Finite Group Databasebeta

← #20244375

Subgroups — #20244375

Order 6016.

260 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 87 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×#13094023C211yesmaximal, characteristic
2#15689146C211yesmaximal, characteristic
3M16×Dic47C211yesmaximal, characteristic
4#15688892C211yesmaximal, characteristic
5#15688891C211yesmaximal, characteristic
6#15688891C211yesmaximal, characteristic
7C47×#343C211yesmaximal, characteristic
8C22×Dic94C412yes—
9C2×#10625329C2211yescharacteristic
10C2×#10625329C2211yescharacteristic
11#13094023—21no—
12#13094023—21no—
13#13094023—21no—
14#13094023—21no—
15C2×C4⋊Dic47C2211yescharacteristic
16C2×Dic47⋊C4C412yes—
17C2×C4×Dic47C2211yescharacteristic
18Dic47⋊C8—21no—
19Dic47⋊C8—21no—
20#13093934—21no—
21C8×Dic47—21no—
22C2×M16×C47C2211yescharacteristic
23C2×M16×C47C2211yescharacteristic
24C2×C4⋊C4×C47C2211yescharacteristic
25C22×C4×C47C2×C412yes—
26C22×C4×C47C2311yescharacteristic
27C22×Dic47C2×C411yescharacteristic
28C22×Dic47C2×C411yescharacteristic
29C22×Dic47C2×C412yes—
30C2×Dic94—22no—
31C2×Dic94—22no—
32C2×Dic94—44no—
33M16×C47—21no—
34M16×C47—21no—
35M16×C47—21no—
36M16×C47Q812yescomplemented
37C2×C8×C47—21no—
38C2×C8×C47—21no—
39C4⋊C4×C47—21no—
40C4⋊C4×C47—21no—
41C4⋊Dic47—21no—
42C4⋊Dic47—21no—
43Dic47⋊C4—22no—
44Dic47⋊C4—22no—
45C4×Dic47D411yescharacteristic
46C4×Dic47D411yescharacteristic
47C4×Dic47D411yescharacteristic
48C4×Dic47D411yescharacteristic
49#10625329—21no—
50#10625329—21no—
51#10625329—21no—
52#10625329Q812yescomplemented
53C2×C47⋊C8—21no—
54C2×C47⋊C8—21no—
55C23×C47C22×C411yescharacteristic
56C2×C4×C47—22no—
57C2×C4×C47—42no—
58C2×C4×C47C2×D411yescharacteristic
59C2×C4×C47C2×D411yescharacteristic
60C2×C4×C47C2×Q811yescharacteristic
61C2×C4×C47C2×Q811yescharacteristic
62C2×C4×C47#4111yescharacteristic
63C2×C4×C47#4111yescharacteristic
64C2×Dic47—22no—
65C2×Dic47—22no—
66C2×Dic47—22no—
67C2×Dic47—42no—
68C2×Dic47C22⋊C411yescharacteristic
69C2×Dic47C22⋊C411yescharacteristic
70C2×Dic47C22⋊C411yescharacteristic
71C2×Dic47C22⋊C411yescharacteristic
72Dic94—44no—
73Dic94—44no—
74C8×C47—22no—
75C8×C47—41no—
76C47⋊C8—22no—
77C47⋊C8—41no—
78C22×C47—21no—
79C22×C47—21no—
80C22×C47C2×C22⋊C411yescharacteristic
81C22×C47C4×Q811yescharacteristic
82C22×C47C4×Q811yescharacteristic
83C4×C47—42no—
84C4×C47C22⋊Q811yescharacteristic
85C4×C47C22⋊Q811yescharacteristic
86C4×C47#12411yescharacteristic
87C4×C47C4⋊Q811yescharacteristic
88Dic47—21no—
89Dic47—21no—
90Dic47—42no—
91Dic47#10012yes—
92Dic47#10112yes—
93#1997—471nomaximal, Sylow
94C2×C47—21no—
95C2×C47—21no—
96C2×C47#39111yescharacteristic
97C2×C47C2×#10011yescharacteristic
98C2×C47C2×#10111yescharacteristic
99C2×C4⋊Q8—471no—
100#423—471no—
101C4×M16—471no—
102#343—471no—
103#343—471no—
104#343—471no—
105#343D4711yescharacteristic
106C47#199711yescharacteristic, complemented, Sylow
107C22×Q8—472no—
108C2×M16—471no—
109C2×M16—471no—
110C2×M16C2×D4711yescharacteristic
111C2×M16C2×D4711yescharacteristic
112C4⋊Q8—941no—
113C4⋊Q8—941no—
114C4⋊Q8—941no—
115C4⋊Q8—941no—
116C2×C4⋊C4—472no—
117C2×C4⋊C4—471no—
118C2×C4⋊C4C2×D4711yescharacteristic
119C2×C42—471no—
120C4⋊C8—941no—
121C4⋊C8—941no—
122#97—941no—
123C4×C8—941no—
124C2×Q8—942no—
125C2×Q8—942no—
126C2×Q8—1884no—
127C22×C4—471no—
128C22×C4—471no—
129C22×C4—472no—
130C22×C4C4×D4712yes—
131C22×C4C22×D4711yescharacteristic
132M16—21no—
133M16—21no—
134M16—21no—
135M16—472no—
136M16—941no—
137M16—941no—
138M16—941no—
139M16Dic9412yescomplemented
140C2×C8—21no—
141C2×C8—21no—
142C2×C8—941no—
143C2×C8—941no—
144C4⋊C4—21no—
145C4⋊C4—21no—
146C4⋊C4—942no—
147C4⋊C4—942no—
148C4⋊C4—941no—
149C4⋊C4—941no—
150C42—471no—
151C42—471no—
152C42—471no—
153C42—471no—
154C23C2×C4×D4711yescharacteristic
155Q8—1884no—
156Q8—1884no—
157C2×C4—22no—
158C2×C4—42no—
159C2×C4—471no—
160C2×C4—471no—
161C2×C4—471no—
162C2×C4—471no—
163C2×C4—942no—
164C2×C4—942no—
165C2×C4—942no—
166C2×C4—1882no—
167C2×C4C2×Dic9411yescharacteristic
168C2×C4#1062535011yescharacteristic
169C2×C4D4×D4711yescharacteristic
170C2×C4D4×D4711yescharacteristic
171C2×C4#1062535211yescharacteristic
172C2×C4Q8×D4711yescharacteristic
173C8—22no—
174C8—41no—
175C8—942no—
176C8—1881no—
177C22—21no—
178C22—21no—
179C22C22⋊C4×D4711yescharacteristic
180C22#1309398911yescharacteristic
181C22C4×Dic9411yescharacteristic
182C4—42no—
183C4—472no—
184C4—472no—
185C4—941no—
186C4—941no—
187C4—1882no—
188C4#1309400111yescharacteristic
189C4#1309400211yescharacteristic
190C4#1309401011yescharacteristic
191C4#1309402311yescharacteristic
192C2—21no—
193C2—21no—
194C2#1568902711yescharacteristic
195C2#100×D4711yescharacteristic
196C2#101×D4711yescharacteristic
subgroupG/H
centerC22C22⋊C4×D47
commutatorC23×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#343C2
socleC22×C47C2×C22⋊C4
hypercenter#343D47
hypocenterC47#1997
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
36. M16×C47Q8semidirect
52. #10625329Q8semidirect
106. C47#1997semidirect
139. M16Dic94semidirect