteristic
401Q8—21no—
402Q8—21no—
403Q8—42no—
404Q8—41no—
405Q8—41no—
406Q8—42no—
407Q8—81no—
408Q8—82no—
409D4—21no—
410D4—42no—
411D4AGL(1,ℤ/8)×C4112yes—
412C2×C4—21no—
413C2×C4—22no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—41no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—42no—
424C2×C4—81no—
425C2×C4—82no—
426C2×C4#121×C4111yescharacteristic
427C2×C4#121×C4111yescharacteristic
428C2×C4#121×C4111yescharacteristic
429C2×C4C22×D4×C4111yescharacteristic
430C2×C4C22×D4×C4111yescharacteristic
431C2×C4C2×#41×C4111yescharacteristic
432C8—22no—
433C8—42no—
434C8—41no—
435C8—42no—
436C8—41no—
437C8#137×C4114yescomplemented
438C22—21no—
439C22—21no—
440C22—22no—
441C22—21no—
442C22—41no—
443C22—41no—
444C22C2×#121×C4111yescharacteristic
445C4—21no—
446C4—21no—
447C4—21no—
448C4—21no—
449C4—41no—
450C4—41no—
451C4—41no—
452C4—82no—
453C4—81no—
454C4—81no—
455C4C2×AGL(1,ℤ/8)×C4111yescharacteristic
456C4C2×#137×C4112yes—
457C4C41×#57511yescharacteristic
458C2—41no—
459C2—42no—
460C2C41×#303911yescharacteristic
461C2C41×#305511yescharacteristic
462C2C41×#306911yescharacteristic
subgroupG/H
center, socleC22×C41C2×#121
commutator, Frattini, cosocleC42C24×C41
prime radicalC2×#41×C41D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C41 ◁ C2×C42×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C41×#3165C2semidirect
5. C41×#1694C2semidirect
6. C41×#1692C2semidirect
7. C41×#1673C2semidirect
8. C41×#1671C2semidirect
9. C41×#1569C2semidirect
10. C41×#1559C2semidirect
11. C41×#1556C2semidirect
205. C8×C41#137semidirect
206. #19314C41direct (N × H)
227. #3165C2×C41semidirect
231. #1694C2×C41semidirect
232. #1692C2×C41semidirect
233. #1673C2×C41semidirect
234. #1671C2×C41semidirect
235. #1569C2×C41semidirect
236. #1559C2×C41semidirect
237. #1556C2×C41semidirect
280. C41#19314direct (N × H)
437. C8#137×C41semidirect

Maximal subgroups

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

subgroupindex
C41×#31652
C41×#31162
C41×#30392
C41×#29702
C41×#16942
C41×#16922
C41×#16732
C41×#16712
C41×#15692
C41×#15592
C41×#15562
#1931441