Finite Group Databasebeta

← C41×#33916 #23810117

Subgroups — C41×#33916 #23810117

Order 10496.

464 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3342C211yesmaximal, characteristic
2C41×#3336C211yesmaximal, characteristic
3C41×#2255C211yesmaximal, characteristic, complemented
4C41×#2237C211yesmaximal, characteristic, complemented
5C41×#2237C211yesmaximal, characteristic, complemented
6C41×#2237C211yesmaximal, characteristic, complemented
7C41×#2236C211yesmaximal, characteristic, complemented
8C41×#2229C211yesmaximal, characteristic, complemented
9C41×#2227C211yesmaximal, characteristic, complemented
10C41×#2219C211yesmaximal, characteristic, complemented
11C41×#2216C211yesmaximal, characteristic, complemented
12C41×#2176C211yesmaximal, characteristic, complemented
13C41×#2168C211yesmaximal, characteristic
14C41×#2159C211yesmaximal, characteristic, complemented
15C41×#2158C211yesmaximal, characteristic, complemented
16C41×#556—21no—
17C41×#552—21no—
18C2×Q32×C41C2211yescharacteristic
19C2×M32×C41C2211yescharacteristic
20C22×C16×C41C2211yescharacteristic
21C41×#500C2211yescharacteristic
22C41×#499C2211yescharacteristic
23C41×#485—21no—
24C41×#485—21no—
25C41×#485—21no—
26C41×#483—21no—
27C41×#479—21no—
28C41×#475—21no—
29C41×#467C2211yescharacteristic
30C41×#467C2211yescharacteristic
31C41×#467C2211yescharacteristic
32C41×#467C2211yescharacteristic
33C4×Q16×C41C2211yescharacteristic
34C4×Q16×C41C2211yescharacteristic
35C8×D4×C41C2211yescharacteristic
36C41×#427C2211yescharacteristic
37C41×#427C2211yescharacteristic
38C41×#427C2211yescharacteristic
39C2×#107×C41C2211yescharacteristic
40C41×#367C2211yescharacteristic
41C41×#367C2211yescharacteristic
42C41×#367C2211yescharacteristic
43C41×#367C2211yescharacteristic
44C41×#366C2211yescharacteristic
45C41×#366C2211yescharacteristic
46C41×#366C2211yescharacteristic
47C41×#366C2211yescharacteristic
48C41×#366C2211yescharacteristic
49C41×C4⋊C16C2211yescharacteristic
50C41×#358C2211yescharacteristic
51C41×#358C2211yescharacteristic
52C41×#358C2211yescharacteristic
53C41×#358C2211yescharacteristic
54C41×#358C2211yescharacteristic
55C41×#358C2211yescharacteristic
56C41×C22⋊C16C2211yescharacteristic
57C41×C22⋊C16C2211yescharacteristic
58C41×#346C2211yescharacteristic
59C2×Q16×C41C2311yescharacteristic
60C2×Q16×C41C2311yescharacteristic
61C22×C8×C41C2311yescharacteristic
62C22×C8×C41C2311yescharacteristic
63C4⋊Q8×C41—21no—
64#126×C41—41no—
65#126×C41—41no—
66#126×C41—41no—
67#125×C41—21no—
68#125×C41—41no—
69#124×C41—41no—
70#123×C41—41no—
71C22⋊Q8×C41—21no—
72C22⋊Q8×C41—21no—
73C22⋊Q8×C41—21no—
74C22⋊Q8×C41—21no—
75C4×Q8×C41—21no—
76C4×Q8×C41—21no—
77C4×Q8×C41—41no—
78C4×D4×C41D411yescharacteristic
79#117×C41—21no—
80#117×C41—21no—
81#117×C41—21no—
82#117×C41—41no—
83C2×C4⋊C4×C41—21no—
84Q32×C41—22no—
85M32×C41—22no—
86C2×C16×C41—22no—
87C2×C16×C41C2311yescharacteristic
88C2×C16×C41C2311yescharacteristic
89C2×C16×C41C2311yescharacteristic
90C2×C16×C41C2311yescharacteristic
91#107×C41—21no—
92#107×C41—21no—
93#107×C41C2311yescharacteristic
94#107×C41C2311yescharacteristic
95#107×C41C2311yescharacteristic
96#107×C41C2311yescharacteristic
97#107×C41C2311yescharacteristic
98#107×C41C2311yescharacteristic
99#106×C41—21no—
100#106×C41—21no—
101#106×C41—21no—
102#106×C41—21no—
103C4⋊C8×C41D411yescharacteristic
104#103×C41—21no—
105#103×C41—21no—
106#103×C41—21no—
107#103×C41—21no—
108#103×C41—21no—
109#103×C41—21no—
110C22⋊C8×C41D411yescharacteristic
111C22⋊C8×C41D411yescharacteristic
112C4×C8×C41C2311yescharacteristic
113C2×Q8×C41—21no—
114C2×Q8×C41—21no—
115C2×Q8×C41—41no—
116C2×D4×C41D811yescharacteristic
117C22×C4×C41—41no—
118C22×C4×C41C2×D411yescharacteristic
119C22×C4×C41C2×D411yescharacteristic
120Q16×C41—21no—
121Q16×C41—21no—
122Q16×C41—21no—
123Q16×C41—21no—
124C2×C8×C41—21no—
125C2×C8×C41—21no—
126C2×C8×C41—21no—
127C2×C8×C41—21no—
128C2×C8×C41C2×D411yescharacteristic
129C2×C8×C41C2×D411yescharacteristic
130C2×C8×C41C2×D411yescharacteristic
131C2×C8×C41C2411yescharacteristic
132C4⋊C4×C41—21no—
133C4⋊C4×C41—21no—
134C4⋊C4×C41—21no—
135C4⋊C4×C41—21no—
136C4⋊C4×C41—21no—
137C4⋊C4×C41—21no—
138C4⋊C4×C41—41no—
139C4⋊C4×C41—41no—
140C4⋊C4×C41—41no—
141C4⋊C4×C41—41no—
142C4⋊C4×C41—41no—
143C4⋊C4×C41—41no—
144C4⋊C4×C41—41no—
145C4⋊C4×C41—41no—
146C4⋊C4×C41—41no—
147C4⋊C4×C41—41no—
148C4⋊C4×C41D811yescharacteristic
149C22⋊C4×C41—41no—
150C22⋊C4×C41—41no—
151C22⋊C4×C41—41no—
152C22⋊C4×C41—41no—
153C22⋊C4×C41—41no—
154C22⋊C4×C41—41no—
155C22⋊C4×C41—41no—
156C22⋊C4×C41D811yescharacteristic
157C22⋊C4×C41D811yescharacteristic
158C42×C41—41no—
159C42×C41—41no—
160C42×C41—41no—
161C42×C41—41no—
162C42×C41—41no—
163C42×C41C2×D411yescharacteristic
164C16×C41—21no—
165C16×C41—21no—
166C16×C41—21no—
167C16×C41#4112yes—
168C23×C41C2×D811yescharacteristic
169C23×C41C2×D811yescharacteristic
170Q8×C41—41no—
171Q8×C41—41no—
172Q8×C41—41no—
173Q8×C41—41no—
174Q8×C41—82no—
175D4×C41—41no—
176C2×C4×C41—21no—
177C2×C4×C41—21no—
178C2×C4×C41—21no—
179C2×C4×C41—21no—
180C2×C4×C41—41no—
181C2×C4×C41—41no—
182C2×C4×C41—41no—
183C2×C4×C41—41no—
184C2×C4×C41—41no—
185C2×C4×C41—41no—
186C2×C4×C41—41no—
187C2×C4×C41—41no—
188C2×C4×C41—82no—
189C2×C4×C41C2×D811yescharacteristic
190C2×C4×C41C2×D811yescharacteristic
191C2×C4×C41C2×D811yescharacteristic
192C2×C4×C41C2×D811yescharacteristic
193C2×C4×C41C22×D411yescharacteristic
194C8×C41—21no—
195C8×C41—21no—
196C8×C41—21no—
197C8×C41C2×#4111yescharacteristic
198C8×C412−1+411yescharacteristic
199#33916C4111yesmaximal, characteristic, direct product factor, Sylow
200C22×C41—21no—
201C22×C41—21no—
202C22×C41—21no—
203C22×C41—21no—
204C22×C41—21no—
205C22×C41—21no—
206C22×C41C22×D811yescharacteristic
207C4×C41—21no—
208C4×C41—21no—
209C4×C41—21no—
210C4×C41—21no—
211C4×C41—81no—
212C4×C41—81no—
213C4×C41—81no—
214C4×C41—81no—
215C4×C41—81no—
216C4×C41—81no—
217C4×C41—81no—
218C4×C41—81no—
219C4×C41#54711yescharacteristic
220C4×C41#57811yescharacteristic
221#3342C2×C4111yescharacteristic
222#3336C2×C4111yescharacteristic
223#2255C2×C4111yescharacteristic, complemented
224#2237C2×C4111yescharacteristic, complemented
225#2237C2×C4111yescharacteristic, complemented
226#2237C2×C4111yescharacteristic, complemented
227#2236C2×C4111yescharacteristic, complemented
228#2229C2×C4111yescharacteristic, complemented
229#2227C2×C4111yescharacteristic, complemented
230#2219C2×C4111yescharacteristic, complemented
231#2216C2×C4111yescharacteristic, complemented
232#2176C2×C4111yescharacteristic, complemented
233#2168C2×C4111yescharacteristic
234#2159C2×C4111yescharacteristic, complemented
235#2158C2×C4111yescharacteristic, complemented
236C2×C41—41no—
237C2×C41—41no—
238C2×C41#333411yescharacteristic
239C2×C41#341411yescharacteristic
240C2×C41#341711yescharacteristic
241#556—21no—
242#552—21no—
243C2×Q32C22×C4111yescharacteristic
244C2×M32C22×C4111yescharacteristic
245C22×C16C22×C4111yescharacteristic
246#500C22×C4111yescharacteristic
247#499C22×C4111yescharacteristic
248#485—21no—
249#485—21no—
250#485—21no—
251#483—21no—
252#479—21no—
253#475—21no—
254#467C22×C4111yescharacteristic
255#467C22×C4111yescharacteristic
256#467C22×C4111yescharacteristic
257#467C22×C4111yescharacteristic
258C4×Q16C22×C4111yescharacteristic
259C4×Q16C22×C4111yescharacteristic
260C8×D4C22×C4111yescharacteristic
261#427C22×C4111yescharacteristic
262#427C22×C4111yescharacteristic
263#427C22×C4111yescharacteristic
264C2×#107C22×C4111yescharacteristic
265#367C22×C4111yescharacteristic
266#367C22×C4111yescharacteristic
267#367C22×C4111yescharacteristic
268#367C22×C4111yescharacteristic
269#366C22×C4111yescharacteristic
270#366C22×C4111yescharacteristic
271#366C22×C4111yescharacteristic
272#366C22×C4111yescharacteristic
273#366C22×C4111yescharacteristic
274C4⋊C16C22×C4111yescharacteristic
275#358C22×C4111yescharacteristic
276#358C22×C4111yescharacteristic
277#358C22×C4111yescharacteristic
278#358C22×C4111yescharacteristic
279#358C22×C4111yescharacteristic
280#358C22×C4111yescharacteristic
281C22⋊C16C22×C4111yescharacteristic
282C22⋊C16C22×C4111yescharacteristic
283#346C22×C4111yescharacteristic
284C41#3391611yescharacteristic, direct product factor, Sylow
285C2×Q16C23×C4111yescharacteristic
286C2×Q16C23×C4111yescharacteristic
287C22×C8C23×C4111yescharacteristic
288C22×C8C23×C4111yescharacteristic
289C4⋊Q8—21no—
290#126—41no—
291#126—41no—
292#126—41no—
293#125—21no—
294#125—41no—
295#124—41no—
296#123—41no—
297C22⋊Q8—21no—
298C22⋊Q8—21no—
299C22⋊Q8—21no—
300C22⋊Q8—21no—
301C4×Q8—21no—
302C4×Q8—21no—
303C4×Q8—41no—
304C4×D4D4×C4111yescharacteristic
305#117—21no—
306#117—21no—
307#117—21no—
308#117—41no—
309C2×C4⋊C4—21no—
310Q32—22no—
311M32—22no—
312C2×C16—22no—
313C2×C16C23×C4111yescharacteristic
314C2×C16C23×C4111yescharacteristic
315C2×C16C23×C4111yescharacteristic
316C2×C16C23×C4111yescharacteristic
317#107—21no—
318#107—21no—
319#107C23×C4111yescharacteristic
320#107C23×C4111yescharacteristic
321#107C23×C4111yescharacteristic
322#107C23×C4111yescharacteristic
323#107C23×C4111yescharacteristic
324#107C23×C4111yescharacteristic
325#106—21no—
326#106—21no—
327#106—21no—
328#106—21no—
329C4⋊C8D4×C4111yescharacteristic
330#103—21no—
331#103—21no—
332#103—21no—
333#103—21no—
334#103—21no—
335#103—21no—
336C22⋊C8D4×C4111yescharacteristic
337C22⋊C8D4×C4111yescharacteristic
338C4×C8C23×C4111yescharacteristic
339C2×Q8—21no—
340C2×Q8—21no—
341C2×Q8—41no—
342C2×D4D8×C4111yescharacteristic
343C22×C4—41no—
344C22×C4C2×D4×C4111yescharacteristic
345C22×C4C2×D4×C4111yescharacteristic
346Q16—21no—
347Q16—21no—
348Q16—21no—
349Q16—21no—
350C2×C8—21no—
351C2×C8—21no—
352C2×C8—21no—
353C2×C8—21no—
354C2×C8C2×D4×C4111yescharacteristic
355C2×C8C2×D4×C4111yescharacteristic
356C2×C8C2×D4×C4111yescharacteristic
357C2×C8C24×C4111yescharacteristic
358C4⋊C4—21no—
359C4⋊C4—21no—
360C4⋊C4—21no—
361C4⋊C4—21no—
362C4⋊C4—21no—
363C4⋊C4—21no—
364C4⋊C4—41no—
365C4⋊C4—41no—
366C4⋊C4—41no—
367C4⋊C4—41no—
368C4⋊C4—41no—
369C4⋊C4—41no—
370C4⋊C4—41no—
371C4⋊C4—41no—
372C4⋊C4—41no—
373C4⋊C4—41no—
374C4⋊C4D8×C4111yescharacteristic
375C22⋊C4—41no—
376C22⋊C4—41no—
377C22⋊C4—41no—
378C22⋊C4—41no—
379C22⋊C4—41no—
380C22⋊C4—41no—
381C22⋊C4—41no—
382C22⋊C4D8×C4111yescharacteristic
383C22⋊C4D8×C4111yescharacteristic
384C42—41no—
385C42—41no—
386C42—41no—
387C42—41no—
388C42—41no—
389C42C2×D4×C4111yescharacteristic
390C16—21no—
391C16—21no—
392C16—21no—
393C16#41×C4112yes—
394C23C2×D8×C4111yescharacteristic
395C23C2×D8×C4111yescharacteristic
396Q8—41no—
397Q8—41no—
398Q8—41no—
399Q8—41no—
400Q8—82no—
401D4—41no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—82no—
415C2×C4C2×D8×C4111yescharacteristic
416C2×C4C2×D8×C4111yescharacteristic
417C2×C4C2×D8×C4111yescharacteristic
418C2×C4C2×D8×C4111yescharacteristic
419C2×C4C22×D4×C4111yescharacteristic
420C8—21no—
421C8—21no—
422C8—21no—
423C8C2×#41×C4111yescharacteristic
424C82−1+4×C4111yescharacteristic
425C22—21no—
426C22—21no—
427C22—21no—
428C22—21no—
429C22—21no—
430C22—21no—
431C22C22×D8×C4111yescharacteristic
432C4—21no—
433C4—21no—
434C4—21no—
435C4—21no—
436C4—81no—
437C4—81no—
438C4—81no—
439C4—81no—
440C4—81no—
441C4—81no—
442C4—81no—
443C4—81no—
444C4C41×#54711yescharacteristic
445C4C41×#57811yescharacteristic
446C2—41no—
447C2—41no—
448C2C41×#333411yescharacteristic
449C2C41×#341411yescharacteristic
450C2C41×#341711yescharacteristic
subgroupG/H
center, socleC22×C41C22×D8
commutator, Frattini, cosocleC2×C8C24×C41
prime radicalC2×D4×C41D8
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C41 ◁ C4×D4×C41 ◁ C8×D4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
3. C41×#2255C2semidirect
4. C41×#2237C2semidirect
5. C41×#2237C2semidirect
6. C41×#2237C2semidirect
7. C41×#2236C2semidirect
8. C41×#2229C2semidirect
9. C41×#2227C2semidirect
10. C41×#2219C2semidirect
11. C41×#2216C2semidirect
12. C41×#2176C2semidirect
14. C41×#2159C2semidirect
15. C41×#2158C2semidirect
199. #33916C41direct (N × H)
223. #2255C2×C41semidirect
224. #2237C2×C41semidirect
225. #2237C2×C41semidirect
226. #2237C2×C41semidirect
227. #2236C2×C41semidirect
228. #2229C2×C41semidirect
229. #2227C2×C41semidirect
230. #2219C2×C41semidirect
231. #2216C2×C41semidirect
232. #2176C2×C41semidirect
234. #2159C2×C41semidirect
235. #2158C2×C41semidirect
284. C41#33916direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#33422
C41×#33362
C41×#22552
C41×#22372
C41×#22362
C41×#22292
C41×#22272
C41×#22192
C41×#22162
C41×#21762
C41×#21682
C41×#21592
C41×#21582
#3391641