Finite Group Databasebeta

← #20242514

Subgroups — #20242514

Order 6016.

256 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 55 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#15689794C211yesmaximal, characteristic
2#15689497C211yesmaximal, characteristic, complemented
3#15689415C211yesmaximal, characteristic, complemented
4#15688866C211yesmaximal, characteristic, complemented
5#15688853C211yesmaximal, characteristic, complemented
6D4⋊(C47⋊C8)C211yesmaximal, characteristic, complemented
7C47×#476C211yesmaximal, characteristic, complemented
8C2×#10625350—21no—
9C2×#10625336—22no—
10#13094021C2211yescharacteristic
11#13094020—21no—
12#13093998—21no—
13#13093997—22no—
14C4×Dic94C2211yescharacteristic
15#13093986—21no—
16#13093957—21no—
17C4⋊(C47⋊C8)C2211yescharacteristic
18#13093947—21no—
19C4×C47⋊C8C2211yescharacteristic
20C4⋊Q8×C47C2211yescharacteristic
21C4×D4×C47C2211yescharacteristic
22#106×C47—21no—
23C4⋊C8×C47C2211yescharacteristic
24#102×C47—21no—
25C2×Q8×C47—21no—
26C2×D4×C47D411yescharacteristic
27C22×C4×C47—21no—
28C2×C22⋊D47—22no—
29C2×C22⋊D47—22no—
30#10625350—42no—
31#10625350—42no—
32C2×D188—21no—
33C2×D188—21no—
34C2×D188D412yes—
35C2×C4×D47—22no—
36C2×Dic94D411yescharacteristic
37C2×C8×C47—21no—
38C4⋊C4×C47—21no—
39C4⋊C4×C47—21no—
40C4⋊C4×C47D411yescharacteristic
41C22⋊C4×C47—21no—
42C42×C47C2311yescharacteristic
43#10625336—44no—
44(C2×D47)⋊C4—22no—
45C4⋊Dic47D411yescharacteristic
46Dic47⋊C4—21no—
47C4×Dic47—21no—
48C2×C47⋊C8—21no—
49C2×C47⋊C8—21no—
50C23×C47—21no—
51C22×D47—22no—
52Q8×C47—42no—
53D4×C47—21no—
54D4×C47—21no—
55C2×C4×C47—21no—
56C2×C4×C47—41no—
57C2×C4×C47—41no—
58C2×C4×C47—41no—
59C2×C4×C47C2×D411yescharacteristic
60C2×C4×C47C2×D411yescharacteristic
61C2×C4×C47C2×D411yescharacteristic
62C22⋊D47—44no—
63C22⋊D47—82no—
64C2×Dic47—21no—
65C2×Dic47—21no—
66D188—42no—
67D188—41no—
68D188—41no—
69D188—41no—
70D188—41no—
71C4×D47—44no—
72Dic94—21no—
73Dic94SD1612yescomplemented
74C8×C47—41no—
75C47⋊C8—22no—
76C47⋊C8—41no—
77C22×C47—41no—
78C22×C47—41no—
79C22×C47—41no—
80C22×C47#12011yescharacteristic
81C2×D47—42no—
82C2×D47—42no—
83C2×D47—42no—
84C4×C47—21no—
85C4×C47—41no—
86C4×C47—81no—
87C4×C47C2×SD1611yescharacteristic
88C4×C47#13511yescharacteristic
89C4×C47AGL(1,ℤ/8)11yescharacteristic
90C4×C47#13711yescharacteristic
91Dic47—22no—
92Dic47—41no—
93#1631—471nomaximal, Sylow
94C2×C47—81no—
95C2×C47#45011yescharacteristic
96C2×C47#45211yescharacteristic
97C2×C47#45311yescharacteristic
98D47—82no—
99#550—471no—
100#492—471no—
101#477—471no—
102#476D4711yescharacteristic, complemented
103#331—471no—
104Q8⋊C8—471no—
105D4⋊C8—471no—
106C47#163111yescharacteristic, complemented, Sylow
107C2×#41—941no—
108C2×SD16—942no—
109C4⋊Q8C2×D4711yescharacteristic
110#127—471no—
111#127—941no—
112#121—942no—
113#121—941no—
114C4×Q8—471no—
115C4×D4—941no—
116C4×D4C2×D4711yescharacteristic
117#107—941no—
118#106—21no—
119C4⋊C8—471no—
120C4⋊C8C2×D4711yescharacteristic
121#103—941no—
122#102—21no—
123C4×C8—471no—
124#41—1882no—
125#41—1882no—
126C2×Q8—21no—
127C2×Q8—471no—
128C2×D4—472no—
129C2×D4—942no—
130C2×D4—942no—
131C2×D4—941no—
132C2×D4—941no—
133C2×D4C22⋊D4711yescharacteristic
134C22×C4—21no—
135C22×C4—942no—
136SD16—1884no—
137C2×C8—21no—
138C2×C8—941no—
139C2×C8—941no—
140C4⋊C4—21no—
141C4⋊C4—21no—
142C4⋊C4—471no—
143C4⋊C4—941no—
144C4⋊C4C22⋊D4711yescharacteristic
145C22⋊C4—21no—
146C22⋊C4—942no—
147C42—941no—
148C42C22×D4711yescharacteristic
149C23—21no—
150C23—942no—
151Q8—42no—
152Q8—472no—
153Q8—941no—
154D4—21no—
155D4—21no—
156D4—3762no—
157D4—1882no—
158D4—1884no—
159D4—1881no—
160D4—1881no—
161D4—1881no—
162D4—1881no—
163C2×C4—21no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—941no—
168C2×C4—941no—
169C2×C4—1884no—
170C2×C4D4×D4711yescharacteristic
171C2×C4D4×D4711yescharacteristic
172C2×C4C2×C22⋊D4711yescharacteristic
173C8—41no—
174C8—942no—
175C8—1881no—
176C22—41no—
177C22—41no—
178C22—41no—
179C22—1882no—
180C22—1882no—
181C22—1882no—
182C22#1309399211yescharacteristic
183C4—21no—
184C4—41no—
185C4—81no—
186C4—942no—
187C4—1881no—
188C4SD16×D4711yescharacteristic
189C4#1309404411yescharacteristic
190C4#1309405111yescharacteristic
191C4#1309405511yescharacteristic
192C2—81no—
193C2—3762no—
194C2#1568927211yescharacteristic
195C2#1568928311yescharacteristic
196C2#1568928911yescharacteristic
subgroupG/H
centerC22#13093992
commutatorC42×C47C23
FrattiniC42C22×D47
FittingC47×#476C2
socleC22×C47#120
hypercenter#476D47
hypocenterC47#1631
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
2. #15689497C2semidirect
3. #15689415C2semidirect
4. #15688866C2semidirect
5. #15688853C2semidirect
6. D4⋊(C47⋊C8)C2semidirect
7. C47×#476C2semidirect
73. Dic94SD16semidirect
102. #476D47semidirect
106. C47#1631semidirect