Finite Group Databasebeta

← #20244167

Subgroups — #20244167

Order 6016.

196 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 83 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
1C2×#13093959C211yesmaximal, characteristic
2#15689165C211yesmaximal, characteristic
3#15689163C211yesmaximal, characteristic
4C2×#13093955C211yesmaximal, characteristic
5#15689081C211yesmaximal, characteristic
6#15688891C211yesmaximal, characteristic
7C47×#343C211yesmaximal, characteristic
8C2×#10625329C2211yescharacteristic
9C22×C47⋊C8C2211yescharacteristic
10#13093983C2211yescharacteristic
11C2×C4⋊Dic47C2211yescharacteristic
12#13093959C414yescomplemented
13#13093958—21no—
14#13093957—21no—
15#13093956—21no—
16#13093955—21no—
17#13093955—21no—
18#13093955—21no—
19#13093934—21no—
20C8×Dic47—21no—
21C2×M16×C47C2211yescharacteristic
22C2×M16×C47C2211yescharacteristic
23C2×C4⋊C4×C47C2211yescharacteristic
24C22×C4×C47—21no—
25C22×C4×C47C2311yescharacteristic
26C22×Dic47—21no—
27M16×C47—21no—
28M16×C47—21no—
29M16×C47C2×C412yes—
30M16×C47Q812yes—
31C2×C8×C47—21no—
32C2×C8×C47—21no—
33C4⋊C4×C47—21no—
34C4⋊C4×C47—21no—
35C22⋊Dic47—21no—
36C4⋊Dic47—21no—
37C4⋊Dic47—21no—
38C4⋊Dic47D411yescharacteristic
39C4⋊Dic47D411yescharacteristic
40C4×Dic47—21no—
41#10625329—21no—
42#10625329C2×C412yes—
43C2×C47⋊C8—21no—
44C2×C47⋊C8C2×C412yes—
45C2×C47⋊C8D411yescharacteristic
46C2×C47⋊C8D411yescharacteristic
47C2×C47⋊C8Q812yes—
48C23×C47#4111yescharacteristic
49C2×C4×C47—41no—
50C2×C4×C47—81no—
51C2×C4×C47C22×C411yescharacteristic
52C2×C4×C47C2×D411yescharacteristic
53C2×C4×C47C2×D411yescharacteristic
54C2×C4×C47C2×Q811yescharacteristic
55C2×C4×C47C2×Q811yescharacteristic
56C2×C4×C47#4111yescharacteristic
57C2×Dic47—21no—
58C2×Dic47—21no—
59C2×Dic47—41no—
60C2×Dic47—81no—
61C8×C47—22no—
62C8×C47—22no—
63C47⋊C8—22no—
64C47⋊C8C4⋊C412yes—
65C47⋊C8C4⋊C412yes—
66C22×C47—21no—
67C22×C47—21no—
68C22×C47C4×Q811yescharacteristic
69C22×C47#12111yescharacteristic
70C22×C47#12511yescharacteristic
71C4×C47—81no—
72C4×C47C2×C4⋊C411yescharacteristic
73C4×C47C4×D411yescharacteristic
74C4×C47C22⋊Q811yescharacteristic
75C4×C47C4⋊Q811yescharacteristic
76Dic47—41no—
77Dic47—41no—
78Dic47—81no—
79#1951—471nomaximal, Sylow
80C2×C47—21no—
81C2×C47—21no—
82C2×C47#38911yescharacteristic
83C2×C47#47111yescharacteristic
84C2×C47#47111yescharacteristic
85C2×#108—471no—
86#428—471no—
87#428—471no—
88C2×#106—471no—
89#405—471no—
90#343—471no—
91#343D4711yescharacteristic
92C47#195111yescharacteristic, complemented, Sylow
93C2×M16—471no—
94C2×M16C2×D4711yescharacteristic
95C2×M16C2×D4711yescharacteristic
96C22×C8—471no—
97#117—471no—
98C2×C4⋊C4—471no—
99C2×C4⋊C4C2×D4711yescharacteristic
100#108—474no—
101#107—941no—
102#107—941no—
103#106—941no—
104#106—941no—
105#106—941no—
106#106—941no—
107#97—941no—
108C4×C8—941no—
109C22×C4—21no—
110C22×C4—941no—
111C22×C4C22×D4711yescharacteristic
112M16—21no—
113M16—21no—
114M16—472no—
115M16—941no—
116M16Dic9412yes—
117M16C4×D4712yes—
118C2×C8—21no—
119C2×C8—21no—
120C2×C8—472no—
121C2×C8—471no—
122C2×C8—471no—
123C2×C8—472no—
124C2×C8—941no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—471no—
128C4⋊C4—471no—
129C4⋊C4—941no—
130C4⋊C4—941no—
131C22⋊C4—941no—
132C42—941no—
133C23#1062535011yescharacteristic
134C2×C4—41no—
135C2×C4—81no—
136C2×C4—941no—
137C2×C4—941no—
138C2×C4—3761no—
139C2×C4—1881no—
140C2×C4C2×Dic9411yescharacteristic
141C2×C4C2×C4×D4711yescharacteristic
142C2×C4D4×D4711yescharacteristic
143C2×C4D4×D4711yescharacteristic
144C2×C4#1062535211yescharacteristic
145C2×C4Q8×D4711yescharacteristic
146C8—22no—
147C8—22no—
148C8—472no—
149C8—472no—
150C8—942no—
151C22—21no—
152C22—21no—
153C22C4×Dic9411yescharacteristic
154C22#1309399711yescharacteristic
155C22#1309401411yescharacteristic
156C4—81no—
157C4—3761no—
158C4—1881no—
159C4—1881no—
160C4C4⋊C4×D4711yescharacteristic
161C4(C22⋊D47)⋊C411yescharacteristic
162C4#1309400111yescharacteristic
163C4#1309402311yescharacteristic
164C2—21no—
165C2—21no—
166C2#1568902011yescharacteristic
167C2#1568938511yescharacteristic
168C2#1568938911yescharacteristic
subgroupG/H
centerC22#13093997
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#343C2
socleC22×C47#121
hypercenter#343D47
hypocenterC47#1951
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
12. #13093959C4semidirect
92. C47#1951semidirect