Finite Group Databasebeta

← #20244663

Subgroups — #20244663

Order 6016.

274 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 65 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×#13094052C211yesmaximal, characteristic
2#15689139C211yesmaximal, characteristic, complemented
3#15689129C211yesmaximal, characteristic, complemented
4#15689105C211yesmaximal, characteristic, complemented
5C2×#13093940C211yesmaximal, characteristic, complemented
6#15688895C211yesmaximal, characteristic, complemented
7C47×#430C211yesmaximal, characteristic, complemented
8C2×#10625350C2211yescharacteristic
9C22×D188C2211yescharacteristic
10#13094052—22no—
11#13094052—22no—
12C2×#10625325—21no—
13C2×D376—21no—
14C2×#10625329C2211yescharacteristic
15#13093983C2211yescharacteristic
16#13093950—22no—
17#13093946—22no—
18#13093942—21no—
19#13093940—21no—
20#13093940—22no—
21C2×M16×C47C2211yescharacteristic
22C2×M16×C47C2211yescharacteristic
23C2×M16×C47C2211yescharacteristic
24#108×C47—22no—
25C23×D47—21no—
26C22×C4×C47C2311yescharacteristic
27C2×C22⋊D47—21no—
28#10625350—21no—
29#10625350—21no—
30#10625350—21no—
31#10625350—21no—
32C2×D188—21no—
33C2×D188—21no—
34C2×D188—21no—
35C2×D188—21no—
36C2×D188—21no—
37C2×D188D411yescharacteristic
38C2×D188D412yes—
39C2×C4×D47—21no—
40C2×Dic94D411yescharacteristic
41M16×C47—21no—
42M16×C47—21no—
43M16×C47—21no—
44M16×C47—21no—
45M16×C47D412yes—
46M16×C47D412yes—
47C2×C8×C47—21no—
48C2×C8×C47—21no—
49C2×C8×C47—21no—
50C22⋊Dic47—21no—
51C4⋊Dic47—21no—
52C4×Dic47—21no—
53#10625329—21no—
54#10625329—21no—
55C2×C47⋊C8—21no—
56D376—24no—
57#10625325—24no—
58C23×C47#4111yescharacteristic
59C22×D47—22no—
60C22×D47—21no—
61C22×D47—41no—
62C22×D47—41no—
63C22×D47—82no—
64C2×C4×C47C2×D411yescharacteristic
65C2×C4×C47C2×D411yescharacteristic
66C2×C4×C47C2×D411yescharacteristic
67C2×C4×C47C2×D411yescharacteristic
68C2×C4×C47#4111yescharacteristic
69C2×C4×C47#4111yescharacteristic
70C22⋊D47—41no—
71C22⋊D47—41no—
72C2×Dic47—21no—
73C2×Dic47—41no—
74D188—22no—
75D188—21no—
76D188—21no—
77D188—22no—
78D188—41no—
79D188—41no—
80C4×D47—41no—
81C4×D47—41no—
82Dic94—21no—
83Dic94—21no—
84C8×C47—22no—
85C8×C47—22no—
86C8×C47—41no—
87C47⋊C8—41no—
88C22×C47—41no—
89C22×C47#12111yescharacteristic
90C22×C47#12311yescharacteristic
91C22×C47#12411yescharacteristic
92C2×D47—41no—
93C2×D47—42no—
94C2×D47—82no—
95C2×D47—82no—
96C2×D47—81no—
97C2×D47—82no—
98C4×C47#12011yescharacteristic
99C4×C47#12111yescharacteristic
100C4×C47#12111yescharacteristic
101C4×C47#12311yescharacteristic
102Dic47—41no—
103Dic47—81no—
104#2048—471nomaximal, Sylow
105C2×C47—21no—
106C2×C47—21no—
107C2×C47—21no—
108C2×C47#39411yescharacteristic
109D47—81no—
110D47—82no—
111C2×AGL(1,ℤ/8)—471no—
112#430D4711yescharacteristic, complemented
113#421—471no—
114#418—471no—
115#413—471no—
116C2×#100—471no—
117#344—471no—
118C47#204811yescharacteristic, complemented, Sylow
119C2×#41—471no—
120C22×D4—471no—
121AGL(1,ℤ/8)—942no—
122AGL(1,ℤ/8)—942no—
123C2×SD16—941no—
124C2×D8—941no—
125C2×M16—471no—
126C2×M16C2×D4711yescharacteristic
127C2×M16C2×D4711yescharacteristic
128C2×M16C2×D4711yescharacteristic
129#117—471no—
130#108—22no—
131#104—942no—
132#102—942no—
133#101—941no—
134#100—941no—
135#100—942no—
136C24—941no—
137#41—941no—
138#41—941no—
139#41—941no—
140#41—941no—
141C2×Q8—471no—
142C2×D4—471no—
143C2×D4—472no—
144C2×D4—941no—
145C2×D4—941no—
146C2×D4—941no—
147C2×D4—941no—
148C2×D4—941no—
149C2×D4—941no—
150C22×C4—941no—
151C22×C4C22×D4711yescharacteristic
152SD16—944no—
153D8—944no—
154M16—21no—
155M16—21no—
156M16—21no—
157M16—21no—
158M16—941no—
159M16—941no—
160M16D18812yes—
161M16C22⋊D4712yes—
162C2×C8—21no—
163C2×C8—21no—
164C2×C8—21no—
165C2×C8—941no—
166C4⋊C4—941no—
167C22⋊C4—941no—
168C42—941no—
169C23—942no—
170C23—941no—
171C23—3762no—
172C23—1881no—
173C23—1881no—
174C23#1062535411yescharacteristic
175Q8—941no—
176Q8—941no—
177D4—941no—
178D4—942no—
179D4—941no—
180D4—942no—
181D4—1881no—
182D4—1881no—
183D4—1881no—
184D4—1881no—
185C2×C4—941no—
186C2×C4—1881no—
187C2×C4—1881no—
188C2×C4—1881no—
189C2×C4C2×D18811yescharacteristic
190C2×C4#1062535011yescharacteristic
191C2×C4D4×D4711yescharacteristic
192C2×C4D4×D4711yescharacteristic
193C2×C4#1062535411yescharacteristic
194C2×C4C2×C22⋊D4711yescharacteristic
195C8—22no—
196C8—22no—
197C8—41no—
198C8—1881no—
199C22—41no—
200C22—3762no—
201C22—3761no—
202C22—3762no—
203C22—3762no—
204C22—1881no—
205C22—1882no—
206C22#1309399911yescharacteristic
207C22#1309400911yescharacteristic
208C22#1309401311yescharacteristic
209C4—3761no—
210C4—1881no—
211C4#1309399211yescharacteristic
212C4#1309399811yescharacteristic
213C4#1309399911yescharacteristic
214C4#1309400911yescharacteristic
215C2—21no—
216C2—21no—
217C2—21no—
218C2—3762no—
219C2—3761no—
220C2#1568904011yescharacteristic
subgroupG/H
centerC2#15689040
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#430C2
socleC2×C47#394
hypercenter#430D47
hypocenterC47#2048
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C22×C4 ◁ #430

Complements

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

NH ≅ G/Ntype
2. #15689139C2semidirect
3. #15689129C2semidirect
4. #15689105C2semidirect
5. C2×#13093940C2semidirect
6. #15688895C2semidirect
7. C47×#430C2semidirect
112. #430D47semidirect
118. C47#2048semidirect