Finite Group Databasebeta

← #20242523

Subgroups — #20242523

Order 6016.

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

normal subgroups only

This group has 214 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#15689834C211yesmaximal, characteristic
2#15689502C211yesmaximal, characteristic, complemented
3#15689419C211yesmaximal, characteristic, complemented
4#15689414C211yesmaximal, characteristic
5#15688853C211yesmaximal, characteristic, complemented
6#15688850C211yesmaximal, characteristic
7C47×#333C211yesmaximal, characteristic, complemented
8C2×#10625337—22no—
9#13094024C2211yescharacteristic
10#13094015—21no—
11#13094004—21no—
12#13094000—22no—
13C4×Dic94C2211yescharacteristic
14C4×D188C2211yescharacteristic
15#13093986—21no—
16C4⋊C4×D47—21no—
17#13093958—21no—
18#13093956—21no—
19#13093949—21no—
20#13093946—21no—
21C4×C47⋊C8C2211yescharacteristic
22C4⋊Q8×C47C2211yescharacteristic
23C4⋊C8×C47C2211yescharacteristic
24C4⋊C8×C47C2211yescharacteristic
25C2×Q8×C47D412yes—
26C2×D188D411yescharacteristic
27C2×C4×D47—21no—
28C2×C4×D47—22no—
29C2×Dic94—21no—
30C2×Dic94D411yescharacteristic
31C2×C8×C47—21no—
32C2×C8×C47—21no—
33C4⋊C4×C47—21no—
34C4⋊C4×C47—21no—
35C42×C47C2311yescharacteristic
36#10625337—44no—
37(C2×D47)⋊C4—22no—
38(C2×D47)⋊C4—21no—
39C4⋊Dic47—22no—
40C4⋊Dic47—21no—
41C4⋊Dic47—21no—
42C4⋊Dic47D411yescharacteristic
43C4⋊Dic47D411yescharacteristic
44Dic47⋊C4—22no—
45Dic47⋊C4—21no—
46C4×Dic47—21no—
47C2×C47⋊C8—21no—
48C22×D47—21no—
49Q8×C47—42no—
50C2×C4×C47—22no—
51C2×C4×C47C2×D411yescharacteristic
52C2×C4×C47C2×D411yescharacteristic
53C2×C4×C47C2×D411yescharacteristic
54C2×Dic47—21no—
55C2×Dic47—21no—
56C2×Dic47—21no—
57C2×Dic47—41no—
58D188—21no—
59D188Q1612yescomplemented
60C4×D47—41no—
61C4×D47—41no—
62C4×D47—82no—
63Dic94—21no—
64Dic94—21no—
65Dic94—42no—
66C8×C47—41no—
67C8×C47—41no—
68C47⋊C8—22no—
69C22×C47#12011yescharacteristic
70C2×D47—22no—
71C2×D47—41no—
72C2×D47—41no—
73C4×C47—21no—
74C4×C47—42no—
75C4×C47C2×Q1611yescharacteristic
76C4×C47#13511yescharacteristic
77C4×C47#13711yescharacteristic
78C4×C47#13711yescharacteristic
79Dic47—41no—
80Dic47—41no—
81Dic47—41no—
82Dic47—81no—
83#1632—471nomaximal, Sylow
84C2×C47#45111yescharacteristic
85C2×C47#45211yescharacteristic
86C2×C47#45311yescharacteristic
87D47—42no—
88#554—471no—
89#494—471no—
90#477—471no—
91#476—471no—
92#333D4711yescharacteristic, complemented
93Q8⋊C8—471no—
94D4⋊C8—471no—
95C47#163211yescharacteristic, complemented, Sylow
96C2×Q16—942no—
97C4⋊Q8—471no—
98C4⋊Q8C2×D4711yescharacteristic
99#125—941no—
100C22⋊Q8—941no—
101C22⋊Q8—942no—
102C4×Q8—471no—
103C4×D4—471no—
104C4×D4—941no—
105C2×C4⋊C4—941no—
106#107—941no—
107#106—941no—
108C4⋊C8C2×D4711yescharacteristic
109C4⋊C8C2×D4711yescharacteristic
110#103—941no—
111#102—941no—
112C4×C8—471no—
113C2×Q8—471no—
114C2×Q8—941no—
115C2×Q8D18812yes—
116C2×D4—471no—
117C22×C4—942no—
118C22×C4—941no—
119Q16—1884no—
120C2×C8—21no—
121C2×C8—21no—
122C2×C8—941no—
123C4⋊C4—21no—
124C4⋊C4—21no—
125C4⋊C4—471no—
126C4⋊C4—471no—
127C4⋊C4—942no—
128C4⋊C4—942no—
129C4⋊C4—941no—
130C4⋊C4—941no—
131C4⋊C4—941no—
132C22⋊C4—942no—
133C22⋊C4—941no—
134C42—941no—
135C42C22×D4711yescharacteristic
136C23—941no—
137Q8—42no—
138Q8—941no—
139Q8—941no—
140Q8—1882no—
141D4—472no—
142D4—941no—
143C2×C4—22no—
144C2×C4—941no—
145C2×C4—941no—
146C2×C4—941no—
147C2×C4—3762no—
148C2×C4—1881no—
149C2×C4—1881no—
150C2×C4—1881no—
151C2×C4C2×D18811yescharacteristic
152C2×C4D4×D4711yescharacteristic
153C2×C4D4×D4711yescharacteristic
154C8—41no—
155C8—41no—
156C8—942no—
157C22—942no—
158C22—1881no—
159C22—1881no—
160C22#1309399411yescharacteristic
161C4—21no—
162C4—42no—
163C4—3761no—
164C4—1881no—
165C4—1881no—
166C4—1881no—
167C4Q16×D4711yescharacteristic
168C4#1309404511yescharacteristic
169C4#1309405311yescharacteristic
170C4#1309405611yescharacteristic
171C2—1882no—
172C2#1568928011yescharacteristic
173C2#1568928811yescharacteristic
174C2#1568929311yescharacteristic
subgroupG/H
centerC22#13093994
commutatorC42×C47C23
FrattiniC42C22×D47
FittingC47×#333C2
socleC22×C47#120
hypercenter#333D47
hypocenterC47#1632
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
2. #15689502C2semidirect
3. #15689419C2semidirect
5. #15688853C2semidirect
7. C47×#333C2semidirect
59. D188Q16semidirect
92. #333D47semidirect
95. C47#1632semidirect