Finite Group Databasebeta

← C2×C47×#1412 #26053291

Subgroups — C2×C47×#1412 #26053291

Order 12032.

390 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 94 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
1C2×C47×#490C211yesmaximal, characteristic
2C2×C47×#353C212yesmaximal
3C47×#1412C214yesmaximal, direct product factor
4C2×#127×C47C2211yescharacteristic
5C2×#125×C47C411yescharacteristic, complemented
6C47×#490—22no—
7C47×#490C412yescomplemented
8C47×#490C2212yes—
9C2×#102×C47—22no—
10C2×#99×C47—22no—
11C2×#97×C47C411yescharacteristic, complemented
12C47×#353—22no—
13C47×#353C2214yes—
14C22×D4×C47—41no—
15C22×D4×C47D412yes—
16C22×C8×C47—21no—
17#127×C47—41no—
18#127×C47C2×C411yescharacteristic
19#127×C47D412yes—
20#127×C47C2311yescharacteristic
21#125×C47—21no—
22#125×C47—41no—
23#125×C47C2×C412yescomplemented
24C2×C4⋊C4×C47—21no—
25C2×C4⋊C4×C47—41no—
26C2×C22⋊C4×C47—42no—
27C2×C42×C47C2×C411yescharacteristic
28#102×C47—24no—
29#102×C47—24no—
30#99×C47—24no—
31#99×C47—42no—
32#97×C47—21no—
33#97×C47C2×C412yescomplemented
34C24×C47—22no—
35C2×D4×C47—22no—
36C2×D4×C47—42no—
37C2×D4×C47—42no—
38C2×D4×C47—41no—
39C2×D4×C47—42no—
40C2×D4×C47—41no—
41C2×D4×C47—84no—
42C2×D4×C47C22⋊C412yes—
43C2×D4×C47C2×D412yes—
44C22×C4×C47—21no—
45C22×C4×C47—41no—
46C22×C4×C47—82no—
47C22×C4×C47C22⋊C411yescharacteristic
48C2×C8×C47—22no—
49C2×C8×C47—41no—
50C2×C8×C47—41no—
51C4⋊C4×C47—22no—
52C4⋊C4×C47—42no—
53C4⋊C4×C47—42no—
54C4⋊C4×C47—41no—
55C22⋊C4×C47—44no—
56C22⋊C4×C47—82no—
57C42×C47—21no—
58C42×C47C22⋊C411yescharacteristic
59C42×C47C22×C411yescharacteristic
60C23×C47—22no—
61C23×C47—22no—
62C23×C47—42no—
63C23×C47—42no—
64C23×C47—84no—
65C23×C47#9911yescharacteristic
66D4×C47—42no—
67D4×C47—42no—
68D4×C47—82no—
69D4×C47—82no—
70D4×C47—84no—
71D4×C47—82no—
72C2×C4×C47—21no—
73C2×C4×C47—21no—
74C2×C4×C47—21no—
75C2×C4×C47—21no—
76C2×C4×C47—42no—
77C2×C4×C47—42no—
78C2×C4×C47—82no—
79C2×C4×C47—84no—
80C2×C4×C47—164no—
81C2×C4×C47#9911yescharacteristic
82C2×C4×C47C2×C22⋊C411yescharacteristic
83C8×C47—42no—
84C2×#1412C4711yesmaximal, characteristic, direct product factor, Sylow
85C22×C47—22no—
86C22×C47—42no—
87C22×C47—42no—
88C22×C47—82no—
89C22×C47—82no—
90C22×C47—84no—
91C22×C47—162no—
92C22×C47#35411yescharacteristic
93C22×C47#35411yescharacteristic
94C22×C47C2×#9911yescharacteristic
95C4×C47—21no—
96C4×C47—21no—
97C4×C47—41no—
98C4×C47—41no—
99C4×C47—82no—
100C4×C47—164no—
101C2×#490C2×C4711yescharacteristic
102C2×#353C2×C4712yes—
103#1412C2×C4714yesdirect product factor
104C2×C47—21no—
105C2×C47—21no—
106C2×C47—82no—
107C2×C47—82no—
108C2×C47#141212yesdirect product factor
109C2×C47C2×#35411yescharacteristic
110C2×#127C22×C4711yescharacteristic
111C2×#125C4×C4711yescharacteristic, complemented
112#490—22no—
113#490C4×C4712yescomplemented
114#490C22×C4712yes—
115C2×#102—22no—
116C2×#99—22no—
117C2×#97C4×C4711yescharacteristic, complemented
118#353—22no—
119#353C22×C4714yes—
120C47C2×#141211yescharacteristic, direct product factor, Sylow
121C22×D4—41no—
122C22×D4D4×C4712yes—
123C22×C8—21no—
124#127—41no—
125#127C2×C4×C4711yescharacteristic
126#127D4×C4712yes—
127#127C23×C4711yescharacteristic
128#125—21no—
129#125—41no—
130#125C2×C4×C4712yescomplemented
131C2×C4⋊C4—21no—
132C2×C4⋊C4—41no—
133C2×C22⋊C4—42no—
134C2×C42C2×C4×C4711yescharacteristic
135#102—24no—
136#102—24no—
137#99—24no—
138#99—42no—
139#97—21no—
140#97C2×C4×C4712yescomplemented
141C24—22no—
142C2×D4—22no—
143C2×D4—42no—
144C2×D4—42no—
145C2×D4—41no—
146C2×D4—42no—
147C2×D4—41no—
148C2×D4—84no—
149C2×D4C22⋊C4×C4712yes—
150C2×D4C2×D4×C4712yes—
151C22×C4—21no—
152C22×C4—41no—
153C22×C4—82no—
154C22×C4C22⋊C4×C4711yescharacteristic
155C2×C8—22no—
156C2×C8—41no—
157C2×C8—41no—
158C4⋊C4—22no—
159C4⋊C4—42no—
160C4⋊C4—42no—
161C4⋊C4—41no—
162C22⋊C4—44no—
163C22⋊C4—82no—
164C42—21no—
165C42C22⋊C4×C4711yescharacteristic
166C42C22×C4×C4711yescharacteristic
167C23—22no—
168C23—22no—
169C23—42no—
170C23—42no—
171C23—84no—
172C23#99×C4711yescharacteristic
173D4—42no—
174D4—42no—
175D4—82no—
176D4—82no—
177D4—84no—
178D4—82no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—82no—
186C2×C4—84no—
187C2×C4—164no—
188C2×C4#99×C4711yescharacteristic
189C2×C4C2×C22⋊C4×C4711yescharacteristic
190C8—42no—
191C22—22no—
192C22—42no—
193C22—42no—
194C22—82no—
195C22—82no—
196C22—84no—
197C22—162no—
198C22C47×#35411yescharacteristic
199C22C47×#35411yescharacteristic
200C22C2×#99×C4711yescharacteristic
201C4—21no—
202C4—21no—
203C4—41no—
204C4—41no—
205C4—82no—
206C4—164no—
207C2—21no—
208C2—21no—
209C2—82no—
210C2—82no—
211C2C47×#141212yesdirect product factor
212C2C2×C47×#35411yescharacteristic
subgroupG/H
center, socleC22×C47#354
commutatorC42C22×C4×C47
Frattini, cosocle#127C23×C47
prime radicalC2×#127×C47C22
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C47 ◁ C23×C47 ◁ C22×C4×C47 ◁ C2×#127×C47 ◁ G

Complements

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

NH ≅ G/Ntype
3. C47×#1412C2direct (N × H)
5. C2×#125×C47C4semidirect
7. C47×#490C4semidirect
11. C2×#97×C47C4semidirect
23. #125×C47C2×C4semidirect
33. #97×C47C2×C4semidirect
84. C2×#1412C47direct (N × H)
103. #1412C2×C47direct (N × H)
108. C2×C47#1412direct (N × H)
111. C2×#125C4×C47semidirect
113. #490C4×C47semidirect
117. C2×#97C4×C47semidirect
120. C47C2×#1412direct (N × H)
130. #125C2×C4×C47semidirect
140. #97C2×C4×C47semidirect
211. C2C47×#1412direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C47×#4902
C2×C47×#3532
C47×#14122
C2×#141247