Finite Group Databasebeta

← #20254859

Subgroups — #20254859

Order 6016.

346 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 117 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
1#15689744C212yesmaximal, complemented
2#15689414C212yesmaximal, complemented
3#15689409C212yesmaximal, complemented
4#15689381C211yesmaximal, characteristic, complemented
5#15689376C211yesmaximal, characteristic
6#15689352C212yesmaximal, complemented
7#15689346C212yesmaximal, complemented
8#15689339C212yesmaximal, complemented
9C47×#424C211yesmaximal, characteristic, complemented
10C2×Dic188C2211yescharacteristic
11C2×#10625325C2212yes—
12C2×D376C2211yescharacteristic
13#13094024C2212yes—
14#13094019—22no—
15#13094012C2212yes—
16#13094010—22no—
17#13094006—22no—
18#13094003C2212yes—
19#13094002—22no—
20#13093998C2212yes—
21C4×Dic94C2212yes—
22C4×D188C2212yes—
23#13093956C2212yes—
24#13093956C2211yescharacteristic
25#13093956C2211yescharacteristic
26#13093949C2212yes—
27#13093949C2212yes—
28#13093946C2212yes—
29#13093946C2212yes—
30C2×M16×C47C2211yescharacteristic
31C22×C8×C47C2211yescharacteristic
32#117×C47C2211yescharacteristic
33C4⋊C8×C47C2212yes—
34C4⋊C8×C47C2212yes—
35C22×C4×C47C2311yescharacteristic
36C2×C22⋊D47—22no—
37C2×D188C2312yes—
38C2×C4×D47—22no—
39C2×Dic94—22no—
40C2×Dic94C2312yes—
41M16×C47—41no—
42C2×C8×C47—41no—
43C2×C8×C47C2312yes—
44C2×C8×C47C2311yescharacteristic
45C2×C8×C47C2311yescharacteristic
46C4⋊C4×C47D412yes—
47C22⋊C4×C47D411yescharacteristic
48C22⋊C4×C47D411yescharacteristic
49C42×C47C2312yes—
50C22⋊Dic47—22no—
51(C2×D47)⋊C4—22no—
52(C2×D47)⋊C4—22no—
53(C2×D47)⋊C4—22no—
54(C2×D47)⋊C4—22no—
55C4⋊Dic47—22no—
56C4⋊Dic47C2312yes—
57C4⋊Dic47C2312yes—
58Dic47⋊C4—22no—
59Dic47⋊C4—22no—
60C4×Dic47—22no—
61Dic188—41no—
62D376—41no—
63#10625325—42no—
64C23×C47C2×D411yescharacteristic
65C22×D47—22no—
66C2×C4×C47—21no—
67C2×C4×C47—21no—
68C2×C4×C47C2×D412yes—
69C2×C4×C47C2×D411yescharacteristic
70C2×C4×C47C2×D412yes—
71C2×C4×C47C2411yescharacteristic
72C22⋊D47—82no—
73C2×Dic47—22no—
74C2×Dic47—22no—
75C2×Dic47—22no—
76D188—22no—
77D188—22no—
78C4×D47—82no—
79Dic94—22no—
80Dic94—22no—
81Dic94—82no—
82C8×C47—22no—
83C8×C47—21no—
84C8×C47—21no—
85C22×C47—21no—
86C22×C47—22no—
87C22×C47C22×D411yescharacteristic
88C2×D47—42no—
89C2×D47—42no—
90C2×D47—42no—
91C4×C47—21no—
92C4×C47—22no—
93C4×C47—22no—
94C4×C47H(5,𝔽2)11yescharacteristic
95C4×C472−1+411yescharacteristic
96Dic47—42no—
97Dic47—42no—
98Dic47—42no—
99#3263—471nomaximal, Sylow
100C2×C47—41no—
101C2×C47#53711yescharacteristic
102C2×C47#57712yes—
103D47—82no—
104#542—472no—
105#476—472no—
106#475—472no—
107#470—471no—
108#469—471no—
109#465—472no—
110#464—472no—
111#463—472no—
112#424D4711yescharacteristic, complemented
113C47#326311yescharacteristic, complemented, Sylow
114C2×Q16—471no—
115C2×SD16—472no—
116C2×D8—471no—
117C2×M16C2×D4711yescharacteristic
118C22×C8C2×D4711yescharacteristic
119C4⋊Q8—472no—
120#126—942no—
121#124—472no—
122#124—942no—
123#123—942no—
124C22⋊Q8—472no—
125C22⋊Q8—942no—
126#121—472no—
127C4×Q8—472no—
128C4×D4—472no—
129#117C2×D4711yescharacteristic
130#106—472no—
131#106—471no—
132#106—471no—
133C4⋊C8C2×D4712yes—
134C4⋊C8C2×D4712yes—
135#103—472no—
136#103—472no—
137#102—472no—
138#102—472no—
139C2×Q8—472no—
140C2×Q8—942no—
141C2×D4—472no—
142C2×D4—942no—
143C22×C4—942no—
144C22×C4C22×D4711yescharacteristic
145Q16—1881no—
146SD16—1882no—
147D8—1881no—
148M16—41no—
149C2×C8—41no—
150C2×C8C22×D4711yescharacteristic
151C2×C8C22×D4712yes—
152C2×C8C22×D4711yescharacteristic
153C4⋊C4—472no—
154C4⋊C4—472no—
155C4⋊C4—942no—
156C4⋊C4—942no—
157C4⋊C4—942no—
158C4⋊C4D18812yes—
159C22⋊C4—942no—
160C22⋊C4—942no—
161C22⋊C4—942no—
162C22⋊C4—942no—
163C22⋊C4—942no—
164C22⋊C4D18811yescharacteristic
165C22⋊C4D18811yescharacteristic
166C42—942no—
167C42C22×D4712yes—
168C23—942no—
169C23C2×D18811yescharacteristic
170Q8—942no—
171Q8—942no—
172Q8—3762no—
173D4—942no—
174D4—942no—
175D4—3762no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—942no—
179C2×C4—942no—
180C2×C4—942no—
181C2×C4—3762no—
182C2×C4C2×D18812yes—
183C2×C4C2×D18812yes—
184C2×C4C2×D18811yescharacteristic
185C2×C4C23×D4711yescharacteristic
186C8—22no—
187C8—21no—
188C8—21no—
189C22—22no—
190C22—21no—
191C22—1882no—
192C22—1882no—
193C22—1882no—
194C22C22×D18811yescharacteristic
195C4—22no—
196C4—22no—
197C4—21no—
198C4—1882no—
199C4—1882no—
200C4—1882no—
201C4#1309406911yescharacteristic
202C4#1309407211yescharacteristic
203C2—41no—
204C2—3762no—
205C2#1568970411yescharacteristic
206C2#1568993512yes—
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#424C2
socleC22×C47C22×D4
hypercenter#424D47
hypocenterC47#3263
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ #117 ◁ #424

Complements

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

NH ≅ G/Ntype
1. #15689744C2semidirect
2. #15689414C2semidirect
3. #15689409C2semidirect
4. #15689381C2semidirect
6. #15689352C2semidirect
7. #15689346C2semidirect
8. #15689339C2semidirect
9. C47×#424C2semidirect
112. #424D47semidirect
113. C47#3263semidirect