Finite Group Databasebeta

← #20244557

Subgroups — #20244557

Order 6016.

244 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 67 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#15689141C211yesmaximal, characteristic
2C2×#13093952C211yesmaximal, characteristic
3#15689096C211yesmaximal, characteristic
4#15688893C211yesmaximal, characteristic, complemented
5#15688883C211yesmaximal, characteristic, complemented
6#15688879C211yesmaximal, characteristic, complemented
7C47×#533C211yesmaximal, characteristic, complemented
8C2×#10625350C2211yescharacteristic
9C2×#10625329C2211yescharacteristic
10C2×#10625329C2211yescharacteristic
11#13093983C2211yescharacteristic
12#13093952—21no—
13#13093952—21no—
14#13093952—22no—
15#13093938—22no—
16C4⋊Q8×C47—21no—
17#125×C47—21no—
18C22⋊Q8×C47—22no—
19C4×Q8×C47—22no—
20#117×C47C2211yescharacteristic
21#117×C47C2211yescharacteristic
22C2×C42×C47C2211yescharacteristic
23C2×Q8×C47—22no—
24C22×C4×C47—21no—
25C22×C4×C47C2311yescharacteristic
26C2×C22⋊D47—21no—
27#10625350—21no—
28#10625350—21no—
29#10625350—21no—
30#10625350—21no—
31C2×D188Q811yescharacteristic, complemented
32C2×C4×D47—21no—
33C2×Dic94Q811yescharacteristic, complemented
34C4⋊C4×C47—24no—
35C4⋊C4×C47—22no—
36C4⋊C4×C47—21no—
37C4⋊C4×C47—21no—
38C22⋊C4×C47—21no—
39C22⋊C4×C47D412yes—
40C42×C47—21no—
41C42×C47—21no—
42C42×C47D411yescharacteristic
43C42×C47D411yescharacteristic
44C42×C47D412yes—
45C22⋊Dic47—21no—
46C4⋊Dic47—21no—
47C4×Dic47—21no—
48#10625329—21no—
49#10625329—21no—
50#10625329—21no—
51#10625329—21no—
52C2×C47⋊C8—21no—
53C2×C47⋊C8—21no—
54C23×C47C2×D411yescharacteristic
55C22×D47—21no—
56Q8×C47—44no—
57C2×C4×C47—21no—
58C2×C4×C47—21no—
59C2×C4×C47—22no—
60C2×C4×C47—22no—
61C2×C4×C47—42no—
62C2×C4×C47C2×D411yescharacteristic
63C2×C4×C47C2×D411yescharacteristic
64C2×C4×C47C2×Q811yescharacteristic
65C2×C4×C47#4111yescharacteristic
66C2×C4×C47#4111yescharacteristic
67C2×C4×C47#4111yescharacteristic
68C22⋊D47—41no—
69C22⋊D47—41no—
70C2×Dic47—21no—
71C2×Dic47—41no—
72D188—21no—
73D188—21no—
74C4×D47—41no—
75C4×D47—41no—
76Dic94—21no—
77Dic94—21no—
78C47⋊C8—41no—
79C47⋊C8—41no—
80C22×C47—41no—
81C22×C47#12011yescharacteristic
82C22×C47C22⋊Q811yescharacteristic
83C22×C47#12411yescharacteristic
84C2×D47—41no—
85C2×D47—81no—
86C4×C47—22no—
87C4×C47—41no—
88C4×C47—42no—
89C4×C47—42no—
90C4×C47C22⋊Q811yescharacteristic
91C4×C47C22⋊Q811yescharacteristic
92C4×C47#12411yescharacteristic
93C4×C47#12411yescharacteristic
94Dic47—41no—
95Dic47—81no—
96#2031—471nomaximal, Sylow
97C2×C47—21no—
98C2×C47—21no—
99C2×C47—21no—
100C2×C47#39311yescharacteristic
101D47—81no—
102#533D4711yescharacteristic, complemented
103#421—471no—
104C2×#104—471no—
105#410—471no—
106#344—471no—
107#339—471no—
108H(3,ℤ/4)—471no—
109C47#203111yescharacteristic, complemented, Sylow
110C2×#41—471no—
111C2×M16—471no—
112C2×M16—471no—
113C4⋊Q8—21no—
114#125—21no—
115C22⋊Q8—22no—
116C4×Q8—22no—
117#117—471no—
118#117C2×D4711yescharacteristic
119#117C2×D4711yescharacteristic
120C2×C42C2×D4711yescharacteristic
121#104—941no—
122#104—941no—
123#104—942no—
124#99—942no—
125#41—941no—
126#41—941no—
127#41—941no—
128#41—941no—
129C2×Q8—22no—
130C2×Q8—471no—
131C2×D4—471no—
132C2×D4—941no—
133C22×C4—21no—
134C22×C4—941no—
135C22×C4C22×D4711yescharacteristic
136M16—941no—
137M16—941no—
138M16—941no—
139M16—941no—
140C2×C8—941no—
141C2×C8—941no—
142C4⋊C4—24no—
143C4⋊C4—22no—
144C4⋊C4—21no—
145C4⋊C4—21no—
146C4⋊C4—941no—
147C22⋊C4—21no—
148C22⋊C4—941no—
149C22⋊C4C22⋊D4712yes—
150C42—21no—
151C42—21no—
152C42—941no—
153C42C22⋊D4711yescharacteristic
154C42C22⋊D4711yescharacteristic
155C42C22⋊D4712yes—
156C23—941no—
157C23C2×C22⋊D4711yescharacteristic
158Q8—44no—
159Q8—941no—
160Q8—941no—
161D4—941no—
162D4—941no—
163D4—1881no—
164D4—1881no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—42no—
170C2×C4—941no—
171C2×C4—1881no—
172C2×C4—1881no—
173C2×C4—1881no—
174C2×C4Q8×D4711yescharacteristic
175C2×C4#1062535411yescharacteristic
176C2×C4#1062535411yescharacteristic
177C2×C4#1062535411yescharacteristic
178C2×C4C2×C22⋊D4711yescharacteristic
179C2×C4C2×C22⋊D4711yescharacteristic
180C8—1881no—
181C8—1881no—
182C22—41no—
183C22—3761no—
184C22—1881no—
185C22#1309399311yescharacteristic
186C22#1309400011yescharacteristic
187C22#1309401311yescharacteristic
188C4—22no—
189C4—41no—
190C4—42no—
191C4—42no—
192C4—3761no—
193C4—1881no—
194C4#1309400011yescharacteristic
195C4#1309400011yescharacteristic
196C4#1309401311yescharacteristic
197C4#1309401311yescharacteristic
198C2—21no—
199C2—21no—
200C2—21no—
201C2—3761no—
202C2#1568903411yescharacteristic
subgroupG/H
centerC4#13094013
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#533C2
socleC2×C47#393
hypercenter#533D47
hypocenterC47#2031
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C22×C4 ◁ #533

Complements

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

NH ≅ G/Ntype
4. #15688893C2semidirect
5. #15688883C2semidirect
6. #15688879C2semidirect
7. C47×#533C2semidirect
31. C2×D188Q8semidirect
33. C2×Dic94Q8semidirect
102. #533D47semidirect
109. C47#2031semidirect