Finite Group Databasebeta

← #20243591

Subgroups — #20243591

Order 6016.

278 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 85 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×M16×D47C211yesmaximal, characteristic
2C2×#13093959C211yesmaximal, characteristic, complemented
3#15689086C211yesmaximal, characteristic
4C2×(C2×D47)⋊C8C211yesmaximal, characteristic
5#15688888C211yesmaximal, characteristic, complemented
6#15688887C211yesmaximal, characteristic, complemented
7C2×#108×C47C211yesmaximal, characteristic, complemented
8C22×C4×D47C2211yescharacteristic
9C2×#10625329C2211yescharacteristic
10C2×#10625329C2211yescharacteristic
11C2×#10625324—21no—
12M16×D47—22no—
13M16×D47—22no—
14C22×C47⋊C8C2211yescharacteristic
15C2×C8×D47—21no—
16#13093959—22no—
17(C2×D47)⋊C8—21no—
18(C2×D47)⋊C8—21no—
19(C2×D47)⋊C8C412yes—
20(C2×D47)⋊C8C412yes—
21C2×M16×C47C2211yescharacteristic
22C2×M16×C47C2211yescharacteristic
23C22×C8×C47C2211yescharacteristic
24#108×C47—22no—
25C23×D47Q811yescharacteristic
26C22×C4×C47C2311yescharacteristic
27C22×Dic47Q811yescharacteristic
28C2×C4×D47—21no—
29C2×C4×D47—21no—
30C2×C4×D47—21no—
31C2×C4×D47—21no—
32C2×C4×D47C2×C411yescharacteristic
33C2×C4×D47C2×C411yescharacteristic
34C2×C4×D47D411yescharacteristic
35C2×C4×D47D411yescharacteristic
36M16×C47—21no—
37M16×C47—21no—
38M16×C47—21no—
39M16×C47D412yes—
40C2×C8×C47—21no—
41C2×C8×C47—21no—
42C2×C8×C47—21no—
43C2×C8×C47—21no—
44C2×C8×C47C2×C412yes—
45#10625329—21no—
46#10625329—21no—
47#10625329—21no—
48#10625329D412yes—
49C2×C47⋊C8—21no—
50C2×C47⋊C8—21no—
51C2×C47⋊C8—21no—
52C2×C47⋊C8—21no—
53C2×C47⋊C8C2×C412yes—
54#10625324—24no—
55C8×D47—24no—
56C23×C47C2×Q811yescharacteristic
57C22×D47—21no—
58C22×D47—21no—
59C22×D47—22no—
60C22×D47—41no—
61C22×D47C4⋊C411yescharacteristic
62C22×D47C4⋊C411yescharacteristic
63C2×C4×C47C22×C411yescharacteristic
64C2×C4×C47C2×D411yescharacteristic
65C2×C4×C47C2×D411yescharacteristic
66C2×C4×C47C2×D411yescharacteristic
67C2×C4×C47#4111yescharacteristic
68C2×C4×C47#4111yescharacteristic
69C2×Dic47—21no—
70C2×Dic47—21no—
71C2×Dic47C4⋊C411yescharacteristic
72C2×Dic47C4⋊C411yescharacteristic
73C4×D47—21no—
74C4×D47—21no—
75C4×D47—21no—
76C4×D47—21no—
77C4×D47—21no—
78C4×D47—21no—
79C4×D47—21no—
80C4×D47—21no—
81C8×C47—22no—
82C8×C47—22no—
83C8×C47—41no—
84C47⋊C8—22no—
85C47⋊C8—22no—
86C47⋊C8—41no—
87C22×C47—21no—
88C22×C47—21no—
89C22×C47C2×C4⋊C411yescharacteristic
90C22×C47C22⋊Q811yescharacteristic
91C22×C47C22⋊Q811yescharacteristic
92C2×D47—21no—
93C2×D47—21no—
94C2×D47—21no—
95C2×D47—21no—
96C2×D47—21no—
97C2×D47—42no—
98C2×D47—42no—
99C2×D47#10812yescomplemented
100C4×C47C4×D411yescharacteristic
101C4×C47C4×D411yescharacteristic
102C4×C47#12011yescharacteristic
103C4×C47#12311yescharacteristic
104Dic47—21no—
105Dic47—21no—
106#1855—471nomaximal, Sylow
107C2×C47—21no—
108C2×C47—21no—
109C2×C47#38511yescharacteristic
110C2×C47C2×#10811yescharacteristic
111C2×C47#43011yescharacteristic
112D47—22no—
113D47—41no—
114C22×M16—471no—
115C2×#108—471no—
116C2×#108D4711yescharacteristic, complemented
117#407—471no—
118C2×C22⋊C8—471no—
119#341—471no—
120#341—471no—
121C47#185511yescharacteristic, complemented, Sylow
122C23×C4—471no—
123C2×M16—471no—
124C2×M16—471no—
125C2×M16—941no—
126C2×M16—942no—
127C2×M16—942no—
128C2×M16C2×D4711yescharacteristic
129C2×M16C2×D4711yescharacteristic
130C22×C8—471no—
131C22×C8—941no—
132C22×C8C2×D4711yescharacteristic
133#108—22no—
134#108—942no—
135C22⋊C8—472no—
136C22⋊C8—472no—
137C22⋊C8—941no—
138C22⋊C8—941no—
139C24—471no—
140C22×C4—471no—
141C22×C4—471no—
142C22×C4—471no—
143C22×C4—471no—
144C22×C4—471no—
145C22×C4—941no—
146C22×C4—941no—
147C22×C4—941no—
148C22×C4—941no—
149C22×C4C22×D4711yescharacteristic
150M16—21no—
151M16—21no—
152M16—21no—
153M16—472no—
154M16—944no—
155M16—941no—
156M16—941no—
157M16—941no—
158M16C22⋊D4712yes—
159C2×C8—21no—
160C2×C8—21no—
161C2×C8—21no—
162C2×C8—21no—
163C2×C8—472no—
164C2×C8—944no—
165C2×C8—941no—
166C2×C8—941no—
167C2×C8—941no—
168C2×C8—941no—
169C2×C8C4×D4712yes—
170C23—471no—
171C23—471no—
172C23—942no—
173C23—941no—
174C23—941no—
175C23—1881no—
176C23Q8×D4711yescharacteristic
177C2×C4—471no—
178C2×C4—471no—
179C2×C4—941no—
180C2×C4—941no—
181C2×C4—941no—
182C2×C4—941no—
183C2×C4—941no—
184C2×C4—941no—
185C2×C4—941no—
186C2×C4—941no—
187C2×C4—941no—
188C2×C4—941no—
189C2×C4C2×C4×D4711yescharacteristic
190C2×C4#1062535011yescharacteristic
191C2×C4D4×D4711yescharacteristic
192C2×C4D4×D4711yescharacteristic
193C2×C4#1062535411yescharacteristic
194C2×C4C2×C22⋊D4711yescharacteristic
195C8—22no—
196C8—22no—
197C8—41no—
198C8—942no—
199C8—942no—
200C8—1881no—
201C22—21no—
202C22—21no—
203C22—472no—
204C22—941no—
205C22—941no—
206C22—941no—
207C22—941no—
208C22—941no—
209C22—1882no—
210C22—1882no—
211C22C4⋊C4×D4711yescharacteristic
212C22#1309400011yescharacteristic
213C22#1309400211yescharacteristic
214C4—941no—
215C4—941no—
216C4C4×C22⋊D4711yescharacteristic
217C4#1309398611yescharacteristic
218C4#1309399211yescharacteristic
219C4#1309400911yescharacteristic
220C2—21no—
221C2—21no—
222C2—942no—
223C2—1881no—
224C2#1568899411yescharacteristic
225C2#108×D4711yescharacteristic
226C2#1568917011yescharacteristic
subgroupG/H
centerC2×C4D4×D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC2×#108×C47C2
socleC22×C47C2×C4⋊C4
hypercenterC2×#108D47
hypocenterC47#1855
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#108

Complements

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

NH ≅ G/Ntype
2. C2×#13093959C2semidirect
5. #15688888C2semidirect
6. #15688887C2semidirect
7. C2×#108×C47C2semidirect
99. C2×D47#108semidirect
116. C2×#108D47semidirect
121. C47#1855semidirect