Finite Group Databasebeta

← C41×#7408 #23783609

Subgroups — C41×#7408 #23783609

Order 10496.

298 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 298 conjugacy classes of subgroups — too many to draw. Only its 46 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#2006C211yesmaximal, characteristic
2C41×#1393C211yesmaximal, characteristic, complemented
3C41×#1270C211yesmaximal, characteristic, complemented
4C2×AGL(1,ℤ/8)×C41—21no—
5C41×#537C411yescharacteristic, complemented
6C2×#104×C41—21no—
7C2×#99×C41—21no—
8C41×#390C2211yescharacteristic
9C41×#343C411yescharacteristic, complemented
10C41×#336—21no—
11C2×#41×C41—21no—
12C22×D4×C41D411yescharacteristic
13AGL(1,ℤ/8)×C41—42no—
14AGL(1,ℤ/8)×C41—41no—
15AGL(1,ℤ/8)×C41—41no—
16C2×SD16×C41—41no—
17C2×D8×C41—41no—
18C2×M16×C41—21no—
19C22×C8×C41—41no—
20C22⋊Q8×C41—41no—
21#121×C41—41no—
22#121×C41—41no—
23C2×C4⋊C4×C41C2×C411yescharacteristic
24C2×C22⋊C4×C41—41no—
25C2×C22⋊C4×C41—41no—
26C2×C42×C41D411yescharacteristic
27#104×C41—42no—
28#99×C41—22no—
29#99×C41—41no—
30C24×C41—21no—
31#41×C41—41no—
32#41×C41—41no—
33#41×C41—41no—
34#41×C41—41no—
35C2×Q8×C41—21no—
36C2×D4×C41—21no—
37C2×D4×C41—21no—
38C2×D4×C41—41no—
39C2×D4×C41—41no—
40C2×D4×C41—41no—
41C2×D4×C41—41no—
42C2×D4×C41D811yescharacteristic
43C2×D4×C41SD1611yescharacteristic
44C22×C4×C41—21no—
45C22×C4×C41—21no—
46C22×C4×C41—41no—
47C22×C4×C41—81no—
48C22×C4×C41C22⋊C411yescharacteristic
49SD16×C41—42no—
50SD16×C41—42no—
51D8×C41—42no—
52D8×C41—42no—
53M16×C41—22no—
54M16×C41—41no—
55C2×C8×C41—41no—
56C2×C8×C41—42no—
57C2×C8×C41—81no—
58C2×C8×C41—81no—
59C4⋊C4×C41—41no—
60C4⋊C4×C41—41no—
61C22⋊C4×C41—42no—
62C22⋊C4×C41—42no—
63C22⋊C4×C41—81no—
64C22⋊C4×C41—81no—
65C22⋊C4×C41—81no—
66C42×C41—41no—
67C23×C41—21no—
68C23×C41—21no—
69C23×C41—41no—
70C23×C41—41no—
71C23×C41—41no—
72C23×C41—81no—
73C23×C41—81no—
74C23×C41#9911yescharacteristic
75Q8×C41—41no—
76Q8×C41—41no—
77D4×C41—41no—
78D4×C41—41no—
79D4×C41—41no—
80D4×C41—41no—
81D4×C41—81no—
82D4×C41—81no—
83D4×C41—81no—
84D4×C41—161no—
85C2×C4×C41—21no—
86C2×C4×C41—21no—
87C2×C4×C41—21no—
88C2×C4×C41—21no—
89C2×C4×C41—41no—
90C2×C4×C41—41no—
91C2×C4×C41—41no—
92C2×C4×C41—41no—
93C2×C4×C41—81no—
94C2×C4×C41—81no—
95C2×C4×C41—81no—
96C2×C4×C41—82no—
97C2×C4×C41—161no—
98C2×C4×C41—161no—
99C2×C4×C41#10211yescharacteristic
100C2×C4×C41#10411yescharacteristic
101C8×C41—42no—
102C8×C41—82no—
103#7408C4111yesmaximal, characteristic, direct product factor, Sylow
104C22×C41—21no—
105C22×C41—21no—
106C22×C41—41no—
107C22×C41—41no—
108C22×C41—81no—
109C22×C41—81no—
110C22×C41—81no—
111C22×C41—81no—
112C22×C41—81no—
113C22×C41—81no—
114C22×C41—81no—
115C22×C41—161no—
116C22×C41#32711yescharacteristic
117C22×C41AΣL(1,𝔽16)11yescharacteristic
118C22×C41#35311yescharacteristic
119C4×C41—21no—
120C4×C41—21no—
121C4×C41—41no—
122C4×C41—41no—
123C4×C41—81no—
124C4×C41—81no—
125C4×C41—162no—
126#2006C2×C4111yescharacteristic
127#1393C2×C4111yescharacteristic, complemented
128#1270C2×C4111yescharacteristic, complemented
129C2×C41—21no—
130C2×C41—21no—
131C2×C41—81no—
132C2×C41—81no—
133C2×C41—161no—
134C2×C41#134311yescharacteristic
135C2×C41#140211yescharacteristic
136C2×C41#140411yescharacteristic
137C2×AGL(1,ℤ/8)—21no—
138#537C4×C4111yescharacteristic, complemented
139C2×#104—21no—
140C2×#99—21no—
141#390C22×C4111yescharacteristic
142#343C4×C4111yescharacteristic, complemented
143#336—21no—
144C41#740811yescharacteristic, direct product factor, Sylow
145C2×#41—21no—
146C22×D4D4×C4111yescharacteristic
147AGL(1,ℤ/8)—42no—
148AGL(1,ℤ/8)—41no—
149AGL(1,ℤ/8)—41no—
150C2×SD16—41no—
151C2×D8—41no—
152C2×M16—21no—
153C22×C8—41no—
154C22⋊Q8—41no—
155#121—41no—
156#121—41no—
157C2×C4⋊C4C2×C4×C4111yescharacteristic
158C2×C22⋊C4—41no—
159C2×C22⋊C4—41no—
160C2×C42D4×C4111yescharacteristic
161#104—42no—
162#99—22no—
163#99—41no—
164C24—21no—
165#41—41no—
166#41—41no—
167#41—41no—
168#41—41no—
169C2×Q8—21no—
170C2×D4—21no—
171C2×D4—21no—
172C2×D4—41no—
173C2×D4—41no—
174C2×D4—41no—
175C2×D4—41no—
176C2×D4D8×C4111yescharacteristic
177C2×D4SD16×C4111yescharacteristic
178C22×C4—21no—
179C22×C4—21no—
180C22×C4—41no—
181C22×C4—81no—
182C22×C4C22⋊C4×C4111yescharacteristic
183SD16—42no—
184SD16—42no—
185D8—42no—
186D8—42no—
187M16—22no—
188M16—41no—
189C2×C8—41no—
190C2×C8—42no—
191C2×C8—81no—
192C2×C8—81no—
193C4⋊C4—41no—
194C4⋊C4—41no—
195C22⋊C4—42no—
196C22⋊C4—42no—
197C22⋊C4—81no—
198C22⋊C4—81no—
199C22⋊C4—81no—
200C42—41no—
201C23—21no—
202C23—21no—
203C23—41no—
204C23—41no—
205C23—41no—
206C23—81no—
207C23—81no—
208C23#99×C4111yescharacteristic
209Q8—41no—
210Q8—41no—
211D4—41no—
212D4—41no—
213D4—41no—
214D4—41no—
215D4—81no—
216D4—81no—
217D4—81no—
218D4—161no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—81no—
228C2×C4—81no—
229C2×C4—81no—
230C2×C4—82no—
231C2×C4—161no—
232C2×C4—161no—
233C2×C4#102×C4111yescharacteristic
234C2×C4#104×C4111yescharacteristic
235C8—42no—
236C8—82no—
237C22—21no—
238C22—21no—
239C22—41no—
240C22—41no—
241C22—81no—
242C22—81no—
243C22—81no—
244C22—81no—
245C22—81no—
246C22—81no—
247C22—81no—
248C22—161no—
249C22C41×#32711yescharacteristic
250C22C41×AΣL(1,𝔽16)11yescharacteristic
251C22C41×#35311yescharacteristic
252C4—21no—
253C4—21no—
254C4—41no—
255C4—41no—
256C4—81no—
257C4—81no—
258C4—162no—
259C2—21no—
260C2—21no—
261C2—81no—
262C2—81no—
263C2—161no—
264C2C41×#134311yescharacteristic
265C2C41×#140211yescharacteristic
266C2C41×#140411yescharacteristic
subgroupG/H
center, socleC22×C41AΣL(1,𝔽16)
commutatorC2×C4⋊C4C2×C4×C41
Frattini, cosocle#390C22×C41
prime radicalC41×#2006C2
LCSG ▷ C2×C4⋊C4 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C41 ◁ C23×C41 ◁ C22×C4×C41 ◁ C41×#390 ◁ G

Complements

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

NH ≅ G/Ntype
2. C41×#1393C2semidirect
3. C41×#1270C2semidirect
5. C41×#537C4semidirect
9. C41×#343C4semidirect
103. #7408C41direct (N × H)
127. #1393C2×C41semidirect
128. #1270C2×C41semidirect
138. #537C4×C41semidirect
142. #343C4×C41semidirect
144. C41#7408direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#20062
C41×#13932
C41×#12702
#740841