Finite Group Databasebeta

← #20241975

Subgroups — #20241975

Order 6016.

234 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 61 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#15689658C211yesmaximal, characteristic
2#15689075C211yesmaximal, characteristic, complemented
3#97×D47C211yesmaximal, characteristic, complemented
4#15688865C211yesmaximal, characteristic, complemented
5#15688862C211yesmaximal, characteristic, complemented
6#15688862C211yesmaximal, characteristic, complemented
7C47×#330C211yesmaximal, characteristic, complemented
8C2×#10625324—21no—
9C2×C8×D47—21no—
10#13094019—21no—
11#13094012C2211yescharacteristic
12#13094009—21no—
13#13094004C411yescharacteristic
14#13093999C411yescharacteristic
15#13093989C411yescharacteristic
16#13093986—21no—
17#13093986C411yescharacteristic
18#13093982—21no—
19C42×D47C2211yescharacteristic
20#13093935C2211yescharacteristic
21#13093935C2211yescharacteristic
22#13093934—21no—
23C8×Dic47—21no—
24#125×C47C2211yescharacteristic
25#97×C47C2211yescharacteristic
26#97×C47C2211yescharacteristic
27C2×D188—21no—
28C2×D188C2×C411yescharacteristic
29C2×C4×D47—21no—
30C2×C4×D47C2×C411yescharacteristic
31C2×C4×D47D411yescharacteristic
32C2×C4×D47D411yescharacteristic
33C2×Dic94C2×C411yescharacteristic
34C2×C8×C47—21no—
35C2×C8×C47—21no—
36C4⋊C4×C47—21no—
37C4⋊C4×C47—21no—
38C4⋊C4×C47C2×C411yescharacteristic
39C4⋊C4×C47C2×C411yescharacteristic
40C42×C47C2311yescharacteristic
41(C2×D47)⋊C4—21no—
42(C2×D47)⋊C4—21no—
43(C2×D47)⋊C4—21no—
44(C2×D47)⋊C4—21no—
45(C2×D47)⋊C4—21no—
46C4⋊Dic47—21no—
47Dic47⋊C4—21no—
48C4×Dic47—21no—
49C4×Dic47C2×C411yescharacteristic
50C4×Dic47D411yescharacteristic
51C4×Dic47D411yescharacteristic
52C2×C47⋊C8—21no—
53C2×C47⋊C8—21no—
54#10625324—24no—
55C8×D47—24no—
56C22×D47—21no—
57C22×D47C22⋊C411yescharacteristic
58C2×C4×C47—21no—
59C2×C4×C47—21no—
60C2×C4×C47C22×C411yescharacteristic
61C2×C4×C47C2×D411yescharacteristic
62C2×C4×C47C2×D411yescharacteristic
63C2×Dic47—21no—
64C2×Dic47C22⋊C411yescharacteristic
65C2×Dic47C22⋊C411yescharacteristic
66C2×Dic47C22⋊C411yescharacteristic
67D188—41no—
68D188—42no—
69C4×D47—22no—
70C4×D47—22no—
71C4×D47—41no—
72C4×D47—42no—
73Dic94—41no—
74C8×C47—22no—
75C8×C47—22no—
76C47⋊C8—22no—
77C47⋊C8—22no—
78C22×C47C2×C22⋊C411yescharacteristic
79C2×D47—21no—
80C2×D47—21no—
81C2×D47—41no—
82C2×D47—41no—
83C2×D47—41no—
84C2×D47#10412yes—
85C4×C47—21no—
86C4×C47—21no—
87C4×C47—21no—
88C4×C47—41no—
89C4×C47—41no—
90Dic47—21no—
91Dic47—21no—
92Dic47—41no—
93Dic47#10412yes—
94#1524—471nomaximal, Sylow
95C2×C47#41311yescharacteristic
96C2×C47C2×#10411yescharacteristic
97C2×C47C2×#10411yescharacteristic
98D47—22no—
99D47—81no—
100#529—471no—
101C4×M16—471no—
102C2×#97—471no—
103#330—471no—
104#330D4711yescharacteristic, complemented
105#329—471no—
106#329—471no—
107C47#152411yescharacteristic, complemented, Sylow
108C2×M16—941no—
109C22×C8—941no—
110#126—941no—
111#125C2×D4711yescharacteristic
112#124—471no—
113#123—941no—
114C22⋊Q8—471no—
115#121—471no—
116C4×Q8—471no—
117C4×D4—471no—
118C4×D4—941no—
119#117—941no—
120C2×C42—471no—
121#97—471no—
122#97—471no—
123#97—941no—
124#97C2×D4711yescharacteristic
125#97C2×D4711yescharacteristic
126C4×C8—941no—
127C2×Q8—471no—
128C2×D4—471no—
129C2×D4—941no—
130C22×C4—471no—
131C22×C4—471no—
132C22×C4—471no—
133C22×C4—941no—
134M16—944no—
135C2×C8—21no—
136C2×C8—21no—
137C2×C8—944no—
138C2×C8—941no—
139C2×C8—941no—
140C4⋊C4—21no—
141C4⋊C4—21no—
142C4⋊C4—941no—
143C4⋊C4—941no—
144C4⋊C4C4×D4711yescharacteristic
145C4⋊C4C4×D4711yescharacteristic
146C22⋊C4—941no—
147C22⋊C4—941no—
148C22⋊C4—941no—
149C22⋊C4—941no—
150C22⋊C4—941no—
151C42—471no—
152C42—471no—
153C42—471no—
154C42—941no—
155C42C22×D4711yescharacteristic
156C23—471no—
157C23—941no—
158Q8—1881no—
159D4—1881no—
160D4—1882no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—471no—
164C2×C4—471no—
165C2×C4—471no—
166C2×C4—942no—
167C2×C4—942no—
168C2×C4—941no—
169C2×C4—1881no—
170C2×C4—1882no—
171C2×C4C2×C4×D4711yescharacteristic
172C2×C4D4×D4711yescharacteristic
173C2×C4D4×D4711yescharacteristic
174C8—22no—
175C8—22no—
176C8—942no—
177C8—942no—
178C22—472no—
179C22—941no—
180C22—941no—
181C22—1881no—
182C22—1881no—
183C22—1881no—
184C22C22⋊C4×D4711yescharacteristic
185C4—21no—
186C4—21no—
187C4—21no—
188C4—41no—
189C4—41no—
190C4—472no—
191C4—941no—
192C4—941no—
193C4—1881no—
194C2—942no—
195C2—3761no—
196C2#1568910611yescharacteristic
197C2#104×D4711yescharacteristic
198C2#104×D4711yescharacteristic
subgroupG/H
centerC22C22⋊C4×D47
commutatorC2×C4×C47C22×C4
FrattiniC42C22×D47
FittingC47×#330C2
socleC22×C47C2×C22⋊C4
hypercenter#330D47
hypocenterC47#1524
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
2. #15689075C2semidirect
3. #97×D47C2semidirect
4. #15688865C2semidirect
5. #15688862C2semidirect
6. #15688862C2semidirect
7. C47×#330C2semidirect
104. #330D47semidirect
107. C47#1524semidirect