Finite Group Databasebeta

← #20244688

Subgroups — #20244688

Order 6016.

262 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 69 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×#13094055C211yesmaximal, characteristic
2C2×#13093960C211yesmaximal, characteristic, complemented
3#15689122C211yesmaximal, characteristic
4C2×#13093943C211yesmaximal, characteristic, complemented
5#15689089C211yesmaximal, characteristic
6#15688892C211yesmaximal, characteristic, complemented
7C2×#103×C47C211yesmaximal, characteristic, complemented
8C2×#10625350C2211yescharacteristic
9#13094055—22no—
10#13094055—22no—
11C2×#10625337—21no—
12C2×#10625336—21no—
13C2×#10625329C2211yescharacteristic
14C2×#10625329C2211yescharacteristic
15C2×#10625329C2211yescharacteristic
16#13093960—22no—
17#13093947—21no—
18#13093944—21no—
19#13093943—22no—
20(C2×D47)⋊C8—22no—
21C22×Q8×C47C2211yescharacteristic
22C22×C8×C47C2211yescharacteristic
23C2×C4⋊C4×C47C2211yescharacteristic
24#103×C47—22no—
25C2×Q8×C47—21no—
26C2×Q8×C47—21no—
27C2×Q8×C47—21no—
28C2×Q8×C47—21no—
29C2×Q8×C47—21no—
30C2×Q8×C47D412yes—
31C22×C4×C47—21no—
32C22×C4×C47—21no—
33C22×C4×C47C2311yescharacteristic
34C2×C22⋊D47—21no—
35#10625350—21no—
36#10625350—21no—
37#10625350—21no—
38#10625350—21no—
39C2×D188D411yescharacteristic
40C2×C4×D47—21no—
41C2×Dic94D411yescharacteristic
42C2×C8×C47—21no—
43C2×C8×C47—21no—
44C2×C8×C47D412yes—
45C4⋊C4×C47—21no—
46C4⋊C4×C47—21no—
47#10625337—24no—
48#10625336—24no—
49#10625329—21no—
50#10625329—21no—
51#10625329—21no—
52#10625329—21no—
53#10625329—21no—
54#10625329D412yes—
55C2×C47⋊C8—21no—
56C2×C47⋊C8—21no—
57C2×C47⋊C8—21no—
58C23×C47#4111yescharacteristic
59C22×D47—21no—
60Q8×C47—22no—
61Q8×C47—22no—
62Q8×C47—41no—
63Q8×C47—41no—
64C2×C4×C47—22no—
65C2×C4×C47—41no—
66C2×C4×C47—41no—
67C2×C4×C47—41no—
68C2×C4×C47—81no—
69C2×C4×C47C2×D411yescharacteristic
70C2×C4×C47C2×D411yescharacteristic
71C2×C4×C47C2×D411yescharacteristic
72C2×C4×C47C2×D411yescharacteristic
73C2×C4×C47#4111yescharacteristic
74C2×C4×C47#4111yescharacteristic
75C22⋊D47—41no—
76C22⋊D47—41no—
77C2×Dic47—21no—
78D188—21no—
79D188—21no—
80C4×D47—41no—
81C4×D47—41no—
82Dic94—21no—
83Dic94—21no—
84C8×C47—22no—
85C47⋊C8—22no—
86C47⋊C8—41no—
87C47⋊C8—41no—
88C22×C47—21no—
89C22×C47—21no—
90C22×C47#12111yescharacteristic
91C22×C47#12311yescharacteristic
92C22×C47#12411yescharacteristic
93C2×D47—41no—
94C2×D47—41no—
95C2×D47—41no—
96C4×C47—42no—
97C4×C47—81no—
98C4×C47#12011yescharacteristic
99C4×C47#12111yescharacteristic
100C4×C47#12111yescharacteristic
101C4×C47#12311yescharacteristic
102Dic47—41no—
103#2052—471nomaximal, Sylow
104C2×C47—21no—
105C2×C47—21no—
106C2×C47#39411yescharacteristic
107C2×C47#47111yescharacteristic
108C2×C47#47311yescharacteristic
109D47—81no—
110C2×#137—471no—
111C2×#108—471no—
112#417—471no—
113C2×#103D4711yescharacteristic, complemented
114C2×#101—471no—
115#408—471no—
116#343—471no—
117C47#205211yescharacteristic, complemented, Sylow
118C2×#41—471no—
119C22×Q8C2×D4711yescharacteristic
120#137—942no—
121#137—942no—
122C2×Q16—941no—
123C2×SD16—941no—
124C2×M16—471no—
125C2×M16—471no—
126C2×M16—471no—
127C22×C8C2×D4711yescharacteristic
128C2×C4⋊C4C2×D4711yescharacteristic
129#108—942no—
130#103—22no—
131#103—941no—
132#102—941no—
133#101—942no—
134C22⋊C8—942no—
135#41—941no—
136#41—941no—
137#41—941no—
138#41—941no—
139C2×Q8—21no—
140C2×Q8—21no—
141C2×Q8—21no—
142C2×Q8—21no—
143C2×Q8—21no—
144C2×Q8—471no—
145C2×Q8D18812yes—
146C2×D4—471no—
147C2×D4—941no—
148C22×C4—21no—
149C22×C4—21no—
150C22×C4—941no—
151C22×C4C22×D4711yescharacteristic
152Q16—944no—
153SD16—944no—
154M16—472no—
155M16—941no—
156M16—941no—
157M16—941no—
158M16—941no—
159M16—941no—
160C2×C8—21no—
161C2×C8—21no—
162C2×C8—941no—
163C2×C8—941no—
164C2×C8—941no—
165C2×C8C22⋊D4712yes—
166C4⋊C4—21no—
167C4⋊C4—21no—
168C23—941no—
169C23#1062535211yescharacteristic
170Q8—22no—
171Q8—22no—
172Q8—41no—
173Q8—41no—
174Q8—941no—
175Q8—941no—
176D4—941no—
177D4—941no—
178D4—1881no—
179D4—1881no—
180C2×C4—22no—
181C2×C4—41no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—81no—
185C2×C4—941no—
186C2×C4—1881no—
187C2×C4—1881no—
188C2×C4C2×D18811yescharacteristic
189C2×C4#1062535011yescharacteristic
190C2×C4D4×D4711yescharacteristic
191C2×C4D4×D4711yescharacteristic
192C2×C4#1062535211yescharacteristic
193C2×C4C2×C22⋊D4711yescharacteristic
194C8—22no—
195C8—942no—
196C8—1881no—
197C8—1881no—
198C22—21no—
199C22—21no—
200C22—1881no—
201C22—1881no—
202C22—1881no—
203C22#1309399511yescharacteristic
204C22#1309400811yescharacteristic
205C22#1309401011yescharacteristic
206C4—42no—
207C4—81no—
208C4—1881no—
209C4#1309399411yescharacteristic
210C4#1309399611yescharacteristic
211C4#1309399811yescharacteristic
212C4#1309400611yescharacteristic
213C2—21no—
214C2—21no—
215C2—3761no—
216C2#1568903911yescharacteristic
217C2#1568938311yescharacteristic
218C2#1568939511yescharacteristic
subgroupG/H
centerC22#13093995
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC2×#103×C47C2
socleC22×C47#121
hypercenterC2×#103D47
hypocenterC47#2052
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
2. C2×#13093960C2semidirect
4. C2×#13093943C2semidirect
6. #15688892C2semidirect
7. C2×#103×C47C2semidirect
113. C2×#103D47semidirect
117. C47#2052semidirect