Finite Group Databasebeta

← #20249209

Subgroups — #20249209

Order 6016.

488 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 165 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
2#15689062C212yesmaximal, complemented
3#15689059C212yesmaximal
4#15689043C212yesmaximal, complemented
5#15689035C212yesmaximal
6#15689021C212yesmaximal, complemented
7#15688989C211yesmaximal, characteristic, complemented
8#15688983C212yesmaximal
9C2×#117×C47C211yesmaximal, characteristic
10C22×Dic94C2212yes—
11#13094024—24no—
12C2×C4⋊Dic47C2212yes—
13C2×C4⋊Dic47C2212yes—
14C2×C4⋊Dic47C2212yes—
15C2×Dic47⋊C4C2214yes—
16C2×C22⋊Dic47C2214yes—
17C47⋊#95C2214yes—
18C47⋊#95C2212yes—
19C47⋊#95C2212yes—
20C47⋊#95C2214yes—
21C23×C4×C47C2211yescharacteristic
22#117×C47—24no—
23C2×C4⋊C4×C47C2211yescharacteristic
24C2×C4⋊C4×C47C2211yescharacteristic
25C2×C22⋊C4×C47C2211yescharacteristic
26C2×C22⋊C4×C47C2211yescharacteristic
27C2×C42×C47C2211yescharacteristic
28C2×C42×C47C2211yescharacteristic
29C24×C47C2311yescharacteristic
30C22×C4×C47—22no—
31C22×C4×C47—22no—
32C22×C4×C47Q814yescomplemented
33C22×C4×C47C2311yescharacteristic
34C22×C4×C47C2311yescharacteristic
35C22×C4×C47C2311yescharacteristic
36C22×C4×C47C2311yescharacteristic
37C22×C4×C47C2311yescharacteristic
38C22×C4×C47C2311yescharacteristic
39C22×Dic47C2314yes—
40C22×Dic47C2314yes—
41C2×Dic94—24no—
42C2×Dic94—44no—
43C4⋊C4×C47—22no—
44C4⋊C4×C47—22no—
45C22⋊C4×C47—22no—
46C22⋊C4×C47—22no—
47C42×C47—22no—
48C42×C47D414yes—
49C22⋊Dic47—44no—
50C4⋊Dic47—24no—
51C4⋊Dic47—24no—
52C4⋊Dic47—24no—
53Dic47⋊C4—44no—
54C23×C47—21no—
55C23×C47—21no—
56C23×C47—22no—
57C23×C47—22no—
58C23×C47C2×Q812yes—
59C23×C47C2411yescharacteristic
60C2×C4×C47—21no—
61C2×C4×C47—21no—
62C2×C4×C47—22no—
63C2×C4×C47—22no—
64C2×C4×C47—28no—
65C2×C4×C47—21no—
66C2×C4×C47—21no—
67C2×C4×C47—22no—
68C2×C4×C47—22no—
69C2×C4×C47C2×D412yes—
70C2×C4×C47C2×D412yes—
71C2×C4×C47C2×D412yes—
72C2×C4×C47C2×Q812yes—
73C2×C4×C47C2×Q812yes—
74C2×C4×C47#4112yes—
75C2×Dic47—24no—
76C2×Dic47—24no—
77C2×Dic47—24no—
78C2×Dic47—24no—
79C2×Dic47—24no—
80C2×Dic47—24no—
81Dic94—48no—
82C22×C47—22no—
83C22×C47—24no—
84C22×C47—41no—
85C22×C47—41no—
86C22×C47—42no—
87C22×C47C22×D411yescharacteristic
88C22×C47C22×Q811yescharacteristic
89C22×C47C2×#4111yescharacteristic
90C22×C47H(5,𝔽2)12yes—
91C22×C472−1+412yes—
92C4×C47—22no—
93C4×C47—22no—
94C4×C47—22no—
95C4×C47—41no—
96C4×C47—41no—
97C4×C47C22⋊Q814yes—
98Dic47—44no—
99Dic47—44no—
100#2628—471nomaximal, Sylow
101C2×C47—42no—
102C2×C47C2×C22⋊Q811yescharacteristic
103C2×C47#53511yescharacteristic
104C2×C47#53611yescharacteristic
105C2×C47#54212yes—
106C2×C47#54412yes—
107C2×C4⋊Q8—471no—
108C2×#117D4711yescharacteristic
109#400—472no—
110#399—472no—
111#395—472no—
112#393—472no—
113#389—472no—
114#382—471no—
115#380—472no—
116C47#262811yescharacteristic, complemented, Sylow
117C22×Q8—472no—
118C23×C4C2×D4711yescharacteristic
119C4⋊Q8—944no—
120#117—24no—
121C2×C4⋊C4—472no—
122C2×C4⋊C4—472no—
123C2×C4⋊C4—472no—
124C2×C4⋊C4—474no—
125C2×C4⋊C4C2×D4711yescharacteristic
126C2×C4⋊C4C2×D4711yescharacteristic
127C2×C22⋊C4—474no—
128C2×C22⋊C4C2×D4711yescharacteristic
129C2×C22⋊C4C2×D4711yescharacteristic
130C2×C42C2×D4711yescharacteristic
131C2×C42C2×D4711yescharacteristic
132#95—474no—
133#95—472no—
134#95—472no—
135#95—474no—
136C24C22×D4711yescharacteristic
137C2×Q8—944no—
138C2×Q8—1884no—
139C22×C4—22no—
140C22×C4—22no—
141C22×C4—474no—
142C22×C4—474no—
143C22×C4Dic9414yescomplemented
144C22×C4C22×D4711yescharacteristic
145C22×C4C22×D4711yescharacteristic
146C22×C4C22×D4711yescharacteristic
147C22×C4C22×D4711yescharacteristic
148C22×C4C22×D4711yescharacteristic
149C22×C4C22×D4711yescharacteristic
150C4⋊C4—22no—
151C4⋊C4—22no—
152C4⋊C4—944no—
153C4⋊C4—944no—
154C4⋊C4—944no—
155C4⋊C4—1884no—
156C22⋊C4—22no—
157C22⋊C4—22no—
158C22⋊C4—1884no—
159C42—22no—
160C42C22⋊D4714yes—
161C23—21no—
162C23—21no—
163C23—22no—
164C23—22no—
165C23C2×Dic9412yes—
166C23C23×D4711yescharacteristic
167Q8—1888no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—28no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—944no—
178C2×C4—944no—
179C2×C4—944no—
180C2×C4—944no—
181C2×C4—944no—
182C2×C4—944no—
183C2×C4C2×Dic9412yes—
184C2×C4C2×Dic9412yes—
185C2×C4#1062535012yes—
186C2×C4C2×C22⋊D4712yes—
187C2×C4C2×C22⋊D4712yes—
188C2×C4C2×C22⋊D4712yes—
189C22—24no—
190C22—22no—
191C22—42no—
192C22—41no—
193C22—41no—
194C22C22×C22⋊D4711yescharacteristic
195C22C22×Dic9411yescharacteristic
196C22C2×#1062535011yescharacteristic
197C22#1309407012yes—
198C22#1309407112yes—
199C4—22no—
200C4—22no—
201C4—22no—
202C4—41no—
203C4—41no—
204C4—1884no—
205C4—1884no—
206C4#1309400314yes—
207C2—42no—
208C2C2×#1309400311yescharacteristic
209C2#1568968711yescharacteristic
210C2#1568969411yescharacteristic
211C2#1568974412yes—
212C2#1568975112yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC2×#117×C47C2
hypercenterC2×#117D47
hypocenterC47#2628
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
1. C2×#13094024C2semidirect
2. #15689062C2semidirect
4. #15689043C2semidirect
6. #15689021C2semidirect
7. #15688989C2semidirect
32. C22×C4×C47Q8semidirect
116. C47#2628semidirect
143. C22×C4Dic94semidirect