Finite Group Databasebeta

← C41×#8518 #23784719

Subgroups — C41×#8518 #23784719

Order 10496.

818 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 818 conjugacy classes of subgroups — too many to draw. Only its 142 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
1C2×C41×#540C211yesmaximal, characteristic
2C41×#1822C211yesmaximal, characteristic, complemented
3C41×#1820C211yesmaximal, characteristic, complemented
4C41×#1510C214yesmaximal, complemented
5C41×#540—28no—
6C2×#127×C41C411yescharacteristic, complemented
7C2×#125×C41C411yescharacteristic, complemented
8C2×#123×C41—22no—
9C2×#121×C41—22no—
10C2×#121×C41C2212yes—
11C2×C4×D4×C41C412yescomplemented
12C2×#117×C41C2211yescharacteristic
13C41×#407C2212yes—
14C41×#381C2212yes—
15C41×#343—22no—
16C41×#342—22no—
17C41×#327—28no—
18C22×D4×C41—22no—
19C22×D4×C41—22no—
20C22×D4×C41C2×C412yes—
21C23×C4×C41—22no—
22C23×C4×C41C2311yescharacteristic
23C2×M16×C41—22no—
24#127×C41—24no—
25#125×C41—24no—
26#123×C41—216no—
27#121×C41—216no—
28#121×C41—24no—
29#121×C41D418yes—
30C4×D4×C41—24no—
31C4×D4×C41—24no—
32#117×C41—24no—
33C2×C4⋊C4×C41—22no—
34C2×C4⋊C4×C41C2×C412yes—
35C2×C4⋊C4×C41D412yes—
36C2×C22⋊C4×C41—22no—
37C2×C22⋊C4×C41—22no—
38C2×C22⋊C4×C41—22no—
39C2×C22⋊C4×C41D412yes—
40C2×C42×C41C2×C411yescharacteristic
41C2×C42×C41C2×C411yescharacteristic
42C22⋊C8×C41—24no—
43#95×C41—24no—
44C24×C41—22no—
45C24×C41C2×D411yescharacteristic
46C2×D4×C41—28no—
47C2×D4×C41—28no—
48C2×D4×C41—22no—
49C2×D4×C41—44no—
50C2×D4×C41—84no—
51C2×D4×C41—84no—
52C2×D4×C41C22⋊C414yes—
53C22×C4×C41—22no—
54C22×C4×C41—28no—
55C22×C4×C41—42no—
56C22×C4×C41—42no—
57C22×C4×C41—84no—
58C22×C4×C41C22⋊C412yes—
59C22×C4×C41C22⋊C412yes—
60C22×C4×C41C22×C411yescharacteristic
61C22×C4×C41C2×D411yescharacteristic
62C22×C4×C41C2×D414yes—
63M16×C41—44no—
64C2×C8×C41—42no—
65C4⋊C4×C41—28no—
66C4⋊C4×C41—22no—
67C4⋊C4×C41—24no—
68C4⋊C4×C41C22⋊C414yes—
69C22⋊C4×C41—28no—
70C22⋊C4×C41—24no—
71C22⋊C4×C41—28no—
72C22⋊C4×C41—44no—
73C42×C41—22no—
74C42×C41—22no—
75C23×C41—22no—
76C23×C41—24no—
77C23×C41—42no—
78C23×C41—44no—
79C23×C41—44no—
80C23×C41—44no—
81C23×C41C2×C22⋊C411yescharacteristic
82C23×C41#12012yes—
83D4×C41—44no—
84D4×C41—44no—
85D4×C41—88no—
86D4×C41—88no—
87C2×C4×C41—22no—
88C2×C4×C41—22no—
89C2×C4×C41—22no—
90C2×C4×C41—22no—
91C2×C4×C41—24no—
92C2×C4×C41—44no—
93C2×C4×C41—44no—
94C2×C4×C41—42no—
95C2×C4×C41—42no—
96C2×C4×C41—88no—
97C2×C4×C41—82no—
98C2×C4×C41—84no—
99C2×C4×C41C2×C22⋊C412yes—
100C2×C4×C41#12012yes—
101C8×C41—82no—
102#8518C4111yesmaximal, characteristic, direct product factor, Sylow
103C22×C41—22no—
104C22×C41—24no—
105C22×C41—22no—
106C22×C41—44no—
107C22×C41—44no—
108C22×C41—44no—
109C22×C41—82no—
110C22×C41—88no—
111C22×C41#37911yescharacteristic
112C22×C41#41012yes—
113C4×C41—22no—
114C4×C41—22no—
115C4×C41—44no—
116C4×C41—42no—
117C4×C41—42no—
118C4×C41—162no—
119C2×#540C2×C4111yescharacteristic
120#1822C2×C4111yescharacteristic, complemented
121#1820C2×C4111yescharacteristic, complemented
122#1510C2×C4114yescomplemented
123C2×C41—22no—
124C2×C41—42no—
125C2×C41—84no—
126C2×C41#178211yescharacteristic
127C2×C41#179512yes—
128#540—28no—
129C2×#127C4×C4111yescharacteristic, complemented
130C2×#125C4×C4111yescharacteristic, complemented
131C2×#123—22no—
132C2×#121—22no—
133C2×#121C22×C4112yes—
134C2×C4×D4C4×C4112yescomplemented
135C2×#117C22×C4111yescharacteristic
136#407C22×C4112yes—
137#381C22×C4112yes—
138#343—22no—
139#342—22no—
140#327—28no—
141C41#851811yescharacteristic, direct product factor, Sylow
142C22×D4—22no—
143C22×D4—22no—
144C22×D4C2×C4×C4112yes—
145C23×C4—22no—
146C23×C4C23×C4111yescharacteristic
147C2×M16—22no—
148#127—24no—
149#125—24no—
150#123—216no—
151#121—216no—
152#121—24no—
153#121D4×C4118yes—
154C4×D4—24no—
155C4×D4—24no—
156#117—24no—
157C2×C4⋊C4—22no—
158C2×C4⋊C4C2×C4×C4112yes—
159C2×C4⋊C4D4×C4112yes—
160C2×C22⋊C4—22no—
161C2×C22⋊C4—22no—
162C2×C22⋊C4—22no—
163C2×C22⋊C4D4×C4112yes—
164C2×C42C2×C4×C4111yescharacteristic
165C2×C42C2×C4×C4111yescharacteristic
166C22⋊C8—24no—
167#95—24no—
168C24—22no—
169C24C2×D4×C4111yescharacteristic
170C2×D4—28no—
171C2×D4—28no—
172C2×D4—22no—
173C2×D4—44no—
174C2×D4—84no—
175C2×D4—84no—
176C2×D4C22⋊C4×C4114yes—
177C22×C4—22no—
178C22×C4—28no—
179C22×C4—42no—
180C22×C4—42no—
181C22×C4—84no—
182C22×C4C22⋊C4×C4112yes—
183C22×C4C22⋊C4×C4112yes—
184C22×C4C22×C4×C4111yescharacteristic
185C22×C4C2×D4×C4111yescharacteristic
186C22×C4C2×D4×C4114yes—
187M16—44no—
188C2×C8—42no—
189C4⋊C4—28no—
190C4⋊C4—22no—
191C4⋊C4—24no—
192C4⋊C4C22⋊C4×C4114yes—
193C22⋊C4—28no—
194C22⋊C4—24no—
195C22⋊C4—28no—
196C22⋊C4—44no—
197C42—22no—
198C42—22no—
199C23—22no—
200C23—24no—
201C23—42no—
202C23—44no—
203C23—44no—
204C23—44no—
205C23C2×C22⋊C4×C4111yescharacteristic
206C23#120×C4112yes—
207D4—44no—
208D4—44no—
209D4—88no—
210D4—88no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—24no—
216C2×C4—44no—
217C2×C4—44no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—88no—
221C2×C4—82no—
222C2×C4—84no—
223C2×C4C2×C22⋊C4×C4112yes—
224C2×C4#120×C4112yes—
225C8—82no—
226C22—22no—
227C22—22no—
228C22—24no—
229C22—44no—
230C22—44no—
231C22—44no—
232C22—82no—
233C22—88no—
234C22C41×#37911yescharacteristic
235C22C41×#41012yes—
236C4—22no—
237C4—22no—
238C4—44no—
239C4—42no—
240C4—42no—
241C4—162no—
242C2—22no—
243C2—42no—
244C2—84no—
245C2C41×#178211yescharacteristic
246C2C41×#179512yes—
subgroupG/H
center, socleC22×C41#379
commutatorC22×C4C22×C4×C41
Frattini, cosocleC23×C4C23×C41
prime radicalC2×C41×#540C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C41 ◁ C23×C4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C41×#1822C2semidirect
3. C41×#1820C2semidirect
4. C41×#1510C2semidirect
6. C2×#127×C41C4semidirect
7. C2×#125×C41C4semidirect
11. C2×C4×D4×C41C4semidirect
102. #8518C41direct (N × H)
120. #1822C2×C41semidirect
121. #1820C2×C41semidirect
122. #1510C2×C41semidirect
129. C2×#127C4×C41semidirect
130. C2×#125C4×C41semidirect
134. C2×C4×D4C4×C41semidirect
141. C41#8518direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C41×#5402
C41×#18222
C41×#18202
C41×#15102
#851841