Finite Group Databasebeta

← C41×#34012 #23810213

Subgroups — C41×#34012 #23810213

Order 10496.

3158 conjugacy classes of subgroups.

The subgroup lattice has 198 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C42×C41C211yesmaximal, characteristic
2C41×#2285C216yesmaximal, complemented
3C41×#2283C2112yesmaximal, complemented
4C41×#2280C216yesmaximal
5C4×#117×C41C216yesmaximal, complemented
6C24×C4×C41C2213yes—
7C2×#117×C41C22112yes—
8C22×C42×C41C4116yescomplemented
9C22×C42×C41C2216yes—
10C22×C42×C41C2213yes—
11C22×C42×C41C2213yes—
12C41×#384C2214yescomplemented
13C41×#383C2218yescomplemented
14C41×#382C22112yescomplemented
15C41×#381C22112yes—
16C41×#380C22124yes—
17C41×#379C2214yes—
18C4×C4⋊C4×C41C22124yescomplemented
19C4×C22⋊C4×C41C22124yes—
20C41×#376C22112yescomplemented
21C43×C41C2214yescomplemented
22C25×C41C2311yescharacteristic
23C23×C4×C41—224no—
24C23×C4×C41C2×C4124yes—
25C23×C4×C41C2316yes—
26C23×C4×C41C2316yes—
27C23×C4×C41C2313yes—
28C23×C4×C41C2313yes—
29#117×C41—248no—
30C2×C4⋊C4×C41C23124yes—
31C2×C22⋊C4×C41C23124yes—
32C2×C42×C41C2×C4148yes—
33C2×C42×C41C2×C4124yes—
34C2×C42×C41C2×C4124yes—
35C2×C42×C41C23124yes—
36C2×C42×C41C2313yes—
37C2×C42×C41C2316yes—
38C2×C42×C41C2313yes—
39C2×C42×C41C2312yes—
40C2×C42×C41C2311yescharacteristic
41C2×C42×C41C2311yescharacteristic
42#95×C41C23148yes—
43C24×C41—212no—
44C24×C41C22×C414yes—
45C24×C41C2413yes—
46C22×C4×C41—212no—
47C22×C4×C41—296no—
48C22×C4×C41—224no—
49C22×C4×C41—224no—
50C22×C4×C41C22×C4112yes—
51C22×C4×C41C22×C4124yes—
52C22×C4×C41C22×C4124yes—
53C22×C4×C41C22×C4112yes—
54C22×C4×C41#41124yes—
55C22×C4×C41C24116yes—
56C22×C4×C41C2416yes—
57C22×C4×C41C2413yes—
58C22×C4×C41C2413yes—
59C4⋊C4×C41—248no—
60C22⋊C4×C41—248no—
61C42×C41—248no—
62C42×C41C22×C418yes—
63C42×C41C22×C4112yes—
64C42×C41C22×C4112yes—
65C42×C41C22×C4124yes—
66C42×C41C22×C414yes—
67C42×C41C22×C414yes—
68C23×C41—232no—
69C23×C41—224no—
70C23×C41—212no—
71C23×C41C23×C416yes—
72C23×C41C2×#41112yes—
73C23×C41C2511yescharacteristic
74C2×C4×C41—224no—
75C2×C4×C41—212no—
76C2×C4×C41—248no—
77C2×C4×C41—248no—
78C2×C4×C41—248no—
79C2×C4×C41#117148yescomplemented
80C2×C4×C41C23×C4112yes—
81C2×C4×C41C23×C416yes—
82C2×C4×C41C23×C416yes—
83C2×C4×C41C2×#41112yes—
84C2×C4×C41C2×#41112yes—
85#34012C4111yesmaximal, characteristic, direct product factor, Sylow
86C22×C41—232no—
87C22×C41—212no—
88C22×C41—224no—
89C22×C41C2×#117112yes—
90C22×C41C24×C411yescharacteristic
91C22×C41C22×#4116yes—
92C4×C41—212no—
93C4×C41—416no—
94C4×C41C2×#117112yes—
95C4×C41C2×#117112yes—
96C23×C42C2×C4111yescharacteristic
97#2285C2×C4116yescomplemented
98#2283C2×C41112yescomplemented
99#2280C2×C4116yes—
100C4×#117C2×C4116yescomplemented
101C2×C41—212no—
102C2×C41C22×#11713yes—
103C2×C41#344414yes—
104C24×C4C22×C4113yes—
105C2×#117C22×C41112yes—
106C22×C42C4×C41116yescomplemented
107C22×C42C22×C4113yes—
108C22×C42C22×C4116yes—
109C22×C42C22×C4113yes—
110#384C22×C4114yescomplemented
111#383C22×C4118yescomplemented
112#382C22×C41112yescomplemented
113#381C22×C41112yes—
114#380C22×C41124yes—
115#379C22×C4114yes—
116C4×C4⋊C4C22×C41124yescomplemented
117C4×C22⋊C4C22×C41124yes—
118#376C22×C41112yescomplemented
119C43C22×C4114yescomplemented
120C41#3401211yescharacteristic, direct product factor, Sylow
121C25C23×C4111yescharacteristic
122C23×C4—224no—
123C23×C4C2×C4×C41124yes—
124C23×C4C23×C4116yes—
125C23×C4C23×C4116yes—
126C23×C4C23×C4113yes—
127C23×C4C23×C4113yes—
128#117—248no—
129C2×C4⋊C4C23×C41124yes—
130C2×C22⋊C4C23×C41124yes—
131C2×C42C2×C4×C41148yes—
132C2×C42C2×C4×C41124yes—
133C2×C42C2×C4×C41124yes—
134C2×C42C23×C41124yes—
135C2×C42C23×C4111yescharacteristic
136C2×C42C23×C4113yes—
137C2×C42C23×C4116yes—
138C2×C42C23×C4113yes—
139C2×C42C23×C4112yes—
140C2×C42C23×C4111yescharacteristic
141#95C23×C41148yes—
142C24—212no—
143C24C22×C4×C4114yes—
144C24C24×C4113yes—
145C22×C4—212no—
146C22×C4—296no—
147C22×C4—224no—
148C22×C4—224no—
149C22×C4C22×C4×C41112yes—
150C22×C4C22×C4×C41124yes—
151C22×C4C22×C4×C41124yes—
152C22×C4C22×C4×C41112yes—
153C22×C4#41×C41124yes—
154C22×C4C24×C41116yes—
155C22×C4C24×C4116yes—
156C22×C4C24×C4113yes—
157C22×C4C24×C4113yes—
158C4⋊C4—248no—
159C22⋊C4—248no—
160C42—248no—
161C42C22×C4×C4118yes—
162C42C22×C4×C41112yes—
163C42C22×C4×C41112yes—
164C42C22×C4×C41124yes—
165C42C22×C4×C4114yes—
166C42C22×C4×C4114yes—
167C23—232no—
168C23—224no—
169C23—212no—
170C23C23×C4×C4116yes—
171C23C2×#41×C41112yes—
172C23C25×C4111yescharacteristic
173C2×C4—224no—
174C2×C4—212no—
175C2×C4—248no—
176C2×C4—248no—
177C2×C4—248no—
178C2×C4#117×C41148yescomplemented
179C2×C4C23×C4×C41112yes—
180C2×C4C23×C4×C4116yes—
181C2×C4C23×C4×C4116yes—
182C2×C4C2×#41×C41112yes—
183C2×C4C2×#41×C41112yes—
184C22—232no—
185C22—212no—
186C22—224no—
187C22C2×#117×C41112yes—
188C22C24×C4×C4111yescharacteristic
189C22C22×#41×C4116yes—
190C4—212no—
191C4—416no—
192C4C2×#117×C41112yes—
193C4C2×#117×C41112yes—
194C2—212no—
195C2C22×#117×C4113yes—
196C2C41×#344414yes—
subgroupG/H
centerC2×C42×C41C23
commutatorC22C24×C4×C41
Frattini, cosocleC23C25×C41
socleC23×C41C25
prime radicalC25×C41C23
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C2×C42×C41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C41×#2285C2semidirect
3. C41×#2283C2semidirect
5. C4×#117×C41C2semidirect
8. C22×C42×C41C4semidirect
12. C41×#384C22semidirect
13. C41×#383C22semidirect
14. C41×#382C22semidirect
18. C4×C4⋊C4×C41C22semidirect
20. C41×#376C22semidirect
21. C43×C41C22semidirect
79. C2×C4×C41#117semidirect
85. #34012C41direct (N × H)
97. #2285C2×C41semidirect
98. #2283C2×C41semidirect
100. C4×#117C2×C41semidirect
106. C22×C42C4×C41semidirect
110. #384C22×C41semidirect
111. #383C22×C41semidirect
112. #382C22×C41semidirect
116. C4×C4⋊C4C22×C41semidirect
118. #376C22×C41semidirect
119. C43C22×C41semidirect
120. C41#34012direct (N × H)
178. C2×C4#117×C41semidirect

Maximal subgroups

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

subgroupindex
C23×C42×C412
C41×#22852
C41×#22832
C41×#22802
C4×#117×C412
#3401241