Finite Group Databasebeta

← C41×#23641 #23799842

Subgroups — C41×#23641 #23799842

Order 10496.

1014 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#427C211yesmaximal, characteristic, complemented
2C2×C41×#408C211yesmaximal, characteristic
3C41×#2311C212yesmaximal
4C41×#2077C214yesmaximal, complemented
5C41×#2076C212yesmaximal, complemented
6C41×#2075C212yesmaximal, complemented
7C41×#1736C212yesmaximal, complemented
8C2×C41×#340C211yesmaximal, characteristic, complemented
9C22×#41×C41C2211yescharacteristic
10C22×M16×C41C2211yescharacteristic
11C23×C8×C41C2211yescharacteristic
12C2×#117×C41C2212yes—
13C22×C4⋊C4×C41C2212yes—
14C41×#427—24no—
15C2×#107×C41C2211yescharacteristic
16C2×#107×C41C2211yescharacteristic
17C2×#106×C41C2212yes—
18C41×#408—24no—
19C2×C22⋊C8×C41C2212yes—
20C2×C22⋊C8×C41C2212yes—
21C41×#391—22no—
22C41×#390—22no—
23C41×#386—24no—
24C41×#380C2214yes—
25C41×#380C2214yes—
26C41×#340C2212yes—
27C41×#340C2214yes—
28C41×#340C2214yes—
29C41×#340C2212yes—
30C2×#41×C41—22no—
31C2×#41×C41—22no—
32C2×#41×C41—24no—
33C2×#41×C41—24no—
34C22×Q8×C41D411yescharacteristic
35C22×D4×C41D412yes—
36C22×D4×C41D411yescharacteristic
37C23×C4×C41—22no—
38C23×C4×C41C2312yes—
39C23×C4×C41C2311yescharacteristic
40C2×M16×C41—22no—
41C2×M16×C41—24no—
42C22×C8×C41—24no—
43C22×C8×C41D414yes—
44C22×C8×C41C2312yes—
45C22×C8×C41C2311yescharacteristic
46C22×C8×C41C2311yescharacteristic
47#117×C41—24no—
48#117×C41—24no—
49C2×C4⋊C4×C41—24no—
50C2×C4⋊C4×C41—24no—
51C2×C4⋊C4×C41—22no—
52C2×C4⋊C4×C41C2314yes—
53C2×C4⋊C4×C41C2312yes—
54C2×C4⋊C4×C41C2312yes—
55C2×C22⋊C4×C41—22no—
56C2×C22⋊C4×C41—24no—
57C2×C22⋊C4×C41—24no—
58C2×C42×C41—22no—
59#107×C41—22no—
60#107×C41—22no—
61#106×C41—24no—
62C22⋊C8×C41—24no—
63C22⋊C8×C41—24no—
64#95×C41—24no—
65#95×C41—24no—
66C24×C41C2×D412yes—
67C24×C41C2×D411yescharacteristic
68#41×C41—44no—
69#41×C41—44no—
70#41×C41—48no—
71C2×Q8×C41—22no—
72C2×Q8×C41—24no—
73C2×D4×C41—24no—
74C2×D4×C41—28no—
75C2×D4×C41—22no—
76C2×D4×C41—24no—
77C22×C4×C41—22no—
78C22×C4×C41—22no—
79C22×C4×C41—24no—
80C22×C4×C41—24no—
81C22×C4×C41—22no—
82C22×C4×C41—22no—
83C22×C4×C41—24no—
84C22×C4×C41—44no—
85C22×C4×C41—82no—
86C22×C4×C41—82no—
87C22×C4×C41C2×D412yes—
88C22×C4×C41C2×D411yescharacteristic
89C22×C4×C41C2×D412yes—
90C22×C4×C41#4112yes—
91C22×C4×C41#4114yes—
92C22×C4×C41#4114yes—
93C22×C4×C41C2411yescharacteristic
94M16×C41—44no—
95C2×C8×C41—28no—
96C2×C8×C41—22no—
97C2×C8×C41—22no—
98C2×C8×C41—22no—
99C2×C8×C41—24no—
100C2×C8×C41C2×D412yes—
101C2×C8×C41C2×D412yes—
102C4⋊C4×C41—22no—
103C4⋊C4×C41—22no—
104C4⋊C4×C41—24no—
105C4⋊C4×C41—24no—
106C4⋊C4×C41—22no—
107C4⋊C4×C41—22no—
108C4⋊C4×C41—44no—
109C22⋊C4×C41—44no—
110C22⋊C4×C41—84no—
111C22⋊C4×C41—84no—
112C42×C41—44no—
113C23×C41—21no—
114C23×C41—22no—
115C23×C41—21no—
116C23×C41—22no—
117C23×C41—24no—
118C23×C41—22no—
119C23×C41—24no—
120C23×C41—22no—
121C23×C41#12112yes—
122C23×C41#12314yes—
123C23×C41C22×D411yescharacteristic
124Q8×C41—44no—
125D4×C41—48no—
126D4×C41—44no—
127C2×C4×C41—22no—
128C2×C4×C41—24no—
129C2×C4×C41—42no—
130C2×C4×C41—42no—
131C2×C4×C41—44no—
132C2×C4×C41—42no—
133C2×C4×C41—42no—
134C2×C4×C41—44no—
135C2×C4×C41—42no—
136C2×C4×C41—44no—
137C2×C4×C41—42no—
138C2×C4×C41—44no—
139C2×C4×C41—42no—
140C2×C4×C41—42no—
141C2×C4×C41—88no—
142C2×C4×C41#12112yes—
143C2×C4×C41#12314yes—
144C2×C4×C41#12314yes—
145C2×C4×C41#12414yes—
146C2×C4×C41#12618yes—
147C2×C4×C41C22×D411yescharacteristic
148C2×C4×C41C2×#4112yes—
149C2×C4×C41C2×#4112yes—
150C2×C4×C41C2×#4111yescharacteristic
151C8×C41—22no—
152C8×C41—22no—
153C8×C41—42no—
154#23641C4111yesmaximal, characteristic, direct product factor, Sylow
155C22×C41—24no—
156C22×C41—24no—
157C22×C41—22no—
158C22×C41—22no—
159C22×C41—44no—
160C22×C41—44no—
161C22×C41—42no—
162C22×C41—42no—
163C22×C41—42no—
164C22×C41#39714yes—
165C22×C41C2×#12111yescharacteristic
166C22×C41C2×#12312yes—
167C22×C41#57611yescharacteristic
168C22×C41#57712yes—
169C22×C41#57811yescharacteristic
170C4×C41—42no—
171C4×C41—84no—
172C4×C41—82no—
173C4×C41—82no—
174C4×C41#39714yes—
175C4×C41C2×#12311yescharacteristic
176C4×C41C2×#12411yescharacteristic
177C4×C41C2×#12612yes—
178C2×#427C2×C4111yescharacteristic, complemented
179C2×#408C2×C4111yescharacteristic
180#2311C2×C4112yes—
181#2077C2×C4114yescomplemented
182#2076C2×C4112yescomplemented
183#2075C2×C4112yescomplemented
184#1736C2×C4112yescomplemented
185C2×#340C2×C4111yescharacteristic, complemented
186C2×C41—24no—
187C2×C41—82no—
188C2×C41C2×#39711yescharacteristic
189C2×C41#306011yescharacteristic
190C2×C41#306111yescharacteristic
191C2×C41#309612yes—
192C2×C41#309712yes—
193C22×#41C22×C4111yescharacteristic
194C22×M16C22×C4111yescharacteristic
195C23×C8C22×C4111yescharacteristic
196C2×#117C22×C4112yes—
197C22×C4⋊C4C22×C4112yes—
198#427—24no—
199C2×#107C22×C4111yescharacteristic
200C2×#107C22×C4111yescharacteristic
201C2×#106C22×C4112yes—
202#408—24no—
203C2×C22⋊C8C22×C4112yes—
204C2×C22⋊C8C22×C4112yes—
205#391—22no—
206#390—22no—
207#386—24no—
208#380C22×C4114yes—
209#380C22×C4114yes—
210#340C22×C4112yes—
211#340C22×C4114yes—
212#340C22×C4114yes—
213#340C22×C4112yes—
214C41#2364111yescharacteristic, direct product factor, Sylow
215C2×#41—22no—
216C2×#41—22no—
217C2×#41—24no—
218C2×#41—24no—
219C22×Q8D4×C4111yescharacteristic
220C22×D4D4×C4112yes—
221C22×D4D4×C4111yescharacteristic
222C23×C4—22no—
223C23×C4C23×C4112yes—
224C23×C4C23×C4111yescharacteristic
225C2×M16—22no—
226C2×M16—24no—
227C22×C8—24no—
228C22×C8D4×C4114yes—
229C22×C8C23×C4112yes—
230C22×C8C23×C4111yescharacteristic
231C22×C8C23×C4111yescharacteristic
232#117—24no—
233#117—24no—
234C2×C4⋊C4—24no—
235C2×C4⋊C4—24no—
236C2×C4⋊C4—22no—
237C2×C4⋊C4C23×C4114yes—
238C2×C4⋊C4C23×C4112yes—
239C2×C4⋊C4C23×C4112yes—
240C2×C22⋊C4—22no—
241C2×C22⋊C4—24no—
242C2×C22⋊C4—24no—
243C2×C42—22no—
244#107—22no—
245#107—22no—
246#106—24no—
247C22⋊C8—24no—
248C22⋊C8—24no—
249#95—24no—
250#95—24no—
251C24C2×D4×C4112yes—
252C24C2×D4×C4111yescharacteristic
253#41—44no—
254#41—44no—
255#41—48no—
256C2×Q8—22no—
257C2×Q8—24no—
258C2×D4—24no—
259C2×D4—28no—
260C2×D4—22no—
261C2×D4—24no—
262C22×C4—22no—
263C22×C4—22no—
264C22×C4—24no—
265C22×C4—24no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—24no—
269C22×C4—44no—
270C22×C4—82no—
271C22×C4—82no—
272C22×C4C2×D4×C4112yes—
273C22×C4C2×D4×C4111yescharacteristic
274C22×C4C2×D4×C4112yes—
275C22×C4#41×C4112yes—
276C22×C4#41×C4114yes—
277C22×C4#41×C4114yes—
278C22×C4C24×C4111yescharacteristic
279M16—44no—
280C2×C8—28no—
281C2×C8—22no—
282C2×C8—22no—
283C2×C8—22no—
284C2×C8—24no—
285C2×C8C2×D4×C4112yes—
286C2×C8C2×D4×C4112yes—
287C4⋊C4—22no—
288C4⋊C4—22no—
289C4⋊C4—24no—
290C4⋊C4—24no—
291C4⋊C4—22no—
292C4⋊C4—22no—
293C4⋊C4—44no—
294C22⋊C4—44no—
295C22⋊C4—84no—
296C22⋊C4—84no—
297C42—44no—
298C23—21no—
299C23—22no—
300C23—21no—
301C23—22no—
302C23—24no—
303C23—22no—
304C23—24no—
305C23—22no—
306C23#121×C4112yes—
307C23#123×C4114yes—
308C23C22×D4×C4111yescharacteristic
309Q8—44no—
310D4—48no—
311D4—44no—
312C2×C4—22no—
313C2×C4—24no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—44no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—44no—
320C2×C4—42no—
321C2×C4—44no—
322C2×C4—42no—
323C2×C4—44no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—88no—
327C2×C4#121×C4112yes—
328C2×C4#123×C4114yes—
329C2×C4#123×C4114yes—
330C2×C4#124×C4114yes—
331C2×C4#126×C4118yes—
332C2×C4C22×D4×C4111yescharacteristic
333C2×C4C2×#41×C4112yes—
334C2×C4C2×#41×C4112yes—
335C2×C4C2×#41×C4111yescharacteristic
336C8—22no—
337C8—22no—
338C8—42no—
339C22—22no—
340C22—22no—
341C22—24no—
342C22—24no—
343C22—42no—
344C22—42no—
345C22—44no—
346C22—44no—
347C22—42no—
348C22C41×#39714yes—
349C22C2×#121×C4111yescharacteristic
350C22C2×#123×C4112yes—
351C22C41×#57611yescharacteristic
352C22C41×#57712yes—
353C22C41×#57811yescharacteristic
354C4—42no—
355C4—82no—
356C4—82no—
357C4—84no—
358C4C41×#39714yes—
359C4C2×#123×C4111yescharacteristic
360C4C2×#124×C4111yescharacteristic
361C4C2×#126×C4112yes—
362C2—24no—
363C2—82no—
364C2C2×C41×#39711yescharacteristic
365C2C41×#306011yescharacteristic
366C2C41×#306111yescharacteristic
367C2C41×#309612yes—
368C2C41×#309712yes—
subgroupG/H
center, socleC23×C41C22×D4
commutator, Frattini, cosocleC22×C4C24×C41
prime radicalC22×#41×C41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C41 ◁ C22×#41×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C41×#427C2semidirect
4. C41×#2077C2semidirect
5. C41×#2076C2semidirect
6. C41×#2075C2semidirect
7. C41×#1736C2semidirect
8. C2×C41×#340C2semidirect
154. #23641C41direct (N × H)
178. C2×#427C2×C41semidirect
181. #2077C2×C41semidirect
182. #2076C2×C41semidirect
183. #2075C2×C41semidirect
184. #1736C2×C41semidirect
185. C2×#340C2×C41semidirect
214. C41#23641direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C41×#4272
C2×C41×#4082
C41×#23112
C41×#20772
C41×#20762
C41×#20752
C41×#17362
C2×C41×#3402
#2364141