Finite Group Databasebeta

← #20241208

Subgroups — #20241208

Order 6016.

202 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 61 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#15689025C211yesmaximal, characteristic
2#15688878C211yesmaximal, characteristic, complemented
3C47×#336C211yesmaximal, characteristic, complemented
4C22×D188C411yescharacteristic
5C22×C47⋊C8—21no—
6C2×C4⋊Dic47C411yescharacteristic
7C2×(C2×D47)⋊C4—21no—
8C2×(C2×D47)⋊C4—21no—
9C22×C8×C47—21no—
10C2×C42×C47C2211yescharacteristic
11C23×D47—21no—
12C22×C4×C47C2×C411yescharacteristic
13C22×C4×C47D411yescharacteristic
14C22×C4×C47D411yescharacteristic
15C22×Dic47—21no—
16C2×D188—21no—
17C2×D188—41no—
18C2×D188—41no—
19C2×D188C812yescomplemented
20C2×C8×C47—22no—
21C2×C8×C47—41no—
22C2×C8×C47—41no—
23C42×C47—41no—
24(C2×D47)⋊C4—41no—
25(C2×D47)⋊C4—41no—
26(C2×D47)⋊C4—41no—
27(C2×D47)⋊C4—41no—
28C4⋊Dic47—41no—
29C2×C47⋊C8—22no—
30C2×C47⋊C8—41no—
31C2×C47⋊C8—41no—
32C23×C47C22⋊C411yescharacteristic
33C22×D47—22no—
34C22×D47—41no—
35C22×D47—41no—
36C22×D47—41no—
37C22×D47—41no—
38C22×D47—41no—
39C22×D47—41no—
40C2×C4×C47—21no—
41C2×C4×C47—21no—
42C2×C4×C47—21no—
43C2×C4×C47—21no—
44C2×C4×C47—21no—
45C2×C4×C47—21no—
46C2×C4×C47C2×C811yescharacteristic
47C2×C4×C47M1611yescharacteristic
48C2×C4×C47D811yescharacteristic
49C2×C4×C47D811yescharacteristic
50C2×C4×C47SD1611yescharacteristic
51C2×C4×C47SD1611yescharacteristic
52C2×Dic47—41no—
53C2×Dic47—41no—
54C2×Dic47—41no—
55D188—42no—
56D188—42no—
57C8×C47—42no—
58C47⋊C8—42no—
59C22×C47C22⋊C811yescharacteristic
60C22×C47#9911yescharacteristic
61C22×C47#10011yescharacteristic
62C22×C47#10211yescharacteristic
63C22×C47#10211yescharacteristic
64C22×C47#10411yescharacteristic
65C22×C47#10411yescharacteristic
66C2×D47—42no—
67C2×D47—42no—
68C2×D47—42no—
69C2×D47—81no—
70C2×D47—81no—
71C2×D47—81no—
72C2×D47—81no—
73C4×C47—21no—
74C4×C47—21no—
75C4×C47—21no—
76C4×C47—21no—
77C4×C47—21no—
78C4×C47—21no—
79Dic47—81no—
80#1270—471nomaximal, Sylow
81C2×C47#32311yescharacteristic
82C2×C47D4⋊C811yescharacteristic
83C2×C47D4⋊C811yescharacteristic
84C2×C47#32711yescharacteristic
85C2×C47#32711yescharacteristic
86C2×C47#32911yescharacteristic
87C2×C47#33111yescharacteristic
88D47—82no—
89#390—471no—
90#336—471no—
91#336D4711yescharacteristic, complemented
92C47#127011yescharacteristic, complemented, Sylow
93C22×D4—471no—
94C22×C8—21no—
95C22×C8—941no—
96C2×C4⋊C4—471no—
97C2×C22⋊C4—941no—
98C2×C22⋊C4—941no—
99C2×C42C2×D4711yescharacteristic
100C24—941no—
101C2×D4—472no—
102C2×D4—941no—
103C2×D4—1881no—
104C2×D4—1881no—
105C22×C4—941no—
106C22×C4C4×D4711yescharacteristic
107C22×C4D18811yescharacteristic
108C22×C4C22⋊D4711yescharacteristic
109C2×C8—22no—
110C2×C8—41no—
111C2×C8—41no—
112C2×C8—942no—
113C2×C8—1881no—
114C2×C8—1881no—
115C4⋊C4—1881no—
116C22⋊C4—1881no—
117C22⋊C4—1881no—
118C22⋊C4—1881no—
119C22⋊C4—1881no—
120C42—41no—
121C23—942no—
122C23—1881no—
123C23—1881no—
124C23—1881no—
125C23—1881no—
126C23—1881no—
127C23—1881no—
128C23(C2×D47)⋊C411yescharacteristic
129D4—1882no—
130D4—1882no—
131C2×C4—21no—
132C2×C4—21no—
133C2×C4—21no—
134C2×C4—21no—
135C2×C4—21no—
136C2×C4—21no—
137C2×C4—1881no—
138C2×C4—1881no—
139C2×C4—1881no—
140C2×C4C8×D4711yescharacteristic
141C2×C4#1062532411yescharacteristic
142C2×C4#1062532511yescharacteristic
143C2×C4D37611yescharacteristic
144C2×C4#1062533411yescharacteristic
145C2×C4#1062533611yescharacteristic
146C8—42no—
147C8—1882no—
148C22—3761no—
149C22—3761no—
150C22—3761no—
151C22—3761no—
152C22—1882no—
153C22—1882no—
154C22—1882no—
155C22(C2×D47)⋊C811yescharacteristic
156C22#1309393811yescharacteristic
157C22#1309394011yescharacteristic
158C22#1309394411yescharacteristic
159C22#1309394611yescharacteristic
160C22#1309395011yescharacteristic
161C22#1309395211yescharacteristic
162C4—21no—
163C4—21no—
164C4—21no—
165C4—21no—
166C4—21no—
167C4—21no—
168C4—3761no—
169C2—3762no—
170C2#1568884611yescharacteristic
171C2#1568885011yescharacteristic
172C2#1568885211yescharacteristic
173C2#1568885611yescharacteristic
174C2#1568885811yescharacteristic
175C2#1568886211yescharacteristic
176C2#1568886611yescharacteristic
subgroupG/H
centerC23(C2×D47)⋊C4
commutatorC2×C4×C47C2×C8
FrattiniC2×C42C2×D47
FittingC47×#336C2
socleC23×C47C22⋊C4
hypercenter#336D47
hypocenterC47#1270
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #336

Complements

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

NH ≅ G/Ntype
2. #15688878C2semidirect
3. C47×#336C2semidirect
19. C2×D188C8semidirect
91. #336D47semidirect
92. C47#1270semidirect