Finite Group Databasebeta

← #20242652

Subgroups — #20242652

Order 6016.

234 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 57 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#15689788C211yesmaximal, characteristic
2#15689519C211yesmaximal, characteristic, complemented
3#15689409C211yesmaximal, characteristic, complemented
4#15689329C211yesmaximal, characteristic
5#15688853C211yesmaximal, characteristic, complemented
6#15688850C211yesmaximal, characteristic
7C47×#332C211yesmaximal, characteristic, complemented
8C2×Q8×D47—21no—
9C2×#10625325—21no—
10#13094024C2211yescharacteristic
11#13094023—21no—
12#13094002—22no—
13#13094000—21no—
14C4×Dic94C2211yescharacteristic
15C4×D188C2211yescharacteristic
16#13093986—21no—
17#13093956—21no—
18#13093955—22no—
19#13093949—21no—
20#13093949—21no—
21C4×C47⋊C8C2211yescharacteristic
22C4⋊Q8×C47C2211yescharacteristic
23C4⋊C8×C47C2211yescharacteristic
24C4⋊C8×C47C2211yescharacteristic
25C2×Q8×C47—21no—
26Q8×D47—42no—
27Q8×D47—42no—
28C2×D188D411yescharacteristic
29C2×C4×D47—22no—
30C2×C4×D47—21no—
31C2×Dic94—22no—
32C2×Dic94—21no—
33C2×Dic94D411yescharacteristic
34C2×C8×C47—21no—
35C2×C8×C47—21no—
36C4⋊C4×C47—21no—
37C4⋊C4×C47D412yes—
38C42×C47C2311yescharacteristic
39(C2×D47)⋊C4—22no—
40(C2×D47)⋊C4—21no—
41C4⋊Dic47—21no—
42C4⋊Dic47—21no—
43C4⋊Dic47D411yescharacteristic
44C4⋊Dic47D411yescharacteristic
45Dic47⋊C4—22no—
46Dic47⋊C4—21no—
47C4×Dic47—21no—
48C2×C47⋊C8—21no—
49#10625325—42no—
50C22×D47—21no—
51Q8×C47—41no—
52Q8×C47—41no—
53C2×C4×C47—22no—
54C2×C4×C47C2×D411yescharacteristic
55C2×C4×C47C2×D411yescharacteristic
56C2×C4×C47C2×D411yescharacteristic
57C2×Dic47—21no—
58C2×Dic47—21no—
59C2×Dic47—21no—
60C2×Dic47—41no—
61D188—21no—
62D188SD1612yes—
63C4×D47—44no—
64C4×D47—41no—
65C4×D47—41no—
66Dic94—21no—
67Dic94—44no—
68Dic94—41no—
69Dic94—41no—
70Dic94SD1612yescomplemented
71C8×C47—41no—
72C8×C47—41no—
73C47⋊C8—22no—
74C22×C47#12011yescharacteristic
75C2×D47—22no—
76C2×D47—41no—
77C2×D47—41no—
78C4×C47—21no—
79C4×C47—42no—
80C4×C47C2×SD1611yescharacteristic
81C4×C47C2×SD1611yescharacteristic
82C4×C47AGL(1,ℤ/8)11yescharacteristic
83C4×C47#13711yescharacteristic
84Dic47—22no—
85Dic47—41no—
86Dic47—41no—
87Dic47—81no—
88#1651—471nomaximal, Sylow
89C2×C47#44811yescharacteristic
90C2×C47#45011yescharacteristic
91C2×C47#45611yescharacteristic
92D47—42no—
93D4×Q8—471no—
94#498—471no—
95#475—471no—
96#461—471no—
97#332D4711yescharacteristic, complemented
98Q8⋊C8—471no—
99D4⋊C8—471no—
100C47#165111yescharacteristic, complemented, Sylow
101C22×Q8—941no—
102C2×SD16—941no—
103C4⋊Q8—471no—
104C4⋊Q8—941no—
105C4⋊Q8C2×D4711yescharacteristic
106C22⋊Q8—941no—
107C22⋊Q8—942no—
108C4×Q8—471no—
109C4×D4—471no—
110C4×D4—941no—
111#106—941no—
112#106—942no—
113C4⋊C8C2×D4711yescharacteristic
114C4⋊C8C2×D4711yescharacteristic
115#103—941no—
116#103—941no—
117C4×C8—471no—
118C2×Q8—21no—
119C2×Q8—471no—
120C2×Q8—942no—
121C2×Q8—941no—
122C2×Q8—1882no—
123C2×Q8—1882no—
124C2×D4—471no—
125C22×C4—942no—
126C22×C4—941no—
127SD16—1882no—
128C2×C8—21no—
129C2×C8—21no—
130C2×C8—941no—
131C4⋊C4—21no—
132C4⋊C4—471no—
133C4⋊C4—471no—
134C4⋊C4—942no—
135C4⋊C4—941no—
136C4⋊C4—941no—
137C4⋊C4—941no—
138C4⋊C4D18812yes—
139C22⋊C4—942no—
140C22⋊C4—941no—
141C42—941no—
142C42C22×D4711yescharacteristic
143C23—941no—
144Q8—41no—
145Q8—41no—
146Q8—472no—
147Q8—941no—
148Q8—1884no—
149Q8—1881no—
150Q8—1881no—
151D4—472no—
152D4—941no—
153C2×C4—22no—
154C2×C4—941no—
155C2×C4—941no—
156C2×C4—941no—
157C2×C4—1884no—
158C2×C4—1881no—
159C2×C4—1881no—
160C2×C4—1881no—
161C2×C4C2×D18811yescharacteristic
162C2×C4D4×D4711yescharacteristic
163C2×C4D4×D4711yescharacteristic
164C8—41no—
165C8—41no—
166C8—942no—
167C22—942no—
168C22—1881no—
169C22—1881no—
170C22#1309399411yescharacteristic
171C4—21no—
172C4—42no—
173C4—942no—
174C4—3761no—
175C4—1881no—
176C4—1881no—
177C4SD16×D4711yescharacteristic
178C4SD16×D4711yescharacteristic
179C4#1309404811yescharacteristic
180C4#1309405611yescharacteristic
181C2—1882no—
182C2#1568926311yescharacteristic
183C2#1568927511yescharacteristic
184C2#1568930811yescharacteristic
subgroupG/H
centerC22#13093994
commutatorC42×C47C23
FrattiniC42C22×D47
FittingC47×#332C2
socleC22×C47#120
hypercenter#332D47
hypocenterC47#1651
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #15689519C2semidirect
3. #15689409C2semidirect
5. #15688853C2semidirect
7. C47×#332C2semidirect
70. Dic94SD16semidirect
97. #332D47semidirect
100. C47#1651semidirect