Finite Group Databasebeta

← C41×#60143 #23836344

Subgroups — C41×#60143 #23836344

Order 10496.

2706 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#568C212yesmaximal, complemented
2C41×#3449C211yesmaximal, characteristic
3C41×#2933C2116yesmaximal, complemented
4C41×#2932C214yesmaximal, complemented
5C41×#2931C214yesmaximal, complemented
6C41×#2905C211yesmaximal, characteristic, complemented
7C2×C41×#408C212yesmaximal, complemented
8C2×C41×#405C211yesmaximal, characteristic, complemented
9C22×#41×C41C2212yes—
10C41×#568—216no—
11C2×#131×C41C2218yes—
12C2×#131×C41C2218yescomplemented
13C22×M16×C41C2212yes—
14C22×M16×C41C2211yescharacteristic
15C22×M16×C41C2218yescomplemented
16C23×C8×C41C2211yescharacteristic
17C41×#537C414yes—
18C41×#536C414yes—
19C41×#535C414yes—
20C41×#534C414yes—
21C41×#532C2214yes—
22C41×#525C2218yes—
23C2×#117×C41C2211yescharacteristic
24C41×#436C22116yescomplemented
25C41×#435C22132yescomplemented
26C8×D4×C41C22116yescomplemented
27C41×#424C2218yescomplemented
28C41×#423C2214yescomplemented
29C41×#408C2218yes—
30C41×#408C2214yescomplemented
31C41×#408C2214yescomplemented
32C2×C22⋊C8×C41C2218yescomplemented
33C41×#405C2218yescomplemented
34C2×#97×C41C2212yescomplemented
35C2×C4×C8×C41C2212yescomplemented
36C2×#41×C41—28no—
37C2×#41×C41—28no—
38C2×#41×C41C2×C414yes—
39C2×#41×C41C2×C414yes—
40C2×#41×C41C2314yes—
41C2×#41×C41C2314yes—
42C22×Q8×C41C2×C412yes—
43C22×D4×C41C2×C414yes—
44C22×D4×C41C2×C412yes—
45C23×C4×C41C2314yes—
46C23×C4×C41C2311yescharacteristic
47#131×C41—232no—
48#131×C41—232no—
49C2×M16×C41—28no—
50C2×M16×C41—232no—
51C2×M16×C41D418yescomplemented
52C2×M16×C41C2314yes—
53C2×M16×C41C2314yes—
54C2×M16×C41C23116yes—
55C2×M16×C41C2314yes—
56C22×C8×C41—24no—
57C22×C8×C41C2311yescharacteristic
58C22×C8×C41C2311yescharacteristic
59C22×C8×C41C2314yes—
60C22×C8×C41C2314yes—
61C22×C8×C41C23116yes—
62C22×C8×C41C2312yes—
63C4⋊Q8×C41C2×C414yes—
64#127×C41C2×C414yes—
65#124×C41C2×C418yes—
66#123×C41C2×C4116yes—
67C22⋊Q8×C41C2×C4116yes—
68#121×C41C2×C4116yes—
69#121×C41C2×C4116yes—
70#120×C41C2×C4116yes—
71C4×D4×C41C23116yes—
72#117×C41C2×C414yes—
73#117×C41C2314yes—
74C2×C4⋊C4×C41C2×C412yes—
75C2×C22⋊C4×C41C2×C412yes—
76C2×C42×C41C2312yes—
77C4⋊C8×C41C23116yes—
78C22⋊C8×C41C23116yes—
79C22⋊C8×C41C23116yes—
80#97×C41C2318yes—
81C4×C8×C41C2318yes—
82C24×C41C22×C414yes—
83C24×C41C22×C411yescharacteristic
84#41×C41—216no—
85#41×C41—216no—
86#41×C41—28no—
87#41×C41—28no—
88#41×C41—28no—
89#41×C41—28no—
90C2×Q8×C41—28no—
91C2×Q8×C41C22×C414yes—
92C2×Q8×C41C22×C414yes—
93C2×D4×C41—216no—
94C2×D4×C41—28no—
95C2×D4×C41C22×C418yes—
96C2×D4×C41C22×C418yes—
97C2×D4×C41C22×C414yes—
98C2×D4×C41C22×C414yes—
99C2×D4×C41C22×C4116yes—
100C22×C4×C41—28no—
101C22×C4×C41—28no—
102C22×C4×C41C22×C418yes—
103C22×C4×C41C22×C414yes—
104C22×C4×C41C22×C414yes—
105C22×C4×C41C22×C411yescharacteristic
106C22×C4×C41C22×C412yes—
107C22×C4×C41C2×D414yes—
108C22×C4×C41#4114yes—
109C22×C4×C41C2418yes—
110C22×C4×C41C2411yescharacteristic
111C22×C4×C41C2412yes—
112M16×C41—28no—
113M16×C41—28no—
114M16×C41—232no—
115M16×C41C2×D4116yes—
116C2×C8×C41—28no—
117C2×C8×C41—28no—
118C2×C8×C41—22no—
119C2×C8×C41—22no—
120C2×C8×C41—232no—
121C2×C8×C41C2×D418yes—
122C2×C8×C41C2412yes—
123C2×C8×C41C2412yes—
124C2×C8×C41C2418yes—
125C2×C8×C41C2414yes—
126C4⋊C4×C41C22×C418yes—
127C4⋊C4×C41C22×C4116yes—
128C22⋊C4×C41C22×C418yes—
129C22⋊C4×C41C22×C4132yes—
130C42×C41C22×C414yes—
131C42×C41C2414yes—
132C23×C41—28no—
133C23×C41—42no—
134C23×C41—48no—
135C23×C41C4×D414yes—
136C23×C41C23×C418yes—
137C23×C41C23×C412yes—
138C23×C41C23×C411yescharacteristic
139Q8×C41—28no—
140Q8×C41—28no—
141D4×C41—216no—
142D4×C41—216no—
143D4×C41—28no—
144D4×C41—28no—
145D4×C41—416no—
146C2×C4×C41—28no—
147C2×C4×C41—216no—
148C2×C4×C41—28no—
149C2×C4×C41—28no—
150C2×C4×C41—44no—
151C2×C4×C41C4×D418yes—
152C2×C4×C41C4×D414yes—
153C2×C4×C41C23×C418yes—
154C2×C4×C41C23×C418yes—
155C2×C4×C41C23×C411yescharacteristic
156C2×C4×C41C23×C412yes—
157C2×C4×C41C22×D414yes—
158C2×C4×C41C22×D412yes—
159C2×C4×C41C2×#4114yes—
160C2×C4×C41C2×#4112yes—
161C2×C4×C41C2511yescharacteristic
162C8×C41—28no—
163C8×C41—22no—
164C8×C41—22no—
165C8×C41C22×D418yes—
166#60143C4111yesmaximal, characteristic, direct product factor, Sylow
167C22×C41—22no—
168C22×C41—24no—
169C22×C41—28no—
170C22×C41—216no—
171C22×C41—44no—
172C22×C41—88no—
173C22×C41C2×C4×D414yes—
174C22×C41C2×C4×D412yes—
175C22×C41C24×C411yescharacteristic
176C4×C41—28no—
177C4×C41—28no—
178C4×C41C2×C4×D414yes—
179C4×C41C2×C4×D412yes—
180C4×C41C23×D411yescharacteristic
181C4×C41C22×#4111yescharacteristic
182C2×#568C2×C4112yescomplemented
183#3449C2×C4111yescharacteristic
184#2933C2×C41116yescomplemented
185#2932C2×C4114yescomplemented
186#2931C2×C4114yescomplemented
187#2905C2×C4111yescharacteristic, complemented
188C2×#408C2×C4112yescomplemented
189C2×#405C2×C4111yescharacteristic, complemented
190C2×C41—24no—
191C2×C41—22no—
192C2×C41—48no—
193C2×C41C22×C4×D411yescharacteristic
194C2×C41#357312yes—
195C22×#41C22×C4112yes—
196#568—216no—
197C2×#131C22×C4118yes—
198C2×#131C22×C4118yescomplemented
199C22×M16C22×C4112yes—
200C22×M16C22×C4111yescharacteristic
201C22×M16C22×C4118yescomplemented
202C23×C8C22×C4111yescharacteristic
203#537C4×C4114yes—
204#536C4×C4114yes—
205#535C4×C4114yes—
206#534C4×C4114yes—
207#532C22×C4114yes—
208#525C22×C4118yes—
209C2×#117C22×C4111yescharacteristic
210#436C22×C41116yescomplemented
211#435C22×C41132yescomplemented
212C8×D4C22×C41116yescomplemented
213#424C22×C4118yescomplemented
214#423C22×C4114yescomplemented
215#408C22×C4118yes—
216#408C22×C4114yescomplemented
217#408C22×C4114yescomplemented
218C2×C22⋊C8C22×C4118yescomplemented
219#405C22×C4118yescomplemented
220C2×#97C22×C4112yescomplemented
221C2×C4×C8C22×C4112yescomplemented
222C41#6014311yescharacteristic, direct product factor, Sylow
223C2×#41—28no—
224C2×#41—28no—
225C2×#41C2×C4×C4114yes—
226C2×#41C2×C4×C4114yes—
227C2×#41C23×C4114yes—
228C2×#41C23×C4114yes—
229C22×Q8C2×C4×C4112yes—
230C22×D4C2×C4×C4114yes—
231C22×D4C2×C4×C4112yes—
232C23×C4C23×C4114yes—
233C23×C4C23×C4111yescharacteristic
234#131—232no—
235#131—232no—
236C2×M16—28no—
237C2×M16—232no—
238C2×M16D4×C4118yescomplemented
239C2×M16C23×C4114yes—
240C2×M16C23×C4114yes—
241C2×M16C23×C41116yes—
242C2×M16C23×C4114yes—
243C22×C8—24no—
244C22×C8C23×C4111yescharacteristic
245C22×C8C23×C4111yescharacteristic
246C22×C8C23×C4114yes—
247C22×C8C23×C4114yes—
248C22×C8C23×C41116yes—
249C22×C8C23×C4112yes—
250C4⋊Q8C2×C4×C4114yes—
251#127C2×C4×C4114yes—
252#124C2×C4×C4118yes—
253#123C2×C4×C41116yes—
254C22⋊Q8C2×C4×C41116yes—
255#121C2×C4×C41116yes—
256#121C2×C4×C41116yes—
257#120C2×C4×C41116yes—
258C4×D4C23×C41116yes—
259#117C2×C4×C4114yes—
260#117C23×C4114yes—
261C2×C4⋊C4C2×C4×C4112yes—
262C2×C22⋊C4C2×C4×C4112yes—
263C2×C42C23×C4112yes—
264C4⋊C8C23×C41116yes—
265C22⋊C8C23×C41116yes—
266C22⋊C8C23×C41116yes—
267#97C23×C4118yes—
268C4×C8C23×C4118yes—
269C24C22×C4×C4114yes—
270C24C22×C4×C4111yescharacteristic
271#41—216no—
272#41—216no—
273#41—28no—
274#41—28no—
275#41—28no—
276#41—28no—
277C2×Q8—28no—
278C2×Q8C22×C4×C4114yes—
279C2×Q8C22×C4×C4114yes—
280C2×D4—216no—
281C2×D4—28no—
282C2×D4C22×C4×C4118yes—
283C2×D4C22×C4×C4118yes—
284C2×D4C22×C4×C4114yes—
285C2×D4C22×C4×C4114yes—
286C2×D4C22×C4×C41116yes—
287C22×C4—28no—
288C22×C4—28no—
289C22×C4C22×C4×C4118yes—
290C22×C4C22×C4×C4114yes—
291C22×C4C22×C4×C4114yes—
292C22×C4C22×C4×C4111yescharacteristic
293C22×C4C22×C4×C4112yes—
294C22×C4C2×D4×C4114yes—
295C22×C4#41×C4114yes—
296C22×C4C24×C4118yes—
297C22×C4C24×C4111yescharacteristic
298C22×C4C24×C4112yes—
299M16—28no—
300M16—28no—
301M16—232no—
302M16C2×D4×C41116yes—
303C2×C8—28no—
304C2×C8—28no—
305C2×C8—22no—
306C2×C8—22no—
307C2×C8—232no—
308C2×C8C2×D4×C4118yes—
309C2×C8C24×C4112yes—
310C2×C8C24×C4112yes—
311C2×C8C24×C4118yes—
312C2×C8C24×C4114yes—
313C4⋊C4C22×C4×C4118yes—
314C4⋊C4C22×C4×C41116yes—
315C22⋊C4C22×C4×C4118yes—
316C22⋊C4C22×C4×C41132yes—
317C42C22×C4×C4114yes—
318C42C24×C4114yes—
319C23—28no—
320C23—42no—
321C23—48no—
322C23C4×D4×C4114yes—
323C23C23×C4×C4118yes—
324C23C23×C4×C4112yes—
325C23C23×C4×C4111yescharacteristic
326Q8—28no—
327Q8—28no—
328D4—216no—
329D4—216no—
330D4—28no—
331D4—28no—
332D4—416no—
333C2×C4—28no—
334C2×C4—216no—
335C2×C4—28no—
336C2×C4—28no—
337C2×C4—44no—
338C2×C4C4×D4×C4118yes—
339C2×C4C4×D4×C4114yes—
340C2×C4C23×C4×C4118yes—
341C2×C4C23×C4×C4118yes—
342C2×C4C23×C4×C4111yescharacteristic
343C2×C4C23×C4×C4112yes—
344C2×C4C22×D4×C4114yes—
345C2×C4C22×D4×C4112yes—
346C2×C4C2×#41×C4114yes—
347C2×C4C2×#41×C4112yes—
348C2×C4C25×C4111yescharacteristic
349C8—28no—
350C8—22no—
351C8—22no—
352C8C22×D4×C4118yes—
353C22—22no—
354C22—24no—
355C22—216no—
356C22—28no—
357C22—44no—
358C22—88no—
359C22C2×C4×D4×C4114yes—
360C22C2×C4×D4×C4112yes—
361C22C24×C4×C4111yescharacteristic
362C4—28no—
363C4—28no—
364C4C2×C4×D4×C4114yes—
365C4C2×C4×D4×C4112yes—
366C4C23×D4×C4111yescharacteristic
367C4C22×#41×C4111yescharacteristic
368C2—24no—
369C2—22no—
370C2—48no—
371C2C22×C4×D4×C4111yescharacteristic
372C2C41×#357312yes—
subgroupG/H
centerC2×C4×C41C25
commutatorC22C24×C4×C41
Frattini, cosocleC2×C4C25×C41
socleC22×C41C24×C4
prime radicalC41×#3449C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C41×#568C2semidirect
3. C41×#2933C2semidirect
4. C41×#2932C2semidirect
5. C41×#2931C2semidirect
6. C41×#2905C2semidirect
7. C2×C41×#408C2semidirect
8. C2×C41×#405C2semidirect
12. C2×#131×C41C22semidirect
15. C22×M16×C41C22semidirect
24. C41×#436C22semidirect
25. C41×#435C22semidirect
26. C8×D4×C41C22semidirect
27. C41×#424C22semidirect
28. C41×#423C22semidirect
30. C41×#408C22semidirect
31. C41×#408C22semidirect
32. C2×C22⋊C8×C41C22semidirect
33. C41×#405C22semidirect
34. C2×#97×C41C22semidirect
35. C2×C4×C8×C41C22semidirect
51. C2×M16×C41D4semidirect
166. #60143C41direct (N × H)
182. C2×#568C2×C41semidirect
184. #2933C2×C41semidirect
185. #2932C2×C41semidirect
186. #2931C2×C41semidirect
187. #2905C2×C41semidirect
188. C2×#408C2×C41semidirect
189. C2×#405C2×C41semidirect
198. C2×#131C22×C41semidirect
201. C22×M16C22×C41semidirect
210. #436C22×C41semidirect
211. #435C22×C41semidirect
212. C8×D4C22×C41semidirect
213. #424C22×C41semidirect
214. #423C22×C41semidirect
216. #408C22×C41semidirect
217. #408C22×C41semidirect
218. C2×C22⋊C8C22×C41semidirect
219. #405C22×C41semidirect
220. C2×#97C22×C41semidirect
221. C2×C4×C8C22×C41semidirect
222. C41#60143direct (N × H)
238. C2×M16D4×C41semidirect

Maximal subgroups

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

subgroupindex
C2×C41×#5682
C41×#34492
C41×#29332
C41×#29322
C41×#29312
C41×#29052
C2×C41×#4082
C2×C41×#4052
#6014341