Finite Group Databasebeta

← C41×#33606 #23809807

Subgroups — C41×#33606 #23809807

Order 10496.

686 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#510C211yesmaximal, characteristic, complemented
2C22×M32×C41C211yesmaximal, characteristic, complemented
3C41×#3050C211yesmaximal, characteristic
4C2×C41×#467C211yesmaximal, characteristic, complemented
5C41×#2220C212yesmaximal, complemented
6C41×#2219C212yesmaximal, complemented
7C41×#2217C212yesmaximal, complemented
8C41×#2216C212yesmaximal, complemented
9C41×#2159C211yesmaximal, characteristic, complemented
10C41×#2141C211yesmaximal, characteristic, complemented
11C41×#2139C211yesmaximal, characteristic, complemented
12C2×#135×C41C2211yescharacteristic
13C22×Q16×C41C2211yescharacteristic
14C23×C8×C41C2211yescharacteristic
15C41×#525—21no—
16C2×C22⋊Q8×C41—21no—
17C41×#510—24no—
18C2×Q32×C41C2212yescomplemented
19C2×SD32×C41C2212yescomplemented
20C2×M32×C41—24no—
21C2×M32×C41C2211yescharacteristic
22C2×M32×C41C2212yes—
23C2×M32×C41C2211yescharacteristic
24C22×C16×C41C2212yes—
25C41×#467—21no—
26C41×#467—21no—
27C41×#467C2212yes—
28C41×#467C2212yes—
29C41×#467C2211yescharacteristic
30C41×#467C2211yescharacteristic
31C41×#466C2211yescharacteristic
32C41×#466C2211yescharacteristic
33C41×#465—21no—
34C41×#465—21no—
35C41×#427C2211yescharacteristic
36C2×#107×C41C2211yescharacteristic
37C41×#416—21no—
38C2×#103×C41—21no—
39C41×#367C2212yescomplemented
40C41×#366C2212yescomplemented
41C41×#358C2212yescomplemented
42C41×#358C2212yescomplemented
43C41×#358C2212yescomplemented
44C41×#357C2212yescomplemented
45C2×#41×C41—21no—
46C22×Q8×C41—21no—
47C23×C4×C41D411yescharacteristic
48#135×C41—22no—
49#135×C41—22no—
50C2×Q16×C41—22no—
51C2×Q16×C41—21no—
52C2×Q16×C41—22no—
53C2×Q16×C41C2312yes—
54C2×Q16×C41C2311yescharacteristic
55C2×SD16×C41—21no—
56C2×D8×C41C2311yescharacteristic
57C22×C8×C41—22no—
58C22×C8×C41—22no—
59C22×C8×C41D411yescharacteristic
60C22×C8×C41D411yescharacteristic
61C22×C8×C41D411yescharacteristic
62C22×C8×C41C2311yescharacteristic
63C22×C8×C41C2311yescharacteristic
64C22×C8×C41C2311yescharacteristic
65#123×C41—41no—
66C22⋊Q8×C41—22no—
67C22⋊Q8×C41—22no—
68C22⋊Q8×C41—21no—
69C22⋊Q8×C41—21no—
70C22⋊Q8×C41—41no—
71C22⋊Q8×C41—41no—
72#121×C41—21no—
73#121×C41—21no—
74#120×C41—41no—
75C4×D4×C41—41no—
76C4×D4×C41—41no—
77#117×C41—21no—
78C2×C4⋊C4×C41—21no—
79C2×C4⋊C4×C41—41no—
80C2×C22⋊C4×C41—41no—
81Q32×C41—24no—
82SD32×C41—24no—
83M32×C41—22no—
84M32×C41—24no—
85M32×C41D414yescomplemented
86C2×C16×C41—24no—
87C2×C16×C41C2312yes—
88C2×C16×C41C2312yes—
89#107×C41—21no—
90#107×C41C2312yes—
91#107×C41C2311yescharacteristic
92#107×C41C2311yescharacteristic
93#106×C41—21no—
94#103×C41—22no—
95#103×C41—22no—
96#103×C41—21no—
97#103×C41—21no—
98#102×C41—21no—
99#102×C41—21no—
100C24×C41D811yescharacteristic
101#41×C41—42no—
102#41×C41—42no—
103C2×Q8×C41—21no—
104C2×Q8×C41—22no—
105C2×Q8×C41—41no—
106C2×Q8×C41—42no—
107C2×Q8×C41—42no—
108C2×D4×C41—21no—
109C2×D4×C41—41no—
110C2×D4×C41—41no—
111C2×D4×C41—41no—
112C22×C4×C41—22no—
113C22×C4×C41—22no—
114C22×C4×C41—41no—
115C22×C4×C41—41no—
116C22×C4×C41—41no—
117C22×C4×C41D811yescharacteristic
118C22×C4×C41D811yescharacteristic
119C22×C4×C41D811yescharacteristic
120C22×C4×C41C2×D411yescharacteristic
121C22×C4×C41C2×D411yescharacteristic
122C22×C4×C41C2×D411yescharacteristic
123Q16×C41—22no—
124Q16×C41—21no—
125Q16×C41—22no—
126Q16×C41—21no—
127Q16×C41—42no—
128SD16×C41—42no—
129D8×C41—21no—
130D8×C41—21no—
131C2×C8×C41—22no—
132C2×C8×C41—22no—
133C2×C8×C41—22no—
134C2×C8×C41—21no—
135C2×C8×C41—21no—
136C2×C8×C41—21no—
137C2×C8×C41—21no—
138C2×C8×C41C2×D411yescharacteristic
139C2×C8×C41C2×D411yescharacteristic
140C2×C8×C41C2×D411yescharacteristic
141C2×C8×C41C2×D412yes—
142C2×C8×C41#4112yes—
143C2×C8×C41C2411yescharacteristic
144C4⋊C4×C41—21no—
145C4⋊C4×C41—21no—
146C4⋊C4×C41—22no—
147C4⋊C4×C41—41no—
148C4⋊C4×C41—42no—
149C4⋊C4×C41—42no—
150C4⋊C4×C41—41no—
151C4⋊C4×C41—41no—
152C22⋊C4×C41—42no—
153C22⋊C4×C41—42no—
154C22⋊C4×C41—41no—
155C22⋊C4×C41—41no—
156C22⋊C4×C41—41no—
157C22⋊C4×C41—41no—
158C22⋊C4×C41—41no—
159C42×C41—41no—
160C16×C41—22no—
161C16×C41C2×D414yes—
162C23×C41—22no—
163C23×C41—22no—
164C23×C41—41no—
165C23×C41—41no—
166C23×C41C2×D811yescharacteristic
167C23×C41C2×D811yescharacteristic
168C23×C41C2×D811yescharacteristic
169Q8×C41—41no—
170Q8×C41—42no—
171Q8×C41—42no—
172Q8×C41—41no—
173Q8×C41—82no—
174D4×C41—41no—
175D4×C41—41no—
176D4×C41—82no—
177D4×C41—82no—
178D4×C41—82no—
179C2×C4×C41—22no—
180C2×C4×C41—21no—
181C2×C4×C41—21no—
182C2×C4×C41—21no—
183C2×C4×C41—21no—
184C2×C4×C41—22no—
185C2×C4×C41—22no—
186C2×C4×C41—41no—
187C2×C4×C41—41no—
188C2×C4×C41—42no—
189C2×C4×C41—41no—
190C2×C4×C41—42no—
191C2×C4×C41—82no—
192C2×C4×C41—82no—
193C2×C4×C41—82no—
194C2×C4×C41#12112yes—
195C2×C4×C41C2×D811yescharacteristic
196C2×C4×C41C2×D811yescharacteristic
197C2×C4×C41C2×D811yescharacteristic
198C2×C4×C41#13512yes—
199C2×C4×C41C22×D411yescharacteristic
200C8×C41—21no—
201C8×C41—21no—
202C8×C41#12112yes—
203C8×C41C22×D411yescharacteristic
204C8×C41C2×#4111yescharacteristic
205#33606C4111yesmaximal, characteristic, direct product factor, Sylow
206C22×C41—21no—
207C22×C41—21no—
208C22×C41—21no—
209C22×C41—21no—
210C22×C41—21no—
211C22×C41—21no—
212C22×C41—21no—
213C22×C41—44no—
214C22×C41—81no—
215C22×C41—81no—
216C22×C41—81no—
217C22×C41#46612yes—
218C22×C41#51012yescomplemented
219C22×C41C22×D811yescharacteristic
220C4×C41—21no—
221C4×C41—21no—
222C4×C41—81no—
223C4×C41—82no—
224C4×C41—81no—
225C4×C41—81no—
226C4×C41—82no—
227C4×C41#46612yes—
228C4×C41C2×#12111yescharacteristic
229C4×C41C2×#13511yescharacteristic
230C2×#510C2×C4111yescharacteristic, complemented
231C22×M32C2×C4111yescharacteristic, complemented
232#3050C2×C4111yescharacteristic
233C2×#467C2×C4111yescharacteristic, complemented
234#2220C2×C4112yescomplemented
235#2219C2×C4112yescomplemented
236#2217C2×C4112yescomplemented
237#2216C2×C4112yescomplemented
238#2159C2×C4111yescharacteristic, complemented
239#2141C2×C4111yescharacteristic, complemented
240#2139C2×C4111yescharacteristic, complemented
241C2×C41—22no—
242C2×C41—22no—
243C2×C41—41no—
244C2×C41—161no—
245C2×C41C2×#46611yescharacteristic
246C2×C41C2×#51011yescharacteristic
247C2×C41#341411yescharacteristic
248C2×#135C22×C4111yescharacteristic
249C22×Q16C22×C4111yescharacteristic
250C23×C8C22×C4111yescharacteristic
251#525—21no—
252C2×C22⋊Q8—21no—
253#510—24no—
254C2×Q32C22×C4112yescomplemented
255C2×SD32C22×C4112yescomplemented
256C2×M32—24no—
257C2×M32C22×C4111yescharacteristic
258C2×M32C22×C4112yes—
259C2×M32C22×C4111yescharacteristic
260C22×C16C22×C4112yes—
261#467—21no—
262#467—21no—
263#467C22×C4111yescharacteristic
264#467C22×C4112yes—
265#467C22×C4111yescharacteristic
266#467C22×C4112yes—
267#466C22×C4111yescharacteristic
268#466C22×C4111yescharacteristic
269#465—21no—
270#465—21no—
271#427C22×C4111yescharacteristic
272C2×#107C22×C4111yescharacteristic
273#416—21no—
274C2×#103—21no—
275#367C22×C4112yescomplemented
276#366C22×C4112yescomplemented
277#358C22×C4112yescomplemented
278#358C22×C4112yescomplemented
279#358C22×C4112yescomplemented
280#357C22×C4112yescomplemented
281C41#3360611yescharacteristic, direct product factor, Sylow
282C2×#41—21no—
283C22×Q8—21no—
284C23×C4D4×C4111yescharacteristic
285#135—22no—
286#135—22no—
287C2×Q16—22no—
288C2×Q16—21no—
289C2×Q16—22no—
290C2×Q16C23×C4112yes—
291C2×Q16C23×C4111yescharacteristic
292C2×SD16—21no—
293C2×D8C23×C4111yescharacteristic
294C22×C8—22no—
295C22×C8—22no—
296C22×C8D4×C4111yescharacteristic
297C22×C8D4×C4111yescharacteristic
298C22×C8D4×C4111yescharacteristic
299C22×C8C23×C4111yescharacteristic
300C22×C8C23×C4111yescharacteristic
301C22×C8C23×C4111yescharacteristic
302#123—41no—
303C22⋊Q8—22no—
304C22⋊Q8—22no—
305C22⋊Q8—21no—
306C22⋊Q8—21no—
307C22⋊Q8—41no—
308C22⋊Q8—41no—
309#121—21no—
310#121—21no—
311#120—41no—
312C4×D4—41no—
313C4×D4—41no—
314#117—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—41no—
317C2×C22⋊C4—41no—
318Q32—24no—
319SD32—24no—
320M32—22no—
321M32—24no—
322M32D4×C4114yescomplemented
323C2×C16—24no—
324C2×C16C23×C4112yes—
325C2×C16C23×C4112yes—
326#107—21no—
327#107C23×C4112yes—
328#107C23×C4111yescharacteristic
329#107C23×C4111yescharacteristic
330#106—21no—
331#103—22no—
332#103—22no—
333#103—21no—
334#103—21no—
335#102—21no—
336#102—21no—
337C24D8×C4111yescharacteristic
338#41—42no—
339#41—42no—
340C2×Q8—21no—
341C2×Q8—22no—
342C2×Q8—41no—
343C2×Q8—42no—
344C2×Q8—42no—
345C2×D4—21no—
346C2×D4—41no—
347C2×D4—41no—
348C2×D4—41no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—41no—
352C22×C4—41no—
353C22×C4—41no—
354C22×C4D8×C4111yescharacteristic
355C22×C4D8×C4111yescharacteristic
356C22×C4D8×C4111yescharacteristic
357C22×C4C2×D4×C4111yescharacteristic
358C22×C4C2×D4×C4111yescharacteristic
359C22×C4C2×D4×C4111yescharacteristic
360Q16—22no—
361Q16—21no—
362Q16—22no—
363Q16—21no—
364Q16—42no—
365SD16—42no—
366D8—21no—
367D8—21no—
368C2×C8—22no—
369C2×C8—22no—
370C2×C8—22no—
371C2×C8—21no—
372C2×C8—21no—
373C2×C8—21no—
374C2×C8—21no—
375C2×C8C2×D4×C4111yescharacteristic
376C2×C8C2×D4×C4111yescharacteristic
377C2×C8C2×D4×C4111yescharacteristic
378C2×C8C2×D4×C4112yes—
379C2×C8#41×C4112yes—
380C2×C8C24×C4111yescharacteristic
381C4⋊C4—21no—
382C4⋊C4—21no—
383C4⋊C4—22no—
384C4⋊C4—41no—
385C4⋊C4—42no—
386C4⋊C4—42no—
387C4⋊C4—41no—
388C4⋊C4—41no—
389C22⋊C4—42no—
390C22⋊C4—42no—
391C22⋊C4—41no—
392C22⋊C4—41no—
393C22⋊C4—41no—
394C22⋊C4—41no—
395C22⋊C4—41no—
396C42—41no—
397C16—22no—
398C16C2×D4×C4114yes—
399C23—22no—
400C23—22no—
401C23—41no—
402C23—41no—
403C23C2×D8×C4111yescharacteristic
404C23C2×D8×C4111yescharacteristic
405C23C2×D8×C4111yescharacteristic
406Q8—41no—
407Q8—42no—
408Q8—42no—
409Q8—41no—
410Q8—82no—
411D4—41no—
412D4—41no—
413D4—82no—
414D4—82no—
415D4—82no—
416C2×C4—22no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—42no—
426C2×C4—41no—
427C2×C4—42no—
428C2×C4—82no—
429C2×C4—82no—
430C2×C4—82no—
431C2×C4#121×C4112yes—
432C2×C4C2×D8×C4111yescharacteristic
433C2×C4C2×D8×C4111yescharacteristic
434C2×C4C2×D8×C4111yescharacteristic
435C2×C4#135×C4112yes—
436C2×C4C22×D4×C4111yescharacteristic
437C8—21no—
438C8—21no—
439C8#121×C4112yes—
440C8C22×D4×C4111yescharacteristic
441C8C2×#41×C4111yescharacteristic
442C22—21no—
443C22—21no—
444C22—21no—
445C22—21no—
446C22—21no—
447C22—21no—
448C22—21no—
449C22—44no—
450C22—81no—
451C22—81no—
452C22—81no—
453C22C41×#46612yes—
454C22C41×#51012yescomplemented
455C22C22×D8×C4111yescharacteristic
456C4—21no—
457C4—21no—
458C4—81no—
459C4—82no—
460C4—81no—
461C4—82no—
462C4—81no—
463C4C41×#46612yes—
464C4C2×#121×C4111yescharacteristic
465C4C2×#135×C4111yescharacteristic
466C2—22no—
467C2—22no—
468C2—41no—
469C2—161no—
470C2C2×C41×#46611yescharacteristic
471C2C2×C41×#51011yescharacteristic
472C2C41×#341411yescharacteristic
subgroupG/H
center, socleC22×C41C22×D8
commutator, Frattini, cosocleC2×C8C24×C41
prime radicalC41×#3050C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C41 ◁ C23×C4×C41 ◁ C23×C8×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C41×#510C2semidirect
2. C22×M32×C41C2semidirect
4. C2×C41×#467C2semidirect
5. C41×#2220C2semidirect
6. C41×#2219C2semidirect
7. C41×#2217C2semidirect
8. C41×#2216C2semidirect
9. C41×#2159C2semidirect
10. C41×#2141C2semidirect
11. C41×#2139C2semidirect
18. C2×Q32×C41C22semidirect
19. C2×SD32×C41C22semidirect
39. C41×#367C22semidirect
40. C41×#366C22semidirect
41. C41×#358C22semidirect
42. C41×#358C22semidirect
43. C41×#358C22semidirect
44. C41×#357C22semidirect
85. M32×C41D4semidirect
205. #33606C41direct (N × H)
218. C22×C41#510semidirect
230. C2×#510C2×C41semidirect
231. C22×M32C2×C41semidirect
233. C2×#467C2×C41semidirect
234. #2220C2×C41semidirect
235. #2219C2×C41semidirect
236. #2217C2×C41semidirect
237. #2216C2×C41semidirect
238. #2159C2×C41semidirect
239. #2141C2×C41semidirect
240. #2139C2×C41semidirect
254. C2×Q32C22×C41semidirect
255. C2×SD32C22×C41semidirect
275. #367C22×C41semidirect
276. #366C22×C41semidirect
277. #358C22×C41semidirect
278. #358C22×C41semidirect
279. #358C22×C41semidirect
280. #357C22×C41semidirect
281. C41#33606direct (N × H)
322. M32D4×C41semidirect
454. C22C41×#510semidirect

Maximal subgroups

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

subgroupindex
C2×C41×#5102
C22×M32×C412
C41×#30502
C2×C41×#4672
C41×#22202
C41×#22192
C41×#22172
C41×#22162
C41×#21592
C41×#21412
C41×#21392
#3360641