Finite Group Databasebeta

← #20243189

Subgroups — #20243189

Order 6016.

284 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 109 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×#13094030C211yesmaximal, characteristic
2#15689105C211yesmaximal, characteristic
3#15689096C211yesmaximal, characteristic
4#15689078C211yesmaximal, characteristic, complemented
5#15688895C211yesmaximal, characteristic, complemented
6#15688893C211yesmaximal, characteristic, complemented
7C47×#405C211yesmaximal, characteristic, complemented
8C2×#10625350C2211yescharacteristic
9#13094030—21no—
10#13094030—21no—
11#13094030—21no—
12#13094030—21no—
13C2×#10625329C2211yescharacteristic
14C2×#10625329C2211yescharacteristic
15C2×#10625324C412yescomplemented
16C2×C8×D47C412yescomplemented
17#13093983C2211yescharacteristic
18#13093942C412yescomplemented
19#13093940C412yescomplemented
20#13093938C414yes—
21#13093934—21no—
22C8×Dic47—21no—
23C2×M16×C47C2211yescharacteristic
24C22×C8×C47C2211yescharacteristic
25#117×C47C2211yescharacteristic
26#97×C47—21no—
27C4×C8×C47—21no—
28C22×C4×C47C2311yescharacteristic
29C2×C22⋊D47C2×C412yes—
30#10625350—21no—
31#10625350—21no—
32#10625350—21no—
33#10625350—21no—
34C2×D188C2×C411yescharacteristic
35C2×C4×D47C2×C412yes—
36C2×Dic94C2×C411yescharacteristic
37M16×C47—21no—
38M16×C47C2×C412yes—
39C2×C8×C47—21no—
40C2×C8×C47C2×C411yescharacteristic
41C2×C8×C47C2×C411yescharacteristic
42C2×C8×C47D411yescharacteristic
43C2×C8×C47D411yescharacteristic
44C2×C8×C47D411yescharacteristic
45C2×C8×C47D411yescharacteristic
46C4⋊C4×C47—21no—
47C22⋊C4×C47C2×C412yes—
48C42×C47—21no—
49C22⋊Dic47C2×C412yes—
50C4⋊Dic47—21no—
51C4×Dic47—21no—
52#10625329—21no—
53#10625329—21no—
54#10625329—21no—
55#10625329C2×C412yes—
56C2×C47⋊C8—21no—
57C2×C47⋊C8C2×C412yes—
58#10625324—22no—
59#10625324—22no—
60C8×D47—22no—
61C8×D47—22no—
62C23×C47C22×C411yescharacteristic
63C22×D47C4212yes—
64C2×C4×C47—22no—
65C2×C4×C47C22×C411yescharacteristic
66C2×C4×C47C22×C411yescharacteristic
67C2×C4×C47C2×D411yescharacteristic
68C2×C4×C47C2×D411yescharacteristic
69C2×C4×C47#4111yescharacteristic
70C2×C4×C47#4111yescharacteristic
71C22⋊D47—22no—
72C22⋊D47—22no—
73C2×Dic47—22no—
74C2×Dic47C4212yes—
75D188—21no—
76D188—21no—
77C4×D47—22no—
78C4×D47—22no—
79Dic94—21no—
80Dic94—21no—
81C8×C47—22no—
82C8×C47C22⋊C411yescharacteristic
83C8×C47C22⋊C411yescharacteristic
84C8×C47C22⋊C411yescharacteristic
85C8×C47C22⋊C411yescharacteristic
86C47⋊C8—22no—
87C47⋊C8—22no—
88C22×C47—41no—
89C22×C47C2×C4211yescharacteristic
90C22×C47C4×D411yescharacteristic
91C22×C47C4×D411yescharacteristic
92C2×D47—22no—
93C2×D47—42no—
94C4×C47—42no—
95C4×C47C2×C22⋊C411yescharacteristic
96C4×C47#11711yescharacteristic
97C4×C47C4×D411yescharacteristic
98C4×C47C4×D411yescharacteristic
99Dic47—22no—
100Dic47—42no—
101#1757—471nomaximal, Sylow
102C2×C47—21no—
103C2×C47—21no—
104C2×C47—21no—
105C2×C47C4×C22⋊C411yescharacteristic
106D47—42no—
107C2×#131—471no—
108#413—471no—
109#410—471no—
110#405—471no—
111#405D4711yescharacteristic, complemented
112#344—471no—
113#344—471no—
114C47#175711yescharacteristic, complemented, Sylow
115C2×#41—471no—
116#131—941no—
117#131—941no—
118#131—941no—
119#131—941no—
120C2×M16—471no—
121C2×M16—472no—
122C2×M16—471no—
123C2×M16C2×D4711yescharacteristic
124C22×C8—472no—
125C22×C8C2×D4711yescharacteristic
126#117—471no—
127#117C2×D4711yescharacteristic
128#101—472no—
129#100—472no—
130#99—474no—
131#97—21no—
132#97—941no—
133C4×C8—21no—
134C4×C8—941no—
135#41—941no—
136#41—941no—
137#41—941no—
138#41—941no—
139C2×Q8—471no—
140C2×D4—472no—
141C2×D4—471no—
142C22×C4—472no—
143C22×C4C22×D4711yescharacteristic
144M16—21no—
145M16—472no—
146M16—941no—
147M16—941no—
148M16—941no—
149M16—942no—
150M16—942no—
151M16C4×D4712yes—
152C2×C8—21no—
153C2×C8—472no—
154C2×C8—941no—
155C2×C8—942no—
156C2×C8—942no—
157C2×C8C4×D4711yescharacteristic
158C2×C8C4×D4711yescharacteristic
159C2×C8D18811yescharacteristic
160C2×C8D18811yescharacteristic
161C2×C8C22⋊D4711yescharacteristic
162C2×C8C22⋊D4711yescharacteristic
163C4⋊C4—21no—
164C4⋊C4—941no—
165C22⋊C4—472no—
166C22⋊C4C4×D4712yes—
167C42—21no—
168C42—941no—
169C23—472no—
170C23C2×C4×D4711yescharacteristic
171Q8—941no—
172Q8—941no—
173D4—942no—
174D4—942no—
175D4—941no—
176D4—941no—
177C2×C4—22no—
178C2×C4—472no—
179C2×C4—942no—
180C2×C4—942no—
181C2×C4—942no—
182C2×C4C2×C4×D4711yescharacteristic
183C2×C4C2×C4×D4711yescharacteristic
184C2×C4C2×D18811yescharacteristic
185C2×C4#1062535011yescharacteristic
186C2×C4#1062535011yescharacteristic
187C2×C4C2×C22⋊D4711yescharacteristic
188C8—22no—
189C8—942no—
190C8—942no—
191C8(C2×D47)⋊C411yescharacteristic
192C8(C2×D47)⋊C411yescharacteristic
193C8(C2×D47)⋊C411yescharacteristic
194C8(C2×D47)⋊C411yescharacteristic
195C22—41no—
196C22—942no—
197C22—1882no—
198C22C42×D4711yescharacteristic
199C22C4×C22⋊D4711yescharacteristic
200C22C4×D18811yescharacteristic
201C4—42no—
202C4—942no—
203C4—1882no—
204C4C2×(C2×D47)⋊C411yescharacteristic
205C4#1309398111yescharacteristic
206C4C4×C22⋊D4711yescharacteristic
207C4C4×D18811yescharacteristic
208C2—21no—
209C2—21no—
210C2—21no—
211C2—1882no—
212C2C4×(C2×D47)⋊C411yescharacteristic
subgroupG/H
centerC8(C2×D47)⋊C4
commutatorC22×C47C2×C42
FrattiniC22×C4C22×D47
FittingC47×#405C2
socleC2×C47C4×C22⋊C4
hypercenter#405D47
hypocenterC47#1757
LCSG ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C8 ◁ C22×C8 ◁ #405

Complements

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

NH ≅ G/Ntype
4. #15689078C2semidirect
5. #15688895C2semidirect
6. #15688893C2semidirect
7. C47×#405C2semidirect
15. C2×#10625324C4semidirect
16. C2×C8×D47C4semidirect
18. #13093942C4semidirect
19. #13093940C4semidirect
111. #405D47semidirect
114. C47#1757semidirect