Finite Group Databasebeta

← C41×#33879 #23810080

Subgroups — C41×#33879 #23810080

Order 10496.

536 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3336C211yesmaximal, characteristic
2D4×Q16×C41C211yesmaximal, characteristic
3C41×#2245C211yesmaximal, characteristic, complemented
4C41×#2237C211yesmaximal, characteristic, complemented
5C41×#2235C211yesmaximal, characteristic, complemented
6C41×#2229C211yesmaximal, characteristic, complemented
7C41×#2219C211yesmaximal, characteristic, complemented
8C41×#2216C211yesmaximal, characteristic, complemented
9C41×#2209C211yesmaximal, characteristic, complemented
10C41×#2188C211yesmaximal, characteristic, complemented
11C41×#2188C211yesmaximal, characteristic, complemented
12C41×#2176C211yesmaximal, characteristic, complemented
13C41×#2168C211yesmaximal, characteristic
14C41×#2141C211yesmaximal, characteristic, complemented
15C2×C41×#358C211yesmaximal, characteristic, complemented
16C22×Q16×C41C2211yescharacteristic
17C22×Q16×C41C2211yescharacteristic
18C41×#552—21no—
19D4×Q8×C41—21no—
20C2×Q32×C41C2211yescharacteristic
21C2×Q32×C41C2211yescharacteristic
22C2×Q32×C41C2211yescharacteristic
23C2×M32×C41C2211yescharacteristic
24C22×C16×C41C2211yescharacteristic
25C41×#499C2211yescharacteristic
26C41×#494C2211yescharacteristic
27C41×#485—21no—
28C41×#483—21no—
29C41×#479—21no—
30C41×#467C2211yescharacteristic
31C41×#467C2211yescharacteristic
32C41×#467C2211yescharacteristic
33C41×#467C2211yescharacteristic
34C41×#462—21no—
35C41×#451—21no—
36C41×#451—21no—
37C4×Q16×C41C2211yescharacteristic
38C4×Q16×C41C2211yescharacteristic
39C8×D4×C41C2211yescharacteristic
40C41×#427C2211yescharacteristic
41C2×#107×C41C2211yescharacteristic
42C41×#367C2211yescharacteristic
43C41×#367C2211yescharacteristic
44C41×#366C2211yescharacteristic
45C41×C4⋊C16C2211yescharacteristic
46C41×#358C2211yescharacteristic
47C41×#358C2211yescharacteristic
48C41×#358C2211yescharacteristic
49C41×#358C2211yescharacteristic
50C41×#358C2211yescharacteristic
51C41×#358C2211yescharacteristic
52C41×#358C2211yescharacteristic
53C41×#358C2211yescharacteristic
54C41×#358C2211yescharacteristic
55C41×#358C2211yescharacteristic
56C41×C22⋊C16C2211yescharacteristic
57C41×C22⋊C16C2211yescharacteristic
58C41×#346C2211yescharacteristic
59C22×Q8×C41—21no—
60C22×Q8×C41—21no—
61C2×Q16×C41—22no—
62C2×Q16×C41—22no—
63C2×Q16×C41—21no—
64C2×Q16×C41—21no—
65C2×Q16×C41—21no—
66C2×Q16×C41—41no—
67C2×Q16×C41—41no—
68C2×Q16×C41C2311yescharacteristic
69C2×Q16×C41C2311yescharacteristic
70C2×Q16×C41C2311yescharacteristic
71C2×Q16×C41C2311yescharacteristic
72C22×C8×C41C2311yescharacteristic
73C22×C8×C41C2311yescharacteristic
74C4⋊Q8×C41—21no—
75C4⋊Q8×C41—41no—
76#126×C41—41no—
77#125×C41—21no—
78#125×C41—41no—
79#123×C41—41no—
80C22⋊Q8×C41—21no—
81C22⋊Q8×C41—21no—
82C22⋊Q8×C41—21no—
83C22⋊Q8×C41—21no—
84C22⋊Q8×C41—41no—
85C22⋊Q8×C41—41no—
86C4×Q8×C41—21no—
87C4×Q8×C41—21no—
88C4×D4×C41—41no—
89C4×D4×C41D411yescharacteristic
90#117×C41—21no—
91#117×C41—41no—
92C2×C4⋊C4×C41—21no—
93Q32×C41—22no—
94Q32×C41—41no—
95Q32×C41—41no—
96M32×C41—41no—
97C2×C16×C41—41no—
98C2×C16×C41C2311yescharacteristic
99C2×C16×C41C2311yescharacteristic
100C2×C16×C41C2311yescharacteristic
101C2×C16×C41C2311yescharacteristic
102#107×C41—21no—
103#107×C41C2311yescharacteristic
104#107×C41C2311yescharacteristic
105#107×C41C2311yescharacteristic
106#107×C41C2311yescharacteristic
107#106×C41—21no—
108#106×C41—21no—
109C4⋊C8×C41D411yescharacteristic
110#103×C41—21no—
111#103×C41—21no—
112#103×C41—21no—
113#103×C41—21no—
114#103×C41—21no—
115#103×C41—21no—
116C22⋊C8×C41D411yescharacteristic
117C22⋊C8×C41D411yescharacteristic
118C4×C8×C41C2311yescharacteristic
119C2×Q8×C41—21no—
120C2×Q8×C41—21no—
121C2×Q8×C41—21no—
122C2×Q8×C41—21no—
123C2×Q8×C41—42no—
124C2×Q8×C41—42no—
125C2×Q8×C41—41no—
126C2×Q8×C41—41no—
127C2×Q8×C41—81no—
128C2×Q8×C41—81no—
129C2×D4×C41D811yescharacteristic
130C22×C4×C41—41no—
131C22×C4×C41—41no—
132C22×C4×C41—41no—
133C22×C4×C41C2×D411yescharacteristic
134C22×C4×C41C2×D411yescharacteristic
135Q16×C41—21no—
136Q16×C41—21no—
137Q16×C41—21no—
138Q16×C41—21no—
139Q16×C41—21no—
140Q16×C41—21no—
141Q16×C41—21no—
142Q16×C41—42no—
143Q16×C41—42no—
144Q16×C41—81no—
145Q16×C41#4112yes—
146C2×C8×C41—21no—
147C2×C8×C41—21no—
148C2×C8×C41—21no—
149C2×C8×C41—21no—
150C2×C8×C41C2×D411yescharacteristic
151C2×C8×C41C2×D411yescharacteristic
152C2×C8×C41C2×D411yescharacteristic
153C2×C8×C41C2411yescharacteristic
154C4⋊C4×C41—21no—
155C4⋊C4×C41—21no—
156C4⋊C4×C41—21no—
157C4⋊C4×C41—21no—
158C4⋊C4×C41—41no—
159C4⋊C4×C41—41no—
160C4⋊C4×C41—41no—
161C4⋊C4×C41—41no—
162C4⋊C4×C41—41no—
163C4⋊C4×C41—41no—
164C4⋊C4×C41—41no—
165C4⋊C4×C41—41no—
166C4⋊C4×C41—41no—
167C4⋊C4×C41—41no—
168C4⋊C4×C41—41no—
169C4⋊C4×C41D811yescharacteristic
170C22⋊C4×C41—41no—
171C22⋊C4×C41—41no—
172C22⋊C4×C41—41no—
173C22⋊C4×C41—41no—
174C22⋊C4×C41—41no—
175C22⋊C4×C41D811yescharacteristic
176C22⋊C4×C41D811yescharacteristic
177C42×C41—41no—
178C42×C41—41no—
179C42×C41—41no—
180C42×C41C2×D411yescharacteristic
181C16×C41—21no—
182C16×C41—21no—
183C16×C41—21no—
184C16×C41—21no—
185C23×C41C2×D811yescharacteristic
186C23×C41C2×D811yescharacteristic
187Q8×C41—22no—
188Q8×C41—41no—
189Q8×C41—41no—
190Q8×C41—41no—
191Q8×C41—41no—
192Q8×C41—41no—
193Q8×C41—41no—
194Q8×C41—41no—
195Q8×C41—82no—
196Q8×C41—82no—
197D4×C41—22no—
198C2×C4×C41—21no—
199C2×C4×C41—21no—
200C2×C4×C41—21no—
201C2×C4×C41—21no—
202C2×C4×C41—41no—
203C2×C4×C41—41no—
204C2×C4×C41—41no—
205C2×C4×C41—41no—
206C2×C4×C41—41no—
207C2×C4×C41—41no—
208C2×C4×C41—41no—
209C2×C4×C41—41no—
210C2×C4×C41—82no—
211C2×C4×C41—82no—
212C2×C4×C41—82no—
213C2×C4×C41C2×D811yescharacteristic
214C2×C4×C41C2×D811yescharacteristic
215C2×C4×C41C2×D811yescharacteristic
216C2×C4×C41C2×D811yescharacteristic
217C2×C4×C41C22×D411yescharacteristic
218C8×C41—21no—
219C8×C41—21no—
220C8×C41—21no—
221C8×C41C2×#4111yescharacteristic
222C8×C41H(5,𝔽2)11yescharacteristic
223#33879C4111yesmaximal, characteristic, direct product factor, Sylow
224C22×C41—21no—
225C22×C41—21no—
226C22×C41—21no—
227C22×C41—21no—
228C22×C41—21no—
229C22×C41#51012yes—
230C22×C41C22×D811yescharacteristic
231C4×C41—21no—
232C4×C41—21no—
233C4×C41—21no—
234C4×C41—21no—
235C4×C41—42no—
236C4×C41—81no—
237C4×C41—81no—
238C4×C41—81no—
239C4×C41—81no—
240C4×C41—81no—
241C4×C41—81no—
242C4×C41—81no—
243C4×C41#54611yescharacteristic
244C4×C41#57711yescharacteristic
245#3336C2×C4111yescharacteristic
246D4×Q16C2×C4111yescharacteristic
247#2245C2×C4111yescharacteristic, complemented
248#2237C2×C4111yescharacteristic, complemented
249#2235C2×C4111yescharacteristic, complemented
250#2229C2×C4111yescharacteristic, complemented
251#2219C2×C4111yescharacteristic, complemented
252#2216C2×C4111yescharacteristic, complemented
253#2209C2×C4111yescharacteristic, complemented
254#2188C2×C4111yescharacteristic, complemented
255#2188C2×C4111yescharacteristic, complemented
256#2176C2×C4111yescharacteristic, complemented
257#2168C2×C4111yescharacteristic
258#2141C2×C4111yescharacteristic, complemented
259C2×#358C2×C4111yescharacteristic, complemented
260C2×C41—22no—
261C2×C41—41no—
262C2×C41#329411yescharacteristic
263C2×C41C2×#51011yescharacteristic
264C2×C41#341711yescharacteristic
265C22×Q16C22×C4111yescharacteristic
266C22×Q16C22×C4111yescharacteristic
267#552—21no—
268D4×Q8—21no—
269C2×Q32C22×C4111yescharacteristic
270C2×Q32C22×C4111yescharacteristic
271C2×Q32C22×C4111yescharacteristic
272C2×M32C22×C4111yescharacteristic
273C22×C16C22×C4111yescharacteristic
274#499C22×C4111yescharacteristic
275#494C22×C4111yescharacteristic
276#485—21no—
277#483—21no—
278#479—21no—
279#467C22×C4111yescharacteristic
280#467C22×C4111yescharacteristic
281#467C22×C4111yescharacteristic
282#467C22×C4111yescharacteristic
283#462—21no—
284#451—21no—
285#451—21no—
286C4×Q16C22×C4111yescharacteristic
287C4×Q16C22×C4111yescharacteristic
288C8×D4C22×C4111yescharacteristic
289#427C22×C4111yescharacteristic
290C2×#107C22×C4111yescharacteristic
291#367C22×C4111yescharacteristic
292#367C22×C4111yescharacteristic
293#366C22×C4111yescharacteristic
294C4⋊C16C22×C4111yescharacteristic
295#358C22×C4111yescharacteristic
296#358C22×C4111yescharacteristic
297#358C22×C4111yescharacteristic
298#358C22×C4111yescharacteristic
299#358C22×C4111yescharacteristic
300#358C22×C4111yescharacteristic
301#358C22×C4111yescharacteristic
302#358C22×C4111yescharacteristic
303#358C22×C4111yescharacteristic
304#358C22×C4111yescharacteristic
305C22⋊C16C22×C4111yescharacteristic
306C22⋊C16C22×C4111yescharacteristic
307#346C22×C4111yescharacteristic
308C41#3387911yescharacteristic, direct product factor, Sylow
309C22×Q8—21no—
310C22×Q8—21no—
311C2×Q16—22no—
312C2×Q16—22no—
313C2×Q16—21no—
314C2×Q16—21no—
315C2×Q16—21no—
316C2×Q16—41no—
317C2×Q16—41no—
318C2×Q16C23×C4111yescharacteristic
319C2×Q16C23×C4111yescharacteristic
320C2×Q16C23×C4111yescharacteristic
321C2×Q16C23×C4111yescharacteristic
322C22×C8C23×C4111yescharacteristic
323C22×C8C23×C4111yescharacteristic
324C4⋊Q8—21no—
325C4⋊Q8—41no—
326#126—41no—
327#125—21no—
328#125—41no—
329#123—41no—
330C22⋊Q8—21no—
331C22⋊Q8—21no—
332C22⋊Q8—21no—
333C22⋊Q8—21no—
334C22⋊Q8—41no—
335C22⋊Q8—41no—
336C4×Q8—21no—
337C4×Q8—21no—
338C4×D4—41no—
339C4×D4D4×C4111yescharacteristic
340#117—21no—
341#117—41no—
342C2×C4⋊C4—21no—
343Q32—22no—
344Q32—41no—
345Q32—41no—
346M32—41no—
347C2×C16—41no—
348C2×C16C23×C4111yescharacteristic
349C2×C16C23×C4111yescharacteristic
350C2×C16C23×C4111yescharacteristic
351C2×C16C23×C4111yescharacteristic
352#107—21no—
353#107C23×C4111yescharacteristic
354#107C23×C4111yescharacteristic
355#107C23×C4111yescharacteristic
356#107C23×C4111yescharacteristic
357#106—21no—
358#106—21no—
359C4⋊C8D4×C4111yescharacteristic
360#103—21no—
361#103—21no—
362#103—21no—
363#103—21no—
364#103—21no—
365#103—21no—
366C22⋊C8D4×C4111yescharacteristic
367C22⋊C8D4×C4111yescharacteristic
368C4×C8C23×C4111yescharacteristic
369C2×Q8—21no—
370C2×Q8—21no—
371C2×Q8—21no—
372C2×Q8—21no—
373C2×Q8—42no—
374C2×Q8—42no—
375C2×Q8—41no—
376C2×Q8—41no—
377C2×Q8—81no—
378C2×Q8—81no—
379C2×D4D8×C4111yescharacteristic
380C22×C4—41no—
381C22×C4—41no—
382C22×C4—41no—
383C22×C4C2×D4×C4111yescharacteristic
384C22×C4C2×D4×C4111yescharacteristic
385Q16—21no—
386Q16—21no—
387Q16—21no—
388Q16—21no—
389Q16—21no—
390Q16—21no—
391Q16—21no—
392Q16—42no—
393Q16—42no—
394Q16—81no—
395Q16#41×C4112yes—
396C2×C8—21no—
397C2×C8—21no—
398C2×C8—21no—
399C2×C8—21no—
400C2×C8C2×D4×C4111yescharacteristic
401C2×C8C2×D4×C4111yescharacteristic
402C2×C8C2×D4×C4111yescharacteristic
403C2×C8C24×C4111yescharacteristic
404C4⋊C4—21no—
405C4⋊C4—21no—
406C4⋊C4—21no—
407C4⋊C4—21no—
408C4⋊C4—41no—
409C4⋊C4—41no—
410C4⋊C4—41no—
411C4⋊C4—41no—
412C4⋊C4—41no—
413C4⋊C4—41no—
414C4⋊C4—41no—
415C4⋊C4—41no—
416C4⋊C4—41no—
417C4⋊C4—41no—
418C4⋊C4—41no—
419C4⋊C4D8×C4111yescharacteristic
420C22⋊C4—41no—
421C22⋊C4—41no—
422C22⋊C4—41no—
423C22⋊C4—41no—
424C22⋊C4—41no—
425C22⋊C4D8×C4111yescharacteristic
426C22⋊C4D8×C4111yescharacteristic
427C42—41no—
428C42—41no—
429C42—41no—
430C42C2×D4×C4111yescharacteristic
431C16—21no—
432C16—21no—
433C16—21no—
434C16—21no—
435C23C2×D8×C4111yescharacteristic
436C23C2×D8×C4111yescharacteristic
437Q8—22no—
438Q8—41no—
439Q8—41no—
440Q8—41no—
441Q8—41no—
442Q8—41no—
443Q8—41no—
444Q8—41no—
445Q8—82no—
446Q8—82no—
447D4—22no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—82no—
461C2×C4—82no—
462C2×C4—82no—
463C2×C4C2×D8×C4111yescharacteristic
464C2×C4C2×D8×C4111yescharacteristic
465C2×C4C2×D8×C4111yescharacteristic
466C2×C4C2×D8×C4111yescharacteristic
467C2×C4C22×D4×C4111yescharacteristic
468C8—21no—
469C8—21no—
470C8—21no—
471C8C2×#41×C4111yescharacteristic
472C8H(5,𝔽2)×C4111yescharacteristic
473C22—21no—
474C22—21no—
475C22—21no—
476C22—21no—
477C22—21no—
478C22C41×#51012yes—
479C22C22×D8×C4111yescharacteristic
480C4—21no—
481C4—21no—
482C4—21no—
483C4—21no—
484C4—42no—
485C4—81no—
486C4—81no—
487C4—81no—
488C4—81no—
489C4—81no—
490C4—81no—
491C4—81no—
492C4C41×#54611yescharacteristic
493C4C41×#57711yescharacteristic
494C2—22no—
495C2—41no—
496C2C41×#329411yescharacteristic
497C2C2×C41×#51011yescharacteristic
498C2C41×#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×#2245C2semidirect
4. C41×#2237C2semidirect
5. C41×#2235C2semidirect
6. C41×#2229C2semidirect
7. C41×#2219C2semidirect
8. C41×#2216C2semidirect
9. C41×#2209C2semidirect
10. C41×#2188C2semidirect
11. C41×#2188C2semidirect
12. C41×#2176C2semidirect
14. C41×#2141C2semidirect
15. C2×C41×#358C2semidirect
223. #33879C41direct (N × H)
247. #2245C2×C41semidirect
248. #2237C2×C41semidirect
249. #2235C2×C41semidirect
250. #2229C2×C41semidirect
251. #2219C2×C41semidirect
252. #2216C2×C41semidirect
253. #2209C2×C41semidirect
254. #2188C2×C41semidirect
255. #2188C2×C41semidirect
256. #2176C2×C41semidirect
258. #2141C2×C41semidirect
259. C2×#358C2×C41semidirect
308. C41#33879direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#33362
D4×Q16×C412
C41×#22452
C41×#22372
C41×#22352
C41×#22292
C41×#22192
C41×#22162
C41×#22092
C41×#21882
C41×#21762
C41×#21682
C41×#21412
C2×C41×#3582
#3387941