Finite Group Databasebeta

← C41×#12164 #23788365

Subgroups — C41×#12164 #23788365

Order 10496.

374 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 74 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×#2184C212yesmaximal, complemented
3C41×#2045C211yesmaximal, characteristic, complemented
4C41×#1349C212yesmaximal, complemented
5C41×#1323C211yesmaximal, characteristic, complemented
6C22×D8×C41C2211yescharacteristic
7C41×#540—21no—
8C2×D16×C41—22no—
9C41×#478—22no—
10C41×#469—21no—
11C41×#466C2212yes—
12C41×#459—22no—
13C41×#424C2211yescharacteristic
14C41×#418—21no—
15C2×#100×C41—21no—
16C41×#357—22no—
17C41×C22⋊C16C2212yes—
18C41×#341C2211yescharacteristic
19C22×D4×C41—21no—
20C2×D8×C41—21no—
21C2×D8×C41—22no—
22C2×D8×C41—42no—
23C2×D8×C41D412yes—
24C2×M16×C41—21no—
25C2×M16×C41D411yescharacteristic
26C22×C8×C41C2311yescharacteristic
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×C41D411yescharacteristic
34D16×C41—44no—
35C2×C16×C41—22no—
36#107×C41D412yes—
37#106×C41—21no—
38C4⋊C8×C41—22no—
39#102×C41—22no—
40#102×C41—22no—
41#102×C41—42no—
42#100×C41—42no—
43C24×C41—41no—
44C2×D4×C41—22no—
45C2×D4×C41—22no—
46C2×D4×C41—41no—
47C2×D4×C41—41no—
48C2×D4×C41—41no—
49C2×D4×C41—42no—
50C2×D4×C41—42no—
51C2×D4×C41—41no—
52C2×D4×C41—41no—
53C22×C4×C41—42no—
54C22×C4×C41C2×D411yescharacteristic
55D8×C41—24no—
56D8×C41—42no—
57D8×C41—42no—
58D8×C41—81no—
59M16×C41—41no—
60M16×C41—41no—
61M16×C41—41no—
62C2×C8×C41—21no—
63C2×C8×C41—41no—
64C2×C8×C41—41no—
65C2×C8×C41C2×D412yes—
66C4⋊C4×C41—22no—
67C4⋊C4×C41—42no—
68C4⋊C4×C41D812yes—
69C22⋊C4×C41—21no—
70C22⋊C4×C41—42no—
71C22⋊C4×C41—42no—
72C42×C41—21no—
73C16×C41—42no—
74C23×C41—42no—
75C23×C41—42no—
76C23×C41—81no—
77C23×C41—81no—
78C23×C41—162no—
79C23×C41AGL(1,ℤ/8)11yescharacteristic
80D4×C41—42no—
81D4×C41—42no—
82D4×C41—42no—
83D4×C41—42no—
84D4×C41—81no—
85D4×C41—81no—
86D4×C41—162no—
87D4×C41—162no—
88C2×C4×C41—21no—
89C2×C4×C41—21no—
90C2×C4×C41—22no—
91C2×C4×C41—42no—
92C2×C4×C41—162no—
93C2×C4×C41#12011yescharacteristic
94C2×C4×C41C2×D811yescharacteristic
95C8×C41—22no—
96C8×C41—41no—
97C8×C41—81no—
98#12164C4111yesmaximal, characteristic, direct product factor, Sylow
99C22×C41—21no—
100C22×C41—22no—
101C22×C41—82no—
102C22×C41—82no—
103C22×C41—82no—
104C22×C41—82no—
105C22×C41—162no—
106C22×C41—162no—
107C22×C41—162no—
108C22×C41#44711yescharacteristic
109C4×C41—21no—
110C4×C41—42no—
111C4×C41—82no—
112C4×C41#45411yescharacteristic
113C4×C41B(4,𝔽2)11yescharacteristic
114#3259C2×C4111yescharacteristic, complemented
115#2184C2×C4112yescomplemented
116#2045C2×C4111yescharacteristic, complemented
117#1349C2×C4112yescomplemented
118#1323C2×C4111yescharacteristic, complemented
119C2×C41—41no—
120C2×C41—162no—
121C2×C41—162no—
122C2×C41#159811yescharacteristic
123C2×C41#219212yes—
124C22×D8C22×C4111yescharacteristic
125#540—21no—
126C2×D16—22no—
127#478—22no—
128#469—21no—
129#466C22×C4112yes—
130#459—22no—
131#424C22×C4111yescharacteristic
132#418—21no—
133C2×#100—21no—
134#357—22no—
135C22⋊C16C22×C4112yes—
136#341C22×C4111yescharacteristic
137C41#1216411yescharacteristic, direct product factor, Sylow
138C22×D4—21no—
139C2×D8—21no—
140C2×D8—22no—
141C2×D8—42no—
142C2×D8D4×C4112yes—
143C2×M16—21no—
144C2×M16D4×C4111yescharacteristic
145C22×C8C23×C4111yescharacteristic
146#127—21no—
147#125—21no—
148#123—42no—
149#121—22no—
150#121—42no—
151C4×D4—22no—
152#117D4×C4111yescharacteristic
153D16—44no—
154C2×C16—22no—
155#107D4×C4112yes—
156#106—21no—
157C4⋊C8—22no—
158#102—22no—
159#102—22no—
160#102—42no—
161#100—42no—
162C24—41no—
163C2×D4—22no—
164C2×D4—22no—
165C2×D4—41no—
166C2×D4—41no—
167C2×D4—41no—
168C2×D4—42no—
169C2×D4—42no—
170C2×D4—41no—
171C2×D4—41no—
172C22×C4—42no—
173C22×C4C2×D4×C4111yescharacteristic
174D8—24no—
175D8—42no—
176D8—42no—
177D8—81no—
178M16—41no—
179M16—41no—
180M16—41no—
181C2×C8—21no—
182C2×C8—41no—
183C2×C8—41no—
184C2×C8C2×D4×C4112yes—
185C4⋊C4—22no—
186C4⋊C4—42no—
187C4⋊C4D8×C4112yes—
188C22⋊C4—21no—
189C22⋊C4—42no—
190C22⋊C4—42no—
191C42—21no—
192C16—42no—
193C23—42no—
194C23—42no—
195C23—81no—
196C23—81no—
197C23—162no—
198C23AGL(1,ℤ/8)×C4111yescharacteristic
199D4—42no—
200D4—42no—
201D4—42no—
202D4—42no—
203D4—81no—
204D4—81no—
205D4—162no—
206D4—162no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—22no—
210C2×C4—42no—
211C2×C4—162no—
212C2×C4#120×C4111yescharacteristic
213C2×C4C2×D8×C4111yescharacteristic
214C8—22no—
215C8—41no—
216C8—81no—
217C22—21no—
218C22—22no—
219C22—82no—
220C22—82no—
221C22—82no—
222C22—82no—
223C22—162no—
224C22—162no—
225C22—162no—
226C22C41×#44711yescharacteristic
227C4—21no—
228C4—42no—
229C4—82no—
230C4C41×#45411yescharacteristic
231C4C41×B(4,𝔽2)11yescharacteristic
232C2—41no—
233C2—162no—
234C2—162no—
235C2C41×#159811yescharacteristic
236C2C41×#219212yes—
subgroupG/H
center, socleC22×C41#447
commutator, Frattini, cosocleC22×C8C23×C41
LCSG ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C41 ◁ C22×C4×C41 ◁ C41×#424 ◁ G

Complements

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

NH ≅ G/Ntype
1. C41×#3259C2semidirect
2. C41×#2184C2semidirect
3. C41×#2045C2semidirect
4. C41×#1349C2semidirect
5. C41×#1323C2semidirect
98. #12164C41direct (N × H)
114. #3259C2×C41semidirect
115. #2184C2×C41semidirect
116. #2045C2×C41semidirect
117. #1349C2×C41semidirect
118. #1323C2×C41semidirect
137. C41#12164direct (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×#21842
C41×#20452
C41×#13492
C41×#13232
#1216441