Finite Group Databasebeta

← C41×#10795 #23786996

Subgroups — C41×#10795 #23786996

Order 10496.

1062 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×C41C211yesmaximal, characteristic
2C2×C41×#336C212yesmaximal
3C2×C41×#336C212yesmaximal
4C2×C41×#336C212yesmaximal
5C23×C8×C41C2214yes—
6C22×C42×C41C412yes—
7C22×C42×C41C412yes—
8C22×C42×C41C2211yescharacteristic
9C22×C42×C41C2211yescharacteristic
10C22×C42×C41C2211yescharacteristic
11C43×C41—24no—
12C41×#336—24no—
13C41×#336—24no—
14C41×#336C418yescomplemented
15C23×C4×C41C2×C411yescharacteristic
16C23×C4×C41C2×C411yescharacteristic
17C23×C4×C41C2×C412yes—
18C23×C4×C41C2×C412yes—
19C23×C4×C41C2311yescharacteristic
20C22×C8×C41—24no—
21C22×C8×C41—24no—
22C22×C8×C41—24no—
23C22×C8×C41—24no—
24C22×C8×C41—24no—
25C22×C8×C41—24no—
26C22×C8×C41C2×C418yes—
27C2×C42×C41—24no—
28C2×C42×C41—24no—
29C2×C42×C41—24no—
30C2×C42×C41—24no—
31C2×C42×C41—24no—
32C2×C42×C41—22no—
33C2×C42×C41—22no—
34C2×C42×C41—22no—
35C2×C42×C41—22no—
36C2×C42×C41—22no—
37C2×C42×C41—22no—
38C2×C42×C41C818yescomplemented
39C2×C42×C41C2×C414yes—
40C2×C42×C41D414yes—
41C2×C42×C41D412yes—
42C2×C42×C41Q812yes—
43C24×C41C22×C411yescharacteristic
44C22×C4×C41—21no—
45C22×C4×C41—21no—
46C22×C4×C41—22no—
47C22×C4×C41—21no—
48C22×C4×C41—21no—
49C22×C4×C41—22no—
50C22×C4×C41—22no—
51C22×C4×C41—22no—
52C22×C4×C41—22no—
53C22×C4×C41—22no—
54C22×C4×C41—22no—
55C22×C4×C41—22no—
56C22×C4×C41—22no—
57C22×C4×C41—22no—
58C22×C4×C41C4212yes—
59C22×C4×C41C4212yes—
60C22×C4×C41C22⋊C414yes—
61C22×C4×C41C4⋊C414yes—
62C22×C4×C41C2×C814yes—
63C22×C4×C41C2×C814yes—
64C22×C4×C41C2×C814yes—
65C22×C4×C41M1614yes—
66C22×C4×C41M1614yes—
67C22×C4×C41M1614yes—
68C22×C4×C41C22×C412yes—
69C22×C4×C41C2×D411yescharacteristic
70C22×C4×C41C2×D412yes—
71C22×C4×C41C2×Q811yescharacteristic
72C22×C4×C41#4112yes—
73C22×C4×C41#4112yes—
74C22×C4×C41#4112yes—
75C22×C4×C41#4112yes—
76C2×C8×C41—28no—
77C2×C8×C41—28no—
78C2×C8×C41—28no—
79C2×C8×C41—44no—
80C2×C8×C41—44no—
81C2×C8×C41—44no—
82C2×C8×C41—44no—
83C42×C41—216no—
84C42×C41—216no—
85C42×C41—28no—
86C42×C41—24no—
87C42×C41—24no—
88C42×C41—28no—
89C23×C41C2×C4211yescharacteristic
90C23×C41C2×C22⋊C411yescharacteristic
91C23×C41C2×C4⋊C411yescharacteristic
92C23×C41#11711yescharacteristic
93C23×C41#11711yescharacteristic
94C23×C41#11711yescharacteristic
95C23×C41#11711yescharacteristic
96C23×C41C22×C812yes—
97C23×C41C2×M1612yes—
98C23×C41C2×M1612yes—
99C23×C41C2×M1612yes—
100C2×C4×C41—22no—
101C2×C4×C41—22no—
102C2×C4×C41—24no—
103C2×C4×C41—24no—
104C2×C4×C41—22no—
105C2×C4×C41—22no—
106C2×C4×C41—24no—
107C2×C4×C41—24no—
108C2×C4×C41—24no—
109C2×C4×C41—24no—
110C2×C4×C41—24no—
111C2×C4×C41—24no—
112C2×C4×C41—24no—
113C2×C4×C41—24no—
114C2×C4×C41—24no—
115C2×C4×C41—24no—
116C2×C4×C41—24no—
117C2×C4×C41—24no—
118C2×C4×C41—24no—
119C2×C4×C41—24no—
120C2×C4×C41C4×C814yes—
121C2×C4×C41#9714yes—
122C2×C4×C41C22⋊C818yes—
123C2×C4×C41C4⋊C818yes—
124C2×C4×C41#11714yes—
125C2×C4×C41C4×D414yes—
126C2×C4×C41C4×D412yes—
127C2×C4×C41C4×Q812yes—
128C2×C4×C41#12112yes—
129C2×C4×C41C22⋊Q812yes—
130C2×C4×C41#12314yes—
131C2×C4×C41#12412yes—
132C2×C4×C41#12512yes—
133C2×C4×C41#12614yes—
134C8×C41—48no—
135#10795C4111yesmaximal, characteristic, direct product factor, Sylow
136C22×C41#37611yescharacteristic
137C22×C41C4×C22⋊C411yescharacteristic
138C22×C41C4×C4⋊C411yescharacteristic
139C22×C41#38011yescharacteristic
140C22×C41#38111yescharacteristic
141C22×C41#38211yescharacteristic
142C22×C41#38311yescharacteristic
143C22×C41C2×C4×C811yescharacteristic
144C22×C41C2×#9711yescharacteristic
145C22×C41C4×M1611yescharacteristic
146C22×C41C4×M1611yescharacteristic
147C22×C41C2×C22⋊C812yes—
148C22×C41#40712yes—
149C22×C41C2×C4⋊C812yes—
150C22×C41#42312yes—
151C22×C41#43112yes—
152C22×C41#43112yes—
153C22×C41#43112yes—
154C22×C41#43112yes—
155C22×C41#43212yes—
156C22×C41#43212yes—
157C22×C41#43212yes—
158C22×C41#43212yes—
159C4×C41—28no—
160C4×C41—28no—
161C4×C41—24no—
162C4×C41—24no—
163C4×C41#38714yes—
164C4×C41#38814yes—
165C2×C43C2×C4111yescharacteristic
166C2×#336C2×C4112yes—
167C2×#336C2×C4112yes—
168C2×#336C2×C4112yes—
169C2×C41#143411yescharacteristic
170C2×C41#174411yescharacteristic
171C2×C41#174511yescharacteristic
172C2×C41C4×C22⋊C811yescharacteristic
173C2×C41#174911yescharacteristic
174C2×C41C4×C4⋊C811yescharacteristic
175C2×C41#176711yescharacteristic
176C2×C41#179712yes—
177C2×C41#181712yes—
178C2×C41#183112yes—
179C2×C41#183912yes—
180C23×C8C22×C4114yes—
181C22×C42C4×C4112yes—
182C22×C42C4×C4112yes—
183C22×C42C22×C4111yescharacteristic
184C22×C42C22×C4111yescharacteristic
185C22×C42C22×C4111yescharacteristic
186C43—24no—
187#336—24no—
188#336—24no—
189#336C4×C4118yescomplemented
190C41#1079511yescharacteristic, direct product factor, Sylow
191C23×C4C2×C4×C4111yescharacteristic
192C23×C4C2×C4×C4111yescharacteristic
193C23×C4C2×C4×C4112yes—
194C23×C4C2×C4×C4112yes—
195C23×C4C23×C4111yescharacteristic
196C22×C8—24no—
197C22×C8—24no—
198C22×C8—24no—
199C22×C8—24no—
200C22×C8—24no—
201C22×C8—24no—
202C22×C8C2×C4×C4118yes—
203C2×C42—24no—
204C2×C42—24no—
205C2×C42—24no—
206C2×C42—24no—
207C2×C42—24no—
208C2×C42—22no—
209C2×C42—22no—
210C2×C42—22no—
211C2×C42—22no—
212C2×C42—22no—
213C2×C42—22no—
214C2×C42C8×C4118yescomplemented
215C2×C42C2×C4×C4114yes—
216C2×C42D4×C4114yes—
217C2×C42D4×C4112yes—
218C2×C42Q8×C4112yes—
219C24C22×C4×C4111yescharacteristic
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—22no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—22no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—22no—
230C22×C4—22no—
231C22×C4—22no—
232C22×C4—22no—
233C22×C4—22no—
234C22×C4C42×C4112yes—
235C22×C4C42×C4112yes—
236C22×C4C22⋊C4×C4114yes—
237C22×C4C4⋊C4×C4114yes—
238C22×C4C2×C8×C4114yes—
239C22×C4C2×C8×C4114yes—
240C22×C4C2×C8×C4114yes—
241C22×C4M16×C4114yes—
242C22×C4M16×C4114yes—
243C22×C4M16×C4114yes—
244C22×C4C22×C4×C4112yes—
245C22×C4C2×D4×C4111yescharacteristic
246C22×C4C2×D4×C4112yes—
247C22×C4C2×Q8×C4111yescharacteristic
248C22×C4#41×C4112yes—
249C22×C4#41×C4112yes—
250C22×C4#41×C4112yes—
251C22×C4#41×C4112yes—
252C2×C8—28no—
253C2×C8—28no—
254C2×C8—28no—
255C2×C8—44no—
256C2×C8—44no—
257C2×C8—44no—
258C2×C8—44no—
259C42—216no—
260C42—216no—
261C42—28no—
262C42—24no—
263C42—24no—
264C42—28no—
265C23C2×C42×C4111yescharacteristic
266C23C2×C22⋊C4×C4111yescharacteristic
267C23C2×C4⋊C4×C4111yescharacteristic
268C23#117×C4111yescharacteristic
269C23#117×C4111yescharacteristic
270C23#117×C4111yescharacteristic
271C23#117×C4111yescharacteristic
272C23C22×C8×C4112yes—
273C23C2×M16×C4112yes—
274C23C2×M16×C4112yes—
275C23C2×M16×C4112yes—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—24no—
279C2×C4—24no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—24no—
283C2×C4—24no—
284C2×C4—24no—
285C2×C4—24no—
286C2×C4—24no—
287C2×C4—24no—
288C2×C4—24no—
289C2×C4—24no—
290C2×C4—24no—
291C2×C4—24no—
292C2×C4—24no—
293C2×C4—24no—
294C2×C4—24no—
295C2×C4—24no—
296C2×C4C4×C8×C4114yes—
297C2×C4#97×C4114yes—
298C2×C4C22⋊C8×C4118yes—
299C2×C4C4⋊C8×C4118yes—
300C2×C4#117×C4114yes—
301C2×C4C4×D4×C4114yes—
302C2×C4C4×D4×C4112yes—
303C2×C4C4×Q8×C4112yes—
304C2×C4#121×C4112yes—
305C2×C4C22⋊Q8×C4112yes—
306C2×C4#123×C4114yes—
307C2×C4#124×C4112yes—
308C2×C4#125×C4112yes—
309C2×C4#126×C4114yes—
310C8—48no—
311C22C41×#37611yescharacteristic
312C22C4×C22⋊C4×C4111yescharacteristic
313C22C4×C4⋊C4×C4111yescharacteristic
314C22C41×#38011yescharacteristic
315C22C41×#38111yescharacteristic
316C22C41×#38211yescharacteristic
317C22C41×#38311yescharacteristic
318C22C2×C4×C8×C4111yescharacteristic
319C22C2×#97×C4111yescharacteristic
320C22C4×M16×C4111yescharacteristic
321C22C4×M16×C4111yescharacteristic
322C22C2×C22⋊C8×C4112yes—
323C22C41×#40712yes—
324C22C2×C4⋊C8×C4112yes—
325C22C41×#42312yes—
326C22C41×#43112yes—
327C22C41×#43112yes—
328C22C41×#43112yes—
329C22C41×#43112yes—
330C22C41×#43212yes—
331C22C41×#43212yes—
332C22C41×#43212yes—
333C22C41×#43212yes—
334C4—28no—
335C4—28no—
336C4—24no—
337C4—24no—
338C4C41×#38714yes—
339C4C41×#38814yes—
340C2C41×#143411yescharacteristic
341C2C41×#174411yescharacteristic
342C2C41×#174511yescharacteristic
343C2C4×C22⋊C8×C4111yescharacteristic
344C2C41×#174911yescharacteristic
345C2C4×C4⋊C8×C4111yescharacteristic
346C2C41×#176711yescharacteristic
347C2C41×#179712yes—
348C2C41×#181712yes—
349C2C41×#183112yes—
350C2C41×#183912yes—
subgroupG/H
centerC23×C4×C41C23
commutatorC22C2×C4×C8×C41
Frattini, cosocleC23×C4C23×C41
socle, prime radicalC24×C41C22×C4
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
14. C41×#336C4semidirect
38. C2×C42×C41C8semidirect
135. #10795C41direct (N × H)
189. #336C4×C41semidirect
190. C41#10795direct (N × H)
214. C2×C42C8×C41semidirect

Maximal subgroups

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

subgroupindex
C2×C43×C412
C2×C41×#3362
#1079541