Finite Group Databasebeta

← C41×#9057 #23785258

Subgroups — C41×#9057 #23785258

Order 10496.

690 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
1C2×C41×#486C211yesmaximal, characteristic
2C41×#2366C211yesmaximal, characteristic
3C41×#1988C211yesmaximal, characteristic, complemented
4C41×#1981C211yesmaximal, characteristic, complemented
5C2×C41×#331C211yesmaximal, characteristic
6C41×#1279C211yesmaximal, characteristic, complemented
7C41×#1279C211yesmaximal, characteristic, complemented
8C2×C4⋊Q8×C41C2211yescharacteristic
9C2×#127×C41C2211yescharacteristic
10C2×C4×D4×C41—21no—
11C2×C4×D4×C41—21no—
12C41×#486—22no—
13C41×#486C414yescomplemented
14C2×C4⋊C8×C41C2211yescharacteristic
15C2×C4⋊C8×C41C2211yescharacteristic
16C2×#103×C41—21no—
17C2×#103×C41—21no—
18C2×#102×C41—22no—
19C2×C4×C8×C41C2211yescharacteristic
20C41×#390—21no—
21C41×#390—21no—
22C41×#386—22no—
23C4×C4⋊C4×C41C2211yescharacteristic
24C4×C4⋊C4×C41C2211yescharacteristic
25C41×#340—21no—
26C41×#340—21no—
27C41×#331—22no—
28C22×Q8×C41—21no—
29C22×D4×C41—21no—
30C22×D4×C41—21no—
31C22×D4×C41D412yes—
32C23×C4×C41—22no—
33C22×C8×C41—21no—
34C22×C8×C41—21no—
35C22×C8×C41—21no—
36C4⋊Q8×C41—21no—
37C4⋊Q8×C41—21no—
38C4⋊Q8×C41—21no—
39C4⋊Q8×C41C2×C412yescomplemented
40#127×C41—21no—
41#127×C41—21no—
42#127×C41C2×C412yes—
43#127×C41D412yes—
44C4×D4×C41—42no—
45C4×D4×C41—42no—
46C4×D4×C41—42no—
47C4×D4×C41—42no—
48C2×C4⋊C4×C41—21no—
49C2×C4⋊C4×C41—21no—
50C2×C4⋊C4×C41D411yescharacteristic
51C2×C4⋊C4×C41D411yescharacteristic
52C2×C4⋊C4×C41D411yescharacteristic
53C2×C4⋊C4×C41D411yescharacteristic
54C2×C22⋊C4×C41—22no—
55C2×C22⋊C4×C41—22no—
56C2×C22⋊C4×C41—22no—
57C2×C42×C41—21no—
58C2×C42×C41—21no—
59C2×C42×C41C2311yescharacteristic
60C4⋊C8×C41—21no—
61C4⋊C8×C41—21no—
62C4⋊C8×C41—21no—
63C4⋊C8×C41—21no—
64#103×C41—42no—
65#103×C41—42no—
66#102×C41—28no—
67C4×C8×C41—21no—
68C4×C8×C41C2×C412yescomplemented
69#95×C41—21no—
70#95×C41—21no—
71C24×C41—22no—
72C2×Q8×C41—22no—
73C2×Q8×C41—41no—
74C2×Q8×C41—41no—
75C2×Q8×C41—41no—
76C2×Q8×C41—41no—
77C2×Q8×C41—41no—
78C2×D4×C41—22no—
79C2×D4×C41—22no—
80C2×D4×C41—22no—
81C2×D4×C41—22no—
82C2×D4×C41—22no—
83C2×D4×C41—42no—
84C2×D4×C41—42no—
85C2×D4×C41—41no—
86C2×D4×C41—41no—
87C2×D4×C41—41no—
88C2×D4×C41—41no—
89C2×D4×C41—41no—
90C2×D4×C41—41no—
91C2×D4×C41—41no—
92C2×D4×C41—41no—
93C2×D4×C41C22⋊C414yes—
94C22×C4×C41—21no—
95C22×C4×C41—21no—
96C22×C4×C41—21no—
97C22×C4×C41—21no—
98C22×C4×C41—44no—
99C22×C4×C41—44no—
100C22×C4×C41—41no—
101C22×C4×C41—82no—
102C22×C4×C41C2×D411yescharacteristic
103C22×C4×C41C2×D411yescharacteristic
104C22×C4×C41C2×D411yescharacteristic
105C2×C8×C41—22no—
106C2×C8×C41—41no—
107C2×C8×C41—41no—
108C2×C8×C41—41no—
109C2×C8×C41—41no—
110C2×C8×C41—41no—
111C2×C8×C41—41no—
112C2×C8×C41—41no—
113C2×C8×C41—41no—
114C4⋊C4×C41—21no—
115C4⋊C4×C41—21no—
116C4⋊C4×C41—22no—
117C4⋊C4×C41—22no—
118C4⋊C4×C41—21no—
119C4⋊C4×C41—21no—
120C4⋊C4×C41—21no—
121C4⋊C4×C41—21no—
122C4⋊C4×C41—41no—
123C4⋊C4×C41—41no—
124C4⋊C4×C41D812yes—
125C4⋊C4×C41SD1612yes—
126C22⋊C4×C41—44no—
127C22⋊C4×C41—44no—
128C22⋊C4×C41—82no—
129C42×C41—41no—
130C42×C41—41no—
131C42×C41—41no—
132C42×C41—41no—
133C42×C41C22×C411yescharacteristic
134C42×C41C2×D411yescharacteristic
135C42×C41#4111yescharacteristic
136C42×C41#4111yescharacteristic
137C23×C41—24no—
138C23×C41—42no—
139C23×C41—42no—
140C23×C41—42no—
141C23×C41—42no—
142C23×C41—42no—
143C23×C41—42no—
144C23×C41#12011yescharacteristic
145Q8×C41—42no—
146Q8×C41—42no—
147Q8×C41—81no—
148Q8×C41—81no—
149D4×C41—44no—
150D4×C41—42no—
151D4×C41—42no—
152D4×C41—42no—
153D4×C41—42no—
154D4×C41—42no—
155D4×C41—42no—
156D4×C41—42no—
157D4×C41—42no—
158D4×C41—82no—
159C2×C4×C41—21no—
160C2×C4×C41—21no—
161C2×C4×C41—22no—
162C2×C4×C41—22no—
163C2×C4×C41—41no—
164C2×C4×C41—41no—
165C2×C4×C41—41no—
166C2×C4×C41—41no—
167C2×C4×C41—42no—
168C2×C4×C41—41no—
169C2×C4×C41—41no—
170C2×C4×C41—41no—
171C2×C4×C41—41no—
172C2×C4×C41—41no—
173C2×C4×C41—41no—
174C2×C4×C41—88no—
175C2×C4×C41—81no—
176C2×C4×C41—81no—
177C2×C4×C41C2×C22⋊C411yescharacteristic
178C2×C4×C41C4×D411yescharacteristic
179C2×C4×C41C4×D411yescharacteristic
180C2×C4×C41#12111yescharacteristic
181C2×C4×C41#12111yescharacteristic
182C2×C4×C41#12311yescharacteristic
183C2×C4×C41C2×D811yescharacteristic
184C2×C4×C41C2×SD1611yescharacteristic
185C2×C4×C41#13511yescharacteristic
186C2×C4×C41#13511yescharacteristic
187C2×C4×C41AGL(1,ℤ/8)11yescharacteristic
188C2×C4×C41AGL(1,ℤ/8)11yescharacteristic
189C2×C4×C41AGL(1,ℤ/8)11yescharacteristic
190C2×C4×C41#13711yescharacteristic
191C8×C41—42no—
192C8×C41—81no—
193C8×C41—81no—
194#9057C4111yesmaximal, characteristic, direct product factor, Sylow
195C22×C41—44no—
196C22×C41—44no—
197C22×C41—44no—
198C22×C41—82no—
199C22×C41—82no—
200C22×C41—82no—
201C22×C41—82no—
202C22×C41#38611yescharacteristic
203C22×C41#44711yescharacteristic
204C22×C41#44911yescharacteristic
205C22×C41#45011yescharacteristic
206C22×C41#45211yescharacteristic
207C22×C41#45511yescharacteristic
208C22×C41#45511yescharacteristic
209C4×C41—21no—
210C4×C41—21no—
211C4×C41—42no—
212C4×C41—42no—
213C4×C41—82no—
214C4×C41—81no—
215C4×C41—81no—
216C4×C41C4×D811yescharacteristic
217C4×C41C4×SD1611yescharacteristic
218C4×C41#44011yescharacteristic
219C4×C41#44211yescharacteristic
220C4×C41#45911yescharacteristic
221C4×C41#46111yescharacteristic
222C4×C41#46311yescharacteristic
223C4×C41#46311yescharacteristic
224C2×#486C2×C4111yescharacteristic
225#2366C2×C4111yescharacteristic
226#1988C2×C4111yescharacteristic, complemented
227#1981C2×C4111yescharacteristic, complemented
228C2×#331C2×C4111yescharacteristic
229#1279C2×C4111yescharacteristic, complemented
230#1279C2×C4111yescharacteristic, complemented
231C2×C41—84no—
232C2×C41#163911yescharacteristic
233C2×C41#164011yescharacteristic
234C2×C41#164111yescharacteristic
235C2×C41#164211yescharacteristic
236C2×C41#187711yescharacteristic
237C2×C41#187911yescharacteristic
238C2×C41#188511yescharacteristic
239C2×C4⋊Q8C22×C4111yescharacteristic
240C2×#127C22×C4111yescharacteristic
241C2×C4×D4—21no—
242C2×C4×D4—21no—
243#486—22no—
244#486C4×C4114yescomplemented
245C2×C4⋊C8C22×C4111yescharacteristic
246C2×C4⋊C8C22×C4111yescharacteristic
247C2×#103—21no—
248C2×#103—21no—
249C2×#102—22no—
250C2×C4×C8C22×C4111yescharacteristic
251#390—21no—
252#390—21no—
253#386—22no—
254C4×C4⋊C4C22×C4111yescharacteristic
255C4×C4⋊C4C22×C4111yescharacteristic
256#340—21no—
257#340—21no—
258#331—22no—
259C41#905711yescharacteristic, direct product factor, Sylow
260C22×Q8—21no—
261C22×D4—21no—
262C22×D4—21no—
263C22×D4D4×C4112yes—
264C23×C4—22no—
265C22×C8—21no—
266C22×C8—21no—
267C22×C8—21no—
268C4⋊Q8—21no—
269C4⋊Q8—21no—
270C4⋊Q8—21no—
271C4⋊Q8C2×C4×C4112yescomplemented
272#127—21no—
273#127—21no—
274#127C2×C4×C4112yes—
275#127D4×C4112yes—
276C4×D4—42no—
277C4×D4—42no—
278C4×D4—42no—
279C4×D4—42no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4D4×C4111yescharacteristic
283C2×C4⋊C4D4×C4111yescharacteristic
284C2×C4⋊C4D4×C4111yescharacteristic
285C2×C4⋊C4D4×C4111yescharacteristic
286C2×C22⋊C4—22no—
287C2×C22⋊C4—22no—
288C2×C22⋊C4—22no—
289C2×C42—21no—
290C2×C42—21no—
291C2×C42C23×C4111yescharacteristic
292C4⋊C8—21no—
293C4⋊C8—21no—
294C4⋊C8—21no—
295C4⋊C8—21no—
296#103—42no—
297#103—42no—
298#102—28no—
299C4×C8—21no—
300C4×C8C2×C4×C4112yescomplemented
301#95—21no—
302#95—21no—
303C24—22no—
304C2×Q8—22no—
305C2×Q8—41no—
306C2×Q8—41no—
307C2×Q8—41no—
308C2×Q8—41no—
309C2×Q8—41no—
310C2×D4—22no—
311C2×D4—22no—
312C2×D4—22no—
313C2×D4—22no—
314C2×D4—22no—
315C2×D4—42no—
316C2×D4—42no—
317C2×D4—41no—
318C2×D4—41no—
319C2×D4—41no—
320C2×D4—41no—
321C2×D4—41no—
322C2×D4—41no—
323C2×D4—41no—
324C2×D4—41no—
325C2×D4C22⋊C4×C4114yes—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—44no—
331C22×C4—44no—
332C22×C4—41no—
333C22×C4—82no—
334C22×C4C2×D4×C4111yescharacteristic
335C22×C4C2×D4×C4111yescharacteristic
336C22×C4C2×D4×C4111yescharacteristic
337C2×C8—22no—
338C2×C8—41no—
339C2×C8—41no—
340C2×C8—41no—
341C2×C8—41no—
342C2×C8—41no—
343C2×C8—41no—
344C2×C8—41no—
345C2×C8—41no—
346C4⋊C4—21no—
347C4⋊C4—21no—
348C4⋊C4—22no—
349C4⋊C4—22no—
350C4⋊C4—21no—
351C4⋊C4—21no—
352C4⋊C4—21no—
353C4⋊C4—21no—
354C4⋊C4—41no—
355C4⋊C4—41no—
356C4⋊C4D8×C4112yes—
357C4⋊C4SD16×C4112yes—
358C22⋊C4—44no—
359C22⋊C4—44no—
360C22⋊C4—82no—
361C42—41no—
362C42—41no—
363C42—41no—
364C42—41no—
365C42C22×C4×C4111yescharacteristic
366C42C2×D4×C4111yescharacteristic
367C42#41×C4111yescharacteristic
368C42#41×C4111yescharacteristic
369C23—24no—
370C23—42no—
371C23—42no—
372C23—42no—
373C23—42no—
374C23—42no—
375C23—42no—
376C23#120×C4111yescharacteristic
377Q8—42no—
378Q8—42no—
379Q8—81no—
380Q8—81no—
381D4—44no—
382D4—42no—
383D4—42no—
384D4—42no—
385D4—42no—
386D4—42no—
387D4—42no—
388D4—42no—
389D4—42no—
390D4—82no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—42no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—88no—
407C2×C4—81no—
408C2×C4—81no—
409C2×C4C2×C22⋊C4×C4111yescharacteristic
410C2×C4C4×D4×C4111yescharacteristic
411C2×C4C4×D4×C4111yescharacteristic
412C2×C4#121×C4111yescharacteristic
413C2×C4#121×C4111yescharacteristic
414C2×C4#123×C4111yescharacteristic
415C2×C4C2×D8×C4111yescharacteristic
416C2×C4C2×SD16×C4111yescharacteristic
417C2×C4#135×C4111yescharacteristic
418C2×C4#135×C4111yescharacteristic
419C2×C4AGL(1,ℤ/8)×C4111yescharacteristic
420C2×C4AGL(1,ℤ/8)×C4111yescharacteristic
421C2×C4AGL(1,ℤ/8)×C4111yescharacteristic
422C2×C4#137×C4111yescharacteristic
423C8—42no—
424C8—81no—
425C8—81no—
426C22—44no—
427C22—44no—
428C22—44no—
429C22—82no—
430C22—82no—
431C22—82no—
432C22—82no—
433C22C41×#38611yescharacteristic
434C22C41×#44711yescharacteristic
435C22C41×#44911yescharacteristic
436C22C41×#45011yescharacteristic
437C22C41×#45211yescharacteristic
438C22C41×#45511yescharacteristic
439C22C41×#45511yescharacteristic
440C4—21no—
441C4—21no—
442C4—42no—
443C4—42no—
444C4—82no—
445C4—81no—
446C4—81no—
447C4C4×D8×C4111yescharacteristic
448C4C4×SD16×C4111yescharacteristic
449C4C41×#44011yescharacteristic
450C4C41×#44211yescharacteristic
451C4C41×#45911yescharacteristic
452C4C41×#46111yescharacteristic
453C4C41×#46311yescharacteristic
454C4C41×#46311yescharacteristic
455C2—84no—
456C2C41×#163911yescharacteristic
457C2C41×#164011yescharacteristic
458C2C41×#164111yescharacteristic
459C2C41×#164211yescharacteristic
460C2C41×#187711yescharacteristic
461C2C41×#187911yescharacteristic
462C2C41×#188511yescharacteristic
subgroupG/H
center, socleC23×C41#120
commutatorC42C22×C4×C41
Frattini, cosocleC2×C42C23×C41
prime radicalC2×#127×C41C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C41 ◁ C2×C42×C41 ◁ G

Complements

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

NH ≅ G/Ntype
3. C41×#1988C2semidirect
4. C41×#1981C2semidirect
6. C41×#1279C2semidirect
7. C41×#1279C2semidirect
13. C41×#486C4semidirect
39. C4⋊Q8×C41C2×C4semidirect
68. C4×C8×C41C2×C4semidirect
194. #9057C41direct (N × H)
226. #1988C2×C41semidirect
227. #1981C2×C41semidirect
229. #1279C2×C41semidirect
230. #1279C2×C41semidirect
244. #486C4×C41semidirect
259. C41#9057direct (N × H)
271. C4⋊Q8C2×C4×C41semidirect
300. C4×C8C2×C4×C41semidirect

Maximal subgroups

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

subgroupindex
C2×C41×#4862
C41×#23662
C41×#19882
C41×#19812
C2×C41×#3312
C41×#12792
#905741