Finite Group Databasebeta

← #20242452

Subgroups — #20242452

Order 6016.

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

normal subgroups only

This group has 278 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, complemented
2#15689499C211yesmaximal, characteristic, complemented
3#15689320C211yesmaximal, characteristic, complemented
4#15688866C211yesmaximal, characteristic, complemented
5#15688853C211yesmaximal, characteristic, complemented
6D4⋊(C47⋊C8)C211yesmaximal, characteristic, complemented
7C47×#459C211yesmaximal, characteristic, complemented
8C2×#10625350—21no—
9C2×#10625335—21no—
10C2×#10625334—22no—
11#13094021C2211yescharacteristic
12#13094020—21no—
13#13093998—21no—
14#13093997—22no—
15C4×Dic94C2211yescharacteristic
16#13093986—21no—
17C4⋊(C47⋊C8)C2211yescharacteristic
18#13093945—21no—
19C4×C47⋊C8C2211yescharacteristic
20C2×D8×C47—21no—
21#127×C47C2211yescharacteristic
22C4×D4×C47C2211yescharacteristic
23C4⋊C8×C47C2211yescharacteristic
24#102×C47—21no—
25C2×D4×C47—21no—
26C2×D4×C47—21no—
27C2×D4×C47—21no—
28C2×D4×C47D411yescharacteristic
29C22×C4×C47—21no—
30C2×C22⋊D47—22no—
31C2×C22⋊D47—22no—
32#10625350—42no—
33#10625350—42no—
34C2×D188—21no—
35C2×D188—21no—
36C2×D188D412yes—
37C2×C4×D47—22no—
38C2×Dic94D411yescharacteristic
39D8×C47—42no—
40C2×C8×C47—21no—
41C4⋊C4×C47D411yescharacteristic
42C22⋊C4×C47—21no—
43C42×C47C2311yescharacteristic
44#10625335—42no—
45#10625334—44no—
46(C2×D47)⋊C4—22no—
47C4⋊Dic47D411yescharacteristic
48Dic47⋊C4—21no—
49C4×Dic47—21no—
50C2×C47⋊C8—21no—
51C2×C47⋊C8—21no—
52C23×C47—21no—
53C23×C47—41no—
54C22×D47—22no—
55D4×C47—21no—
56D4×C47—21no—
57D4×C47—42no—
58D4×C47—41no—
59D4×C47—41no—
60D4×C47—41no—
61D4×C47—41no—
62C2×C4×C47—21no—
63C2×C4×C47—41no—
64C2×C4×C47—41no—
65C2×C4×C47C2×D411yescharacteristic
66C2×C4×C47C2×D411yescharacteristic
67C2×C4×C47C2×D411yescharacteristic
68C22⋊D47—44no—
69C22⋊D47—82no—
70C2×Dic47—21no—
71C2×Dic47—21no—
72D188—42no—
73D188—41no—
74D188—41no—
75D188—41no—
76D188—41no—
77C4×D47—44no—
78Dic94—21no—
79Dic94D812yescomplemented
80C8×C47—41no—
81C47⋊C8—22no—
82C47⋊C8—41no—
83C22×C47—41no—
84C22×C47—41no—
85C22×C47—41no—
86C22×C47—81no—
87C22×C47—81no—
88C22×C47—81no—
89C22×C47#12011yescharacteristic
90C2×D47—42no—
91C2×D47—42no—
92C2×D47—42no—
93C4×C47—21no—
94C4×C47—41no—
95C4×C47C2×D811yescharacteristic
96C4×C47#13511yescharacteristic
97C4×C47AGL(1,ℤ/8)11yescharacteristic
98C4×C47AGL(1,ℤ/8)11yescharacteristic
99Dic47—22no—
100Dic47—41no—
101#1621—471nomaximal, Sylow
102C2×C47—81no—
103C2×C47—161no—
104C2×C47#44711yescharacteristic
105C2×C47#44911yescharacteristic
106C2×C47#45311yescharacteristic
107D47—82no—
108#550—471no—
109#493—471no—
110#460—471no—
111#459D4711yescharacteristic, complemented
112#331—471no—
113Q8⋊C8—471no—
114D4⋊C8—471no—
115C47#162111yescharacteristic, complemented, Sylow
116C2×#41—941no—
117C2×SD16—941no—
118C2×D8—21no—
119C2×D8—942no—
120#127—471no—
121#127—941no—
122#127C2×D4711yescharacteristic
123#121—942no—
124#121—941no—
125C4×Q8—471no—
126C4×D4—941no—
127C4×D4C2×D4711yescharacteristic
128C4⋊C8—471no—
129C4⋊C8C2×D4711yescharacteristic
130#102—21no—
131#102—941no—
132C4×C8—471no—
133#41—1882no—
134#41—1882no—
135C2×Q8—471no—
136C2×D4—21no—
137C2×D4—21no—
138C2×D4—21no—
139C2×D4—472no—
140C2×D4—942no—
141C2×D4—942no—
142C2×D4—941no—
143C2×D4—941no—
144C2×D4C22⋊D4711yescharacteristic
145C22×C4—21no—
146C22×C4—942no—
147SD16—1882no—
148D8—42no—
149D8—1884no—
150C2×C8—21no—
151C2×C8—941no—
152C2×C8—941no—
153C4⋊C4—471no—
154C4⋊C4—941no—
155C4⋊C4C22⋊D4711yescharacteristic
156C22⋊C4—21no—
157C22⋊C4—942no—
158C42—941no—
159C42C22×D4711yescharacteristic
160C23—21no—
161C23—41no—
162C23—942no—
163Q8—472no—
164Q8—941no—
165D4—21no—
166D4—21no—
167D4—42no—
168D4—41no—
169D4—41no—
170D4—41no—
171D4—41no—
172D4—3762no—
173D4—1882no—
174D4—1884no—
175D4—1881no—
176D4—1881no—
177D4—1881no—
178D4—1881no—
179C2×C4—21no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—941no—
183C2×C4—941no—
184C2×C4—1884no—
185C2×C4D4×D4711yescharacteristic
186C2×C4D4×D4711yescharacteristic
187C2×C4C2×C22⋊D4711yescharacteristic
188C8—41no—
189C8—942no—
190C8—1881no—
191C22—41no—
192C22—41no—
193C22—41no—
194C22—81no—
195C22—81no—
196C22—81no—
197C22—1882no—
198C22—1882no—
199C22—1882no—
200C22#1309399211yescharacteristic
201C4—21no—
202C4—41no—
203C4—942no—
204C4—1881no—
205C4D8×D4711yescharacteristic
206C4#1309404411yescharacteristic
207C4#1309404811yescharacteristic
208C4#1309405011yescharacteristic
209C2—81no—
210C2—161no—
211C2—3762no—
212C2#1568925511yescharacteristic
213C2#1568926611yescharacteristic
214C2#1568928911yescharacteristic
subgroupG/H
centerC22#13093992
commutatorC42×C47C23
FrattiniC42C22×D47
FittingC47×#459C2
socleC22×C47#120
hypercenter#459D47
hypocenterC47#1621
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #15689794C2semidirect
2. #15689499C2semidirect
3. #15689320C2semidirect
4. #15688866C2semidirect
5. #15688853C2semidirect
6. D4⋊(C47⋊C8)C2semidirect
7. C47×#459C2semidirect
79. Dic94D8semidirect
111. #459D47semidirect
115. C47#1621semidirect