Finite Group Databasebeta

← C47×#10574 #26050272

Subgroups — C47×#10574 #26050272

Order 12032.

494 conjugacy classes of subgroups; only the 162 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 162 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
1C47×#2551C211yesmaximal, characteristic
2C47×#1948C212yesmaximal
3C47×#1844C211yesmaximal, characteristic
4C47×#1296C211yesmaximal, characteristic
5C47×#1279C212yesmaximal
6C2×C4⋊Q8×C47—22no—
7C2×#106×C47—22no—
8C2×#106×C47—22no—
9C2×C4⋊C8×C47C2212yes—
10C2×C4×C8×C47C2211yescharacteristic
11C47×#395—22no—
12C47×#389—22no—
13C47×#384C2211yescharacteristic
14C47×#384C2211yescharacteristic
15C4×C4⋊C4×C47C2212yes—
16C47×#340—22no—
17C22×Q8×C47—22no—
18C22×C8×C47—21no—
19C22×C8×C47—22no—
20C4⋊Q8×C47—44no—
21C4⋊Q8×C47—44no—
22C2×C4⋊C4×C47—24no—
23C2×C4⋊C4×C47—22no—
24C2×C4⋊C4×C47—22no—
25C2×C4⋊C4×C47—21no—
26C2×C4⋊C4×C47D412yes—
27C2×C4⋊C4×C47D412yes—
28C2×C4⋊C4×C47D412yes—
29C2×C42×C47—22no—
30C2×C42×C47C2311yescharacteristic
31#106×C47—44no—
32#106×C47—44no—
33C4⋊C8×C47—22no—
34C4⋊C8×C47Q814yescomplemented
35C4×C8×C47—21no—
36C4×C8×C47Q812yescomplemented
37#95×C47—22no—
38#95×C47—22no—
39C2×Q8×C47—48no—
40C2×Q8×C47—82no—
41C22×C4×C47—22no—
42C22×C4×C47—22no—
43C22×C4×C47—22no—
44C22×C4×C47—41no—
45C22×C4×C47C2×D411yescharacteristic
46C22×C4×C47C2×D412yes—
47C2×C8×C47—22no—
48C2×C8×C47—22no—
49C2×C8×C47—22no—
50C2×C8×C47—24no—
51C2×C8×C47—42no—
52C2×C8×C47—42no—
53C4⋊C4×C47—22no—
54C4⋊C4×C47—22no—
55C4⋊C4×C47—48no—
56C4⋊C4×C47—42no—
57C4⋊C4×C47—42no—
58C4⋊C4×C47—42no—
59C4⋊C4×C47—42no—
60C4⋊C4×C47—42no—
61C4⋊C4×C47—42no—
62C4⋊C4×C47SD1614yes—
63C4⋊C4×C47SD1614yes—
64C42×C47—42no—
65C42×C47—42no—
66C42×C47C2×Q812yes—
67C42×C47C2×Q811yescharacteristic
68C42×C47#4111yescharacteristic
69C23×C47#12011yescharacteristic
70Q8×C47—88no—
71C2×C4×C47—21no—
72C2×C4×C47—21no—
73C2×C4×C47—24no—
74C2×C4×C47—24no—
75C2×C4×C47—42no—
76C2×C4×C47—42no—
77C2×C4×C47—42no—
78C2×C4×C47—42no—
79C2×C4×C47—44no—
80C2×C4×C47—42no—
81C2×C4×C47—82no—
82C2×C4×C47—81no—
83C2×C4×C47C22⋊Q811yescharacteristic
84C2×C4×C47C22⋊Q812yes—
85C2×C4×C47C4⋊Q811yescharacteristic
86C2×C4×C47C4⋊Q812yes—
87C2×C4×C47C2×SD1612yes—
88C2×C4×C47C2×SD1612yes—
89C2×C4×C47AGL(1,ℤ/8)12yes—
90C2×C4×C47#13712yes—
91C8×C47—24no—
92C8×C47—44no—
93#10574C4711yesmaximal, characteristic, direct product factor, Sylow
94C22×C47#39511yescharacteristic
95C22×C47#44812yes—
96C22×C47#45012yes—
97C22×C47#45311yescharacteristic
98C22×C47#45611yescharacteristic
99C4×C47—21no—
100C4×C47—21no—
101C4×C47—44no—
102C4×C47—44no—
103C4×C47—82no—
104C4×C47—161no—
105C4×C47#47512yes—
106C4×C47#47612yes—
107C4×C47#49812yes—
108C4×C47#50112yes—
109#2551C2×C4711yescharacteristic
110#1948C2×C4712yes—
111#1844C2×C4711yescharacteristic
112#1296C2×C4711yescharacteristic
113#1279C2×C4712yes—
114C2×C47#162311yescharacteristic
115C2×C47#162911yescharacteristic
116C2×C47#165112yes—
117C2×C47#205812yes—
118C2×C47#206011yescharacteristic
119C2×C4⋊Q8—22no—
120C2×#106—22no—
121C2×#106—22no—
122C2×C4⋊C8C22×C4712yes—
123C2×C4×C8C22×C4711yescharacteristic
124#395—22no—
125#389—22no—
126#384C22×C4711yescharacteristic
127#384C22×C4711yescharacteristic
128C4×C4⋊C4C22×C4712yes—
129#340—22no—
130C47#1057411yescharacteristic, direct product factor, Sylow
131C22×Q8—22no—
132C22×C8—21no—
133C22×C8—22no—
134C4⋊Q8—44no—
135C4⋊Q8—44no—
136C2×C4⋊C4—24no—
137C2×C4⋊C4—22no—
138C2×C4⋊C4—22no—
139C2×C4⋊C4—21no—
140C2×C4⋊C4D4×C4712yes—
141C2×C4⋊C4D4×C4712yes—
142C2×C4⋊C4D4×C4712yes—
143C2×C42—22no—
144C2×C42C23×C4711yescharacteristic
145#106—44no—
146#106—44no—
147C4⋊C8—22no—
148C4⋊C8Q8×C4714yescomplemented
149C4×C8—21no—
150C4×C8Q8×C4712yescomplemented
151#95—22no—
152#95—22no—
153C2×Q8—48no—
154C2×Q8—82no—
155C22×C4—22no—
156C22×C4—22no—
157C22×C4—22no—
158C22×C4—41no—
159C22×C4C2×D4×C4711yescharacteristic
160C22×C4C2×D4×C4712yes—
161C2×C8—22no—
162C2×C8—22no—
163C2×C8—22no—
164C2×C8—24no—
165C2×C8—42no—
166C2×C8—42no—
167C4⋊C4—22no—
168C4⋊C4—22no—
169C4⋊C4—42no—
170C4⋊C4—48no—
171C4⋊C4—42no—
172C4⋊C4—42no—
173C4⋊C4—42no—
174C4⋊C4—42no—
175C4⋊C4—42no—
176C4⋊C4SD16×C4714yes—
177C4⋊C4SD16×C4714yes—
178C42—42no—
179C42—42no—
180C42C2×Q8×C4711yescharacteristic
181C42C2×Q8×C4712yes—
182C42#41×C4711yescharacteristic
183C23#120×C4711yescharacteristic
184Q8—88no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—24no—
188C2×C4—24no—
189C2×C4—42no—
190C2×C4—42no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4—44no—
194C2×C4—42no—
195C2×C4—81no—
196C2×C4—82no—
197C2×C4C22⋊Q8×C4711yescharacteristic
198C2×C4C22⋊Q8×C4712yes—
199C2×C4C4⋊Q8×C4711yescharacteristic
200C2×C4C4⋊Q8×C4712yes—
201C2×C4C2×SD16×C4712yes—
202C2×C4C2×SD16×C4712yes—
203C2×C4AGL(1,ℤ/8)×C4712yes—
204C2×C4#137×C4712yes—
205C8—24no—
206C8—44no—
207C22C47×#39511yescharacteristic
208C22C47×#44812yes—
209C22C47×#45012yes—
210C22C47×#45311yescharacteristic
211C22C47×#45611yescharacteristic
212C4—21no—
213C4—21no—
214C4—44no—
215C4—44no—
216C4—82no—
217C4—161no—
218C4C47×#47512yes—
219C4C47×#47612yes—
220C4C47×#49812yes—
221C4C47×#50112yes—
222C2C47×#162311yescharacteristic
223C2C47×#162911yescharacteristic
224C2C47×#165112yes—
225C2C47×#205812yes—
226C2C47×#206011yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C47#120
commutator, Frattini, cosocleC2×C42C23×C47
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C47 ◁ C2×C42×C47 ◁ G

Complements

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

NH ≅ G/Ntype
34. C4⋊C8×C47Q8semidirect
36. C4×C8×C47Q8semidirect
93. #10574C47direct (N × H)
130. C47#10574direct (N × H)
148. C4⋊C8Q8×C47semidirect
150. C4×C8Q8×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#25512
C47×#19482
C47×#18442
C47×#12962
C47×#12792
#1057447