Finite Group Databasebeta

← #20249212

Subgroups — #20249212

Order 6016.

488 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 157 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×#13094024C211yesmaximal, characteristic, complemented
2C2×#13093981C211yesmaximal, characteristic
3#15689063C212yesmaximal, complemented
4#15689060C212yesmaximal
5#15689044C212yesmaximal, complemented
6#15689036C212yesmaximal
7#15689022C212yesmaximal, complemented
8#15688980C212yesmaximal
9C47×#382C211yesmaximal, characteristic, complemented
10C22×Dic94C2212yes—
11C22×C4×D47C2211yescharacteristic
12#13094024—24no—
13#13093981—24no—
14C2×C4⋊Dic47C2212yes—
15C2×C4⋊Dic47C2212yes—
16C2×C4⋊Dic47C2214yes—
17C2×Dic47⋊C4C2211yescharacteristic
18C2×Dic47⋊C4C2211yescharacteristic
19C2×(C2×D47)⋊C4C2211yescharacteristic
20C2×(C2×D47)⋊C4C2211yescharacteristic
21C2×(C2×D47)⋊C4C2214yes—
22C2×C4×Dic47C2211yescharacteristic
23C47⋊#95C2214yes—
24C47⋊#95C2214yes—
25C2×C4⋊C4×C47C2212yes—
26C2×C42×C47C2211yescharacteristic
27#95×C47C2212yes—
28#95×C47C2212yes—
29C23×D47C2311yescharacteristic
30C22×C4×C47C2314yes—
31C22×C4×C47C2311yescharacteristic
32C22×C4×C47C2311yescharacteristic
33C22×C4×C47C2311yescharacteristic
34C22×Dic47C2311yescharacteristic
35C22×Dic47C2314yes—
36C22×Dic47C2311yescharacteristic
37C22×Dic47C2311yescharacteristic
38C2×C4×D47—22no—
39C2×C4×D47—22no—
40C2×C4×D47Q814yescomplemented
41C2×Dic94—24no—
42C2×Dic94—44no—
43C4⋊C4×C47—24no—
44C42×C47D414yes—
45(C2×D47)⋊C4—22no—
46(C2×D47)⋊C4—22no—
47(C2×D47)⋊C4—44no—
48C4⋊Dic47—24no—
49C4⋊Dic47—24no—
50C4⋊Dic47—44no—
51Dic47⋊C4—22no—
52Dic47⋊C4—22no—
53C4×Dic47—22no—
54C23×C47C2411yescharacteristic
55C22×D47—21no—
56C22×D47—21no—
57C22×D47—22no—
58C22×D47—22no—
59C22×D47C2×Q812yes—
60C2×C4×C47—22no—
61C2×C4×C47—22no—
62C2×C4×C47—24no—
63C2×C4×C47—24no—
64C2×C4×C47—24no—
65C2×C4×C47C2×D412yes—
66C2×C4×C47C2×D412yes—
67C2×C4×C47C2×D412yes—
68C2×C4×C47C2×Q812yes—
69C2×C4×C47#4112yes—
70C2×Dic47—21no—
71C2×Dic47—21no—
72C2×Dic47—21no—
73C2×Dic47—21no—
74C2×Dic47—24no—
75C2×Dic47—22no—
76C2×Dic47—24no—
77C2×Dic47—24no—
78C2×Dic47—22no—
79C2×Dic47C2×Q812yes—
80C4×D47—28no—
81Dic94—48no—
82C22×C47C22×D411yescharacteristic
83C22×C47C22×Q811yescharacteristic
84C22×C47C2×#4111yescharacteristic
85C22×C47H(5,𝔽2)12yes—
86C22×C472−1+412yes—
87C2×D47—22no—
88C2×D47—24no—
89C2×D47—41no—
90C2×D47—41no—
91C2×D47—42no—
92C4×C47—22no—
93C4×C47—22no—
94C4×C47—44no—
95C4×C47C22⋊Q814yes—
96Dic47—22no—
97Dic47—44no—
98Dic47—41no—
99Dic47—41no—
100#2628—471nomaximal, Sylow
101C2×C47C2×C22⋊Q811yescharacteristic
102C2×C47#53511yescharacteristic
103C2×C47#53611yescharacteristic
104C2×C47#54212yes—
105C2×C47#54412yes—
106D47—42no—
107C2×C4⋊Q8—471no—
108C2×#117—471no—
109#400—472no—
110#399—472no—
111#395—472no—
112#393—472no—
113#389—472no—
114#382D4711yescharacteristic, complemented
115#380—472no—
116C47#262811yescharacteristic, complemented, Sylow
117C22×Q8—472no—
118C23×C4—471no—
119C4⋊Q8—944no—
120#117—944no—
121C2×C4⋊C4—471no—
122C2×C4⋊C4—471no—
123C2×C4⋊C4—472no—
124C2×C4⋊C4—472no—
125C2×C4⋊C4—474no—
126C2×C4⋊C4C2×D4712yes—
127C2×C22⋊C4—471no—
128C2×C22⋊C4—471no—
129C2×C22⋊C4—474no—
130C2×C42—471no—
131C2×C42C2×D4711yescharacteristic
132#95—474no—
133#95—474no—
134#95C2×D4712yes—
135#95C2×D4712yes—
136C24—471no—
137C2×Q8—944no—
138C2×Q8—1884no—
139C22×C4—471no—
140C22×C4—474no—
141C22×C4—471no—
142C22×C4—474no—
143C22×C4—471no—
144C22×C4—942no—
145C22×C4—942no—
146C22×C4C22×D4714yes—
147C22×C4C22×D4711yescharacteristic
148C22×C4C22×D4711yescharacteristic
149C22×C4C22×D4711yescharacteristic
150C4⋊C4—24no—
151C4⋊C4—942no—
152C4⋊C4—942no—
153C4⋊C4—944no—
154C4⋊C4—944no—
155C4⋊C4—1884no—
156C22⋊C4—942no—
157C22⋊C4—942no—
158C22⋊C4—1884no—
159C42—942no—
160C42D18814yes—
161C23—472no—
162C23—941no—
163C23—941no—
164C23—942no—
165C23—942no—
166C23C23×D4711yescharacteristic
167Q8—1888no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—24no—
171C2×C4—24no—
172C2×C4—24no—
173C2×C4—472no—
174C2×C4—941no—
175C2×C4—941no—
176C2×C4—948no—
177C2×C4—941no—
178C2×C4—941no—
179C2×C4—944no—
180C2×C4—944no—
181C2×C4—942no—
182C2×C4—944no—
183C2×C4—942no—
184C2×C4C2×D18812yes—
185C2×C4C2×D18812yes—
186C2×C4C2×D18812yes—
187C2×C4#1062535212yes—
188C2×C4Q8×D4712yes—
189C22—944no—
190C22—942no—
191C22—1882no—
192C22—1881no—
193C22—1881no—
194C22C22×D18811yescharacteristic
195C22C2×Q8×D4711yescharacteristic
196C22C2×#1062535211yescharacteristic
197C22#1309407012yes—
198C22#1309407112yes—
199C4—22no—
200C4—22no—
201C4—44no—
202C4—942no—
203C4—1884no—
204C4—1881no—
205C4—1881no—
206C4#1309400414yes—
207C2—1882no—
208C2C2×#1309400411yescharacteristic
209C2#1568969211yescharacteristic
210C2#1568969911yescharacteristic
211C2#1568974212yes—
212C2#1568975312yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#382C2
hypercenter#382D47
hypocenterC47#2628
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
1. C2×#13094024C2semidirect
3. #15689063C2semidirect
5. #15689044C2semidirect
7. #15689022C2semidirect
9. C47×#382C2semidirect
40. C2×C4×D47Q8semidirect
114. #382D47semidirect
116. C47#2628semidirect