Finite Group Databasebeta

← C47×#34642 #26074340

Subgroups — C47×#34642 #26074340

Order 12032.

2110 conjugacy classes of subgroups.

The subgroup lattice has 210 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#533C212yesmaximal
2C47×#2660C218yesmaximal, complemented
3C47×#2659C218yesmaximal
4C47×#2399C218yesmaximal, complemented
5C47×#2285C214yesmaximal
6C2×C47×#376C211yesmaximal, characteristic
7C47×#533—216no—
8C2×C4⋊Q8×C47C2214yes—
9C2×#125×C47C2214yes—
10C2×C22⋊Q8×C47C2218yes—
11C2×C4×Q8×C47C2218yes—
12C2×#117×C47C2214yes—
13C22×C42×C47C2211yescharacteristic
14C22×C42×C47C2212yes—
15C47×#398C22132yes—
16C47×#395C22132yes—
17C47×#384C2218yes—
18C47×#382C2218yes—
19C47×#380C22116yes—
20C4×C4⋊C4×C47C22116yes—
21C47×#376C2214yes—
22C47×#376C2214yes—
23C2×#95×C47C2214yes—
24C22×Q8×C47C2318yes—
25C23×C4×C47C2312yes—
26C23×C4×C47C2314yes—
27C23×C4×C47C2311yescharacteristic
28C4⋊Q8×C47—216no—
29#125×C47—216no—
30C22⋊Q8×C47—232no—
31C4×Q8×C47—232no—
32#117×C47—216no—
33C2×C4⋊C4×C47C2318yes—
34C2×C4⋊C4×C47C23116yes—
35C2×C4⋊C4×C47C2318yes—
36C2×C4⋊C4×C47C23132yes—
37C2×C22⋊C4×C47C2318yes—
38C2×C42×C47D418yes—
39C2×C42×C47Q8116yescomplemented
40C2×C42×C47C2318yes—
41C2×C42×C47C2312yes—
42C2×C42×C47C2312yes—
43C2×C42×C47C2314yes—
44C2×C42×C47C2314yes—
45#95×C47C23116yes—
46#95×C47C23132yes—
47C24×C47C2411yescharacteristic
48C2×Q8×C47—216no—
49C2×Q8×C47—416no—
50C22×C4×C47—48no—
51C22×C4×C47—44no—
52C22×C4×C47C2×D418yes—
53C22×C4×C47C2×D414yes—
54C22×C4×C47C2×Q8116yes—
55C22×C4×C47C2×Q818yes—
56C22×C4×C47C24116yes—
57C22×C4×C47C2414yes—
58C22×C4×C47C2418yes—
59C22×C4×C47C2411yescharacteristic
60C22×C4×C47C2411yescharacteristic
61C4⋊C4×C47—216no—
62C4⋊C4×C47—232no—
63C4⋊C4×C47—216no—
64C4⋊C4×C47—432no—
65C22⋊C4×C47—216no—
66C42×C47—216no—
67C42×C47C2×D418yes—
68C42×C47C2×D418yes—
69C42×C47C2×Q8116yes—
70C42×C47C2×Q8116yes—
71C23×C47—24no—
72C23×C47C22×D412yes—
73C23×C47C22×Q814yes—
74C23×C47C2511yescharacteristic
75Q8×C47—432no—
76C2×C4×C47—216no—
77C2×C4×C47—28no—
78C2×C4×C47—216no—
79C2×C4×C47—232no—
80C2×C4×C47—48no—
81C2×C4×C47—416no—
82C2×C4×C47C4⋊Q8116yes—
83C2×C4×C47C22×D418yes—
84C2×C4×C47C22×D412yes—
85C2×C4×C47C22×D412yes—
86C2×C4×C47C22×Q8116yes—
87C2×C4×C47C22×Q814yes—
88C2×C4×C47C22×Q814yes—
89#34642C4711yesmaximal, characteristic, direct product factor, Sylow
90C22×C47—24no—
91C22×C47—28no—
92C22×C47C2×C4⋊Q814yes—
93C22×C47C23×D411yescharacteristic
94C22×C47C23×Q812yes—
95C22×C47#58514yes—
96C4×C47—28no—
97C4×C47—216no—
98C4×C47—416no—
99C4×C47C2×C4⋊Q814yes—
100C4×C47C2×C4⋊Q814yes—
101C2×#533C2×C4712yes—
102#2660C2×C4718yescomplemented
103#2659C2×C4718yes—
104#2399C2×C4718yescomplemented
105#2285C2×C4714yes—
106C2×#376C2×C4711yescharacteristic
107C2×C47—24no—
108C2×C47C22×C4⋊Q811yescharacteristic
109C2×C47#344912yes—
110C2×C47#345814yes—
111#533—216no—
112C2×C4⋊Q8C22×C4714yes—
113C2×#125C22×C4714yes—
114C2×C22⋊Q8C22×C4718yes—
115C2×C4×Q8C22×C4718yes—
116C2×#117C22×C4714yes—
117C22×C42C22×C4711yescharacteristic
118C22×C42C22×C4712yes—
119#398C22×C47132yes—
120#395C22×C47132yes—
121#384C22×C4718yes—
122#382C22×C4718yes—
123#380C22×C47116yes—
124C4×C4⋊C4C22×C47116yes—
125#376C22×C4714yes—
126#376C22×C4714yes—
127C2×#95C22×C4714yes—
128C47#3464211yescharacteristic, direct product factor, Sylow
129C22×Q8C23×C4718yes—
130C23×C4C23×C4712yes—
131C23×C4C23×C4714yes—
132C23×C4C23×C4711yescharacteristic
133C4⋊Q8—216no—
134#125—216no—
135C22⋊Q8—232no—
136C4×Q8—232no—
137#117—216no—
138C2×C4⋊C4C23×C4718yes—
139C2×C4⋊C4C23×C47116yes—
140C2×C4⋊C4C23×C4718yes—
141C2×C4⋊C4C23×C47132yes—
142C2×C22⋊C4C23×C4718yes—
143C2×C42D4×C4718yes—
144C2×C42Q8×C47116yescomplemented
145C2×C42C23×C4718yes—
146C2×C42C23×C4712yes—
147C2×C42C23×C4712yes—
148C2×C42C23×C4714yes—
149C2×C42C23×C4714yes—
150#95C23×C47116yes—
151#95C23×C47132yes—
152C24C24×C4711yescharacteristic
153C2×Q8—216no—
154C2×Q8—416no—
155C22×C4—48no—
156C22×C4—44no—
157C22×C4C2×D4×C4718yes—
158C22×C4C2×D4×C4714yes—
159C22×C4C2×Q8×C47116yes—
160C22×C4C2×Q8×C4718yes—
161C22×C4C24×C47116yes—
162C22×C4C24×C4714yes—
163C22×C4C24×C4718yes—
164C22×C4C24×C4711yescharacteristic
165C22×C4C24×C4711yescharacteristic
166C4⋊C4—216no—
167C4⋊C4—232no—
168C4⋊C4—216no—
169C4⋊C4—432no—
170C22⋊C4—216no—
171C42—216no—
172C42C2×D4×C4718yes—
173C42C2×D4×C4718yes—
174C42C2×Q8×C47116yes—
175C42C2×Q8×C47116yes—
176C23—24no—
177C23C22×D4×C4712yes—
178C23C22×Q8×C4714yes—
179C23C25×C4711yescharacteristic
180Q8—432no—
181C2×C4—216no—
182C2×C4—28no—
183C2×C4—216no—
184C2×C4—232no—
185C2×C4—48no—
186C2×C4—416no—
187C2×C4C4⋊Q8×C47116yes—
188C2×C4C22×D4×C4718yes—
189C2×C4C22×D4×C4712yes—
190C2×C4C22×D4×C4712yes—
191C2×C4C22×Q8×C47116yes—
192C2×C4C22×Q8×C4714yes—
193C2×C4C22×Q8×C4714yes—
194C22—24no—
195C22—28no—
196C22C2×C4⋊Q8×C4714yes—
197C22C23×D4×C4711yescharacteristic
198C22C23×Q8×C4712yes—
199C22C47×#58514yes—
200C4—28no—
201C4—216no—
202C4—416no—
203C4C2×C4⋊Q8×C4714yes—
204C4C2×C4⋊Q8×C4714yes—
205C2—24no—
206C2C22×C4⋊Q8×C4711yescharacteristic
207C2C47×#344912yes—
208C2C47×#345814yes—
subgroupG/H
centerC22×C4×C47C24
commutator, Frattini, cosocleC23C25×C47
socleC23×C47C25
prime radicalC24×C47C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C47×#2660C2semidirect
4. C47×#2399C2semidirect
39. C2×C42×C47Q8semidirect
89. #34642C47direct (N × H)
102. #2660C2×C47semidirect
104. #2399C2×C47semidirect
128. C47#34642direct (N × H)
144. C2×C42Q8×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#5332
C47×#26602
C47×#26592
C47×#23992
C47×#22852
C2×C47×#3762
#3464247