Finite Group Databasebeta

← C2×C31×#2371 #21490905

Subgroups — C2×C31×#2371 #21490905

Order 7936.

2422 conjugacy classes of subgroups.

The subgroup lattice has 220 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#125C211yesmaximal, characteristic
2C31×#2371C2116yesmaximal, direct product factor
3C2×C31×#387C214yesmaximal
4C2×C31×#387C214yesmaximal
5C2×C4×C4⋊C4×C31C214yesmaximal
6C2×C31×#376C212yesmaximal
7C2×C31×#125C4116yescomplemented
8C2×C31×#125C2218yes—
9C22×C4⋊C4×C31C2214yes—
10C22×C4⋊C4×C31C2214yes—
11C22×C4⋊C4×C31C2212yes—
12C22×C42×C31C2214yes—
13C22×C42×C31C2214yes—
14C22×C42×C31C2211yescharacteristic
15C31×#387C22132yes—
16C31×#387C22132yes—
17C4×C4⋊C4×C31C22132yes—
18C31×#376C22116yes—
19C2×C31×#95C2212yes—
20C2×C31×#95C2212yes—
21C2×C31×#95C2214yes—
22C2×C31×#95C2214yes—
23C2×C31×#95C2214yes—
24C23×C4×C31C2314yes—
25C23×C4×C31C2312yes—
26C23×C4×C31C2314yes—
27C23×C4×C31C2311yescharacteristic
28C23×C4×C31C2314yes—
29C31×#125C2×C4164yescomplemented
30C2×C4⋊C4×C31—216no—
31C2×C4⋊C4×C31C2×C4132yes—
32C2×C4⋊C4×C31C2×C4116yes—
33C2×C4⋊C4×C31C23116yes—
34C2×C4⋊C4×C31C23116yes—
35C2×C4⋊C4×C31C2318yes—
36C2×C42×C31—216no—
37C2×C42×C31—216no—
38C2×C42×C31C2×C418yes—
39C2×C42×C31C23116yes—
40C2×C42×C31C23116yes—
41C2×C42×C31C2314yes—
42C31×#95C2318yes—
43C31×#95C2318yes—
44C31×#95C23116yes—
45C31×#95C23116yes—
46C31×#95C23116yes—
47C24×C31C2411yescharacteristic
48C22×C4×C31—28no—
49C22×C4×C31—28no—
50C22×C4×C31—28no—
51C22×C4×C31—28no—
52C22×C4×C31—24no—
53C22×C4×C31—28no—
54C22×C4×C31—28no—
55C22×C4×C31—28no—
56C22×C4×C31—28no—
57C22×C4×C31C22×C418yes—
58C22×C4×C31C22×C414yes—
59C22×C4×C31C22×C4116yes—
60C22×C4×C31#41116yes—
61C22×C4×C31C2418yes—
62C22×C4×C31C2412yes—
63C22×C4×C31C2414yes—
64C22×C4×C31C2418yes—
65C22×C4×C31C2418yes—
66C4⋊C4×C31—232no—
67C4⋊C4×C31C22×C4164yes—
68C4⋊C4×C31C22×C4132yes—
69C42×C31—232no—
70C42×C31—232no—
71C42×C31C22×C4116yes—
72C2×#2371C3111yesmaximal, characteristic, direct product factor, Sylow
73C23×C31C23×C412yes—
74C23×C31C2×#4118yes—
75C23×C312−1+414yes—
76C23×C31C2511yescharacteristic
77C2×C4×C31—216no—
78C2×C4×C31—232no—
79C2×C4×C31—28no—
80C2×C4×C31—232no—
81C2×C4×C31—28no—
82C2×C4×C31—28no—
83C2×C4×C31—28no—
84C2×C4×C31—28no—
85C2×C4×C31—24no—
86C2×C4×C31—28no—
87C2×C4×C31—28no—
88C2×C4×C31—28no—
89C2×C4×C31—28no—
90C2×C4×C31—416no—
91C2×C4×C31C23×C418yes—
92C2×C4×C31C23×C414yes—
93C2×C4×C31C23×C4116yes—
94C2×C4×C31C2×#41116yes—
95C22×#125C2×C3111yescharacteristic
96#2371C2×C31116yesdirect product factor
97C2×#387C2×C3114yes—
98C2×#387C2×C3114yes—
99C2×C4×C4⋊C4C2×C3114yes—
100C2×#376C2×C3112yes—
101C22×C31C4×#4118yes—
102C22×C31#51914yes—
103C22×C31#552116yes—
104C22×C31C24×C411yescharacteristic
105C22×C31C22×#4114yes—
106C22×C31C2×2−1+412yes—
107C4×C31—28no—
108C4×C31—216no—
109C4×C31—24no—
110C4×C31—216no—
111C4×C31—48no—
112C2×#125C4×C31116yescomplemented
113C2×#125C22×C3118yes—
114C22×C4⋊C4C22×C3114yes—
115C22×C4⋊C4C22×C3114yes—
116C22×C4⋊C4C22×C3112yes—
117C22×C42C22×C3114yes—
118C22×C42C22×C3114yes—
119C22×C42C22×C3111yescharacteristic
120#387C22×C31132yes—
121#387C22×C31132yes—
122C4×C4⋊C4C22×C31132yes—
123#376C22×C31116yes—
124C2×#95C22×C3112yes—
125C2×#95C22×C3112yes—
126C2×#95C22×C3114yes—
127C2×#95C22×C3114yes—
128C2×#95C22×C3114yes—
129C2×C31#237118yesdirect product factor
130C2×C31C2×C4×#4112yes—
131C2×C31C2×#51911yescharacteristic
132C2×C31C2×#55214yes—
133C23×C4C23×C3114yes—
134C23×C4C23×C3114yes—
135C23×C4C23×C3111yescharacteristic
136C23×C4C23×C3112yes—
137C23×C4C23×C3114yes—
138#125C2×C4×C31164yescomplemented
139C2×C4⋊C4—216no—
140C2×C4⋊C4C2×C4×C31132yes—
141C2×C4⋊C4C2×C4×C31116yes—
142C2×C4⋊C4C23×C31116yes—
143C2×C4⋊C4C23×C31116yes—
144C2×C4⋊C4C23×C3118yes—
145C2×C42—216no—
146C2×C42—216no—
147C2×C42C2×C4×C3118yes—
148C2×C42C23×C31116yes—
149C2×C42C23×C31116yes—
150C2×C42C23×C3114yes—
151#95C23×C3118yes—
152#95C23×C3118yes—
153#95C23×C31116yes—
154#95C23×C31116yes—
155#95C23×C31116yes—
156C31C2×#237111yescharacteristic, direct product factor, Sylow
157C24C24×C3111yescharacteristic
158C22×C4—28no—
159C22×C4—28no—
160C22×C4—28no—
161C22×C4—28no—
162C22×C4—24no—
163C22×C4—28no—
164C22×C4—28no—
165C22×C4—28no—
166C22×C4—28no—
167C22×C4C22×C4×C3118yes—
168C22×C4C22×C4×C3114yes—
169C22×C4C22×C4×C31116yes—
170C22×C4#41×C31116yes—
171C22×C4C24×C3118yes—
172C22×C4C24×C3112yes—
173C22×C4C24×C3114yes—
174C22×C4C24×C3118yes—
175C22×C4C24×C3118yes—
176C4⋊C4—232no—
177C4⋊C4C22×C4×C31164yes—
178C4⋊C4C22×C4×C31132yes—
179C42—232no—
180C42—232no—
181C42C22×C4×C31116yes—
182C23C23×C4×C3112yes—
183C23C2×#41×C3118yes—
184C23C31×2−1+414yes—
185C23C25×C3111yescharacteristic
186C2×C4—216no—
187C2×C4—232no—
188C2×C4—28no—
189C2×C4—232no—
190C2×C4—28no—
191C2×C4—28no—
192C2×C4—28no—
193C2×C4—28no—
194C2×C4—24no—
195C2×C4—28no—
196C2×C4—28no—
197C2×C4—28no—
198C2×C4—28no—
199C2×C4—416no—
200C2×C4C23×C4×C3118yes—
201C2×C4C23×C4×C3114yes—
202C2×C4C23×C4×C31116yes—
203C2×C4C2×#41×C31116yes—
204C22C4×#41×C3118yes—
205C22C31×#51914yes—
206C22C31×#552116yes—
207C22C24×C4×C3111yescharacteristic
208C22C22×#41×C3114yes—
209C22C2×C31×2−1+412yes—
210C4—28no—
211C4—216no—
212C4—24no—
213C4—216no—
214C4—48no—
215C2C31×#237118yesdirect product factor
216C2C2×C4×#41×C3112yes—
217C2C2×C31×#51911yescharacteristic
218C2C2×C31×#55214yes—
subgroupG/H
center, socle, prime radicalC24×C31C24
commutatorC22C24×C4×C31
Frattini, cosocleC23C25×C31
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#2371C2direct (N × H)
7. C2×C31×#125C4semidirect
29. C31×#125C2×C4semidirect
72. C2×#2371C31direct (N × H)
96. #2371C2×C31direct (N × H)
112. C2×#125C4×C31semidirect
129. C2×C31#2371direct (N × H)
138. #125C2×C4×C31semidirect
156. C31C2×#2371direct (N × H)
215. C2C31×#2371direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C31×#1252
C31×#23712
C2×C31×#3872
C2×C4×C4⋊C4×C312
C2×C31×#3762
C2×#237131