Finite Group Databasebeta

← #20242702

Subgroups — #20242702

Order 6016.

208 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 45 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#15689867C211yesmaximal, characteristic
2#15689529C211yesmaximal, characteristic, complemented
3#15689485C211yesmaximal, characteristic, complemented
4#15688864C211yesmaximal, characteristic, complemented
5#15688863C211yesmaximal, characteristic, complemented
6#15688862C211yesmaximal, characteristic, complemented
7C47×#497C211yesmaximal, characteristic, complemented
8#13094016C2211yescharacteristic
9#13094012C2211yescharacteristic
10#13094008—21no—
11#13094006—21no—
12#13094001—21no—
13#13094000—21no—
14#13093997—21no—
15#13093996—21no—
16#13093957—21no—
17#13093955—21no—
18#13093947—21no—
19#13093944—21no—
20#13093935C2211yescharacteristic
21#13093935C2211yescharacteristic
22C2×Q16×C47—21no—
23C2×SD16×C47—21no—
24C4⋊Q8×C47C2211yescharacteristic
25#124×C47C2211yescharacteristic
26#97×C47C2211yescharacteristic
27C2×Q8×C47—21no—
28C2×Q8×C47D411yescharacteristic
29C2×D4×C47D411yescharacteristic
30C2×C22⋊D47—21no—
31C2×C22⋊D47—21no—
32C22×Dic47—21no—
33C2×D188D411yescharacteristic
34C2×C4×D47—21no—
35C2×Dic94D411yescharacteristic
36Q16×C47—42no—
37SD16×C47—42no—
38C2×C8×C47—21no—
39C4⋊C4×C47—21no—
40C4⋊C4×C47—21no—
41C22⋊C4×C47—21no—
42C22⋊C4×C47—21no—
43C42×C47C2311yescharacteristic
44C22⋊Dic47—21no—
45(C2×D47)⋊C4—21no—
46(C2×D47)⋊C4—21no—
47(C2×D47)⋊C4—21no—
48C4⋊Dic47—21no—
49C4⋊Dic47D411yescharacteristic
50C4⋊Dic47D411yescharacteristic
51Dic47⋊C4—21no—
52Dic47⋊C4—21no—
53Dic47⋊C4—21no—
54C2×C47⋊C8—21no—
55C2×C47⋊C8—21no—
56C23×C47—21no—
57C22×D47—21no—
58Q8×C47—41no—
59Q8×C47—41no—
60Q8×C47—41no—
61D4×C47—41no—
62C2×C4×C47—21no—
63C2×C4×C47—41no—
64C2×C4×C47C2×D411yescharacteristic
65C2×C4×C47C2×D411yescharacteristic
66C2×C4×C47C2×D411yescharacteristic
67C22⋊D47—81no—
68C22⋊D47—81no—
69C2×Dic47—21no—
70C2×Dic47—21no—
71C2×Dic47—21no—
72C2×Dic47—81no—
73D188—41no—
74C4×D47—81no—
75Dic94—41no—
76C8×C47—22no—
77C47⋊C8—22no—
78C47⋊C8—41no—
79C22×C47—41no—
80C22×C47—41no—
81C22×C47—41no—
82C22×C47#12011yescharacteristic
83C2×D47—41no—
84C2×D47—41no—
85C2×D47—41no—
86C4×C47—21no—
87C4×C47—21no—
88C4×C47—21no—
89C4×C47—41no—
90C4×C47—81no—
91Dic47—41no—
92Dic47—41no—
93Dic47—41no—
94#1661—471nomaximal, Sylow
95C2×C47—81no—
96C2×C47#45311yescharacteristic
97C2×C47#45511yescharacteristic
98C2×C47#45611yescharacteristic
99D47—81no—
100#562—471no—
101#501—471no—
102#497D4711yescharacteristic, complemented
103#489—471no—
104#330—471no—
105#329—471no—
106#329—471no—
107C47#166111yescharacteristic, complemented, Sylow
108C2×Q16—21no—
109C2×SD16—21no—
110C4⋊Q8C2×D4711yescharacteristic
111#125—471no—
112#124—471no—
113#124C2×D4711yescharacteristic
114#123—941no—
115#123—941no—
116C22⋊Q8—941no—
117C22⋊Q8—941no—
118#121—941no—
119#121—941no—
120#107—941no—
121#106—941no—
122#103—941no—
123#102—941no—
124#97—471no—
125#97—471no—
126#97C2×D4711yescharacteristic
127C2×Q8—21no—
128C2×Q8—471no—
129C2×Q8C22⋊D4711yescharacteristic
130C2×D4—471no—
131C2×D4—941no—
132C2×D4—941no—
133C2×D4C22⋊D4711yescharacteristic
134C22×C4—941no—
135C22×C4—941no—
136Q16—42no—
137SD16—42no—
138C2×C8—21no—
139C2×C8—941no—
140C2×C8—941no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—471no—
144C4⋊C4—471no—
145C4⋊C4—941no—
146C4⋊C4—941no—
147C4⋊C4—941no—
148C4⋊C4—941no—
149C22⋊C4—21no—
150C22⋊C4—21no—
151C22⋊C4—941no—
152C22⋊C4—941no—
153C22⋊C4—941no—
154C22⋊C4—941no—
155C42C22×D4711yescharacteristic
156C23—21no—
157C23—941no—
158Q8—41no—
159Q8—41no—
160Q8—41no—
161Q8—1881no—
162D4—41no—
163D4—3761no—
164D4—3761no—
165D4—1881no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—941no—
169C2×C4—941no—
170C2×C4—941no—
171C2×C4—3761no—
172C2×C4—3761no—
173C2×C4D4×D4711yescharacteristic
174C2×C4D4×D4711yescharacteristic
175C2×C4C2×C22⋊D4711yescharacteristic
176C8—22no—
177C8—942no—
178C8—1881no—
179C22—41no—
180C22—41no—
181C22—41no—
182C22—1881no—
183C22—1881no—
184C22—1881no—
185C22#1309399211yescharacteristic
186C4—21no—
187C4—21no—
188C4—21no—
189C4—41no—
190C4—81no—
191C4—1881no—
192C4—1881no—
193C4—1881no—
194C2—81no—
195C2—3761no—
196C2#1568929011yescharacteristic
197C2#1568929911yescharacteristic
198C2#1568930411yescharacteristic
subgroupG/H
centerC22#13093992
commutatorC42×C47C23
FrattiniC42C22×D47
FittingC47×#497C2
socleC22×C47#120
hypercenter#497D47
hypocenterC47#1661
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

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

NH ≅ G/Ntype
2. #15689529C2semidirect
3. #15689485C2semidirect
4. #15688864C2semidirect
5. #15688863C2semidirect
6. #15688862C2semidirect
7. C47×#497C2semidirect
102. #497D47semidirect
107. C47#1661semidirect