Finite Group Databasebeta

← C41×#12170 #23788371

Subgroups — C41×#12170 #23788371

Order 10496.

356 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 70 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×#3259C211yesmaximal, characteristic, complemented
2C41×#2190C212yesmaximal, complemented
3C41×#2053C211yesmaximal, characteristic, complemented
4C41×#1339C212yesmaximal, complemented
5C41×#1328C211yesmaximal, characteristic, complemented
6C41×#575C2211yescharacteristic
7C41×#540—21no—
8C41×#509—22no—
9C41×#478—22no—
10C41×#469C2212yes—
11C41×#466—21no—
12C41×#459—22no—
13C41×#424C2211yescharacteristic
14C41×#416—21no—
15C41×#410—21no—
16C41×#360—22no—
17C41×#349C2212yes—
18C41×H(3,ℤ/4)C2211yescharacteristic
19C2×#41×C41—21no—
20#137×C41—41no—
21AGL(1,ℤ/8)×C41—41no—
22#135×C41—22no—
23C2×D8×C41—21no—
24C2×D8×C41D412yes—
25C2×M16×C41C2311yescharacteristic
26C22×C8×C41D411yescharacteristic
27#127×C41—21no—
28#125×C41—21no—
29#123×C41—42no—
30#121×C41—22no—
31#121×C41—42no—
32C4×D4×C41—22no—
33#117×C41—21no—
34#117×C41D411yescharacteristic
35SD32×C41—42no—
36D16×C41—42no—
37M32×C41—22no—
38#107×C41—21no—
39#106×C41D412yes—
40C4⋊C8×C41—22no—
41#103×C41—41no—
42#102×C41—22no—
43#102×C41—22no—
44#102×C41—41no—
45#99×C41—42no—
46#41×C41—41no—
47#41×C41—41no—
48#41×C41—41no—
49#41×C41—41no—
50C2×Q8×C41—21no—
51C2×D4×C41—21no—
52C2×D4×C41—22no—
53C2×D4×C41—42no—
54C2×D4×C41—41no—
55C2×D4×C41—42no—
56C22×C4×C41—41no—
57C22×C4×C41—42no—
58C22×C4×C41C2×D411yescharacteristic
59Q16×C41—22no—
60SD16×C41—42no—
61D8×C41—22no—
62D8×C41—42no—
63D8×C41—81no—
64M16×C41—41no—
65C2×C8×C41—21no—
66C2×C8×C41—41no—
67C2×C8×C41C2×D412yes—
68C4⋊C4×C41—21no—
69C4⋊C4×C41—22no—
70C4⋊C4×C41—42no—
71C4⋊C4×C41—41no—
72C22⋊C4×C41—42no—
73C22⋊C4×C41—42no—
74C22⋊C4×C41—41no—
75C22⋊C4×C41D812yes—
76C42×C41—21no—
77C42×C41—41no—
78C16×C41—42no—
79C23×C41—41no—
80C23×C41—42no—
81C23×C41C2×D811yescharacteristic
82Q8×C41—41no—
83Q8×C41—41no—
84D4×C41—41no—
85D4×C41—42no—
86D4×C41—41no—
87D4×C41—42no—
88D4×C41—81no—
89D4×C41—81no—
90D4×C41—162no—
91D4×C41—162no—
92C2×C4×C41—21no—
93C2×C4×C41—21no—
94C2×C4×C41—22no—
95C2×C4×C41—41no—
96C2×C4×C41—42no—
97C2×C4×C41—81no—
98C2×C4×C41—81no—
99C2×C4×C41—81no—
100C2×C4×C41—162no—
101C2×C4×C41#12011yescharacteristic
102C2×C4×C41AGL(1,ℤ/8)11yescharacteristic
103C8×C41—22no—
104C8×C41—41no—
105#12170C4111yesmaximal, characteristic, direct product factor, Sylow
106C22×C41—21no—
107C22×C41—41no—
108C22×C41—82no—
109C22×C41—82no—
110C22×C41—81no—
111C22×C41—82no—
112C22×C41—161no—
113C22×C41#44711yescharacteristic
114C4×C41—21no—
115C4×C41—42no—
116C4×C41—82no—
117C4×C41—81no—
118C4×C41—161no—
119C4×C41#45411yescharacteristic
120C4×C41B(4,𝔽2)11yescharacteristic
121#3259C2×C4111yescharacteristic, complemented
122#2190C2×C4112yescomplemented
123#2053C2×C4111yescharacteristic, complemented
124#1339C2×C4112yescomplemented
125#1328C2×C4111yescharacteristic, complemented
126C2×C41—21no—
127C2×C41—41no—
128C2×C41—162no—
129C2×C41—161no—
130C2×C41#159811yescharacteristic
131#575C22×C4111yescharacteristic
132#540—21no—
133#509—22no—
134#478—22no—
135#469C22×C4112yes—
136#466—21no—
137#459—22no—
138#424C22×C4111yescharacteristic
139#416—21no—
140#410—21no—
141#360—22no—
142#349C22×C4112yes—
143H(3,ℤ/4)C22×C4111yescharacteristic
144C41#1217011yescharacteristic, direct product factor, Sylow
145C2×#41—21no—
146#137—41no—
147AGL(1,ℤ/8)—41no—
148#135—22no—
149C2×D8—21no—
150C2×D8D4×C4112yes—
151C2×M16C23×C4111yescharacteristic
152C22×C8D4×C4111yescharacteristic
153#127—21no—
154#125—21no—
155#123—42no—
156#121—22no—
157#121—42no—
158C4×D4—22no—
159#117—21no—
160#117D4×C4111yescharacteristic
161SD32—42no—
162D16—42no—
163M32—22no—
164#107—21no—
165#106D4×C4112yes—
166C4⋊C8—22no—
167#103—41no—
168#102—22no—
169#102—22no—
170#102—41no—
171#99—42no—
172#41—41no—
173#41—41no—
174#41—41no—
175#41—41no—
176C2×Q8—21no—
177C2×D4—21no—
178C2×D4—22no—
179C2×D4—42no—
180C2×D4—41no—
181C2×D4—42no—
182C22×C4—41no—
183C22×C4—42no—
184C22×C4C2×D4×C4111yescharacteristic
185Q16—22no—
186SD16—42no—
187D8—22no—
188D8—42no—
189D8—81no—
190M16—41no—
191C2×C8—21no—
192C2×C8—41no—
193C2×C8C2×D4×C4112yes—
194C4⋊C4—21no—
195C4⋊C4—22no—
196C4⋊C4—42no—
197C4⋊C4—41no—
198C22⋊C4—42no—
199C22⋊C4—42no—
200C22⋊C4—41no—
201C22⋊C4D8×C4112yes—
202C42—21no—
203C42—41no—
204C16—42no—
205C23—41no—
206C23—42no—
207C23C2×D8×C4111yescharacteristic
208Q8—41no—
209Q8—41no—
210D4—41no—
211D4—42no—
212D4—41no—
213D4—42no—
214D4—81no—
215D4—81no—
216D4—162no—
217D4—162no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—41no—
222C2×C4—42no—
223C2×C4—81no—
224C2×C4—81no—
225C2×C4—81no—
226C2×C4—162no—
227C2×C4#120×C4111yescharacteristic
228C2×C4AGL(1,ℤ/8)×C4111yescharacteristic
229C8—22no—
230C8—41no—
231C22—21no—
232C22—41no—
233C22—82no—
234C22—82no—
235C22—81no—
236C22—82no—
237C22—161no—
238C22C41×#44711yescharacteristic
239C4—21no—
240C4—42no—
241C4—82no—
242C4—81no—
243C4—161no—
244C4C41×#45411yescharacteristic
245C4C41×B(4,𝔽2)11yescharacteristic
246C2—21no—
247C2—41no—
248C2—162no—
249C2—161no—
250C2C41×#159811yescharacteristic
subgroupG/H
center, socleC2×C41#1598
commutator, Frattini, cosocleC2×M16C23×C41
LCSG ▷ C2×M16 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C41 ◁ C2×C4×C41 ◁ C2×M16×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C41×#3259C2semidirect
2. C41×#2190C2semidirect
3. C41×#2053C2semidirect
4. C41×#1339C2semidirect
5. C41×#1328C2semidirect
105. #12170C41direct (N × H)
121. #3259C2×C41semidirect
122. #2190C2×C41semidirect
123. #2053C2×C41semidirect
124. #1339C2×C41semidirect
125. #1328C2×C41semidirect
144. C41#12170direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#32592
C41×#21902
C41×#20532
C41×#13392
C41×#13282
#1217041