Finite Group Databasebeta

← #20244684

Subgroups — #20244684

Order 6016.

262 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 71 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×#13093959C211yesmaximal, characteristic, complemented
2#15689124C211yesmaximal, characteristic
3C2×#13093948C211yesmaximal, characteristic, complemented
4C2×#13093943C211yesmaximal, characteristic, complemented
5#15689090C211yesmaximal, characteristic
6#15688891C211yesmaximal, characteristic, complemented
7C2×#137×C47C211yesmaximal, characteristic
8C2×#10625329C2211yescharacteristic
9C2×#10625329C2211yescharacteristic
10C22×C47⋊C8C2211yescharacteristic
11C2×C4⋊Dic47C2211yescharacteristic
12#13093959—22no—
13#13093948—21no—
14#13093948—22no—
15#13093945—21no—
16#13093943—22no—
17C22⋊(C47⋊C8)—22no—
18C2×#41×C47C2211yescharacteristic
19C22×Q8×C47C2211yescharacteristic
20#137×C47—22no—
21#137×C47—22no—
22C2×Q16×C47—21no—
23C2×SD16×C47—21no—
24C2×M16×C47C2211yescharacteristic
25#41×C47—21no—
26#41×C47—21no—
27#41×C47—21no—
28#41×C47—21no—
29C2×Q8×C47—21no—
30C2×Q8×C47—21no—
31C2×Q8×C47—21no—
32C2×Q8×C47—21no—
33C2×Q8×C47—21no—
34C2×Q8×C47D411yescharacteristic
35C2×Q8×C47D412yes—
36C2×D4×C47—21no—
37C2×D4×C47D411yescharacteristic
38C22×C4×C47—21no—
39C22×C4×C47—21no—
40C22×C4×C47C2311yescharacteristic
41C22×Dic47—21no—
42Q16×C47—24no—
43SD16×C47—24no—
44M16×C47—21no—
45M16×C47D412yes—
46C2×C8×C47—21no—
47C4⋊Dic47—21no—
48C4⋊Dic47—21no—
49#10625329—21no—
50#10625329—21no—
51#10625329—21no—
52#10625329—21no—
53C2×C47⋊C8—21no—
54C2×C47⋊C8—21no—
55C2×C47⋊C8—21no—
56C2×C47⋊C8—21no—
57C2×C47⋊C8D412yes—
58C23×C47—21no—
59C23×C47#4111yescharacteristic
60Q8×C47—22no—
61Q8×C47—21no—
62Q8×C47—22no—
63Q8×C47—21no—
64Q8×C47—41no—
65Q8×C47—41no—
66D4×C47—21no—
67D4×C47—21no—
68D4×C47—41no—
69D4×C47—41no—
70C2×C4×C47—21no—
71C2×C4×C47—22no—
72C2×C4×C47—41no—
73C2×C4×C47—41no—
74C2×C4×C47—41no—
75C2×C4×C47—41no—
76C2×C4×C47C2×D411yescharacteristic
77C2×C4×C47C2×D411yescharacteristic
78C2×C4×C47C2×D411yescharacteristic
79C2×C4×C47C2×D411yescharacteristic
80C2×C4×C47#4111yescharacteristic
81C2×C4×C47#4111yescharacteristic
82C2×Dic47—41no—
83C2×Dic47—81no—
84C8×C47—22no—
85C47⋊C8—22no—
86C47⋊C8—41no—
87C47⋊C8—41no—
88C22×C47—21no—
89C22×C47—21no—
90C22×C47—41no—
91C22×C47—41no—
92C22×C47—41no—
93C22×C47#12111yescharacteristic
94C22×C47#12311yescharacteristic
95C22×C47#12411yescharacteristic
96C4×C47—41no—
97C4×C47—42no—
98C4×C47#12011yescharacteristic
99C4×C47#12111yescharacteristic
100C4×C47#12111yescharacteristic
101C4×C47#12311yescharacteristic
102Dic47—81no—
103#2052—471nomaximal, Sylow
104C2×C47—21no—
105C2×C47—21no—
106C2×C47—81no—
107C2×C47#39411yescharacteristic
108C2×C47#47111yescharacteristic
109C2×C47#47311yescharacteristic
110C2×#137D4711yescharacteristic
111C2×#108—471no—
112#417—471no—
113C2×#103—471no—
114C2×#101—471no—
115#408—471no—
116#343—471no—
117C47#205211yescharacteristic, complemented, Sylow
118C2×#41C2×D4711yescharacteristic
119C22×Q8C2×D4711yescharacteristic
120#137—22no—
121#137—22no—
122C2×Q16—21no—
123C2×SD16—21no—
124C2×M16—471no—
125C2×M16—471no—
126C2×M16C2×D4711yescharacteristic
127C22×C8—471no—
128C2×C4⋊C4—471no—
129#108—942no—
130#103—942no—
131#103—941no—
132#102—941no—
133#101—942no—
134C22⋊C8—942no—
135#41—21no—
136#41—21no—
137#41—21no—
138#41—21no—
139C2×Q8—21no—
140C2×Q8—21no—
141C2×Q8—21no—
142C2×Q8—21no—
143C2×Q8—21no—
144C2×Q8C22⋊D4712yes—
145C2×Q8C22⋊D4711yescharacteristic
146C2×D4—21no—
147C2×D4C22⋊D4711yescharacteristic
148C22×C4—21no—
149C22×C4—21no—
150C22×C4—941no—
151C22×C4C22×D4711yescharacteristic
152Q16—24no—
153SD16—24no—
154M16—21no—
155M16—941no—
156M16—941no—
157M16—941no—
158M16—941no—
159M16C22⋊D4712yes—
160C2×C8—21no—
161C2×C8—472no—
162C2×C8—941no—
163C2×C8—941no—
164C2×C8—941no—
165C2×C8—941no—
166C4⋊C4—941no—
167C4⋊C4—941no—
168C23—21no—
169C23#1062535211yescharacteristic
170Q8—22no—
171Q8—21no—
172Q8—22no—
173Q8—21no—
174Q8—41no—
175Q8—41no—
176D4—21no—
177D4—21no—
178D4—41no—
179D4—41no—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—3761no—
187C2×C4—1881no—
188C2×C4D4×D4711yescharacteristic
189C2×C4#1062535211yescharacteristic
190C2×C4#1062535211yescharacteristic
191C2×C4C2×C22⋊D4711yescharacteristic
192C2×C4C2×C22⋊D4711yescharacteristic
193C2×C4C2×C22⋊D4711yescharacteristic
194C8—22no—
195C8—942no—
196C8—1881no—
197C8—1881no—
198C22—21no—
199C22—21no—
200C22—41no—
201C22—41no—
202C22—41no—
203C22#1309399611yescharacteristic
204C22#1309400511yescharacteristic
205C22#1309401111yescharacteristic
206C4—41no—
207C4—42no—
208C4—3761no—
209C4#1309399311yescharacteristic
210C4#1309399511yescharacteristic
211C4#1309399611yescharacteristic
212C4#1309400511yescharacteristic
213C2—21no—
214C2—21no—
215C2—81no—
216C2#1568903711yescharacteristic
217C2#1568938811yescharacteristic
218C2#1568939611yescharacteristic
subgroupG/H
centerC22#13093996
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC2×#137×C47C2
socleC22×C47#121
hypercenterC2×#137D47
hypocenterC47#2052
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×#13093959C2semidirect
3. C2×#13093948C2semidirect
4. C2×#13093943C2semidirect
6. #15688891C2semidirect
117. C47#2052semidirect