Finite Group Databasebeta

← C41×#9325 #23785526

Subgroups — C41×#9325 #23785526

Order 10496.

650 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×#3109C211yesmaximal, characteristic
2C41×#2275C211yesmaximal, characteristic, complemented
3C41×#1980C211yesmaximal, characteristic, complemented
4C41×#1505C211yesmaximal, characteristic, complemented
5C41×#1490C211yesmaximal, characteristic, complemented
6C41×#1300C211yesmaximal, characteristic, complemented
7C41×#1285C211yesmaximal, characteristic, complemented
8C41×#532C2211yescharacteristic
9C2×C4×D4×C41—21no—
10C2×C4×D4×C41C2211yescharacteristic
11C41×#481—21no—
12C41×#476C412yescomplemented
13C41×#459C412yescomplemented
14C41×#447—21no—
15C41×#442—22no—
16C41×#432C2211yescharacteristic
17C41×#432C2211yescharacteristic
18C2×#104×C41—22no—
19C4×M16×C41C2211yescharacteristic
20C4×C4⋊C4×C41—21no—
21C4×C4⋊C4×C41C2211yescharacteristic
22C4×C22⋊C4×C41—22no—
23C4×C22⋊C4×C41—21no—
24C41×#376C2211yescharacteristic
25C2×#95×C41—21no—
26C41×#327—21no—
27C41×#327—21no—
28C41×D4⋊C8—22no—
29C2×#41×C41—21no—
30C22×D4×C41D411yescharacteristic
31C23×C4×C41—22no—
32C23×C4×C41—21no—
33C2×D8×C41—22no—
34C2×M16×C41—21no—
35C4⋊Q8×C41C2×C411yescharacteristic, complemented
36#127×C41C2×C411yescharacteristic, complemented
37#124×C41—21no—
38#121×C41—21no—
39#121×C41—21no—
40C4×D4×C41—28no—
41C4×D4×C41—21no—
42C4×D4×C41—21no—
43C4×D4×C41—21no—
44C4×D4×C41—21no—
45C4×D4×C41C2×C412yes—
46C4×D4×C41D412yes—
47C2×C4⋊C4×C41—21no—
48C2×C4⋊C4×C41D411yescharacteristic
49C2×C22⋊C4×C41—22no—
50C2×C22⋊C4×C41—21no—
51C2×C42×C41—21no—
52C2×C42×C41—22no—
53C2×C42×C41D412yes—
54C2×C42×C41C2311yescharacteristic
55#106×C41—22no—
56C4⋊C8×C41—21no—
57C4⋊C8×C41C2×C412yescomplemented
58#104×C41—44no—
59#102×C41—22no—
60#102×C41—22no—
61C22⋊C8×C41—21no—
62C22⋊C8×C41—21no—
63#97×C41—21no—
64#97×C41—21no—
65#97×C41—21no—
66C4×C8×C41—21no—
67#95×C41—22no—
68#95×C41—21no—
69#95×C41—21no—
70#95×C41D411yescharacteristic
71#95×C41D411yescharacteristic
72C24×C41—21no—
73#41×C41—42no—
74#41×C41—42no—
75C2×Q8×C41—21no—
76C2×D4×C41—24no—
77C2×D4×C41—21no—
78C2×D4×C41—21no—
79C2×D4×C41—21no—
80C2×D4×C41—21no—
81C2×D4×C41—41no—
82C2×D4×C41C22⋊C412yes—
83C22×C4×C41—21no—
84C22×C4×C41—21no—
85C22×C4×C41—22no—
86C22×C4×C41—21no—
87C22×C4×C41—28no—
88C22×C4×C41—22no—
89C22×C4×C41—22no—
90C22×C4×C41—41no—
91C22×C4×C41—82no—
92C22×C4×C41—82no—
93C22×C4×C41—82no—
94C22×C4×C41C2×D411yescharacteristic
95C22×C4×C41C2×D411yescharacteristic
96C22×C4×C41C2×D411yescharacteristic
97D8×C41—44no—
98M16×C41—22no—
99M16×C41—41no—
100C2×C8×C41—22no—
101C2×C8×C41—41no—
102C2×C8×C41—41no—
103C4⋊C4×C41—24no—
104C4⋊C4×C41—21no—
105C4⋊C4×C41—21no—
106C4⋊C4×C41—21no—
107C4⋊C4×C41C22⋊C412yes—
108C22⋊C4×C41—28no—
109C22⋊C4×C41—22no—
110C22⋊C4×C41—22no—
111C22⋊C4×C41—41no—
112C22⋊C4×C41—41no—
113C42×C41—24no—
114C42×C41—42no—
115C42×C41—82no—
116C42×C41C22×C411yescharacteristic
117C42×C41C2×D411yescharacteristic
118C42×C41#4111yescharacteristic
119C42×C41#4111yescharacteristic
120C23×C41—24no—
121C23×C41—22no—
122C23×C41—42no—
123C23×C41—41no—
124C23×C41—41no—
125C23×C41—41no—
126C23×C41#12011yescharacteristic
127Q8×C41—42no—
128D4×C41—24no—
129D4×C41—22no—
130D4×C41—42no—
131D4×C41—42no—
132D4×C41—81no—
133D4×C41—81no—
134D4×C41—81no—
135D4×C41#10414yescomplemented
136C2×C4×C41—21no—
137C2×C4×C41—21no—
138C2×C4×C41—22no—
139C2×C4×C41—22no—
140C2×C4×C41—22no—
141C2×C4×C41—24no—
142C2×C4×C41—22no—
143C2×C4×C41—41no—
144C2×C4×C41—41no—
145C2×C4×C41—42no—
146C2×C4×C41—42no—
147C2×C4×C41—41no—
148C2×C4×C41—42no—
149C2×C4×C41—41no—
150C2×C4×C41—41no—
151C2×C4×C41—41no—
152C2×C4×C41—82no—
153C2×C4×C41—82no—
154C2×C4×C41—82no—
155C2×C4×C41—88no—
156C2×C4×C41C2×C22⋊C411yescharacteristic
157C2×C4×C41C4×D411yescharacteristic
158C2×C4×C41C4×D411yescharacteristic
159C2×C4×C41#12111yescharacteristic
160C2×C4×C41#12111yescharacteristic
161C2×C4×C41#12311yescharacteristic
162C8×C41—42no—
163C8×C41—42no—
164C8×C41—81no—
165#9325C4111yesmaximal, characteristic, direct product factor, Sylow
166C22×C41—21no—
167C22×C41—21no—
168C22×C41—24no—
169C22×C41—44no—
170C22×C41—44no—
171C22×C41—42no—
172C22×C41—42no—
173C22×C41—81no—
174C22×C41—81no—
175C22×C41—81no—
176C22×C41#38611yescharacteristic
177C22×C41#45311yescharacteristic
178C22×C41#45411yescharacteristic
179C4×C41—21no—
180C4×C41—21no—
181C4×C41—21no—
182C4×C41—21no—
183C4×C41—21no—
184C4×C41—42no—
185C4×C41—44no—
186C4×C41—42no—
187C4×C41—42no—
188C4×C41—81no—
189C4×C41C2×#10412yes—
190#3109C2×C4111yescharacteristic
191#2275C2×C4111yescharacteristic, complemented
192#1980C2×C4111yescharacteristic, complemented
193#1505C2×C4111yescharacteristic, complemented
194#1490C2×C4111yescharacteristic, complemented
195#1300C2×C4111yescharacteristic, complemented
196#1285C2×C4111yescharacteristic, complemented
197C2×C41—21no—
198C2×C41—21no—
199C2×C41—44no—
200C2×C41—161no—
201C2×C41#188311yescharacteristic
202C2×C41#189611yescharacteristic
203C2×C41#190411yescharacteristic
204#532C22×C4111yescharacteristic
205C2×C4×D4—21no—
206C2×C4×D4C22×C4111yescharacteristic
207#481—21no—
208#476C4×C4112yescomplemented
209#459C4×C4112yescomplemented
210#447—21no—
211#442—22no—
212#432C22×C4111yescharacteristic
213#432C22×C4111yescharacteristic
214C2×#104—22no—
215C4×M16C22×C4111yescharacteristic
216C4×C4⋊C4—21no—
217C4×C4⋊C4C22×C4111yescharacteristic
218C4×C22⋊C4—22no—
219C4×C22⋊C4—21no—
220#376C22×C4111yescharacteristic
221C2×#95—21no—
222#327—21no—
223#327—21no—
224D4⋊C8—22no—
225C41#932511yescharacteristic, direct product factor, Sylow
226C2×#41—21no—
227C22×D4D4×C4111yescharacteristic
228C23×C4—22no—
229C23×C4—21no—
230C2×D8—22no—
231C2×M16—21no—
232C4⋊Q8C2×C4×C4111yescharacteristic, complemented
233#127C2×C4×C4111yescharacteristic, complemented
234#124—21no—
235#121—21no—
236#121—21no—
237C4×D4—28no—
238C4×D4—21no—
239C4×D4—21no—
240C4×D4—21no—
241C4×D4—21no—
242C4×D4C2×C4×C4112yes—
243C4×D4D4×C4112yes—
244C2×C4⋊C4—21no—
245C2×C4⋊C4D4×C4111yescharacteristic
246C2×C22⋊C4—22no—
247C2×C22⋊C4—21no—
248C2×C42—21no—
249C2×C42—22no—
250C2×C42D4×C4112yes—
251C2×C42C23×C4111yescharacteristic
252#106—22no—
253C4⋊C8—21no—
254C4⋊C8C2×C4×C4112yescomplemented
255#104—44no—
256#102—22no—
257#102—22no—
258C22⋊C8—21no—
259C22⋊C8—21no—
260#97—21no—
261#97—21no—
262#97—21no—
263C4×C8—21no—
264#95—22no—
265#95—21no—
266#95—21no—
267#95D4×C4111yescharacteristic
268#95D4×C4111yescharacteristic
269C24—21no—
270#41—42no—
271#41—42no—
272C2×Q8—21no—
273C2×D4—24no—
274C2×D4—21no—
275C2×D4—21no—
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—41no—
279C2×D4C22⋊C4×C4112yes—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—22no—
283C22×C4—21no—
284C22×C4—28no—
285C22×C4—22no—
286C22×C4—22no—
287C22×C4—41no—
288C22×C4—82no—
289C22×C4—82no—
290C22×C4—82no—
291C22×C4C2×D4×C4111yescharacteristic
292C22×C4C2×D4×C4111yescharacteristic
293C22×C4C2×D4×C4111yescharacteristic
294D8—44no—
295M16—22no—
296M16—41no—
297C2×C8—22no—
298C2×C8—41no—
299C2×C8—41no—
300C4⋊C4—24no—
301C4⋊C4—21no—
302C4⋊C4—21no—
303C4⋊C4—21no—
304C4⋊C4C22⋊C4×C4112yes—
305C22⋊C4—28no—
306C22⋊C4—22no—
307C22⋊C4—22no—
308C22⋊C4—41no—
309C22⋊C4—41no—
310C42—24no—
311C42—42no—
312C42—82no—
313C42C22×C4×C4111yescharacteristic
314C42C2×D4×C4111yescharacteristic
315C42#41×C4111yescharacteristic
316C42#41×C4111yescharacteristic
317C23—24no—
318C23—22no—
319C23—42no—
320C23—41no—
321C23—41no—
322C23—41no—
323C23#120×C4111yescharacteristic
324Q8—42no—
325D4—24no—
326D4—22no—
327D4—42no—
328D4—42no—
329D4—81no—
330D4—81no—
331D4—81no—
332D4#104×C4114yescomplemented
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—24no—
339C2×C4—22no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—41no—
345C2×C4—42no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—82no—
350C2×C4—82no—
351C2×C4—82no—
352C2×C4—88no—
353C2×C4C2×C22⋊C4×C4111yescharacteristic
354C2×C4C4×D4×C4111yescharacteristic
355C2×C4C4×D4×C4111yescharacteristic
356C2×C4#121×C4111yescharacteristic
357C2×C4#121×C4111yescharacteristic
358C2×C4#123×C4111yescharacteristic
359C8—42no—
360C8—42no—
361C8—81no—
362C22—21no—
363C22—21no—
364C22—24no—
365C22—44no—
366C22—44no—
367C22—42no—
368C22—42no—
369C22—81no—
370C22—81no—
371C22—81no—
372C22C41×#38611yescharacteristic
373C22C41×#45311yescharacteristic
374C22C41×#45411yescharacteristic
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—21no—
380C4—42no—
381C4—44no—
382C4—42no—
383C4—42no—
384C4—81no—
385C4C2×#104×C4112yes—
386C2—21no—
387C2—21no—
388C2—44no—
389C2—161no—
390C2C41×#188311yescharacteristic
391C2C41×#189611yescharacteristic
392C2C41×#190411yescharacteristic
subgroupG/H
center, socleC22×C41#386
commutatorC42C22×C4×C41
Frattini, cosocleC2×C42C23×C41
prime radicalC41×#3109C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C41 ◁ C2×C42×C41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C41×#2275C2semidirect
3. C41×#1980C2semidirect
4. C41×#1505C2semidirect
5. C41×#1490C2semidirect
6. C41×#1300C2semidirect
7. C41×#1285C2semidirect
12. C41×#476C4semidirect
13. C41×#459C4semidirect
35. C4⋊Q8×C41C2×C4semidirect
36. #127×C41C2×C4semidirect
57. C4⋊C8×C41C2×C4semidirect
135. D4×C41#104semidirect
165. #9325C41direct (N × H)
191. #2275C2×C41semidirect
192. #1980C2×C41semidirect
193. #1505C2×C41semidirect
194. #1490C2×C41semidirect
195. #1300C2×C41semidirect
196. #1285C2×C41semidirect
208. #476C4×C41semidirect
209. #459C4×C41semidirect
225. C41#9325direct (N × H)
232. C4⋊Q8C2×C4×C41semidirect
233. #127C2×C4×C41semidirect
254. C4⋊C8C2×C4×C41semidirect
332. D4#104×C41semidirect

Maximal subgroups

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

subgroupindex
C41×#31092
C41×#22752
C41×#19802
C41×#15052
C41×#14902
C41×#13002
C41×#12852
#932541