Finite Group Databasebeta

← C2×C47×#2399 #26074244

Subgroups — C2×C47×#2399 #26074244

Order 12032.

2814 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×C4×Q8×C47C212yesmaximal
2C47×#2399C2116yesmaximal, direct product factor
3C2×C47×#398C214yesmaximal
4C2×C47×#395C214yesmaximal
5C2×C4×C4⋊C4×C47C214yesmaximal
6C2×C47×#376C211yesmaximal, characteristic
7C23×Q8×C47C2212yes—
8C2×C4×Q8×C47—216no—
9C2×C4×Q8×C47C22116yes—
10C22×C4⋊C4×C47C2218yes—
11C22×C4⋊C4×C47C2214yes—
12C22×C4⋊C4×C47C2212yes—
13C22×C42×C47C2214yes—
14C22×C42×C47C2211yescharacteristic
15C22×C42×C47C2212yes—
16C47×#398C22132yes—
17C47×#395C22132yes—
18C4×C4⋊C4×C47C22132yes—
19C47×#376C2218yes—
20C2×#95×C47C2214yes—
21C2×#95×C47C2214yes—
22C2×#95×C47C2214yes—
23C22×Q8×C47—28no—
24C22×Q8×C47—216no—
25C22×Q8×C47C2318yes—
26C23×C4×C47C2314yes—
27C23×C4×C47C2312yes—
28C23×C4×C47C2314yes—
29C23×C4×C47C2314yes—
30C23×C4×C47C2311yescharacteristic
31C4×Q8×C47—264no—
32C2×C4⋊C4×C47—216no—
33C2×C4⋊C4×C47—28no—
34C2×C4⋊C4×C47—232no—
35C2×C4⋊C4×C47C23116yes—
36C2×C4⋊C4×C47C2318yes—
37C2×C4⋊C4×C47C23132yes—
38C2×C42×C47—216no—
39C2×C42×C47D418yes—
40C2×C42×C47Q8116yescomplemented
41C2×C42×C47C23116yes—
42C2×C42×C47C2314yes—
43C2×C42×C47C2318yes—
44#95×C47C23116yes—
45#95×C47C23116yes—
46#95×C47C23116yes—
47C24×C47C2411yescharacteristic
48C2×Q8×C47—264no—
49C2×Q8×C47—216no—
50C2×Q8×C47—232no—
51C22×C4×C47—28no—
52C22×C4×C47—216no—
53C22×C4×C47—28no—
54C22×C4×C47—28no—
55C22×C4×C47—28no—
56C22×C4×C47—216no—
57C22×C4×C47C2×D418yes—
58C22×C4×C47C2×D414yes—
59C22×C4×C47C2×Q8116yes—
60C22×C4×C47C2×Q818yes—
61C22×C4×C47#41116yes—
62C22×C4×C47C2418yes—
63C22×C4×C47C2414yes—
64C22×C4×C47C2418yes—
65C22×C4×C47C2418yes—
66C22×C4×C47C2412yes—
67C4⋊C4×C47—232no—
68C4⋊C4×C47—216no—
69C4⋊C4×C47—264no—
70C42×C47—232no—
71C42×C47C2×D4116yes—
72C42×C47C2×Q8132yescomplemented
73C23×C47C22×D412yes—
74C23×C47C22×Q814yes—
75C23×C47C2×#4118yes—
76C23×C47C2511yescharacteristic
77Q8×C47—264no—
78C2×C4×C47—216no—
79C2×C4×C47—232no—
80C2×C4×C47—232no—
81C2×C4×C47—28no—
82C2×C4×C47—216no—
83C2×C4×C47—28no—
84C2×C4×C47—28no—
85C2×C4×C47—28no—
86C2×C4×C47—216no—
87C2×C4×C47—416no—
88C2×C4×C47C4⋊Q8116yes—
89C2×C4×C47C22×D418yes—
90C2×C4×C47C22×D414yes—
91C2×C4×C47C22×Q8116yes—
92C2×C4×C47C22×Q818yes—
93C2×C4×C47C2×#41116yes—
94C2×#2399C4711yesmaximal, characteristic, direct product factor, Sylow
95C22×C47#52518yes—
96C22×C47C2×C4⋊Q814yes—
97C22×C47#533116yes—
98C22×C47C23×D411yescharacteristic
99C22×C47C23×Q812yes—
100C22×C47C22×#4114yes—
101C4×C47—28no—
102C4×C47—216no—
103C4×C47—216no—
104C4×C47—48no—
105C4×C47C2×C4⋊Q818yes—
106C22×C4×Q8C2×C4712yes—
107#2399C2×C47116yesdirect product factor
108C2×#398C2×C4714yes—
109C2×#395C2×C4714yes—
110C2×C4×C4⋊C4C2×C4714yes—
111C2×#376C2×C4711yescharacteristic
112C2×C47#239918yesdirect product factor
113C2×C47C2×#52512yes—
114C2×C47C22×C4⋊Q811yescharacteristic
115C2×C47C2×#53314yes—
116C23×Q8C22×C4712yes—
117C2×C4×Q8—216no—
118C2×C4×Q8C22×C47116yes—
119C22×C4⋊C4C22×C4714yes—
120C22×C4⋊C4C22×C4718yes—
121C22×C4⋊C4C22×C4712yes—
122C22×C42C22×C4714yes—
123C22×C42C22×C4711yescharacteristic
124C22×C42C22×C4712yes—
125#398C22×C47132yes—
126#395C22×C47132yes—
127C4×C4⋊C4C22×C47132yes—
128#376C22×C4718yes—
129C2×#95C22×C4714yes—
130C2×#95C22×C4714yes—
131C2×#95C22×C4714yes—
132C47C2×#239911yescharacteristic, direct product factor, Sylow
133C22×Q8—28no—
134C22×Q8—216no—
135C22×Q8C23×C4718yes—
136C23×C4C23×C4714yes—
137C23×C4C23×C4712yes—
138C23×C4C23×C4714yes—
139C23×C4C23×C4714yes—
140C23×C4C23×C4711yescharacteristic
141C4×Q8—264no—
142C2×C4⋊C4—216no—
143C2×C4⋊C4—28no—
144C2×C4⋊C4—232no—
145C2×C4⋊C4C23×C47116yes—
146C2×C4⋊C4C23×C4718yes—
147C2×C4⋊C4C23×C47132yes—
148C2×C42—216no—
149C2×C42D4×C4718yes—
150C2×C42Q8×C47116yescomplemented
151C2×C42C23×C47116yes—
152C2×C42C23×C4714yes—
153C2×C42C23×C4718yes—
154#95C23×C47116yes—
155#95C23×C47116yes—
156#95C23×C47116yes—
157C24C24×C4711yescharacteristic
158C2×Q8—264no—
159C2×Q8—216no—
160C2×Q8—232no—
161C22×C4—28no—
162C22×C4—216no—
163C22×C4—28no—
164C22×C4—28no—
165C22×C4—28no—
166C22×C4—216no—
167C22×C4C2×D4×C4718yes—
168C22×C4C2×D4×C4714yes—
169C22×C4C2×Q8×C47116yes—
170C22×C4C2×Q8×C4718yes—
171C22×C4#41×C47116yes—
172C22×C4C24×C4718yes—
173C22×C4C24×C4714yes—
174C22×C4C24×C4718yes—
175C22×C4C24×C4718yes—
176C22×C4C24×C4712yes—
177C4⋊C4—232no—
178C4⋊C4—216no—
179C4⋊C4—264no—
180C42—232no—
181C42C2×D4×C47116yes—
182C42C2×Q8×C47132yescomplemented
183C23C22×D4×C4712yes—
184C23C22×Q8×C4714yes—
185C23C2×#41×C4718yes—
186C23C25×C4711yescharacteristic
187Q8—264no—
188C2×C4—216no—
189C2×C4—232no—
190C2×C4—232no—
191C2×C4—28no—
192C2×C4—216no—
193C2×C4—28no—
194C2×C4—28no—
195C2×C4—28no—
196C2×C4—216no—
197C2×C4—416no—
198C2×C4C4⋊Q8×C47116yes—
199C2×C4C22×D4×C4718yes—
200C2×C4C22×D4×C4714yes—
201C2×C4C22×Q8×C47116yes—
202C2×C4C22×Q8×C4718yes—
203C2×C4C2×#41×C47116yes—
204C22C47×#52518yes—
205C22C2×C4⋊Q8×C4714yes—
206C22C47×#533116yes—
207C22C23×D4×C4711yescharacteristic
208C22C23×Q8×C4712yes—
209C22C22×#41×C4714yes—
210C4—28no—
211C4—216no—
212C4—216no—
213C4—48no—
214C4C2×C4⋊Q8×C4718yes—
215C2C47×#239918yesdirect product factor
216C2C2×C47×#52512yes—
217C2C22×C4⋊Q8×C4711yescharacteristic
218C2C2×C47×#53314yes—
subgroupG/H
centerC23×C4×C47C23
commutator, Frattini, cosocleC23C25×C47
socle, prime radicalC24×C47C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C47×#2399C2direct (N × H)
40. C2×C42×C47Q8semidirect
72. C42×C47C2×Q8semidirect
94. C2×#2399C47direct (N × H)
107. #2399C2×C47direct (N × H)
112. C2×C47#2399direct (N × H)
132. C47C2×#2399direct (N × H)
150. C2×C42Q8×C47semidirect
182. C42C2×Q8×C47semidirect
215. C2C47×#2399direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×Q8×C472
C47×#23992
C2×C47×#3982
C2×C47×#3952
C2×C4×C4⋊C4×C472
C2×C47×#3762
C2×#239947