Finite Group Databasebeta

← #20244783

Subgroups — #20244783

Order 6016.

248 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 89 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×#13093957C211yesmaximal, characteristic
2C2×C4⋊(C47⋊C8)C211yesmaximal, characteristic
3C2×#13093948C211yesmaximal, characteristic
4C2×#13093948C211yesmaximal, characteristic
5#15689021C211yesmaximal, characteristic
6#15688885C211yesmaximal, characteristic
7C47×#391C211yesmaximal, characteristic
8C22×C47⋊C8C2211yescharacteristic
9C22×C47⋊C8C2211yescharacteristic
10C2×C4⋊Dic47C2211yescharacteristic
11C2×C4⋊Dic47C2211yescharacteristic
12C2×Dic47⋊C4—21no—
13#13093957—22no—
14C4⋊(C47⋊C8)—22no—
15#13093948—22no—
16#13093948—22no—
17C47⋊#95—21no—
18C22×Q8×C47C2211yescharacteristic
19C2×C4⋊C4×C47C2211yescharacteristic
20C2×C42×C47C2211yescharacteristic
21#95×C47—21no—
22#95×C47—21no—
23C2×Q8×C47—21no—
24C2×Q8×C47—21no—
25C2×Q8×C47—21no—
26C2×Q8×C47—21no—
27C2×Q8×C47—21no—
28C2×Q8×C47Q812yes—
29C22×C4×C47—21no—
30C22×C4×C47—21no—
31C22×C4×C47D411yescharacteristic
32C22×C4×C47D411yescharacteristic
33C22×C4×C47C2311yescharacteristic
34C22×Dic47—21no—
35C22×Dic47—21no—
36C4⋊C4×C47—21no—
37C4⋊C4×C47—21no—
38C42×C47—21no—
39C42×C47—21no—
40C4⋊Dic47—21no—
41C4⋊Dic47—21no—
42C4⋊Dic47—21no—
43C4⋊Dic47D412yes—
44Dic47⋊C4—42no—
45C2×C47⋊C8—21no—
46C2×C47⋊C8—21no—
47C2×C47⋊C8—21no—
48C2×C47⋊C8—21no—
49C2×C47⋊C8—21no—
50C2×C47⋊C8D412yes—
51C23×C47C2×D411yescharacteristic
52Q8×C47—22no—
53Q8×C47—22no—
54Q8×C47—41no—
55Q8×C47—41no—
56C2×C4×C47—21no—
57C2×C4×C47—21no—
58C2×C4×C47—21no—
59C2×C4×C47—22no—
60C2×C4×C47—21no—
61C2×C4×C47—21no—
62C2×C4×C47—41no—
63C2×C4×C47—41no—
64C2×C4×C47—41no—
65C2×C4×C47—41no—
66C2×C4×C47—41no—
67C2×C4×C47Q1612yes—
68C2×C4×C47C2×D411yescharacteristic
69C2×C4×C47C2×D411yescharacteristic
70C2×C4×C47C2×Q811yescharacteristic
71C2×C4×C47#4111yescharacteristic
72C2×C4×C47#4111yescharacteristic
73C2×C4×C47#4111yescharacteristic
74C2×Dic47—22no—
75C2×Dic47—41no—
76C2×Dic47—41no—
77C2×Dic47—41no—
78C2×Dic47—41no—
79C2×Dic47—41no—
80C47⋊C8—22no—
81C47⋊C8—41no—
82C22×C47#12111yescharacteristic
83C22×C47#12111yescharacteristic
84C22×C47C22⋊Q811yescharacteristic
85C22×C47C2×Q1611yescharacteristic
86C22×C47#13511yescharacteristic
87C22×C47AGL(1,ℤ/8)11yescharacteristic
88C22×C47#13711yescharacteristic
89C4×C47—22no—
90C4×C47—42no—
91C4×C47—41no—
92C4×C47—81no—
93C4×C47#12111yescharacteristic
94C4×C47C22⋊Q811yescharacteristic
95C4×C47C22⋊Q811yescharacteristic
96C4×C47#12611yescharacteristic
97Dic47—42no—
98Dic47—81no—
99#2068—471nomaximal, Sylow
100C2×C47#39611yescharacteristic
101C2×C47#46211yescharacteristic
102C2×C47#46311yescharacteristic
103C2×C47#46711yescharacteristic
104C2×C47#46811yescharacteristic
105C2×C47#47711yescharacteristic
106C2×C47#47911yescharacteristic
107C2×#107—471no—
108C2×C4⋊C8—471no—
109C2×#103—471no—
110C2×#103—471no—
111#391D4711yescharacteristic
112#389—471no—
113#340—471no—
114C47#206811yescharacteristic, complemented, Sylow
115C22×Q8C2×D4711yescharacteristic
116C22×C8—471no—
117C22×C8—471no—
118C2×C4⋊C4—471no—
119C2×C4⋊C4—471no—
120C2×C4⋊C4—941no—
121C2×C4⋊C4C2×D4711yescharacteristic
122C2×C42C2×D4711yescharacteristic
123#107—942no—
124C4⋊C8—942no—
125#103—942no—
126#103—942no—
127#95—21no—
128#95—21no—
129#95—941no—
130C2×Q8—21no—
131C2×Q8—21no—
132C2×Q8—21no—
133C2×Q8—21no—
134C2×Q8—21no—
135C2×Q8Dic9412yes—
136C22×C4—21no—
137C22×C4—21no—
138C22×C4—941no—
139C22×C4—941no—
140C22×C4C22⋊D4711yescharacteristic
141C22×C4C22⋊D4711yescharacteristic
142C22×C4C22×D4711yescharacteristic
143C2×C8—472no—
144C2×C8—941no—
145C2×C8—941no—
146C2×C8—941no—
147C2×C8—941no—
148C2×C8—941no—
149C4⋊C4—21no—
150C4⋊C4—21no—
151C4⋊C4—472no—
152C4⋊C4—941no—
153C4⋊C4—941no—
154C4⋊C4—941no—
155C4⋊C4—1882no—
156C42—21no—
157C42—21no—
158C23C2×C22⋊D4711yescharacteristic
159Q8—22no—
160Q8—22no—
161Q8—41no—
162Q8—41no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—22no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—942no—
175C2×C4—1881no—
176C2×C4—1881no—
177C2×C4—1881no—
178C2×C4—1881no—
179C2×C4—1881no—
180C2×C4#1062533712yes—
181C2×C4C2×Dic9411yescharacteristic
182C2×C4#1062535011yescharacteristic
183C2×C4D4×D4711yescharacteristic
184C2×C4D4×D4711yescharacteristic
185C2×C4#1062535211yescharacteristic
186C2×C4#1062535211yescharacteristic
187C8—942no—
188C8—1881no—
189C22#1309399511yescharacteristic
190C22#1309399611yescharacteristic
191C22#1309400311yescharacteristic
192C22C2×#1062533711yescharacteristic
193C22#1309404411yescharacteristic
194C22#1309404911yescharacteristic
195C22#1309405511yescharacteristic
196C4—22no—
197C4—42no—
198C4—41no—
199C4—81no—
200C4—3761no—
201C4—1882no—
202C4#1309399711yescharacteristic
203C4#1309400111yescharacteristic
204C4#1309400111yescharacteristic
205C4#1309401711yescharacteristic
206C2#1568904611yescharacteristic
207C2#1568933011yescharacteristic
208C2#1568933511yescharacteristic
209C2#1568936211yescharacteristic
210C2#1568937111yescharacteristic
211C2#1568941811yescharacteristic
212C2#1568943011yescharacteristic
subgroupG/H
centerC23C2×C22⋊D47
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#391C2
socleC23×C47C2×D4
hypercenter#391D47
hypocenterC47#2068
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #391

Complements

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

NH ≅ G/Ntype
114. C47#2068semidirect