Finite Group Databasebeta

← #20249210

Subgroups — #20249210

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×#13093981C211yesmaximal, characteristic
2#15689061C212yesmaximal, complemented
3#15689058C212yesmaximal
4#15689042C212yesmaximal, complemented
5#15689034C212yesmaximal
6#15689019C212yesmaximal, complemented
7#15688989C211yesmaximal, characteristic, complemented
8#15688980C212yesmaximal
9C2×C4⋊Q8×C47C211yesmaximal, characteristic, complemented
10C22×C4×D47C2211yescharacteristic
11#13093981—24no—
12C2×C4⋊Dic47C2212yes—
13C2×Dic47⋊C4C2211yescharacteristic
14C2×Dic47⋊C4C2211yescharacteristic
15C2×Dic47⋊C4C2214yes—
16C2×(C2×D47)⋊C4C2211yescharacteristic
17C2×(C2×D47)⋊C4C2211yescharacteristic
18C2×(C2×D47)⋊C4C2214yes—
19C2×C4×Dic47C2211yescharacteristic
20C47⋊#95C2214yes—
21C47⋊#95C2212yes—
22C47⋊#95C2212yes—
23C47⋊#95C2214yes—
24C22×Q8×C47C2212yes—
25C4⋊Q8×C47—24no—
26C2×C4⋊C4×C47C2212yes—
27C2×C4⋊C4×C47C2212yes—
28C2×C42×C47C2211yescharacteristic
29C23×D47C2311yescharacteristic
30C2×Q8×C47—24no—
31C2×Q8×C47—44no—
32C22×C4×C47C2314yes—
33C22×C4×C47C2311yescharacteristic
34C22×C4×C47C2311yescharacteristic
35C22×C4×C47C2311yescharacteristic
36C22×Dic47C2311yescharacteristic
37C22×Dic47C2314yes—
38C22×Dic47C2311yescharacteristic
39C22×Dic47C2311yescharacteristic
40C2×C4×D47—22no—
41C2×C4×D47—22no—
42C2×C4×D47Q814yescomplemented
43C4⋊C4×C47—24no—
44C4⋊C4×C47—24no—
45C42×C47D414yes—
46(C2×D47)⋊C4—22no—
47(C2×D47)⋊C4—22no—
48(C2×D47)⋊C4—44no—
49C4⋊Dic47—24no—
50Dic47⋊C4—22no—
51Dic47⋊C4—22no—
52Dic47⋊C4—44no—
53C4×Dic47—22no—
54C23×C47C2411yescharacteristic
55C22×D47—21no—
56C22×D47—21no—
57C22×D47—22no—
58C22×D47—22no—
59C22×D47C2×Q812yes—
60Q8×C47—48no—
61C2×C4×C47—22no—
62C2×C4×C47—22no—
63C2×C4×C47—24no—
64C2×C4×C47—24no—
65C2×C4×C47—24no—
66C2×C4×C47C2×D412yes—
67C2×C4×C47C2×D412yes—
68C2×C4×C47C2×D412yes—
69C2×C4×C47C2×Q812yes—
70C2×C4×C47#4112yes—
71C2×Dic47—21no—
72C2×Dic47—21no—
73C2×Dic47—21no—
74C2×Dic47—21no—
75C2×Dic47—24no—
76C2×Dic47—22no—
77C2×Dic47—24no—
78C2×Dic47—22no—
79C2×Dic47—24no—
80C2×Dic47C2×Q812yes—
81C4×D47—28no—
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—41no—
98Dic47—41no—
99Dic47—44no—
100#2628—471nomaximal, Sylow
101C2×C47C2×C22⋊Q811yescharacteristic
102C2×C47#53511yescharacteristic
103C2×C47#53611yescharacteristic
104C2×C47#54212yes—
105C2×C47#54412yes—
106D47—42no—
107C2×C4⋊Q8D4711yescharacteristic, complemented
108C2×#117—471no—
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×Q8C2×D4712yes—
118C23×C4—471no—
119C4⋊Q8—24no—
120#117—944no—
121C2×C4⋊C4—471no—
122C2×C4⋊C4—471no—
123C2×C4⋊C4—472no—
124C2×C4⋊C4—474no—
125C2×C4⋊C4C2×D4712yes—
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—472no—
134#95—472no—
135#95—474no—
136C24—471no—
137C2×Q8—24no—
138C2×Q8—44no—
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—24no—
152C4⋊C4—944no—
153C4⋊C4—942no—
154C4⋊C4—942no—
155C4⋊C4—1884no—
156C22⋊C4—942no—
157C22⋊C4—942no—
158C22⋊C4—1884no—
159C42—942no—
160C42C22⋊D4714yes—
161C23—472no—
162C23—941no—
163C23—941no—
164C23—942no—
165C23—942no—
166C23C23×D4711yescharacteristic
167Q8—48no—
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×C4Q8×D4712yes—
185C2×C4#1062535412yes—
186C2×C4C2×C22⋊D4712yes—
187C2×C4C2×C22⋊D4712yes—
188C2×C4C2×C22⋊D4712yes—
189C22—944no—
190C22—942no—
191C22—1882no—
192C22—1881no—
193C22—1881no—
194C22C22×C22⋊D4711yescharacteristic
195C22C2×Q8×D4711yescharacteristic
196C22C2×#1062535411yescharacteristic
197C22#1309406912yes—
198C22#1309407212yes—
199C4—22no—
200C4—22no—
201C4—44no—
202C4—942no—
203C4—1884no—
204C4—1881no—
205C4—1881no—
206C4#1309400014yes—
207C2—1882no—
208C2C2×#1309400011yescharacteristic
209C2#1568969011yescharacteristic
210C2#1568969711yescharacteristic
211C2#1568974712yes—
212C2#1568975012yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC2×C4⋊Q8×C47C2
hypercenterC2×C4⋊Q8D47
hypocenterC47#2628
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #15689061C2semidirect
4. #15689042C2semidirect
6. #15689019C2semidirect
7. #15688989C2semidirect
9. C2×C4⋊Q8×C47C2semidirect
42. C2×C4×D47Q8semidirect
107. C2×C4⋊Q8D47semidirect
116. C47#2628semidirect