Finite Group Databasebeta

← C41×#9273 #23785474

Subgroups — C41×#9273 #23785474

Order 10496.

560 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3205C211yesmaximal, characteristic
2C41×#2935C211yesmaximal, characteristic, complemented
3C41×#1965C211yesmaximal, characteristic, complemented
4C41×#1547C211yesmaximal, characteristic, complemented
5C2×C41×#331C211yesmaximal, characteristic, complemented
6C41×#1301C211yesmaximal, characteristic, complemented
7C41×#1283C211yesmaximal, characteristic, complemented
8C2×#131×C41—21no—
9C41×#532C2211yescharacteristic
10C2×#127×C41C2211yescharacteristic
11C41×#493—21no—
12C41×#486—21no—
13C41×#459—22no—
14C41×#447C414yes—
15C41×#436—21no—
16C41×#435—22no—
17C8×D4×C41—21no—
18C41×#431C2211yescharacteristic
19C41×#423C2211yescharacteristic
20C2×C4⋊C8×C41C2211yescharacteristic
21C2×C4⋊C8×C41C2211yescharacteristic
22C2×#100×C41—21no—
23C2×#100×C41—21no—
24C41×#408—21no—
25C4×M16×C41C2211yescharacteristic
26C41×#332—21no—
27C41×#331—21no—
28C41×#331—21no—
29C41×#331—21no—
30C2×#41×C41—21no—
31C22×D4×C41—21no—
32C22×D4×C41—21no—
33C22×D4×C41C2×C412yes—
34C2×D8×C41—24no—
35#131×C41—42no—
36#131×C41—42no—
37C2×M16×C41—22no—
38C2×M16×C41—21no—
39C2×M16×C41D411yescharacteristic
40C2×M16×C41D411yescharacteristic
41C22×C8×C41—22no—
42C22×C8×C41—21no—
43C22×C8×C41—21no—
44C4⋊Q8×C41D411yescharacteristic
45#127×C41—21no—
46#127×C41—21no—
47#127×C41—21no—
48#127×C41—21no—
49#127×C41D411yescharacteristic
50#124×C41—21no—
51#121×C41—21no—
52#121×C41C2×C412yes—
53C4×D4×C41—21no—
54C4×D4×C41D412yes—
55C2×C42×C41C2311yescharacteristic
56C4⋊C8×C41—21no—
57C4⋊C8×C41—21no—
58C4⋊C8×C41—21no—
59C4⋊C8×C41—21no—
60C4⋊C8×C41—21no—
61C4⋊C8×C41—21no—
62C4⋊C8×C41D411yescharacteristic
63C4⋊C8×C41D411yescharacteristic
64#102×C41—24no—
65#100×C41—42no—
66#100×C41—42no—
67C22⋊C8×C41—22no—
68C22⋊C8×C41—22no—
69C22⋊C8×C41C2×C412yes—
70#97×C41—21no—
71C4×C8×C41—21no—
72C4×C8×C41—21no—
73C24×C41—22no—
74#41×C41—41no—
75#41×C41—41no—
76#41×C41—41no—
77#41×C41—41no—
78C2×Q8×C41—21no—
79C2×D4×C41—22no—
80C2×D4×C41—22no—
81C2×D4×C41—22no—
82C2×D4×C41—21no—
83C2×D4×C41—21no—
84C2×D4×C41—41no—
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—81no—
93C2×D4×C41—81no—
94C2×D4×C41—82no—
95C2×D4×C41C22⋊C412yes—
96C22×C4×C41—22no—
97C22×C4×C41C22×C411yescharacteristic
98C22×C4×C41C2×D411yescharacteristic
99C22×C4×C41#4111yescharacteristic
100D8×C41—84no—
101M16×C41—21no—
102M16×C41—21no—
103M16×C41—21no—
104M16×C41—44no—
105M16×C41—41no—
106M16×C41—41no—
107M16×C41D812yescomplemented
108C2×C8×C41—21no—
109C2×C8×C41—22no—
110C2×C8×C41—21no—
111C2×C8×C41—21no—
112C2×C8×C41—21no—
113C2×C8×C41—44no—
114C2×C8×C41—41no—
115C2×C8×C41—41no—
116C2×C8×C41—41no—
117C2×C8×C41—41no—
118C2×C8×C41—81no—
119C4⋊C4×C41—21no—
120C4⋊C4×C41C22⋊C412yes—
121C22⋊C4×C41—22no—
122C22⋊C4×C41—22no—
123C42×C41C2×D411yescharacteristic
124C42×C41C2×D411yescharacteristic
125C42×C41C2×D411yescharacteristic
126C42×C41#4111yescharacteristic
127C23×C41—22no—
128C23×C41—42no—
129C23×C41—42no—
130C23×C41—42no—
131C23×C41—82no—
132C23×C41—82no—
133C23×C41C4×D411yescharacteristic
134Q8×C41—41no—
135Q8×C41—41no—
136D4×C41—42no—
137D4×C41—44no—
138D4×C41—42no—
139D4×C41—42no—
140D4×C41—41no—
141D4×C41—41no—
142D4×C41—41no—
143D4×C41—41no—
144D4×C41—82no—
145D4×C41—82no—
146D4×C41—81no—
147D4×C41—81no—
148D4×C41—81no—
149D4×C41—81no—
150D4×C41—81no—
151D4×C41—81no—
152C2×C4×C41—21no—
153C2×C4×C41—21no—
154C2×C4×C41—22no—
155C2×C4×C41—41no—
156C2×C4×C41—42no—
157C2×C4×C41—42no—
158C2×C4×C41C2×C22⋊C411yescharacteristic
159C2×C4×C41C4×D411yescharacteristic
160C2×C4×C41#12011yescharacteristic
161C2×C4×C41#12111yescharacteristic
162C2×C4×C41#12111yescharacteristic
163C2×C4×C41#12311yescharacteristic
164C2×C4×C41C2×D811yescharacteristic
165C2×C4×C41#13511yescharacteristic
166C2×C4×C41AGL(1,ℤ/8)11yescharacteristic
167C2×C4×C41AGL(1,ℤ/8)11yescharacteristic
168C8×C41—22no—
169C8×C41—42no—
170C8×C41—41no—
171C8×C41—41no—
172C8×C41—41no—
173C8×C41—81no—
174C8×C41—81no—
175#9273C4111yesmaximal, characteristic, direct product factor, Sylow
176C22×C41—21no—
177C22×C41—21no—
178C22×C41—42no—
179C22×C41—42no—
180C22×C41—42no—
181C22×C41—82no—
182C22×C41—82no—
183C22×C41—82no—
184C22×C41—162no—
185C22×C41—162no—
186C22×C41#38611yescharacteristic
187C22×C41C4×D811yescharacteristic
188C22×C41#44211yescharacteristic
189C4×C41—21no—
190C4×C41—21no—
191C4×C41—21no—
192C4×C41—42no—
193C4×C41#44711yescharacteristic
194C4×C41#44911yescharacteristic
195C4×C41#45911yescharacteristic
196C4×C41#46311yescharacteristic
197C4×C41#47111yescharacteristic
198C4×C41#47211yescharacteristic
199#3205C2×C4111yescharacteristic
200#2935C2×C4111yescharacteristic, complemented
201#1965C2×C4111yescharacteristic, complemented
202#1547C2×C4111yescharacteristic, complemented
203C2×#331C2×C4111yescharacteristic, complemented
204#1301C2×C4111yescharacteristic, complemented
205#1283C2×C4111yescharacteristic, complemented
206C2×C41—21no—
207C2×C41—21no—
208C2×C41—82no—
209C2×C41—162no—
210C2×C41#187911yescharacteristic
211C2×C41#190711yescharacteristic
212C2×C41#191411yescharacteristic
213C2×#131—21no—
214#532C22×C4111yescharacteristic
215C2×#127C22×C4111yescharacteristic
216#493—21no—
217#486—21no—
218#459—22no—
219#447C4×C4114yes—
220#436—21no—
221#435—22no—
222C8×D4—21no—
223#431C22×C4111yescharacteristic
224#423C22×C4111yescharacteristic
225C2×C4⋊C8C22×C4111yescharacteristic
226C2×C4⋊C8C22×C4111yescharacteristic
227C2×#100—21no—
228C2×#100—21no—
229#408—21no—
230C4×M16C22×C4111yescharacteristic
231#332—21no—
232#331—21no—
233#331—21no—
234#331—21no—
235C41#927311yescharacteristic, direct product factor, Sylow
236C2×#41—21no—
237C22×D4—21no—
238C22×D4—21no—
239C22×D4C2×C4×C4112yes—
240C2×D8—24no—
241#131—42no—
242#131—42no—
243C2×M16—22no—
244C2×M16—21no—
245C2×M16D4×C4111yescharacteristic
246C2×M16D4×C4111yescharacteristic
247C22×C8—22no—
248C22×C8—21no—
249C22×C8—21no—
250C4⋊Q8D4×C4111yescharacteristic
251#127—21no—
252#127—21no—
253#127—21no—
254#127—21no—
255#127D4×C4111yescharacteristic
256#124—21no—
257#121—21no—
258#121C2×C4×C4112yes—
259C4×D4—21no—
260C4×D4D4×C4112yes—
261C2×C42C23×C4111yescharacteristic
262C4⋊C8—21no—
263C4⋊C8—21no—
264C4⋊C8—21no—
265C4⋊C8—21no—
266C4⋊C8—21no—
267C4⋊C8—21no—
268C4⋊C8D4×C4111yescharacteristic
269C4⋊C8D4×C4111yescharacteristic
270#102—24no—
271#100—42no—
272#100—42no—
273C22⋊C8—22no—
274C22⋊C8—22no—
275C22⋊C8C2×C4×C4112yes—
276#97—21no—
277C4×C8—21no—
278C4×C8—21no—
279C24—22no—
280#41—41no—
281#41—41no—
282#41—41no—
283#41—41no—
284C2×Q8—21no—
285C2×D4—22no—
286C2×D4—22no—
287C2×D4—22no—
288C2×D4—21no—
289C2×D4—21no—
290C2×D4—41no—
291C2×D4—41no—
292C2×D4—41no—
293C2×D4—41no—
294C2×D4—41no—
295C2×D4—41no—
296C2×D4—41no—
297C2×D4—41no—
298C2×D4—81no—
299C2×D4—81no—
300C2×D4—82no—
301C2×D4C22⋊C4×C4112yes—
302C22×C4—22no—
303C22×C4C22×C4×C4111yescharacteristic
304C22×C4C2×D4×C4111yescharacteristic
305C22×C4#41×C4111yescharacteristic
306D8—84no—
307M16—21no—
308M16—21no—
309M16—21no—
310M16—44no—
311M16—41no—
312M16—41no—
313M16D8×C4112yescomplemented
314C2×C8—21no—
315C2×C8—22no—
316C2×C8—21no—
317C2×C8—21no—
318C2×C8—21no—
319C2×C8—44no—
320C2×C8—41no—
321C2×C8—41no—
322C2×C8—41no—
323C2×C8—41no—
324C2×C8—81no—
325C4⋊C4—21no—
326C4⋊C4C22⋊C4×C4112yes—
327C22⋊C4—22no—
328C22⋊C4—22no—
329C42C2×D4×C4111yescharacteristic
330C42C2×D4×C4111yescharacteristic
331C42C2×D4×C4111yescharacteristic
332C42#41×C4111yescharacteristic
333C23—22no—
334C23—42no—
335C23—42no—
336C23—42no—
337C23—82no—
338C23—82no—
339C23C4×D4×C4111yescharacteristic
340Q8—41no—
341Q8—41no—
342D4—42no—
343D4—44no—
344D4—42no—
345D4—42no—
346D4—41no—
347D4—41no—
348D4—41no—
349D4—41no—
350D4—82no—
351D4—82no—
352D4—81no—
353D4—81no—
354D4—81no—
355D4—81no—
356D4—81no—
357D4—81no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—22no—
361C2×C4—41no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4C2×C22⋊C4×C4111yescharacteristic
365C2×C4C4×D4×C4111yescharacteristic
366C2×C4#120×C4111yescharacteristic
367C2×C4#121×C4111yescharacteristic
368C2×C4#121×C4111yescharacteristic
369C2×C4#123×C4111yescharacteristic
370C2×C4C2×D8×C4111yescharacteristic
371C2×C4#135×C4111yescharacteristic
372C2×C4AGL(1,ℤ/8)×C4111yescharacteristic
373C2×C4AGL(1,ℤ/8)×C4111yescharacteristic
374C8—22no—
375C8—42no—
376C8—41no—
377C8—41no—
378C8—41no—
379C8—81no—
380C8—81no—
381C22—21no—
382C22—21no—
383C22—42no—
384C22—42no—
385C22—42no—
386C22—82no—
387C22—82no—
388C22—82no—
389C22—162no—
390C22—162no—
391C22C41×#38611yescharacteristic
392C22C4×D8×C4111yescharacteristic
393C22C41×#44211yescharacteristic
394C4—21no—
395C4—21no—
396C4—21no—
397C4—42no—
398C4C41×#44711yescharacteristic
399C4C41×#44911yescharacteristic
400C4C41×#45911yescharacteristic
401C4C41×#46311yescharacteristic
402C4C41×#47111yescharacteristic
403C4C41×#47211yescharacteristic
404C2—21no—
405C2—21no—
406C2—82no—
407C2—162no—
408C2C41×#187911yescharacteristic
409C2C41×#190711yescharacteristic
410C2C41×#191411yescharacteristic
subgroupG/H
center, socleC22×C41#386
commutatorC22×C4C22×C4×C41
Frattini, cosocleC2×C42C23×C41
prime radicalC41×#3205C2
LCSG ▷ C22×C4 ▷ 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×#2935C2semidirect
3. C41×#1965C2semidirect
4. C41×#1547C2semidirect
5. C2×C41×#331C2semidirect
6. C41×#1301C2semidirect
7. C41×#1283C2semidirect
107. M16×C41D8semidirect
175. #9273C41direct (N × H)
200. #2935C2×C41semidirect
201. #1965C2×C41semidirect
202. #1547C2×C41semidirect
203. C2×#331C2×C41semidirect
204. #1301C2×C41semidirect
205. #1283C2×C41semidirect
235. C41#9273direct (N × H)
313. M16D8×C41semidirect

Maximal subgroups

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

subgroupindex
C41×#32052
C41×#29352
C41×#19652
C41×#15472
C2×C41×#3312
C41×#13012
C41×#12832
#927341