Finite Group Databasebeta

← C41×#24989 #23801190

Subgroups — C41×#24989 #23801190

Order 10496.

620 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#473C211yesmaximal, characteristic
2C41×#2950C211yesmaximal, characteristic, complemented
3C41×#2082C212yesmaximal, complemented
4C41×#2049C212yesmaximal
5C41×#1979C211yesmaximal, characteristic, complemented
6C41×#1953C211yesmaximal, characteristic, complemented
7C41×#1905C212yesmaximal
8C41×#1833C211yesmaximal, characteristic, complemented
9C41×#1830C212yesmaximal, complemented
10C41×#1814C211yesmaximal, characteristic
11C41×#1757C211yesmaximal, characteristic
12C2×#137×C41C2212yes—
13C22×Q16×C41C2211yescharacteristic
14C2×#131×C41C2211yescharacteristic
15C41×#519C2212yes—
16C41×#473—22no—
17C41×#473—22no—
18C41×#441—22no—
19C4×Q16×C41—22no—
20C41×#430C2212yes—
21C2×#108×C41C2211yescharacteristic
22C2×#108×C41C2211yescharacteristic
23C41×#427C2211yescharacteristic
24C41×#421C2212yes—
25C41×#419C2212yes—
26C41×#419C2212yes—
27C41×#413C2211yescharacteristic
28C2×#101×C41C2212yes—
29C2×#101×C41C2212yes—
30C41×#410C2211yescharacteristic
31C41×#405C2211yescharacteristic
32C41×#405C2211yescharacteristic
33C41×#344C2211yescharacteristic
34C41×#344C2211yescharacteristic
35C41×#344C2212yes—
36C41×#344C2212yes—
37C41×#344C2212yes—
38C41×H(3,ℤ/4)C2212yes—
39C2×#41×C41C2311yescharacteristic
40C22×Q8×C41C2312yes—
41#137×C41—24no—
42#137×C41—42no—
43C2×Q16×C41—22no—
44C2×Q16×C41—21no—
45C2×Q16×C41—21no—
46C2×Q16×C41—21no—
47C2×Q16×C41—21no—
48C2×Q16×C41D412yes—
49C2×Q16×C41D412yes—
50C2×SD16×C41—22no—
51#131×C41—21no—
52#131×C41—21no—
53#131×C41—21no—
54#131×C41—21no—
55C2×M16×C41—21no—
56C2×M16×C41C2311yescharacteristic
57C2×M16×C41C2312yes—
58C2×M16×C41C2311yescharacteristic
59C2×M16×C41C2312yes—
60C2×M16×C41C2311yescharacteristic
61C22×C8×C41—21no—
62C22×C8×C41C2311yescharacteristic
63C4×Q8×C41—24no—
64C4×Q8×C41—42no—
65#117×C41—24no—
66#117×C41C2312yes—
67#117×C41C2311yescharacteristic
68#117×C41C2311yescharacteristic
69#108×C41—21no—
70#108×C41—21no—
71#108×C41—21no—
72#108×C41—21no—
73#108×C41—42no—
74#107×C41—21no—
75#106×C41—21no—
76#104×C41—42no—
77#103×C41—24no—
78#103×C41—42no—
79#101×C41—24no—
80#101×C41—21no—
81#101×C41—42no—
82#100×C41—21no—
83#99×C41—22no—
84#97×C41—21no—
85#97×C41—21no—
86C4×C8×C41—21no—
87C4×C8×C41—21no—
88#41×C41—21no—
89#41×C41—21no—
90#41×C41—21no—
91#41×C41—21no—
92C2×Q8×C41—22no—
93C2×Q8×C41—22no—
94C2×Q8×C41—22no—
95C2×Q8×C41—22no—
96C2×Q8×C41—22no—
97C2×Q8×C41C2×D414yes—
98C2×Q8×C41#4111yescharacteristic
99C2×D4×C41—21no—
100C2×D4×C41#4111yescharacteristic
101C22×C4×C41—22no—
102C22×C4×C41—21no—
103C22×C4×C41C2411yescharacteristic
104Q16×C41—22no—
105Q16×C41—22no—
106Q16×C41—22no—
107Q16×C41—22no—
108Q16×C41—44no—
109SD16×C41—44no—
110M16×C41—21no—
111M16×C41—22no—
112M16×C41—21no—
113M16×C41—21no—
114M16×C41—22no—
115M16×C41—21no—
116M16×C41—21no—
117M16×C41—22no—
118M16×C41—21no—
119M16×C41—22no—
120M16×C41—41no—
121M16×C41—41no—
122C2×C8×C41—21no—
123C2×C8×C41—21no—
124C2×C8×C41—21no—
125C2×C8×C41—22no—
126C2×C8×C41—22no—
127C2×C8×C41—41no—
128C2×C8×C41—41no—
129C2×C8×C41C2×D411yescharacteristic
130C2×C8×C41C2×D411yescharacteristic
131C2×C8×C41#4111yescharacteristic
132C2×C8×C41#4111yescharacteristic
133C2×C8×C41#4111yescharacteristic
134C2×C8×C41#4111yescharacteristic
135C4⋊C4×C41—21no—
136C4⋊C4×C41—22no—
137C4⋊C4×C41—21no—
138C4⋊C4×C41—44no—
139C22⋊C4×C41—21no—
140C22⋊C4×C41—22no—
141C22⋊C4×C41#4112yes—
142C42×C41—21no—
143C42×C41—21no—
144C42×C41—22no—
145C42×C41—44no—
146C23×C41—21no—
147C23×C41C2×#4111yescharacteristic
148Q8×C41—24no—
149Q8×C41—24no—
150Q8×C41—21no—
151Q8×C41—21no—
152Q8×C41—42no—
153Q8×C41—42no—
154D4×C41—21no—
155D4×C41—21no—
156D4×C41—41no—
157D4×C41—41no—
158C2×C4×C41—21no—
159C2×C4×C41—22no—
160C2×C4×C41—24no—
161C2×C4×C41—42no—
162C2×C4×C41—42no—
163C2×C4×C41—41no—
164C2×C4×C41—41no—
165C2×C4×C41—42no—
166C2×C4×C41—41no—
167C2×C4×C41C22×D411yescharacteristic
168C2×C4×C41C2×#4111yescharacteristic
169C2×C4×C41C2×#4111yescharacteristic
170C2×C4×C41C2×#4111yescharacteristic
171C2×C4×C41H(5,𝔽2)11yescharacteristic
172C2×C4×C41H(5,𝔽2)11yescharacteristic
173C8×C41—41no—
174C8×C41—42no—
175C8×C41—41no—
176C8×C41—42no—
177C8×C41—41no—
178C8×C41#12311yescharacteristic
179C8×C41#12311yescharacteristic
180C8×C41#12311yescharacteristic
181C8×C41#12311yescharacteristic
182#24989C4111yesmaximal, characteristic, direct product factor, Sylow
183C22×C41—41no—
184C22×C41—41no—
185C22×C41—81no—
186C22×C41#52911yescharacteristic
187C22×C41#54611yescharacteristic
188C22×C41#55511yescharacteristic
189C4×C41—42no—
190C4×C41—41no—
191C4×C41—44no—
192C4×C41—82no—
193C4×C41—81no—
194C4×C41C2×#12311yescharacteristic
195C4×C41#54011yescharacteristic
196C4×C41#54611yescharacteristic
197C4×C41#55311yescharacteristic
198C2×#473C2×C4111yescharacteristic
199#2950C2×C4111yescharacteristic, complemented
200#2082C2×C4112yescomplemented
201#2049C2×C4112yes—
202#1979C2×C4111yescharacteristic, complemented
203#1953C2×C4111yescharacteristic, complemented
204#1905C2×C4112yes—
205#1833C2×C4111yescharacteristic, complemented
206#1830C2×C4112yescomplemented
207#1814C2×C4111yescharacteristic
208#1757C2×C4111yescharacteristic
209C2×C41—21no—
210C2×C41—21no—
211C2×C41—21no—
212C2×C41—81no—
213C2×C41#242011yescharacteristic
214C2×#137C22×C4112yes—
215C22×Q16C22×C4111yescharacteristic
216C2×#131C22×C4111yescharacteristic
217#519C22×C4112yes—
218#473—22no—
219#473—22no—
220#441—22no—
221C4×Q16—22no—
222#430C22×C4112yes—
223C2×#108C22×C4111yescharacteristic
224C2×#108C22×C4111yescharacteristic
225#427C22×C4111yescharacteristic
226#421C22×C4112yes—
227#419C22×C4112yes—
228#419C22×C4112yes—
229#413C22×C4111yescharacteristic
230C2×#101C22×C4112yes—
231C2×#101C22×C4112yes—
232#410C22×C4111yescharacteristic
233#405C22×C4111yescharacteristic
234#405C22×C4111yescharacteristic
235#344C22×C4112yes—
236#344C22×C4112yes—
237#344C22×C4111yescharacteristic
238#344C22×C4111yescharacteristic
239#344C22×C4112yes—
240H(3,ℤ/4)C22×C4112yes—
241C41#2498911yescharacteristic, direct product factor, Sylow
242C2×#41C23×C4111yescharacteristic
243C22×Q8C23×C4112yes—
244#137—24no—
245#137—42no—
246C2×Q16—22no—
247C2×Q16—21no—
248C2×Q16—21no—
249C2×Q16—21no—
250C2×Q16—21no—
251C2×Q16D4×C4112yes—
252C2×Q16D4×C4112yes—
253C2×SD16—22no—
254#131—21no—
255#131—21no—
256#131—21no—
257#131—21no—
258C2×M16—21no—
259C2×M16C23×C4111yescharacteristic
260C2×M16C23×C4112yes—
261C2×M16C23×C4111yescharacteristic
262C2×M16C23×C4112yes—
263C2×M16C23×C4111yescharacteristic
264C22×C8—21no—
265C22×C8C23×C4111yescharacteristic
266C4×Q8—24no—
267C4×Q8—42no—
268#117—24no—
269#117C23×C4112yes—
270#117C23×C4111yescharacteristic
271#117C23×C4111yescharacteristic
272#108—21no—
273#108—21no—
274#108—21no—
275#108—21no—
276#108—42no—
277#107—21no—
278#106—21no—
279#104—42no—
280#103—24no—
281#103—42no—
282#101—24no—
283#101—21no—
284#101—42no—
285#100—21no—
286#99—22no—
287#97—21no—
288#97—21no—
289C4×C8—21no—
290C4×C8—21no—
291#41—21no—
292#41—21no—
293#41—21no—
294#41—21no—
295C2×Q8—22no—
296C2×Q8—22no—
297C2×Q8—22no—
298C2×Q8—22no—
299C2×Q8—22no—
300C2×Q8C2×D4×C4114yes—
301C2×Q8#41×C4111yescharacteristic
302C2×D4—21no—
303C2×D4#41×C4111yescharacteristic
304C22×C4—22no—
305C22×C4—21no—
306C22×C4C24×C4111yescharacteristic
307Q16—22no—
308Q16—22no—
309Q16—22no—
310Q16—22no—
311Q16—44no—
312SD16—44no—
313M16—21no—
314M16—22no—
315M16—21no—
316M16—21no—
317M16—22no—
318M16—21no—
319M16—21no—
320M16—22no—
321M16—21no—
322M16—22no—
323M16—41no—
324M16—41no—
325C2×C8—21no—
326C2×C8—21no—
327C2×C8—21no—
328C2×C8—22no—
329C2×C8—22no—
330C2×C8—41no—
331C2×C8—41no—
332C2×C8C2×D4×C4111yescharacteristic
333C2×C8C2×D4×C4111yescharacteristic
334C2×C8#41×C4111yescharacteristic
335C2×C8#41×C4111yescharacteristic
336C2×C8#41×C4111yescharacteristic
337C2×C8#41×C4111yescharacteristic
338C4⋊C4—21no—
339C4⋊C4—22no—
340C4⋊C4—21no—
341C4⋊C4—44no—
342C22⋊C4—21no—
343C22⋊C4—22no—
344C22⋊C4#41×C4112yes—
345C42—21no—
346C42—21no—
347C42—22no—
348C42—44no—
349C23—21no—
350C23C2×#41×C4111yescharacteristic
351Q8—24no—
352Q8—24no—
353Q8—21no—
354Q8—21no—
355Q8—42no—
356Q8—42no—
357D4—21no—
358D4—21no—
359D4—41no—
360D4—41no—
361C2×C4—21no—
362C2×C4—22no—
363C2×C4—24no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—42no—
369C2×C4—41no—
370C2×C4C22×D4×C4111yescharacteristic
371C2×C4C2×#41×C4111yescharacteristic
372C2×C4C2×#41×C4111yescharacteristic
373C2×C4C2×#41×C4111yescharacteristic
374C2×C4H(5,𝔽2)×C4111yescharacteristic
375C2×C4H(5,𝔽2)×C4111yescharacteristic
376C8—41no—
377C8—42no—
378C8—42no—
379C8—41no—
380C8—41no—
381C8#123×C4111yescharacteristic
382C8#123×C4111yescharacteristic
383C8#123×C4111yescharacteristic
384C8#123×C4111yescharacteristic
385C22—41no—
386C22—41no—
387C22—81no—
388C22C41×#52911yescharacteristic
389C22C41×#54611yescharacteristic
390C22C41×#55511yescharacteristic
391C4—42no—
392C4—41no—
393C4—44no—
394C4—82no—
395C4—81no—
396C4C2×#123×C4111yescharacteristic
397C4C41×#54011yescharacteristic
398C4C41×#54611yescharacteristic
399C4C41×#55311yescharacteristic
400C2—21no—
401C2—21no—
402C2—21no—
403C2—81no—
404C2C41×#242011yescharacteristic
subgroupG/H
center, socleC2×C41#2420
commutator, Frattini, cosocleC22×C4C24×C41
prime radicalC2×#41×C41C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C41 ◁ C22×C4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C41×#2950C2semidirect
3. C41×#2082C2semidirect
5. C41×#1979C2semidirect
6. C41×#1953C2semidirect
8. C41×#1833C2semidirect
9. C41×#1830C2semidirect
182. #24989C41direct (N × H)
199. #2950C2×C41semidirect
200. #2082C2×C41semidirect
202. #1979C2×C41semidirect
203. #1953C2×C41semidirect
205. #1833C2×C41semidirect
206. #1830C2×C41semidirect
241. C41#24989direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C41×#4732
C41×#29502
C41×#20822
C41×#20492
C41×#19792
C41×#19532
C41×#19052
C41×#18332
C41×#18302
C41×#18142
C41×#17572
#2498941