Finite Group Databasebeta

← #20244046

Subgroups — #20244046

Order 6016.

212 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 75 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#15689166C211yesmaximal, characteristic
2C2×#13093948C211yesmaximal, characteristic
3C2×#13093943C211yesmaximal, characteristic
4#15689079C211yesmaximal, characteristic
5#15688891C211yesmaximal, characteristic
6#15688887C211yesmaximal, characteristic
7C47×#419C211yesmaximal, characteristic
8C2×#10625329C2211yescharacteristic
9C2×#10625329C2211yescharacteristic
10C22×C47⋊C8C2211yescharacteristic
11C2×C4⋊Dic47C2211yescharacteristic
12#13093957—21no—
13#13093955—21no—
14#13093948—21no—
15#13093948—21no—
16#13093943C414yescomplemented
17#13093935—21no—
18C4×C47⋊C8—21no—
19C22×Q8×C47C2211yescharacteristic
20C2×M16×C47C2211yescharacteristic
21#117×C47C2211yescharacteristic
22#103×C47—21no—
23#103×C47—21no—
24C2×Q8×C47—21no—
25C2×Q8×C47—21no—
26C2×Q8×C47—21no—
27C2×Q8×C47—21no—
28C2×Q8×C47—21no—
29C2×Q8×C47C2×C412yes—
30C22×C4×C47—21no—
31C22×C4×C47C2311yescharacteristic
32C22×Dic47—21no—
33M16×C47—21no—
34M16×C47—21no—
35C2×C8×C47—21no—
36C4⋊C4×C47D411yescharacteristic
37C4⋊C4×C47D411yescharacteristic
38C22⋊C4×C47—21no—
39C42×C47—21no—
40C4⋊Dic47—21no—
41C4⋊Dic47—21no—
42#10625329—21no—
43#10625329—21no—
44#10625329C2×C412yes—
45#10625329C2×C412yes—
46C2×C47⋊C8—21no—
47C2×C47⋊C8—21no—
48C2×C47⋊C8—21no—
49C2×C47⋊C8—21no—
50C2×C47⋊C8D411yescharacteristic
51C2×C47⋊C8D411yescharacteristic
52C23×C47#4111yescharacteristic
53Q8×C47—22no—
54Q8×C47—22no—
55Q8×C47—41no—
56Q8×C47—41no—
57C2×C4×C47—22no—
58C2×C4×C47—21no—
59C2×C4×C47—21no—
60C2×C4×C47—41no—
61C2×C4×C47—41no—
62C2×C4×C47C22×C411yescharacteristic
63C2×C4×C47C2×D411yescharacteristic
64C2×C4×C47C2×D411yescharacteristic
65C2×C4×C47#4111yescharacteristic
66C2×C4×C47#4111yescharacteristic
67C2×C4×C47#4111yescharacteristic
68C2×Dic47—41no—
69C2×Dic47—81no—
70C8×C47—41no—
71C47⋊C8—22no—
72C47⋊C8—22no—
73C47⋊C8—21no—
74C47⋊C8—21no—
75C22×C47—21no—
76C22×C47—21no—
77C22×C47#11711yescharacteristic
78C22×C47#12111yescharacteristic
79C22×C47#12611yescharacteristic
80C4×C47—42no—
81C4×C47—41no—
82C4×C47—41no—
83C4×C47C4×D411yescharacteristic
84C4×C47C4×D411yescharacteristic
85C4×C47#12311yescharacteristic
86C4×C47#12411yescharacteristic
87Dic47—81no—
88#1930—471nomaximal, Sylow
89C2×C47—21no—
90C2×C47—21no—
91C2×C47#38811yescharacteristic
92C2×C47#47111yescharacteristic
93C2×C47#47311yescharacteristic
94#428—471no—
95#419D4711yescharacteristic
96C2×#103—471no—
97C2×#101—471no—
98#405—471no—
99#343—471no—
100#341—471no—
101C47#193011yescharacteristic, complemented, Sylow
102C22×Q8C2×D4711yescharacteristic
103C2×M16—471no—
104C2×M16—471no—
105C2×M16C2×D4711yescharacteristic
106C22×C8—471no—
107#117C2×D4711yescharacteristic
108C2×C4⋊C4—471no—
109#107—941no—
110#106—941no—
111#103—21no—
112#103—21no—
113#103—941no—
114#103—941no—
115#101—474no—
116#97—941no—
117C4×C8—941no—
118C2×Q8—21no—
119C2×Q8—21no—
120C2×Q8—21no—
121C2×Q8—21no—
122C2×Q8—21no—
123C2×Q8C4×D4712yes—
124C22×C4—21no—
125C22×C4—941no—
126C22×C4C22×D4711yescharacteristic
127M16—21no—
128M16—21no—
129M16—472no—
130M16—472no—
131M16—941no—
132M16—941no—
133C2×C8—21no—
134C2×C8—471no—
135C2×C8—471no—
136C2×C8—941no—
137C2×C8—941no—
138C2×C8—941no—
139C2×C8—941no—
140C4⋊C4—941no—
141C4⋊C4—941no—
142C4⋊C4C22⋊D4711yescharacteristic
143C4⋊C4C22⋊D4711yescharacteristic
144C22⋊C4—21no—
145C42—21no—
146C23#1062535211yescharacteristic
147Q8—22no—
148Q8—22no—
149Q8—41no—
150Q8—41no—
151C2×C4—22no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—3761no—
157C2×C4—1881no—
158C2×C4C2×C4×D4711yescharacteristic
159C2×C4#1062535011yescharacteristic
160C2×C4D4×D4711yescharacteristic
161C2×C4#1062535211yescharacteristic
162C2×C4#1062535211yescharacteristic
163C2×C4C2×C22⋊D4711yescharacteristic
164C8—41no—
165C8—942no—
166C8—942no—
167C8—941no—
168C8—941no—
169C22—21no—
170C22—21no—
171C22#1309398011yescharacteristic
172C22#1309399611yescharacteristic
173C22#1309401711yescharacteristic
174C4—42no—
175C4—41no—
176C4—41no—
177C4—3761no—
178C4(C22⋊D47)⋊C411yescharacteristic
179C4C4×C22⋊D4711yescharacteristic
180C4#1309400611yescharacteristic
181C4#1309401111yescharacteristic
182C2—21no—
183C2—21no—
184C2#1568901711yescharacteristic
185C2#1568938811yescharacteristic
186C2#1568939611yescharacteristic
subgroupG/H
centerC22#13093996
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#419C2
socleC22×C47#121
hypercenter#419D47
hypocenterC47#1930
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
16. #13093943C4semidirect
101. C47#1930semidirect