Finite Group Databasebeta

← C41×#12990 #23789191

Subgroups — C41×#12990 #23789191

Order 10496.

518 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3050C211yesmaximal, characteristic
2C22×#108×C41C211yesmaximal, characteristic, complemented
3C2×C41×#359C212yesmaximal, complemented
4C2×C41×C22⋊C16C211yesmaximal, characteristic, complemented
5C41×#1382C212yesmaximal, complemented
6C2×#135×C41C2211yescharacteristic
7C22×M16×C41—21no—
8C23×C8×C41C2211yescharacteristic
9C41×#525—21no—
10C22×C16×C41C2212yes—
11C41×#467C411yescharacteristic
12C41×#467C411yescharacteristic
13C41×#466C411yescharacteristic
14C41×#466C411yescharacteristic
15C41×#465—21no—
16C41×#465—21no—
17C2×#108×C41—21no—
18C2×#108×C41—24no—
19C2×#108×C41C2212yes—
20C41×#427C2211yescharacteristic
21C41×#416—21no—
22C41×#359—24no—
23C41×C22⋊C16—21no—
24C41×C22⋊C16—21no—
25C2×#41×C41—21no—
26C23×C4×C41D411yescharacteristic
27#135×C41—22no—
28#135×C41—22no—
29C2×Q16×C41C2×C411yescharacteristic
30C2×SD16×C41—21no—
31C2×D8×C41C2×C411yescharacteristic
32C2×M16×C41—24no—
33C2×M16×C41—22no—
34C2×M16×C41—42no—
35C2×M16×C41—41no—
36C22×C8×C41—22no—
37C22×C8×C41—22no—
38C22×C8×C41—41no—
39C22×C8×C41C2×C411yescharacteristic
40C22×C8×C41C2×C411yescharacteristic
41C22×C8×C41D411yescharacteristic
42C22×C8×C41D411yescharacteristic
43C22×C8×C41D411yescharacteristic
44C22×C8×C41C2311yescharacteristic
45#123×C41—41no—
46C22⋊Q8×C41—21no—
47C22⋊Q8×C41—21no—
48#121×C41—21no—
49#121×C41—21no—
50#120×C41—41no—
51C4×D4×C41—41no—
52C4×D4×C41—41no—
53#117×C41—21no—
54C2×C16×C41—22no—
55C2×C16×C41—22no—
56C2×C16×C41—22no—
57#108×C41—24no—
58#108×C41—22no—
59#108×C41D414yescomplemented
60#107×C41C2×C411yescharacteristic
61#107×C41C2×C411yescharacteristic
62#106×C41—21no—
63#103×C41—21no—
64#103×C41—21no—
65#102×C41—21no—
66#102×C41—21no—
67C24×C41SD1611yescharacteristic
68#41×C41—41no—
69#41×C41—41no—
70#41×C41—41no—
71#41×C41—41no—
72C2×Q8×C41—21no—
73C2×D4×C41—21no—
74C2×D4×C41—41no—
75C2×D4×C41—41no—
76C2×D4×C41—41no—
77C22×C4×C41—21no—
78C22×C4×C41—21no—
79C22×C4×C41—21no—
80C22×C4×C41—21no—
81C22×C4×C41—41no—
82C22×C4×C41C22⋊C411yescharacteristic
83C22×C4×C41C22⋊C411yescharacteristic
84C22×C4×C41D811yescharacteristic
85C22×C4×C41D811yescharacteristic
86C22×C4×C41SD1611yescharacteristic
87C22×C4×C41C2×D411yescharacteristic
88Q16×C41—22no—
89SD16×C41—42no—
90D8×C41—22no—
91M16×C41—24no—
92M16×C41—44no—
93M16×C41—42no—
94C2×C8×C41—21no—
95C2×C8×C41—21no—
96C2×C8×C41—22no—
97C2×C8×C41—22no—
98C2×C8×C41—22no—
99C2×C8×C41—22no—
100C2×C8×C41—44no—
101C2×C8×C41—42no—
102C2×C8×C41C22⋊C411yescharacteristic
103C2×C8×C41C22⋊C411yescharacteristic
104C2×C8×C41C22×C411yescharacteristic
105C2×C8×C41C2×D412yes—
106C2×C8×C41C2×D411yescharacteristic
107C2×C8×C41#4112yes—
108C4⋊C4×C41—21no—
109C4⋊C4×C41—21no—
110C4⋊C4×C41—41no—
111C4⋊C4×C41—41no—
112C22⋊C4×C41—41no—
113C22⋊C4×C41—41no—
114C22⋊C4×C41—41no—
115C22⋊C4×C41—41no—
116C22⋊C4×C41—41no—
117C42×C41—41no—
118C16×C41—42no—
119C23×C41—22no—
120C23×C41—21no—
121C23×C41—21no—
122C23×C41—41no—
123C23×C41—41no—
124C23×C41#10211yescharacteristic
125C23×C41#10211yescharacteristic
126C23×C41C2×SD1611yescharacteristic
127Q8×C41—41no—
128Q8×C41—41no—
129D4×C41—41no—
130D4×C41—41no—
131D4×C41—82no—
132D4×C41—82no—
133D4×C41—81no—
134D4×C41—81no—
135C2×C4×C41—21no—
136C2×C4×C41—21no—
137C2×C4×C41—21no—
138C2×C4×C41—21no—
139C2×C4×C41—21no—
140C2×C4×C41—21no—
141C2×C4×C41—21no—
142C2×C4×C41—21no—
143C2×C4×C41—21no—
144C2×C4×C41—21no—
145C2×C4×C41—41no—
146C2×C4×C41—41no—
147C2×C4×C41—41no—
148C2×C4×C41—81no—
149C2×C4×C41—81no—
150C2×C4×C41#10211yescharacteristic
151C2×C4×C41#10211yescharacteristic
152C2×C4×C41C2×C22⋊C411yescharacteristic
153C2×C4×C41#12011yescharacteristic
154C2×C4×C41#12311yescharacteristic
155C2×C4×C41C2×D811yescharacteristic
156C2×C4×C41AGL(1,ℤ/8)11yescharacteristic
157C2×C4×C41#13711yescharacteristic
158C8×C41—21no—
159C8×C41—21no—
160C8×C41—44no—
161C8×C41C4×D412yes—
162C8×C41#12112yes—
163#12990C4111yesmaximal, characteristic, direct product factor, Sylow
164C22×C41—21no—
165C22×C41—21no—
166C22×C41—21no—
167C22×C41—21no—
168C22×C41—21no—
169C22×C41—21no—
170C22×C41—21no—
171C22×C41—42no—
172C22×C41—42no—
173C22×C41—81no—
174C22×C41—81no—
175C22×C41—81no—
176C22×C41#35912yescomplemented
177C22×C41C2×#10211yescharacteristic
178C22×C41#44811yescharacteristic
179C22×C41#48111yescharacteristic
180C4×C41—21no—
181C4×C41—21no—
182C4×C41—81no—
183C4×C41—81no—
184C4×C41—81no—
185C4×C41#38611yescharacteristic
186C4×C41#41711yescharacteristic
187C4×C41#44711yescharacteristic
188C4×C41#48011yescharacteristic
189#3050C2×C4111yescharacteristic
190C22×#108C2×C4111yescharacteristic, complemented
191C2×#359C2×C4112yescomplemented
192C2×C22⋊C16C2×C4111yescharacteristic, complemented
193#1382C2×C4112yescomplemented
194C2×C41—22no—
195C2×C41—21no—
196C2×C41—21no—
197C2×C41—41no—
198C2×C41—161no—
199C2×C41#187411yescharacteristic
200C2×C41C2×#35911yescharacteristic
201C2×C41#214311yescharacteristic
202C2×#135C22×C4111yescharacteristic
203C22×M16—21no—
204C23×C8C22×C4111yescharacteristic
205#525—21no—
206C22×C16C22×C4112yes—
207#467C4×C4111yescharacteristic
208#467C4×C4111yescharacteristic
209#466C4×C4111yescharacteristic
210#466C4×C4111yescharacteristic
211#465—21no—
212#465—21no—
213C2×#108—21no—
214C2×#108—24no—
215C2×#108C22×C4112yes—
216#427C22×C4111yescharacteristic
217#416—21no—
218#359—24no—
219C22⋊C16—21no—
220C22⋊C16—21no—
221C41#1299011yescharacteristic, direct product factor, Sylow
222C2×#41—21no—
223C23×C4D4×C4111yescharacteristic
224#135—22no—
225#135—22no—
226C2×Q16C2×C4×C4111yescharacteristic
227C2×SD16—21no—
228C2×D8C2×C4×C4111yescharacteristic
229C2×M16—24no—
230C2×M16—22no—
231C2×M16—42no—
232C2×M16—41no—
233C22×C8—22no—
234C22×C8—22no—
235C22×C8—41no—
236C22×C8C2×C4×C4111yescharacteristic
237C22×C8C2×C4×C4111yescharacteristic
238C22×C8D4×C4111yescharacteristic
239C22×C8D4×C4111yescharacteristic
240C22×C8D4×C4111yescharacteristic
241C22×C8C23×C4111yescharacteristic
242#123—41no—
243C22⋊Q8—21no—
244C22⋊Q8—21no—
245#121—21no—
246#121—21no—
247#120—41no—
248C4×D4—41no—
249C4×D4—41no—
250#117—21no—
251C2×C16—22no—
252C2×C16—22no—
253C2×C16—22no—
254#108—24no—
255#108—22no—
256#108D4×C4114yescomplemented
257#107C2×C4×C4111yescharacteristic
258#107C2×C4×C4111yescharacteristic
259#106—21no—
260#103—21no—
261#103—21no—
262#102—21no—
263#102—21no—
264C24SD16×C4111yescharacteristic
265#41—41no—
266#41—41no—
267#41—41no—
268#41—41no—
269C2×Q8—21no—
270C2×D4—21no—
271C2×D4—41no—
272C2×D4—41no—
273C2×D4—41no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—41no—
279C22×C4C22⋊C4×C4111yescharacteristic
280C22×C4C22⋊C4×C4111yescharacteristic
281C22×C4D8×C4111yescharacteristic
282C22×C4D8×C4111yescharacteristic
283C22×C4SD16×C4111yescharacteristic
284C22×C4C2×D4×C4111yescharacteristic
285Q16—22no—
286SD16—42no—
287D8—22no—
288M16—24no—
289M16—44no—
290M16—42no—
291C2×C8—21no—
292C2×C8—21no—
293C2×C8—22no—
294C2×C8—22no—
295C2×C8—22no—
296C2×C8—22no—
297C2×C8—44no—
298C2×C8—42no—
299C2×C8C22⋊C4×C4111yescharacteristic
300C2×C8C22⋊C4×C4111yescharacteristic
301C2×C8C22×C4×C4111yescharacteristic
302C2×C8C2×D4×C4112yes—
303C2×C8C2×D4×C4111yescharacteristic
304C2×C8#41×C4112yes—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C22⋊C4—41no—
310C22⋊C4—41no—
311C22⋊C4—41no—
312C22⋊C4—41no—
313C22⋊C4—41no—
314C42—41no—
315C16—42no—
316C23—22no—
317C23—21no—
318C23—21no—
319C23—41no—
320C23—41no—
321C23#102×C4111yescharacteristic
322C23#102×C4111yescharacteristic
323C23C2×SD16×C4111yescharacteristic
324Q8—41no—
325Q8—41no—
326D4—41no—
327D4—41no—
328D4—82no—
329D4—82no—
330D4—81no—
331D4—81no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—81no—
346C2×C4—81no—
347C2×C4#102×C4111yescharacteristic
348C2×C4#102×C4111yescharacteristic
349C2×C4C2×C22⋊C4×C4111yescharacteristic
350C2×C4#120×C4111yescharacteristic
351C2×C4#123×C4111yescharacteristic
352C2×C4C2×D8×C4111yescharacteristic
353C2×C4AGL(1,ℤ/8)×C4111yescharacteristic
354C2×C4#137×C4111yescharacteristic
355C8—21no—
356C8—21no—
357C8—44no—
358C8C4×D4×C4112yes—
359C8#121×C4112yes—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—42no—
368C22—42no—
369C22—81no—
370C22—81no—
371C22—81no—
372C22C41×#35912yescomplemented
373C22C2×#102×C4111yescharacteristic
374C22C41×#44811yescharacteristic
375C22C41×#48111yescharacteristic
376C4—21no—
377C4—21no—
378C4—81no—
379C4—81no—
380C4—81no—
381C4C41×#38611yescharacteristic
382C4C41×#41711yescharacteristic
383C4C41×#44711yescharacteristic
384C4C41×#48011yescharacteristic
385C2—22no—
386C2—21no—
387C2—21no—
388C2—41no—
389C2—161no—
390C2C41×#187411yescharacteristic
391C2C2×C41×#35911yescharacteristic
392C2C41×#214311yescharacteristic
subgroupG/H
centerC2×C4×C41C2×D8
commutatorC2×C8C22×C4×C41
Frattini, cosocleC22×C8C23×C41
socleC22×C41C2×#102
prime radicalC41×#3050C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C41 ◁ C23×C4×C41 ◁ C23×C8×C41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×#108×C41C2semidirect
3. C2×C41×#359C2semidirect
4. C2×C41×C22⋊C16C2semidirect
5. C41×#1382C2semidirect
59. #108×C41D4semidirect
163. #12990C41direct (N × H)
176. C22×C41#359semidirect
190. C22×#108C2×C41semidirect
191. C2×#359C2×C41semidirect
192. C2×C22⋊C16C2×C41semidirect
193. #1382C2×C41semidirect
221. C41#12990direct (N × H)
256. #108D4×C41semidirect
372. C22C41×#359semidirect

Maximal subgroups

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

subgroupindex
C41×#30502
C22×#108×C412
C2×C41×#3592
C2×C41×C22⋊C162
C41×#13822
#1299041