Finite Group Databasebeta

← C41×#13027 #23789228

Subgroups — C41×#13027 #23789228

Order 10496.

484 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3414C211yesmaximal, characteristic
2C4×#135×C41C211yesmaximal, characteristic, complemented
3C41×#2145C211yesmaximal, characteristic, complemented
4C41×#2143C211yesmaximal, characteristic, complemented
5C41×#1974C211yesmaximal, characteristic, complemented
6C41×#1389C211yesmaximal, characteristic, complemented
7C41×#1376C211yesmaximal, characteristic, complemented
8C2×#135×C41C2211yescharacteristic
9C2×#135×C41C2211yescharacteristic
10C4×#41×C41—21no—
11C41×#510—21no—
12C41×#510C412yescomplemented
13C41×#509—21no—
14C41×#509C412yescomplemented
15C41×#508—22no—
16C2×M32×C41C2211yescharacteristic
17C2×M32×C41C2211yescharacteristic
18C4×Q16×C41—21no—
19C4×SD16×C41—22no—
20C4×D8×C41—21no—
21C2×#108×C41C2211yescharacteristic
22C41×#427C2211yescharacteristic
23C2×#104×C41—21no—
24C41×#416—21no—
25C41×#408—21no—
26C2×C4×C8×C41C2211yescharacteristic
27C41×#360—22no—
28C41×#359—22no—
29C2×#41×C41—21no—
30C2×#41×C41—21no—
31#135×C41—21no—
32#135×C41—21no—
33#135×C41—21no—
34#135×C41—21no—
35#135×C41—21no—
36#135×C41—21no—
37#135×C41C2×C412yes—
38#135×C41D412yes—
39C2×Q16×C41C2×C411yescharacteristic, complemented
40C2×Q16×C41D411yescharacteristic
41C2×SD16×C41—21no—
42C2×SD16×C41—21no—
43C2×D8×C41C2×C411yescharacteristic, complemented
44C2×D8×C41D411yescharacteristic
45C2×M16×C41—21no—
46C22×C8×C41D411yescharacteristic
47C22×C8×C41C2311yescharacteristic
48C4×Q8×C41—22no—
49C4×D4×C41—22no—
50C4×D4×C41—42no—
51#117×C41—21no—
52#117×C41—41no—
53C2×C42×C41—41no—
54C2×C42×C41D411yescharacteristic
55Q32×C41—22no—
56SD32×C41—22no—
57SD32×C41—22no—
58D16×C41—22no—
59M32×C41—21no—
60M32×C41—21no—
61M32×C41—21no—
62M32×C41C2×C412yescomplemented
63C2×C16×C41—21no—
64C2×C16×C41—21no—
65#108×C41—21no—
66#108×C41—21no—
67#107×C41—21no—
68#106×C41D412yes—
69#104×C41—41no—
70#104×C41—41no—
71#103×C41—22no—
72#102×C41—22no—
73C22⋊C8×C41—42no—
74C4×C8×C41—21no—
75C4×C8×C41—21no—
76#41×C41—22no—
77#41×C41—22no—
78#41×C41—41no—
79#41×C41—41no—
80#41×C41—41no—
81#41×C41—41no—
82#41×C41—41no—
83#41×C41—41no—
84C2×Q8×C41—21no—
85C2×Q8×C41—21no—
86C2×D4×C41—21no—
87C2×D4×C41—21no—
88C2×D4×C41—41no—
89C2×D4×C41—41no—
90C22×C4×C41—21no—
91C22×C4×C41—42no—
92C22×C4×C41—41no—
93C22×C4×C41—41no—
94C22×C4×C41C2×D411yescharacteristic
95Q16×C41—21no—
96Q16×C41—21no—
97Q16×C41—21no—
98Q16×C41C22⋊C412yes—
99SD16×C41—22no—
100SD16×C41—22no—
101SD16×C41—41no—
102SD16×C41—41no—
103D8×C41—21no—
104D8×C41—21no—
105D8×C41—21no—
106D8×C41C22⋊C412yes—
107M16×C41—41no—
108M16×C41—41no—
109C2×C8×C41—21no—
110C2×C8×C41—21no—
111C2×C8×C41—21no—
112C2×C8×C41—41no—
113C2×C8×C41C22×C411yescharacteristic
114C2×C8×C41C2×D411yescharacteristic
115C2×C8×C41C2×D411yescharacteristic
116C2×C8×C41C2×D411yescharacteristic
117C2×C8×C41#4111yescharacteristic
118C2×C8×C41#4111yescharacteristic
119C4⋊C4×C41—22no—
120C4⋊C4×C41—42no—
121C22⋊C4×C41—42no—
122C22⋊C4×C41—41no—
123C42×C41—21no—
124C42×C41—42no—
125C42×C41—41no—
126C42×C41D811yescharacteristic
127C42×C41D811yescharacteristic
128C16×C41—22no—
129C16×C41—41no—
130C23×C41—41no—
131C23×C41—41no—
132C23×C41AGL(1,ℤ/8)11yescharacteristic
133Q8×C41—22no—
134Q8×C41—41no—
135Q8×C41—41no—
136Q8×C41—41no—
137D4×C41—22no—
138D4×C41—42no—
139D4×C41—42no—
140D4×C41—41no—
141D4×C41—41no—
142D4×C41—41no—
143D4×C41—81no—
144D4×C41—81no—
145C2×C4×C41—21no—
146C2×C4×C41—21no—
147C2×C4×C41—42no—
148C2×C4×C41—41no—
149C2×C4×C41—42no—
150C2×C4×C41—42no—
151C2×C4×C41—41no—
152C2×C4×C41—42no—
153C2×C4×C41—84no—
154C2×C4×C41—81no—
155C2×C4×C41—81no—
156C2×C4×C41C4×D411yescharacteristic
157C2×C4×C41#12011yescharacteristic
158C2×C4×C41#12111yescharacteristic
159C2×C4×C41C2×D811yescharacteristic
160C2×C4×C41#13511yescharacteristic
161C2×C4×C41AGL(1,ℤ/8)11yescharacteristic
162C8×C41—41no—
163C8×C41—81no—
164C8×C41C2×C22⋊C411yescharacteristic
165C8×C41C4×D411yescharacteristic
166C8×C41#12111yescharacteristic
167C8×C41#12311yescharacteristic
168#13027C4111yesmaximal, characteristic, direct product factor, Sylow
169C22×C41—41no—
170C22×C41—42no—
171C22×C41—82no—
172C22×C41—82no—
173C22×C41—81no—
174C22×C41#44211yescharacteristic
175C22×C41#44711yescharacteristic
176C22×C41#46311yescharacteristic
177C4×C41—22no—
178C4×C41—41no—
179C4×C41—42no—
180C4×C41—82no—
181C4×C41—81no—
182C4×C41#38611yescharacteristic
183C4×C41C4×D811yescharacteristic
184C4×C41#44911yescharacteristic
185C4×C41#45911yescharacteristic
186#3414C2×C4111yescharacteristic
187C4×#135C2×C4111yescharacteristic, complemented
188#2145C2×C4111yescharacteristic, complemented
189#2143C2×C4111yescharacteristic, complemented
190#1974C2×C4111yescharacteristic, complemented
191#1389C2×C4111yescharacteristic, complemented
192#1376C2×C4111yescharacteristic, complemented
193C2×C41—21no—
194C2×C41—21no—
195C2×C41—21no—
196C2×C41—82no—
197C2×C41—161no—
198C2×C41#187911yescharacteristic
199C2×#135C22×C4111yescharacteristic
200C2×#135C22×C4111yescharacteristic
201C4×#41—21no—
202#510—21no—
203#510C4×C4112yescomplemented
204#509—21no—
205#509C4×C4112yescomplemented
206#508—22no—
207C2×M32C22×C4111yescharacteristic
208C2×M32C22×C4111yescharacteristic
209C4×Q16—21no—
210C4×SD16—22no—
211C4×D8—21no—
212C2×#108C22×C4111yescharacteristic
213#427C22×C4111yescharacteristic
214C2×#104—21no—
215#416—21no—
216#408—21no—
217C2×C4×C8C22×C4111yescharacteristic
218#360—22no—
219#359—22no—
220C41#1302711yescharacteristic, direct product factor, Sylow
221C2×#41—21no—
222C2×#41—21no—
223#135—21no—
224#135—21no—
225#135—21no—
226#135—21no—
227#135—21no—
228#135—21no—
229#135C2×C4×C4112yes—
230#135D4×C4112yes—
231C2×Q16C2×C4×C4111yescharacteristic, complemented
232C2×Q16D4×C4111yescharacteristic
233C2×SD16—21no—
234C2×SD16—21no—
235C2×D8C2×C4×C4111yescharacteristic, complemented
236C2×D8D4×C4111yescharacteristic
237C2×M16—21no—
238C22×C8D4×C4111yescharacteristic
239C22×C8C23×C4111yescharacteristic
240C4×Q8—22no—
241C4×D4—22no—
242C4×D4—42no—
243#117—21no—
244#117—41no—
245C2×C42—41no—
246C2×C42D4×C4111yescharacteristic
247Q32—22no—
248SD32—22no—
249SD32—22no—
250D16—22no—
251M32—21no—
252M32—21no—
253M32—21no—
254M32C2×C4×C4112yescomplemented
255C2×C16—21no—
256C2×C16—21no—
257#108—21no—
258#108—21no—
259#107—21no—
260#106D4×C4112yes—
261#104—41no—
262#104—41no—
263#103—22no—
264#102—22no—
265C22⋊C8—42no—
266C4×C8—21no—
267C4×C8—21no—
268#41—22no—
269#41—22no—
270#41—41no—
271#41—41no—
272#41—41no—
273#41—41no—
274#41—41no—
275#41—41no—
276C2×Q8—21no—
277C2×Q8—21no—
278C2×D4—21no—
279C2×D4—21no—
280C2×D4—41no—
281C2×D4—41no—
282C22×C4—21no—
283C22×C4—42no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4C2×D4×C4111yescharacteristic
287Q16—21no—
288Q16—21no—
289Q16—21no—
290Q16C22⋊C4×C4112yes—
291SD16—22no—
292SD16—22no—
293SD16—41no—
294SD16—41no—
295D8—21no—
296D8—21no—
297D8—21no—
298D8C22⋊C4×C4112yes—
299M16—41no—
300M16—41no—
301C2×C8—21no—
302C2×C8—21no—
303C2×C8—21no—
304C2×C8—41no—
305C2×C8C22×C4×C4111yescharacteristic
306C2×C8C2×D4×C4111yescharacteristic
307C2×C8C2×D4×C4111yescharacteristic
308C2×C8C2×D4×C4111yescharacteristic
309C2×C8#41×C4111yescharacteristic
310C2×C8#41×C4111yescharacteristic
311C4⋊C4—22no—
312C4⋊C4—42no—
313C22⋊C4—42no—
314C22⋊C4—41no—
315C42—21no—
316C42—42no—
317C42—41no—
318C42D8×C4111yescharacteristic
319C42D8×C4111yescharacteristic
320C16—22no—
321C16—41no—
322C23—41no—
323C23—41no—
324C23AGL(1,ℤ/8)×C4111yescharacteristic
325Q8—22no—
326Q8—41no—
327Q8—41no—
328Q8—41no—
329D4—22no—
330D4—42no—
331D4—42no—
332D4—41no—
333D4—41no—
334D4—41no—
335D4—81no—
336D4—81no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—42no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—41no—
344C2×C4—42no—
345C2×C4—84no—
346C2×C4—81no—
347C2×C4—81no—
348C2×C4C4×D4×C4111yescharacteristic
349C2×C4#120×C4111yescharacteristic
350C2×C4#121×C4111yescharacteristic
351C2×C4C2×D8×C4111yescharacteristic
352C2×C4#135×C4111yescharacteristic
353C2×C4AGL(1,ℤ/8)×C4111yescharacteristic
354C8—41no—
355C8—81no—
356C8C2×C22⋊C4×C4111yescharacteristic
357C8C4×D4×C4111yescharacteristic
358C8#121×C4111yescharacteristic
359C8#123×C4111yescharacteristic
360C22—41no—
361C22—42no—
362C22—82no—
363C22—82no—
364C22—81no—
365C22C41×#44211yescharacteristic
366C22C41×#44711yescharacteristic
367C22C41×#46311yescharacteristic
368C4—22no—
369C4—41no—
370C4—42no—
371C4—82no—
372C4—81no—
373C4C41×#38611yescharacteristic
374C4C4×D8×C4111yescharacteristic
375C4C41×#44911yescharacteristic
376C4C41×#45911yescharacteristic
377C2—21no—
378C2—21no—
379C2—21no—
380C2—82no—
381C2—161no—
382C2C41×#187911yescharacteristic
subgroupG/H
centerC4×C41#459
commutatorC2×C8C22×C4×C41
Frattini, cosocleC22×C8C23×C41
socleC2×C41#1879
prime radicalC41×#3414C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C41 ◁ C22×C4×C41 ◁ C2×C4×C8×C41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C4×#135×C41C2semidirect
3. C41×#2145C2semidirect
4. C41×#2143C2semidirect
5. C41×#1974C2semidirect
6. C41×#1389C2semidirect
7. C41×#1376C2semidirect
12. C41×#510C4semidirect
14. C41×#509C4semidirect
39. C2×Q16×C41C2×C4semidirect
43. C2×D8×C41C2×C4semidirect
62. M32×C41C2×C4semidirect
168. #13027C41direct (N × H)
187. C4×#135C2×C41semidirect
188. #2145C2×C41semidirect
189. #2143C2×C41semidirect
190. #1974C2×C41semidirect
191. #1389C2×C41semidirect
192. #1376C2×C41semidirect
203. #510C4×C41semidirect
205. #509C4×C41semidirect
220. C41#13027direct (N × H)
231. C2×Q16C2×C4×C41semidirect
235. C2×D8C2×C4×C41semidirect
254. M32C2×C4×C41semidirect

Maximal subgroups

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

subgroupindex
C41×#34142
C4×#135×C412
C41×#21452
C41×#21432
C41×#19742
C41×#13892
C41×#13762
#1302741